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GenUtils.jl
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GenUtils.jl
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module GenUtils
importall Base
export eq,eqsize,eqlength,
diagonal, Centering,
check, prevent,
argumentsmatch,
@elapsedloop,
promote_eltype, accepts, isscalar,
randw,
max1,max2, dott, logsumexp
######### Patches #####################################
# fixed: https://github.com/JuliaLang/julia/issues/3202
# convert(::Type{Rational},x::Integer) = convert(Rational{typeof(x)},x)
# fixed: https://github.com/JuliaLang/julia/issues/3246
# import Base.power_by_squaring
# ^{T<:FloatingPoint}(z::Complex{T}, n::Bool) = n ? z : one(z)
# ^{T<:Rational}(z::Complex{T}, n::Bool) = n ? z : one(z)
# ^{T<:Integer}(z::Complex{T}, n::Bool) = n ? z : one(z)
# ^{T<:FloatingPoint}(z::Complex{T}, n::Integer) = n>=0?power_by_squaring(z,n):power_by_squaring(inv(z),-n)
# ^{T<:Rational}(z::Complex{T}, n::Integer) = n>=0?power_by_squaring(z,n):power_by_squaring(inv(z),-n)
# ^{T<:Integer}(z::Complex{T}, n::Integer) = power_by_squaring(z,n) # DomainError for n<0
#######################################################
abstract TagType
# Below we will overload some operators to accept TagTypes as arguments, to do new things.
#######################################################
#base has: |(x,f::Function) = f(x)
|(args::NTuple, f::Function) = f(args...)
########################################################
eq{T}(msg::String,a1::T,args::T...) = all(map(x->x==a1,args))?a1:error(msg)
eq{N}(sz1::NTuple{N,Int},sizes::NTuple{N,Int}...) = eq("size mismatch",sz1,sizes...)
eq(d1::Int,dims::Int...) = eq("dimension mismatch",d1,dims...)
eqsize(args...) = eq(map(size,args)...)
eqlength(args...) = eq("length mismatch",map(length,args)...)
########################################################
isscalar(X) = ndims(X) == 0
promote_eltype(args::AbstractArray...) = promote_type(map(eltype,args)...)
# predicts which conversions will not throw inexact error or similar
# Note, things like
typealias IntFlavours{T<:Integer} Union(T,Complex{T})
typealias RatFlavours{T<:Rational} Union(T,Complex{T})
typealias FloatFlavours{T<:FloatingPoint} Union(T,Complex{T})
willconvert{D<:Number,S<:Number}(::Type{D},::Type{S}) = true
willconvert{D<:Real,S<:Complex}(::Type{D},::Type{S}) = false
willconvert{D<:IntFlavours,S<:RatFlavours}(::Type{D},::Type{S}) = false
willconvert{D<:IntFlavours,S<:FloatFlavours}(::Type{D},::Type{S}) = false
accepts{D<:Number,S<:Number}(A::Array{D},::Type{S}) = willconvert(D,S)
accepts{D<:Number,S<:Number}(A::Array{D},::S) = willconvert(D,S)
############### precondition checking #######################
check(ok::Bool, msg="precondition failed") = ok?true:error(msg)
prevent(notok::Bool, msg="precondition failed") = notok?error(msg):true
# Follow check or prevent by &&
# - for assignment, use brackets: check(condition)&&(x=5), or check(condition)&&(x=5;true)
# Also provide a user-definable check for user-defined operators.
# Users can supply argumentsmatch
check(op::Function,A,B) = check(argumentsmatch(op,A,B))
#default argumentsmatch for matrix arguments
function argumentsmatch(f::Function,A,B)
if ( contains({+,-},f) && size(A) != size(B) ) ||
( contains({*,/,\},f) && size(A,2) != size(B,1) )
error("arguments do not match: $(summary(A)) $(f) $(summary(B))")
else
return true
end
end
# just use assert() to check postconditions, or if you want to chain further, use check/prevent
#lest(notok::Function) = x-> notok(x)?error("assertion failed"):x #latin "ne"
#sothat(ok::Function) = x-> ok(x)?x:error("assertion failed") #latin "ut"
########################################################
# getindex(A::Array, f::Function) = f(A)
# setindex!(A::Array, X, f::Function) = f(A,X)
########################################################
immutable diagonal <: TagType
k::Int
end
getindex(M::Matrix,::Type{diagonal}) = M[diagind(M)]
setindex!(M::Matrix,X,::Type{diagonal}) = setindex!(M,X,diagind(M))
getindex(M::Matrix,d::diagonal) = M[diagind(M,d.k)]
setindex!(M::Matrix,X,d::diagonal) = setindex!(M,X,diagind(M,d.k))
########################################################
immutable Centering <: TagType
n::Int
end
summary(C::Centering) = "Centering($(C.n))"
full(C::Centering) = (n = C.n; F = fill(-1/n,n,n); F[diagonal] = (n-1)/n; F )
full(::Type{Rational},C::Centering) = (n = C.n; F = fill(-1//n,n,n); F[diagonal] = (n-1)//n; F )
size(C::Centering) = (C.n,C.n)
size(C::Centering,i::Int) = 1<=i<=2?C.n:1
length(C::Centering) = C.n^2
ndims(C::Centering) = 2
getindex(C::Centering,i::Int,j::Int) = (n=C.n; all(1.<[i,j].<n)?(i==j?(n-1)/n:-1/n):error("index out of bounds") )
*(::Type{Centering},v::Vector) = v - mean(v)
*(::Type{Centering},M::Matrix) = M .- mean(M,1)
*(M::Matrix,::Type{Centering}) = M .- mean(M,2)
*(C::Centering,v::Vector) = check(*,C,v)&& v - mean(v)
*(C::Centering,M::Matrix) = check(*,C,M)&& M .- mean(M,1)
*(M::Matrix,C::Centering) = check(*,M,C)&& M .- mean(M,2)
*(::Type{Centering},::Type{Centering}) = Centering
*(C::Centering,::Type{Centering}) = C
*(::Type{Centering},C::Centering) = C
*(A::Centering,B::Centering) = Centering(eq(A.n,B.n))
########################################################
randw(d,n) = (R = randn(d,n); R*R')
randw(d) = randw(d,d+1)
########################################################
macro elapsedloop(n,ex)
quote
local s = 0.0
for i=1:$(esc(n))
local t0 = time_ns()
local val = $(esc(ex))
s += (time_ns()-t0)/1e9
end
s
end
end
########################################################
max1{T}(A::Matrix{T})=(
(m,n) = size(A); @assert m>0 && n>0;
s = Array(T,n);
for j=1:n
t=A[1,j]
for i=2:m e = A[i,j]; if e>t t = e end end
s[j] = t
end;
reshape(s,1,n)
)
max2(A::Matrix)=(
(m,n)=size(A); @assert m>0 && n>0;
s = A[:,1];
for j=2:n, i=1:m
si = s[i]; e = A[i,j]
if e > si s[i] = e end
end;
reshape(s,m,1)
)
########################################################
# dot without conjugation
dott(x::Vector, y::Vector) = (reshape(x,1,length(x))*y)[1]
dott{T<:Real}(x::Vector{T}, y::Vector{T}) = dot(x,y)
function logsumexp(X::Matrix)
# Mathematically the same as y=log(sum(exp(x),1)),
# but guards against numerical overflow of exp(x).
m,n = size(X)
y = Array(promote_type(eltype(X),Float64),n)
for j=1:n
mx = real(X[1,j])
for i=2:m e = real(X[i,j]); if e>mx mx = e end end
s = zero(eltype(y))
for i=1:m s += exp(X[i,j]-mx) end
y[j] = mx + log(s);
end
return reshape(y,1,n)
end
##########################################################
end