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abstractarraymath.jl
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abstractarraymath.jl
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# This file is a part of Julia. License is MIT: http:https://julialang.org/license
## Basic functions ##
isinteger(x::AbstractArray) = all(isinteger,x)
isinteger{T<:Integer,n}(x::AbstractArray{T,n}) = true
isreal(x::AbstractArray) = all(isreal,x)
isreal{T<:Real,n}(x::AbstractArray{T,n}) = true
ctranspose(a::AbstractArray) = error("ctranspose not implemented for $(typeof(a)). Consider adding parentheses, e.g. A*(B*C') instead of A*B*C' to avoid explicit calculation of the transposed matrix.")
transpose(a::AbstractArray) = error("transpose not implemented for $(typeof(a)). Consider adding parentheses, e.g. A*(B*C.') instead of A*B*C' to avoid explicit calculation of the transposed matrix.")
## Constructors ##
vec(a::AbstractArray) = reshape(a,length(a))
vec(a::AbstractVector) = a
_sub(::Tuple{}, ::Tuple{}) = ()
_sub(t::Tuple, ::Tuple{}) = t
_sub(t::Tuple, s::Tuple) = _sub(tail(t), tail(s))
function squeeze(A::AbstractArray, dims::Dims)
for i in 1:length(dims)
1 <= dims[i] <= ndims(A) || throw(ArgumentError("squeezed dims must be in range 1:ndims(A)"))
size(A, dims[i]) == 1 || throw(ArgumentError("squeezed dims must all be size 1"))
for j = 1:i-1
dims[j] == dims[i] && throw(ArgumentError("squeezed dims must be unique"))
end
end
d = ()
for i = 1:ndims(A)
if !in(i, dims)
d = tuple(d..., size(A, i))
end
end
reshape(A, d::typeof(_sub(size(A), dims)))
end
squeeze(A::AbstractArray, dim::Integer) = squeeze(A, (Int(dim),))
## Unary operators ##
conj{T<:Real}(x::AbstractArray{T}) = x
conj!{T<:Real}(x::AbstractArray{T}) = x
real{T<:Real}(x::AbstractArray{T}) = x
imag{T<:Real}(x::AbstractArray{T}) = zero(x)
+{T<:Number}(x::AbstractArray{T}) = x
*{T<:Number}(x::AbstractArray{T,2}) = x
## Binary arithmetic operators ##
*(A::Number, B::AbstractArray) = A .* B
*(A::AbstractArray, B::Number) = A .* B
/(A::AbstractArray, B::Number) = A ./ B
\(A::Number, B::AbstractArray) = B ./ A
# index A[:,:,...,i,:,:,...] where "i" is in dimension "d"
# TODO: more optimized special cases
slicedim(A::AbstractArray, d::Integer, i) =
A[[ n==d ? i : (1:size(A,n)) for n in 1:ndims(A) ]...]
function flipdim(A::AbstractVector, d::Integer)
d > 0 || throw(ArgumentError("dimension to flip must be positive"))
d == 1 || return copy(A)
reverse(A)
end
function flipdim(A::AbstractArray, d::Integer)
nd = ndims(A)
sd = d > nd ? 1 : size(A, d)
if sd == 1 || isempty(A)
return copy(A)
end
B = similar(A)
nnd = 0
for i = 1:nd
nnd += Int(size(A,i)==1 || i==d)
end
if nnd==nd
# flip along the only non-singleton dimension
for i = 1:sd
B[i] = A[sd+1-i]
end
return B
end
alli = [ 1:size(B,n) for n in 1:nd ]
for i = 1:sd
B[[ n==d ? sd+1-i : alli[n] for n in 1:nd ]...] = slicedim(A, d, i)
end
return B
end
circshift(a::AbstractArray, shiftamt::Real) = circshift(a, [Integer(shiftamt)])
function circshift{T,N}(a::AbstractArray{T,N}, shiftamts)
I = ()
for i=1:N
s = size(a,i)
d = i<=length(shiftamts) ? shiftamts[i] : 0
I = tuple(I..., d==0 ? [1:s;] : mod([-d:s-1-d;], s).+1)
end
a[(I::NTuple{N,Vector{Int}})...]
end
# Uses K-B-N summation
function cumsum_kbn{T<:AbstractFloat}(v::AbstractVector{T})
n = length(v)
r = similar(v, n)
if n == 0; return r; end
s = r[1] = v[1]
c = zero(T)
for i=2:n
vi = v[i]
t = s + vi
if abs(s) >= abs(vi)
c += ((s-t) + vi)
else
c += ((vi-t) + s)
end
s = t
r[i] = s+c
end
return r
end
# Uses K-B-N summation
function cumsum_kbn{T<:AbstractFloat}(A::AbstractArray{T}, axis::Integer=1)
dimsA = size(A)
ndimsA = ndims(A)
axis_size = dimsA[axis]
axis_stride = 1
for i = 1:(axis-1)
axis_stride *= size(A,i)
end
if axis_size <= 1
return A
end
B = similar(A)
C = similar(A)
for i = 1:length(A)
if div(i-1, axis_stride) % axis_size == 0
B[i] = A[i]
C[i] = zero(T)
else
s = B[i-axis_stride]
Ai = A[i]
B[i] = t = s + Ai
if abs(s) >= abs(Ai)
C[i] = C[i-axis_stride] + ((s-t) + Ai)
else
C[i] = C[i-axis_stride] + ((Ai-t) + s)
end
end
end
return B + C
end
## ipermutedims in terms of permutedims ##
function ipermutedims(A::AbstractArray,perm)
iperm = Array(Int,length(perm))
for i = 1:length(perm)
iperm[perm[i]] = i
end
return permutedims(A,iperm)
end
## Other array functions ##
function repmat(a::AbstractVecOrMat, m::Int, n::Int=1)
o, p = size(a,1), size(a,2)
b = similar(a, o*m, p*n)
for j=1:n
d = (j-1)*p+1
R = d:d+p-1
for i=1:m
c = (i-1)*o+1
b[c:c+o-1, R] = a
end
end
return b
end
function repmat(a::AbstractVector, m::Int)
o = length(a)
b = similar(a, o*m)
for i=1:m
c = (i-1)*o+1
b[c:c+o-1] = a
end
return b
end
# Generalized repmat
function repeat{T}(A::Array{T};
inner::Array{Int} = ones(Int, ndims(A)),
outer::Array{Int} = ones(Int, ndims(A)))
ndims_in = ndims(A)
length_inner = length(inner)
length_outer = length(outer)
ndims_out = max(ndims_in, length_inner, length_outer)
if length_inner < ndims_in || length_outer < ndims_in
throw(ArgumentError("inner/outer repetitions must be set for all input dimensions"))
end
inner = vcat(inner, ones(Int,ndims_out-length_inner))
outer = vcat(outer, ones(Int,ndims_out-length_outer))
size_in = size(A)
size_out = ntuple(i->inner[i]*size(A,i)*outer[i],ndims_out)::Dims
inner_size_out = ntuple(i->inner[i]*size(A,i),ndims_out)::Dims
indices_in = Array(Int, ndims_in)
indices_out = Array(Int, ndims_out)
length_out = prod(size_out)
R = Array(T, size_out)
for index_out in 1:length_out
ind2sub!(indices_out, size_out, index_out)
for t in 1:ndims_in
# "Project" outer repetitions into inner repetitions
indices_in[t] = mod1(indices_out[t], inner_size_out[t])
# Find inner repetitions using flooring division
if inner[t] != 1
indices_in[t] = fld1(indices_in[t], inner[t])
end
end
index_in = sub2ind(size_in, indices_in...)
R[index_out] = A[index_in]
end
return R
end