From 96fd3164d8319c2100cee62740c0adcdea715d3f Mon Sep 17 00:00:00 2001 From: Mike Innes Date: Mon, 29 Jun 2015 20:51:22 -0400 Subject: [PATCH 01/10] fix identation --- doc/stdlib/linalg.rst | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/doc/stdlib/linalg.rst b/doc/stdlib/linalg.rst index 6e2b85a231eee..ac42f9dddf848 100644 --- a/doc/stdlib/linalg.rst +++ b/doc/stdlib/linalg.rst @@ -48,7 +48,7 @@ Linear algebra functions in Julia are largely implemented by calling functions f .. function:: full(F) - Reconstruct the matrix ``A`` from the factorization ``F=factorize(A)``. + Reconstruct the matrix ``A`` from the factorization ``F=factorize(A)``. .. function:: lu(A) -> L, U, p From 4a86729aca0e2a0408a61330a2db26a0a3613b16 Mon Sep 17 00:00:00 2001 From: Mike Innes Date: Mon, 29 Jun 2015 18:27:40 -0400 Subject: [PATCH 02/10] newdoc.jl generates docs/helpdb.jl --- doc/newdoc.jl | 103 ++++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 103 insertions(+) create mode 100644 doc/newdoc.jl diff --git a/doc/newdoc.jl b/doc/newdoc.jl new file mode 100644 index 0000000000000..4694edc040bcb --- /dev/null +++ b/doc/newdoc.jl @@ -0,0 +1,103 @@ +cd(dirname(@__FILE__)) + +# Load docs from RST into memory + +typealias Docs Dict{UTF8String, Vector{UTF8String}} + +function parsedoc!(docs::Dict{UTF8String, Docs}, file) + doccing = false + mod = "Base" + func = "" + doc = IOBuffer() + for l in split(readall(file), "\n") + + if doccing && (startswith(l, " ") || ismatch(r"^\s*$", l)) + println(doc, startswith(l, " ") ? l[4:end] : l) + else + doccing = false + func != "" && + push!(get!(get!(docs, mod, Docs()), func, UTF8String[]), rstrip(takebuf_string(doc))) + func = "" + end + + if startswith(l, ".. function::") + name = match(r"^\.\. function:: (@?[^\(\s\{]+)", l) + name == nothing && (warn("bad function $l"); continue) + doccing = true + func = name.captures[1] + println(doc, "::") + println(doc, " "^11, l[15:end]) + elseif ismatch(r"^\.\. (current)?module::", l) + mod = match(r"^\.\. (current)?module:: ([\w\.]+)", l).captures[2] + end + end + func != "" && + push!(get!(get!(docs, mod, Docs()), func, UTF8String[]), rstrip(takebuf_string(doc))) + return docs +end + +function alldocs() + docs = Dict{UTF8String, Docs}() + for folder in ["stdlib", "manual", "devdocs"] + for f in readdir(folder) + parsedoc!(docs, "$folder/$f") + end + end + return docs +end + +map(kv->length(kv[2]), alldocs()) |> sum +map(kv -> sum(map(kv -> length(kv[2]), kv[2])), alldocs()) |> sum + +# Dump in helpdb.jl + +exceptions = ["ans", "CPU_CORES", "JULIA_HOME", "STDOUT", "STDERR", "STDIN", + "help", "apropos", "Help", "x", "build_sysimg", ".\\\\", "\\:", + "\\", "\\\\", "munmap", "mmap", "FormatMessage", "GetLastError"] + +qualify = ["ccall", "in", "<:", "|>", "*", "\\", "*", "/", "^", ".+", ".-", ".*", + "./", ".\\", ".^", "//", "<<", ">>", ">>>", "==", "!=", "===", "!==", + "<", "<=", ">", ">=", ".==", ".!=", ".<", ".<=", ".>", ".>=", "|", "*", + "^", ":", "!"] + +isop(func) = ismatch(r"[^\w@!.]|^!$", func) + +identifier(mod, func) = + func in qualify ? "$mod.$(isop(func) ? "(:($func))" : func)" : + mod == "Base" ? func : + "$(replace(mod, "Base.", "")).$func" + +macquote(n) = + startswith(n, "@") ? ":$n" : + contains(n, "@") ? ":($n)" : + n + +open("../base/docs/helpdb.jl", "w") do io + for (mod, docs) in alldocs() + println(io, "# $mod\n") + for (func, docs) in docs + func in exceptions && continue + println(io, "doc\"\"\"\n```rst") + for (i, doc) in enumerate(docs) + println(io, doc) + i < length(docs) && println(io) + end + println(io, "```\n\"\"\"") + println(io, macquote(identifier(mod, func))) + println(io) + end + end +end + +# let count = 0, hand = 0 +# for (mod, docs) in alldocs() +# for (func, docs) in docs +# count += 1 +# doc = join(docs, "\n") +# if ismatch(r":\w+:", doc) +# hand += 1 +# end +# end +# end +# hand, count +# end From bc1d8529441c067d028eecdf3ef866fec60603a1 Mon Sep 17 00:00:00 2001 From: Mike Innes Date: Fri, 31 Jul 2015 11:21:52 +0100 Subject: [PATCH 03/10] generate new helpdb --- base/docs/helpdb.jl | 16331 ++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 16331 insertions(+) create mode 100644 base/docs/helpdb.jl diff --git a/base/docs/helpdb.jl b/base/docs/helpdb.jl new file mode 100644 index 0000000000000..4aac2bf32f5ff --- /dev/null +++ b/base/docs/helpdb.jl @@ -0,0 +1,16331 @@ +# Base.LinAlg.BLAS + +doc""" +```rst +:: + ger!(alpha, x, y, A) + +Rank-1 update of the matrix ``A`` with vectors ``x`` and +``y`` as ``alpha*x*y' + A``. +``` +""" +LinAlg.BLAS.ger! + +doc""" +```rst +:: + gbmv!(trans, m, kl, ku, alpha, A, x, beta, y) + +Update vector ``y`` as ``alpha*A*x + beta*y`` or ``alpha*A'*x + +beta*y`` according to ``trans`` ('N' or 'T'). The matrix ``A`` is +a general band matrix of dimension ``m`` by ``size(A,2)`` with +``kl`` sub-diagonals and ``ku`` super-diagonals. Returns the +updated ``y``. +``` +""" +LinAlg.BLAS.gbmv! + +doc""" +```rst +:: + gbmv(trans, m, kl, ku, alpha, A, x, beta, y) + +Returns ``alpha*A*x`` or ``alpha*A'*x`` according to ``trans`` ('N' +or 'T'). The matrix ``A`` is a general band matrix of dimension +``m`` by ``size(A,2)`` with ``kl`` sub-diagonals and +``ku`` super-diagonals. +``` +""" +LinAlg.BLAS.gbmv + +doc""" +```rst +:: + gemm!(tA, tB, alpha, A, B, beta, C) + +Update ``C`` as ``alpha*A*B + beta*C`` or the other three variants +according to ``tA`` (transpose ``A``) and ``tB``. Returns the +updated ``C``. +``` +""" +LinAlg.BLAS.gemm! + +doc""" +```rst +:: + gemv!(tA, alpha, A, x, beta, y) + +Update the vector ``y`` as ``alpha*A*x + beta*y`` or +``alpha*A'x + beta*y`` according to ``tA`` (transpose ``A``). +Returns the updated ``y``. +``` +""" +LinAlg.BLAS.gemv! + +doc""" +```rst +:: + blascopy!(n, X, incx, Y, incy) + +Copy ``n`` elements of array ``X`` with stride ``incx`` to array +``Y`` with stride ``incy``. Returns ``Y``. +``` +""" +LinAlg.BLAS.blascopy! + +doc""" +```rst +:: + scal!(n, a, X, incx) + +Overwrite ``X`` with ``a*X``. Returns ``X``. +``` +""" +LinAlg.BLAS.scal! + +doc""" +```rst +:: + gemv(tA, alpha, A, x) + +Returns ``alpha*A*x`` or ``alpha*A'x`` according to ``tA`` +(transpose ``A``). + +:: + gemv(tA, A, x) + +Returns ``A*x`` or ``A'x`` according to ``tA`` (transpose ``A``). +``` +""" +LinAlg.BLAS.gemv + +doc""" +```rst +:: + syr!(uplo, alpha, x, A) + +Rank-1 update of the symmetric matrix ``A`` with vector +``x`` as ``alpha*x*x.' + A``. When ``uplo`` is 'U' the +upper triangle of ``A`` is updated ('L' for lower triangle). +Returns ``A``. +``` +""" +LinAlg.BLAS.syr! + +doc""" +```rst +:: + trsm!(side, ul, tA, dA, alpha, A, B) + +Overwrite ``B`` with the solution to ``A*X = alpha*B`` or one of +the other three variants determined by ``side`` (A on left or +right of ``X``) and ``tA`` (transpose A). Only the ``ul`` triangle +of ``A`` is used. ``dA`` indicates if ``A`` is unit-triangular +(the diagonal is assumed to be all ones). Returns the updated ``B``. +``` +""" +LinAlg.BLAS.trsm! + +doc""" +```rst +:: + trsv!(ul, tA, dA, A, b) + +Overwrite ``b`` with the solution to ``A*x = b`` or one of the other two +variants determined by ``tA`` (transpose A) and ``ul`` (triangle of ``A`` +used). ``dA`` indicates if ``A`` is unit-triangular (the diagonal is assumed +to be all ones). Returns the updated ``b``. +``` +""" +LinAlg.BLAS.trsv! + +doc""" +```rst +:: + her!(uplo, alpha, x, A) + +Methods for complex arrays only. Rank-1 update of the Hermitian +matrix ``A`` with vector ``x`` as ``alpha*x*x' + A``. When +``uplo`` is 'U' the upper triangle of ``A`` is updated +('L' for lower triangle). Returns ``A``. +``` +""" +LinAlg.BLAS.her! + +doc""" +```rst +:: + trsv(ul, tA, dA, A, b) + +Returns the solution to ``A*x = b`` or one of the other two variants +determined by ``tA`` (transpose A) and ``ul`` (triangle of ``A`` is used.) +``dA`` indicates if ``A`` is unit-triangular (the diagonal is assumed to be +all ones). +``` +""" +LinAlg.BLAS.trsv + +doc""" +```rst +:: + dot(n, X, incx, Y, incy) + +Dot product of two vectors consisting of ``n`` elements of array +``X`` with stride ``incx`` and ``n`` elements of array ``Y`` with +stride ``incy``. +``` +""" +LinAlg.BLAS.dot + +doc""" +```rst +:: + dotu(n, X, incx, Y, incy) + +Dot function for two complex vectors. +``` +""" +LinAlg.BLAS.dotu + +doc""" +```rst +:: + herk!(uplo, trans, alpha, A, beta, C) + +Methods for complex arrays only. Rank-k update of the Hermitian +matrix ``C`` as ``alpha*A*A' + beta*C`` or ``alpha*A'*A + beta*C`` +according to whether ``trans`` is 'N' or 'T'. When ``uplo`` is 'U' +the upper triangle of ``C`` is updated ('L' for lower triangle). +Returns ``C``. +``` +""" +LinAlg.BLAS.herk! + +doc""" +```rst +:: + trmv(side, ul, tA, dA, alpha, A, b) + +Returns ``alpha*A*b`` or one of the other three variants +determined by ``side`` (A on left or right) and ``tA`` (transpose A). +Only the ``ul`` triangle of ``A`` is used. ``dA`` indicates if +``A`` is unit-triangular (the diagonal is assumed to be all ones). +``` +""" +LinAlg.BLAS.trmv + +doc""" +```rst +:: + symv(ul, alpha, A, x) + +Returns ``alpha*A*x``. ``A`` is assumed to be symmetric. Only the +``ul`` triangle of ``A`` is used. + +:: + symv(ul, A, x) + +Returns ``A*x``. ``A`` is assumed to be symmetric. Only the +``ul`` triangle of ``A`` is used. +``` +""" +LinAlg.BLAS.symv + +doc""" +```rst +:: + dotc(n, X, incx, U, incy) + +Dot function for two complex vectors conjugating the first vector. +``` +""" +LinAlg.BLAS.dotc + +doc""" +```rst +:: + axpy!(a, X, Y) + +Overwrite ``Y`` with ``a*X + Y``. Returns ``Y``. +``` +""" +LinAlg.BLAS.axpy! + +doc""" +```rst +:: + syrk!(uplo, trans, alpha, A, beta, C) + +Rank-k update of the symmetric matrix ``C`` as ``alpha*A*A.' + +beta*C`` or ``alpha*A.'*A + beta*C`` according to whether ``trans`` +is 'N' or 'T'. When ``uplo`` is 'U' the upper triangle of ``C`` is +updated ('L' for lower triangle). Returns ``C``. +``` +""" +LinAlg.BLAS.syrk! + +doc""" +```rst +:: + sbmv(uplo, k, alpha, A, x) + +Returns ``alpha*A*x`` where ``A`` is a symmetric band matrix of +order ``size(A,2)`` with ``k`` super-diagonals stored in the +argument ``A``. + +:: + sbmv(uplo, k, A, x) + +Returns ``A*x`` where ``A`` is a symmetric band matrix of +order ``size(A,2)`` with ``k`` super-diagonals stored in the +argument ``A``. +``` +""" +LinAlg.BLAS.sbmv + +doc""" +```rst +:: + sbmv!(uplo, k, alpha, A, x, beta, y) + +Update vector ``y`` as ``alpha*A*x + beta*y`` where ``A`` is a +a symmetric band matrix of order ``size(A,2)`` with +``k`` super-diagonals stored in the argument ``A``. The storage +layout for ``A`` is described the reference BLAS module, level-2 +BLAS at http://www.netlib.org/lapack/explore-html/. + +Returns the updated ``y``. +``` +""" +LinAlg.BLAS.sbmv! + +doc""" +```rst +:: + symv!(ul, alpha, A, x, beta, y) + +Update the vector ``y`` as ``alpha*A*x + beta*y``. ``A`` is assumed +to be symmetric. Only the ``ul`` triangle of ``A`` is used. +Returns the updated ``y``. +``` +""" +LinAlg.BLAS.symv! + +doc""" +```rst +:: + symm(side, ul, alpha, A, B) + +Returns ``alpha*A*B`` or ``alpha*B*A`` according to ``side``. +``A`` is assumed to be symmetric. Only the ``ul`` triangle of +``A`` is used. + +:: + symm(side, ul, A, B) + +Returns ``A*B`` or ``B*A`` according to ``side``. ``A`` is assumed +to be symmetric. Only the ``ul`` triangle of ``A`` is used. + +:: + symm(tA, tB, alpha, A, B) + +Returns ``alpha*A*B`` or the other three variants +according to ``tA`` (transpose ``A``) and ``tB``. +``` +""" +LinAlg.BLAS.symm + +doc""" +```rst +:: + herk(uplo, trans, alpha, A) + +Methods for complex arrays only. Returns either the upper triangle +or the lower triangle, according to ``uplo`` ('U' or 'L'), of +``alpha*A*A'`` or ``alpha*A'*A``, according to ``trans`` ('N' or 'T'). +``` +""" +LinAlg.BLAS.herk + +doc""" +```rst +:: + syrk(uplo, trans, alpha, A) + +Returns either the upper triangle or the lower triangle, according +to ``uplo`` ('U' or 'L'), of ``alpha*A*A.'`` or ``alpha*A.'*A``, +according to ``trans`` ('N' or 'T'). +``` +""" +LinAlg.BLAS.syrk + +doc""" +```rst +:: + trsm(side, ul, tA, dA, alpha, A, B) + +Returns the solution to ``A*X = alpha*B`` or one of +the other three variants determined by ``side`` (A on left or +right of ``X``) and ``tA`` (transpose A). Only the ``ul`` triangle +of ``A`` is used. ``dA`` indicates if ``A`` is unit-triangular +(the diagonal is assumed to be all ones). +``` +""" +LinAlg.BLAS.trsm + +doc""" +```rst +:: + blas_set_num_threads(n) + +Set the number of threads the BLAS library should use. +``` +""" +LinAlg.BLAS.blas_set_num_threads + +doc""" +```rst +:: + asum(n, X, incx) + +sum of the absolute values of the first ``n`` elements of array ``X`` with +stride ``incx``. +``` +""" +LinAlg.BLAS.asum + +doc""" +```rst +:: + trmv!(side, ul, tA, dA, alpha, A, b) + +Update ``b`` as ``alpha*A*b`` or one of the other three variants +determined by ``side`` (A on left or right) and ``tA`` (transpose A). +Only the ``ul`` triangle of ``A`` is used. ``dA`` indicates if +``A`` is unit-triangular (the diagonal is assumed to be all ones). +Returns the updated ``b``. +``` +""" +LinAlg.BLAS.trmv! + +doc""" +```rst +:: + gemm(tA, tB, alpha, A, B) + +Returns ``alpha*A*B`` or the other three variants +according to ``tA`` (transpose ``A``) and ``tB``. + +:: + gemm(tA, tB, A, B) + +Returns ``A*B`` or the other three variants +according to ``tA`` (transpose ``A``) and ``tB``. +``` +""" +LinAlg.BLAS.gemm + +doc""" +```rst +:: + symm!(side, ul, alpha, A, B, beta, C) + +Update ``C`` as ``alpha*A*B + beta*C`` or ``alpha*B*A + beta*C`` +according to ``side``. ``A`` is assumed to be symmetric. Only the +``ul`` triangle of ``A`` is used. Returns the updated ``C``. +``` +""" +LinAlg.BLAS.symm! + +doc""" +```rst +:: + scal(n, a, X, incx) + +Returns ``a*X``. +``` +""" +LinAlg.BLAS.scal + +doc""" +```rst +:: + nrm2(n, X, incx) + +2-norm of a vector consisting of ``n`` elements of array ``X`` with +stride ``incx``. +``` +""" +LinAlg.BLAS.nrm2 + +doc""" +```rst +:: + trmm!(side, ul, tA, dA, alpha, A, B) + +Update ``B`` as ``alpha*A*B`` or one of the other three variants +determined by ``side`` (A on left or right) and ``tA`` (transpose A). +Only the ``ul`` triangle of ``A`` is used. ``dA`` indicates if +``A`` is unit-triangular (the diagonal is assumed to be all ones). +Returns the updated ``B``. +``` +""" +LinAlg.BLAS.trmm! + +doc""" +```rst +:: + trmm(side, ul, tA, dA, alpha, A, B) + +Returns ``alpha*A*B`` or one of the other three variants +determined by ``side`` (A on left or right) and ``tA`` (transpose A). +Only the ``ul`` triangle of ``A`` is used. ``dA`` indicates if +``A`` is unit-triangular (the diagonal is assumed to be all ones). +``` +""" +LinAlg.BLAS.trmm + +# Libdl + +doc""" +```rst +:: + dlopen(libfile::AbstractString [, flags::Integer]) + +Load a shared library, returning an opaque handle. + +The optional flags argument is a bitwise-or of zero or more of +``RTLD_LOCAL``, ``RTLD_GLOBAL``, ``RTLD_LAZY``, ``RTLD_NOW``, ``RTLD_NODELETE``, +``RTLD_NOLOAD``, ``RTLD_DEEPBIND``, and ``RTLD_FIRST``. These are converted to +the corresponding flags of the POSIX (and/or GNU libc and/or MacOS) +dlopen command, if possible, or are ignored if the specified +functionality is not available on the current platform. The +default flags are platform specific. On MacOS the default ``dlopen`` flags are +``RTLD_LAZY|RTLD_DEEPBIND|RTLD_GLOBAL`` while on other platforms the +defaults are ``RTLD_LAZY|RTLD_DEEPBIND|RTLD_LOCAL``. An important usage +of these flags is to specify non default behavior for when the dynamic library loader +binds library references to exported symbols and if the bound references are put into +process local or global scope. For instance ``RTLD_LAZY|RTLD_DEEPBIND|RTLD_GLOBAL`` +allows the library's symbols to be available for usage in other shared libraries, addressing +situations where there are dependencies between shared libraries. +``` +""" +Libdl.dlopen + +doc""" +```rst +:: + dlclose(handle) + +Close shared library referenced by handle. +``` +""" +Libdl.dlclose + +doc""" +```rst +:: + dlsym_e(handle, sym) + +Look up a symbol from a shared library handle, silently return NULL pointer on lookup failure. +``` +""" +Libdl.dlsym_e + +doc""" +```rst +:: + dlopen_e(libfile::AbstractString [, flags::Integer]) + +Similar to :func:`dlopen`, except returns a ``NULL`` pointer instead of raising errors. +``` +""" +Libdl.dlopen_e + +doc""" +```rst +:: + find_library(names, locations) + +Searches for the first library in ``names`` in the paths in the ``locations`` list, ``DL_LOAD_PATH``, or system +library paths (in that order) which can successfully be dlopen'd. On success, the return value will be one of +the names (potentially prefixed by one of the paths in locations). This string can be assigned to a ``global const`` +and used as the library name in future ``ccall``'s. On failure, it returns the empty string. +``` +""" +Libdl.find_library + +doc""" +```rst +:: + dlsym(handle, sym) + +Look up a symbol from a shared library handle, return callable function pointer on success. +``` +""" +Libdl.dlsym + +# Libc + +doc""" +```rst +:: + TmStruct([seconds]) + +Convert a number of seconds since the epoch to broken-down format, with fields ``sec``, ``min``, ``hour``, ``mday``, ``month``, ``year``, ``wday``, ``yday``, and ``isdst``. +``` +""" +Libc.TmStruct + +doc""" +```rst +:: + time(t::TmStruct) + +Converts a ``TmStruct`` struct to a number of seconds since the epoch. +``` +""" +Libc.time + +doc""" +```rst +:: + calloc(num::Integer, size::Integer) -> Ptr{Void} + +Call ``calloc`` from the C standard library. +``` +""" +Libc.calloc + +doc""" +```rst +:: + strerror(n=errno()) + +Convert a system call error code to a descriptive string +``` +""" +Libc.strerror + +doc""" +```rst +:: + realloc(addr::Ptr, size::Integer) -> Ptr{Void} + +Call ``realloc`` from the C standard library. + +See warning in the documentation for ``free`` regarding only using this on memory originally obtained from ``malloc``. +``` +""" +Libc.realloc + +doc""" +```rst +:: + free(addr::Ptr) + +Call ``free`` from the C standard library. Only use this on memory obtained from ``malloc``, +not on pointers retrieved from other C libraries. +``Ptr`` objects obtained from C libraries should be freed by the free functions defined in that library, +to avoid assertion failures if multiple ``libc`` libraries exist on the system. +``` +""" +Libc.free + +doc""" +```rst +:: + strftime([format], time) + +Convert time, given as a number of seconds since the epoch or a ``TmStruct``, to a formatted string using the given format. Supported formats are the same as those in the standard C library. +``` +""" +Libc.strftime + +doc""" +```rst +:: + errno([code]) + +Get the value of the C library's ``errno``. If an argument is specified, it is +used to set the value of ``errno``. + +The value of ``errno`` is only valid immediately after a ``ccall`` to a C +library routine that sets it. Specifically, you cannot call ``errno`` at the next +prompt in a REPL, because lots of code is executed between prompts. +``` +""" +Libc.errno + +doc""" +```rst +:: + malloc(size::Integer) -> Ptr{Void} + +Call ``malloc`` from the C standard library. +``` +""" +Libc.malloc + +doc""" +```rst +:: + strptime([format], timestr) + +Parse a formatted time string into a ``TmStruct`` giving the seconds, minute, hour, date, etc. Supported formats are the same as those in the standard C library. On some platforms, timezones will not be parsed correctly. If the result of this function will be passed to ``time`` to convert it to seconds since the epoch, the ``isdst`` field should be filled in manually. Setting it to ``-1`` will tell the C library to use the current system settings to determine the timezone. +``` +""" +Libc.strptime + +doc""" +```rst +:: + flush_cstdio() + +Flushes the C ``stdout`` and ``stderr`` streams (which may have been +written to by external C code). +``` +""" +Libc.flush_cstdio + +doc""" +```rst +:: + msync(ptr, len, [flags]) + +Forces synchronization of the :func:`mmap`\ ped memory region from ``ptr`` to ``ptr+len``. Flags defaults to ``MS_SYNC``, but can be a combination of ``MS_ASYNC``, ``MS_SYNC``, or ``MS_INVALIDATE``. See your platform man page for specifics. The flags argument is not valid on Windows. + +You may not need to call ``msync``, because synchronization is performed at intervals automatically by the operating system. However, you can call this directly if, for example, you are concerned about losing the result of a long-running calculation. +``` +""" +Libc.msync + +# Base.Collections + +doc""" +```rst +:: + PriorityQueue(K, V, [ord]) + +Construct a new :obj:`PriorityQueue`, with keys of type ``K`` and values/priorites of +type ``V``. If an order is not given, the priority queue is min-ordered using +the default comparison for ``V``. +``` +""" +Collections.PriorityQueue + +doc""" +```rst +:: + enqueue!(pq, k, v) + +Insert the a key ``k`` into a priority queue ``pq`` with priority ``v``. +``` +""" +Collections.enqueue! + +doc""" +```rst +:: + dequeue!(pq) + +Remove and return the lowest priority key from a priority queue. +``` +""" +Collections.dequeue! + +doc""" +```rst +:: + peek(pq) + +Return the lowest priority key from a priority queue without removing that key from the queue. +``` +""" +Collections.peek + +doc""" +```rst +:: + heapify!(v, [ord]) + +In-place :func:`heapify`. +``` +""" +Collections.heapify! + +doc""" +```rst +:: + heappush!(v, x, [ord]) + +Given a binary heap-ordered array, push a new element ``x``, preserving the heap +property. For efficiency, this function does not check that the array is +indeed heap-ordered. +``` +""" +Collections.heappush! + +doc""" +```rst +:: + heappop!(v, [ord]) + +Given a binary heap-ordered array, remove and return the lowest ordered +element. For efficiency, this function does not check that the array is +indeed heap-ordered. +``` +""" +Collections.heappop! + +doc""" +```rst +:: + heapify(v, [ord]) + +Return a new vector in binary heap order, optionally using the given +ordering. +``` +""" +Collections.heapify + +doc""" +```rst +:: + isheap(v, [ord]) + +Return true iff an array is heap-ordered according to the given order. +``` +""" +Collections.isheap + +# Base.Test + +doc""" +```rst +:: + @test_throws(extype, ex) + +Test that the expression ``ex`` throws an exception of type ``extype`` and calls the current handler to handle the result. +The default handler returns the exception if it is of the expected type. +``` +""" +:(Test.@test_throws) + +doc""" +```rst +:: + @test_approx_eq_eps(a, b, tol) + +Test two floating point numbers ``a`` and ``b`` for equality taking in account +a margin of tolerance given by ``tol``. +``` +""" +:(Test.@test_approx_eq_eps) + +doc""" +```rst +:: + @test(ex) + +Test the expression ``ex`` and calls the current handler to handle the result. +``` +""" +:(Test.@test) + +doc""" +```rst +:: + @test_approx_eq(a, b) + +Test two floating point numbers ``a`` and ``b`` for equality taking in account +small numerical errors. +``` +""" +:(Test.@test_approx_eq) + +doc""" +```rst +:: + with_handler(f, handler) + +Run the function ``f`` using the ``handler`` as the handler. +``` +""" +Test.with_handler + +# Base.FFTW + +doc""" +```rst +:: + r2r(A, kind [, dims]) + +Performs a multidimensional real-input/real-output (r2r) transform +of type ``kind`` of the array ``A``, as defined in the FFTW manual. +``kind`` specifies either a discrete cosine transform of various types +(``FFTW.REDFT00``, ``FFTW.REDFT01``, ``FFTW.REDFT10``, or +``FFTW.REDFT11``), a discrete sine transform of various types +(``FFTW.RODFT00``, ``FFTW.RODFT01``, ``FFTW.RODFT10``, or +``FFTW.RODFT11``), a real-input DFT with halfcomplex-format output +(``FFTW.R2HC`` and its inverse ``FFTW.HC2R``), or a discrete +Hartley transform (``FFTW.DHT``). The ``kind`` argument may be +an array or tuple in order to specify different transform types +along the different dimensions of ``A``; ``kind[end]`` is used +for any unspecified dimensions. See the FFTW manual for precise +definitions of these transform types, at http://www.fftw.org/doc. + +The optional ``dims`` argument specifies an iterable subset of +dimensions (e.g. an integer, range, tuple, or array) to transform +along. ``kind[i]`` is then the transform type for ``dims[i]``, +with ``kind[end]`` being used for ``i > length(kind)``. + +See also :func:`plan_r2r` to pre-plan optimized r2r transforms. +``` +""" +FFTW.r2r + +doc""" +```rst +:: + r2r!(A, kind [, dims]) + +Same as :func:`r2r`, but operates in-place on ``A``, which must be +an array of real or complex floating-point numbers. +``` +""" +FFTW.r2r! + +doc""" +```rst +:: + plan_r2r!(A, kind [, dims [, flags [, timelimit]]]) + +Similar to :func:`Base.plan_fft`, but corresponds to :func:`r2r!`. +``` +""" +FFTW.plan_r2r! + +doc""" +```rst +:: + plan_r2r(A, kind [, dims [, flags [, timelimit]]]) + +Pre-plan an optimized r2r transform, similar to :func:`Base.plan_fft` +except that the transforms (and the first three arguments) +correspond to :func:`r2r` and :func:`r2r!`, respectively. +``` +""" +FFTW.plan_r2r + +# Base.Profile + +doc""" +```rst +:: + print([io::IO = STDOUT,] [data::Vector]; format = :tree, C = false, combine = true, cols = tty_cols()) + +Prints profiling results to ``io`` (by default, ``STDOUT``). If you +do not supply a ``data`` vector, the internal buffer of accumulated +backtraces will be used. ``format`` can be ``:tree`` or +``:flat``. If ``C==true``, backtraces from C and Fortran code are +shown. ``combine==true`` merges instruction pointers that +correspond to the same line of code. ``cols`` controls the width +of the display. + +:: + print([io::IO = STDOUT,] data::Vector, lidict::Dict; format = :tree, combine = true, cols = tty_cols()) + +Prints profiling results to ``io``. This variant is used to examine +results exported by a previous call to :func:`retrieve`. +Supply the vector ``data`` of backtraces and a dictionary +``lidict`` of line information. +``` +""" +Profile.print + +doc""" +```rst +:: + init(; n::Integer, delay::Float64) + +Configure the ``delay`` between backtraces (measured in seconds), +and the number ``n`` of instruction pointers that may be +stored. Each instruction pointer corresponds to a single line of +code; backtraces generally consist of a long list of instruction +pointers. Default settings can be obtained by calling this function +with no arguments, and each can be set independently using keywords +or in the order ``(n, delay)``. +``` +""" +Profile.init + +doc""" +```rst +:: + clear_malloc_data() + +Clears any stored memory allocation data when running julia with +``--track-allocation``. Execute the command(s) you want to test +(to force JIT-compilation), then call :func:`clear_malloc_data`. +Then execute your command(s) again, quit Julia, and examine the +resulting ``*.mem`` files. +``` +""" +Profile.clear_malloc_data + +doc""" +```rst +:: + callers(funcname, [data, lidict], [filename=], [linerange=]) -> Vector{Tuple{count, linfo}} + +Given a previous profiling run, determine who called a particular +function. Supplying the filename (and optionally, range of line +numbers over which the function is defined) allows you to +disambiguate an overloaded method. The returned value is a vector +containing a count of the number of calls and line information +about the caller. One can optionally supply backtrace data +obtained from :func:`retrieve`; otherwise, the current internal profile +buffer is used. +``` +""" +Profile.callers + +doc""" +```rst +:: + fetch() -> data + +Returns a reference to the internal buffer of backtraces. Note that +subsequent operations, like :func:`clear`, can affect +``data`` unless you first make a copy. Note that the values in +``data`` have meaning only on this machine in the current session, +because it depends on the exact memory addresses used in +JIT-compiling. This function is primarily for internal use; +:func:`retrieve` may be a better choice for most users. +``` +""" +Profile.fetch + +doc""" +```rst +:: + retrieve() -> data, lidict + +"Exports" profiling results in a portable format, returning the set +of all backtraces (``data``) and a dictionary that maps the +(session-specific) instruction pointers in ``data`` to ``LineInfo`` +values that store the file name, function name, and line +number. This function allows you to save profiling results for +future analysis. +``` +""" +Profile.retrieve + +doc""" +```rst +:: + clear() + +Clear any existing backtraces from the internal buffer. +``` +""" +Profile.clear + +# Base.Cartesian + +doc""" +```rst +:: + @nall N expr + + ``@nall 3 d->(i_d > 1)`` would generate the expression + ``(i_1 > 1 && i_2 > 1 && i_3 > 1)``. This can be convenient for + bounds-checking. +``` +""" +:(Cartesian.@nall) + +doc""" +```rst +:: + @nloops N itersym rangeexpr bodyexpr + @nloops N itersym rangeexpr preexpr bodyexpr + @nloops N itersym rangeexpr preexpr postexpr bodyexpr + + Generate ``N`` nested loops, using ``itersym`` as the prefix for + the iteration variables. ``rangeexpr`` may be an + anonymous-function expression, or a simple symbol ``var`` in which + case the range is ``1:size(var,d)`` for dimension ``d``. + + Optionally, you can provide "pre" and "post" expressions. These + get executed first and last, respectively, in the body of each + loop. For example, + :: + + @nloops 2 i A d->j_d=min(i_d,5) begin + s += @nref 2 A j + end + + would generate + :: + + for i_2 = 1:size(A, 2) + j_2 = min(i_2, 5) + for i_1 = 1:size(A, 1) + j_1 = min(i_1, 5) + s += A[j_1,j_2] + end + end + + If you want just a post-expression, supply + ``nothing`` for the pre-expression. Using parenthesis and + semicolons, you can supply multi-statement expressions. +``` +""" +:(Cartesian.@nloops) + +doc""" +```rst +:: + @ntuple N expr + + Generates an ``N``-tuple. ``@ntuple 2 i`` would generate ``(i_1, i_2)``, and ``@ntuple 2 k->k+1`` would generate ``(2,3)``. +``` +""" +:(Cartesian.@ntuple) + +doc""" +```rst +:: + @nif N conditionexpr expr + @nif N conditionexpr expr elseexpr + + Generates a sequence of ``if ... elseif ... else ... end`` statements. For example:: + + @nif 3 d->(i_d >= size(A,d)) d->(error("Dimension ", d, " too big")) d->println("All OK") + + would generate:: + + if i_1 > size(A, 1) +``` +""" +:(Cartesian.@nif) + +doc""" +```rst +:: + @nref N A indexexpr + + Generate expressions like ``A[i_1,i_2,...]``. ``indexexpr`` can + either be an iteration-symbol prefix, or an anonymous-function + expression. +``` +""" +:(Cartesian.@nref) + +doc""" +```rst +:: + @nexprs N expr + + Generate ``N`` expressions. ``expr`` should be an + anonymous-function expression. +``` +""" +:(Cartesian.@nexprs) + +# Base + +doc""" +```rst +:: + @time + +A macro to execute an expression, printing the time it took to execute, the number of allocations, and the total number of bytes its execution caused to be allocated, before returning the value of the expression. +``` +""" +:@time + +doc""" +```rst +:: + systemerror(sysfunc, iftrue) + +Raises a ``SystemError`` for ``errno`` with the descriptive string ``sysfunc`` if ``bool`` is true +``` +""" +systemerror + +doc""" +```rst +:: + writedlm(f, A, delim='\\t') + +Write ``A`` (a vector, matrix or an iterable collection of iterable rows) as text to ``f`` (either a filename string or an ``IO`` stream) using the given delimeter ``delim`` (which defaults to tab, but can be any printable Julia object, typically a ``Char`` or ``AbstractString``). + +For example, two vectors ``x`` and ``y`` of the same length can +be written as two columns of tab-delimited text to ``f`` by +either ``writedlm(f, [x y])`` or by ``writedlm(f, zip(x, y))``. +``` +""" +writedlm + +doc""" +```rst +:: + cholfact(A, [LU=:U[,pivot=Val{false}]][;tol=-1.0]) -> Cholesky + +Compute the Cholesky factorization of a dense symmetric positive (semi)definite matrix ``A`` and return either a ``Cholesky`` if ``pivot==Val{false}`` or ``CholeskyPivoted`` if ``pivot==Val{true}``. ``LU`` may be ``:L`` for using the lower part or ``:U`` for the upper part. The default is to use ``:U``. The triangular matrix can be obtained from the factorization ``F`` with: ``F[:L]`` and ``F[:U]``. The following functions are available for ``Cholesky`` objects: ``size``, ``\``, ``inv``, ``det``. For ``CholeskyPivoted`` there is also defined a ``rank``. If ``pivot==Val{false}`` a ``PosDefException`` exception is thrown in case the matrix is not positive definite. The argument ``tol`` determines the tolerance for determining the rank. For negative values, the tolerance is the machine precision. + +:: + cholfact(A; shift=0, perm=Int[]) -> CHOLMOD.Factor + +Compute the Cholesky factorization of a sparse positive definite +matrix ``A``. A fill-reducing permutation is used. ``F = +cholfact(A)`` is most frequently used to solve systems of equations +with ``F\b``, but also the methods ``diag``, ``det``, ``logdet`` +are defined for ``F``. You can also extract individual factors +from ``F``, using ``F[:L]``. However, since pivoting is on by +default, the factorization is internally represented as ``A == +P'*L*L'*P`` with a permutation matrix ``P``; using just ``L`` +without accounting for ``P`` will give incorrect answers. To +include the effects of permutation, it's typically preferable to +extact "combined" factors like ``PtL = F[:PtL]`` (the equivalent of +``P'*L``) and ``LtP = F[:UP]`` (the equivalent of ``L'*P``). + +Setting optional ``shift`` keyword argument computes the factorization +of ``A+shift*I`` instead of ``A``. If the ``perm`` argument is nonempty, +it should be a permutation of `1:size(A,1)` giving the ordering to use +(instead of CHOLMOD's default AMD ordering). + +The function calls the C library CHOLMOD and many other functions +from the library are wrapped but not exported. +``` +""" +cholfact + +doc""" +```rst +:: + digamma(x) + +Compute the digamma function of ``x`` (the logarithmic derivative of ``gamma(x)``) +``` +""" +digamma + +doc""" +```rst +:: + fill!(A, x) + +Fill array ``A`` with the value ``x``. If ``x`` is an object reference, all elements will refer to the same object. +``fill!(A, Foo())`` will return ``A`` filled with the result of evaluating ``Foo()`` once. +``` +""" +fill! + +doc""" +```rst +:: + read!(stream, array::Array) + +Read binary data from a stream, filling in the argument ``array``. +``` +""" +read! + +doc""" +```rst +:: + empty!(collection) -> collection + +Remove all elements from a ``collection``. +``` +""" +empty! + +doc""" +```rst +:: + asin(x) + +Compute the inverse sine of ``x``, where the output is in radians +``` +""" +asin + +doc""" +```rst +:: + <:(T1, T2) + +Subtype operator, equivalent to ``issubtype(T1,T2)``. +``` +""" +Base.(:(<:)) + +doc""" +```rst +:: + schedule(t::Task, [val]; error=false) + +Add a task to the scheduler's queue. This causes the task to run constantly +when the system is otherwise idle, unless the task performs a blocking +operation such as ``wait``. + +If a second argument is provided, it will be passed to the task (via the +return value of ``yieldto``) when it runs again. If ``error`` is true, +the value is raised as an exception in the woken task. +``` +""" +schedule + +doc""" +```rst +:: + step(r) + +Get the step size of a :obj:`Range` object. +``` +""" +step + +doc""" +```rst +:: + utf32(s) + +Create a UTF-32 string from a byte array, array of ``Char`` or ``UInt32``, or +any other string type. (Conversions of byte arrays check for a +byte-order marker in the first four bytes, and do not include it in +the resulting string.) + +Note that the resulting ``UTF32String`` data is terminated by the NUL +codepoint (32-bit zero), which is not treated as a character in the +string (so that it is mostly invisible in Julia); this allows the +string to be passed directly to external functions requiring +NUL-terminated data. This NUL is appended automatically by the +`utf32(s)` conversion function. If you have a ``Char`` or ``UInt32`` array +``A`` that is already NUL-terminated UTF-32 data, then you +can instead use `UTF32String(A)`` to construct the string without +making a copy of the data and treating the NUL as a terminator +rather than as part of the string. + +:: + utf32(::Union{Ptr{Char},Ptr{UInt32},Ptr{Int32}} [, length]) + +Create a string from the address of a NUL-terminated UTF-32 string. A copy is made; the pointer can be safely freed. If ``length`` is specified, the string does not have to be NUL-terminated. +``` +""" +utf32 + +doc""" +```rst +:: + takebuf_array(b::IOBuffer) + +Obtain the contents of an ``IOBuffer`` as an array, without copying. Afterwards, the IOBuffer is reset to its initial state. +``` +""" +takebuf_array + +doc""" +```rst +:: + download(url,[localfile]) + +Download a file from the given url, optionally renaming it to the given local file name. +Note that this function relies on the availability of external tools such as ``curl``, +``wget`` or ``fetch`` to download the file and is provided for convenience. For production +use or situations in which more options are need, please use a package that provides the +desired functionality instead. +``` +""" +download + +doc""" +```rst +:: + @everywhere + + Execute an expression on all processes. Errors on any of the processes are + collected into a `CompositeException` and thrown. +``` +""" +:@everywhere + +doc""" +```rst +:: + lstrip(string, [chars]) + +Return ``string`` with any leading whitespace removed. If ``chars`` (a character, or vector or set of characters) is provided, instead remove characters contained in it. +``` +""" +lstrip + +doc""" +```rst +:: + reenable_sigint(f::Function) + +Re-enable Ctrl-C handler during execution of a function. Temporarily +reverses the effect of ``disable_sigint``. +``` +""" +reenable_sigint + +doc""" +```rst +:: + indmin(itr) -> Integer + +Returns the index of the minimum element in a collection. +``` +""" +indmin + +doc""" +```rst +:: + powermod(x, p, m) + +Compute :math:`x^p \pmod m` +``` +""" +powermod + +doc""" +```rst +:: + typeintersect(T, S) + +Compute a type that contains the intersection of ``T`` and ``S``. Usually this will be the smallest such type or one close to it. +``` +""" +typeintersect + +doc""" +```rst +:: + plan_bfft!(A [, dims]; flags=FFTW.ESTIMATE; timelimit=Inf) + +Same as :func:`plan_bfft`, but operates in-place on ``A``. +``` +""" +plan_bfft! + +doc""" +```rst +:: + pointer(array [, index]) + +Get the native address of an array or string element. Be careful to +ensure that a julia reference to ``a`` exists as long as this +pointer will be used. This function is "unsafe" like ``unsafe_convert``. + +Calling ``Ref(array[, index])`` is generally preferable to this function. +``` +""" +pointer + +doc""" +```rst +:: + countnz(A) + +Counts the number of nonzero values in array A (dense or sparse). Note that this is not a constant-time operation. For sparse matrices, one should usually use ``nnz``, which returns the number of stored values. +``` +""" +countnz + +doc""" +```rst +:: + isnan(f) -> Bool + +Test whether a floating point number is not a number (NaN) +``` +""" +isnan + +doc""" +```rst +:: + plan_irfft(A, d [, dims]; flags=FFTW.ESTIMATE; timelimit=Inf) + +Pre-plan an optimized inverse real-input FFT, similar to :func:`plan_rfft` +except for :func:`irfft` and :func:`brfft`, respectively. The first +three arguments have the same meaning as for :func:`irfft`. +``` +""" +plan_irfft + +doc""" +```rst +:: + println(x) + +Print (using :func:`print`) ``x`` followed by a newline. +``` +""" +println + +doc""" +```rst +:: + besselj(nu, x) + +Bessel function of the first kind of order ``nu``, :math:`J_\nu(x)`. +``` +""" +besselj + +doc""" +```rst +:: + @code_lowered + +Evaluates the arguments to the function call, determines their types, and calls :func:`code_lowered` on the resulting expression +``` +""" +:@code_lowered + +doc""" +```rst +:: + //(num, den) + +Divide two integers or rational numbers, giving a ``Rational`` result. +``` +""" +Base.(:(//)) + +doc""" +```rst +:: + At_mul_B(...) + +Matrix operator A\ :sup:`T` B +``` +""" +At_mul_B + +doc""" +```rst +:: + methods(f, [types]) + +Returns the method table for ``f``. + +If ``types`` is specified, returns an array of methods whose types match. +``` +""" +methods + +doc""" +```rst +:: + pmap(f, lsts...; err_retry=true, err_stop=false, pids=workers()) + +Transform collections ``lsts`` by applying ``f`` to each element in parallel. +(Note that ``f`` must be made available to all worker processes; see :ref:`Code Availability and Loading Packages ` for details.) +If ``nprocs() > 1``, the calling process will be dedicated to assigning tasks. +All other available processes will be used as parallel workers, or on the processes specified by ``pids``. + +If ``err_retry`` is true, it retries a failed application of ``f`` on a different worker. +If ``err_stop`` is true, it takes precedence over the value of ``err_retry`` and ``pmap`` stops execution on the first error. +``` +""" +pmap + +doc""" +```rst +:: + workers() + +Returns a list of all worker process identifiers. +``` +""" +workers + +doc""" +```rst +:: + isinteger(x) -> Bool + +Test whether ``x`` or all its elements are numerically equal to some integer +``` +""" +isinteger + +doc""" +```rst +:: + sortrows(A, [alg=,] [by=,] [lt=,] [rev=false]) + +Sort the rows of matrix ``A`` lexicographically. +``` +""" +sortrows + +doc""" +```rst +:: + ./(x, y) + +Element-wise right division operator. +``` +""" +Base.(:(./)) + +doc""" +```rst +:: + IPv6(host::Integer) -> IPv6 + +Returns IPv6 object from ip address formatted as Integer +``` +""" +IPv6 + +doc""" +```rst +:: + prod!(r, A) + +Multiply elements of ``A`` over the singleton dimensions of ``r``, +and write results to ``r``. +``` +""" +prod! + +doc""" +```rst +:: + hist2d!(counts, M, e1, e2) -> (e1, e2, counts) + +Compute a "2d histogram" with respect to the bins delimited by the edges given +in ``e1`` and ``e2``. This function writes the results to a pre-allocated +array ``counts``. +``` +""" +hist2d! + +doc""" +```rst +:: + fieldtype(type, name::Symbol | index::Int) + +Determine the declared type of a field (specified by name or index) in a composite type. +``` +""" +fieldtype + +doc""" +```rst +:: + hypot(x, y) + +Compute the :math:`\sqrt{x^2+y^2}` avoiding overflow and underflow +``` +""" +hypot + +doc""" +```rst +:: + airybi(x) + +Airy function :math:`\operatorname{Bi}(x)`. +``` +""" +airybi + +doc""" +```rst +:: + gensym([tag]) + +Generates a symbol which will not conflict with other variable names. +``` +""" +gensym + +doc""" +```rst +:: + cummin(A, [dim]) + +Cumulative minimum along a dimension. +The dimension defaults to 1. +``` +""" +cummin + +doc""" +```rst +:: + minabs!(r, A) + +Compute the minimum absolute values over the singleton dimensions of ``r``, +and write values to ``r``. +``` +""" +minabs! + +doc""" +```rst +:: + prevprod([k_1,k_2,...], n) + +Previous integer not greater than ``n`` that can be written as :math:`\prod k_i^{p_i}` for integers :math:`p_1`, :math:`p_2`, etc. +``` +""" +prevprod + +doc""" +```rst +:: + @evalpoly(z, c...) + +Evaluate the polynomial :math:`\sum_k c[k] z^{k-1}` for the +coefficients ``c[1]``, ``c[2]``, ...; that is, the coefficients are +given in ascending order by power of ``z``. This macro expands to +efficient inline code that uses either Horner's method or, for +complex ``z``, a more efficient Goertzel-like algorithm. +``` +""" +:@evalpoly + +doc""" +```rst +:: + eigfact!(A, [B]) + +Same as :func:`eigfact`, but saves space by overwriting the input ``A`` (and +``B``), instead of creating a copy. +``` +""" +eigfact! + +doc""" +```rst +:: + cosh(x) + +Compute hyperbolic cosine of ``x`` +``` +""" +cosh + +doc""" +```rst +:: + ipermutedims(A, perm) + +Like :func:`permutedims`, except the inverse of the given permutation is applied. +``` +""" +ipermutedims + +doc""" +```rst +:: + dirname(path::AbstractString) -> AbstractString + +Get the directory part of a path. +``` +""" +dirname + +doc""" +```rst +:: + isfile(path) -> Bool + +Returns ``true`` if ``path`` is a regular file, ``false`` otherwise. +``` +""" +isfile + +doc""" +```rst +:: + symlink(target, link) + +Creates a symbolic link to ``target`` with the name ``link``. + +.. note:: + + This function raises an error under operating systems that do not support + soft symbolic links, such as Windows XP. +``` +""" +symlink + +doc""" +```rst +:: + task_local_storage(symbol) + +Look up the value of a symbol in the current task's task-local storage. + +:: + task_local_storage(symbol, value) + +Assign a value to a symbol in the current task's task-local storage. + +:: + task_local_storage(body, symbol, value) + +Call the function ``body`` with a modified task-local storage, in which +``value`` is assigned to ``symbol``; the previous value of ``symbol``, or +lack thereof, is restored afterwards. Useful for emulating dynamic scoping. +``` +""" +task_local_storage + +doc""" +```rst +:: + diff(A, [dim]) + +Finite difference operator of matrix or vector. +``` +""" +diff + +doc""" +```rst +:: + precision(num::AbstractFloat) + +Get the precision of a floating point number, as defined by the effective number of bits in the mantissa. +``` +""" +precision + +doc""" +```rst +:: + cor(v1[, v2][, vardim=1, mean=nothing]) + +Compute the Pearson correlation between the vector(s) in ``v1`` and ``v2``. + +Users can use the keyword argument ``vardim`` to specify the variable +dimension, and ``mean`` to supply pre-computed mean values. +``` +""" +cor + +doc""" +```rst +:: + partitions(n) + +Generate all integer arrays that sum to ``n``. Because the number of +partitions can be very large, this function returns an iterator +object. Use ``collect(partitions(n))`` to get an array of all +partitions. The number of partitions to generate can be efficiently +computed using ``length(partitions(n))``. + +:: + partitions(n, m) + +Generate all arrays of ``m`` integers that sum to ``n``. Because +the number of partitions can be very large, this function returns an +iterator object. Use ``collect(partitions(n,m))`` to get an array of +all partitions. The number of partitions to generate can be efficiently +computed using ``length(partitions(n,m))``. + +:: + partitions(array) + +Generate all set partitions of the elements of an array, +represented as arrays of arrays. Because the number of partitions +can be very large, this function returns an iterator object. Use +``collect(partitions(array))`` to get an array of all partitions. +The number of partitions to generate can be efficiently +computed using ``length(partitions(array))``. + +:: + partitions(array, m) + +Generate all set partitions of the elements of an array into exactly m +subsets, represented as arrays of arrays. Because the number of +partitions can be very large, this function returns an iterator object. +Use ``collect(partitions(array,m))`` to get an array of all partitions. +The number of partitions into m subsets is equal to the Stirling number +of the second kind and can be efficiently computed using +``length(partitions(array,m))``. +``` +""" +partitions + +doc""" +```rst +:: + readlines(stream) + +Read all lines as an array. +``` +""" +readlines + +doc""" +```rst +:: + findnz(A) + +Return a tuple ``(I, J, V)`` where ``I`` and ``J`` are the row and +column indexes of the non-zero values in matrix ``A``, and ``V`` is +a vector of the non-zero values. +``` +""" +findnz + +doc""" +```rst +:: + RemoteRef() + +Make an uninitialized remote reference on the local machine. + +:: + RemoteRef(n) + +Make an uninitialized remote reference on process ``n``. +``` +""" +RemoteRef + +doc""" +```rst +:: + foldl(op, v0, itr) + +Like :func:`reduce`, but with guaranteed left associativity. ``v0`` +will be used exactly once. + +:: + foldl(op, itr) + +Like ``foldl(op, v0, itr)``, but using the first element of ``itr`` +as ``v0``. In general, this cannot be used with empty collections +(see ``reduce(op, itr)``). +``` +""" +foldl + +doc""" +```rst +:: + airybiprime(x) + +Airy function derivative :math:`\operatorname{Bi}'(x)`. +``` +""" +airybiprime + +doc""" +```rst +:: + Ac_rdiv_B(a,b) + +Matrix operator A\ :sup:`H` / B +``` +""" +Ac_rdiv_B + +doc""" +```rst +:: + set_rounding(T, mode) + +Set the rounding mode of floating point type ``T``, controlling the +rounding of basic arithmetic functions (:func:`+`, :func:`-`, :func:`*`, +:func:`/` and :func:`sqrt`) and type conversion. + +Note that this may affect other types, for instance changing the rounding +mode of ``Float64`` will change the rounding mode of ``Float32``. See +``get_rounding`` for available modes +``` +""" +set_rounding + +doc""" +```rst +:: + linspace(start, stop, n=100) + +Construct a range of ``n`` linearly spaced elements from ``start`` to ``stop``. +``` +""" +linspace + +doc""" +```rst +:: + promote_type(type1, type2) + +Determine a type big enough to hold values of each argument type without loss, whenever possible. In some cases, where no type exists to which both types can be promoted losslessly, some loss is tolerated; for example, ``promote_type(Int64,Float64)`` returns ``Float64`` even though strictly, not all ``Int64`` values can be represented exactly as ``Float64`` values. +``` +""" +promote_type + +doc""" +```rst +:: + ind2sub(dims, index) -> subscripts + +Returns a tuple of subscripts into an array with dimensions ``dims``, corresponding to the linear index ``index`` + +**Example** ``i, j, ... = ind2sub(size(A), indmax(A))`` provides the indices of the maximum element + +:: + ind2sub(a, index) -> subscripts + +Returns a tuple of subscripts into array ``a`` corresponding to the linear index ``index`` +``` +""" +ind2sub + +doc""" +```rst +:: + .*(x, y) + +Element-wise multiplication operator. +``` +""" +Base.(:(.*)) + +doc""" +```rst +:: + ror!(dest::BitArray{1}, src::BitArray{1}, i::Integer) -> BitArray{1} + +Performs a right rotation operation on ``src`` and put the result into ``dest``. + +:: + ror!(B::BitArray{1}, i::Integer) -> BitArray{1} + +Performs a right rotation operation on B. +``` +""" +ror! + +doc""" +```rst +:: + range(start, [step], length) + +Construct a range by length, given a starting value and optional step (defaults to 1). +``` +""" +range + +doc""" +```rst +:: + eltype(type) + +Determine the type of the elements generated by iterating a collection of the +given ``type``. +For associative collection types, this will be a ``(key,value)`` tuple type. +The definition ``eltype(x) = eltype(typeof(x))`` is provided for convenience so +that instances can be passed instead of types. However the form that accepts +a type argument should be defined for new types. +``` +""" +eltype + +doc""" +```rst +:: + edit(file::AbstractString, [line]) + +Edit a file optionally providing a line number to edit at. Returns to the julia prompt when you quit the editor. + +:: + edit(function, [types]) + +Edit the definition of a function, optionally specifying a tuple of types to indicate which method to edit. +``` +""" +edit + +doc""" +```rst +:: + backtrace() + +Get a backtrace object for the current program point. +``` +""" +backtrace + +doc""" +```rst +:: + ignorestatus(command) + +Mark a command object so that running it will not throw an error if the +result code is non-zero. +``` +""" +ignorestatus + +doc""" +```rst +:: + reducedim(f, A, dims[, initial]) + +Reduce 2-argument function ``f`` along dimensions of ``A``. ``dims`` is a +vector specifying the dimensions to reduce, and ``initial`` is the initial +value to use in the reductions. For `+`, `*`, `max` and `min` the `initial` +argument is optional. + +The associativity of the reduction is implementation-dependent; if you +need a particular associativity, e.g. left-to-right, you should write +your own loop. See documentation for ``reduce``. +``` +""" +reducedim + +doc""" +```rst +:: + -(x) + +Unary minus operator. + +:: + -(x, y) + +Subtraction operator. +``` +""" +- + +doc""" +```rst +:: + mapfoldr(f, op, v0, itr) + +Like :func:`mapreduce`, but with guaranteed right associativity. ``v0`` +will be used exactly once. + +:: + mapfoldr(f, op, itr) + +Like ``mapfoldr(f, op, v0, itr)``, but using the first element of +``itr`` as ``v0``. In general, this cannot be used with empty +collections (see ``reduce(op, itr)``). +``` +""" +mapfoldr + +doc""" +```rst +:: + broadcast_setindex!(A, X, inds...) + +Broadcasts the ``X`` and ``inds`` arrays to a common size and stores the value from each position in ``X`` at the indices given by the same positions in ``inds``. +``` +""" +broadcast_setindex! + +doc""" +```rst +:: + Nullable(x) + +Wrap value ``x`` in an object of type ``Nullable``, which indicates whether a value is present. +``Nullable(x)`` yields a non-empty wrapper, and ``Nullable{T}()`` yields an empty instance +of a wrapper that might contain a value of type ``T``. +``` +""" +Nullable + +doc""" +```rst +:: + bits(n) + +A string giving the literal bit representation of a number. +``` +""" +bits + +doc""" +```rst +:: + launch(manager::FooManager, params::Dict, launched::Vector{WorkerConfig}, launch_ntfy::Condition) + + Implemented by cluster managers. For every Julia worker launched by this function, it should append a ``WorkerConfig`` entry + to ``launched`` and notify ``launch_ntfy``. The function MUST exit once all workers, requested by ``manager`` have been launched. + ``params`` is a dictionary of all keyword arguments ``addprocs`` was called with. +``` +""" +launch + +doc""" +```rst +:: + @code_typed + +Evaluates the arguments to the function call, determines their types, and calls :func:`code_typed` on the resulting expression +``` +""" +:@code_typed + +doc""" +```rst +:: + invdigamma(x) + +Compute the inverse digamma function of ``x``. +``` +""" +invdigamma + +doc""" +```rst +:: + getindex(type[, elements...]) + +Construct a 1-d array of the specified type. This is usually called with the syntax ``Type[]``. Element values can be specified using ``Type[a,b,c,...]``. + +:: + getindex(A, inds...) + +Returns a subset of array ``A`` as specified by ``inds``, where each ``ind`` may be an ``Int``, a ``Range``, or a ``Vector``. See the manual section on :ref:`array indexing ` for details. + +:: + getindex(collection, key...) + +Retrieve the value(s) stored at the given key or index within a collection. +The syntax ``a[i,j,...]`` is converted by the compiler to +``getindex(a, i, j, ...)``. +``` +""" +getindex + +doc""" +```rst +:: + cconvert(T,x) + +Convert "x" to a value of type "T", typically by calling ``convert(T,x)`` + +In cases where "x" cannot be safely converted to "T", unlike ``convert``, +``cconvert`` may return an object of a type different from "T", +which however is suitable for ``unsafe_convert`` to handle. + +Neither ``convert`` nor ``cconvert`` should take a Julia object and turn it into a ``Ptr``. +``` +""" +cconvert + +doc""" +```rst +:: + |>(x, f) + +Applies a function to the preceding argument. This allows for easy function chaining. + +.. doctest:: + + julia> [1:5;] |> x->x.^2 |> sum |> inv + 0.01818181818181818 +``` +""" +Base.(:(|>)) + +doc""" +```rst +:: + assert(cond) + +Throw an ``AssertionError`` if ``cond`` is false. Also available as the macro ``@assert expr``. +``` +""" +assert + +doc""" +```rst +:: + sech(x) + +Compute the hyperbolic secant of ``x`` +``` +""" +sech + +doc""" +```rst +:: + nworkers() + +Get the number of available worker processes. This is one less than nprocs(). Equal to nprocs() if nprocs() == 1. +``` +""" +nworkers + +doc""" +```rst +:: + filemode(file) + +Equivalent to stat(file).mode +``` +""" +filemode + +doc""" +```rst +:: + print_joined(io, items, delim, [last]) + +Print elements of ``items`` to ``io`` with ``delim`` between them. If ``last`` is specified, it is used as the final delimiter instead of ``delim``. +``` +""" +print_joined + +doc""" +```rst +:: + lfact(x) + +Compute the logarithmic factorial of ``x`` +``` +""" +lfact + +doc""" +```rst +:: + deconv(b,a) + +Construct vector ``c`` such that ``b = conv(a,c) + r``. Equivalent to polynomial division. +``` +""" +deconv + +doc""" +```rst +:: + insert!(collection, index, item) + +Insert an ``item`` into ``collection`` at the given ``index``. +``index`` is the index of ``item`` in the resulting ``collection``. + +.. doctest:: + + julia> insert!([6, 5, 4, 2, 1], 4, 3) + 6-element Array{Int64,1}: + 6 + 5 + 4 + 3 + 2 + 1 +``` +""" +insert! + +doc""" +```rst +:: + repmat(A, n, m) + +Construct a matrix by repeating the given matrix ``n`` times in dimension 1 and ``m`` times in dimension 2. +``` +""" +repmat + +doc""" +```rst +:: + acos(x) + +Compute the inverse cosine of ``x``, where the output is in radians +``` +""" +acos + +doc""" +```rst +:: + nzrange(A, col) + +Return the range of indices to the structural nonzero values of a sparse matrix column. In conjunction with ``nonzeros(A)`` and ``rowvals(A)``, this allows for convenient iterating over a sparse matrix :: + + A = sparse(I,J,V) + rows = rowvals(A) + vals = nonzeros(A) + m, n = size(A) + for i = 1:n + for j in nzrange(A, i) + row = rows[j] + val = vals[j] + # perform sparse wizardry... + end + end +``` +""" +nzrange + +doc""" +```rst +:: + ispath(path) -> Bool + +Returns ``true`` if ``path`` is a valid filesystem path, ``false`` otherwise. +``` +""" +ispath + +doc""" +```rst +:: + fdio([name::AbstractString, ]fd::Integer[, own::Bool]) -> IOStream + +Create an ``IOStream`` object from an integer file descriptor. If ``own`` is true, closing this object will close the underlying descriptor. By default, an ``IOStream`` is closed when it is garbage collected. ``name`` allows you to associate the descriptor with a named file. +``` +""" +fdio + +doc""" +```rst +:: + unsafe_copy!(dest::Ptr{T}, src::Ptr{T}, N) + +Copy ``N`` elements from a source pointer to a destination, with no checking. The +size of an element is determined by the type of the pointers. + +The ``unsafe`` prefix on this function indicates that no validation is performed +on the pointers ``dest`` and ``src`` to ensure that they are valid. +Incorrect usage may corrupt or segfault your program, in the same manner as C. + +:: + unsafe_copy!(dest::Array, do, src::Array, so, N) + +Copy ``N`` elements from a source array to a destination, starting at offset ``so`` +in the source and ``do`` in the destination (1-indexed). + +The ``unsafe`` prefix on this function indicates that no validation is performed +to ensure that N is inbounds on either array. Incorrect usage may corrupt or segfault +your program, in the same manner as C. +``` +""" +unsafe_copy! + +doc""" +```rst +:: + diag(M[, k]) + +The ``k``\ th diagonal of a matrix, as a vector. Use ``diagm`` to construct a diagonal matrix. +``` +""" +diag + +doc""" +```rst +:: + .^(x, y) + +Element-wise exponentiation operator. +``` +""" +Base.(:(.^)) + +doc""" +```rst +:: + isspace(c::Union{Char,AbstractString}) -> Bool + +Tests whether a character is any whitespace character. Includes ASCII characters '\\t', '\\n', '\\v', '\\f', '\\r', and ' ', Latin-1 character U+0085, and characters in Unicode category Zs. For strings, tests whether this is true for all elements of the string. +``` +""" +isspace + +doc""" +```rst +:: + splitext(path::AbstractString) -> (AbstractString,AbstractString) + +If the last component of a path contains a dot, split the path into everything +before the dot and everything including and after the dot. Otherwise, return +a tuple of the argument unmodified and the empty string. +``` +""" +splitext + +doc""" +```rst +:: + gethostname() -> AbstractString + +Get the local machine's host name. +``` +""" +gethostname + +doc""" +```rst +:: + code_typed(f, types; optimize=true) + +Returns an array of lowered and type-inferred ASTs for the methods matching the given generic function and type signature. The keyword argument ``optimize`` controls whether additional optimizations, such as inlining, are also applied. +``` +""" +code_typed + +doc""" +```rst +:: + hankelh1x(nu, x) + +Scaled Bessel function of the third kind of order ``nu``, :math:`H^{(1)}_\nu(x) e^{-x i}`. +``` +""" +hankelh1x + +doc""" +```rst +:: + blkdiag(A...) + +Concatenate matrices block-diagonally. Currently only implemented for sparse matrices. +``` +""" +blkdiag + +doc""" +```rst +:: + replace(string, pat, r[, n]) + +Search for the given pattern ``pat``, and replace each occurrence with ``r``. If ``n`` is provided, replace at most ``n`` occurrences. As with search, the second argument may be a single character, a vector or a set of characters, a string, or a regular expression. If ``r`` is a function, each occurrence is replaced with ``r(s)`` where ``s`` is the matched substring. If ``pat`` is a regular expression and ``r`` is a ``SubstitutionString``, then capture group references in ``r`` are replaced with the corresponding matched text. +``` +""" +replace + +doc""" +```rst +:: + randexp([rng], [dims...]) + +Generate a random number according to the exponential distribution with scale 1. Optionally generate an array of such random numbers. +``` +""" +randexp + +doc""" +```rst +:: + chop(string) + +Remove the last character from a string +``` +""" +chop + +doc""" +```rst +:: + Float32(x [, mode::RoundingMode]) + +Create a Float32 from ``x``. If ``x`` is not exactly representable then +``mode`` determines how ``x`` is rounded. + +.. doctest:: + + julia> Float32(1/3, RoundDown) + 0.3333333f0 + + julia> Float32(1/3, RoundUp) + 0.33333334f0 + +See ``get_rounding`` for available rounding modes. +``` +""" +Float32 + +doc""" +```rst +:: + readuntil(stream, delim) + +Read a string, up to and including the given delimiter byte. +``` +""" +readuntil + +doc""" +```rst +:: + isimmutable(v) + +True if value ``v`` is immutable. See :ref:`man-immutable-composite-types` for a discussion of immutability. +Note that this function works on values, so if you give it a type, it will tell you that a value of ``DataType`` is mutable. +``` +""" +isimmutable + +doc""" +```rst +:: + macroexpand(x) + +Takes the expression x and returns an equivalent expression with all macros removed (expanded). +``` +""" +macroexpand + +doc""" +```rst +:: + issticky(path) -> Bool + +Returns ``true`` if ``path`` has the sticky bit set, ``false`` otherwise. +``` +""" +issticky + +doc""" +```rst +:: + rol(B::BitArray{1}, i::Integer) -> BitArray{1} + +Performs a left rotation operation. +``` +""" +rol + +doc""" +```rst +:: + Mmap.mmap(io::Union(IOStream,AbstractString,Mmap.AnonymousMmap)[, type::Type{Array{T,N}}, dims, offset]; grow::Bool=true, shared::Bool=true) + Mmap.mmap(type::Type{Array{T,N}}, dims) + +Create an ``Array`` whose values are linked to a file, using memory-mapping. This provides a convenient way of working with data too large to fit in the computer's memory. + +The type is an ``Array{T,N}`` with a bits-type element of ``T`` and dimension ``N`` that determines how the bytes of the array are interpreted. Note that the file must be stored in binary format, and no format conversions are possible (this is a limitation of operating systems, not Julia). + +``dims`` is a tuple or single ``Integer`` specifying the size or length of the array. + +The file is passed via the stream argument, either as an open ``IOStream`` or filename string. When you initialize the stream, use ``"r"`` for a "read-only" array, and ``"w+"`` to create a new array used to write values to disk. + +If no ``type`` argument is specified, the default is ``Vector{UInt8}``. + +Optionally, you can specify an offset (in bytes) if, for example, you want to skip over a header in the file. The default value for the offset is the current stream position for an ``IOStream``. + +The ``grow`` keyword argument specifies whether the disk file should be grown to accomodate the requested size of array (if the total file size is < requested array size). Write privileges are required to grow the file. + +The ``shared`` keyword argument specifies whether the resulting ``Array`` and changes made to it will be visible to other processes mapping the same file. + +For example, the following code:: + + # Create a file for mmapping + # (you could alternatively use mmap to do this step, too) + A = rand(1:20, 5, 30) + s = open("/tmp/mmap.bin", "w+") + # We'll write the dimensions of the array as the first two Ints in the file + write(s, size(A,1)) + write(s, size(A,2)) + # Now write the data + write(s, A) + close(s) + + # Test by reading it back in + s = open("/tmp/mmap.bin") # default is read-only + m = read(s, Int) + n = read(s, Int) + A2 = Mmap.mmap(s, Matrix{Int}, (m,n)) + +creates a ``m``-by-``n`` ``Matrix{Int}``, linked to the file associated with stream ``s``. + +A more portable file would need to encode the word size---32 bit or 64 bit---and endianness information in the header. In practice, consider encoding binary data using standard formats like HDF5 (which can be used with memory-mapping). + +:: + Mmap.mmap(io, BitArray, [dims, offset]) + +Create a ``BitArray`` whose values are linked to a file, using memory-mapping; it has the same purpose, works in the same way, and has the same arguments, as :func:`mmap`, but the byte representation is different. + +**Example**: ``B = Mmap.mmap(s, BitArray, (25,30000))`` + +This would create a 25-by-30000 ``BitArray``, linked to the file associated with stream ``s``. +``` +""" +Mmap.mmap + +doc""" +```rst +:: + airyprime(x) + +Airy function derivative :math:`\operatorname{Ai}'(x)`. +``` +""" +airyprime + +doc""" +```rst +:: + bessely0(x) + +Bessel function of the second kind of order 0, :math:`Y_0(x)`. +``` +""" +bessely0 + +doc""" +```rst +:: + any!(r, A) + +Test whether any values in ``A`` along the singleton dimensions of ``r`` are true, +and write results to ``r``. +``` +""" +any! + +doc""" +```rst +:: + falses(dims) + +Create a ``BitArray`` with all values set to false +``` +""" +falses + +doc""" +```rst +:: + filter!(function, collection) + +Update ``collection``, removing elements for which ``function`` is false. +For associative collections, the function is passed two arguments (key and value). +``` +""" +filter! + +doc""" +```rst +:: + schurfact(A) -> Schur + +Computes the Schur factorization of the matrix ``A``. The (quasi) triangular Schur factor can be obtained from the ``Schur`` object ``F`` with either ``F[:Schur]`` or ``F[:T]`` and the unitary/orthogonal Schur vectors can be obtained with ``F[:vectors]`` or ``F[:Z]`` such that ``A=F[:vectors]*F[:Schur]*F[:vectors]'``. The eigenvalues of ``A`` can be obtained with ``F[:values]``. + +:: + schurfact(A, B) -> GeneralizedSchur + +Computes the Generalized Schur (or QZ) factorization of the matrices ``A`` and ``B``. The (quasi) triangular Schur factors can be obtained from the ``Schur`` object ``F`` with ``F[:S]`` and ``F[:T]``, the left unitary/orthogonal Schur vectors can be obtained with ``F[:left]`` or ``F[:Q]`` and the right unitary/orthogonal Schur vectors can be obtained with ``F[:right]`` or ``F[:Z]`` such that ``A=F[:left]*F[:S]*F[:right]'`` and ``B=F[:left]*F[:T]*F[:right]'``. The generalized eigenvalues of ``A`` and ``B`` can be obtained with ``F[:alpha]./F[:beta]``. +``` +""" +schurfact + +doc""" +```rst +:: + base64decode(string) + +Decodes the base64-encoded ``string`` and returns a ``Vector{UInt8}`` +of the decoded bytes. +``` +""" +base64decode + +doc""" +```rst +:: + besselkx(nu, x) + +Scaled modified Bessel function of the second kind of order ``nu``, :math:`K_\nu(x) e^x`. +``` +""" +besselkx + +doc""" +```rst +:: + myid() + +Get the id of the current process. +``` +""" +myid + +doc""" +```rst +:: + oct(n, [pad]) + +Convert an integer to an octal string, optionally specifying a number of digits to pad to. +``` +""" +oct + +doc""" +```rst +:: + timedwait(testcb::Function, secs::Float64; pollint::Float64=0.1) + +Waits till ``testcb`` returns ``true`` or for ``secs``` seconds, whichever is earlier. +``testcb`` is polled every ``pollint`` seconds. +``` +""" +timedwait + +doc""" +```rst +:: + sizeof(type) + +Size, in bytes, of the canonical binary representation of the given type, if any. + +:: + sizeof(s::AbstractString) + +The number of bytes in string ``s``. +``` +""" +sizeof + +doc""" +```rst +:: + ===(x, y) + ≡(x,y) + +See the :func:`is` operator +``` +""" +Base.(:(===)) + +doc""" +```rst +:: + ReadOnlyMemoryError() + +An operation tried to write to memory that is read-only. +``` +""" +ReadOnlyMemoryError + +doc""" +```rst +:: + startswith(string, prefix | chars) + +Returns ``true`` if ``string`` starts with ``prefix``. If the second argument is a vector or set of characters, tests whether the first character of ``string`` belongs to that set. +``` +""" +startswith + +doc""" +```rst +:: + permutedims!(dest, src, perm) + +Permute the dimensions of array ``src`` and store the result in the array ``dest``. ``perm`` is a vector specifying a permutation of length ``ndims(src)``. The preallocated array ``dest`` should have ``size(dest) == size(src)[perm]`` and is completely overwritten. No in-place permutation is supported and unexpected results will happen if `src` and `dest` have overlapping memory regions. +``` +""" +permutedims! + +doc""" +```rst +:: + functionloc(f::Function, types) + +Returns a tuple ``(filename,line)`` giving the location of a method definition. + +:: + functionloc(m::Method) + +Returns a tuple ``(filename,line)`` giving the location of a method definition. +``` +""" +functionloc + +doc""" +```rst +:: + stride(A, k) + +Returns the distance in memory (in number of elements) between adjacent elements in dimension k +``` +""" +stride + +doc""" +```rst +:: + last(coll) + +Get the last element of an ordered collection, if it can be computed in O(1) time. +This is accomplished by calling :func:`endof` to get the last index. +Returns the end point of a :obj:`Range` even if it is empty. +``` +""" +last + +doc""" +```rst +:: + islink(path) -> Bool + +Returns ``true`` if ``path`` is a symbolic link, ``false`` otherwise. +``` +""" +islink + +doc""" +```rst +:: + istril(A) -> Bool + +Test whether a matrix is lower triangular. +``` +""" +istril + +doc""" +```rst +:: + lgamma(x) + +Compute the logarithm of the absolute value of :func:`gamma` for +:obj:`Real` ``x``, while for :obj:`Complex` ``x`` it computes the +logarithm of ``gamma(x)``. +``` +""" +lgamma + +doc""" +```rst +:: + bin(n, [pad]) + +Convert an integer to a binary string, optionally specifying a number of digits to pad to. +``` +""" +bin + +doc""" +```rst +:: + cis(z) + +Return :math:`\exp(iz)`. +``` +""" +cis + +doc""" +```rst +:: + isapprox(x::Number, y::Number; rtol::Real=cbrt(maxeps), atol::Real=sqrt(maxeps)) + +Inexact equality comparison - behaves slightly different depending on types of input args: + +* For ``AbstractFloat`` numbers, ``isapprox`` returns ``true`` if ``abs(x-y) <= atol + rtol*max(abs(x), abs(y))``. + +* For ``Integer`` and ``Rational`` numbers, ``isapprox`` returns ``true`` if ``abs(x-y) <= atol``. The `rtol` argument is ignored. If one of ``x`` and ``y`` is ``AbstractFloat``, the other is promoted, and the method above is called instead. + +* For ``Complex`` numbers, the distance in the complex plane is compared, using the same criterion as above. + +For default tolerance arguments, ``maxeps = max(eps(abs(x)), eps(abs(y)))``. +``` +""" +isapprox + +doc""" +```rst +:: + primes(n) + +Returns a collection of the prime numbers <= ``n``. +``` +""" +primes + +doc""" +```rst +:: + sinh(x) + +Compute hyperbolic sine of ``x`` +``` +""" +sinh + +doc""" +```rst +:: + permutations(array) + +Generate all permutations of an indexable object. Because the +number of permutations can be very large, this function returns an +iterator object. Use ``collect(permutations(array))`` to get an array +of all permutations. +``` +""" +permutations + +doc""" +```rst +:: + ceil([T,] x, [digits, [base]]) + +``ceil(x)`` returns the nearest integral value of the same type as ``x`` +that is greater than or equal to ``x``. + +``ceil(T, x)`` converts the result to type ``T``, throwing an +``InexactError`` if the value is not representable. + +``digits`` and ``base`` work as for :func:`round`. +``` +""" +ceil + +doc""" +```rst +:: + mapslices(f, A, dims) + +Transform the given dimensions of array ``A`` using function ``f``. ``f`` +is called on each slice of ``A`` of the form ``A[...,:,...,:,...]``. +``dims`` is an integer vector specifying where the colons go in this +expression. The results are concatenated along the remaining dimensions. +For example, if ``dims`` is ``[1,2]`` and A is 4-dimensional, ``f`` is +called on ``A[:,:,i,j]`` for all ``i`` and ``j``. +``` +""" +mapslices + +doc""" +```rst +:: + spdiagm(B, d[, m, n]) + +Construct a sparse diagonal matrix. ``B`` is a tuple of vectors containing the diagonals and ``d`` is a tuple containing the positions of the diagonals. In the case the input contains only one diagonaly, ``B`` can be a vector (instead of a tuple) and ``d`` can be the diagonal position (instead of a tuple), defaulting to 0 (diagonal). Optionally, ``m`` and ``n`` specify the size of the resulting sparse matrix. +``` +""" +spdiagm + +doc""" +```rst +:: + svdvals(A) + +Returns the singular values of ``A``. + +:: + svdvals(A, B) + +Return only the singular values from the generalized singular value decomposition of ``A`` and ``B``. +``` +""" +svdvals + +doc""" +```rst +:: + issocket(path) -> Bool + +Returns ``true`` if ``path`` is a socket, ``false`` otherwise. +``` +""" +issocket + +doc""" +```rst +:: + srand([rng], [seed]) + +Reseed the random number generator. If a ``seed`` is provided, the RNG will give a reproducible sequence of numbers, otherwise Julia will get entropy from the system. +For ``MersenneTwister``, the ``seed`` may be a non-negative integer, a vector of ``UInt32`` integers or a filename, in which case the seed is read from a file. +``RandomDevice`` does not support seeding. +``` +""" +srand + +doc""" +```rst +:: + schur(A) -> Schur[:T], Schur[:Z], Schur[:values] + +See :func:`schurfact` + +:: + schur(A,B) -> GeneralizedSchur[:S], GeneralizedSchur[:T], GeneralizedSchur[:Q], GeneralizedSchur[:Z] + +See :func:`schurfact` +``` +""" +schur + +doc""" +```rst +:: + isexecutable(path) -> Bool + +Returns ``true`` if the current user has permission to execute ``path``, +``false`` otherwise. +``` +""" +isexecutable + +doc""" +```rst +:: + acot(x) + +Compute the inverse cotangent of ``x``, where the output is in radians +``` +""" +acot + +doc""" +```rst +:: + middle(x) + +Compute the middle of a scalar value, which is equivalent to ``x`` itself, +but of the type of ``middle(x, x)`` for consistency. + +:: + middle(x, y) + +Compute the middle of two reals ``x`` and ``y``, which is equivalent +in both value and type to computing their mean (``(x + y) / 2``). + +:: + middle(range) + +Compute the middle of a range, which consists in computing the mean of its extrema. +Since a range is sorted, the mean is performed with the first and last element. + +:: + middle(array) + +Compute the middle of an array, which consists in finding its extrema and +then computing their mean. +``` +""" +middle + +doc""" +```rst +:: + oftype(x, y) + +Convert ``y`` to the type of ``x`` (``convert(typeof(x), y)``). +``` +""" +oftype + +doc""" +```rst +:: + maxabs!(r, A) + +Compute the maximum absolute values over the singleton dimensions of ``r``, +and write values to ``r``. +``` +""" +maxabs! + +doc""" +```rst +:: + nullspace(M) + +Basis for nullspace of ``M``. +``` +""" +nullspace + +doc""" +```rst +:: + isfinite(f) -> Bool + +Test whether a number is finite +``` +""" +isfinite + +doc""" +```rst +:: + push!(collection, items...) -> collection + +Insert one or more ``items`` at the end of ``collection``. + +.. doctest:: + + julia> push!([1, 2, 3], 4, 5, 6) + 6-element Array{Int64,1}: + 1 + 2 + 3 + 4 + 5 + 6 + +Use :func:`append!` to add all the elements of another collection to +``collection``. +The result of the preceding example is equivalent to +``append!([1, 2, 3], [4, 5, 6])``. +``` +""" +push! + +doc""" +```rst +:: + prevpow(a, x) + +The largest ``a^n`` not greater than ``x``, where ``n`` is a non-negative integer. +``a`` must be greater than 1, and ``x`` must not be less than 1. +``` +""" +prevpow + +doc""" +```rst +:: + indexin(a, b) + +Returns a vector containing the highest index in ``b`` +for each value in ``a`` that is a member of ``b`` . +The output vector contains 0 wherever ``a`` is not a member of ``b``. +``` +""" +indexin + +doc""" +```rst +:: + permutedims(A, perm) + +Permute the dimensions of array ``A``. ``perm`` is a vector specifying a permutation of length ``ndims(A)``. This is a generalization of transpose for multi-dimensional arrays. Transpose is equivalent to ``permutedims(A, [2,1])``. +``` +""" +permutedims + +doc""" +```rst +:: + shuffle!([rng,] v) + +In-place version of :func:`shuffle`. +``` +""" +shuffle! + +doc""" +```rst +:: + fldmod(x, y) + +The floored quotient and modulus after division. Equivalent to ``(fld(x,y), mod(x,y))``. +``` +""" +fldmod + +doc""" +```rst +:: + promote(xs...) + +Convert all arguments to their common promotion type (if any), and return them all (as a tuple). +``` +""" +promote + +doc""" +```rst +:: + @schedule + +Wrap an expression in a Task and add it to the scheduler's queue. +``` +""" +:@schedule + +doc""" +```rst +:: + bessely(nu, x) + +Bessel function of the second kind of order ``nu``, :math:`Y_\nu(x)`. +``` +""" +bessely + +doc""" +```rst +:: + gradient(F, [h]) + +Compute differences along vector ``F``, using ``h`` as the spacing between points. +The default spacing is one. +``` +""" +gradient + +doc""" +```rst +:: + tan(x) + +Compute tangent of ``x``, where ``x`` is in radians +``` +""" +tan + +doc""" +```rst +:: + sprint(f::Function, args...) + +Call the given function with an I/O stream and the supplied extra arguments. +Everything written to this I/O stream is returned as a string. +``` +""" +sprint + +doc""" +```rst +:: + fd(stream) + +Returns the file descriptor backing the stream or file. Note that this function only applies to synchronous `File`'s and `IOStream`'s +not to any of the asynchronous streams. +``` +""" +fd + +doc""" +```rst +:: + require(module::Symbol) + +This function is part of the implementation of ``using`` / ``import``, if a module is not already defined in ``Main``. It can also be called directly to force reloading a module, regardless of whether it has been loaded before (for exmple, when interactively developing libraries). + +Loads a source files, in the context of the ``Main`` module, on every active node, searching standard locations for files. ``require`` is considered a top-level operation, so it sets the current ``include`` path but does not use it to search for files (see help for ``include``). This function is typically used to load library code, and is implicitly called by ``using`` to load packages. + +When searching for files, ``require`` first looks in the current working directory, then looks for package code under ``Pkg.dir()``, then tries paths in the global array ``LOAD_PATH``. +``` +""" +require + +doc""" +```rst +:: + $(x, y) + +Bitwise exclusive or +``` +""" +$ + +doc""" +```rst +:: + expand(x) + +Takes the expression x and returns an equivalent expression in lowered form +``` +""" +expand + +doc""" +```rst +:: + peakflops(n; parallel=false) + +``peakflops`` computes the peak flop rate of the computer by using double precision :func:`Base.LinAlg.BLAS.gemm!`. By default, if no arguments are specified, it multiplies a matrix of size ``n x n``, where ``n = 2000``. If the underlying BLAS is using multiple threads, higher flop rates are realized. The number of BLAS threads can be set with ``blas_set_num_threads(n)``. + +If the keyword argument ``parallel`` is set to ``true``, ``peakflops`` is run in parallel on all the worker processors. The flop rate of the entire parallel computer is returned. When running in parallel, only 1 BLAS thread is used. The argument ``n`` still refers to the size of the problem that is solved on each processor. +``` +""" +peakflops + +doc""" +```rst +:: + svd(A, [thin=true]) -> U, S, V + +Wrapper around ``svdfact`` extracting all parts the factorization to a tuple. Direct use of ``svdfact`` is therefore generally more efficient. Computes the SVD of A, returning ``U``, vector ``S``, and ``V`` such that ``A == U*diagm(S)*V'``. If ``thin`` is ``true``, an economy mode decomposition is returned. The default is to produce a thin decomposition. + +:: + svd(A, B) -> U, V, Q, D1, D2, R0 + +Wrapper around ``svdfact`` extracting all parts the factorization to a tuple. Direct use of ``svdfact`` is therefore generally more efficient. The function returns the generalized SVD of ``A`` and ``B``, returning ``U``, ``V``, ``Q``, ``D1``, ``D2``, and ``R0`` such that ``A = U*D1*R0*Q'`` and ``B = V*D2*R0*Q'``. +``` +""" +svd + +doc""" +```rst +:: + ones(type, dims) + +Create an array of all ones of specified type. The type defaults to Float64 if not specified. + +:: + ones(A) + +Create an array of all ones with the same element type and shape as A. +``` +""" +ones + +doc""" +```rst +:: + ind2chr(string, i) + +Convert a byte index to a character index +``` +""" +ind2chr + +doc""" +```rst +:: + reshape(A, dims) + +Create an array with the same data as the given array, but with different dimensions. An implementation for a particular type of array may choose whether the data is copied or shared. +``` +""" +reshape + +doc""" +```rst +:: + randsubseq!(S, A, p) + +Like ``randsubseq``, but the results are stored in ``S`` (which is +resized as needed). +``` +""" +randsubseq! + +doc""" +```rst +:: + maximum(itr) + +Returns the largest element in a collection. + +:: + maximum(A, dims) + +Compute the maximum value of an array over the given dimensions. +``` +""" +maximum + +doc""" +```rst +:: + redisplay(x) + redisplay(d::Display, x) + redisplay(mime, x) + redisplay(d::Display, mime, x) + +By default, the ``redisplay`` functions simply call ``display``. However, +some display backends may override ``redisplay`` to modify an existing +display of ``x`` (if any). Using ``redisplay`` is also a hint to the +backend that ``x`` may be redisplayed several times, and the backend +may choose to defer the display until (for example) the next interactive +prompt. +``` +""" +redisplay + +doc""" +```rst +:: + A_mul_Bc(...) + +Matrix operator A B\ :sup:`H` +``` +""" +A_mul_Bc + +doc""" +```rst +:: + searchsorted(a, x, [by=,] [lt=,] [rev=false]) + +Returns the range of indices of ``a`` which compare as equal to ``x`` according to the +order specified by the ``by``, ``lt`` and ``rev`` keywords, assuming that ``a`` is +already sorted in that order. Returns an empty range located at the insertion point if +``a`` does not contain values equal to ``x``. +``` +""" +searchsorted + +doc""" +```rst +:: + /(x, y) + +Right division operator: multiplication of ``x`` by the inverse of ``y`` on the right. +Gives floating-point results for integer arguments. +``` +""" +Base.(:(/)) + +doc""" +```rst +:: + ldltfact(A) -> LDLtFactorization + +Compute a factorization of a positive definite matrix ``A`` such that ``A=L*Diagonal(d)*L'`` where ``L`` is a unit lower triangular matrix and ``d`` is a vector with non-negative elements. + +:: + ldltfact(A; shift=0, perm=Int[]) -> CHOLMOD.Factor + +Compute the LDLt factorization of a sparse symmetric or Hermitian +matrix ``A``. A fill-reducing permutation is used. ``F = +ldltfact(A)`` is most frequently used to solve systems of equations +with ``F\b``, but also the methods ``diag``, ``det``, ``logdet`` +are defined for ``F``. You can also extract individual factors from +``F``, using ``F[:L]``. However, since pivoting is on by default, +the factorization is internally represented as ``A == P'*L*D*L'*P`` +with a permutation matrix ``P``; using just ``L`` without +accounting for ``P`` will give incorrect answers. To include the +effects of permutation, it's typically preferable to extact +"combined" factors like ``PtL = F[:PtL]`` (the equivalent of +``P'*L``) and ``LtP = F[:UP]`` (the equivalent of ``L'*P``). The +complete list of supported factors is ``:L, :PtL, :D, :UP, :U, :LD, +:DU, :PtLD, :DUP``. + +Setting optional ``shift`` keyword argument computes the factorization +of ``A+shift*I`` instead of ``A``. If the ``perm`` argument is nonempty, +it should be a permutation of `1:size(A,1)` giving the ordering to use +(instead of CHOLMOD's default AMD ordering). + +The function calls the C library CHOLMOD and many other functions +from the library are wrapped but not exported. +``` +""" +ldltfact + +doc""" +```rst +:: + connect([host],port) -> TcpSocket + +Connect to the host ``host`` on port ``port`` + +:: + connect(path) -> Pipe + +Connect to the Named Pipe/Domain Socket at ``path`` + +:: + connect(manager::FooManager, pid::Int, config::WorkerConfig) -> (instrm::AsyncStream, outstrm::AsyncStream) + + Implemented by cluster managers using custom transports. It should establish a logical connection to worker with id ``pid``, + specified by ``config`` and return a pair of ``AsyncStream`` objects. Messages from ``pid`` to current process will be read + off ``instrm``, while messages to be sent to ``pid`` will be written to ``outstrm``. The custom transport implementation + must ensure that messages are delivered and received completely and in order. ``Base.connect(manager::ClusterManager.....)`` + sets up TCP/IP socket connections in-between workers. +``` +""" +connect + +doc""" +```rst +:: + mean(v[, region]) + +Compute the mean of whole array ``v``, or optionally along the dimensions in ``region``. +Note: Julia does not ignore ``NaN`` values in the computation. +For applications requiring the handling of missing data, the ``DataArray`` +package is recommended. +``` +""" +mean + +doc""" +```rst +:: + split(string, [chars]; limit=0, keep=true) + +Return an array of substrings by splitting the given string on occurrences of the given character delimiters, which may be specified in any of the formats allowed by ``search``'s second argument (i.e. a single character, collection of characters, string, or regular expression). If ``chars`` is omitted, it defaults to the set of all space characters, and ``keep`` is taken to be false. The two keyword arguments are optional: they are are a maximum size for the result and a flag determining whether empty fields should be kept in the result. +``` +""" +split + +doc""" +```rst +:: + dump(x) + +Show all user-visible structure of a value. +``` +""" +dump + +doc""" +```rst +:: + sumabs(itr) + +Sum absolute values of all elements in a collection. This is +equivalent to `sum(abs(itr))` but faster. + +:: + sumabs(A, dims) + +Sum absolute values of elements of an array over the given +dimensions. +``` +""" +sumabs + +doc""" +```rst +:: + svdvals!(A) + +Returns the singular values of ``A``, while saving space by overwriting the input. +``` +""" +svdvals! + +doc""" +```rst +:: + collect(collection) + +Return an array of all items in a collection. For associative collections, returns (key, value) tuples. + +:: + collect(element_type, collection) + +Return an array of type ``Array{element_type,1}`` of all items in a collection. +``` +""" +collect + +doc""" +```rst +:: + consume(task, values...) + +Receive the next value passed to ``produce`` by the specified task. +Additional arguments may be passed, to be returned from the last ``produce`` call +in the producer. +``` +""" +consume + +doc""" +```rst +:: + hankelh2x(nu, x) + +Scaled Bessel function of the third kind of order ``nu``, :math:`H^{(2)}_\nu(x) e^{x i}`. +``` +""" +hankelh2x + +doc""" +```rst +:: + ndigits(n, b) + +Compute the number of digits in number ``n`` written in base ``b``. +``` +""" +ndigits + +doc""" +```rst +:: + cummax(A, [dim]) + +Cumulative maximum along a dimension. +The dimension defaults to 1. +``` +""" +cummax + +doc""" +```rst +:: + watch_file(path, timeout_s::Real) + +Watch file or directory ``s`` for changes until a change occurs or ``timeout_s`` seconds have elapsed. + +The returned value is an object with boolean fields ``changed``, ``renamed``, +and ``timedout``, giving the result of watching the file. + +This behavior of this function varies slightly across platforms. +See https://nodejs.org/api/fs.html#fs_caveat for more detailed information. +``` +""" +watch_file + +doc""" +```rst +:: + At_rdiv_Bt(a,b) + +Matrix operator A\ :sup:`T` / B\ :sup:`T` +``` +""" +At_rdiv_Bt + +doc""" +```rst +:: + isinteractive() -> Bool + +Determine whether Julia is running an interactive session. +``` +""" +isinteractive + +doc""" +```rst +:: + At_mul_Bt(...) + +Matrix operator A\ :sup:`T` B\ :sup:`T` +``` +""" +At_mul_Bt + +doc""" +```rst +:: + sum!(r, A) + +Sum elements of ``A`` over the singleton dimensions of ``r``, +and write results to ``r``. +``` +""" +sum! + +doc""" +```rst +:: + close(stream) + +Close an I/O stream. Performs a ``flush`` first. + +:: + close(Channel) + + Closes a channel. An exception is thrown by: + + * ``put!`` on a on a closed channel. + + * ``take!`` and ``fetch`` on an empty, closed channel. +``` +""" +close + +doc""" +```rst +:: + cospi(x) + +Compute :math:`\cos(\pi x)` more accurately than ``cos(pi*x)``, especially for large ``x``. +``` +""" +cospi + +doc""" +```rst +:: + parentindexes(A) + +From an array view ``A``, returns the corresponding indexes in the parent +``` +""" +parentindexes + +doc""" +```rst +:: + spones(S) + +Create a sparse matrix with the same structure as that of ``S``, but with every nonzero element having the value ``1.0``. +``` +""" +spones + +doc""" +```rst +:: + display(x) + display(d::Display, x) + display(mime, x) + display(d::Display, mime, x) + +Display ``x`` using the topmost applicable display in the display stack, +typically using the richest supported multimedia output for ``x``, with +plain-text ``STDOUT`` output as a fallback. The ``display(d, x)`` variant +attempts to display ``x`` on the given display ``d`` only, throwing +a ``MethodError`` if ``d`` cannot display objects of this type. + +There are also two variants with a ``mime`` argument (a MIME type +string, such as ``"image/png"``), which attempt to display ``x`` using the +requested MIME type *only*, throwing a ``MethodError`` if this type +is not supported by either the display(s) or by ``x``. With these +variants, one can also supply the "raw" data in the requested MIME +type by passing ``x::AbstractString`` (for MIME types with text-based storage, +such as text/html or application/postscript) or ``x::Vector{UInt8}`` +(for binary MIME types). +``` +""" +display + +doc""" +```rst +:: + @spawnat + +Accepts two arguments, ``p`` and an expression. A closure is created around +the expression and run asynchronously on process ``p``. Returns a ``RemoteRef`` +to the result. +``` +""" +:@spawnat + +doc""" +```rst +:: + print_shortest(io, x) + +Print the shortest possible representation, with the minimum number of consecutive non-zero digits, of number ``x``, ensuring that it would parse to the exact same number. +``` +""" +print_shortest + +doc""" +```rst +:: + merge(collection, others...) + +Construct a merged collection from the given collections. If necessary, the types of the resulting collection will be promoted to accommodate the types of the merged collections. If the same key is present in another collection, the value for that key will be the value it has in the last collection listed. + +.. doctest:: + + julia> a = Dict("foo" => 0.0, "bar" => 42.0) + Dict{ASCIIString,Float64} with 2 entries: + "bar" => 42.0 + "foo" => 0.0 + + julia> b = Dict(utf8("baz") => 17, utf8("bar") => 4711) + Dict{UTF8String,Int64} with 2 entries: + "bar" => 4711 + "baz" => 17 + + julia> merge(a, b) + Dict{UTF8String,Float64} with 3 entries: + "bar" => 4711.0 + "baz" => 17.0 + "foo" => 0.0 + + julia> merge(b, a) + Dict{UTF8String,Float64} with 3 entries: + "bar" => 42.0 + "baz" => 17.0 + "foo" => 0.0 +``` +""" +merge + +doc""" +```rst +:: + circshift(A,shifts) + +Circularly shift the data in an array. The second argument is a vector giving the amount to shift in each dimension. +``` +""" +circshift + +doc""" +```rst +:: + fieldnames(x::DataType) + +Get an array of the fields of a data type. +``` +""" +fieldnames + +doc""" +```rst +:: + yield() + +Switch to the scheduler to allow another scheduled task to run. A task that calls this function is still runnable, and will be restarted immediately if there are no other runnable tasks. +``` +""" +yield + +doc""" +```rst +:: + transpose!(dest,src) + +Transpose array ``src`` and store the result in the preallocated array ``dest``, which should have a size corresponding to ``(size(src,2),size(src,1))``. No in-place transposition is supported and unexpected results will happen if `src` and `dest` have overlapping memory regions. +``` +""" +transpose! + +doc""" +```rst +:: + isconst([m::Module], s::Symbol) -> Bool + +Determine whether a global is declared ``const`` in a given module. +The default module argument is ``current_module()``. +``` +""" +isconst + +doc""" +```rst +:: + open(command, mode::AbstractString="r", stdio=DevNull) + +Start running ``command`` asynchronously, and return a tuple +``(stream,process)``. If ``mode`` is ``"r"``, then ``stream`` +reads from the process's standard output and ``stdio`` optionally +specifies the process's standard input stream. If ``mode`` is +``"w"``, then ``stream`` writes to the process's standard input +and ``stdio`` optionally specifies the process's standard output +stream. + +:: + open(f::Function, command, mode::AbstractString="r", stdio=DevNull) + +Similar to ``open(command, mode, stdio)``, but calls ``f(stream)`` +on the resulting read or write stream, then closes the stream +and waits for the process to complete. Returns the value returned +by ``f``. + +:: + open(file_name, [read, write, create, truncate, append]) -> IOStream + +Open a file in a mode specified by five boolean arguments. The default is to open files for reading only. Returns a stream for accessing the file. + +:: + open(file_name, [mode]) -> IOStream + +Alternate syntax for open, where a string-based mode specifier is used instead of the five booleans. The values of ``mode`` correspond to those from ``fopen(3)`` or Perl ``open``, and are equivalent to setting the following boolean groups: + +==== ================================= + r read + r+ read, write + w write, create, truncate + w+ read, write, create, truncate + a write, create, append + a+ read, write, create, append +==== ================================= + +:: + open(f::function, args...) + +Apply the function ``f`` to the result of ``open(args...)`` and close the resulting file descriptor upon completion. + +**Example**: ``open(readall, "file.txt")`` +``` +""" +open + +doc""" +```rst +:: + sort(v, [alg=,] [by=,] [lt=,] [rev=false]) + +Variant of ``sort!`` that returns a sorted copy of ``v`` leaving ``v`` itself unmodified. + +:: + sort(A, dim, [alg=,] [by=,] [lt=,] [rev=false]) + +Sort a multidimensional array ``A`` along the given dimension. +``` +""" +sort + +doc""" +```rst +:: + kron(A, B) + +Kronecker tensor product of two vectors or two matrices. +``` +""" +kron + +doc""" +```rst +:: + >>(x, n) + +Right bit shift operator, preserving the sign of ``x``. +``` +""" +Base.(:(>>)) + +doc""" +```rst +:: + fieldoffsets(type) + +The byte offset of each field of a type relative to the data start. For example, we could use it +in the following manner to summarize information about a struct type: + +.. doctest:: + + julia> structinfo(T) = [zip(fieldoffsets(T),fieldnames(T),T.types)...]; + + julia> structinfo(StatStruct) + 12-element Array{Tuple{Int64,Symbol,DataType},1}: + (0,:device,UInt64) + (8,:inode,UInt64) + (16,:mode,UInt64) + (24,:nlink,Int64) + (32,:uid,UInt64) + (40,:gid,UInt64) + (48,:rdev,UInt64) + (56,:size,Int64) + (64,:blksize,Int64) + (72,:blocks,Int64) + (80,:mtime,Float64) + (88,:ctime,Float64) +``` +""" +fieldoffsets + +doc""" +```rst +:: + fft!(A [, dims]) + +Same as :func:`fft`, but operates in-place on ``A``, +which must be an array of complex floating-point numbers. +``` +""" +fft! + +doc""" +```rst +:: + symdiff!(s, n) + +The set ``s`` is destructively modified to toggle the inclusion of integer ``n``. + +:: + symdiff!(s, itr) + +For each element in ``itr``, destructively toggle its inclusion in set ``s``. + +:: + symdiff!(s1, s2) + +Construct the symmetric difference of sets ``s1`` and ``s2``, storing the result in ``s1``. +``` +""" +symdiff! + +doc""" +```rst +:: + randn([rng], [dims...]) + +Generate a normally-distributed random number with mean 0 and standard deviation 1. Optionally generate an array of normally-distributed random numbers. +``` +""" +randn + +doc""" +```rst +:: + process_exited(p::Process) + +Determine whether a process has exited. +``` +""" +process_exited + +doc""" +```rst +:: + tuple(xs...) + +Construct a tuple of the given objects. +``` +""" +tuple + +doc""" +```rst +:: + quantile(v, p) + +Compute the quantiles of a vector ``v`` at a specified set of probability values ``p``. +Note: Julia does not ignore ``NaN`` values in the computation. + +:: + quantile(v, p) + +Compute the quantile of a vector ``v`` at the probability ``p``. +Note: Julia does not ignore ``NaN`` values in the computation. +``` +""" +quantile + +doc""" +```rst +:: + besseli(nu, x) + +Modified Bessel function of the first kind of order ``nu``, :math:`I_\nu(x)`. +``` +""" +besseli + +doc""" +```rst +:: + ifftshift(x, [dim]) + +Undoes the effect of ``fftshift``. +``` +""" +ifftshift + +doc""" +```rst +:: + eachmatch(r::Regex, s::AbstractString[, overlap::Bool=false]) + +Search for all matches of a the regular expression ``r`` in ``s`` and return a iterator over the matches. If overlap is true, the matching sequences are allowed to overlap indices in the original string, otherwise they must be from distinct character ranges. +``` +""" +eachmatch + +doc""" +```rst +:: + log10(x) + +Compute the logarithm of ``x`` to base 10. Throws ``DomainError`` for negative ``Real`` arguments. +``` +""" +log10 + +doc""" +```rst +:: + @profile + +``@profile `` runs your expression while taking +periodic backtraces. These are appended to an internal buffer of +backtraces. +``` +""" +:@profile + +doc""" +```rst +:: + extrema(itr) + + Compute both the minimum and maximum element in a single pass, and + return them as a 2-tuple. +``` +""" +extrema + +doc""" +```rst +:: + isdigit(c::Union{Char,AbstractString}) -> Bool + +Tests whether a character is a numeric digit (0-9), or whether this +is true for all elements of a string. +``` +""" +isdigit + +doc""" +```rst +:: + @windows + +Given ``@windows? a : b``, do ``a`` on Windows and ``b`` elsewhere. See documentation for Handling Platform Variations +in the Calling C and Fortran Code section of the manual. +``` +""" +:@windows + +doc""" +```rst +:: + @unix + +Given ``@unix? a : b``, do ``a`` on Unix systems (including Linux and OS X) and ``b`` elsewhere. See documentation +for Handling Platform Variations in the Calling C and Fortran Code section of the manual. +``` +""" +:@unix + +doc""" +```rst +:: + num2hex(f) + +Get a hexadecimal string of the binary representation of a floating point number +``` +""" +num2hex + +doc""" +```rst +:: + speye(type,m[,n]) + +Create a sparse identity matrix of specified type of size ``m x m``. In case ``n`` is supplied, create a sparse identity matrix of size ``m x n``. +``` +""" +speye + +doc""" +```rst +:: + count_ones(x::Integer) -> Integer + +Number of ones in the binary representation of ``x``. + +.. doctest:: + + julia> count_ones(7) + 3 +``` +""" +count_ones + +doc""" +```rst +:: + reim(z) + +Return both the real and imaginary parts of the complex number ``z`` +``` +""" +reim + +doc""" +```rst +:: + displayable(mime) -> Bool + displayable(d::Display, mime) -> Bool + +Returns a boolean value indicating whether the given ``mime`` type (string) +is displayable by any of the displays in the current display stack, or +specifically by the display ``d`` in the second variant. +``` +""" +displayable + +doc""" +```rst +:: + sdata(S::SharedArray) + +Returns the actual ``Array`` object backing ``S`` +``` +""" +sdata + +doc""" +```rst +:: + truncate(file,n) + +Resize the file or buffer given by the first argument to exactly `n` bytes, filling previously unallocated space with '\\0' +if the file or buffer is grown +``` +""" +truncate + +doc""" +```rst +:: + stat(file) + +Returns a structure whose fields contain information about the file. The fields of the structure are: + +========= ====================================================================== + size The size (in bytes) of the file + device ID of the device that contains the file + inode The inode number of the file + mode The protection mode of the file + nlink The number of hard links to the file + uid The user id of the owner of the file + gid The group id of the file owner + rdev If this file refers to a device, the ID of the device it refers to + blksize The file-system preferred block size for the file + blocks The number of such blocks allocated + mtime Unix timestamp of when the file was last modified + ctime Unix timestamp of when the file was created +========= ====================================================================== +``` +""" +stat + +doc""" +```rst +:: + exp10(x) + +Compute :math:`10^x` +``` +""" +exp10 + +doc""" +```rst +:: + &(x, y) + +Bitwise and +``` +""" +& + +doc""" +```rst +:: + besselyx(nu, x) + +Scaled Bessel function of the second kind of order ``nu``, :math:`Y_\nu(x) e^{- | \operatorname{Im}(x) |}`. +``` +""" +besselyx + +doc""" +```rst +:: + eigmax(A) + +Returns the largest eigenvalue of ``A``. +``` +""" +eigmax + +doc""" +```rst +:: + PipeBuffer() + +An IOBuffer that allows reading and performs writes by appending. Seeking and truncating are not supported. See IOBuffer for the available constructors. + +:: + PipeBuffer(data::Vector{UInt8},[maxsize]) + +Create a PipeBuffer to operate on a data vector, optionally specifying a size beyond which the underlying Array may not be grown. +``` +""" +PipeBuffer + +doc""" +```rst +:: + eigs(A, [B,]; nev=6, which="LM", tol=0.0, maxiter=300, sigma=nothing, ritzvec=true, v0=zeros((0,))) -> (d,[v,],nconv,niter,nmult,resid) + +Computes eigenvalues ``d`` of ``A`` using Lanczos or Arnoldi iterations for +real symmetric or general nonsymmetric matrices respectively. If ``B`` is +provided, the generalized eigenproblem is solved. + +The following keyword arguments are supported: + * ``nev``: Number of eigenvalues + * ``ncv``: Number of Krylov vectors used in the computation; should satisfy + ``nev+1 <= ncv <= n`` for real symmetric problems and ``nev+2 <= ncv <= n`` + for other problems, where ``n`` is the size of the input matrix ``A``. + The default is ``ncv = max(20,2*nev+1)``. + Note that these restrictions limit the input matrix ``A`` to be of + dimension at least 2. + * ``which``: type of eigenvalues to compute. See the note below. + + ========= ====================================================================================================================== + ``which`` type of eigenvalues + --------- ---------------------------------------------------------------------------------------------------------------------- + ``:LM`` eigenvalues of largest magnitude (default) + ``:SM`` eigenvalues of smallest magnitude + ``:LR`` eigenvalues of largest real part + ``:SR`` eigenvalues of smallest real part + ``:LI`` eigenvalues of largest imaginary part (nonsymmetric or complex ``A`` only) + ``:SI`` eigenvalues of smallest imaginary part (nonsymmetric or complex ``A`` only) + ``:BE`` compute half of the eigenvalues from each end of the spectrum, biased in favor of the high end. (real symmetric ``A`` only) + ========= ====================================================================================================================== + + * ``tol``: tolerance (:math:`tol \le 0.0` defaults to ``DLAMCH('EPS')``) + * ``maxiter``: Maximum number of iterations (default = 300) + * ``sigma``: Specifies the level shift used in inverse iteration. If ``nothing`` (default), defaults to ordinary (forward) iterations. Otherwise, find eigenvalues close to ``sigma`` using shift and invert iterations. + * ``ritzvec``: Returns the Ritz vectors ``v`` (eigenvectors) if ``true`` + * ``v0``: starting vector from which to start the iterations + +``eigs`` returns the ``nev`` requested eigenvalues in ``d``, the corresponding Ritz vectors ``v`` (only if ``ritzvec=true``), the number of converged eigenvalues ``nconv``, the number of iterations ``niter`` and the number of matrix vector multiplications ``nmult``, as well as the final residual vector ``resid``. + +.. note:: The ``sigma`` and ``which`` keywords interact: the description of eigenvalues searched for by ``which`` do _not_ necessarily refer to the eigenvalues of ``A``, but rather the linear operator constructed by the specification of the iteration mode implied by ``sigma``. + + =============== ================================== ================================== + ``sigma`` iteration mode ``which`` refers to eigenvalues of + --------------- ---------------------------------- ---------------------------------- + ``nothing`` ordinary (forward) :math:`A` + real or complex inverse with level shift ``sigma`` :math:`(A - \sigma I )^{-1}` + =============== ================================== ================================== +``` +""" +eigs + +doc""" +```rst +:: + sortperm(v, [alg=,] [by=,] [lt=,] [rev=false]) + +Return a permutation vector of indices of ``v`` that puts it in sorted order. +Specify ``alg`` to choose a particular sorting algorithm (see `Sorting Algorithms`_). +``MergeSort`` is used by default, and since it is stable, the resulting permutation +will be the lexicographically first one that puts the input array into sorted order – +i.e. indices of equal elements appear in ascending order. If you choose a non-stable +sorting algorithm such as ``QuickSort``, a different permutation that puts the array +into order may be returned. The order is specified using the same keywords as ``sort!``. + +See also :func:`sortperm!` +``` +""" +sortperm + +doc""" +```rst +:: + mod2pi(x) + +Modulus after division by 2pi, returning in the range [0,2pi). + +This function computes a floating point representation of the modulus after +division by numerically exact 2pi, and is therefore not exactly the same as +mod(x,2pi), which would compute the modulus of x relative to division by the +floating-point number 2pi. +``` +""" +mod2pi + +doc""" +```rst +:: + cumsum!(B, A, [dim]) + +Cumulative sum of ``A`` along a dimension, storing the result in ``B``. +The dimension defaults to 1. +``` +""" +cumsum! + +doc""" +```rst +:: + logdet(M) + +Log of matrix determinant. Equivalent to ``log(det(M))``, but may provide increased accuracy and/or speed. +``` +""" +logdet + +doc""" +```rst +:: + hcat(A...) + +Concatenate along dimension 2 +``` +""" +hcat + +doc""" +```rst +:: + select(v, k, [by=,] [lt=,] [rev=false]) + +Variant of ``select!`` which copies ``v`` before partially sorting it, thereby +returning the same thing as ``select!`` but leaving ``v`` unmodified. +``` +""" +select + +doc""" +```rst +:: + lpad(string, n, p) + +Make a string at least ``n`` columns wide when printed, by padding on the left with copies of ``p``. +``` +""" +lpad + +doc""" +```rst +:: + mapreduce(f, op, v0, itr) + +Apply function ``f`` to each element in ``itr``, and then reduce +the result using the binary function ``op``. ``v0`` must be a +neutral element for ``op`` that will be returned for empty +collections. It is unspecified whether ``v0`` is used for non-empty +collections. + +:func:`mapreduce` is functionally equivalent to calling ``reduce(op, +v0, map(f, itr))``, but will in general execute faster since no +intermediate collection needs to be created. See documentation for +:func:`reduce` and :func:`map`. + +.. doctest:: + + julia> mapreduce(x->x^2, +, [1:3;]) # == 1 + 4 + 9 + 14 + +The associativity of the reduction is implementation-dependent. +Additionally, some implementations may reuse the return value of +``f`` for elements that appear multiple times in ``itr``. +Use :func:`mapfoldl` or :func:`mapfoldr` instead for guaranteed +left or right associativity and invocation of ``f`` for every value. + +:: + mapreduce(f, op, itr) + +Like ``mapreduce(f, op, v0, itr)``. In general, this cannot be used +with empty collections (see ``reduce(op, itr)``). +``` +""" +mapreduce + +doc""" +```rst +:: + quantile!(v, p) + +Like ``quantile``, but overwrites the input vector. +``` +""" +quantile! + +doc""" +```rst +:: + accept(server[,client]) + +Accepts a connection on the given server and returns a connection to the client. An uninitialized client +stream may be provided, in which case it will be used instead of creating a new stream. +``` +""" +accept + +doc""" +```rst +:: + ordschur(Q, T, select) -> Schur + +Reorders the Schur factorization of a real matrix ``A=Q*T*Q'`` according to the logical array ``select`` returning a Schur object ``F``. The selected eigenvalues appear in the leading diagonal of ``F[:Schur]`` and the the corresponding leading columns of ``F[:vectors]`` form an orthonormal basis of the corresponding right invariant subspace. A complex conjugate pair of eigenvalues must be either both included or excluded via ``select``. + +:: + ordschur(S, select) -> Schur + +Reorders the Schur factorization ``S`` of type ``Schur``. + +:: + ordschur(S, T, Q, Z, select) -> GeneralizedSchur + +Reorders the Generalized Schur factorization of a matrix ``(A, B) = (Q*S*Z^{H}, Q*T*Z^{H})`` according to the logical array ``select`` and returns a GeneralizedSchur object ``GS``. The selected eigenvalues appear in the leading diagonal of both``(GS[:S], GS[:T])`` and the left and right unitary/orthogonal Schur vectors are also reordered such that ``(A, B) = GS[:Q]*(GS[:S], GS[:T])*GS[:Z]^{H}`` still holds and the generalized eigenvalues of ``A`` and ``B`` can still be obtained with ``GS[:alpha]./GS[:beta]``. + +:: + ordschur(GS, select) -> GeneralizedSchur + +Reorders the Generalized Schur factorization of a Generalized Schur object. See :func:`ordschur`. +``` +""" +ordschur + +doc""" +```rst +:: + triu!(M) + +Upper triangle of a matrix, overwriting ``M`` in the process. + +:: + triu!(M, k) + +Returns the upper triangle of ``M`` starting from the ``k``\ th superdiagonal, overwriting ``M`` in the process. +``` +""" +triu! + +doc""" +```rst +:: + readall(stream::IO) + +Read the entire contents of an I/O stream as a string. + +:: + readall(filename::AbstractString) + +Open ``filename``, read the entire contents as a string, then close the file. +Equivalent to ``open(readall, filename)``. +``` +""" +readall + +doc""" +```rst +:: + poll_file(path, interval_s::Real, timeout_s::Real) -> (previous::StatStruct, current::StatStruct) + +Monitor a file for changes by polling every ``interval_s`` seconds until a change occurs or ``timeout_s`` seconds have elapsed. +The `interval_s` should be a long period; the default is 5.007 seconds. + +Returns a pair of ``StatStruct`` objects ``(previous, current)`` when a change is detected. + +To determine when a file was modified, compare `mtime(prev) != mtime(current)` to detect notification of changes. +However, using ``watch_file`` for this operation is preferred, since it is more reliable and efficient, +although in some situations it may not be available. +``` +""" +poll_file + +doc""" +```rst +:: + eachline(stream) + +Create an iterable object that will yield each line from a stream. +``` +""" +eachline + +doc""" +```rst +:: + isposdef!(A) -> Bool + +Test whether a matrix is positive definite, overwriting ``A`` in the processes. +``` +""" +isposdef! + +doc""" +```rst +:: + complex(r, [i]) + +Convert real numbers or arrays to complex. ``i`` defaults to zero. +``` +""" +complex + +doc""" +```rst +:: + setopt(sock::UDPSocket; multicast_loop = nothing, multicast_ttl=nothing, enable_broadcast=nothing, ttl=nothing) + +Set UDP socket options. ``multicast_loop``: loopback for multicast packets (default: true). ``multicast_ttl``: TTL for multicast packets. ``enable_broadcast``: flag must be set to true if socket will be used for broadcast messages, or else the UDP system will return an access error (default: false). ``ttl``: Time-to-live of packets sent on the socket. +``` +""" +setopt + +doc""" +```rst +:: + Mmap.Anonymous(name, readonly, create) + +Create an ``IO``-like object for creating zeroed-out mmapped-memory that is not tied to a file for use in ``Mmap.mmap``. Used by ``SharedArray`` for creating shared memory arrays. +``` +""" +Mmap.Anonymous + +doc""" +```rst +:: + A_rdiv_Bc(...) + +Matrix operator A / B\ :sup:`H` +``` +""" +A_rdiv_Bc + +doc""" +```rst +:: + sparse(I,J,V,[m,n,combine]) + +Create a sparse matrix ``S`` of dimensions ``m x n`` such that ``S[I[k], J[k]] = V[k]``. The ``combine`` function is used to combine duplicates. If ``m`` and ``n`` are not specified, they are set to ``max(I)`` and ``max(J)`` respectively. If the ``combine`` function is not supplied, duplicates are added by default. + +:: + sparse(A) + +Convert an AbstractMatrix ``A`` into a sparse matrix. +``` +""" +sparse + +doc""" +```rst +:: + round([T,] x, [digits, [base]], [r::RoundingMode]) + +``round(x)`` rounds ``x`` to an integer value according to the default +rounding mode (see :func:`get_rounding`), returning a value of the same type as +``x``. By default (:obj:`RoundNearest`), this will round to the nearest +integer, with ties (fractional values of 0.5) being rounded to the even +integer. + +.. doctest:: + + julia> round(1.7) + 2.0 + + julia> round(1.5) + 2.0 + + julia> round(2.5) + 2.0 + +The optional :obj:`RoundingMode` argument will change how the number gets rounded. + +``round(T, x, [r::RoundingMode])`` converts the result to type ``T``, throwing an +:exc:`InexactError` if the value is not representable. + +``round(x, digits)`` rounds to the specified number of digits after the +decimal place (or before if negative). ``round(x, digits, base)`` rounds +using a base other than 10. + + .. doctest:: + +:: + round(z, RoundingModeReal, RoundingModeImaginary) + +Returns the nearest integral value of the same type as the complex-valued +``z`` to ``z``, breaking ties using the specified :obj:`RoundingMode`\ s. +The first :obj:`RoundingMode` is used for rounding the real components while +the second is used for rounding the imaginary components. +``` +""" +round + +doc""" +```rst +:: + strwidth(s) + +Gives the number of columns needed to print a string. +``` +""" +strwidth + +doc""" +```rst +:: + function_module(f::Function, types) -> Module + +Determine the module containing a given definition of a generic function. +``` +""" +function_module + +doc""" +```rst +:: + hex(n, [pad]) + +Convert an integer to a hexadecimal string, optionally specifying a number of digits to pad to. +``` +""" +hex + +doc""" +```rst +:: + workspace() + +Replace the top-level module (``Main``) with a new one, providing a clean workspace. +The previous ``Main`` module is made available as ``LastMain``. A previously-loaded +package can be accessed using a statement such as ``using LastMain.Package``. + +This function should only be used interactively. +``` +""" +workspace + +doc""" +```rst +:: + tempdir() + +Obtain the path of a temporary directory (possibly shared with other processes). +``` +""" +tempdir + +doc""" +```rst +:: + reduce(op, v0, itr) + +Reduce the given collection ``ìtr`` with the given binary operator +``op``. ``v0`` must be a neutral element for ``op`` that will be +returned for empty collections. It is unspecified whether ``v0`` is +used for non-empty collections. + +Reductions for certain commonly-used operators have special +implementations which should be used instead: ``maximum(itr)``, +``minimum(itr)``, ``sum(itr)``, ``prod(itr)``, ``any(itr)``, +``all(itr)``. + +The associativity of the reduction is implementation dependent. +This means that you can't use non-associative operations like ``-`` +because it is undefined whether ``reduce(-,[1,2,3])`` should be +evaluated as ``(1-2)-3`` or ``1-(2-3)``. Use ``foldl`` or ``foldr`` +instead for guaranteed left or right associativity. + +Some operations accumulate error, and parallelism will also be +easier if the reduction can be executed in groups. Future versions +of Julia might change the algorithm. Note that the elements are not +reordered if you use an ordered collection. + +:: + reduce(op, itr) + +Like ``reduce(op, v0, itr)``. This cannot be used with empty +collections, except for some special cases (e.g. when ``op`` is one +of ``+``, ``*``, ``max``, ``min``, ``&``, ``|``) when Julia can +determine the neutral element of ``op``. +``` +""" +reduce + +doc""" +```rst +:: + .>=(x, y) + .≥(x,y) + +Element-wise greater-than-or-equals comparison operator. +``` +""" +Base.(:(.>=)) + +doc""" +```rst +:: + stdm(v, m) + +Compute the sample standard deviation of a vector ``v`` with known mean ``m``. +Note: Julia does not ignore ``NaN`` values in the computation. +``` +""" +stdm + +doc""" +```rst +:: + mv(src::AbstractString,dst::AbstractString; remove_destination::Bool=false) + +Move the file, link, or directory from *src* to *dest*. +\"remove_destination=true\" will first remove an existing `dst`. +``` +""" +mv + +doc""" +```rst +:: + erfi(x) + +Compute the imaginary error function of ``x``, +defined by :math:`-i \operatorname{erf}(ix)`. +``` +""" +erfi + +doc""" +```rst +:: + floor([T,] x, [digits, [base]]) + +``floor(x)`` returns the nearest integral value of the same type as ``x`` +that is less than or equal to ``x``. + +``floor(T, x)`` converts the result to type ``T``, throwing an +``InexactError`` if the value is not representable. + +``digits`` and ``base`` work as for :func:`round`. +``` +""" +floor + +doc""" +```rst +:: + tril!(M) + +Lower triangle of a matrix, overwriting ``M`` in the process. + +:: + tril!(M, k) + +Returns the lower triangle of ``M`` starting from the ``k``\ th subdiagonal, overwriting ``M`` in the process. +``` +""" +tril! + +doc""" +```rst +:: + divrem(x, y) + +The quotient and remainder from Euclidean division. Equivalent to ``(x÷y, x%y)``. +``` +""" +divrem + +doc""" +```rst +:: + ErrorException(msg) + +Generic error type. The error message, in the `.msg` field, may provide more specific details. +``` +""" +ErrorException + +doc""" +```rst +:: + reverse(v [, start=1 [, stop=length(v) ]] ) + +Return a copy of ``v`` reversed from start to stop. +``` +""" +reverse + +doc""" +```rst +:: + reverse!(v [, start=1 [, stop=length(v) ]]) -> v + +In-place version of :func:`reverse`. +``` +""" +reverse! + +doc""" +```rst +:: + flipdim(A, d) + +Reverse ``A`` in dimension ``d``. +``` +""" +flipdim + +doc""" +```rst +:: + num(x) + +Numerator of the rational representation of ``x`` +``` +""" +num + +doc""" +```rst +:: + eachindex(A...) + +Creates an iterable object for visiting each index of an AbstractArray ``A`` in an efficient manner. For array types that have opted into fast linear indexing (like ``Array``), this is simply the range ``1:length(A)``. For other array types, this returns a specialized Cartesian range to efficiently index into the array with indices specified for every dimension. For other iterables, including strings and dictionaries, this returns an iterator object supporting arbitrary index types (e.g. unevenly spaced or non-integer indices). + +Example for a sparse 2-d array:: + + julia> A = sprand(2, 3, 0.5) + 2x3 sparse matrix with 4 Float64 entries: + [1, 1] = 0.598888 + [1, 2] = 0.0230247 + [1, 3] = 0.486499 + [2, 3] = 0.809041 + + julia> for iter in eachindex(A) + @show iter.I_1, iter.I_2 + @show A[iter] + end + (iter.I_1,iter.I_2) = (1,1) + A[iter] = 0.5988881393454597 + (iter.I_1,iter.I_2) = (2,1) + A[iter] = 0.0 + (iter.I_1,iter.I_2) = (1,2) + A[iter] = 0.02302469881746183 + (iter.I_1,iter.I_2) = (2,2) + A[iter] = 0.0 + (iter.I_1,iter.I_2) = (1,3) + A[iter] = 0.4864987874354343 + (iter.I_1,iter.I_2) = (2,3) + A[iter] = 0.8090413606455655 +``` +""" +eachindex + +doc""" +```rst +:: + .<(x, y) + +Element-wise less-than comparison operator. +``` +""" +Base.(:(.<)) + +doc""" +```rst +:: + UndefRefError() + +The item or field is not defined for the given object. +``` +""" +UndefRefError + +doc""" +```rst +:: + bessely1(x) + +Bessel function of the second kind of order 1, :math:`Y_1(x)`. +``` +""" +bessely1 + +doc""" +```rst +:: + cumprod(A, [dim]) + +Cumulative product along a dimension ``dim`` (defaults to 1). +See also :func:`cumprod!` to use a preallocated output array, +both for performance and to control the precision of the +output (e.g. to avoid overflow). +``` +""" +cumprod + +doc""" +```rst +:: + besseljx(nu, x) + +Scaled Bessel function of the first kind of order ``nu``, :math:`J_\nu(x) e^{- | \operatorname{Im}(x) |}`. +``` +""" +besseljx + +doc""" +```rst +:: + print(x) + +Write (to the default output stream) a canonical (un-decorated) text representation of a value if there is one, otherwise call ``show``. +The representation used by ``print`` includes minimal formatting and tries to avoid Julia-specific details. +``` +""" +print + +doc""" +```rst +:: + filt(b, a, x, [si]) + +Apply filter described by vectors ``a`` and ``b`` to vector ``x``, with an +optional initial filter state vector ``si`` (defaults to zeros). +``` +""" +filt + +doc""" +```rst +:: + indexpids(S::SharedArray) + +Returns the index of the current worker into the ``pids`` vector, i.e., the list of workers mapping +the SharedArray +``` +""" +indexpids + +doc""" +```rst +:: + remotecall_wait(id, func, args...) + +Perform ``wait(remotecall(...))`` in one message. +``` +""" +remotecall_wait + +doc""" +```rst +:: + dct(A [, dims]) + +Performs a multidimensional type-II discrete cosine transform (DCT) +of the array ``A``, using the unitary normalization of the DCT. +The optional ``dims`` argument specifies an iterable subset of +dimensions (e.g. an integer, range, tuple, or array) to transform +along. Most efficient if the size of ``A`` along the transformed +dimensions is a product of small primes; see :func:`nextprod`. See +also :func:`plan_dct` for even greater efficiency. +``` +""" +dct + +doc""" +```rst +:: + append!(collection, collection2) -> collection. + +Add the elements of ``collection2`` to the end of ``collection``. + +.. doctest:: + + julia> append!([1],[2,3]) + 3-element Array{Int64,1}: + 1 + 2 + 3 + +.. doctest:: + + julia> append!([1, 2, 3], [4, 5, 6]) + 6-element Array{Int64,1}: + 1 + 2 + 3 + 4 + 5 + 6 + +Use :func:`push!` to add individual items to ``collection`` which are not +already themselves in another collection. +The result is of the preceding example is equivalent to +``push!([1, 2, 3], 4, 5, 6)``. +``` +""" +append! + +doc""" +```rst +:: + find(A) + +Return a vector of the linear indexes of the non-zeros in ``A`` +(determined by ``A[i]!=0``). A common use of this is to convert a +boolean array to an array of indexes of the ``true`` +elements. + +:: + find(f,A) + +Return a vector of the linear indexes of ``A`` where ``f`` returns true. +``` +""" +find + +doc""" +```rst +:: + ctranspose(A) + +The conjugate transposition operator (``'``). +``` +""" +ctranspose + +doc""" +```rst +:: + skip(s, offset) + +Seek a stream relative to the current position. +``` +""" +skip + +doc""" +```rst +:: + bfft(A [, dims]) + +Similar to :func:`ifft`, but computes an unnormalized inverse (backward) +transform, which must be divided by the product of the sizes of the +transformed dimensions in order to obtain the inverse. (This is slightly +more efficient than :func:`ifft` because it omits a scaling step, which in +some applications can be combined with other computational steps elsewhere.) + +.. math:: + + \operatorname{BDFT}(A)[k] = \operatorname{length}(A) \operatorname{IDFT}(A)[k] +``` +""" +bfft + +doc""" +```rst +:: + lu(A) -> L, U, p + +Compute the LU factorization of ``A``, such that ``A[p,:] = L*U``. +``` +""" +lu + +doc""" +```rst +:: + @task + +Wrap an expression in a Task without executing it, and return the Task. This +only creates a task, and does not run it. +``` +""" +:@task + +doc""" +```rst +:: + fld(x, y) + +Largest integer less than or equal to ``x/y``. +``` +""" +fld + +doc""" +```rst +:: + indmax(itr) -> Integer + +Returns the index of the maximum element in a collection. +``` +""" +indmax + +doc""" +```rst +:: + writecsv(filename, A) + +Equivalent to ``writedlm`` with ``delim`` set to comma. +``` +""" +writecsv + +doc""" +```rst +:: + wstring(s) + +This is a synonym for either ``utf32(s)`` or ``utf16(s)``, +depending on whether ``Cwchar_t`` is 32 or 16 bits, respectively. +The synonym ``WString`` for ``UTF32String`` or ``UTF16String`` +is also provided. +``` +""" +wstring + +doc""" +```rst +:: + withenv(f::Function, kv::Pair...) + +Execute ``f()`` in an environment that is temporarily modified (not replaced as in ``setenv``) by zero or more ``"var"=>val`` arguments ``kv``. ``withenv`` is generally used via the ``withenv(kv...) do ... end`` syntax. A value of ``nothing`` can be used to temporarily unset an environment variable (if it is set). When ``withenv`` returns, the original environment has been restored. +``` +""" +withenv + +doc""" +```rst +:: + setdiff!(s, iterable) + +Remove each element of ``iterable`` from set ``s`` in-place. +``` +""" +setdiff! + +doc""" +```rst +:: + EOFError() + +No more data was available to read from a file or stream. +``` +""" +EOFError + +doc""" +```rst +:: + isascii(c::Union{Char,AbstractString}) -> Bool + +Tests whether a character belongs to the ASCII character set, or whether this +is true for all elements of a string. +``` +""" +isascii + +doc""" +```rst +:: + ucfirst(string) + +Returns ``string`` with the first character converted to uppercase. +``` +""" +ucfirst + +doc""" +```rst +:: + copysign(x, y) + +Return ``x`` such that it has the same sign as ``y`` +``` +""" +copysign + +doc""" +```rst +:: + getaddrinfo(host) + +Gets the IP address of the ``host`` (may have to do a DNS lookup) +``` +""" +getaddrinfo + +doc""" +```rst +:: + @show + +Show an expression and result, returning the result +``` +""" +:@show + +doc""" +```rst +:: + showcompact(x) + +Show a more compact representation of a value. This is used for printing +array elements. If a new type has a different compact representation, it +should overload ``showcompact(io, x)`` where the first argument is a stream. +``` +""" +showcompact + +doc""" +```rst +:: + isleaftype(T) + +Determine whether ``T`` is a concrete type that can have instances, meaning +its only subtypes are itself and ``None`` (but ``T`` itself is not +``None``). +``` +""" +isleaftype + +doc""" +```rst +:: + svdfact(A, [thin=true]) -> SVD + +Compute the Singular Value Decomposition (SVD) of ``A`` and return an ``SVD`` object. ``U``, ``S``, ``V`` and ``Vt`` can be obtained from the factorization ``F`` with ``F[:U]``, ``F[:S]``, ``F[:V]`` and ``F[:Vt]``, such that ``A = U*diagm(S)*Vt``. If ``thin`` is ``true``, an economy mode decomposition is returned. The algorithm produces ``Vt`` and hence ``Vt`` is more efficient to extract than ``V``. The default is to produce a thin decomposition. + +:: + svdfact(A, B) -> GeneralizedSVD + +Compute the generalized SVD of ``A`` and ``B``, returning a ``GeneralizedSVD`` Factorization object ``F``, such that ``A = F[:U]*F[:D1]*F[:R0]*F[:Q]'`` and ``B = F[:V]*F[:D2]*F[:R0]*F[:Q]'``. +``` +""" +svdfact + +doc""" +```rst +:: + string(xs...) + +Create a string from any values using the ``print`` function. +``` +""" +string + +doc""" +```rst +:: + erfc(x) + +Compute the complementary error function of ``x``, +defined by :math:`1 - \operatorname{erf}(x)`. +``` +""" +erfc + +doc""" +```rst +:: + prevfloat(f) -> AbstractFloat + +Get the previous floating point number in lexicographic order +``` +""" +prevfloat + +doc""" +```rst +:: + rest(iter, state) + +An iterator that yields the same elements as ``iter``, but starting at the given ``state``. +``` +""" +rest + +doc""" +```rst +:: + getfield(value, name::Symbol) + +Extract a named field from a value of composite type. The syntax ``a.b`` calls +``getfield(a, :b)``, and the syntax ``a.(b)`` calls ``getfield(a, b)``. +``` +""" +getfield + +doc""" +```rst +:: + utf8(::Array{UInt8,1}) + +Create a UTF-8 string from a byte array. + +:: + utf8(::Ptr{UInt8}, [length]) + +Create a UTF-8 string from the address of a C (0-terminated) string encoded in UTF-8. A copy is made; the ptr can be safely freed. If ``length`` is specified, the string does not have to be 0-terminated. + +:: + utf8(s) + +Convert a string to a contiguous UTF-8 string (all characters must be valid UTF-8 characters). +``` +""" +utf8 + +doc""" +```rst +:: + hvcat(rows::Tuple{Vararg{Int}}, values...) + +Horizontal and vertical concatenation in one call. This function is called for +block matrix syntax. The first argument specifies the number of arguments to +concatenate in each block row. +For example, ``[a b;c d e]`` calls ``hvcat((2,3),a,b,c,d,e)``. + +If the first argument is a single integer ``n``, then all block rows are assumed to have ``n`` block columns. +``` +""" +hvcat + +doc""" +```rst +:: + besselj1(x) + +Bessel function of the first kind of order 1, :math:`J_1(x)`. +``` +""" +besselj1 + +doc""" +```rst +:: + sinpi(x) + +Compute :math:`\sin(\pi x)` more accurately than ``sin(pi*x)``, especially for large ``x``. +``` +""" +sinpi + +doc""" +```rst +:: + select!(v, k, [by=,] [lt=,] [rev=false]) + +Partially sort the vector ``v`` in place, according to the order specified by ``by``, +``lt`` and ``rev`` so that the value at index ``k`` (or range of adjacent values if +``k`` is a range) occurs at the position where it would appear if the array were +fully sorted via a non-stable algorithm. If ``k`` is a single index, that value +is returned; if ``k`` is a range, an array of values at those indices is returned. +Note that ``select!`` does not fully sort the input array. +``` +""" +select! + +doc""" +```rst +:: + maximum!(r, A) + +Compute the maximum value of ``A`` over the singleton dimensions of ``r``, +and write results to ``r``. +``` +""" +maximum! + +doc""" +```rst +:: + prod(itr) + +Returns the product of all elements of a collection. + +:: + prod(A, dims) + +Multiply elements of an array over the given dimensions. +``` +""" +prod + +doc""" +```rst +:: + Base.linearindexing(A) + +``linearindexing`` defines how an AbstractArray most efficiently accesses its elements. If ``Base.linearindexing(A)`` returns ``Base.LinearFast()``, this means that linear indexing with only one index is an efficient operation. If it instead returns ``Base.LinearSlow()`` (by default), this means that the array intrinsically accesses its elements with indices specified for every dimension. Since converting a linear index to multiple indexing subscripts is typically very expensive, this provides a traits-based mechanism to enable efficient generic code for all array types. + +An abstract array subtype ``MyArray`` that wishes to opt into fast linear indexing behaviors should define ``linearindexing`` in the type-domain:: + + Base.linearindexing{T<:MyArray}(::Type{T}) = Base.LinearFast() +``` +""" +Base.linearindexing + +doc""" +```rst +:: + isqrt(n) + +Integer square root: the largest integer ``m`` such that ``m*m <= n``. +``` +""" +isqrt + +doc""" +```rst +:: + log1p(x) + +Accurate natural logarithm of ``1+x``. Throws ``DomainError`` for ``Real`` arguments less than -1. + +There is an experimental variant in the ``Base.Math.JuliaLibm`` module, +which is typically faster and more accurate. +``` +""" +log1p + +doc""" +```rst +:: + flipsign(x, y) + +Return ``x`` with its sign flipped if ``y`` is negative. For example ``abs(x) = flipsign(x,x)``. +``` +""" +flipsign + +doc""" +```rst +:: + lbeta(x, y) + +Natural logarithm of the absolute value of the beta function :math:`\log(|\operatorname{B}(x,y)|)`. +``` +""" +lbeta + +doc""" +```rst +:: + randstring([rng,] len=8) + +Create a random ASCII string of length ``len``, consisting of upper- and +lower-case letters and the digits 0-9. The optional ``rng`` argument +specifies a random number generator, see :ref:`Random Numbers `. +``` +""" +randstring + +doc""" +```rst +:: + Float64(x [, mode::RoundingMode]) + +Create a Float64 from ``x``. If ``x`` is not exactly representable then +``mode`` determines how ``x`` is rounded. + +.. doctest:: + + julia> Float64(pi, RoundDown) + 3.141592653589793 + + julia> Float64(pi, RoundUp) + 3.1415926535897936 + +See ``get_rounding`` for available rounding modes. +``` +""" +Float64 + +doc""" +```rst +:: + function_name(f::Function) -> Symbol + +Get the name of a generic function as a symbol, or ``:anonymous``. +``` +""" +function_name + +doc""" +```rst +:: + addprocs(n::Integer; exeflags=``) -> List of process identifiers + +Launches workers using the in-built ``LocalManager`` which only launches workers on the local host. +This can be used to take advantage of multiple cores. ``addprocs(4)`` will add 4 processes on the local machine. + +:: + addprocs() -> List of process identifiers + + Equivalent to ``addprocs(CPU_CORES)`` + +:: + addprocs(machines; tunnel=false, sshflags=``, max_parallel=10, exeflags=``) -> List of process identifiers + +Add processes on remote machines via SSH. +Requires julia to be installed in the same location on each node, or to be available via a shared file system. + +``machines`` is a vector of machine specifications. Worker are started for each specification. + +A machine specification is either a string ``machine_spec`` or a tuple - ``(machine_spec, count)`` + +``machine_spec`` is a string of the form ``[user@]host[:port] [bind_addr[:port]]``. ``user`` defaults +to current user, ``port`` to the standard ssh port. If ``[bind_addr[:port]]`` is specified, other +workers will connect to this worker at the specified ``bind_addr`` and ``port``. + +``count`` is the number of workers to be launched on the specified host. If specified as ``:auto`` +it will launch as many workers as the number of cores on the specific host. + + +Keyword arguments: + +``tunnel`` : if ``true`` then SSH tunneling will be used to connect to the worker from the master process. + +``sshflags`` : specifies additional ssh options, e.g. :literal:`sshflags=\`-i /home/foo/bar.pem\`` . + +``max_parallel`` : specifies the maximum number of workers connected to in parallel at a host. Defaults to 10. + +``dir`` : specifies the working directory on the workers. Defaults to the host's current directory (as found by `pwd()`) + +``exename`` : name of the julia executable. Defaults to "$JULIA_HOME/julia" or "$JULIA_HOME/julia-debug" as the case may be. + +``exeflags`` : additional flags passed to the worker processes. + +Environment variables : + +If the master process fails to establish a connection with a newly launched worker within 60.0 seconds, +the worker treats it a fatal situation and terminates. This timeout can be controlled via environment +variable ``JULIA_WORKER_TIMEOUT``. The value of ``JULIA_WORKER_TIMEOUT`` on the master process, specifies +the number of seconds a newly launched worker waits for connection establishment. + +:: + addprocs(manager::ClusterManager; kwargs...) -> List of process identifiers + +Launches worker processes via the specified cluster manager. + +For example Beowulf clusters are supported via a custom cluster manager implemented +in package ``ClusterManagers``. + +The number of seconds a newly launched worker waits for connection establishment from the master can be +specified via variable ``JULIA_WORKER_TIMEOUT`` in the worker process's environment. Relevant only when +using TCP/IP as transport. +``` +""" +addprocs + +doc""" +```rst +:: + mkpath(path, [mode]) + +Create all directories in the given ``path``, with permissions ``mode``. +``mode`` defaults to 0o777, modified by the current file creation mask. +``` +""" +mkpath + +doc""" +```rst +:: + lufact(A [,pivot=Val{true}]) -> F + +Compute the LU factorization of ``A``. The return type of ``F`` depends on the type of ``A``. In most cases, if ``A`` is a subtype ``S`` of AbstractMatrix with an element type ``T``` supporting ``+``, ``-``, ``*`` and ``/`` the return type is ``LU{T,S{T}}``. If pivoting is chosen (default) the element type should also support ``abs`` and ``<``. When ``A`` is sparse and have element of type ``Float32``, ``Float64``, ``Complex{Float32}``, or ``Complex{Float64}`` the return type is ``UmfpackLU``. Some examples are shown in the table below. + + ======================= ========================= ======================================== + Type of input ``A`` Type of output ``F`` Relationship between ``F`` and ``A`` + ----------------------- ------------------------- ---------------------------------------- + :func:`Matrix` ``LU`` ``F[:L]*F[:U] == A[F[:p], :]`` + :func:`Tridiagonal` ``LU{T,Tridiagonal{T}}`` ``F[:L]*F[:U] == A[F[:p], :]`` + :func:`SparseMatrixCSC` ``UmfpackLU`` ``F[:L]*F[:U] == (F[:Rs] .* A)[F[:p], F[:q]]`` + ======================= ========================= ======================================== + +The individual components of the factorization ``F`` can be accessed by indexing: + + =========== ======================================= ====== ======================== ============= + Component Description ``LU`` ``LU{T,Tridiagonal{T}}`` ``UmfpackLU`` + ----------- --------------------------------------- ------ ------------------------ ------------- + ``F[:L]`` ``L`` (lower triangular) part of ``LU`` ✓ ✓ ✓ + ``F[:U]`` ``U`` (upper triangular) part of ``LU`` ✓ ✓ ✓ + ``F[:p]`` (right) permutation ``Vector`` ✓ ✓ ✓ + ``F[:P]`` (right) permutation ``Matrix`` ✓ ✓ + ``F[:q]`` left permutation ``Vector`` ✓ + ``F[:Rs]`` ``Vector`` of scaling factors ✓ + ``F[:(:)]`` ``(L,U,p,q,Rs)`` components ✓ + =========== ======================================= ====== ======================== ============= + + ================== ====== ======================== ============= + Supported function ``LU`` ``LU{T,Tridiagonal{T}}`` ``UmfpackLU`` + ------------------ ------ ------------------------ ------------- + ``/`` ✓ + ``\`` ✓ ✓ ✓ + ``cond`` ✓ ✓ + ``det`` ✓ ✓ ✓ + ``logdet`` ✓ ✓ + ``logabsdet`` ✓ ✓ + ``size`` ✓ ✓ + ================== ====== ======================== ============= +``` +""" +lufact + +doc""" +```rst +:: + besselix(nu, x) + +Scaled modified Bessel function of the first kind of order ``nu``, :math:`I_\nu(x) e^{- | \operatorname{Re}(x) |}`. +``` +""" +besselix + +doc""" +```rst +:: + union(s1,s2...) + ∪(s1,s2) + +Construct the union of two or more sets. Maintains order with arrays. +``` +""" +union + +doc""" +```rst +:: + lstat(file) + +Like stat, but for symbolic links gets the info for the link itself rather than the file it refers to. This function must be called on a file path rather than a file object or a file descriptor. +``` +""" +lstat + +doc""" +```rst +:: + mapfoldl(f, op, v0, itr) + +Like :func:`mapreduce`, but with guaranteed left associativity. ``v0`` +will be used exactly once. + +:: + mapfoldl(f, op, itr) + +Like ``mapfoldl(f, op, v0, itr)``, but using the first element of +``itr`` as ``v0``. In general, this cannot be used with empty +collections (see ``reduce(op, itr)``). +``` +""" +mapfoldl + +doc""" +```rst +:: + realmax(type) + +The highest finite value representable by the given floating-point type +``` +""" +realmax + +doc""" +```rst +:: + takebuf_string(b::IOBuffer) + +Obtain the contents of an ``IOBuffer`` as a string, without copying. Afterwards, the IOBuffer is reset to its initial state. +``` +""" +takebuf_string + +doc""" +```rst +:: + pipe(from, to, ...) + +Create a pipeline from a data source to a destination. The source and destination can +be commands, I/O streams, strings, or results of other ``pipe`` calls. At least one +argument must be a command. Strings refer to filenames. +When called with more than two arguments, they are chained together from left to right. +For example ``pipe(a,b,c)`` is equivalent to ``pipe(pipe(a,b),c)``. This provides a more +concise way to specify multi-stage pipelines. + +**Examples**: + * ``run(pipe(`ls`, `grep xyz`))`` + * ``run(pipe(`ls`, "out.txt"))`` + * ``run(pipe("out.txt", `grep xyz`))`` + +:: + pipe(command; stdin, stdout, stderr, append=false) + +Redirect I/O to or from the given ``command``. Keyword arguments specify which of +the command's streams should be redirected. ``append`` controls whether file output +appends to the file. +This is a more general version of the 2-argument ``pipe`` function. +``pipe(from, to)`` is equivalent to ``pipe(from, stdout=to)`` when ``from`` is a +command, and to ``pipe(to, stdin=from)`` when ``from`` is another kind of +data source. + +**Examples**: + * ``run(pipe(`dothings`, stdout="out.txt", stderr="errs.txt"))`` + * ``run(pipe(`update`, stdout="log.txt", append=true))`` +``` +""" +pipe + +doc""" +```rst +:: + serialize(stream, value) + +Write an arbitrary value to a stream in an opaque format, such that it can +be read back by ``deserialize``. The read-back value will be as identical as +possible to the original. In general, this process will not work if the +reading and writing are done by different versions of Julia, or +an instance of Julia with a different system image. +``` +""" +serialize + +doc""" +```rst +:: + sum(itr) + +Returns the sum of all elements in a collection. + +:: + sum(A, dims) + +Sum elements of an array over the given dimensions. + +:: + sum(f, itr) + +Sum the results of calling function ``f`` on each element of ``itr``. +``` +""" +sum + +doc""" +```rst +:: + typemin(type) + +The lowest value representable by the given (real) numeric type. +``` +""" +typemin + +doc""" +```rst +:: + call(x, args...) + +If ``x`` is not a ``Function``, then ``x(args...)`` is equivalent to +``call(x, args...)``. This means that function-like behavior can be +added to any type by defining new ``call`` methods. +``` +""" +call + +doc""" +```rst +:: + countfrom(start=1, step=1) + +An iterator that counts forever, starting at ``start`` and incrementing by ``step``. +``` +""" +countfrom + +doc""" +```rst +:: + eof(stream) -> Bool + +Tests whether an I/O stream is at end-of-file. If the stream is not yet +exhausted, this function will block to wait for more data if necessary, and +then return ``false``. Therefore it is always safe to read one byte after +seeing ``eof`` return ``false``. ``eof`` will return ``false`` as long +as buffered data is still available, even if the remote end of a +connection is closed. +``` +""" +eof + +doc""" +```rst +:: + mktempdir([parent=tempdir()]) + +Create a temporary directory in the ``parent`` directory and return its path. +``` +""" +mktempdir + +doc""" +```rst +:: + tril(M) + +Lower triangle of a matrix. + +:: + tril(M, k) + +Returns the lower triangle of ``M`` starting from the ``k``\ th subdiagonal. +``` +""" +tril + +doc""" +```rst +:: + @edit + +Evaluates the arguments to the function call, determines their types, and calls the ``edit`` function on the resulting expression +``` +""" +:@edit + +doc""" +```rst +:: + subtypes(T::DataType) + +Return a list of immediate subtypes of DataType T. Note that all currently loaded subtypes are included, including those not visible in the current module. +``` +""" +subtypes + +doc""" +```rst +:: + digits(n, [base], [pad]) + +Returns an array of the digits of ``n`` in the given base, optionally padded with +zeros to a specified size. More significant digits are at higher indexes, such +that ``n == sum([digits[k]*base^(k-1) for k=1:length(digits)])``. +``` +""" +digits + +doc""" +```rst +:: + bytes2hex(bin_arr::Array{UInt8, 1}) + +Convert an array of bytes to its hexadecimal representation. All characters are in lower-case. Returns an ASCIIString. +``` +""" +bytes2hex + +doc""" +```rst +:: + unlock(l::ReentrantLock) + +Releases ownership of the lock by the current task. If the lock had been acquired before, +it just decrements an internal counter and returns immediately. +``` +""" +unlock + +doc""" +```rst +:: + BigFloat(x) + +Create an arbitrary precision floating point number. ``x`` may be +an ``Integer``, a ``Float64`` or a ``BigInt``. The +usual mathematical operators are defined for this type, and results +are promoted to a ``BigFloat``. + +Note that because decimal literals are converted to floating point numbers +when parsed, ``BigFloat(2.1)`` may not yield what you expect. You may instead +prefer to initialize constants from strings via :func:`parse`, or using the +``big`` string literal. + +.. doctest:: + + julia> BigFloat(2.1) + 2.100000000000000088817841970012523233890533447265625000000000000000000000000000 + + julia> big"2.1" + 2.099999999999999999999999999999999999999999999999999999999999999999999999999986 +``` +""" +BigFloat + +doc""" +```rst +:: + xcorr(u,v) + +Compute the cross-correlation of two vectors. +``` +""" +xcorr + +doc""" +```rst +:: + typeof(x) + +Get the concrete type of ``x``. +``` +""" +typeof + +doc""" +```rst +:: + drop(iter, n) + +An iterator that generates all but the first ``n`` elements of ``iter``. +``` +""" +drop + +doc""" +```rst +:: + acsc(x) + +Compute the inverse cosecant of ``x``, where the output is in radians +``` +""" +acsc + +doc""" +```rst +:: + log(x) + +Compute the natural logarithm of ``x``. Throws ``DomainError`` for negative +``Real`` arguments. Use complex negative arguments to obtain complex +results. + +There is an experimental variant in the ``Base.Math.JuliaLibm`` module, +which is typically faster and more accurate. + +:: + log(b,x) + +Compute the base ``b`` logarithm of ``x``. Throws ``DomainError`` for negative ``Real`` arguments. +``` +""" +log + +doc""" +```rst +:: + trunc([T,] x, [digits, [base]]) + +``trunc(x)`` returns the nearest integral value of the same type as ``x`` whose absolute +value is less than or equal to ``x``. + +``trunc(T, x)`` converts the result to type ``T``, throwing an +``InexactError`` if the value is not representable. + +``digits`` and ``base`` work as for :func:`round`. +``` +""" +trunc + +doc""" +```rst +:: + @less + +Evaluates the arguments to the function call, determines their types, and calls the ``less`` function on the resulting expression +``` +""" +:@less + +doc""" +```rst +:: + broadcast_function(f) + +Returns a function ``broadcast_f`` such that ``broadcast_function(f)(As...) === broadcast(f, As...)``. Most useful in the form ``const broadcast_f = broadcast_function(f)``. +``` +""" +broadcast_function + +doc""" +```rst +:: + unsafe_convert(T,x) + +Convert "x" to a value of type "T" + +In cases where ``convert`` would need to take a Julia object and turn it into a ``Ptr``, +this function should be used to define and perform that conversion. + +Be careful to ensure that a julia reference to ``x`` exists as long as the result of this function will be used. +Accordingly, the argument ``x`` to this function should never be an expression, +only a variable name or field reference. +For example, ``x=a.b.c`` is acceptable, but ``x=[a,b,c]`` is not. + +The ``unsafe`` prefix on this function indicates that using the result of this function +after the ``x`` argument to this function is no longer accessible to the program may cause +undefined behavior, including program corruption or segfaults, at any later time. +``` +""" +unsafe_convert + +doc""" +```rst +:: + warn(msg) + +Display a warning. +``` +""" +warn + +doc""" +```rst +:: + erfinv(x) + +Compute the inverse error function of a real ``x``, +defined by :math:`\operatorname{erf}(\operatorname{erfinv}(x)) = x`. +``` +""" +erfinv + +doc""" +```rst +:: + @async + +Wraps an expression in a closure and schedules it to run on the local machine. Also +adds it to the set of items that the nearest enclosing ``@sync`` waits for. +``` +""" +:@async + +doc""" +```rst +:: + rotr90(A) + +Rotate matrix ``A`` right 90 degrees. + +:: + rotr90(A, k) + +Rotate matrix ``A`` right 90 degrees an integer ``k`` number of times. If ``k`` +is zero or a multiple of four, this is equivalent to a ``copy``. +``` +""" +rotr90 + +doc""" +```rst +:: + readdir([dir]) -> Vector{ByteString} + +Returns the files and directories in the directory `dir` (or the current working directory if not given). +``` +""" +readdir + +doc""" +```rst +:: + seek(s, pos) + +Seek a stream to the given position. +``` +""" +seek + +doc""" +```rst +:: + acosd(x) + +Compute the inverse cosine of ``x``, where the output is in degrees +``` +""" +acosd + +doc""" +```rst +:: + triu(M) + +Upper triangle of a matrix. + +:: + triu(M, k) + +Returns the upper triangle of ``M`` starting from the ``k``\ th superdiagonal. +``` +""" +triu + +doc""" +```rst +:: + instances(T::Type) + +Return a collection of all instances of the given type, if applicable. +Mostly used for enumerated types (see ``@enum``). +``` +""" +instances + +doc""" +```rst +:: + besselj0(x) + +Bessel function of the first kind of order 0, :math:`J_0(x)`. +``` +""" +besselj0 + +doc""" +```rst +:: + erfcinv(x) + +Compute the inverse error complementary function of a real ``x``, +defined by :math:`\operatorname{erfc}(\operatorname{erfcinv}(x)) = x`. +``` +""" +erfcinv + +doc""" +```rst +:: + minabs(itr) + +Compute the minimum absolute value of a collection of values. + +:: + minabs(A, dims) + +Compute the minimum absolute values over given dimensions. +``` +""" +minabs + +doc""" +```rst +:: + popdisplay() + popdisplay(d::Display) + +Pop the topmost backend off of the display-backend stack, or the +topmost copy of ``d`` in the second variant. +``` +""" +popdisplay + +doc""" +```rst +:: + readdlm(source, delim::Char, T::Type, eol::Char; header=false, skipstart=0, skipblanks=true, use_mmap, ignore_invalid_chars=false, quotes=true, dims, comments=true, comment_char='#') + +Read a matrix from the source where each line (separated by ``eol``) gives one row, with elements separated by the given delimeter. The source can be a text file, stream or byte array. Memory mapped files can be used by passing the byte array representation of the mapped segment as source. + +If ``T`` is a numeric type, the result is an array of that type, with any non-numeric elements as ``NaN`` for floating-point types, or zero. Other useful values of ``T`` include ``ASCIIString``, ``AbstractString``, and ``Any``. + +If ``header`` is ``true``, the first row of data will be read as header and the tuple ``(data_cells, header_cells)`` is returned instead of only ``data_cells``. + +Specifying ``skipstart`` will ignore the corresponding number of initial lines from the input. + +If ``skipblanks`` is ``true``, blank lines in the input will be ignored. + +If ``use_mmap`` is ``true``, the file specified by ``source`` is memory mapped for potential speedups. Default is ``true`` except on Windows. On Windows, you may want to specify ``true`` if the file is large, and is only read once and not written to. + +If ``ignore_invalid_chars`` is ``true``, bytes in ``source`` with invalid character encoding will be ignored. Otherwise an error is thrown indicating the offending character position. + +If ``quotes`` is ``true``, column enclosed within double-quote (``) characters are allowed to contain new lines and column delimiters. Double-quote characters within a quoted field must be escaped with another double-quote. + +Specifying ``dims`` as a tuple of the expected rows and columns (including header, if any) may speed up reading of large files. + +If ``comments`` is ``true``, lines beginning with ``comment_char`` and text following ``comment_char`` in any line are ignored. + +:: + readdlm(source, delim::Char, eol::Char; options...) + +If all data is numeric, the result will be a numeric array. If some elements cannot be parsed as numbers, a cell array of numbers and strings is returned. + +:: + readdlm(source, delim::Char, T::Type; options...) + +The end of line delimiter is taken as ``\n``. + +:: + readdlm(source, delim::Char; options...) + +The end of line delimiter is taken as ``\n``. If all data is numeric, the result will be a numeric array. If some elements cannot be parsed as numbers, a cell array of numbers and strings is returned. + +:: + readdlm(source, T::Type; options...) + +The columns are assumed to be separated by one or more whitespaces. The end of line delimiter is taken as ``\n``. + +:: + readdlm(source; options...) + +The columns are assumed to be separated by one or more whitespaces. The end of line delimiter is taken as ``\n``. If all data is numeric, the result will be a numeric array. If some elements cannot be parsed as numbers, a cell array of numbers and strings is returned. +``` +""" +readdlm + +doc""" +```rst +:: + filesize(path...) + +Equivalent to stat(file).size +``` +""" +filesize + +doc""" +```rst +:: + sinc(x) + +Compute :math:`\sin(\pi x) / (\pi x)` if :math:`x \neq 0`, and :math:`1` if :math:`x = 0`. +``` +""" +sinc + +doc""" +```rst +:: + utf16(s) + +Create a UTF-16 string from a byte array, array of ``UInt16``, or +any other string type. (Data must be valid UTF-16. Conversions of +byte arrays check for a byte-order marker in the first two bytes, +and do not include it in the resulting string.) + +Note that the resulting ``UTF16String`` data is terminated by the NUL +codepoint (16-bit zero), which is not treated as a character in the +string (so that it is mostly invisible in Julia); this allows the +string to be passed directly to external functions requiring +NUL-terminated data. This NUL is appended automatically by the +`utf16(s)` conversion function. If you have a ``UInt16`` array +``A`` that is already NUL-terminated valid UTF-16 data, then you +can instead use `UTF16String(A)`` to construct the string without +making a copy of the data and treating the NUL as a terminator +rather than as part of the string. + +:: + utf16(::Union{Ptr{UInt16},Ptr{Int16}} [, length]) + +Create a string from the address of a NUL-terminated UTF-16 string. A copy is made; the pointer can be safely freed. If ``length`` is specified, the string does not have to be NUL-terminated. +``` +""" +utf16 + +doc""" +```rst +:: + median(v[, region]) + +Compute the median of whole array ``v``, or optionally along the dimensions +in ``region``. ``NaN`` is returned if the data contains any ``NaN`` values. +For applications requiring the handling of missing data, the ``DataArrays`` +package is recommended. +``` +""" +median + +doc""" +```rst +:: + cglobal((symbol, library) [, type=Void]) + +Obtain a pointer to a global variable in a C-exported shared library, specified exactly as in ``ccall``. Returns a ``Ptr{Type}``, defaulting to ``Ptr{Void}`` if no Type argument is supplied. The values can be read or written by ``unsafe_load`` or ``unsafe_store!``, respectively. +``` +""" +cglobal + +doc""" +```rst +:: + one(x) + +Get the multiplicative identity element for the type of x (x can also specify the type itself). For matrices, returns an identity matrix of the appropriate size and type. +``` +""" +one + +doc""" +```rst +:: + parseip(addr) + +Parse a string specifying an IPv4 or IPv6 ip address. +``` +""" +parseip + +doc""" +```rst +:: + rationalize([Type=Int,] x; tol=eps(x)) + +Approximate floating point number ``x`` as a Rational number with components of the given +integer type. The result will differ from ``x`` by no more than ``tol``. +``` +""" +rationalize + +doc""" +```rst +:: + splice!(collection, index, [replacement]) -> item + +Remove the item at the given index, and return the removed item. Subsequent items +are shifted down to fill the resulting gap. If specified, replacement values from +an ordered collection will be spliced in place of the removed item. + +.. doctest:: + + julia> A = [6, 5, 4, 3, 2, 1]; splice!(A, 5) + 2 + + julia> A + 5-element Array{Int64,1}: + 6 + 5 + 4 + 3 + 1 + + julia> splice!(A, 5, -1) + 1 + + julia> A + 5-element Array{Int64,1}: + 6 + 5 + 4 + 3 + -1 + + julia> splice!(A, 1, [-1, -2, -3]) + 6 + + julia> A + 7-element Array{Int64,1}: + -1 + -2 + -3 + 5 + 4 + 3 + -1 + +To insert ``replacement`` before an index ``n`` without removing any items, use +``splice!(collection, n:n-1, replacement)``. + +:: + splice!(collection, range, [replacement]) -> items + +Remove items in the specified index range, and return a collection containing the +removed items. Subsequent items are shifted down to fill the resulting gap. +If specified, replacement values from an ordered collection will be spliced in place +of the removed items. + +To insert ``replacement`` before an index ``n`` without removing any items, use +``splice!(collection, n:n-1, replacement)``. + +.. doctest:: + + julia> splice!(A, 4:3, 2) + 0-element Array{Int64,1} + + julia> A + 8-element Array{Int64,1}: + -1 + -2 + -3 + 2 + 5 + 4 + 3 + -1 +``` +""" +splice! + +doc""" +```rst +:: + endof(collection) -> Integer + +Returns the last index of the collection. + +.. doctest:: + + julia> endof([1,2,4]) + 3 +``` +""" +endof + +doc""" +```rst +:: + isfifo(path) -> Bool + +Returns ``true`` if ``path`` is a FIFO, ``false`` otherwise. +``` +""" +isfifo + +doc""" +```rst +:: + Channel{T}(sz::Int) + +Constructs a Channel that can hold a maximum of ``sz`` objects of type ``T``. ``put!`` calls +on a full channel block till an object is removed with ``take!``. + +Other constructors: + ``Channel()`` - equivalent to ``Channel{Any}(32)`` + ``Channel(sz::Int)`` equivalent to ``Channel{Any}(sz)`` +``` +""" +Channel + +doc""" +```rst +:: + next(iter, state) -> item, state + +For a given iterable object and iteration state, return the current item and the next iteration state +``` +""" +next + +doc""" +```rst +:: + irfft(A, d [, dims]) + +Inverse of :func:`rfft`: for a complex array ``A``, gives the +corresponding real array whose FFT yields ``A`` in the first half. +As for :func:`rfft`, ``dims`` is an optional subset of dimensions +to transform, defaulting to ``1:ndims(A)``. + +``d`` is the length of the transformed real array along the ``dims[1]`` +dimension, which must satisfy ``div(d,2)+1 == size(A,dims[1])``. +(This parameter cannot be inferred from ``size(A)`` since both +``2*size(A,dims[1])-2`` as well as ``2*size(A,dims[1])-1`` are valid sizes +for the transformed real array.) +``` +""" +irfft + +doc""" +```rst +:: + nnz(A) + +Returns the number of stored (filled) elements in a sparse matrix. +``` +""" +nnz + +doc""" +```rst +:: + unshift!(collection, items...) -> collection + +Insert one or more ``items`` at the beginning of ``collection``. + +.. doctest:: + + julia> unshift!([1, 2, 3, 4], 5, 6) + 6-element Array{Int64,1}: + 5 + 6 + 1 + 2 + 3 + 4 +``` +""" +unshift! + +doc""" +```rst +:: + log2(x) + +Compute the logarithm of ``x`` to base 2. Throws ``DomainError`` for negative ``Real`` arguments. +``` +""" +log2 + +doc""" +```rst +:: + SymTridiagonal(d, du) + +Construct a real symmetric tridiagonal matrix from the diagonal and upper diagonal, respectively. The result is of type ``SymTridiagonal`` and provides efficient specialized eigensolvers, but may be converted into a regular matrix with :func:`full`. +``` +""" +SymTridiagonal + +doc""" +```rst +:: + spzeros(m,n) + +Create a sparse matrix of size ``m x n``. This sparse matrix will not contain any nonzero values. No storage will be allocated for nonzero values during construction. +``` +""" +spzeros + +doc""" +```rst +:: + colon(start, [step], stop) + +Called by ``:`` syntax for constructing ranges. +``` +""" +colon + +doc""" +```rst +:: + Base64EncodePipe(ostream) + +Returns a new write-only I/O stream, which converts any bytes written +to it into base64-encoded ASCII bytes written to ``ostream``. Calling +``close`` on the ``Base64Pipe`` stream is necessary to complete the +encoding (but does not close ``ostream``). +``` +""" +Base64EncodePipe + +doc""" +```rst +:: + issetgid(path) -> Bool + +Returns ``true`` if ``path`` has the setgid flag set, ``false`` otherwise. +``` +""" +issetgid + +doc""" +```rst +:: + isnull(x) + +Is the ``Nullable`` object ``x`` null, i.e. missing a value? +``` +""" +isnull + +doc""" +```rst +:: + abs2(x) + +Squared absolute value of ``x`` +``` +""" +abs2 + +doc""" +```rst +:: + write(stream, x) + +Write the canonical binary representation of a value to the given stream. +``` +""" +write + +doc""" +```rst +:: + sizehint!(s, n) + +Suggest that collection ``s`` reserve capacity for at least ``n`` elements. This can improve performance. +``` +""" +sizehint! + +doc""" +```rst +:: + permute!(v, p) + +Permute vector ``v`` in-place, according to permutation ``p``. No +checking is done to verify that ``p`` is a permutation. + +To return a new permutation, use ``v[p]``. Note that this is +generally faster than ``permute!(v,p)`` for large vectors. +``` +""" +permute! + +doc""" +```rst +:: + ifelse(condition::Bool, x, y) + +Return ``x`` if ``condition`` is true, otherwise return ``y``. This +differs from ``?`` or ``if`` in that it is an ordinary function, so +all the arguments are evaluated first. In some cases, using +``ifelse`` instead of an ``if`` statement can eliminate the branch +in generated code and provide higher performance in tight loops. +``` +""" +ifelse + +doc""" +```rst +:: + ispow2(n) -> Bool + +Test whether ``n`` is a power of two +``` +""" +ispow2 + +doc""" +```rst +:: + vcat(A...) + +Concatenate along dimension 1 +``` +""" +vcat + +doc""" +```rst +:: + isgraph(c::Union{Char,AbstractString}) -> Bool + +Tests whether a character is printable, and not a space, or whether this +is true for all elements of a string. Any character that would cause a printer +to use ink should be classified with isgraph(c)==true. +``` +""" +isgraph + +doc""" +```rst +:: + OutOfMemoryError() + +An operation allocated too much memory for either the system or the garbage collector to handle properly. +``` +""" +OutOfMemoryError + +doc""" +```rst +:: + zip(iters...) + +For a set of iterable objects, returns an iterable of tuples, where the ``i``\ th tuple contains the ``i``\ th component of each input iterable. + +Note that :func:`zip` is its own inverse: ``collect(zip(zip(a...)...)) == collect(a)``. +``` +""" +zip + +doc""" +```rst +:: + SystemError(prefix::AbstractString, [errnum::Int32]) + +A system call failed with an error code (in the ``errno`` global variable). +``` +""" +SystemError + +doc""" +```rst +:: + binomial(n,k) + +Number of ways to choose ``k`` out of ``n`` items +``` +""" +binomial + +doc""" +```rst +:: + rot180(A) + +Rotate matrix ``A`` 180 degrees. + +:: + rot180(A, k) + +Rotate matrix ``A`` 180 degrees an integer ``k`` number of times. +If ``k`` is even, this is equivalent to a ``copy``. +``` +""" +rot180 + +doc""" +```rst +:: + .<=(x, y) + .≤(x,y) + +Element-wise less-than-or-equals comparison operator. +``` +""" +Base.(:(.<=)) + +doc""" +```rst +:: + checkbounds(array, indexes...) + +Throw an error if the specified indexes are not in bounds for the given array. +``` +""" +checkbounds + +doc""" +```rst +:: + asec(x) + +Compute the inverse secant of ``x``, where the output is in radians +``` +""" +asec + +doc""" +```rst +:: + rank(M) + +Compute the rank of a matrix. +``` +""" +rank + +doc""" +```rst +:: + max(x, y, ...) + +Return the maximum of the arguments. Operates elementwise over arrays. +``` +""" +max + +doc""" +```rst +:: + versioninfo([verbose::Bool]) + +Print information about the version of Julia in use. If the ``verbose`` argument +is true, detailed system information is shown as well. +``` +""" +versioninfo + +doc""" +```rst +:: + DimensionMismatch([msg]) + +The objects called do not have matching dimensionality. +``` +""" +DimensionMismatch + +doc""" +```rst +:: + take!(RemoteRef) + +Fetch the value of a remote reference, removing it so that the reference is empty again. + +:: + take!(Channel) + +Removes and returns a value from a ``Channel``. Blocks till data is available. +``` +""" +take! + +doc""" +```rst +:: + ifft!(A [, dims]) + +Same as :func:`ifft`, but operates in-place on ``A``. +``` +""" +ifft! + +doc""" +```rst +:: + sort!(v, [alg=,] [by=,] [lt=,] [rev=false]) + +Sort the vector ``v`` in place. ``QuickSort`` is used by default for numeric arrays +while ``MergeSort`` is used for other arrays. You can specify an algorithm to use via +the ``alg`` keyword (see `Sorting Algorithms`_ for available algorithms). The ``by`` +keyword lets you provide a function that will be applied to each element before +comparison; the ``lt`` keyword allows providing a custom "less than" function; use +``rev=true`` to reverse the sorting order. These options are independent and can be +used together in all possible combinations: if both ``by`` and ``lt`` are specified, +the ``lt`` function is applied to the result of the ``by`` function; ``rev=true`` +reverses whatever ordering specified via the ``by`` and ``lt`` keywords. +``` +""" +sort! + +doc""" +```rst +:: + kill(p::Process, signum=SIGTERM) + +Send a signal to a process. The default is to terminate the process. + +:: + kill(manager::FooManager, pid::Int, config::WorkerConfig) + + Implemented by cluster managers. It is called on the master process, by ``rmprocs``. It should cause the remote worker specified + by ``pid`` to exit. ``Base.kill(manager::ClusterManager.....)`` executes a remote ``exit()`` on ``pid`` +``` +""" +kill + +doc""" +```rst +:: + logm(A) + +Compute the matrix logarithm of ``A``. +``` +""" +logm + +doc""" +```rst +:: + sylvester(A, B, C) + +Computes the solution ``X`` to the Sylvester equation ``AX + XB + C = 0``, where ``A``, ``B`` and ``C`` have compatible dimensions and ``A`` and ``-B`` have no eigenvalues with equal real part. +``` +""" +sylvester + +doc""" +```rst +:: + broadcast!(f, dest, As...) + +Like ``broadcast``, but store the result of ``broadcast(f, As...)`` in the ``dest`` array. +Note that ``dest`` is only used to store the result, and does not supply arguments to +``f`` unless it is also listed in the ``As``, as in ``broadcast!(f, A, A, B)`` to perform +``A[:] = broadcast(f, A, B)``. +``` +""" +broadcast! + +doc""" +```rst +:: + cross(x, y) + ×(x,y) + +Compute the cross product of two 3-vectors. +``` +""" +cross + +doc""" +```rst +:: + strides(A) + +Returns a tuple of the memory strides in each dimension +``` +""" +strides + +doc""" +```rst +:: + keys(collection) + +Return an iterator over all keys in a collection. ``collect(keys(d))`` returns an array of keys. +``` +""" +keys + +doc""" +```rst +:: + repeat(A, inner = Int[], outer = Int[]) + +Construct an array by repeating the entries of ``A``. The i-th element of ``inner`` specifies the number of times that the individual entries of the i-th dimension of ``A`` should be repeated. The i-th element of ``outer`` specifies the number of times that a slice along the i-th dimension of ``A`` should be repeated. +``` +""" +repeat + +doc""" +```rst +:: + scale(A, b) + +:: + scale(b, A) + +Scale an array ``A`` by a scalar ``b``, returning a new array. + +If ``A`` is a matrix and ``b`` is a vector, then ``scale(A,b)`` +scales each column ``i`` of ``A`` by ``b[i]`` (similar to +``A*diagm(b)``), while ``scale(b,A)`` scales each row ``i`` of +``A`` by ``b[i]`` (similar to ``diagm(b)*A``), returning a new array. + +Note: for large ``A``, ``scale`` can be much faster than ``A .* b`` or +``b .* A``, due to the use of BLAS. +``` +""" +scale + +doc""" +```rst +:: + ReentrantLock() + +Creates a reentrant lock. The same task can acquire the lock as many times +as required. Each lock must be matched with an unlock. +``` +""" +ReentrantLock + +doc""" +```rst +:: + real(z) + +Return the real part of the complex number ``z`` +``` +""" +real + +doc""" +```rst +:: + gperm(file) + +Like uperm but gets the permissions of the group owning the file +``` +""" +gperm + +doc""" +```rst +:: + idct(A [, dims]) + +Computes the multidimensional inverse discrete cosine transform (DCT) +of the array ``A`` (technically, a type-III DCT with the unitary +normalization). +The optional ``dims`` argument specifies an iterable subset of +dimensions (e.g. an integer, range, tuple, or array) to transform +along. Most efficient if the size of ``A`` along the transformed +dimensions is a product of small primes; see :func:`nextprod`. See +also :func:`plan_idct` for even greater efficiency. +``` +""" +idct + +doc""" +```rst +:: + nb_available(stream) + +Returns the number of bytes available for reading before a read from this stream or buffer will block. +``` +""" +nb_available + +doc""" +```rst +:: + finalize(x) + +Immediately run finalizers registered for object ``x``. +``` +""" +finalize + +doc""" +```rst +:: + rand([rng], [S], [dims...]) + +Pick a random element or array of random elements from the set of values specified by ``S``; ``S`` can be + +* an indexable collection (for example ``1:n`` or ``['x','y','z']``), or + +* a type: the set of values to pick from is then equivalent to ``typemin(S):typemax(S)`` for integers (this is not applicable to ``BigInt``), and to [0,1) for floating point numbers; + +``S`` defaults to ``Float64``. +``` +""" +rand + +doc""" +```rst +:: + bitpack(A::AbstractArray{T,N}) -> BitArray + +Converts a numeric array to a packed boolean array +``` +""" +bitpack + +doc""" +```rst +:: + base(base, n, [pad]) + +Convert an integer to a string in the given base, optionally specifying a number of digits to pad to. The base can be specified as either an integer, or as a ``UInt8`` array of character values to use as digit symbols. +``` +""" +base + +doc""" +```rst +:: + Timer(callback::Function, delay, repeat=0) + +Create a timer to call the given callback function. +The callback is passed one argument, the timer object itself. +The callback will be invoked after the specified initial delay, +and then repeating with the given ``repeat`` interval. +If ``repeat`` is ``0``, the timer is only triggered once. +Times are in seconds. +A timer is stopped and has its resources freed by calling ``close`` on it. + +:: + Timer(delay, repeat=0) + +Create a timer that wakes up tasks waiting for it (by calling ``wait`` on +the timer object) at a specified interval. +Waiting tasks are also woken up when the timer is closed (by ``close``). +Use ``isopen`` to check whether a timer is still active after a wakeup. +``` +""" +Timer + +doc""" +```rst +:: + BoundsError([a],[i]) + +An indexing operation into an array, ``a``, tried to access an out-of-bounds element, ``i``. +``` +""" +BoundsError + +doc""" +```rst +:: + disable_sigint(f::Function) + +Disable Ctrl-C handler during execution of a function, for calling +external code that is not interrupt safe. Intended to be called using ``do`` +block syntax as follows:: + + disable_sigint() do + # interrupt-unsafe code + ... + end +``` +""" +disable_sigint + +doc""" +```rst +:: + svdfact!(A, [thin=true]) -> SVD + +``svdfact!`` is the same as :func:`svdfact`, but saves space by overwriting the input A, instead of creating a copy. If ``thin`` is ``true``, an economy mode decomposition is returned. The default is to produce a thin decomposition. +``` +""" +svdfact! + +doc""" +```rst +:: + cartesianmap(f, dims) + +Given a ``dims`` tuple of integers ``(m, n, ...)``, call ``f`` on all combinations of +integers in the ranges ``1:m``, ``1:n``, etc. + +.. doctest:: + + julia> cartesianmap(println, (2,2)) + 11 + 21 + 12 + 22 +``` +""" +cartesianmap + +doc""" +```rst +:: + hist2d(M, e1, e2) -> (edge1, edge2, counts) + +Compute a "2d histogram" of a set of N points specified by N-by-2 matrix ``M``. +Arguments ``e1`` and ``e2`` are bins for each dimension, specified either as +integer bin counts or vectors of bin edges. The result is a tuple of +``edge1`` (the bin edges used in the first dimension), ``edge2`` (the bin edges +used in the second dimension), and ``counts``, a histogram matrix of size +``(length(edge1)-1, length(edge2)-1)``. +Note: Julia does not ignore ``NaN`` values in the computation. +``` +""" +hist2d + +doc""" +```rst +:: + which(f, types) + +Returns the method of ``f`` (a ``Method`` object) that would be called for arguments of the given types. + +If ``types`` is an abstract type, then the method that would be called by ``invoke`` +is returned. + +:: + which(symbol) + +Return the module in which the binding for the variable referenced +by ``symbol`` was created. +``` +""" +which + +doc""" +```rst +:: + conv2(u,v,A) + +2-D convolution of the matrix ``A`` with the 2-D separable kernel generated by +the vectors ``u`` and ``v``. Uses 2-D FFT algorithm + +:: + conv2(B,A) + +2-D convolution of the matrix ``B`` with the matrix ``A``. Uses 2-D FFT algorithm +``` +""" +conv2 + +doc""" +```rst +:: + broadcast_getindex(A, inds...) + +Broadcasts the ``inds`` arrays to a common size like ``broadcast``, and returns an array of the results ``A[ks...]``, where ``ks`` goes over the positions in the broadcast. +``` +""" +broadcast_getindex + +doc""" +```rst +:: + findn(A) + +Return a vector of indexes for each dimension giving the locations of the non-zeros in ``A`` (determined by ``A[i]!=0``). +``` +""" +findn + +doc""" +```rst +:: + invoke(f, (types...), args...) + +Invoke a method for the given generic function matching the specified types (as a tuple), on the specified arguments. The arguments must be compatible with the specified types. This allows invoking a method other than the most specific matching method, which is useful when the behavior of a more general definition is explicitly needed (often as part of the implementation of a more specific method of the same function). +``` +""" +invoke + +doc""" +```rst +:: + parse(str, start; greedy=true, raise=true) + +Parse the expression string and return an expression (which could later be passed to eval for execution). Start is the index of the first character to start parsing. If ``greedy`` is true (default), ``parse`` will try to consume as much input as it can; otherwise, it will stop as soon as it has parsed a valid expression. Incomplete but otherwise syntactically valid expressions will return ``Expr(:incomplete, "(error message)")``. If ``raise`` is true (default), syntax errors other than incomplete expressions will raise an error. If ``raise`` is false, ``parse`` will return an expression that will raise an error upon evaluation. + +:: + parse(str; raise=true) + +Parse the whole string greedily, returning a single expression. An error is thrown if there are additional characters after the first expression. If ``raise`` is true (default), syntax errors will raise an error; otherwise, ``parse`` will return an expression that will raise an error upon evaluation. + +:: + parse(type, str, [base]) + +Parse a string as a number. If the type is an integer type, then a base can be specified (the default is 10). If the type is a floating point type, the string is parsed as a decimal floating point number. +If the string does not contain a valid number, an error is raised. +``` +""" +parse + +doc""" +```rst +:: + touch(path::AbstractString) + +Update the last-modified timestamp on a file to the current time. +``` +""" +touch + +doc""" +```rst +:: + bkfact!(A) -> BunchKaufman + +``bkfact!`` is the same as :func:`bkfact`, but saves space by overwriting the input ``A``, instead of creating a copy. +``` +""" +bkfact! + +doc""" +```rst +:: + ^(x, y) + +Exponentiation operator. + +:: + ^(s, n) + +Repeat ``n`` times the string ``s``. The ``^`` operator is an alias to this function. + +.. doctest:: + + julia> "Test "^3 + "Test Test Test " +``` +""" +Base.(:(^)) + +doc""" +```rst +:: + position(s) + +Get the current position of a stream. +``` +""" +position + +doc""" +```rst +:: + selectperm(v, k, [alg=,] [by=,] [lt=,] [rev=false]) + +Return a partial permutation of the the vector ``v``, according to the order +specified by ``by``, ``lt`` and ``rev``, so that ``v[output]`` returns the +first ``k`` (or range of adjacent values if ``k`` is a range) values of a +fully sorted version of ``v``. If ``k`` is a single index (Integer), an +array of the first ``k`` indices is returned; if ``k`` is a range, an array +of those indices is returned. Note that the handling of integer values for +``k`` is different from ``select`` in that it returns a vector of ``k`` +elements instead of just the ``k`` th element. Also note that this is +equivalent to, but more efficient than, calling ``sortperm(...)[k]`` +``` +""" +selectperm + +doc""" +```rst +:: + isabspath(path::AbstractString) -> Bool + +Determines whether a path is absolute (begins at the root directory). +``` +""" +isabspath + +doc""" +```rst +:: + hex2bytes(s::ASCIIString) + +Convert an arbitrarily long hexadecimal string to its binary representation. Returns an Array{UInt8, 1}, i.e. an array of bytes. +``` +""" +hex2bytes + +doc""" +```rst +:: + fft(A [, dims]) + +Performs a multidimensional FFT of the array ``A``. The optional ``dims`` +argument specifies an iterable subset of dimensions (e.g. an integer, +range, tuple, or array) to transform along. Most efficient if the +size of ``A`` along the transformed dimensions is a product of small +primes; see :func:`nextprod`. See also :func:`plan_fft` for even +greater efficiency. + +A one-dimensional FFT computes the one-dimensional discrete Fourier +transform (DFT) as defined by + +.. math:: + + \operatorname{DFT}(A)[k] = \sum_{n=1}^{\operatorname{length}(A)} + \exp\left(-i\frac{2\pi (n-1)(k-1)}{\operatorname{length}(A)} \right) + A[n]. + +A multidimensional FFT simply performs this operation along each transformed +dimension of ``A``. + +Higher performance is usually possible with multi-threading. Use +`FFTW.set_num_threads(np)` to use `np` threads, if you have `np` +processors. +``` +""" +fft + +doc""" +```rst +:: + isdir(path) -> Bool + +Returns ``true`` if ``path`` is a directory, ``false`` otherwise. +``` +""" +isdir + +doc""" +```rst +:: + reinterpret(type, A) + +Change the type-interpretation of a block of memory. For example, ``reinterpret(Float32, UInt32(7))`` interprets the 4 bytes corresponding to ``UInt32(7)`` as a ``Float32``. For arrays, this constructs an array with the same binary data as the given array, but with the specified element type. +``` +""" +reinterpret + +doc""" +```rst +:: + squeeze(A, dims) + +Remove the dimensions specified by ``dims`` from array ``A``. Elements of +``dims`` must be unique and within the range ``1:ndims(A)``. +``` +""" +squeeze + +doc""" +```rst +:: + ~(x) + +Bitwise not +``` +""" +~ + +doc""" +```rst +:: + hankelh1(nu, x) + +Bessel function of the third kind of order ``nu``, :math:`H^{(1)}_\nu(x)`. +``` +""" +hankelh1 + +doc""" +```rst +:: + hessfact(A) + +Compute the Hessenberg decomposition of ``A`` and return a ``Hessenberg`` object. If ``F`` is the factorization object, the unitary matrix can be accessed with ``F[:Q]`` and the Hessenberg matrix with ``F[:H]``. When ``Q`` is extracted, the resulting type is the ``HessenbergQ`` object, and may be converted to a regular matrix with :func:`full`. +``` +""" +hessfact + +doc""" +```rst +:: + gcdx(x,y) + +Computes the greatest common (positive) divisor of ``x`` and ``y`` and their Bézout coefficients, i.e. the integer coefficients ``u`` and ``v`` that satisfy :math:`ux+vy = d = gcd(x,y)`. + +.. doctest:: + + julia> gcdx(12, 42) + (6,-3,1) + +.. doctest:: + + julia> gcdx(240, 46) + (2,-9,47) + +.. note:: + + Bézout coefficients are *not* uniquely defined. ``gcdx`` returns the minimal Bézout coefficients that are computed by the extended Euclid algorithm. (Ref: D. Knuth, TAoCP, 2/e, p. 325, Algorithm X.) These coefficients ``u`` and ``v`` are minimal in the sense that :math:`|u| < |\frac y d` and :math:`|v| < |\frac x d`. Furthermore, the signs of ``u`` and ``v`` are chosen so that ``d`` is positive. +``` +""" +gcdx + +doc""" +```rst +:: + rem(x, y) + %(x, y) + +Remainder from Euclidean division, returning a value of the same sign +as``x``, and smaller in magnitude than ``y``. This value is always exact. +``` +""" +rem + +doc""" +```rst +:: + rotl90(A) + +Rotate matrix ``A`` left 90 degrees. + +:: + rotl90(A, k) + +Rotate matrix ``A`` left 90 degrees an integer ``k`` number of times. If ``k`` +is zero or a multiple of four, this is equivalent to a ``copy``. +``` +""" +rotl90 + +doc""" +```rst +:: + info(msg) + +Display an informational message. +``` +""" +info + +doc""" +```rst +:: + eigmin(A) + +Returns the smallest eigenvalue of ``A``. +``` +""" +eigmin + +doc""" +```rst +:: + acscd(x) + +Compute the inverse cosecant of ``x``, where the output is in degrees +``` +""" +acscd + +doc""" +```rst +:: + ltoh(x) + +Converts the endianness of a value from Little-endian to that used by the +Host. +``` +""" +ltoh + +doc""" +```rst +:: + evalfile(path::AbstractString) + +Load the file using ``include``, evaluate all expressions, and return the value of the last one. +``` +""" +evalfile + +doc""" +```rst +:: + success(command) + +Run a command object, constructed with backticks, and tell whether it was successful (exited with a code of 0). An exception is raised if the process cannot be started. +``` +""" +success + +doc""" +```rst +:: + sortperm!(ix, v, [alg=,] [by=,] [lt=,] [rev=false,] [initialized=false]) + +Like ``sortperm``, but accepts a preallocated index vector ``ix``. If ``initialized`` is ``false`` +(the default), ix is initialized to contain the values ``1:length(v)``. + +See also :func:`sortperm` +``` +""" +sortperm! + +doc""" +```rst +:: + isodd(x::Integer) -> Bool + +Returns ``true`` if ``x`` is odd (that is, not divisible by 2), and ``false`` otherwise. + +.. doctest:: + + julia> isodd(9) + true + + julia> isodd(10) + false +``` +""" +isodd + +doc""" +```rst +:: + normalize_string(s, normalform::Symbol) + +Normalize the string ``s`` according to one of the four "normal +forms" of the Unicode standard: ``normalform`` can be ``:NFC``, +``:NFD``, ``:NFKC``, or ``:NFKD``. Normal forms C (canonical +composition) and D (canonical decomposition) convert different +visually identical representations of the same abstract string into +a single canonical form, with form C being more compact. Normal +forms KC and KD additionally canonicalize "compatibility +equivalents": they convert characters that are abstractly similar +but visually distinct into a single canonical choice (e.g. they expand +ligatures into the individual characters), with form KC being more compact. + +Alternatively, finer control and additional transformations may be +be obtained by calling `normalize_string(s; keywords...)`, where +any number of the following boolean keywords options (which all default +to ``false`` except for ``compose``) are specified: + +* ``compose=false``: do not perform canonical composition +* ``decompose=true``: do canonical decomposition instead of canonical composition (``compose=true`` is ignored if present) +* ``compat=true``: compatibility equivalents are canonicalized +* ``casefold=true``: perform Unicode case folding, e.g. for case-insensitive string comparison +* ``newline2lf=true``, ``newline2ls=true``, or ``newline2ps=true``: convert various newline sequences (LF, CRLF, CR, NEL) into a linefeed (LF), line-separation (LS), or paragraph-separation (PS) character, respectively +* ``stripmark=true``: strip diacritical marks (e.g. accents) +* ``stripignore=true``: strip Unicode's "default ignorable" characters (e.g. the soft hyphen or the left-to-right marker) +* ``stripcc=true``: strip control characters; horizontal tabs and form feeds are converted to spaces; newlines are also converted to spaces unless a newline-conversion flag was specified +* ``rejectna=true``: throw an error if unassigned code points are found +* ``stable=true``: enforce Unicode Versioning Stability + +For example, NFKC corresponds to the options ``compose=true, compat=true, stable=true``. +``` +""" +normalize_string + +doc""" +```rst +:: + cd(dir::AbstractString) + +Set the current working directory. + +:: + cd(f, [dir]) + +Temporarily changes the current working directory (HOME if not specified) and applies function f before returning. +``` +""" +cd + +doc""" +```rst +:: + hton(x) + +Converts the endianness of a value from that used by the Host to Network +byte order (big-endian). +``` +""" +hton + +doc""" +```rst +:: + is(x, y) -> Bool + ===(x,y) -> Bool + ≡(x,y) -> Bool + +Determine whether ``x`` and ``y`` are identical, in the sense that no program could distinguish them. Compares mutable objects by address in memory, and compares immutable objects (such as numbers) by contents at the bit level. This function is sometimes called ``egal``. +``` +""" +is + +doc""" +```rst +:: + mark(s) + +Add a mark at the current position of stream ``s``. Returns the marked position. + +See also :func:`unmark`, :func:`reset`, :func:`ismarked` +``` +""" +mark + +doc""" +```rst +:: + cp(src::AbstractString, dst::AbstractString; remove_destination::Bool=false, follow_symlinks::Bool=false) + +Copy the file, link, or directory from *src* to *dest*. +\"remove_destination=true\" will first remove an existing `dst`. + +If `follow_symlinks=false`, and src is a symbolic link, dst will be created as a symbolic link. +If `follow_symlinks=true` and src is a symbolic link, dst will be a copy of the file or directory +`src` refers to. +``` +""" +cp + +doc""" +```rst +:: + bswap(n) + +Byte-swap an integer +``` +""" +bswap + +doc""" +```rst +:: + manage(manager::FooManager, pid::Int, config::WorkerConfig. op::Symbol) + + Implemented by cluster managers. It is called on the master process, during a worker's lifetime, + with appropriate ``op`` values: + + - with ``:register``/``:deregister`` when a worker is added / removed + from the Julia worker pool. + - with ``:interrupt`` when ``interrupt(workers)`` is called. The + :class:`ClusterManager` should signal the appropriate worker with an + interrupt signal. + - with ``:finalize`` for cleanup purposes. +``` +""" +manage + +doc""" +```rst +:: + resize!(collection, n) -> collection + +Resize ``collection`` to contain ``n`` elements. +If ``n`` is smaller than the current collection length, the first ``n`` +elements will be retained. If ``n`` is larger, the new elements are not +guaranteed to be initialized. + +.. doctest:: + + julia> resize!([6, 5, 4, 3, 2, 1], 3) + 3-element Array{Int64,1}: + 6 + 5 + 4 + +.. code-block:: julia + + julia> resize!([6, 5, 4, 3, 2, 1], 8) + 8-element Array{Int64,1}: + 6 + 5 + 4 + 3 + 2 + 1 + 0 + 0 +``` +""" +resize! + +doc""" +```rst +:: + sumabs2!(r, A) + +Sum squared absolute values of elements of ``A`` over the singleton +dimensions of ``r``, and write results to ``r``. +``` +""" +sumabs2! + +doc""" +```rst +:: + IPv4(host::Integer) -> IPv4 + +Returns IPv4 object from ip address formatted as Integer +``` +""" +IPv4 + +doc""" +```rst +:: + trailing_zeros(x::Integer) -> Integer + +Number of zeros trailing the binary representation of ``x``. + +.. doctest:: + + julia> trailing_zeros(2) + 1 +``` +""" +trailing_zeros + +doc""" +```rst +:: + etree(A[, post]) + +Compute the elimination tree of a symmetric sparse matrix ``A`` from ``triu(A)`` and, optionally, its post-ordering permutation. +``` +""" +etree + +doc""" +```rst +:: + isalnum(c::Union{Char,AbstractString}) -> Bool + +Tests whether a character is alphanumeric, or whether this +is true for all elements of a string. A character is classified as alphabetic +if it belongs to the Unicode general category Letter or Number, i.e. a character whose +category code begins with 'L' or 'N'. +``` +""" +isalnum + +doc""" +```rst +:: + dct!(A [, dims]) + +Same as :func:`dct!`, except that it operates in-place +on ``A``, which must be an array of real or complex floating-point +values. +``` +""" +dct! + +doc""" +```rst +:: + @sprintf("%Fmt", args...) + +Return ``@printf`` formatted output as string. +julia> s = @sprintf "this is a %s %15.1f" "test" 34.567; + +julia> println(s) +this is a test 34.6 +``` +""" +:@sprintf + +doc""" +```rst +:: + tanh(x) + +Compute hyperbolic tangent of ``x`` +``` +""" +tanh + +doc""" +```rst +:: + repr(x) + +Create a string from any value using the ``showall`` function. +``` +""" +repr + +doc""" +```rst +:: + maxintfloat(type) + +The largest integer losslessly representable by the given floating-point type +``` +""" +maxintfloat + +doc""" +```rst +:: + promote_shape(s1, s2) + +Check two array shapes for compatibility, allowing trailing singleton dimensions, +and return whichever shape has more dimensions. +``` +""" +promote_shape + +doc""" +```rst +:: + methodswith(typ[, module or function][, showparents]) + +Return an array of methods with an argument of type ``typ``. If optional +``showparents`` is ``true``, also return arguments with a parent type +of ``typ``, excluding type ``Any``. + +The optional second argument restricts the search to a particular module +or function. +``` +""" +methodswith + +doc""" +```rst +:: + foldr(op, v0, itr) + +Like :func:`reduce`, but with guaranteed right associativity. ``v0`` +will be used exactly once. + +:: + foldr(op, itr) + +Like ``foldr(op, v0, itr)``, but using the last element of ``itr`` +as ``v0``. In general, this cannot be used with empty collections +(see ``reduce(op, itr)``). +``` +""" +foldr + +doc""" +```rst +:: + chol(A, [LU]) -> F + +Compute the Cholesky factorization of a symmetric positive definite matrix ``A`` and return the matrix ``F``. If ``LU`` is ``Val{:U}`` (Upper), ``F`` is of type ``UpperTriangular`` and ``A = F'*F``. If ``LU`` is ``Val{:L}`` (Lower), ``F`` is of type ``LowerTriangular`` and ``A = F*F'``. ``LU`` defaults to ``Val{:U}``. +``` +""" +chol + +doc""" +```rst +:: + ParseError(msg) + +The expression passed to the `parse` function could not be interpreted as a valid Julia expression. +``` +""" +ParseError + +doc""" +```rst +:: + delete!(collection, key) + +Delete the mapping for the given key in a collection, and return the collection. +``` +""" +delete! + +doc""" +```rst +:: + interrupt([pids...]) + +Interrupt the current executing task on the specified workers. This is +equivalent to pressing Ctrl-C on the local machine. If no arguments are given, +all workers are interrupted. +``` +""" +interrupt + +doc""" +```rst +:: + std(v[, region]) + +Compute the sample standard deviation of a vector or array ``v``, optionally along dimensions in ``region``. The algorithm returns an estimator of the generative distribution's standard deviation under the assumption that each entry of ``v`` is an IID drawn from that generative distribution. This computation is equivalent to calculating ``sqrt(sum((v - mean(v)).^2) / (length(v) - 1))``. +Note: Julia does not ignore ``NaN`` values in the computation. +For applications requiring the handling of missing data, the ``DataArray`` +package is recommended. +``` +""" +std + +doc""" +```rst +:: + chr2ind(string, i) + +Convert a character index to a byte index +``` +""" +chr2ind + +doc""" +```rst +:: + fullname(m::Module) + +Get the fully-qualified name of a module as a tuple of symbols. For example, +``fullname(Base.Pkg)`` gives ``(:Base,:Pkg)``, and ``fullname(Main)`` gives ``()``. +``` +""" +fullname + +doc""" +```rst +:: + isreadable(path) -> Bool + +Returns ``true`` if the current user has permission to read ``path``, +``false`` otherwise. +``` +""" +isreadable + +doc""" +```rst +:: + eps([type]) + +The distance between 1.0 and the next larger representable floating-point value of ``type``. Only floating-point types are sensible arguments. If ``type`` is omitted, then ``eps(Float64)`` is returned. + +:: + eps(x) + +The distance between ``x`` and the next larger representable floating-point value of the same type as ``x``. +``` +""" +eps + +doc""" +```rst +:: + rem1(x,m) + +Remainder after division, returning in the range (0,m] +``` +""" +rem1 + +doc""" +```rst +:: + sparsevec(I, V, [m, combine]) + +Create a sparse matrix ``S`` of size ``m x 1`` such that ``S[I[k]] = V[k]``. Duplicates are combined using the ``combine`` function, which defaults to ``+`` if it is not provided. In julia, sparse vectors are really just sparse matrices with one column. Given Julia's Compressed Sparse Columns (CSC) storage format, a sparse column matrix with one column is sparse, whereas a sparse row matrix with one row ends up being dense. + +:: + sparsevec(D::Dict, [m]) + +Create a sparse matrix of size ``m x 1`` where the row values are keys from the dictionary, and the nonzero values are the values from the dictionary. + +:: + sparsevec(A) + +Convert a dense vector ``A`` into a sparse matrix of size ``m x 1``. In julia, sparse vectors are really just sparse matrices with one column. +``` +""" +sparsevec + +doc""" +```rst +:: + isalpha(c::Union{Char,AbstractString}) -> Bool + +Tests whether a character is alphabetic, or whether this +is true for all elements of a string. A character is classified as alphabetic +if it belongs to the Unicode general category Letter, i.e. a character whose +category code begins with 'L'. +``` +""" +isalpha + +doc""" +```rst +:: + lock(l::ReentrantLock) + +Associates ``l`` with the current task. If ``l`` is already locked by a different +task, waits for it to become available. The same task can acquire the lock multiple +times. Each "lock" must be matched by an "unlock" +``` +""" +lock + +doc""" +```rst +:: + transpose(A) + +The transposition operator (``.'``). +``` +""" +transpose + +doc""" +```rst +:: + searchsortedfirst(a, x, [by=,] [lt=,] [rev=false]) + +Returns the index of the first value in ``a`` greater than or equal to ``x``, +according to the specified order. Returns ``length(a)+1`` if ``x`` is greater +than all values in ``a``. +``` +""" +searchsortedfirst + +doc""" +```rst +:: + big(x) + +Convert a number to a maximum precision representation (typically ``BigInt`` or ``BigFloat``). See ``BigFloat`` for information about some pitfalls with floating-point numbers. +``` +""" +big + +doc""" +```rst +:: + names(x::Module[, all=false[, imported=false]]) + +Get an array of the names exported by a module, with optionally more module +globals according to the additional parameters. +``` +""" +names + +doc""" +```rst +:: + quit() + +Quit the program indicating that the processes completed successfully. This function calls ``exit(0)`` (see :func:`exit`). +``` +""" +quit + +doc""" +```rst +:: + init_worker(manager::FooManager) + + Called by cluster managers implementing custom transports. It initializes a newly launched process as a worker. + Command line argument ``--worker`` has the effect of initializing a process as a worker using TCP/IP sockets + for transport. +``` +""" +init_worker + +doc""" +```rst +:: + print_escaped(io, str::AbstractString, esc::AbstractString) + +General escaping of traditional C and Unicode escape sequences, plus any characters in esc are also escaped (with a backslash). +``` +""" +print_escaped + +doc""" +```rst +:: + typejoin(T, S) + +Compute a type that contains both ``T`` and ``S``. +``` +""" +typejoin + +doc""" +```rst +:: + summary(x) + +Return a string giving a brief description of a value. By default returns +``string(typeof(x))``. For arrays, returns strings like "2x2 Float64 Array". +``` +""" +summary + +doc""" +```rst +:: + Base64DecodePipe(istream) + +Returns a new read-only I/O stream, which decodes base64-encoded data +read from ``istream``. +``` +""" +Base64DecodePipe + +doc""" +```rst +:: + module_parent(m::Module) -> Module + +Get a module's enclosing module. ``Main`` is its own parent. +``` +""" +module_parent + +doc""" +```rst +:: + airyaiprime(x) + +Airy function derivative :math:`\operatorname{Ai}'(x)`. +``` +""" +airyaiprime + +doc""" +```rst +:: + besselh(nu, k, x) + +Bessel function of the third kind of order ``nu`` (Hankel function). +``k`` is either 1 or 2, selecting ``hankelh1`` or ``hankelh2``, respectively. +``` +""" +besselh + +doc""" +```rst +:: + prepend!(collection, items) -> collection + +Insert the elements of ``items`` to the beginning of ``collection``. + +.. doctest:: + + julia> prepend!([3],[1,2]) + 3-element Array{Int64,1}: + 1 + 2 + 3 +``` +""" +prepend! + +doc""" +```rst +:: + sum_kbn(A) + +Returns the sum of all array elements, using the Kahan-Babuska-Neumaier compensated summation algorithm for additional accuracy. +``` +""" +sum_kbn + +doc""" +```rst +:: + beta(x, y) + +Euler integral of the first kind :math:`\operatorname{B}(x,y) = \Gamma(x)\Gamma(y)/\Gamma(x+y)`. +``` +""" +beta + +doc""" +```rst +:: + eye(n) + +n-by-n identity matrix + +:: + eye(m, n) + +m-by-n identity matrix + +:: + eye(A) + +Constructs an identity matrix of the same dimensions and type as ``A``. +``` +""" +eye + +doc""" +```rst +:: + diagind(M[, k]) + +A ``Range`` giving the indices of the ``k``\ th diagonal of the matrix ``M``. +``` +""" +diagind + +doc""" +```rst +:: + include_string(code::AbstractString, [filename]) + +Like ``include``, except reads code from the given string rather than from a file. Since there is no file path involved, no path processing or fetching from node 1 is done. +``` +""" +include_string + +doc""" +```rst +:: + chmod(path, mode) + +Change the permissions mode of ``path`` to ``mode``. Only integer ``mode``\ s +(e.g. 0o777) are currently supported. +``` +""" +chmod + +doc""" +```rst +:: + gamma(x) + +Compute the gamma function of ``x`` +``` +""" +gamma + +doc""" +```rst +:: + sin(x) + +Compute sine of ``x``, where ``x`` is in radians +``` +""" +sin + +doc""" +```rst +:: + ordschur!(Q, T, select) -> Schur + +Reorders the Schur factorization of a real matrix ``A=Q*T*Q'``, overwriting ``Q`` and ``T`` in the process. See :func:`ordschur` + +:: + ordschur!(S, select) -> Schur + +Reorders the Schur factorization ``S`` of type ``Schur``, overwriting ``S`` in the process. See :func:`ordschur` + +:: + ordschur!(S, T, Q, Z, select) -> GeneralizedSchur + +Reorders the Generalized Schur factorization of a matrix by overwriting the matrices ``(S, T, Q, Z)`` in the process. See :func:`ordschur`. + +:: + ordschur!(GS, select) -> GeneralizedSchur + +Reorders the Generalized Schur factorization of a Generalized Schur object by overwriting the object with the new factorization. See :func:`ordschur`. +``` +""" +ordschur! + +doc""" +```rst +:: + whos([Module,] [pattern::Regex]) + +Print information about exported global variables in a module, optionally restricted +to those matching ``pattern``. +``` +""" +whos + +doc""" +```rst +:: + compile(module::Symbol) + +Creates a precompiled cache file for module (see help for ``require``) and all of its dependencies. This can be used to reduce package load times. Cache files are stored in LOAD_CACHE_PATH[1], which defaults to `~/.julia/lib/VERSION`. See the manual section `Module initialization and precompilation` (under `Modules`) for important notes. +``` +""" +compile + +doc""" +```rst +:: + clipboard(x) + +Send a printed form of ``x`` to the operating system clipboard ("copy"). + +:: + clipboard() -> AbstractString + +Return a string with the contents of the operating system clipboard ("paste"). +``` +""" +clipboard + +doc""" +```rst +:: + code_lowered(f, types) + +Returns an array of lowered ASTs for the methods matching the given generic function and type signature. +``` +""" +code_lowered + +doc""" +```rst +:: + nthperm(v, k) + +Compute the kth lexicographic permutation of a vector. + +:: + nthperm(p) + +Return the ``k`` that generated permutation ``p``. +Note that ``nthperm(nthperm([1:n], k)) == k`` for ``1 <= k <= factorial(n)``. +``` +""" +nthperm + +doc""" +```rst +:: + values(collection) + +Return an iterator over all values in a collection. ``collect(values(d))`` returns an array of values. +``` +""" +values + +doc""" +```rst +:: + A_mul_B!(Y, A, B) -> Y + + +Calculates the matrix-matrix or matrix-vector product *A B* and stores the +result in *Y*, overwriting the existing value of *Y*. + +.. doctest:: + + julia> A=[1.0 2.0; 3.0 4.0]; B=[1.0 1.0; 1.0 1.0]; A_mul_B!(B, A, B); + + julia> B + 2x2 Array{Float64,2}: + 3.0 3.0 + 7.0 7.0 +``` +""" +A_mul_B! + +doc""" +```rst +:: + ntuple(f::Function, n) + +Create a tuple of length ``n``, computing each element as ``f(i)``, where ``i`` is the index of the element. +``` +""" +ntuple + +doc""" +```rst +:: + idct!(A [, dims]) + +Same as :func:`idct!`, but operates in-place on ``A``. +``` +""" +idct! + +doc""" +```rst +:: + Ac_rdiv_Bc(a,b) + +Matrix operator A\ :sup:`H` / B\ :sup:`H` +``` +""" +Ac_rdiv_Bc + +doc""" +```rst +:: + selectperm!(ix, v, k, [alg=,] [by=,] [lt=,] [rev=false,] [initialized=false]) + +Like ``selectperm``, but accepts a preallocated index vector ``ix``. If +``initialized`` is ``false`` (the default), ix is initialized to contain the +values ``1:length(ix)``. +``` +""" +selectperm! + +doc""" +```rst +:: + istaskdone(task) -> Bool + +Tell whether a task has exited. +``` +""" +istaskdone + +doc""" +```rst +:: + .>(x, y) + +Element-wise greater-than comparison operator. +``` +""" +Base.(:(.>)) + +doc""" +```rst +:: + search(string, chars, [start]) + +Search for the first occurrence of the given characters within the given string. The second argument may be a single character, a vector or a set of characters, a string, or a regular expression (though regular expressions are only allowed on contiguous strings, such as ASCII or UTF-8 strings). The third argument optionally specifies a starting index. The return value is a range of indexes where the matching sequence is found, such that ``s[search(s,x)] == x``: + +``search(string, "substring")`` = ``start:end`` such that ``string[start:end] == "substring"``, or ``0:-1`` if unmatched. + +``search(string, 'c')`` = ``index`` such that ``string[index] == 'c'``, or ``0`` if unmatched. +``` +""" +search + +doc""" +```rst +:: + remotecall_fetch(id, func, args...) + +Perform ``fetch(remotecall(...))`` in one message. Any remote exceptions are captured in a ``RemoteException`` +and thrown. +``` +""" +remotecall_fetch + +doc""" +```rst +:: + contains(haystack, needle) + +Determine whether the second argument is a substring of the first. +``` +""" +contains + +doc""" +```rst +:: + flush(stream) + +Commit all currently buffered writes to the given stream. +``` +""" +flush + +doc""" +```rst +:: + detach(command) + +Mark a command object so that it will be run in a new process group, +allowing it to outlive the julia process, and not have Ctrl-C interrupts +passed to it. +``` +""" +detach + +doc""" +```rst +:: + precompile(f,args::Tuple{Vararg{Any}}) + +Compile the given function ``f`` for the argument tuple (of types) ``args``, but do not execute it. +``` +""" +precompile + +doc""" +```rst +:: + toc() + +Print and return the time elapsed since the last :func:`tic`. +``` +""" +toc + +doc""" +```rst +:: + asinh(x) + +Compute the inverse hyperbolic sine of ``x`` +``` +""" +asinh + +doc""" +```rst +:: + count(p, itr) -> Integer + +Count the number of elements in ``itr`` for which predicate ``p`` returns true. +``` +""" +count + +doc""" +```rst +:: + atreplinit(f) + +Register a one-argument function to be called before the REPL interface is initialized in interactive sessions; this is useful to customize the interface. The argument of ``f`` is the REPL object. +This function should be called from within the ``.juliarc.jl`` initialization file. +``` +""" +atreplinit + +doc""" +```rst +:: + strip(string, [chars]) + +Return ``string`` with any leading and trailing whitespace removed. If ``chars`` (a character, or vector or set of characters) is provided, instead remove characters contained in it. +``` +""" +strip + +doc""" +```rst +:: + findin(a, b) + +Returns the indices of elements in collection ``a`` that appear in collection ``b`` +``` +""" +findin + +doc""" +```rst +:: + minimum(itr) + +Returns the smallest element in a collection. + +:: + minimum(A, dims) + +Compute the minimum value of an array over the given dimensions. +``` +""" +minimum + +doc""" +```rst +:: + var(v[, region]) + +Compute the sample variance of a vector or array ``v``, optionally along dimensions in ``region``. The algorithm will return an estimator of the generative distribution's variance under the assumption that each entry of ``v`` is an IID drawn from that generative distribution. This computation is equivalent to calculating ``sum((v - mean(v)).^2) / (length(v) - 1)``. +Note: Julia does not ignore ``NaN`` values in the computation. +For applications requiring the handling of missing data, the ``DataArray`` +package is recommended. +``` +""" +var + +doc""" +```rst +:: + lcfirst(string) + +Returns ``string`` with the first character converted to lowercase. +``` +""" +lcfirst + +doc""" +```rst +:: + @code_native + +Evaluates the arguments to the function call, determines their types, and calls :func:`code_native` on the resulting expression +``` +""" +:@code_native + +doc""" +```rst +:: + flipbits!(B::BitArray{N}) -> BitArray{N} + +Performs a bitwise not operation on B. See :ref:`~ operator <~>`. +``` +""" +flipbits! + +doc""" +```rst +:: + readlink(path) -> AbstractString + +Returns the value of a symbolic link ``path``. +``` +""" +readlink + +doc""" +```rst +:: + @code_warntype + +Evaluates the arguments to the function call, determines their types, and calls :func:`code_warntype` on the resulting expression +``` +""" +:@code_warntype + +doc""" +```rst +:: + deg2rad(x) + +Convert ``x`` from degrees to radians +``` +""" +deg2rad + +doc""" +```rst +:: + redirect_stdin([stream]) + +Like redirect_stdout, but for STDIN. Note that the order of the return tuple is still (rd,wr), i.e. data to be read +from STDIN, may be written to wr. +``` +""" +redirect_stdin + +doc""" +```rst +:: + minmax(x, y) + +Return ``(min(x,y), max(x,y))``. +See also: :func:`extrema` that returns ``(minimum(x), maximum(x))`` +``` +""" +minmax + +doc""" +```rst +:: + mktemp([parent=tempdir()]) + +Returns ``(path, io)``, where ``path`` is the path of a new temporary file +in ``parent`` and ``io`` is an open file object for this path. +``` +""" +mktemp + +doc""" +```rst +:: + isreadonly(stream) -> Bool + +Determine whether a stream is read-only. +``` +""" +isreadonly + +doc""" +```rst +:: + get_rounding(T) + +Get the current floating point rounding mode for type ``T``, controlling +the rounding of basic arithmetic functions (:func:`+`, :func:`-`, +:func:`*`, :func:`/` and :func:`sqrt`) and type conversion. + +Valid modes are ``RoundNearest``, ``RoundToZero``, ``RoundUp``, +``RoundDown``, and ``RoundFromZero`` (``BigFloat`` only). +``` +""" +get_rounding + +doc""" +```rst +:: + code_llvm(f, types) + +Prints the LLVM bitcodes generated for running the method matching the given generic function and type signature to :const:`STDOUT`. + +All metadata and dbg.* calls are removed from the printed bitcode. Use code_llvm_raw for the full IR. +``` +""" +code_llvm + +doc""" +```rst +:: + Bidiagonal(dv, ev, isupper) + +Constructs an upper (``isupper=true``) or lower (``isupper=false``) bidiagonal matrix +using the given diagonal (``dv``) and off-diagonal (``ev``) vectors. The result is of type ``Bidiagonal`` and provides efficient specialized linear solvers, but may be converted into a regular matrix with :func:`full`. +``` +""" +Bidiagonal + +doc""" +```rst +:: + notify(condition, val=nothing; all=true, error=false) + +Wake up tasks waiting for a condition, passing them ``val``. +If ``all`` is true (the default), all waiting tasks are woken, otherwise +only one is. If ``error`` is true, the passed value is raised as an +exception in the woken tasks. +``` +""" +notify + +doc""" +```rst +:: + fftshift(x) + +Swap the first and second halves of each dimension of ``x``. + +:: + fftshift(x,dim) + +Swap the first and second halves of the given dimension of array ``x``. +``` +""" +fftshift + +doc""" +```rst +:: + unique(itr[, dim]) + +Returns an array containing only the unique elements of the iterable ``itr``, in +the order that the first of each set of equivalent elements originally appears. +If ``dim`` is specified, returns unique regions of the array ``itr`` along ``dim``. +``` +""" +unique + +doc""" +```rst +:: + sub(A, inds...) + +Like :func:`getindex`, but returns a view into the parent array ``A`` with the given indices instead of making a copy. Calling :func:`getindex` or :func:`setindex!` on the returned :obj:`SubArray` computes the indices to the parent array on the fly without checking bounds. +``` +""" +sub + +doc""" +```rst +:: + cholfact!(A [,LU=:U [,pivot=Val{false}]][;tol=-1.0]) -> Cholesky + +``cholfact!`` is the same as :func:`cholfact`, but saves space by overwriting the input ``A``, instead of creating a copy. ``cholfact!`` can also reuse the symbolic factorization from a different matrix ``F`` with the same structure when used as: ``cholfact!(F::CholmodFactor, A)``. +``` +""" +cholfact! + +doc""" +```rst +:: + expanduser(path::AbstractString) -> AbstractString + +On Unix systems, replace a tilde character at the start of a path with the +current user's home directory. +``` +""" +expanduser + +doc""" +```rst +:: + haskey(collection, key) -> Bool + +Determine whether a collection has a mapping for a given key. +``` +""" +haskey + +doc""" +```rst +:: + cot(x) + +Compute the cotangent of ``x``, where ``x`` is in radians +``` +""" +cot + +doc""" +```rst +:: + get(x) + +Attempt to access the value of the ``Nullable`` object, ``x``. Returns the +value if it is present; otherwise, throws a ``NullException``. + +:: + get(x, y) + +Attempt to access the value of the ``Nullable{T}`` object, ``x``. Returns +the value if it is present; otherwise, returns ``convert(T, y)``. + +:: + get(collection, key, default) + +Return the value stored for the given key, or the given default value if no mapping for the key is present. + +:: + get(f::Function, collection, key) + +Return the value stored for the given key, or if no mapping for the key is present, return ``f()``. Use :func:`get!` to also store the default value in the dictionary. + +This is intended to be called using ``do`` block syntax:: + + get(dict, key) do + # default value calculated here +``` +""" +get + +doc""" +```rst +:: + .!=(x, y) + .≠(x,y) + +Element-wise not-equals comparison operator. +``` +""" +Base.(:(.!=)) + +doc""" +```rst +:: + lufact!(A) -> LU + +``lufact!`` is the same as :func:`lufact`, but saves space by overwriting the input A, instead of creating a copy. For sparse ``A`` the ``nzval`` field is not overwritten but the index fields, ``colptr`` and ``rowval`` are decremented in place, converting from 1-based indices to 0-based indices. +``` +""" +lufact! + +doc""" +```rst +:: + IOBuffer() -> IOBuffer + +Create an in-memory I/O stream. + +:: + IOBuffer(size::Int) + +Create a fixed size IOBuffer. The buffer will not grow dynamically. + +:: + IOBuffer(string) + +Create a read-only IOBuffer on the data underlying the given string + +:: + IOBuffer([data,],[readable,writable,[maxsize]]) + +Create an IOBuffer, which may optionally operate on a pre-existing array. If the readable/writable arguments are given, +they restrict whether or not the buffer may be read from or written to respectively. By default the buffer is readable +but not writable. The last argument optionally specifies a size beyond which the buffer may not be grown. +``` +""" +IOBuffer + +doc""" +```rst +:: + plan_dct!(A [, dims [, flags [, timelimit]]]) + +Same as :func:`plan_dct`, but operates in-place on ``A``. +``` +""" +plan_dct! + +doc""" +```rst +:: + findmax(itr) -> (x, index) + +Returns the maximum element and its index. + +:: + findmax(A, dims) -> (maxval, index) + +For an array input, returns the value and index of the maximum over +the given dimensions. +``` +""" +findmax + +doc""" +```rst +:: + tempname() + +Generate a unique temporary file path. +``` +""" +tempname + +doc""" +```rst +:: + poll_fd(fd, timeout_s::Real; readable=false, writable=false) + +Monitor a file descriptor ``fd`` for changes in the read or write availability, and with a timeout given by ``timeout_s`` seconds. + +The keyword arguments determine which of read and/or write status should be monitored; at least one of them must be set to true. + +The returned value is an object with boolean fields ``readable``, ``writable``, and +``timedout``, giving the result of the polling. +``` +""" +poll_fd + +doc""" +```rst +:: + prevpow2(n) + +The largest power of two not greater than ``n``. Returns 0 for ``n==0``, and returns +``-prevpow2(-n)`` for negative arguments. +``` +""" +prevpow2 + +doc""" +```rst +:: + code_warntype(f, types) + +Displays lowered and type-inferred ASTs for the methods matching the given generic function and type signature. The ASTs are annotated in such a way as to cause "non-leaf" types to be emphasized (if color is available, displayed in red). This serves as a warning of potential type instability. Not all non-leaf types are particularly problematic for performance, so the results need to be used judiciously. See :ref:`man-code-warntype` for more information. +``` +""" +code_warntype + +doc""" +```rst +:: + broadcast!_function(f) + +Like ``broadcast_function``, but for ``broadcast!``. +``` +""" +broadcast!_function + +doc""" +```rst +:: + with_rounding(f::Function, T, mode) + +Change the rounding mode of floating point type ``T`` for the duration of ``f``. It is logically equivalent to:: + + old = get_rounding(T) + set_rounding(T, mode) + f() + set_rounding(T, old) + +See ``get_rounding`` for available rounding modes. +``` +""" +with_rounding + +doc""" +```rst +:: + sleep(seconds) + +Block the current task for a specified number of seconds. The minimum sleep +time is 1 millisecond or input of ``0.001``. +``` +""" +sleep + +doc""" +```rst +:: + Mmap.sync!(array) + +Forces synchronization between the in-memory version of a memory-mapped ``Array`` or ``BitArray`` and the on-disk version. +``` +""" +Mmap.sync! + +doc""" +```rst +:: + csc(x) + +Compute the cosecant of ``x``, where ``x`` is in radians +``` +""" +csc + +doc""" +```rst +:: + hash(x[, h]) + +Compute an integer hash code such that ``isequal(x,y)`` implies ``hash(x)==hash(y)``. +The optional second argument ``h`` is a hash code to be mixed with the result. + +New types should implement the 2-argument form, typically by calling the 2-argument ``hash`` method recursively in order to mix hashes of the contents with each other (and with ``h``). Typically, any type that implements ``hash`` should also implement its own ``==`` (hence ``isequal``) to guarantee the property mentioned above. +``` +""" +hash + +doc""" +```rst +:: + atan2(y, x) + +Compute the inverse tangent of ``y/x``, using the signs of both ``x`` and ``y`` to determine the quadrant of the return value. +``` +""" +atan2 + +doc""" +```rst +:: + send(socket::UDPSocket, host::IPv4, port::Integer, msg) + +Send ``msg`` over ``socket to ``host:port``. +``` +""" +send + +doc""" +```rst +:: + atanh(x) + +Compute the inverse hyperbolic tangent of ``x`` +``` +""" +atanh + +doc""" +```rst +:: + deleteat!(collection, index) + +Remove the item at the given ``index`` and return the modified ``collection``. +Subsequent items are shifted to fill the resulting gap. + +.. doctest:: + + julia> deleteat!([6, 5, 4, 3, 2, 1], 2) + 5-element Array{Int64,1}: + 6 + 4 + 3 + 2 + 1 + +:: + deleteat!(collection, itr) + +Remove the items at the indices given by ``itr``, and return the modified ``collection``. +Subsequent items are shifted to fill the resulting gap. ``itr`` must be sorted and unique. + +.. doctest:: + + julia> deleteat!([6, 5, 4, 3, 2, 1], 1:2:5) + 3-element Array{Int64,1}: + 5 + 3 + 1 + +.. doctest:: + + julia> deleteat!([6, 5, 4, 3, 2, 1], (2, 2)) + ERROR: ArgumentError: indices must be unique and sorted + in deleteat! at array.jl:533 +``` +""" +deleteat! + +doc""" +```rst +:: + schurfact!(A) + +Computes the Schur factorization of ``A``, overwriting ``A`` in the process. See :func:`schurfact` +``` +""" +schurfact! + +doc""" +```rst +:: + read(stream, type) + +Read a value of the given type from a stream, in canonical binary representation. + +:: + read(stream, type, dims) + +Read a series of values of the given type from a stream, in canonical binary representation. ``dims`` is either a tuple or a series of integer arguments specifying the size of ``Array`` to return. +``` +""" +read + +doc""" +```rst +:: + plan_rfft(A [, dims]; flags=FFTW.ESTIMATE; timelimit=Inf) + +Pre-plan an optimized real-input FFT, similar to :func:`plan_fft` +except for :func:`rfft` instead of :func:`fft`. The first two +arguments, and the size of the transformed result, are the same as +for :func:`rfft`. +``` +""" +plan_rfft + +doc""" +```rst +:: + @timev + +This is a verbose version of the ``@time`` macro, it first prints the same information as ``@time``, then any non-zero memory allocation counters, and then returns the value of the expression. +``` +""" +:@timev + +doc""" +```rst +:: + isopen(object) -> Bool + +Determine whether an object - such as a stream, timer, or mmap -- is not yet closed. +Once an object is closed, it will never produce a new event. +However, a closed stream may still have data to read in its buffer, +use ``eof`` to check for the ability to read data. +Use ``poll_fd`` to be notified when a stream might be writable or readable. +``` +""" +isopen + +doc""" +```rst +:: + shift!(collection) -> item + +Remove the first ``item`` from ``collection``. + +.. doctest:: + + julia> A = [1, 2, 3, 4, 5, 6] + 6-element Array{Int64,1}: + 1 + 2 + 3 + 4 + 5 + 6 + + julia> shift!(A) + 1 + + julia> A + 5-element Array{Int64,1}: + 2 + 3 + 4 + 5 + 6 +``` +""" +shift! + +doc""" +```rst +:: + @fetch + +Equivalent to ``fetch(@spawn expr)``. +``` +""" +:@fetch + +doc""" +```rst +:: + spawn(command) + +Run a command object asynchronously, returning the resulting ``Process`` object. +``` +""" +spawn + +doc""" +```rst +:: + isposdef(A) -> Bool + +Test whether a matrix is positive definite. +``` +""" +isposdef + +doc""" +```rst +:: + nextind(str, i) + +Get the next valid string index after ``i``. Returns a value greater than ``endof(str)`` +at or after the end of the string. +``` +""" +nextind + +doc""" +```rst +:: + >>>(x, n) + +Unsigned right bit shift operator. +``` +""" +Base.(:(>>>)) + +doc""" +```rst +:: + @timed + +A macro to execute an expression, and return the value of the expression, elapsed time, total bytes allocated, garbage collection time, and an object with various memory allocation counters. +``` +""" +:@timed + +doc""" +```rst +:: + code_native(f, types) + +Prints the native assembly instructions generated for running the method matching the given generic function and type signature to STDOUT. +``` +""" +code_native + +doc""" +```rst +:: + isgeneric(f::Function) -> Bool + +Determine whether a function is generic. +``` +""" +isgeneric + +doc""" +```rst +:: + symdiff(s1,s2...) + +Construct the symmetric difference of elements in the passed in sets or arrays. Maintains order with arrays. +``` +""" +symdiff + +doc""" +```rst +:: + bfft!(A [, dims]) + +Same as :func:`bfft`, but operates in-place on ``A``. +``` +""" +bfft! + +doc""" +```rst +:: + histrange(v, n) + +Compute *nice* bin ranges for the edges of a histogram of ``v``, using +approximately ``n`` bins. The resulting step sizes will be 1, 2 or 5 +multiplied by a power of 10. +Note: Julia does not ignore ``NaN`` values in the computation. +``` +""" +histrange + +doc""" +```rst +:: + eta(x) + +Dirichlet eta function :math:`\eta(s) = \sum^\infty_{n=1}(-)^{n-1}/n^{s}`. +``` +""" +eta + +doc""" +```rst +:: + isdefined([object,] index | symbol) + +Tests whether an assignable location is defined. The arguments can be an +array and index, a composite object and field name (as a symbol), or a +module and a symbol. +With a single symbol argument, tests whether a global variable with that +name is defined in ``current_module()``. +``` +""" +isdefined + +doc""" +```rst +:: + cotd(x) + +Compute the cotangent of ``x``, where ``x`` is in degrees +``` +""" +cotd + +doc""" +```rst +:: + dec(n, [pad]) + +Convert an integer to a decimal string, optionally specifying a number of digits to pad to. +``` +""" +dec + +doc""" +```rst +:: + wait([x]) + +Block the current task until some event occurs, depending on the type +of the argument: + +* ``RemoteRef``: Wait for a value to become available for the specified remote reference. + +* ``Channel``: Wait for a value to be appended to the channel. + +* ``Condition``: Wait for ``notify`` on a condition. + +* ``Process``: Wait for a process or process chain to exit. The ``exitcode`` field of a process can be used to determine success or failure. + +* ``Task``: Wait for a ``Task`` to finish, returning its result value. If the task fails with an exception, the exception is propagated (re-thrown in the task that called ``wait``). + +* ``RawFD``: Wait for changes on a file descriptor (see `poll_fd` for keyword arguments and return code) + +If no argument is passed, the task blocks for an undefined period. If the task's +state is set to ``:waiting``, it can only be restarted by an explicit call to +``schedule`` or ``yieldto``. If the task's state is ``:runnable``, it might be +restarted unpredictably. + +Often ``wait`` is called within a ``while`` loop to ensure a waited-for condition +is met before proceeding. +``` +""" +wait + +doc""" +```rst +:: + shuffle([rng,] v) + +Return a randomly permuted copy of ``v``. The optional ``rng`` argument +specifies a random number generator, see :ref:`Random Numbers +`. +``` +""" +shuffle + +doc""" +```rst +:: + Dict([itr]) + +``Dict{K,V}()`` constructs a hash table with keys of type ``K`` and values of type ``V``. + +Given a single iterable argument, constructs a :obj:`Dict` whose key-value pairs +are taken from 2-tuples ``(key,value)`` generated by the argument. + +.. doctest:: + + julia> Dict([("A", 1), ("B", 2)]) + Dict{ASCIIString,Int64} with 2 entries: + "B" => 2 + "A" => 1 + +Alternatively, a sequence of pair arguments may be passed. + +.. doctest:: + + julia> Dict("A"=>1, "B"=>2) + Dict{ASCIIString,Int64} with 2 entries: + "B" => 2 + "A" => 1 +``` +""" +Dict + +doc""" +```rst +:: + sqrt(x) + +Return :math:`\sqrt{x}`. Throws ``DomainError`` for negative ``Real`` arguments. Use complex negative arguments instead. The prefix operator ``√`` is equivalent to ``sqrt``. +``` +""" +sqrt + +doc""" +```rst +:: + atexit(f) + +Register a zero-argument function to be called at exit. +``` +""" +atexit + +doc""" +```rst +:: + besselk(nu, x) + +Modified Bessel function of the second kind of order ``nu``, :math:`K_\nu(x)`. +``` +""" +besselk + +doc""" +```rst +:: + readchomp(x) + +Read the entirety of x as a string but remove trailing newlines. Equivalent to chomp(readall(x)). +``` +""" +readchomp + +doc""" +```rst +:: + pinv(M[, tol]) + +Computes the Moore-Penrose pseudoinverse. + +For matrices ``M`` with floating point elements, it is convenient to compute +the pseudoinverse by inverting only singular values above a given threshold, +``tol``. + +The optimal choice of ``tol`` varies both with the value of ``M`` +and the intended application of the pseudoinverse. The default value of +``tol`` is ``eps(real(float(one(eltype(M)))))*maximum(size(A))``, +which is essentially machine epsilon for the real part of a matrix element +multiplied by the larger matrix dimension. +For inverting dense ill-conditioned matrices in a least-squares sense, +``tol = sqrt(eps(real(float(one(eltype(M))))))`` is recommended. + +For more information, see [8859]_, [B96]_, [S84]_, [KY88]_. + +.. [8859] Issue 8859, "Fix least squares", https://github.com/JuliaLang/julia/pull/8859 +.. [B96] Åke Björck, "Numerical Methods for Least Squares Problems", + SIAM Press, Philadelphia, 1996, "Other Titles in Applied Mathematics", Vol. 51. + `doi:10.1137/1.9781611971484 `_ +.. [S84] G. W. Stewart, "Rank Degeneracy", SIAM Journal on + Scientific and Statistical Computing, 5(2), 1984, 403-413. + `doi:10.1137/0905030 `_ +.. [KY88] Konstantinos Konstantinides and Kung Yao, "Statistical analysis + of effective singular values in matrix rank determination", IEEE + Transactions on Acoustics, Speech and Signal Processing, 36(5), 1988, + 757-763. + `doi:10.1109/29.1585 `_ +``` +""" +pinv + +doc""" +```rst +:: + asecd(x) + +Compute the inverse secant of ``x``, where the output is in degrees +``` +""" +asecd + +doc""" +```rst +:: + readbytes!(stream, b::Vector{UInt8}, nb=length(b); all=true) + +Read at most ``nb`` bytes from the stream into ``b``, returning the +number of bytes read (increasing the size of ``b`` as needed). + +See ``readbytes`` for a description of the ``all`` option. +``` +""" +readbytes! + +doc""" +```rst +:: + basename(path::AbstractString) -> AbstractString + +Get the file name part of a path. +``` +""" +basename + +doc""" +```rst +:: + issparse(S) + +Returns ``true`` if ``S`` is sparse, and ``false`` otherwise. +``` +""" +issparse + +doc""" +```rst +:: + ArgumentError(msg) + +The parameters to a function call do not match a valid signature. +``` +""" +ArgumentError + +doc""" +```rst +:: + atand(x) + +Compute the inverse tangent of ``x``, where the output is in degrees +``` +""" +atand + +doc""" +```rst +:: + KeyError(key) + +An indexing operation into an ``Associative`` (``Dict``) or ``Set`` like object tried to access or delete a non-existent element. +``` +""" +KeyError + +doc""" +```rst +:: + isdiag(A) -> Bool + +Test whether a matrix is diagonal. +``` +""" +isdiag + +doc""" +```rst +:: + !==(x, y) + ≢(x,y) + +Equivalent to ``!is(x, y)`` +``` +""" +Base.(:(!==)) + +doc""" +```rst +:: + trailing_ones(x::Integer) -> Integer + +Number of ones trailing the binary representation of ``x``. + +.. doctest:: + + julia> trailing_ones(3) + 2 +``` +""" +trailing_ones + +doc""" +```rst +:: + repeated(x[, n::Int]) + +An iterator that generates the value ``x`` forever. If ``n`` is specified, generates +``x`` that many times (equivalent to ``take(repeated(x), n)``). +``` +""" +repeated + +doc""" +```rst +:: + isnumber(c::Union{Char,AbstractString}) -> Bool + +Tests whether a character is numeric, or whether this +is true for all elements of a string. A character is classified as numeric +if it belongs to the Unicode general category Number, i.e. a character whose +category code begins with 'N'. +``` +""" +isnumber + +doc""" +```rst +:: + similar(array, element_type, dims) + +Create an uninitialized array of the same type as the given array, but with the specified element type and dimensions. The second and third arguments are both optional. The ``dims`` argument may be a tuple or a series of integer arguments. For some special ``AbstractArray`` objects which are not real containers (like ranges), this function returns a standard ``Array`` to allow operating on elements. +``` +""" +similar + +doc""" +```rst +:: + copy(x) + +Create a shallow copy of ``x``: the outer structure is copied, but not all internal values. For example, copying an array produces a new array with identically-same elements as the original. +``` +""" +copy + +doc""" +```rst +:: + isempty(collection) -> Bool + +Determine whether a collection is empty (has no elements). + +.. doctest:: + + julia> isempty([]) + true + + julia> isempty([1 2 3]) + false +``` +""" +isempty + +doc""" +```rst +:: + sumabs!(r, A) + +Sum absolute values of elements of ``A`` over the singleton +dimensions of ``r``, and write results to ``r``. +``` +""" +sumabs! + +doc""" +```rst +:: + abs(x) + +Absolute value of ``x`` +``` +""" +abs + +doc""" +```rst +:: + Sys.set_process_title(title::AbstractString) + +Set the process title. No-op on some operating systems. (not exported) +``` +""" +Sys.set_process_title + +doc""" +```rst +:: + htol(x) + +Converts the endianness of a value from that used by the Host to +Little-endian. +``` +""" +htol + +doc""" +```rst +:: + ctime(file) + +Equivalent to stat(file).ctime +``` +""" +ctime + +doc""" +```rst +:: + normpath(path::AbstractString) -> AbstractString + +Normalize a path, removing "." and ".." entries. +``` +""" +normpath + +doc""" +```rst +:: + unmark(s) + +Remove a mark from stream ``s``. +Returns ``true`` if the stream was marked, ``false`` otherwise. + +See also :func:`mark`, :func:`reset`, :func:`ismarked` +``` +""" +unmark + +doc""" +```rst +:: + module_name(m::Module) -> Symbol + +Get the name of a module as a symbol. +``` +""" +module_name + +doc""" +```rst +:: + reset(s) + +Reset a stream ``s`` to a previously marked position, and remove the mark. +Returns the previously marked position. +Throws an error if the stream is not marked. + +See also :func:`mark`, :func:`unmark`, :func:`ismarked` +``` +""" +reset + +doc""" +```rst +:: + modf(x) + +Return a tuple (fpart,ipart) of the fractional and integral parts of a +number. Both parts have the same sign as the argument. +``` +""" +modf + +doc""" +```rst +:: + hex2num(str) + +Convert a hexadecimal string to the floating point number it represents +``` +""" +hex2num + +doc""" +```rst +:: + ndims(A) -> Integer + +Returns the number of dimensions of A +``` +""" +ndims + +doc""" +```rst +:: + @osx + +Given ``@osx? a : b``, do ``a`` on OS X and ``b`` elsewhere. See documentation for Handling Platform Variations +in the Calling C and Fortran Code section of the manual. +``` +""" +:@osx + +doc""" +```rst +:: + ishermitian(A) -> Bool + +Test whether a matrix is Hermitian. +``` +""" +ishermitian + +doc""" +```rst +:: + sind(x) + +Compute sine of ``x``, where ``x`` is in degrees +``` +""" +sind + +doc""" +```rst +:: + iseltype(A,T) + +Tests whether A or its elements are of type T +``` +""" +iseltype + +doc""" +```rst +:: + symperm(A, p) + +Return the symmetric permutation of A, which is ``A[p,p]``. A should be symmetric and sparse, where only the upper triangular part of the matrix is stored. This algorithm ignores the lower triangular part of the matrix. Only the upper triangular part of the result is returned as well. +``` +""" +symperm + +doc""" +```rst +:: + min(x, y, ...) + +Return the minimum of the arguments. Operates elementwise over arrays. +``` +""" +min + +doc""" +```rst +:: + isready(r::RemoteRef) + +Determine whether a ``RemoteRef`` has a value stored to it. Note that this function +can cause race conditions, since by the time you receive its result it may +no longer be true. It is recommended that this function only be used on a +``RemoteRef`` that is assigned once. + +If the argument ``RemoteRef`` is owned by a different node, this call will block to +wait for the answer. It is recommended to wait for ``r`` in a separate task instead, +or to use a local ``RemoteRef`` as a proxy:: + + rr = RemoteRef() + @async put!(rr, remotecall_fetch(p, long_computation)) + isready(rr) # will not block +``` +""" +isready + +doc""" +```rst +:: + InexactError() + +Type conversion cannot be done exactly. +``` +""" +InexactError + +doc""" +```rst +:: + @sync + +Wait until all dynamically-enclosed uses of ``@async``, ``@spawn``, +``@spawnat`` and ``@parallel`` are complete. All exceptions thrown by +enclosed async operations are collected and thrown as a ``CompositeException``. +``` +""" +:@sync + +doc""" +```rst +:: + typemax(type) + +The highest value representable by the given (real) numeric type. +``` +""" +typemax + +doc""" +```rst +:: + all(itr) -> Bool + +Test whether all elements of a boolean collection are true. + +:: + all(A, dims) + +Test whether all values along the given dimensions of an array are true. + +:: + all(p, itr) -> Bool + +Determine whether predicate ``p`` returns true for all elements of ``itr``. + +.. doctest:: + + julia> all(i->(4<=i<=6), [4,5,6]) + true +``` +""" +all + +doc""" +```rst +:: + bind(socket::Union{UDPSocket, TCPSocket}, host::IPv4, port::Integer) + +Bind ``socket`` to the given ``host:port``. Note that `0.0.0.0` will listen on all devices. +``` +""" +bind + +doc""" +```rst +:: + cld(x, y) + +Smallest integer larger than or equal to ``x/y``. +``` +""" +cld + +doc""" +```rst +:: + issetuid(path) -> Bool + +Returns ``true`` if ``path`` has the setuid flag set, ``false`` otherwise. +``` +""" +issetuid + +doc""" +```rst +:: + ccall((symbol, library) or function_pointer, ReturnType, (ArgumentType1, ...), ArgumentValue1, ...) + +Call function in C-exported shared library, specified by ``(function name, library)`` tuple, +where each component is an AbstractString or :Symbol. + +Note that the argument type tuple must be a literal tuple, and not a tuple-valued variable or expression. +Alternatively, ccall may also be used to call a function pointer, such as one returned by dlsym. + +Each ``ArgumentValue`` to the ``ccall`` will be converted to the corresponding ``ArgumentType``, +by automatic insertion of calls to ``unsafe_convert(ArgumentType, cconvert(ArgumentType, ArgumentValue))``. +(see also the documentation for each of these functions for further details). +In most cases, this simply results in a call to ``convert(ArgumentType, ArgumentValue)`` +``` +""" +Base.ccall + +doc""" +```rst +:: + scale!(A, b) + +:: + scale!(b, A) + +Scale an array ``A`` by a scalar ``b``, similar to :func:`scale` but +overwriting ``A`` in-place. + +If ``A`` is a matrix and ``b`` is a vector, then ``scale!(A,b)`` +scales each column ``i`` of ``A`` by ``b[i]`` (similar to +``A*diagm(b)``), while ``scale!(b,A)`` scales each row ``i`` of +``A`` by ``b[i]`` (similar to ``diagm(b)*A``), again operating in-place +on ``A``. +``` +""" +scale! + +doc""" +```rst +:: + DomainError() + +The arguments to a function or constructor are outside the valid domain. +``` +""" +DomainError + +doc""" +```rst +:: + issym(A) -> Bool + +Test whether a matrix is symmetric. +``` +""" +issym + +doc""" +```rst +:: + svds(A; nsv=6, ritzvec=true, tol=0.0, maxiter=1000) -> (left_sv, s, right_sv, nconv, niter, nmult, resid) + +``svds`` computes largest singular values ``s`` of ``A`` using Lanczos or Arnoldi iterations. +Uses :func:`eigs` underneath. + +Inputs are: + * ``A``: Linear operator. It can either subtype of ``AbstractArray`` (e.g., sparse matrix) or duck typed. For duck typing ``A`` has to support ``size(A)``, ``eltype(A)``, ``A * vector`` and ``A' * vector``. + * ``nsv``: Number of singular values. + * ``ritzvec``: Whether to return the left and right singular vectors ``left_sv`` and ``right_sv``, default is ``true``. If ``false`` the singular vectors are omitted from the output. + * ``tol``: tolerance, see :func:`eigs`. + * ``maxiter``: Maximum number of iterations, see :func:`eigs`. + +**Example**:: + + X = sprand(10, 5, 0.2) + svds(X, nsv = 2) +``` +""" +svds + +doc""" +```rst +:: + acosh(x) + +Compute the inverse hyperbolic cosine of ``x`` +``` +""" +acosh + +doc""" +```rst +:: + IntSet([itr]) + +Construct a sorted set of the integers generated by the given iterable object, or an empty set. Implemented as a bit string, and therefore designed for dense integer sets. Only non-negative integers can be stored. If the set will be sparse (for example holding a single very large integer), use :obj:`Set` instead. +``` +""" +IntSet + +doc""" +```rst +:: + Task(func) + +Create a ``Task`` (i.e. thread, or coroutine) to execute the given function (which must be callable with no arguments). The task exits when this function returns. +``` +""" +Task + +doc""" +```rst +:: + pushdisplay(d::Display) + +Pushes a new display ``d`` on top of the global display-backend +stack. Calling ``display(x)`` or ``display(mime, x)`` will display +``x`` on the topmost compatible backend in the stack (i.e., the +topmost backend that does not throw a ``MethodError``). +``` +""" +pushdisplay + +doc""" +```rst +:: + randexp!([rng], A::Array{Float64,N}) + +Fill the array A with random numbers following the exponential distribution (with scale 1). +``` +""" +randexp! + +doc""" +```rst +:: + prevind(str, i) + +Get the previous valid string index before ``i``. Returns a value less than ``1`` at +the beginning of the string. +``` +""" +prevind + +doc""" +```rst +:: + setenv(command, env; dir=working_dir) + +Set environment variables to use when running the given +command. ``env`` is either a dictionary mapping strings to strings, +an array of strings of the form ``"var=val"``, or zero or more +``"var"=>val`` pair arguments. In order to modify (rather than +replace) the existing environment, create ``env`` by ``copy(ENV)`` +and then setting ``env["var"]=val`` as desired, or use ``withenv``. + +The ``dir`` keyword argument can be used to specify a working +directory for the command. +``` +""" +setenv + +doc""" +```rst +:: + invperm(v) + +Return the inverse permutation of v. +``` +""" +invperm + +doc""" +```rst +:: + lowercase(string) + +Returns ``string`` with all characters converted to lowercase. +``` +""" +lowercase + +doc""" +```rst +:: + produce(value) + +Send the given value to the last ``consume`` call, switching to the consumer task. +If the next ``consume`` call passes any values, they are returned by ``produce``. +``` +""" +produce + +doc""" +```rst +:: + ifft(A [, dims]) + +Multidimensional inverse FFT. + +A one-dimensional inverse FFT computes + +.. math:: + + \operatorname{IDFT}(A)[k] = \frac{1}{\operatorname{length}(A)} + \sum_{n=1}^{\operatorname{length}(A)} \exp\left(+i\frac{2\pi (n-1)(k-1)} + {\operatorname{length}(A)} \right) A[n]. + +A multidimensional inverse FFT simply performs this operation along each +transformed dimension of ``A``. +``` +""" +ifft + +doc""" +```rst +:: + StackOverflowError() + +The function call grew beyond the size of the call stack. This usually happens when a call recurses infinitely. +``` +""" +StackOverflowError + +doc""" +```rst +:: + acsch(x) + +Compute the inverse hyperbolic cosecant of ``x`` +``` +""" +acsch + +doc""" +```rst +:: + process_running(p::Process) + +Determine whether a process is currently running. +``` +""" +process_running + +doc""" +```rst +:: + BigInt(x) + +Create an arbitrary precision integer. ``x`` may be an ``Int`` (or anything +that can be converted to an ``Int``). The usual mathematical operators are +defined for this type, and results are promoted to a ``BigInt``. + +Instances can be constructed from strings via :func:`parse`, or using the +``big`` string literal. +``` +""" +BigInt + +doc""" +```rst +:: + rsearch(string, chars, [start]) + +Similar to ``search``, but returning the last occurrence of the given characters within the given string, searching in reverse from ``start``. +``` +""" +rsearch + +doc""" +```rst +:: + isdirpath(path::AbstractString) -> Bool + +Determines whether a path refers to a directory (for example, ends with a path separator). +``` +""" +isdirpath + +doc""" +```rst +:: + in(item, collection) -> Bool + ∈(item,collection) -> Bool + ∋(collection,item) -> Bool + ∉(item,collection) -> Bool + ∌(collection,item) -> Bool + +Determine whether an item is in the given collection, in the sense that it is +``==`` to one of the values generated by iterating over the collection. +Some collections need a slightly different definition; for example :obj:`Set`\ s +check whether the item :func:`isequal` to one of the elements. :obj:`Dict`\ s look for +``(key,value)`` pairs, and the key is compared using :func:`isequal`. To test +for the presence of a key in a dictionary, use :func:`haskey` or +``k in keys(dict)``. +``` +""" +Base.in + +doc""" +```rst +:: + isblockdev(path) -> Bool + +Returns ``true`` if ``path`` is a block device, ``false`` otherwise. +``` +""" +isblockdev + +doc""" +```rst +:: + ==(x, y) + +Generic equality operator, giving a single ``Bool`` result. Falls back to ``===``. +Should be implemented for all types with a notion of equality, based +on the abstract value that an instance represents. For example, all numeric types are compared +by numeric value, ignoring type. Strings are compared as sequences of characters, ignoring +encoding. + +Follows IEEE semantics for floating-point numbers. + +Collections should generally implement ``==`` by calling ``==`` recursively on all contents. + +New numeric types should implement this function for two arguments of the new type, and handle +comparison to other types via promotion rules where possible. +``` +""" +Base.(:(==)) + +doc""" +```rst +:: + mapreducedim(f, op, A, dims[, initial]) + +Evaluates to the same as `reducedim(op, map(f, A), dims, f(initial))`, but +is generally faster because the intermediate array is avoided. +``` +""" +mapreducedim + +doc""" +```rst +:: + seekstart(s) + +Seek a stream to its beginning. +``` +""" +seekstart + +doc""" +```rst +:: + nfields(x::DataType) -> Int + +Get the number of fields of a data type. +``` +""" +nfields + +doc""" +```rst +:: + toq() + +Return, but do not print, the time elapsed since the last :func:`tic`. +``` +""" +toq + +doc""" +```rst +:: + writemime(stream, mime, x) + +The ``display`` functions ultimately call ``writemime`` in order to +write an object ``x`` as a given ``mime`` type to a given I/O +``stream`` (usually a memory buffer), if possible. In order to +provide a rich multimedia representation of a user-defined type +``T``, it is only necessary to define a new ``writemime`` method for +``T``, via: ``writemime(stream, ::MIME"mime", x::T) = ...``, where +``mime`` is a MIME-type string and the function body calls +``write`` (or similar) to write that representation of ``x`` to +``stream``. (Note that the ``MIME""`` notation only supports literal +strings; to construct ``MIME`` types in a more flexible manner use +``MIME{symbol("")}``.) + +For example, if you define a ``MyImage`` type and know how to write +it to a PNG file, you could define a function ``writemime(stream, +::MIME"image/png", x::MyImage) = ...``` to allow your images to +be displayed on any PNG-capable ``Display`` (such as IJulia). +As usual, be sure to ``import Base.writemime`` in order to add +new methods to the built-in Julia function ``writemime``. + +Technically, the ``MIME"mime"`` macro defines a singleton type for +the given ``mime`` string, which allows us to exploit Julia's +dispatch mechanisms in determining how to display objects of any +given type. +``` +""" +writemime + +doc""" +```rst +:: + mean!(r, v) + +Compute the mean of ``v`` over the singleton dimensions of ``r``, and write results to ``r``. +``` +""" +mean! + +doc""" +```rst +:: + join(strings, delim, [last]) + +Join an array of ``strings`` into a single string, inserting the given delimiter between adjacent strings. +If ``last`` is given, it will be used instead of ``delim`` between the last two strings. +For example, ``join(["apples", "bananas", "pineapples"], ", ", " and ") == "apples, bananas and pineapples"``. + +``strings`` can be any iterable over elements ``x`` which are convertible to strings via ``print(io::IOBuffer, x)``. +``` +""" +join + +doc""" +```rst +:: + linreg(x, y) -> [a; b] + +Linear Regression. Returns ``a`` and ``b`` such that ``a+b*x`` is the closest line to the given points ``(x,y)``. In other words, this function determines parameters ``[a, b]`` that minimize the squared error between ``y`` and ``a+b*x``. + +**Example**:: + + using PyPlot; + x = float([1:12]) + y = [5.5; 6.3; 7.6; 8.8; 10.9; 11.79; 13.48; 15.02; 17.77; 20.81; 22.0; 22.99] + a, b = linreg(x,y) # Linear regression + plot(x, y, "o") # Plot (x,y) points + plot(x, [a+b*i for i in x]) # Plot the line determined by the linear regression + +:: + linreg(x, y, w) + +Weighted least-squares linear regression. +``` +""" +linreg + +doc""" +```rst +:: + polygamma(m, x) + +Compute the polygamma function of order ``m`` of argument ``x`` (the ``(m+1)th`` derivative of the logarithm of ``gamma(x)``) +``` +""" +polygamma + +doc""" +```rst +:: + isless(x, y) + +Test whether ``x`` is less than ``y``, according to a canonical total order. +Values that are normally unordered, such as ``NaN``, are ordered in an arbitrary but consistent fashion. This is the default comparison used by ``sort``. Non-numeric types with a canonical total order should implement this function. Numeric types only need to implement it if they have special values such as ``NaN``. +``` +""" +isless + +doc""" +```rst +:: + expm1(x) + +Accurately compute :math:`e^x-1` +``` +""" +expm1 + +doc""" +```rst +:: + showerror(io, e) + +Show a descriptive representation of an exception object. +``` +""" +showerror + +doc""" +```rst +:: + setdiff(s1,s2) + +Construct the set of elements in ``s1`` but not ``s2``. Maintains order with arrays. +Note that both arguments must be collections, and both will be iterated over. +In particular, ``setdiff(set,element)`` where ``element`` is a potential member of +``set``, will not work in general. +``` +""" +setdiff + +doc""" +```rst +:: + airyai(x) + +Airy function :math:`\operatorname{Ai}(x)`. +``` +""" +airyai + +doc""" +```rst +:: + error(message::AbstractString) + +Raise an ``ErrorException`` with the given message +``` +""" +error + +doc""" +```rst +:: + less(file::AbstractString, [line]) + +Show a file using the default pager, optionally providing a starting line number. Returns to the julia prompt when you quit the pager. + +:: + less(function, [types]) + +Show the definition of a function using the default pager, optionally specifying a tuple of types to indicate which method to see. +``` +""" +less + +doc""" +```rst +:: + sqrtm(A) + +Compute the matrix square root of ``A``. If ``B = sqrtm(A)``, then ``B*B == A`` within roundoff error. + +``sqrtm`` uses a polyalgorithm, computing the matrix square root using Schur factorizations (:func:`schurfact`) unless it detects the matrix to be Hermitian or real symmetric, in which case it computes the matrix square root from an eigendecomposition (:func:`eigfact`). In the latter situation for positive definite matrices, the matrix square root has ``Real`` elements, otherwise it has ``Complex`` elements. +``` +""" +sqrtm + +doc""" +```rst +:: + conv(u,v) + +Convolution of two vectors. Uses FFT algorithm. +``` +""" +conv + +doc""" +```rst +:: + unsafe_store!(p::Ptr{T},x,i::Integer) + +Store a value of type ``T`` to the address of the ith element (1-indexed) +starting at ``p``. This is equivalent to the C expression ``p[i-1] = x``. + +The ``unsafe`` prefix on this function indicates that no validation is performed +on the pointer ``p`` to ensure that it is valid. Incorrect usage may corrupt +or segfault your program, in the same manner as C. +``` +""" +unsafe_store! + +doc""" +```rst +:: + expm(A) + +Compute the matrix exponential of ``A``. +``` +""" +expm + +doc""" +```rst +:: + hessfact!(A) + +``hessfact!`` is the same as :func:`hessfact`, but saves space by overwriting the input A, instead of creating a copy. +``` +""" +hessfact! + +doc""" +```rst +:: + Sys.get_process_title() + +Get the process title. On some systems, will always return empty string. (not exported) +``` +""" +Sys.get_process_title + +doc""" +```rst +:: + readcsv(source, [T::Type]; options...) + +Equivalent to ``readdlm`` with ``delim`` set to comma. +``` +""" +readcsv + +doc""" +```rst +:: + current_module() -> Module + +Get the *dynamically* current module, which is the module code is currently being +read from. In general, this is not the same as the module containing the call to +this function. +``` +""" +current_module + +doc""" +```rst +:: + erfcx(x) + +Compute the scaled complementary error function of ``x``, +defined by :math:`e^{x^2} \operatorname{erfc}(x)`. Note +also that :math:`\operatorname{erfcx}(-ix)` computes the +Faddeeva function :math:`w(x)`. +``` +""" +erfcx + +doc""" +```rst +:: + UndefVarError(var::Symbol) + +A symbol in the current scope is not defined. +``` +""" +UndefVarError + +doc""" +```rst +:: + gc() + +Perform garbage collection. This should not generally be used. +``` +""" +gc + +doc""" +```rst +:: + iscntrl(c::Union{Char,AbstractString}) -> Bool + +Tests whether a character is a control character, or whether this +is true for all elements of a string. Control characters are the +non-printing characters of the Latin-1 subset of Unicode. +``` +""" +iscntrl + +doc""" +```rst +:: + hist!(counts, v, e) -> e, counts + +Compute the histogram of ``v``, using a vector/range ``e`` as the edges for the bins. +This function writes the resultant counts to a pre-allocated array ``counts``. +``` +""" +hist! + +doc""" +```rst +:: + minimum!(r, A) + +Compute the minimum value of ``A`` over the singleton dimensions of ``r``, +and write results to ``r``. +``` +""" +minimum! + +doc""" +```rst +:: + diagm(v[, k]) + +Construct a diagonal matrix and place ``v`` on the ``k``\ th diagonal. +``` +""" +diagm + +doc""" +```rst +:: + .-(x, y) + +Element-wise subtraction operator. +``` +""" +Base.(:(.-)) + +doc""" +```rst +:: + imag(z) + +Return the imaginary part of the complex number ``z`` +``` +""" +imag + +doc""" +```rst +:: + unsafe_trunc(T, x) + +``unsafe_trunc(T, x)`` returns the nearest integral value of type ``T`` whose absolute +value is less than or equal to ``x``. If the value is not representable by +``T``, an arbitrary value will be returned. +``` +""" +unsafe_trunc + +doc""" +```rst +:: + parent(A) + +Returns the "parent array" of an array view type (e.g., SubArray), or the array itself if it is not a view +``` +""" +parent + +doc""" +```rst +:: + <(x, y) + +Less-than comparison operator. New numeric types should implement this function +for two arguments of the new type. +Because of the behavior of floating-point NaN values, ``<`` implements a +partial order. Types with a canonical partial order should implement ``<``, and +types with a canonical total order should implement ``isless``. +``` +""" +Base.(:(<)) + +doc""" +```rst +:: + EnvHash() -> EnvHash + +A singleton of this type provides a hash table interface to environment variables. +``` +""" +EnvHash + +doc""" +```rst +:: + method_exists(f, Tuple type) -> Bool + +Determine whether the given generic function has a method matching the given :obj:`Tuple` of argument types. + +.. doctest:: + + julia> method_exists(length, Tuple{Array}) + true +``` +""" +method_exists + +doc""" +```rst +:: + nextpow(a, x) + +The smallest ``a^n`` not less than ``x``, where ``n`` is a non-negative integer. +``a`` must be greater than 1, and ``x`` must be greater than 0. +``` +""" +nextpow + +doc""" +```rst +:: + rad2deg(x) + +Convert ``x`` from radians to degrees +``` +""" +rad2deg + +doc""" +```rst +:: + gc_enable(on::Bool) + +Control whether garbage collection is enabled using a boolean argument (true for +enabled, false for disabled). +Returns previous GC state. +Disabling garbage collection should be used only with extreme caution, +as it can cause memory use to grow without bound. +``` +""" +gc_enable + +doc""" +```rst +:: + sub2ind(dims, i, j, k...) -> index + +The inverse of ``ind2sub``, returns the linear index corresponding to the provided subscripts +``` +""" +sub2ind + +doc""" +```rst +:: + isperm(v) -> Bool + +Returns true if v is a valid permutation. +``` +""" +isperm + +doc""" +```rst +:: + super(T::DataType) + +Return the supertype of DataType T +``` +""" +super + +doc""" +```rst +:: + readline(stream=STDIN) + +Read a single line of text, including a trailing newline character (if one is reached before the end of the input), from the given ``stream`` (defaults to ``STDIN``), +``` +""" +readline + +doc""" +```rst +:: + atan(x) + +Compute the inverse tangent of ``x``, where the output is in radians +``` +""" +atan + +doc""" +```rst +:: + logabsdet(M) + +Log of absolute value of determinant of real matrix. Equivalent to ``(log(abs(det(M))), sign(det(M)))``, but may provide increased accuracy and/or speed. +``` +""" +logabsdet + +doc""" +```rst +:: + joinpath(parts...) -> AbstractString + +Join path components into a full path. If some argument is an absolute +path, then prior components are dropped. +``` +""" +joinpath + +doc""" +```rst +:: + get_bigfloat_precision() + +Get the precision (in bits) currently used for BigFloat arithmetic. +``` +""" +get_bigfloat_precision + +doc""" +```rst +:: + homedir() -> AbstractString + +Return the current user's home directory. +``` +""" +homedir + +doc""" +```rst +:: + count_zeros(x::Integer) -> Integer + +Number of zeros in the binary representation of ``x``. + +.. doctest:: + + julia> count_zeros(Int32(2 ^ 16 - 1)) + 16 +``` +""" +count_zeros + +doc""" +```rst +:: + isinf(f) -> Bool + +Test whether a number is infinite +``` +""" +isinf + +doc""" +```rst +:: + @fetchfrom + +Equivalent to ``fetch(@spawnat p expr)``. +``` +""" +:@fetchfrom + +doc""" +```rst +:: + secd(x) + +Compute the secant of ``x``, where ``x`` is in degrees +``` +""" +secd + +doc""" +```rst +:: + varm(v, m) + +Compute the sample variance of a vector ``v`` with known mean ``m``. +Note: Julia does not ignore ``NaN`` values in the computation. +``` +""" +varm + +doc""" +```rst +:: + OverflowError() + +The result of an expression is too large for the specified type and will cause a wraparound. +``` +""" +OverflowError + +doc""" +```rst +:: + redirect_stderr([stream]) + +Like redirect_stdout, but for STDERR +``` +""" +redirect_stderr + +doc""" +```rst +:: + ctranspose!(dest,src) + +Conjugate transpose array ``src`` and store the result in the preallocated array ``dest``, which should have a size corresponding to ``(size(src,2),size(src,1))``. No in-place transposition is supported and unexpected results will happen if `src` and `dest` have overlapping memory regions. +``` +""" +ctranspose! + +doc""" +```rst +:: + object_id(x) + +Get a unique integer id for ``x``. ``object_id(x)==object_id(y)`` if and only if ``is(x,y)``. +``` +""" +object_id + +doc""" +```rst +:: + norm(A, [p]) + +Compute the ``p``-norm of a vector or the operator norm of a matrix ``A``, defaulting to the ``p=2``-norm. + +For vectors, ``p`` can assume any numeric value (even though not all values produce a mathematically valid vector norm). In particular, ``norm(A, Inf)`` returns the largest value in ``abs(A)``, whereas ``norm(A, -Inf)`` returns the smallest. + +For matrices, valid values of ``p`` are ``1``, ``2``, or ``Inf``. (Note that for sparse matrices, ``p=2`` is currently not implemented.) Use :func:`vecnorm` to compute the Frobenius norm. +``` +""" +norm + +doc""" +```rst +:: + print_unescaped(io, s::AbstractString) + +General unescaping of traditional C and Unicode escape sequences. Reverse of :func:`print_escaped`. +``` +""" +print_unescaped + +doc""" +```rst +:: + digits!(array, n, [base]) + + Fills an array of the digits of ``n`` in the given base. More significant digits are at higher indexes. + If the array length is insufficient, the least significant digits are filled up to the array length. + If the array length is excessive, the excess portion is filled with zeros. +``` +""" +digits! + +doc""" +```rst +:: + MethodError(f, args) + +A method with the required type signature does not exist in the given generic function. +``` +""" +MethodError + +doc""" +```rst +:: + cat(dims, A...) + +Concatenate the input arrays along the specified dimensions in the iterable ``dims``. For dimensions not in ``dims``, all input arrays should have the same size, which will also be the size of the output array along that dimension. For dimensions in ``dims``, the size of the output array is the sum of the sizes of the input arrays along that dimension. If ``dims`` is a single number, the different arrays are tightly stacked along that dimension. If ``dims`` is an iterable containing several dimensions, this allows to construct block diagonal matrices and their higher-dimensional analogues by simultaneously increasing several dimensions for every new input array and putting zero blocks elsewhere. For example, `cat([1,2], matrices...)` builds a block diagonal matrix, i.e. a block matrix with `matrices[1]`, `matrices[2]`, ... as diagonal blocks and matching zero blocks away from the diagonal. +``` +""" +cat + +doc""" +```rst +:: + factorial(n) + +Factorial of ``n``. If ``n`` is an :obj:`Integer`, the factorial +is computed as an integer (promoted to at least 64 bits). Note +that this may overflow if ``n`` is not small, but you can use +``factorial(big(n))`` to compute the result exactly in arbitrary +precision. If ``n`` is not an ``Integer``, ``factorial(n)`` is +equivalent to :func:`gamma(n+1) `. + +:: + factorial(n,k) + +Compute ``factorial(n)/factorial(k)`` +``` +""" +factorial + +doc""" +```rst +:: + bitrand([rng], [dims...]) + +Generate a ``BitArray`` of random boolean values. +``` +""" +bitrand + +doc""" +```rst +:: + randcycle([rng,] n) + +Construct a random cyclic permutation of length ``n``. The optional ``rng`` +argument specifies a random number generator, see :ref:`Random Numbers +`. +``` +""" +randcycle + +doc""" +```rst +:: + leading_zeros(x::Integer) -> Integer + +Number of zeros leading the binary representation of ``x``. + +.. doctest:: + + julia> leading_zeros(Int32(1)) + 31 +``` +""" +leading_zeros + +doc""" +```rst +:: + hankelh2(nu, x) + +Bessel function of the third kind of order ``nu``, :math:`H^{(2)}_\nu(x)`. +``` +""" +hankelh2 + +doc""" +```rst +:: + lexcmp(x, y) + +Compare ``x`` and ``y`` lexicographically and return -1, 0, or 1 depending on whether ``x`` is less than, equal to, or greater than ``y``, respectively. +This function should be defined for lexicographically comparable types, and ``lexless`` will call ``lexcmp`` by default. +``` +""" +lexcmp + +doc""" +```rst +:: + inf(f) + +Returns positive infinity of the floating point type ``f`` or of the same floating point type as ``f`` +``` +""" +inf + +doc""" +```rst +:: + isupper(c::Union{Char,AbstractString}) -> Bool + +Tests whether a character is an uppercase letter, or whether this +is true for all elements of a string. A character is classified as uppercase +if it belongs to Unicode category Lu, Letter: Uppercase, or Lt, Letter: Titlecase. +``` +""" +isupper + +doc""" +```rst +:: + pointer_to_array(pointer, dims[, take_ownership::Bool]) + +Wrap a native pointer as a Julia Array object. The pointer element type determines +the array element type. ``own`` optionally specifies whether Julia should take +ownership of the memory, calling ``free`` on the pointer when the array is no +longer referenced. +``` +""" +pointer_to_array + +doc""" +```rst +:: + show(x) + +Write an informative text representation of a value to the current output stream. New types should overload ``show(io, x)`` where the first argument is a stream. +The representation used by ``show`` generally includes Julia-specific formatting and type information. +``` +""" +show + +doc""" +```rst +:: + @allocated + +A macro to evaluate an expression, discarding the resulting value, instead returning the total number of bytes allocated during evaluation of the expression. +Note: the expression is evaluated inside a local function, instead of the current context, in order to eliminate the effects of compilation, +however, there still may be some allocations due to JIT compilation. This also makes the results inconsistent with the ``@time`` macros, +which do not try to adjust for the effects of compilation. +``` +""" +:@allocated + +doc""" +```rst +:: + Array(dims) + +``Array{T}(dims)`` constructs an uninitialized dense array with element type ``T``. +``dims`` may be a tuple or a series of integer arguments. +The syntax ``Array(T, dims)`` is also available, but deprecated. +``` +""" +Array + +doc""" +```rst +:: + isreal(x) -> Bool + +Test whether ``x`` or all its elements are numerically equal to some real number +``` +""" +isreal + +doc""" +```rst +:: + randsubseq(A, p) -> Vector + +Return a vector consisting of a random subsequence of the given array ``A``, +where each element of ``A`` is included (in order) with independent +probability ``p``. (Complexity is linear in ``p*length(A)``, so this +function is efficient even if ``p`` is small and ``A`` is large.) Technically, +this process is known as "Bernoulli sampling" of ``A``. +``` +""" +randsubseq + +doc""" +```rst +:: + issubtype(type1, type2) + +True if and only if all values of ``type1`` are also of ``type2``. Can also be written using the ``<:`` infix operator as ``type1 <: type2``. +``` +""" +issubtype + +doc""" +```rst +:: + finalizer(x, function) + +Register a function ``f(x)`` to be called when there are no program-accessible references to ``x``. The behavior of this function is unpredictable if ``x`` is of a bits type. +``` +""" +finalizer + +doc""" +```rst +:: + nextprod([k_1,k_2,...], n) + +Next integer not less than ``n`` that can be written as :math:`\prod k_i^{p_i}` for integers :math:`p_1`, :math:`p_2`, etc. +``` +""" +nextprod + +doc""" +```rst +:: + <<(x, n) + +Left bit shift operator. +``` +""" +Base.(:(<<)) + +doc""" +```rst +:: + csch(x) + +Compute the hyperbolic cosecant of ``x`` +``` +""" +csch + +doc""" +```rst +:: + isequal(x, y) + +Similar to ``==``, except treats all floating-point ``NaN`` values as equal to each other, +and treats ``-0.0`` as unequal to ``0.0``. +The default implementation of ``isequal`` calls ``==``, so if you have a type that doesn't have these floating-point subtleties then you probably only need to define ``==``. + +``isequal`` is the comparison function used by hash tables (``Dict``). +``isequal(x,y)`` must imply that ``hash(x) == hash(y)``. + +This typically means that if you define your own ``==`` function then you must define a corresponding ``hash`` (and vice versa). Collections typically implement ``isequal`` by calling ``isequal`` recursively on +all contents. + +Scalar types generally do not need to implement ``isequal`` separate from ``==``, unless they +represent floating-point numbers amenable to a more efficient implementation +than that provided as a generic fallback (based on ``isnan``, ``signbit``, and ``==``). +``` +""" +isequal + +doc""" +```rst +:: + lyap(A, C) + +Computes the solution ``X`` to the continuous Lyapunov equation ``AX + XA' + C = 0``, where no eigenvalue of ``A`` has a zero real part and no two eigenvalues are negative complex conjugates of each other. +``` +""" +lyap + +doc""" +```rst +:: + condskeel(M, [x, p]) + +.. math:: + \kappa_S(M, p) & = \left\Vert \left\vert M \right\vert \left\vert M^{-1} \right\vert \right\Vert_p \\ + \kappa_S(M, x, p) & = \left\Vert \left\vert M \right\vert \left\vert M^{-1} \right\vert \left\vert x \right\vert \right\Vert_p + +Skeel condition number :math:`\kappa_S` of the matrix ``M``, optionally with respect to the vector ``x``, as computed using the operator ``p``-norm. ``p`` is ``Inf`` by default, if not provided. Valid values for ``p`` are ``1``, ``2``, or ``Inf``. + +This quantity is also known in the literature as the Bauer condition number, relative condition number, or componentwise relative condition number. +``` +""" +condskeel + +doc""" +```rst +:: + sec(x) + +Compute the secant of ``x``, where ``x`` is in radians +``` +""" +sec + +doc""" +```rst +:: + recv(socket::UDPSocket) + +Read a UDP packet from the specified socket, and return the bytes received. This call blocks. +``` +""" +recv + +doc""" +```rst +:: + acoth(x) + +Compute the inverse hyperbolic cotangent of ``x`` +``` +""" +acoth + +doc""" +```rst +:: + det(M) + +Matrix determinant +``` +""" +det + +doc""" +```rst +:: + TypeError(func::Symbol, context::AbstractString, expected::Type, got) + +A type assertion failure, or calling an intrinsic function with an incorrect argument type. +``` +""" +TypeError + +doc""" +```rst +:: + plan_fft(A [, dims]; flags=FFTW.ESTIMATE; timelimit=Inf) + +Pre-plan an optimized FFT along given dimensions (``dims``) of arrays +matching the shape and type of ``A``. (The first two arguments have +the same meaning as for :func:`fft`.) Returns an object ``P`` which +represents the linear operator computed by the FFT, and which contains +all of the information needed to compute ``fft(A, dims)`` quickly. + +To apply ``P`` to an array ``A``, use ``P * A``; in general, the +syntax for applying plans is much like that of matrices. (A plan +can only be applied to arrays of the same size as the ``A`` for +which the plan was created.) You can also apply a plan with a +preallocated output array ``Â`` by calling ``A_mul_B!(Â, plan, +A)``. You can compute the inverse-transform plan by ``inv(P)`` and +apply the inverse plan with ``P \ Â`` (the inverse plan is cached +and reused for subsequent calls to ``inv`` or ``\``), and apply the +inverse plan to a pre-allocated output array ``A`` with +``A_ldiv_B!(A, P, Â)``. + +The ``flags`` argument is a bitwise-or of FFTW planner flags, defaulting +to ``FFTW.ESTIMATE``. e.g. passing ``FFTW.MEASURE`` or ``FFTW.PATIENT`` +will instead spend several seconds (or more) benchmarking different +possible FFT algorithms and picking the fastest one; see the FFTW manual +for more information on planner flags. The optional ``timelimit`` argument +specifies a rough upper bound on the allowed planning time, in seconds. +Passing ``FFTW.MEASURE`` or ``FFTW.PATIENT`` may cause the input array ``A`` +to be overwritten with zeros during plan creation. + +:func:`plan_fft!` is the same as :func:`plan_fft` but creates a plan +that operates in-place on its argument (which must be an array of +complex floating-point numbers). :func:`plan_ifft` and so on +are similar but produce plans that perform the equivalent of +the inverse transforms :func:`ifft` and so on. +``` +""" +plan_fft + +doc""" +```rst +:: + A_rdiv_Bt(a,b) + +Matrix operator A / B\ :sup:`T` +``` +""" +A_rdiv_Bt + +doc""" +```rst +:: + pwd() -> AbstractString + +Get the current working directory. +``` +""" +pwd + +doc""" +```rst +:: + getipaddr() -> AbstractString + +Get the IP address of the local machine, as a string of the form "x.x.x.x". +``` +""" +getipaddr + +doc""" +```rst +:: + uppercase(string) + +Returns ``string`` with all characters converted to uppercase. +``` +""" +uppercase + +doc""" +```rst +:: + cosd(x) + +Compute cosine of ``x``, where ``x`` is in degrees +``` +""" +cosd + +doc""" +```rst +:: + brfft(A, d [, dims]) + +Similar to :func:`irfft` but computes an unnormalized inverse transform +(similar to :func:`bfft`), which must be divided by the product +of the sizes of the transformed dimensions (of the real output array) +in order to obtain the inverse transform. +``` +""" +brfft + +doc""" +```rst +:: + cycle(iter) + +An iterator that cycles through ``iter`` forever. +``` +""" +cycle + +doc""" +```rst +:: + put!(RemoteRef, value) + +Store a value to a remote reference. Implements "shared queue of length 1" semantics: if a value is already present, blocks until the value is removed with ``take!``. Returns its first argument. + +:: + put!(Channel, value) + + Appends an item to the channel. Blocks if the channel is full. +``` +""" +put! + +doc""" +```rst +:: + operm(file) + +Like uperm but gets the permissions for people who neither own the file nor are a +member of the group owning the file +``` +""" +operm + +doc""" +```rst +:: + cumsum(A, [dim]) + +Cumulative sum along a dimension ``dim`` (defaults to 1). +See also :func:`cumsum!` to use a preallocated output array, +both for performance and to control the precision of the +output (e.g. to avoid overflow). +``` +""" +cumsum + +doc""" +```rst +:: + rmprocs(pids...) + +Removes the specified workers. +``` +""" +rmprocs + +doc""" +```rst +:: + rpad(string, n, p) + +Make a string at least ``n`` columns wide when printed, by padding on the right with copies of ``p``. +``` +""" +rpad + +doc""" +```rst +:: + setfield!(value, name::Symbol, x) + +Assign ``x`` to a named field in ``value`` of composite type. +The syntax ``a.b = c`` calls ``setfield!(a, :b, c)``, and the syntax ``a.(b) = c`` +calls ``setfield!(a, b, c)``. +``` +""" +setfield! + +doc""" +```rst +:: + @printf([io::IOStream], "%Fmt", args...) + +Print arg(s) using C ``printf()`` style format specification string. Optionally, an IOStream may be passed as the first argument to redirect output. +``` +""" +:@printf + +doc""" +```rst +:: + rstrip(string, [chars]) + +Return ``string`` with any trailing whitespace removed. If ``chars`` (a character, or vector or set of characters) is provided, instead remove characters contained in it. +``` +""" +rstrip + +doc""" +```rst +:: + countlines(io,[eol::Char]) + +Read ``io`` until the end of the stream/file and count the number of lines. To specify a file pass the filename as the first +argument. EOL markers other than '\\n' are supported by passing them as the second argument. +``` +""" +countlines + +doc""" +```rst +:: + *(A, B) +:noindex: + +Matrix multiplication + +:: + *(x, y...) + +Multiplication operator. ``x*y*z*...`` calls this function with all arguments, i.e. +``*(x, y, z, ...)``. + +:: + *(s, t) + +Concatenate strings. The ``*`` operator is an alias to this function. + +.. doctest:: +``` +""" +Base.(:(*)) + +doc""" +```rst +:: + complement!(s) + +Mutates :obj:`IntSet` ``s`` into its set-complement. +``` +""" +complement! + +doc""" +```rst +:: + slice(A, inds...) + +Returns a view of array ``A`` with the given indices like :func:`sub`, but drops all dimensions indexed with scalars. +``` +""" +slice + +doc""" +```rst +:: + time() + +Get the system time in seconds since the epoch, with fairly high (typically, microsecond) resolution. +``` +""" +time + +doc""" +```rst +:: + procs() + +Returns a list of all process identifiers. + +:: + procs(S::SharedArray) + +Get the vector of processes that have mapped the shared array +``` +""" +procs + +doc""" +```rst +:: + plan_bfft(A [, dims]; flags=FFTW.ESTIMATE; timelimit=Inf) + +Same as :func:`plan_fft`, but produces a plan that performs an unnormalized +backwards transform :func:`bfft`. +``` +""" +plan_bfft + +doc""" +```rst +:: + mod(x, y) + +Modulus after division, returning in the range [0,``y``), if ``y`` is +positive, or (``y``,0] if ``y`` is negative. +``` +""" +mod + +doc""" +```rst +:: + trues(dims) + +Create a ``BitArray`` with all values set to true +``` +""" +trues + +doc""" +```rst +:: + qr(A [,pivot=Val{false}][;thin=true]) -> Q, R, [p] + +Compute the (pivoted) QR factorization of ``A`` such that either ``A = Q*R`` or ``A[:,p] = Q*R``. Also see ``qrfact``. The default is to compute a thin factorization. Note that ``R`` is not extended with zeros when the full ``Q`` is requested. +``` +""" +qr + +doc""" +```rst +:: + invmod(x,m) + +Take the inverse of ``x`` modulo ``m``: ``y`` such that :math:`xy = 1 \pmod m` +``` +""" +invmod + +doc""" +```rst +:: + TextDisplay(stream) + +Returns a ``TextDisplay <: Display``, which can display any object +as the text/plain MIME type (only), writing the text representation +to the given I/O stream. (The text representation is the same +as the way an object is printed in the Julia REPL.) +``` +""" +TextDisplay + +doc""" +```rst +:: + factor(n) -> Dict + +Compute the prime factorization of an integer ``n``. Returns a dictionary. The keys of the dictionary correspond to the factors, and hence are of the same type as ``n``. The value associated with each key indicates the number of times the factor appears in the factorization. + +.. doctest:: + + julia> factor(100) # == 2*2*5*5 + Dict{Int64,Int64} with 2 entries: + 2 => 2 + 5 => 2 +``` +""" +factor + +doc""" +```rst +:: + ismatch(r::Regex, s::AbstractString) -> Bool + +Test whether a string contains a match of the given regular expression. +``` +""" +ismatch + +doc""" +```rst +:: + exp(x) + +Compute :math:`e^x` +``` +""" +exp + +doc""" +```rst +:: + with_bigfloat_precision(f::Function,precision::Integer) + +Change the BigFloat arithmetic precision (in bits) for the duration of ``f``. It is logically equivalent to:: + + old = get_bigfloat_precision() + set_bigfloat_precision(precision) + f() + set_bigfloat_precision(old) +``` +""" +with_bigfloat_precision + +doc""" +```rst +:: + searchindex(string, substring, [start]) + +Similar to ``search``, but return only the start index at which the substring is found, or 0 if it is not. +``` +""" +searchindex + +doc""" +```rst +:: + listenany(port_hint) -> (UInt16,TcpServer) + +Create a TcpServer on any port, using hint as a starting point. Returns a tuple of the actual port that the server +was created on and the server itself. +``` +""" +listenany + +doc""" +```rst +:: + getpid() -> Int32 + +Get julia's process ID. +``` +""" +getpid + +doc""" +```rst +:: + cbrt(x) + +Return :math:`x^{1/3}`. The prefix operator ``∛`` is equivalent to ``cbrt``. +``` +""" +cbrt + +doc""" +```rst +:: + Tridiagonal(dl, d, du) + +Construct a tridiagonal matrix from the lower diagonal, diagonal, and upper diagonal, respectively. The result is of type ``Tridiagonal`` and provides efficient specialized linear solvers, but may be converted into a regular matrix with :func:`full`. +``` +""" +Tridiagonal + +doc""" +```rst +:: + findprev(A, i) + +Find the previous index <= ``i`` of a non-zero element of ``A``, or 0 if not found. + +:: + findprev(predicate, A, i) + +Find the previous index <= ``i`` of an element of ``A`` for which ``predicate`` returns true, or ``0`` if not found. + +:: + findprev(A, v, i) + +Find the previous index <= ``i`` of an element of ``A`` equal to ``v`` (using ``==``), +or ``0`` if not found. +``` +""" +findprev + +doc""" +```rst +:: + matchall(r::Regex, s::AbstractString[, overlap::Bool=false]) -> Vector{AbstractString} + +Return a vector of the matching substrings from eachmatch. +``` +""" +matchall + +doc""" +```rst +:: + get!(collection, key, default) + +Return the value stored for the given key, or if no mapping for the key is present, store ``key => default``, and return ``default``. + +:: + get!(f::Function, collection, key) + +Return the value stored for the given key, or if no mapping for the key is present, store ``key => f()``, and return ``f()``. + +This is intended to be called using ``do`` block syntax:: + + get!(dict, key) do + # default value calculated here +``` +""" +get! + +doc""" +```rst +:: + inv(M) + +Matrix inverse +``` +""" +inv + +doc""" +```rst +:: + mod1(x,m) + +Modulus after division, returning in the range (0,m] +``` +""" +mod1 + +doc""" +```rst +:: + @assert cond [text] + +Throw an ``AssertionError`` if ``cond`` is false. Preferred syntax for writing assertions. +``` +""" +:@assert + +doc""" +```rst +:: + intersect!(s1, s2) + +Intersects sets ``s1`` and ``s2`` and overwrites the set ``s1`` with the result. If needed, ``s1`` will be expanded to the size of ``s2``. +``` +""" +intersect! + +doc""" +```rst +:: + listen([addr,]port) -> TcpServer + +Listen on port on the address specified by ``addr``. By default this listens on localhost only. +To listen on all interfaces pass, ``IPv4(0)`` or ``IPv6(0)`` as appropriate. + +:: + listen(path) -> PipeServer + +Listens on/Creates a Named Pipe/Domain Socket +``` +""" +listen + +doc""" +```rst +:: + leading_ones(x::Integer) -> Integer + +Number of ones leading the binary representation of ``x``. + +.. doctest:: + + julia> leading_ones(UInt32(2 ^ 32 - 2)) + 31 +``` +""" +leading_ones + +doc""" +```rst +:: + deserialize(stream) + +Read a value written by ``serialize``. +``` +""" +deserialize + +doc""" +```rst +:: + asech(x) + +Compute the inverse hyperbolic secant of ``x`` +``` +""" +asech + +doc""" +```rst +:: + sprandn(m,n,p) + +Create a random ``m`` by ``n`` sparse matrix with the specified (independent) probability ``p`` of any entry being nonzero, where nonzero values are sampled from the normal distribution. +``` +""" +sprandn + +doc""" +```rst +:: + ismarked(s) + +Returns true if stream ``s`` is marked. + +See also :func:`mark`, :func:`unmark`, :func:`reset` +``` +""" +ismarked + +doc""" +```rst +:: + first(coll) + +Get the first element of an iterable collection. Returns the start point of a :obj:`Range` +even if it is empty. +``` +""" +first + +doc""" +```rst +:: + median!(v) + +Like ``median``, but may overwrite the input vector. +``` +""" +median! + +doc""" +```rst +:: + cumprod!(B, A, [dim]) + +Cumulative product of ``A`` along a dimension, storing the result in ``B``. +The dimension defaults to 1. +``` +""" +cumprod! + +doc""" +```rst +:: + @linux + +Given ``@linux? a : b``, do ``a`` on Linux and ``b`` elsewhere. See documentation for Handling Platform Variations +in the Calling C and Fortran Code section of the manual. +``` +""" +:@linux + +doc""" +```rst +:: + complement(s) + +Returns the set-complement of :obj:`IntSet` ``s``. +``` +""" +complement + +doc""" +```rst +:: + rethrow([e]) + +Throw an object without changing the current exception backtrace. +The default argument is the current exception (if called within a +``catch`` block). +``` +""" +rethrow + +doc""" +```rst +:: + reprmime(mime, x) + +Returns an ``AbstractString`` or ``Vector{UInt8}`` containing the +representation of ``x`` in the requested ``mime`` type, as written +by ``writemime`` (throwing a ``MethodError`` if no appropriate +``writemime`` is available). An ``AbstractString`` is returned for MIME +types with textual representations (such as ``"text/html"`` or +``"application/postscript"``), whereas binary data is returned as +``Vector{UInt8}``. (The function ``istext(mime)`` returns whether +or not Julia treats a given ``mime`` type as text.) + +As a special case, if ``x`` is an ``AbstractString`` (for textual MIME types) +or a ``Vector{UInt8}`` (for binary MIME types), the ``reprmime`` function +assumes that ``x`` is already in the requested ``mime`` format and +simply returns ``x``. +``` +""" +reprmime + +doc""" +```rst +:: + rm(path::AbstractString; recursive=false) + +Delete the file, link, or empty directory at the given path. If ``recursive=true`` is +passed and the path is a directory, then all contents are removed recursively. +``` +""" +rm + +doc""" +```rst +:: + MersenneTwister([seed]) + +Create a ``MersenneTwister`` RNG object. Different RNG objects can have their own seeds, which may be useful for generating different streams of random numbers. +``` +""" +MersenneTwister + +doc""" +```rst +:: + graphemes(s) -> iterator over substrings of s + +Returns an iterator over substrings of ``s`` that correspond to +the extended graphemes in the string, as defined by Unicode UAX #29. +(Roughly, these are what users would perceive as single characters, +even though they may contain more than one codepoint; for example +a letter combined with an accent mark is a single grapheme.) +``` +""" +graphemes + +doc""" +```rst +:: + @__FILE__() -> AbstractString + +``@__FILE__`` expands to a string with the absolute path and file name of the script being run. +Returns ``nothing`` if run from a REPL or an empty string if evaluated by ``julia -e ``. +``` +""" +:@__FILE__ + +doc""" +```rst +:: + charwidth(c) + +Gives the number of columns needed to print a character. +``` +""" +charwidth + +doc""" +```rst +:: + abspath(path::AbstractString) -> AbstractString + +Convert a path to an absolute path by adding the current directory if +necessary. +``` +""" +abspath + +doc""" +```rst +:: + ispunct(c::Union{Char,AbstractString}) -> Bool + +Tests whether a character belongs to the Unicode general category Punctuation, i.e. a character whose category code begins with 'P'. For strings, tests whether this is true for all elements of the string. +``` +""" +ispunct + +doc""" +```rst +:: + bitunpack(B::BitArray{N}) -> Array{Bool,N} + +Converts a packed boolean array to an array of booleans +``` +""" +bitunpack + +doc""" +```rst +:: + @which + +Applied to a function call, it evaluates the arguments to the +specified function call, and returns the ``Method`` object for the +method that would be called for those arguments. Applied to a +variable, it returns the module in which the variable was bound. It +calls out to the ``which`` function. +``` +""" +:@which + +doc""" +```rst +:: + size(A, [dim...]) + +Returns a tuple containing the dimensions of A. Optionally you can specify the dimension(s) you want the length of, and get the length of that dimension, or a tuple of the lengths of dimensions you asked for.:: + + julia> A = rand(2,3,4); + + julia> size(A, 2) + 3 + + julia> size(A,3,2) + (4,3) +``` +""" +size + +doc""" +```rst +:: + trigamma(x) + +Compute the trigamma function of ``x`` (the logarithmic second derivative of ``gamma(x)``) +``` +""" +trigamma + +doc""" +```rst +:: + findmin(itr) -> (x, index) + +Returns the minimum element and its index. + +:: + findmin(A, dims) -> (minval, index) + +For an array input, returns the value and index of the minimum over +the given dimensions. +``` +""" +findmin + +doc""" +```rst +:: + ismount(path) -> Bool + +Returns ``true`` if ``path`` is a mount point, ``false`` otherwise. +``` +""" +ismount + +doc""" +```rst +:: + endswith(string, suffix | chars) + +Returns ``true`` if ``string`` ends with ``suffix``. If the second argument is a vector or set of characters, tests whether the last character of ``string`` belongs to that set. +``` +""" +endswith + +doc""" +```rst +:: + airy(k,x) + +kth derivative of the Airy function :math:`\operatorname{Ai}(x)`. +``` +""" +airy + +doc""" +```rst +:: + !(x) + +Boolean not +``` +""" +Base.(:(!)) + +doc""" +```rst +:: + length(A) -> Integer + +Returns the number of elements in A + +:: + length(collection) -> Integer + +For ordered, indexable collections, the maximum index ``i`` for which ``getindex(collection, i)`` is valid. For unordered collections, the number of elements. + +:: + length(s) + +The number of characters in string ``s``. +``` +""" +length + +doc""" +```rst +:: + rand!([rng], A, [coll]) + +Populate the array A with random values. If the indexable collection ``coll`` is specified, the values are picked randomly from ``coll``. This is equivalent to ``copy!(A, rand(rng, coll, size(A)))`` or ``copy!(A, rand(rng, eltype(A), size(A)))`` but without allocating a new array. +``` +""" +rand! + +doc""" +```rst +:: + bkfact(A) -> BunchKaufman + +Compute the Bunch-Kaufman [Bunch1977]_ factorization of a real symmetric or complex Hermitian matrix ``A`` and return a ``BunchKaufman`` object. The following functions are available for ``BunchKaufman`` objects: ``size``, ``\``, ``inv``, ``issym``, ``ishermitian``. +``` +""" +bkfact + +doc""" +```rst +:: + searchsortedlast(a, x, [by=,] [lt=,] [rev=false]) + +Returns the index of the last value in ``a`` less than or equal to ``x``, +according to the specified order. Returns ``0`` if ``x`` is less than all +values in ``a``. +``` +""" +searchsortedlast + +doc""" +```rst +:: + InterruptException() + +The process was stopped by a terminal interrupt (CTRL+C). +``` +""" +InterruptException + +doc""" +```rst +:: + cov(v1[, v2][, vardim=1, corrected=true, mean=nothing]) + +Compute the Pearson covariance between the vector(s) in ``v1`` and ``v2``. +Here, ``v1`` and ``v2`` can be either vectors or matrices. + +This function accepts three keyword arguments: + +- ``vardim``: the dimension of variables. When ``vardim = 1``, variables + are considered in columns while observations in rows; when ``vardim = 2``, + variables are in rows while observations in columns. By default, it is + set to ``1``. + +- ``corrected``: whether to apply Bessel's correction (divide by ``n-1`` + instead of ``n``). By default, it is set to ``true``. + +- ``mean``: allow users to supply mean values that are known. By default, + it is set to ``nothing``, which indicates that the mean(s) are unknown, + and the function will compute the mean. Users can use ``mean=0`` to + indicate that the input data are centered, and hence there's no need to + subtract the mean. + +The size of the result depends on the size of ``v1`` and ``v2``. When both +``v1`` and ``v2`` are vectors, it returns the covariance between them as a +scalar. When either one is a matrix, it returns a covariance matrix of size +``(n1, n2)``, where ``n1`` and ``n2`` are the numbers of slices in ``v1`` and +``v2``, which depend on the setting of ``vardim``. + +Note: ``v2`` can be omitted, which indicates ``v2 = v1``. +``` +""" +cov + +doc""" +```rst +:: + den(x) + +Denominator of the rational representation of ``x`` +``` +""" +den + +doc""" +```rst +:: + issubnormal(f) -> Bool + +Test whether a floating point number is subnormal +``` +""" +issubnormal + +doc""" +```rst +:: + Ac_ldiv_B(...) + +Matrix operator A\ :sup:`H` \\ B +``` +""" +Ac_ldiv_B + +doc""" +```rst +:: + NullException() + +An attempted access to a ``Nullable`` with no defined value. +``` +""" +NullException + +doc""" +```rst +:: + .==(x, y) + +Element-wise equality comparison operator. +``` +""" +Base.(:(.==)) + +doc""" +```rst +:: + cfunction(function::Function, ReturnType::Type, (ArgumentTypes...)) + +Generate C-callable function pointer from Julia function. Type annotation of the return value in the +callback function is a must for situations where Julia cannot infer the return type automatically. + +For example:: + + function foo() + # body + + retval::Float64 + end + + bar = cfunction(foo, Float64, ()) +``` +""" +cfunction + +doc""" +```rst +:: + recvfrom(socket::UDPSocket) -> (address, data) + + Read a UDP packet from the specified socket, returning a tuple of (address, data), where address will be either IPv4 or IPv6 as appropriate. +``` +""" +recvfrom + +doc""" +```rst +:: + @code_llvm + +Evaluates the arguments to the function call, determines their types, and calls :func:`code_llvm` on the resulting expression +``` +""" +:@code_llvm + +doc""" +```rst +:: + nextfloat(f) + +Get the next floating point number in lexicographic order +``` +""" +nextfloat + +doc""" +```rst +:: + intersect(s1,s2...) + ∩(s1,s2) + +Construct the intersection of two or more sets. Maintains order and multiplicity of the first argument for arrays and ranges. +``` +""" +intersect + +doc""" +```rst +:: + !=(x, y) + ≠(x,y) + +Not-equals comparison operator. Always gives the opposite answer as ``==``. +New types should generally not implement this, and rely on the fallback +definition ``!=(x,y) = !(x==y)`` instead. +``` +""" +Base.(:(!=)) + +doc""" +```rst +:: + @spawn + +Creates a closure around an expression and runs it on an automatically-chosen process, returning a +``RemoteRef`` to the result. +``` +""" +:@spawn + +doc""" +```rst +:: + findfirst(A) + +Return the index of the first non-zero value in ``A`` (determined by ``A[i]!=0``). + +:: + findfirst(A,v) + +Return the index of the first element equal to ``v`` in ``A``. + +:: + findfirst(predicate, A) + +Return the index of the first element of ``A`` for which ``predicate`` returns true. +``` +""" +findfirst + +doc""" +```rst +:: + factorize(A) + +Compute a convenient factorization (including LU, Cholesky, Bunch-Kaufman, LowerTriangular, UpperTriangular) of A, based upon the type of the input matrix. The return value can then be reused for efficient solving of multiple systems. For example: ``A=factorize(A); x=A\b; y=A\C``. +``` +""" +factorize + +doc""" +```rst +:: + promote_rule(type1, type2) + +Specifies what type should be used by ``promote`` when given values of types +``type1`` and ``type2``. This function should not be called directly, but +should have definitions added to it for new types as appropriate. +``` +""" +promote_rule + +doc""" +```rst +:: + mtime(file) + +Equivalent to stat(file).mtime +``` +""" +mtime + +doc""" +```rst +:: + SharedArray(T::Type, dims::NTuple; init=false, pids=Int[]) + + Construct a SharedArray of a bitstype ``T`` and size ``dims`` across the processes + specified by ``pids`` - all of which have to be on the same host. + + If ``pids`` is left unspecified, the shared array will be mapped across all processes + on the current host, including the master. But, ``localindexes`` and ``indexpids`` + will only refer to worker processes. This facilitates work distribution code to use + workers for actual computation with the master process acting as a driver. + + If an ``init`` function of the type ``initfn(S::SharedArray)`` is specified, + it is called on all the participating workers. +``` +""" +SharedArray + +doc""" +```rst +:: + logspace(start, stop, n=50) + +Construct a vector of ``n`` logarithmically spaced numbers from ``10^start`` to ``10^stop``. +``` +""" +logspace + +doc""" +```rst +:: + @gensym + +Generates a gensym symbol for a variable. For example, ``@gensym x y`` is transformed into ``x = gensym("x"); y = gensym("y")``. +``` +""" +:@gensym + +doc""" +```rst +:: + sumabs2(itr) + +Sum squared absolute values of all elements in a collection. This +is equivalent to `sum(abs2(itr))` but faster. + +:: + sumabs2(A, dims) + +Sum squared absolute values of elements of an array over the given +dimensions. +``` +""" +sumabs2 + +doc""" +```rst +:: + uperm(file) + +Gets the permissions of the owner of the file as a bitfield of + +==== ===================== + 01 Execute Permission + 02 Write Permission + 04 Read Permission +==== ===================== + +For allowed arguments, see ``stat``. +``` +""" +uperm + +doc""" +```rst +:: + run(command) + +Run a command object, constructed with backticks. Throws an error if anything goes wrong, including the process exiting with a non-zero status. +``` +""" +run + +doc""" +```rst +:: + showall(x) + +Similar to ``show``, except shows all elements of arrays. +``` +""" +showall + +doc""" +```rst +:: + mimewritable(mime, x) + +Returns a boolean value indicating whether or not the object ``x`` +can be written as the given ``mime`` type. (By default, this +is determined automatically by the existence of the corresponding +``writemime`` function for ``typeof(x)``.) +``` +""" +mimewritable + +doc""" +```rst +:: + vecdot(x, y) + +For any iterable containers ``x`` and ``y`` (including arrays of +any dimension) of numbers (or any element type for which ``dot`` is +defined), compute the Euclidean dot product (the sum of +``dot(x[i],y[i])``) as if they were vectors. +``` +""" +vecdot + +doc""" +```rst +:: + isprime(x::Integer) -> Bool + +Returns ``true`` if ``x`` is prime, and ``false`` otherwise. + +.. doctest:: + + julia> isprime(3) + true + +:: + isprime(x::BigInt, [reps = 25]) -> Bool + +Probabilistic primality test. Returns ``true`` if ``x`` is prime; and +``false`` if ``x`` is not prime with high probability. The false positive +rate is about ``0.25^reps``. ``reps = 25`` is considered safe for +cryptographic applications (Knuth, Seminumerical Algorithms). + +.. doctest:: + + julia> isprime(big(3)) + true +``` +""" +isprime + +doc""" +```rst +:: + >(x, y) + +Greater-than comparison operator. Generally, new types should implement ``<`` +instead of this function, and rely on the fallback definition ``>(x,y) = y)) + +doc""" +```rst +:: + match(r::Regex, s::AbstractString[, idx::Integer[, addopts]]) + +Search for the first match of the regular expression ``r`` in ``s`` and return a RegexMatch object containing the match, or nothing if the match failed. The matching substring can be retrieved by accessing ``m.match`` and the captured sequences can be retrieved by accessing ``m.captures`` The optional ``idx`` argument specifies an index at which to start the search. +``` +""" +match + +doc""" +```rst +:: + nprocs() + +Get the number of available processes. +``` +""" +nprocs + +doc""" +```rst +:: + Ac_mul_B(...) + +Matrix operator A\ :sup:`H` B +``` +""" +Ac_mul_B + +doc""" +```rst +:: + qrfact!(A [,pivot=Val{false}]) + +``qrfact!`` is the same as :func:`qrfact` when A is a subtype of ``StridedMatrix``, but saves space by overwriting the input ``A``, instead of creating a copy. +``` +""" +qrfact! + +doc""" +```rst +:: + At_rdiv_B(a,b) + +Matrix operator A\ :sup:`T` / B +``` +""" +At_rdiv_B + +doc""" +```rst +:: + coth(x) + +Compute the hyperbolic cotangent of ``x`` +``` +""" +coth + +doc""" +```rst +:: + conj(z) + +Compute the complex conjugate of a complex number ``z`` +``` +""" +conj + +doc""" +```rst +:: + conj!(A) + +Convert an array to its complex conjugate in-place +``` +""" +conj! + +doc""" +```rst +:: + start(iter) -> state + +Get initial iteration state for an iterable object +``` +""" +start + +doc""" +```rst +:: + div(x, y) + ÷(x, y) + +The quotient from Euclidean division. Computes ``x/y``, truncated to an integer. +``` +""" +div + +doc""" +```rst +:: + relpath(path::AbstractString, startpath::AbstractString = ".") -> AbstractString + +Return a relative filepath to path either from the current directory or from an optional +start directory. +This is a path computation: the filesystem is not accessed to confirm the existence or +nature of path or startpath. +``` +""" +relpath + +doc""" +```rst +:: + readavailable(stream) + +Read all available data on the stream, blocking the task only if no data is available. The result is a ``Vector{UInt8,1}``. +``` +""" +readavailable + +doc""" +```rst +:: + remotecall(id, func, args...) + +Call a function asynchronously on the given arguments on the specified process. Returns a ``RemoteRef``. +``` +""" +remotecall + +doc""" +```rst +:: + slicedim(A, d, i) + +Return all the data of ``A`` where the index for dimension ``d`` equals ``i``. Equivalent to ``A[:,:,...,i,:,:,...]`` where ``i`` is in position ``d``. +``` +""" +slicedim + +doc""" +```rst +:: + isa(x, type) -> Bool + +Determine whether ``x`` is of the given ``type``. +``` +""" +isa + +doc""" +```rst +:: + <=(x, y) + ≤(x,y) + +Less-than-or-equals comparison operator. +``` +""" +Base.(:(<=)) + +doc""" +```rst +:: + ProcessExitedException() + +After a client Julia process has exited, further attempts to reference the dead child will throw this exception. +``` +""" +ProcessExitedException + +doc""" +```rst +:: + unsafe_load(p::Ptr{T},i::Integer) + +Load a value of type ``T`` from the address of the ith element (1-indexed) +starting at ``p``. This is equivalent to the C expression ``p[i-1]``. + +The ``unsafe`` prefix on this function indicates that no validation is +performed on the pointer ``p`` to ensure that it is valid. Incorrect usage +may segfault your program or return garbage answers, in the same manner as +C. +``` +""" +unsafe_load + +doc""" +```rst +:: + catch_backtrace() + +Get the backtrace of the current exception, for use within ``catch`` +blocks. +``` +""" +catch_backtrace + +doc""" +```rst +:: + airyx(k,x) + +scaled kth derivative of the Airy function, return :math:`\operatorname{Ai}(x) e^{\frac{2}{3} x \sqrt{x}}` for ``k == 0 || k == 1``, and :math:`\operatorname{Ai}(x) e^{- \left| \operatorname{Re} \left( \frac{2}{3} x \sqrt{x} \right) \right|}` for ``k == 2 || k == 3``. +``` +""" +airyx + +doc""" +```rst +:: + get_zero_subnormals() -> Bool + +Returns ``false`` if operations on subnormal floating-point values +("denormals") obey rules for IEEE arithmetic, and ``true`` if they +might be converted to zeros. +``` +""" +get_zero_subnormals + +doc""" +```rst +:: + cos(x) + +Compute cosine of ``x``, where ``x`` is in radians +``` +""" +cos + +doc""" +```rst +:: + base64encode(writefunc, args...) + base64encode(args...) + +Given a ``write``-like function ``writefunc``, which takes an I/O +stream as its first argument, ``base64(writefunc, args...)`` +calls ``writefunc`` to write ``args...`` to a base64-encoded string, +and returns the string. ``base64(args...)`` is equivalent to +``base64(write, args...)``: it converts its arguments into bytes +using the standard ``write`` functions and returns the base64-encoded +string. +``` +""" +base64encode + +doc""" +```rst +:: + Condition() + +Create an edge-triggered event source that tasks can wait for. Tasks +that call ``wait`` on a ``Condition`` are suspended and queued. +Tasks are woken up when ``notify`` is later called on the ``Condition``. +Edge triggering means that only tasks waiting at the time ``notify`` is +called can be woken up. For level-triggered notifications, you must +keep extra state to keep track of whether a notification has happened. +The ``Channel`` type does this, and so can be used for level-triggered +events. +``` +""" +Condition + +doc""" +```rst +:: + filt!(out, b, a, x, [si]) + +Same as :func:`filt` but writes the result into the ``out`` argument, +which may alias the input ``x`` to modify it in-place. +``` +""" +filt! + +doc""" +```rst +:: + ascii(::Array{UInt8,1}) + +Create an ASCII string from a byte array. + +:: + ascii(s) + +Convert a string to a contiguous ASCII string (all characters must be valid ASCII characters). + +:: + ascii(::Ptr{UInt8}, [length]) + +Create an ASCII string from the address of a C (0-terminated) string encoded in ASCII. A copy is made; the ptr can be safely freed. If ``length`` is specified, the string does not have to be 0-terminated. +``` +""" +ascii + +doc""" +```rst +:: + plan_idct(A [, dims [, flags [, timelimit]]]) + +Pre-plan an optimized inverse discrete cosine transform (DCT), similar to +:func:`plan_fft` except producing a function that computes :func:`idct`. +The first two arguments have the same meaning as for :func:`idct`. +``` +""" +plan_idct + +doc""" +```rst +:: + maxabs(itr) + +Compute the maximum absolute value of a collection of values. + +:: + maxabs(A, dims) + +Compute the maximum absolute values over given dimensions. +``` +""" +maxabs + +doc""" +```rst +:: + done(iter, state) -> Bool + +Test whether we are done iterating +``` +""" +done + +doc""" +```rst +:: + convert(T, x) + +Convert ``x`` to a value of type ``T``. + +If ``T`` is an ``Integer`` type, an :exc:`InexactError` will be raised if +``x`` is not representable by ``T``, for example if ``x`` is not +integer-valued, or is outside the range supported by ``T``. + +.. doctest:: + + julia> convert(Int, 3.0) + 3 + + julia> convert(Int, 3.5) + ERROR: InexactError() + in convert at int.jl:205 + +If ``T`` is a :obj:`AbstractFloat` or :obj:`Rational` type, then it will return +the closest value to ``x`` representable by ``T``. + +.. doctest:: + + julia> x = 1/3 + 0.3333333333333333 + + julia> convert(Float32, x) + 0.33333334f0 + + julia> convert(Rational{Int32}, x) + 1//3 + + julia> convert(Rational{Int64}, x) + 6004799503160661//18014398509481984 +``` +""" +convert + +doc""" +```rst +:: + A_ldiv_Bt(a,b) + +Matrix operator A \\ B\ :sup:`T` +``` +""" +A_ldiv_Bt + +doc""" +```rst +:: + applicable(f, args...) -> Bool + +Determine whether the given generic function has a method applicable to the given arguments. + +.. doctest:: + + julia> function f(x, y) + x + y + end; + + julia> applicable(f, 1) + false + + julia> applicable(f, 1, 2) + true +``` +""" +applicable + +doc""" +```rst +:: + xdump(x) + +Show all structure of a value, including all fields of objects. +``` +""" +xdump + +doc""" +```rst +:: + Base.process_messages(instrm::AsyncStream, outstrm::AsyncStream) + + Called by cluster managers using custom transports. It should be called when the custom transport implementation receives the + first message from a remote worker. The custom transport must manage a logical connection to the remote worker and provide two + AsyncStream objects, one for incoming messages and the other for messages addressed to the remote worker. +``` +""" +Base.process_messages + +doc""" +```rst +:: + RandomDevice() + +Create a ``RandomDevice`` RNG object. Two such objects will always generate different streams of random numbers. +``` +""" +RandomDevice + +doc""" +```rst +:: + plan_fft!(A [, dims]; flags=FFTW.ESTIMATE; timelimit=Inf) + +Same as :func:`plan_fft`, but operates in-place on ``A``. +``` +""" +plan_fft! + +doc""" +```rst +:: + fma(x, y, z) + +Computes ``x*y+z`` without rounding the intermediate result +``x*y``. On some systems this is significantly more expensive than +``x*y+z``. ``fma`` is used to improve accuracy in certain +algorithms. See ``muladd``. +``` +""" +fma + +doc""" +```rst +:: + eigvals(A,[irange,][vl,][vu]) + +Returns the eigenvalues of ``A``. If ``A`` is :class:`Symmetric`, +:class:`Hermitian` or :class:`SymTridiagonal`, it is possible to calculate +only a subset of the eigenvalues by specifying either a :class:`UnitRange` +``irange`` covering indices of the sorted eigenvalues, or a pair ``vl`` and +``vu`` for the lower and upper boundaries of the eigenvalues. + +For general non-symmetric matrices it is possible to specify how the matrix +is balanced before the eigenvector calculation. The option ``permute=true`` +permutes the matrix to become closer to upper triangular, and ``scale=true`` +scales the matrix by its diagonal elements to make rows and columns more +equal in norm. The default is ``true`` for both options. +``` +""" +eigvals + +doc""" +```rst +:: + A_ldiv_Bc(a,b) + +Matrix operator A \\ B\ :sup:`H` +``` +""" +A_ldiv_Bc + +doc""" +```rst +:: + escape_string(str::AbstractString) -> AbstractString + +General escaping of traditional C and Unicode escape sequences. See :func:`print_escaped` for more general escaping. +``` +""" +escape_string + +doc""" +```rst +:: + significand(x) + +Extract the significand(s) (a.k.a. mantissa), in binary representation, of +a floating-point number or array. If ``x`` is a non-zero finite number, +than the result will be a number of the same type on the interval +[1,2). Otherwise ``x`` is returned. + +.. doctest:: + + julia> significand(15.2)/15.2 + 0.125 + + julia> significand(15.2)*8 + 15.2 +``` +""" +significand + +doc""" +```rst +:: + pointer_from_objref(object_instance) + +Get the memory address of a Julia object as a ``Ptr``. The existence of the resulting +``Ptr`` will not protect the object from garbage collection, so you must ensure +that the object remains referenced for the whole time that the ``Ptr`` will be used. +``` +""" +pointer_from_objref + +doc""" +```rst +:: + cumsum_kbn(A, [dim]) + +Cumulative sum along a dimension, using the Kahan-Babuska-Neumaier +compensated summation algorithm for additional accuracy. +The dimension defaults to 1. +``` +""" +cumsum_kbn + +doc""" +```rst +:: + cmp(x,y) + +Return -1, 0, or 1 depending on whether ``x`` is less than, equal to, or greater +than ``y``, respectively. Uses the total order implemented by ``isless``. For +floating-point numbers, uses ``<`` but throws an error for unordered arguments. +``` +""" +cmp + +doc""" +```rst +:: + tand(x) + +Compute tangent of ``x``, where ``x`` is in degrees +``` +""" +tand + +doc""" +```rst +:: + issorted(v, [by=,] [lt=,] [rev=false]) + +Test whether a vector is in sorted order. The ``by``, ``lt`` and ``rev`` +keywords modify what order is considered to be sorted just as they do for ``sort``. +``` +""" +issorted + +doc""" +```rst +:: + set_bigfloat_precision(x::Int64) + +Set the precision (in bits) to be used to BigFloat arithmetic. +``` +""" +set_bigfloat_precision + +doc""" +```rst +:: + isbits(T) + +True if ``T`` is a "plain data" type, meaning it is immutable and contains no references to other values. Typical examples are numeric types such as ``UInt8``, ``Float64``, and ``Complex{Float64}``. + +.. doctest:: + + julia> isbits(Complex{Float64}) + true + + julia> isbits(Complex) + false +``` +""" +isbits + +doc""" +```rst +:: + findlast(A) + +Return the index of the last non-zero value in ``A`` (determined by ``A[i]!=0``). + +:: + findlast(A, v) + +Return the index of the last element equal to ``v`` in ``A``. + +:: + findlast(predicate, A) + +Return the index of the last element of ``A`` for which ``predicate`` returns true. +``` +""" +findlast + +doc""" +```rst +:: + @elapsed + +A macro to evaluate an expression, discarding the resulting value, instead returning the number of seconds it took to execute as a floating-point number. +``` +""" +:@elapsed + +doc""" +```rst +:: + findnext(A, i) + +Find the next index >= ``i`` of a non-zero element of ``A``, or ``0`` if not found. + +:: + findnext(predicate, A, i) + +Find the next index >= ``i`` of an element of ``A`` for which ``predicate`` returns true, or ``0`` if not found. + +:: + findnext(A, v, i) + +Find the next index >= ``i`` of an element of ``A`` equal to ``v`` (using ``==``), +or ``0`` if not found. +``` +""" +findnext + +doc""" +```rst +:: + fetch(x) + +Waits and fetches a value from ``x`` depending on the type of ``x``. Does not remove the item fetched: + +* ``RemoteRef``: Wait for and get the value of a remote reference. If the remote value is an exception, + throws a ``RemoteException`` which captures the remote exception and backtrace. + +* ``Channel`` : Wait for and get the first available item from the channel. +``` +""" +fetch + +doc""" +```rst +:: + angle(z) + +Compute the phase angle in radians of a complex number ``z`` +``` +""" +angle + +doc""" +```rst +:: + tic() + +Set a timer to be read by the next call to :func:`toc` or :func:`toq`. The macro call ``@time expr`` can also be used to time evaluation. +``` +""" +tic + +doc""" +```rst +:: + LoadError(file::AbstractString, line::Int, error) + +An error occurred while `including`, `requiring`, or `using` a file. The error specifics should be available in the `.error` field. +``` +""" +LoadError + +doc""" +```rst +:: + vec(Array) -> Vector + +Vectorize an array using column-major convention. +``` +""" +vec + +doc""" +```rst +:: + copy!(dest, src) + +Copy all elements from collection ``src`` to array ``dest``. Returns ``dest``. + +:: + copy!(dest, do, src, so, N) + +Copy ``N`` elements from collection ``src`` starting at offset ``so``, to +array ``dest`` starting at offset ``do``. Returns ``dest``. +``` +""" +copy! + +doc""" +```rst +:: + broadcast(f, As...) + +Broadcasts the arrays ``As`` to a common size by expanding singleton dimensions, and returns an array of the results ``f(as...)`` for each position. +``` +""" +broadcast + +doc""" +```rst +:: + eigvecs(A, [eigvals,][permute=true,][scale=true]) -> Matrix + +Returns a matrix ``M`` whose columns are the eigenvectors of ``A``. +(The ``k``\ th eigenvector can be obtained from the slice ``M[:, k]``.) +The ``permute`` and ``scale`` keywords are the same as for :func:`eigfact`. + +For :class:`SymTridiagonal` matrices, if the optional vector of eigenvalues +``eigvals`` is specified, returns the specific corresponding eigenvectors. +``` +""" +eigvecs + +doc""" +```rst +:: + ntoh(x) + +Converts the endianness of a value from Network byte order (big-endian) to +that used by the Host. +``` +""" +ntoh + +doc""" +```rst +:: + qrfact(A [,pivot=Val{false}]) -> F + +Computes the QR factorization of ``A``. The return type of ``F`` depends on the element type of ``A`` and whether pivoting is specified (with ``pivot==Val{true}``). + + ================ ================= ============== ===================================== + Return type ``eltype(A)`` ``pivot`` Relationship between ``F`` and ``A`` + ---------------- ----------------- -------------- ------------------------------------- + ``QR`` not ``BlasFloat`` either ``A==F[:Q]*F[:R]`` + ``QRCompactWY`` ``BlasFloat`` ``Val{false}`` ``A==F[:Q]*F[:R]`` + ``QRPivoted`` ``BlasFloat`` ``Val{true}`` ``A[:,F[:p]]==F[:Q]*F[:R]`` + ================ ================= ============== ===================================== + +``BlasFloat`` refers to any of: ``Float32``, ``Float64``, ``Complex64`` or ``Complex128``. + +The individual components of the factorization ``F`` can be accessed by indexing: + + =========== ============================================= ================== ===================== ================== + Component Description ``QR`` ``QRCompactWY`` ``QRPivoted`` + ----------- --------------------------------------------- ------------------ --------------------- ------------------ + ``F[:Q]`` ``Q`` (orthogonal/unitary) part of ``QR`` ✓ (``QRPackedQ``) ✓ (``QRCompactWYQ``) ✓ (``QRPackedQ``) + ``F[:R]`` ``R`` (upper right triangular) part of ``QR`` ✓ ✓ ✓ + ``F[:p]`` pivot ``Vector`` ✓ + ``F[:P]`` (pivot) permutation ``Matrix`` ✓ + =========== ============================================= ================== ===================== ================== + +The following functions are available for the ``QR`` objects: ``size``, ``\``. When ``A`` is rectangular, ``\`` will return a least squares solution and if the solution is not unique, the one with smallest norm is returned. + +Multiplication with respect to either thin or full ``Q`` is allowed, i.e. both ``F[:Q]*F[:R]`` and ``F[:Q]*A`` are supported. A ``Q`` matrix can be converted into a regular matrix with :func:`full` which has a named argument ``thin``. + +.. note:: + + ``qrfact`` returns multiple types because LAPACK uses several representations that minimize the memory storage requirements of products of Householder elementary reflectors, so that the ``Q`` and ``R`` matrices can be stored compactly rather as two separate dense matrices. + + The data contained in ``QR`` or ``QRPivoted`` can be used to construct the ``QRPackedQ`` type, which is a compact representation of the rotation matrix: + + .. math:: + + Q = \prod_{i=1}^{\min(m,n)} (I - \tau_i v_i v_i^T) + + where :math:`\tau_i` is the scale factor and :math:`v_i` is the projection vector associated with the :math:`i^{th}` Householder elementary reflector. + + The data contained in ``QRCompactWY`` can be used to construct the ``QRCompactWYQ`` type, which is a compact representation of the rotation matrix + + .. math:: + + Q = I + Y T Y^T + + where ``Y`` is :math:`m \times r` lower trapezoidal and ``T`` is :math:`r \times r` upper triangular. The *compact WY* representation [Schreiber1989]_ is not to be confused with the older, *WY* representation [Bischof1987]_. (The LAPACK documentation uses ``V`` in lieu of ``Y``.) + +.. [Bischof1987] C Bischof and C Van Loan, The WY representation for products of Householder matrices, SIAM J Sci Stat Comput 8 (1987), s2-s13. doi:10.1137/0908009 +.. [Schreiber1989] R Schreiber and C Van Loan, A storage-efficient WY representation for products of Householder transformations, SIAM J Sci Stat Comput 10 (1989), 53-57. doi:10.1137/0910005 + +:: + qrfact(A) -> SPQR.Factorization + +Compute the QR factorization of a sparse matrix ``A``. A fill-reducing permutation is used. The main application of this type is to solve least squares problems with ``\``. The function calls the C library SPQR and a few additional functions from the library are wrapped but not exported. +``` +""" +qrfact + +doc""" +```rst +:: + +(x, y...) + +Addition operator. ``x+y+z+...`` calls this function with all arguments, i.e. +``+(x, y, z, ...)``. +``` +""" ++ + +doc""" +```rst +:: + identity(x) + +The identity function. Returns its argument. +``` +""" +identity + +doc""" +```rst +:: + iseven(x::Integer) -> Bool + +Returns ``true`` is ``x`` is even (that is, divisible by 2), and ``false`` otherwise. + +.. doctest:: + + julia> iseven(9) + false + + julia> iseven(10) + true +``` +""" +iseven + +doc""" +```rst +:: + setindex!(A, X, inds...) + +Store values from array ``X`` within some subset of ``A`` as specified by ``inds``. + +:: + setindex!(collection, value, key...) + +Store the given value at the given key or index within a collection. +The syntax ``a[i,j,...] = x`` is converted by the compiler to +``setindex!(a, x, i, j, ...)``. +``` +""" +setindex! + +doc""" +```rst +:: + signif(x, digits, [base]) + +Rounds (in the sense of ``round``) ``x`` so that there are ``digits`` significant digits, under a base ``base`` representation, default 10. E.g., ``signif(123.456, 2)`` is ``120.0``, and ``signif(357.913, 4, 2)`` is ``352.0``. +``` +""" +signif + +doc""" +```rst +:: + sprandbool(m,n,p) + +Create a random ``m`` by ``n`` sparse boolean matrix with the specified (independent) probability ``p`` of any entry being ``true``. +``` +""" +sprandbool + +doc""" +```rst +:: + nextpow2(n) + +The smallest power of two not less than ``n``. Returns 0 for ``n==0``, and returns +``-nextpow2(-n)`` for negative arguments. +``` +""" +nextpow2 + +doc""" +```rst +:: + ipermute!(v, p) + +Like permute!, but the inverse of the given permutation is applied. +``` +""" +ipermute! + +doc""" +```rst +:: + full(S) + +Convert a sparse matrix ``S`` into a dense matrix. + +:: + full(F) + +Reconstruct the matrix ``A`` from the factorization ``F=factorize(A)``. + +:: + full(QRCompactWYQ[, thin=true]) -> Matrix + +Converts an orthogonal or unitary matrix stored as a ``QRCompactWYQ`` +object, i.e. in the compact WY format [Bischof1987]_, to a dense matrix. + +Optionally takes a ``thin`` Boolean argument, which if ``true`` omits the +columns that span the rows of ``R`` in the QR factorization that are zero. +The resulting matrix is the ``Q`` in a thin QR factorization (sometimes +called the reduced QR factorization). If ``false``, returns a ``Q`` that +spans all rows of ``R`` in its corresponding QR factorization. +``` +""" +full + +doc""" +```rst +:: + map(f, c...) -> collection + +Transform collection ``c`` by applying ``f`` to each element. +For multiple collection arguments, apply ``f`` elementwise. + +.. doctest:: + + julia> map((x) -> x * 2, [1, 2, 3]) + 3-element Array{Int64,1}: + 2 + 4 + 6 + + julia> map(+, [1, 2, 3], [10, 20, 30]) + 3-element Array{Int64,1}: + 11 + 22 + 33 +``` +""" +map + +doc""" +```rst +:: + @parallel + +A parallel for loop of the form :: + + @parallel [reducer] for var = range + body + end + +The specified range is partitioned and locally executed across all workers. +In case an optional reducer function is specified, @parallel performs local +reductions on each worker with a final reduction on the calling process. + +Note that without a reducer function, @parallel executes asynchronously, +i.e. it spawns independent tasks on all available workers and returns +immediately without waiting for completion. To wait for completion, prefix +the call with ``@sync``, like :: + + @sync @parallel for var = range + body + end +``` +""" +:@parallel + +doc""" +```rst +:: + throw(e) + +Throw an object as an exception +``` +""" +throw + +doc""" +```rst +:: + isxdigit(c::Union{Char,AbstractString}) -> Bool + +Tests whether a character is a valid hexadecimal digit, or whether this +is true for all elements of a string. +``` +""" +isxdigit + +doc""" +```rst +:: + fill(x, dims) + +Create an array filled with the value ``x``. +For example, ``fill(1.0, (10,10))`` returns a 10x10 array of floats, with each +element initialized to 1.0. + +If ``x`` is an object reference, all elements will refer to the same object. +``fill(Foo(), dims)`` will return an array filled with the result of evaluating ``Foo()`` once. +``` +""" +fill + +doc""" +```rst +:: + rol!(dest::BitArray{1}, src::BitArray{1}, i::Integer) -> BitArray{1} + +Performs a left rotation operation on ``src`` and put the result into ``dest``. + +:: + rol!(B::BitArray{1}, i::Integer) -> BitArray{1} + +Performs a left rotation operation on B. +``` +""" +rol! + +doc""" +```rst +:: + issubset(a, b) + ⊆(A,S) -> Bool + ⊈(A,S) -> Bool + ⊊(A,S) -> Bool + +Determine whether every element of ``a`` is also in ``b``, using :func:`in`. + +:: + issubset(A, S) -> Bool + ⊆(A,S) -> Bool + +True if A is a subset of or equal to S. +``` +""" +issubset + +doc""" +```rst +:: + istriu(A) -> Bool + +Test whether a matrix is upper triangular. +``` +""" +istriu + +doc""" +```rst +:: + map!(function, collection) + +In-place version of :func:`map`. + +:: + map!(function, destination, collection...) + +Like :func:`map`, but stores the result in ``destination`` rather than a +new collection. ``destination`` must be at least as large as the first +collection. +``` +""" +map! + +doc""" +```rst +:: + unescape_string(s::AbstractString) -> AbstractString + +General unescaping of traditional C and Unicode escape sequences. Reverse of :func:`escape_string`. See also :func:`print_unescaped`. +``` +""" +unescape_string + +doc""" +```rst +:: + redirect_stdout() + +Create a pipe to which all C and Julia level STDOUT output will be redirected. Returns a tuple (rd,wr) +representing the pipe ends. Data written to STDOUT may now be read from the rd end of the pipe. The +wr end is given for convenience in case the old STDOUT object was cached by the user and needs to be +replaced elsewhere. + +:: + redirect_stdout(stream) + +Replace STDOUT by stream for all C and julia level output to STDOUT. Note that `stream` must be a TTY, a Pipe or a +TcpSocket. +``` +""" +redirect_stdout + +doc""" +```rst +:: + print_with_color(color::Symbol, [io], strings...) + +Print strings in a color specified as a symbol, for example ``:red`` or ``:blue``. +``` +""" +print_with_color + +doc""" +```rst +:: + stringmime(mime, x) + +Returns an ``AbstractString`` containing the representation of ``x`` in the +requested ``mime`` type. This is similar to ``reprmime`` except +that binary data is base64-encoded as an ASCII string. +``` +""" +stringmime + +doc""" +```rst +:: + ischardev(path) -> Bool + +Returns ``true`` if ``path`` is a character device, ``false`` otherwise. +``` +""" +ischardev + +doc""" +```rst +:: + zero(x) + +Get the additive identity element for the type of x (x can also specify the type itself). +``` +""" +zero + +doc""" +```rst +:: + any(itr) -> Bool + +Test whether any elements of a boolean collection are true. + +:: + any(A, dims) + +Test whether any values along the given dimensions of an array are true. + +:: + any(p, itr) -> Bool + +Determine whether predicate ``p`` returns true for any elements of ``itr``. +``` +""" +any + +doc""" +```rst +:: + plan_ifft(A [, dims]; flags=FFTW.ESTIMATE; timelimit=Inf) + +Same as :func:`plan_fft`, but produces a plan that performs inverse transforms +:func:`ifft`. +``` +""" +plan_ifft + +doc""" +```rst +:: + cosc(x) + +Compute :math:`\cos(\pi x) / x - \sin(\pi x) / (\pi x^2)` if :math:`x \neq 0`, and :math:`0` +if :math:`x = 0`. This is the derivative of ``sinc(x)``. +``` +""" +cosc + +doc""" +```rst +:: + getkey(collection, key, default) + +Return the key matching argument ``key`` if one exists in ``collection``, otherwise return ``default``. +``` +""" +getkey + +doc""" +```rst +:: + At_ldiv_Bt(...) + +Matrix operator A\ :sup:`T` \\ B\ :sup:`T` +``` +""" +At_ldiv_Bt + +doc""" +```rst +:: + Ac_mul_Bc(...) + +Matrix operator A\ :sup:`H` B\ :sup:`H` +``` +""" +Ac_mul_Bc + +doc""" +```rst +:: + acotd(x) + +Compute the inverse cotangent of ``x``, where the output is in degrees +``` +""" +acotd + +doc""" +```rst +:: + zeros(type, dims) + +Create an array of all zeros of specified type. The type defaults to Float64 if not specified. + +:: + zeros(A) + +Create an array of all zeros with the same element type and shape as A. +``` +""" +zeros + +doc""" +```rst +:: + symbol(x...) -> Symbol + +Create a ``Symbol`` by concatenating the string representations of the arguments together. +``` +""" +symbol + +doc""" +```rst +:: + zeta(s) + +Riemann zeta function :math:`\zeta(s)`. + +:: + zeta(s, z) + +Hurwitz zeta function :math:`\zeta(s, z)`. (This is equivalent to +the Riemann zeta function :math:`\zeta(s)` for the case of ``z=1``.) +``` +""" +zeta + +doc""" +```rst +:: + sprand([rng,] m,n,p [,rfn]) + +Create a random ``m`` by ``n`` sparse matrix, in which the probability of any element being nonzero is independently given by ``p`` (and hence the mean density of nonzeros is also exactly ``p``). Nonzero values are sampled from the distribution specified by ``rfn``. The uniform distribution is used in case ``rfn`` is not specified. The optional ``rng`` argument specifies a random number generator, see :ref:`Random Numbers `. +``` +""" +sprand + +doc""" +```rst +:: + A_mul_Bt(...) + +Matrix operator A B\ :sup:`T` +``` +""" +A_mul_Bt + +doc""" +```rst +:: + vecnorm(A, [p]) + +For any iterable container ``A`` (including arrays of any +dimension) of numbers (or any element type for which ``norm`` is +defined), compute the ``p``-norm (defaulting to ``p=2``) as if +``A`` were a vector of the corresponding length. + +For example, if ``A`` is a matrix and ``p=2``, then this is equivalent +to the Frobenius norm. +``` +""" +vecnorm + +doc""" +```rst +:: + isvalid(value) -> Bool + +Returns true if the given value is valid for its type, +which currently can be one of ``Char``, ``ASCIIString``, ``UTF8String``, ``UTF16String``, or ``UTF32String`` + +:: + isvalid(T, value) -> Bool + +Returns true if the given value is valid for that type. +Types currently can be ``Char``, ``ASCIIString``, ``UTF8String``, ``UTF16String``, or ``UTF32String`` +Values for ``Char`` can be of type ``Char`` or ``UInt32`` +Values for ``ASCIIString`` and ``UTF8String`` can be of that type, or ``Vector{UInt8}`` +Values for ``UTF16String`` can be ``UTF16String`` or ``Vector{UInt16}`` +Values for ``UTF32String`` can be ``UTF32String``, ``Vector{Char}`` or ``Vector{UInt32}`` + +:: + isvalid(str, i) + +Tells whether index ``i`` is valid for the given string +``` +""" +isvalid + +doc""" +```rst +:: + esc(e::ANY) + +Only valid in the context of an Expr returned from a macro. Prevents the macro hygiene pass from turning embedded variables into gensym variables. See the :ref:`man-macros` +section of the Metaprogramming chapter of the manual for more details and examples. +``` +""" +esc + +doc""" +```rst +:: + bitbroadcast(f, As...) + +Like ``broadcast``, but allocates a ``BitArray`` to store the result, rather then an ``Array``. +``` +""" +bitbroadcast + +doc""" +```rst +:: + set_zero_subnormals(yes::Bool) -> Bool + +If ``yes`` is ``false``, subsequent floating-point operations follow +rules for IEEE arithmetic on subnormal values ("denormals"). +Otherwise, floating-point operations are permitted (but not required) +to convert subnormal inputs or outputs to zero. Returns ``true`` +unless ``yes==true`` but the hardware does not support zeroing of +subnormal numbers. + +``set_zero_subnormals(true)`` can speed up some computations on +some hardware. However, it can break identities such as +``(x-y==0) == (x==y)``. +``` +""" +set_zero_subnormals + +doc""" +```rst +:: + take(iter, n) + +An iterator that generates at most the first ``n`` elements of ``iter``. +``` +""" +take + +doc""" +```rst +:: + combinations(array, n) + +Generate all combinations of ``n`` elements from an indexable +object. Because the number of combinations can be very large, this +function returns an iterator object. Use +``collect(combinations(array,n))`` to get an array of all combinations. +``` +""" +combinations + +doc""" +```rst +:: + frexp(val) + +Return ``(x,exp)`` such that ``x`` has a magnitude in the interval ``[1/2, 1)`` or 0, +and val = :math:`x \times 2^{exp}`. +``` +""" +frexp + +doc""" +```rst +:: + sortcols(A, [alg=,] [by=,] [lt=,] [rev=false]) + +Sort the columns of matrix ``A`` lexicographically. +``` +""" +sortcols + +doc""" +```rst +:: + rsplit(string, [chars]; limit=0, keep=true) + +Similar to ``split``, but starting from the end of the string. +``` +""" +rsplit + +doc""" +```rst +:: + trace(M) + +Matrix trace +``` +""" +trace + +doc""" +```rst +:: + runtests([tests=["all"] [, numcores=iceil(CPU_CORES/2) ]]) + +Run the Julia unit tests listed in ``tests``, which can be either a +string or an array of strings, using ``numcores`` processors. (not exported) +``` +""" +runtests + +doc""" +```rst +:: + time_ns() + +Get the time in nanoseconds. The time corresponding to 0 is undefined, and wraps every 5.8 years. +``` +""" +time_ns + +doc""" +```rst +:: + exponent(x) -> Int + +Get the exponent of a normalized floating-point number. +``` +""" +exponent + +doc""" +```rst +:: + rsearchindex(string, substring, [start]) + +Similar to ``rsearch``, but return only the start index at which the substring is found, or 0 if it is not. +``` +""" +rsearchindex + +doc""" +```rst +:: + muladd(x, y, z) + +Combined multiply-add, computes ``x*y+z`` in an efficient manner. +This may on some systems be equivalent to ``x*y+z``, or to +``fma(x,y,z)``. ``muladd`` is used to improve performance. See +``fma``. +``` +""" +muladd + +doc""" +```rst +:: + unsigned(x) -> Unsigned + +Convert a number to an unsigned integer. If the argument is signed, it is reinterpreted as unsigned without checking for negative values. +``` +""" +unsigned + +doc""" +```rst +:: + eigfact(A,[irange,][vl,][vu,][permute=true,][scale=true]) -> Eigen + +Computes the eigenvalue decomposition of ``A``, returning an ``Eigen`` +factorization object ``F`` which contains the eigenvalues in ``F[:values]`` +and the eigenvectors in the columns of the matrix ``F[:vectors]``. +(The ``k``\ th eigenvector can be obtained from the slice ``F[:vectors][:, k]``.) + +The following functions are available for ``Eigen`` objects: ``inv``, +``det``. + +If ``A`` is :class:`Symmetric`, :class:`Hermitian` or :class:`SymTridiagonal`, +it is possible to calculate only a subset of the eigenvalues by specifying +either a :class:`UnitRange` ``irange`` covering indices of the sorted +eigenvalues or a pair ``vl`` and ``vu`` for the lower and upper boundaries +of the eigenvalues. + +For general nonsymmetric matrices it is possible to specify how the matrix +is balanced before the eigenvector calculation. The option ``permute=true`` +permutes the matrix to become closer to upper triangular, and ``scale=true`` +scales the matrix by its diagonal elements to make rows and columns more +equal in norm. The default is ``true`` for both options. + +:: + eigfact(A, B) -> GeneralizedEigen + +Computes the generalized eigenvalue decomposition of ``A`` and ``B``, +returning a ``GeneralizedEigen`` factorization object ``F`` which contains +the generalized eigenvalues in ``F[:values]`` and the generalized +eigenvectors in the columns of the matrix ``F[:vectors]``. (The ``k``\ th +generalized eigenvector can be obtained from the slice ``F[:vectors][:, +k]``.) +``` +""" +eigfact + +doc""" +```rst +:: + plan_brfft(A, d [, dims]; flags=FFTW.ESTIMATE; timelimit=Inf) + +Pre-plan an optimized real-input unnormalized transform, similar to +:func:`plan_rfft` except for :func:`brfft` instead of :func:`rfft`. +The first two arguments and the size of the transformed result, are +the same as for :func:`brfft`. +``` +""" +plan_brfft + +doc""" +```rst +:: + rowvals(A) + +Return a vector of the row indices of ``A``, and any modifications to the returned vector will mutate ``A`` as well. Given the internal storage format of sparse matrices, providing access to how the row indices are stored internally can be useful in conjuction with iterating over structural nonzero values. See ``nonzeros(A)`` and ``nzrange(A, col)``. +``` +""" +rowvals + +doc""" +```rst +:: + mkdir(path, [mode]) + +Make a new directory with name ``path`` and permissions ``mode``. +``mode`` defaults to 0o777, modified by the current file creation mask. +``` +""" +mkdir + +doc""" +```rst +:: + bytestring(::Ptr{UInt8}, [length]) + +Create a string from the address of a C (0-terminated) string encoded in ASCII or UTF-8. A copy is made; the ptr can be safely freed. If ``length`` is specified, the string does not have to be 0-terminated. + +:: + bytestring(s) + +Convert a string to a contiguous byte array representation appropriate for passing it to C functions. The string will be encoded as either ASCII or UTF-8. +``` +""" +bytestring + +doc""" +```rst +:: + midpoints(e) + +Compute the midpoints of the bins with edges ``e``. The result is a +vector/range of length ``length(e) - 1``. +Note: Julia does not ignore ``NaN`` values in the computation. +``` +""" +midpoints + +doc""" +```rst +:: + .+(x, y) + +Element-wise addition operator. +``` +""" +Base.(:(.+)) + +doc""" +```rst +:: + reverseind(v, i) + +Given an index ``i`` in ``reverse(v)``, return the corresponding +index in ``v`` so that ``v[reverseind(v,i)] == reverse(v)[i]``. +(This can be nontrivial in the case where ``v`` is a Unicode string.) +``` +""" +reverseind + +doc""" +```rst +:: + nan(f) + +Returns NaN (not-a-number) of the floating point type ``f`` or of the same floating point type as ``f`` +``` +""" +nan + +doc""" +```rst +:: + float(x) + +Convert a number, array, or string to a ``AbstractFloat`` data type. For numeric data, the smallest suitable ``AbstractFloat`` type is used. Converts strings to ``Float64``. +``` +""" +float + +doc""" +```rst +:: + include(path::AbstractString) + +Evaluate the contents of a source file in the current context. During including, a task-local include path is set to the directory containing the file. Nested calls to ``include`` will search relative to that path. All paths refer to files on node 1 when running in parallel, and files will be fetched from node 1. This function is typically used to load source interactively, or to combine files in packages that are broken into multiple source files. +``` +""" +include + +doc""" +```rst +:: + randn!([rng], A::Array{Float64,N}) + +Fill the array A with normally-distributed (mean 0, standard deviation 1) random numbers. Also see the rand function. +``` +""" +randn! + +doc""" +```rst +:: + ldexp(x, n) + +Compute :math:`x \times 2^n` +``` +""" +ldexp + +doc""" +```rst +:: + quadgk(f, a,b,c...; reltol=sqrt(eps), abstol=0, maxevals=10^7, order=7, norm=vecnorm) + +Numerically integrate the function ``f(x)`` from ``a`` to ``b``, +and optionally over additional intervals ``b`` to ``c`` and so on. +Keyword options include a relative error tolerance ``reltol`` (defaults +to ``sqrt(eps)`` in the precision of the endpoints), an absolute error +tolerance ``abstol`` (defaults to 0), a maximum number of function +evaluations ``maxevals`` (defaults to ``10^7``), and the ``order`` +of the integration rule (defaults to 7). + +Returns a pair ``(I,E)`` of the estimated integral ``I`` and an +estimated upper bound on the absolute error ``E``. If ``maxevals`` +is not exceeded then ``E <= max(abstol, reltol*norm(I))`` will hold. +(Note that it is useful to specify a positive ``abstol`` in cases where +``norm(I)`` may be zero.) + +The endpoints ``a`` etcetera can also be complex (in which case the +integral is performed over straight-line segments in the complex +plane). If the endpoints are ``BigFloat``, then the integration +will be performed in ``BigFloat`` precision as well (note: it is +advisable to increase the integration ``order`` in rough proportion +to the precision, for smooth integrands). More generally, the +precision is set by the precision of the integration endpoints +(promoted to floating-point types). + +The integrand ``f(x)`` can return any numeric scalar, vector, or matrix +type, or in fact any type supporting ``+``, ``-``, multiplication +by real values, and a ``norm`` (i.e., any normed vector space). +Alternatively, a different norm can be specified by passing a `norm`-like +function as the `norm` keyword argument (which defaults to `vecnorm`). + +[Only one-dimensional integrals are provided by this function. For +multi-dimensional integration (cubature), there are many different +algorithms (often much better than simple nested 1d integrals) +and the optimal choice tends to be very problem-dependent. See +the Julia external-package listing for available algorithms for +multidimensional integration or other specialized tasks (such as +integrals of highly oscillatory or singular functions).] + +The algorithm is an adaptive Gauss-Kronrod integration technique: +the integral in each interval is estimated using a Kronrod rule +(``2*order+1`` points) and the error is estimated using an embedded +Gauss rule (``order`` points). The interval with the largest +error is then subdivided into two intervals and the process is repeated +until the desired error tolerance is achieved. + +These quadrature rules work best for smooth functions within each +interval, so if your function has a known discontinuity or other +singularity, it is best to subdivide your interval to put the +singularity at an endpoint. For example, if ``f`` has a discontinuity +at ``x=0.7`` and you want to integrate from 0 to 1, you should use +``quadgk(f, 0,0.7,1)`` to subdivide the interval at the point of +discontinuity. The integrand is never evaluated exactly at the endpoints +of the intervals, so it is possible to integrate functions that diverge +at the endpoints as long as the singularity is integrable (for example, +a ``log(x)`` or ``1/sqrt(x)`` singularity). + +For real-valued endpoints, the starting and/or ending points may be +infinite. (A coordinate transformation is performed internally to +map the infinite interval to a finite one.) +``` +""" +quadgk + +doc""" +```rst +:: + hist(v[, n]) -> e, counts + +Compute the histogram of ``v``, optionally using approximately ``n`` +bins. The return values are a range ``e``, which correspond to the +edges of the bins, and ``counts`` containing the number of elements of +``v`` in each bin. +Note: Julia does not ignore ``NaN`` values in the computation. + +:: + hist(v, e) -> e, counts + +Compute the histogram of ``v`` using a vector/range ``e`` as the edges for +the bins. The result will be a vector of length ``length(e) - 1``, such that the +element at location ``i`` satisfies ``sum(e[i] .< v .<= e[i+1])``. +Note: Julia does not ignore ``NaN`` values in the computation. +``` +""" +hist + +doc""" +```rst +:: + islower(c::Union{Char,AbstractString}) -> Bool + +Tests whether a character is a lowercase letter, or whether this +is true for all elements of a string. A character is classified as lowercase +if it belongs to Unicode category Ll, Letter: Lowercase. +``` +""" +islower + +doc""" +```rst +:: + nthperm!(v, k) + +In-place version of :func:`nthperm`. +``` +""" +nthperm! + +doc""" +```rst +:: + cell(dims) + +Construct an uninitialized cell array (heterogeneous array). ``dims`` can be either a tuple or a series of integer arguments. +``` +""" +cell + +doc""" +```rst +:: + readbytes(stream, nb=typemax(Int); all=true) + +Read at most ``nb`` bytes from the stream, returning a ``Vector{UInt8}`` of the bytes read. + +If ``all`` is true (the default), this function will block repeatedly +trying to read all requested bytes, until an error or end-of-file +occurs. +If ``all`` is false, at most one ``read`` call is performed, and the +amount of data returned is device-dependent. +Note that not all stream types support the ``all`` option. +``` +""" +readbytes + +doc""" +```rst +:: + eig(A,[irange,][vl,][vu,][permute=true,][scale=true]) -> D, V + +Computes eigenvalues and eigenvectors of ``A``. See :func:`eigfact` for +details on the ``balance`` keyword argument. + +.. doctest:: + + julia> eig([1.0 0.0 0.0; 0.0 3.0 0.0; 0.0 0.0 18.0]) + ([1.0,3.0,18.0], + 3x3 Array{Float64,2}: + 1.0 0.0 0.0 + 0.0 1.0 0.0 + 0.0 0.0 1.0) + +``eig`` is a wrapper around :func:`eigfact`, extracting all parts of the +factorization to a tuple; where possible, using :func:`eigfact` is +recommended. + +:: + eig(A, B) -> D, V + +Computes generalized eigenvalues and vectors of ``A`` with respect to ``B``. + +``eig`` is a wrapper around :func:`eigfact`, extracting all parts of the +factorization to a tuple; where possible, using :func:`eigfact` is +recommended. +``` +""" +eig + +doc""" +```rst +:: + exp2(x) + +Compute :math:`2^x` +``` +""" +exp2 + +doc""" +```rst +:: + gcd(x,y) + +Greatest common (positive) divisor (or zero if x and y are both zero). +``` +""" +gcd + +doc""" +```rst +:: + signbit(x) + +Returns ``true`` if the value of the sign of ``x`` is negative, otherwise ``false``. +``` +""" +signbit + +doc""" +```rst +:: + istaskstarted(task) -> Bool + +Tell whether a task has started executing. +``` +""" +istaskstarted + +doc""" +```rst +:: + clamp(x, lo, hi) + +Return x if ``lo <= x <= hi``. If ``x < lo``, return ``lo``. If ``x > hi``, return ``hi``. Arguments are promoted to a common type. Operates elementwise over ``x`` if it is an array. +``` +""" +clamp + +doc""" +```rst +:: + plan_dct(A [, dims [, flags [, timelimit]]]) + +Pre-plan an optimized discrete cosine transform (DCT), similar to +:func:`plan_fft` except producing a function that computes :func:`dct`. +The first two arguments have the same meaning as for :func:`dct`. +``` +""" +plan_dct + +doc""" +```rst +:: + cscd(x) + +Compute the cosecant of ``x``, where ``x`` is in degrees +``` +""" +cscd + +doc""" +```rst +:: + tryparse(type, str, [base]) + +Like ``parse``, but returns a ``Nullable`` of the requested type. +The result will be null if the string does not contain a valid number. +``` +""" +tryparse + +doc""" +```rst +:: + lexless(x, y) + +Determine whether ``x`` is lexicographically less than ``y``. +``` +""" +lexless + +doc""" +```rst +:: + all!(r, A) + +Test whether all values in ``A`` along the singleton dimensions of ``r`` are true, +and write results to ``r``. +``` +""" +all! + +doc""" +```rst +:: + is_assigned_char(c) -> Bool + +Returns true if the given char or integer is an assigned Unicode code point. +``` +""" +is_assigned_char + +doc""" +```rst +:: + exit([code]) + +Quit (or control-D at the prompt). The default exit code is zero, indicating that the processes completed successfully. +``` +""" +exit + +doc""" +```rst +:: + nonzeros(A) + +Return a vector of the structural nonzero values in sparse matrix ``A``. This includes zeros that are explicitly stored in the sparse matrix. The returned vector points directly to the internal nonzero storage of ``A``, and any modifications to the returned vector will mutate ``A`` as well. See ``rowvals(A)`` and ``nzrange(A, col)``. +``` +""" +nonzeros + +doc""" +```rst +:: + istext(m::MIME) + +Determine whether a MIME type is text data. +``` +""" +istext + +doc""" +```rst +:: + merge!(collection, others...) + +Update collection with pairs from the other collections +``` +""" +merge! + +doc""" +```rst +:: + realpath(path::AbstractString) -> AbstractString + +Canonicalize a path by expanding symbolic links and removing "." and ".." entries. +``` +""" +realpath + +doc""" +```rst +:: + skipchars(stream, predicate; linecomment::Char) + +Advance the stream until before the first character for which ``predicate`` returns false. For example ``skipchars(stream, isspace)`` will skip all whitespace. If keyword argument ``linecomment`` is specified, characters from that character through the end of a line will also be skipped. +``` +""" +skipchars + +doc""" +```rst +:: + realmin(type) + +The smallest in absolute value non-subnormal value representable by the given floating-point type +``` +""" +realmin + +doc""" +```rst +:: + union!(s, iterable) + +Union each element of ``iterable`` into set ``s`` in-place. +``` +""" +union! + +doc""" +```rst +:: + At_ldiv_B(...) + +Matrix operator A\ :sup:`T` \\ B +``` +""" +At_ldiv_B + +doc""" +```rst +:: + dot(x, y) + ⋅(x,y) + +Compute the dot product. For complex vectors, the first vector is conjugated. +``` +""" +dot + +doc""" +```rst +:: + cond(M, [p]) + +Condition number of the matrix ``M``, computed using the operator ``p``-norm. Valid values for ``p`` are ``1``, ``2`` (default), or ``Inf``. +``` +""" +cond + +doc""" +```rst +:: + deepcopy(x) + +Create a deep copy of ``x``: everything is copied recursively, resulting in a fully independent object. For example, deep-copying an array produces a new array whose elements are deep copies of the original elements. Calling `deepcopy` on an object should generally have the same effect as serializing and then deserializing it. + +As a special case, functions can only be actually deep-copied if they are anonymous, otherwise they are just copied. The difference is only relevant in the case of closures, i.e. functions which may contain hidden internal references. + +While it isn't normally necessary, user-defined types can override the default ``deepcopy`` behavior by defining a specialized version of the function ``deepcopy_internal(x::T, dict::ObjectIdDict)`` (which shouldn't otherwise be used), where ``T`` is the type to be specialized for, and ``dict`` keeps track of objects copied so far within the recursion. Within the definition, ``deepcopy_internal`` should be used in place of ``deepcopy``, and the ``dict`` variable should be updated as appropriate before returning. +``` +""" +deepcopy + +doc""" +```rst +:: + widen(type | x) + +If the argument is a type, return a "larger" type (for numeric types, this will be +a type with at least as much range and precision as the argument, and usually more). +Otherwise the argument ``x`` is converted to ``widen(typeof(x))``. + +.. doctest:: + + julia> widen(Int32) + Int64 + +.. doctest:: + + julia> widen(1.5f0) + 1.5 +``` +""" +widen + +doc""" +```rst +:: + @eval + +Evaluate an expression and return the value. +``` +""" +:@eval + +doc""" +```rst +:: + eval([m::Module], expr::Expr) + +Evaluate an expression in the given module and return the result. +Every module (except those defined with ``baremodule``) has its own 1-argument definition +of ``eval``, which evaluates expressions in that module. +``` +""" +eval + +doc""" +```rst +:: + Set([itr]) + +Construct a :obj:`Set` of the values generated by the given iterable object, or an empty set. +Should be used instead of :obj:`IntSet` for sparse integer sets, or for sets of arbitrary objects. +``` +""" +Set + +doc""" +```rst +:: + erf(x) + +Compute the error function of ``x``, defined by +:math:`\frac{2}{\sqrt{\pi}} \int_0^x e^{-t^2} dt` +for arbitrary complex ``x``. +``` +""" +erf + +doc""" +```rst +:: + lcm(x,y) + +Least common (non-negative) multiple. +``` +""" +lcm + +doc""" +```rst +:: + isprint(c::Union{Char,AbstractString}) -> Bool + +Tests whether a character is printable, including spaces, but not a control character. For strings, tests whether this is true for all elements of the string. +``` +""" +isprint + +doc""" +```rst +:: + splitdir(path::AbstractString) -> (AbstractString,AbstractString) + +Split a path into a tuple of the directory name and file name. +``` +""" +splitdir + +doc""" +```rst +:: + sign(x) + +Return ``+1`` if ``x`` is positive, ``0`` if ``x == 0``, and ``-1`` if ``x`` is negative. +``` +""" +sign + +doc""" +```rst +:: + signed(x) + +Convert a number to a signed integer. If the argument is unsigned, it is reinterpreted as signed without checking for overflow. +``` +""" +signed + +doc""" +```rst +:: + Val{c} + +Create a "value type" out of ``c``, which must be an ``isbits`` +value. The intent of this construct is to be able to dispatch on +constants, e.g., ``f(Val{false})`` allows you to dispatch directly +(at compile-time) to an implementation ``f(::Type{Val{false}})``, +without having to test the boolean value at runtime. +``` +""" +Val + +doc""" +```rst +:: + iswritable(path) -> Bool + +Returns ``true`` if the current user has permission to write to ``path``, +``false`` otherwise. +``` +""" +iswritable + +doc""" +```rst +:: + |(x, y) + +Bitwise or +``` +""" +Base.(:(|)) + +doc""" +```rst +:: + yieldto(task, arg = nothing) + +Switch to the given task. The first time a task is switched to, the task's function is called with no arguments. On subsequent switches, ``arg`` is returned from the task's last call to ``yieldto``. This is a low-level call that only switches tasks, not considering states or scheduling in any way. Its use is discouraged. +``` +""" +yieldto + +doc""" +```rst +:: + readandwrite(command) + +Starts running a command asynchronously, and returns a tuple (stdout,stdin,process) of the output stream and input stream of the process, and the process object itself. +``` +""" +readandwrite + +doc""" +```rst +:: + splitdrive(path::AbstractString) -> (AbstractString,AbstractString) + +On Windows, split a path into the drive letter part and the path part. On Unix +systems, the first component is always the empty string. +``` +""" +splitdrive + +doc""" +```rst +:: + pop!(collection, key[, default]) + +Delete and return the mapping for ``key`` if it exists in ``collection``, otherwise return ``default``, or throw an error if default is not specified. + +:: + pop!(collection) -> item + +Remove the last item in ``collection`` and return it. + +.. doctest:: + + julia> A=[1, 2, 3, 4, 5, 6] + 6-element Array{Int64,1}: + 1 + 2 + 3 + 4 + 5 + 6 + + julia> pop!(A) + 6 + + julia> A + 5-element Array{Int64,1}: + 1 + 2 + 3 + 4 + 5 +``` +""" +pop! + +doc""" +```rst +:: + filter(function, collection) + +Return a copy of ``collection``, removing elements for which ``function`` is false. +For associative collections, the function is passed two arguments (key and value). +``` +""" +filter + +doc""" +```rst +:: + plan_idct!(A [, dims [, flags [, timelimit]]]) + +Same as :func:`plan_idct`, but operates in-place on ``A``. +``` +""" +plan_idct! + +doc""" +```rst +:: + randperm([rng,] n) + +Construct a random permutation of length ``n``. The optional ``rng`` argument +specifies a random number generator, see :ref:`Random Numbers `. +``` +""" +randperm + +doc""" +```rst +:: + seekend(s) + +Seek a stream to its end. +``` +""" +seekend + +doc""" +```rst +:: + plan_ifft!(A [, dims]; flags=FFTW.ESTIMATE; timelimit=Inf) + +Same as :func:`plan_ifft`, but operates in-place on ``A``. +``` +""" +plan_ifft! + +doc""" +```rst +:: + DivideError() + +Integer division was attempted with a denominator value of 0. +``` +""" +DivideError + +doc""" +```rst +:: + AssertionError([msg]) + +The asserted condition did not evalutate to ``true``. +``` +""" +AssertionError + +doc""" +```rst +:: + ror(B::BitArray{1}, i::Integer) -> BitArray{1} + +Performs a right rotation operation. +``` +""" +ror + +doc""" +```rst +:: + Ac_ldiv_Bc(...) + +Matrix operator A\ :sup:`H` \\ B\ :sup:`H` +``` +""" +Ac_ldiv_Bc + +doc""" +```rst +:: + rfft(A [, dims]) + +Multidimensional FFT of a real array A, exploiting the fact that +the transform has conjugate symmetry in order to save roughly half +the computational time and storage costs compared with :func:`fft`. +If ``A`` has size ``(n_1, ..., n_d)``, the result has size +``(div(n_1,2)+1, ..., n_d)``. + +The optional ``dims`` argument specifies an iterable subset of one or +more dimensions of ``A`` to transform, similar to :func:`fft`. Instead +of (roughly) halving the first dimension of ``A`` in the result, the +``dims[1]`` dimension is (roughly) halved in the same way. +``` +""" +rfft + +doc""" +```rst +:: + @enum EnumName EnumValue1[=x] EnumValue2[=y] + +Create an :obj:`Enum` type with name ``EnumName`` and enum member values of ``EnumValue1`` and ``EnumValue2`` with optional assigned values of ``x`` and ``y``, respectively. ``EnumName`` can be used just like other types and enum member values as regular values, such as + +.. doctest:: + + julia> @enum FRUIT apple=1 orange=2 kiwi=3 + + julia> f(x::FRUIT) = "I'm a FRUIT with value: $(Int(x))" + f (generic function with 1 method) + + julia> f(apple) + "I'm a FRUIT with value: 1" +``` +""" +:@enum + +doc""" +```rst +:: + asind(x) + +Compute the inverse sine of ``x``, where the output is in degrees +``` +""" +asind + +doc""" +```rst +:: + widemul(x, y) + +Multiply ``x`` and ``y``, giving the result as a larger type. +``` +""" +widemul + +doc""" +```rst +:: + unsafe_pointer_to_objref(p::Ptr) + +Convert a ``Ptr`` to an object reference. Assumes the pointer refers to a +valid heap-allocated Julia object. If this is not the case, undefined behavior +results, hence this function is considered "unsafe" and should be used with care. +``` +""" +unsafe_pointer_to_objref + +doc""" +```rst +:: + chomp(string) + +Remove a trailing newline from a string +``` +""" +chomp + +doc""" +```rst +:: + enumerate(iter) + +An iterator that yields ``(i, x)`` where ``i`` is an index starting at 1, and ``x`` is the ``i``\ th value from the given iterator. It's useful when you need not only the values ``x`` over which you are iterating, but also the index ``i`` of the iterations. + +.. doctest:: + + julia> a = ["a", "b", "c"]; + + julia> for (index, value) in enumerate(a) + println("$index $value") + end + 1 a + 2 b + 3 c +``` +""" +enumerate + +doc""" +```rst +:: + >=(x, y) + ≥(x,y) + +Greater-than-or-equals comparison operator. +``` +""" +Base.(:(>=)) + +doc""" +```rst +:: + dawson(x) + +Compute the Dawson function (scaled imaginary error function) of ``x``, +defined by :math:`\frac{\sqrt{\pi}}{2} e^{-x^2} \operatorname{erfi}(x)`. +``` +""" +dawson + +doc""" +```rst +:: + current_task() + +Get the currently running Task. +``` +""" +current_task + +# Dates + +doc""" +```rst +:: + firstdayofweek(dt::TimeType) -> TimeType + + Adjusts ``dt`` to the Monday of its week. +``` +""" +Dates.firstdayofweek + +doc""" +```rst +:: + datetime2unix(dt::DateTime) -> Float64 + +Takes the given DateTime and returns the number of seconds since +the unix epoch as a ``Float64``. +``` +""" +Dates.datetime2unix + +doc""" +```rst +:: + dayofweekofmonth(dt::TimeType) -> Int + + For the day of week of ``dt``, returns which number it is in ``dt``'s month. + So if the day of the week of ``dt`` is Monday, then ``1 = First Monday of the month, + 2 = Second Monday of the month, etc.`` In the range 1:5. +``` +""" +Dates.dayofweekofmonth + +doc""" +```rst +:: + monthabbr(dt::TimeType; locale="english") -> AbstractString + +Return the abbreviated month name of the Date or DateTime in the given ``locale``. +``` +""" +Dates.monthabbr + +doc""" +```rst +:: + datetime2julian(dt::DateTime) -> Float64 + +Takes the given DateTime and returns the number of Julian calendar days +since the julian epoch as a ``Float64``. +``` +""" +Dates.datetime2julian + +doc""" +```rst +:: + dayabbr(dt::TimeType; locale="english") -> AbstractString + +Return the abbreviated name corresponding to the day of the week +of the Date or DateTime in the given ``locale``. +``` +""" +Dates.dayabbr + +doc""" +```rst +:: + DateTime(y, [m, d, h, mi, s, ms]) -> DateTime + +Construct a DateTime type by parts. Arguments must be convertible to +``Int64``. + +:: + DateTime(periods::Period...) -> DateTime + +Constuct a DateTime type by ``Period`` type parts. Arguments may be in any order. +DateTime parts not provided will default to the value of ``Dates.default(period)``. + +:: + DateTime(f::Function, y[, m, d, h, mi, s]; step=Day(1), negate=false, limit=10000) -> DateTime + + Create a DateTime through the adjuster API. The starting point will be constructed from the + provided ``y, m, d...`` arguments, and will be adjusted until ``f::Function`` returns true. The step size in + adjusting can be provided manually through the ``step`` keyword. If ``negate=true``, then the adjusting + will stop when ``f::Function`` returns false instead of true. ``limit`` provides a limit to + the max number of iterations the adjustment API will pursue before throwing an error (in the case that ``f::Function`` + is never satisfied). + +:: + DateTime(dt::Date) -> DateTime + + Converts a ``Date`` type to a ``DateTime``. The hour, minute, second, and millisecond + parts of the new ``DateTime`` are assumed to be zero. + +:: + DateTime(dt::AbstractString, format::AbstractString; locale="english") -> DateTime + +Construct a DateTime type by parsing the ``dt`` date string following the pattern given in +the ``format`` string. The following codes can be used for constructing format strings: + +=============== ========= =============================================================== +Code Matches Comment +--------------- --------- --------------------------------------------------------------- +``y`` 1996, 96 Returns year of 1996, 0096 +``m`` 1, 01 Matches 1 or 2-digit months +``u`` Jan Matches abbreviated months according to the ``locale`` keyword +``U`` January Matches full month names according to the ``locale`` keyword +``d`` 1, 01 Matches 1 or 2-digit days +``H`` 00 Matches hours +``M`` 00 Matches minutes +``S`` 00 Matches seconds +``s`` .500 Matches milliseconds +``e`` Mon, Tues Matches abbreviated days of the week +``E`` Monday Matches full name days of the week +``yyyymmdd`` 19960101 Matches fixed-width year, month, and day +=============== ========= =============================================================== + +All characters not listed above are treated as delimiters between date and time slots. +So a ``dt`` string of "1996-01-15T00:00:00.0" would have a ``format`` string +like "y-m-dTH:M:S.s". + +:: + DateTime(dt::AbstractString, df::DateFormat) -> DateTime + +Similar form as above for parsing a ``DateTime``, but passes a ``DateFormat`` object instead of a raw formatting string. It is more efficient if similarly formatted date strings will be parsed repeatedly to first create a ``DateFormat`` object then use this method for parsing. +``` +""" +Dates.DateTime + +doc""" +```rst +:: + datetime2rata(dt::TimeType) -> Int64 + +Returns the number of Rata Die days since epoch from the +given Date or DateTime. +``` +""" +Dates.datetime2rata + +doc""" +```rst +:: + monthname(dt::TimeType; locale="english") -> AbstractString + +Return the full name of the month of the Date or DateTime in the given ``locale``. +``` +""" +Dates.monthname + +doc""" +```rst +:: + dayname(dt::TimeType; locale="english") -> AbstractString + +Return the full day name corresponding to the day of the week +of the Date or DateTime in the given ``locale``. +``` +""" +Dates.dayname + +doc""" +```rst +:: + Date(y, [m, d]) -> Date + +Construct a ``Date`` type by parts. Arguments must be convertible to +``Int64``. + +:: + Date(period::Period...) -> Date + +Constuct a Date type by ``Period`` type parts. Arguments may be in any order. +Date parts not provided will default to the value of ``Dates.default(period)``. + +:: + Date(f::Function, y[, m]; step=Day(1), negate=false, limit=10000) -> Date + + Create a Date through the adjuster API. The starting point will be constructed from the + provided ``y, m`` arguments, and will be adjusted until ``f::Function`` returns true. The step size in + adjusting can be provided manually through the ``step`` keyword. If ``negate=true``, then the adjusting + will stop when ``f::Function`` returns false instead of true. ``limit`` provides a limit to + the max number of iterations the adjustment API will pursue before throwing an error (given that ``f::Function`` + is never satisfied). + +:: + Date(dt::DateTime) -> Date + + Converts a ``DateTime`` type to a ``Date``. The hour, minute, second, and millisecond + parts of the ``DateTime`` are truncated, so only the year, month and day parts are used in construction. + +:: + Date(dt::AbstractString, format::AbstractString; locale="english") -> Date + +Construct a Date type by parsing a ``dt`` date string following the pattern given in +the ``format`` string. Follows the same conventions as ``DateTime`` above. + +:: + Date(dt::AbstractString, df::DateFormat) -> Date + +Parse a date from a date string ``dt`` using a ``DateFormat`` object ``df``. +``` +""" +Dates.Date + +doc""" +```rst +:: + firstdayofmonth(dt::TimeType) -> TimeType + + Adjusts ``dt`` to the first day of its month. +``` +""" +Dates.firstdayofmonth + +doc""" +```rst +:: + tonext(dt::TimeType,dow::Int;same::Bool=false) -> TimeType + + Adjusts ``dt`` to the next day of week corresponding to ``dow`` with + ``1 = Monday, 2 = Tuesday, etc``. Setting ``same=true`` allows the current + ``dt`` to be considered as the next ``dow``, allowing for no adjustment to occur. + +:: + tonext(func::Function,dt::TimeType;step=Day(1),negate=false,limit=10000,same=false) -> TimeType + + Adjusts ``dt`` by iterating at most ``limit`` iterations by ``step`` increments until + ``func`` returns true. ``func`` must take a single ``TimeType`` argument and return a ``Bool``. + ``same`` allows ``dt`` to be considered in satisfying ``func``. ``negate`` will make the adjustment + process terminate when ``func`` returns false instead of true. +``` +""" +Dates.tonext + +doc""" +```rst +:: + dayofyear(dt::TimeType) -> Int + + Returns the day of the year for ``dt`` with January 1st being day 1. +``` +""" +Dates.dayofyear + +doc""" +```rst +:: + tolast(dt::TimeType,dow::Int;of=Month) -> TimeType + + Adjusts ``dt`` to the last ``dow`` of its month. Alternatively, ``of=Year`` + will adjust to the last ``dow`` of the year. +``` +""" +Dates.tolast + +doc""" +```rst +:: + firstdayofquarter(dt::TimeType) -> TimeType + + Adjusts ``dt`` to the first day of its quarter. +``` +""" +Dates.firstdayofquarter + +doc""" +```rst +:: + julian2datetime(julian_days) -> DateTime + +Takes the number of Julian calendar days since epoch +``-4713-11-24T12:00:00`` and returns the corresponding DateTime. +``` +""" +Dates.julian2datetime + +doc""" +```rst +:: + year(dt::TimeType) -> Int64 + month(dt::TimeType) -> Int64 + week(dt::TimeType) -> Int64 + day(dt::TimeType) -> Int64 + hour(dt::TimeType) -> Int64 + minute(dt::TimeType) -> Int64 + second(dt::TimeType) -> Int64 + millisecond(dt::TimeType) -> Int64 + +Return the field part of a Date or DateTime as an ``Int64``. +``` +""" +Dates.year + +doc""" +```rst +:: + toprev(dt::TimeType,dow::Int;same::Bool=false) -> TimeType + + Adjusts ``dt`` to the previous day of week corresponding to ``dow`` with + ``1 = Monday, 2 = Tuesday, etc``. Setting ``same=true`` allows the current + ``dt`` to be considered as the previous ``dow``, allowing for no adjustment to occur. + +:: + toprev(func::Function,dt::TimeType;step=Day(-1),negate=false,limit=10000,same=false) -> TimeType + + Adjusts ``dt`` by iterating at most ``limit`` iterations by ``step`` increments until + ``func`` returns true. ``func`` must take a single ``TimeType`` argument and return a ``Bool``. + ``same`` allows ``dt`` to be considered in satisfying ``func``. ``negate`` will make the adjustment + process terminate when ``func`` returns false instead of true. +``` +""" +Dates.toprev + +doc""" +```rst +:: + daysinyear(dt::TimeType) -> Int + + Returns 366 if the year of ``dt`` is a leap year, otherwise returns 365. +``` +""" +Dates.daysinyear + +doc""" +```rst +:: + trunc(dt::TimeType, ::Type{Period}) -> TimeType + + Truncates the value of ``dt`` according to the provided ``Period`` type. + E.g. if ``dt`` is ``1996-01-01T12:30:00``, then ``trunc(dt,Day) == 1996-01-01T00:00:00``. +``` +""" +Dates.trunc + +doc""" +```rst +:: + daysinmonth(dt::TimeType) -> Int + + Returns the number of days in the month of ``dt``. Value will be 28, 29, 30, or 31. +``` +""" +Dates.daysinmonth + +doc""" +```rst +:: + yearmonth(dt::TimeType) -> (Int64, Int64) + + Simultaneously return the year and month parts of a Date or DateTime. +``` +""" +Dates.yearmonth + +doc""" +```rst +:: + daysofweekinmonth(dt::TimeType) -> Int + + For the day of week of ``dt``, returns the total number of that day of the week + in ``dt``'s month. Returns 4 or 5. Useful in temporal expressions for specifying + the last day of a week in a month by including ``dayofweekofmonth(dt) == daysofweekinmonth(dt)`` + in the adjuster function. +``` +""" +Dates.daysofweekinmonth + +doc""" +```rst +:: + yearmonthday(dt::TimeType) -> (Int64, Int64, Int64) + + Simultaneously return the year, month, and day parts of a Date or DateTime. +``` +""" +Dates.yearmonthday + +doc""" +```rst +:: + Dates.DateFormat(format::AbstractString) -> DateFormat + +Construct a date formatting object that can be passed repeatedly for parsing similarly formatted date strings. ``format`` is a format string in the form described above (e.g. ``"yyyy-mm-dd"``). +``` +""" +Dates.Dates.DateFormat + +doc""" +```rst +:: + lastdayofweek(dt::TimeType) -> TimeType + + Adjusts ``dt`` to the Sunday of its week. +``` +""" +Dates.lastdayofweek + +doc""" +```rst +:: + recur{T<:TimeType}(func::Function,dr::StepRange{T};negate=false,limit=10000) -> Vector{T} + + ``func`` takes a single TimeType argument and returns a ``Bool`` indicating whether the input + should be "included" in the final set. ``recur`` applies ``func`` over each element in the + range of ``dr``, including those elements for which ``func`` returns ``true`` in the resulting + Array, unless ``negate=true``, then only elements where ``func`` returns ``false`` are included. +``` +""" +Dates.recur + +doc""" +```rst +:: + monthday(dt::TimeType) -> (Int64, Int64) + + Simultaneously return the month and day parts of a Date or DateTime. +``` +""" +Dates.monthday + +doc""" +```rst +:: + default(p::Period) -> Period + + Returns a sensible "default" value for the input Period by returning + ``one(p)`` for Year, Month, and Day, and ``zero(p)`` for Hour, Minute, + Second, and Millisecond. +``` +""" +Dates.default + +doc""" +```rst +:: + unix2datetime(x) -> DateTime + +Takes the number of seconds since unix epoch ``1970-01-01T00:00:00`` +and converts to the corresponding DateTime. +``` +""" +Dates.unix2datetime + +doc""" +```rst +:: + eps(::DateTime) -> Millisecond + eps(::Date) -> Day + +Returns ``Millisecond(1)`` for ``DateTime`` values and ``Day(1)`` for ``Date`` values. +``` +""" +Dates.eps + +doc""" +```rst +:: + firstdayofyear(dt::TimeType) -> TimeType + + Adjusts ``dt`` to the first day of its year. +``` +""" +Dates.firstdayofyear + +doc""" +```rst +:: + rata2datetime(days) -> DateTime + +Takes the number of Rata Die days since epoch ``0000-12-31T00:00:00`` +and returns the corresponding DateTime. +``` +""" +Dates.rata2datetime + +doc""" +```rst +:: + now() -> DateTime + +Returns a DateTime corresponding to the user's system +time including the system timezone locale. + +:: + now(::Type{UTC}) -> DateTime + +Returns a DateTime corresponding to the user's system +time as UTC/GMT. +``` +""" +Dates.now + +doc""" +```rst +:: + isleapyear(dt::TimeType) -> Bool + + Returns true if the year of ``dt`` is a leap year. +``` +""" +Dates.isleapyear + +doc""" +```rst +:: + today() -> Date + + Returns the date portion of ``now()``. +``` +""" +Dates.today + +doc""" +```rst +:: + lastdayofyear(dt::TimeType) -> TimeType + + Adjusts ``dt`` to the last day of its year. +``` +""" +Dates.lastdayofyear + +doc""" +```rst +:: + tofirst(dt::TimeType,dow::Int;of=Month) -> TimeType + + Adjusts ``dt`` to the first ``dow`` of its month. Alternatively, ``of=Year`` + will adjust to the first ``dow`` of the year. +``` +""" +Dates.tofirst + +doc""" +```rst +:: + lastdayofmonth(dt::TimeType) -> TimeType + + Adjusts ``dt`` to the last day of its month. +``` +""" +Dates.lastdayofmonth + +doc""" +```rst +:: + dayofweek(dt::TimeType) -> Int64 + + Returns the day of the week as an ``Int64`` with ``1 = Monday, 2 = Tuesday, etc.``. +``` +""" +Dates.dayofweek + +doc""" +```rst +:: + Year(dt::TimeType) -> Year + Month(dt::TimeType) -> Month + Week(dt::TimeType) -> Week + Day(dt::TimeType) -> Day + Hour(dt::TimeType) -> Hour + Minute(dt::TimeType) -> Minute + Second(dt::TimeType) -> Second + Millisecond(dt::TimeType) -> Millisecond + +Return the field part of a Date or DateTime as a ``Period`` type. + +:: + Year(v) + Month(v) + Week(v) + Day(v) + Hour(v) + Minute(v) + Second(v) + Millisecond(v) + +Construct a ``Period`` type with the given ``v`` value. +Input must be losslessly convertible to an ``Int64``. +``` +""" +Dates.Year + +doc""" +```rst +:: + quarterofyear(dt::TimeType) -> Int + + Returns the quarter that ``dt`` resides in. Range of value is 1:4. +``` +""" +Dates.quarterofyear + +doc""" +```rst +:: + dayofquarter(dt::TimeType) -> Int + + Returns the day of the current quarter of ``dt``. Range of value is 1:92. +``` +""" +Dates.dayofquarter + +doc""" +```rst +:: + lastdayofquarter(dt::TimeType) -> TimeType + + Adjusts ``dt`` to the last day of its quarter. +``` +""" +Dates.lastdayofquarter + +# Base.Pkg + +doc""" +```rst +:: + build() + +Run the build scripts for all installed packages in depth-first recursive order. + +:: + build(pkgs...) + +Run the build script in "deps/build.jl" for each package in ``pkgs`` and all of their dependencies in depth-first recursive order. +This is called automatically by ``Pkg.resolve()`` on all installed or updated packages. +``` +""" +Pkg.build + +doc""" +```rst +:: + init(meta::AbstractString=DEFAULT_META, branch::AbstractString=META_BRANCH) + +Initialize ``Pkg.dir()`` as a package directory. +This will be done automatically when the ``JULIA_PKGDIR`` is not set and ``Pkg.dir()`` uses its default value. +As part of this process, clones a local METADATA git repository from the site and branch specified by its arguments, which +are typically not provided. Explicit (non-default) arguments can be used to support a custom METADATA setup. +``` +""" +Pkg.init + +doc""" +```rst +:: + publish() + +For each new package version tagged in ``METADATA`` not already published, make sure that the tagged package commits have been pushed to the repo at the registered URL for the package and if they all have, open a pull request to ``METADATA``. +``` +""" +Pkg.publish + +doc""" +```rst +:: + pin(pkg) + +Pin ``pkg`` at the current version. +To go back to using the newest compatible released version, use ``Pkg.free(pkg)`` + +:: + pin(pkg, version) + +Pin ``pkg`` at registered version ``version``. +``` +""" +Pkg.pin + +doc""" +```rst +:: + resolve() + +Determines an optimal, consistent set of package versions to install or upgrade to. +The optimal set of package versions is based on the contents of ``Pkg.dir("REQUIRE")`` and the state of installed packages in ``Pkg.dir()``, +Packages that are no longer required are moved into ``Pkg.dir(".trash")``. +``` +""" +Pkg.resolve + +doc""" +```rst +:: + available() -> Vector{ASCIIString} + +Returns the names of available packages. + +:: + available(pkg) -> Vector{VersionNumber} + +Returns the version numbers available for package ``pkg``. +``` +""" +Pkg.available + +doc""" +```rst +:: + register(pkg, [url]) + +Register ``pkg`` at the git URL ``url``, defaulting to the configured origin URL of the git repo ``Pkg.dir(pkg)``. +``` +""" +Pkg.register + +doc""" +```rst +:: + rm(pkg) + +Remove all requirement entries for ``pkg`` from ``Pkg.dir("REQUIRE")`` and call ``Pkg.resolve()``. +``` +""" +Pkg.rm + +doc""" +```rst +:: + free(pkg) + +Free the package ``pkg`` to be managed by the package manager again. +It calls ``Pkg.resolve()`` to determine optimal package versions after. +This is an inverse for both ``Pkg.checkout`` and ``Pkg.pin``. + +You can also supply an iterable collection of package names, e.g., +``Pkg.free(("Pkg1", "Pkg2"))`` to free multiple packages at once. +``` +""" +Pkg.free + +doc""" +```rst +:: + status() + +Prints out a summary of what packages are installed and what version and state they're in. +``` +""" +Pkg.status + +doc""" +```rst +:: + edit() + +Opens ``Pkg.dir("REQUIRE")`` in the editor specified by the ``VISUAL`` or ``EDITOR`` environment variables; +when the editor command returns, it runs ``Pkg.resolve()`` to determine and install a new optimal set of installed package versions. +``` +""" +Pkg.edit + +doc""" +```rst +:: + clone(url, [pkg]) + +Clone a package directly from the git URL ``url``. +The package does not need to be a registered in ``Pkg.dir("METADATA")``. +The package repo is cloned by the name ``pkg`` if provided; +if not provided, ``pkg`` is determined automatically from ``url``. + +:: + clone(pkg) + +If ``pkg`` has a URL registered in ``Pkg.dir("METADATA")``, clone it from that URL on the default branch. +The package does not need to have any registered versions. +``` +""" +Pkg.clone + +doc""" +```rst +:: + checkout(pkg, [branch="master"]) + +Checkout the ``Pkg.dir(pkg)`` repo to the branch ``branch``. +Defaults to checking out the "master" branch. +To go back to using the newest compatible released version, use ``Pkg.free(pkg)`` +``` +""" +Pkg.checkout + +doc""" +```rst +:: + update() + +Update package the metadata repo – kept in ``Pkg.dir("METADATA")`` – then update any fixed packages that can safely be pulled from their origin; +then call ``Pkg.resolve()`` to determine a new optimal set of packages versions. +``` +""" +Pkg.update + +doc""" +```rst +:: + add(pkg, vers...) + +Add a requirement entry for ``pkg`` to ``Pkg.dir("REQUIRE")`` and call ``Pkg.resolve()``. +If ``vers`` are given, they must be ``VersionNumber`` objects and they specify acceptable version intervals for ``pkg``. +``` +""" +Pkg.add + +doc""" +```rst +:: + tag(pkg, [ver, [commit]]) + +Tag ``commit`` as version ``ver`` of package ``pkg`` and create a version entry in ``METADATA``. +If not provided, ``commit`` defaults to the current commit of the ``pkg`` repo. +If ``ver`` is one of the symbols ``:patch``, ``:minor``, ``:major`` the next patch, minor or major version is used. +If ``ver`` is not provided, it defaults to ``:patch``. +``` +""" +Pkg.tag + +doc""" +```rst +:: + test() + +Run the tests for all installed packages ensuring that each package's test dependencies are installed for the duration of the test. A package is tested by running its ``test/runtests.jl`` file and test dependencies are specified in ``test/REQUIRE``. + +:: + test(pkgs...) + +Run the tests for each package in ``pkgs`` ensuring that each package's test dependencies are installed for the duration of the test. A package is tested by running its ``test/runtests.jl`` file and test dependencies are specified in ``test/REQUIRE``. +``` +""" +Pkg.test + +doc""" +```rst +:: + generate(pkg,license) + +Generate a new package named ``pkg`` with one of these license keys: ``"MIT"``, ``"BSD"`` or ``"ASL"``. +If you want to make a package with a different license, you can edit it afterwards. +Generate creates a git repo at ``Pkg.dir(pkg)`` for the package and inside it ``LICENSE.md``, ``README.md``, ``REQUIRE``, the julia entrypoint ``$pkg/src/$pkg.jl``, and Travis and AppVeyor CI configuration files ``.travis.yml`` and ``appveyor.yml``. +``` +""" +Pkg.generate + +doc""" +```rst +:: + dir() -> AbstractString + +Returns the absolute path of the package directory. +This defaults to ``joinpath(homedir(),".julia","v$(VERSION.major).$(VERSION.minor)")`` on all platforms +(i.e. ``~/.julia/v0.4`` in UNIX shell syntax). If the ``JULIA_PKGDIR`` environment variable is set, then +that path is used in the returned value as ``joinpath(ENV["JULIA_PKGDIR"],"v$(VERSION.major).$(VERSION.minor)")``. +If ``JULIA_PKGDIR`` is a relative path, it is interpreted relative to whatever the current working directory is. + +:: + dir(names...) -> AbstractString + +Equivalent to ``normpath(Pkg.dir(),names...)`` – i.e. it appends path components to the package directory and normalizes the resulting path. +In particular, ``Pkg.dir(pkg)`` returns the path to the package ``pkg``. +``` +""" +Pkg.dir + +doc""" +```rst +:: + installed() -> Dict{ASCIIString,VersionNumber} + +Returns a dictionary mapping installed package names to the installed version number of each package. + +:: + installed(pkg) -> Void | VersionNumber + +If ``pkg`` is installed, return the installed version number, otherwise return ``nothing``. +``` +""" +Pkg.installed + From 1d97152eb91644ac3848f76f1f3905042d70180a Mon Sep 17 00:00:00 2001 From: Mike Innes Date: Tue, 7 Jul 2015 21:06:21 +0100 Subject: [PATCH 04/10] include helpdb.jl --- base/sysimg.jl | 1 + 1 file changed, 1 insertion(+) diff --git a/base/sysimg.jl b/base/sysimg.jl index ccb0da02f56dd..c2a416bdb0566 100644 --- a/base/sysimg.jl +++ b/base/sysimg.jl @@ -301,6 +301,7 @@ import .Dates: Date, DateTime, now include("deprecated.jl") # Some basic documentation +include("docs/helpdb.jl") include("docs/basedocs.jl") function __init__() From fa4110d44558a730faba5d7bc4b7cd0acc367c00 Mon Sep 17 00:00:00 2001 From: Mike Innes Date: Fri, 31 Jul 2015 11:26:09 +0100 Subject: [PATCH 05/10] remove newdoc.jl --- doc/newdoc.jl | 103 -------------------------------------------------- 1 file changed, 103 deletions(-) delete mode 100644 doc/newdoc.jl diff --git a/doc/newdoc.jl b/doc/newdoc.jl deleted file mode 100644 index 4694edc040bcb..0000000000000 --- a/doc/newdoc.jl +++ /dev/null @@ -1,103 +0,0 @@ -cd(dirname(@__FILE__)) - -# Load docs from RST into memory - -typealias Docs Dict{UTF8String, Vector{UTF8String}} - -function parsedoc!(docs::Dict{UTF8String, Docs}, file) - doccing = false - mod = "Base" - func = "" - doc = IOBuffer() - for l in split(readall(file), "\n") - - if doccing && (startswith(l, " ") || ismatch(r"^\s*$", l)) - println(doc, startswith(l, " ") ? l[4:end] : l) - else - doccing = false - func != "" && - push!(get!(get!(docs, mod, Docs()), func, UTF8String[]), rstrip(takebuf_string(doc))) - func = "" - end - - if startswith(l, ".. function::") - name = match(r"^\.\. function:: (@?[^\(\s\{]+)", l) - name == nothing && (warn("bad function $l"); continue) - doccing = true - func = name.captures[1] - println(doc, "::") - println(doc, " "^11, l[15:end]) - elseif ismatch(r"^\.\. (current)?module::", l) - mod = match(r"^\.\. (current)?module:: ([\w\.]+)", l).captures[2] - end - end - func != "" && - push!(get!(get!(docs, mod, Docs()), func, UTF8String[]), rstrip(takebuf_string(doc))) - return docs -end - -function alldocs() - docs = Dict{UTF8String, Docs}() - for folder in ["stdlib", "manual", "devdocs"] - for f in readdir(folder) - parsedoc!(docs, "$folder/$f") - end - end - return docs -end - -map(kv->length(kv[2]), alldocs()) |> sum -map(kv -> sum(map(kv -> length(kv[2]), kv[2])), alldocs()) |> sum - -# Dump in helpdb.jl - -exceptions = ["ans", "CPU_CORES", "JULIA_HOME", "STDOUT", "STDERR", "STDIN", - "help", "apropos", "Help", "x", "build_sysimg", ".\\\\", "\\:", - "\\", "\\\\", "munmap", "mmap", "FormatMessage", "GetLastError"] - -qualify = ["ccall", "in", "<:", "|>", "*", "\\", "*", "/", "^", ".+", ".-", ".*", - "./", ".\\", ".^", "//", "<<", ">>", ">>>", "==", "!=", "===", "!==", - "<", "<=", ">", ">=", ".==", ".!=", ".<", ".<=", ".>", ".>=", "|", "*", - "^", ":", "!"] - -isop(func) = ismatch(r"[^\w@!.]|^!$", func) - -identifier(mod, func) = - func in qualify ? "$mod.$(isop(func) ? "(:($func))" : func)" : - mod == "Base" ? func : - "$(replace(mod, "Base.", "")).$func" - -macquote(n) = - startswith(n, "@") ? ":$n" : - contains(n, "@") ? ":($n)" : - n - -open("../base/docs/helpdb.jl", "w") do io - for (mod, docs) in alldocs() - println(io, "# $mod\n") - for (func, docs) in docs - func in exceptions && continue - println(io, "doc\"\"\"\n```rst") - for (i, doc) in enumerate(docs) - println(io, doc) - i < length(docs) && println(io) - end - println(io, "```\n\"\"\"") - println(io, macquote(identifier(mod, func))) - println(io) - end - end -end - -# let count = 0, hand = 0 -# for (mod, docs) in alldocs() -# for (func, docs) in docs -# count += 1 -# doc = join(docs, "\n") -# if ismatch(r":\w+:", doc) -# hand += 1 -# end -# end -# end -# hand, count -# end From 6636796c4a78b2974d51cec40f9942f350fa764e Mon Sep 17 00:00:00 2001 From: Stefan Karpinski Date: Sun, 28 Jun 2015 01:04:42 -0400 Subject: [PATCH 06/10] new doc city: remove traces of the old helpdb.jl --- CONTRIBUTING.md | 2 +- Makefile | 8 +- base/docs/Docs.jl | 5 +- base/help.jl | 226 - base/sysimg.jl | 3 - doc/Makefile | 7 +- doc/README.md | 2 - doc/helpdb.jl | 13387 -------------------------------------------- test/docs.jl | 67 - 9 files changed, 5 insertions(+), 13702 deletions(-) delete mode 100644 base/help.jl delete mode 100644 doc/helpdb.jl diff --git a/CONTRIBUTING.md b/CONTRIBUTING.md index 358ae2f82bc48..1bfa2080d087f 100644 --- a/CONTRIBUTING.md +++ b/CONTRIBUTING.md @@ -154,7 +154,7 @@ Make sure that [Travis](http://www.travis-ci.org) greenlights the pull request w - Try to [squash](http://gitready.com/advanced/2009/02/10/squashing-commits-with-rebase.html) together small commits that make repeated changes to the same section of code so your pull request is easier to review, and Julia's history won't have any broken intermediate commits. A reasonable number of separate well-factored commits is fine, especially for larger changes. - If any conflicts arise due to changes in Julia's `master`, prefer updating your pull request branch with `git rebase` versus `git merge` or `git pull`, since the latter will introduce merge commits that clutter the git history with noise that makes your changes more difficult to review. - If you see any unrelated changes to submodules like `deps/libuv`, `deps/openlibm`, etc., try running `git submodule update` first. - - Avoid committing changes to auto-generated files such as `doc/helpdb.jl`, which is a frequent source of conflicts and can be re-generated later. + - Avoid committing changes to auto-generated files such as `doc/stdlib/*.rst`, which is a frequent source of conflicts and can be re-generated later. - Descriptive commit messages are good. - Using `git add -p` or `git add -i` can be useful to avoid accidentally committing unrelated changes. - GitHub does not send notifications when you push a new commit to a pull request, so please add a comment to the pull request thread to let reviewers know when you've made changes. diff --git a/Makefile b/Makefile index e59d65a8c22b3..d63b083949fb0 100644 --- a/Makefile +++ b/Makefile @@ -48,7 +48,7 @@ endif julia-deps: | $(DIRS) $(build_datarootdir)/julia/base $(build_datarootdir)/julia/test $(build_docdir) $(build_sysconfdir)/julia/juliarc.jl $(build_man1dir)/julia.1 @$(MAKE) $(QUIET_MAKE) -C deps -julia-base: julia-deps $(build_docdir)/helpdb.jl +julia-base: julia-deps @$(MAKE) $(QUIET_MAKE) -C base julia-libccalltest: @@ -96,7 +96,6 @@ release-candidate: release testall @$(MAKE) -C doc latex SPHINXOPTS="-n" #Rebuild Julia PDF docs pedantically @$(MAKE) -C doc doctest #Run Julia doctests @$(MAKE) -C doc linkcheck #Check all links - @$(MAKE) -C doc helpdb.jl #Rebuild Julia online documentation for help(), apropos(), etc... @# Check to see if the above make invocations changed anything important @if [ -n "$$(git status --porcelain)" ]; then \ @@ -124,9 +123,6 @@ release-candidate: release testall @echo 10. Change master to release-0.X in base/version.jl and base/version_git.sh as in 4cb1e20 @echo -$(build_docdir)/helpdb.jl: doc/helpdb.jl | $(build_docdir) - @cp $< $@ - $(build_man1dir)/julia.1: doc/man/julia.1 | $(build_man1dir) @mkdir -p $(build_man1dir) @cp $< $@ @@ -183,7 +179,7 @@ $(build_private_libdir)/inference.ji: $(build_private_libdir)/inference0.ji COMMA:=, define sysimg_builder -$$(build_private_libdir)/sys$1.o: $$(build_private_libdir)/inference.ji VERSION $$(BASE_SRCS) $$(build_docdir)/helpdb.jl +$$(build_private_libdir)/sys$1.o: $$(build_private_libdir)/inference.ji VERSION $$(BASE_SRCS) @$$(call PRINT_JULIA, cd base && \ $$(call spawn,$2) -C $$(JULIA_CPU_TARGET) --output-o $$(call cygpath_w,$$@) $$(JULIA_SYSIMG_BUILD_FLAGS) -f \ -J $$(call cygpath_w,$$<) sysimg.jl \ diff --git a/base/docs/Docs.jl b/base/docs/Docs.jl index 96708c7cba168..2f87b90eaccc4 100644 --- a/base/docs/Docs.jl +++ b/base/docs/Docs.jl @@ -527,10 +527,7 @@ macro repl(ex) if $(isfield(ex) ? :(isa($(esc(ex.args[1])), DataType)) : false) $(isfield(ex) ? :(fielddoc($(esc(ex.args[1])), $(ex.args[2]))) : nothing) else - # Backwards-compatible with the previous help system, for now - let doc = @doc $(esc(ex)) - doc ≠ nothing ? doc : Base.Help.@help_ $(esc(ex)) - end + @doc $(esc(ex)) end end end diff --git a/base/help.jl b/base/help.jl deleted file mode 100644 index f0d6e8cca7039..0000000000000 --- a/base/help.jl +++ /dev/null @@ -1,226 +0,0 @@ -# This file is a part of Julia. License is MIT: http://julialang.org/license - -module Help - -export help, apropos, @help - -MODULE_DICT = nothing -FUNCTION_DICT = nothing - -function clear_cache() - global MODULE_DICT = nothing - global FUNCTION_DICT = nothing -end - -function decor_help_desc(func::AbstractString, mfunc::AbstractString, desc::AbstractString) - sd = convert(Array{ByteString,1}, split(desc, '\n')) - for i = 1:length(sd) - if startswith(sd[i], func) - sd[i] = mfunc * sd[i][length(func)+1:end] - else - break - end - end - return join(sd, '\n') -end - -function helpdb_filename() - file = "helpdb.jl" - for loc in [Base.locale()] - fn = joinpath(JULIA_HOME, Base.DOCDIR, loc, file) - if isfile(fn) - return fn - end - end - joinpath(JULIA_HOME, Base.DOCDIR, file) -end - -function init_help() - global MODULE_DICT, FUNCTION_DICT - if FUNCTION_DICT == nothing - helpdb = evalfile(helpdb_filename()) - MODULE_DICT = Dict() - FUNCTION_DICT = Dict() - for (mod,func,desc) in helpdb - if !isempty(mod) - mfunc = mod * "." * func - desc = decor_help_desc(func, mfunc, desc) - else - mfunc = func - end - if !haskey(FUNCTION_DICT, mfunc) - FUNCTION_DICT[mfunc] = [] - end - push!(FUNCTION_DICT[mfunc], desc) - if !haskey(MODULE_DICT, func) - MODULE_DICT[func] = [] - end - if !in(mod, MODULE_DICT[func]) - push!(MODULE_DICT[func], mod) - end - end - end -end - -function help(io::IO) - print(io, """ - - Welcome to Julia. The full manual is available at - - http://docs.julialang.org - - To get help, try help(function), help("@macro"), or help("variable"). - To search all help text, try apropos("string"). - """) -end - -function print_help_entries(io::IO, entries) - first = true - for desc in entries - if !first - println(io) - end - println(io, strip(desc)) - first = false - end -end - -func_expr_from_symbols(s::Vector{Symbol}) = length(s) == 1 ? s[1] : Expr(:., func_expr_from_symbols(s[1:end-1]), Expr(:quote, s[end])) - -module_defined(x::Symbol) = isdefined(x) -module_defined(x::Expr) = - x.head == :. && - module_defined(x.args[1]) && - isdefined(eval(x.args[1]), x.args[2].value) - -function is_defined_in_module(name::AbstractString, obj::DataType, mod::AbstractString) - module_defined(parse(mod)) && - isdefined(eval(parse(mod)), symbol(name)) && - eval(parse("$mod.$name")) == obj -end - -function help(io::IO, fname::AbstractString, obj=0) - init_help() - found = false - if haskey(FUNCTION_DICT, fname) - print_help_entries(io, FUNCTION_DICT[fname]) - found = true - elseif haskey(MODULE_DICT, fname) - allmods = MODULE_DICT[fname] - alldesc = [] - for mod in allmods - mfname = isempty(mod) ? fname : mod * "." * fname - if isgeneric(obj) - mf = eval(func_expr_from_symbols(map(symbol, split(mfname, r"(? 0 - print(io, " subtypes : ") - showcompact(io, st) - println(io) - end - end - fields = fieldnames(obj) - if !isempty(fields) - println(io, " fields : ", fields) - end - elseif isgeneric(obj) - writemime(io, "text/plain", obj); println() - else - println(io, "Symbol not found. Falling back on apropos search ...") - apropos(io, fname) - end - end -end - -apropos() = help() - -apropos(s::AbstractString) = apropos(STDOUT, s) -function apropos(io::IO, txt::AbstractString) - init_help() - n = 0 - r = Regex("\\Q$txt", "i") - for (func, entries) in FUNCTION_DICT - if ismatch(r, func) || any(e->ismatch(r,e), entries) - for desc in entries - nl = search(desc,'\n') - if nl != 0 - println(io, desc[1:(nl-1)]) - else - println(io, desc) - end - end - n+=1 - end - end - if n == 0 - println(io, "No help information found.") - end -end - -typename(t::DataType) = t.name.name - -help(io::IO, f::Function) = help(io, string(f), f) -help(io::IO, t::DataType) = help(io, string(typename(t)), t) -help(io::IO, t::Module) = help(io, string(t)) - -function help(io::IO, x) - show(io, x) - t = typeof(x) - if isa(t,DataType) - println(io, " is of type") - help(io, t) - else - println(io, " is of type $t") - end -end - -help(args...) = help(STDOUT, args...) -help(::IO, args...) = throw(ArgumentError("too many arguments to help()")) - -# check whether an expression is a qualified name, e.g. Base.FFTW.FORWARD -isname(n::Symbol) = true -isname(ex::Expr) = ((ex.head == :. && isname(ex.args[1]) && isname(ex.args[2])) - || (ex.head == :quote && isname(ex.args[1]))) - -macro help_(ex) - if ex === :? || ex === :help - return Expr(:call, :help) - elseif !isa(ex, Expr) || isname(ex) - return Expr(:call, :help, esc(ex)) - elseif ex.head == :macrocall && length(ex.args) == 1 - # e.g., "julia> @help @printf" - return Expr(:call, :help, string(ex.args[1])) - else - return Expr(:macrocall, symbol("@which"), esc(ex)) - end -end - -end # module diff --git a/base/sysimg.jl b/base/sysimg.jl index c2a416bdb0566..4e3590518c9e0 100644 --- a/base/sysimg.jl +++ b/base/sysimg.jl @@ -227,10 +227,7 @@ include("interactiveutil.jl") include("replutil.jl") include("test.jl") include("i18n.jl") -include("help.jl") using .I18n -using .Help -push!(I18n.CALLBACKS, Help.clear_cache) # frontend include("Terminals.jl") diff --git a/doc/Makefile b/doc/Makefile index 66de60c379880..94c546a17c7b1 100644 --- a/doc/Makefile +++ b/doc/Makefile @@ -1,6 +1,6 @@ # Makefile for Sphinx documentation -default: helpdb.jl html +default: html # You can set these variables from the command line. SPHINXOPTS = @@ -35,7 +35,6 @@ SPHINXBUILD = . $(ACTIVATE) && sphinx-build help: @echo "Please use 'make ' where is one of" - @echo " helpdb.jl to make the REPL help db" @echo " html to make standalone HTML files" @echo " dirhtml to make HTML files named index.html in directories" @echo " singlehtml to make a single large HTML file" @@ -172,10 +171,6 @@ doctest: $(SPHINX_BUILD) @echo "Testing of doctests in the sources finished, look at the " \ "results in _build/doctest/output.txt." -helpdb.jl: stdlib/*.rst $(SPHINX_BUILD) - $(SPHINXBUILD) -b jlhelp $(ALLSPHINXOPTS) _build/jlhelp - mv _build/jlhelp/jlhelp.jl helpdb.jl - manual/unicode-input-table.rst: $(JULIAHOME)/base/latex_symbols.jl $(JULIA_EXECUTABLE) tabcomplete.jl > manual/unicode-input-table.rst diff --git a/doc/README.md b/doc/README.md index a6e1e4085e902..627feb73b262b 100644 --- a/doc/README.md +++ b/doc/README.md @@ -25,7 +25,6 @@ Building the documentation Build the documentation by running - $ make helpdb.jl $ make html $ make latexpdf @@ -34,7 +33,6 @@ File layout ----------- conf.py Sphinx configuration - helpdb.jl REPL help database stdlib/ Julia standard library documentation UNDOCUMENTED.rst Undocumented functions (to be filled in and copied to the correct location in stdlib/) diff --git a/doc/helpdb.jl b/doc/helpdb.jl deleted file mode 100644 index 74ef81f9010c9..0000000000000 --- a/doc/helpdb.jl +++ /dev/null @@ -1,13387 +0,0 @@ -# automatically generated from files in doc/stdlib/ -- do not edit here - -Any[ - -("Base","ndims","ndims(A) -> Integer - - Returns the number of dimensions of A - -"), - -("Base","size","size(A[, dim...]) - - Returns a tuple containing the dimensions of A. Optionally you can - specify the dimension(s) you want the length of, and get the length - of that dimension, or a tuple of the lengths of dimensions you - asked for.: - - julia> A = rand(2,3,4); - - julia> size(A, 2) - 3 - - julia> size(A,3,2) - (4,3) - -"), - -("Base","iseltype","iseltype(A, T) - - Tests whether A or its elements are of type T - -"), - -("Base","length","length(A) -> Integer - - Returns the number of elements in A - -"), - -("Base","eachindex","eachindex(A...) - - Creates an iterable object for visiting each index of an - AbstractArray \"A\" in an efficient manner. For array types that - have opted into fast linear indexing (like \"Array\"), this is - simply the range \"1:length(A)\". For other array types, this - returns a specialized Cartesian range to efficiently index into the - array with indices specified for every dimension. For other - iterables, including strings and dictionaries, this returns an - iterator object supporting arbitrary index types (e.g. unevenly - spaced or non-integer indices). - - Example for a sparse 2-d array: - - julia> A = sprand(2, 3, 0.5) - 2x3 sparse matrix with 4 Float64 entries: - [1, 1] = 0.598888 - [1, 2] = 0.0230247 - [1, 3] = 0.486499 - [2, 3] = 0.809041 - - julia> for iter in eachindex(A) - @show iter.I_1, iter.I_2 - @show A[iter] - end - (iter.I_1,iter.I_2) = (1,1) - A[iter] = 0.5988881393454597 - (iter.I_1,iter.I_2) = (2,1) - A[iter] = 0.0 - (iter.I_1,iter.I_2) = (1,2) - A[iter] = 0.02302469881746183 - (iter.I_1,iter.I_2) = (2,2) - A[iter] = 0.0 - (iter.I_1,iter.I_2) = (1,3) - A[iter] = 0.4864987874354343 - (iter.I_1,iter.I_2) = (2,3) - A[iter] = 0.8090413606455655 - -"), - -("Base","Base","Base.linearindexing(A) - - \"linearindexing\" defines how an AbstractArray most efficiently - accesses its elements. If \"Base.linearindexing(A)\" returns - \"Base.LinearFast()\", this means that linear indexing with only - one index is an efficient operation. If it instead returns - \"Base.LinearSlow()\" (by default), this means that the array - intrinsically accesses its elements with indices specified for - every dimension. Since converting a linear index to multiple - indexing subscripts is typically very expensive, this provides a - traits-based mechanism to enable efficient generic code for all - array types. - - An abstract array subtype \"MyArray\" that wishes to opt into fast - linear indexing behaviors should define \"linearindexing\" in the - type-domain: - - Base.linearindexing{T<:MyArray}(::Type{T}) = Base.LinearFast() - -"), - -("Base","countnz","countnz(A) - - Counts the number of nonzero values in array A (dense or sparse). - Note that this is not a constant-time operation. For sparse - matrices, one should usually use \"nnz\", which returns the number - of stored values. - -"), - -("Base","conj!","conj!(A) - - Convert an array to its complex conjugate in-place - -"), - -("Base","stride","stride(A, k) - - Returns the distance in memory (in number of elements) between - adjacent elements in dimension k - -"), - -("Base","strides","strides(A) - - Returns a tuple of the memory strides in each dimension - -"), - -("Base","ind2sub","ind2sub(dims, index) -> subscripts - - Returns a tuple of subscripts into an array with dimensions - \"dims\", corresponding to the linear index \"index\" - - **Example** \"i, j, ... = ind2sub(size(A), indmax(A))\" provides - the indices of the maximum element - -"), - -("Base","ind2sub","ind2sub(a, index) -> subscripts - - Returns a tuple of subscripts into array \"a\" corresponding to the - linear index \"index\" - -"), - -("Base","sub2ind","sub2ind(dims, i, j, k...) -> index - - The inverse of \"ind2sub\", returns the linear index corresponding - to the provided subscripts - -"), - -("Base","Array","Array(dims) - - \"Array{T}(dims)\" constructs an uninitialized dense array with - element type \"T\". \"dims\" may be a tuple or a series of integer - arguments. The syntax \"Array(T, dims)\" is also available, but - deprecated. - -"), - -("Base","getindex","getindex(type[, elements...]) - - Construct a 1-d array of the specified type. This is usually called - with the syntax \"Type[]\". Element values can be specified using - \"Type[a,b,c,...]\". - -"), - -("Base","cell","cell(dims) - - Construct an uninitialized cell array (heterogeneous array). - \"dims\" can be either a tuple or a series of integer arguments. - -"), - -("Base","zeros","zeros(type, dims) - - Create an array of all zeros of specified type. The type defaults - to Float64 if not specified. - -"), - -("Base","zeros","zeros(A) - - Create an array of all zeros with the same element type and shape - as A. - -"), - -("Base","ones","ones(type, dims) - - Create an array of all ones of specified type. The type defaults to - Float64 if not specified. - -"), - -("Base","ones","ones(A) - - Create an array of all ones with the same element type and shape as - A. - -"), - -("Base","trues","trues(dims) - - Create a \"BitArray\" with all values set to true - -"), - -("Base","falses","falses(dims) - - Create a \"BitArray\" with all values set to false - -"), - -("Base","fill","fill(x, dims) - - Create an array filled with the value \"x\". For example, - \"fill(1.0, (10,10))\" returns a 10x10 array of floats, with each - element initialized to 1.0. - - If \"x\" is an object reference, all elements will refer to the - same object. \"fill(Foo(), dims)\" will return an array filled with - the result of evaluating \"Foo()\" once. - -"), - -("Base","fill!","fill!(A, x) - - Fill array \"A\" with the value \"x\". If \"x\" is an object - reference, all elements will refer to the same object. \"fill!(A, - Foo())\" will return \"A\" filled with the result of evaluating - \"Foo()\" once. - -"), - -("Base","reshape","reshape(A, dims) - - Create an array with the same data as the given array, but with - different dimensions. An implementation for a particular type of - array may choose whether the data is copied or shared. - -"), - -("Base","similar","similar(array, element_type, dims) - - Create an uninitialized array of the same type as the given array, - but with the specified element type and dimensions. The second and - third arguments are both optional. The \"dims\" argument may be a - tuple or a series of integer arguments. For some special - \"AbstractArray\" objects which are not real containers (like - ranges), this function returns a standard \"Array\" to allow - operating on elements. - -"), - -("Base","reinterpret","reinterpret(type, A) - - Change the type-interpretation of a block of memory. For example, - \"reinterpret(Float32, UInt32(7))\" interprets the 4 bytes - corresponding to \"UInt32(7)\" as a \"Float32\". For arrays, this - constructs an array with the same binary data as the given array, - but with the specified element type. - -"), - -("Base","eye","eye(n) - - n-by-n identity matrix - -"), - -("Base","eye","eye(m, n) - - m-by-n identity matrix - -"), - -("Base","eye","eye(A) - - Constructs an identity matrix of the same dimensions and type as - \"A\". - -"), - -("Base","linspace","linspace(start, stop, n=100) - - Construct a range of \"n\" linearly spaced elements from \"start\" - to \"stop\". - -"), - -("Base","logspace","logspace(start, stop, n=50) - - Construct a vector of \"n\" logarithmically spaced numbers from - \"10^start\" to \"10^stop\". - -"), - -("Base","broadcast","broadcast(f, As...) - - Broadcasts the arrays \"As\" to a common size by expanding - singleton dimensions, and returns an array of the results - \"f(as...)\" for each position. - -"), - -("Base","broadcast!","broadcast!(f, dest, As...) - - Like \"broadcast\", but store the result of \"broadcast(f, As...)\" - in the \"dest\" array. Note that \"dest\" is only used to store the - result, and does not supply arguments to \"f\" unless it is also - listed in the \"As\", as in \"broadcast!(f, A, A, B)\" to perform - \"A[:] = broadcast(f, A, B)\". - -"), - -("Base","bitbroadcast","bitbroadcast(f, As...) - - Like \"broadcast\", but allocates a \"BitArray\" to store the - result, rather then an \"Array\". - -"), - -("Base","broadcast_function","broadcast_function(f) - - Returns a function \"broadcast_f\" such that - \"broadcast_function(f)(As...) === broadcast(f, As...)\". Most - useful in the form \"const broadcast_f = broadcast_function(f)\". - -"), - -("Base","broadcast!_function","broadcast!_function(f) - - Like \"broadcast_function\", but for \"broadcast!\". - -"), - -("Base","getindex","getindex(A, inds...) - - Returns a subset of array \"A\" as specified by \"inds\", where - each \"ind\" may be an \"Int\", a \"Range\", or a \"Vector\". See - the manual section on *array indexing* for details. - -"), - -("Base","sub","sub(A, inds...) - - Like \"getindex()\", but returns a view into the parent array \"A\" - with the given indices instead of making a copy. Calling - \"getindex()\" or \"setindex!()\" on the returned \"SubArray\" - computes the indices to the parent array on the fly without - checking bounds. - -"), - -("Base","parent","parent(A) - - Returns the \"parent array\" of an array view type (e.g., - SubArray), or the array itself if it is not a view - -"), - -("Base","parentindexes","parentindexes(A) - - From an array view \"A\", returns the corresponding indexes in the - parent - -"), - -("Base","slicedim","slicedim(A, d, i) - - Return all the data of \"A\" where the index for dimension \"d\" - equals \"i\". Equivalent to \"A[:,:,...,i,:,:,...]\" where \"i\" is - in position \"d\". - -"), - -("Base","slice","slice(A, inds...) - - Returns a view of array \"A\" with the given indices like - \"sub()\", but drops all dimensions indexed with scalars. - -"), - -("Base","setindex!","setindex!(A, X, inds...) - - Store values from array \"X\" within some subset of \"A\" as - specified by \"inds\". - -"), - -("Base","broadcast_getindex","broadcast_getindex(A, inds...) - - Broadcasts the \"inds\" arrays to a common size like \"broadcast\", - and returns an array of the results \"A[ks...]\", where \"ks\" goes - over the positions in the broadcast. - -"), - -("Base","broadcast_setindex!","broadcast_setindex!(A, X, inds...) - - Broadcasts the \"X\" and \"inds\" arrays to a common size and - stores the value from each position in \"X\" at the indices given - by the same positions in \"inds\". - -"), - -("Base","cat","cat(dims, A...) - - Concatenate the input arrays along the specified dimensions in the - iterable \"dims\". For dimensions not in \"dims\", all input arrays - should have the same size, which will also be the size of the - output array along that dimension. For dimensions in \"dims\", the - size of the output array is the sum of the sizes of the input - arrays along that dimension. If \"dims\" is a single number, the - different arrays are tightly stacked along that dimension. If - \"dims\" is an iterable containing several dimensions, this allows - to construct block diagonal matrices and their higher-dimensional - analogues by simultaneously increasing several dimensions for every - new input array and putting zero blocks elsewhere. For example, - *cat([1,2], matrices...)* builds a block diagonal matrix, i.e. a - block matrix with *matrices[1]*, *matrices[2]*, ... as diagonal - blocks and matching zero blocks away from the diagonal. - -"), - -("Base","vcat","vcat(A...) - - Concatenate along dimension 1 - -"), - -("Base","hcat","hcat(A...) - - Concatenate along dimension 2 - -"), - -("Base","hvcat","hvcat(rows::Tuple{Vararg{Int}}, values...) - - Horizontal and vertical concatenation in one call. This function is - called for block matrix syntax. The first argument specifies the - number of arguments to concatenate in each block row. For example, - \"[a b;c d e]\" calls \"hvcat((2,3),a,b,c,d,e)\". - - If the first argument is a single integer \"n\", then all block - rows are assumed to have \"n\" block columns. - -"), - -("Base","flipdim","flipdim(A, d) - - Reverse \"A\" in dimension \"d\". - -"), - -("Base","circshift","circshift(A, shifts) - - Circularly shift the data in an array. The second argument is a - vector giving the amount to shift in each dimension. - -"), - -("Base","find","find(A) - - Return a vector of the linear indexes of the non-zeros in \"A\" - (determined by \"A[i]!=0\"). A common use of this is to convert a - boolean array to an array of indexes of the \"true\" elements. - -"), - -("Base","find","find(f, A) - - Return a vector of the linear indexes of \"A\" where \"f\" returns - true. - -"), - -("Base","findn","findn(A) - - Return a vector of indexes for each dimension giving the locations - of the non-zeros in \"A\" (determined by \"A[i]!=0\"). - -"), - -("Base","findnz","findnz(A) - - Return a tuple \"(I, J, V)\" where \"I\" and \"J\" are the row and - column indexes of the non-zero values in matrix \"A\", and \"V\" is - a vector of the non-zero values. - -"), - -("Base","findfirst","findfirst(A) - - Return the index of the first non-zero value in \"A\" (determined - by \"A[i]!=0\"). - -"), - -("Base","findfirst","findfirst(A, v) - - Return the index of the first element equal to \"v\" in \"A\". - -"), - -("Base","findfirst","findfirst(predicate, A) - - Return the index of the first element of \"A\" for which - \"predicate\" returns true. - -"), - -("Base","findlast","findlast(A) - - Return the index of the last non-zero value in \"A\" (determined by - \"A[i]!=0\"). - -"), - -("Base","findlast","findlast(A, v) - - Return the index of the last element equal to \"v\" in \"A\". - -"), - -("Base","findlast","findlast(predicate, A) - - Return the index of the last element of \"A\" for which - \"predicate\" returns true. - -"), - -("Base","findnext","findnext(A, i) - - Find the next index >= \"i\" of a non-zero element of \"A\", or - \"0\" if not found. - -"), - -("Base","findnext","findnext(predicate, A, i) - - Find the next index >= \"i\" of an element of \"A\" for which - \"predicate\" returns true, or \"0\" if not found. - -"), - -("Base","findnext","findnext(A, v, i) - - Find the next index >= \"i\" of an element of \"A\" equal to \"v\" - (using \"==\"), or \"0\" if not found. - -"), - -("Base","findprev","findprev(A, i) - - Find the previous index <= \"i\" of a non-zero element of \"A\", or - 0 if not found. - -"), - -("Base","findprev","findprev(predicate, A, i) - - Find the previous index <= \"i\" of an element of \"A\" for which - \"predicate\" returns true, or \"0\" if not found. - -"), - -("Base","findprev","findprev(A, v, i) - - Find the previous index <= \"i\" of an element of \"A\" equal to - \"v\" (using \"==\"), or \"0\" if not found. - -"), - -("Base","permutedims","permutedims(A, perm) - - Permute the dimensions of array \"A\". \"perm\" is a vector - specifying a permutation of length \"ndims(A)\". This is a - generalization of transpose for multi-dimensional arrays. Transpose - is equivalent to \"permutedims(A, [2,1])\". - -"), - -("Base","ipermutedims","ipermutedims(A, perm) - - Like \"permutedims()\", except the inverse of the given permutation - is applied. - -"), - -("Base","permutedims!","permutedims!(dest, src, perm) - - Permute the dimensions of array \"src\" and store the result in the - array \"dest\". \"perm\" is a vector specifying a permutation of - length \"ndims(src)\". The preallocated array \"dest\" should have - \"size(dest) == size(src)[perm]\" and is completely overwritten. No - in-place permutation is supported and unexpected results will - happen if *src* and *dest* have overlapping memory regions. - -"), - -("Base","squeeze","squeeze(A, dims) - - Remove the dimensions specified by \"dims\" from array \"A\". - Elements of \"dims\" must be unique and within the range - \"1:ndims(A)\". - -"), - -("Base","vec","vec(Array) -> Vector - - Vectorize an array using column-major convention. - -"), - -("Base","promote_shape","promote_shape(s1, s2) - - Check two array shapes for compatibility, allowing trailing - singleton dimensions, and return whichever shape has more - dimensions. - -"), - -("Base","checkbounds","checkbounds(array, indexes...) - - Throw an error if the specified indexes are not in bounds for the - given array. - -"), - -("Base","randsubseq","randsubseq(A, p) -> Vector - - Return a vector consisting of a random subsequence of the given - array \"A\", where each element of \"A\" is included (in order) - with independent probability \"p\". (Complexity is linear in - \"p*length(A)\", so this function is efficient even if \"p\" is - small and \"A\" is large.) Technically, this process is known as - \"Bernoulli sampling\" of \"A\". - -"), - -("Base","randsubseq!","randsubseq!(S, A, p) - - Like \"randsubseq\", but the results are stored in \"S\" (which is - resized as needed). - -"), - -("Base","cumprod","cumprod(A[, dim]) - - Cumulative product along a dimension \"dim\" (defaults to 1). See - also \"cumprod!()\" to use a preallocated output array, both for - performance and to control the precision of the output (e.g. to - avoid overflow). - -"), - -("Base","cumprod!","cumprod!(B, A[, dim]) - - Cumulative product of \"A\" along a dimension, storing the result - in \"B\". The dimension defaults to 1. - -"), - -("Base","cumsum","cumsum(A[, dim]) - - Cumulative sum along a dimension \"dim\" (defaults to 1). See also - \"cumsum!()\" to use a preallocated output array, both for - performance and to control the precision of the output (e.g. to - avoid overflow). - -"), - -("Base","cumsum!","cumsum!(B, A[, dim]) - - Cumulative sum of \"A\" along a dimension, storing the result in - \"B\". The dimension defaults to 1. - -"), - -("Base","cumsum_kbn","cumsum_kbn(A[, dim]) - - Cumulative sum along a dimension, using the Kahan-Babuska-Neumaier - compensated summation algorithm for additional accuracy. The - dimension defaults to 1. - -"), - -("Base","cummin","cummin(A[, dim]) - - Cumulative minimum along a dimension. The dimension defaults to 1. - -"), - -("Base","cummax","cummax(A[, dim]) - - Cumulative maximum along a dimension. The dimension defaults to 1. - -"), - -("Base","diff","diff(A[, dim]) - - Finite difference operator of matrix or vector. - -"), - -("Base","gradient","gradient(F[, h]) - - Compute differences along vector \"F\", using \"h\" as the spacing - between points. The default spacing is one. - -"), - -("Base","rot180","rot180(A) - - Rotate matrix \"A\" 180 degrees. - -"), - -("Base","rot180","rot180(A, k) - - Rotate matrix \"A\" 180 degrees an integer \"k\" number of times. - If \"k\" is even, this is equivalent to a \"copy\". - -"), - -("Base","rotl90","rotl90(A) - - Rotate matrix \"A\" left 90 degrees. - -"), - -("Base","rotl90","rotl90(A, k) - - Rotate matrix \"A\" left 90 degrees an integer \"k\" number of - times. If \"k\" is zero or a multiple of four, this is equivalent - to a \"copy\". - -"), - -("Base","rotr90","rotr90(A) - - Rotate matrix \"A\" right 90 degrees. - -"), - -("Base","rotr90","rotr90(A, k) - - Rotate matrix \"A\" right 90 degrees an integer \"k\" number of - times. If \"k\" is zero or a multiple of four, this is equivalent - to a \"copy\". - -"), - -("Base","reducedim","reducedim(f, A, dims[, initial]) - - Reduce 2-argument function \"f\" along dimensions of \"A\". - \"dims\" is a vector specifying the dimensions to reduce, and - \"initial\" is the initial value to use in the reductions. For *+*, - ***, *max* and *min* the *initial* argument is optional. - - The associativity of the reduction is implementation-dependent; if - you need a particular associativity, e.g. left-to-right, you should - write your own loop. See documentation for \"reduce\". - -"), - -("Base","mapreducedim","mapreducedim(f, op, A, dims[, initial]) - - Evaluates to the same as *reducedim(op, map(f, A), dims, - f(initial))*, but is generally faster because the intermediate - array is avoided. - -"), - -("Base","mapslices","mapslices(f, A, dims) - - Transform the given dimensions of array \"A\" using function \"f\". - \"f\" is called on each slice of \"A\" of the form - \"A[...,:,...,:,...]\". \"dims\" is an integer vector specifying - where the colons go in this expression. The results are - concatenated along the remaining dimensions. For example, if - \"dims\" is \"[1,2]\" and A is 4-dimensional, \"f\" is called on - \"A[:,:,i,j]\" for all \"i\" and \"j\". - -"), - -("Base","sum_kbn","sum_kbn(A) - - Returns the sum of all array elements, using the Kahan-Babuska- - Neumaier compensated summation algorithm for additional accuracy. - -"), - -("Base","cartesianmap","cartesianmap(f, dims) - - Given a \"dims\" tuple of integers \"(m, n, ...)\", call \"f\" on - all combinations of integers in the ranges \"1:m\", \"1:n\", etc. - - julia> cartesianmap(println, (2,2)) - 11 - 21 - 12 - 22 - -"), - -("Base","nthperm","nthperm(v, k) - - Compute the kth lexicographic permutation of a vector. - -"), - -("Base","nthperm","nthperm(p) - - Return the \"k\" that generated permutation \"p\". Note that - \"nthperm(nthperm([1:n], k)) == k\" for \"1 <= k <= factorial(n)\". - -"), - -("Base","nthperm!","nthperm!(v, k) - - In-place version of \"nthperm()\". - -"), - -("Base","randperm","randperm([rng], n) - - Construct a random permutation of length \"n\". The optional - \"rng\" argument specifies a random number generator, see *Random - Numbers*. - -"), - -("Base","invperm","invperm(v) - - Return the inverse permutation of v. - -"), - -("Base","isperm","isperm(v) -> Bool - - Returns true if v is a valid permutation. - -"), - -("Base","permute!","permute!(v, p) - - Permute vector \"v\" in-place, according to permutation \"p\". No - checking is done to verify that \"p\" is a permutation. - - To return a new permutation, use \"v[p]\". Note that this is - generally faster than \"permute!(v,p)\" for large vectors. - -"), - -("Base","ipermute!","ipermute!(v, p) - - Like permute!, but the inverse of the given permutation is applied. - -"), - -("Base","randcycle","randcycle([rng], n) - - Construct a random cyclic permutation of length \"n\". The optional - \"rng\" argument specifies a random number generator, see *Random - Numbers*. - -"), - -("Base","shuffle","shuffle([rng], v) - - Return a randomly permuted copy of \"v\". The optional \"rng\" - argument specifies a random number generator, see *Random Numbers*. - -"), - -("Base","shuffle!","shuffle!([rng], v) - - In-place version of \"shuffle()\". - -"), - -("Base","reverse","reverse(v[, start=1[, stop=length(v)]]) - - Return a copy of \"v\" reversed from start to stop. - -"), - -("Base","reverseind","reverseind(v, i) - - Given an index \"i\" in \"reverse(v)\", return the corresponding - index in \"v\" so that \"v[reverseind(v,i)] == reverse(v)[i]\". - (This can be nontrivial in the case where \"v\" is a Unicode - string.) - -"), - -("Base","reverse!","reverse!(v[, start=1[, stop=length(v)]]) -> v - - In-place version of \"reverse()\". - -"), - -("Base","combinations","combinations(array, n) - - Generate all combinations of \"n\" elements from an indexable - object. Because the number of combinations can be very large, this - function returns an iterator object. Use - \"collect(combinations(array,n))\" to get an array of all - combinations. - -"), - -("Base","permutations","permutations(array) - - Generate all permutations of an indexable object. Because the - number of permutations can be very large, this function returns an - iterator object. Use \"collect(permutations(array))\" to get an - array of all permutations. - -"), - -("Base","partitions","partitions(n) - - Generate all integer arrays that sum to \"n\". Because the number - of partitions can be very large, this function returns an iterator - object. Use \"collect(partitions(n))\" to get an array of all - partitions. The number of partitions to generate can be efficiently - computed using \"length(partitions(n))\". - -"), - -("Base","partitions","partitions(n, m) - - Generate all arrays of \"m\" integers that sum to \"n\". Because - the number of partitions can be very large, this function returns - an iterator object. Use \"collect(partitions(n,m))\" to get an - array of all partitions. The number of partitions to generate can - be efficiently computed using \"length(partitions(n,m))\". - -"), - -("Base","partitions","partitions(array) - - Generate all set partitions of the elements of an array, - represented as arrays of arrays. Because the number of partitions - can be very large, this function returns an iterator object. Use - \"collect(partitions(array))\" to get an array of all partitions. - The number of partitions to generate can be efficiently computed - using \"length(partitions(array))\". - -"), - -("Base","partitions","partitions(array, m) - - Generate all set partitions of the elements of an array into - exactly m subsets, represented as arrays of arrays. Because the - number of partitions can be very large, this function returns an - iterator object. Use \"collect(partitions(array,m))\" to get an - array of all partitions. The number of partitions into m subsets is - equal to the Stirling number of the second kind and can be - efficiently computed using \"length(partitions(array,m))\". - -"), - -("Base","bitpack","bitpack(A::AbstractArray{T, N}) -> BitArray - - Converts a numeric array to a packed boolean array - -"), - -("Base","bitunpack","bitunpack(B::BitArray{N}) -> Array{Bool,N} - - Converts a packed boolean array to an array of booleans - -"), - -("Base","flipbits!","flipbits!(B::BitArray{N}) -> BitArray{N} - - Performs a bitwise not operation on B. See *~ operator*. - -"), - -("Base","rol!","rol!(dest::BitArray{1}, src::BitArray{1}, i::Integer) -> BitArray{1} - - Performs a left rotation operation on \"src\" and put the result - into \"dest\". - -"), - -("Base","rol!","rol!(B::BitArray{1}, i::Integer) -> BitArray{1} - - Performs a left rotation operation on B. - -"), - -("Base","rol","rol(B::BitArray{1}, i::Integer) -> BitArray{1} - - Performs a left rotation operation. - -"), - -("Base","ror!","ror!(dest::BitArray{1}, src::BitArray{1}, i::Integer) -> BitArray{1} - - Performs a right rotation operation on \"src\" and put the result - into \"dest\". - -"), - -("Base","ror!","ror!(B::BitArray{1}, i::Integer) -> BitArray{1} - - Performs a right rotation operation on B. - -"), - -("Base","ror","ror(B::BitArray{1}, i::Integer) -> BitArray{1} - - Performs a right rotation operation. - -"), - -("Base","sparse","sparse(I, J, V[, m, n, combine]) - - Create a sparse matrix \"S\" of dimensions \"m x n\" such that - \"S[I[k], J[k]] = V[k]\". The \"combine\" function is used to - combine duplicates. If \"m\" and \"n\" are not specified, they are - set to \"max(I)\" and \"max(J)\" respectively. If the \"combine\" - function is not supplied, duplicates are added by default. - -"), - -("Base","sparsevec","sparsevec(I, V[, m, combine]) - - Create a sparse matrix \"S\" of size \"m x 1\" such that \"S[I[k]] - = V[k]\". Duplicates are combined using the \"combine\" function, - which defaults to \"+\" if it is not provided. In julia, sparse - vectors are really just sparse matrices with one column. Given - Julia's Compressed Sparse Columns (CSC) storage format, a sparse - column matrix with one column is sparse, whereas a sparse row - matrix with one row ends up being dense. - -"), - -("Base","sparsevec","sparsevec(D::Dict[, m]) - - Create a sparse matrix of size \"m x 1\" where the row values are - keys from the dictionary, and the nonzero values are the values - from the dictionary. - -"), - -("Base","issparse","issparse(S) - - Returns \"true\" if \"S\" is sparse, and \"false\" otherwise. - -"), - -("Base","sparse","sparse(A) - - Convert an AbstractMatrix \"A\" into a sparse matrix. - -"), - -("Base","sparsevec","sparsevec(A) - - Convert a dense vector \"A\" into a sparse matrix of size \"m x - 1\". In julia, sparse vectors are really just sparse matrices with - one column. - -"), - -("Base","full","full(S) - - Convert a sparse matrix \"S\" into a dense matrix. - -"), - -("Base","nnz","nnz(A) - - Returns the number of stored (filled) elements in a sparse matrix. - -"), - -("Base","spzeros","spzeros(m, n) - - Create a sparse matrix of size \"m x n\". This sparse matrix will - not contain any nonzero values. No storage will be allocated for - nonzero values during construction. - -"), - -("Base","spones","spones(S) - - Create a sparse matrix with the same structure as that of \"S\", - but with every nonzero element having the value \"1.0\". - -"), - -("Base","speye","speye(type, m[, n]) - - Create a sparse identity matrix of specified type of size \"m x - m\". In case \"n\" is supplied, create a sparse identity matrix of - size \"m x n\". - -"), - -("Base","spdiagm","spdiagm(B, d[, m, n]) - - Construct a sparse diagonal matrix. \"B\" is a tuple of vectors - containing the diagonals and \"d\" is a tuple containing the - positions of the diagonals. In the case the input contains only one - diagonaly, \"B\" can be a vector (instead of a tuple) and \"d\" can - be the diagonal position (instead of a tuple), defaulting to 0 - (diagonal). Optionally, \"m\" and \"n\" specify the size of the - resulting sparse matrix. - -"), - -("Base","sprand","sprand([rng], m, n, p[, rfn]) - - Create a random \"m\" by \"n\" sparse matrix, in which the - probability of any element being nonzero is independently given by - \"p\" (and hence the mean density of nonzeros is also exactly - \"p\"). Nonzero values are sampled from the distribution specified - by \"rfn\". The uniform distribution is used in case \"rfn\" is not - specified. The optional \"rng\" argument specifies a random number - generator, see *Random Numbers*. - -"), - -("Base","sprandn","sprandn(m, n, p) - - Create a random \"m\" by \"n\" sparse matrix with the specified - (independent) probability \"p\" of any entry being nonzero, where - nonzero values are sampled from the normal distribution. - -"), - -("Base","sprandbool","sprandbool(m, n, p) - - Create a random \"m\" by \"n\" sparse boolean matrix with the - specified (independent) probability \"p\" of any entry being - \"true\". - -"), - -("Base","etree","etree(A[, post]) - - Compute the elimination tree of a symmetric sparse matrix \"A\" - from \"triu(A)\" and, optionally, its post-ordering permutation. - -"), - -("Base","symperm","symperm(A, p) - - Return the symmetric permutation of A, which is \"A[p,p]\". A - should be symmetric and sparse, where only the upper triangular - part of the matrix is stored. This algorithm ignores the lower - triangular part of the matrix. Only the upper triangular part of - the result is returned as well. - -"), - -("Base","nonzeros","nonzeros(A) - - Return a vector of the structural nonzero values in sparse matrix - \"A\". This includes zeros that are explicitly stored in the sparse - matrix. The returned vector points directly to the internal nonzero - storage of \"A\", and any modifications to the returned vector will - mutate \"A\" as well. See \"rowvals(A)\" and \"nzrange(A, col)\". - -"), - -("Base","rowvals","rowvals(A) - - Return a vector of the row indices of \"A\", and any modifications - to the returned vector will mutate \"A\" as well. Given the - internal storage format of sparse matrices, providing access to how - the row indices are stored internally can be useful in conjuction - with iterating over structural nonzero values. See \"nonzeros(A)\" - and \"nzrange(A, col)\". - -"), - -("Base","nzrange","nzrange(A, col) - - Return the range of indices to the structural nonzero values of a - sparse matrix column. In conjunction with \"nonzeros(A)\" and - \"rowvals(A)\", this allows for convenient iterating over a sparse - matrix - - A = sparse(I,J,V) - rows = rowvals(A) - vals = nonzeros(A) - m, n = size(A) - for i = 1:n - for j in nzrange(A, i) - row = rows[j] - val = vals[j] - # perform sparse wizardry... - end - end - -"), - -("Base","exit","exit([code]) - - Quit (or control-D at the prompt). The default exit code is zero, - indicating that the processes completed successfully. - -"), - -("Base","quit","quit() - - Quit the program indicating that the processes completed - successfully. This function calls \"exit(0)\" (see \"exit()\"). - -"), - -("Base","atexit","atexit(f) - - Register a zero-argument function to be called at exit. - -"), - -("Base","atreplinit","atreplinit(f) - - Register a one-argument function to be called before the REPL - interface is initialized in interactive sessions; this is useful to - customize the interface. The argument of \"f\" is the REPL object. - This function should be called from within the \".juliarc.jl\" - initialization file. - -"), - -("Base","isinteractive","isinteractive() -> Bool - - Determine whether Julia is running an interactive session. - -"), - -("Base","whos","whos([Module,] [pattern::Regex]) - - Print information about exported global variables in a module, - optionally restricted to those matching \"pattern\". - -"), - -("Base","edit","edit(file::AbstractString[, line]) - - Edit a file optionally providing a line number to edit at. Returns - to the julia prompt when you quit the editor. - -"), - -("Base","edit","edit(function[, types]) - - Edit the definition of a function, optionally specifying a tuple of - types to indicate which method to edit. - -"), - -("Base","@edit","@edit() - - Evaluates the arguments to the function call, determines their - types, and calls the \"edit\" function on the resulting expression - -"), - -("Base","less","less(file::AbstractString[, line]) - - Show a file using the default pager, optionally providing a - starting line number. Returns to the julia prompt when you quit the - pager. - -"), - -("Base","less","less(function[, types]) - - Show the definition of a function using the default pager, - optionally specifying a tuple of types to indicate which method to - see. - -"), - -("Base","@less","@less() - - Evaluates the arguments to the function call, determines their - types, and calls the \"less\" function on the resulting expression - -"), - -("Base","clipboard","clipboard(x) - - Send a printed form of \"x\" to the operating system clipboard - (\"copy\"). - -"), - -("Base","clipboard","clipboard() -> AbstractString - - Return a string with the contents of the operating system clipboard - (\"paste\"). - -"), - -("Base","require","require(module::Symbol) - - This function is part of the implementation of \"using\" / - \"import\", if a module is not already defined in \"Main\". It can - also be called directly to force reloading a module, regardless of - whether it has been loaded before (for exmple, when interactively - developing libraries). - - Loads a source files, in the context of the \"Main\" module, on - every active node, searching standard locations for files. - \"require\" is considered a top-level operation, so it sets the - current \"include\" path but does not use it to search for files - (see help for \"include\"). This function is typically used to load - library code, and is implicitly called by \"using\" to load - packages. - - When searching for files, \"require\" first looks in the current - working directory, then looks for package code under \"Pkg.dir()\", - then tries paths in the global array \"LOAD_PATH\". - -"), - -("Base","compile","compile(module::Symbol) - - Creates a precompiled cache file for module (see help for - \"require\") and all of its dependencies. This can be used to - reduce package load times. Cache files are stored in - LOAD_CACHE_PATH[1], which defaults to *~/.julia/lib/VERSION*. See - the manual section *Module initialization and precompilation* - (under *Modules*) for important notes. - -"), - -("Base","include","include(path::AbstractString) - - Evaluate the contents of a source file in the current context. - During including, a task-local include path is set to the directory - containing the file. Nested calls to \"include\" will search - relative to that path. All paths refer to files on node 1 when - running in parallel, and files will be fetched from node 1. This - function is typically used to load source interactively, or to - combine files in packages that are broken into multiple source - files. - -"), - -("Base","include_string","include_string(code::AbstractString[, filename]) - - Like \"include\", except reads code from the given string rather - than from a file. Since there is no file path involved, no path - processing or fetching from node 1 is done. - -"), - -("Base","help","help(name) - - Get help for a function. \"name\" can be an object or a string. - -"), - -("Base","apropos","apropos(string) - - Search documentation for functions related to \"string\". - -"), - -("Base","which","which(f, types) - - Returns the method of \"f\" (a \"Method\" object) that would be - called for arguments of the given types. - - If \"types\" is an abstract type, then the method that would be - called by \"invoke\" is returned. - -"), - -("Base","which","which(symbol) - - Return the module in which the binding for the variable referenced - by \"symbol\" was created. - -"), - -("Base","@which","@which() - - Applied to a function call, it evaluates the arguments to the - specified function call, and returns the \"Method\" object for the - method that would be called for those arguments. Applied to a - variable, it returns the module in which the variable was bound. It - calls out to the \"which\" function. - -"), - -("Base","methods","methods(f[, types]) - - Returns the method table for \"f\". - - If \"types\" is specified, returns an array of methods whose types - match. - -"), - -("Base","methodswith","methodswith(typ[, module or function][, showparents]) - - Return an array of methods with an argument of type \"typ\". If - optional \"showparents\" is \"true\", also return arguments with a - parent type of \"typ\", excluding type \"Any\". - - The optional second argument restricts the search to a particular - module or function. - -"), - -("Base","@show","@show() - - Show an expression and result, returning the result - -"), - -("Base","versioninfo","versioninfo([verbose::Bool]) - - Print information about the version of Julia in use. If the - \"verbose\" argument is true, detailed system information is shown - as well. - -"), - -("Base","workspace","workspace() - - Replace the top-level module (\"Main\") with a new one, providing a - clean workspace. The previous \"Main\" module is made available as - \"LastMain\". A previously-loaded package can be accessed using a - statement such as \"using LastMain.Package\". - - This function should only be used interactively. - -"), - -("Base","ans","ans - - A variable referring to the last computed value, automatically set - at the interactive prompt. - -"), - -("Base","is","is(x, y) -> Bool -===(x, y) -> Bool -≡(x, y) -> Bool - - Determine whether \"x\" and \"y\" are identical, in the sense that - no program could distinguish them. Compares mutable objects by - address in memory, and compares immutable objects (such as numbers) - by contents at the bit level. This function is sometimes called - \"egal\". - -"), - -("Base","isa","isa(x, type) -> Bool - - Determine whether \"x\" is of the given \"type\". - -"), - -("Base","isequal","isequal(x, y) - - Similar to \"==\", except treats all floating-point \"NaN\" values - as equal to each other, and treats \"-0.0\" as unequal to \"0.0\". - The default implementation of \"isequal\" calls \"==\", so if you - have a type that doesn't have these floating-point subtleties then - you probably only need to define \"==\". - - \"isequal\" is the comparison function used by hash tables - (\"Dict\"). \"isequal(x,y)\" must imply that \"hash(x) == - hash(y)\". - - This typically means that if you define your own \"==\" function - then you must define a corresponding \"hash\" (and vice versa). - Collections typically implement \"isequal\" by calling \"isequal\" - recursively on all contents. - - Scalar types generally do not need to implement \"isequal\" - separate from \"==\", unless they represent floating-point numbers - amenable to a more efficient implementation than that provided as a - generic fallback (based on \"isnan\", \"signbit\", and \"==\"). - -"), - -("Base","isless","isless(x, y) - - Test whether \"x\" is less than \"y\", according to a canonical - total order. Values that are normally unordered, such as \"NaN\", - are ordered in an arbitrary but consistent fashion. This is the - default comparison used by \"sort\". Non-numeric types with a - canonical total order should implement this function. Numeric types - only need to implement it if they have special values such as - \"NaN\". - -"), - -("Base","ifelse","ifelse(condition::Bool, x, y) - - Return \"x\" if \"condition\" is true, otherwise return \"y\". This - differs from \"?\" or \"if\" in that it is an ordinary function, so - all the arguments are evaluated first. In some cases, using - \"ifelse\" instead of an \"if\" statement can eliminate the branch - in generated code and provide higher performance in tight loops. - -"), - -("Base","lexcmp","lexcmp(x, y) - - Compare \"x\" and \"y\" lexicographically and return -1, 0, or 1 - depending on whether \"x\" is less than, equal to, or greater than - \"y\", respectively. This function should be defined for - lexicographically comparable types, and \"lexless\" will call - \"lexcmp\" by default. - -"), - -("Base","lexless","lexless(x, y) - - Determine whether \"x\" is lexicographically less than \"y\". - -"), - -("Base","typeof","typeof(x) - - Get the concrete type of \"x\". - -"), - -("Base","tuple","tuple(xs...) - - Construct a tuple of the given objects. - -"), - -("Base","ntuple","ntuple(f::Function, n) - - Create a tuple of length \"n\", computing each element as \"f(i)\", - where \"i\" is the index of the element. - -"), - -("Base","object_id","object_id(x) - - Get a unique integer id for \"x\". \"object_id(x)==object_id(y)\" - if and only if \"is(x,y)\". - -"), - -("Base","hash","hash(x[, h]) - - Compute an integer hash code such that \"isequal(x,y)\" implies - \"hash(x)==hash(y)\". The optional second argument \"h\" is a hash - code to be mixed with the result. - - New types should implement the 2-argument form, typically by - calling the 2-argument \"hash\" method recursively in order to mix - hashes of the contents with each other (and with \"h\"). - Typically, any type that implements \"hash\" should also implement - its own \"==\" (hence \"isequal\") to guarantee the property - mentioned above. - -"), - -("Base","finalizer","finalizer(x, function) - - Register a function \"f(x)\" to be called when there are no - program-accessible references to \"x\". The behavior of this - function is unpredictable if \"x\" is of a bits type. - -"), - -("Base","finalize","finalize(x) - - Immediately run finalizers registered for object \"x\". - -"), - -("Base","copy","copy(x) - - Create a shallow copy of \"x\": the outer structure is copied, but - not all internal values. For example, copying an array produces a - new array with identically-same elements as the original. - -"), - -("Base","deepcopy","deepcopy(x) - - Create a deep copy of \"x\": everything is copied recursively, - resulting in a fully independent object. For example, deep-copying - an array produces a new array whose elements are deep copies of the - original elements. Calling *deepcopy* on an object should generally - have the same effect as serializing and then deserializing it. - - As a special case, functions can only be actually deep-copied if - they are anonymous, otherwise they are just copied. The difference - is only relevant in the case of closures, i.e. functions which may - contain hidden internal references. - - While it isn't normally necessary, user-defined types can override - the default \"deepcopy\" behavior by defining a specialized version - of the function \"deepcopy_internal(x::T, dict::ObjectIdDict)\" - (which shouldn't otherwise be used), where \"T\" is the type to be - specialized for, and \"dict\" keeps track of objects copied so far - within the recursion. Within the definition, \"deepcopy_internal\" - should be used in place of \"deepcopy\", and the \"dict\" variable - should be updated as appropriate before returning. - -"), - -("Base","isdefined","isdefined([object], index | symbol) - - Tests whether an assignable location is defined. The arguments can - be an array and index, a composite object and field name (as a - symbol), or a module and a symbol. With a single symbol argument, - tests whether a global variable with that name is defined in - \"current_module()\". - -"), - -("Base","convert","convert(T, x) - - Convert \"x\" to a value of type \"T\". - - If \"T\" is an \"Integer\" type, an \"InexactError\" will be raised - if \"x\" is not representable by \"T\", for example if \"x\" is not - integer-valued, or is outside the range supported by \"T\". - - julia> convert(Int, 3.0) - 3 - - julia> convert(Int, 3.5) - ERROR: InexactError() - in convert at int.jl:196 - - If \"T\" is a \"AbstractFloat\" or \"Rational\" type, then it will - return the closest value to \"x\" representable by \"T\". - - julia> x = 1/3 - 0.3333333333333333 - - julia> convert(Float32, x) - 0.33333334f0 - - julia> convert(Rational{Int32}, x) - 1//3 - - julia> convert(Rational{Int64}, x) - 6004799503160661//18014398509481984 - -"), - -("Base","promote","promote(xs...) - - Convert all arguments to their common promotion type (if any), and - return them all (as a tuple). - -"), - -("Base","oftype","oftype(x, y) - - Convert \"y\" to the type of \"x\" (\"convert(typeof(x), y)\"). - -"), - -("Base","widen","widen(type | x) - - If the argument is a type, return a \"larger\" type (for numeric - types, this will be a type with at least as much range and - precision as the argument, and usually more). Otherwise the - argument \"x\" is converted to \"widen(typeof(x))\". - - julia> widen(Int32) - Int64 - - julia> widen(1.5f0) - 1.5 - -"), - -("Base","identity","identity(x) - - The identity function. Returns its argument. - -"), - -("Base","super","super(T::DataType) - - Return the supertype of DataType T - -"), - -("Base","issubtype","issubtype(type1, type2) - - True if and only if all values of \"type1\" are also of \"type2\". - Can also be written using the \"<:\" infix operator as \"type1 <: - type2\". - -"), - -("Base","<:","<:(T1, T2) - - Subtype operator, equivalent to \"issubtype(T1,T2)\". - -"), - -("Base","subtypes","subtypes(T::DataType) - - Return a list of immediate subtypes of DataType T. Note that all - currently loaded subtypes are included, including those not visible - in the current module. - -"), - -("Base","typemin","typemin(type) - - The lowest value representable by the given (real) numeric type. - -"), - -("Base","typemax","typemax(type) - - The highest value representable by the given (real) numeric type. - -"), - -("Base","realmin","realmin(type) - - The smallest in absolute value non-subnormal value representable by - the given floating-point type - -"), - -("Base","realmax","realmax(type) - - The highest finite value representable by the given floating-point - type - -"), - -("Base","maxintfloat","maxintfloat(type) - - The largest integer losslessly representable by the given floating- - point type - -"), - -("Base","sizeof","sizeof(type) - - Size, in bytes, of the canonical binary representation of the given - type, if any. - -"), - -("Base","eps","eps([type]) - - The distance between 1.0 and the next larger representable - floating-point value of \"type\". Only floating-point types are - sensible arguments. If \"type\" is omitted, then \"eps(Float64)\" - is returned. - -"), - -("Base","eps","eps(x) - - The distance between \"x\" and the next larger representable - floating-point value of the same type as \"x\". - -"), - -("Base","promote_type","promote_type(type1, type2) - - Determine a type big enough to hold values of each argument type - without loss, whenever possible. In some cases, where no type - exists to which both types can be promoted losslessly, some loss is - tolerated; for example, \"promote_type(Int64,Float64)\" returns - \"Float64\" even though strictly, not all \"Int64\" values can be - represented exactly as \"Float64\" values. - -"), - -("Base","promote_rule","promote_rule(type1, type2) - - Specifies what type should be used by \"promote\" when given values - of types \"type1\" and \"type2\". This function should not be - called directly, but should have definitions added to it for new - types as appropriate. - -"), - -("Base","getfield","getfield(value, name::Symbol) - - Extract a named field from a value of composite type. The syntax - \"a.b\" calls \"getfield(a, :b)\", and the syntax \"a.(b)\" calls - \"getfield(a, b)\". - -"), - -("Base","setfield!","setfield!(value, name::Symbol, x) - - Assign \"x\" to a named field in \"value\" of composite type. The - syntax \"a.b = c\" calls \"setfield!(a, :b, c)\", and the syntax - \"a.(b) = c\" calls \"setfield!(a, b, c)\". - -"), - -("Base","fieldoffsets","fieldoffsets(type) - - The byte offset of each field of a type relative to the data start. - For example, we could use it in the following manner to summarize - information about a struct type: - - julia> structinfo(T) = [zip(fieldoffsets(T),fieldnames(T),T.types)...]; - - julia> structinfo(StatStruct) - 12-element Array{Tuple{Int64,Symbol,DataType},1}: - (0,:device,UInt64) - (8,:inode,UInt64) - (16,:mode,UInt64) - (24,:nlink,Int64) - (32,:uid,UInt64) - (40,:gid,UInt64) - (48,:rdev,UInt64) - (56,:size,Int64) - (64,:blksize,Int64) - (72,:blocks,Int64) - (80,:mtime,Float64) - (88,:ctime,Float64) - -"), - -("Base","fieldtype","fieldtype(type, name::Symbol | index::Int) - - Determine the declared type of a field (specified by name or index) - in a composite type. - -"), - -("Base","isimmutable","isimmutable(v) - - True if value \"v\" is immutable. See *Immutable Composite Types* - for a discussion of immutability. Note that this function works on - values, so if you give it a type, it will tell you that a value of - \"DataType\" is mutable. - -"), - -("Base","isbits","isbits(T) - - True if \"T\" is a \"plain data\" type, meaning it is immutable and - contains no references to other values. Typical examples are - numeric types such as \"UInt8\", \"Float64\", and - \"Complex{Float64}\". - - julia> isbits(Complex{Float64}) - true - - julia> isbits(Complex) - false - -"), - -("Base","isleaftype","isleaftype(T) - - Determine whether \"T\" is a concrete type that can have instances, - meaning its only subtypes are itself and \"None\" (but \"T\" itself - is not \"None\"). - -"), - -("Base","typejoin","typejoin(T, S) - - Compute a type that contains both \"T\" and \"S\". - -"), - -("Base","typeintersect","typeintersect(T, S) - - Compute a type that contains the intersection of \"T\" and \"S\". - Usually this will be the smallest such type or one close to it. - -"), - -("Base","Val{c}","Val{c}() - - Create a \"value type\" out of \"c\", which must be an \"isbits\" - value. The intent of this construct is to be able to dispatch on - constants, e.g., \"f(Val{false})\" allows you to dispatch directly - (at compile-time) to an implementation \"f(::Type{Val{false}})\", - without having to test the boolean value at runtime. - -"), - -("","@enum EnumName EnumValue1[=x] EnumValue2[=y]","@enum EnumName EnumValue1[=x] EnumValue2[=y] - - Create an \"Enum\" type with name \"EnumName\" and enum member - values of \"EnumValue1\" and \"EnumValue2\" with optional assigned - values of \"x\" and \"y\", respectively. \"EnumName\" can be used - just like other types and enum member values as regular values, - such as - - julia> @enum FRUIT apple=1 orange=2 kiwi=3 - - julia> f(x::FRUIT) = \"I'm a FRUIT with value: \$(Int(x))\" - f (generic function with 1 method) - - julia> f(apple) - \"I'm a FRUIT with value: 1\" - -"), - -("Base","instances","instances(T::Type) - - Return a collection of all instances of the given type, if - applicable. Mostly used for enumerated types (see \"@enum\"). - -"), - -("Base","method_exists","method_exists(f, Tuple type) -> Bool - - Determine whether the given generic function has a method matching - the given \"Tuple\" of argument types. - - julia> method_exists(length, Tuple{Array}) - true - -"), - -("Base","applicable","applicable(f, args...) -> Bool - - Determine whether the given generic function has a method - applicable to the given arguments. - - julia> function f(x, y) - x + y - end; - - julia> applicable(f, 1) - false - - julia> applicable(f, 1, 2) - true - -"), - -("Base","invoke","invoke(f, (types...), args...) - - Invoke a method for the given generic function matching the - specified types (as a tuple), on the specified arguments. The - arguments must be compatible with the specified types. This allows - invoking a method other than the most specific matching method, - which is useful when the behavior of a more general definition is - explicitly needed (often as part of the implementation of a more - specific method of the same function). - -"), - -("Base","|>","|>(x, f) - - Applies a function to the preceding argument. This allows for easy - function chaining. - - julia> [1:5;] |> x->x.^2 |> sum |> inv - 0.01818181818181818 - -"), - -("Base","call","call(x, args...) - - If \"x\" is not a \"Function\", then \"x(args...)\" is equivalent - to \"call(x, args...)\". This means that function-like behavior - can be added to any type by defining new \"call\" methods. - -"), - -("Base","eval","eval([m::Module], expr::Expr) - - Evaluate an expression in the given module and return the result. - Every module (except those defined with \"baremodule\") has its own - 1-argument definition of \"eval\", which evaluates expressions in - that module. - -"), - -("Base","@eval","@eval() - - Evaluate an expression and return the value. - -"), - -("Base","evalfile","evalfile(path::AbstractString) - - Load the file using \"include\", evaluate all expressions, and - return the value of the last one. - -"), - -("Base","esc","esc(e::ANY) - - Only valid in the context of an Expr returned from a macro. - Prevents the macro hygiene pass from turning embedded variables - into gensym variables. See the *Macros* section of the - Metaprogramming chapter of the manual for more details and - examples. - -"), - -("Base","gensym","gensym([tag]) - - Generates a symbol which will not conflict with other variable - names. - -"), - -("Base","@gensym","@gensym() - - Generates a gensym symbol for a variable. For example, \"@gensym x - y\" is transformed into \"x = gensym(\"x\"); y = gensym(\"y\")\". - -"), - -("Base","parse","parse(str, start; greedy=true, raise=true) - - Parse the expression string and return an expression (which could - later be passed to eval for execution). Start is the index of the - first character to start parsing. If \"greedy\" is true (default), - \"parse\" will try to consume as much input as it can; otherwise, - it will stop as soon as it has parsed a valid expression. - Incomplete but otherwise syntactically valid expressions will - return \"Expr(:incomplete, \"(error message)\")\". If \"raise\" is - true (default), syntax errors other than incomplete expressions - will raise an error. If \"raise\" is false, \"parse\" will return - an expression that will raise an error upon evaluation. - -"), - -("Base","parse","parse(str; raise=true) - - Parse the whole string greedily, returning a single expression. An - error is thrown if there are additional characters after the first - expression. If \"raise\" is true (default), syntax errors will - raise an error; otherwise, \"parse\" will return an expression that - will raise an error upon evaluation. - -"), - -("Base","Nullable","Nullable(x) - - Wrap value \"x\" in an object of type \"Nullable\", which indicates - whether a value is present. \"Nullable(x)\" yields a non-empty - wrapper, and \"Nullable{T}()\" yields an empty instance of a - wrapper that might contain a value of type \"T\". - -"), - -("Base","get","get(x) - - Attempt to access the value of the \"Nullable\" object, \"x\". - Returns the value if it is present; otherwise, throws a - \"NullException\". - -"), - -("Base","get","get(x, y) - - Attempt to access the value of the \"Nullable{T}\" object, \"x\". - Returns the value if it is present; otherwise, returns \"convert(T, - y)\". - -"), - -("Base","isnull","isnull(x) - - Is the \"Nullable\" object \"x\" null, i.e. missing a value? - -"), - -("Base","run","run(command) - - Run a command object, constructed with backticks. Throws an error - if anything goes wrong, including the process exiting with a non- - zero status. - -"), - -("Base","spawn","spawn(command) - - Run a command object asynchronously, returning the resulting - \"Process\" object. - -"), - -("Base","DevNull","DevNull - - Used in a stream redirect to discard all data written to it. - Essentially equivalent to /dev/null on Unix or NUL on Windows. - Usage: \"run(`cat test.txt` |> DevNull)\" - -"), - -("Base","success","success(command) - - Run a command object, constructed with backticks, and tell whether - it was successful (exited with a code of 0). An exception is raised - if the process cannot be started. - -"), - -("Base","process_running","process_running(p::Process) - - Determine whether a process is currently running. - -"), - -("Base","process_exited","process_exited(p::Process) - - Determine whether a process has exited. - -"), - -("Base","kill","kill(p::Process, signum=SIGTERM) - - Send a signal to a process. The default is to terminate the - process. - -"), - -("Base","open","open(command, mode::AbstractString=\"r\", stdio=DevNull) - - Start running \"command\" asynchronously, and return a tuple - \"(stream,process)\". If \"mode\" is \"\"r\"\", then \"stream\" - reads from the process's standard output and \"stdio\" optionally - specifies the process's standard input stream. If \"mode\" is - \"\"w\"\", then \"stream\" writes to the process's standard input - and \"stdio\" optionally specifies the process's standard output - stream. - -"), - -("Base","open","open(f::Function, command, mode::AbstractString=\"r\", stdio=DevNull) - - Similar to \"open(command, mode, stdio)\", but calls \"f(stream)\" - on the resulting read or write stream, then closes the stream and - waits for the process to complete. Returns the value returned by - \"f\". - -"), - -("Base","Sys","Sys.set_process_title(title::AbstractString) - - Set the process title. No-op on some operating systems. (not - exported) - -"), - -("Base","Sys","Sys.get_process_title() - - Get the process title. On some systems, will always return empty - string. (not exported) - -"), - -("Base","readandwrite","readandwrite(command) - - Starts running a command asynchronously, and returns a tuple - (stdout,stdin,process) of the output stream and input stream of the - process, and the process object itself. - -"), - -("Base","ignorestatus","ignorestatus(command) - - Mark a command object so that running it will not throw an error if - the result code is non-zero. - -"), - -("Base","detach","detach(command) - - Mark a command object so that it will be run in a new process - group, allowing it to outlive the julia process, and not have - Ctrl-C interrupts passed to it. - -"), - -("Base","setenv","setenv(command, env; dir=working_dir) - - Set environment variables to use when running the given command. - \"env\" is either a dictionary mapping strings to strings, an array - of strings of the form \"\"var=val\"\", or zero or more - \"\"var\"=>val\" pair arguments. In order to modify (rather than - replace) the existing environment, create \"env\" by \"copy(ENV)\" - and then setting \"env[\"var\"]=val\" as desired, or use - \"withenv\". - - The \"dir\" keyword argument can be used to specify a working - directory for the command. - -"), - -("Base","withenv","withenv(f::Function, kv::Pair...) - - Execute \"f()\" in an environment that is temporarily modified (not - replaced as in \"setenv\") by zero or more \"\"var\"=>val\" - arguments \"kv\". \"withenv\" is generally used via the - \"withenv(kv...) do ... end\" syntax. A value of \"nothing\" can - be used to temporarily unset an environment variable (if it is - set). When \"withenv\" returns, the original environment has been - restored. - -"), - -("Base","pipe","pipe(from, to, ...) - - Create a pipeline from a data source to a destination. The source - and destination can be commands, I/O streams, strings, or results - of other \"pipe\" calls. At least one argument must be a command. - Strings refer to filenames. When called with more than two - arguments, they are chained together from left to right. For - example \"pipe(a,b,c)\" is equivalent to \"pipe(pipe(a,b),c)\". - This provides a more concise way to specify multi-stage pipelines. - - **Examples**: - * \"run(pipe(`ls`, `grep xyz`))\" - - * \"run(pipe(`ls`, \"out.txt\"))\" - - * \"run(pipe(\"out.txt\", `grep xyz`))\" - -"), - -("Base","pipe","pipe(command; stdin, stdout, stderr, append=false) - - Redirect I/O to or from the given \"command\". Keyword arguments - specify which of the command's streams should be redirected. - \"append\" controls whether file output appends to the file. This - is a more general version of the 2-argument \"pipe\" function. - \"pipe(from, to)\" is equivalent to \"pipe(from, stdout=to)\" when - \"from\" is a command, and to \"pipe(to, stdin=from)\" when - \"from\" is another kind of data source. - - **Examples**: - * \"run(pipe(`dothings`, stdout=\"out.txt\", - stderr=\"errs.txt\"))\" - - * \"run(pipe(`update`, stdout=\"log.txt\", append=true))\" - -"), - -("Base","gethostname","gethostname() -> AbstractString - - Get the local machine's host name. - -"), - -("Base","getipaddr","getipaddr() -> AbstractString - - Get the IP address of the local machine, as a string of the form - \"x.x.x.x\". - -"), - -("Base","getpid","getpid() -> Int32 - - Get julia's process ID. - -"), - -("Base","time","time() - - Get the system time in seconds since the epoch, with fairly high - (typically, microsecond) resolution. - -"), - -("Base","time_ns","time_ns() - - Get the time in nanoseconds. The time corresponding to 0 is - undefined, and wraps every 5.8 years. - -"), - -("Base","tic","tic() - - Set a timer to be read by the next call to \"toc()\" or \"toq()\". - The macro call \"@time expr\" can also be used to time evaluation. - -"), - -("Base","toc","toc() - - Print and return the time elapsed since the last \"tic()\". - -"), - -("Base","toq","toq() - - Return, but do not print, the time elapsed since the last - \"tic()\". - -"), - -("Base","@time","@time() - - A macro to execute an expression, printing the time it took to - execute, the number of allocations, and the total number of bytes - its execution caused to be allocated, before returning the value of - the expression. - -"), - -("Base","@timev","@timev() - - This is a verbose version of the \"@time\" macro, it first prints - the same information as \"@time\", then any non-zero memory - allocation counters, and then returns the value of the expression. - -"), - -("Base","@timed","@timed() - - A macro to execute an expression, and return the value of the - expression, elapsed time, total bytes allocated, garbage collection - time, and an object with various memory allocation counters. - -"), - -("Base","@elapsed","@elapsed() - - A macro to evaluate an expression, discarding the resulting value, - instead returning the number of seconds it took to execute as a - floating-point number. - -"), - -("Base","@allocated","@allocated() - - A macro to evaluate an expression, discarding the resulting value, - instead returning the total number of bytes allocated during - evaluation of the expression. Note: the expression is evaluated - inside a local function, instead of the current context, in order - to eliminate the effects of compilation, however, there still may - be some allocations due to JIT compilation. This also makes the - results inconsistent with the \"@time\" macros, which do not try to - adjust for the effects of compilation. - -"), - -("Base","EnvHash","EnvHash() -> EnvHash - - A singleton of this type provides a hash table interface to - environment variables. - -"), - -("Base","ENV","ENV - - Reference to the singleton \"EnvHash\", providing a dictionary - interface to system environment variables. - -"), - -("Base","@unix","@unix() - - Given \"@unix? a : b\", do \"a\" on Unix systems (including Linux - and OS X) and \"b\" elsewhere. See documentation for Handling - Platform Variations in the Calling C and Fortran Code section of - the manual. - -"), - -("Base","@osx","@osx() - - Given \"@osx? a : b\", do \"a\" on OS X and \"b\" elsewhere. See - documentation for Handling Platform Variations in the Calling C and - Fortran Code section of the manual. - -"), - -("Base","@linux","@linux() - - Given \"@linux? a : b\", do \"a\" on Linux and \"b\" elsewhere. See - documentation for Handling Platform Variations in the Calling C and - Fortran Code section of the manual. - -"), - -("Base","@windows","@windows() - - Given \"@windows? a : b\", do \"a\" on Windows and \"b\" elsewhere. - See documentation for Handling Platform Variations in the Calling C - and Fortran Code section of the manual. - -"), - -("Base","error","error(message::AbstractString) - - Raise an \"ErrorException\" with the given message - -"), - -("Base","throw","throw(e) - - Throw an object as an exception - -"), - -("Base","rethrow","rethrow([e]) - - Throw an object without changing the current exception backtrace. - The default argument is the current exception (if called within a - \"catch\" block). - -"), - -("Base","backtrace","backtrace() - - Get a backtrace object for the current program point. - -"), - -("Base","catch_backtrace","catch_backtrace() - - Get the backtrace of the current exception, for use within - \"catch\" blocks. - -"), - -("Base","assert","assert(cond) - - Throw an \"AssertionError\" if \"cond\" is false. Also available as - the macro \"@assert expr\". - -"), - -("","@assert cond [text]","@assert cond [text] - - Throw an \"AssertionError\" if \"cond\" is false. Preferred syntax - for writing assertions. - -"), - -("Base","ArgumentError","ArgumentError(msg) - - The parameters to a function call do not match a valid signature. - -"), - -("Base","AssertionError","AssertionError([msg]) - - The asserted condition did not evalutate to \"true\". - -"), - -("Base","BoundsError","BoundsError([a][, i]) - - An indexing operation into an array, \"a\", tried to access an out- - of-bounds element, \"i\". - -"), - -("Base","DimensionMismatch","DimensionMismatch([msg]) - - The objects called do not have matching dimensionality. - -"), - -("Base","DivideError","DivideError() - - Integer division was attempted with a denominator value of 0. - -"), - -("Base","DomainError","DomainError() - - The arguments to a function or constructor are outside the valid - domain. - -"), - -("Base","EOFError","EOFError() - - No more data was available to read from a file or stream. - -"), - -("Base","ErrorException","ErrorException(msg) - - Generic error type. The error message, in the *.msg* field, may - provide more specific details. - -"), - -("Base","InexactError","InexactError() - - Type conversion cannot be done exactly. - -"), - -("Base","InterruptException","InterruptException() - - The process was stopped by a terminal interrupt (CTRL+C). - -"), - -("Base","KeyError","KeyError(key) - - An indexing operation into an \"Associative\" (\"Dict\") or \"Set\" - like object tried to access or delete a non-existent element. - -"), - -("Base","LoadError","LoadError(file::AbstractString, line::Int, error) - - An error occurred while *including*, *requiring*, or *using* a - file. The error specifics should be available in the *.error* - field. - -"), - -("Base","MethodError","MethodError(f, args) - - A method with the required type signature does not exist in the - given generic function. - -"), - -("Base","NullException","NullException() - - An attempted access to a \"Nullable\" with no defined value. - -"), - -("Base","OutOfMemoryError","OutOfMemoryError() - - An operation allocated too much memory for either the system or the - garbage collector to handle properly. - -"), - -("Base","ReadOnlyMemoryError","ReadOnlyMemoryError() - - An operation tried to write to memory that is read-only. - -"), - -("Base","OverflowError","OverflowError() - - The result of an expression is too large for the specified type and - will cause a wraparound. - -"), - -("Base","ParseError","ParseError(msg) - - The expression passed to the *parse* function could not be - interpreted as a valid Julia expression. - -"), - -("Base","ProcessExitedException","ProcessExitedException() - - After a client Julia process has exited, further attempts to - reference the dead child will throw this exception. - -"), - -("Base","StackOverflowError","StackOverflowError() - - The function call grew beyond the size of the call stack. This - usually happens when a call recurses infinitely. - -"), - -("Base","SystemError","SystemError(prefix::AbstractString[, errnum::Int32]) - - A system call failed with an error code (in the \"errno\" global - variable). - -"), - -("Base","TypeError","TypeError(func::Symbol, context::AbstractString, expected::Type, got) - - A type assertion failure, or calling an intrinsic function with an - incorrect argument type. - -"), - -("Base","UndefRefError","UndefRefError() - - The item or field is not defined for the given object. - -"), - -("Base","UndefVarError","UndefVarError(var::Symbol) - - A symbol in the current scope is not defined. - -"), - -("Base","Timer","Timer(callback::Function, delay, repeat=0) - - Create a timer to call the given callback function. The callback is - passed one argument, the timer object itself. The callback will be - invoked after the specified initial delay, and then repeating with - the given \"repeat\" interval. If \"repeat\" is \"0\", the timer is - only triggered once. Times are in seconds. A timer is stopped and - has its resources freed by calling \"close\" on it. - -"), - -("Base","Timer","Timer(delay, repeat=0) - - Create a timer that wakes up tasks waiting for it (by calling - \"wait\" on the timer object) at a specified interval. Waiting - tasks are also woken up when the timer is closed (by \"close\"). - Use \"isopen\" to check whether a timer is still active after a - wakeup. - -"), - -("Base","module_name","module_name(m::Module) -> Symbol - - Get the name of a module as a symbol. - -"), - -("Base","module_parent","module_parent(m::Module) -> Module - - Get a module's enclosing module. \"Main\" is its own parent. - -"), - -("Base","current_module","current_module() -> Module - - Get the *dynamically* current module, which is the module code is - currently being read from. In general, this is not the same as the - module containing the call to this function. - -"), - -("Base","fullname","fullname(m::Module) - - Get the fully-qualified name of a module as a tuple of symbols. For - example, \"fullname(Base.Pkg)\" gives \"(:Base,:Pkg)\", and - \"fullname(Main)\" gives \"()\". - -"), - -("Base","names","names(x::Module[, all=false[, imported=false]]) - - Get an array of the names exported by a module, with optionally - more module globals according to the additional parameters. - -"), - -("Base","nfields","nfields(x::DataType) -> Int - - Get the number of fields of a data type. - -"), - -("Base","fieldnames","fieldnames(x::DataType) - - Get an array of the fields of a data type. - -"), - -("Base","isconst","isconst([m::Module], s::Symbol) -> Bool - - Determine whether a global is declared \"const\" in a given module. - The default module argument is \"current_module()\". - -"), - -("Base","isgeneric","isgeneric(f::Function) -> Bool - - Determine whether a function is generic. - -"), - -("Base","function_name","function_name(f::Function) -> Symbol - - Get the name of a generic function as a symbol, or \":anonymous\". - -"), - -("Base","function_module","function_module(f::Function, types) -> Module - - Determine the module containing a given definition of a generic - function. - -"), - -("Base","functionloc","functionloc(f::Function, types) - - Returns a tuple \"(filename,line)\" giving the location of a method - definition. - -"), - -("Base","functionloc","functionloc(m::Method) - - Returns a tuple \"(filename,line)\" giving the location of a method - definition. - -"), - -("Base","gc","gc() - - Perform garbage collection. This should not generally be used. - -"), - -("Base","gc_enable","gc_enable(on::Bool) - - Control whether garbage collection is enabled using a boolean - argument (true for enabled, false for disabled). Returns previous - GC state. Disabling garbage collection should be used only with - extreme caution, as it can cause memory use to grow without bound. - -"), - -("Base","macroexpand","macroexpand(x) - - Takes the expression x and returns an equivalent expression with - all macros removed (expanded). - -"), - -("Base","expand","expand(x) - - Takes the expression x and returns an equivalent expression in - lowered form - -"), - -("Base","code_lowered","code_lowered(f, types) - - Returns an array of lowered ASTs for the methods matching the given - generic function and type signature. - -"), - -("Base","@code_lowered","@code_lowered() - - Evaluates the arguments to the function call, determines their - types, and calls \"code_lowered()\" on the resulting expression - -"), - -("Base","code_typed","code_typed(f, types; optimize=true) - - Returns an array of lowered and type-inferred ASTs for the methods - matching the given generic function and type signature. The keyword - argument \"optimize\" controls whether additional optimizations, - such as inlining, are also applied. - -"), - -("Base","@code_typed","@code_typed() - - Evaluates the arguments to the function call, determines their - types, and calls \"code_typed()\" on the resulting expression - -"), - -("Base","code_warntype","code_warntype(f, types) - - Displays lowered and type-inferred ASTs for the methods matching - the given generic function and type signature. The ASTs are - annotated in such a way as to cause \"non-leaf\" types to be - emphasized (if color is available, displayed in red). This serves - as a warning of potential type instability. Not all non-leaf types - are particularly problematic for performance, so the results need - to be used judiciously. See *@code_warntype* for more information. - -"), - -("Base","@code_warntype","@code_warntype() - - Evaluates the arguments to the function call, determines their - types, and calls \"code_warntype()\" on the resulting expression - -"), - -("Base","code_llvm","code_llvm(f, types) - - Prints the LLVM bitcodes generated for running the method matching - the given generic function and type signature to \"STDOUT\". - - All metadata and dbg.* calls are removed from the printed bitcode. - Use code_llvm_raw for the full IR. - -"), - -("Base","@code_llvm","@code_llvm() - - Evaluates the arguments to the function call, determines their - types, and calls \"code_llvm()\" on the resulting expression - -"), - -("Base","code_native","code_native(f, types) - - Prints the native assembly instructions generated for running the - method matching the given generic function and type signature to - STDOUT. - -"), - -("Base","@code_native","@code_native() - - Evaluates the arguments to the function call, determines their - types, and calls \"code_native()\" on the resulting expression - -"), - -("Base","precompile","precompile(f, args::Tuple{Vararg{Any}}) - - Compile the given function \"f\" for the argument tuple (of types) - \"args\", but do not execute it. - -"), - -("Base","ccall","ccall((symbol, library) or function_pointer, ReturnType, (ArgumentType1, ...), ArgumentValue1, ...) - - Call function in C-exported shared library, specified by - \"(function name, library)\" tuple, where each component is an - AbstractString or :Symbol. - - Note that the argument type tuple must be a literal tuple, and not - a tuple-valued variable or expression. Alternatively, ccall may - also be used to call a function pointer, such as one returned by - dlsym. - - Each \"ArgumentValue\" to the \"ccall\" will be converted to the - corresponding \"ArgumentType\", by automatic insertion of calls to - \"unsafe_convert(ArgumentType, cconvert(ArgumentType, - ArgumentValue))\". (see also the documentation for each of these - functions for further details). In most cases, this simply results - in a call to \"convert(ArgumentType, ArgumentValue)\" - -"), - -("Base","cglobal","cglobal((symbol, library)[, type=Void]) - - Obtain a pointer to a global variable in a C-exported shared - library, specified exactly as in \"ccall\". Returns a - \"Ptr{Type}\", defaulting to \"Ptr{Void}\" if no Type argument is - supplied. The values can be read or written by \"unsafe_load\" or - \"unsafe_store!\", respectively. - -"), - -("Base","cfunction","cfunction(function::Function, ReturnType::Type, (ArgumentTypes...)) - - Generate C-callable function pointer from Julia function. Type - annotation of the return value in the callback function is a must - for situations where Julia cannot infer the return type - automatically. - - For example: - - function foo() - # body - - retval::Float64 - end - - bar = cfunction(foo, Float64, ()) - -"), - -("Base","unsafe_convert","unsafe_convert(T, x) - - Convert \"x\" to a value of type \"T\" - - In cases where \"convert\" would need to take a Julia object and - turn it into a \"Ptr\", this function should be used to define and - perform that conversion. - - Be careful to ensure that a julia reference to \"x\" exists as long - as the result of this function will be used. Accordingly, the - argument \"x\" to this function should never be an expression, only - a variable name or field reference. For example, \"x=a.b.c\" is - acceptable, but \"x=[a,b,c]\" is not. - - The \"unsafe\" prefix on this function indicates that using the - result of this function after the \"x\" argument to this function - is no longer accessible to the program may cause undefined - behavior, including program corruption or segfaults, at any later - time. - -"), - -("Base","cconvert","cconvert(T, x) - - Convert \"x\" to a value of type \"T\", typically by calling - \"convert(T,x)\" - - In cases where \"x\" cannot be safely converted to \"T\", unlike - \"convert\", \"cconvert\" may return an object of a type different - from \"T\", which however is suitable for \"unsafe_convert\" to - handle. - - Neither \"convert\" nor \"cconvert\" should take a Julia object and - turn it into a \"Ptr\". - -"), - -("Base","unsafe_load","unsafe_load(p::Ptr{T}, i::Integer) - - Load a value of type \"T\" from the address of the ith element - (1-indexed) starting at \"p\". This is equivalent to the C - expression \"p[i-1]\". - - The \"unsafe\" prefix on this function indicates that no validation - is performed on the pointer \"p\" to ensure that it is valid. - Incorrect usage may segfault your program or return garbage - answers, in the same manner as C. - -"), - -("Base","unsafe_store!","unsafe_store!(p::Ptr{T}, x, i::Integer) - - Store a value of type \"T\" to the address of the ith element - (1-indexed) starting at \"p\". This is equivalent to the C - expression \"p[i-1] = x\". - - The \"unsafe\" prefix on this function indicates that no validation - is performed on the pointer \"p\" to ensure that it is valid. - Incorrect usage may corrupt or segfault your program, in the same - manner as C. - -"), - -("Base","unsafe_copy!","unsafe_copy!(dest::Ptr{T}, src::Ptr{T}, N) - - Copy \"N\" elements from a source pointer to a destination, with no - checking. The size of an element is determined by the type of the - pointers. - - The \"unsafe\" prefix on this function indicates that no validation - is performed on the pointers \"dest\" and \"src\" to ensure that - they are valid. Incorrect usage may corrupt or segfault your - program, in the same manner as C. - -"), - -("Base","unsafe_copy!","unsafe_copy!(dest::Array, do, src::Array, so, N) - - Copy \"N\" elements from a source array to a destination, starting - at offset \"so\" in the source and \"do\" in the destination - (1-indexed). - - The \"unsafe\" prefix on this function indicates that no validation - is performed to ensure that N is inbounds on either array. - Incorrect usage may corrupt or segfault your program, in the same - manner as C. - -"), - -("Base","copy!","copy!(dest, src) - - Copy all elements from collection \"src\" to array \"dest\". - Returns \"dest\". - -"), - -("Base","copy!","copy!(dest, do, src, so, N) - - Copy \"N\" elements from collection \"src\" starting at offset - \"so\", to array \"dest\" starting at offset \"do\". Returns - \"dest\". - -"), - -("Base","pointer","pointer(array[, index]) - - Get the native address of an array or string element. Be careful to - ensure that a julia reference to \"a\" exists as long as this - pointer will be used. This function is \"unsafe\" like - \"unsafe_convert\". - - Calling \"Ref(array[, index])\" is generally preferable to this - function. - -"), - -("Base","pointer_to_array","pointer_to_array(pointer, dims[, take_ownership::Bool]) - - Wrap a native pointer as a Julia Array object. The pointer element - type determines the array element type. \"own\" optionally - specifies whether Julia should take ownership of the memory, - calling \"free\" on the pointer when the array is no longer - referenced. - -"), - -("Base","pointer_from_objref","pointer_from_objref(object_instance) - - Get the memory address of a Julia object as a \"Ptr\". The - existence of the resulting \"Ptr\" will not protect the object from - garbage collection, so you must ensure that the object remains - referenced for the whole time that the \"Ptr\" will be used. - -"), - -("Base","unsafe_pointer_to_objref","unsafe_pointer_to_objref(p::Ptr) - - Convert a \"Ptr\" to an object reference. Assumes the pointer - refers to a valid heap-allocated Julia object. If this is not the - case, undefined behavior results, hence this function is considered - \"unsafe\" and should be used with care. - -"), - -("Base","disable_sigint","disable_sigint(f::Function) - - Disable Ctrl-C handler during execution of a function, for calling - external code that is not interrupt safe. Intended to be called - using \"do\" block syntax as follows: - - disable_sigint() do - # interrupt-unsafe code - ... - end - -"), - -("Base","reenable_sigint","reenable_sigint(f::Function) - - Re-enable Ctrl-C handler during execution of a function. - Temporarily reverses the effect of \"disable_sigint\". - -"), - -("Base","systemerror","systemerror(sysfunc, iftrue) - - Raises a \"SystemError\" for \"errno\" with the descriptive string - \"sysfunc\" if \"bool\" is true - -"), - -("Base","Ptr{T}","Ptr{T} - - A memory address referring to data of type \"T\". However, there is - no guarantee that the memory is actually valid, or that it actually - represents data of the specified type. - -"), - -("Base","Ref{T}","Ref{T} - - An object that safely references data of type \"T\". This type is - guaranteed to point to valid, Julia-allocated memory of the correct - type. The underlying data is protected from freeing by the garbage - collector as long as the \"Ref\" itself is referenced. - - When passed as a \"ccall\" argument (either as a \"Ptr\" or \"Ref\" - type), a \"Ref\" object will be converted to a native pointer to - the data it references. - - There is no invalid (NULL) \"Ref\". - -"), - -("Base","Cchar","Cchar - - Equivalent to the native \"char\" c-type - -"), - -("Base","Cuchar","Cuchar - - Equivalent to the native \"unsigned char\" c-type (UInt8) - -"), - -("Base","Cshort","Cshort - - Equivalent to the native \"signed short\" c-type (Int16) - -"), - -("Base","Cushort","Cushort - - Equivalent to the native \"unsigned short\" c-type (UInt16) - -"), - -("Base","Cint","Cint - - Equivalent to the native \"signed int\" c-type (Int32) - -"), - -("Base","Cuint","Cuint - - Equivalent to the native \"unsigned int\" c-type (UInt32) - -"), - -("Base","Clong","Clong - - Equivalent to the native \"signed long\" c-type - -"), - -("Base","Culong","Culong - - Equivalent to the native \"unsigned long\" c-type - -"), - -("Base","Clonglong","Clonglong - - Equivalent to the native \"signed long long\" c-type (Int64) - -"), - -("Base","Culonglong","Culonglong - - Equivalent to the native \"unsigned long long\" c-type (UInt64) - -"), - -("Base","Cintmax_t","Cintmax_t - - Equivalent to the native \"intmax_t\" c-type (Int64) - -"), - -("Base","Cuintmax_t","Cuintmax_t - - Equivalent to the native \"uintmax_t\" c-type (UInt64) - -"), - -("Base","Csize_t","Csize_t - - Equivalent to the native \"size_t\" c-type (UInt) - -"), - -("Base","Cssize_t","Cssize_t - - Equivalent to the native \"ssize_t\" c-type - -"), - -("Base","Cptrdiff_t","Cptrdiff_t - - Equivalent to the native \"ptrdiff_t\" c-type (Int) - -"), - -("Base","Coff_t","Coff_t - - Equivalent to the native \"off_t\" c-type - -"), - -("Base","Cwchar_t","Cwchar_t - - Equivalent to the native \"wchar_t\" c-type (Int32) - -"), - -("Base","Cfloat","Cfloat - - Equivalent to the native \"float\" c-type (Float32) - -"), - -("Base","Cdouble","Cdouble - - Equivalent to the native \"double\" c-type (Float64) - -"), - -("Base","start","start(iter) -> state - - Get initial iteration state for an iterable object - -"), - -("Base","done","done(iter, state) -> Bool - - Test whether we are done iterating - -"), - -("Base","next","next(iter, state) -> item, state - - For a given iterable object and iteration state, return the current - item and the next iteration state - -"), - -("Base","zip","zip(iters...) - - For a set of iterable objects, returns an iterable of tuples, where - the \"i\"th tuple contains the \"i\"th component of each input - iterable. - - Note that \"zip()\" is its own inverse: - \"collect(zip(zip(a...)...)) == collect(a)\". - -"), - -("Base","enumerate","enumerate(iter) - - An iterator that yields \"(i, x)\" where \"i\" is an index starting - at 1, and \"x\" is the \"i\"th value from the given iterator. It's - useful when you need not only the values \"x\" over which you are - iterating, but also the index \"i\" of the iterations. - - julia> a = [\"a\", \"b\", \"c\"]; - - julia> for (index, value) in enumerate(a) - println(\"\$index \$value\") - end - 1 a - 2 b - 3 c - -"), - -("Base","rest","rest(iter, state) - - An iterator that yields the same elements as \"iter\", but starting - at the given \"state\". - -"), - -("Base","countfrom","countfrom(start=1, step=1) - - An iterator that counts forever, starting at \"start\" and - incrementing by \"step\". - -"), - -("Base","take","take(iter, n) - - An iterator that generates at most the first \"n\" elements of - \"iter\". - -"), - -("Base","drop","drop(iter, n) - - An iterator that generates all but the first \"n\" elements of - \"iter\". - -"), - -("Base","cycle","cycle(iter) - - An iterator that cycles through \"iter\" forever. - -"), - -("Base","repeated","repeated(x[, n::Int]) - - An iterator that generates the value \"x\" forever. If \"n\" is - specified, generates \"x\" that many times (equivalent to - \"take(repeated(x), n)\"). - -"), - -("Base","isempty","isempty(collection) -> Bool - - Determine whether a collection is empty (has no elements). - - julia> isempty([]) - true - - julia> isempty([1 2 3]) - false - -"), - -("Base","empty!","empty!(collection) -> collection - - Remove all elements from a \"collection\". - -"), - -("Base","length","length(collection) -> Integer - - For ordered, indexable collections, the maximum index \"i\" for - which \"getindex(collection, i)\" is valid. For unordered - collections, the number of elements. - -"), - -("Base","endof","endof(collection) -> Integer - - Returns the last index of the collection. - - julia> endof([1,2,4]) - 3 - -"), - -("Base","in","in(item, collection) -> Bool -∈(item, collection) -> Bool -∋(collection, item) -> Bool -∉(item, collection) -> Bool -∌(collection, item) -> Bool - - Determine whether an item is in the given collection, in the sense - that it is \"==\" to one of the values generated by iterating over - the collection. Some collections need a slightly different - definition; for example \"Set\"s check whether the item - \"isequal()\" to one of the elements. \"Dict\"s look for - \"(key,value)\" pairs, and the key is compared using \"isequal()\". - To test for the presence of a key in a dictionary, use \"haskey()\" - or \"k in keys(dict)\". - -"), - -("Base","eltype","eltype(type) - - Determine the type of the elements generated by iterating a - collection of the given \"type\". For associative collection types, - this will be a \"(key,value)\" tuple type. The definition - \"eltype(x) = eltype(typeof(x))\" is provided for convenience so - that instances can be passed instead of types. However the form - that accepts a type argument should be defined for new types. - -"), - -("Base","indexin","indexin(a, b) - - Returns a vector containing the highest index in \"b\" for each - value in \"a\" that is a member of \"b\" . The output vector - contains 0 wherever \"a\" is not a member of \"b\". - -"), - -("Base","findin","findin(a, b) - - Returns the indices of elements in collection \"a\" that appear in - collection \"b\" - -"), - -("Base","unique","unique(itr[, dim]) - - Returns an array containing only the unique elements of the - iterable \"itr\", in the order that the first of each set of - equivalent elements originally appears. If \"dim\" is specified, - returns unique regions of the array \"itr\" along \"dim\". - -"), - -("Base","reduce","reduce(op, v0, itr) - - Reduce the given collection \"ìtr\" with the given binary operator - \"op\". \"v0\" must be a neutral element for \"op\" that will be - returned for empty collections. It is unspecified whether \"v0\" is - used for non-empty collections. - - Reductions for certain commonly-used operators have special - implementations which should be used instead: \"maximum(itr)\", - \"minimum(itr)\", \"sum(itr)\", \"prod(itr)\", \"any(itr)\", - \"all(itr)\". - - The associativity of the reduction is implementation dependent. - This means that you can't use non-associative operations like \"-\" - because it is undefined whether \"reduce(-,[1,2,3])\" should be - evaluated as \"(1-2)-3\" or \"1-(2-3)\". Use \"foldl\" or \"foldr\" - instead for guaranteed left or right associativity. - - Some operations accumulate error, and parallelism will also be - easier if the reduction can be executed in groups. Future versions - of Julia might change the algorithm. Note that the elements are not - reordered if you use an ordered collection. - -"), - -("Base","reduce","reduce(op, itr) - - Like \"reduce(op, v0, itr)\". This cannot be used with empty - collections, except for some special cases (e.g. when \"op\" is one - of \"+\", \"*\", \"max\", \"min\", \"&\", \"|\") when Julia can - determine the neutral element of \"op\". - -"), - -("Base","foldl","foldl(op, v0, itr) - - Like \"reduce()\", but with guaranteed left associativity. \"v0\" - will be used exactly once. - -"), - -("Base","foldl","foldl(op, itr) - - Like \"foldl(op, v0, itr)\", but using the first element of \"itr\" - as \"v0\". In general, this cannot be used with empty collections - (see \"reduce(op, itr)\"). - -"), - -("Base","foldr","foldr(op, v0, itr) - - Like \"reduce()\", but with guaranteed right associativity. \"v0\" - will be used exactly once. - -"), - -("Base","foldr","foldr(op, itr) - - Like \"foldr(op, v0, itr)\", but using the last element of \"itr\" - as \"v0\". In general, this cannot be used with empty collections - (see \"reduce(op, itr)\"). - -"), - -("Base","maximum","maximum(itr) - - Returns the largest element in a collection. - -"), - -("Base","maximum","maximum(A, dims) - - Compute the maximum value of an array over the given dimensions. - -"), - -("Base","maximum!","maximum!(r, A) - - Compute the maximum value of \"A\" over the singleton dimensions of - \"r\", and write results to \"r\". - -"), - -("Base","minimum","minimum(itr) - - Returns the smallest element in a collection. - -"), - -("Base","minimum","minimum(A, dims) - - Compute the minimum value of an array over the given dimensions. - -"), - -("Base","minimum!","minimum!(r, A) - - Compute the minimum value of \"A\" over the singleton dimensions of - \"r\", and write results to \"r\". - -"), - -("Base","extrema","extrema(itr) - - Compute both the minimum and maximum element in a single pass, and - return them as a 2-tuple. - -"), - -("Base","indmax","indmax(itr) -> Integer - - Returns the index of the maximum element in a collection. - -"), - -("Base","indmin","indmin(itr) -> Integer - - Returns the index of the minimum element in a collection. - -"), - -("Base","findmax","findmax(itr) -> (x, index) - - Returns the maximum element and its index. - -"), - -("Base","findmax","findmax(A, dims) -> (maxval, index) - - For an array input, returns the value and index of the maximum over - the given dimensions. - -"), - -("Base","findmin","findmin(itr) -> (x, index) - - Returns the minimum element and its index. - -"), - -("Base","findmin","findmin(A, dims) -> (minval, index) - - For an array input, returns the value and index of the minimum over - the given dimensions. - -"), - -("Base","maxabs","maxabs(itr) - - Compute the maximum absolute value of a collection of values. - -"), - -("Base","maxabs","maxabs(A, dims) - - Compute the maximum absolute values over given dimensions. - -"), - -("Base","maxabs!","maxabs!(r, A) - - Compute the maximum absolute values over the singleton dimensions - of \"r\", and write values to \"r\". - -"), - -("Base","minabs","minabs(itr) - - Compute the minimum absolute value of a collection of values. - -"), - -("Base","minabs","minabs(A, dims) - - Compute the minimum absolute values over given dimensions. - -"), - -("Base","minabs!","minabs!(r, A) - - Compute the minimum absolute values over the singleton dimensions - of \"r\", and write values to \"r\". - -"), - -("Base","sum","sum(itr) - - Returns the sum of all elements in a collection. - -"), - -("Base","sum","sum(A, dims) - - Sum elements of an array over the given dimensions. - -"), - -("Base","sum!","sum!(r, A) - - Sum elements of \"A\" over the singleton dimensions of \"r\", and - write results to \"r\". - -"), - -("Base","sum","sum(f, itr) - - Sum the results of calling function \"f\" on each element of - \"itr\". - -"), - -("Base","sumabs","sumabs(itr) - - Sum absolute values of all elements in a collection. This is - equivalent to *sum(abs(itr))* but faster. - -"), - -("Base","sumabs","sumabs(A, dims) - - Sum absolute values of elements of an array over the given - dimensions. - -"), - -("Base","sumabs!","sumabs!(r, A) - - Sum absolute values of elements of \"A\" over the singleton - dimensions of \"r\", and write results to \"r\". - -"), - -("Base","sumabs2","sumabs2(itr) - - Sum squared absolute values of all elements in a collection. This - is equivalent to *sum(abs2(itr))* but faster. - -"), - -("Base","sumabs2","sumabs2(A, dims) - - Sum squared absolute values of elements of an array over the given - dimensions. - -"), - -("Base","sumabs2!","sumabs2!(r, A) - - Sum squared absolute values of elements of \"A\" over the singleton - dimensions of \"r\", and write results to \"r\". - -"), - -("Base","prod","prod(itr) - - Returns the product of all elements of a collection. - -"), - -("Base","prod","prod(A, dims) - - Multiply elements of an array over the given dimensions. - -"), - -("Base","prod!","prod!(r, A) - - Multiply elements of \"A\" over the singleton dimensions of \"r\", - and write results to \"r\". - -"), - -("Base","any","any(itr) -> Bool - - Test whether any elements of a boolean collection are true. - -"), - -("Base","any","any(A, dims) - - Test whether any values along the given dimensions of an array are - true. - -"), - -("Base","any!","any!(r, A) - - Test whether any values in \"A\" along the singleton dimensions of - \"r\" are true, and write results to \"r\". - -"), - -("Base","all","all(itr) -> Bool - - Test whether all elements of a boolean collection are true. - -"), - -("Base","all","all(A, dims) - - Test whether all values along the given dimensions of an array are - true. - -"), - -("Base","all!","all!(r, A) - - Test whether all values in \"A\" along the singleton dimensions of - \"r\" are true, and write results to \"r\". - -"), - -("Base","count","count(p, itr) -> Integer - - Count the number of elements in \"itr\" for which predicate \"p\" - returns true. - -"), - -("Base","any","any(p, itr) -> Bool - - Determine whether predicate \"p\" returns true for any elements of - \"itr\". - -"), - -("Base","all","all(p, itr) -> Bool - - Determine whether predicate \"p\" returns true for all elements of - \"itr\". - - julia> all(i->(4<=i<=6), [4,5,6]) - true - -"), - -("Base","map","map(f, c...) -> collection - - Transform collection \"c\" by applying \"f\" to each element. For - multiple collection arguments, apply \"f\" elementwise. - - julia> map((x) -> x * 2, [1, 2, 3]) - 3-element Array{Int64,1}: - 2 - 4 - 6 - - julia> map(+, [1, 2, 3], [10, 20, 30]) - 3-element Array{Int64,1}: - 11 - 22 - 33 - -"), - -("Base","map!","map!(function, collection) - - In-place version of \"map()\". - -"), - -("Base","map!","map!(function, destination, collection...) - - Like \"map()\", but stores the result in \"destination\" rather - than a new collection. \"destination\" must be at least as large as - the first collection. - -"), - -("Base","mapreduce","mapreduce(f, op, v0, itr) - - Apply function \"f\" to each element in \"itr\", and then reduce - the result using the binary function \"op\". \"v0\" must be a - neutral element for \"op\" that will be returned for empty - collections. It is unspecified whether \"v0\" is used for non-empty - collections. - - \"mapreduce()\" is functionally equivalent to calling \"reduce(op, - v0, map(f, itr))\", but will in general execute faster since no - intermediate collection needs to be created. See documentation for - \"reduce()\" and \"map()\". - - julia> mapreduce(x->x^2, +, [1:3;]) # == 1 + 4 + 9 - 14 - - The associativity of the reduction is implementation-dependent. - Additionally, some implementations may reuse the return value of - \"f\" for elements that appear multiple times in \"itr\". Use - \"mapfoldl()\" or \"mapfoldr()\" instead for guaranteed left or - right associativity and invocation of \"f\" for every value. - -"), - -("Base","mapreduce","mapreduce(f, op, itr) - - Like \"mapreduce(f, op, v0, itr)\". In general, this cannot be used - with empty collections (see \"reduce(op, itr)\"). - -"), - -("Base","mapfoldl","mapfoldl(f, op, v0, itr) - - Like \"mapreduce()\", but with guaranteed left associativity. - \"v0\" will be used exactly once. - -"), - -("Base","mapfoldl","mapfoldl(f, op, itr) - - Like \"mapfoldl(f, op, v0, itr)\", but using the first element of - \"itr\" as \"v0\". In general, this cannot be used with empty - collections (see \"reduce(op, itr)\"). - -"), - -("Base","mapfoldr","mapfoldr(f, op, v0, itr) - - Like \"mapreduce()\", but with guaranteed right associativity. - \"v0\" will be used exactly once. - -"), - -("Base","mapfoldr","mapfoldr(f, op, itr) - - Like \"mapfoldr(f, op, v0, itr)\", but using the first element of - \"itr\" as \"v0\". In general, this cannot be used with empty - collections (see \"reduce(op, itr)\"). - -"), - -("Base","first","first(coll) - - Get the first element of an iterable collection. Returns the start - point of a \"Range\" even if it is empty. - -"), - -("Base","last","last(coll) - - Get the last element of an ordered collection, if it can be - computed in O(1) time. This is accomplished by calling \"endof()\" - to get the last index. Returns the end point of a \"Range\" even if - it is empty. - -"), - -("Base","step","step(r) - - Get the step size of a \"Range\" object. - -"), - -("Base","collect","collect(collection) - - Return an array of all items in a collection. For associative - collections, returns (key, value) tuples. - -"), - -("Base","collect","collect(element_type, collection) - - Return an array of type \"Array{element_type,1}\" of all items in a - collection. - -"), - -("Base","issubset","issubset(a, b) -⊆(A, S) -> Bool -⊈(A, S) -> Bool -⊊(A, S) -> Bool - - Determine whether every element of \"a\" is also in \"b\", using - \"in()\". - -"), - -("Base","filter","filter(function, collection) - - Return a copy of \"collection\", removing elements for which - \"function\" is false. For associative collections, the function is - passed two arguments (key and value). - -"), - -("Base","filter!","filter!(function, collection) - - Update \"collection\", removing elements for which \"function\" is - false. For associative collections, the function is passed two - arguments (key and value). - -"), - -("Base","getindex","getindex(collection, key...) - - Retrieve the value(s) stored at the given key or index within a - collection. The syntax \"a[i,j,...]\" is converted by the compiler - to \"getindex(a, i, j, ...)\". - -"), - -("Base","setindex!","setindex!(collection, value, key...) - - Store the given value at the given key or index within a - collection. The syntax \"a[i,j,...] = x\" is converted by the - compiler to \"setindex!(a, x, i, j, ...)\". - -"), - -("Base","Dict","Dict([itr]) - - \"Dict{K,V}()\" constructs a hash table with keys of type \"K\" and - values of type \"V\". - - Given a single iterable argument, constructs a \"Dict\" whose key- - value pairs are taken from 2-tuples \"(key,value)\" generated by - the argument. - - julia> Dict([(\"A\", 1), (\"B\", 2)]) - Dict{ASCIIString,Int64} with 2 entries: - \"B\" => 2 - \"A\" => 1 - - Alternatively, a sequence of pair arguments may be passed. - - julia> Dict(\"A\"=>1, \"B\"=>2) - Dict{ASCIIString,Int64} with 2 entries: - \"B\" => 2 - \"A\" => 1 - -"), - -("Base","haskey","haskey(collection, key) -> Bool - - Determine whether a collection has a mapping for a given key. - -"), - -("Base","get","get(collection, key, default) - - Return the value stored for the given key, or the given default - value if no mapping for the key is present. - -"), - -("Base","get","get(f::Function, collection, key) - - Return the value stored for the given key, or if no mapping for the - key is present, return \"f()\". Use \"get!()\" to also store the - default value in the dictionary. - - This is intended to be called using \"do\" block syntax: - - get(dict, key) do - # default value calculated here - time() - end - -"), - -("Base","get!","get!(collection, key, default) - - Return the value stored for the given key, or if no mapping for the - key is present, store \"key => default\", and return \"default\". - -"), - -("Base","get!","get!(f::Function, collection, key) - - Return the value stored for the given key, or if no mapping for the - key is present, store \"key => f()\", and return \"f()\". - - This is intended to be called using \"do\" block syntax: - - get!(dict, key) do - # default value calculated here - time() - end - -"), - -("Base","getkey","getkey(collection, key, default) - - Return the key matching argument \"key\" if one exists in - \"collection\", otherwise return \"default\". - -"), - -("Base","delete!","delete!(collection, key) - - Delete the mapping for the given key in a collection, and return - the collection. - -"), - -("Base","pop!","pop!(collection, key[, default]) - - Delete and return the mapping for \"key\" if it exists in - \"collection\", otherwise return \"default\", or throw an error if - default is not specified. - -"), - -("Base","keys","keys(collection) - - Return an iterator over all keys in a collection. - \"collect(keys(d))\" returns an array of keys. - -"), - -("Base","values","values(collection) - - Return an iterator over all values in a collection. - \"collect(values(d))\" returns an array of values. - -"), - -("Base","merge","merge(collection, others...) - - Construct a merged collection from the given collections. If - necessary, the types of the resulting collection will be promoted - to accommodate the types of the merged collections. If the same key - is present in another collection, the value for that key will be - the value it has in the last collection listed. - - julia> a = Dict(\"foo\" => 0.0, \"bar\" => 42.0) - Dict{ASCIIString,Float64} with 2 entries: - \"bar\" => 42.0 - \"foo\" => 0.0 - - julia> b = Dict(utf8(\"baz\") => 17, utf8(\"bar\") => 4711) - Dict{UTF8String,Int64} with 2 entries: - \"bar\" => 4711 - \"baz\" => 17 - - julia> merge(a, b) - Dict{UTF8String,Float64} with 3 entries: - \"bar\" => 4711.0 - \"baz\" => 17.0 - \"foo\" => 0.0 - - julia> merge(b, a) - Dict{UTF8String,Float64} with 3 entries: - \"bar\" => 42.0 - \"baz\" => 17.0 - \"foo\" => 0.0 - -"), - -("Base","merge!","merge!(collection, others...) - - Update collection with pairs from the other collections - -"), - -("Base","sizehint!","sizehint!(s, n) - - Suggest that collection \"s\" reserve capacity for at least \"n\" - elements. This can improve performance. - -"), - -("Base","Set","Set([itr]) - - Construct a \"Set\" of the values generated by the given iterable - object, or an empty set. Should be used instead of \"IntSet\" for - sparse integer sets, or for sets of arbitrary objects. - -"), - -("Base","IntSet","IntSet([itr]) - - Construct a sorted set of the integers generated by the given - iterable object, or an empty set. Implemented as a bit string, and - therefore designed for dense integer sets. Only non-negative - integers can be stored. If the set will be sparse (for example - holding a single very large integer), use \"Set\" instead. - -"), - -("Base","union","union(s1, s2...) -∪(s1, s2) - - Construct the union of two or more sets. Maintains order with - arrays. - -"), - -("Base","union!","union!(s, iterable) - - Union each element of \"iterable\" into set \"s\" in-place. - -"), - -("Base","intersect","intersect(s1, s2...) -∩(s1, s2) - - Construct the intersection of two or more sets. Maintains order and - multiplicity of the first argument for arrays and ranges. - -"), - -("Base","setdiff","setdiff(s1, s2) - - Construct the set of elements in \"s1\" but not \"s2\". Maintains - order with arrays. Note that both arguments must be collections, - and both will be iterated over. In particular, - \"setdiff(set,element)\" where \"element\" is a potential member of - \"set\", will not work in general. - -"), - -("Base","setdiff!","setdiff!(s, iterable) - - Remove each element of \"iterable\" from set \"s\" in-place. - -"), - -("Base","symdiff","symdiff(s1, s2...) - - Construct the symmetric difference of elements in the passed in - sets or arrays. Maintains order with arrays. - -"), - -("Base","symdiff!","symdiff!(s, n) - - The set \"s\" is destructively modified to toggle the inclusion of - integer \"n\". - -"), - -("Base","symdiff!","symdiff!(s, itr) - - For each element in \"itr\", destructively toggle its inclusion in - set \"s\". - -"), - -("Base","symdiff!","symdiff!(s1, s2) - - Construct the symmetric difference of sets \"s1\" and \"s2\", - storing the result in \"s1\". - -"), - -("Base","complement","complement(s) - - Returns the set-complement of \"IntSet\" \"s\". - -"), - -("Base","complement!","complement!(s) - - Mutates \"IntSet\" \"s\" into its set-complement. - -"), - -("Base","intersect!","intersect!(s1, s2) - - Intersects sets \"s1\" and \"s2\" and overwrites the set \"s1\" - with the result. If needed, \"s1\" will be expanded to the size of - \"s2\". - -"), - -("Base","issubset","issubset(A, S) -> Bool -⊆(A, S) -> Bool - - True if A is a subset of or equal to S. - -"), - -("Base","push!","push!(collection, items...) -> collection - - Insert one or more \"items\" at the end of \"collection\". - - julia> push!([1, 2, 3], 4, 5, 6) - 6-element Array{Int64,1}: - 1 - 2 - 3 - 4 - 5 - 6 - - Use \"append!()\" to add all the elements of another collection to - \"collection\". The result of the preceding example is equivalent - to \"append!([1, 2, 3], [4, 5, 6])\". - -"), - -("Base","pop!","pop!(collection) -> item - - Remove the last item in \"collection\" and return it. - - julia> A=[1, 2, 3, 4, 5, 6] - 6-element Array{Int64,1}: - 1 - 2 - 3 - 4 - 5 - 6 - - julia> pop!(A) - 6 - - julia> A - 5-element Array{Int64,1}: - 1 - 2 - 3 - 4 - 5 - -"), - -("Base","unshift!","unshift!(collection, items...) -> collection - - Insert one or more \"items\" at the beginning of \"collection\". - - julia> unshift!([1, 2, 3, 4], 5, 6) - 6-element Array{Int64,1}: - 5 - 6 - 1 - 2 - 3 - 4 - -"), - -("Base","shift!","shift!(collection) -> item - - Remove the first \"item\" from \"collection\". - - julia> A = [1, 2, 3, 4, 5, 6] - 6-element Array{Int64,1}: - 1 - 2 - 3 - 4 - 5 - 6 - - julia> shift!(A) - 1 - - julia> A - 5-element Array{Int64,1}: - 2 - 3 - 4 - 5 - 6 - -"), - -("Base","insert!","insert!(collection, index, item) - - Insert an \"item\" into \"collection\" at the given \"index\". - \"index\" is the index of \"item\" in the resulting \"collection\". - - julia> insert!([6, 5, 4, 2, 1], 4, 3) - 6-element Array{Int64,1}: - 6 - 5 - 4 - 3 - 2 - 1 - -"), - -("Base","deleteat!","deleteat!(collection, index) - - Remove the item at the given \"index\" and return the modified - \"collection\". Subsequent items are shifted to fill the resulting - gap. - - julia> deleteat!([6, 5, 4, 3, 2, 1], 2) - 5-element Array{Int64,1}: - 6 - 4 - 3 - 2 - 1 - -"), - -("Base","deleteat!","deleteat!(collection, itr) - - Remove the items at the indices given by \"itr\", and return the - modified \"collection\". Subsequent items are shifted to fill the - resulting gap. \"itr\" must be sorted and unique. - - julia> deleteat!([6, 5, 4, 3, 2, 1], 1:2:5) - 3-element Array{Int64,1}: - 5 - 3 - 1 - - julia> deleteat!([6, 5, 4, 3, 2, 1], (2, 2)) - ERROR: ArgumentError: indices must be unique and sorted - in deleteat! at array.jl:631 - -"), - -("Base","splice!","splice!(collection, index[, replacement]) -> item - - Remove the item at the given index, and return the removed item. - Subsequent items are shifted down to fill the resulting gap. If - specified, replacement values from an ordered collection will be - spliced in place of the removed item. - - julia> A = [6, 5, 4, 3, 2, 1]; splice!(A, 5) - 2 - - julia> A - 5-element Array{Int64,1}: - 6 - 5 - 4 - 3 - 1 - - julia> splice!(A, 5, -1) - 1 - - julia> A - 5-element Array{Int64,1}: - 6 - 5 - 4 - 3 - -1 - - julia> splice!(A, 1, [-1, -2, -3]) - 6 - - julia> A - 7-element Array{Int64,1}: - -1 - -2 - -3 - 5 - 4 - 3 - -1 - - To insert \"replacement\" before an index \"n\" without removing - any items, use \"splice!(collection, n:n-1, replacement)\". - -"), - -("Base","splice!","splice!(collection, range[, replacement]) -> items - - Remove items in the specified index range, and return a collection - containing the removed items. Subsequent items are shifted down to - fill the resulting gap. If specified, replacement values from an - ordered collection will be spliced in place of the removed items. - - To insert \"replacement\" before an index \"n\" without removing - any items, use \"splice!(collection, n:n-1, replacement)\". - - julia> splice!(A, 4:3, 2) - 0-element Array{Int64,1} - - julia> A - 8-element Array{Int64,1}: - -1 - -2 - -3 - 2 - 5 - 4 - 3 - -1 - -"), - -("Base","resize!","resize!(collection, n) -> collection - - Resize \"collection\" to contain \"n\" elements. If \"n\" is - smaller than the current collection length, the first \"n\" - elements will be retained. If \"n\" is larger, the new elements are - not guaranteed to be initialized. - - julia> resize!([6, 5, 4, 3, 2, 1], 3) - 3-element Array{Int64,1}: - 6 - 5 - 4 - - julia> resize!([6, 5, 4, 3, 2, 1], 8) - 8-element Array{Int64,1}: - 6 - 5 - 4 - 3 - 2 - 1 - 0 - 0 - -"), - -("Base","append!","append!(collection, collection2) -> collection. - - Add the elements of \"collection2\" to the end of \"collection\". - - julia> append!([1],[2,3]) - 3-element Array{Int64,1}: - 1 - 2 - 3 - - julia> append!([1, 2, 3], [4, 5, 6]) - 6-element Array{Int64,1}: - 1 - 2 - 3 - 4 - 5 - 6 - - Use \"push!()\" to add individual items to \"collection\" which are - not already themselves in another collection. The result is of the - preceding example is equivalent to \"push!([1, 2, 3], 4, 5, 6)\". - -"), - -("Base","prepend!","prepend!(collection, items) -> collection - - Insert the elements of \"items\" to the beginning of - \"collection\". - - julia> prepend!([3],[1,2]) - 3-element Array{Int64,1}: - 1 - 2 - 3 - -"), - -("Base.Collections","PriorityQueue","PriorityQueue(K, V[, ord]) - - Construct a new \"PriorityQueue\", with keys of type \"K\" and - values/priorites of type \"V\". If an order is not given, the - priority queue is min-ordered using the default comparison for - \"V\". - -"), - -("Base.Collections","enqueue!","enqueue!(pq, k, v) - - Insert the a key \"k\" into a priority queue \"pq\" with priority - \"v\". - -"), - -("Base.Collections","dequeue!","dequeue!(pq) - - Remove and return the lowest priority key from a priority queue. - -"), - -("Base.Collections","peek","peek(pq) - - Return the lowest priority key from a priority queue without - removing that key from the queue. - -"), - -("Base.Collections","heapify","heapify(v[, ord]) - - Return a new vector in binary heap order, optionally using the - given ordering. - -"), - -("Base.Collections","heapify!","heapify!(v[, ord]) - - In-place \"heapify()\". - -"), - -("Base.Collections","isheap","isheap(v[, ord]) - - Return true iff an array is heap-ordered according to the given - order. - -"), - -("Base.Collections","heappush!","heappush!(v, x[, ord]) - - Given a binary heap-ordered array, push a new element \"x\", - preserving the heap property. For efficiency, this function does - not check that the array is indeed heap-ordered. - -"), - -("Base.Collections","heappop!","heappop!(v[, ord]) - - Given a binary heap-ordered array, remove and return the lowest - ordered element. For efficiency, this function does not check that - the array is indeed heap-ordered. - -"), - -("Base","nothing","nothing - - The singleton instance of type \"Void\", used by convention when - there is no value to return (as in a C \"void\" function). Can be - converted to an empty \"Nullable\" value. - -"), - -("Base","OS_NAME","OS_NAME - - A symbol representing the name of the operating system. Possible - values are \":Linux\", \":Darwin\" (OS X), or \":Windows\". - -"), - -("Base","ARGS","ARGS - - An array of the command line arguments passed to Julia, as strings. - -"), - -("Base","C_NULL","C_NULL - - The C null pointer constant, sometimes used when calling external - code. - -"), - -("Base","CPU_CORES","CPU_CORES - - The number of CPU cores in the system. - -"), - -("Base","WORD_SIZE","WORD_SIZE - - Standard word size on the current machine, in bits. - -"), - -("Base","VERSION","VERSION - - An object describing which version of Julia is in use. - -"), - -("Base","LOAD_PATH","LOAD_PATH - - An array of paths (as strings) where the \"require\" function looks - for code. - -"), - -("Base","JULIA_HOME","JULIA_HOME - - A string containing the full path to the directory containing the - \"julia\" executable. - -"), - -("Base","ANY","ANY - - Equivalent to \"Any\" for dispatch purposes, but signals the - compiler to skip code generation specialization for that field - -"), - -("Dates","Period","Period - -"), - -("Dates","Year","Year - -"), - -("Dates","Month","Month - -"), - -("Dates","Week","Week - -"), - -("Dates","Day","Day - -"), - -("Dates","Hour","Hour - -"), - -("Dates","Minute","Minute - -"), - -("Dates","Second","Second - -"), - -("Dates","Millisecond","Millisecond - - \"Period\" types represent discrete, human representations of time. - -"), - -("Dates","Instant","Instant - - \"Instant\" types represent integer-based, machine representations - of time as continuous timelines starting from an epoch. - -"), - -("Dates","UTInstant{T}","UTInstant{T} - - The \"UTInstant\" represents a machine timeline based on *UT* time - (1 day = one revolution of the earth). The \"{T}\" is a \"Period\" - parameter that indicates the resolution or precision of the - instant. - -"), - -("Dates","TimeType","TimeType - - \"TimeType\" types wrap \"Instant\" machine instances to provide - human representations of the machine instant. - -"), - -("Dates","DateTime","DateTime - - \"DateTime\" wraps a \"UTInstant{Millisecond}\" and interprets it - according to the proleptic Gregorian calendar. - -"), - -("Dates","Date","Date - - \"Date\" wraps a \"UTInstant{Day}\" and interprets it according to - the proleptic Gregorian calendar. - -"), - -("Dates","DateTime","DateTime(y[, m, d, h, mi, s, ms]) -> DateTime - - Construct a DateTime type by parts. Arguments must be convertible - to \"Int64\". - -"), - -("Dates","DateTime","DateTime(periods::Period...) -> DateTime - - Constuct a DateTime type by \"Period\" type parts. Arguments may be - in any order. DateTime parts not provided will default to the value - of \"Dates.default(period)\". - -"), - -("Dates","DateTime","DateTime(f::Function, y[, m, d, h, mi, s]; step=Day(1), negate=false, limit=10000) -> DateTime - - Create a DateTime through the adjuster API. The starting point will - be constructed from the provided \"y, m, d...\" arguments, and will - be adjusted until \"f::Function\" returns true. The step size in - adjusting can be provided manually through the \"step\" keyword. If - \"negate=true\", then the adjusting will stop when \"f::Function\" - returns false instead of true. \"limit\" provides a limit to the - max number of iterations the adjustment API will pursue before - throwing an error (in the case that \"f::Function\" is never - satisfied). - -"), - -("Dates","DateTime","DateTime(dt::Date) -> DateTime - - Converts a \"Date\" type to a \"DateTime\". The hour, minute, - second, and millisecond parts of the new \"DateTime\" are assumed - to be zero. - -"), - -("Dates","DateTime","DateTime(dt::AbstractString, format::AbstractString; locale=\"english\") -> DateTime - - Construct a DateTime type by parsing the \"dt\" date string - following the pattern given in the \"format\" string. The following - codes can be used for constructing format strings: - - +-----------------+-----------+-----------------------------------------------------------------+ - | Code | Matches | Comment | - +-----------------+-----------+-----------------------------------------------------------------+ - | \\\"y\\\" | 1996, 96 | Returns year of 1996, 0096 | - +-----------------+-----------+-----------------------------------------------------------------+ - | \\\"m\\\" | 1, 01 | Matches 1 or 2-digit months | - +-----------------+-----------+-----------------------------------------------------------------+ - | \\\"u\\\" | Jan | Matches abbreviated months according to the \\\"locale\\\" keyword | - +-----------------+-----------+-----------------------------------------------------------------+ - | \\\"U\\\" | January | Matches full month names according to the \\\"locale\\\" keyword | - +-----------------+-----------+-----------------------------------------------------------------+ - | \\\"d\\\" | 1, 01 | Matches 1 or 2-digit days | - +-----------------+-----------+-----------------------------------------------------------------+ - | \\\"H\\\" | 00 | Matches hours | - +-----------------+-----------+-----------------------------------------------------------------+ - | \\\"M\\\" | 00 | Matches minutes | - +-----------------+-----------+-----------------------------------------------------------------+ - | \\\"S\\\" | 00 | Matches seconds | - +-----------------+-----------+-----------------------------------------------------------------+ - | \\\"s\\\" | .500 | Matches milliseconds | - +-----------------+-----------+-----------------------------------------------------------------+ - | \\\"e\\\" | Mon, Tues | Matches abbreviated days of the week | - +-----------------+-----------+-----------------------------------------------------------------+ - | \\\"E\\\" | Monday | Matches full name days of the week | - +-----------------+-----------+-----------------------------------------------------------------+ - | \\\"yyyymmdd\\\" | 19960101 | Matches fixed-width year, month, and day | - +-----------------+-----------+-----------------------------------------------------------------+ - - All characters not listed above are treated as delimiters between - date and time slots. So a \"dt\" string of - \"1996-01-15T00:00:00.0\" would have a \"format\" string like - \"y-m-dTH:M:S.s\". - -"), - -("Dates","Dates","Dates.DateFormat(format::AbstractString) -> DateFormat - - Construct a date formatting object that can be passed repeatedly - for parsing similarly formatted date strings. \"format\" is a - format string in the form described above (e.g. \"\"yyyy-mm- - dd\"\"). - -"), - -("Dates","DateTime","DateTime(dt::AbstractString, df::DateFormat) -> DateTime - - Similar form as above for parsing a \"DateTime\", but passes a - \"DateFormat\" object instead of a raw formatting string. It is - more efficient if similarly formatted date strings will be parsed - repeatedly to first create a \"DateFormat\" object then use this - method for parsing. - -"), - -("Dates","Date","Date(y[, m, d]) -> Date - - Construct a \"Date\" type by parts. Arguments must be convertible - to \"Int64\". - -"), - -("Dates","Date","Date(period::Period...) -> Date - - Constuct a Date type by \"Period\" type parts. Arguments may be in - any order. Date parts not provided will default to the value of - \"Dates.default(period)\". - -"), - -("Dates","Date","Date(f::Function, y[, m]; step=Day(1), negate=false, limit=10000) -> Date - - Create a Date through the adjuster API. The starting point will be - constructed from the provided \"y, m\" arguments, and will be - adjusted until \"f::Function\" returns true. The step size in - adjusting can be provided manually through the \"step\" keyword. If - \"negate=true\", then the adjusting will stop when \"f::Function\" - returns false instead of true. \"limit\" provides a limit to the - max number of iterations the adjustment API will pursue before - throwing an error (given that \"f::Function\" is never satisfied). - -"), - -("Dates","Date","Date(dt::DateTime) -> Date - - Converts a \"DateTime\" type to a \"Date\". The hour, minute, - second, and millisecond parts of the \"DateTime\" are truncated, so - only the year, month and day parts are used in construction. - -"), - -("Dates","Date","Date(dt::AbstractString, format::AbstractString; locale=\"english\") -> Date - - Construct a Date type by parsing a \"dt\" date string following the - pattern given in the \"format\" string. Follows the same - conventions as \"DateTime\" above. - -"), - -("Dates","Date","Date(dt::AbstractString, df::DateFormat) -> Date - - Parse a date from a date string \"dt\" using a \"DateFormat\" - object \"df\". - -"), - -("Dates","now","now() -> DateTime - - Returns a DateTime corresponding to the user's system time - including the system timezone locale. - -"), - -("Dates","now","now(::Type{UTC}) -> DateTime - - Returns a DateTime corresponding to the user's system time as - UTC/GMT. - -"), - -("Dates","eps","eps(::DateTime) -> Millisecond -eps(::Date) -> Day - - Returns \"Millisecond(1)\" for \"DateTime\" values and \"Day(1)\" - for \"Date\" values. - -"), - -("Dates","year","year(dt::TimeType) -> Int64 -month(dt::TimeType) -> Int64 -week(dt::TimeType) -> Int64 -day(dt::TimeType) -> Int64 -hour(dt::TimeType) -> Int64 -minute(dt::TimeType) -> Int64 -second(dt::TimeType) -> Int64 -millisecond(dt::TimeType) -> Int64 - - Return the field part of a Date or DateTime as an \"Int64\". - -"), - -("Dates","Year","Year(dt::TimeType) -> Year -Month(dt::TimeType) -> Month -Week(dt::TimeType) -> Week -Day(dt::TimeType) -> Day -Hour(dt::TimeType) -> Hour -Minute(dt::TimeType) -> Minute -Second(dt::TimeType) -> Second -Millisecond(dt::TimeType) -> Millisecond - - Return the field part of a Date or DateTime as a \"Period\" type. - -"), - -("Dates","yearmonth","yearmonth(dt::TimeType) -> (Int64, Int64) - - Simultaneously return the year and month parts of a Date or - DateTime. - -"), - -("Dates","monthday","monthday(dt::TimeType) -> (Int64, Int64) - - Simultaneously return the month and day parts of a Date or - DateTime. - -"), - -("Dates","yearmonthday","yearmonthday(dt::TimeType) -> (Int64, Int64, Int64) - - Simultaneously return the year, month, and day parts of a Date or - DateTime. - -"), - -("Dates","dayname","dayname(dt::TimeType; locale=\"english\") -> AbstractString - - Return the full day name corresponding to the day of the week of - the Date or DateTime in the given \"locale\". - -"), - -("Dates","dayabbr","dayabbr(dt::TimeType; locale=\"english\") -> AbstractString - - Return the abbreviated name corresponding to the day of the week of - the Date or DateTime in the given \"locale\". - -"), - -("Dates","dayofweek","dayofweek(dt::TimeType) -> Int64 - - Returns the day of the week as an \"Int64\" with \"1 = Monday, 2 = - Tuesday, etc.\". - -"), - -("Dates","dayofweekofmonth","dayofweekofmonth(dt::TimeType) -> Int - - For the day of week of \"dt\", returns which number it is in - \"dt\"'s month. So if the day of the week of \"dt\" is Monday, then - \"1 = First Monday of the month, 2 = Second Monday of the month, - etc.\" In the range 1:5. - -"), - -("Dates","daysofweekinmonth","daysofweekinmonth(dt::TimeType) -> Int - - For the day of week of \"dt\", returns the total number of that day - of the week in \"dt\"'s month. Returns 4 or 5. Useful in temporal - expressions for specifying the last day of a week in a month by - including \"dayofweekofmonth(dt) == daysofweekinmonth(dt)\" in the - adjuster function. - -"), - -("Dates","monthname","monthname(dt::TimeType; locale=\"english\") -> AbstractString - - Return the full name of the month of the Date or DateTime in the - given \"locale\". - -"), - -("Dates","monthabbr","monthabbr(dt::TimeType; locale=\"english\") -> AbstractString - - Return the abbreviated month name of the Date or DateTime in the - given \"locale\". - -"), - -("Dates","daysinmonth","daysinmonth(dt::TimeType) -> Int - - Returns the number of days in the month of \"dt\". Value will be - 28, 29, 30, or 31. - -"), - -("Dates","isleapyear","isleapyear(dt::TimeType) -> Bool - - Returns true if the year of \"dt\" is a leap year. - -"), - -("Dates","dayofyear","dayofyear(dt::TimeType) -> Int - - Returns the day of the year for \"dt\" with January 1st being day - 1. - -"), - -("Dates","daysinyear","daysinyear(dt::TimeType) -> Int - - Returns 366 if the year of \"dt\" is a leap year, otherwise returns - 365. - -"), - -("Dates","quarterofyear","quarterofyear(dt::TimeType) -> Int - - Returns the quarter that \"dt\" resides in. Range of value is 1:4. - -"), - -("Dates","dayofquarter","dayofquarter(dt::TimeType) -> Int - - Returns the day of the current quarter of \"dt\". Range of value is - 1:92. - -"), - -("Dates","trunc","trunc(dt::TimeType, ::Type{Period}) -> TimeType - - Truncates the value of \"dt\" according to the provided \"Period\" - type. E.g. if \"dt\" is \"1996-01-01T12:30:00\", then - \"trunc(dt,Day) == 1996-01-01T00:00:00\". - -"), - -("Dates","firstdayofweek","firstdayofweek(dt::TimeType) -> TimeType - - Adjusts \"dt\" to the Monday of its week. - -"), - -("Dates","lastdayofweek","lastdayofweek(dt::TimeType) -> TimeType - - Adjusts \"dt\" to the Sunday of its week. - -"), - -("Dates","firstdayofmonth","firstdayofmonth(dt::TimeType) -> TimeType - - Adjusts \"dt\" to the first day of its month. - -"), - -("Dates","lastdayofmonth","lastdayofmonth(dt::TimeType) -> TimeType - - Adjusts \"dt\" to the last day of its month. - -"), - -("Dates","firstdayofyear","firstdayofyear(dt::TimeType) -> TimeType - - Adjusts \"dt\" to the first day of its year. - -"), - -("Dates","lastdayofyear","lastdayofyear(dt::TimeType) -> TimeType - - Adjusts \"dt\" to the last day of its year. - -"), - -("Dates","firstdayofquarter","firstdayofquarter(dt::TimeType) -> TimeType - - Adjusts \"dt\" to the first day of its quarter. - -"), - -("Dates","lastdayofquarter","lastdayofquarter(dt::TimeType) -> TimeType - - Adjusts \"dt\" to the last day of its quarter. - -"), - -("Dates","tonext","tonext(dt::TimeType, dow::Int;same::Bool=false) -> TimeType - - Adjusts \"dt\" to the next day of week corresponding to \"dow\" - with \"1 = Monday, 2 = Tuesday, etc\". Setting \"same=true\" allows - the current \"dt\" to be considered as the next \"dow\", allowing - for no adjustment to occur. - -"), - -("Dates","toprev","toprev(dt::TimeType, dow::Int;same::Bool=false) -> TimeType - - Adjusts \"dt\" to the previous day of week corresponding to \"dow\" - with \"1 = Monday, 2 = Tuesday, etc\". Setting \"same=true\" allows - the current \"dt\" to be considered as the previous \"dow\", - allowing for no adjustment to occur. - -"), - -("Dates","tofirst","tofirst(dt::TimeType, dow::Int;of=Month) -> TimeType - - Adjusts \"dt\" to the first \"dow\" of its month. Alternatively, - \"of=Year\" will adjust to the first \"dow\" of the year. - -"), - -("Dates","tolast","tolast(dt::TimeType, dow::Int;of=Month) -> TimeType - - Adjusts \"dt\" to the last \"dow\" of its month. Alternatively, - \"of=Year\" will adjust to the last \"dow\" of the year. - -"), - -("Dates","tonext","tonext(func::Function, dt::TimeType;step=Day(1), negate=false, limit=10000, same=false) -> TimeType - - Adjusts \"dt\" by iterating at most \"limit\" iterations by - \"step\" increments until \"func\" returns true. \"func\" must take - a single \"TimeType\" argument and return a \"Bool\". \"same\" - allows \"dt\" to be considered in satisfying \"func\". \"negate\" - will make the adjustment process terminate when \"func\" returns - false instead of true. - -"), - -("Dates","toprev","toprev(func::Function, dt::TimeType;step=Day(-1), negate=false, limit=10000, same=false) -> TimeType - - Adjusts \"dt\" by iterating at most \"limit\" iterations by - \"step\" increments until \"func\" returns true. \"func\" must take - a single \"TimeType\" argument and return a \"Bool\". \"same\" - allows \"dt\" to be considered in satisfying \"func\". \"negate\" - will make the adjustment process terminate when \"func\" returns - false instead of true. - -"), - -("Dates","recur{T<:TimeType}","recur{T<:TimeType}(func::Function, dr::StepRange{T};negate=false, limit=10000) -> Vector{T} - - \"func\" takes a single TimeType argument and returns a \"Bool\" - indicating whether the input should be \"included\" in the final - set. \"recur\" applies \"func\" over each element in the range of - \"dr\", including those elements for which \"func\" returns - \"true\" in the resulting Array, unless \"negate=true\", then only - elements where \"func\" returns \"false\" are included. - -"), - -("Dates","Year","Year(v) -Month(v) -Week(v) -Day(v) -Hour(v) -Minute(v) -Second(v) -Millisecond(v) - - Construct a \"Period\" type with the given \"v\" value. Input must - be losslessly convertible to an \"Int64\". - -"), - -("Dates","default","default(p::Period) -> Period - - Returns a sensible \"default\" value for the input Period by - returning \"one(p)\" for Year, Month, and Day, and \"zero(p)\" for - Hour, Minute, Second, and Millisecond. - -"), - -("Dates","today","today() -> Date - - Returns the date portion of \"now()\". - -"), - -("Dates","unix2datetime","unix2datetime(x) -> DateTime - - Takes the number of seconds since unix epoch - \"1970-01-01T00:00:00\" and converts to the corresponding DateTime. - -"), - -("Dates","datetime2unix","datetime2unix(dt::DateTime) -> Float64 - - Takes the given DateTime and returns the number of seconds since - the unix epoch as a \"Float64\". - -"), - -("Dates","julian2datetime","julian2datetime(julian_days) -> DateTime - - Takes the number of Julian calendar days since epoch - \"-4713-11-24T12:00:00\" and returns the corresponding DateTime. - -"), - -("Dates","datetime2julian","datetime2julian(dt::DateTime) -> Float64 - - Takes the given DateTime and returns the number of Julian calendar - days since the julian epoch as a \"Float64\". - -"), - -("Dates","rata2datetime","rata2datetime(days) -> DateTime - - Takes the number of Rata Die days since epoch - \"0000-12-31T00:00:00\" and returns the corresponding DateTime. - -"), - -("Dates","datetime2rata","datetime2rata(dt::TimeType) -> Int64 - - Returns the number of Rata Die days since epoch from the given Date - or DateTime. - -"), - -("Base","pwd","pwd() -> AbstractString - - Get the current working directory. - -"), - -("Base","cd","cd(dir::AbstractString) - - Set the current working directory. - -"), - -("Base","cd","cd(f[, dir]) - - Temporarily changes the current working directory (HOME if not - specified) and applies function f before returning. - -"), - -("Base","readdir","readdir([dir]) -> Vector{ByteString} - - Returns the files and directories in the directory *dir* (or the - current working directory if not given). - -"), - -("Base","mkdir","mkdir(path[, mode]) - - Make a new directory with name \"path\" and permissions \"mode\". - \"mode\" defaults to 0o777, modified by the current file creation - mask. - -"), - -("Base","mkpath","mkpath(path[, mode]) - - Create all directories in the given \"path\", with permissions - \"mode\". \"mode\" defaults to 0o777, modified by the current file - creation mask. - -"), - -("Base","symlink","symlink(target, link) - - Creates a symbolic link to \"target\" with the name \"link\". - - Note: This function raises an error under operating systems that - do not support soft symbolic links, such as Windows XP. - -"), - -("Base","readlink","readlink(path) -> AbstractString - - Returns the value of a symbolic link \"path\". - -"), - -("Base","chmod","chmod(path, mode) - - Change the permissions mode of \"path\" to \"mode\". Only integer - \"mode\"s (e.g. 0o777) are currently supported. - -"), - -("Base","stat","stat(file) - - Returns a structure whose fields contain information about the - file. The fields of the structure are: - - +-----------+------------------------------------------------------------------------+ - | size | The size (in bytes) of the file | - +-----------+------------------------------------------------------------------------+ - | device | ID of the device that contains the file | - +-----------+------------------------------------------------------------------------+ - | inode | The inode number of the file | - +-----------+------------------------------------------------------------------------+ - | mode | The protection mode of the file | - +-----------+------------------------------------------------------------------------+ - | nlink | The number of hard links to the file | - +-----------+------------------------------------------------------------------------+ - | uid | The user id of the owner of the file | - +-----------+------------------------------------------------------------------------+ - | gid | The group id of the file owner | - +-----------+------------------------------------------------------------------------+ - | rdev | If this file refers to a device, the ID of the device it refers to | - +-----------+------------------------------------------------------------------------+ - | blksize | The file-system preferred block size for the file | - +-----------+------------------------------------------------------------------------+ - | blocks | The number of such blocks allocated | - +-----------+------------------------------------------------------------------------+ - | mtime | Unix timestamp of when the file was last modified | - +-----------+------------------------------------------------------------------------+ - | ctime | Unix timestamp of when the file was created | - +-----------+------------------------------------------------------------------------+ - -"), - -("Base","lstat","lstat(file) - - Like stat, but for symbolic links gets the info for the link itself - rather than the file it refers to. This function must be called on - a file path rather than a file object or a file descriptor. - -"), - -("Base","ctime","ctime(file) - - Equivalent to stat(file).ctime - -"), - -("Base","mtime","mtime(file) - - Equivalent to stat(file).mtime - -"), - -("Base","filemode","filemode(file) - - Equivalent to stat(file).mode - -"), - -("Base","filesize","filesize(path...) - - Equivalent to stat(file).size - -"), - -("Base","uperm","uperm(file) - - Gets the permissions of the owner of the file as a bitfield of - - +------+-----------------------+ - | 01 | Execute Permission | - +------+-----------------------+ - | 02 | Write Permission | - +------+-----------------------+ - | 04 | Read Permission | - +------+-----------------------+ - - For allowed arguments, see \"stat\". - -"), - -("Base","gperm","gperm(file) - - Like uperm but gets the permissions of the group owning the file - -"), - -("Base","operm","operm(file) - - Like uperm but gets the permissions for people who neither own the - file nor are a member of the group owning the file - -"), - -("Base","cp","cp(src::AbstractString, dst::AbstractString; remove_destination::Bool=false, follow_symlinks::Bool=false) - - Copy the file, link, or directory from *src* to *dest*. - \"remove_destination=true\" will first remove an existing *dst*. - - If *follow_symlinks=false*, and src is a symbolic link, dst will be - created as a symbolic link. If *follow_symlinks=true* and src is a - symbolic link, dst will be a copy of the file or directory *src* - refers to. - -"), - -("Base","download","download(url[, localfile]) - - Download a file from the given url, optionally renaming it to the - given local file name. Note that this function relies on the - availability of external tools such as \"curl\", \"wget\" or - \"fetch\" to download the file and is provided for convenience. For - production use or situations in which more options are need, please - use a package that provides the desired functionality instead. - -"), - -("Base","mv","mv(src::AbstractString, dst::AbstractString; remove_destination::Bool=false) - - Move the file, link, or directory from *src* to *dest*. - \"remove_destination=true\" will first remove an existing *dst*. - -"), - -("Base","rm","rm(path::AbstractString; recursive=false) - - Delete the file, link, or empty directory at the given path. If - \"recursive=true\" is passed and the path is a directory, then all - contents are removed recursively. - -"), - -("Base","touch","touch(path::AbstractString) - - Update the last-modified timestamp on a file to the current time. - -"), - -("Base","tempname","tempname() - - Generate a unique temporary file path. - -"), - -("Base","tempdir","tempdir() - - Obtain the path of a temporary directory (possibly shared with - other processes). - -"), - -("Base","mktemp","mktemp([parent=tempdir()]) - - Returns \"(path, io)\", where \"path\" is the path of a new - temporary file in \"parent\" and \"io\" is an open file object for - this path. - -"), - -("Base","mktempdir","mktempdir([parent=tempdir()]) - - Create a temporary directory in the \"parent\" directory and return - its path. - -"), - -("Base","isblockdev","isblockdev(path) -> Bool - - Returns \"true\" if \"path\" is a block device, \"false\" - otherwise. - -"), - -("Base","ischardev","ischardev(path) -> Bool - - Returns \"true\" if \"path\" is a character device, \"false\" - otherwise. - -"), - -("Base","isdir","isdir(path) -> Bool - - Returns \"true\" if \"path\" is a directory, \"false\" otherwise. - -"), - -("Base","isexecutable","isexecutable(path) -> Bool - - Returns \"true\" if the current user has permission to execute - \"path\", \"false\" otherwise. - -"), - -("Base","isfifo","isfifo(path) -> Bool - - Returns \"true\" if \"path\" is a FIFO, \"false\" otherwise. - -"), - -("Base","isfile","isfile(path) -> Bool - - Returns \"true\" if \"path\" is a regular file, \"false\" - otherwise. - -"), - -("Base","islink","islink(path) -> Bool - - Returns \"true\" if \"path\" is a symbolic link, \"false\" - otherwise. - -"), - -("Base","ismount","ismount(path) -> Bool - - Returns \"true\" if \"path\" is a mount point, \"false\" otherwise. - -"), - -("Base","ispath","ispath(path) -> Bool - - Returns \"true\" if \"path\" is a valid filesystem path, \"false\" - otherwise. - -"), - -("Base","isreadable","isreadable(path) -> Bool - - Returns \"true\" if the current user has permission to read - \"path\", \"false\" otherwise. - -"), - -("Base","issetgid","issetgid(path) -> Bool - - Returns \"true\" if \"path\" has the setgid flag set, \"false\" - otherwise. - -"), - -("Base","issetuid","issetuid(path) -> Bool - - Returns \"true\" if \"path\" has the setuid flag set, \"false\" - otherwise. - -"), - -("Base","issocket","issocket(path) -> Bool - - Returns \"true\" if \"path\" is a socket, \"false\" otherwise. - -"), - -("Base","issticky","issticky(path) -> Bool - - Returns \"true\" if \"path\" has the sticky bit set, \"false\" - otherwise. - -"), - -("Base","iswritable","iswritable(path) -> Bool - - Returns \"true\" if the current user has permission to write to - \"path\", \"false\" otherwise. - -"), - -("Base","homedir","homedir() -> AbstractString - - Return the current user's home directory. - -"), - -("Base","dirname","dirname(path::AbstractString) -> AbstractString - - Get the directory part of a path. - -"), - -("Base","basename","basename(path::AbstractString) -> AbstractString - - Get the file name part of a path. - -"), - -("Base","@__FILE__","@__FILE__() -> AbstractString - - \"@__FILE__\" expands to a string with the absolute path and file - name of the script being run. Returns \"nothing\" if run from a - REPL or an empty string if evaluated by \"julia -e \". - -"), - -("Base","isabspath","isabspath(path::AbstractString) -> Bool - - Determines whether a path is absolute (begins at the root - directory). - -"), - -("Base","isdirpath","isdirpath(path::AbstractString) -> Bool - - Determines whether a path refers to a directory (for example, ends - with a path separator). - -"), - -("Base","joinpath","joinpath(parts...) -> AbstractString - - Join path components into a full path. If some argument is an - absolute path, then prior components are dropped. - -"), - -("Base","abspath","abspath(path::AbstractString) -> AbstractString - - Convert a path to an absolute path by adding the current directory - if necessary. - -"), - -("Base","normpath","normpath(path::AbstractString) -> AbstractString - - Normalize a path, removing \".\" and \"..\" entries. - -"), - -("Base","realpath","realpath(path::AbstractString) -> AbstractString - - Canonicalize a path by expanding symbolic links and removing \".\" - and \"..\" entries. - -"), - -("Base","relpath","relpath(path::AbstractString, startpath::AbstractString = \".\") -> AbstractString - - Return a relative filepath to path either from the current - directory or from an optional start directory. This is a path - computation: the filesystem is not accessed to confirm the - existence or nature of path or startpath. - -"), - -("Base","expanduser","expanduser(path::AbstractString) -> AbstractString - - On Unix systems, replace a tilde character at the start of a path - with the current user's home directory. - -"), - -("Base","splitdir","splitdir(path::AbstractString) -> (AbstractString, AbstractString) - - Split a path into a tuple of the directory name and file name. - -"), - -("Base","splitdrive","splitdrive(path::AbstractString) -> (AbstractString, AbstractString) - - On Windows, split a path into the drive letter part and the path - part. On Unix systems, the first component is always the empty - string. - -"), - -("Base","splitext","splitext(path::AbstractString) -> (AbstractString, AbstractString) - - If the last component of a path contains a dot, split the path into - everything before the dot and everything including and after the - dot. Otherwise, return a tuple of the argument unmodified and the - empty string. - -"), - - -("Base","STDOUT","STDOUT - - Global variable referring to the standard out stream. - -"), - -("Base","STDERR","STDERR - - Global variable referring to the standard error stream. - -"), - -("Base","STDIN","STDIN - - Global variable referring to the standard input stream. - -"), - -("Base","open","open(file_name[, read, write, create, truncate, append]) -> IOStream - - Open a file in a mode specified by five boolean arguments. The - default is to open files for reading only. Returns a stream for - accessing the file. - -"), - -("Base","open","open(file_name[, mode]) -> IOStream - - Alternate syntax for open, where a string-based mode specifier is - used instead of the five booleans. The values of \"mode\" - correspond to those from \"fopen(3)\" or Perl \"open\", and are - equivalent to setting the following boolean groups: - - +------+-----------------------------------+ - | r | read | - +------+-----------------------------------+ - | r+ | read, write | - +------+-----------------------------------+ - | w | write, create, truncate | - +------+-----------------------------------+ - | w+ | read, write, create, truncate | - +------+-----------------------------------+ - | a | write, create, append | - +------+-----------------------------------+ - | a+ | read, write, create, append | - +------+-----------------------------------+ - -"), - -("Base","open","open(f::function, args...) - - Apply the function \"f\" to the result of \"open(args...)\" and - close the resulting file descriptor upon completion. - - **Example**: \"open(readall, \"file.txt\")\" - -"), - -("Base","IOBuffer","IOBuffer() -> IOBuffer - - Create an in-memory I/O stream. - -"), - -("Base","IOBuffer","IOBuffer(size::Int) - - Create a fixed size IOBuffer. The buffer will not grow dynamically. - -"), - -("Base","IOBuffer","IOBuffer(string) - - Create a read-only IOBuffer on the data underlying the given string - -"), - -("Base","IOBuffer","IOBuffer([data][, readable, writable[, maxsize]]) - - Create an IOBuffer, which may optionally operate on a pre-existing - array. If the readable/writable arguments are given, they restrict - whether or not the buffer may be read from or written to - respectively. By default the buffer is readable but not writable. - The last argument optionally specifies a size beyond which the - buffer may not be grown. - -"), - -("Base","takebuf_array","takebuf_array(b::IOBuffer) - - Obtain the contents of an \"IOBuffer\" as an array, without - copying. Afterwards, the IOBuffer is reset to its initial state. - -"), - -("Base","takebuf_string","takebuf_string(b::IOBuffer) - - Obtain the contents of an \"IOBuffer\" as a string, without - copying. Afterwards, the IOBuffer is reset to its initial state. - -"), - -("Base","fdio","fdio([name::AbstractString], fd::Integer[, own::Bool]) -> IOStream - - Create an \"IOStream\" object from an integer file descriptor. If - \"own\" is true, closing this object will close the underlying - descriptor. By default, an \"IOStream\" is closed when it is - garbage collected. \"name\" allows you to associate the descriptor - with a named file. - -"), - -("Base","flush","flush(stream) - - Commit all currently buffered writes to the given stream. - -"), - -("Base","close","close(stream) - - Close an I/O stream. Performs a \"flush\" first. - -"), - -("Base","write","write(stream, x) - - Write the canonical binary representation of a value to the given - stream. - -"), - -("Base","read","read(stream, type) - - Read a value of the given type from a stream, in canonical binary - representation. - -"), - -("Base","read","read(stream, type, dims) - - Read a series of values of the given type from a stream, in - canonical binary representation. \"dims\" is either a tuple or a - series of integer arguments specifying the size of \"Array\" to - return. - -"), - -("Base","read!","read!(stream, array::Array) - - Read binary data from a stream, filling in the argument \"array\". - -"), - -("Base","readbytes!","readbytes!(stream, b::Vector{UInt8}, nb=length(b); all=true) - - Read at most \"nb\" bytes from the stream into \"b\", returning the - number of bytes read (increasing the size of \"b\" as needed). - - See \"readbytes\" for a description of the \"all\" option. - -"), - -("Base","readbytes","readbytes(stream, nb=typemax(Int); all=true) - - Read at most \"nb\" bytes from the stream, returning a - \"Vector{UInt8}\" of the bytes read. - - If \"all\" is true (the default), this function will block - repeatedly trying to read all requested bytes, until an error or - end-of-file occurs. If \"all\" is false, at most one \"read\" call - is performed, and the amount of data returned is device-dependent. - Note that not all stream types support the \"all\" option. - -"), - -("Base","position","position(s) - - Get the current position of a stream. - -"), - -("Base","seek","seek(s, pos) - - Seek a stream to the given position. - -"), - -("Base","seekstart","seekstart(s) - - Seek a stream to its beginning. - -"), - -("Base","seekend","seekend(s) - - Seek a stream to its end. - -"), - -("Base","skip","skip(s, offset) - - Seek a stream relative to the current position. - -"), - -("Base","mark","mark(s) - - Add a mark at the current position of stream \"s\". Returns the - marked position. - - See also \"unmark()\", \"reset()\", \"ismarked()\" - -"), - -("Base","unmark","unmark(s) - - Remove a mark from stream \"s\". Returns \"true\" if the stream was - marked, \"false\" otherwise. - - See also \"mark()\", \"reset()\", \"ismarked()\" - -"), - -("Base","reset","reset(s) - - Reset a stream \"s\" to a previously marked position, and remove - the mark. Returns the previously marked position. Throws an error - if the stream is not marked. - - See also \"mark()\", \"unmark()\", \"ismarked()\" - -"), - -("Base","ismarked","ismarked(s) - - Returns true if stream \"s\" is marked. - - See also \"mark()\", \"unmark()\", \"reset()\" - -"), - -("Base","eof","eof(stream) -> Bool - - Tests whether an I/O stream is at end-of-file. If the stream is not - yet exhausted, this function will block to wait for more data if - necessary, and then return \"false\". Therefore it is always safe - to read one byte after seeing \"eof\" return \"false\". \"eof\" - will return \"false\" as long as buffered data is still available, - even if the remote end of a connection is closed. - -"), - -("Base","isreadonly","isreadonly(stream) -> Bool - - Determine whether a stream is read-only. - -"), - -("Base","isopen","isopen(object) -> Bool - - Determine whether an object - such as a stream, timer, or mmap -- - is not yet closed. Once an object is closed, it will never produce - a new event. However, a closed stream may still have data to read - in its buffer, use \"eof\" to check for the ability to read data. - Use \"poll_fd\" to be notified when a stream might be writable or - readable. - -"), - -("Base","serialize","serialize(stream, value) - - Write an arbitrary value to a stream in an opaque format, such that - it can be read back by \"deserialize\". The read-back value will be - as identical as possible to the original. In general, this process - will not work if the reading and writing are done by different - versions of Julia, or an instance of Julia with a different system - image. - -"), - -("Base","deserialize","deserialize(stream) - - Read a value written by \"serialize\". - -"), - -("Base","print_escaped","print_escaped(io, str::AbstractString, esc::AbstractString) - - General escaping of traditional C and Unicode escape sequences, - plus any characters in esc are also escaped (with a backslash). - -"), - -("Base","print_unescaped","print_unescaped(io, s::AbstractString) - - General unescaping of traditional C and Unicode escape sequences. - Reverse of \"print_escaped()\". - -"), - -("Base","print_joined","print_joined(io, items, delim[, last]) - - Print elements of \"items\" to \"io\" with \"delim\" between them. - If \"last\" is specified, it is used as the final delimiter instead - of \"delim\". - -"), - -("Base","print_shortest","print_shortest(io, x) - - Print the shortest possible representation, with the minimum number - of consecutive non-zero digits, of number \"x\", ensuring that it - would parse to the exact same number. - -"), - -("Base","fd","fd(stream) - - Returns the file descriptor backing the stream or file. Note that - this function only applies to synchronous *File*'s and *IOStream*'s - not to any of the asynchronous streams. - -"), - -("Base","redirect_stdout","redirect_stdout() - - Create a pipe to which all C and Julia level STDOUT output will be - redirected. Returns a tuple (rd,wr) representing the pipe ends. - Data written to STDOUT may now be read from the rd end of the pipe. - The wr end is given for convenience in case the old STDOUT object - was cached by the user and needs to be replaced elsewhere. - -"), - -("Base","redirect_stdout","redirect_stdout(stream) - - Replace STDOUT by stream for all C and julia level output to - STDOUT. Note that *stream* must be a TTY, a Pipe or a TcpSocket. - -"), - -("Base","redirect_stderr","redirect_stderr([stream]) - - Like redirect_stdout, but for STDERR - -"), - -("Base","redirect_stdin","redirect_stdin([stream]) - - Like redirect_stdout, but for STDIN. Note that the order of the - return tuple is still (rd,wr), i.e. data to be read from STDIN, may - be written to wr. - -"), - -("Base","readchomp","readchomp(x) - - Read the entirety of x as a string but remove trailing newlines. - Equivalent to chomp(readall(x)). - -"), - -("Base","truncate","truncate(file, n) - - Resize the file or buffer given by the first argument to exactly - *n* bytes, filling previously unallocated space with '\\0' if the - file or buffer is grown - -"), - -("Base","skipchars","skipchars(stream, predicate; linecomment::Char) - - Advance the stream until before the first character for which - \"predicate\" returns false. For example \"skipchars(stream, - isspace)\" will skip all whitespace. If keyword argument - \"linecomment\" is specified, characters from that character - through the end of a line will also be skipped. - -"), - -("Base","countlines","countlines(io[, eol::Char]) - - Read \"io\" until the end of the stream/file and count the number - of lines. To specify a file pass the filename as the first - argument. EOL markers other than '\\n' are supported by passing - them as the second argument. - -"), - -("Base","PipeBuffer","PipeBuffer() - - An IOBuffer that allows reading and performs writes by appending. - Seeking and truncating are not supported. See IOBuffer for the - available constructors. - -"), - -("Base","PipeBuffer","PipeBuffer(data::Vector{UInt8}[, maxsize]) - - Create a PipeBuffer to operate on a data vector, optionally - specifying a size beyond which the underlying Array may not be - grown. - -"), - -("Base","readavailable","readavailable(stream) - - Read all available data on the stream, blocking the task only if no - data is available. The result is a \"Vector{UInt8,1}\". - -"), - -("Base","show","show(x) - - Write an informative text representation of a value to the current - output stream. New types should overload \"show(io, x)\" where the - first argument is a stream. The representation used by \"show\" - generally includes Julia-specific formatting and type information. - -"), - -("Base","showcompact","showcompact(x) - - Show a more compact representation of a value. This is used for - printing array elements. If a new type has a different compact - representation, it should overload \"showcompact(io, x)\" where the - first argument is a stream. - -"), - -("Base","showall","showall(x) - - Similar to \"show\", except shows all elements of arrays. - -"), - -("Base","summary","summary(x) - - Return a string giving a brief description of a value. By default - returns \"string(typeof(x))\". For arrays, returns strings like - \"2x2 Float64 Array\". - -"), - -("Base","print","print(x) - - Write (to the default output stream) a canonical (un-decorated) - text representation of a value if there is one, otherwise call - \"show\". The representation used by \"print\" includes minimal - formatting and tries to avoid Julia-specific details. - -"), - -("Base","println","println(x) - - Print (using \"print()\") \"x\" followed by a newline. - -"), - -("Base","print_with_color","print_with_color(color::Symbol[, io], strings...) - - Print strings in a color specified as a symbol, for example - \":red\" or \":blue\". - -"), - -("Base","info","info(msg) - - Display an informational message. - -"), - -("Base","warn","warn(msg) - - Display a warning. - -"), - -("Base","@printf","@printf([io::IOStream], \"%Fmt\", args...) - - Print arg(s) using C \"printf()\" style format specification - string. Optionally, an IOStream may be passed as the first argument - to redirect output. - -"), - -("Base","@sprintf","@sprintf(\"%Fmt\", args...) - - Return \"@printf\" formatted output as string. - -"), - -("Base","sprint","sprint(f::Function, args...) - - Call the given function with an I/O stream and the supplied extra - arguments. Everything written to this I/O stream is returned as a - string. - -"), - -("Base","showerror","showerror(io, e) - - Show a descriptive representation of an exception object. - -"), - -("Base","dump","dump(x) - - Show all user-visible structure of a value. - -"), - -("Base","xdump","xdump(x) - - Show all structure of a value, including all fields of objects. - -"), - -("Base","readall","readall(stream::IO) - - Read the entire contents of an I/O stream as a string. - -"), - -("Base","readall","readall(filename::AbstractString) - - Open \"filename\", read the entire contents as a string, then close - the file. Equivalent to \"open(readall, filename)\". - -"), - -("Base","readline","readline(stream=STDIN) - - Read a single line of text, including a trailing newline character - (if one is reached before the end of the input), from the given - \"stream\" (defaults to \"STDIN\"), - -"), - -("Base","readuntil","readuntil(stream, delim) - - Read a string, up to and including the given delimiter byte. - -"), - -("Base","readlines","readlines(stream) - - Read all lines as an array. - -"), - -("Base","eachline","eachline(stream) - - Create an iterable object that will yield each line from a stream. - -"), - -("Base","readdlm","readdlm(source, delim::Char, T::Type, eol::Char; header=false, skipstart=0, skipblanks=true, use_mmap, ignore_invalid_chars=false, quotes=true, dims, comments=true, comment_char='#') - - Read a matrix from the source where each line (separated by - \"eol\") gives one row, with elements separated by the given - delimeter. The source can be a text file, stream or byte array. - Memory mapped files can be used by passing the byte array - representation of the mapped segment as source. - - If \"T\" is a numeric type, the result is an array of that type, - with any non-numeric elements as \"NaN\" for floating-point types, - or zero. Other useful values of \"T\" include \"ASCIIString\", - \"AbstractString\", and \"Any\". - - If \"header\" is \"true\", the first row of data will be read as - header and the tuple \"(data_cells, header_cells)\" is returned - instead of only \"data_cells\". - - Specifying \"skipstart\" will ignore the corresponding number of - initial lines from the input. - - If \"skipblanks\" is \"true\", blank lines in the input will be - ignored. - - If \"use_mmap\" is \"true\", the file specified by \"source\" is - memory mapped for potential speedups. Default is \"true\" except on - Windows. On Windows, you may want to specify \"true\" if the file - is large, and is only read once and not written to. - - If \"ignore_invalid_chars\" is \"true\", bytes in \"source\" with - invalid character encoding will be ignored. Otherwise an error is - thrown indicating the offending character position. - - If \"quotes\" is \"true\", column enclosed within double-quote (``) - characters are allowed to contain new lines and column delimiters. - Double-quote characters within a quoted field must be escaped with - another double-quote. - - Specifying \"dims\" as a tuple of the expected rows and columns - (including header, if any) may speed up reading of large files. - - If \"comments\" is \"true\", lines beginning with \"comment_char\" - and text following \"comment_char\" in any line are ignored. - -"), - -("Base","readdlm","readdlm(source, delim::Char, eol::Char; options...) - - If all data is numeric, the result will be a numeric array. If some - elements cannot be parsed as numbers, a cell array of numbers and - strings is returned. - -"), - -("Base","readdlm","readdlm(source, delim::Char, T::Type; options...) - - The end of line delimiter is taken as \"\\n\". - -"), - -("Base","readdlm","readdlm(source, delim::Char; options...) - - The end of line delimiter is taken as \"\\n\". If all data is - numeric, the result will be a numeric array. If some elements - cannot be parsed as numbers, a cell array of numbers and strings is - returned. - -"), - -("Base","readdlm","readdlm(source, T::Type; options...) - - The columns are assumed to be separated by one or more whitespaces. - The end of line delimiter is taken as \"\\n\". - -"), - -("Base","readdlm","readdlm(source; options...) - - The columns are assumed to be separated by one or more whitespaces. - The end of line delimiter is taken as \"\\n\". If all data is - numeric, the result will be a numeric array. If some elements - cannot be parsed as numbers, a cell array of numbers and strings is - returned. - -"), - -("Base","writedlm","writedlm(f, A, delim='\\t') - - Write \"A\" (a vector, matrix or an iterable collection of iterable - rows) as text to \"f\" (either a filename string or an \"IO\" - stream) using the given delimeter \"delim\" (which defaults to tab, - but can be any printable Julia object, typically a \"Char\" or - \"AbstractString\"). - - For example, two vectors \"x\" and \"y\" of the same length can be - written as two columns of tab-delimited text to \"f\" by either - \"writedlm(f, [x y])\" or by \"writedlm(f, zip(x, y))\". - -"), - -("Base","readcsv","readcsv(source, [T::Type]; options...) - - Equivalent to \"readdlm\" with \"delim\" set to comma. - -"), - -("Base","writecsv","writecsv(filename, A) - - Equivalent to \"writedlm\" with \"delim\" set to comma. - -"), - -("Base","Base64EncodePipe","Base64EncodePipe(ostream) - - Returns a new write-only I/O stream, which converts any bytes - written to it into base64-encoded ASCII bytes written to - \"ostream\". Calling \"close\" on the \"Base64Pipe\" stream is - necessary to complete the encoding (but does not close - \"ostream\"). - -"), - -("Base","Base64DecodePipe","Base64DecodePipe(istream) - - Returns a new read-only I/O stream, which decodes base64-encoded - data read from \"istream\". - -"), - -("Base","base64encode","base64encode(writefunc, args...) -base64encode(args...) - - Given a \"write\"-like function \"writefunc\", which takes an I/O - stream as its first argument, \"base64(writefunc, args...)\" calls - \"writefunc\" to write \"args...\" to a base64-encoded string, and - returns the string. \"base64(args...)\" is equivalent to - \"base64(write, args...)\": it converts its arguments into bytes - using the standard \"write\" functions and returns the - base64-encoded string. - -"), - -("Base","base64decode","base64decode(string) - - Decodes the base64-encoded \"string\" and returns a - \"Vector{UInt8}\" of the decoded bytes. - -"), - -("Base","display","display(x) -display(d::Display, x) -display(mime, x) -display(d::Display, mime, x) - - Display \"x\" using the topmost applicable display in the display - stack, typically using the richest supported multimedia output for - \"x\", with plain-text \"STDOUT\" output as a fallback. The - \"display(d, x)\" variant attempts to display \"x\" on the given - display \"d\" only, throwing a \"MethodError\" if \"d\" cannot - display objects of this type. - - There are also two variants with a \"mime\" argument (a MIME type - string, such as \"\"image/png\"\"), which attempt to display \"x\" - using the requested MIME type *only*, throwing a \"MethodError\" if - this type is not supported by either the display(s) or by \"x\". - With these variants, one can also supply the \"raw\" data in the - requested MIME type by passing \"x::AbstractString\" (for MIME - types with text-based storage, such as text/html or - application/postscript) or \"x::Vector{UInt8}\" (for binary MIME - types). - -"), - -("Base","redisplay","redisplay(x) -redisplay(d::Display, x) -redisplay(mime, x) -redisplay(d::Display, mime, x) - - By default, the \"redisplay\" functions simply call \"display\". - However, some display backends may override \"redisplay\" to modify - an existing display of \"x\" (if any). Using \"redisplay\" is - also a hint to the backend that \"x\" may be redisplayed several - times, and the backend may choose to defer the display until (for - example) the next interactive prompt. - -"), - -("Base","displayable","displayable(mime) -> Bool -displayable(d::Display, mime) -> Bool - - Returns a boolean value indicating whether the given \"mime\" type - (string) is displayable by any of the displays in the current - display stack, or specifically by the display \"d\" in the second - variant. - -"), - -("Base","writemime","writemime(stream, mime, x) - - The \"display\" functions ultimately call \"writemime\" in order to - write an object \"x\" as a given \"mime\" type to a given I/O - \"stream\" (usually a memory buffer), if possible. In order to - provide a rich multimedia representation of a user-defined type - \"T\", it is only necessary to define a new \"writemime\" method - for \"T\", via: \"writemime(stream, ::MIME\"mime\", x::T) = ...\", - where \"mime\" is a MIME-type string and the function body calls - \"write\" (or similar) to write that representation of \"x\" to - \"stream\". (Note that the \"MIME\"\"\" notation only supports - literal strings; to construct \"MIME\" types in a more flexible - manner use \"MIME{symbol(\"\")}\".) - - For example, if you define a \"MyImage\" type and know how to write - it to a PNG file, you could define a function \"writemime(stream, - ::MIME\"image/png\", x::MyImage) = ...`\" to allow your images to - be displayed on any PNG-capable \"Display\" (such as IJulia). As - usual, be sure to \"import Base.writemime\" in order to add new - methods to the built-in Julia function \"writemime\". - - Technically, the \"MIME\"mime\"\" macro defines a singleton type - for the given \"mime\" string, which allows us to exploit Julia's - dispatch mechanisms in determining how to display objects of any - given type. - -"), - -("Base","mimewritable","mimewritable(mime, x) - - Returns a boolean value indicating whether or not the object \"x\" - can be written as the given \"mime\" type. (By default, this is - determined automatically by the existence of the corresponding - \"writemime\" function for \"typeof(x)\".) - -"), - -("Base","reprmime","reprmime(mime, x) - - Returns an \"AbstractString\" or \"Vector{UInt8}\" containing the - representation of \"x\" in the requested \"mime\" type, as written - by \"writemime\" (throwing a \"MethodError\" if no appropriate - \"writemime\" is available). An \"AbstractString\" is returned for - MIME types with textual representations (such as \"\"text/html\"\" - or \"\"application/postscript\"\"), whereas binary data is returned - as \"Vector{UInt8}\". (The function \"istext(mime)\" returns - whether or not Julia treats a given \"mime\" type as text.) - - As a special case, if \"x\" is an \"AbstractString\" (for textual - MIME types) or a \"Vector{UInt8}\" (for binary MIME types), the - \"reprmime\" function assumes that \"x\" is already in the - requested \"mime\" format and simply returns \"x\". - -"), - -("Base","stringmime","stringmime(mime, x) - - Returns an \"AbstractString\" containing the representation of - \"x\" in the requested \"mime\" type. This is similar to - \"reprmime\" except that binary data is base64-encoded as an ASCII - string. - -"), - -("Base","pushdisplay","pushdisplay(d::Display) - - Pushes a new display \"d\" on top of the global display-backend - stack. Calling \"display(x)\" or \"display(mime, x)\" will display - \"x\" on the topmost compatible backend in the stack (i.e., the - topmost backend that does not throw a \"MethodError\"). - -"), - -("Base","popdisplay","popdisplay() -popdisplay(d::Display) - - Pop the topmost backend off of the display-backend stack, or the - topmost copy of \"d\" in the second variant. - -"), - -("Base","TextDisplay","TextDisplay(stream) - - Returns a \"TextDisplay <: Display\", which can display any object - as the text/plain MIME type (only), writing the text representation - to the given I/O stream. (The text representation is the same as - the way an object is printed in the Julia REPL.) - -"), - -("Base","istext","istext(m::MIME) - - Determine whether a MIME type is text data. - -"), - -("Base","Mmap","Mmap.Anonymous(name, readonly, create) - - Create an \"IO\"-like object for creating zeroed-out mmapped-memory - that is not tied to a file for use in \"Mmap.mmap\". Used by - \"SharedArray\" for creating shared memory arrays. - -"), - -("Base","Mmap","Mmap.mmap(io::Union(IOStream,AbstractString,Mmap.AnonymousMmap)[, type::Type{Array{T,N}}, dims, offset]; grow::Bool=true, shared::Bool=true) -Mmap.mmap(type::Type{Array{T, N}}, dims) - - Create an \"Array\" whose values are linked to a file, using - memory-mapping. This provides a convenient way of working with data - too large to fit in the computer's memory. - - The type is an \"Array{T,N}\" with a bits-type element of \"T\" and - dimension \"N\" that determines how the bytes of the array are - interpreted. Note that the file must be stored in binary format, - and no format conversions are possible (this is a limitation of - operating systems, not Julia). - - \"dims\" is a tuple or single \"Integer\" specifying the size or - length of the array. - - The file is passed via the stream argument, either as an open - \"IOStream\" or filename string. When you initialize the stream, - use \"\"r\"\" for a \"read-only\" array, and \"\"w+\"\" to create a - new array used to write values to disk. - - If no \"type\" argument is specified, the default is - \"Vector{UInt8}\". - - Optionally, you can specify an offset (in bytes) if, for example, - you want to skip over a header in the file. The default value for - the offset is the current stream position for an \"IOStream\". - - The \"grow\" keyword argument specifies whether the disk file - should be grown to accomodate the requested size of array (if the - total file size is < requested array size). Write privileges are - required to grow the file. - - The \"shared\" keyword argument specifies whether the resulting - \"Array\" and changes made to it will be visible to other processes - mapping the same file. - - For example, the following code: - - # Create a file for mmapping - # (you could alternatively use mmap to do this step, too) - A = rand(1:20, 5, 30) - s = open(\"/tmp/mmap.bin\", \"w+\") - # We'll write the dimensions of the array as the first two Ints in the file - write(s, size(A,1)) - write(s, size(A,2)) - # Now write the data - write(s, A) - close(s) - - # Test by reading it back in - s = open(\"/tmp/mmap.bin\") # default is read-only - m = read(s, Int) - n = read(s, Int) - A2 = Mmap.mmap(s, Matrix{Int}, (m,n)) - - creates a \"m\"-by-\"n\" \"Matrix{Int}\", linked to the file - associated with stream \"s\". - - A more portable file would need to encode the word size---32 bit or - 64 bit---and endianness information in the header. In practice, - consider encoding binary data using standard formats like HDF5 - (which can be used with memory-mapping). - -"), - -("Base","Mmap","Mmap.mmap(io, BitArray[, dims, offset]) - - Create a \"BitArray\" whose values are linked to a file, using - memory-mapping; it has the same purpose, works in the same way, and - has the same arguments, as \"mmap()\", but the byte representation - is different. - - **Example**: \"B = Mmap.mmap(s, BitArray, (25,30000))\" - - This would create a 25-by-30000 \"BitArray\", linked to the file - associated with stream \"s\". - -"), - -("Base","Mmap","Mmap.sync!(array) - - Forces synchronization between the in-memory version of a memory- - mapped \"Array\" or \"BitArray\" and the on-disk version. - -"), - -("Base","connect","connect([host], port) -> TcpSocket - - Connect to the host \"host\" on port \"port\" - -"), - -("Base","connect","connect(path) -> Pipe - - Connect to the Named Pipe/Domain Socket at \"path\" - -"), - -("Base","listen","listen([addr], port) -> TcpServer - - Listen on port on the address specified by \"addr\". By default - this listens on localhost only. To listen on all interfaces pass, - \"IPv4(0)\" or \"IPv6(0)\" as appropriate. - -"), - -("Base","listen","listen(path) -> PipeServer - - Listens on/Creates a Named Pipe/Domain Socket - -"), - -("Base","getaddrinfo","getaddrinfo(host) - - Gets the IP address of the \"host\" (may have to do a DNS lookup) - -"), - -("Base","parseip","parseip(addr) - - Parse a string specifying an IPv4 or IPv6 ip address. - -"), - -("Base","IPv4","IPv4(host::Integer) -> IPv4 - - Returns IPv4 object from ip address formatted as Integer - -"), - -("Base","IPv6","IPv6(host::Integer) -> IPv6 - - Returns IPv6 object from ip address formatted as Integer - -"), - -("Base","nb_available","nb_available(stream) - - Returns the number of bytes available for reading before a read - from this stream or buffer will block. - -"), - -("Base","accept","accept(server[, client]) - - Accepts a connection on the given server and returns a connection - to the client. An uninitialized client stream may be provided, in - which case it will be used instead of creating a new stream. - -"), - -("Base","listenany","listenany(port_hint) -> (UInt16, TcpServer) - - Create a TcpServer on any port, using hint as a starting point. - Returns a tuple of the actual port that the server was created on - and the server itself. - -"), - -("Base","watch_file","watch_file(cb=false, s; poll=false) - - Watch file or directory \"s\" and run callback \"cb\" when \"s\" is - modified. The \"poll\" parameter specifies whether to use file - system event monitoring or polling. The callback function \"cb\" - should accept 3 arguments: \"(filename, events, status)\" where - \"filename\" is the name of file that was modified, \"events\" is - an object with boolean fields \"changed\" and \"renamed\" when - using file system event monitoring, or \"readable\" and - \"writable\" when using polling, and \"status\" is always 0. Pass - \"false\" for \"cb\" to not use a callback function. - -"), - -("Base","poll_fd","poll_fd(fd, seconds::Real; readable=false, writable=false) - - Poll a file descriptor fd for changes in the read or write - availability and with a timeout given by the second argument. If - the timeout is not needed, use \"wait(fd)\" instead. The keyword - arguments determine which of read and/or write status should be - monitored and at least one of them needs to be set to true. The - returned value is an object with boolean fields \"readable\", - \"writable\", and \"timedout\", giving the result of the polling. - -"), - -("Base","poll_file","poll_file(s, interval_seconds::Real, seconds::Real) - - Monitor a file for changes by polling every *interval_seconds* - seconds for *seconds* seconds. A return value of true indicates the - file changed, a return value of false indicates a timeout. - -"), - -("Base","bind","bind(socket::Union{UDPSocket, TCPSocket}, host::IPv4, port::Integer) - - Bind \"socket\" to the given \"host:port\". Note that *0.0.0.0* - will listen on all devices. - -"), - -("Base","send","send(socket::UDPSocket, host::IPv4, port::Integer, msg) - - Send \"msg\" over \"socket to ``host:port\". - -"), - -("Base","recv","recv(socket::UDPSocket) - - Read a UDP packet from the specified socket, and return the bytes - received. This call blocks. - -"), - -("Base","recvfrom","recvfrom(socket::UDPSocket) -> (address, data) - - Read a UDP packet from the specified socket, returning a tuple of - (address, data), where address will be either IPv4 or IPv6 as - appropriate. - -"), - -("Base","setopt","setopt(sock::UDPSocket; multicast_loop = nothing, multicast_ttl=nothing, enable_broadcast=nothing, ttl=nothing) - - Set UDP socket options. \"multicast_loop\": loopback for multicast - packets (default: true). \"multicast_ttl\": TTL for multicast - packets. \"enable_broadcast\": flag must be set to true if socket - will be used for broadcast messages, or else the UDP system will - return an access error (default: false). \"ttl\": Time-to-live of - packets sent on the socket. - -"), - -("Base","ntoh","ntoh(x) - - Converts the endianness of a value from Network byte order (big- - endian) to that used by the Host. - -"), - -("Base","hton","hton(x) - - Converts the endianness of a value from that used by the Host to - Network byte order (big-endian). - -"), - -("Base","ltoh","ltoh(x) - - Converts the endianness of a value from Little-endian to that used - by the Host. - -"), - -("Base","htol","htol(x) - - Converts the endianness of a value from that used by the Host to - Little-endian. - -"), - -("Base","ENDIAN_BOM","ENDIAN_BOM - - The 32-bit byte-order-mark indicates the native byte order of the - host machine. Little-endian machines will contain the value - 0x04030201. Big-endian machines will contain the value 0x01020304. - -"), - -("Libc","malloc","malloc(size::Integer) -> Ptr{Void} - - Call \"malloc\" from the C standard library. - -"), - -("Libc","calloc","calloc(num::Integer, size::Integer) -> Ptr{Void} - - Call \"calloc\" from the C standard library. - -"), - -("Libc","realloc","realloc(addr::Ptr, size::Integer) -> Ptr{Void} - - Call \"realloc\" from the C standard library. - - See warning in the documentation for \"free\" regarding only using - this on memory originally obtained from \"malloc\". - -"), - -("Libc","free","free(addr::Ptr) - - Call \"free\" from the C standard library. Only use this on memory - obtained from \"malloc\", not on pointers retrieved from other C - libraries. \"Ptr\" objects obtained from C libraries should be - freed by the free functions defined in that library, to avoid - assertion failures if multiple \"libc\" libraries exist on the - system. - -"), - -("Libc","errno","errno([code]) - - Get the value of the C library's \"errno\". If an argument is - specified, it is used to set the value of \"errno\". - - The value of \"errno\" is only valid immediately after a \"ccall\" - to a C library routine that sets it. Specifically, you cannot call - \"errno\" at the next prompt in a REPL, because lots of code is - executed between prompts. - -"), - -("Libc","strerror","strerror(n) - - Convert a system call error code to a descriptive string - -"), - -("Libc","time","time(t::TmStruct) - - Converts a \"TmStruct\" struct to a number of seconds since the - epoch. - -"), - -("Libc","strftime","strftime([format], time) - - Convert time, given as a number of seconds since the epoch or a - \"TmStruct\", to a formatted string using the given format. - Supported formats are the same as those in the standard C library. - -"), - -("Libc","strptime","strptime([format], timestr) - - Parse a formatted time string into a \"TmStruct\" giving the - seconds, minute, hour, date, etc. Supported formats are the same as - those in the standard C library. On some platforms, timezones will - not be parsed correctly. If the result of this function will be - passed to \"time\" to convert it to seconds since the epoch, the - \"isdst\" field should be filled in manually. Setting it to \"-1\" - will tell the C library to use the current system settings to - determine the timezone. - -"), - -("Libc","TmStruct","TmStruct([seconds]) - - Convert a number of seconds since the epoch to broken-down format, - with fields \"sec\", \"min\", \"hour\", \"mday\", \"month\", - \"year\", \"wday\", \"yday\", and \"isdst\". - -"), - -("Libc","flush_cstdio","flush_cstdio() - - Flushes the C \"stdout\" and \"stderr\" streams (which may have - been written to by external C code). - -"), - -("Libc","msync","msync(ptr, len[, flags]) - - Forces synchronization of the \"mmap()\"ped memory region from - \"ptr\" to \"ptr+len\". Flags defaults to \"MS_SYNC\", but can be a - combination of \"MS_ASYNC\", \"MS_SYNC\", or \"MS_INVALIDATE\". See - your platform man page for specifics. The flags argument is not - valid on Windows. - - You may not need to call \"msync\", because synchronization is - performed at intervals automatically by the operating system. - However, you can call this directly if, for example, you are - concerned about losing the result of a long-running calculation. - -"), - -("Libc","MS_ASYNC","MS_ASYNC - - Enum constant for \"msync()\". See your platform man page for - details. (not available on Windows). - -"), - -("Libc","MS_SYNC","MS_SYNC - - Enum constant for \"msync()\". See your platform man page for - details. (not available on Windows). - -"), - -("Libc","MS_INVALIDATE","MS_INVALIDATE - - Enum constant for \"msync()\". See your platform man page for - details. (not available on Windows). - -"), - -("Libc","mmap","mmap(len, prot, flags, fd, offset) - - Low-level interface to the \"mmap\" system call. See the man page. - -"), - -("Libc","munmap","munmap(pointer, len) - - Low-level interface for unmapping memory (see the man page). With - \"mmap_array()\" you do not need to call this directly; the memory - is unmapped for you when the array goes out of scope. - -"), - -("Libdl","dlopen","dlopen(libfile::AbstractString[, flags::Integer]) - - Load a shared library, returning an opaque handle. - - The optional flags argument is a bitwise-or of zero or more of - \"RTLD_LOCAL\", \"RTLD_GLOBAL\", \"RTLD_LAZY\", \"RTLD_NOW\", - \"RTLD_NODELETE\", \"RTLD_NOLOAD\", \"RTLD_DEEPBIND\", and - \"RTLD_FIRST\". These are converted to the corresponding flags of - the POSIX (and/or GNU libc and/or MacOS) dlopen command, if - possible, or are ignored if the specified functionality is not - available on the current platform. The default flags are platform - specific. On MacOS the default \"dlopen\" flags are - \"RTLD_LAZY|RTLD_DEEPBIND|RTLD_GLOBAL\" while on other platforms - the defaults are \"RTLD_LAZY|RTLD_DEEPBIND|RTLD_LOCAL\". An - important usage of these flags is to specify non default behavior - for when the dynamic library loader binds library references to - exported symbols and if the bound references are put into process - local or global scope. For instance - \"RTLD_LAZY|RTLD_DEEPBIND|RTLD_GLOBAL\" allows the library's - symbols to be available for usage in other shared libraries, - addressing situations where there are dependencies between shared - libraries. - -"), - -("Libdl","dlopen_e","dlopen_e(libfile::AbstractString[, flags::Integer]) - - Similar to \"dlopen()\", except returns a \"NULL\" pointer instead - of raising errors. - -"), - -("Libdl","RTLD_DEEPBIND","RTLD_DEEPBIND - - Enum constant for \"dlopen()\". See your platform man page for - details, if applicable. - -"), - -("Libdl","RTLD_FIRST","RTLD_FIRST - - Enum constant for \"dlopen()\". See your platform man page for - details, if applicable. - -"), - -("Libdl","RTLD_GLOBAL","RTLD_GLOBAL - - Enum constant for \"dlopen()\". See your platform man page for - details, if applicable. - -"), - -("Libdl","RTLD_LAZY","RTLD_LAZY - - Enum constant for \"dlopen()\". See your platform man page for - details, if applicable. - -"), - -("Libdl","RTLD_LOCAL","RTLD_LOCAL - - Enum constant for \"dlopen()\". See your platform man page for - details, if applicable. - -"), - -("Libdl","RTLD_NODELETE","RTLD_NODELETE - - Enum constant for \"dlopen()\". See your platform man page for - details, if applicable. - -"), - -("Libdl","RTLD_NOLOAD","RTLD_NOLOAD - - Enum constant for \"dlopen()\". See your platform man page for - details, if applicable. - -"), - -("Libdl","RTLD_NOW","RTLD_NOW - - Enum constant for \"dlopen()\". See your platform man page for - details, if applicable. - -"), - -("Libdl","dlsym","dlsym(handle, sym) - - Look up a symbol from a shared library handle, return callable - function pointer on success. - -"), - -("Libdl","dlsym_e","dlsym_e(handle, sym) - - Look up a symbol from a shared library handle, silently return NULL - pointer on lookup failure. - -"), - -("Libdl","dlclose","dlclose(handle) - - Close shared library referenced by handle. - -"), - -("Libdl","find_library","find_library(names, locations) - - Searches for the first library in \"names\" in the paths in the - \"locations\" list, \"DL_LOAD_PATH\", or system library paths (in - that order) which can successfully be dlopen'd. On success, the - return value will be one of the names (potentially prefixed by one - of the paths in locations). This string can be assigned to a - \"global const\" and used as the library name in future - \"ccall\"'s. On failure, it returns the empty string. - -"), - -("Libdl","DL_LOAD_PATH","DL_LOAD_PATH - - When calling \"dlopen\", the paths in this list will be searched - first, in order, before searching the system locations for a valid - library handle. - -"), - -("Base","*","*(A, B) - - Matrix multiplication - -"), - -("Base","\\","\\(A, B) - - Matrix division using a polyalgorithm. For input matrices \"A\" and - \"B\", the result \"X\" is such that \"A*X == B\" when \"A\" is - square. The solver that is used depends upon the structure of - \"A\". A direct solver is used for upper- or lower triangular - \"A\". For Hermitian \"A\" (equivalent to symmetric \"A\" for non- - complex \"A\") the \"BunchKaufman\" factorization is used. - Otherwise an LU factorization is used. For rectangular \"A\" the - result is the minimum-norm least squares solution computed by a - pivoted QR factorization of \"A\" and a rank estimate of A based on - the R factor. - - When \"A\" is sparse, a similar polyalgorithm is used. For - indefinite matrices, the LDLt factorization does not use pivoting - during the numerical factorization and therefore the procedure can - fail even for invertible matrices. - -"), - -("Base","dot","dot(x, y) -⋅(x, y) - - Compute the dot product. For complex vectors, the first vector is - conjugated. - -"), - -("Base","vecdot","vecdot(x, y) - - For any iterable containers \"x\" and \"y\" (including arrays of - any dimension) of numbers (or any element type for which \"dot\" is - defined), compute the Euclidean dot product (the sum of - \"dot(x[i],y[i])\") as if they were vectors. - -"), - -("Base","cross","cross(x, y) -×(x, y) - - Compute the cross product of two 3-vectors. - -"), - -("Base","factorize","factorize(A) - - Compute a convenient factorization (including LU, Cholesky, Bunch- - Kaufman, LowerTriangular, UpperTriangular) of A, based upon the - type of the input matrix. The return value can then be reused for - efficient solving of multiple systems. For example: - \"A=factorize(A); x=A\\\\b; y=A\\\\C\". - -"), - -("Base","full","full(F) - - Reconstruct the matrix \"A\" from the factorization - \"F=factorize(A)\". - -"), - -("Base","lu","lu(A) -> L, U, p - - Compute the LU factorization of \"A\", such that \"A[p,:] = L*U\". - -"), - -("Base","lufact","lufact(A[, pivot=Val{true}]) -> F - - Compute the LU factorization of \"A\". The return type of \"F\" - depends on the type of \"A\". In most cases, if \"A\" is a subtype - \"S\" of AbstractMatrix with an element type \"T`\" supporting - \"+\", \"-\", \"*\" and \"/\" the return type is \"LU{T,S{T}}\". If - pivoting is chosen (default) the element type should also support - \"abs\" and \"<\". When \"A\" is sparse and have element of type - \"Float32\", \"Float64\", \"Complex{Float32}\", or - \"Complex{Float64}\" the return type is \"UmfpackLU\". Some - examples are shown in the table below. - - +-------------------------+---------------------------+------------------------------------------------+ - | Type of input \\\"A\\\" | Type of output \\\"F\\\" | Relationship between \\\"F\\\" and \\\"A\\\" | - +-------------------------+---------------------------+------------------------------------------------+ - | \\\"Matrix()\\\" | \\\"LU\\\" | \\\"F[:L]*F[:U] == A[F[:p], :]\\\" | - +-------------------------+---------------------------+------------------------------------------------+ - | \\\"Tridiagonal()\\\" | \\\"LU{T,Tridiagonal{T}}\\\" | \\\"F[:L]*F[:U] == A[F[:p], :]\\\" | - +-------------------------+---------------------------+------------------------------------------------+ - | \\\"SparseMatrixCSC()\\\" | \\\"UmfpackLU\\\" | \\\"F[:L]*F[:U] == (F[:Rs] .* A)[F[:p], F[:q]]\\\" | - +-------------------------+---------------------------+------------------------------------------------+ - - The individual components of the factorization \"F\" can be - accessed by indexing: - - +-------------+-----------------------------------------+--------+--------------------------+---------------+ - | Component | Description | \\\"LU\\\" | \\\"LU{T,Tridiagonal{T}}\\\" | \\\"UmfpackLU\\\" | - +-------------+-----------------------------------------+--------+--------------------------+---------------+ - | \\\"F[:L]\\\" | \\\"L\\\" (lower triangular) part of \\\"LU\\\" | ✓ | ✓ | ✓ | - +-------------+-----------------------------------------+--------+--------------------------+---------------+ - | \\\"F[:U]\\\" | \\\"U\\\" (upper triangular) part of \\\"LU\\\" | ✓ | ✓ | ✓ | - +-------------+-----------------------------------------+--------+--------------------------+---------------+ - | \\\"F[:p]\\\" | (right) permutation \\\"Vector\\\" | ✓ | ✓ | ✓ | - +-------------+-----------------------------------------+--------+--------------------------+---------------+ - | \\\"F[:P]\\\" | (right) permutation \\\"Matrix\\\" | ✓ | ✓ | | - +-------------+-----------------------------------------+--------+--------------------------+---------------+ - | \\\"F[:q]\\\" | left permutation \\\"Vector\\\" | | | ✓ | - +-------------+-----------------------------------------+--------+--------------------------+---------------+ - | \\\"F[:Rs]\\\" | \\\"Vector\\\" of scaling factors | | | ✓ | - +-------------+-----------------------------------------+--------+--------------------------+---------------+ - | \\\"F[:(:)]\\\" | \\\"(L,U,p,q,Rs)\\\" components | | | ✓ | - +-------------+-----------------------------------------+--------+--------------------------+---------------+ - - +--------------------+--------+--------------------------+---------------+ - | Supported function | \\\"LU\\\" | \\\"LU{T,Tridiagonal{T}}\\\" | \\\"UmfpackLU\\\" | - +--------------------+--------+--------------------------+---------------+ - | \\\"/\\\" | ✓ | | | - +--------------------+--------+--------------------------+---------------+ - | \\\"\\\\\\\" | ✓ | ✓ | ✓ | - +--------------------+--------+--------------------------+---------------+ - | \\\"cond\\\" | ✓ | | ✓ | - +--------------------+--------+--------------------------+---------------+ - | \\\"det\\\" | ✓ | ✓ | ✓ | - +--------------------+--------+--------------------------+---------------+ - | \\\"logdet\\\" | ✓ | ✓ | | - +--------------------+--------+--------------------------+---------------+ - | \\\"logabsdet\\\" | ✓ | ✓ | | - +--------------------+--------+--------------------------+---------------+ - | \\\"size\\\" | ✓ | ✓ | | - +--------------------+--------+--------------------------+---------------+ - -"), - -("Base","lufact!","lufact!(A) -> LU - - \"lufact!\" is the same as \"lufact()\", but saves space by - overwriting the input A, instead of creating a copy. For sparse - \"A\" the \"nzval\" field is not overwritten but the index fields, - \"colptr\" and \"rowval\" are decremented in place, converting from - 1-based indices to 0-based indices. - -"), - -("Base","chol","chol(A[, LU]) -> F - - Compute the Cholesky factorization of a symmetric positive definite - matrix \"A\" and return the matrix \"F\". If \"LU\" is \"Val{:U}\" - (Upper), \"F\" is of type \"UpperTriangular\" and \"A = F'*F\". If - \"LU\" is \"Val{:L}\" (Lower), \"F\" is of type \"LowerTriangular\" - and \"A = F*F'\". \"LU\" defaults to \"Val{:U}\". - -"), - -("Base","cholfact","cholfact(A, [LU=:U[,pivot=Val{false}]][;tol=-1.0]) -> Cholesky - - Compute the Cholesky factorization of a dense symmetric positive - (semi)definite matrix \"A\" and return either a \"Cholesky\" if - \"pivot==Val{false}\" or \"CholeskyPivoted\" if - \"pivot==Val{true}\". \"LU\" may be \":L\" for using the lower part - or \":U\" for the upper part. The default is to use \":U\". The - triangular matrix can be obtained from the factorization \"F\" - with: \"F[:L]\" and \"F[:U]\". The following functions are - available for \"Cholesky\" objects: \"size\", \"\\\", \"inv\", - \"det\". For \"CholeskyPivoted\" there is also defined a \"rank\". - If \"pivot==Val{false}\" a \"PosDefException\" exception is thrown - in case the matrix is not positive definite. The argument \"tol\" - determines the tolerance for determining the rank. For negative - values, the tolerance is the machine precision. - -"), - -("Base","cholfact","cholfact(A; shift=0, perm=Int[]) -> CHOLMOD.Factor - - Compute the Cholesky factorization of a sparse positive definite - matrix \"A\". A fill-reducing permutation is used. \"F = - cholfact(A)\" is most frequently used to solve systems of equations - with \"F\\b\", but also the methods \"diag\", \"det\", \"logdet\" - are defined for \"F\". You can also extract individual factors - from \"F\", using \"F[:L]\". However, since pivoting is on by - default, the factorization is internally represented as \"A == - P'*L*L'*P\" with a permutation matrix \"P\"; using just \"L\" - without accounting for \"P\" will give incorrect answers. To - include the effects of permutation, it's typically preferable to - extact \"combined\" factors like \"PtL = F[:PtL]\" (the equivalent - of \"P'*L\") and \"LtP = F[:UP]\" (the equivalent of \"L'*P\"). - - Setting optional \"shift\" keyword argument computes the - factorization of \"A+shift*I\" instead of \"A\". If the \"perm\" - argument is nonempty, it should be a permutation of *1:size(A,1)* - giving the ordering to use (instead of CHOLMOD's default AMD - ordering). - - The function calls the C library CHOLMOD and many other functions - from the library are wrapped but not exported. - -"), - -("Base","cholfact!","cholfact!(A [,LU=:U [,pivot=Val{false}]][;tol=-1.0]) -> Cholesky - - \"cholfact!\" is the same as \"cholfact()\", but saves space by - overwriting the input \"A\", instead of creating a copy. - \"cholfact!\" can also reuse the symbolic factorization from a - different matrix \"F\" with the same structure when used as: - \"cholfact!(F::CholmodFactor, A)\". - -"), - -("Base","ldltfact","ldltfact(A) -> LDLtFactorization - - Compute a factorization of a positive definite matrix \"A\" such - that \"A=L*Diagonal(d)*L'\" where \"L\" is a unit lower triangular - matrix and \"d\" is a vector with non-negative elements. - -"), - -("Base","ldltfact","ldltfact(A; shift=0, perm=Int[]) -> CHOLMOD.Factor - - Compute the LDLt factorization of a sparse symmetric or Hermitian - matrix \"A\". A fill-reducing permutation is used. \"F = - ldltfact(A)\" is most frequently used to solve systems of equations - with \"F\\b\", but also the methods \"diag\", \"det\", \"logdet\" - are defined for \"F\". You can also extract individual factors from - \"F\", using \"F[:L]\". However, since pivoting is on by default, - the factorization is internally represented as \"A == P'*L*D*L'*P\" - with a permutation matrix \"P\"; using just \"L\" without - accounting for \"P\" will give incorrect answers. To include the - effects of permutation, it's typically preferable to extact - \"combined\" factors like \"PtL = F[:PtL]\" (the equivalent of - \"P'*L\") and \"LtP = F[:UP]\" (the equivalent of \"L'*P\"). The - complete list of supported factors is \":L, :PtL, :D, :UP, :U, :LD, - :DU, :PtLD, :DUP\". - - Setting optional \"shift\" keyword argument computes the - factorization of \"A+shift*I\" instead of \"A\". If the \"perm\" - argument is nonempty, it should be a permutation of *1:size(A,1)* - giving the ordering to use (instead of CHOLMOD's default AMD - ordering). - - The function calls the C library CHOLMOD and many other functions - from the library are wrapped but not exported. - -"), - -("Base","qr","qr(A[, pivot=Val{false}][;thin=true]) -> Q, R, [p] - - Compute the (pivoted) QR factorization of \"A\" such that either - \"A = Q*R\" or \"A[:,p] = Q*R\". Also see \"qrfact\". The default - is to compute a thin factorization. Note that \"R\" is not extended - with zeros when the full \"Q\" is requested. - -"), - -("Base","qrfact","qrfact(A[, pivot=Val{false}]) -> F - - Computes the QR factorization of \"A\". The return type of \"F\" - depends on the element type of \"A\" and whether pivoting is - specified (with \"pivot==Val{true}\"). - - +------------------+-------------------+----------------+---------------------------------------+ - | Return type | \\\"eltype(A)\\\" | \\\"pivot\\\" | Relationship between \\\"F\\\" and \\\"A\\\" | - +------------------+-------------------+----------------+---------------------------------------+ - | \\\"QR\\\" | not \\\"BlasFloat\\\" | either | \\\"A==F[:Q]*F[:R]\\\" | - +------------------+-------------------+----------------+---------------------------------------+ - | \\\"QRCompactWY\\\" | \\\"BlasFloat\\\" | \\\"Val{false}\\\" | \\\"A==F[:Q]*F[:R]\\\" | - +------------------+-------------------+----------------+---------------------------------------+ - | \\\"QRPivoted\\\" | \\\"BlasFloat\\\" | \\\"Val{true}\\\" | \\\"A[:,F[:p]]==F[:Q]*F[:R]\\\" | - +------------------+-------------------+----------------+---------------------------------------+ - - \"BlasFloat\" refers to any of: \"Float32\", \"Float64\", - \"Complex64\" or \"Complex128\". - - The individual components of the factorization \"F\" can be - accessed by indexing: - - +-------------+-----------------------------------------------+--------------------+-----------------------+--------------------+ - | Component | Description | \\\"QR\\\" | \\\"QRCompactWY\\\" | \\\"QRPivoted\\\" | - +-------------+-----------------------------------------------+--------------------+-----------------------+--------------------+ - | \\\"F[:Q]\\\" | \\\"Q\\\" (orthogonal/unitary) part of \\\"QR\\\" | ✓ (\\\"QRPackedQ\\\") | ✓ (\\\"QRCompactWYQ\\\") | ✓ (\\\"QRPackedQ\\\") | - +-------------+-----------------------------------------------+--------------------+-----------------------+--------------------+ - | \\\"F[:R]\\\" | \\\"R\\\" (upper right triangular) part of \\\"QR\\\" | ✓ | ✓ | ✓ | - +-------------+-----------------------------------------------+--------------------+-----------------------+--------------------+ - | \\\"F[:p]\\\" | pivot \\\"Vector\\\" | | | ✓ | - +-------------+-----------------------------------------------+--------------------+-----------------------+--------------------+ - | \\\"F[:P]\\\" | (pivot) permutation \\\"Matrix\\\" | | | ✓ | - +-------------+-----------------------------------------------+--------------------+-----------------------+--------------------+ - - The following functions are available for the \"QR\" objects: - \"size\", \"\\\". When \"A\" is rectangular, \"\\\" will return a - least squares solution and if the solution is not unique, the one - with smallest norm is returned. - - Multiplication with respect to either thin or full \"Q\" is - allowed, i.e. both \"F[:Q]*F[:R]\" and \"F[:Q]*A\" are supported. A - \"Q\" matrix can be converted into a regular matrix with \"full()\" - which has a named argument \"thin\". - - Note: \"qrfact\" returns multiple types because LAPACK uses - several representations that minimize the memory storage - requirements of products of Householder elementary reflectors, so - that the \"Q\" and \"R\" matrices can be stored compactly rather - as two separate dense matrices.The data contained in \"QR\" or - \"QRPivoted\" can be used to construct the \"QRPackedQ\" type, - which is a compact representation of the rotation matrix: - - Q = \\prod_{i=1}^{\\min(m,n)} (I - \\tau_i v_i v_i^T) - - where \\tau_i is the scale factor and v_i is the projection - vector associated with the i^{th} Householder elementary - reflector.The data contained in \"QRCompactWY\" can be used to - construct the \"QRCompactWYQ\" type, which is a compact - representation of the rotation matrix - - Q = I + Y T Y^T - - where \"Y\" is m \\times r lower trapezoidal and \"T\" is r - \\times r upper triangular. The *compact WY* representation - [Schreiber1989] is not to be confused with the older, *WY* - representation [Bischof1987]. (The LAPACK documentation uses - \"V\" in lieu of \"Y\".) - - [Bischof1987] C Bischof and C Van Loan, The WY - representation for products of Householder matrices, - SIAM J Sci Stat Comput 8 (1987), s2-s13. - doi:10.1137/0908009 - - [Schreiber1989] R Schreiber and C Van Loan, A - storage-efficient WY representation for products of - Householder transformations, SIAM J Sci Stat Comput - 10 (1989), 53-57. doi:10.1137/0910005 - -"), - -("Base","qrfact","qrfact(A) -> SPQR.Factorization - - Compute the QR factorization of a sparse matrix \"A\". A fill- - reducing permutation is used. The main application of this type is - to solve least squares problems with \"\\\". The function calls the - C library SPQR and a few additional functions from the library are - wrapped but not exported. - -"), - -("Base","qrfact!","qrfact!(A[, pivot=Val{false}]) - - \"qrfact!\" is the same as \"qrfact()\" when A is a subtype of - \"StridedMatrix\", but saves space by overwriting the input \"A\", - instead of creating a copy. - -"), - -("Base","full","full(QRCompactWYQ[, thin=true]) -> Matrix - - Converts an orthogonal or unitary matrix stored as a - \"QRCompactWYQ\" object, i.e. in the compact WY format - [Bischof1987], to a dense matrix. - - Optionally takes a \"thin\" Boolean argument, which if \"true\" - omits the columns that span the rows of \"R\" in the QR - factorization that are zero. The resulting matrix is the \"Q\" in a - thin QR factorization (sometimes called the reduced QR - factorization). If \"false\", returns a \"Q\" that spans all rows - of \"R\" in its corresponding QR factorization. - -"), - -("Base","bkfact","bkfact(A) -> BunchKaufman - - Compute the Bunch-Kaufman [Bunch1977] factorization of a real - symmetric or complex Hermitian matrix \"A\" and return a - \"BunchKaufman\" object. The following functions are available for - \"BunchKaufman\" objects: \"size\", \"\\\", \"inv\", \"issym\", - \"ishermitian\". - -"), - -("Base","bkfact!","bkfact!(A) -> BunchKaufman - - \"bkfact!\" is the same as \"bkfact()\", but saves space by - overwriting the input \"A\", instead of creating a copy. - -"), - -("Base","sqrtm","sqrtm(A) - - Compute the matrix square root of \"A\". If \"B = sqrtm(A)\", then - \"B*B == A\" within roundoff error. - - \"sqrtm\" uses a polyalgorithm, computing the matrix square root - using Schur factorizations (\"schurfact()\") unless it detects the - matrix to be Hermitian or real symmetric, in which case it computes - the matrix square root from an eigendecomposition (\"eigfact()\"). - In the latter situation for positive definite matrices, the matrix - square root has \"Real\" elements, otherwise it has \"Complex\" - elements. - -"), - -("Base","eig","eig(A,[irange,][vl,][vu,][permute=true,][scale=true]) -> D, V - - Computes eigenvalues and eigenvectors of \"A\". See \"eigfact()\" - for details on the \"balance\" keyword argument. - - julia> eig([1.0 0.0 0.0; 0.0 3.0 0.0; 0.0 0.0 18.0]) - ([1.0,3.0,18.0], - 3x3 Array{Float64,2}: - 1.0 0.0 0.0 - 0.0 1.0 0.0 - 0.0 0.0 1.0) - - \"eig\" is a wrapper around \"eigfact()\", extracting all parts of - the factorization to a tuple; where possible, using \"eigfact()\" - is recommended. - -"), - -("Base","eig","eig(A, B) -> D, V - - Computes generalized eigenvalues and vectors of \"A\" with respect - to \"B\". - - \"eig\" is a wrapper around \"eigfact()\", extracting all parts of - the factorization to a tuple; where possible, using \"eigfact()\" - is recommended. - -"), - -("Base","eigvals","eigvals(A,[irange,][vl,][vu]) - - Returns the eigenvalues of \"A\". If \"A\" is \"Symmetric\", - \"Hermitian\" or \"SymTridiagonal\", it is possible to calculate - only a subset of the eigenvalues by specifying either a - \"UnitRange\" \"irange\" covering indices of the sorted - eigenvalues, or a pair \"vl\" and \"vu\" for the lower and upper - boundaries of the eigenvalues. - - For general non-symmetric matrices it is possible to specify how - the matrix is balanced before the eigenvector calculation. The - option \"permute=true\" permutes the matrix to become closer to - upper triangular, and \"scale=true\" scales the matrix by its - diagonal elements to make rows and columns more equal in norm. The - default is \"true\" for both options. - -"), - -("Base","eigmax","eigmax(A) - - Returns the largest eigenvalue of \"A\". - -"), - -("Base","eigmin","eigmin(A) - - Returns the smallest eigenvalue of \"A\". - -"), - -("Base","eigvecs","eigvecs(A, [eigvals,][permute=true,][scale=true]) -> Matrix - - Returns a matrix \"M\" whose columns are the eigenvectors of \"A\". - (The \"k\"th eigenvector can be obtained from the slice \"M[:, - k]\".) The \"permute\" and \"scale\" keywords are the same as for - \"eigfact()\". - - For \"SymTridiagonal\" matrices, if the optional vector of - eigenvalues \"eigvals\" is specified, returns the specific - corresponding eigenvectors. - -"), - -("Base","eigfact","eigfact(A,[irange,][vl,][vu,][permute=true,][scale=true]) -> Eigen - - Computes the eigenvalue decomposition of \"A\", returning an - \"Eigen\" factorization object \"F\" which contains the eigenvalues - in \"F[:values]\" and the eigenvectors in the columns of the matrix - \"F[:vectors]\". (The \"k\"th eigenvector can be obtained from the - slice \"F[:vectors][:, k]\".) - - The following functions are available for \"Eigen\" objects: - \"inv\", \"det\". - - If \"A\" is \"Symmetric\", \"Hermitian\" or \"SymTridiagonal\", it - is possible to calculate only a subset of the eigenvalues by - specifying either a \"UnitRange\" \"irange\" covering indices of - the sorted eigenvalues or a pair \"vl\" and \"vu\" for the lower - and upper boundaries of the eigenvalues. - - For general nonsymmetric matrices it is possible to specify how the - matrix is balanced before the eigenvector calculation. The option - \"permute=true\" permutes the matrix to become closer to upper - triangular, and \"scale=true\" scales the matrix by its diagonal - elements to make rows and columns more equal in norm. The default - is \"true\" for both options. - -"), - -("Base","eigfact","eigfact(A, B) -> GeneralizedEigen - - Computes the generalized eigenvalue decomposition of \"A\" and - \"B\", returning a \"GeneralizedEigen\" factorization object \"F\" - which contains the generalized eigenvalues in \"F[:values]\" and - the generalized eigenvectors in the columns of the matrix - \"F[:vectors]\". (The \"k\"th generalized eigenvector can be - obtained from the slice \"F[:vectors][:, k]\".) - -"), - -("Base","eigfact!","eigfact!(A[, B]) - - Same as \"eigfact()\", but saves space by overwriting the input - \"A\" (and \"B\"), instead of creating a copy. - -"), - -("Base","hessfact","hessfact(A) - - Compute the Hessenberg decomposition of \"A\" and return a - \"Hessenberg\" object. If \"F\" is the factorization object, the - unitary matrix can be accessed with \"F[:Q]\" and the Hessenberg - matrix with \"F[:H]\". When \"Q\" is extracted, the resulting type - is the \"HessenbergQ\" object, and may be converted to a regular - matrix with \"full()\". - -"), - -("Base","hessfact!","hessfact!(A) - - \"hessfact!\" is the same as \"hessfact()\", but saves space by - overwriting the input A, instead of creating a copy. - -"), - -("Base","schurfact","schurfact(A) -> Schur - - Computes the Schur factorization of the matrix \"A\". The (quasi) - triangular Schur factor can be obtained from the \"Schur\" object - \"F\" with either \"F[:Schur]\" or \"F[:T]\" and the - unitary/orthogonal Schur vectors can be obtained with - \"F[:vectors]\" or \"F[:Z]\" such that - \"A=F[:vectors]*F[:Schur]*F[:vectors]'\". The eigenvalues of \"A\" - can be obtained with \"F[:values]\". - -"), - -("Base","schurfact!","schurfact!(A) - - Computes the Schur factorization of \"A\", overwriting \"A\" in the - process. See \"schurfact()\" - -"), - -("Base","schur","schur(A) -> Schur[:T], Schur[:Z], Schur[:values] - - See \"schurfact()\" - -"), - -("Base","ordschur","ordschur(Q, T, select) -> Schur - - Reorders the Schur factorization of a real matrix \"A=Q*T*Q'\" - according to the logical array \"select\" returning a Schur object - \"F\". The selected eigenvalues appear in the leading diagonal of - \"F[:Schur]\" and the the corresponding leading columns of - \"F[:vectors]\" form an orthonormal basis of the corresponding - right invariant subspace. A complex conjugate pair of eigenvalues - must be either both included or excluded via \"select\". - -"), - -("Base","ordschur!","ordschur!(Q, T, select) -> Schur - - Reorders the Schur factorization of a real matrix \"A=Q*T*Q'\", - overwriting \"Q\" and \"T\" in the process. See \"ordschur()\" - -"), - -("Base","ordschur","ordschur(S, select) -> Schur - - Reorders the Schur factorization \"S\" of type \"Schur\". - -"), - -("Base","ordschur!","ordschur!(S, select) -> Schur - - Reorders the Schur factorization \"S\" of type \"Schur\", - overwriting \"S\" in the process. See \"ordschur()\" - -"), - -("Base","schurfact","schurfact(A, B) -> GeneralizedSchur - - Computes the Generalized Schur (or QZ) factorization of the - matrices \"A\" and \"B\". The (quasi) triangular Schur factors can - be obtained from the \"Schur\" object \"F\" with \"F[:S]\" and - \"F[:T]\", the left unitary/orthogonal Schur vectors can be - obtained with \"F[:left]\" or \"F[:Q]\" and the right - unitary/orthogonal Schur vectors can be obtained with \"F[:right]\" - or \"F[:Z]\" such that \"A=F[:left]*F[:S]*F[:right]'\" and - \"B=F[:left]*F[:T]*F[:right]'\". The generalized eigenvalues of - \"A\" and \"B\" can be obtained with \"F[:alpha]./F[:beta]\". - -"), - -("Base","schur","schur(A, B) -> GeneralizedSchur[:S], GeneralizedSchur[:T], GeneralizedSchur[:Q], GeneralizedSchur[:Z] - - See \"schurfact()\" - -"), - -("Base","ordschur","ordschur(S, T, Q, Z, select) -> GeneralizedSchur - - Reorders the Generalized Schur factorization of a matrix \"(A, B) = - (Q*S*Z^{H}, Q*T*Z^{H})\" according to the logical array \"select\" - and returns a GeneralizedSchur object \"GS\". The selected - eigenvalues appear in the leading diagonal of both``(GS[:S], - GS[:T])`` and the left and right unitary/orthogonal Schur vectors - are also reordered such that \"(A, B) = GS[:Q]*(GS[:S], - GS[:T])*GS[:Z]^{H}\" still holds and the generalized eigenvalues of - \"A\" and \"B\" can still be obtained with - \"GS[:alpha]./GS[:beta]\". - -"), - -("Base","ordschur!","ordschur!(S, T, Q, Z, select) -> GeneralizedSchur - - Reorders the Generalized Schur factorization of a matrix by - overwriting the matrices \"(S, T, Q, Z)\" in the process. See - \"ordschur()\". - -"), - -("Base","ordschur","ordschur(GS, select) -> GeneralizedSchur - - Reorders the Generalized Schur factorization of a Generalized Schur - object. See \"ordschur()\". - -"), - -("Base","ordschur!","ordschur!(GS, select) -> GeneralizedSchur - - Reorders the Generalized Schur factorization of a Generalized Schur - object by overwriting the object with the new factorization. See - \"ordschur()\". - -"), - -("Base","svdfact","svdfact(A[, thin=true]) -> SVD - - Compute the Singular Value Decomposition (SVD) of \"A\" and return - an \"SVD\" object. \"U\", \"S\", \"V\" and \"Vt\" can be obtained - from the factorization \"F\" with \"F[:U]\", \"F[:S]\", \"F[:V]\" - and \"F[:Vt]\", such that \"A = U*diagm(S)*Vt\". If \"thin\" is - \"true\", an economy mode decomposition is returned. The algorithm - produces \"Vt\" and hence \"Vt\" is more efficient to extract than - \"V\". The default is to produce a thin decomposition. - -"), - -("Base","svdfact!","svdfact!(A[, thin=true]) -> SVD - - \"svdfact!\" is the same as \"svdfact()\", but saves space by - overwriting the input A, instead of creating a copy. If \"thin\" is - \"true\", an economy mode decomposition is returned. The default is - to produce a thin decomposition. - -"), - -("Base","svd","svd(A[, thin=true]) -> U, S, V - - Wrapper around \"svdfact\" extracting all parts the factorization - to a tuple. Direct use of \"svdfact\" is therefore generally more - efficient. Computes the SVD of A, returning \"U\", vector \"S\", - and \"V\" such that \"A == U*diagm(S)*V'\". If \"thin\" is - \"true\", an economy mode decomposition is returned. The default is - to produce a thin decomposition. - -"), - -("Base","svdvals","svdvals(A) - - Returns the singular values of \"A\". - -"), - -("Base","svdvals!","svdvals!(A) - - Returns the singular values of \"A\", while saving space by - overwriting the input. - -"), - -("Base","svdfact","svdfact(A, B) -> GeneralizedSVD - - Compute the generalized SVD of \"A\" and \"B\", returning a - \"GeneralizedSVD\" Factorization object \"F\", such that \"A = - F[:U]*F[:D1]*F[:R0]*F[:Q]'\" and \"B = - F[:V]*F[:D2]*F[:R0]*F[:Q]'\". - -"), - -("Base","svd","svd(A, B) -> U, V, Q, D1, D2, R0 - - Wrapper around \"svdfact\" extracting all parts the factorization - to a tuple. Direct use of \"svdfact\" is therefore generally more - efficient. The function returns the generalized SVD of \"A\" and - \"B\", returning \"U\", \"V\", \"Q\", \"D1\", \"D2\", and \"R0\" - such that \"A = U*D1*R0*Q'\" and \"B = V*D2*R0*Q'\". - -"), - -("Base","svdvals","svdvals(A, B) - - Return only the singular values from the generalized singular value - decomposition of \"A\" and \"B\". - -"), - -("Base","triu","triu(M) - - Upper triangle of a matrix. - -"), - -("Base","triu","triu(M, k) - - Returns the upper triangle of \"M\" starting from the \"k\"th - superdiagonal. - -"), - -("Base","triu!","triu!(M) - - Upper triangle of a matrix, overwriting \"M\" in the process. - -"), - -("Base","triu!","triu!(M, k) - - Returns the upper triangle of \"M\" starting from the \"k\"th - superdiagonal, overwriting \"M\" in the process. - -"), - -("Base","tril","tril(M) - - Lower triangle of a matrix. - -"), - -("Base","tril","tril(M, k) - - Returns the lower triangle of \"M\" starting from the \"k\"th - subdiagonal. - -"), - -("Base","tril!","tril!(M) - - Lower triangle of a matrix, overwriting \"M\" in the process. - -"), - -("Base","tril!","tril!(M, k) - - Returns the lower triangle of \"M\" starting from the \"k\"th - subdiagonal, overwriting \"M\" in the process. - -"), - -("Base","diagind","diagind(M[, k]) - - A \"Range\" giving the indices of the \"k\"th diagonal of the - matrix \"M\". - -"), - -("Base","diag","diag(M[, k]) - - The \"k\"th diagonal of a matrix, as a vector. Use \"diagm\" to - construct a diagonal matrix. - -"), - -("Base","diagm","diagm(v[, k]) - - Construct a diagonal matrix and place \"v\" on the \"k\"th - diagonal. - -"), - -("Base","scale","scale(A, b) - -"), - -("Base","scale","scale(b, A) - - Scale an array \"A\" by a scalar \"b\", returning a new array. - - If \"A\" is a matrix and \"b\" is a vector, then \"scale(A,b)\" - scales each column \"i\" of \"A\" by \"b[i]\" (similar to - \"A*diagm(b)\"), while \"scale(b,A)\" scales each row \"i\" of - \"A\" by \"b[i]\" (similar to \"diagm(b)*A\"), returning a new - array. - - Note: for large \"A\", \"scale\" can be much faster than \"A .* b\" - or \"b .* A\", due to the use of BLAS. - -"), - -("Base","scale!","scale!(A, b) - -"), - -("Base","scale!","scale!(b, A) - - Scale an array \"A\" by a scalar \"b\", similar to \"scale()\" but - overwriting \"A\" in-place. - - If \"A\" is a matrix and \"b\" is a vector, then \"scale!(A,b)\" - scales each column \"i\" of \"A\" by \"b[i]\" (similar to - \"A*diagm(b)\"), while \"scale!(b,A)\" scales each row \"i\" of - \"A\" by \"b[i]\" (similar to \"diagm(b)*A\"), again operating in- - place on \"A\". - -"), - -("Base","Tridiagonal","Tridiagonal(dl, d, du) - - Construct a tridiagonal matrix from the lower diagonal, diagonal, - and upper diagonal, respectively. The result is of type - \"Tridiagonal\" and provides efficient specialized linear solvers, - but may be converted into a regular matrix with \"full()\". - -"), - -("Base","Bidiagonal","Bidiagonal(dv, ev, isupper) - - Constructs an upper (\"isupper=true\") or lower (\"isupper=false\") - bidiagonal matrix using the given diagonal (\"dv\") and off- - diagonal (\"ev\") vectors. The result is of type \"Bidiagonal\" - and provides efficient specialized linear solvers, but may be - converted into a regular matrix with \"full()\". - -"), - -("Base","SymTridiagonal","SymTridiagonal(d, du) - - Construct a real symmetric tridiagonal matrix from the diagonal and - upper diagonal, respectively. The result is of type - \"SymTridiagonal\" and provides efficient specialized eigensolvers, - but may be converted into a regular matrix with \"full()\". - -"), - -("Base","rank","rank(M) - - Compute the rank of a matrix. - -"), - -("Base","norm","norm(A[, p]) - - Compute the \"p\"-norm of a vector or the operator norm of a matrix - \"A\", defaulting to the \"p=2\"-norm. - - For vectors, \"p\" can assume any numeric value (even though not - all values produce a mathematically valid vector norm). In - particular, \"norm(A, Inf)\" returns the largest value in - \"abs(A)\", whereas \"norm(A, -Inf)\" returns the smallest. - - For matrices, valid values of \"p\" are \"1\", \"2\", or \"Inf\". - (Note that for sparse matrices, \"p=2\" is currently not - implemented.) Use \"vecnorm()\" to compute the Frobenius norm. - -"), - -("Base","vecnorm","vecnorm(A[, p]) - - For any iterable container \"A\" (including arrays of any - dimension) of numbers (or any element type for which \"norm\" is - defined), compute the \"p\"-norm (defaulting to \"p=2\") as if - \"A\" were a vector of the corresponding length. - - For example, if \"A\" is a matrix and \"p=2\", then this is - equivalent to the Frobenius norm. - -"), - -("Base","cond","cond(M[, p]) - - Condition number of the matrix \"M\", computed using the operator - \"p\"-norm. Valid values for \"p\" are \"1\", \"2\" (default), or - \"Inf\". - -"), - -("Base","condskeel","condskeel(M[, x, p]) - - \\kappa_S(M, p) & = \\left\\Vert \\left\\vert M \\right\\vert - \\left\\vert M^{-1} \\right\\vert \\right\\Vert_p \\\\ - \\kappa_S(M, x, p) & = \\left\\Vert \\left\\vert M \\right\\vert - \\left\\vert M^{-1} \\right\\vert \\left\\vert x \\right\\vert - \\right\\Vert_p - - Skeel condition number \\kappa_S of the matrix \"M\", optionally - with respect to the vector \"x\", as computed using the operator - \"p\"-norm. \"p\" is \"Inf\" by default, if not provided. Valid - values for \"p\" are \"1\", \"2\", or \"Inf\". - - This quantity is also known in the literature as the Bauer - condition number, relative condition number, or componentwise - relative condition number. - -"), - -("Base","trace","trace(M) - - Matrix trace - -"), - -("Base","det","det(M) - - Matrix determinant - -"), - -("Base","logdet","logdet(M) - - Log of matrix determinant. Equivalent to \"log(det(M))\", but may - provide increased accuracy and/or speed. - -"), - -("Base","logabsdet","logabsdet(M) - - Log of absolute value of determinant of real matrix. Equivalent to - \"(log(abs(det(M))), sign(det(M)))\", but may provide increased - accuracy and/or speed. - -"), - -("Base","inv","inv(M) - - Matrix inverse - -"), - -("Base","pinv","pinv(M[, tol]) - - Computes the Moore-Penrose pseudoinverse. - - For matrices \"M\" with floating point elements, it is convenient - to compute the pseudoinverse by inverting only singular values - above a given threshold, \"tol\". - - The optimal choice of \"tol\" varies both with the value of \"M\" - and the intended application of the pseudoinverse. The default - value of \"tol\" is - \"eps(real(float(one(eltype(M)))))*maximum(size(A))\", which is - essentially machine epsilon for the real part of a matrix element - multiplied by the larger matrix dimension. For inverting dense ill- - conditioned matrices in a least-squares sense, \"tol = - sqrt(eps(real(float(one(eltype(M))))))\" is recommended. - - For more information, see [8859], [B96], [S84], [KY88]. - - [8859] Issue 8859, \"Fix least squares\", - https://github.com/JuliaLang/julia/pull/8859 - - [B96] Åke Björck, \"Numerical Methods for Least Squares - Problems\", SIAM Press, Philadelphia, 1996, \"Other Titles in - Applied Mathematics\", Vol. 51. doi:10.1137/1.9781611971484 - - [S84] G. W. Stewart, \"Rank Degeneracy\", SIAM Journal on - Scientific and Statistical Computing, 5(2), 1984, 403-413. - doi:10.1137/0905030 - - [KY88] Konstantinos Konstantinides and Kung Yao, - \"Statistical analysis of effective singular values in - matrix rank determination\", IEEE Transactions on Acoustics, - Speech and Signal Processing, 36(5), 1988, 757-763. - doi:10.1109/29.1585 - -"), - -("Base","nullspace","nullspace(M) - - Basis for nullspace of \"M\". - -"), - -("Base","repmat","repmat(A, n, m) - - Construct a matrix by repeating the given matrix \"n\" times in - dimension 1 and \"m\" times in dimension 2. - -"), - -("Base","repeat","repeat(A, inner = Int[], outer = Int[]) - - Construct an array by repeating the entries of \"A\". The i-th - element of \"inner\" specifies the number of times that the - individual entries of the i-th dimension of \"A\" should be - repeated. The i-th element of \"outer\" specifies the number of - times that a slice along the i-th dimension of \"A\" should be - repeated. - -"), - -("Base","kron","kron(A, B) - - Kronecker tensor product of two vectors or two matrices. - -"), - -("Base","blkdiag","blkdiag(A...) - - Concatenate matrices block-diagonally. Currently only implemented - for sparse matrices. - -"), - -("Base","linreg","linreg(x, y) -> [a; b] - - Linear Regression. Returns \"a\" and \"b\" such that \"a+b*x\" is - the closest line to the given points \"(x,y)\". In other words, - this function determines parameters \"[a, b]\" that minimize the - squared error between \"y\" and \"a+b*x\". - - **Example**: - - using PyPlot; - x = float([1:12]) - y = [5.5; 6.3; 7.6; 8.8; 10.9; 11.79; 13.48; 15.02; 17.77; 20.81; 22.0; 22.99] - a, b = linreg(x,y) # Linear regression - plot(x, y, \"o\") # Plot (x,y) points - plot(x, [a+b*i for i in x]) # Plot the line determined by the linear regression - -"), - -("Base","linreg","linreg(x, y, w) - - Weighted least-squares linear regression. - -"), - -("Base","expm","expm(A) - - Matrix exponential. - -"), - -("Base","logm","logm(A) - - Matrix logarithm. - -"), - -("Base","lyap","lyap(A, C) - - Computes the solution \"X\" to the continuous Lyapunov equation - \"AX + XA' + C = 0\", where no eigenvalue of \"A\" has a zero real - part and no two eigenvalues are negative complex conjugates of each - other. - -"), - -("Base","sylvester","sylvester(A, B, C) - - Computes the solution \"X\" to the Sylvester equation \"AX + XB + C - = 0\", where \"A\", \"B\" and \"C\" have compatible dimensions and - \"A\" and \"-B\" have no eigenvalues with equal real part. - -"), - -("Base","issym","issym(A) -> Bool - - Test whether a matrix is symmetric. - -"), - -("Base","isposdef","isposdef(A) -> Bool - - Test whether a matrix is positive definite. - -"), - -("Base","isposdef!","isposdef!(A) -> Bool - - Test whether a matrix is positive definite, overwriting \"A\" in - the processes. - -"), - -("Base","istril","istril(A) -> Bool - - Test whether a matrix is lower triangular. - -"), - -("Base","istriu","istriu(A) -> Bool - - Test whether a matrix is upper triangular. - -"), - -("Base","isdiag","isdiag(A) -> Bool - - Test whether a matrix is diagonal. - -"), - -("Base","ishermitian","ishermitian(A) -> Bool - - Test whether a matrix is Hermitian. - -"), - -("Base","transpose","transpose(A) - - The transposition operator (\".'\"). - -"), - -("Base","transpose!","transpose!(dest, src) - - Transpose array \"src\" and store the result in the preallocated - array \"dest\", which should have a size corresponding to - \"(size(src,2),size(src,1))\". No in-place transposition is - supported and unexpected results will happen if *src* and *dest* - have overlapping memory regions. - -"), - -("Base","ctranspose","ctranspose(A) - - The conjugate transposition operator (\"'\"). - -"), - -("Base","ctranspose!","ctranspose!(dest, src) - - Conjugate transpose array \"src\" and store the result in the - preallocated array \"dest\", which should have a size corresponding - to \"(size(src,2),size(src,1))\". No in-place transposition is - supported and unexpected results will happen if *src* and *dest* - have overlapping memory regions. - -"), - -("Base","eigs","eigs(A[, B], ; nev=6, which=\"LM\", tol=0.0, maxiter=300, sigma=nothing, ritzvec=true, v0=zeros((0, ))) -> (d[, v], nconv, niter, nmult, resid) - - Computes eigenvalues \"d\" of \"A\" using Lanczos or Arnoldi - iterations for real symmetric or general nonsymmetric matrices - respectively. If \"B\" is provided, the generalized eigenproblem is - solved. - - The following keyword arguments are supported: - * \"nev\": Number of eigenvalues - - * \"ncv\": Number of Krylov vectors used in the computation; - should satisfy - - \"nev+1 <= ncv <= n\" for real symmetric problems and - \"nev+2 <= ncv <= n\" for other problems, where \"n\" is - the size of the input matrix \"A\". The default is \"ncv = - max(20,2*nev+1)\". Note that these restrictions limit the - input matrix \"A\" to be of dimension at least 2. - - * \"which\": type of eigenvalues to compute. See the note - below. - - +-----------+-----------------------------------------------------------------------------------------------------------------------------+ - | \\\"which\\\" | type of eigenvalues | - +-----------+-----------------------------------------------------------------------------------------------------------------------------+ - | \\\":LM\\\" | eigenvalues of largest magnitude (default) | - +-----------+-----------------------------------------------------------------------------------------------------------------------------+ - | \\\":SM\\\" | eigenvalues of smallest magnitude | - +-----------+-----------------------------------------------------------------------------------------------------------------------------+ - | \\\":LR\\\" | eigenvalues of largest real part | - +-----------+-----------------------------------------------------------------------------------------------------------------------------+ - | \\\":SR\\\" | eigenvalues of smallest real part | - +-----------+-----------------------------------------------------------------------------------------------------------------------------+ - | \\\":LI\\\" | eigenvalues of largest imaginary part (nonsymmetric or complex \\\"A\\\" only) | - +-----------+-----------------------------------------------------------------------------------------------------------------------------+ - | \\\":SI\\\" | eigenvalues of smallest imaginary part (nonsymmetric or complex \\\"A\\\" only) | - +-----------+-----------------------------------------------------------------------------------------------------------------------------+ - | \\\":BE\\\" | compute half of the eigenvalues from each end of the spectrum, biased in favor of the high end. (real symmetric \\\"A\\\" only) | - +-----------+-----------------------------------------------------------------------------------------------------------------------------+ - - * \"tol\": tolerance (tol \\le 0.0 defaults to - \"DLAMCH('EPS')\") - - * \"maxiter\": Maximum number of iterations (default = 300) - - * \"sigma\": Specifies the level shift used in inverse - iteration. If \"nothing\" (default), defaults to ordinary - (forward) iterations. Otherwise, find eigenvalues close to - \"sigma\" using shift and invert iterations. - - * \"ritzvec\": Returns the Ritz vectors \"v\" (eigenvectors) - if \"true\" - - * \"v0\": starting vector from which to start the iterations - - \"eigs\" returns the \"nev\" requested eigenvalues in \"d\", the - corresponding Ritz vectors \"v\" (only if \"ritzvec=true\"), the - number of converged eigenvalues \"nconv\", the number of iterations - \"niter\" and the number of matrix vector multiplications - \"nmult\", as well as the final residual vector \"resid\". - - Note: The \"sigma\" and \"which\" keywords interact: the - description of eigenvalues searched for by \"which\" do _not_ - necessarily refer to the eigenvalues of \"A\", but rather the - linear operator constructed by the specification of the iteration - mode implied by \"sigma\". - - +-----------------+------------------------------------+------------------------------------+ - | \\\"sigma\\\" | iteration mode | \\\"which\\\" refers to eigenvalues of | - +-----------------+------------------------------------+------------------------------------+ - | \\\"nothing\\\" | ordinary (forward) | A | - +-----------------+------------------------------------+------------------------------------+ - | real or complex | inverse with level shift \\\"sigma\\\" | (A - \\\\sigma I )^{-1} | - +-----------------+------------------------------------+------------------------------------+ - -"), - -("Base","svds","svds(A; nsv=6, ritzvec=true, tol=0.0, maxiter=1000) -> (left_sv, s, right_sv, nconv, niter, nmult, resid) - - \"svds\" computes largest singular values \"s\" of \"A\" using - Lanczos or Arnoldi iterations. Uses \"eigs()\" underneath. - - Inputs are: - * \"A\": Linear operator. It can either subtype of - \"AbstractArray\" (e.g., sparse matrix) or duck typed. For - duck typing \"A\" has to support \"size(A)\", \"eltype(A)\", - \"A * vector\" and \"A' * vector\". - - * \"nsv\": Number of singular values. - - * \"ritzvec\": Whether to return the left and right singular - vectors \"left_sv\" and \"right_sv\", default is \"true\". If - \"false\" the singular vectors are omitted from the output. - - * \"tol\": tolerance, see \"eigs()\". - - * \"maxiter\": Maximum number of iterations, see \"eigs()\". - - **Example**: - - X = sprand(10, 5, 0.2) - svds(X, nsv = 2) - -"), - -("Base","peakflops","peakflops(n; parallel=false) - - \"peakflops\" computes the peak flop rate of the computer by using - double precision \"Base.LinAlg.BLAS.gemm!()\". By default, if no - arguments are specified, it multiplies a matrix of size \"n x n\", - where \"n = 2000\". If the underlying BLAS is using multiple - threads, higher flop rates are realized. The number of BLAS threads - can be set with \"blas_set_num_threads(n)\". - - If the keyword argument \"parallel\" is set to \"true\", - \"peakflops\" is run in parallel on all the worker processors. The - flop rate of the entire parallel computer is returned. When running - in parallel, only 1 BLAS thread is used. The argument \"n\" still - refers to the size of the problem that is solved on each processor. - -"), - -("Base.LinAlg.BLAS","dot","dot(n, X, incx, Y, incy) - - Dot product of two vectors consisting of \"n\" elements of array - \"X\" with stride \"incx\" and \"n\" elements of array \"Y\" with - stride \"incy\". - -"), - -("Base.LinAlg.BLAS","dotu","dotu(n, X, incx, Y, incy) - - Dot function for two complex vectors. - -"), - -("Base.LinAlg.BLAS","dotc","dotc(n, X, incx, U, incy) - - Dot function for two complex vectors conjugating the first vector. - -"), - -("Base.LinAlg.BLAS","blascopy!","blascopy!(n, X, incx, Y, incy) - - Copy \"n\" elements of array \"X\" with stride \"incx\" to array - \"Y\" with stride \"incy\". Returns \"Y\". - -"), - -("Base.LinAlg.BLAS","nrm2","nrm2(n, X, incx) - - 2-norm of a vector consisting of \"n\" elements of array \"X\" with - stride \"incx\". - -"), - -("Base.LinAlg.BLAS","asum","asum(n, X, incx) - - sum of the absolute values of the first \"n\" elements of array - \"X\" with stride \"incx\". - -"), - -("Base.LinAlg.BLAS","axpy!","axpy!(a, X, Y) - - Overwrite \"Y\" with \"a*X + Y\". Returns \"Y\". - -"), - -("Base.LinAlg.BLAS","scal!","scal!(n, a, X, incx) - - Overwrite \"X\" with \"a*X\". Returns \"X\". - -"), - -("Base.LinAlg.BLAS","scal","scal(n, a, X, incx) - - Returns \"a*X\". - -"), - -("Base.LinAlg.BLAS","ger!","ger!(alpha, x, y, A) - - Rank-1 update of the matrix \"A\" with vectors \"x\" and \"y\" as - \"alpha*x*y' + A\". - -"), - -("Base.LinAlg.BLAS","syr!","syr!(uplo, alpha, x, A) - - Rank-1 update of the symmetric matrix \"A\" with vector \"x\" as - \"alpha*x*x.' + A\". When \"uplo\" is 'U' the upper triangle of - \"A\" is updated ('L' for lower triangle). Returns \"A\". - -"), - -("Base.LinAlg.BLAS","syrk!","syrk!(uplo, trans, alpha, A, beta, C) - - Rank-k update of the symmetric matrix \"C\" as \"alpha*A*A.' + - beta*C\" or \"alpha*A.'*A + beta*C\" according to whether \"trans\" - is 'N' or 'T'. When \"uplo\" is 'U' the upper triangle of \"C\" is - updated ('L' for lower triangle). Returns \"C\". - -"), - -("Base.LinAlg.BLAS","syrk","syrk(uplo, trans, alpha, A) - - Returns either the upper triangle or the lower triangle, according - to \"uplo\" ('U' or 'L'), of \"alpha*A*A.'\" or \"alpha*A.'*A\", - according to \"trans\" ('N' or 'T'). - -"), - -("Base.LinAlg.BLAS","her!","her!(uplo, alpha, x, A) - - Methods for complex arrays only. Rank-1 update of the Hermitian - matrix \"A\" with vector \"x\" as \"alpha*x*x' + A\". When - \"uplo\" is 'U' the upper triangle of \"A\" is updated ('L' for - lower triangle). Returns \"A\". - -"), - -("Base.LinAlg.BLAS","herk!","herk!(uplo, trans, alpha, A, beta, C) - - Methods for complex arrays only. Rank-k update of the Hermitian - matrix \"C\" as \"alpha*A*A' + beta*C\" or \"alpha*A'*A + beta*C\" - according to whether \"trans\" is 'N' or 'T'. When \"uplo\" is 'U' - the upper triangle of \"C\" is updated ('L' for lower triangle). - Returns \"C\". - -"), - -("Base.LinAlg.BLAS","herk","herk(uplo, trans, alpha, A) - - Methods for complex arrays only. Returns either the upper triangle - or the lower triangle, according to \"uplo\" ('U' or 'L'), of - \"alpha*A*A'\" or \"alpha*A'*A\", according to \"trans\" ('N' or - 'T'). - -"), - -("Base.LinAlg.BLAS","gbmv!","gbmv!(trans, m, kl, ku, alpha, A, x, beta, y) - - Update vector \"y\" as \"alpha*A*x + beta*y\" or \"alpha*A'*x + - beta*y\" according to \"trans\" ('N' or 'T'). The matrix \"A\" is - a general band matrix of dimension \"m\" by \"size(A,2)\" with - \"kl\" sub-diagonals and \"ku\" super-diagonals. Returns the - updated \"y\". - -"), - -("Base.LinAlg.BLAS","gbmv","gbmv(trans, m, kl, ku, alpha, A, x, beta, y) - - Returns \"alpha*A*x\" or \"alpha*A'*x\" according to \"trans\" ('N' - or 'T'). The matrix \"A\" is a general band matrix of dimension - \"m\" by \"size(A,2)\" with \"kl\" sub-diagonals and \"ku\" super- - diagonals. - -"), - -("Base.LinAlg.BLAS","sbmv!","sbmv!(uplo, k, alpha, A, x, beta, y) - - Update vector \"y\" as \"alpha*A*x + beta*y\" where \"A\" is a a - symmetric band matrix of order \"size(A,2)\" with \"k\" super- - diagonals stored in the argument \"A\". The storage layout for - \"A\" is described the reference BLAS module, level-2 BLAS at - http://www.netlib.org/lapack/explore-html/. - - Returns the updated \"y\". - -"), - -("Base.LinAlg.BLAS","sbmv","sbmv(uplo, k, alpha, A, x) - - Returns \"alpha*A*x\" where \"A\" is a symmetric band matrix of - order \"size(A,2)\" with \"k\" super-diagonals stored in the - argument \"A\". - -"), - -("Base.LinAlg.BLAS","sbmv","sbmv(uplo, k, A, x) - - Returns \"A*x\" where \"A\" is a symmetric band matrix of order - \"size(A,2)\" with \"k\" super-diagonals stored in the argument - \"A\". - -"), - -("Base.LinAlg.BLAS","gemm!","gemm!(tA, tB, alpha, A, B, beta, C) - - Update \"C\" as \"alpha*A*B + beta*C\" or the other three variants - according to \"tA\" (transpose \"A\") and \"tB\". Returns the - updated \"C\". - -"), - -("Base.LinAlg.BLAS","gemm","gemm(tA, tB, alpha, A, B) - - Returns \"alpha*A*B\" or the other three variants according to - \"tA\" (transpose \"A\") and \"tB\". - -"), - -("Base.LinAlg.BLAS","gemm","gemm(tA, tB, A, B) - - Returns \"A*B\" or the other three variants according to \"tA\" - (transpose \"A\") and \"tB\". - -"), - -("Base.LinAlg.BLAS","gemv!","gemv!(tA, alpha, A, x, beta, y) - - Update the vector \"y\" as \"alpha*A*x + beta*y\" or \"alpha*A'x + - beta*y\" according to \"tA\" (transpose \"A\"). Returns the updated - \"y\". - -"), - -("Base.LinAlg.BLAS","gemv","gemv(tA, alpha, A, x) - - Returns \"alpha*A*x\" or \"alpha*A'x\" according to \"tA\" - (transpose \"A\"). - -"), - -("Base.LinAlg.BLAS","gemv","gemv(tA, A, x) - - Returns \"A*x\" or \"A'x\" according to \"tA\" (transpose \"A\"). - -"), - -("Base.LinAlg.BLAS","symm!","symm!(side, ul, alpha, A, B, beta, C) - - Update \"C\" as \"alpha*A*B + beta*C\" or \"alpha*B*A + beta*C\" - according to \"side\". \"A\" is assumed to be symmetric. Only the - \"ul\" triangle of \"A\" is used. Returns the updated \"C\". - -"), - -("Base.LinAlg.BLAS","symm","symm(side, ul, alpha, A, B) - - Returns \"alpha*A*B\" or \"alpha*B*A\" according to \"side\". \"A\" - is assumed to be symmetric. Only the \"ul\" triangle of \"A\" is - used. - -"), - -("Base.LinAlg.BLAS","symm","symm(side, ul, A, B) - - Returns \"A*B\" or \"B*A\" according to \"side\". \"A\" is assumed - to be symmetric. Only the \"ul\" triangle of \"A\" is used. - -"), - -("Base.LinAlg.BLAS","symm","symm(tA, tB, alpha, A, B) - - Returns \"alpha*A*B\" or the other three variants according to - \"tA\" (transpose \"A\") and \"tB\". - -"), - -("Base.LinAlg.BLAS","symv!","symv!(ul, alpha, A, x, beta, y) - - Update the vector \"y\" as \"alpha*A*x + beta*y\". \"A\" is assumed - to be symmetric. Only the \"ul\" triangle of \"A\" is used. - Returns the updated \"y\". - -"), - -("Base.LinAlg.BLAS","symv","symv(ul, alpha, A, x) - - Returns \"alpha*A*x\". \"A\" is assumed to be symmetric. Only the - \"ul\" triangle of \"A\" is used. - -"), - -("Base.LinAlg.BLAS","symv","symv(ul, A, x) - - Returns \"A*x\". \"A\" is assumed to be symmetric. Only the - \"ul\" triangle of \"A\" is used. - -"), - -("Base.LinAlg.BLAS","trmm!","trmm!(side, ul, tA, dA, alpha, A, B) - - Update \"B\" as \"alpha*A*B\" or one of the other three variants - determined by \"side\" (A on left or right) and \"tA\" (transpose - A). Only the \"ul\" triangle of \"A\" is used. \"dA\" indicates if - \"A\" is unit-triangular (the diagonal is assumed to be all ones). - Returns the updated \"B\". - -"), - -("Base.LinAlg.BLAS","trmm","trmm(side, ul, tA, dA, alpha, A, B) - - Returns \"alpha*A*B\" or one of the other three variants determined - by \"side\" (A on left or right) and \"tA\" (transpose A). Only the - \"ul\" triangle of \"A\" is used. \"dA\" indicates if \"A\" is - unit-triangular (the diagonal is assumed to be all ones). - -"), - -("Base.LinAlg.BLAS","trsm!","trsm!(side, ul, tA, dA, alpha, A, B) - - Overwrite \"B\" with the solution to \"A*X = alpha*B\" or one of - the other three variants determined by \"side\" (A on left or right - of \"X\") and \"tA\" (transpose A). Only the \"ul\" triangle of - \"A\" is used. \"dA\" indicates if \"A\" is unit-triangular (the - diagonal is assumed to be all ones). Returns the updated \"B\". - -"), - -("Base.LinAlg.BLAS","trsm","trsm(side, ul, tA, dA, alpha, A, B) - - Returns the solution to \"A*X = alpha*B\" or one of the other three - variants determined by \"side\" (A on left or right of \"X\") and - \"tA\" (transpose A). Only the \"ul\" triangle of \"A\" is used. - \"dA\" indicates if \"A\" is unit-triangular (the diagonal is - assumed to be all ones). - -"), - -("Base.LinAlg.BLAS","trmv!","trmv!(side, ul, tA, dA, alpha, A, b) - - Update \"b\" as \"alpha*A*b\" or one of the other three variants - determined by \"side\" (A on left or right) and \"tA\" (transpose - A). Only the \"ul\" triangle of \"A\" is used. \"dA\" indicates if - \"A\" is unit-triangular (the diagonal is assumed to be all ones). - Returns the updated \"b\". - -"), - -("Base.LinAlg.BLAS","trmv","trmv(side, ul, tA, dA, alpha, A, b) - - Returns \"alpha*A*b\" or one of the other three variants determined - by \"side\" (A on left or right) and \"tA\" (transpose A). Only the - \"ul\" triangle of \"A\" is used. \"dA\" indicates if \"A\" is - unit-triangular (the diagonal is assumed to be all ones). - -"), - -("Base.LinAlg.BLAS","trsv!","trsv!(ul, tA, dA, A, b) - - Overwrite \"b\" with the solution to \"A*x = b\" or one of the - other two variants determined by \"tA\" (transpose A) and \"ul\" - (triangle of \"A\" used). \"dA\" indicates if \"A\" is unit- - triangular (the diagonal is assumed to be all ones). Returns the - updated \"b\". - -"), - -("Base.LinAlg.BLAS","trsv","trsv(ul, tA, dA, A, b) - - Returns the solution to \"A*x = b\" or one of the other two - variants determined by \"tA\" (transpose A) and \"ul\" (triangle of - \"A\" is used.) \"dA\" indicates if \"A\" is unit-triangular (the - diagonal is assumed to be all ones). - -"), - -("Base.LinAlg.BLAS","blas_set_num_threads","blas_set_num_threads(n) - - Set the number of threads the BLAS library should use. - -"), - -("Base.LinAlg.BLAS","I","I - - An object of type \"UniformScaling\", representing an identity - matrix of any size. - -"), - -("Base","-","-(x) - - Unary minus operator. - -"), - -("Base","+","+(x, y...) - - Addition operator. \"x+y+z+...\" calls this function with all - arguments, i.e. \"+(x, y, z, ...)\". - -"), - -("Base","-","-(x, y) - - Subtraction operator. - -"), - -("Base","*","*(x, y...) - - Multiplication operator. \"x*y*z*...\" calls this function with all - arguments, i.e. \"*(x, y, z, ...)\". - -"), - -("Base","/","/(x, y) - - Right division operator: multiplication of \"x\" by the inverse of - \"y\" on the right. Gives floating-point results for integer - arguments. - -"), - -("Base","\\","\\(x, y) - - Left division operator: multiplication of \"y\" by the inverse of - \"x\" on the left. Gives floating-point results for integer - arguments. - -"), - -("Base","^","^(x, y) - - Exponentiation operator. - -"), - -("Base",".+",".+(x, y) - - Element-wise addition operator. - -"), - -("Base",".-",".-(x, y) - - Element-wise subtraction operator. - -"), - -("Base",".*",".*(x, y) - - Element-wise multiplication operator. - -"), - -("Base","./","./(x, y) - - Element-wise right division operator. - -"), - -("Base",".\\",".\\(x, y) - - Element-wise left division operator. - -"), - -("Base",".^",".^(x, y) - - Element-wise exponentiation operator. - -"), - -("Base","fma","fma(x, y, z) - - Computes \"x*y+z\" without rounding the intermediate result - \"x*y\". On some systems this is significantly more expensive than - \"x*y+z\". \"fma\" is used to improve accuracy in certain - algorithms. See \"muladd\". - -"), - -("Base","muladd","muladd(x, y, z) - - Combined multiply-add, computes \"x*y+z\" in an efficient manner. - This may on some systems be equivalent to \"x*y+z\", or to - \"fma(x,y,z)\". \"muladd\" is used to improve performance. See - \"fma\". - -"), - -("Base","div","div(x, y) -÷(x, y) - - The quotient from Euclidean division. Computes \"x/y\", truncated - to an integer. - -"), - -("Base","fld","fld(x, y) - - Largest integer less than or equal to \"x/y\". - -"), - -("Base","cld","cld(x, y) - - Smallest integer larger than or equal to \"x/y\". - -"), - -("Base","mod","mod(x, y) - - Modulus after division, returning in the range [0,``y``), if \"y\" - is positive, or (\"y\",0] if \"y\" is negative. - -"), - -("Base","mod2pi","mod2pi(x) - - Modulus after division by 2pi, returning in the range [0,2pi). - - This function computes a floating point representation of the - modulus after division by numerically exact 2pi, and is therefore - not exactly the same as mod(x,2pi), which would compute the modulus - of x relative to division by the floating-point number 2pi. - -"), - -("Base","rem","rem(x, y) -%(x, y) - - Remainder from Euclidean division, returning a value of the same - sign as``x``, and smaller in magnitude than \"y\". This value is - always exact. - -"), - -("Base","divrem","divrem(x, y) - - The quotient and remainder from Euclidean division. Equivalent to - \"(x÷y, x%y)\". - -"), - -("Base","fldmod","fldmod(x, y) - - The floored quotient and modulus after division. Equivalent to - \"(fld(x,y), mod(x,y))\". - -"), - -("Base","mod1","mod1(x, m) - - Modulus after division, returning in the range (0,m] - -"), - -("Base","rem1","rem1(x, m) - - Remainder after division, returning in the range (0,m] - -"), - -("Base","//","//(num, den) - - Divide two integers or rational numbers, giving a \"Rational\" - result. - -"), - -("Base","rationalize","rationalize([Type=Int], x; tol=eps(x)) - - Approximate floating point number \"x\" as a Rational number with - components of the given integer type. The result will differ from - \"x\" by no more than \"tol\". - -"), - -("Base","num","num(x) - - Numerator of the rational representation of \"x\" - -"), - -("Base","den","den(x) - - Denominator of the rational representation of \"x\" - -"), - -("Base","<<","<<(x, n) - - Left bit shift operator. - -"), - -("Base",">>",">>(x, n) - - Right bit shift operator, preserving the sign of \"x\". - -"), - -("Base",">>>",">>>(x, n) - - Unsigned right bit shift operator. - -"), - -("Base",":",":(start[, step], stop) - - Range operator. \"a:b\" constructs a range from \"a\" to \"b\" with - a step size of 1, and \"a:s:b\" is similar but uses a step size of - \"s\". These syntaxes call the function \"colon\". The colon is - also used in indexing to select whole dimensions. - -"), - -("Base","colon","colon(start[, step], stop) - - Called by \":\" syntax for constructing ranges. - -"), - -("Base","range","range(start[, step], length) - - Construct a range by length, given a starting value and optional - step (defaults to 1). - -"), - -("Base","==","==(x, y) - - Generic equality operator, giving a single \"Bool\" result. Falls - back to \"===\". Should be implemented for all types with a notion - of equality, based on the abstract value that an instance - represents. For example, all numeric types are compared by numeric - value, ignoring type. Strings are compared as sequences of - characters, ignoring encoding. - - Follows IEEE semantics for floating-point numbers. - - Collections should generally implement \"==\" by calling \"==\" - recursively on all contents. - - New numeric types should implement this function for two arguments - of the new type, and handle comparison to other types via promotion - rules where possible. - -"), - -("Base","!=","!=(x, y) -≠(x, y) - - Not-equals comparison operator. Always gives the opposite answer as - \"==\". New types should generally not implement this, and rely on - the fallback definition \"!=(x,y) = !(x==y)\" instead. - -"), - -("Base","===","===(x, y) -≡(x, y) - - See the \"is()\" operator - -"), - -("Base","!==","!==(x, y) -≢(x, y) - - Equivalent to \"!is(x, y)\" - -"), - -("Base","<","<(x, y) - - Less-than comparison operator. New numeric types should implement - this function for two arguments of the new type. Because of the - behavior of floating-point NaN values, \"<\" implements a partial - order. Types with a canonical partial order should implement \"<\", - and types with a canonical total order should implement \"isless\". - -"), - -("Base","<=","<=(x, y) -≤(x, y) - - Less-than-or-equals comparison operator. - -"), - -("Base",">",">(x, y) - - Greater-than comparison operator. Generally, new types should - implement \"<\" instead of this function, and rely on the fallback - definition \">(x,y) = y=",">=(x, y) -≥(x, y) - - Greater-than-or-equals comparison operator. - -"), - -("Base",".==",".==(x, y) - - Element-wise equality comparison operator. - -"), - -("Base",".!=",".!=(x, y) -.≠(x, y) - - Element-wise not-equals comparison operator. - -"), - -("Base",".<",".<(x, y) - - Element-wise less-than comparison operator. - -"), - -("Base",".<=",".<=(x, y) -.≤(x, y) - - Element-wise less-than-or-equals comparison operator. - -"), - -("Base",".>",".>(x, y) - - Element-wise greater-than comparison operator. - -"), - -("Base",".>=",".>=(x, y) -.≥(x, y) - - Element-wise greater-than-or-equals comparison operator. - -"), - -("Base","cmp","cmp(x, y) - - Return -1, 0, or 1 depending on whether \"x\" is less than, equal - to, or greater than \"y\", respectively. Uses the total order - implemented by \"isless\". For floating-point numbers, uses \"<\" - but throws an error for unordered arguments. - -"), - -("Base","~","~(x) - - Bitwise not - -"), - -("Base","&","&(x, y) - - Bitwise and - -"), - -("Base","|","|(x, y) - - Bitwise or - -"), - -("Base","\$","\$(x, y) - - Bitwise exclusive or - -"), - -("Base","!","!(x) - - Boolean not - -"), - -("","x && y","x && y - - Short-circuiting boolean and - -"), - -("","x || y","x || y - - Short-circuiting boolean or - -"), - -("Base","A_ldiv_Bc","A_ldiv_Bc(a, b) - - Matrix operator A \\ B^H - -"), - -("Base","A_ldiv_Bt","A_ldiv_Bt(a, b) - - Matrix operator A \\ B^T - -"), - -("Base","A_mul_B!","A_mul_B!(Y, A, B) -> Y - - Calculates the matrix-matrix or matrix-vector product *A B* and - stores the result in *Y*, overwriting the existing value of *Y*. - - julia> A=[1.0 2.0; 3.0 4.0]; B=[1.0 1.0; 1.0 1.0]; A_mul_B!(B, A, B); - - julia> B - 2x2 Array{Float64,2}: - 3.0 3.0 - 7.0 7.0 - -"), - -("Base","A_mul_Bc","A_mul_Bc(...) - - Matrix operator A B^H - -"), - -("Base","A_mul_Bt","A_mul_Bt(...) - - Matrix operator A B^T - -"), - -("Base","A_rdiv_Bc","A_rdiv_Bc(...) - - Matrix operator A / B^H - -"), - -("Base","A_rdiv_Bt","A_rdiv_Bt(a, b) - - Matrix operator A / B^T - -"), - -("Base","Ac_ldiv_B","Ac_ldiv_B(...) - - Matrix operator A^H \\ B - -"), - -("Base","Ac_ldiv_Bc","Ac_ldiv_Bc(...) - - Matrix operator A^H \\ B^H - -"), - -("Base","Ac_mul_B","Ac_mul_B(...) - - Matrix operator A^H B - -"), - -("Base","Ac_mul_Bc","Ac_mul_Bc(...) - - Matrix operator A^H B^H - -"), - -("Base","Ac_rdiv_B","Ac_rdiv_B(a, b) - - Matrix operator A^H / B - -"), - -("Base","Ac_rdiv_Bc","Ac_rdiv_Bc(a, b) - - Matrix operator A^H / B^H - -"), - -("Base","At_ldiv_B","At_ldiv_B(...) - - Matrix operator A^T \\ B - -"), - -("Base","At_ldiv_Bt","At_ldiv_Bt(...) - - Matrix operator A^T \\ B^T - -"), - -("Base","At_mul_B","At_mul_B(...) - - Matrix operator A^T B - -"), - -("Base","At_mul_Bt","At_mul_Bt(...) - - Matrix operator A^T B^T - -"), - -("Base","At_rdiv_B","At_rdiv_B(a, b) - - Matrix operator A^T / B - -"), - -("Base","At_rdiv_Bt","At_rdiv_Bt(a, b) - - Matrix operator A^T / B^T - -"), - -("Base","isapprox","isapprox(x::Number, y::Number; rtol::Real=cbrt(maxeps), atol::Real=sqrt(maxeps)) - - Inexact equality comparison - behaves slightly different depending - on types of input args: - - * For \"AbstractFloat\" numbers, \"isapprox\" returns \"true\" if - \"abs(x-y) <= atol + rtol*max(abs(x), abs(y))\". - - * For \"Integer\" and \"Rational\" numbers, \"isapprox\" returns - \"true\" if \"abs(x-y) <= atol\". The *rtol* argument is ignored. - If one of \"x\" and \"y\" is \"AbstractFloat\", the other is - promoted, and the method above is called instead. - - * For \"Complex\" numbers, the distance in the complex plane is - compared, using the same criterion as above. - - For default tolerance arguments, \"maxeps = max(eps(abs(x)), - eps(abs(y)))\". - -"), - -("Base","sin","sin(x) - - Compute sine of \"x\", where \"x\" is in radians - -"), - -("Base","cos","cos(x) - - Compute cosine of \"x\", where \"x\" is in radians - -"), - -("Base","tan","tan(x) - - Compute tangent of \"x\", where \"x\" is in radians - -"), - -("Base","sind","sind(x) - - Compute sine of \"x\", where \"x\" is in degrees - -"), - -("Base","cosd","cosd(x) - - Compute cosine of \"x\", where \"x\" is in degrees - -"), - -("Base","tand","tand(x) - - Compute tangent of \"x\", where \"x\" is in degrees - -"), - -("Base","sinpi","sinpi(x) - - Compute \\sin(\\pi x) more accurately than \"sin(pi*x)\", - especially for large \"x\". - -"), - -("Base","cospi","cospi(x) - - Compute \\cos(\\pi x) more accurately than \"cos(pi*x)\", - especially for large \"x\". - -"), - -("Base","sinh","sinh(x) - - Compute hyperbolic sine of \"x\" - -"), - -("Base","cosh","cosh(x) - - Compute hyperbolic cosine of \"x\" - -"), - -("Base","tanh","tanh(x) - - Compute hyperbolic tangent of \"x\" - -"), - -("Base","asin","asin(x) - - Compute the inverse sine of \"x\", where the output is in radians - -"), - -("Base","acos","acos(x) - - Compute the inverse cosine of \"x\", where the output is in radians - -"), - -("Base","atan","atan(x) - - Compute the inverse tangent of \"x\", where the output is in - radians - -"), - -("Base","atan2","atan2(y, x) - - Compute the inverse tangent of \"y/x\", using the signs of both - \"x\" and \"y\" to determine the quadrant of the return value. - -"), - -("Base","asind","asind(x) - - Compute the inverse sine of \"x\", where the output is in degrees - -"), - -("Base","acosd","acosd(x) - - Compute the inverse cosine of \"x\", where the output is in degrees - -"), - -("Base","atand","atand(x) - - Compute the inverse tangent of \"x\", where the output is in - degrees - -"), - -("Base","sec","sec(x) - - Compute the secant of \"x\", where \"x\" is in radians - -"), - -("Base","csc","csc(x) - - Compute the cosecant of \"x\", where \"x\" is in radians - -"), - -("Base","cot","cot(x) - - Compute the cotangent of \"x\", where \"x\" is in radians - -"), - -("Base","secd","secd(x) - - Compute the secant of \"x\", where \"x\" is in degrees - -"), - -("Base","cscd","cscd(x) - - Compute the cosecant of \"x\", where \"x\" is in degrees - -"), - -("Base","cotd","cotd(x) - - Compute the cotangent of \"x\", where \"x\" is in degrees - -"), - -("Base","asec","asec(x) - - Compute the inverse secant of \"x\", where the output is in radians - -"), - -("Base","acsc","acsc(x) - - Compute the inverse cosecant of \"x\", where the output is in - radians - -"), - -("Base","acot","acot(x) - - Compute the inverse cotangent of \"x\", where the output is in - radians - -"), - -("Base","asecd","asecd(x) - - Compute the inverse secant of \"x\", where the output is in degrees - -"), - -("Base","acscd","acscd(x) - - Compute the inverse cosecant of \"x\", where the output is in - degrees - -"), - -("Base","acotd","acotd(x) - - Compute the inverse cotangent of \"x\", where the output is in - degrees - -"), - -("Base","sech","sech(x) - - Compute the hyperbolic secant of \"x\" - -"), - -("Base","csch","csch(x) - - Compute the hyperbolic cosecant of \"x\" - -"), - -("Base","coth","coth(x) - - Compute the hyperbolic cotangent of \"x\" - -"), - -("Base","asinh","asinh(x) - - Compute the inverse hyperbolic sine of \"x\" - -"), - -("Base","acosh","acosh(x) - - Compute the inverse hyperbolic cosine of \"x\" - -"), - -("Base","atanh","atanh(x) - - Compute the inverse hyperbolic tangent of \"x\" - -"), - -("Base","asech","asech(x) - - Compute the inverse hyperbolic secant of \"x\" - -"), - -("Base","acsch","acsch(x) - - Compute the inverse hyperbolic cosecant of \"x\" - -"), - -("Base","acoth","acoth(x) - - Compute the inverse hyperbolic cotangent of \"x\" - -"), - -("Base","sinc","sinc(x) - - Compute \\sin(\\pi x) / (\\pi x) if x \\neq 0, and 1 if x = 0. - -"), - -("Base","cosc","cosc(x) - - Compute \\cos(\\pi x) / x - \\sin(\\pi x) / (\\pi x^2) if x \\neq - 0, and 0 if x = 0. This is the derivative of \"sinc(x)\". - -"), - -("Base","deg2rad","deg2rad(x) - - Convert \"x\" from degrees to radians - -"), - -("Base","rad2deg","rad2deg(x) - - Convert \"x\" from radians to degrees - -"), - -("Base","hypot","hypot(x, y) - - Compute the \\sqrt{x^2+y^2} avoiding overflow and underflow - -"), - -("Base","log","log(x) - - Compute the natural logarithm of \"x\". Throws \"DomainError\" for - negative \"Real\" arguments. Use complex negative arguments to - obtain complex results. - - There is an experimental variant in the \"Base.Math.JuliaLibm\" - module, which is typically faster and more accurate. - -"), - -("Base","log","log(b, x) - - Compute the base \"b\" logarithm of \"x\". Throws \"DomainError\" - for negative \"Real\" arguments. - -"), - -("Base","log2","log2(x) - - Compute the logarithm of \"x\" to base 2. Throws \"DomainError\" - for negative \"Real\" arguments. - -"), - -("Base","log10","log10(x) - - Compute the logarithm of \"x\" to base 10. Throws \"DomainError\" - for negative \"Real\" arguments. - -"), - -("Base","log1p","log1p(x) - - Accurate natural logarithm of \"1+x\". Throws \"DomainError\" for - \"Real\" arguments less than -1. - - There is an experimental variant in the \"Base.Math.JuliaLibm\" - module, which is typically faster and more accurate. - -"), - -("Base","frexp","frexp(val) - - Return \"(x,exp)\" such that \"x\" has a magnitude in the interval - \"[1/2, 1)\" or 0, and val = x \\times 2^{exp}. - -"), - -("Base","exp","exp(x) - - Compute e^x - -"), - -("Base","exp2","exp2(x) - - Compute 2^x - -"), - -("Base","exp10","exp10(x) - - Compute 10^x - -"), - -("Base","ldexp","ldexp(x, n) - - Compute x \\times 2^n - -"), - -("Base","modf","modf(x) - - Return a tuple (fpart,ipart) of the fractional and integral parts - of a number. Both parts have the same sign as the argument. - -"), - -("Base","expm1","expm1(x) - - Accurately compute e^x-1 - -"), - -("Base","round","round([T], x[, digits[, base]][, r::RoundingMode]) - - \"round(x)\" rounds \"x\" to an integer value according to the - default rounding mode (see \"get_rounding()\"), returning a value - of the same type as \"x\". By default (\"RoundNearest\"), this will - round to the nearest integer, with ties (fractional values of 0.5) - being rounded to the even integer. - - julia> round(1.7) - 2.0 - - julia> round(1.5) - 2.0 - - julia> round(2.5) - 2.0 - - The optional \"RoundingMode\" argument will change how the number - gets rounded. - - \"round(T, x, [r::RoundingMode])\" converts the result to type - \"T\", throwing an \"InexactError\" if the value is not - representable. - - \"round(x, digits)\" rounds to the specified number of digits after - the decimal place (or before if negative). \"round(x, digits, - base)\" rounds using a base other than 10. - - julia> round(pi, 2) - 3.14 - - julia> round(pi, 3, 2) - 3.125 - - Note: Rounding to specified digits in bases other than 2 can be - inexact when operating on binary floating point numbers. For - example, the \"Float64\" value represented by \"1.15\" is - actually *less* than 1.15, yet will be rounded to 1.2. - - julia> x = 1.15 - 1.15 - - julia> @sprintf \"%.20f\" x - \"1.14999999999999991118\" - - julia> x < 115//100 - true - - julia> round(x, 1) - 1.2 - -"), - -("Base","RoundingMode","RoundingMode - - A type which controls rounding behavior. Currently supported - rounding modes are: - - * \"RoundNearest\" (default) - - * \"RoundNearestTiesAway\" - - * \"RoundNearestTiesUp\" - - * \"RoundToZero\" - - * \"RoundUp\" - - * \"RoundDown\" - -"), - -("Base","RoundNearest","RoundNearest - - The default rounding mode. Rounds to the nearest integer, with ties - (fractional values of 0.5) being rounded to the nearest even - integer. - -"), - -("Base","RoundNearestTiesAway","RoundNearestTiesAway - - Rounds to nearest integer, with ties rounded away from zero (C/C++ - \"round()\" behaviour). - -"), - -("Base","RoundNearestTiesUp","RoundNearestTiesUp - - Rounds to nearest integer, with ties rounded toward positive - infinity (Java/JavaScript \"round()\" behaviour). - -"), - -("Base","RoundToZero","RoundToZero - - \"round()\" using this rounding mode is an alias for \"trunc()\". - -"), - -("Base","RoundUp","RoundUp - - \"round()\" using this rounding mode is an alias for \"ceil()\". - -"), - -("Base","RoundDown","RoundDown - - \"round()\" using this rounding mode is an alias for \"floor()\". - -"), - -("Base","round","round(z, RoundingModeReal, RoundingModeImaginary) - - Returns the nearest integral value of the same type as the complex- - valued \"z\" to \"z\", breaking ties using the specified - \"RoundingMode\"s. The first \"RoundingMode\" is used for rounding - the real components while the second is used for rounding the - imaginary components. - -"), - -("Base","ceil","ceil([T], x[, digits[, base]]) - - \"ceil(x)\" returns the nearest integral value of the same type as - \"x\" that is greater than or equal to \"x\". - - \"ceil(T, x)\" converts the result to type \"T\", throwing an - \"InexactError\" if the value is not representable. - - \"digits\" and \"base\" work as for \"round()\". - -"), - -("Base","floor","floor([T], x[, digits[, base]]) - - \"floor(x)\" returns the nearest integral value of the same type as - \"x\" that is less than or equal to \"x\". - - \"floor(T, x)\" converts the result to type \"T\", throwing an - \"InexactError\" if the value is not representable. - - \"digits\" and \"base\" work as for \"round()\". - -"), - -("Base","trunc","trunc([T], x[, digits[, base]]) - - \"trunc(x)\" returns the nearest integral value of the same type as - \"x\" whose absolute value is less than or equal to \"x\". - - \"trunc(T, x)\" converts the result to type \"T\", throwing an - \"InexactError\" if the value is not representable. - - \"digits\" and \"base\" work as for \"round()\". - -"), - -("Base","unsafe_trunc","unsafe_trunc(T, x) - - \"unsafe_trunc(T, x)\" returns the nearest integral value of type - \"T\" whose absolute value is less than or equal to \"x\". If the - value is not representable by \"T\", an arbitrary value will be - returned. - -"), - -("Base","signif","signif(x, digits[, base]) - - Rounds (in the sense of \"round\") \"x\" so that there are - \"digits\" significant digits, under a base \"base\" - representation, default 10. E.g., \"signif(123.456, 2)\" is - \"120.0\", and \"signif(357.913, 4, 2)\" is \"352.0\". - -"), - -("Base","min","min(x, y, ...) - - Return the minimum of the arguments. Operates elementwise over - arrays. - -"), - -("Base","max","max(x, y, ...) - - Return the maximum of the arguments. Operates elementwise over - arrays. - -"), - -("Base","minmax","minmax(x, y) - - Return \"(min(x,y), max(x,y))\". See also: \"extrema()\" that - returns \"(minimum(x), maximum(x))\" - -"), - -("Base","clamp","clamp(x, lo, hi) - - Return x if \"lo <= x <= hi\". If \"x < lo\", return \"lo\". If \"x - > hi\", return \"hi\". Arguments are promoted to a common type. - Operates elementwise over \"x\" if it is an array. - -"), - -("Base","abs","abs(x) - - Absolute value of \"x\" - -"), - -("Base","abs2","abs2(x) - - Squared absolute value of \"x\" - -"), - -("Base","copysign","copysign(x, y) - - Return \"x\" such that it has the same sign as \"y\" - -"), - -("Base","sign","sign(x) - - Return \"+1\" if \"x\" is positive, \"0\" if \"x == 0\", and \"-1\" - if \"x\" is negative. - -"), - -("Base","signbit","signbit(x) - - Returns \"true\" if the value of the sign of \"x\" is negative, - otherwise \"false\". - -"), - -("Base","flipsign","flipsign(x, y) - - Return \"x\" with its sign flipped if \"y\" is negative. For - example \"abs(x) = flipsign(x,x)\". - -"), - -("Base","sqrt","sqrt(x) - - Return \\sqrt{x}. Throws \"DomainError\" for negative \"Real\" - arguments. Use complex negative arguments instead. The prefix - operator \"√\" is equivalent to \"sqrt\". - -"), - -("Base","isqrt","isqrt(n) - - Integer square root: the largest integer \"m\" such that \"m*m <= - n\". - -"), - -("Base","cbrt","cbrt(x) - - Return x^{1/3}. The prefix operator \"∛\" is equivalent to - \"cbrt\". - -"), - -("Base","erf","erf(x) - - Compute the error function of \"x\", defined by - \\frac{2}{\\sqrt{\\pi}} \\int_0^x e^{-t^2} dt for arbitrary complex - \"x\". - -"), - -("Base","erfc","erfc(x) - - Compute the complementary error function of \"x\", defined by 1 - - \\operatorname{erf}(x). - -"), - -("Base","erfcx","erfcx(x) - - Compute the scaled complementary error function of \"x\", defined - by e^{x^2} \\operatorname{erfc}(x). Note also that - \\operatorname{erfcx}(-ix) computes the Faddeeva function w(x). - -"), - -("Base","erfi","erfi(x) - - Compute the imaginary error function of \"x\", defined by -i - \\operatorname{erf}(ix). - -"), - -("Base","dawson","dawson(x) - - Compute the Dawson function (scaled imaginary error function) of - \"x\", defined by \\frac{\\sqrt{\\pi}}{2} e^{-x^2} - \\operatorname{erfi}(x). - -"), - -("Base","erfinv","erfinv(x) - - Compute the inverse error function of a real \"x\", defined by - \\operatorname{erf}(\\operatorname{erfinv}(x)) = x. - -"), - -("Base","erfcinv","erfcinv(x) - - Compute the inverse error complementary function of a real \"x\", - defined by \\operatorname{erfc}(\\operatorname{erfcinv}(x)) = x. - -"), - -("Base","real","real(z) - - Return the real part of the complex number \"z\" - -"), - -("Base","imag","imag(z) - - Return the imaginary part of the complex number \"z\" - -"), - -("Base","reim","reim(z) - - Return both the real and imaginary parts of the complex number - \"z\" - -"), - -("Base","conj","conj(z) - - Compute the complex conjugate of a complex number \"z\" - -"), - -("Base","angle","angle(z) - - Compute the phase angle in radians of a complex number \"z\" - -"), - -("Base","cis","cis(z) - - Return \\exp(iz). - -"), - -("Base","binomial","binomial(n, k) - - Number of ways to choose \"k\" out of \"n\" items - -"), - -("Base","factorial","factorial(n) - - Factorial of \"n\". If \"n\" is an \"Integer\", the factorial is - computed as an integer (promoted to at least 64 bits). Note that - this may overflow if \"n\" is not small, but you can use - \"factorial(big(n))\" to compute the result exactly in arbitrary - precision. If \"n\" is not an \"Integer\", \"factorial(n)\" is - equivalent to \"gamma(n+1)\". - -"), - -("Base","factorial","factorial(n, k) - - Compute \"factorial(n)/factorial(k)\" - -"), - -("Base","factor","factor(n) -> Dict - - Compute the prime factorization of an integer \"n\". Returns a - dictionary. The keys of the dictionary correspond to the factors, - and hence are of the same type as \"n\". The value associated with - each key indicates the number of times the factor appears in the - factorization. - - julia> factor(100) # == 2*2*5*5 - Dict{Int64,Int64} with 2 entries: - 2 => 2 - 5 => 2 - -"), - -("Base","gcd","gcd(x, y) - - Greatest common (positive) divisor (or zero if x and y are both - zero). - -"), - -("Base","lcm","lcm(x, y) - - Least common (non-negative) multiple. - -"), - -("Base","gcdx","gcdx(x, y) - - Computes the greatest common (positive) divisor of \"x\" and \"y\" - and their Bézout coefficients, i.e. the integer coefficients \"u\" - and \"v\" that satisfy ux+vy = d = gcd(x,y). - - julia> gcdx(12, 42) - (6,-3,1) - - julia> gcdx(240, 46) - (2,-9,47) - - Note: Bézout coefficients are *not* uniquely defined. \"gcdx\" - returns the minimal Bézout coefficients that are computed by the - extended Euclid algorithm. (Ref: D. Knuth, TAoCP, 2/e, p. 325, - Algorithm X.) These coefficients \"u\" and \"v\" are minimal in - the sense that |u| < |\\frac y d and |v| < |\\frac x d. - Furthermore, the signs of \"u\" and \"v\" are chosen so that - \"d\" is positive. - -"), - -("Base","ispow2","ispow2(n) -> Bool - - Test whether \"n\" is a power of two - -"), - -("Base","nextpow2","nextpow2(n) - - The smallest power of two not less than \"n\". Returns 0 for - \"n==0\", and returns \"-nextpow2(-n)\" for negative arguments. - -"), - -("Base","prevpow2","prevpow2(n) - - The largest power of two not greater than \"n\". Returns 0 for - \"n==0\", and returns \"-prevpow2(-n)\" for negative arguments. - -"), - -("Base","nextpow","nextpow(a, x) - - The smallest \"a^n\" not less than \"x\", where \"n\" is a non- - negative integer. \"a\" must be greater than 1, and \"x\" must be - greater than 0. - -"), - -("Base","prevpow","prevpow(a, x) - - The largest \"a^n\" not greater than \"x\", where \"n\" is a non- - negative integer. \"a\" must be greater than 1, and \"x\" must not - be less than 1. - -"), - -("Base","nextprod","nextprod([k_1, k_2, ...], n) - - Next integer not less than \"n\" that can be written as \\prod - k_i^{p_i} for integers p_1, p_2, etc. - -"), - -("Base","prevprod","prevprod([k_1, k_2, ...], n) - - Previous integer not greater than \"n\" that can be written as - \\prod k_i^{p_i} for integers p_1, p_2, etc. - -"), - -("Base","invmod","invmod(x, m) - - Take the inverse of \"x\" modulo \"m\": \"y\" such that xy = 1 - \\pmod m - -"), - -("Base","powermod","powermod(x, p, m) - - Compute x^p \\pmod m - -"), - -("Base","gamma","gamma(x) - - Compute the gamma function of \"x\" - -"), - -("Base","lgamma","lgamma(x) - - Compute the logarithm of the absolute value of \"gamma()\" for - \"Real\" \"x\", while for \"Complex\" \"x\" it computes the - logarithm of \"gamma(x)\". - -"), - -("Base","lfact","lfact(x) - - Compute the logarithmic factorial of \"x\" - -"), - -("Base","digamma","digamma(x) - - Compute the digamma function of \"x\" (the logarithmic derivative - of \"gamma(x)\") - -"), - -("Base","invdigamma","invdigamma(x) - - Compute the inverse digamma function of \"x\". - -"), - -("Base","trigamma","trigamma(x) - - Compute the trigamma function of \"x\" (the logarithmic second - derivative of \"gamma(x)\") - -"), - -("Base","polygamma","polygamma(m, x) - - Compute the polygamma function of order \"m\" of argument \"x\" - (the \"(m+1)th\" derivative of the logarithm of \"gamma(x)\") - -"), - -("Base","airy","airy(k, x) - - kth derivative of the Airy function \\operatorname{Ai}(x). - -"), - -("Base","airyai","airyai(x) - - Airy function \\operatorname{Ai}(x). - -"), - -("Base","airyprime","airyprime(x) - - Airy function derivative \\operatorname{Ai}'(x). - -"), - -("Base","airyaiprime","airyaiprime(x) - - Airy function derivative \\operatorname{Ai}'(x). - -"), - -("Base","airybi","airybi(x) - - Airy function \\operatorname{Bi}(x). - -"), - -("Base","airybiprime","airybiprime(x) - - Airy function derivative \\operatorname{Bi}'(x). - -"), - -("Base","airyx","airyx(k, x) - - scaled kth derivative of the Airy function, return - \\operatorname{Ai}(x) e^{\\frac{2}{3} x \\sqrt{x}} for \"k == 0 || - k == 1\", and \\operatorname{Ai}(x) e^{- \\left| \\operatorname{Re} - \\left( \\frac{2}{3} x \\sqrt{x} \\right) \\right|} for \"k == 2 || - k == 3\". - -"), - -("Base","besselj0","besselj0(x) - - Bessel function of the first kind of order 0, J_0(x). - -"), - -("Base","besselj1","besselj1(x) - - Bessel function of the first kind of order 1, J_1(x). - -"), - -("Base","besselj","besselj(nu, x) - - Bessel function of the first kind of order \"nu\", J_\\nu(x). - -"), - -("Base","besseljx","besseljx(nu, x) - - Scaled Bessel function of the first kind of order \"nu\", J_\\nu(x) - e^{- | \\operatorname{Im}(x) |}. - -"), - -("Base","bessely0","bessely0(x) - - Bessel function of the second kind of order 0, Y_0(x). - -"), - -("Base","bessely1","bessely1(x) - - Bessel function of the second kind of order 1, Y_1(x). - -"), - -("Base","bessely","bessely(nu, x) - - Bessel function of the second kind of order \"nu\", Y_\\nu(x). - -"), - -("Base","besselyx","besselyx(nu, x) - - Scaled Bessel function of the second kind of order \"nu\", - Y_\\nu(x) e^{- | \\operatorname{Im}(x) |}. - -"), - -("Base","hankelh1","hankelh1(nu, x) - - Bessel function of the third kind of order \"nu\", H^{(1)}_\\nu(x). - -"), - -("Base","hankelh1x","hankelh1x(nu, x) - - Scaled Bessel function of the third kind of order \"nu\", - H^{(1)}_\\nu(x) e^{-x i}. - -"), - -("Base","hankelh2","hankelh2(nu, x) - - Bessel function of the third kind of order \"nu\", H^{(2)}_\\nu(x). - -"), - -("Base","hankelh2x","hankelh2x(nu, x) - - Scaled Bessel function of the third kind of order \"nu\", - H^{(2)}_\\nu(x) e^{x i}. - -"), - -("Base","besselh","besselh(nu, k, x) - - Bessel function of the third kind of order \"nu\" (Hankel - function). \"k\" is either 1 or 2, selecting \"hankelh1\" or - \"hankelh2\", respectively. - -"), - -("Base","besseli","besseli(nu, x) - - Modified Bessel function of the first kind of order \"nu\", - I_\\nu(x). - -"), - -("Base","besselix","besselix(nu, x) - - Scaled modified Bessel function of the first kind of order \"nu\", - I_\\nu(x) e^{- | \\operatorname{Re}(x) |}. - -"), - -("Base","besselk","besselk(nu, x) - - Modified Bessel function of the second kind of order \"nu\", - K_\\nu(x). - -"), - -("Base","besselkx","besselkx(nu, x) - - Scaled modified Bessel function of the second kind of order \"nu\", - K_\\nu(x) e^x. - -"), - -("Base","beta","beta(x, y) - - Euler integral of the first kind \\operatorname{B}(x,y) = - \\Gamma(x)\\Gamma(y)/\\Gamma(x+y). - -"), - -("Base","lbeta","lbeta(x, y) - - Natural logarithm of the absolute value of the beta function - \\log(|\\operatorname{B}(x,y)|). - -"), - -("Base","eta","eta(x) - - Dirichlet eta function \\eta(s) = - \\sum^\\infty_{n=1}(-)^{n-1}/n^{s}. - -"), - -("Base","zeta","zeta(s) - - Riemann zeta function \\zeta(s). - -"), - -("Base","zeta","zeta(s, z) - - Hurwitz zeta function \\zeta(s, z). (This is equivalent to the - Riemann zeta function \\zeta(s) for the case of \"z=1\".) - -"), - -("Base","ndigits","ndigits(n, b) - - Compute the number of digits in number \"n\" written in base \"b\". - -"), - -("Base","widemul","widemul(x, y) - - Multiply \"x\" and \"y\", giving the result as a larger type. - -"), - -("Base","@evalpoly","@evalpoly(z, c...) - - Evaluate the polynomial \\sum_k c[k] z^{k-1} for the coefficients - \"c[1]\", \"c[2]\", ...; that is, the coefficients are given in - ascending order by power of \"z\". This macro expands to efficient - inline code that uses either Horner's method or, for complex \"z\", - a more efficient Goertzel-like algorithm. - -"), - -("Base","mean","mean(v[, region]) - - Compute the mean of whole array \"v\", or optionally along the - dimensions in \"region\". Note: Julia does not ignore \"NaN\" - values in the computation. For applications requiring the handling - of missing data, the \"DataArray\" package is recommended. - -"), - -("Base","mean!","mean!(r, v) - - Compute the mean of \"v\" over the singleton dimensions of \"r\", - and write results to \"r\". - -"), - -("Base","std","std(v[, region]) - - Compute the sample standard deviation of a vector or array \"v\", - optionally along dimensions in \"region\". The algorithm returns an - estimator of the generative distribution's standard deviation under - the assumption that each entry of \"v\" is an IID drawn from that - generative distribution. This computation is equivalent to - calculating \"sqrt(sum((v - mean(v)).^2) / (length(v) - 1))\". - Note: Julia does not ignore \"NaN\" values in the computation. For - applications requiring the handling of missing data, the - \"DataArray\" package is recommended. - -"), - -("Base","stdm","stdm(v, m) - - Compute the sample standard deviation of a vector \"v\" with known - mean \"m\". Note: Julia does not ignore \"NaN\" values in the - computation. - -"), - -("Base","var","var(v[, region]) - - Compute the sample variance of a vector or array \"v\", optionally - along dimensions in \"region\". The algorithm will return an - estimator of the generative distribution's variance under the - assumption that each entry of \"v\" is an IID drawn from that - generative distribution. This computation is equivalent to - calculating \"sum((v - mean(v)).^2) / (length(v) - 1)\". Note: - Julia does not ignore \"NaN\" values in the computation. For - applications requiring the handling of missing data, the - \"DataArray\" package is recommended. - -"), - -("Base","varm","varm(v, m) - - Compute the sample variance of a vector \"v\" with known mean - \"m\". Note: Julia does not ignore \"NaN\" values in the - computation. - -"), - -("Base","middle","middle(x) - - Compute the middle of a scalar value, which is equivalent to \"x\" - itself, but of the type of \"middle(x, x)\" for consistency. - -"), - -("Base","middle","middle(x, y) - - Compute the middle of two reals \"x\" and \"y\", which is - equivalent in both value and type to computing their mean (\"(x + - y) / 2\"). - -"), - -("Base","middle","middle(range) - - Compute the middle of a range, which consists in computing the mean - of its extrema. Since a range is sorted, the mean is performed with - the first and last element. - -"), - -("Base","middle","middle(array) - - Compute the middle of an array, which consists in finding its - extrema and then computing their mean. - -"), - -("Base","median","median(v[, region]) - - Compute the median of whole array \"v\", or optionally along the - dimensions in \"region\". \"NaN\" is returned if the data contains - any \"NaN\" values. For applications requiring the handling of - missing data, the \"DataArrays\" package is recommended. - -"), - -("Base","median!","median!(v) - - Like \"median\", but may overwrite the input vector. - -"), - -("Base","hist","hist(v[, n]) -> e, counts - - Compute the histogram of \"v\", optionally using approximately - \"n\" bins. The return values are a range \"e\", which correspond - to the edges of the bins, and \"counts\" containing the number of - elements of \"v\" in each bin. Note: Julia does not ignore \"NaN\" - values in the computation. - -"), - -("Base","hist","hist(v, e) -> e, counts - - Compute the histogram of \"v\" using a vector/range \"e\" as the - edges for the bins. The result will be a vector of length - \"length(e) - 1\", such that the element at location \"i\" - satisfies \"sum(e[i] .< v .<= e[i+1])\". Note: Julia does not - ignore \"NaN\" values in the computation. - -"), - -("Base","hist!","hist!(counts, v, e) -> e, counts - - Compute the histogram of \"v\", using a vector/range \"e\" as the - edges for the bins. This function writes the resultant counts to a - pre-allocated array \"counts\". - -"), - -("Base","hist2d","hist2d(M, e1, e2) -> (edge1, edge2, counts) - - Compute a \"2d histogram\" of a set of N points specified by N-by-2 - matrix \"M\". Arguments \"e1\" and \"e2\" are bins for each - dimension, specified either as integer bin counts or vectors of bin - edges. The result is a tuple of \"edge1\" (the bin edges used in - the first dimension), \"edge2\" (the bin edges used in the second - dimension), and \"counts\", a histogram matrix of size - \"(length(edge1)-1, length(edge2)-1)\". Note: Julia does not ignore - \"NaN\" values in the computation. - -"), - -("Base","hist2d!","hist2d!(counts, M, e1, e2) -> (e1, e2, counts) - - Compute a \"2d histogram\" with respect to the bins delimited by - the edges given in \"e1\" and \"e2\". This function writes the - results to a pre-allocated array \"counts\". - -"), - -("Base","histrange","histrange(v, n) - - Compute *nice* bin ranges for the edges of a histogram of \"v\", - using approximately \"n\" bins. The resulting step sizes will be 1, - 2 or 5 multiplied by a power of 10. Note: Julia does not ignore - \"NaN\" values in the computation. - -"), - -("Base","midpoints","midpoints(e) - - Compute the midpoints of the bins with edges \"e\". The result is a - vector/range of length \"length(e) - 1\". Note: Julia does not - ignore \"NaN\" values in the computation. - -"), - -("Base","quantile","quantile(v, p) - - Compute the quantiles of a vector \"v\" at a specified set of - probability values \"p\". Note: Julia does not ignore \"NaN\" - values in the computation. - -"), - -("Base","quantile","quantile(v, p) - - Compute the quantile of a vector \"v\" at the probability \"p\". - Note: Julia does not ignore \"NaN\" values in the computation. - -"), - -("Base","quantile!","quantile!(v, p) - - Like \"quantile\", but overwrites the input vector. - -"), - -("Base","cov","cov(v1[, v2][, vardim=1, corrected=true, mean=nothing]) - - Compute the Pearson covariance between the vector(s) in \"v1\" and - \"v2\". Here, \"v1\" and \"v2\" can be either vectors or matrices. - - This function accepts three keyword arguments: - - * \"vardim\": the dimension of variables. When \"vardim = 1\", - variables are considered in columns while observations in rows; - when \"vardim = 2\", variables are in rows while observations in - columns. By default, it is set to \"1\". - - * \"corrected\": whether to apply Bessel's correction (divide by - \"n-1\" instead of \"n\"). By default, it is set to \"true\". - - * \"mean\": allow users to supply mean values that are known. By - default, it is set to \"nothing\", which indicates that the - mean(s) are unknown, and the function will compute the mean. - Users can use \"mean=0\" to indicate that the input data are - centered, and hence there's no need to subtract the mean. - - The size of the result depends on the size of \"v1\" and \"v2\". - When both \"v1\" and \"v2\" are vectors, it returns the covariance - between them as a scalar. When either one is a matrix, it returns a - covariance matrix of size \"(n1, n2)\", where \"n1\" and \"n2\" are - the numbers of slices in \"v1\" and \"v2\", which depend on the - setting of \"vardim\". - - Note: \"v2\" can be omitted, which indicates \"v2 = v1\". - -"), - -("Base","cor","cor(v1[, v2][, vardim=1, mean=nothing]) - - Compute the Pearson correlation between the vector(s) in \"v1\" and - \"v2\". - - Users can use the keyword argument \"vardim\" to specify the - variable dimension, and \"mean\" to supply pre-computed mean - values. - -"), - -("Base","fft","fft(A[, dims]) - - Performs a multidimensional FFT of the array \"A\". The optional - \"dims\" argument specifies an iterable subset of dimensions (e.g. - an integer, range, tuple, or array) to transform along. Most - efficient if the size of \"A\" along the transformed dimensions is - a product of small primes; see \"nextprod()\". See also - \"plan_fft()\" for even greater efficiency. - - A one-dimensional FFT computes the one-dimensional discrete Fourier - transform (DFT) as defined by - - \\operatorname{DFT}(A)[k] = - \\sum_{n=1}^{\\operatorname{length}(A)} - \\exp\\left(-i\\frac{2\\pi - (n-1)(k-1)}{\\operatorname{length}(A)} \\right) A[n]. - - A multidimensional FFT simply performs this operation along each - transformed dimension of \"A\". - - Higher performance is usually possible with multi-threading. Use - *FFTW.set_num_threads(np)* to use *np* threads, if you have *np* - processors. - -"), - -("Base","fft!","fft!(A[, dims]) - - Same as \"fft()\", but operates in-place on \"A\", which must be an - array of complex floating-point numbers. - -"), - -("Base","ifft","ifft(A[, dims]) - - Multidimensional inverse FFT. - - A one-dimensional inverse FFT computes - - \\operatorname{IDFT}(A)[k] = - \\frac{1}{\\operatorname{length}(A)} - \\sum_{n=1}^{\\operatorname{length}(A)} - \\exp\\left(+i\\frac{2\\pi (n-1)(k-1)} - {\\operatorname{length}(A)} \\right) A[n]. - - A multidimensional inverse FFT simply performs this operation along - each transformed dimension of \"A\". - -"), - -("Base","ifft!","ifft!(A[, dims]) - - Same as \"ifft()\", but operates in-place on \"A\". - -"), - -("Base","bfft","bfft(A[, dims]) - - Similar to \"ifft()\", but computes an unnormalized inverse - (backward) transform, which must be divided by the product of the - sizes of the transformed dimensions in order to obtain the inverse. - (This is slightly more efficient than \"ifft()\" because it omits a - scaling step, which in some applications can be combined with other - computational steps elsewhere.) - - \\operatorname{BDFT}(A)[k] = \\operatorname{length}(A) - \\operatorname{IDFT}(A)[k] - -"), - -("Base","bfft!","bfft!(A[, dims]) - - Same as \"bfft()\", but operates in-place on \"A\". - -"), - -("Base","plan_fft","plan_fft(A [, dims]; flags=FFTW.ESTIMATE; timelimit=Inf) - - Pre-plan an optimized FFT along given dimensions (\"dims\") of - arrays matching the shape and type of \"A\". (The first two - arguments have the same meaning as for \"fft()\".) Returns an - object \"P\" which represents the linear operator computed by the - FFT, and which contains all of the information needed to compute - \"fft(A, dims)\" quickly. - - To apply \"P\" to an array \"A\", use \"P * A\"; in general, the - syntax for applying plans is much like that of matrices. (A plan - can only be applied to arrays of the same size as the \"A\" for - which the plan was created.) You can also apply a plan with a - preallocated output array \"Â\" by calling \"A_mul_B!(Â, plan, - A)\". You can compute the inverse-transform plan by \"inv(P)\" and - apply the inverse plan with \"P \\ Â\" (the inverse plan is cached - and reused for subsequent calls to \"inv\" or \"\\\"), and apply - the inverse plan to a pre-allocated output array \"A\" with - \"A_ldiv_B!(A, P, Â)\". - - The \"flags\" argument is a bitwise-or of FFTW planner flags, - defaulting to \"FFTW.ESTIMATE\". e.g. passing \"FFTW.MEASURE\" or - \"FFTW.PATIENT\" will instead spend several seconds (or more) - benchmarking different possible FFT algorithms and picking the - fastest one; see the FFTW manual for more information on planner - flags. The optional \"timelimit\" argument specifies a rough upper - bound on the allowed planning time, in seconds. Passing - \"FFTW.MEASURE\" or \"FFTW.PATIENT\" may cause the input array - \"A\" to be overwritten with zeros during plan creation. - - \"plan_fft!()\" is the same as \"plan_fft()\" but creates a plan - that operates in-place on its argument (which must be an array of - complex floating-point numbers). \"plan_ifft()\" and so on are - similar but produce plans that perform the equivalent of the - inverse transforms \"ifft()\" and so on. - -"), - -("Base","plan_ifft","plan_ifft(A [, dims]; flags=FFTW.ESTIMATE; timelimit=Inf) - - Same as \"plan_fft()\", but produces a plan that performs inverse - transforms \"ifft()\". - -"), - -("Base","plan_bfft","plan_bfft(A [, dims]; flags=FFTW.ESTIMATE; timelimit=Inf) - - Same as \"plan_fft()\", but produces a plan that performs an - unnormalized backwards transform \"bfft()\". - -"), - -("Base","plan_fft!","plan_fft!(A [, dims]; flags=FFTW.ESTIMATE; timelimit=Inf) - - Same as \"plan_fft()\", but operates in-place on \"A\". - -"), - -("Base","plan_ifft!","plan_ifft!(A [, dims]; flags=FFTW.ESTIMATE; timelimit=Inf) - - Same as \"plan_ifft()\", but operates in-place on \"A\". - -"), - -("Base","plan_bfft!","plan_bfft!(A [, dims]; flags=FFTW.ESTIMATE; timelimit=Inf) - - Same as \"plan_bfft()\", but operates in-place on \"A\". - -"), - -("Base","rfft","rfft(A[, dims]) - - Multidimensional FFT of a real array A, exploiting the fact that - the transform has conjugate symmetry in order to save roughly half - the computational time and storage costs compared with \"fft()\". - If \"A\" has size \"(n_1, ..., n_d)\", the result has size - \"(div(n_1,2)+1, ..., n_d)\". - - The optional \"dims\" argument specifies an iterable subset of one - or more dimensions of \"A\" to transform, similar to \"fft()\". - Instead of (roughly) halving the first dimension of \"A\" in the - result, the \"dims[1]\" dimension is (roughly) halved in the same - way. - -"), - -("Base","irfft","irfft(A, d[, dims]) - - Inverse of \"rfft()\": for a complex array \"A\", gives the - corresponding real array whose FFT yields \"A\" in the first half. - As for \"rfft()\", \"dims\" is an optional subset of dimensions to - transform, defaulting to \"1:ndims(A)\". - - \"d\" is the length of the transformed real array along the - \"dims[1]\" dimension, which must satisfy \"div(d,2)+1 == - size(A,dims[1])\". (This parameter cannot be inferred from - \"size(A)\" since both \"2*size(A,dims[1])-2\" as well as - \"2*size(A,dims[1])-1\" are valid sizes for the transformed real - array.) - -"), - -("Base","brfft","brfft(A, d[, dims]) - - Similar to \"irfft()\" but computes an unnormalized inverse - transform (similar to \"bfft()\"), which must be divided by the - product of the sizes of the transformed dimensions (of the real - output array) in order to obtain the inverse transform. - -"), - -("Base","plan_rfft","plan_rfft(A [, dims]; flags=FFTW.ESTIMATE; timelimit=Inf) - - Pre-plan an optimized real-input FFT, similar to \"plan_fft()\" - except for \"rfft()\" instead of \"fft()\". The first two - arguments, and the size of the transformed result, are the same as - for \"rfft()\". - -"), - -("Base","plan_brfft","plan_brfft(A, d [, dims]; flags=FFTW.ESTIMATE; timelimit=Inf) - - Pre-plan an optimized real-input unnormalized transform, similar to - \"plan_rfft()\" except for \"brfft()\" instead of \"rfft()\". The - first two arguments and the size of the transformed result, are the - same as for \"brfft()\". - -"), - -("Base","plan_irfft","plan_irfft(A, d [, dims]; flags=FFTW.ESTIMATE; timelimit=Inf) - - Pre-plan an optimized inverse real-input FFT, similar to - \"plan_rfft()\" except for \"irfft()\" and \"brfft()\", - respectively. The first three arguments have the same meaning as - for \"irfft()\". - -"), - -("Base","dct","dct(A[, dims]) - - Performs a multidimensional type-II discrete cosine transform (DCT) - of the array \"A\", using the unitary normalization of the DCT. The - optional \"dims\" argument specifies an iterable subset of - dimensions (e.g. an integer, range, tuple, or array) to transform - along. Most efficient if the size of \"A\" along the transformed - dimensions is a product of small primes; see \"nextprod()\". See - also \"plan_dct()\" for even greater efficiency. - -"), - -("Base","dct!","dct!(A[, dims]) - - Same as \"dct!()\", except that it operates in-place on \"A\", - which must be an array of real or complex floating-point values. - -"), - -("Base","idct","idct(A[, dims]) - - Computes the multidimensional inverse discrete cosine transform - (DCT) of the array \"A\" (technically, a type-III DCT with the - unitary normalization). The optional \"dims\" argument specifies an - iterable subset of dimensions (e.g. an integer, range, tuple, or - array) to transform along. Most efficient if the size of \"A\" - along the transformed dimensions is a product of small primes; see - \"nextprod()\". See also \"plan_idct()\" for even greater - efficiency. - -"), - -("Base","idct!","idct!(A[, dims]) - - Same as \"idct!()\", but operates in-place on \"A\". - -"), - -("Base","plan_dct","plan_dct(A[, dims[, flags[, timelimit]]]) - - Pre-plan an optimized discrete cosine transform (DCT), similar to - \"plan_fft()\" except producing a function that computes \"dct()\". - The first two arguments have the same meaning as for \"dct()\". - -"), - -("Base","plan_dct!","plan_dct!(A[, dims[, flags[, timelimit]]]) - - Same as \"plan_dct()\", but operates in-place on \"A\". - -"), - -("Base","plan_idct","plan_idct(A[, dims[, flags[, timelimit]]]) - - Pre-plan an optimized inverse discrete cosine transform (DCT), - similar to \"plan_fft()\" except producing a function that computes - \"idct()\". The first two arguments have the same meaning as for - \"idct()\". - -"), - -("Base","plan_idct!","plan_idct!(A[, dims[, flags[, timelimit]]]) - - Same as \"plan_idct()\", but operates in-place on \"A\". - -"), - -("Base","fftshift","fftshift(x) - - Swap the first and second halves of each dimension of \"x\". - -"), - -("Base","fftshift","fftshift(x, dim) - - Swap the first and second halves of the given dimension of array - \"x\". - -"), - -("Base","ifftshift","ifftshift(x[, dim]) - - Undoes the effect of \"fftshift\". - -"), - -("Base","filt","filt(b, a, x[, si]) - - Apply filter described by vectors \"a\" and \"b\" to vector \"x\", - with an optional initial filter state vector \"si\" (defaults to - zeros). - -"), - -("Base","filt!","filt!(out, b, a, x[, si]) - - Same as \"filt()\" but writes the result into the \"out\" argument, - which may alias the input \"x\" to modify it in-place. - -"), - -("Base","deconv","deconv(b, a) - - Construct vector \"c\" such that \"b = conv(a,c) + r\". Equivalent - to polynomial division. - -"), - -("Base","conv","conv(u, v) - - Convolution of two vectors. Uses FFT algorithm. - -"), - -("Base","conv2","conv2(u, v, A) - - 2-D convolution of the matrix \"A\" with the 2-D separable kernel - generated by the vectors \"u\" and \"v\". Uses 2-D FFT algorithm - -"), - -("Base","conv2","conv2(B, A) - - 2-D convolution of the matrix \"B\" with the matrix \"A\". Uses - 2-D FFT algorithm - -"), - -("Base","xcorr","xcorr(u, v) - - Compute the cross-correlation of two vectors. - -"), - -("Base.FFTW","r2r","r2r(A, kind[, dims]) - - Performs a multidimensional real-input/real-output (r2r) transform - of type \"kind\" of the array \"A\", as defined in the FFTW manual. - \"kind\" specifies either a discrete cosine transform of various - types (\"FFTW.REDFT00\", \"FFTW.REDFT01\", \"FFTW.REDFT10\", or - \"FFTW.REDFT11\"), a discrete sine transform of various types - (\"FFTW.RODFT00\", \"FFTW.RODFT01\", \"FFTW.RODFT10\", or - \"FFTW.RODFT11\"), a real-input DFT with halfcomplex-format output - (\"FFTW.R2HC\" and its inverse \"FFTW.HC2R\"), or a discrete - Hartley transform (\"FFTW.DHT\"). The \"kind\" argument may be an - array or tuple in order to specify different transform types along - the different dimensions of \"A\"; \"kind[end]\" is used for any - unspecified dimensions. See the FFTW manual for precise - definitions of these transform types, at http://www.fftw.org/doc. - - The optional \"dims\" argument specifies an iterable subset of - dimensions (e.g. an integer, range, tuple, or array) to transform - along. \"kind[i]\" is then the transform type for \"dims[i]\", with - \"kind[end]\" being used for \"i > length(kind)\". - - See also \"plan_r2r()\" to pre-plan optimized r2r transforms. - -"), - -("Base.FFTW","r2r!","r2r!(A, kind[, dims]) - - Same as \"r2r()\", but operates in-place on \"A\", which must be an - array of real or complex floating-point numbers. - -"), - -("Base.FFTW","plan_r2r","plan_r2r(A, kind[, dims[, flags[, timelimit]]]) - - Pre-plan an optimized r2r transform, similar to \"Base.plan_fft()\" - except that the transforms (and the first three arguments) - correspond to \"r2r()\" and \"r2r!()\", respectively. - -"), - -("Base.FFTW","plan_r2r!","plan_r2r!(A, kind[, dims[, flags[, timelimit]]]) - - Similar to \"Base.plan_fft()\", but corresponds to \"r2r!()\". - -"), - -("Base","quadgk","quadgk(f, a, b, c...; reltol=sqrt(eps), abstol=0, maxevals=10^7, order=7, norm=vecnorm) - - Numerically integrate the function \"f(x)\" from \"a\" to \"b\", - and optionally over additional intervals \"b\" to \"c\" and so on. - Keyword options include a relative error tolerance \"reltol\" - (defaults to \"sqrt(eps)\" in the precision of the endpoints), an - absolute error tolerance \"abstol\" (defaults to 0), a maximum - number of function evaluations \"maxevals\" (defaults to \"10^7\"), - and the \"order\" of the integration rule (defaults to 7). - - Returns a pair \"(I,E)\" of the estimated integral \"I\" and an - estimated upper bound on the absolute error \"E\". If \"maxevals\" - is not exceeded then \"E <= max(abstol, reltol*norm(I))\" will - hold. (Note that it is useful to specify a positive \"abstol\" in - cases where \"norm(I)\" may be zero.) - - The endpoints \"a\" etcetera can also be complex (in which case the - integral is performed over straight-line segments in the complex - plane). If the endpoints are \"BigFloat\", then the integration - will be performed in \"BigFloat\" precision as well (note: it is - advisable to increase the integration \"order\" in rough proportion - to the precision, for smooth integrands). More generally, the - precision is set by the precision of the integration endpoints - (promoted to floating-point types). - - The integrand \"f(x)\" can return any numeric scalar, vector, or - matrix type, or in fact any type supporting \"+\", \"-\", - multiplication by real values, and a \"norm\" (i.e., any normed - vector space). Alternatively, a different norm can be specified by - passing a *norm*-like function as the *norm* keyword argument - (which defaults to *vecnorm*). - - [Only one-dimensional integrals are provided by this function. For - multi-dimensional integration (cubature), there are many different - algorithms (often much better than simple nested 1d integrals) and - the optimal choice tends to be very problem-dependent. See the - Julia external-package listing for available algorithms for - multidimensional integration or other specialized tasks (such as - integrals of highly oscillatory or singular functions).] - - The algorithm is an adaptive Gauss-Kronrod integration technique: - the integral in each interval is estimated using a Kronrod rule - (\"2*order+1\" points) and the error is estimated using an embedded - Gauss rule (\"order\" points). The interval with the largest - error is then subdivided into two intervals and the process is - repeated until the desired error tolerance is achieved. - - These quadrature rules work best for smooth functions within each - interval, so if your function has a known discontinuity or other - singularity, it is best to subdivide your interval to put the - singularity at an endpoint. For example, if \"f\" has a - discontinuity at \"x=0.7\" and you want to integrate from 0 to 1, - you should use \"quadgk(f, 0,0.7,1)\" to subdivide the interval at - the point of discontinuity. The integrand is never evaluated - exactly at the endpoints of the intervals, so it is possible to - integrate functions that diverge at the endpoints as long as the - singularity is integrable (for example, a \"log(x)\" or - \"1/sqrt(x)\" singularity). - - For real-valued endpoints, the starting and/or ending points may be - infinite. (A coordinate transformation is performed internally to - map the infinite interval to a finite one.) - -"), - -("Base","bin","bin(n[, pad]) - - Convert an integer to a binary string, optionally specifying a - number of digits to pad to. - -"), - -("Base","hex","hex(n[, pad]) - - Convert an integer to a hexadecimal string, optionally specifying a - number of digits to pad to. - -"), - -("Base","dec","dec(n[, pad]) - - Convert an integer to a decimal string, optionally specifying a - number of digits to pad to. - -"), - -("Base","oct","oct(n[, pad]) - - Convert an integer to an octal string, optionally specifying a - number of digits to pad to. - -"), - -("Base","base","base(base, n[, pad]) - - Convert an integer to a string in the given base, optionally - specifying a number of digits to pad to. The base can be specified - as either an integer, or as a \"UInt8\" array of character values - to use as digit symbols. - -"), - -("Base","digits","digits(n[, base][, pad]) - - Returns an array of the digits of \"n\" in the given base, - optionally padded with zeros to a specified size. More significant - digits are at higher indexes, such that \"n == - sum([digits[k]*base^(k-1) for k=1:length(digits)])\". - -"), - -("Base","digits!","digits!(array, n[, base]) - - Fills an array of the digits of \"n\" in the given base. More - significant digits are at higher indexes. If the array length is - insufficient, the least significant digits are filled up to the - array length. If the array length is excessive, the excess portion - is filled with zeros. - -"), - -("Base","bits","bits(n) - - A string giving the literal bit representation of a number. - -"), - -("Base","parse","parse(type, str[, base]) - - Parse a string as a number. If the type is an integer type, then a - base can be specified (the default is 10). If the type is a - floating point type, the string is parsed as a decimal floating - point number. If the string does not contain a valid number, an - error is raised. - -"), - -("Base","tryparse","tryparse(type, str[, base]) - - Like \"parse\", but returns a \"Nullable\" of the requested type. - The result will be null if the string does not contain a valid - number. - -"), - -("Base","big","big(x) - - Convert a number to a maximum precision representation (typically - \"BigInt\" or \"BigFloat\"). See \"BigFloat\" for information about - some pitfalls with floating-point numbers. - -"), - -("Base","signed","signed(x) - - Convert a number to a signed integer. If the argument is unsigned, - it is reinterpreted as signed without checking for overflow. - -"), - -("Base","unsigned","unsigned(x) -> Unsigned - - Convert a number to an unsigned integer. If the argument is signed, - it is reinterpreted as unsigned without checking for negative - values. - -"), - -("Base","float","float(x) - - Convert a number, array, or string to a \"AbstractFloat\" data - type. For numeric data, the smallest suitable \"AbstractFloat\" - type is used. Converts strings to \"Float64\". - -"), - -("Base","significand","significand(x) - - Extract the significand(s) (a.k.a. mantissa), in binary - representation, of a floating-point number or array. If \"x\" is a - non-zero finite number, than the result will be a number of the - same type on the interval [1,2). Otherwise \"x\" is returned. - - julia> significand(15.2)/15.2 - 0.125 - - julia> significand(15.2)*8 - 15.2 - -"), - -("Base","exponent","exponent(x) -> Int - - Get the exponent of a normalized floating-point number. - -"), - -("Base","complex","complex(r[, i]) - - Convert real numbers or arrays to complex. \"i\" defaults to zero. - -"), - -("Base","bswap","bswap(n) - - Byte-swap an integer - -"), - -("Base","num2hex","num2hex(f) - - Get a hexadecimal string of the binary representation of a floating - point number - -"), - -("Base","hex2num","hex2num(str) - - Convert a hexadecimal string to the floating point number it - represents - -"), - -("Base","hex2bytes","hex2bytes(s::ASCIIString) - - Convert an arbitrarily long hexadecimal string to its binary - representation. Returns an Array{UInt8, 1}, i.e. an array of bytes. - -"), - -("Base","bytes2hex","bytes2hex(bin_arr::Array{UInt8, 1}) - - Convert an array of bytes to its hexadecimal representation. All - characters are in lower-case. Returns an ASCIIString. - -"), - -("Base","one","one(x) - - Get the multiplicative identity element for the type of x (x can - also specify the type itself). For matrices, returns an identity - matrix of the appropriate size and type. - -"), - -("Base","zero","zero(x) - - Get the additive identity element for the type of x (x can also - specify the type itself). - -"), - -("Base","pi","pi -π - - The constant pi - -"), - -("Base","im","im - - The imaginary unit - -"), - -("Base","e","e -eu - - The constant e - -"), - -("Base","catalan","catalan - - Catalan's constant - -"), - -("Base","γ","γ -eulergamma - - Euler's constant - -"), - -("Base","φ","φ -golden - - The golden ratio - -"), - -("Base","Inf","Inf - - Positive infinity of type Float64 - -"), - -("Base","Inf32","Inf32 - - Positive infinity of type Float32 - -"), - -("Base","Inf16","Inf16 - - Positive infinity of type Float16 - -"), - -("Base","NaN","NaN - - A not-a-number value of type Float64 - -"), - -("Base","NaN32","NaN32 - - A not-a-number value of type Float32 - -"), - -("Base","NaN16","NaN16 - - A not-a-number value of type Float16 - -"), - -("Base","issubnormal","issubnormal(f) -> Bool - - Test whether a floating point number is subnormal - -"), - -("Base","isfinite","isfinite(f) -> Bool - - Test whether a number is finite - -"), - -("Base","isinf","isinf(f) -> Bool - - Test whether a number is infinite - -"), - -("Base","isnan","isnan(f) -> Bool - - Test whether a floating point number is not a number (NaN) - -"), - -("Base","inf","inf(f) - - Returns positive infinity of the floating point type \"f\" or of - the same floating point type as \"f\" - -"), - -("Base","nan","nan(f) - - Returns NaN (not-a-number) of the floating point type \"f\" or of - the same floating point type as \"f\" - -"), - -("Base","nextfloat","nextfloat(f) - - Get the next floating point number in lexicographic order - -"), - -("Base","prevfloat","prevfloat(f) -> AbstractFloat - - Get the previous floating point number in lexicographic order - -"), - -("Base","isinteger","isinteger(x) -> Bool - - Test whether \"x\" or all its elements are numerically equal to - some integer - -"), - -("Base","isreal","isreal(x) -> Bool - - Test whether \"x\" or all its elements are numerically equal to - some real number - -"), - -("Base","Float32","Float32(x[, mode::RoundingMode]) - - Create a Float32 from \"x\". If \"x\" is not exactly representable - then \"mode\" determines how \"x\" is rounded. - - julia> Float32(1/3, RoundDown) - 0.3333333f0 - - julia> Float32(1/3, RoundUp) - 0.33333334f0 - - See \"get_rounding\" for available rounding modes. - -"), - -("Base","Float64","Float64(x[, mode::RoundingMode]) - - Create a Float64 from \"x\". If \"x\" is not exactly representable - then \"mode\" determines how \"x\" is rounded. - - julia> Float64(pi, RoundDown) - 3.141592653589793 - - julia> Float64(pi, RoundUp) - 3.1415926535897936 - - See \"get_rounding\" for available rounding modes. - -"), - -("Base","BigInt","BigInt(x) - - Create an arbitrary precision integer. \"x\" may be an \"Int\" (or - anything that can be converted to an \"Int\"). The usual - mathematical operators are defined for this type, and results are - promoted to a \"BigInt\". - - Instances can be constructed from strings via \"parse()\", or using - the \"big\" string literal. - -"), - -("Base","BigFloat","BigFloat(x) - - Create an arbitrary precision floating point number. \"x\" may be - an \"Integer\", a \"Float64\" or a \"BigInt\". The usual - mathematical operators are defined for this type, and results are - promoted to a \"BigFloat\". - - Note that because decimal literals are converted to floating point - numbers when parsed, \"BigFloat(2.1)\" may not yield what you - expect. You may instead prefer to initialize constants from strings - via \"parse()\", or using the \"big\" string literal. - - julia> big\"2.1\" - 2.099999999999999999999999999999999999999999999999999999999999999999999999999986e+00 with 256 bits of precision - -"), - -("Base","get_rounding","get_rounding(T) - - Get the current floating point rounding mode for type \"T\", - controlling the rounding of basic arithmetic functions (\"+()\", - \"-()\", \"*()\", \"/()\" and \"sqrt()\") and type conversion. - - Valid modes are \"RoundNearest\", \"RoundToZero\", \"RoundUp\", - \"RoundDown\", and \"RoundFromZero\" (\"BigFloat\" only). - -"), - -("Base","set_rounding","set_rounding(T, mode) - - Set the rounding mode of floating point type \"T\", controlling the - rounding of basic arithmetic functions (\"+()\", \"-()\", \"*()\", - \"/()\" and \"sqrt()\") and type conversion. - - Note that this may affect other types, for instance changing the - rounding mode of \"Float64\" will change the rounding mode of - \"Float32\". See \"get_rounding\" for available modes - -"), - -("Base","with_rounding","with_rounding(f::Function, T, mode) - - Change the rounding mode of floating point type \"T\" for the - duration of \"f\". It is logically equivalent to: - - old = get_rounding(T) - set_rounding(T, mode) - f() - set_rounding(T, old) - - See \"get_rounding\" for available rounding modes. - -"), - -("Base","get_zero_subnormals","get_zero_subnormals() -> Bool - - Returns \"false\" if operations on subnormal floating-point values - (\"denormals\") obey rules for IEEE arithmetic, and \"true\" if - they might be converted to zeros. - -"), - -("Base","set_zero_subnormals","set_zero_subnormals(yes::Bool) -> Bool - - If \"yes\" is \"false\", subsequent floating-point operations - follow rules for IEEE arithmetic on subnormal values - (\"denormals\"). Otherwise, floating-point operations are permitted - (but not required) to convert subnormal inputs or outputs to zero. - Returns \"true\" unless \"yes==true\" but the hardware does not - support zeroing of subnormal numbers. - - \"set_zero_subnormals(true)\" can speed up some computations on - some hardware. However, it can break identities such as \"(x-y==0) - == (x==y)\". - -"), - -("Base","count_ones","count_ones(x::Integer) -> Integer - - Number of ones in the binary representation of \"x\". - - julia> count_ones(7) - 3 - -"), - -("Base","count_zeros","count_zeros(x::Integer) -> Integer - - Number of zeros in the binary representation of \"x\". - - julia> count_zeros(Int32(2 ^ 16 - 1)) - 16 - -"), - -("Base","leading_zeros","leading_zeros(x::Integer) -> Integer - - Number of zeros leading the binary representation of \"x\". - - julia> leading_zeros(Int32(1)) - 31 - -"), - -("Base","leading_ones","leading_ones(x::Integer) -> Integer - - Number of ones leading the binary representation of \"x\". - - julia> leading_ones(UInt32(2 ^ 32 - 2)) - 31 - -"), - -("Base","trailing_zeros","trailing_zeros(x::Integer) -> Integer - - Number of zeros trailing the binary representation of \"x\". - - julia> trailing_zeros(2) - 1 - -"), - -("Base","trailing_ones","trailing_ones(x::Integer) -> Integer - - Number of ones trailing the binary representation of \"x\". - - julia> trailing_ones(3) - 2 - -"), - -("Base","isprime","isprime(x::Integer) -> Bool - - Returns \"true\" if \"x\" is prime, and \"false\" otherwise. - - julia> isprime(3) - true - -"), - -("Base","isprime","isprime(x::BigInt[, reps = 25]) -> Bool - - Probabilistic primality test. Returns \"true\" if \"x\" is prime; - and \"false\" if \"x\" is not prime with high probability. The - false positive rate is about \"0.25^reps\". \"reps = 25\" is - considered safe for cryptographic applications (Knuth, - Seminumerical Algorithms). - - julia> isprime(big(3)) - true - -"), - -("Base","primes","primes(n) - - Returns a collection of the prime numbers <= \"n\". - -"), - -("Base","isodd","isodd(x::Integer) -> Bool - - Returns \"true\" if \"x\" is odd (that is, not divisible by 2), and - \"false\" otherwise. - - julia> isodd(9) - true - - julia> isodd(10) - false - -"), - -("Base","iseven","iseven(x::Integer) -> Bool - - Returns \"true\" is \"x\" is even (that is, divisible by 2), and - \"false\" otherwise. - - julia> iseven(9) - false - - julia> iseven(10) - true - -"), - -("Base","precision","precision(num::AbstractFloat) - - Get the precision of a floating point number, as defined by the - effective number of bits in the mantissa. - -"), - -("Base","get_bigfloat_precision","get_bigfloat_precision() - - Get the precision (in bits) currently used for BigFloat arithmetic. - -"), - -("Base","set_bigfloat_precision","set_bigfloat_precision(x::Int64) - - Set the precision (in bits) to be used to BigFloat arithmetic. - -"), - -("Base","with_bigfloat_precision","with_bigfloat_precision(f::Function, precision::Integer) - - Change the BigFloat arithmetic precision (in bits) for the duration - of \"f\". It is logically equivalent to: - - old = get_bigfloat_precision() - set_bigfloat_precision(precision) - f() - set_bigfloat_precision(old) - -"), - -("Base","srand","srand([rng][, seed]) - - Reseed the random number generator. If a \"seed\" is provided, the - RNG will give a reproducible sequence of numbers, otherwise Julia - will get entropy from the system. For \"MersenneTwister\", the - \"seed\" may be a non-negative integer, a vector of \"UInt32\" - integers or a filename, in which case the seed is read from a file. - \"RandomDevice\" does not support seeding. - -"), - -("Base","MersenneTwister","MersenneTwister([seed]) - - Create a \"MersenneTwister\" RNG object. Different RNG objects can - have their own seeds, which may be useful for generating different - streams of random numbers. - -"), - -("Base","RandomDevice","RandomDevice() - - Create a \"RandomDevice\" RNG object. Two such objects will always - generate different streams of random numbers. - -"), - -("Base","rand","rand([rng][, S][, dims...]) - - Pick a random element or array of random elements from the set of - values specified by \"S\"; \"S\" can be - - * an indexable collection (for example \"1:n\" or - \"['x','y','z']\"), or - - * a type: the set of values to pick from is then equivalent to - \"typemin(S):typemax(S)\" for integers (this is not applicable to - \"BigInt\"), and to [0,1) for floating point numbers; - - \"S\" defaults to \"Float64\". - -"), - -("Base","rand!","rand!([rng], A[, coll]) - - Populate the array A with random values. If the indexable - collection \"coll\" is specified, the values are picked randomly - from \"coll\". This is equivalent to \"copy!(A, rand(rng, coll, - size(A)))\" or \"copy!(A, rand(rng, eltype(A), size(A)))\" but - without allocating a new array. - -"), - -("Base","bitrand","bitrand([rng][, dims...]) - - Generate a \"BitArray\" of random boolean values. - -"), - -("Base","randn","randn([rng][, dims...]) - - Generate a normally-distributed random number with mean 0 and - standard deviation 1. Optionally generate an array of normally- - distributed random numbers. - -"), - -("Base","randn!","randn!([rng], A::Array{Float64, N}) - - Fill the array A with normally-distributed (mean 0, standard - deviation 1) random numbers. Also see the rand function. - -"), - -("Base","randexp","randexp([rng][, dims...]) - - Generate a random number according to the exponential distribution - with scale 1. Optionally generate an array of such random numbers. - -"), - -("Base","randexp!","randexp!([rng], A::Array{Float64, N}) - - Fill the array A with random numbers following the exponential - distribution (with scale 1). - -"), - -("Base","Task","Task(func) - - Create a \"Task\" (i.e. thread, or coroutine) to execute the given - function (which must be callable with no arguments). The task exits - when this function returns. - -"), - -("Base","yieldto","yieldto(task, arg = nothing) - - Switch to the given task. The first time a task is switched to, the - task's function is called with no arguments. On subsequent - switches, \"arg\" is returned from the task's last call to - \"yieldto\". This is a low-level call that only switches tasks, not - considering states or scheduling in any way. Its use is - discouraged. - -"), - -("Base","current_task","current_task() - - Get the currently running Task. - -"), - -("Base","istaskdone","istaskdone(task) -> Bool - - Tell whether a task has exited. - -"), - -("Base","istaskstarted","istaskstarted(task) -> Bool - - Tell whether a task has started executing. - -"), - -("Base","consume","consume(task, values...) - - Receive the next value passed to \"produce\" by the specified task. - Additional arguments may be passed, to be returned from the last - \"produce\" call in the producer. - -"), - -("Base","produce","produce(value) - - Send the given value to the last \"consume\" call, switching to the - consumer task. If the next \"consume\" call passes any values, they - are returned by \"produce\". - -"), - -("Base","yield","yield() - - Switch to the scheduler to allow another scheduled task to run. A - task that calls this function is still runnable, and will be - restarted immediately if there are no other runnable tasks. - -"), - -("Base","task_local_storage","task_local_storage(symbol) - - Look up the value of a symbol in the current task's task-local - storage. - -"), - -("Base","task_local_storage","task_local_storage(symbol, value) - - Assign a value to a symbol in the current task's task-local - storage. - -"), - -("Base","task_local_storage","task_local_storage(body, symbol, value) - - Call the function \"body\" with a modified task-local storage, in - which \"value\" is assigned to \"symbol\"; the previous value of - \"symbol\", or lack thereof, is restored afterwards. Useful for - emulating dynamic scoping. - -"), - -("Base","Condition","Condition() - - Create an edge-triggered event source that tasks can wait for. - Tasks that call \"wait\" on a \"Condition\" are suspended and - queued. Tasks are woken up when \"notify\" is later called on the - \"Condition\". Edge triggering means that only tasks waiting at the - time \"notify\" is called can be woken up. For level-triggered - notifications, you must keep extra state to keep track of whether a - notification has happened. The \"RemoteRef\" type does this, and so - can be used for level-triggered events. - -"), - -("Base","notify","notify(condition, val=nothing; all=true, error=false) - - Wake up tasks waiting for a condition, passing them \"val\". If - \"all\" is true (the default), all waiting tasks are woken, - otherwise only one is. If \"error\" is true, the passed value is - raised as an exception in the woken tasks. - -"), - -("Base","schedule","schedule(t::Task, [val]; error=false) - - Add a task to the scheduler's queue. This causes the task to run - constantly when the system is otherwise idle, unless the task - performs a blocking operation such as \"wait\". - - If a second argument is provided, it will be passed to the task - (via the return value of \"yieldto\") when it runs again. If - \"error\" is true, the value is raised as an exception in the woken - task. - -"), - -("Base","@schedule","@schedule() - - Wrap an expression in a Task and add it to the scheduler's queue. - -"), - -("Base","@task","@task() - - Wrap an expression in a Task without executing it, and return the - Task. This only creates a task, and does not run it. - -"), - -("Base","sleep","sleep(seconds) - - Block the current task for a specified number of seconds. The - minimum sleep time is 1 millisecond or input of \"0.001\". - -"), - -("Base","ReentrantLock","ReentrantLock() - - Creates a reentrant lock. The same task can acquire the lock as - many times as required. Each lock must be matched with an unlock. - -"), - -("Base","lock","lock(l::ReentrantLock) - - Associates \"l\" with the current task. If \"l\" is already locked - by a different task, waits for it to become available. The same - task can acquire the lock multiple times. Each \"lock\" must be - matched by an \"unlock\" - -"), - -("Base","unlock","unlock(l::ReentrantLock) - - Releases ownership of the lock by the current task. If the lock had - been acquired before, it just decrements an internal counter and - returns immediately. - -"), - -("Base","addprocs","addprocs(n::Integer; exeflags=``) -> List of process identifiers - - Launches workers using the in-built \"LocalManager\" which only - launches workers on the local host. This can be used to take - advantage of multiple cores. \"addprocs(4)\" will add 4 processes - on the local machine. - -"), - -("Base","addprocs","addprocs() -> List of process identifiers - - Equivalent to \"addprocs(CPU_CORES)\" - -"), - -("Base","addprocs","addprocs(machines; tunnel=false, sshflags=``, max_parallel=10, exeflags=``) -> List of process identifiers - - Add processes on remote machines via SSH. Requires julia to be - installed in the same location on each node, or to be available via - a shared file system. - - \"machines\" is a vector of machine specifications. Worker are - started for each specification. - - A machine specification is either a string \"machine_spec\" or a - tuple - \"(machine_spec, count)\" - - \"machine_spec\" is a string of the form \"[user@]host[:port] - [bind_addr[:port]]\". \"user\" defaults to current user, \"port\" - to the standard ssh port. If \"[bind_addr[:port]]\" is specified, - other workers will connect to this worker at the specified - \"bind_addr\" and \"port\". - - \"count\" is the number of workers to be launched on the specified - host. If specified as \":auto\" it will launch as many workers as - the number of cores on the specific host. - - Keyword arguments: - - \"tunnel\" : if \"true\" then SSH tunneling will be used to connect - to the worker from the master process. - - \"sshflags\" : specifies additional ssh options, e.g. - \"sshflags=`-i /home/foo/bar.pem`\" . - - \"max_parallel\" : specifies the maximum number of workers - connected to in parallel at a host. Defaults to 10. - - \"dir\" : specifies the working directory on the workers. Defaults - to the host's current directory (as found by *pwd()*) - - \"exename\" : name of the julia executable. Defaults to - \"\$JULIA_HOME/julia\" or \"\$JULIA_HOME/julia-debug\" as the case - may be. - - \"exeflags\" : additional flags passed to the worker processes. - - Environment variables : - - If the master process fails to establish a connection with a newly - launched worker within 60.0 seconds, the worker treats it a fatal - situation and terminates. This timeout can be controlled via - environment variable \"JULIA_WORKER_TIMEOUT\". The value of - \"JULIA_WORKER_TIMEOUT\" on the master process, specifies the - number of seconds a newly launched worker waits for connection - establishment. - -"), - -("Base","addprocs","addprocs(manager::ClusterManager; kwargs...) -> List of process identifiers - - Launches worker processes via the specified cluster manager. - - For example Beowulf clusters are supported via a custom cluster - manager implemented in package \"ClusterManagers\". - - The number of seconds a newly launched worker waits for connection - establishment from the master can be specified via variable - \"JULIA_WORKER_TIMEOUT\" in the worker process's environment. - Relevant only when using TCP/IP as transport. - -"), - -("Base","nprocs","nprocs() - - Get the number of available processes. - -"), - -("Base","nworkers","nworkers() - - Get the number of available worker processes. This is one less than - nprocs(). Equal to nprocs() if nprocs() == 1. - -"), - -("Base","procs","procs() - - Returns a list of all process identifiers. - -"), - -("Base","workers","workers() - - Returns a list of all worker process identifiers. - -"), - -("Base","rmprocs","rmprocs(pids...) - - Removes the specified workers. - -"), - -("Base","interrupt","interrupt([pids...]) - - Interrupt the current executing task on the specified workers. This - is equivalent to pressing Ctrl-C on the local machine. If no - arguments are given, all workers are interrupted. - -"), - -("Base","myid","myid() - - Get the id of the current process. - -"), - -("Base","pmap","pmap(f, lsts...; err_retry=true, err_stop=false, pids=workers()) - - Transform collections \"lsts\" by applying \"f\" to each element in - parallel. If \"nprocs() > 1\", the calling process will be - dedicated to assigning tasks. All other available processes will be - used as parallel workers, or on the processes specified by - \"pids\". - - If \"err_retry\" is true, it retries a failed application of \"f\" - on a different worker. If \"err_stop\" is true, it takes precedence - over the value of \"err_retry\" and \"pmap\" stops execution on the - first error. - -"), - -("Base","remotecall","remotecall(id, func, args...) - - Call a function asynchronously on the given arguments on the - specified process. Returns a \"RemoteRef\". - -"), - -("Base","wait","wait([x]) - - Block the current task until some event occurs, depending on the - type of the argument: - - * \"RemoteRef\": Wait for a value to become available for the - specified remote reference. - - * \"Condition\": Wait for \"notify\" on a condition. - - * \"Process\": Wait for a process or process chain to exit. The - \"exitcode\" field of a process can be used to determine success - or failure. - - * \"Task\": Wait for a \"Task\" to finish, returning its result - value. If the task fails with an exception, the exception is - propagated (re-thrown in the task that called \"wait\"). - - * \"RawFD\": Wait for changes on a file descriptor (see *poll_fd* - for keyword arguments and return code) - - If no argument is passed, the task blocks for an undefined period. - If the task's state is set to \":waiting\", it can only be - restarted by an explicit call to \"schedule\" or \"yieldto\". If - the task's state is \":runnable\", it might be restarted - unpredictably. - - Often \"wait\" is called within a \"while\" loop to ensure a - waited-for condition is met before proceeding. - -"), - -("Base","fetch","fetch(RemoteRef) - - Wait for and get the value of a remote reference. - -"), - -("Base","remotecall_wait","remotecall_wait(id, func, args...) - - Perform \"wait(remotecall(...))\" in one message. - -"), - -("Base","remotecall_fetch","remotecall_fetch(id, func, args...) - - Perform \"fetch(remotecall(...))\" in one message. - -"), - -("Base","put!","put!(RemoteRef, value) - - Store a value to a remote reference. Implements \"shared queue of - length 1\" semantics: if a value is already present, blocks until - the value is removed with \"take!\". Returns its first argument. - -"), - -("Base","take!","take!(RemoteRef) - - Fetch the value of a remote reference, removing it so that the - reference is empty again. - -"), - -("Base","isready","isready(r::RemoteRef) - - Determine whether a \"RemoteRef\" has a value stored to it. Note - that this function can cause race conditions, since by the time you - receive its result it may no longer be true. It is recommended that - this function only be used on a \"RemoteRef\" that is assigned - once. - - If the argument \"RemoteRef\" is owned by a different node, this - call will block to wait for the answer. It is recommended to wait - for \"r\" in a separate task instead, or to use a local - \"RemoteRef\" as a proxy: - - rr = RemoteRef() - @async put!(rr, remotecall_fetch(p, long_computation)) - isready(rr) # will not block - -"), - -("Base","RemoteRef","RemoteRef() - - Make an uninitialized remote reference on the local machine. - -"), - -("Base","RemoteRef","RemoteRef(n) - - Make an uninitialized remote reference on process \"n\". - -"), - -("Base","timedwait","timedwait(testcb::Function, secs::Float64; pollint::Float64=0.1) - - Waits till \"testcb\" returns \"true\" or for \"secs`\" seconds, - whichever is earlier. \"testcb\" is polled every \"pollint\" - seconds. - -"), - -("Base","@spawn","@spawn() - - Execute an expression on an automatically-chosen process, returning - a \"RemoteRef\" to the result. - -"), - -("Base","@spawnat","@spawnat() - - Accepts two arguments, \"p\" and an expression, and runs the - expression asynchronously on process \"p\", returning a - \"RemoteRef\" to the result. - -"), - -("Base","@fetch","@fetch() - - Equivalent to \"fetch(@spawn expr)\". - -"), - -("Base","@fetchfrom","@fetchfrom() - - Equivalent to \"fetch(@spawnat p expr)\". - -"), - -("Base","@async","@async() - - Schedule an expression to run on the local machine, also adding it - to the set of items that the nearest enclosing \"@sync\" waits for. - -"), - -("Base","@sync","@sync() - - Wait until all dynamically-enclosed uses of \"@async\", \"@spawn\", - \"@spawnat\" and \"@parallel\" are complete. - -"), - -("Base","@parallel","@parallel() - - A parallel for loop of the form - - @parallel [reducer] for var = range - body - end - - The specified range is partitioned and locally executed across all - workers. In case an optional reducer function is specified, - @parallel performs local reductions on each worker with a final - reduction on the calling process. - - Note that without a reducer function, @parallel executes - asynchronously, i.e. it spawns independent tasks on all available - workers and returns immediately without waiting for completion. To - wait for completion, prefix the call with \"@sync\", like - - @sync @parallel for var = range - body - end - -"), - -("Base","SharedArray","SharedArray(T::Type, dims::NTuple; init=false, pids=Int[]) - - Construct a SharedArray of a bitstype \"T\" and size \"dims\" - across the processes specified by \"pids\" - all of which have to - be on the same host. - - If \"pids\" is left unspecified, the shared array will be mapped - across all processes on the current host, including the master. - But, \"localindexes\" and \"indexpids\" will only refer to worker - processes. This facilitates work distribution code to use workers - for actual computation with the master process acting as a driver. - - If an \"init\" function of the type \"initfn(S::SharedArray)\" is - specified, it is called on all the participating workers. - -"), - -("Base","procs","procs(S::SharedArray) - - Get the vector of processes that have mapped the shared array - -"), - -("Base","sdata","sdata(S::SharedArray) - - Returns the actual \"Array\" object backing \"S\" - -"), - -("Base","indexpids","indexpids(S::SharedArray) - - Returns the index of the current worker into the \"pids\" vector, - i.e., the list of workers mapping the SharedArray - -"), - -("Base","launch","launch(manager::FooManager, params::Dict, launched::Vector{WorkerConfig}, launch_ntfy::Condition) - - Implemented by cluster managers. For every Julia worker launched by - this function, it should append a \"WorkerConfig\" entry to - \"launched\" and notify \"launch_ntfy\". The function MUST exit - once all workers, requested by \"manager\" have been launched. - \"params\" is a dictionary of all keyword arguments \"addprocs\" - was called with. - -"), - -("Base","manage","manage(manager::FooManager, pid::Int, config::WorkerConfig. op::Symbol) - - Implemented by cluster managers. It is called on the master - process, during a worker's lifetime, with appropriate \"op\" - values: - - * with \":register\"/\":deregister\" when a worker is added / - removed from the Julia worker pool. - - * with \":interrupt\" when \"interrupt(workers)\" is called. - The \"ClusterManager\" should signal the appropriate worker - with an interrupt signal. - - * with \":finalize\" for cleanup purposes. - -"), - -("Base","kill","kill(manager::FooManager, pid::Int, config::WorkerConfig) - - Implemented by cluster managers. It is called on the master - process, by \"rmprocs\". It should cause the remote worker - specified by \"pid\" to exit. - \"Base.kill(manager::ClusterManager.....)\" executes a remote - \"exit()\" on \"pid\" - -"), - -("Base","init_worker","init_worker(manager::FooManager) - - Called by cluster managers implementing custom transports. It - initializes a newly launched process as a worker. Command line - argument \"--worker\" has the effect of initializing a process as a - worker using TCP/IP sockets for transport. - -"), - -("Base","connect","connect(manager::FooManager, pid::Int, config::WorkerConfig) -> (instrm::AsyncStream, outstrm::AsyncStream) - - Implemented by cluster managers using custom transports. It should - establish a logical connection to worker with id \"pid\", specified - by \"config\" and return a pair of \"AsyncStream\" objects. - Messages from \"pid\" to current process will be read off - \"instrm\", while messages to be sent to \"pid\" will be written to - \"outstrm\". The custom transport implementation must ensure that - messages are delivered and received completely and in order. - \"Base.connect(manager::ClusterManager.....)\" sets up TCP/IP - socket connections in-between workers. - -"), - -("Base","Base","Base.process_messages(instrm::AsyncStream, outstrm::AsyncStream) - - Called by cluster managers using custom transports. It should be - called when the custom transport implementation receives the first - message from a remote worker. The custom transport must manage a - logical connection to the remote worker and provide two AsyncStream - objects, one for incoming messages and the other for messages - addressed to the remote worker. - -"), - -("Base.Pkg","dir","dir() -> AbstractString - - Returns the absolute path of the package directory. This defaults - to \"joinpath(homedir(),\".julia\",\"v\$(VERSION.major).\$(VERSION - .minor)\")\" on all platforms (i.e. \"~/.julia/v0.4\" in UNIX shell - syntax). If the \"JULIA_PKGDIR\" environment variable is set, then - that path is used in the returned value as \"joinpath(ENV[\"JULIA_ - PKGDIR\"],\"v\$(VERSION.major).\$(VERSION.minor)\")\". If - \"JULIA_PKGDIR\" is a relative path, it is interpreted relative to - whatever the current working directory is. - -"), - -("Base.Pkg","dir","dir(names...) -> AbstractString - - Equivalent to \"normpath(Pkg.dir(),names...)\" – i.e. it appends - path components to the package directory and normalizes the - resulting path. In particular, \"Pkg.dir(pkg)\" returns the path to - the package \"pkg\". - -"), - -("Base.Pkg","init","init(meta::AbstractString=DEFAULT_META, branch::AbstractString=META_BRANCH) - - Initialize \"Pkg.dir()\" as a package directory. This will be done - automatically when the \"JULIA_PKGDIR\" is not set and - \"Pkg.dir()\" uses its default value. As part of this process, - clones a local METADATA git repository from the site and branch - specified by its arguments, which are typically not provided. - Explicit (non-default) arguments can be used to support a custom - METADATA setup. - -"), - -("Base.Pkg","resolve","resolve() - - Determines an optimal, consistent set of package versions to - install or upgrade to. The optimal set of package versions is based - on the contents of \"Pkg.dir(\"REQUIRE\")\" and the state of - installed packages in \"Pkg.dir()\", Packages that are no longer - required are moved into \"Pkg.dir(\".trash\")\". - -"), - -("Base.Pkg","edit","edit() - - Opens \"Pkg.dir(\"REQUIRE\")\" in the editor specified by the - \"VISUAL\" or \"EDITOR\" environment variables; when the editor - command returns, it runs \"Pkg.resolve()\" to determine and install - a new optimal set of installed package versions. - -"), - -("Base.Pkg","add","add(pkg, vers...) - - Add a requirement entry for \"pkg\" to \"Pkg.dir(\"REQUIRE\")\" and - call \"Pkg.resolve()\". If \"vers\" are given, they must be - \"VersionNumber\" objects and they specify acceptable version - intervals for \"pkg\". - -"), - -("Base.Pkg","rm","rm(pkg) - - Remove all requirement entries for \"pkg\" from - \"Pkg.dir(\"REQUIRE\")\" and call \"Pkg.resolve()\". - -"), - -("Base.Pkg","clone","clone(url[, pkg]) - - Clone a package directly from the git URL \"url\". The package does - not need to be a registered in \"Pkg.dir(\"METADATA\")\". The - package repo is cloned by the name \"pkg\" if provided; if not - provided, \"pkg\" is determined automatically from \"url\". - -"), - -("Base.Pkg","clone","clone(pkg) - - If \"pkg\" has a URL registered in \"Pkg.dir(\"METADATA\")\", clone - it from that URL on the default branch. The package does not need - to have any registered versions. - -"), - -("Base.Pkg","available","available() -> Vector{ASCIIString} - - Returns the names of available packages. - -"), - -("Base.Pkg","available","available(pkg) -> Vector{VersionNumber} - - Returns the version numbers available for package \"pkg\". - -"), - -("Base.Pkg","installed","installed() -> Dict{ASCIIString,VersionNumber} - - Returns a dictionary mapping installed package names to the - installed version number of each package. - -"), - -("Base.Pkg","installed","installed(pkg) -> Void | VersionNumber - - If \"pkg\" is installed, return the installed version number, - otherwise return \"nothing\". - -"), - -("Base.Pkg","status","status() - - Prints out a summary of what packages are installed and what - version and state they're in. - -"), - -("Base.Pkg","update","update() - - Update package the metadata repo – kept in - \"Pkg.dir(\"METADATA\")\" – then update any fixed packages that can - safely be pulled from their origin; then call \"Pkg.resolve()\" to - determine a new optimal set of packages versions. - -"), - -("Base.Pkg","checkout","checkout(pkg[, branch=\"master\"]) - - Checkout the \"Pkg.dir(pkg)\" repo to the branch \"branch\". - Defaults to checking out the \"master\" branch. To go back to using - the newest compatible released version, use \"Pkg.free(pkg)\" - -"), - -("Base.Pkg","pin","pin(pkg) - - Pin \"pkg\" at the current version. To go back to using the newest - compatible released version, use \"Pkg.free(pkg)\" - -"), - -("Base.Pkg","pin","pin(pkg, version) - - Pin \"pkg\" at registered version \"version\". - -"), - -("Base.Pkg","free","free(pkg) - - Free the package \"pkg\" to be managed by the package manager - again. It calls \"Pkg.resolve()\" to determine optimal package - versions after. This is an inverse for both \"Pkg.checkout\" and - \"Pkg.pin\". - - You can also supply an iterable collection of package names, e.g., - \"Pkg.free((\"Pkg1\", \"Pkg2\"))\" to free multiple packages at - once. - -"), - -("Base.Pkg","build","build() - - Run the build scripts for all installed packages in depth-first - recursive order. - -"), - -("Base.Pkg","build","build(pkgs...) - - Run the build script in \"deps/build.jl\" for each package in - \"pkgs\" and all of their dependencies in depth-first recursive - order. This is called automatically by \"Pkg.resolve()\" on all - installed or updated packages. - -"), - -("Base.Pkg","generate","generate(pkg, license) - - Generate a new package named \"pkg\" with one of these license - keys: \"\"MIT\"\", \"\"BSD\"\" or \"\"ASL\"\". If you want to make - a package with a different license, you can edit it afterwards. - Generate creates a git repo at \"Pkg.dir(pkg)\" for the package and - inside it \"LICENSE.md\", \"README.md\", \"REQUIRE\", the julia - entrypoint \"\$pkg/src/\$pkg.jl\", and Travis and AppVeyor CI - configuration files \".travis.yml\" and \"appveyor.yml\". - -"), - -("Base.Pkg","register","register(pkg[, url]) - - Register \"pkg\" at the git URL \"url\", defaulting to the - configured origin URL of the git repo \"Pkg.dir(pkg)\". - -"), - -("Base.Pkg","tag","tag(pkg[, ver[, commit]]) - - Tag \"commit\" as version \"ver\" of package \"pkg\" and create a - version entry in \"METADATA\". If not provided, \"commit\" defaults - to the current commit of the \"pkg\" repo. If \"ver\" is one of the - symbols \":patch\", \":minor\", \":major\" the next patch, minor or - major version is used. If \"ver\" is not provided, it defaults to - \":patch\". - -"), - -("Base.Pkg","publish","publish() - - For each new package version tagged in \"METADATA\" not already - published, make sure that the tagged package commits have been - pushed to the repo at the registered URL for the package and if - they all have, open a pull request to \"METADATA\". - -"), - -("Base.Pkg","test","test() - - Run the tests for all installed packages ensuring that each - package's test dependencies are installed for the duration of the - test. A package is tested by running its \"test/runtests.jl\" file - and test dependencies are specified in \"test/REQUIRE\". - -"), - -("Base.Pkg","test","test(pkgs...) - - Run the tests for each package in \"pkgs\" ensuring that each - package's test dependencies are installed for the duration of the - test. A package is tested by running its \"test/runtests.jl\" file - and test dependencies are specified in \"test/REQUIRE\". - -"), - -("Base","@profile","@profile() - - \"@profile \" runs your expression while taking - periodic backtraces. These are appended to an internal buffer of - backtraces. - -"), - -("Base.Profile","clear","clear() - - Clear any existing backtraces from the internal buffer. - -"), - -("Base.Profile","print","print([io::IO = STDOUT], [data::Vector]; format = :tree, C = false, combine = true, cols = tty_cols()) - - Prints profiling results to \"io\" (by default, \"STDOUT\"). If you - do not supply a \"data\" vector, the internal buffer of accumulated - backtraces will be used. \"format\" can be \":tree\" or \":flat\". - If \"C==true\", backtraces from C and Fortran code are shown. - \"combine==true\" merges instruction pointers that correspond to - the same line of code. \"cols\" controls the width of the display. - -"), - -("Base.Profile","print","print([io::IO = STDOUT], data::Vector, lidict::Dict; format = :tree, combine = true, cols = tty_cols()) - - Prints profiling results to \"io\". This variant is used to examine - results exported by a previous call to \"retrieve()\". Supply the - vector \"data\" of backtraces and a dictionary \"lidict\" of line - information. - -"), - -("Base.Profile","init","init(; n::Integer, delay::Float64) - - Configure the \"delay\" between backtraces (measured in seconds), - and the number \"n\" of instruction pointers that may be stored. - Each instruction pointer corresponds to a single line of code; - backtraces generally consist of a long list of instruction - pointers. Default settings can be obtained by calling this function - with no arguments, and each can be set independently using keywords - or in the order \"(n, delay)\". - -"), - -("Base.Profile","fetch","fetch() -> data - - Returns a reference to the internal buffer of backtraces. Note that - subsequent operations, like \"clear()\", can affect \"data\" unless - you first make a copy. Note that the values in \"data\" have - meaning only on this machine in the current session, because it - depends on the exact memory addresses used in JIT-compiling. This - function is primarily for internal use; \"retrieve()\" may be a - better choice for most users. - -"), - -("Base.Profile","retrieve","retrieve() -> data, lidict - - \"Exports\" profiling results in a portable format, returning the - set of all backtraces (\"data\") and a dictionary that maps the - (session-specific) instruction pointers in \"data\" to \"LineInfo\" - values that store the file name, function name, and line number. - This function allows you to save profiling results for future - analysis. - -"), - -("Base.Profile","callers","callers(funcname[, data, lidict][, filename=][, linerange=]) -> Vector{Tuple{count, linfo}} - - Given a previous profiling run, determine who called a particular - function. Supplying the filename (and optionally, range of line - numbers over which the function is defined) allows you to - disambiguate an overloaded method. The returned value is a vector - containing a count of the number of calls and line information - about the caller. One can optionally supply backtrace data - obtained from \"retrieve()\"; otherwise, the current internal - profile buffer is used. - -"), - -("Base.Profile","clear_malloc_data","clear_malloc_data() - - Clears any stored memory allocation data when running julia with \" - --track-allocation\". Execute the command(s) you want to test (to - force JIT-compilation), then call \"clear_malloc_data()\". Then - execute your command(s) again, quit Julia, and examine the - resulting \"*.mem\" files. - -"), - - -("Base","sort!","sort!(v, [alg=,] [by=,] [lt=,] [rev=false]) - - Sort the vector \"v\" in place. \"QuickSort\" is used by default - for numeric arrays while \"MergeSort\" is used for other arrays. - You can specify an algorithm to use via the \"alg\" keyword (see - Sorting Algorithms for available algorithms). The \"by\" keyword - lets you provide a function that will be applied to each element - before comparison; the \"lt\" keyword allows providing a custom - \"less than\" function; use \"rev=true\" to reverse the sorting - order. These options are independent and can be used together in - all possible combinations: if both \"by\" and \"lt\" are specified, - the \"lt\" function is applied to the result of the \"by\" - function; \"rev=true\" reverses whatever ordering specified via the - \"by\" and \"lt\" keywords. - -"), - -("Base","sort","sort(v, [alg=,] [by=,] [lt=,] [rev=false]) - - Variant of \"sort!\" that returns a sorted copy of \"v\" leaving - \"v\" itself unmodified. - -"), - -("Base","sort","sort(A, dim, [alg=,] [by=,] [lt=,] [rev=false]) - - Sort a multidimensional array \"A\" along the given dimension. - -"), - -("Base","sortperm","sortperm(v, [alg=,] [by=,] [lt=,] [rev=false]) - - Return a permutation vector of indices of \"v\" that puts it in - sorted order. Specify \"alg\" to choose a particular sorting - algorithm (see Sorting Algorithms). \"MergeSort\" is used by - default, and since it is stable, the resulting permutation will be - the lexicographically first one that puts the input array into - sorted order – i.e. indices of equal elements appear in ascending - order. If you choose a non-stable sorting algorithm such as - \"QuickSort\", a different permutation that puts the array into - order may be returned. The order is specified using the same - keywords as \"sort!\". - - See also \"sortperm!()\" - -"), - -("Base","sortperm!","sortperm!(ix, v, [alg=,] [by=,] [lt=,] [rev=false,] [initialized=false]) - - Like \"sortperm\", but accepts a preallocated index vector \"ix\". - If \"initialized\" is \"false\" (the default), ix is initialized to - contain the values \"1:length(v)\". - - See also \"sortperm()\" - -"), - -("Base","sortrows","sortrows(A, [alg=,] [by=,] [lt=,] [rev=false]) - - Sort the rows of matrix \"A\" lexicographically. - -"), - -("Base","sortcols","sortcols(A, [alg=,] [by=,] [lt=,] [rev=false]) - - Sort the columns of matrix \"A\" lexicographically. - -"), - -("Base","issorted","issorted(v, [by=,] [lt=,] [rev=false]) - - Test whether a vector is in sorted order. The \"by\", \"lt\" and - \"rev\" keywords modify what order is considered to be sorted just - as they do for \"sort\". - -"), - -("Base","searchsorted","searchsorted(a, x, [by=,] [lt=,] [rev=false]) - - Returns the range of indices of \"a\" which compare as equal to - \"x\" according to the order specified by the \"by\", \"lt\" and - \"rev\" keywords, assuming that \"a\" is already sorted in that - order. Returns an empty range located at the insertion point if - \"a\" does not contain values equal to \"x\". - -"), - -("Base","searchsortedfirst","searchsortedfirst(a, x, [by=,] [lt=,] [rev=false]) - - Returns the index of the first value in \"a\" greater than or equal - to \"x\", according to the specified order. Returns \"length(a)+1\" - if \"x\" is greater than all values in \"a\". - -"), - -("Base","searchsortedlast","searchsortedlast(a, x, [by=,] [lt=,] [rev=false]) - - Returns the index of the last value in \"a\" less than or equal to - \"x\", according to the specified order. Returns \"0\" if \"x\" is - less than all values in \"a\". - -"), - -("Base","select!","select!(v, k, [by=,] [lt=,] [rev=false]) - - Partially sort the vector \"v\" in place, according to the order - specified by \"by\", \"lt\" and \"rev\" so that the value at index - \"k\" (or range of adjacent values if \"k\" is a range) occurs at - the position where it would appear if the array were fully sorted - via a non-stable algorithm. If \"k\" is a single index, that value - is returned; if \"k\" is a range, an array of values at those - indices is returned. Note that \"select!\" does not fully sort the - input array. - -"), - -("Base","select","select(v, k, [by=,] [lt=,] [rev=false]) - - Variant of \"select!\" which copies \"v\" before partially sorting - it, thereby returning the same thing as \"select!\" but leaving - \"v\" unmodified. - -"), - -("Base","selectperm","selectperm(v, k, [alg=,] [by=,] [lt=,] [rev=false]) - - Return a partial permutation of the the vector \"v\", according to - the order specified by \"by\", \"lt\" and \"rev\", so that - \"v[output]\" returns the first \"k\" (or range of adjacent values - if \"k\" is a range) values of a fully sorted version of \"v\". If - \"k\" is a single index (Integer), an array of the first \"k\" - indices is returned; if \"k\" is a range, an array of those indices - is returned. Note that the handling of integer values for \"k\" is - different from \"select\" in that it returns a vector of \"k\" - elements instead of just the \"k\" th element. Also note that this - is equivalent to, but more efficient than, calling - \"sortperm(...)[k]\" - -"), - -("Base","selectperm!","selectperm!(ix, v, k, [alg=,] [by=,] [lt=,] [rev=false,] [initialized=false]) - - Like \"selectperm\", but accepts a preallocated index vector - \"ix\". If \"initialized\" is \"false\" (the default), ix is - initialized to contain the values \"1:length(ix)\". - -"), - -("Base","length","length(s) - - The number of characters in string \"s\". - -"), - -("Base","sizeof","sizeof(s::AbstractString) - - The number of bytes in string \"s\". - -"), - -("Base","*","*(s, t) - - Concatenate strings. The \"*\" operator is an alias to this - function. - - julia> \"Hello \" * \"world\" - \"Hello world\" - -"), - -("Base","^","^(s, n) - - Repeat \"n\" times the string \"s\". The \"^\" operator is an alias - to this function. - - julia> \"Test \"^3 - \"Test Test Test \" - -"), - -("Base","string","string(xs...) - - Create a string from any values using the \"print\" function. - -"), - -("Base","repr","repr(x) - - Create a string from any value using the \"showall\" function. - -"), - -("Base","bytestring","bytestring(::Ptr{UInt8}[, length]) - - Create a string from the address of a C (0-terminated) string - encoded in ASCII or UTF-8. A copy is made; the ptr can be safely - freed. If \"length\" is specified, the string does not have to be - 0-terminated. - -"), - -("Base","bytestring","bytestring(s) - - Convert a string to a contiguous byte array representation - appropriate for passing it to C functions. The string will be - encoded as either ASCII or UTF-8. - -"), - -("Base","ascii","ascii(::Array{UInt8, 1}) - - Create an ASCII string from a byte array. - -"), - -("Base","ascii","ascii(s) - - Convert a string to a contiguous ASCII string (all characters must - be valid ASCII characters). - -"), - -("Base","ascii","ascii(::Ptr{UInt8}[, length]) - - Create an ASCII string from the address of a C (0-terminated) - string encoded in ASCII. A copy is made; the ptr can be safely - freed. If \"length\" is specified, the string does not have to be - 0-terminated. - -"), - -("Base","utf8","utf8(::Array{UInt8, 1}) - - Create a UTF-8 string from a byte array. - -"), - -("Base","utf8","utf8(::Ptr{UInt8}[, length]) - - Create a UTF-8 string from the address of a C (0-terminated) string - encoded in UTF-8. A copy is made; the ptr can be safely freed. If - \"length\" is specified, the string does not have to be - 0-terminated. - -"), - -("Base","utf8","utf8(s) - - Convert a string to a contiguous UTF-8 string (all characters must - be valid UTF-8 characters). - -"), - -("Base","normalize_string","normalize_string(s, normalform::Symbol) - - Normalize the string \"s\" according to one of the four \"normal - forms\" of the Unicode standard: \"normalform\" can be \":NFC\", - \":NFD\", \":NFKC\", or \":NFKD\". Normal forms C (canonical - composition) and D (canonical decomposition) convert different - visually identical representations of the same abstract string into - a single canonical form, with form C being more compact. Normal - forms KC and KD additionally canonicalize \"compatibility - equivalents\": they convert characters that are abstractly similar - but visually distinct into a single canonical choice (e.g. they - expand ligatures into the individual characters), with form KC - being more compact. - - Alternatively, finer control and additional transformations may be - be obtained by calling *normalize_string(s; keywords...)*, where - any number of the following boolean keywords options (which all - default to \"false\" except for \"compose\") are specified: - - * \"compose=false\": do not perform canonical composition - - * \"decompose=true\": do canonical decomposition instead of - canonical composition (\"compose=true\" is ignored if present) - - * \"compat=true\": compatibility equivalents are canonicalized - - * \"casefold=true\": perform Unicode case folding, e.g. for case- - insensitive string comparison - - * \"newline2lf=true\", \"newline2ls=true\", or - \"newline2ps=true\": convert various newline sequences (LF, CRLF, - CR, NEL) into a linefeed (LF), line-separation (LS), or - paragraph-separation (PS) character, respectively - - * \"stripmark=true\": strip diacritical marks (e.g. accents) - - * \"stripignore=true\": strip Unicode's \"default ignorable\" - characters (e.g. the soft hyphen or the left-to-right marker) - - * \"stripcc=true\": strip control characters; horizontal tabs and - form feeds are converted to spaces; newlines are also converted - to spaces unless a newline-conversion flag was specified - - * \"rejectna=true\": throw an error if unassigned code points are - found - - * \"stable=true\": enforce Unicode Versioning Stability - - For example, NFKC corresponds to the options \"compose=true, - compat=true, stable=true\". - -"), - -("Base","graphemes","graphemes(s) -> iterator over substrings of s - - Returns an iterator over substrings of \"s\" that correspond to the - extended graphemes in the string, as defined by Unicode UAX #29. - (Roughly, these are what users would perceive as single characters, - even though they may contain more than one codepoint; for example a - letter combined with an accent mark is a single grapheme.) - -"), - -("Base","isvalid","isvalid(value) -> Bool - - Returns true if the given value is valid for its type, which - currently can be one of \"Char\", \"ASCIIString\", \"UTF8String\", - \"UTF16String\", or \"UTF32String\" - -"), - -("Base","isvalid","isvalid(T, value) -> Bool - - Returns true if the given value is valid for that type. Types - currently can be \"Char\", \"ASCIIString\", \"UTF8String\", - \"UTF16String\", or \"UTF32String\" Values for \"Char\" can be of - type \"Char\" or \"UInt32\" Values for \"ASCIIString\" and - \"UTF8String\" can be of that type, or \"Vector{UInt8}\" Values for - \"UTF16String\" can be \"UTF16String\" or \"Vector{UInt16}\" Values - for \"UTF32String\" can be \"UTF32String\", \"Vector{Char}\" or - \"Vector{UInt32}\" - -"), - -("Base","is_assigned_char","is_assigned_char(c) -> Bool - - Returns true if the given char or integer is an assigned Unicode - code point. - -"), - -("Base","ismatch","ismatch(r::Regex, s::AbstractString) -> Bool - - Test whether a string contains a match of the given regular - expression. - -"), - -("Base","match","match(r::Regex, s::AbstractString[, idx::Integer[, addopts]]) - - Search for the first match of the regular expression \"r\" in \"s\" - and return a RegexMatch object containing the match, or nothing if - the match failed. The matching substring can be retrieved by - accessing \"m.match\" and the captured sequences can be retrieved - by accessing \"m.captures\" The optional \"idx\" argument specifies - an index at which to start the search. - -"), - -("Base","eachmatch","eachmatch(r::Regex, s::AbstractString[, overlap::Bool=false]) - - Search for all matches of a the regular expression \"r\" in \"s\" - and return a iterator over the matches. If overlap is true, the - matching sequences are allowed to overlap indices in the original - string, otherwise they must be from distinct character ranges. - -"), - -("Base","matchall","matchall(r::Regex, s::AbstractString[, overlap::Bool=false]) -> Vector{AbstractString} - - Return a vector of the matching substrings from eachmatch. - -"), - -("Base","lpad","lpad(string, n, p) - - Make a string at least \"n\" columns wide when printed, by padding - on the left with copies of \"p\". - -"), - -("Base","rpad","rpad(string, n, p) - - Make a string at least \"n\" columns wide when printed, by padding - on the right with copies of \"p\". - -"), - -("Base","search","search(string, chars[, start]) - - Search for the first occurrence of the given characters within the - given string. The second argument may be a single character, a - vector or a set of characters, a string, or a regular expression - (though regular expressions are only allowed on contiguous strings, - such as ASCII or UTF-8 strings). The third argument optionally - specifies a starting index. The return value is a range of indexes - where the matching sequence is found, such that \"s[search(s,x)] == - x\": - - \"search(string, \"substring\")\" = \"start:end\" such that - \"string[start:end] == \"substring\"\", or \"0:-1\" if unmatched. - - \"search(string, 'c')\" = \"index\" such that - \"string[index] == 'c'\", or \"0\" if unmatched. - -"), - -("Base","rsearch","rsearch(string, chars[, start]) - - Similar to \"search\", but returning the last occurrence of the - given characters within the given string, searching in reverse from - \"start\". - -"), - -("Base","searchindex","searchindex(string, substring[, start]) - - Similar to \"search\", but return only the start index at which the - substring is found, or 0 if it is not. - -"), - -("Base","rsearchindex","rsearchindex(string, substring[, start]) - - Similar to \"rsearch\", but return only the start index at which - the substring is found, or 0 if it is not. - -"), - -("Base","contains","contains(haystack, needle) - - Determine whether the second argument is a substring of the first. - -"), - -("Base","replace","replace(string, pat, r[, n]) - - Search for the given pattern \"pat\", and replace each occurrence - with \"r\". If \"n\" is provided, replace at most \"n\" - occurrences. As with search, the second argument may be a single - character, a vector or a set of characters, a string, or a regular - expression. If \"r\" is a function, each occurrence is replaced - with \"r(s)\" where \"s\" is the matched substring. If \"pat\" is a - regular expression and \"r\" is a \"SubstitutionString\", then - capture group references in \"r\" are replaced with the - corresponding matched text. - -"), - -("Base","split","split(string, [chars]; limit=0, keep=true) - - Return an array of substrings by splitting the given string on - occurrences of the given character delimiters, which may be - specified in any of the formats allowed by \"search\"'s second - argument (i.e. a single character, collection of characters, - string, or regular expression). If \"chars\" is omitted, it - defaults to the set of all space characters, and \"keep\" is taken - to be false. The two keyword arguments are optional: they are are a - maximum size for the result and a flag determining whether empty - fields should be kept in the result. - -"), - -("Base","rsplit","rsplit(string, [chars]; limit=0, keep=true) - - Similar to \"split\", but starting from the end of the string. - -"), - -("Base","strip","strip(string[, chars]) - - Return \"string\" with any leading and trailing whitespace removed. - If \"chars\" (a character, or vector or set of characters) is - provided, instead remove characters contained in it. - -"), - -("Base","lstrip","lstrip(string[, chars]) - - Return \"string\" with any leading whitespace removed. If \"chars\" - (a character, or vector or set of characters) is provided, instead - remove characters contained in it. - -"), - -("Base","rstrip","rstrip(string[, chars]) - - Return \"string\" with any trailing whitespace removed. If - \"chars\" (a character, or vector or set of characters) is - provided, instead remove characters contained in it. - -"), - -("Base","startswith","startswith(string, prefix | chars) - - Returns \"true\" if \"string\" starts with \"prefix\". If the - second argument is a vector or set of characters, tests whether the - first character of \"string\" belongs to that set. - -"), - -("Base","endswith","endswith(string, suffix | chars) - - Returns \"true\" if \"string\" ends with \"suffix\". If the second - argument is a vector or set of characters, tests whether the last - character of \"string\" belongs to that set. - -"), - -("Base","uppercase","uppercase(string) - - Returns \"string\" with all characters converted to uppercase. - -"), - -("Base","lowercase","lowercase(string) - - Returns \"string\" with all characters converted to lowercase. - -"), - -("Base","ucfirst","ucfirst(string) - - Returns \"string\" with the first character converted to uppercase. - -"), - -("Base","lcfirst","lcfirst(string) - - Returns \"string\" with the first character converted to lowercase. - -"), - -("Base","join","join(strings, delim[, last]) - - Join an array of \"strings\" into a single string, inserting the - given delimiter between adjacent strings. If \"last\" is given, it - will be used instead of \"delim\" between the last two strings. For - example, \"join([\"apples\", \"bananas\", \"pineapples\"], \", \", - \" and \") == \"apples, bananas and pineapples\"\". - - \"strings\" can be any iterable over elements \"x\" which are - convertible to strings via \"print(io::IOBuffer, x)\". - -"), - -("Base","chop","chop(string) - - Remove the last character from a string - -"), - -("Base","chomp","chomp(string) - - Remove a trailing newline from a string - -"), - -("Base","ind2chr","ind2chr(string, i) - - Convert a byte index to a character index - -"), - -("Base","chr2ind","chr2ind(string, i) - - Convert a character index to a byte index - -"), - -("Base","isvalid","isvalid(str, i) - - Tells whether index \"i\" is valid for the given string - -"), - -("Base","nextind","nextind(str, i) - - Get the next valid string index after \"i\". Returns a value - greater than \"endof(str)\" at or after the end of the string. - -"), - -("Base","prevind","prevind(str, i) - - Get the previous valid string index before \"i\". Returns a value - less than \"1\" at the beginning of the string. - -"), - -("Base","randstring","randstring([rng], len=8) - - Create a random ASCII string of length \"len\", consisting of - upper- and lower-case letters and the digits 0-9. The optional - \"rng\" argument specifies a random number generator, see *Random - Numbers*. - -"), - -("Base","charwidth","charwidth(c) - - Gives the number of columns needed to print a character. - -"), - -("Base","strwidth","strwidth(s) - - Gives the number of columns needed to print a string. - -"), - -("Base","isalnum","isalnum(c::Union{Char, AbstractString}) -> Bool - - Tests whether a character is alphanumeric, or whether this is true - for all elements of a string. A character is classified as - alphabetic if it belongs to the Unicode general category Letter or - Number, i.e. a character whose category code begins with 'L' or - 'N'. - -"), - -("Base","isalpha","isalpha(c::Union{Char, AbstractString}) -> Bool - - Tests whether a character is alphabetic, or whether this is true - for all elements of a string. A character is classified as - alphabetic if it belongs to the Unicode general category Letter, - i.e. a character whose category code begins with 'L'. - -"), - -("Base","isascii","isascii(c::Union{Char, AbstractString}) -> Bool - - Tests whether a character belongs to the ASCII character set, or - whether this is true for all elements of a string. - -"), - -("Base","iscntrl","iscntrl(c::Union{Char, AbstractString}) -> Bool - - Tests whether a character is a control character, or whether this - is true for all elements of a string. Control characters are the - non-printing characters of the Latin-1 subset of Unicode. - -"), - -("Base","isdigit","isdigit(c::Union{Char, AbstractString}) -> Bool - - Tests whether a character is a numeric digit (0-9), or whether this - is true for all elements of a string. - -"), - -("Base","isgraph","isgraph(c::Union{Char, AbstractString}) -> Bool - - Tests whether a character is printable, and not a space, or whether - this is true for all elements of a string. Any character that - would cause a printer to use ink should be classified with - isgraph(c)==true. - -"), - -("Base","islower","islower(c::Union{Char, AbstractString}) -> Bool - - Tests whether a character is a lowercase letter, or whether this is - true for all elements of a string. A character is classified as - lowercase if it belongs to Unicode category Ll, Letter: Lowercase. - -"), - -("Base","isnumber","isnumber(c::Union{Char, AbstractString}) -> Bool - - Tests whether a character is numeric, or whether this is true for - all elements of a string. A character is classified as numeric if - it belongs to the Unicode general category Number, i.e. a character - whose category code begins with 'N'. - -"), - -("Base","isprint","isprint(c::Union{Char, AbstractString}) -> Bool - - Tests whether a character is printable, including spaces, but not a - control character. For strings, tests whether this is true for all - elements of the string. - -"), - -("Base","ispunct","ispunct(c::Union{Char, AbstractString}) -> Bool - - Tests whether a character belongs to the Unicode general category - Punctuation, i.e. a character whose category code begins with 'P'. - For strings, tests whether this is true for all elements of the - string. - -"), - -("Base","isspace","isspace(c::Union{Char, AbstractString}) -> Bool - - Tests whether a character is any whitespace character. Includes - ASCII characters '\\t', '\\n', '\\v', '\\f', '\\r', and ' ', - Latin-1 character U+0085, and characters in Unicode category Zs. - For strings, tests whether this is true for all elements of the - string. - -"), - -("Base","isupper","isupper(c::Union{Char, AbstractString}) -> Bool - - Tests whether a character is an uppercase letter, or whether this - is true for all elements of a string. A character is classified - as uppercase if it belongs to Unicode category Lu, Letter: - Uppercase, or Lt, Letter: Titlecase. - -"), - -("Base","isxdigit","isxdigit(c::Union{Char, AbstractString}) -> Bool - - Tests whether a character is a valid hexadecimal digit, or whether - this is true for all elements of a string. - -"), - -("Base","symbol","symbol(x...) -> Symbol - - Create a \"Symbol\" by concatenating the string representations of - the arguments together. - -"), - -("Base","escape_string","escape_string(str::AbstractString) -> AbstractString - - General escaping of traditional C and Unicode escape sequences. See - \"print_escaped()\" for more general escaping. - -"), - -("Base","unescape_string","unescape_string(s::AbstractString) -> AbstractString - - General unescaping of traditional C and Unicode escape sequences. - Reverse of \"escape_string()\". See also \"print_unescaped()\". - -"), - -("Base","utf16","utf16(s) - - Create a UTF-16 string from a byte array, array of \"UInt16\", or - any other string type. (Data must be valid UTF-16. Conversions of - byte arrays check for a byte-order marker in the first two bytes, - and do not include it in the resulting string.) - - Note that the resulting \"UTF16String\" data is terminated by the - NUL codepoint (16-bit zero), which is not treated as a character in - the string (so that it is mostly invisible in Julia); this allows - the string to be passed directly to external functions requiring - NUL-terminated data. This NUL is appended automatically by the - *utf16(s)* conversion function. If you have a \"UInt16\" array - \"A\" that is already NUL-terminated valid UTF-16 data, then you - can instead use *UTF16String(A)`* to construct the string without - making a copy of the data and treating the NUL as a terminator - rather than as part of the string. - -"), - -("Base","utf16","utf16(::Union{Ptr{UInt16}, Ptr{Int16}}[, length]) - - Create a string from the address of a NUL-terminated UTF-16 string. - A copy is made; the pointer can be safely freed. If \"length\" is - specified, the string does not have to be NUL-terminated. - -"), - -("Base","utf32","utf32(s) - - Create a UTF-32 string from a byte array, array of \"Char\" or - \"UInt32\", or any other string type. (Conversions of byte arrays - check for a byte-order marker in the first four bytes, and do not - include it in the resulting string.) - - Note that the resulting \"UTF32String\" data is terminated by the - NUL codepoint (32-bit zero), which is not treated as a character in - the string (so that it is mostly invisible in Julia); this allows - the string to be passed directly to external functions requiring - NUL-terminated data. This NUL is appended automatically by the - *utf32(s)* conversion function. If you have a \"Char\" or - \"UInt32\" array \"A\" that is already NUL-terminated UTF-32 data, - then you can instead use *UTF32String(A)`* to construct the string - without making a copy of the data and treating the NUL as a - terminator rather than as part of the string. - -"), - -("Base","utf32","utf32(::Union{Ptr{Char}, Ptr{UInt32}, Ptr{Int32}}[, length]) - - Create a string from the address of a NUL-terminated UTF-32 string. - A copy is made; the pointer can be safely freed. If \"length\" is - specified, the string does not have to be NUL-terminated. - -"), - -("Base","wstring","wstring(s) - - This is a synonym for either \"utf32(s)\" or \"utf16(s)\", - depending on whether \"Cwchar_t\" is 32 or 16 bits, respectively. - The synonym \"WString\" for \"UTF32String\" or \"UTF16String\" is - also provided. - -"), - -("Base","runtests","runtests([tests=[\"all\"][, numcores=iceil(CPU_CORES/2)]]) - - Run the Julia unit tests listed in \"tests\", which can be either a - string or an array of strings, using \"numcores\" processors. (not - exported) - -"), - -("Base.Test","@test","@test(ex) - - Test the expression \"ex\" and calls the current handler to handle - the result. - -"), - -("Base.Test","@test_throws","@test_throws(extype, ex) - - Test that the expression \"ex\" throws an exception of type - \"extype\" and calls the current handler to handle the result. The - default handler returns the exception if it is of the expected - type. - -"), - -("Base.Test","@test_approx_eq","@test_approx_eq(a, b) - - Test two floating point numbers \"a\" and \"b\" for equality taking - in account small numerical errors. - -"), - -("Base.Test","@test_approx_eq_eps","@test_approx_eq_eps(a, b, tol) - - Test two floating point numbers \"a\" and \"b\" for equality taking - in account a margin of tolerance given by \"tol\". - -"), - -("Base.Test","with_handler","with_handler(f, handler) - - Run the function \"f\" using the \"handler\" as the handler. - -"), - - -] diff --git a/test/docs.jl b/test/docs.jl index c47eae20fe678..559d8e8cfb1b3 100644 --- a/test/docs.jl +++ b/test/docs.jl @@ -22,73 +22,6 @@ end @test (@doc ModuleMacroDoc) == "I am a module" @test (@doc ModuleMacroDoc.@m) == ["I am a macro"] -# apropos function testing - -@test sprint(apropos, "non-documented object") == "No help information found.\n" - -# issue 11438 (partial) - -for (typ, name) in [ - (RoundingMode, "RoundingMode"), - (Dates.DateTime, "DateTime"), - (Libc.TmStruct, "TmStruct") - ] - @test sprint(help, typ) == sprint(help, name) -end - -module DataTypeHelpTest - -module M - type T end -end - -module N - type T end -end - -module P - module R - type U end - type T end - end - import .R.T -end - -const mod = string(current_module()) - -Base.Help.eval(quote - - init_help() - - import $(parse(mod)) - import $(parse(mod)): M, N, P - - const mod = $mod - - MODULE_DICT["T"] = ["$mod.M","$mod.N","$mod.P"] - MODULE_DICT["U"] = ["$mod.P","$mod.P.R"] - - FUNCTION_DICT["$mod.M.T"] = ["M.T"] - FUNCTION_DICT["$mod.N.T"] = ["N.T"] - FUNCTION_DICT["$mod.P.T"] = ["P.R.T"] - FUNCTION_DICT["$mod.P.U"] = ["P.U"] - FUNCTION_DICT["$mod.P.R.U"] = ["P.R.U"] - -end) - -import Base.Test.@test - -@test sprint(help, M.T) == "M.T\n" -@test sprint(help, N.T) == "N.T\n" -@test sprint(help, P.T) == "P.R.T\n" -@test sprint(help, P.R.U) == "P.R.U\n" -@test sprint(help, "$mod.M.T") == "M.T\n" -@test sprint(help, "$mod.N.T") == "N.T\n" -@test sprint(help, "$mod.P.T") == "P.R.T\n" -@test sprint(help, "$mod.P.R.U") == "P.R.U\n" -@test sprint(help, "T") == "M.T\n\nN.T\n\nP.R.T\n" -end - # General tests for docstrings. module DocsTest From 55339fca71e643db614c459c55fd742fdef8c4d0 Mon Sep 17 00:00:00 2001 From: Mike Innes Date: Fri, 31 Jul 2015 11:21:25 +0100 Subject: [PATCH 07/10] further help removals --- base/docs/basedocs.jl | 2 -- base/exports.jl | 2 -- contrib/BBEditTextWrangler-julia.plist | 2 -- doc/DocCheck.jl | 1 - doc/stdlib/base.rst | 8 -------- 5 files changed, 15 deletions(-) diff --git a/base/docs/basedocs.jl b/base/docs/basedocs.jl index b3db3a11b4f19..55370d22ff81b 100644 --- a/base/docs/basedocs.jl +++ b/base/docs/basedocs.jl @@ -16,8 +16,6 @@ const intro = doc""" For help on a specific function or macro, type `?` followed by its name, e.g. `?fft`, `?@time` or `?html`, and press enter. - - You can also use `apropos("...")` to search the documentation. """ keywords[:help] = keywords[:?] = keywords[:julia] = keywords[:wtf] = intro diff --git a/base/exports.jl b/base/exports.jl index 7794fd0d5ee44..8799710e5ea2a 100644 --- a/base/exports.jl +++ b/base/exports.jl @@ -1076,7 +1076,6 @@ export symbol, # help and reflection - apropos, current_module, edit, code_typed, @@ -1086,7 +1085,6 @@ export code_native, fullname, functionloc, - help, isconst, isgeneric, isinteractive, diff --git a/contrib/BBEditTextWrangler-julia.plist b/contrib/BBEditTextWrangler-julia.plist index 9755f658062e5..2581462dda7e7 100644 --- a/contrib/BBEditTextWrangler-julia.plist +++ b/contrib/BBEditTextWrangler-julia.plist @@ -189,7 +189,6 @@ any any! append! - apropos ascii asec asecd @@ -497,7 +496,6 @@ hash haskey hcat - help hessfact hessfact! hex diff --git a/doc/DocCheck.jl b/doc/DocCheck.jl index 6f1968b9b23aa..59be92428a7ab 100644 --- a/doc/DocCheck.jl +++ b/doc/DocCheck.jl @@ -13,7 +13,6 @@ module DocCheck -import Base.Help: init_help, FUNCTION_DICT, MODULE_DICT import Base: argtype_decl, uncompressed_ast export isdeprecated, isdocumented, undefined_exports, undocumented, undocumented_by_file, undocumented_rst, diff --git a/doc/stdlib/base.rst b/doc/stdlib/base.rst index 6b7fc16454b92..15d04f254a9e2 100644 --- a/doc/stdlib/base.rst +++ b/doc/stdlib/base.rst @@ -98,14 +98,6 @@ Getting Around Like ``include``, except reads code from the given string rather than from a file. Since there is no file path involved, no path processing or fetching from node 1 is done. -.. function:: help(name) - - Get help for a function. ``name`` can be an object or a string. - -.. function:: apropos(string) - - Search documentation for functions related to ``string``. - .. function:: which(f, types) Returns the method of ``f`` (a ``Method`` object) that would be called for arguments of the given types. From be7f7c65fba8ee267d4970b6da25a49e3dabc7c2 Mon Sep 17 00:00:00 2001 From: Mike Innes Date: Mon, 29 Jun 2015 21:07:51 -0400 Subject: [PATCH 08/10] genstdlib.jl regenerates the manual --- doc/genstdlib.jl | 92 ++++++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 92 insertions(+) create mode 100644 doc/genstdlib.jl diff --git a/doc/genstdlib.jl b/doc/genstdlib.jl new file mode 100644 index 0000000000000..0448766162abc --- /dev/null +++ b/doc/genstdlib.jl @@ -0,0 +1,92 @@ +using .Markdown +using Base.Markdown: MD + +cd(dirname(@__FILE__)) + +isop(func) = ismatch(r"[^\w@!.]|^!$", func) + +ident(mod, x) = "$mod.$(isop(x) ? "(:($x))" : x)" + +getdoc(mod, x) = try eval(parse("@doc $(ident(mod, x))")) catch e end + +flat_content(md) = md +flat_content(xs::Vector) = reduce((xs, x) -> vcat(xs,flat_content(x)), [], xs) +flat_content(md::MD) = flat_content(md.content) +flatten(md::MD) = MD(flat_content(md)) + +# issig(md) = isa(md, Markdown.Code) && length(split(md.code, "\n")) == 1 + +# function splitsig(md) +# md = flatten(md) +# sig = nothing +# if !isempty(md.content) && issig(md.content[1]) +# sig = shift!(md.content) +# end +# return md, sig +# end + +isrst(md) = + length(flatten(md).content) == 1 && + isa(flatten(md).content[1], Markdown.Code) && + flatten(md).content[1].language == "rst" + +torst(md) = isrst(md) ? flatten(md).content[1].code : Markdown.rst(md) + +function remsig(l, doc) + sig = l[15:end] + ls = split(doc, "\n") + contains(ls[2], sig) && (ls = ls[3:end]) + while ls[1] == "" shift!(ls) end + startswith(ls[1], " "^11) && (ls = ["::", ls...]) + join(ls, "\n") +end + +function translate(file) + @assert isfile(file) + ls = split(readall(file), "\n")[1:end-1] + doccing = false + func = nothing + mod = "Base" + + open(file, "w+") do io + for l in ls + if ismatch(r"^\.\. (current)?module::", l) + mod = match(r"^\.\. (current)?module:: ([\w\.]+)", l).captures[2] + println(io, l) + elseif startswith(l, ".. function::") + func = match(r".. function:: (@?[^\(\s\{]+)", l) + func == nothing && (warn("bad function $l"); continue) + func = func.captures[1] + doc = getdoc(mod, func) + + if doc == nothing || !isrst(doc) + doc == nothing ? + info("no docs for $(ident(mod, func))") : + info("can't convert docs for $(ident(mod, func))") + println(io, l) + doccing = false + continue + end + + doccing = true + println(io, l) + println(io) + for l in split(remsig(l, torst(doc)), "\n") + ismatch(r"^\s*$", l) ? println(io) : println(io, " ", l) + end + println(io) + elseif doccing && (startswith(l, " ") || ismatch(r"^\s*$", l)) + else + doccing = false + println(io, l) + end + end + end +end + +for folder in ["stdlib", "manual", "devdocs"] + println("\nConverting $folder/\n") + for file in readdir("$folder") + translate("$folder/$file") + end +end From dfc7168696c1ad031db99e43bdb799c271edec0c Mon Sep 17 00:00:00 2001 From: Mike Innes Date: Fri, 31 Jul 2015 11:25:46 +0100 Subject: [PATCH 09/10] regenerate the manual --- doc/devdocs/cartesian.rst | 5 + doc/stdlib/arrays.rst | 562 ++++++++++++++++++++++++++++- doc/stdlib/base.rst | 300 +++++++++++++++- doc/stdlib/c.rst | 37 ++ doc/stdlib/collections.rst | 714 ++++++++++++++++++++++++++++++++++++- doc/stdlib/dates.rst | 612 ++++++++++++++++++++++++++++++- doc/stdlib/file.rst | 18 +- doc/stdlib/io-network.rst | 625 +++++++++++++++++++++++++++++++- doc/stdlib/libc.rst | 5 +- doc/stdlib/linalg.rst | 666 ++++++++++++++++++++++++++++++++++ doc/stdlib/math.rst | 313 +++++++++++++++- doc/stdlib/numbers.rst | 42 ++- doc/stdlib/parallel.rst | 320 ++++++++++++++++- doc/stdlib/pkg.rst | 103 ++++++ doc/stdlib/profile.rst | 24 +- doc/stdlib/sort.rst | 15 +- doc/stdlib/strings.rst | 227 +++++++++++- doc/stdlib/test.rst | 2 - 18 files changed, 4540 insertions(+), 50 deletions(-) diff --git a/doc/devdocs/cartesian.rst b/doc/devdocs/cartesian.rst index 0e0bfd3608e1f..98fad0492420c 100644 --- a/doc/devdocs/cartesian.rst +++ b/doc/devdocs/cartesian.rst @@ -137,6 +137,8 @@ Macro reference ~~~~~~~~~~~~~~~ .. function:: @nloops N itersym rangeexpr bodyexpr + + :: @nloops N itersym rangeexpr preexpr bodyexpr @nloops N itersym rangeexpr preexpr postexpr bodyexpr @@ -191,6 +193,8 @@ Macro reference bounds-checking. .. function:: @nif N conditionexpr expr + + :: @nif N conditionexpr expr elseexpr Generates a sequence of ``if ... elseif ... else ... end`` statements. For example:: @@ -200,6 +204,7 @@ Macro reference would generate:: if i_1 > size(A, 1) + error("Dimension ", 1, " too big") elseif i_2 > size(A, 2) error("Dimension ", 2, " too big") diff --git a/doc/stdlib/arrays.rst b/doc/stdlib/arrays.rst index d137f4fe63974..d23098f5373f1 100644 --- a/doc/stdlib/arrays.rst +++ b/doc/stdlib/arrays.rst @@ -33,6 +33,16 @@ Basic functions Returns the number of elements in A + :: + length(collection) -> Integer + + For ordered, indexable collections, the maximum index ``i`` for which ``getindex(collection, i)`` is valid. For unordered collections, the number of elements. + + :: + length(s) + + The number of characters in string ``s``. + .. function:: eachindex(A...) Creates an iterable object for visiting each index of an AbstractArray ``A`` in an efficient manner. For array types that have opted into fast linear indexing (like ``Array``), this is simply the range ``1:length(A)``. For other array types, this returns a specialized Cartesian range to efficiently index into the array with indices specified for every dimension. For other iterables, including strings and dictionaries, this returns an iterator object supporting arbitrary index types (e.g. unevenly spaced or non-integer indices). @@ -100,8 +110,23 @@ largest range along each dimension. **Example** ``i, j, ... = ind2sub(size(A), indmax(A))`` provides the indices of the maximum element + :: + ind2sub(a, index) -> subscripts + + Returns a tuple of subscripts into array ``a`` corresponding to the linear index ``index`` + .. function:: ind2sub(a, index) -> subscripts + :: + ind2sub(dims, index) -> subscripts + + Returns a tuple of subscripts into an array with dimensions ``dims``, corresponding to the linear index ``index`` + + **Example** ``i, j, ... = ind2sub(size(A), indmax(A))`` provides the indices of the maximum element + + :: + ind2sub(a, index) -> subscripts + Returns a tuple of subscripts into array ``a`` corresponding to the linear index ``index`` .. function:: sub2ind(dims, i, j, k...) -> index @@ -121,23 +146,62 @@ Constructors Construct a 1-d array of the specified type. This is usually called with the syntax ``Type[]``. Element values can be specified using ``Type[a,b,c,...]``. + :: + getindex(A, inds...) + + Returns a subset of array ``A`` as specified by ``inds``, where each ``ind`` may be an ``Int``, a ``Range``, or a ``Vector``. See the manual section on :ref:`array indexing ` for details. + + :: + getindex(collection, key...) + + Retrieve the value(s) stored at the given key or index within a collection. + The syntax ``a[i,j,...]`` is converted by the compiler to + ``getindex(a, i, j, ...)``. + .. function:: cell(dims) Construct an uninitialized cell array (heterogeneous array). ``dims`` can be either a tuple or a series of integer arguments. + .. function:: zeros(type, dims) Create an array of all zeros of specified type. The type defaults to Float64 if not specified. + :: + zeros(A) + + Create an array of all zeros with the same element type and shape as A. + .. function:: zeros(A) + :: + zeros(type, dims) + + Create an array of all zeros of specified type. The type defaults to Float64 if not specified. + + :: + zeros(A) + Create an array of all zeros with the same element type and shape as A. .. function:: ones(type, dims) Create an array of all ones of specified type. The type defaults to Float64 if not specified. + :: + ones(A) + + Create an array of all ones with the same element type and shape as A. + .. function:: ones(A) + :: + ones(type, dims) + + Create an array of all ones of specified type. The type defaults to Float64 if not specified. + + :: + ones(A) + Create an array of all ones with the same element type and shape as A. .. function:: trues(dims) @@ -178,12 +242,48 @@ Constructors n-by-n identity matrix + :: + eye(m, n) + + m-by-n identity matrix + + :: + eye(A) + + Constructs an identity matrix of the same dimensions and type as ``A``. + .. function:: eye(m, n) + :: + eye(n) + + n-by-n identity matrix + + :: + eye(m, n) + m-by-n identity matrix + :: + eye(A) + + Constructs an identity matrix of the same dimensions and type as ``A``. + .. function:: eye(A) + :: + eye(n) + + n-by-n identity matrix + + :: + eye(m, n) + + m-by-n identity matrix + + :: + eye(A) + Constructs an identity matrix of the same dimensions and type as ``A``. .. function:: linspace(start, stop, n=100) @@ -227,8 +327,23 @@ Indexing, Assignment, and Concatenation .. function:: getindex(A, inds...) + :: + getindex(type[, elements...]) + + Construct a 1-d array of the specified type. This is usually called with the syntax ``Type[]``. Element values can be specified using ``Type[a,b,c,...]``. + + :: + getindex(A, inds...) + Returns a subset of array ``A`` as specified by ``inds``, where each ``ind`` may be an ``Int``, a ``Range``, or a ``Vector``. See the manual section on :ref:`array indexing ` for details. + :: + getindex(collection, key...) + + Retrieve the value(s) stored at the given key or index within a collection. + The syntax ``a[i,j,...]`` is converted by the compiler to + ``getindex(a, i, j, ...)``. + .. function:: sub(A, inds...) Like :func:`getindex`, but returns a view into the parent array ``A`` with the given indices instead of making a copy. Calling :func:`getindex` or :func:`setindex!` on the returned :obj:`SubArray` computes the indices to the parent array on the fly without checking bounds. @@ -253,6 +368,13 @@ Indexing, Assignment, and Concatenation Store values from array ``X`` within some subset of ``A`` as specified by ``inds``. + :: + setindex!(collection, value, key...) + + Store the given value at the given key or index within a collection. + The syntax ``a[i,j,...] = x`` is converted by the compiler to + ``setindex!(a, x, i, j, ...)``. + .. function:: broadcast_getindex(A, inds...) Broadcasts the ``inds`` arrays to a common size like ``broadcast``, and returns an array of the results ``A[ks...]``, where ``ks`` goes over the positions in the broadcast. @@ -297,8 +419,24 @@ Indexing, Assignment, and Concatenation boolean array to an array of indexes of the ``true`` elements. + :: + find(f,A) + + Return a vector of the linear indexes of ``A`` where ``f`` returns true. + .. function:: find(f,A) + :: + find(A) + + Return a vector of the linear indexes of the non-zeros in ``A`` + (determined by ``A[i]!=0``). A common use of this is to convert a + boolean array to an array of indexes of the ``true`` + elements. + + :: + find(f,A) + Return a vector of the linear indexes of ``A`` where ``f`` returns true. .. function:: findn(A) @@ -315,36 +453,146 @@ Indexing, Assignment, and Concatenation Return the index of the first non-zero value in ``A`` (determined by ``A[i]!=0``). + :: + findfirst(A,v) + + Return the index of the first element equal to ``v`` in ``A``. + + :: + findfirst(predicate, A) + + Return the index of the first element of ``A`` for which ``predicate`` returns true. + .. function:: findfirst(A,v) + :: + findfirst(A) + + Return the index of the first non-zero value in ``A`` (determined by ``A[i]!=0``). + + :: + findfirst(A,v) + Return the index of the first element equal to ``v`` in ``A``. + :: + findfirst(predicate, A) + + Return the index of the first element of ``A`` for which ``predicate`` returns true. + .. function:: findfirst(predicate, A) + :: + findfirst(A) + + Return the index of the first non-zero value in ``A`` (determined by ``A[i]!=0``). + + :: + findfirst(A,v) + + Return the index of the first element equal to ``v`` in ``A``. + + :: + findfirst(predicate, A) + Return the index of the first element of ``A`` for which ``predicate`` returns true. .. function:: findlast(A) Return the index of the last non-zero value in ``A`` (determined by ``A[i]!=0``). + :: + findlast(A, v) + + Return the index of the last element equal to ``v`` in ``A``. + + :: + findlast(predicate, A) + + Return the index of the last element of ``A`` for which ``predicate`` returns true. + .. function:: findlast(A, v) + :: + findlast(A) + + Return the index of the last non-zero value in ``A`` (determined by ``A[i]!=0``). + + :: + findlast(A, v) + Return the index of the last element equal to ``v`` in ``A``. + :: + findlast(predicate, A) + + Return the index of the last element of ``A`` for which ``predicate`` returns true. + .. function:: findlast(predicate, A) + :: + findlast(A) + + Return the index of the last non-zero value in ``A`` (determined by ``A[i]!=0``). + + :: + findlast(A, v) + + Return the index of the last element equal to ``v`` in ``A``. + + :: + findlast(predicate, A) + Return the index of the last element of ``A`` for which ``predicate`` returns true. .. function:: findnext(A, i) Find the next index >= ``i`` of a non-zero element of ``A``, or ``0`` if not found. + :: + findnext(predicate, A, i) + + Find the next index >= ``i`` of an element of ``A`` for which ``predicate`` returns true, or ``0`` if not found. + + :: + findnext(A, v, i) + + Find the next index >= ``i`` of an element of ``A`` equal to ``v`` (using ``==``), + or ``0`` if not found. + .. function:: findnext(predicate, A, i) + :: + findnext(A, i) + + Find the next index >= ``i`` of a non-zero element of ``A``, or ``0`` if not found. + + :: + findnext(predicate, A, i) + Find the next index >= ``i`` of an element of ``A`` for which ``predicate`` returns true, or ``0`` if not found. + :: + findnext(A, v, i) + + Find the next index >= ``i`` of an element of ``A`` equal to ``v`` (using ``==``), + or ``0`` if not found. + .. function:: findnext(A, v, i) + :: + findnext(A, i) + + Find the next index >= ``i`` of a non-zero element of ``A``, or ``0`` if not found. + + :: + findnext(predicate, A, i) + + Find the next index >= ``i`` of an element of ``A`` for which ``predicate`` returns true, or ``0`` if not found. + + :: + findnext(A, v, i) + Find the next index >= ``i`` of an element of ``A`` equal to ``v`` (using ``==``), or ``0`` if not found. @@ -352,12 +600,50 @@ Indexing, Assignment, and Concatenation Find the previous index <= ``i`` of a non-zero element of ``A``, or 0 if not found. + :: + findprev(predicate, A, i) + + Find the previous index <= ``i`` of an element of ``A`` for which ``predicate`` returns true, or ``0`` if not found. + + :: + findprev(A, v, i) + + Find the previous index <= ``i`` of an element of ``A`` equal to ``v`` (using ``==``), + or ``0`` if not found. + .. function:: findprev(predicate, A, i) + :: + findprev(A, i) + + Find the previous index <= ``i`` of a non-zero element of ``A``, or 0 if not found. + + :: + findprev(predicate, A, i) + Find the previous index <= ``i`` of an element of ``A`` for which ``predicate`` returns true, or ``0`` if not found. + :: + findprev(A, v, i) + + Find the previous index <= ``i`` of an element of ``A`` equal to ``v`` (using ``==``), + or ``0`` if not found. + .. function:: findprev(A, v, i) + :: + findprev(A, i) + + Find the previous index <= ``i`` of a non-zero element of ``A``, or 0 if not found. + + :: + findprev(predicate, A, i) + + Find the previous index <= ``i`` of an element of ``A`` for which ``predicate`` returns true, or ``0`` if not found. + + :: + findprev(A, v, i) + Find the previous index <= ``i`` of an element of ``A`` equal to ``v`` (using ``==``), or ``0`` if not found. @@ -404,7 +690,6 @@ Indexing, Assignment, and Concatenation Like ``randsubseq``, but the results are stored in ``S`` (which is resized as needed). - Array functions --------------- @@ -461,8 +746,22 @@ Array functions Rotate matrix ``A`` 180 degrees. + :: + rot180(A, k) + + Rotate matrix ``A`` 180 degrees an integer ``k`` number of times. + If ``k`` is even, this is equivalent to a ``copy``. + .. function:: rot180(A, k) + :: + rot180(A) + + Rotate matrix ``A`` 180 degrees. + + :: + rot180(A, k) + Rotate matrix ``A`` 180 degrees an integer ``k`` number of times. If ``k`` is even, this is equivalent to a ``copy``. @@ -470,8 +769,22 @@ Array functions Rotate matrix ``A`` left 90 degrees. + :: + rotl90(A, k) + + Rotate matrix ``A`` left 90 degrees an integer ``k`` number of times. If ``k`` + is zero or a multiple of four, this is equivalent to a ``copy``. + .. function:: rotl90(A, k) + :: + rotl90(A) + + Rotate matrix ``A`` left 90 degrees. + + :: + rotl90(A, k) + Rotate matrix ``A`` left 90 degrees an integer ``k`` number of times. If ``k`` is zero or a multiple of four, this is equivalent to a ``copy``. @@ -479,8 +792,22 @@ Array functions Rotate matrix ``A`` right 90 degrees. + :: + rotr90(A, k) + + Rotate matrix ``A`` right 90 degrees an integer ``k`` number of times. If ``k`` + is zero or a multiple of four, this is equivalent to a ``copy``. + .. function:: rotr90(A, k) + :: + rotr90(A) + + Rotate matrix ``A`` right 90 degrees. + + :: + rotr90(A, k) + Rotate matrix ``A`` right 90 degrees an integer ``k`` number of times. If ``k`` is zero or a multiple of four, this is equivalent to a ``copy``. @@ -533,8 +860,22 @@ Combinatorics Compute the kth lexicographic permutation of a vector. + :: + nthperm(p) + + Return the ``k`` that generated permutation ``p``. + Note that ``nthperm(nthperm([1:n], k)) == k`` for ``1 <= k <= factorial(n)``. + .. function:: nthperm(p) + :: + nthperm(v, k) + + Compute the kth lexicographic permutation of a vector. + + :: + nthperm(p) + Return the ``k`` that generated permutation ``p``. Note that ``nthperm(nthperm([1:n], k)) == k`` for ``1 <= k <= factorial(n)``. @@ -619,16 +960,100 @@ Combinatorics partitions. The number of partitions to generate can be efficiently computed using ``length(partitions(n))``. + :: + partitions(n, m) + + Generate all arrays of ``m`` integers that sum to ``n``. Because + the number of partitions can be very large, this function returns an + iterator object. Use ``collect(partitions(n,m))`` to get an array of + all partitions. The number of partitions to generate can be efficiently + computed using ``length(partitions(n,m))``. + + :: + partitions(array) + + Generate all set partitions of the elements of an array, + represented as arrays of arrays. Because the number of partitions + can be very large, this function returns an iterator object. Use + ``collect(partitions(array))`` to get an array of all partitions. + The number of partitions to generate can be efficiently + computed using ``length(partitions(array))``. + + :: + partitions(array, m) + + Generate all set partitions of the elements of an array into exactly m + subsets, represented as arrays of arrays. Because the number of + partitions can be very large, this function returns an iterator object. + Use ``collect(partitions(array,m))`` to get an array of all partitions. + The number of partitions into m subsets is equal to the Stirling number + of the second kind and can be efficiently computed using + ``length(partitions(array,m))``. + .. function:: partitions(n, m) + :: + partitions(n) + + Generate all integer arrays that sum to ``n``. Because the number of + partitions can be very large, this function returns an iterator + object. Use ``collect(partitions(n))`` to get an array of all + partitions. The number of partitions to generate can be efficiently + computed using ``length(partitions(n))``. + + :: + partitions(n, m) + Generate all arrays of ``m`` integers that sum to ``n``. Because the number of partitions can be very large, this function returns an iterator object. Use ``collect(partitions(n,m))`` to get an array of all partitions. The number of partitions to generate can be efficiently computed using ``length(partitions(n,m))``. + :: + partitions(array) + + Generate all set partitions of the elements of an array, + represented as arrays of arrays. Because the number of partitions + can be very large, this function returns an iterator object. Use + ``collect(partitions(array))`` to get an array of all partitions. + The number of partitions to generate can be efficiently + computed using ``length(partitions(array))``. + + :: + partitions(array, m) + + Generate all set partitions of the elements of an array into exactly m + subsets, represented as arrays of arrays. Because the number of + partitions can be very large, this function returns an iterator object. + Use ``collect(partitions(array,m))`` to get an array of all partitions. + The number of partitions into m subsets is equal to the Stirling number + of the second kind and can be efficiently computed using + ``length(partitions(array,m))``. + .. function:: partitions(array) + :: + partitions(n) + + Generate all integer arrays that sum to ``n``. Because the number of + partitions can be very large, this function returns an iterator + object. Use ``collect(partitions(n))`` to get an array of all + partitions. The number of partitions to generate can be efficiently + computed using ``length(partitions(n))``. + + :: + partitions(n, m) + + Generate all arrays of ``m`` integers that sum to ``n``. Because + the number of partitions can be very large, this function returns an + iterator object. Use ``collect(partitions(n,m))`` to get an array of + all partitions. The number of partitions to generate can be efficiently + computed using ``length(partitions(n,m))``. + + :: + partitions(array) + Generate all set partitions of the elements of an array, represented as arrays of arrays. Because the number of partitions can be very large, this function returns an iterator object. Use @@ -636,8 +1061,50 @@ Combinatorics The number of partitions to generate can be efficiently computed using ``length(partitions(array))``. + :: + partitions(array, m) + + Generate all set partitions of the elements of an array into exactly m + subsets, represented as arrays of arrays. Because the number of + partitions can be very large, this function returns an iterator object. + Use ``collect(partitions(array,m))`` to get an array of all partitions. + The number of partitions into m subsets is equal to the Stirling number + of the second kind and can be efficiently computed using + ``length(partitions(array,m))``. + .. function:: partitions(array, m) + :: + partitions(n) + + Generate all integer arrays that sum to ``n``. Because the number of + partitions can be very large, this function returns an iterator + object. Use ``collect(partitions(n))`` to get an array of all + partitions. The number of partitions to generate can be efficiently + computed using ``length(partitions(n))``. + + :: + partitions(n, m) + + Generate all arrays of ``m`` integers that sum to ``n``. Because + the number of partitions can be very large, this function returns an + iterator object. Use ``collect(partitions(n,m))`` to get an array of + all partitions. The number of partitions to generate can be efficiently + computed using ``length(partitions(n,m))``. + + :: + partitions(array) + + Generate all set partitions of the elements of an array, + represented as arrays of arrays. Because the number of partitions + can be very large, this function returns an iterator object. Use + ``collect(partitions(array))`` to get an array of all partitions. + The number of partitions to generate can be efficiently + computed using ``length(partitions(array))``. + + :: + partitions(array, m) + Generate all set partitions of the elements of an array into exactly m subsets, represented as arrays of arrays. Because the number of partitions can be very large, this function returns an iterator object. @@ -665,8 +1132,21 @@ BitArrays Performs a left rotation operation on ``src`` and put the result into ``dest``. + :: + rol!(B::BitArray{1}, i::Integer) -> BitArray{1} + + Performs a left rotation operation on B. + .. function:: rol!(B::BitArray{1}, i::Integer) -> BitArray{1} + :: + rol!(dest::BitArray{1}, src::BitArray{1}, i::Integer) -> BitArray{1} + + Performs a left rotation operation on ``src`` and put the result into ``dest``. + + :: + rol!(B::BitArray{1}, i::Integer) -> BitArray{1} + Performs a left rotation operation on B. .. function:: rol(B::BitArray{1}, i::Integer) -> BitArray{1} @@ -677,8 +1157,21 @@ BitArrays Performs a right rotation operation on ``src`` and put the result into ``dest``. + :: + ror!(B::BitArray{1}, i::Integer) -> BitArray{1} + + Performs a right rotation operation on B. + .. function:: ror!(B::BitArray{1}, i::Integer) -> BitArray{1} + :: + ror!(dest::BitArray{1}, src::BitArray{1}, i::Integer) -> BitArray{1} + + Performs a right rotation operation on ``src`` and put the result into ``dest``. + + :: + ror!(B::BitArray{1}, i::Integer) -> BitArray{1} + Performs a right rotation operation on B. .. function:: ror(B::BitArray{1}, i::Integer) -> BitArray{1} @@ -696,30 +1189,96 @@ Sparse matrices support much of the same set of operations as dense matrices. Th Create a sparse matrix ``S`` of dimensions ``m x n`` such that ``S[I[k], J[k]] = V[k]``. The ``combine`` function is used to combine duplicates. If ``m`` and ``n`` are not specified, they are set to ``max(I)`` and ``max(J)`` respectively. If the ``combine`` function is not supplied, duplicates are added by default. + :: + sparse(A) + + Convert an AbstractMatrix ``A`` into a sparse matrix. + .. function:: sparsevec(I, V, [m, combine]) Create a sparse matrix ``S`` of size ``m x 1`` such that ``S[I[k]] = V[k]``. Duplicates are combined using the ``combine`` function, which defaults to ``+`` if it is not provided. In julia, sparse vectors are really just sparse matrices with one column. Given Julia's Compressed Sparse Columns (CSC) storage format, a sparse column matrix with one column is sparse, whereas a sparse row matrix with one row ends up being dense. + :: + sparsevec(D::Dict, [m]) + + Create a sparse matrix of size ``m x 1`` where the row values are keys from the dictionary, and the nonzero values are the values from the dictionary. + + :: + sparsevec(A) + + Convert a dense vector ``A`` into a sparse matrix of size ``m x 1``. In julia, sparse vectors are really just sparse matrices with one column. + .. function:: sparsevec(D::Dict, [m]) + :: + sparsevec(I, V, [m, combine]) + + Create a sparse matrix ``S`` of size ``m x 1`` such that ``S[I[k]] = V[k]``. Duplicates are combined using the ``combine`` function, which defaults to ``+`` if it is not provided. In julia, sparse vectors are really just sparse matrices with one column. Given Julia's Compressed Sparse Columns (CSC) storage format, a sparse column matrix with one column is sparse, whereas a sparse row matrix with one row ends up being dense. + + :: + sparsevec(D::Dict, [m]) + Create a sparse matrix of size ``m x 1`` where the row values are keys from the dictionary, and the nonzero values are the values from the dictionary. + :: + sparsevec(A) + + Convert a dense vector ``A`` into a sparse matrix of size ``m x 1``. In julia, sparse vectors are really just sparse matrices with one column. + .. function:: issparse(S) Returns ``true`` if ``S`` is sparse, and ``false`` otherwise. .. function:: sparse(A) + :: + sparse(I,J,V,[m,n,combine]) + + Create a sparse matrix ``S`` of dimensions ``m x n`` such that ``S[I[k], J[k]] = V[k]``. The ``combine`` function is used to combine duplicates. If ``m`` and ``n`` are not specified, they are set to ``max(I)`` and ``max(J)`` respectively. If the ``combine`` function is not supplied, duplicates are added by default. + + :: + sparse(A) + Convert an AbstractMatrix ``A`` into a sparse matrix. .. function:: sparsevec(A) + :: + sparsevec(I, V, [m, combine]) + + Create a sparse matrix ``S`` of size ``m x 1`` such that ``S[I[k]] = V[k]``. Duplicates are combined using the ``combine`` function, which defaults to ``+`` if it is not provided. In julia, sparse vectors are really just sparse matrices with one column. Given Julia's Compressed Sparse Columns (CSC) storage format, a sparse column matrix with one column is sparse, whereas a sparse row matrix with one row ends up being dense. + + :: + sparsevec(D::Dict, [m]) + + Create a sparse matrix of size ``m x 1`` where the row values are keys from the dictionary, and the nonzero values are the values from the dictionary. + + :: + sparsevec(A) + Convert a dense vector ``A`` into a sparse matrix of size ``m x 1``. In julia, sparse vectors are really just sparse matrices with one column. .. function:: full(S) Convert a sparse matrix ``S`` into a dense matrix. + :: + full(F) + + Reconstruct the matrix ``A`` from the factorization ``F=factorize(A)``. + + :: + full(QRCompactWYQ[, thin=true]) -> Matrix + + Converts an orthogonal or unitary matrix stored as a ``QRCompactWYQ`` + object, i.e. in the compact WY format [Bischof1987]_, to a dense matrix. + + Optionally takes a ``thin`` Boolean argument, which if ``true`` omits the + columns that span the rows of ``R`` in the QR factorization that are zero. + The resulting matrix is the ``Q`` in a thin QR factorization (sometimes + called the reduced QR factorization). If ``false``, returns a ``Q`` that + spans all rows of ``R`` in its corresponding QR factorization. + .. function:: nnz(A) Returns the number of stored (filled) elements in a sparse matrix. @@ -783,3 +1342,4 @@ Sparse matrices support much of the same set of operations as dense matrices. Th # perform sparse wizardry... end end + diff --git a/doc/stdlib/base.rst b/doc/stdlib/base.rst index 15d04f254a9e2..66a2eb5f30f7b 100644 --- a/doc/stdlib/base.rst +++ b/doc/stdlib/base.rst @@ -50,8 +50,21 @@ Getting Around Edit a file optionally providing a line number to edit at. Returns to the julia prompt when you quit the editor. + :: + edit(function, [types]) + + Edit the definition of a function, optionally specifying a tuple of types to indicate which method to edit. + .. function:: edit(function, [types]) + :: + edit(file::AbstractString, [line]) + + Edit a file optionally providing a line number to edit at. Returns to the julia prompt when you quit the editor. + + :: + edit(function, [types]) + Edit the definition of a function, optionally specifying a tuple of types to indicate which method to edit. .. function:: @edit @@ -62,8 +75,21 @@ Getting Around Show a file using the default pager, optionally providing a starting line number. Returns to the julia prompt when you quit the pager. + :: + less(function, [types]) + + Show the definition of a function using the default pager, optionally specifying a tuple of types to indicate which method to see. + .. function:: less(function, [types]) + :: + less(file::AbstractString, [line]) + + Show a file using the default pager, optionally providing a starting line number. Returns to the julia prompt when you quit the pager. + + :: + less(function, [types]) + Show the definition of a function using the default pager, optionally specifying a tuple of types to indicate which method to see. .. function:: @less @@ -74,8 +100,21 @@ Getting Around Send a printed form of ``x`` to the operating system clipboard ("copy"). + :: + clipboard() -> AbstractString + + Return a string with the contents of the operating system clipboard ("paste"). + .. function:: clipboard() -> AbstractString + :: + clipboard(x) + + Send a printed form of ``x`` to the operating system clipboard ("copy"). + + :: + clipboard() -> AbstractString + Return a string with the contents of the operating system clipboard ("paste"). .. function:: require(module::Symbol) @@ -105,8 +144,25 @@ Getting Around If ``types`` is an abstract type, then the method that would be called by ``invoke`` is returned. + :: + which(symbol) + + Return the module in which the binding for the variable referenced + by ``symbol`` was created. + .. function:: which(symbol) + :: + which(f, types) + + Returns the method of ``f`` (a ``Method`` object) that would be called for arguments of the given types. + + If ``types`` is an abstract type, then the method that would be called by ``invoke`` + is returned. + + :: + which(symbol) + Return the module in which the binding for the variable referenced by ``symbol`` was created. @@ -159,6 +215,8 @@ All Objects ----------- .. function:: is(x, y) -> Bool + + :: ===(x,y) -> Bool ≡(x,y) -> Bool @@ -332,7 +390,10 @@ Types .. function:: <:(T1, T2) - Subtype operator, equivalent to ``issubtype(T1,T2)``. + :: + issubtype(type1, type2) + + True if and only if all values of ``type1`` are also of ``type2``. Can also be written using the ``<:`` infix operator as ``type1 <: type2``. .. function:: subtypes(T::DataType) @@ -362,13 +423,26 @@ Types Size, in bytes, of the canonical binary representation of the given type, if any. + :: + sizeof(s::AbstractString) + + The number of bytes in string ``s``. + .. function:: eps([type]) - The distance between 1.0 and the next larger representable floating-point value of ``type``. Only floating-point types are sensible arguments. If ``type`` is omitted, then ``eps(Float64)`` is returned. + :: + eps(::DateTime) -> Millisecond + eps(::Date) -> Day + + Returns ``Millisecond(1)`` for ``DateTime`` values and ``Day(1)`` for ``Date`` values. .. function:: eps(x) - The distance between ``x`` and the next larger representable floating-point value of the same type as ``x``. + :: + eps(::DateTime) -> Millisecond + eps(::Date) -> Day + + Returns ``Millisecond(1)`` for ``DateTime`` values and ``Day(1)`` for ``Date`` values. .. function:: promote_type(type1, type2) @@ -558,10 +632,34 @@ Syntax Parse the expression string and return an expression (which could later be passed to eval for execution). Start is the index of the first character to start parsing. If ``greedy`` is true (default), ``parse`` will try to consume as much input as it can; otherwise, it will stop as soon as it has parsed a valid expression. Incomplete but otherwise syntactically valid expressions will return ``Expr(:incomplete, "(error message)")``. If ``raise`` is true (default), syntax errors other than incomplete expressions will raise an error. If ``raise`` is false, ``parse`` will return an expression that will raise an error upon evaluation. + :: + parse(str; raise=true) + + Parse the whole string greedily, returning a single expression. An error is thrown if there are additional characters after the first expression. If ``raise`` is true (default), syntax errors will raise an error; otherwise, ``parse`` will return an expression that will raise an error upon evaluation. + + :: + parse(type, str, [base]) + + Parse a string as a number. If the type is an integer type, then a base can be specified (the default is 10). If the type is a floating point type, the string is parsed as a decimal floating point number. + If the string does not contain a valid number, an error is raised. + .. function:: parse(str; raise=true) + :: + parse(str, start; greedy=true, raise=true) + + Parse the expression string and return an expression (which could later be passed to eval for execution). Start is the index of the first character to start parsing. If ``greedy`` is true (default), ``parse`` will try to consume as much input as it can; otherwise, it will stop as soon as it has parsed a valid expression. Incomplete but otherwise syntactically valid expressions will return ``Expr(:incomplete, "(error message)")``. If ``raise`` is true (default), syntax errors other than incomplete expressions will raise an error. If ``raise`` is false, ``parse`` will return an expression that will raise an error upon evaluation. + + :: + parse(str; raise=true) + Parse the whole string greedily, returning a single expression. An error is thrown if there are additional characters after the first expression. If ``raise`` is true (default), syntax errors will raise an error; otherwise, ``parse`` will return an expression that will raise an error upon evaluation. + :: + parse(type, str, [base]) + + Parse a string as a number. If the type is an integer type, then a base can be specified (the default is 10). If the type is a floating point type, the string is parsed as a decimal floating point number. + If the string does not contain a valid number, an error is raised. Nullables --------- @@ -577,16 +675,60 @@ Nullables Attempt to access the value of the ``Nullable`` object, ``x``. Returns the value if it is present; otherwise, throws a ``NullException``. + :: + get(x, y) + + Attempt to access the value of the ``Nullable{T}`` object, ``x``. Returns + the value if it is present; otherwise, returns ``convert(T, y)``. + + :: + get(collection, key, default) + + Return the value stored for the given key, or the given default value if no mapping for the key is present. + + :: + get(f::Function, collection, key) + + Return the value stored for the given key, or if no mapping for the key is present, return ``f()``. Use :func:`get!` to also store the default value in the dictionary. + + This is intended to be called using ``do`` block syntax:: + + get(dict, key) do + # default value calculated here + .. function:: get(x, y) + :: + get(x) + + Attempt to access the value of the ``Nullable`` object, ``x``. Returns the + value if it is present; otherwise, throws a ``NullException``. + + :: + get(x, y) + Attempt to access the value of the ``Nullable{T}`` object, ``x``. Returns the value if it is present; otherwise, returns ``convert(T, y)``. + :: + get(collection, key, default) + + Return the value stored for the given key, or the given default value if no mapping for the key is present. + + :: + get(f::Function, collection, key) + + Return the value stored for the given key, or if no mapping for the key is present, return ``f()``. Use :func:`get!` to also store the default value in the dictionary. + + This is intended to be called using ``do`` block syntax:: + + get(dict, key) do + # default value calculated here + .. function:: isnull(x) Is the ``Nullable`` object ``x`` null, i.e. missing a value? - System ------ @@ -619,6 +761,12 @@ System Send a signal to a process. The default is to terminate the process. + :: + kill(manager::FooManager, pid::Int, config::WorkerConfig) + + Implemented by cluster managers. It is called on the master process, by ``rmprocs``. It should cause the remote worker specified + by ``pid`` to exit. ``Base.kill(manager::ClusterManager.....)`` executes a remote ``exit()`` on ``pid`` + .. function:: open(command, mode::AbstractString="r", stdio=DevNull) Start running ``command`` asynchronously, and return a tuple @@ -629,13 +777,87 @@ System and ``stdio`` optionally specifies the process's standard output stream. + :: + open(f::Function, command, mode::AbstractString="r", stdio=DevNull) + + Similar to ``open(command, mode, stdio)``, but calls ``f(stream)`` + on the resulting read or write stream, then closes the stream + and waits for the process to complete. Returns the value returned + by ``f``. + + :: + open(file_name, [read, write, create, truncate, append]) -> IOStream + + Open a file in a mode specified by five boolean arguments. The default is to open files for reading only. Returns a stream for accessing the file. + + :: + open(file_name, [mode]) -> IOStream + + Alternate syntax for open, where a string-based mode specifier is used instead of the five booleans. The values of ``mode`` correspond to those from ``fopen(3)`` or Perl ``open``, and are equivalent to setting the following boolean groups: + + ==== ================================= + r read + r+ read, write + w write, create, truncate + w+ read, write, create, truncate + a write, create, append + a+ read, write, create, append + ==== ================================= + + :: + open(f::function, args...) + + Apply the function ``f`` to the result of ``open(args...)`` and close the resulting file descriptor upon completion. + + **Example**: ``open(readall, "file.txt")`` + .. function:: open(f::Function, command, mode::AbstractString="r", stdio=DevNull) + :: + open(command, mode::AbstractString="r", stdio=DevNull) + + Start running ``command`` asynchronously, and return a tuple + ``(stream,process)``. If ``mode`` is ``"r"``, then ``stream`` + reads from the process's standard output and ``stdio`` optionally + specifies the process's standard input stream. If ``mode`` is + ``"w"``, then ``stream`` writes to the process's standard input + and ``stdio`` optionally specifies the process's standard output + stream. + + :: + open(f::Function, command, mode::AbstractString="r", stdio=DevNull) + Similar to ``open(command, mode, stdio)``, but calls ``f(stream)`` on the resulting read or write stream, then closes the stream and waits for the process to complete. Returns the value returned by ``f``. + :: + open(file_name, [read, write, create, truncate, append]) -> IOStream + + Open a file in a mode specified by five boolean arguments. The default is to open files for reading only. Returns a stream for accessing the file. + + :: + open(file_name, [mode]) -> IOStream + + Alternate syntax for open, where a string-based mode specifier is used instead of the five booleans. The values of ``mode`` correspond to those from ``fopen(3)`` or Perl ``open``, and are equivalent to setting the following boolean groups: + + ==== ================================= + r read + r+ read, write + w write, create, truncate + w+ read, write, create, truncate + a write, create, append + a+ read, write, create, append + ==== ================================= + + :: + open(f::function, args...) + + Apply the function ``f`` to the result of ``open(args...)`` and close the resulting file descriptor upon completion. + + **Example**: ``open(readall, "file.txt")`` + .. function:: Sys.set_process_title(title::AbstractString) Set the process title. No-op on some operating systems. (not exported) @@ -689,8 +911,41 @@ System * ``run(pipe(`ls`, "out.txt"))`` * ``run(pipe("out.txt", `grep xyz`))`` + :: + pipe(command; stdin, stdout, stderr, append=false) + + Redirect I/O to or from the given ``command``. Keyword arguments specify which of + the command's streams should be redirected. ``append`` controls whether file output + appends to the file. + This is a more general version of the 2-argument ``pipe`` function. + ``pipe(from, to)`` is equivalent to ``pipe(from, stdout=to)`` when ``from`` is a + command, and to ``pipe(to, stdin=from)`` when ``from`` is another kind of + data source. + + **Examples**: + * ``run(pipe(`dothings`, stdout="out.txt", stderr="errs.txt"))`` + * ``run(pipe(`update`, stdout="log.txt", append=true))`` + .. function:: pipe(command; stdin, stdout, stderr, append=false) + :: + pipe(from, to, ...) + + Create a pipeline from a data source to a destination. The source and destination can + be commands, I/O streams, strings, or results of other ``pipe`` calls. At least one + argument must be a command. Strings refer to filenames. + When called with more than two arguments, they are chained together from left to right. + For example ``pipe(a,b,c)`` is equivalent to ``pipe(pipe(a,b),c)``. This provides a more + concise way to specify multi-stage pipelines. + + **Examples**: + * ``run(pipe(`ls`, `grep xyz`))`` + * ``run(pipe(`ls`, "out.txt"))`` + * ``run(pipe("out.txt", `grep xyz`))`` + + :: + pipe(command; stdin, stdout, stderr, append=false) + Redirect I/O to or from the given ``command``. Keyword arguments specify which of the command's streams should be redirected. ``append`` controls whether file output appends to the file. @@ -786,7 +1041,6 @@ System Given ``@windows? a : b``, do ``a`` on Windows and ``b`` elsewhere. See documentation for Handling Platform Variations in the Calling C and Fortran Code section of the manual. - Errors ------ @@ -930,8 +1184,30 @@ Events Times are in seconds. A timer is stopped and has its resources freed by calling ``close`` on it. + :: + Timer(delay, repeat=0) + + Create a timer that wakes up tasks waiting for it (by calling ``wait`` on + the timer object) at a specified interval. + Waiting tasks are also woken up when the timer is closed (by ``close``). + Use ``isopen`` to check whether a timer is still active after a wakeup. + .. function:: Timer(delay, repeat=0) + :: + Timer(callback::Function, delay, repeat=0) + + Create a timer to call the given callback function. + The callback is passed one argument, the timer object itself. + The callback will be invoked after the specified initial delay, + and then repeating with the given ``repeat`` interval. + If ``repeat`` is ``0``, the timer is only triggered once. + Times are in seconds. + A timer is stopped and has its resources freed by calling ``close`` on it. + + :: + Timer(delay, repeat=0) + Create a timer that wakes up tasks waiting for it (by calling ``wait`` on the timer object) at a specified interval. Waiting tasks are also woken up when the timer is closed (by ``close``). @@ -993,8 +1269,21 @@ Reflection Returns a tuple ``(filename,line)`` giving the location of a method definition. + :: + functionloc(m::Method) + + Returns a tuple ``(filename,line)`` giving the location of a method definition. + .. function:: functionloc(m::Method) + :: + functionloc(f::Function, types) + + Returns a tuple ``(filename,line)`` giving the location of a method definition. + + :: + functionloc(m::Method) + Returns a tuple ``(filename,line)`` giving the location of a method definition. Internals @@ -1065,3 +1354,4 @@ Internals .. function:: precompile(f,args::Tuple{Vararg{Any}}) Compile the given function ``f`` for the argument tuple (of types) ``args``, but do not execute it. + diff --git a/doc/stdlib/c.rst b/doc/stdlib/c.rst index 2d24a41c6bb43..81fbf0084b7cc 100644 --- a/doc/stdlib/c.rst +++ b/doc/stdlib/c.rst @@ -90,8 +90,31 @@ on the pointers ``dest`` and ``src`` to ensure that they are valid. Incorrect usage may corrupt or segfault your program, in the same manner as C. + :: + unsafe_copy!(dest::Array, do, src::Array, so, N) + + Copy ``N`` elements from a source array to a destination, starting at offset ``so`` + in the source and ``do`` in the destination (1-indexed). + + The ``unsafe`` prefix on this function indicates that no validation is performed + to ensure that N is inbounds on either array. Incorrect usage may corrupt or segfault + your program, in the same manner as C. + .. function:: unsafe_copy!(dest::Array, do, src::Array, so, N) + :: + unsafe_copy!(dest::Ptr{T}, src::Ptr{T}, N) + + Copy ``N`` elements from a source pointer to a destination, with no checking. The + size of an element is determined by the type of the pointers. + + The ``unsafe`` prefix on this function indicates that no validation is performed + on the pointers ``dest`` and ``src`` to ensure that they are valid. + Incorrect usage may corrupt or segfault your program, in the same manner as C. + + :: + unsafe_copy!(dest::Array, do, src::Array, so, N) + Copy ``N`` elements from a source array to a destination, starting at offset ``so`` in the source and ``do`` in the destination (1-indexed). @@ -103,8 +126,22 @@ Copy all elements from collection ``src`` to array ``dest``. Returns ``dest``. + :: + copy!(dest, do, src, so, N) + + Copy ``N`` elements from collection ``src`` starting at offset ``so``, to + array ``dest`` starting at offset ``do``. Returns ``dest``. + .. function:: copy!(dest, do, src, so, N) + :: + copy!(dest, src) + + Copy all elements from collection ``src`` to array ``dest``. Returns ``dest``. + + :: + copy!(dest, do, src, so, N) + Copy ``N`` elements from collection ``src`` starting at offset ``so``, to array ``dest`` starting at offset ``do``. Returns ``dest``. diff --git a/doc/stdlib/collections.rst b/doc/stdlib/collections.rst index d52c7ab836e41..03e4abe2892d2 100644 --- a/doc/stdlib/collections.rst +++ b/doc/stdlib/collections.rst @@ -125,8 +125,21 @@ General Collections .. function:: length(collection) -> Integer + :: + length(A) -> Integer + + Returns the number of elements in A + + :: + length(collection) -> Integer + For ordered, indexable collections, the maximum index ``i`` for which ``getindex(collection, i)`` is valid. For unordered collections, the number of elements. + :: + length(s) + + The number of characters in string ``s``. + .. function:: endof(collection) -> Integer Returns the last index of the collection. @@ -153,6 +166,8 @@ Iterable Collections -------------------- .. function:: in(item, collection) -> Bool + + :: ∈(item,collection) -> Bool ∋(collection,item) -> Bool ∉(item,collection) -> Bool @@ -214,8 +229,43 @@ Iterable Collections of Julia might change the algorithm. Note that the elements are not reordered if you use an ordered collection. + :: + reduce(op, itr) + + Like ``reduce(op, v0, itr)``. This cannot be used with empty + collections, except for some special cases (e.g. when ``op`` is one + of ``+``, ``*``, ``max``, ``min``, ``&``, ``|``) when Julia can + determine the neutral element of ``op``. + .. function:: reduce(op, itr) + :: + reduce(op, v0, itr) + + Reduce the given collection ``ìtr`` with the given binary operator + ``op``. ``v0`` must be a neutral element for ``op`` that will be + returned for empty collections. It is unspecified whether ``v0`` is + used for non-empty collections. + + Reductions for certain commonly-used operators have special + implementations which should be used instead: ``maximum(itr)``, + ``minimum(itr)``, ``sum(itr)``, ``prod(itr)``, ``any(itr)``, + ``all(itr)``. + + The associativity of the reduction is implementation dependent. + This means that you can't use non-associative operations like ``-`` + because it is undefined whether ``reduce(-,[1,2,3])`` should be + evaluated as ``(1-2)-3`` or ``1-(2-3)``. Use ``foldl`` or ``foldr`` + instead for guaranteed left or right associativity. + + Some operations accumulate error, and parallelism will also be + easier if the reduction can be executed in groups. Future versions + of Julia might change the algorithm. Note that the elements are not + reordered if you use an ordered collection. + + :: + reduce(op, itr) + Like ``reduce(op, v0, itr)``. This cannot be used with empty collections, except for some special cases (e.g. when ``op`` is one of ``+``, ``*``, ``max``, ``min``, ``&``, ``|``) when Julia can @@ -226,8 +276,24 @@ Iterable Collections Like :func:`reduce`, but with guaranteed left associativity. ``v0`` will be used exactly once. + :: + foldl(op, itr) + + Like ``foldl(op, v0, itr)``, but using the first element of ``itr`` + as ``v0``. In general, this cannot be used with empty collections + (see ``reduce(op, itr)``). + .. function:: foldl(op, itr) + :: + foldl(op, v0, itr) + + Like :func:`reduce`, but with guaranteed left associativity. ``v0`` + will be used exactly once. + + :: + foldl(op, itr) + Like ``foldl(op, v0, itr)``, but using the first element of ``itr`` as ``v0``. In general, this cannot be used with empty collections (see ``reduce(op, itr)``). @@ -237,8 +303,24 @@ Iterable Collections Like :func:`reduce`, but with guaranteed right associativity. ``v0`` will be used exactly once. + :: + foldr(op, itr) + + Like ``foldr(op, v0, itr)``, but using the last element of ``itr`` + as ``v0``. In general, this cannot be used with empty collections + (see ``reduce(op, itr)``). + .. function:: foldr(op, itr) + :: + foldr(op, v0, itr) + + Like :func:`reduce`, but with guaranteed right associativity. ``v0`` + will be used exactly once. + + :: + foldr(op, itr) + Like ``foldr(op, v0, itr)``, but using the last element of ``itr`` as ``v0``. In general, this cannot be used with empty collections (see ``reduce(op, itr)``). @@ -247,8 +329,21 @@ Iterable Collections Returns the largest element in a collection. + :: + maximum(A, dims) + + Compute the maximum value of an array over the given dimensions. + .. function:: maximum(A, dims) + :: + maximum(itr) + + Returns the largest element in a collection. + + :: + maximum(A, dims) + Compute the maximum value of an array over the given dimensions. .. function:: maximum!(r, A) @@ -260,8 +355,21 @@ Iterable Collections Returns the smallest element in a collection. + :: + minimum(A, dims) + + Compute the minimum value of an array over the given dimensions. + .. function:: minimum(A, dims) + :: + minimum(itr) + + Returns the smallest element in a collection. + + :: + minimum(A, dims) + Compute the minimum value of an array over the given dimensions. .. function:: minimum!(r, A) @@ -286,8 +394,22 @@ Iterable Collections Returns the maximum element and its index. + :: + findmax(A, dims) -> (maxval, index) + + For an array input, returns the value and index of the maximum over + the given dimensions. + .. function:: findmax(A, dims) -> (maxval, index) + :: + findmax(itr) -> (x, index) + + Returns the maximum element and its index. + + :: + findmax(A, dims) -> (maxval, index) + For an array input, returns the value and index of the maximum over the given dimensions. @@ -295,8 +417,22 @@ Iterable Collections Returns the minimum element and its index. + :: + findmin(A, dims) -> (minval, index) + + For an array input, returns the value and index of the minimum over + the given dimensions. + .. function:: findmin(A, dims) -> (minval, index) + :: + findmin(itr) -> (x, index) + + Returns the minimum element and its index. + + :: + findmin(A, dims) -> (minval, index) + For an array input, returns the value and index of the minimum over the given dimensions. @@ -304,8 +440,21 @@ Iterable Collections Compute the maximum absolute value of a collection of values. + :: + maxabs(A, dims) + + Compute the maximum absolute values over given dimensions. + .. function:: maxabs(A, dims) + :: + maxabs(itr) + + Compute the maximum absolute value of a collection of values. + + :: + maxabs(A, dims) + Compute the maximum absolute values over given dimensions. .. function:: maxabs!(r, A) @@ -317,8 +466,21 @@ Iterable Collections Compute the minimum absolute value of a collection of values. + :: + minabs(A, dims) + + Compute the minimum absolute values over given dimensions. + .. function:: minabs(A, dims) + :: + minabs(itr) + + Compute the minimum absolute value of a collection of values. + + :: + minabs(A, dims) + Compute the minimum absolute values over given dimensions. .. function:: minabs!(r, A) @@ -330,10 +492,33 @@ Iterable Collections Returns the sum of all elements in a collection. + :: + sum(A, dims) + + Sum elements of an array over the given dimensions. + + :: + sum(f, itr) + + Sum the results of calling function ``f`` on each element of ``itr``. + .. function:: sum(A, dims) + :: + sum(itr) + + Returns the sum of all elements in a collection. + + :: + sum(A, dims) + Sum elements of an array over the given dimensions. + :: + sum(f, itr) + + Sum the results of calling function ``f`` on each element of ``itr``. + .. function:: sum!(r, A) Sum elements of ``A`` over the singleton dimensions of ``r``, @@ -341,6 +526,19 @@ Iterable Collections .. function:: sum(f, itr) + :: + sum(itr) + + Returns the sum of all elements in a collection. + + :: + sum(A, dims) + + Sum elements of an array over the given dimensions. + + :: + sum(f, itr) + Sum the results of calling function ``f`` on each element of ``itr``. .. function:: sumabs(itr) @@ -348,8 +546,23 @@ Iterable Collections Sum absolute values of all elements in a collection. This is equivalent to `sum(abs(itr))` but faster. + :: + sumabs(A, dims) + + Sum absolute values of elements of an array over the given + dimensions. + .. function:: sumabs(A, dims) + :: + sumabs(itr) + + Sum absolute values of all elements in a collection. This is + equivalent to `sum(abs(itr))` but faster. + + :: + sumabs(A, dims) + Sum absolute values of elements of an array over the given dimensions. @@ -363,8 +576,23 @@ Iterable Collections Sum squared absolute values of all elements in a collection. This is equivalent to `sum(abs2(itr))` but faster. + :: + sumabs2(A, dims) + + Sum squared absolute values of elements of an array over the given + dimensions. + .. function:: sumabs2(A, dims) + :: + sumabs2(itr) + + Sum squared absolute values of all elements in a collection. This + is equivalent to `sum(abs2(itr))` but faster. + + :: + sumabs2(A, dims) + Sum squared absolute values of elements of an array over the given dimensions. @@ -377,8 +605,21 @@ Iterable Collections Returns the product of all elements of a collection. + :: + prod(A, dims) + + Multiply elements of an array over the given dimensions. + .. function:: prod(A, dims) + :: + prod(itr) + + Returns the product of all elements of a collection. + + :: + prod(A, dims) + Multiply elements of an array over the given dimensions. .. function:: prod!(r, A) @@ -390,10 +631,33 @@ Iterable Collections Test whether any elements of a boolean collection are true. + :: + any(A, dims) + + Test whether any values along the given dimensions of an array are true. + + :: + any(p, itr) -> Bool + + Determine whether predicate ``p`` returns true for any elements of ``itr``. + .. function:: any(A, dims) + :: + any(itr) -> Bool + + Test whether any elements of a boolean collection are true. + + :: + any(A, dims) + Test whether any values along the given dimensions of an array are true. + :: + any(p, itr) -> Bool + + Determine whether predicate ``p`` returns true for any elements of ``itr``. + .. function:: any!(r, A) Test whether any values in ``A`` along the singleton dimensions of ``r`` are true, @@ -403,10 +667,43 @@ Iterable Collections Test whether all elements of a boolean collection are true. + :: + all(A, dims) + + Test whether all values along the given dimensions of an array are true. + + :: + all(p, itr) -> Bool + + Determine whether predicate ``p`` returns true for all elements of ``itr``. + + .. doctest:: + + julia> all(i->(4<=i<=6), [4,5,6]) + true + .. function:: all(A, dims) + :: + all(itr) -> Bool + + Test whether all elements of a boolean collection are true. + + :: + all(A, dims) + Test whether all values along the given dimensions of an array are true. + :: + all(p, itr) -> Bool + + Determine whether predicate ``p`` returns true for all elements of ``itr``. + + .. doctest:: + + julia> all(i->(4<=i<=6), [4,5,6]) + true + .. function:: all!(r, A) Test whether all values in ``A`` along the singleton dimensions of ``r`` are true, @@ -418,10 +715,36 @@ Iterable Collections .. function:: any(p, itr) -> Bool + :: + any(itr) -> Bool + + Test whether any elements of a boolean collection are true. + + :: + any(A, dims) + + Test whether any values along the given dimensions of an array are true. + + :: + any(p, itr) -> Bool + Determine whether predicate ``p`` returns true for any elements of ``itr``. .. function:: all(p, itr) -> Bool + :: + all(itr) -> Bool + + Test whether all elements of a boolean collection are true. + + :: + all(A, dims) + + Test whether all values along the given dimensions of an array are true. + + :: + all(p, itr) -> Bool + Determine whether predicate ``p`` returns true for all elements of ``itr``. .. doctest:: @@ -452,8 +775,23 @@ Iterable Collections In-place version of :func:`map`. + :: + map!(function, destination, collection...) + + Like :func:`map`, but stores the result in ``destination`` rather than a + new collection. ``destination`` must be at least as large as the first + collection. + .. function:: map!(function, destination, collection...) + :: + map!(function, collection) + + In-place version of :func:`map`. + + :: + map!(function, destination, collection...) + Like :func:`map`, but stores the result in ``destination`` rather than a new collection. ``destination`` must be at least as large as the first collection. @@ -482,8 +820,42 @@ Iterable Collections Use :func:`mapfoldl` or :func:`mapfoldr` instead for guaranteed left or right associativity and invocation of ``f`` for every value. + :: + mapreduce(f, op, itr) + + Like ``mapreduce(f, op, v0, itr)``. In general, this cannot be used + with empty collections (see ``reduce(op, itr)``). + .. function:: mapreduce(f, op, itr) + :: + mapreduce(f, op, v0, itr) + + Apply function ``f`` to each element in ``itr``, and then reduce + the result using the binary function ``op``. ``v0`` must be a + neutral element for ``op`` that will be returned for empty + collections. It is unspecified whether ``v0`` is used for non-empty + collections. + + :func:`mapreduce` is functionally equivalent to calling ``reduce(op, + v0, map(f, itr))``, but will in general execute faster since no + intermediate collection needs to be created. See documentation for + :func:`reduce` and :func:`map`. + + .. doctest:: + + julia> mapreduce(x->x^2, +, [1:3;]) # == 1 + 4 + 9 + 14 + + The associativity of the reduction is implementation-dependent. + Additionally, some implementations may reuse the return value of + ``f`` for elements that appear multiple times in ``itr``. + Use :func:`mapfoldl` or :func:`mapfoldr` instead for guaranteed + left or right associativity and invocation of ``f`` for every value. + + :: + mapreduce(f, op, itr) + Like ``mapreduce(f, op, v0, itr)``. In general, this cannot be used with empty collections (see ``reduce(op, itr)``). @@ -492,8 +864,24 @@ Iterable Collections Like :func:`mapreduce`, but with guaranteed left associativity. ``v0`` will be used exactly once. + :: + mapfoldl(f, op, itr) + + Like ``mapfoldl(f, op, v0, itr)``, but using the first element of + ``itr`` as ``v0``. In general, this cannot be used with empty + collections (see ``reduce(op, itr)``). + .. function:: mapfoldl(f, op, itr) + :: + mapfoldl(f, op, v0, itr) + + Like :func:`mapreduce`, but with guaranteed left associativity. ``v0`` + will be used exactly once. + + :: + mapfoldl(f, op, itr) + Like ``mapfoldl(f, op, v0, itr)``, but using the first element of ``itr`` as ``v0``. In general, this cannot be used with empty collections (see ``reduce(op, itr)``). @@ -503,8 +891,24 @@ Iterable Collections Like :func:`mapreduce`, but with guaranteed right associativity. ``v0`` will be used exactly once. + :: + mapfoldr(f, op, itr) + + Like ``mapfoldr(f, op, v0, itr)``, but using the first element of + ``itr`` as ``v0``. In general, this cannot be used with empty + collections (see ``reduce(op, itr)``). + .. function:: mapfoldr(f, op, itr) + :: + mapfoldr(f, op, v0, itr) + + Like :func:`mapreduce`, but with guaranteed right associativity. ``v0`` + will be used exactly once. + + :: + mapfoldr(f, op, itr) + Like ``mapfoldr(f, op, v0, itr)``, but using the first element of ``itr`` as ``v0``. In general, this cannot be used with empty collections (see ``reduce(op, itr)``). @@ -528,17 +932,38 @@ Iterable Collections Return an array of all items in a collection. For associative collections, returns (key, value) tuples. + :: + collect(element_type, collection) + + Return an array of type ``Array{element_type,1}`` of all items in a collection. + .. function:: collect(element_type, collection) + :: + collect(collection) + + Return an array of all items in a collection. For associative collections, returns (key, value) tuples. + + :: + collect(element_type, collection) + Return an array of type ``Array{element_type,1}`` of all items in a collection. .. function:: issubset(a, b) + + :: ⊆(A,S) -> Bool ⊈(A,S) -> Bool ⊊(A,S) -> Bool Determine whether every element of ``a`` is also in ``b``, using :func:`in`. + :: + issubset(A, S) -> Bool + ⊆(A,S) -> Bool + + True if A is a subset of or equal to S. + .. function:: filter(function, collection) Return a copy of ``collection``, removing elements for which ``function`` is false. @@ -549,18 +974,38 @@ Iterable Collections Update ``collection``, removing elements for which ``function`` is false. For associative collections, the function is passed two arguments (key and value). - Indexable Collections --------------------- .. function:: getindex(collection, key...) + :: + getindex(type[, elements...]) + + Construct a 1-d array of the specified type. This is usually called with the syntax ``Type[]``. Element values can be specified using ``Type[a,b,c,...]``. + + :: + getindex(A, inds...) + + Returns a subset of array ``A`` as specified by ``inds``, where each ``ind`` may be an ``Int``, a ``Range``, or a ``Vector``. See the manual section on :ref:`array indexing ` for details. + + :: + getindex(collection, key...) + Retrieve the value(s) stored at the given key or index within a collection. The syntax ``a[i,j,...]`` is converted by the compiler to ``getindex(a, i, j, ...)``. .. function:: setindex!(collection, value, key...) + :: + setindex!(A, X, inds...) + + Store values from array ``X`` within some subset of ``A`` as specified by ``inds``. + + :: + setindex!(collection, value, key...) + Store the given value at the given key or index within a collection. The syntax ``a[i,j,...] = x`` is converted by the compiler to ``setindex!(a, x, i, j, ...)``. @@ -629,16 +1074,62 @@ Given a dictionary ``D``, the syntax ``D[x]`` returns the value of key ``x`` (if .. function:: get(collection, key, default) + :: + get(x) + + Attempt to access the value of the ``Nullable`` object, ``x``. Returns the + value if it is present; otherwise, throws a ``NullException``. + + :: + get(x, y) + + Attempt to access the value of the ``Nullable{T}`` object, ``x``. Returns + the value if it is present; otherwise, returns ``convert(T, y)``. + + :: + get(collection, key, default) + Return the value stored for the given key, or the given default value if no mapping for the key is present. + :: + get(f::Function, collection, key) + + Return the value stored for the given key, or if no mapping for the key is present, return ``f()``. Use :func:`get!` to also store the default value in the dictionary. + + This is intended to be called using ``do`` block syntax:: + + get(dict, key) do + # default value calculated here + .. function:: get(f::Function, collection, key) + :: + get(x) + + Attempt to access the value of the ``Nullable`` object, ``x``. Returns the + value if it is present; otherwise, throws a ``NullException``. + + :: + get(x, y) + + Attempt to access the value of the ``Nullable{T}`` object, ``x``. Returns + the value if it is present; otherwise, returns ``convert(T, y)``. + + :: + get(collection, key, default) + + Return the value stored for the given key, or the given default value if no mapping for the key is present. + + :: + get(f::Function, collection, key) + Return the value stored for the given key, or if no mapping for the key is present, return ``f()``. Use :func:`get!` to also store the default value in the dictionary. This is intended to be called using ``do`` block syntax:: get(dict, key) do # default value calculated here + time() end @@ -646,14 +1137,33 @@ Given a dictionary ``D``, the syntax ``D[x]`` returns the value of key ``x`` (if Return the value stored for the given key, or if no mapping for the key is present, store ``key => default``, and return ``default``. + :: + get!(f::Function, collection, key) + + Return the value stored for the given key, or if no mapping for the key is present, store ``key => f()``, and return ``f()``. + + This is intended to be called using ``do`` block syntax:: + + get!(dict, key) do + # default value calculated here + .. function:: get!(f::Function, collection, key) + :: + get!(collection, key, default) + + Return the value stored for the given key, or if no mapping for the key is present, store ``key => default``, and return ``default``. + + :: + get!(f::Function, collection, key) + Return the value stored for the given key, or if no mapping for the key is present, store ``key => f()``, and return ``f()``. This is intended to be called using ``do`` block syntax:: get!(dict, key) do # default value calculated here + time() end @@ -669,6 +1179,33 @@ Given a dictionary ``D``, the syntax ``D[x]`` returns the value of key ``x`` (if Delete and return the mapping for ``key`` if it exists in ``collection``, otherwise return ``default``, or throw an error if default is not specified. + :: + pop!(collection) -> item + + Remove the last item in ``collection`` and return it. + + .. doctest:: + + julia> A=[1, 2, 3, 4, 5, 6] + 6-element Array{Int64,1}: + 1 + 2 + 3 + 4 + 5 + 6 + + julia> pop!(A) + 6 + + julia> A + 5-element Array{Int64,1}: + 1 + 2 + 3 + 4 + 5 + .. function:: keys(collection) Return an iterator over all keys in a collection. ``collect(keys(d))`` returns an array of keys. @@ -740,6 +1277,8 @@ Set-Like Collections Construct a sorted set of the integers generated by the given iterable object, or an empty set. Implemented as a bit string, and therefore designed for dense integer sets. Only non-negative integers can be stored. If the set will be sparse (for example holding a single very large integer), use :obj:`Set` instead. .. function:: union(s1,s2...) + + :: ∪(s1,s2) Construct the union of two or more sets. Maintains order with arrays. @@ -749,6 +1288,8 @@ Set-Like Collections Union each element of ``iterable`` into set ``s`` in-place. .. function:: intersect(s1,s2...) + + :: ∩(s1,s2) Construct the intersection of two or more sets. Maintains order and multiplicity of the first argument for arrays and ranges. @@ -772,12 +1313,48 @@ Set-Like Collections The set ``s`` is destructively modified to toggle the inclusion of integer ``n``. + :: + symdiff!(s, itr) + + For each element in ``itr``, destructively toggle its inclusion in set ``s``. + + :: + symdiff!(s1, s2) + + Construct the symmetric difference of sets ``s1`` and ``s2``, storing the result in ``s1``. + .. function:: symdiff!(s, itr) + :: + symdiff!(s, n) + + The set ``s`` is destructively modified to toggle the inclusion of integer ``n``. + + :: + symdiff!(s, itr) + For each element in ``itr``, destructively toggle its inclusion in set ``s``. + :: + symdiff!(s1, s2) + + Construct the symmetric difference of sets ``s1`` and ``s2``, storing the result in ``s1``. + .. function:: symdiff!(s1, s2) + :: + symdiff!(s, n) + + The set ``s`` is destructively modified to toggle the inclusion of integer ``n``. + + :: + symdiff!(s, itr) + + For each element in ``itr``, destructively toggle its inclusion in set ``s``. + + :: + symdiff!(s1, s2) + Construct the symmetric difference of sets ``s1`` and ``s2``, storing the result in ``s1``. .. function:: complement(s) @@ -793,6 +1370,17 @@ Set-Like Collections Intersects sets ``s1`` and ``s2`` and overwrites the set ``s1`` with the result. If needed, ``s1`` will be expanded to the size of ``s2``. .. function:: issubset(A, S) -> Bool + + :: + issubset(a, b) + ⊆(A,S) -> Bool + ⊈(A,S) -> Bool + ⊊(A,S) -> Bool + + Determine whether every element of ``a`` is also in ``b``, using :func:`in`. + + :: + issubset(A, S) -> Bool ⊆(A,S) -> Bool True if A is a subset of or equal to S. @@ -831,6 +1419,14 @@ Dequeues .. function:: pop!(collection) -> item + :: + pop!(collection, key[, default]) + + Delete and return the mapping for ``key`` if it exists in ``collection``, otherwise return ``default``, or throw an error if default is not specified. + + :: + pop!(collection) -> item + Remove the last item in ``collection`` and return it. .. doctest:: @@ -927,8 +1523,47 @@ Dequeues 2 1 + :: + deleteat!(collection, itr) + + Remove the items at the indices given by ``itr``, and return the modified ``collection``. + Subsequent items are shifted to fill the resulting gap. ``itr`` must be sorted and unique. + + .. doctest:: + + julia> deleteat!([6, 5, 4, 3, 2, 1], 1:2:5) + 3-element Array{Int64,1}: + 5 + 3 + 1 + + .. doctest:: + + julia> deleteat!([6, 5, 4, 3, 2, 1], (2, 2)) + ERROR: ArgumentError: indices must be unique and sorted + in deleteat! at array.jl:533 + .. function:: deleteat!(collection, itr) + :: + deleteat!(collection, index) + + Remove the item at the given ``index`` and return the modified ``collection``. + Subsequent items are shifted to fill the resulting gap. + + .. doctest:: + + julia> deleteat!([6, 5, 4, 3, 2, 1], 2) + 5-element Array{Int64,1}: + 6 + 4 + 3 + 2 + 1 + + :: + deleteat!(collection, itr) + Remove the items at the indices given by ``itr``, and return the modified ``collection``. Subsequent items are shifted to fill the resulting gap. ``itr`` must be sorted and unique. @@ -992,8 +1627,85 @@ Dequeues To insert ``replacement`` before an index ``n`` without removing any items, use ``splice!(collection, n:n-1, replacement)``. + :: + splice!(collection, range, [replacement]) -> items + + Remove items in the specified index range, and return a collection containing the + removed items. Subsequent items are shifted down to fill the resulting gap. + If specified, replacement values from an ordered collection will be spliced in place + of the removed items. + + To insert ``replacement`` before an index ``n`` without removing any items, use + ``splice!(collection, n:n-1, replacement)``. + + .. doctest:: + + julia> splice!(A, 4:3, 2) + 0-element Array{Int64,1} + + julia> A + 8-element Array{Int64,1}: + -1 + -2 + -3 + 2 + 5 + 4 + 3 + -1 + .. function:: splice!(collection, range, [replacement]) -> items + :: + splice!(collection, index, [replacement]) -> item + + Remove the item at the given index, and return the removed item. Subsequent items + are shifted down to fill the resulting gap. If specified, replacement values from + an ordered collection will be spliced in place of the removed item. + + .. doctest:: + + julia> A = [6, 5, 4, 3, 2, 1]; splice!(A, 5) + 2 + + julia> A + 5-element Array{Int64,1}: + 6 + 5 + 4 + 3 + 1 + + julia> splice!(A, 5, -1) + 1 + + julia> A + 5-element Array{Int64,1}: + 6 + 5 + 4 + 3 + -1 + + julia> splice!(A, 1, [-1, -2, -3]) + 6 + + julia> A + 7-element Array{Int64,1}: + -1 + -2 + -3 + 5 + 4 + 3 + -1 + + To insert ``replacement`` before an index ``n`` without removing any items, use + ``splice!(collection, n:n-1, replacement)``. + + :: + splice!(collection, range, [replacement]) -> items + Remove items in the specified index range, and return a collection containing the removed items. Subsequent items are shifted down to fill the resulting gap. If specified, replacement values from an ordered collection will be spliced in place diff --git a/doc/stdlib/dates.rst b/doc/stdlib/dates.rst index 0d0cbc54c4d10..ba6553e0236f5 100644 --- a/doc/stdlib/dates.rst +++ b/doc/stdlib/dates.rst @@ -52,13 +52,139 @@ alternatively, you could call ``using Dates`` to bring all exported functions in Construct a DateTime type by parts. Arguments must be convertible to ``Int64``. + :: + DateTime(periods::Period...) -> DateTime + + Constuct a DateTime type by ``Period`` type parts. Arguments may be in any order. + DateTime parts not provided will default to the value of ``Dates.default(period)``. + + :: + DateTime(f::Function, y[, m, d, h, mi, s]; step=Day(1), negate=false, limit=10000) -> DateTime + + Create a DateTime through the adjuster API. The starting point will be constructed from the + provided ``y, m, d...`` arguments, and will be adjusted until ``f::Function`` returns true. The step size in + adjusting can be provided manually through the ``step`` keyword. If ``negate=true``, then the adjusting + will stop when ``f::Function`` returns false instead of true. ``limit`` provides a limit to + the max number of iterations the adjustment API will pursue before throwing an error (in the case that ``f::Function`` + is never satisfied). + + :: + DateTime(dt::Date) -> DateTime + + Converts a ``Date`` type to a ``DateTime``. The hour, minute, second, and millisecond + parts of the new ``DateTime`` are assumed to be zero. + + :: + DateTime(dt::AbstractString, format::AbstractString; locale="english") -> DateTime + + Construct a DateTime type by parsing the ``dt`` date string following the pattern given in + the ``format`` string. The following codes can be used for constructing format strings: + + =============== ========= =============================================================== + Code Matches Comment + --------------- --------- --------------------------------------------------------------- + ``y`` 1996, 96 Returns year of 1996, 0096 + ``m`` 1, 01 Matches 1 or 2-digit months + ``u`` Jan Matches abbreviated months according to the ``locale`` keyword + ``U`` January Matches full month names according to the ``locale`` keyword + ``d`` 1, 01 Matches 1 or 2-digit days + ``H`` 00 Matches hours + ``M`` 00 Matches minutes + ``S`` 00 Matches seconds + ``s`` .500 Matches milliseconds + ``e`` Mon, Tues Matches abbreviated days of the week + ``E`` Monday Matches full name days of the week + ``yyyymmdd`` 19960101 Matches fixed-width year, month, and day + =============== ========= =============================================================== + + All characters not listed above are treated as delimiters between date and time slots. + So a ``dt`` string of "1996-01-15T00:00:00.0" would have a ``format`` string + like "y-m-dTH:M:S.s". + + :: + DateTime(dt::AbstractString, df::DateFormat) -> DateTime + + Similar form as above for parsing a ``DateTime``, but passes a ``DateFormat`` object instead of a raw formatting string. It is more efficient if similarly formatted date strings will be parsed repeatedly to first create a ``DateFormat`` object then use this method for parsing. + .. function:: DateTime(periods::Period...) -> DateTime + :: + DateTime(y, [m, d, h, mi, s, ms]) -> DateTime + + Construct a DateTime type by parts. Arguments must be convertible to + ``Int64``. + + :: + DateTime(periods::Period...) -> DateTime + Constuct a DateTime type by ``Period`` type parts. Arguments may be in any order. DateTime parts not provided will default to the value of ``Dates.default(period)``. + :: + DateTime(f::Function, y[, m, d, h, mi, s]; step=Day(1), negate=false, limit=10000) -> DateTime + + Create a DateTime through the adjuster API. The starting point will be constructed from the + provided ``y, m, d...`` arguments, and will be adjusted until ``f::Function`` returns true. The step size in + adjusting can be provided manually through the ``step`` keyword. If ``negate=true``, then the adjusting + will stop when ``f::Function`` returns false instead of true. ``limit`` provides a limit to + the max number of iterations the adjustment API will pursue before throwing an error (in the case that ``f::Function`` + is never satisfied). + + :: + DateTime(dt::Date) -> DateTime + + Converts a ``Date`` type to a ``DateTime``. The hour, minute, second, and millisecond + parts of the new ``DateTime`` are assumed to be zero. + + :: + DateTime(dt::AbstractString, format::AbstractString; locale="english") -> DateTime + + Construct a DateTime type by parsing the ``dt`` date string following the pattern given in + the ``format`` string. The following codes can be used for constructing format strings: + + =============== ========= =============================================================== + Code Matches Comment + --------------- --------- --------------------------------------------------------------- + ``y`` 1996, 96 Returns year of 1996, 0096 + ``m`` 1, 01 Matches 1 or 2-digit months + ``u`` Jan Matches abbreviated months according to the ``locale`` keyword + ``U`` January Matches full month names according to the ``locale`` keyword + ``d`` 1, 01 Matches 1 or 2-digit days + ``H`` 00 Matches hours + ``M`` 00 Matches minutes + ``S`` 00 Matches seconds + ``s`` .500 Matches milliseconds + ``e`` Mon, Tues Matches abbreviated days of the week + ``E`` Monday Matches full name days of the week + ``yyyymmdd`` 19960101 Matches fixed-width year, month, and day + =============== ========= =============================================================== + + All characters not listed above are treated as delimiters between date and time slots. + So a ``dt`` string of "1996-01-15T00:00:00.0" would have a ``format`` string + like "y-m-dTH:M:S.s". + + :: + DateTime(dt::AbstractString, df::DateFormat) -> DateTime + + Similar form as above for parsing a ``DateTime``, but passes a ``DateFormat`` object instead of a raw formatting string. It is more efficient if similarly formatted date strings will be parsed repeatedly to first create a ``DateFormat`` object then use this method for parsing. + .. function:: DateTime(f::Function, y[, m, d, h, mi, s]; step=Day(1), negate=false, limit=10000) -> DateTime + :: + DateTime(y, [m, d, h, mi, s, ms]) -> DateTime + + Construct a DateTime type by parts. Arguments must be convertible to + ``Int64``. + + :: + DateTime(periods::Period...) -> DateTime + + Constuct a DateTime type by ``Period`` type parts. Arguments may be in any order. + DateTime parts not provided will default to the value of ``Dates.default(period)``. + + :: + DateTime(f::Function, y[, m, d, h, mi, s]; step=Day(1), negate=false, limit=10000) -> DateTime + Create a DateTime through the adjuster API. The starting point will be constructed from the provided ``y, m, d...`` arguments, and will be adjusted until ``f::Function`` returns true. The step size in adjusting can be provided manually through the ``step`` keyword. If ``negate=true``, then the adjusting @@ -66,13 +192,139 @@ alternatively, you could call ``using Dates`` to bring all exported functions in the max number of iterations the adjustment API will pursue before throwing an error (in the case that ``f::Function`` is never satisfied). + :: + DateTime(dt::Date) -> DateTime + + Converts a ``Date`` type to a ``DateTime``. The hour, minute, second, and millisecond + parts of the new ``DateTime`` are assumed to be zero. + + :: + DateTime(dt::AbstractString, format::AbstractString; locale="english") -> DateTime + + Construct a DateTime type by parsing the ``dt`` date string following the pattern given in + the ``format`` string. The following codes can be used for constructing format strings: + + =============== ========= =============================================================== + Code Matches Comment + --------------- --------- --------------------------------------------------------------- + ``y`` 1996, 96 Returns year of 1996, 0096 + ``m`` 1, 01 Matches 1 or 2-digit months + ``u`` Jan Matches abbreviated months according to the ``locale`` keyword + ``U`` January Matches full month names according to the ``locale`` keyword + ``d`` 1, 01 Matches 1 or 2-digit days + ``H`` 00 Matches hours + ``M`` 00 Matches minutes + ``S`` 00 Matches seconds + ``s`` .500 Matches milliseconds + ``e`` Mon, Tues Matches abbreviated days of the week + ``E`` Monday Matches full name days of the week + ``yyyymmdd`` 19960101 Matches fixed-width year, month, and day + =============== ========= =============================================================== + + All characters not listed above are treated as delimiters between date and time slots. + So a ``dt`` string of "1996-01-15T00:00:00.0" would have a ``format`` string + like "y-m-dTH:M:S.s". + + :: + DateTime(dt::AbstractString, df::DateFormat) -> DateTime + + Similar form as above for parsing a ``DateTime``, but passes a ``DateFormat`` object instead of a raw formatting string. It is more efficient if similarly formatted date strings will be parsed repeatedly to first create a ``DateFormat`` object then use this method for parsing. + .. function:: DateTime(dt::Date) -> DateTime + :: + DateTime(y, [m, d, h, mi, s, ms]) -> DateTime + + Construct a DateTime type by parts. Arguments must be convertible to + ``Int64``. + + :: + DateTime(periods::Period...) -> DateTime + + Constuct a DateTime type by ``Period`` type parts. Arguments may be in any order. + DateTime parts not provided will default to the value of ``Dates.default(period)``. + + :: + DateTime(f::Function, y[, m, d, h, mi, s]; step=Day(1), negate=false, limit=10000) -> DateTime + + Create a DateTime through the adjuster API. The starting point will be constructed from the + provided ``y, m, d...`` arguments, and will be adjusted until ``f::Function`` returns true. The step size in + adjusting can be provided manually through the ``step`` keyword. If ``negate=true``, then the adjusting + will stop when ``f::Function`` returns false instead of true. ``limit`` provides a limit to + the max number of iterations the adjustment API will pursue before throwing an error (in the case that ``f::Function`` + is never satisfied). + + :: + DateTime(dt::Date) -> DateTime + Converts a ``Date`` type to a ``DateTime``. The hour, minute, second, and millisecond parts of the new ``DateTime`` are assumed to be zero. + :: + DateTime(dt::AbstractString, format::AbstractString; locale="english") -> DateTime + + Construct a DateTime type by parsing the ``dt`` date string following the pattern given in + the ``format`` string. The following codes can be used for constructing format strings: + + =============== ========= =============================================================== + Code Matches Comment + --------------- --------- --------------------------------------------------------------- + ``y`` 1996, 96 Returns year of 1996, 0096 + ``m`` 1, 01 Matches 1 or 2-digit months + ``u`` Jan Matches abbreviated months according to the ``locale`` keyword + ``U`` January Matches full month names according to the ``locale`` keyword + ``d`` 1, 01 Matches 1 or 2-digit days + ``H`` 00 Matches hours + ``M`` 00 Matches minutes + ``S`` 00 Matches seconds + ``s`` .500 Matches milliseconds + ``e`` Mon, Tues Matches abbreviated days of the week + ``E`` Monday Matches full name days of the week + ``yyyymmdd`` 19960101 Matches fixed-width year, month, and day + =============== ========= =============================================================== + + All characters not listed above are treated as delimiters between date and time slots. + So a ``dt`` string of "1996-01-15T00:00:00.0" would have a ``format`` string + like "y-m-dTH:M:S.s". + + :: + DateTime(dt::AbstractString, df::DateFormat) -> DateTime + + Similar form as above for parsing a ``DateTime``, but passes a ``DateFormat`` object instead of a raw formatting string. It is more efficient if similarly formatted date strings will be parsed repeatedly to first create a ``DateFormat`` object then use this method for parsing. + .. function:: DateTime(dt::AbstractString, format::AbstractString; locale="english") -> DateTime + :: + DateTime(y, [m, d, h, mi, s, ms]) -> DateTime + + Construct a DateTime type by parts. Arguments must be convertible to + ``Int64``. + + :: + DateTime(periods::Period...) -> DateTime + + Constuct a DateTime type by ``Period`` type parts. Arguments may be in any order. + DateTime parts not provided will default to the value of ``Dates.default(period)``. + + :: + DateTime(f::Function, y[, m, d, h, mi, s]; step=Day(1), negate=false, limit=10000) -> DateTime + + Create a DateTime through the adjuster API. The starting point will be constructed from the + provided ``y, m, d...`` arguments, and will be adjusted until ``f::Function`` returns true. The step size in + adjusting can be provided manually through the ``step`` keyword. If ``negate=true``, then the adjusting + will stop when ``f::Function`` returns false instead of true. ``limit`` provides a limit to + the max number of iterations the adjustment API will pursue before throwing an error (in the case that ``f::Function`` + is never satisfied). + + :: + DateTime(dt::Date) -> DateTime + + Converts a ``Date`` type to a ``DateTime``. The hour, minute, second, and millisecond + parts of the new ``DateTime`` are assumed to be zero. + + :: + DateTime(dt::AbstractString, format::AbstractString; locale="english") -> DateTime + Construct a DateTime type by parsing the ``dt`` date string following the pattern given in the ``format`` string. The following codes can be used for constructing format strings: @@ -97,12 +349,75 @@ alternatively, you could call ``using Dates`` to bring all exported functions in So a ``dt`` string of "1996-01-15T00:00:00.0" would have a ``format`` string like "y-m-dTH:M:S.s". + :: + DateTime(dt::AbstractString, df::DateFormat) -> DateTime + + Similar form as above for parsing a ``DateTime``, but passes a ``DateFormat`` object instead of a raw formatting string. It is more efficient if similarly formatted date strings will be parsed repeatedly to first create a ``DateFormat`` object then use this method for parsing. + .. function:: Dates.DateFormat(format::AbstractString) -> DateFormat Construct a date formatting object that can be passed repeatedly for parsing similarly formatted date strings. ``format`` is a format string in the form described above (e.g. ``"yyyy-mm-dd"``). .. function:: DateTime(dt::AbstractString, df::DateFormat) -> DateTime + :: + DateTime(y, [m, d, h, mi, s, ms]) -> DateTime + + Construct a DateTime type by parts. Arguments must be convertible to + ``Int64``. + + :: + DateTime(periods::Period...) -> DateTime + + Constuct a DateTime type by ``Period`` type parts. Arguments may be in any order. + DateTime parts not provided will default to the value of ``Dates.default(period)``. + + :: + DateTime(f::Function, y[, m, d, h, mi, s]; step=Day(1), negate=false, limit=10000) -> DateTime + + Create a DateTime through the adjuster API. The starting point will be constructed from the + provided ``y, m, d...`` arguments, and will be adjusted until ``f::Function`` returns true. The step size in + adjusting can be provided manually through the ``step`` keyword. If ``negate=true``, then the adjusting + will stop when ``f::Function`` returns false instead of true. ``limit`` provides a limit to + the max number of iterations the adjustment API will pursue before throwing an error (in the case that ``f::Function`` + is never satisfied). + + :: + DateTime(dt::Date) -> DateTime + + Converts a ``Date`` type to a ``DateTime``. The hour, minute, second, and millisecond + parts of the new ``DateTime`` are assumed to be zero. + + :: + DateTime(dt::AbstractString, format::AbstractString; locale="english") -> DateTime + + Construct a DateTime type by parsing the ``dt`` date string following the pattern given in + the ``format`` string. The following codes can be used for constructing format strings: + + =============== ========= =============================================================== + Code Matches Comment + --------------- --------- --------------------------------------------------------------- + ``y`` 1996, 96 Returns year of 1996, 0096 + ``m`` 1, 01 Matches 1 or 2-digit months + ``u`` Jan Matches abbreviated months according to the ``locale`` keyword + ``U`` January Matches full month names according to the ``locale`` keyword + ``d`` 1, 01 Matches 1 or 2-digit days + ``H`` 00 Matches hours + ``M`` 00 Matches minutes + ``S`` 00 Matches seconds + ``s`` .500 Matches milliseconds + ``e`` Mon, Tues Matches abbreviated days of the week + ``E`` Monday Matches full name days of the week + ``yyyymmdd`` 19960101 Matches fixed-width year, month, and day + =============== ========= =============================================================== + + All characters not listed above are treated as delimiters between date and time slots. + So a ``dt`` string of "1996-01-15T00:00:00.0" would have a ``format`` string + like "y-m-dTH:M:S.s". + + :: + DateTime(dt::AbstractString, df::DateFormat) -> DateTime + Similar form as above for parsing a ``DateTime``, but passes a ``DateFormat`` object instead of a raw formatting string. It is more efficient if similarly formatted date strings will be parsed repeatedly to first create a ``DateFormat`` object then use this method for parsing. .. function:: Date(y, [m, d]) -> Date @@ -110,13 +425,97 @@ alternatively, you could call ``using Dates`` to bring all exported functions in Construct a ``Date`` type by parts. Arguments must be convertible to ``Int64``. + :: + Date(period::Period...) -> Date + + Constuct a Date type by ``Period`` type parts. Arguments may be in any order. + Date parts not provided will default to the value of ``Dates.default(period)``. + + :: + Date(f::Function, y[, m]; step=Day(1), negate=false, limit=10000) -> Date + + Create a Date through the adjuster API. The starting point will be constructed from the + provided ``y, m`` arguments, and will be adjusted until ``f::Function`` returns true. The step size in + adjusting can be provided manually through the ``step`` keyword. If ``negate=true``, then the adjusting + will stop when ``f::Function`` returns false instead of true. ``limit`` provides a limit to + the max number of iterations the adjustment API will pursue before throwing an error (given that ``f::Function`` + is never satisfied). + + :: + Date(dt::DateTime) -> Date + + Converts a ``DateTime`` type to a ``Date``. The hour, minute, second, and millisecond + parts of the ``DateTime`` are truncated, so only the year, month and day parts are used in construction. + + :: + Date(dt::AbstractString, format::AbstractString; locale="english") -> Date + + Construct a Date type by parsing a ``dt`` date string following the pattern given in + the ``format`` string. Follows the same conventions as ``DateTime`` above. + + :: + Date(dt::AbstractString, df::DateFormat) -> Date + + Parse a date from a date string ``dt`` using a ``DateFormat`` object ``df``. + .. function:: Date(period::Period...) -> Date + :: + Date(y, [m, d]) -> Date + + Construct a ``Date`` type by parts. Arguments must be convertible to + ``Int64``. + + :: + Date(period::Period...) -> Date + Constuct a Date type by ``Period`` type parts. Arguments may be in any order. Date parts not provided will default to the value of ``Dates.default(period)``. + :: + Date(f::Function, y[, m]; step=Day(1), negate=false, limit=10000) -> Date + + Create a Date through the adjuster API. The starting point will be constructed from the + provided ``y, m`` arguments, and will be adjusted until ``f::Function`` returns true. The step size in + adjusting can be provided manually through the ``step`` keyword. If ``negate=true``, then the adjusting + will stop when ``f::Function`` returns false instead of true. ``limit`` provides a limit to + the max number of iterations the adjustment API will pursue before throwing an error (given that ``f::Function`` + is never satisfied). + + :: + Date(dt::DateTime) -> Date + + Converts a ``DateTime`` type to a ``Date``. The hour, minute, second, and millisecond + parts of the ``DateTime`` are truncated, so only the year, month and day parts are used in construction. + + :: + Date(dt::AbstractString, format::AbstractString; locale="english") -> Date + + Construct a Date type by parsing a ``dt`` date string following the pattern given in + the ``format`` string. Follows the same conventions as ``DateTime`` above. + + :: + Date(dt::AbstractString, df::DateFormat) -> Date + + Parse a date from a date string ``dt`` using a ``DateFormat`` object ``df``. + .. function:: Date(f::Function, y[, m]; step=Day(1), negate=false, limit=10000) -> Date + :: + Date(y, [m, d]) -> Date + + Construct a ``Date`` type by parts. Arguments must be convertible to + ``Int64``. + + :: + Date(period::Period...) -> Date + + Constuct a Date type by ``Period`` type parts. Arguments may be in any order. + Date parts not provided will default to the value of ``Dates.default(period)``. + + :: + Date(f::Function, y[, m]; step=Day(1), negate=false, limit=10000) -> Date + Create a Date through the adjuster API. The starting point will be constructed from the provided ``y, m`` arguments, and will be adjusted until ``f::Function`` returns true. The step size in adjusting can be provided manually through the ``step`` keyword. If ``negate=true``, then the adjusting @@ -124,18 +523,144 @@ alternatively, you could call ``using Dates`` to bring all exported functions in the max number of iterations the adjustment API will pursue before throwing an error (given that ``f::Function`` is never satisfied). + :: + Date(dt::DateTime) -> Date + + Converts a ``DateTime`` type to a ``Date``. The hour, minute, second, and millisecond + parts of the ``DateTime`` are truncated, so only the year, month and day parts are used in construction. + + :: + Date(dt::AbstractString, format::AbstractString; locale="english") -> Date + + Construct a Date type by parsing a ``dt`` date string following the pattern given in + the ``format`` string. Follows the same conventions as ``DateTime`` above. + + :: + Date(dt::AbstractString, df::DateFormat) -> Date + + Parse a date from a date string ``dt`` using a ``DateFormat`` object ``df``. + .. function:: Date(dt::DateTime) -> Date + :: + Date(y, [m, d]) -> Date + + Construct a ``Date`` type by parts. Arguments must be convertible to + ``Int64``. + + :: + Date(period::Period...) -> Date + + Constuct a Date type by ``Period`` type parts. Arguments may be in any order. + Date parts not provided will default to the value of ``Dates.default(period)``. + + :: + Date(f::Function, y[, m]; step=Day(1), negate=false, limit=10000) -> Date + + Create a Date through the adjuster API. The starting point will be constructed from the + provided ``y, m`` arguments, and will be adjusted until ``f::Function`` returns true. The step size in + adjusting can be provided manually through the ``step`` keyword. If ``negate=true``, then the adjusting + will stop when ``f::Function`` returns false instead of true. ``limit`` provides a limit to + the max number of iterations the adjustment API will pursue before throwing an error (given that ``f::Function`` + is never satisfied). + + :: + Date(dt::DateTime) -> Date + Converts a ``DateTime`` type to a ``Date``. The hour, minute, second, and millisecond parts of the ``DateTime`` are truncated, so only the year, month and day parts are used in construction. + :: + Date(dt::AbstractString, format::AbstractString; locale="english") -> Date + + Construct a Date type by parsing a ``dt`` date string following the pattern given in + the ``format`` string. Follows the same conventions as ``DateTime`` above. + + :: + Date(dt::AbstractString, df::DateFormat) -> Date + + Parse a date from a date string ``dt`` using a ``DateFormat`` object ``df``. + .. function:: Date(dt::AbstractString, format::AbstractString; locale="english") -> Date + :: + Date(y, [m, d]) -> Date + + Construct a ``Date`` type by parts. Arguments must be convertible to + ``Int64``. + + :: + Date(period::Period...) -> Date + + Constuct a Date type by ``Period`` type parts. Arguments may be in any order. + Date parts not provided will default to the value of ``Dates.default(period)``. + + :: + Date(f::Function, y[, m]; step=Day(1), negate=false, limit=10000) -> Date + + Create a Date through the adjuster API. The starting point will be constructed from the + provided ``y, m`` arguments, and will be adjusted until ``f::Function`` returns true. The step size in + adjusting can be provided manually through the ``step`` keyword. If ``negate=true``, then the adjusting + will stop when ``f::Function`` returns false instead of true. ``limit`` provides a limit to + the max number of iterations the adjustment API will pursue before throwing an error (given that ``f::Function`` + is never satisfied). + + :: + Date(dt::DateTime) -> Date + + Converts a ``DateTime`` type to a ``Date``. The hour, minute, second, and millisecond + parts of the ``DateTime`` are truncated, so only the year, month and day parts are used in construction. + + :: + Date(dt::AbstractString, format::AbstractString; locale="english") -> Date + Construct a Date type by parsing a ``dt`` date string following the pattern given in the ``format`` string. Follows the same conventions as ``DateTime`` above. + :: + Date(dt::AbstractString, df::DateFormat) -> Date + + Parse a date from a date string ``dt`` using a ``DateFormat`` object ``df``. + .. function:: Date(dt::AbstractString, df::DateFormat) -> Date + :: + Date(y, [m, d]) -> Date + + Construct a ``Date`` type by parts. Arguments must be convertible to + ``Int64``. + + :: + Date(period::Period...) -> Date + + Constuct a Date type by ``Period`` type parts. Arguments may be in any order. + Date parts not provided will default to the value of ``Dates.default(period)``. + + :: + Date(f::Function, y[, m]; step=Day(1), negate=false, limit=10000) -> Date + + Create a Date through the adjuster API. The starting point will be constructed from the + provided ``y, m`` arguments, and will be adjusted until ``f::Function`` returns true. The step size in + adjusting can be provided manually through the ``step`` keyword. If ``negate=true``, then the adjusting + will stop when ``f::Function`` returns false instead of true. ``limit`` provides a limit to + the max number of iterations the adjustment API will pursue before throwing an error (given that ``f::Function`` + is never satisfied). + + :: + Date(dt::DateTime) -> Date + + Converts a ``DateTime`` type to a ``Date``. The hour, minute, second, and millisecond + parts of the ``DateTime`` are truncated, so only the year, month and day parts are used in construction. + + :: + Date(dt::AbstractString, format::AbstractString; locale="english") -> Date + + Construct a Date type by parsing a ``dt`` date string following the pattern given in + the ``format`` string. Follows the same conventions as ``DateTime`` above. + + :: + Date(dt::AbstractString, df::DateFormat) -> Date + Parse a date from a date string ``dt`` using a ``DateFormat`` object ``df``. .. function:: now() -> DateTime @@ -143,12 +668,29 @@ alternatively, you could call ``using Dates`` to bring all exported functions in Returns a DateTime corresponding to the user's system time including the system timezone locale. + :: + now(::Type{UTC}) -> DateTime + + Returns a DateTime corresponding to the user's system + time as UTC/GMT. + .. function:: now(::Type{UTC}) -> DateTime + :: + now() -> DateTime + + Returns a DateTime corresponding to the user's system + time including the system timezone locale. + + :: + now(::Type{UTC}) -> DateTime + Returns a DateTime corresponding to the user's system time as UTC/GMT. .. function:: eps(::DateTime) -> Millisecond + + :: eps(::Date) -> Day Returns ``Millisecond(1)`` for ``DateTime`` values and ``Day(1)`` for ``Date`` values. @@ -157,6 +699,8 @@ Accessor Functions ~~~~~~~~~~~~~~~~~~ .. function:: year(dt::TimeType) -> Int64 + + :: month(dt::TimeType) -> Int64 week(dt::TimeType) -> Int64 day(dt::TimeType) -> Int64 @@ -168,6 +712,8 @@ Accessor Functions Return the field part of a Date or DateTime as an ``Int64``. .. function:: Year(dt::TimeType) -> Year + + :: Month(dt::TimeType) -> Month Week(dt::TimeType) -> Week Day(dt::TimeType) -> Day @@ -178,6 +724,19 @@ Accessor Functions Return the field part of a Date or DateTime as a ``Period`` type. + :: + Year(v) + Month(v) + Week(v) + Day(v) + Hour(v) + Minute(v) + Second(v) + Millisecond(v) + + Construct a ``Period`` type with the given ``v`` value. + Input must be losslessly convertible to an ``Int64``. + .. function:: yearmonth(dt::TimeType) -> (Int64, Int64) Simultaneously return the year and month parts of a Date or DateTime. @@ -298,12 +857,28 @@ Adjuster Functions ``1 = Monday, 2 = Tuesday, etc``. Setting ``same=true`` allows the current ``dt`` to be considered as the next ``dow``, allowing for no adjustment to occur. + :: + tonext(func::Function,dt::TimeType;step=Day(1),negate=false,limit=10000,same=false) -> TimeType + + Adjusts ``dt`` by iterating at most ``limit`` iterations by ``step`` increments until + ``func`` returns true. ``func`` must take a single ``TimeType`` argument and return a ``Bool``. + ``same`` allows ``dt`` to be considered in satisfying ``func``. ``negate`` will make the adjustment + process terminate when ``func`` returns false instead of true. + .. function:: toprev(dt::TimeType,dow::Int;same::Bool=false) -> TimeType Adjusts ``dt`` to the previous day of week corresponding to ``dow`` with ``1 = Monday, 2 = Tuesday, etc``. Setting ``same=true`` allows the current ``dt`` to be considered as the previous ``dow``, allowing for no adjustment to occur. + :: + toprev(func::Function,dt::TimeType;step=Day(-1),negate=false,limit=10000,same=false) -> TimeType + + Adjusts ``dt`` by iterating at most ``limit`` iterations by ``step`` increments until + ``func`` returns true. ``func`` must take a single ``TimeType`` argument and return a ``Bool``. + ``same`` allows ``dt`` to be considered in satisfying ``func``. ``negate`` will make the adjustment + process terminate when ``func`` returns false instead of true. + .. function:: tofirst(dt::TimeType,dow::Int;of=Month) -> TimeType Adjusts ``dt`` to the first ``dow`` of its month. Alternatively, ``of=Year`` @@ -316,6 +891,16 @@ Adjuster Functions .. function:: tonext(func::Function,dt::TimeType;step=Day(1),negate=false,limit=10000,same=false) -> TimeType + :: + tonext(dt::TimeType,dow::Int;same::Bool=false) -> TimeType + + Adjusts ``dt`` to the next day of week corresponding to ``dow`` with + ``1 = Monday, 2 = Tuesday, etc``. Setting ``same=true`` allows the current + ``dt`` to be considered as the next ``dow``, allowing for no adjustment to occur. + + :: + tonext(func::Function,dt::TimeType;step=Day(1),negate=false,limit=10000,same=false) -> TimeType + Adjusts ``dt`` by iterating at most ``limit`` iterations by ``step`` increments until ``func`` returns true. ``func`` must take a single ``TimeType`` argument and return a ``Bool``. ``same`` allows ``dt`` to be considered in satisfying ``func``. ``negate`` will make the adjustment @@ -323,6 +908,16 @@ Adjuster Functions .. function:: toprev(func::Function,dt::TimeType;step=Day(-1),negate=false,limit=10000,same=false) -> TimeType + :: + toprev(dt::TimeType,dow::Int;same::Bool=false) -> TimeType + + Adjusts ``dt`` to the previous day of week corresponding to ``dow`` with + ``1 = Monday, 2 = Tuesday, etc``. Setting ``same=true`` allows the current + ``dt`` to be considered as the previous ``dow``, allowing for no adjustment to occur. + + :: + toprev(func::Function,dt::TimeType;step=Day(-1),negate=false,limit=10000,same=false) -> TimeType + Adjusts ``dt`` by iterating at most ``limit`` iterations by ``step`` increments until ``func`` returns true. ``func`` must take a single ``TimeType`` argument and return a ``Bool``. ``same`` allows ``dt`` to be considered in satisfying ``func``. ``negate`` will make the adjustment @@ -335,11 +930,25 @@ Adjuster Functions range of ``dr``, including those elements for which ``func`` returns ``true`` in the resulting Array, unless ``negate=true``, then only elements where ``func`` returns ``false`` are included. - Periods ~~~~~~~ .. function:: Year(v) + + :: + Year(dt::TimeType) -> Year + Month(dt::TimeType) -> Month + Week(dt::TimeType) -> Week + Day(dt::TimeType) -> Day + Hour(dt::TimeType) -> Hour + Minute(dt::TimeType) -> Minute + Second(dt::TimeType) -> Second + Millisecond(dt::TimeType) -> Millisecond + + Return the field part of a Date or DateTime as a ``Period`` type. + + :: + Year(v) Month(v) Week(v) Day(v) @@ -394,7 +1003,6 @@ Conversion Functions Returns the number of Rata Die days since epoch from the given Date or DateTime. - Constants ~~~~~~~~~ diff --git a/doc/stdlib/file.rst b/doc/stdlib/file.rst index f53e41b6e3162..23424e96db4f9 100644 --- a/doc/stdlib/file.rst +++ b/doc/stdlib/file.rst @@ -13,8 +13,21 @@ Set the current working directory. + :: + cd(f, [dir]) + + Temporarily changes the current working directory (HOME if not specified) and applies function f before returning. + .. function:: cd(f, [dir]) + :: + cd(dir::AbstractString) + + Set the current working directory. + + :: + cd(f, [dir]) + Temporarily changes the current working directory (HOME if not specified) and applies function f before returning. .. function:: readdir([dir]) -> Vector{ByteString} @@ -112,7 +125,7 @@ .. function:: cp(src::AbstractString, dst::AbstractString; remove_destination::Bool=false, follow_symlinks::Bool=false) Copy the file, link, or directory from *src* to *dest*. - \"remove_destination=true\" will first remove an existing `dst`. + "remove_destination=true" will first remove an existing `dst`. If `follow_symlinks=false`, and src is a symbolic link, dst will be created as a symbolic link. If `follow_symlinks=true` and src is a symbolic link, dst will be a copy of the file or directory @@ -129,7 +142,7 @@ .. function:: mv(src::AbstractString,dst::AbstractString; remove_destination::Bool=false) Move the file, link, or directory from *src* to *dest*. - \"remove_destination=true\" will first remove an existing `dst`. + "remove_destination=true" will first remove an existing `dst`. .. function:: rm(path::AbstractString; recursive=false) @@ -289,3 +302,4 @@ If the last component of a path contains a dot, split the path into everything before the dot and everything including and after the dot. Otherwise, return a tuple of the argument unmodified and the empty string. + diff --git a/doc/stdlib/io-network.rst b/doc/stdlib/io-network.rst index abcc1816b95c7..8d3c12207148e 100644 --- a/doc/stdlib/io-network.rst +++ b/doc/stdlib/io-network.rst @@ -21,10 +21,80 @@ General I/O .. function:: open(file_name, [read, write, create, truncate, append]) -> IOStream + :: + open(command, mode::AbstractString="r", stdio=DevNull) + + Start running ``command`` asynchronously, and return a tuple + ``(stream,process)``. If ``mode`` is ``"r"``, then ``stream`` + reads from the process's standard output and ``stdio`` optionally + specifies the process's standard input stream. If ``mode`` is + ``"w"``, then ``stream`` writes to the process's standard input + and ``stdio`` optionally specifies the process's standard output + stream. + + :: + open(f::Function, command, mode::AbstractString="r", stdio=DevNull) + + Similar to ``open(command, mode, stdio)``, but calls ``f(stream)`` + on the resulting read or write stream, then closes the stream + and waits for the process to complete. Returns the value returned + by ``f``. + + :: + open(file_name, [read, write, create, truncate, append]) -> IOStream + Open a file in a mode specified by five boolean arguments. The default is to open files for reading only. Returns a stream for accessing the file. + :: + open(file_name, [mode]) -> IOStream + + Alternate syntax for open, where a string-based mode specifier is used instead of the five booleans. The values of ``mode`` correspond to those from ``fopen(3)`` or Perl ``open``, and are equivalent to setting the following boolean groups: + + ==== ================================= + r read + r+ read, write + w write, create, truncate + w+ read, write, create, truncate + a write, create, append + a+ read, write, create, append + ==== ================================= + + :: + open(f::function, args...) + + Apply the function ``f`` to the result of ``open(args...)`` and close the resulting file descriptor upon completion. + + **Example**: ``open(readall, "file.txt")`` + .. function:: open(file_name, [mode]) -> IOStream + :: + open(command, mode::AbstractString="r", stdio=DevNull) + + Start running ``command`` asynchronously, and return a tuple + ``(stream,process)``. If ``mode`` is ``"r"``, then ``stream`` + reads from the process's standard output and ``stdio`` optionally + specifies the process's standard input stream. If ``mode`` is + ``"w"``, then ``stream`` writes to the process's standard input + and ``stdio`` optionally specifies the process's standard output + stream. + + :: + open(f::Function, command, mode::AbstractString="r", stdio=DevNull) + + Similar to ``open(command, mode, stdio)``, but calls ``f(stream)`` + on the resulting read or write stream, then closes the stream + and waits for the process to complete. Returns the value returned + by ``f``. + + :: + open(file_name, [read, write, create, truncate, append]) -> IOStream + + Open a file in a mode specified by five boolean arguments. The default is to open files for reading only. Returns a stream for accessing the file. + + :: + open(file_name, [mode]) -> IOStream + Alternate syntax for open, where a string-based mode specifier is used instead of the five booleans. The values of ``mode`` correspond to those from ``fopen(3)`` or Perl ``open``, and are equivalent to setting the following boolean groups: ==== ================================= @@ -36,9 +106,56 @@ General I/O a+ read, write, create, append ==== ================================= + :: + open(f::function, args...) + + Apply the function ``f`` to the result of ``open(args...)`` and close the resulting file descriptor upon completion. + + **Example**: ``open(readall, "file.txt")`` .. function:: open(f::function, args...) + :: + open(command, mode::AbstractString="r", stdio=DevNull) + + Start running ``command`` asynchronously, and return a tuple + ``(stream,process)``. If ``mode`` is ``"r"``, then ``stream`` + reads from the process's standard output and ``stdio`` optionally + specifies the process's standard input stream. If ``mode`` is + ``"w"``, then ``stream`` writes to the process's standard input + and ``stdio`` optionally specifies the process's standard output + stream. + + :: + open(f::Function, command, mode::AbstractString="r", stdio=DevNull) + + Similar to ``open(command, mode, stdio)``, but calls ``f(stream)`` + on the resulting read or write stream, then closes the stream + and waits for the process to complete. Returns the value returned + by ``f``. + + :: + open(file_name, [read, write, create, truncate, append]) -> IOStream + + Open a file in a mode specified by five boolean arguments. The default is to open files for reading only. Returns a stream for accessing the file. + + :: + open(file_name, [mode]) -> IOStream + + Alternate syntax for open, where a string-based mode specifier is used instead of the five booleans. The values of ``mode`` correspond to those from ``fopen(3)`` or Perl ``open``, and are equivalent to setting the following boolean groups: + + ==== ================================= + r read + r+ read, write + w write, create, truncate + w+ read, write, create, truncate + a write, create, append + a+ read, write, create, append + ==== ================================= + + :: + open(f::function, args...) + Apply the function ``f`` to the result of ``open(args...)`` and close the resulting file descriptor upon completion. **Example**: ``open(readall, "file.txt")`` @@ -47,16 +164,91 @@ General I/O Create an in-memory I/O stream. + :: + IOBuffer(size::Int) + + Create a fixed size IOBuffer. The buffer will not grow dynamically. + + :: + IOBuffer(string) + + Create a read-only IOBuffer on the data underlying the given string + + :: + IOBuffer([data,],[readable,writable,[maxsize]]) + + Create an IOBuffer, which may optionally operate on a pre-existing array. If the readable/writable arguments are given, + they restrict whether or not the buffer may be read from or written to respectively. By default the buffer is readable + but not writable. The last argument optionally specifies a size beyond which the buffer may not be grown. + .. function:: IOBuffer(size::Int) + :: + IOBuffer() -> IOBuffer + + Create an in-memory I/O stream. + + :: + IOBuffer(size::Int) + Create a fixed size IOBuffer. The buffer will not grow dynamically. + :: + IOBuffer(string) + + Create a read-only IOBuffer on the data underlying the given string + + :: + IOBuffer([data,],[readable,writable,[maxsize]]) + + Create an IOBuffer, which may optionally operate on a pre-existing array. If the readable/writable arguments are given, + they restrict whether or not the buffer may be read from or written to respectively. By default the buffer is readable + but not writable. The last argument optionally specifies a size beyond which the buffer may not be grown. + .. function:: IOBuffer(string) + :: + IOBuffer() -> IOBuffer + + Create an in-memory I/O stream. + + :: + IOBuffer(size::Int) + + Create a fixed size IOBuffer. The buffer will not grow dynamically. + + :: + IOBuffer(string) + Create a read-only IOBuffer on the data underlying the given string + :: + IOBuffer([data,],[readable,writable,[maxsize]]) + + Create an IOBuffer, which may optionally operate on a pre-existing array. If the readable/writable arguments are given, + they restrict whether or not the buffer may be read from or written to respectively. By default the buffer is readable + but not writable. The last argument optionally specifies a size beyond which the buffer may not be grown. + .. function:: IOBuffer([data,],[readable,writable,[maxsize]]) + :: + IOBuffer() -> IOBuffer + + Create an in-memory I/O stream. + + :: + IOBuffer(size::Int) + + Create a fixed size IOBuffer. The buffer will not grow dynamically. + + :: + IOBuffer(string) + + Create a read-only IOBuffer on the data underlying the given string + + :: + IOBuffer([data,],[readable,writable,[maxsize]]) + Create an IOBuffer, which may optionally operate on a pre-existing array. If the readable/writable arguments are given, they restrict whether or not the buffer may be read from or written to respectively. By default the buffer is readable but not writable. The last argument optionally specifies a size beyond which the buffer may not be grown. @@ -81,6 +273,15 @@ General I/O Close an I/O stream. Performs a ``flush`` first. + :: + close(Channel) + + Closes a channel. An exception is thrown by: + + * ``put!`` on a on a closed channel. + + * ``take!`` and ``fetch`` on an empty, closed channel. + .. function:: write(stream, x) Write the canonical binary representation of a value to the given stream. @@ -89,8 +290,21 @@ General I/O Read a value of the given type from a stream, in canonical binary representation. + :: + read(stream, type, dims) + + Read a series of values of the given type from a stream, in canonical binary representation. ``dims`` is either a tuple or a series of integer arguments specifying the size of ``Array`` to return. + .. function:: read(stream, type, dims) + :: + read(stream, type) + + Read a value of the given type from a stream, in canonical binary representation. + + :: + read(stream, type, dims) + Read a series of values of the given type from a stream, in canonical binary representation. ``dims`` is either a tuple or a series of integer arguments specifying the size of ``Array`` to return. .. function:: read!(stream, array::Array) @@ -223,8 +437,25 @@ General I/O wr end is given for convenience in case the old STDOUT object was cached by the user and needs to be replaced elsewhere. + :: + redirect_stdout(stream) + + Replace STDOUT by stream for all C and julia level output to STDOUT. Note that `stream` must be a TTY, a Pipe or a + TcpSocket. + .. function:: redirect_stdout(stream) + :: + redirect_stdout() + + Create a pipe to which all C and Julia level STDOUT output will be redirected. Returns a tuple (rd,wr) + representing the pipe ends. Data written to STDOUT may now be read from the rd end of the pipe. The + wr end is given for convenience in case the old STDOUT object was cached by the user and needs to be + replaced elsewhere. + + :: + redirect_stdout(stream) + Replace STDOUT by stream for all C and julia level output to STDOUT. Note that `stream` must be a TTY, a Pipe or a TcpSocket. @@ -259,15 +490,27 @@ General I/O An IOBuffer that allows reading and performs writes by appending. Seeking and truncating are not supported. See IOBuffer for the available constructors. + :: + PipeBuffer(data::Vector{UInt8},[maxsize]) + + Create a PipeBuffer to operate on a data vector, optionally specifying a size beyond which the underlying Array may not be grown. + .. function:: PipeBuffer(data::Vector{UInt8},[maxsize]) + :: + PipeBuffer() + + An IOBuffer that allows reading and performs writes by appending. Seeking and truncating are not supported. See IOBuffer for the available constructors. + + :: + PipeBuffer(data::Vector{UInt8},[maxsize]) + Create a PipeBuffer to operate on a data vector, optionally specifying a size beyond which the underlying Array may not be grown. .. function:: readavailable(stream) Read all available data on the stream, blocking the task only if no data is available. The result is a ``Vector{UInt8,1}``. - Text I/O -------- @@ -345,8 +588,22 @@ Text I/O Read the entire contents of an I/O stream as a string. + :: + readall(filename::AbstractString) + + Open ``filename``, read the entire contents as a string, then close the file. + Equivalent to ``open(readall, filename)``. + .. function:: readall(filename::AbstractString) + :: + readall(stream::IO) + + Read the entire contents of an I/O stream as a string. + + :: + readall(filename::AbstractString) + Open ``filename``, read the entire contents as a string, then close the file. Equivalent to ``open(readall, filename)``. @@ -388,24 +645,279 @@ Text I/O If ``comments`` is ``true``, lines beginning with ``comment_char`` and text following ``comment_char`` in any line are ignored. + :: + readdlm(source, delim::Char, eol::Char; options...) + + If all data is numeric, the result will be a numeric array. If some elements cannot be parsed as numbers, a cell array of numbers and strings is returned. + + :: + readdlm(source, delim::Char, T::Type; options...) + + The end of line delimiter is taken as ``\n``. + + :: + readdlm(source, delim::Char; options...) + + The end of line delimiter is taken as ``\n``. If all data is numeric, the result will be a numeric array. If some elements cannot be parsed as numbers, a cell array of numbers and strings is returned. + + :: + readdlm(source, T::Type; options...) + + The columns are assumed to be separated by one or more whitespaces. The end of line delimiter is taken as ``\n``. + + :: + readdlm(source; options...) + + The columns are assumed to be separated by one or more whitespaces. The end of line delimiter is taken as ``\n``. If all data is numeric, the result will be a numeric array. If some elements cannot be parsed as numbers, a cell array of numbers and strings is returned. + .. function:: readdlm(source, delim::Char, eol::Char; options...) + :: + readdlm(source, delim::Char, T::Type, eol::Char; header=false, skipstart=0, skipblanks=true, use_mmap, ignore_invalid_chars=false, quotes=true, dims, comments=true, comment_char='#') + + Read a matrix from the source where each line (separated by ``eol``) gives one row, with elements separated by the given delimeter. The source can be a text file, stream or byte array. Memory mapped files can be used by passing the byte array representation of the mapped segment as source. + + If ``T`` is a numeric type, the result is an array of that type, with any non-numeric elements as ``NaN`` for floating-point types, or zero. Other useful values of ``T`` include ``ASCIIString``, ``AbstractString``, and ``Any``. + + If ``header`` is ``true``, the first row of data will be read as header and the tuple ``(data_cells, header_cells)`` is returned instead of only ``data_cells``. + + Specifying ``skipstart`` will ignore the corresponding number of initial lines from the input. + + If ``skipblanks`` is ``true``, blank lines in the input will be ignored. + + If ``use_mmap`` is ``true``, the file specified by ``source`` is memory mapped for potential speedups. Default is ``true`` except on Windows. On Windows, you may want to specify ``true`` if the file is large, and is only read once and not written to. + + If ``ignore_invalid_chars`` is ``true``, bytes in ``source`` with invalid character encoding will be ignored. Otherwise an error is thrown indicating the offending character position. + + If ``quotes`` is ``true``, column enclosed within double-quote (``) characters are allowed to contain new lines and column delimiters. Double-quote characters within a quoted field must be escaped with another double-quote. + + Specifying ``dims`` as a tuple of the expected rows and columns (including header, if any) may speed up reading of large files. + + If ``comments`` is ``true``, lines beginning with ``comment_char`` and text following ``comment_char`` in any line are ignored. + + :: + readdlm(source, delim::Char, eol::Char; options...) + If all data is numeric, the result will be a numeric array. If some elements cannot be parsed as numbers, a cell array of numbers and strings is returned. + :: + readdlm(source, delim::Char, T::Type; options...) + + The end of line delimiter is taken as ``\n``. + + :: + readdlm(source, delim::Char; options...) + + The end of line delimiter is taken as ``\n``. If all data is numeric, the result will be a numeric array. If some elements cannot be parsed as numbers, a cell array of numbers and strings is returned. + + :: + readdlm(source, T::Type; options...) + + The columns are assumed to be separated by one or more whitespaces. The end of line delimiter is taken as ``\n``. + + :: + readdlm(source; options...) + + The columns are assumed to be separated by one or more whitespaces. The end of line delimiter is taken as ``\n``. If all data is numeric, the result will be a numeric array. If some elements cannot be parsed as numbers, a cell array of numbers and strings is returned. + .. function:: readdlm(source, delim::Char, T::Type; options...) + :: + readdlm(source, delim::Char, T::Type, eol::Char; header=false, skipstart=0, skipblanks=true, use_mmap, ignore_invalid_chars=false, quotes=true, dims, comments=true, comment_char='#') + + Read a matrix from the source where each line (separated by ``eol``) gives one row, with elements separated by the given delimeter. The source can be a text file, stream or byte array. Memory mapped files can be used by passing the byte array representation of the mapped segment as source. + + If ``T`` is a numeric type, the result is an array of that type, with any non-numeric elements as ``NaN`` for floating-point types, or zero. Other useful values of ``T`` include ``ASCIIString``, ``AbstractString``, and ``Any``. + + If ``header`` is ``true``, the first row of data will be read as header and the tuple ``(data_cells, header_cells)`` is returned instead of only ``data_cells``. + + Specifying ``skipstart`` will ignore the corresponding number of initial lines from the input. + + If ``skipblanks`` is ``true``, blank lines in the input will be ignored. + + If ``use_mmap`` is ``true``, the file specified by ``source`` is memory mapped for potential speedups. Default is ``true`` except on Windows. On Windows, you may want to specify ``true`` if the file is large, and is only read once and not written to. + + If ``ignore_invalid_chars`` is ``true``, bytes in ``source`` with invalid character encoding will be ignored. Otherwise an error is thrown indicating the offending character position. + + If ``quotes`` is ``true``, column enclosed within double-quote (``) characters are allowed to contain new lines and column delimiters. Double-quote characters within a quoted field must be escaped with another double-quote. + + Specifying ``dims`` as a tuple of the expected rows and columns (including header, if any) may speed up reading of large files. + + If ``comments`` is ``true``, lines beginning with ``comment_char`` and text following ``comment_char`` in any line are ignored. + + :: + readdlm(source, delim::Char, eol::Char; options...) + + If all data is numeric, the result will be a numeric array. If some elements cannot be parsed as numbers, a cell array of numbers and strings is returned. + + :: + readdlm(source, delim::Char, T::Type; options...) + The end of line delimiter is taken as ``\n``. + :: + readdlm(source, delim::Char; options...) + + The end of line delimiter is taken as ``\n``. If all data is numeric, the result will be a numeric array. If some elements cannot be parsed as numbers, a cell array of numbers and strings is returned. + + :: + readdlm(source, T::Type; options...) + + The columns are assumed to be separated by one or more whitespaces. The end of line delimiter is taken as ``\n``. + + :: + readdlm(source; options...) + + The columns are assumed to be separated by one or more whitespaces. The end of line delimiter is taken as ``\n``. If all data is numeric, the result will be a numeric array. If some elements cannot be parsed as numbers, a cell array of numbers and strings is returned. + .. function:: readdlm(source, delim::Char; options...) + :: + readdlm(source, delim::Char, T::Type, eol::Char; header=false, skipstart=0, skipblanks=true, use_mmap, ignore_invalid_chars=false, quotes=true, dims, comments=true, comment_char='#') + + Read a matrix from the source where each line (separated by ``eol``) gives one row, with elements separated by the given delimeter. The source can be a text file, stream or byte array. Memory mapped files can be used by passing the byte array representation of the mapped segment as source. + + If ``T`` is a numeric type, the result is an array of that type, with any non-numeric elements as ``NaN`` for floating-point types, or zero. Other useful values of ``T`` include ``ASCIIString``, ``AbstractString``, and ``Any``. + + If ``header`` is ``true``, the first row of data will be read as header and the tuple ``(data_cells, header_cells)`` is returned instead of only ``data_cells``. + + Specifying ``skipstart`` will ignore the corresponding number of initial lines from the input. + + If ``skipblanks`` is ``true``, blank lines in the input will be ignored. + + If ``use_mmap`` is ``true``, the file specified by ``source`` is memory mapped for potential speedups. Default is ``true`` except on Windows. On Windows, you may want to specify ``true`` if the file is large, and is only read once and not written to. + + If ``ignore_invalid_chars`` is ``true``, bytes in ``source`` with invalid character encoding will be ignored. Otherwise an error is thrown indicating the offending character position. + + If ``quotes`` is ``true``, column enclosed within double-quote (``) characters are allowed to contain new lines and column delimiters. Double-quote characters within a quoted field must be escaped with another double-quote. + + Specifying ``dims`` as a tuple of the expected rows and columns (including header, if any) may speed up reading of large files. + + If ``comments`` is ``true``, lines beginning with ``comment_char`` and text following ``comment_char`` in any line are ignored. + + :: + readdlm(source, delim::Char, eol::Char; options...) + + If all data is numeric, the result will be a numeric array. If some elements cannot be parsed as numbers, a cell array of numbers and strings is returned. + + :: + readdlm(source, delim::Char, T::Type; options...) + + The end of line delimiter is taken as ``\n``. + + :: + readdlm(source, delim::Char; options...) + The end of line delimiter is taken as ``\n``. If all data is numeric, the result will be a numeric array. If some elements cannot be parsed as numbers, a cell array of numbers and strings is returned. + :: + readdlm(source, T::Type; options...) + + The columns are assumed to be separated by one or more whitespaces. The end of line delimiter is taken as ``\n``. + + :: + readdlm(source; options...) + + The columns are assumed to be separated by one or more whitespaces. The end of line delimiter is taken as ``\n``. If all data is numeric, the result will be a numeric array. If some elements cannot be parsed as numbers, a cell array of numbers and strings is returned. + .. function:: readdlm(source, T::Type; options...) + :: + readdlm(source, delim::Char, T::Type, eol::Char; header=false, skipstart=0, skipblanks=true, use_mmap, ignore_invalid_chars=false, quotes=true, dims, comments=true, comment_char='#') + + Read a matrix from the source where each line (separated by ``eol``) gives one row, with elements separated by the given delimeter. The source can be a text file, stream or byte array. Memory mapped files can be used by passing the byte array representation of the mapped segment as source. + + If ``T`` is a numeric type, the result is an array of that type, with any non-numeric elements as ``NaN`` for floating-point types, or zero. Other useful values of ``T`` include ``ASCIIString``, ``AbstractString``, and ``Any``. + + If ``header`` is ``true``, the first row of data will be read as header and the tuple ``(data_cells, header_cells)`` is returned instead of only ``data_cells``. + + Specifying ``skipstart`` will ignore the corresponding number of initial lines from the input. + + If ``skipblanks`` is ``true``, blank lines in the input will be ignored. + + If ``use_mmap`` is ``true``, the file specified by ``source`` is memory mapped for potential speedups. Default is ``true`` except on Windows. On Windows, you may want to specify ``true`` if the file is large, and is only read once and not written to. + + If ``ignore_invalid_chars`` is ``true``, bytes in ``source`` with invalid character encoding will be ignored. Otherwise an error is thrown indicating the offending character position. + + If ``quotes`` is ``true``, column enclosed within double-quote (``) characters are allowed to contain new lines and column delimiters. Double-quote characters within a quoted field must be escaped with another double-quote. + + Specifying ``dims`` as a tuple of the expected rows and columns (including header, if any) may speed up reading of large files. + + If ``comments`` is ``true``, lines beginning with ``comment_char`` and text following ``comment_char`` in any line are ignored. + + :: + readdlm(source, delim::Char, eol::Char; options...) + + If all data is numeric, the result will be a numeric array. If some elements cannot be parsed as numbers, a cell array of numbers and strings is returned. + + :: + readdlm(source, delim::Char, T::Type; options...) + + The end of line delimiter is taken as ``\n``. + + :: + readdlm(source, delim::Char; options...) + + The end of line delimiter is taken as ``\n``. If all data is numeric, the result will be a numeric array. If some elements cannot be parsed as numbers, a cell array of numbers and strings is returned. + + :: + readdlm(source, T::Type; options...) + The columns are assumed to be separated by one or more whitespaces. The end of line delimiter is taken as ``\n``. + :: + readdlm(source; options...) + + The columns are assumed to be separated by one or more whitespaces. The end of line delimiter is taken as ``\n``. If all data is numeric, the result will be a numeric array. If some elements cannot be parsed as numbers, a cell array of numbers and strings is returned. + .. function:: readdlm(source; options...) + :: + readdlm(source, delim::Char, T::Type, eol::Char; header=false, skipstart=0, skipblanks=true, use_mmap, ignore_invalid_chars=false, quotes=true, dims, comments=true, comment_char='#') + + Read a matrix from the source where each line (separated by ``eol``) gives one row, with elements separated by the given delimeter. The source can be a text file, stream or byte array. Memory mapped files can be used by passing the byte array representation of the mapped segment as source. + + If ``T`` is a numeric type, the result is an array of that type, with any non-numeric elements as ``NaN`` for floating-point types, or zero. Other useful values of ``T`` include ``ASCIIString``, ``AbstractString``, and ``Any``. + + If ``header`` is ``true``, the first row of data will be read as header and the tuple ``(data_cells, header_cells)`` is returned instead of only ``data_cells``. + + Specifying ``skipstart`` will ignore the corresponding number of initial lines from the input. + + If ``skipblanks`` is ``true``, blank lines in the input will be ignored. + + If ``use_mmap`` is ``true``, the file specified by ``source`` is memory mapped for potential speedups. Default is ``true`` except on Windows. On Windows, you may want to specify ``true`` if the file is large, and is only read once and not written to. + + If ``ignore_invalid_chars`` is ``true``, bytes in ``source`` with invalid character encoding will be ignored. Otherwise an error is thrown indicating the offending character position. + + If ``quotes`` is ``true``, column enclosed within double-quote (``) characters are allowed to contain new lines and column delimiters. Double-quote characters within a quoted field must be escaped with another double-quote. + + Specifying ``dims`` as a tuple of the expected rows and columns (including header, if any) may speed up reading of large files. + + If ``comments`` is ``true``, lines beginning with ``comment_char`` and text following ``comment_char`` in any line are ignored. + + :: + readdlm(source, delim::Char, eol::Char; options...) + + If all data is numeric, the result will be a numeric array. If some elements cannot be parsed as numbers, a cell array of numbers and strings is returned. + + :: + readdlm(source, delim::Char, T::Type; options...) + + The end of line delimiter is taken as ``\n``. + + :: + readdlm(source, delim::Char; options...) + + The end of line delimiter is taken as ``\n``. If all data is numeric, the result will be a numeric array. If some elements cannot be parsed as numbers, a cell array of numbers and strings is returned. + + :: + readdlm(source, T::Type; options...) + + The columns are assumed to be separated by one or more whitespaces. The end of line delimiter is taken as ``\n``. + + :: + readdlm(source; options...) + The columns are assumed to be separated by one or more whitespaces. The end of line delimiter is taken as ``\n``. If all data is numeric, the result will be a numeric array. If some elements cannot be parsed as numbers, a cell array of numbers and strings is returned. .. function:: writedlm(f, A, delim='\\t') @@ -437,6 +949,8 @@ Text I/O read from ``istream``. .. function:: base64encode(writefunc, args...) + + :: base64encode(args...) Given a ``write``-like function ``writefunc``, which takes an I/O @@ -474,6 +988,8 @@ displays may be enabled by loading external modules or by using graphical Julia environments (such as the IPython-based IJulia notebook). .. function:: display(x) + + :: display(d::Display, x) display(mime, x) display(d::Display, mime, x) @@ -494,6 +1010,8 @@ Julia environments (such as the IPython-based IJulia notebook). (for binary MIME types). .. function:: redisplay(x) + + :: redisplay(d::Display, x) redisplay(mime, x) redisplay(d::Display, mime, x) @@ -506,6 +1024,8 @@ Julia environments (such as the IPython-based IJulia notebook). prompt. .. function:: displayable(mime) -> Bool + + :: displayable(d::Display, mime) -> Bool Returns a boolean value indicating whether the given ``mime`` type (string) @@ -601,6 +1121,7 @@ stack with: topmost backend that does not throw a ``MethodError``). .. function:: popdisplay() + popdisplay(d::Display) Pop the topmost backend off of the display-backend stack, or the @@ -625,6 +1146,8 @@ Memory-mapped I/O Create an ``IO``-like object for creating zeroed-out mmapped-memory that is not tied to a file for use in ``Mmap.mmap``. Used by ``SharedArray`` for creating shared memory arrays. .. function:: Mmap.mmap(io::Union(IOStream,AbstractString,Mmap.AnonymousMmap)[, type::Type{Array{T,N}}, dims, offset]; grow::Bool=true, shared::Bool=true) + + :: Mmap.mmap(type::Type{Array{T,N}}, dims) Create an ``Array`` whose values are linked to a file, using memory-mapping. This provides a convenient way of working with data too large to fit in the computer's memory. @@ -666,8 +1189,63 @@ Memory-mapped I/O A more portable file would need to encode the word size---32 bit or 64 bit---and endianness information in the header. In practice, consider encoding binary data using standard formats like HDF5 (which can be used with memory-mapping). + :: + Mmap.mmap(io, BitArray, [dims, offset]) + + Create a ``BitArray`` whose values are linked to a file, using memory-mapping; it has the same purpose, works in the same way, and has the same arguments, as :func:`mmap`, but the byte representation is different. + + **Example**: ``B = Mmap.mmap(s, BitArray, (25,30000))`` + + This would create a 25-by-30000 ``BitArray``, linked to the file associated with stream ``s``. + .. function:: Mmap.mmap(io, BitArray, [dims, offset]) + :: + Mmap.mmap(io::Union(IOStream,AbstractString,Mmap.AnonymousMmap)[, type::Type{Array{T,N}}, dims, offset]; grow::Bool=true, shared::Bool=true) + Mmap.mmap(type::Type{Array{T,N}}, dims) + + Create an ``Array`` whose values are linked to a file, using memory-mapping. This provides a convenient way of working with data too large to fit in the computer's memory. + + The type is an ``Array{T,N}`` with a bits-type element of ``T`` and dimension ``N`` that determines how the bytes of the array are interpreted. Note that the file must be stored in binary format, and no format conversions are possible (this is a limitation of operating systems, not Julia). + + ``dims`` is a tuple or single ``Integer`` specifying the size or length of the array. + + The file is passed via the stream argument, either as an open ``IOStream`` or filename string. When you initialize the stream, use ``"r"`` for a "read-only" array, and ``"w+"`` to create a new array used to write values to disk. + + If no ``type`` argument is specified, the default is ``Vector{UInt8}``. + + Optionally, you can specify an offset (in bytes) if, for example, you want to skip over a header in the file. The default value for the offset is the current stream position for an ``IOStream``. + + The ``grow`` keyword argument specifies whether the disk file should be grown to accomodate the requested size of array (if the total file size is < requested array size). Write privileges are required to grow the file. + + The ``shared`` keyword argument specifies whether the resulting ``Array`` and changes made to it will be visible to other processes mapping the same file. + + For example, the following code:: + + # Create a file for mmapping + # (you could alternatively use mmap to do this step, too) + A = rand(1:20, 5, 30) + s = open("/tmp/mmap.bin", "w+") + # We'll write the dimensions of the array as the first two Ints in the file + write(s, size(A,1)) + write(s, size(A,2)) + # Now write the data + write(s, A) + close(s) + + # Test by reading it back in + s = open("/tmp/mmap.bin") # default is read-only + m = read(s, Int) + n = read(s, Int) + A2 = Mmap.mmap(s, Matrix{Int}, (m,n)) + + creates a ``m``-by-``n`` ``Matrix{Int}``, linked to the file associated with stream ``s``. + + A more portable file would need to encode the word size---32 bit or 64 bit---and endianness information in the header. In practice, consider encoding binary data using standard formats like HDF5 (which can be used with memory-mapping). + + :: + Mmap.mmap(io, BitArray, [dims, offset]) + Create a ``BitArray`` whose values are linked to a file, using memory-mapping; it has the same purpose, works in the same way, and has the same arguments, as :func:`mmap`, but the byte representation is different. **Example**: ``B = Mmap.mmap(s, BitArray, (25,30000))`` @@ -685,17 +1263,62 @@ Network I/O Connect to the host ``host`` on port ``port`` + :: + connect(path) -> Pipe + + Connect to the Named Pipe/Domain Socket at ``path`` + + :: + connect(manager::FooManager, pid::Int, config::WorkerConfig) -> (instrm::AsyncStream, outstrm::AsyncStream) + + Implemented by cluster managers using custom transports. It should establish a logical connection to worker with id ``pid``, + specified by ``config`` and return a pair of ``AsyncStream`` objects. Messages from ``pid`` to current process will be read + off ``instrm``, while messages to be sent to ``pid`` will be written to ``outstrm``. The custom transport implementation + must ensure that messages are delivered and received completely and in order. ``Base.connect(manager::ClusterManager.....)`` + sets up TCP/IP socket connections in-between workers. + .. function:: connect(path) -> Pipe + :: + connect([host],port) -> TcpSocket + + Connect to the host ``host`` on port ``port`` + + :: + connect(path) -> Pipe + Connect to the Named Pipe/Domain Socket at ``path`` + :: + connect(manager::FooManager, pid::Int, config::WorkerConfig) -> (instrm::AsyncStream, outstrm::AsyncStream) + + Implemented by cluster managers using custom transports. It should establish a logical connection to worker with id ``pid``, + specified by ``config`` and return a pair of ``AsyncStream`` objects. Messages from ``pid`` to current process will be read + off ``instrm``, while messages to be sent to ``pid`` will be written to ``outstrm``. The custom transport implementation + must ensure that messages are delivered and received completely and in order. ``Base.connect(manager::ClusterManager.....)`` + sets up TCP/IP socket connections in-between workers. + .. function:: listen([addr,]port) -> TcpServer Listen on port on the address specified by ``addr``. By default this listens on localhost only. To listen on all interfaces pass, ``IPv4(0)`` or ``IPv6(0)`` as appropriate. + :: + listen(path) -> PipeServer + + Listens on/Creates a Named Pipe/Domain Socket + .. function:: listen(path) -> PipeServer + :: + listen([addr,]port) -> TcpServer + + Listen on port on the address specified by ``addr``. By default this listens on localhost only. + To listen on all interfaces pass, ``IPv4(0)`` or ``IPv6(0)`` as appropriate. + + :: + listen(path) -> PipeServer + Listens on/Creates a Named Pipe/Domain Socket .. function:: getaddrinfo(host) diff --git a/doc/stdlib/libc.rst b/doc/stdlib/libc.rst index 959be71ab3e35..11f28895c713d 100644 --- a/doc/stdlib/libc.rst +++ b/doc/stdlib/libc.rst @@ -48,7 +48,10 @@ .. function:: time(t::TmStruct) - Converts a ``TmStruct`` struct to a number of seconds since the epoch. + :: + time() + + Get the system time in seconds since the epoch, with fairly high (typically, microsecond) resolution. .. function:: strftime([format], time) diff --git a/doc/stdlib/linalg.rst b/doc/stdlib/linalg.rst index ac42f9dddf848..e332f74009cf9 100644 --- a/doc/stdlib/linalg.rst +++ b/doc/stdlib/linalg.rst @@ -14,10 +14,24 @@ Standard Functions Linear algebra functions in Julia are largely implemented by calling functions from `LAPACK `_. Sparse factorizations call functions from `SuiteSparse `_. .. function:: *(A, B) + :noindex: Matrix multiplication + :: + *(x, y...) + + Multiplication operator. ``x*y*z*...`` calls this function with all arguments, i.e. + ``*(x, y, z, ...)``. + + :: + *(s, t) + + Concatenate strings. The ``*`` operator is an alias to this function. + + .. doctest:: + .. function:: \\(A, B) :noindex: @@ -26,6 +40,8 @@ Linear algebra functions in Julia are largely implemented by calling functions f When ``A`` is sparse, a similar polyalgorithm is used. For indefinite matrices, the LDLt factorization does not use pivoting during the numerical factorization and therefore the procedure can fail even for invertible matrices. .. function:: dot(x, y) + + :: ⋅(x,y) Compute the dot product. For complex vectors, the first vector is conjugated. @@ -38,6 +54,8 @@ Linear algebra functions in Julia are largely implemented by calling functions f ``dot(x[i],y[i])``) as if they were vectors. .. function:: cross(x, y) + + :: ×(x,y) Compute the cross product of two 3-vectors. @@ -48,8 +66,28 @@ Linear algebra functions in Julia are largely implemented by calling functions f .. function:: full(F) + :: + full(S) + + Convert a sparse matrix ``S`` into a dense matrix. + + :: + full(F) + Reconstruct the matrix ``A`` from the factorization ``F=factorize(A)``. + :: + full(QRCompactWYQ[, thin=true]) -> Matrix + + Converts an orthogonal or unitary matrix stored as a ``QRCompactWYQ`` + object, i.e. in the compact WY format [Bischof1987]_, to a dense matrix. + + Optionally takes a ``thin`` Boolean argument, which if ``true`` omits the + columns that span the rows of ``R`` in the QR factorization that are zero. + The resulting matrix is the ``Q`` in a thin QR factorization (sometimes + called the reduced QR factorization). If ``false``, returns a ``Q`` that + spans all rows of ``R`` in its corresponding QR factorization. + .. function:: lu(A) -> L, U, p Compute the LU factorization of ``A``, such that ``A[p,:] = L*U``. @@ -104,8 +142,40 @@ Linear algebra functions in Julia are largely implemented by calling functions f Compute the Cholesky factorization of a dense symmetric positive (semi)definite matrix ``A`` and return either a ``Cholesky`` if ``pivot==Val{false}`` or ``CholeskyPivoted`` if ``pivot==Val{true}``. ``LU`` may be ``:L`` for using the lower part or ``:U`` for the upper part. The default is to use ``:U``. The triangular matrix can be obtained from the factorization ``F`` with: ``F[:L]`` and ``F[:U]``. The following functions are available for ``Cholesky`` objects: ``size``, ``\``, ``inv``, ``det``. For ``CholeskyPivoted`` there is also defined a ``rank``. If ``pivot==Val{false}`` a ``PosDefException`` exception is thrown in case the matrix is not positive definite. The argument ``tol`` determines the tolerance for determining the rank. For negative values, the tolerance is the machine precision. + :: + cholfact(A; shift=0, perm=Int[]) -> CHOLMOD.Factor + + Compute the Cholesky factorization of a sparse positive definite + matrix ``A``. A fill-reducing permutation is used. ``F = + cholfact(A)`` is most frequently used to solve systems of equations + with ``F\b``, but also the methods ``diag``, ``det``, ``logdet`` + are defined for ``F``. You can also extract individual factors + from ``F``, using ``F[:L]``. However, since pivoting is on by + default, the factorization is internally represented as ``A == + P'*L*L'*P`` with a permutation matrix ``P``; using just ``L`` + without accounting for ``P`` will give incorrect answers. To + include the effects of permutation, it's typically preferable to + extact "combined" factors like ``PtL = F[:PtL]`` (the equivalent of + ``P'*L``) and ``LtP = F[:UP]`` (the equivalent of ``L'*P``). + + Setting optional ``shift`` keyword argument computes the factorization + of ``A+shift*I`` instead of ``A``. If the ``perm`` argument is nonempty, + it should be a permutation of `1:size(A,1)` giving the ordering to use + (instead of CHOLMOD's default AMD ordering). + + The function calls the C library CHOLMOD and many other functions + from the library are wrapped but not exported. + .. function:: cholfact(A; shift=0, perm=Int[]) -> CHOLMOD.Factor + :: + cholfact(A, [LU=:U[,pivot=Val{false}]][;tol=-1.0]) -> Cholesky + + Compute the Cholesky factorization of a dense symmetric positive (semi)definite matrix ``A`` and return either a ``Cholesky`` if ``pivot==Val{false}`` or ``CholeskyPivoted`` if ``pivot==Val{true}``. ``LU`` may be ``:L`` for using the lower part or ``:U`` for the upper part. The default is to use ``:U``. The triangular matrix can be obtained from the factorization ``F`` with: ``F[:L]`` and ``F[:U]``. The following functions are available for ``Cholesky`` objects: ``size``, ``\``, ``inv``, ``det``. For ``CholeskyPivoted`` there is also defined a ``rank``. If ``pivot==Val{false}`` a ``PosDefException`` exception is thrown in case the matrix is not positive definite. The argument ``tol`` determines the tolerance for determining the rank. For negative values, the tolerance is the machine precision. + + :: + cholfact(A; shift=0, perm=Int[]) -> CHOLMOD.Factor + Compute the Cholesky factorization of a sparse positive definite matrix ``A``. A fill-reducing permutation is used. ``F = cholfact(A)`` is most frequently used to solve systems of equations @@ -135,8 +205,42 @@ Linear algebra functions in Julia are largely implemented by calling functions f Compute a factorization of a positive definite matrix ``A`` such that ``A=L*Diagonal(d)*L'`` where ``L`` is a unit lower triangular matrix and ``d`` is a vector with non-negative elements. + :: + ldltfact(A; shift=0, perm=Int[]) -> CHOLMOD.Factor + + Compute the LDLt factorization of a sparse symmetric or Hermitian + matrix ``A``. A fill-reducing permutation is used. ``F = + ldltfact(A)`` is most frequently used to solve systems of equations + with ``F\b``, but also the methods ``diag``, ``det``, ``logdet`` + are defined for ``F``. You can also extract individual factors from + ``F``, using ``F[:L]``. However, since pivoting is on by default, + the factorization is internally represented as ``A == P'*L*D*L'*P`` + with a permutation matrix ``P``; using just ``L`` without + accounting for ``P`` will give incorrect answers. To include the + effects of permutation, it's typically preferable to extact + "combined" factors like ``PtL = F[:PtL]`` (the equivalent of + ``P'*L``) and ``LtP = F[:UP]`` (the equivalent of ``L'*P``). The + complete list of supported factors is ``:L, :PtL, :D, :UP, :U, :LD, + :DU, :PtLD, :DUP``. + + Setting optional ``shift`` keyword argument computes the factorization + of ``A+shift*I`` instead of ``A``. If the ``perm`` argument is nonempty, + it should be a permutation of `1:size(A,1)` giving the ordering to use + (instead of CHOLMOD's default AMD ordering). + + The function calls the C library CHOLMOD and many other functions + from the library are wrapped but not exported. + .. function:: ldltfact(A; shift=0, perm=Int[]) -> CHOLMOD.Factor + :: + ldltfact(A) -> LDLtFactorization + + Compute a factorization of a positive definite matrix ``A`` such that ``A=L*Diagonal(d)*L'`` where ``L`` is a unit lower triangular matrix and ``d`` is a vector with non-negative elements. + + :: + ldltfact(A; shift=0, perm=Int[]) -> CHOLMOD.Factor + Compute the LDLt factorization of a sparse symmetric or Hermitian matrix ``A``. A fill-reducing permutation is used. ``F = ldltfact(A)`` is most frequently used to solve systems of equations @@ -216,8 +320,69 @@ Linear algebra functions in Julia are largely implemented by calling functions f .. [Bischof1987] C Bischof and C Van Loan, The WY representation for products of Householder matrices, SIAM J Sci Stat Comput 8 (1987), s2-s13. doi:10.1137/0908009 .. [Schreiber1989] R Schreiber and C Van Loan, A storage-efficient WY representation for products of Householder transformations, SIAM J Sci Stat Comput 10 (1989), 53-57. doi:10.1137/0910005 + :: + qrfact(A) -> SPQR.Factorization + + Compute the QR factorization of a sparse matrix ``A``. A fill-reducing permutation is used. The main application of this type is to solve least squares problems with ``\``. The function calls the C library SPQR and a few additional functions from the library are wrapped but not exported. + .. function:: qrfact(A) -> SPQR.Factorization + :: + qrfact(A [,pivot=Val{false}]) -> F + + Computes the QR factorization of ``A``. The return type of ``F`` depends on the element type of ``A`` and whether pivoting is specified (with ``pivot==Val{true}``). + + ================ ================= ============== ===================================== + Return type ``eltype(A)`` ``pivot`` Relationship between ``F`` and ``A`` + ---------------- ----------------- -------------- ------------------------------------- + ``QR`` not ``BlasFloat`` either ``A==F[:Q]*F[:R]`` + ``QRCompactWY`` ``BlasFloat`` ``Val{false}`` ``A==F[:Q]*F[:R]`` + ``QRPivoted`` ``BlasFloat`` ``Val{true}`` ``A[:,F[:p]]==F[:Q]*F[:R]`` + ================ ================= ============== ===================================== + + ``BlasFloat`` refers to any of: ``Float32``, ``Float64``, ``Complex64`` or ``Complex128``. + + The individual components of the factorization ``F`` can be accessed by indexing: + + =========== ============================================= ================== ===================== ================== + Component Description ``QR`` ``QRCompactWY`` ``QRPivoted`` + ----------- --------------------------------------------- ------------------ --------------------- ------------------ + ``F[:Q]`` ``Q`` (orthogonal/unitary) part of ``QR`` ✓ (``QRPackedQ``) ✓ (``QRCompactWYQ``) ✓ (``QRPackedQ``) + ``F[:R]`` ``R`` (upper right triangular) part of ``QR`` ✓ ✓ ✓ + ``F[:p]`` pivot ``Vector`` ✓ + ``F[:P]`` (pivot) permutation ``Matrix`` ✓ + =========== ============================================= ================== ===================== ================== + + The following functions are available for the ``QR`` objects: ``size``, ``\``. When ``A`` is rectangular, ``\`` will return a least squares solution and if the solution is not unique, the one with smallest norm is returned. + + Multiplication with respect to either thin or full ``Q`` is allowed, i.e. both ``F[:Q]*F[:R]`` and ``F[:Q]*A`` are supported. A ``Q`` matrix can be converted into a regular matrix with :func:`full` which has a named argument ``thin``. + + .. note:: + + ``qrfact`` returns multiple types because LAPACK uses several representations that minimize the memory storage requirements of products of Householder elementary reflectors, so that the ``Q`` and ``R`` matrices can be stored compactly rather as two separate dense matrices. + + The data contained in ``QR`` or ``QRPivoted`` can be used to construct the ``QRPackedQ`` type, which is a compact representation of the rotation matrix: + + .. math:: + + Q = \prod_{i=1}^{\min(m,n)} (I - \tau_i v_i v_i^T) + + where :math:`\tau_i` is the scale factor and :math:`v_i` is the projection vector associated with the :math:`i^{th}` Householder elementary reflector. + + The data contained in ``QRCompactWY`` can be used to construct the ``QRCompactWYQ`` type, which is a compact representation of the rotation matrix + + .. math:: + + Q = I + Y T Y^T + + where ``Y`` is :math:`m \times r` lower trapezoidal and ``T`` is :math:`r \times r` upper triangular. The *compact WY* representation [Schreiber1989]_ is not to be confused with the older, *WY* representation [Bischof1987]_. (The LAPACK documentation uses ``V`` in lieu of ``Y``.) + + .. [Bischof1987] C Bischof and C Van Loan, The WY representation for products of Householder matrices, SIAM J Sci Stat Comput 8 (1987), s2-s13. doi:10.1137/0908009 + .. [Schreiber1989] R Schreiber and C Van Loan, A storage-efficient WY representation for products of Householder transformations, SIAM J Sci Stat Comput 10 (1989), 53-57. doi:10.1137/0910005 + + :: + qrfact(A) -> SPQR.Factorization + Compute the QR factorization of a sparse matrix ``A``. A fill-reducing permutation is used. The main application of this type is to solve least squares problems with ``\``. The function calls the C library SPQR and a few additional functions from the library are wrapped but not exported. .. function:: qrfact!(A [,pivot=Val{false}]) @@ -226,6 +391,19 @@ Linear algebra functions in Julia are largely implemented by calling functions f .. function:: full(QRCompactWYQ[, thin=true]) -> Matrix + :: + full(S) + + Convert a sparse matrix ``S`` into a dense matrix. + + :: + full(F) + + Reconstruct the matrix ``A`` from the factorization ``F=factorize(A)``. + + :: + full(QRCompactWYQ[, thin=true]) -> Matrix + Converts an orthogonal or unitary matrix stored as a ``QRCompactWYQ`` object, i.e. in the compact WY format [Bischof1987]_, to a dense matrix. @@ -263,8 +441,39 @@ Linear algebra functions in Julia are largely implemented by calling functions f factorization to a tuple; where possible, using :func:`eigfact` is recommended. + :: + eig(A, B) -> D, V + + Computes generalized eigenvalues and vectors of ``A`` with respect to ``B``. + + ``eig`` is a wrapper around :func:`eigfact`, extracting all parts of the + factorization to a tuple; where possible, using :func:`eigfact` is + recommended. + .. function:: eig(A, B) -> D, V + :: + eig(A,[irange,][vl,][vu,][permute=true,][scale=true]) -> D, V + + Computes eigenvalues and eigenvectors of ``A``. See :func:`eigfact` for + details on the ``balance`` keyword argument. + + .. doctest:: + + julia> eig([1.0 0.0 0.0; 0.0 3.0 0.0; 0.0 0.0 18.0]) + ([1.0,3.0,18.0], + 3x3 Array{Float64,2}: + 1.0 0.0 0.0 + 0.0 1.0 0.0 + 0.0 0.0 1.0) + + ``eig`` is a wrapper around :func:`eigfact`, extracting all parts of the + factorization to a tuple; where possible, using :func:`eigfact` is + recommended. + + :: + eig(A, B) -> D, V + Computes generalized eigenvalues and vectors of ``A`` with respect to ``B``. ``eig`` is a wrapper around :func:`eigfact`, extracting all parts of the @@ -324,8 +533,44 @@ Linear algebra functions in Julia are largely implemented by calling functions f scales the matrix by its diagonal elements to make rows and columns more equal in norm. The default is ``true`` for both options. + :: + eigfact(A, B) -> GeneralizedEigen + + Computes the generalized eigenvalue decomposition of ``A`` and ``B``, + returning a ``GeneralizedEigen`` factorization object ``F`` which contains + the generalized eigenvalues in ``F[:values]`` and the generalized + eigenvectors in the columns of the matrix ``F[:vectors]``. (The ``k``\ th + generalized eigenvector can be obtained from the slice ``F[:vectors][:, + k]``.) + .. function:: eigfact(A, B) -> GeneralizedEigen + :: + eigfact(A,[irange,][vl,][vu,][permute=true,][scale=true]) -> Eigen + + Computes the eigenvalue decomposition of ``A``, returning an ``Eigen`` + factorization object ``F`` which contains the eigenvalues in ``F[:values]`` + and the eigenvectors in the columns of the matrix ``F[:vectors]``. + (The ``k``\ th eigenvector can be obtained from the slice ``F[:vectors][:, k]``.) + + The following functions are available for ``Eigen`` objects: ``inv``, + ``det``. + + If ``A`` is :class:`Symmetric`, :class:`Hermitian` or :class:`SymTridiagonal`, + it is possible to calculate only a subset of the eigenvalues by specifying + either a :class:`UnitRange` ``irange`` covering indices of the sorted + eigenvalues or a pair ``vl`` and ``vu`` for the lower and upper boundaries + of the eigenvalues. + + For general nonsymmetric matrices it is possible to specify how the matrix + is balanced before the eigenvector calculation. The option ``permute=true`` + permutes the matrix to become closer to upper triangular, and ``scale=true`` + scales the matrix by its diagonal elements to make rows and columns more + equal in norm. The default is ``true`` for both options. + + :: + eigfact(A, B) -> GeneralizedEigen + Computes the generalized eigenvalue decomposition of ``A`` and ``B``, returning a ``GeneralizedEigen`` factorization object ``F`` which contains the generalized eigenvalues in ``F[:values]`` and the generalized @@ -350,6 +595,11 @@ Linear algebra functions in Julia are largely implemented by calling functions f Computes the Schur factorization of the matrix ``A``. The (quasi) triangular Schur factor can be obtained from the ``Schur`` object ``F`` with either ``F[:Schur]`` or ``F[:T]`` and the unitary/orthogonal Schur vectors can be obtained with ``F[:vectors]`` or ``F[:Z]`` such that ``A=F[:vectors]*F[:Schur]*F[:vectors]'``. The eigenvalues of ``A`` can be obtained with ``F[:values]``. + :: + schurfact(A, B) -> GeneralizedSchur + + Computes the Generalized Schur (or QZ) factorization of the matrices ``A`` and ``B``. The (quasi) triangular Schur factors can be obtained from the ``Schur`` object ``F`` with ``F[:S]`` and ``F[:T]``, the left unitary/orthogonal Schur vectors can be obtained with ``F[:left]`` or ``F[:Q]`` and the right unitary/orthogonal Schur vectors can be obtained with ``F[:right]`` or ``F[:Z]`` such that ``A=F[:left]*F[:S]*F[:right]'`` and ``B=F[:left]*F[:T]*F[:right]'``. The generalized eigenvalues of ``A`` and ``B`` can be obtained with ``F[:alpha]./F[:beta]``. + .. function:: schurfact!(A) Computes the Schur factorization of ``A``, overwriting ``A`` in the process. See :func:`schurfact` @@ -358,50 +608,214 @@ Linear algebra functions in Julia are largely implemented by calling functions f See :func:`schurfact` + :: + schur(A,B) -> GeneralizedSchur[:S], GeneralizedSchur[:T], GeneralizedSchur[:Q], GeneralizedSchur[:Z] + + See :func:`schurfact` + .. function:: ordschur(Q, T, select) -> Schur Reorders the Schur factorization of a real matrix ``A=Q*T*Q'`` according to the logical array ``select`` returning a Schur object ``F``. The selected eigenvalues appear in the leading diagonal of ``F[:Schur]`` and the the corresponding leading columns of ``F[:vectors]`` form an orthonormal basis of the corresponding right invariant subspace. A complex conjugate pair of eigenvalues must be either both included or excluded via ``select``. + :: + ordschur(S, select) -> Schur + + Reorders the Schur factorization ``S`` of type ``Schur``. + + :: + ordschur(S, T, Q, Z, select) -> GeneralizedSchur + + Reorders the Generalized Schur factorization of a matrix ``(A, B) = (Q*S*Z^{H}, Q*T*Z^{H})`` according to the logical array ``select`` and returns a GeneralizedSchur object ``GS``. The selected eigenvalues appear in the leading diagonal of both``(GS[:S], GS[:T])`` and the left and right unitary/orthogonal Schur vectors are also reordered such that ``(A, B) = GS[:Q]*(GS[:S], GS[:T])*GS[:Z]^{H}`` still holds and the generalized eigenvalues of ``A`` and ``B`` can still be obtained with ``GS[:alpha]./GS[:beta]``. + + :: + ordschur(GS, select) -> GeneralizedSchur + + Reorders the Generalized Schur factorization of a Generalized Schur object. See :func:`ordschur`. + .. function:: ordschur!(Q, T, select) -> Schur Reorders the Schur factorization of a real matrix ``A=Q*T*Q'``, overwriting ``Q`` and ``T`` in the process. See :func:`ordschur` + :: + ordschur!(S, select) -> Schur + + Reorders the Schur factorization ``S`` of type ``Schur``, overwriting ``S`` in the process. See :func:`ordschur` + + :: + ordschur!(S, T, Q, Z, select) -> GeneralizedSchur + + Reorders the Generalized Schur factorization of a matrix by overwriting the matrices ``(S, T, Q, Z)`` in the process. See :func:`ordschur`. + + :: + ordschur!(GS, select) -> GeneralizedSchur + + Reorders the Generalized Schur factorization of a Generalized Schur object by overwriting the object with the new factorization. See :func:`ordschur`. + .. function:: ordschur(S, select) -> Schur + :: + ordschur(Q, T, select) -> Schur + + Reorders the Schur factorization of a real matrix ``A=Q*T*Q'`` according to the logical array ``select`` returning a Schur object ``F``. The selected eigenvalues appear in the leading diagonal of ``F[:Schur]`` and the the corresponding leading columns of ``F[:vectors]`` form an orthonormal basis of the corresponding right invariant subspace. A complex conjugate pair of eigenvalues must be either both included or excluded via ``select``. + + :: + ordschur(S, select) -> Schur + Reorders the Schur factorization ``S`` of type ``Schur``. + :: + ordschur(S, T, Q, Z, select) -> GeneralizedSchur + + Reorders the Generalized Schur factorization of a matrix ``(A, B) = (Q*S*Z^{H}, Q*T*Z^{H})`` according to the logical array ``select`` and returns a GeneralizedSchur object ``GS``. The selected eigenvalues appear in the leading diagonal of both``(GS[:S], GS[:T])`` and the left and right unitary/orthogonal Schur vectors are also reordered such that ``(A, B) = GS[:Q]*(GS[:S], GS[:T])*GS[:Z]^{H}`` still holds and the generalized eigenvalues of ``A`` and ``B`` can still be obtained with ``GS[:alpha]./GS[:beta]``. + + :: + ordschur(GS, select) -> GeneralizedSchur + + Reorders the Generalized Schur factorization of a Generalized Schur object. See :func:`ordschur`. + .. function:: ordschur!(S, select) -> Schur + :: + ordschur!(Q, T, select) -> Schur + + Reorders the Schur factorization of a real matrix ``A=Q*T*Q'``, overwriting ``Q`` and ``T`` in the process. See :func:`ordschur` + + :: + ordschur!(S, select) -> Schur + Reorders the Schur factorization ``S`` of type ``Schur``, overwriting ``S`` in the process. See :func:`ordschur` + :: + ordschur!(S, T, Q, Z, select) -> GeneralizedSchur + + Reorders the Generalized Schur factorization of a matrix by overwriting the matrices ``(S, T, Q, Z)`` in the process. See :func:`ordschur`. + + :: + ordschur!(GS, select) -> GeneralizedSchur + + Reorders the Generalized Schur factorization of a Generalized Schur object by overwriting the object with the new factorization. See :func:`ordschur`. + .. function:: schurfact(A, B) -> GeneralizedSchur + :: + schurfact(A) -> Schur + + Computes the Schur factorization of the matrix ``A``. The (quasi) triangular Schur factor can be obtained from the ``Schur`` object ``F`` with either ``F[:Schur]`` or ``F[:T]`` and the unitary/orthogonal Schur vectors can be obtained with ``F[:vectors]`` or ``F[:Z]`` such that ``A=F[:vectors]*F[:Schur]*F[:vectors]'``. The eigenvalues of ``A`` can be obtained with ``F[:values]``. + + :: + schurfact(A, B) -> GeneralizedSchur + Computes the Generalized Schur (or QZ) factorization of the matrices ``A`` and ``B``. The (quasi) triangular Schur factors can be obtained from the ``Schur`` object ``F`` with ``F[:S]`` and ``F[:T]``, the left unitary/orthogonal Schur vectors can be obtained with ``F[:left]`` or ``F[:Q]`` and the right unitary/orthogonal Schur vectors can be obtained with ``F[:right]`` or ``F[:Z]`` such that ``A=F[:left]*F[:S]*F[:right]'`` and ``B=F[:left]*F[:T]*F[:right]'``. The generalized eigenvalues of ``A`` and ``B`` can be obtained with ``F[:alpha]./F[:beta]``. .. function:: schur(A,B) -> GeneralizedSchur[:S], GeneralizedSchur[:T], GeneralizedSchur[:Q], GeneralizedSchur[:Z] + :: + schur(A) -> Schur[:T], Schur[:Z], Schur[:values] + + See :func:`schurfact` + + :: + schur(A,B) -> GeneralizedSchur[:S], GeneralizedSchur[:T], GeneralizedSchur[:Q], GeneralizedSchur[:Z] + See :func:`schurfact` .. function:: ordschur(S, T, Q, Z, select) -> GeneralizedSchur + :: + ordschur(Q, T, select) -> Schur + + Reorders the Schur factorization of a real matrix ``A=Q*T*Q'`` according to the logical array ``select`` returning a Schur object ``F``. The selected eigenvalues appear in the leading diagonal of ``F[:Schur]`` and the the corresponding leading columns of ``F[:vectors]`` form an orthonormal basis of the corresponding right invariant subspace. A complex conjugate pair of eigenvalues must be either both included or excluded via ``select``. + + :: + ordschur(S, select) -> Schur + + Reorders the Schur factorization ``S`` of type ``Schur``. + + :: + ordschur(S, T, Q, Z, select) -> GeneralizedSchur + Reorders the Generalized Schur factorization of a matrix ``(A, B) = (Q*S*Z^{H}, Q*T*Z^{H})`` according to the logical array ``select`` and returns a GeneralizedSchur object ``GS``. The selected eigenvalues appear in the leading diagonal of both``(GS[:S], GS[:T])`` and the left and right unitary/orthogonal Schur vectors are also reordered such that ``(A, B) = GS[:Q]*(GS[:S], GS[:T])*GS[:Z]^{H}`` still holds and the generalized eigenvalues of ``A`` and ``B`` can still be obtained with ``GS[:alpha]./GS[:beta]``. + :: + ordschur(GS, select) -> GeneralizedSchur + + Reorders the Generalized Schur factorization of a Generalized Schur object. See :func:`ordschur`. + .. function:: ordschur!(S, T, Q, Z, select) -> GeneralizedSchur + :: + ordschur!(Q, T, select) -> Schur + + Reorders the Schur factorization of a real matrix ``A=Q*T*Q'``, overwriting ``Q`` and ``T`` in the process. See :func:`ordschur` + + :: + ordschur!(S, select) -> Schur + + Reorders the Schur factorization ``S`` of type ``Schur``, overwriting ``S`` in the process. See :func:`ordschur` + + :: + ordschur!(S, T, Q, Z, select) -> GeneralizedSchur + Reorders the Generalized Schur factorization of a matrix by overwriting the matrices ``(S, T, Q, Z)`` in the process. See :func:`ordschur`. + :: + ordschur!(GS, select) -> GeneralizedSchur + + Reorders the Generalized Schur factorization of a Generalized Schur object by overwriting the object with the new factorization. See :func:`ordschur`. + .. function:: ordschur(GS, select) -> GeneralizedSchur + :: + ordschur(Q, T, select) -> Schur + + Reorders the Schur factorization of a real matrix ``A=Q*T*Q'`` according to the logical array ``select`` returning a Schur object ``F``. The selected eigenvalues appear in the leading diagonal of ``F[:Schur]`` and the the corresponding leading columns of ``F[:vectors]`` form an orthonormal basis of the corresponding right invariant subspace. A complex conjugate pair of eigenvalues must be either both included or excluded via ``select``. + + :: + ordschur(S, select) -> Schur + + Reorders the Schur factorization ``S`` of type ``Schur``. + + :: + ordschur(S, T, Q, Z, select) -> GeneralizedSchur + + Reorders the Generalized Schur factorization of a matrix ``(A, B) = (Q*S*Z^{H}, Q*T*Z^{H})`` according to the logical array ``select`` and returns a GeneralizedSchur object ``GS``. The selected eigenvalues appear in the leading diagonal of both``(GS[:S], GS[:T])`` and the left and right unitary/orthogonal Schur vectors are also reordered such that ``(A, B) = GS[:Q]*(GS[:S], GS[:T])*GS[:Z]^{H}`` still holds and the generalized eigenvalues of ``A`` and ``B`` can still be obtained with ``GS[:alpha]./GS[:beta]``. + + :: + ordschur(GS, select) -> GeneralizedSchur + Reorders the Generalized Schur factorization of a Generalized Schur object. See :func:`ordschur`. .. function:: ordschur!(GS, select) -> GeneralizedSchur + :: + ordschur!(Q, T, select) -> Schur + + Reorders the Schur factorization of a real matrix ``A=Q*T*Q'``, overwriting ``Q`` and ``T`` in the process. See :func:`ordschur` + + :: + ordschur!(S, select) -> Schur + + Reorders the Schur factorization ``S`` of type ``Schur``, overwriting ``S`` in the process. See :func:`ordschur` + + :: + ordschur!(S, T, Q, Z, select) -> GeneralizedSchur + + Reorders the Generalized Schur factorization of a matrix by overwriting the matrices ``(S, T, Q, Z)`` in the process. See :func:`ordschur`. + + :: + ordschur!(GS, select) -> GeneralizedSchur + Reorders the Generalized Schur factorization of a Generalized Schur object by overwriting the object with the new factorization. See :func:`ordschur`. .. function:: svdfact(A, [thin=true]) -> SVD Compute the Singular Value Decomposition (SVD) of ``A`` and return an ``SVD`` object. ``U``, ``S``, ``V`` and ``Vt`` can be obtained from the factorization ``F`` with ``F[:U]``, ``F[:S]``, ``F[:V]`` and ``F[:Vt]``, such that ``A = U*diagm(S)*Vt``. If ``thin`` is ``true``, an economy mode decomposition is returned. The algorithm produces ``Vt`` and hence ``Vt`` is more efficient to extract than ``V``. The default is to produce a thin decomposition. + :: + svdfact(A, B) -> GeneralizedSVD + + Compute the generalized SVD of ``A`` and ``B``, returning a ``GeneralizedSVD`` Factorization object ``F``, such that ``A = F[:U]*F[:D1]*F[:R0]*F[:Q]'`` and ``B = F[:V]*F[:D2]*F[:R0]*F[:Q]'``. + .. function:: svdfact!(A, [thin=true]) -> SVD ``svdfact!`` is the same as :func:`svdfact`, but saves space by overwriting the input A, instead of creating a copy. If ``thin`` is ``true``, an economy mode decomposition is returned. The default is to produce a thin decomposition. @@ -410,56 +824,142 @@ Linear algebra functions in Julia are largely implemented by calling functions f Wrapper around ``svdfact`` extracting all parts the factorization to a tuple. Direct use of ``svdfact`` is therefore generally more efficient. Computes the SVD of A, returning ``U``, vector ``S``, and ``V`` such that ``A == U*diagm(S)*V'``. If ``thin`` is ``true``, an economy mode decomposition is returned. The default is to produce a thin decomposition. + :: + svd(A, B) -> U, V, Q, D1, D2, R0 + + Wrapper around ``svdfact`` extracting all parts the factorization to a tuple. Direct use of ``svdfact`` is therefore generally more efficient. The function returns the generalized SVD of ``A`` and ``B``, returning ``U``, ``V``, ``Q``, ``D1``, ``D2``, and ``R0`` such that ``A = U*D1*R0*Q'`` and ``B = V*D2*R0*Q'``. + .. function:: svdvals(A) Returns the singular values of ``A``. + :: + svdvals(A, B) + + Return only the singular values from the generalized singular value decomposition of ``A`` and ``B``. + .. function:: svdvals!(A) Returns the singular values of ``A``, while saving space by overwriting the input. .. function:: svdfact(A, B) -> GeneralizedSVD + :: + svdfact(A, [thin=true]) -> SVD + + Compute the Singular Value Decomposition (SVD) of ``A`` and return an ``SVD`` object. ``U``, ``S``, ``V`` and ``Vt`` can be obtained from the factorization ``F`` with ``F[:U]``, ``F[:S]``, ``F[:V]`` and ``F[:Vt]``, such that ``A = U*diagm(S)*Vt``. If ``thin`` is ``true``, an economy mode decomposition is returned. The algorithm produces ``Vt`` and hence ``Vt`` is more efficient to extract than ``V``. The default is to produce a thin decomposition. + + :: + svdfact(A, B) -> GeneralizedSVD + Compute the generalized SVD of ``A`` and ``B``, returning a ``GeneralizedSVD`` Factorization object ``F``, such that ``A = F[:U]*F[:D1]*F[:R0]*F[:Q]'`` and ``B = F[:V]*F[:D2]*F[:R0]*F[:Q]'``. .. function:: svd(A, B) -> U, V, Q, D1, D2, R0 + :: + svd(A, [thin=true]) -> U, S, V + + Wrapper around ``svdfact`` extracting all parts the factorization to a tuple. Direct use of ``svdfact`` is therefore generally more efficient. Computes the SVD of A, returning ``U``, vector ``S``, and ``V`` such that ``A == U*diagm(S)*V'``. If ``thin`` is ``true``, an economy mode decomposition is returned. The default is to produce a thin decomposition. + + :: + svd(A, B) -> U, V, Q, D1, D2, R0 + Wrapper around ``svdfact`` extracting all parts the factorization to a tuple. Direct use of ``svdfact`` is therefore generally more efficient. The function returns the generalized SVD of ``A`` and ``B``, returning ``U``, ``V``, ``Q``, ``D1``, ``D2``, and ``R0`` such that ``A = U*D1*R0*Q'`` and ``B = V*D2*R0*Q'``. .. function:: svdvals(A, B) + :: + svdvals(A) + + Returns the singular values of ``A``. + + :: + svdvals(A, B) + Return only the singular values from the generalized singular value decomposition of ``A`` and ``B``. .. function:: triu(M) Upper triangle of a matrix. + :: + triu(M, k) + + Returns the upper triangle of ``M`` starting from the ``k``\ th superdiagonal. + .. function:: triu(M, k) + :: + triu(M) + + Upper triangle of a matrix. + + :: + triu(M, k) + Returns the upper triangle of ``M`` starting from the ``k``\ th superdiagonal. .. function:: triu!(M) Upper triangle of a matrix, overwriting ``M`` in the process. + :: + triu!(M, k) + + Returns the upper triangle of ``M`` starting from the ``k``\ th superdiagonal, overwriting ``M`` in the process. + .. function:: triu!(M, k) + :: + triu!(M) + + Upper triangle of a matrix, overwriting ``M`` in the process. + + :: + triu!(M, k) + Returns the upper triangle of ``M`` starting from the ``k``\ th superdiagonal, overwriting ``M`` in the process. .. function:: tril(M) Lower triangle of a matrix. + :: + tril(M, k) + + Returns the lower triangle of ``M`` starting from the ``k``\ th subdiagonal. + .. function:: tril(M, k) + :: + tril(M) + + Lower triangle of a matrix. + + :: + tril(M, k) + Returns the lower triangle of ``M`` starting from the ``k``\ th subdiagonal. .. function:: tril!(M) Lower triangle of a matrix, overwriting ``M`` in the process. + :: + tril!(M, k) + + Returns the lower triangle of ``M`` starting from the ``k``\ th subdiagonal, overwriting ``M`` in the process. + .. function:: tril!(M, k) + :: + tril!(M) + + Lower triangle of a matrix, overwriting ``M`` in the process. + + :: + tril!(M, k) + Returns the lower triangle of ``M`` starting from the ``k``\ th subdiagonal, overwriting ``M`` in the process. .. function:: diagind(M[, k]) @@ -475,8 +975,28 @@ Linear algebra functions in Julia are largely implemented by calling functions f Construct a diagonal matrix and place ``v`` on the ``k``\ th diagonal. .. function:: scale(A, b) + + :: + scale(b, A) + + Scale an array ``A`` by a scalar ``b``, returning a new array. + + If ``A`` is a matrix and ``b`` is a vector, then ``scale(A,b)`` + scales each column ``i`` of ``A`` by ``b[i]`` (similar to + ``A*diagm(b)``), while ``scale(b,A)`` scales each row ``i`` of + ``A`` by ``b[i]`` (similar to ``diagm(b)*A``), returning a new array. + + Note: for large ``A``, ``scale`` can be much faster than ``A .* b`` or + ``b .* A``, due to the use of BLAS. + .. function:: scale(b, A) + :: + scale(A, b) + + :: + scale(b, A) + Scale an array ``A`` by a scalar ``b``, returning a new array. If ``A`` is a matrix and ``b`` is a vector, then ``scale(A,b)`` @@ -488,8 +1008,27 @@ Linear algebra functions in Julia are largely implemented by calling functions f ``b .* A``, due to the use of BLAS. .. function:: scale!(A, b) + + :: + scale!(b, A) + + Scale an array ``A`` by a scalar ``b``, similar to :func:`scale` but + overwriting ``A`` in-place. + + If ``A`` is a matrix and ``b`` is a vector, then ``scale!(A,b)`` + scales each column ``i`` of ``A`` by ``b[i]`` (similar to + ``A*diagm(b)``), while ``scale!(b,A)`` scales each row ``i`` of + ``A`` by ``b[i]`` (similar to ``diagm(b)*A``), again operating in-place + on ``A``. + .. function:: scale!(b, A) + :: + scale!(A, b) + + :: + scale!(b, A) + Scale an array ``A`` by a scalar ``b``, similar to :func:`scale` but overwriting ``A`` in-place. @@ -632,8 +1171,30 @@ Linear algebra functions in Julia are largely implemented by calling functions f plot(x, y, "o") # Plot (x,y) points plot(x, [a+b*i for i in x]) # Plot the line determined by the linear regression + :: + linreg(x, y, w) + + Weighted least-squares linear regression. + .. function:: linreg(x, y, w) + :: + linreg(x, y) -> [a; b] + + Linear Regression. Returns ``a`` and ``b`` such that ``a+b*x`` is the closest line to the given points ``(x,y)``. In other words, this function determines parameters ``[a, b]`` that minimize the squared error between ``y`` and ``a+b*x``. + + **Example**:: + + using PyPlot; + x = float([1:12]) + y = [5.5; 6.3; 7.6; 8.8; 10.9; 11.79; 13.48; 15.02; 17.77; 20.81; 22.0; 22.99] + a, b = linreg(x,y) # Linear regression + plot(x, y, "o") # Plot (x,y) points + plot(x, [a+b*i for i in x]) # Plot the line determined by the linear regression + + :: + linreg(x, y, w) + Weighted least-squares linear regression. .. function:: expm(A) @@ -902,8 +1463,25 @@ Usually a function has 4 methods defined, one each for ``Float64``, order ``size(A,2)`` with ``k`` super-diagonals stored in the argument ``A``. + :: + sbmv(uplo, k, A, x) + + Returns ``A*x`` where ``A`` is a symmetric band matrix of + order ``size(A,2)`` with ``k`` super-diagonals stored in the + argument ``A``. + .. function:: sbmv(uplo, k, A, x) + :: + sbmv(uplo, k, alpha, A, x) + + Returns ``alpha*A*x`` where ``A`` is a symmetric band matrix of + order ``size(A,2)`` with ``k`` super-diagonals stored in the + argument ``A``. + + :: + sbmv(uplo, k, A, x) + Returns ``A*x`` where ``A`` is a symmetric band matrix of order ``size(A,2)`` with ``k`` super-diagonals stored in the argument ``A``. @@ -919,8 +1497,23 @@ Usually a function has 4 methods defined, one each for ``Float64``, Returns ``alpha*A*B`` or the other three variants according to ``tA`` (transpose ``A``) and ``tB``. + :: + gemm(tA, tB, A, B) + + Returns ``A*B`` or the other three variants + according to ``tA`` (transpose ``A``) and ``tB``. + .. function:: gemm(tA, tB, A, B) + :: + gemm(tA, tB, alpha, A, B) + + Returns ``alpha*A*B`` or the other three variants + according to ``tA`` (transpose ``A``) and ``tB``. + + :: + gemm(tA, tB, A, B) + Returns ``A*B`` or the other three variants according to ``tA`` (transpose ``A``) and ``tB``. @@ -935,8 +1528,22 @@ Usually a function has 4 methods defined, one each for ``Float64``, Returns ``alpha*A*x`` or ``alpha*A'x`` according to ``tA`` (transpose ``A``). + :: + gemv(tA, A, x) + + Returns ``A*x`` or ``A'x`` according to ``tA`` (transpose ``A``). + .. function:: gemv(tA, A, x) + :: + gemv(tA, alpha, A, x) + + Returns ``alpha*A*x`` or ``alpha*A'x`` according to ``tA`` + (transpose ``A``). + + :: + gemv(tA, A, x) + Returns ``A*x`` or ``A'x`` according to ``tA`` (transpose ``A``). .. function:: symm!(side, ul, alpha, A, B, beta, C) @@ -951,13 +1558,57 @@ Usually a function has 4 methods defined, one each for ``Float64``, ``A`` is assumed to be symmetric. Only the ``ul`` triangle of ``A`` is used. + :: + symm(side, ul, A, B) + + Returns ``A*B`` or ``B*A`` according to ``side``. ``A`` is assumed + to be symmetric. Only the ``ul`` triangle of ``A`` is used. + + :: + symm(tA, tB, alpha, A, B) + + Returns ``alpha*A*B`` or the other three variants + according to ``tA`` (transpose ``A``) and ``tB``. + .. function:: symm(side, ul, A, B) + :: + symm(side, ul, alpha, A, B) + + Returns ``alpha*A*B`` or ``alpha*B*A`` according to ``side``. + ``A`` is assumed to be symmetric. Only the ``ul`` triangle of + ``A`` is used. + + :: + symm(side, ul, A, B) + Returns ``A*B`` or ``B*A`` according to ``side``. ``A`` is assumed to be symmetric. Only the ``ul`` triangle of ``A`` is used. + :: + symm(tA, tB, alpha, A, B) + + Returns ``alpha*A*B`` or the other three variants + according to ``tA`` (transpose ``A``) and ``tB``. + .. function:: symm(tA, tB, alpha, A, B) + :: + symm(side, ul, alpha, A, B) + + Returns ``alpha*A*B`` or ``alpha*B*A`` according to ``side``. + ``A`` is assumed to be symmetric. Only the ``ul`` triangle of + ``A`` is used. + + :: + symm(side, ul, A, B) + + Returns ``A*B`` or ``B*A`` according to ``side``. ``A`` is assumed + to be symmetric. Only the ``ul`` triangle of ``A`` is used. + + :: + symm(tA, tB, alpha, A, B) + Returns ``alpha*A*B`` or the other three variants according to ``tA`` (transpose ``A``) and ``tB``. @@ -972,8 +1623,23 @@ Usually a function has 4 methods defined, one each for ``Float64``, Returns ``alpha*A*x``. ``A`` is assumed to be symmetric. Only the ``ul`` triangle of ``A`` is used. + :: + symv(ul, A, x) + + Returns ``A*x``. ``A`` is assumed to be symmetric. Only the + ``ul`` triangle of ``A`` is used. + .. function:: symv(ul, A, x) + :: + symv(ul, alpha, A, x) + + Returns ``alpha*A*x``. ``A`` is assumed to be symmetric. Only the + ``ul`` triangle of ``A`` is used. + + :: + symv(ul, A, x) + Returns ``A*x``. ``A`` is assumed to be symmetric. Only the ``ul`` triangle of ``A`` is used. diff --git a/doc/stdlib/math.rst b/doc/stdlib/math.rst index 7bb80d5a049cf..1f42489a76bae 100644 --- a/doc/stdlib/math.rst +++ b/doc/stdlib/math.rst @@ -13,6 +13,11 @@ Mathematical Operators Unary minus operator. + :: + -(x, y) + + Subtraction operator. + .. _+: .. function:: +(x, y...) @@ -22,14 +27,38 @@ Mathematical Operators .. _-: .. function:: -(x, y) + :: + -(x) + + Unary minus operator. + + :: + -(x, y) + Subtraction operator. .. _*: .. function:: *(x, y...) + :: + *(A, B) + :noindex: + + Matrix multiplication + + :: + *(x, y...) + Multiplication operator. ``x*y*z*...`` calls this function with all arguments, i.e. ``*(x, y, z, ...)``. + :: + *(s, t) + + Concatenate strings. The ``*`` operator is an alias to this function. + + .. doctest:: + .. _/: .. function:: /(x, y) @@ -47,6 +76,16 @@ Mathematical Operators Exponentiation operator. + :: + ^(s, n) + + Repeat ``n`` times the string ``s``. The ``^`` operator is an alias to this function. + + .. doctest:: + + julia> "Test "^3 + "Test Test Test " + .. _.+: .. function:: .+(x, y) @@ -92,6 +131,8 @@ Mathematical Operators ``fma``. .. function:: div(x, y) + + :: ÷(x, y) The quotient from Euclidean division. Computes ``x/y``, truncated to an integer. @@ -119,6 +160,8 @@ Mathematical Operators floating-point number 2pi. .. function:: rem(x, y) + + :: %(x, y) Remainder from Euclidean division, returning a value of the same sign @@ -207,6 +250,8 @@ Mathematical Operators .. _!=: .. function:: !=(x, y) + + :: ≠(x,y) Not-equals comparison operator. Always gives the opposite answer as ``==``. @@ -215,12 +260,18 @@ Mathematical Operators .. _===: .. function:: ===(x, y) - ≡(x,y) - See the :func:`is` operator + :: + is(x, y) -> Bool + ===(x,y) -> Bool + ≡(x,y) -> Bool + + Determine whether ``x`` and ``y`` are identical, in the sense that no program could distinguish them. Compares mutable objects by address in memory, and compares immutable objects (such as numbers) by contents at the bit level. This function is sometimes called ``egal``. .. _!==: .. function:: !==(x, y) + + :: ≢(x,y) Equivalent to ``!is(x, y)`` @@ -236,6 +287,8 @@ Mathematical Operators .. _<=: .. function:: <=(x, y) + + :: ≤(x,y) Less-than-or-equals comparison operator. @@ -248,6 +301,8 @@ Mathematical Operators .. _>=: .. function:: >=(x, y) + + :: ≥(x,y) Greater-than-or-equals comparison operator. @@ -259,6 +314,8 @@ Mathematical Operators .. _.!=: .. function:: .!=(x, y) + + :: .≠(x,y) Element-wise not-equals comparison operator. @@ -270,6 +327,8 @@ Mathematical Operators .. _.<=: .. function:: .<=(x, y) + + :: .≤(x,y) Element-wise less-than-or-equals comparison operator. @@ -281,6 +340,8 @@ Mathematical Operators .. _.>=: .. function:: .>=(x, y) + + :: .≥(x,y) Element-wise greater-than-or-equals comparison operator. @@ -336,7 +397,6 @@ Mathematical Operators .. function:: A_mul_B!(Y, A, B) -> Y - Calculates the matrix-matrix or matrix-vector product *A B* and stores the result in *Y*, overwriting the existing value of *Y*. @@ -413,7 +473,6 @@ Mathematical Operators Matrix operator A\ :sup:`T` / B\ :sup:`T` - Mathematical Functions ---------------------- @@ -615,8 +674,26 @@ Mathematical Functions There is an experimental variant in the ``Base.Math.JuliaLibm`` module, which is typically faster and more accurate. + :: + log(b,x) + + Compute the base ``b`` logarithm of ``x``. Throws ``DomainError`` for negative ``Real`` arguments. + .. function:: log(b,x) + :: + log(x) + + Compute the natural logarithm of ``x``. Throws ``DomainError`` for negative + ``Real`` arguments. Use complex negative arguments to obtain complex + results. + + There is an experimental variant in the ``Base.Math.JuliaLibm`` module, + which is typically faster and more accurate. + + :: + log(b,x) + Compute the base ``b`` logarithm of ``x``. Throws ``DomainError`` for negative ``Real`` arguments. .. function:: log2(x) @@ -694,6 +771,14 @@ Mathematical Functions .. doctest:: + :: + round(z, RoundingModeReal, RoundingModeImaginary) + + Returns the nearest integral value of the same type as the complex-valued + ``z`` to ``z``, breaking ties using the specified :obj:`RoundingMode`\ s. + The first :obj:`RoundingMode` is used for rounding the real components while + the second is used for rounding the imaginary components. + julia> round(pi, 2) 3.14 @@ -761,6 +846,40 @@ Mathematical Functions .. function:: round(z, RoundingModeReal, RoundingModeImaginary) + :: + round([T,] x, [digits, [base]], [r::RoundingMode]) + + ``round(x)`` rounds ``x`` to an integer value according to the default + rounding mode (see :func:`get_rounding`), returning a value of the same type as + ``x``. By default (:obj:`RoundNearest`), this will round to the nearest + integer, with ties (fractional values of 0.5) being rounded to the even + integer. + + .. doctest:: + + julia> round(1.7) + 2.0 + + julia> round(1.5) + 2.0 + + julia> round(2.5) + 2.0 + + The optional :obj:`RoundingMode` argument will change how the number gets rounded. + + ``round(T, x, [r::RoundingMode])`` converts the result to type ``T``, throwing an + :exc:`InexactError` if the value is not representable. + + ``round(x, digits)`` rounds to the specified number of digits after the + decimal place (or before if negative). ``round(x, digits, base)`` rounds + using a base other than 10. + + .. doctest:: + + :: + round(z, RoundingModeReal, RoundingModeImaginary) + Returns the nearest integral value of the same type as the complex-valued ``z`` to ``z``, breaking ties using the specified :obj:`RoundingMode`\ s. The first :obj:`RoundingMode` is used for rounding the real components while @@ -788,13 +907,11 @@ Mathematical Functions .. function:: trunc([T,] x, [digits, [base]]) - ``trunc(x)`` returns the nearest integral value of the same type as ``x`` whose absolute - value is less than or equal to ``x``. + :: + trunc(dt::TimeType, ::Type{Period}) -> TimeType - ``trunc(T, x)`` converts the result to type ``T``, throwing an - ``InexactError`` if the value is not representable. - - ``digits`` and ``base`` work as for :func:`round`. + Truncates the value of ``dt`` according to the provided ``Period`` type. + E.g. if ``dt`` is ``1996-01-01T12:30:00``, then ``trunc(dt,Day) == 1996-01-01T00:00:00``. .. function:: unsafe_trunc(T, x) @@ -934,8 +1051,26 @@ Mathematical Functions precision. If ``n`` is not an ``Integer``, ``factorial(n)`` is equivalent to :func:`gamma(n+1) `. + :: + factorial(n,k) + + Compute ``factorial(n)/factorial(k)`` + .. function:: factorial(n,k) + :: + factorial(n) + + Factorial of ``n``. If ``n`` is an :obj:`Integer`, the factorial + is computed as an integer (promoted to at least 64 bits). Note + that this may overflow if ``n`` is not small, but you can use + ``factorial(big(n))`` to compute the result exactly in arbitrary + precision. If ``n`` is not an ``Integer``, ``factorial(n)`` is + equivalent to :func:`gamma(n+1) `. + + :: + factorial(n,k) + Compute ``factorial(n)/factorial(k)`` .. function:: factor(n) -> Dict @@ -1158,8 +1293,22 @@ Mathematical Functions Riemann zeta function :math:`\zeta(s)`. + :: + zeta(s, z) + + Hurwitz zeta function :math:`\zeta(s, z)`. (This is equivalent to + the Riemann zeta function :math:`\zeta(s)` for the case of ``z=1``.) + .. function:: zeta(s, z) + :: + zeta(s) + + Riemann zeta function :math:`\zeta(s)`. + + :: + zeta(s, z) + Hurwitz zeta function :math:`\zeta(s, z)`. (This is equivalent to the Riemann zeta function :math:`\zeta(s)` for the case of ``z=1``.) @@ -1222,18 +1371,99 @@ Statistics Compute the middle of a scalar value, which is equivalent to ``x`` itself, but of the type of ``middle(x, x)`` for consistency. + :: + middle(x, y) + + Compute the middle of two reals ``x`` and ``y``, which is equivalent + in both value and type to computing their mean (``(x + y) / 2``). + + :: + middle(range) + + Compute the middle of a range, which consists in computing the mean of its extrema. + Since a range is sorted, the mean is performed with the first and last element. + + :: + middle(array) + + Compute the middle of an array, which consists in finding its extrema and + then computing their mean. + .. function:: middle(x, y) + :: + middle(x) + + Compute the middle of a scalar value, which is equivalent to ``x`` itself, + but of the type of ``middle(x, x)`` for consistency. + + :: + middle(x, y) + Compute the middle of two reals ``x`` and ``y``, which is equivalent in both value and type to computing their mean (``(x + y) / 2``). + :: + middle(range) + + Compute the middle of a range, which consists in computing the mean of its extrema. + Since a range is sorted, the mean is performed with the first and last element. + + :: + middle(array) + + Compute the middle of an array, which consists in finding its extrema and + then computing their mean. + .. function:: middle(range) + :: + middle(x) + + Compute the middle of a scalar value, which is equivalent to ``x`` itself, + but of the type of ``middle(x, x)`` for consistency. + + :: + middle(x, y) + + Compute the middle of two reals ``x`` and ``y``, which is equivalent + in both value and type to computing their mean (``(x + y) / 2``). + + :: + middle(range) + Compute the middle of a range, which consists in computing the mean of its extrema. Since a range is sorted, the mean is performed with the first and last element. + :: + middle(array) + + Compute the middle of an array, which consists in finding its extrema and + then computing their mean. + .. function:: middle(array) + :: + middle(x) + + Compute the middle of a scalar value, which is equivalent to ``x`` itself, + but of the type of ``middle(x, x)`` for consistency. + + :: + middle(x, y) + + Compute the middle of two reals ``x`` and ``y``, which is equivalent + in both value and type to computing their mean (``(x + y) / 2``). + + :: + middle(range) + + Compute the middle of a range, which consists in computing the mean of its extrema. + Since a range is sorted, the mean is performed with the first and last element. + + :: + middle(array) + Compute the middle of an array, which consists in finding its extrema and then computing their mean. @@ -1256,8 +1486,28 @@ Statistics ``v`` in each bin. Note: Julia does not ignore ``NaN`` values in the computation. + :: + hist(v, e) -> e, counts + + Compute the histogram of ``v`` using a vector/range ``e`` as the edges for + the bins. The result will be a vector of length ``length(e) - 1``, such that the + element at location ``i`` satisfies ``sum(e[i] .< v .<= e[i+1])``. + Note: Julia does not ignore ``NaN`` values in the computation. + .. function:: hist(v, e) -> e, counts + :: + hist(v[, n]) -> e, counts + + Compute the histogram of ``v``, optionally using approximately ``n`` + bins. The return values are a range ``e``, which correspond to the + edges of the bins, and ``counts`` containing the number of elements of + ``v`` in each bin. + Note: Julia does not ignore ``NaN`` values in the computation. + + :: + hist(v, e) -> e, counts + Compute the histogram of ``v`` using a vector/range ``e`` as the edges for the bins. The result will be a vector of length ``length(e) - 1``, such that the element at location ``i`` satisfies ``sum(e[i] .< v .<= e[i+1])``. @@ -1302,8 +1552,20 @@ Statistics Compute the quantiles of a vector ``v`` at a specified set of probability values ``p``. Note: Julia does not ignore ``NaN`` values in the computation. + :: + quantile(v, p) + + Compute the quantile of a vector ``v`` at the probability ``p``. + Note: Julia does not ignore ``NaN`` values in the computation. + .. function:: quantile(v, p) + Compute the quantiles of a vector ``v`` at a specified set of probability values ``p``. + Note: Julia does not ignore ``NaN`` values in the computation. + + :: + quantile(v, p) + Compute the quantile of a vector ``v`` at the probability ``p``. Note: Julia does not ignore ``NaN`` values in the computation. @@ -1340,7 +1602,6 @@ Statistics Note: ``v2`` can be omitted, which indicates ``v2 = v1``. - .. function:: cor(v1[, v2][, vardim=1, mean=nothing]) Compute the Pearson correlation between the vector(s) in ``v1`` and ``v2``. @@ -1348,7 +1609,6 @@ Statistics Users can use the keyword argument ``vardim`` to specify the variable dimension, and ``mean`` to supply pre-computed mean values. - Signal Processing ----------------- @@ -1587,8 +1847,21 @@ multi-threading. Use `FFTW.set_num_threads(np)` to use `np` threads. Swap the first and second halves of each dimension of ``x``. + :: + fftshift(x,dim) + + Swap the first and second halves of the given dimension of array ``x``. + .. function:: fftshift(x,dim) + :: + fftshift(x) + + Swap the first and second halves of each dimension of ``x``. + + :: + fftshift(x,dim) + Swap the first and second halves of the given dimension of array ``x``. .. function:: ifftshift(x, [dim]) @@ -1618,8 +1891,22 @@ multi-threading. Use `FFTW.set_num_threads(np)` to use `np` threads. 2-D convolution of the matrix ``A`` with the 2-D separable kernel generated by the vectors ``u`` and ``v``. Uses 2-D FFT algorithm + :: + conv2(B,A) + + 2-D convolution of the matrix ``B`` with the matrix ``A``. Uses 2-D FFT algorithm + .. function:: conv2(B,A) + :: + conv2(u,v,A) + + 2-D convolution of the matrix ``A`` with the 2-D separable kernel generated by + the vectors ``u`` and ``v``. Uses 2-D FFT algorithm + + :: + conv2(B,A) + 2-D convolution of the matrix ``B`` with the matrix ``A``. Uses 2-D FFT algorithm .. function:: xcorr(u,v) @@ -1669,7 +1956,6 @@ The following functions are defined within the ``Base.FFTW`` module. Similar to :func:`Base.plan_fft`, but corresponds to :func:`r2r!`. .. currentmodule:: Base - Numerical Integration --------------------- @@ -1737,3 +2023,4 @@ some built-in integration support in Julia. For real-valued endpoints, the starting and/or ending points may be infinite. (A coordinate transformation is performed internally to map the infinite interval to a finite one.) + diff --git a/doc/stdlib/numbers.rst b/doc/stdlib/numbers.rst index d7f103dbfbd2a..b58a774379335 100644 --- a/doc/stdlib/numbers.rst +++ b/doc/stdlib/numbers.rst @@ -50,6 +50,19 @@ Data Formats .. function:: parse(type, str, [base]) + :: + parse(str, start; greedy=true, raise=true) + + Parse the expression string and return an expression (which could later be passed to eval for execution). Start is the index of the first character to start parsing. If ``greedy`` is true (default), ``parse`` will try to consume as much input as it can; otherwise, it will stop as soon as it has parsed a valid expression. Incomplete but otherwise syntactically valid expressions will return ``Expr(:incomplete, "(error message)")``. If ``raise`` is true (default), syntax errors other than incomplete expressions will raise an error. If ``raise`` is false, ``parse`` will return an expression that will raise an error upon evaluation. + + :: + parse(str; raise=true) + + Parse the whole string greedily, returning a single expression. An error is thrown if there are additional characters after the first expression. If ``raise`` is true (default), syntax errors will raise an error; otherwise, ``parse`` will return an expression that will raise an error upon evaluation. + + :: + parse(type, str, [base]) + Parse a string as a number. If the type is an integer type, then a base can be specified (the default is 10). If the type is a floating point type, the string is parsed as a decimal floating point number. If the string does not contain a valid number, an error is raised. @@ -117,7 +130,6 @@ Data Formats Convert an array of bytes to its hexadecimal representation. All characters are in lower-case. Returns an ASCIIString. - General Number Functions and Constants -------------------------------------- @@ -280,7 +292,6 @@ General Number Functions and Constants julia> big"2.1" 2.099999999999999999999999999999999999999999999999999999999999999999999999999986 - .. function:: get_rounding(T) Get the current floating point rounding mode for type ``T``, controlling @@ -396,8 +407,34 @@ Integers julia> isprime(3) true + :: + isprime(x::BigInt, [reps = 25]) -> Bool + + Probabilistic primality test. Returns ``true`` if ``x`` is prime; and + ``false`` if ``x`` is not prime with high probability. The false positive + rate is about ``0.25^reps``. ``reps = 25`` is considered safe for + cryptographic applications (Knuth, Seminumerical Algorithms). + + .. doctest:: + + julia> isprime(big(3)) + true + .. function:: isprime(x::BigInt, [reps = 25]) -> Bool + :: + isprime(x::Integer) -> Bool + + Returns ``true`` if ``x`` is prime, and ``false`` otherwise. + + .. doctest:: + + julia> isprime(3) + true + + :: + isprime(x::BigInt, [reps = 25]) -> Bool + Probabilistic primality test. Returns ``true`` if ``x`` is prime; and ``false`` if ``x`` is not prime with high probability. The false positive rate is about ``0.25^reps``. ``reps = 25`` is considered safe for @@ -527,3 +564,4 @@ As ``BigInt`` represents unbounded integers, the interval must be specified (e.g .. function:: randexp!([rng], A::Array{Float64,N}) Fill the array A with random numbers following the exponential distribution (with scale 1). + diff --git a/doc/stdlib/parallel.rst b/doc/stdlib/parallel.rst index 31ec2abfb10ac..8de090be91295 100644 --- a/doc/stdlib/parallel.rst +++ b/doc/stdlib/parallel.rst @@ -46,12 +46,52 @@ Tasks Look up the value of a symbol in the current task's task-local storage. + :: + task_local_storage(symbol, value) + + Assign a value to a symbol in the current task's task-local storage. + + :: + task_local_storage(body, symbol, value) + + Call the function ``body`` with a modified task-local storage, in which + ``value`` is assigned to ``symbol``; the previous value of ``symbol``, or + lack thereof, is restored afterwards. Useful for emulating dynamic scoping. + .. function:: task_local_storage(symbol, value) + :: + task_local_storage(symbol) + + Look up the value of a symbol in the current task's task-local storage. + + :: + task_local_storage(symbol, value) + Assign a value to a symbol in the current task's task-local storage. + :: + task_local_storage(body, symbol, value) + + Call the function ``body`` with a modified task-local storage, in which + ``value`` is assigned to ``symbol``; the previous value of ``symbol``, or + lack thereof, is restored afterwards. Useful for emulating dynamic scoping. + .. function:: task_local_storage(body, symbol, value) + :: + task_local_storage(symbol) + + Look up the value of a symbol in the current task's task-local storage. + + :: + task_local_storage(symbol, value) + + Assign a value to a symbol in the current task's task-local storage. + + :: + task_local_storage(body, symbol, value) + Call the function ``body`` with a modified task-local storage, in which ``value`` is assigned to ``symbol``; the previous value of ``symbol``, or lack thereof, is restored afterwards. Useful for emulating dynamic scoping. @@ -123,7 +163,6 @@ Tasks ``Channel()`` - equivalent to ``Channel{Any}(32)`` ``Channel(sz::Int)`` equivalent to ``Channel{Any}(sz)`` - General Parallel Computing Support ---------------------------------- @@ -132,12 +171,142 @@ General Parallel Computing Support Launches workers using the in-built ``LocalManager`` which only launches workers on the local host. This can be used to take advantage of multiple cores. ``addprocs(4)`` will add 4 processes on the local machine. + :: + addprocs() -> List of process identifiers + + Equivalent to ``addprocs(CPU_CORES)`` + + :: + addprocs(machines; tunnel=false, sshflags=``, max_parallel=10, exeflags=``) -> List of process identifiers + + Add processes on remote machines via SSH. + Requires julia to be installed in the same location on each node, or to be available via a shared file system. + + ``machines`` is a vector of machine specifications. Worker are started for each specification. + + A machine specification is either a string ``machine_spec`` or a tuple - ``(machine_spec, count)`` + + ``machine_spec`` is a string of the form ``[user@]host[:port] [bind_addr[:port]]``. ``user`` defaults + to current user, ``port`` to the standard ssh port. If ``[bind_addr[:port]]`` is specified, other + workers will connect to this worker at the specified ``bind_addr`` and ``port``. + + ``count`` is the number of workers to be launched on the specified host. If specified as ``:auto`` + it will launch as many workers as the number of cores on the specific host. + + + Keyword arguments: + + ``tunnel`` : if ``true`` then SSH tunneling will be used to connect to the worker from the master process. + + ``sshflags`` : specifies additional ssh options, e.g. :literal:`sshflags=\`-i /home/foo/bar.pem\`` . + + ``max_parallel`` : specifies the maximum number of workers connected to in parallel at a host. Defaults to 10. + + ``dir`` : specifies the working directory on the workers. Defaults to the host's current directory (as found by `pwd()`) + + ``exename`` : name of the julia executable. Defaults to "$JULIA_HOME/julia" or "$JULIA_HOME/julia-debug" as the case may be. + + ``exeflags`` : additional flags passed to the worker processes. + + Environment variables : + + If the master process fails to establish a connection with a newly launched worker within 60.0 seconds, + the worker treats it a fatal situation and terminates. This timeout can be controlled via environment + variable ``JULIA_WORKER_TIMEOUT``. The value of ``JULIA_WORKER_TIMEOUT`` on the master process, specifies + the number of seconds a newly launched worker waits for connection establishment. + + :: + addprocs(manager::ClusterManager; kwargs...) -> List of process identifiers + + Launches worker processes via the specified cluster manager. + + For example Beowulf clusters are supported via a custom cluster manager implemented + in package ``ClusterManagers``. + + The number of seconds a newly launched worker waits for connection establishment from the master can be + specified via variable ``JULIA_WORKER_TIMEOUT`` in the worker process's environment. Relevant only when + using TCP/IP as transport. + .. function:: addprocs() -> List of process identifiers + :: + addprocs(n::Integer; exeflags=``) -> List of process identifiers + + Launches workers using the in-built ``LocalManager`` which only launches workers on the local host. + This can be used to take advantage of multiple cores. ``addprocs(4)`` will add 4 processes on the local machine. + + :: + addprocs() -> List of process identifiers + Equivalent to ``addprocs(CPU_CORES)`` + :: + addprocs(machines; tunnel=false, sshflags=``, max_parallel=10, exeflags=``) -> List of process identifiers + + Add processes on remote machines via SSH. + Requires julia to be installed in the same location on each node, or to be available via a shared file system. + + ``machines`` is a vector of machine specifications. Worker are started for each specification. + + A machine specification is either a string ``machine_spec`` or a tuple - ``(machine_spec, count)`` + + ``machine_spec`` is a string of the form ``[user@]host[:port] [bind_addr[:port]]``. ``user`` defaults + to current user, ``port`` to the standard ssh port. If ``[bind_addr[:port]]`` is specified, other + workers will connect to this worker at the specified ``bind_addr`` and ``port``. + + ``count`` is the number of workers to be launched on the specified host. If specified as ``:auto`` + it will launch as many workers as the number of cores on the specific host. + + + Keyword arguments: + + ``tunnel`` : if ``true`` then SSH tunneling will be used to connect to the worker from the master process. + + ``sshflags`` : specifies additional ssh options, e.g. :literal:`sshflags=\`-i /home/foo/bar.pem\`` . + + ``max_parallel`` : specifies the maximum number of workers connected to in parallel at a host. Defaults to 10. + + ``dir`` : specifies the working directory on the workers. Defaults to the host's current directory (as found by `pwd()`) + + ``exename`` : name of the julia executable. Defaults to "$JULIA_HOME/julia" or "$JULIA_HOME/julia-debug" as the case may be. + + ``exeflags`` : additional flags passed to the worker processes. + + Environment variables : + + If the master process fails to establish a connection with a newly launched worker within 60.0 seconds, + the worker treats it a fatal situation and terminates. This timeout can be controlled via environment + variable ``JULIA_WORKER_TIMEOUT``. The value of ``JULIA_WORKER_TIMEOUT`` on the master process, specifies + the number of seconds a newly launched worker waits for connection establishment. + + :: + addprocs(manager::ClusterManager; kwargs...) -> List of process identifiers + + Launches worker processes via the specified cluster manager. + + For example Beowulf clusters are supported via a custom cluster manager implemented + in package ``ClusterManagers``. + + The number of seconds a newly launched worker waits for connection establishment from the master can be + specified via variable ``JULIA_WORKER_TIMEOUT`` in the worker process's environment. Relevant only when + using TCP/IP as transport. + .. function:: addprocs(machines; tunnel=false, sshflags=``, max_parallel=10, exeflags=``) -> List of process identifiers + :: + addprocs(n::Integer; exeflags=``) -> List of process identifiers + + Launches workers using the in-built ``LocalManager`` which only launches workers on the local host. + This can be used to take advantage of multiple cores. ``addprocs(4)`` will add 4 processes on the local machine. + + :: + addprocs() -> List of process identifiers + + Equivalent to ``addprocs(CPU_CORES)`` + + :: + addprocs(machines; tunnel=false, sshflags=``, max_parallel=10, exeflags=``) -> List of process identifiers + Add processes on remote machines via SSH. Requires julia to be installed in the same location on each node, or to be available via a shared file system. @@ -174,9 +343,73 @@ General Parallel Computing Support variable ``JULIA_WORKER_TIMEOUT``. The value of ``JULIA_WORKER_TIMEOUT`` on the master process, specifies the number of seconds a newly launched worker waits for connection establishment. + :: + addprocs(manager::ClusterManager; kwargs...) -> List of process identifiers + + Launches worker processes via the specified cluster manager. + + For example Beowulf clusters are supported via a custom cluster manager implemented + in package ``ClusterManagers``. + + The number of seconds a newly launched worker waits for connection establishment from the master can be + specified via variable ``JULIA_WORKER_TIMEOUT`` in the worker process's environment. Relevant only when + using TCP/IP as transport. .. function:: addprocs(manager::ClusterManager; kwargs...) -> List of process identifiers + :: + addprocs(n::Integer; exeflags=``) -> List of process identifiers + + Launches workers using the in-built ``LocalManager`` which only launches workers on the local host. + This can be used to take advantage of multiple cores. ``addprocs(4)`` will add 4 processes on the local machine. + + :: + addprocs() -> List of process identifiers + + Equivalent to ``addprocs(CPU_CORES)`` + + :: + addprocs(machines; tunnel=false, sshflags=``, max_parallel=10, exeflags=``) -> List of process identifiers + + Add processes on remote machines via SSH. + Requires julia to be installed in the same location on each node, or to be available via a shared file system. + + ``machines`` is a vector of machine specifications. Worker are started for each specification. + + A machine specification is either a string ``machine_spec`` or a tuple - ``(machine_spec, count)`` + + ``machine_spec`` is a string of the form ``[user@]host[:port] [bind_addr[:port]]``. ``user`` defaults + to current user, ``port`` to the standard ssh port. If ``[bind_addr[:port]]`` is specified, other + workers will connect to this worker at the specified ``bind_addr`` and ``port``. + + ``count`` is the number of workers to be launched on the specified host. If specified as ``:auto`` + it will launch as many workers as the number of cores on the specific host. + + + Keyword arguments: + + ``tunnel`` : if ``true`` then SSH tunneling will be used to connect to the worker from the master process. + + ``sshflags`` : specifies additional ssh options, e.g. :literal:`sshflags=\`-i /home/foo/bar.pem\`` . + + ``max_parallel`` : specifies the maximum number of workers connected to in parallel at a host. Defaults to 10. + + ``dir`` : specifies the working directory on the workers. Defaults to the host's current directory (as found by `pwd()`) + + ``exename`` : name of the julia executable. Defaults to "$JULIA_HOME/julia" or "$JULIA_HOME/julia-debug" as the case may be. + + ``exeflags`` : additional flags passed to the worker processes. + + Environment variables : + + If the master process fails to establish a connection with a newly launched worker within 60.0 seconds, + the worker treats it a fatal situation and terminates. This timeout can be controlled via environment + variable ``JULIA_WORKER_TIMEOUT``. The value of ``JULIA_WORKER_TIMEOUT`` on the master process, specifies + the number of seconds a newly launched worker waits for connection establishment. + + :: + addprocs(manager::ClusterManager; kwargs...) -> List of process identifiers + Launches worker processes via the specified cluster manager. For example Beowulf clusters are supported via a custom cluster manager implemented @@ -186,7 +419,6 @@ General Parallel Computing Support specified via variable ``JULIA_WORKER_TIMEOUT`` in the worker process's environment. Relevant only when using TCP/IP as transport. - .. function:: nprocs() Get the number of available processes. @@ -199,6 +431,11 @@ General Parallel Computing Support Returns a list of all process identifiers. + :: + procs(S::SharedArray) + + Get the vector of processes that have mapped the shared array + .. function:: workers() Returns a list of all worker process identifiers. @@ -227,7 +464,6 @@ General Parallel Computing Support If ``err_retry`` is true, it retries a failed application of ``f`` on a different worker. If ``err_stop`` is true, it takes precedence over the value of ``err_retry`` and ``pmap`` stops execution on the first error. - .. function:: remotecall(id, func, args...) Call a function asynchronously on the given arguments on the specified process. Returns a ``RemoteRef``. @@ -279,16 +515,42 @@ General Parallel Computing Support Store a value to a remote reference. Implements "shared queue of length 1" semantics: if a value is already present, blocks until the value is removed with ``take!``. Returns its first argument. + :: + put!(Channel, value) + + Appends an item to the channel. Blocks if the channel is full. + .. function:: put!(Channel, value) + :: + put!(RemoteRef, value) + + Store a value to a remote reference. Implements "shared queue of length 1" semantics: if a value is already present, blocks until the value is removed with ``take!``. Returns its first argument. + + :: + put!(Channel, value) + Appends an item to the channel. Blocks if the channel is full. .. function:: take!(RemoteRef) Fetch the value of a remote reference, removing it so that the reference is empty again. + :: + take!(Channel) + + Removes and returns a value from a ``Channel``. Blocks till data is available. + .. function:: take!(Channel) + :: + take!(RemoteRef) + + Fetch the value of a remote reference, removing it so that the reference is empty again. + + :: + take!(Channel) + Removes and returns a value from a ``Channel``. Blocks till data is available. .. function:: isready(r::RemoteRef) @@ -308,6 +570,14 @@ General Parallel Computing Support .. function:: close(Channel) + :: + close(stream) + + Close an I/O stream. Performs a ``flush`` first. + + :: + close(Channel) + Closes a channel. An exception is thrown by: * ``put!`` on a on a closed channel. @@ -318,8 +588,21 @@ General Parallel Computing Support Make an uninitialized remote reference on the local machine. + :: + RemoteRef(n) + + Make an uninitialized remote reference on process ``n``. + .. function:: RemoteRef(n) + :: + RemoteRef() + + Make an uninitialized remote reference on the local machine. + + :: + RemoteRef(n) + Make an uninitialized remote reference on process ``n``. .. function:: timedwait(testcb::Function, secs::Float64; pollint::Float64=0.1) @@ -401,6 +684,14 @@ Shared Arrays (Experimental, UNIX-only feature) .. function:: procs(S::SharedArray) + :: + procs() + + Returns a list of all process identifiers. + + :: + procs(S::SharedArray) + Get the vector of processes that have mapped the shared array .. function:: sdata(S::SharedArray) @@ -439,6 +730,14 @@ Cluster Manager Interface .. function:: kill(manager::FooManager, pid::Int, config::WorkerConfig) + :: + kill(p::Process, signum=SIGTERM) + + Send a signal to a process. The default is to terminate the process. + + :: + kill(manager::FooManager, pid::Int, config::WorkerConfig) + Implemented by cluster managers. It is called on the master process, by ``rmprocs``. It should cause the remote worker specified by ``pid`` to exit. ``Base.kill(manager::ClusterManager.....)`` executes a remote ``exit()`` on ``pid`` @@ -450,15 +749,28 @@ Cluster Manager Interface .. function:: connect(manager::FooManager, pid::Int, config::WorkerConfig) -> (instrm::AsyncStream, outstrm::AsyncStream) + :: + connect([host],port) -> TcpSocket + + Connect to the host ``host`` on port ``port`` + + :: + connect(path) -> Pipe + + Connect to the Named Pipe/Domain Socket at ``path`` + + :: + connect(manager::FooManager, pid::Int, config::WorkerConfig) -> (instrm::AsyncStream, outstrm::AsyncStream) + Implemented by cluster managers using custom transports. It should establish a logical connection to worker with id ``pid``, specified by ``config`` and return a pair of ``AsyncStream`` objects. Messages from ``pid`` to current process will be read off ``instrm``, while messages to be sent to ``pid`` will be written to ``outstrm``. The custom transport implementation must ensure that messages are delivered and received completely and in order. ``Base.connect(manager::ClusterManager.....)`` sets up TCP/IP socket connections in-between workers. - .. function:: Base.process_messages(instrm::AsyncStream, outstrm::AsyncStream) Called by cluster managers using custom transports. It should be called when the custom transport implementation receives the first message from a remote worker. The custom transport must manage a logical connection to the remote worker and provide two AsyncStream objects, one for incoming messages and the other for messages addressed to the remote worker. + diff --git a/doc/stdlib/pkg.rst b/doc/stdlib/pkg.rst index 57a580fe45d4b..406a71aabdac0 100644 --- a/doc/stdlib/pkg.rst +++ b/doc/stdlib/pkg.rst @@ -15,8 +15,26 @@ to use them, you'll need to prefix each function call with an explicit ``Pkg.``, that path is used in the returned value as ``joinpath(ENV["JULIA_PKGDIR"],"v$(VERSION.major).$(VERSION.minor)")``. If ``JULIA_PKGDIR`` is a relative path, it is interpreted relative to whatever the current working directory is. + :: + dir(names...) -> AbstractString + + Equivalent to ``normpath(Pkg.dir(),names...)`` – i.e. it appends path components to the package directory and normalizes the resulting path. + In particular, ``Pkg.dir(pkg)`` returns the path to the package ``pkg``. + .. function:: dir(names...) -> AbstractString + :: + dir() -> AbstractString + + Returns the absolute path of the package directory. + This defaults to ``joinpath(homedir(),".julia","v$(VERSION.major).$(VERSION.minor)")`` on all platforms + (i.e. ``~/.julia/v0.4`` in UNIX shell syntax). If the ``JULIA_PKGDIR`` environment variable is set, then + that path is used in the returned value as ``joinpath(ENV["JULIA_PKGDIR"],"v$(VERSION.major).$(VERSION.minor)")``. + If ``JULIA_PKGDIR`` is a relative path, it is interpreted relative to whatever the current working directory is. + + :: + dir(names...) -> AbstractString + Equivalent to ``normpath(Pkg.dir(),names...)`` – i.e. it appends path components to the package directory and normalizes the resulting path. In particular, ``Pkg.dir(pkg)`` returns the path to the package ``pkg``. @@ -54,8 +72,25 @@ to use them, you'll need to prefix each function call with an explicit ``Pkg.``, The package repo is cloned by the name ``pkg`` if provided; if not provided, ``pkg`` is determined automatically from ``url``. + :: + clone(pkg) + + If ``pkg`` has a URL registered in ``Pkg.dir("METADATA")``, clone it from that URL on the default branch. + The package does not need to have any registered versions. + .. function:: clone(pkg) + :: + clone(url, [pkg]) + + Clone a package directly from the git URL ``url``. + The package does not need to be a registered in ``Pkg.dir("METADATA")``. + The package repo is cloned by the name ``pkg`` if provided; + if not provided, ``pkg`` is determined automatically from ``url``. + + :: + clone(pkg) + If ``pkg`` has a URL registered in ``Pkg.dir("METADATA")``, clone it from that URL on the default branch. The package does not need to have any registered versions. @@ -63,16 +98,42 @@ to use them, you'll need to prefix each function call with an explicit ``Pkg.``, Returns the names of available packages. + :: + available(pkg) -> Vector{VersionNumber} + + Returns the version numbers available for package ``pkg``. + .. function:: available(pkg) -> Vector{VersionNumber} + :: + available() -> Vector{ASCIIString} + + Returns the names of available packages. + + :: + available(pkg) -> Vector{VersionNumber} + Returns the version numbers available for package ``pkg``. .. function:: installed() -> Dict{ASCIIString,VersionNumber} Returns a dictionary mapping installed package names to the installed version number of each package. + :: + installed(pkg) -> Void | VersionNumber + + If ``pkg`` is installed, return the installed version number, otherwise return ``nothing``. + .. function:: installed(pkg) -> Void | VersionNumber + :: + installed() -> Dict{ASCIIString,VersionNumber} + + Returns a dictionary mapping installed package names to the installed version number of each package. + + :: + installed(pkg) -> Void | VersionNumber + If ``pkg`` is installed, return the installed version number, otherwise return ``nothing``. .. function:: status() @@ -95,8 +156,22 @@ to use them, you'll need to prefix each function call with an explicit ``Pkg.``, Pin ``pkg`` at the current version. To go back to using the newest compatible released version, use ``Pkg.free(pkg)`` + :: + pin(pkg, version) + + Pin ``pkg`` at registered version ``version``. + .. function:: pin(pkg, version) + :: + pin(pkg) + + Pin ``pkg`` at the current version. + To go back to using the newest compatible released version, use ``Pkg.free(pkg)`` + + :: + pin(pkg, version) + Pin ``pkg`` at registered version ``version``. .. function:: free(pkg) @@ -112,8 +187,22 @@ to use them, you'll need to prefix each function call with an explicit ``Pkg.``, Run the build scripts for all installed packages in depth-first recursive order. + :: + build(pkgs...) + + Run the build script in "deps/build.jl" for each package in ``pkgs`` and all of their dependencies in depth-first recursive order. + This is called automatically by ``Pkg.resolve()`` on all installed or updated packages. + .. function:: build(pkgs...) + :: + build() + + Run the build scripts for all installed packages in depth-first recursive order. + + :: + build(pkgs...) + Run the build script in "deps/build.jl" for each package in ``pkgs`` and all of their dependencies in depth-first recursive order. This is called automatically by ``Pkg.resolve()`` on all installed or updated packages. @@ -142,6 +231,20 @@ to use them, you'll need to prefix each function call with an explicit ``Pkg.``, Run the tests for all installed packages ensuring that each package's test dependencies are installed for the duration of the test. A package is tested by running its ``test/runtests.jl`` file and test dependencies are specified in ``test/REQUIRE``. + :: + test(pkgs...) + + Run the tests for each package in ``pkgs`` ensuring that each package's test dependencies are installed for the duration of the test. A package is tested by running its ``test/runtests.jl`` file and test dependencies are specified in ``test/REQUIRE``. + .. function:: test(pkgs...) + :: + test() + + Run the tests for all installed packages ensuring that each package's test dependencies are installed for the duration of the test. A package is tested by running its ``test/runtests.jl`` file and test dependencies are specified in ``test/REQUIRE``. + + :: + test(pkgs...) + Run the tests for each package in ``pkgs`` ensuring that each package's test dependencies are installed for the duration of the test. A package is tested by running its ``test/runtests.jl`` file and test dependencies are specified in ``test/REQUIRE``. + diff --git a/doc/stdlib/profile.rst b/doc/stdlib/profile.rst index 1ab214c5efdb1..9b19d8d2d7214 100644 --- a/doc/stdlib/profile.rst +++ b/doc/stdlib/profile.rst @@ -15,7 +15,6 @@ backtraces. .. currentmodule:: Base.Profile - The methods in :mod:`Base.Profile` are not exported and need to be called e.g. as ``Profile.print()``. .. function:: clear() @@ -32,8 +31,30 @@ The methods in :mod:`Base.Profile` are not exported and need to be called e.g. a correspond to the same line of code. ``cols`` controls the width of the display. + :: + print([io::IO = STDOUT,] data::Vector, lidict::Dict; format = :tree, combine = true, cols = tty_cols()) + + Prints profiling results to ``io``. This variant is used to examine + results exported by a previous call to :func:`retrieve`. + Supply the vector ``data`` of backtraces and a dictionary + ``lidict`` of line information. + .. function:: print([io::IO = STDOUT,] data::Vector, lidict::Dict; format = :tree, combine = true, cols = tty_cols()) + :: + print([io::IO = STDOUT,] [data::Vector]; format = :tree, C = false, combine = true, cols = tty_cols()) + + Prints profiling results to ``io`` (by default, ``STDOUT``). If you + do not supply a ``data`` vector, the internal buffer of accumulated + backtraces will be used. ``format`` can be ``:tree`` or + ``:flat``. If ``C==true``, backtraces from C and Fortran code are + shown. ``combine==true`` merges instruction pointers that + correspond to the same line of code. ``cols`` controls the width + of the display. + + :: + print([io::IO = STDOUT,] data::Vector, lidict::Dict; format = :tree, combine = true, cols = tty_cols()) + Prints profiling results to ``io``. This variant is used to examine results exported by a previous call to :func:`retrieve`. Supply the vector ``data`` of backtraces and a dictionary @@ -86,3 +107,4 @@ The methods in :mod:`Base.Profile` are not exported and need to be called e.g. a (to force JIT-compilation), then call :func:`clear_malloc_data`. Then execute your command(s) again, quit Julia, and examine the resulting ``*.mem`` files. + diff --git a/doc/stdlib/sort.rst b/doc/stdlib/sort.rst index 93d2c42c866fc..d1ff0cceee9bc 100644 --- a/doc/stdlib/sort.rst +++ b/doc/stdlib/sort.rst @@ -133,8 +133,21 @@ Sorting Functions Variant of ``sort!`` that returns a sorted copy of ``v`` leaving ``v`` itself unmodified. + :: + sort(A, dim, [alg=,] [by=,] [lt=,] [rev=false]) + + Sort a multidimensional array ``A`` along the given dimension. + .. function:: sort(A, dim, [alg=,] [by=,] [lt=,] [rev=false]) + :: + sort(v, [alg=,] [by=,] [lt=,] [rev=false]) + + Variant of ``sort!`` that returns a sorted copy of ``v`` leaving ``v`` itself unmodified. + + :: + sort(A, dim, [alg=,] [by=,] [lt=,] [rev=false]) + Sort a multidimensional array ``A`` along the given dimension. .. function:: sortperm(v, [alg=,] [by=,] [lt=,] [rev=false]) @@ -164,7 +177,6 @@ Sorting Functions Sort the columns of matrix ``A`` lexicographically. - Order-Related Functions ----------------------- @@ -224,7 +236,6 @@ Order-Related Functions ``initialized`` is ``false`` (the default), ix is initialized to contain the values ``1:length(ix)``. - Sorting Algorithms ------------------ diff --git a/doc/stdlib/strings.rst b/doc/stdlib/strings.rst index 3649350f8435b..c0a32995829ef 100644 --- a/doc/stdlib/strings.rst +++ b/doc/stdlib/strings.rst @@ -6,14 +6,50 @@ .. function:: length(s) + :: + length(A) -> Integer + + Returns the number of elements in A + + :: + length(collection) -> Integer + + For ordered, indexable collections, the maximum index ``i`` for which ``getindex(collection, i)`` is valid. For unordered collections, the number of elements. + + :: + length(s) + The number of characters in string ``s``. .. function:: sizeof(s::AbstractString) + :: + sizeof(type) + + Size, in bytes, of the canonical binary representation of the given type, if any. + + :: + sizeof(s::AbstractString) + The number of bytes in string ``s``. .. function:: *(s, t) + :: + *(A, B) + :noindex: + + Matrix multiplication + + :: + *(x, y...) + + Multiplication operator. ``x*y*z*...`` calls this function with all arguments, i.e. + ``*(x, y, z, ...)``. + + :: + *(s, t) + Concatenate strings. The ``*`` operator is an alias to this function. .. doctest:: @@ -23,6 +59,14 @@ .. function:: ^(s, n) + :: + ^(x, y) + + Exponentiation operator. + + :: + ^(s, n) + Repeat ``n`` times the string ``s``. The ``^`` operator is an alias to this function. .. doctest:: @@ -42,32 +86,117 @@ Create a string from the address of a C (0-terminated) string encoded in ASCII or UTF-8. A copy is made; the ptr can be safely freed. If ``length`` is specified, the string does not have to be 0-terminated. + :: + bytestring(s) + + Convert a string to a contiguous byte array representation appropriate for passing it to C functions. The string will be encoded as either ASCII or UTF-8. + .. function:: bytestring(s) + :: + bytestring(::Ptr{UInt8}, [length]) + + Create a string from the address of a C (0-terminated) string encoded in ASCII or UTF-8. A copy is made; the ptr can be safely freed. If ``length`` is specified, the string does not have to be 0-terminated. + + :: + bytestring(s) + Convert a string to a contiguous byte array representation appropriate for passing it to C functions. The string will be encoded as either ASCII or UTF-8. .. function:: ascii(::Array{UInt8,1}) Create an ASCII string from a byte array. + :: + ascii(s) + + Convert a string to a contiguous ASCII string (all characters must be valid ASCII characters). + + :: + ascii(::Ptr{UInt8}, [length]) + + Create an ASCII string from the address of a C (0-terminated) string encoded in ASCII. A copy is made; the ptr can be safely freed. If ``length`` is specified, the string does not have to be 0-terminated. + .. function:: ascii(s) + :: + ascii(::Array{UInt8,1}) + + Create an ASCII string from a byte array. + + :: + ascii(s) + Convert a string to a contiguous ASCII string (all characters must be valid ASCII characters). + :: + ascii(::Ptr{UInt8}, [length]) + + Create an ASCII string from the address of a C (0-terminated) string encoded in ASCII. A copy is made; the ptr can be safely freed. If ``length`` is specified, the string does not have to be 0-terminated. + .. function:: ascii(::Ptr{UInt8}, [length]) + :: + ascii(::Array{UInt8,1}) + + Create an ASCII string from a byte array. + + :: + ascii(s) + + Convert a string to a contiguous ASCII string (all characters must be valid ASCII characters). + + :: + ascii(::Ptr{UInt8}, [length]) + Create an ASCII string from the address of a C (0-terminated) string encoded in ASCII. A copy is made; the ptr can be safely freed. If ``length`` is specified, the string does not have to be 0-terminated. .. function:: utf8(::Array{UInt8,1}) Create a UTF-8 string from a byte array. + :: + utf8(::Ptr{UInt8}, [length]) + + Create a UTF-8 string from the address of a C (0-terminated) string encoded in UTF-8. A copy is made; the ptr can be safely freed. If ``length`` is specified, the string does not have to be 0-terminated. + + :: + utf8(s) + + Convert a string to a contiguous UTF-8 string (all characters must be valid UTF-8 characters). + .. function:: utf8(::Ptr{UInt8}, [length]) + :: + utf8(::Array{UInt8,1}) + + Create a UTF-8 string from a byte array. + + :: + utf8(::Ptr{UInt8}, [length]) + Create a UTF-8 string from the address of a C (0-terminated) string encoded in UTF-8. A copy is made; the ptr can be safely freed. If ``length`` is specified, the string does not have to be 0-terminated. + :: + utf8(s) + + Convert a string to a contiguous UTF-8 string (all characters must be valid UTF-8 characters). + .. function:: utf8(s) + :: + utf8(::Array{UInt8,1}) + + Create a UTF-8 string from a byte array. + + :: + utf8(::Ptr{UInt8}, [length]) + + Create a UTF-8 string from the address of a C (0-terminated) string encoded in UTF-8. A copy is made; the ptr can be safely freed. If ``length`` is specified, the string does not have to be 0-terminated. + + :: + utf8(s) + Convert a string to a contiguous UTF-8 string (all characters must be valid UTF-8 characters). .. function:: normalize_string(s, normalform::Symbol) @@ -114,8 +243,32 @@ Returns true if the given value is valid for its type, which currently can be one of ``Char``, ``ASCIIString``, ``UTF8String``, ``UTF16String``, or ``UTF32String`` + :: + isvalid(T, value) -> Bool + + Returns true if the given value is valid for that type. + Types currently can be ``Char``, ``ASCIIString``, ``UTF8String``, ``UTF16String``, or ``UTF32String`` + Values for ``Char`` can be of type ``Char`` or ``UInt32`` + Values for ``ASCIIString`` and ``UTF8String`` can be of that type, or ``Vector{UInt8}`` + Values for ``UTF16String`` can be ``UTF16String`` or ``Vector{UInt16}`` + Values for ``UTF32String`` can be ``UTF32String``, ``Vector{Char}`` or ``Vector{UInt32}`` + + :: + isvalid(str, i) + + Tells whether index ``i`` is valid for the given string + .. function:: isvalid(T, value) -> Bool + :: + isvalid(value) -> Bool + + Returns true if the given value is valid for its type, + which currently can be one of ``Char``, ``ASCIIString``, ``UTF8String``, ``UTF16String``, or ``UTF32String`` + + :: + isvalid(T, value) -> Bool + Returns true if the given value is valid for that type. Types currently can be ``Char``, ``ASCIIString``, ``UTF8String``, ``UTF16String``, or ``UTF32String`` Values for ``Char`` can be of type ``Char`` or ``UInt32`` @@ -123,6 +276,11 @@ Values for ``UTF16String`` can be ``UTF16String`` or ``Vector{UInt16}`` Values for ``UTF32String`` can be ``UTF32String``, ``Vector{Char}`` or ``Vector{UInt32}`` + :: + isvalid(str, i) + + Tells whether index ``i`` is valid for the given string + .. function:: is_assigned_char(c) -> Bool Returns true if the given char or integer is an assigned Unicode code point. @@ -249,6 +407,25 @@ .. function:: isvalid(str, i) + :: + isvalid(value) -> Bool + + Returns true if the given value is valid for its type, + which currently can be one of ``Char``, ``ASCIIString``, ``UTF8String``, ``UTF16String``, or ``UTF32String`` + + :: + isvalid(T, value) -> Bool + + Returns true if the given value is valid for that type. + Types currently can be ``Char``, ``ASCIIString``, ``UTF8String``, ``UTF16String``, or ``UTF32String`` + Values for ``Char`` can be of type ``Char`` or ``UInt32`` + Values for ``ASCIIString`` and ``UTF8String`` can be of that type, or ``Vector{UInt8}`` + Values for ``UTF16String`` can be ``UTF16String`` or ``Vector{UInt16}`` + Values for ``UTF32String`` can be ``UTF32String``, ``Vector{Char}`` or ``Vector{UInt32}`` + + :: + isvalid(str, i) + Tells whether index ``i`` is valid for the given string .. function:: nextind(str, i) @@ -377,31 +554,56 @@ making a copy of the data and treating the NUL as a terminator rather than as part of the string. -.. function:: utf16(::Union{Ptr{UInt16},Ptr{Int16}} [, length]) + :: + utf16(::Union{Ptr{UInt16},Ptr{Int16}} [, length]) Create a string from the address of a NUL-terminated UTF-16 string. A copy is made; the pointer can be safely freed. If ``length`` is specified, the string does not have to be NUL-terminated. -.. function:: utf32(s) +.. function:: utf16(::Union{Ptr{UInt16},Ptr{Int16}} [, length]) - Create a UTF-32 string from a byte array, array of ``Char`` or ``UInt32``, or - any other string type. (Conversions of byte arrays check for a - byte-order marker in the first four bytes, and do not include it in - the resulting string.) + :: + utf16(s) + + Create a UTF-16 string from a byte array, array of ``UInt16``, or + any other string type. (Data must be valid UTF-16. Conversions of + byte arrays check for a byte-order marker in the first two bytes, + and do not include it in the resulting string.) - Note that the resulting ``UTF32String`` data is terminated by the NUL - codepoint (32-bit zero), which is not treated as a character in the + Note that the resulting ``UTF16String`` data is terminated by the NUL + codepoint (16-bit zero), which is not treated as a character in the string (so that it is mostly invisible in Julia); this allows the string to be passed directly to external functions requiring NUL-terminated data. This NUL is appended automatically by the - `utf32(s)` conversion function. If you have a ``Char`` or ``UInt32`` array - ``A`` that is already NUL-terminated UTF-32 data, then you - can instead use `UTF32String(A)`` to construct the string without + `utf16(s)` conversion function. If you have a ``UInt16`` array + ``A`` that is already NUL-terminated valid UTF-16 data, then you + can instead use `UTF16String(A)`` to construct the string without making a copy of the data and treating the NUL as a terminator rather than as part of the string. + :: + utf16(::Union{Ptr{UInt16},Ptr{Int16}} [, length]) + + Create a string from the address of a NUL-terminated UTF-16 string. A copy is made; the pointer can be safely freed. If ``length`` is specified, the string does not have to be NUL-terminated. + +.. function:: utf32(s) + + :: + wstring(s) + + This is a synonym for either ``utf32(s)`` or ``utf16(s)``, + depending on whether ``Cwchar_t`` is 32 or 16 bits, respectively. + The synonym ``WString`` for ``UTF32String`` or ``UTF16String`` + is also provided. + .. function:: utf32(::Union{Ptr{Char},Ptr{UInt32},Ptr{Int32}} [, length]) - Create a string from the address of a NUL-terminated UTF-32 string. A copy is made; the pointer can be safely freed. If ``length`` is specified, the string does not have to be NUL-terminated. + :: + wstring(s) + + This is a synonym for either ``utf32(s)`` or ``utf16(s)``, + depending on whether ``Cwchar_t`` is 32 or 16 bits, respectively. + The synonym ``WString`` for ``UTF32String`` or ``UTF16String`` + is also provided. .. function:: wstring(s) @@ -410,4 +612,3 @@ The synonym ``WString`` for ``UTF32String`` or ``UTF16String`` is also provided. - diff --git a/doc/stdlib/test.rst b/doc/stdlib/test.rst index c8a1266d924df..514cb1a185b48 100644 --- a/doc/stdlib/test.rst +++ b/doc/stdlib/test.rst @@ -17,9 +17,7 @@ binary install, you can run the test suite using ``Base.runtests()``. Run the Julia unit tests listed in ``tests``, which can be either a string or an array of strings, using ``numcores`` processors. (not exported) - .. module:: Base.Test - Test Framework -------------- From b980d09245e891f46f1498f95642c2f079ae7d40 Mon Sep 17 00:00:00 2001 From: Mike Innes Date: Fri, 31 Jul 2015 11:28:52 +0100 Subject: [PATCH 10/10] add stdlib generation to build --- Makefile | 1 + 1 file changed, 1 insertion(+) diff --git a/Makefile b/Makefile index d63b083949fb0..a5da17df850a1 100644 --- a/Makefile +++ b/Makefile @@ -82,6 +82,7 @@ endif release-candidate: release testall @$(JULIA_EXECUTABLE) contrib/add_license_to_files.jl #add license headers + @$(JULIA_EXECUTABLE) doc/genstdlib.jl @#Check documentation @$(JULIA_EXECUTABLE) doc/NEWS-update.jl #Add missing cross-references to NEWS.md @$(MAKE) -C doc unicode #Rebuild Unicode table if necessary