https://github.com/JuliaLang/julia
Tip revision: eb951480b52c9844efc5929ad45b411a523f763c authored by Valentin Churavy on 21 February 2019, 20:36:15 UTC
try integrate runtime system
try integrate runtime system
Tip revision: eb95148
abstractarraymath.jl
# This file is a part of Julia. License is MIT: https://julialang.org/license
## Basic functions ##
isreal(x::AbstractArray) = all(isreal,x)
iszero(x::AbstractArray) = all(iszero,x)
isreal(x::AbstractArray{<:Real}) = true
## Constructors ##
"""
vec(a::AbstractArray) -> AbstractVector
Reshape the array `a` as a one-dimensional column vector. Return `a` if it is
already an `AbstractVector`. The resulting array
shares the same underlying data as `a`, so it will only be mutable if `a` is
mutable, in which case modifying one will also modify the other.
# Examples
```jldoctest
julia> a = [1 2 3; 4 5 6]
2×3 Array{Int64,2}:
1 2 3
4 5 6
julia> vec(a)
6-element Array{Int64,1}:
1
4
2
5
3
6
julia> vec(1:3)
1:3
```
See also [`reshape`](@ref).
"""
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))
"""
dropdims(A; dims)
Remove the dimensions specified by `dims` from array `A`.
Elements of `dims` must be unique and within the range `1:ndims(A)`.
`size(A,i)` must equal 1 for all `i` in `dims`.
# Examples
```jldoctest
julia> a = reshape(Vector(1:4),(2,2,1,1))
2×2×1×1 Array{Int64,4}:
[:, :, 1, 1] =
1 3
2 4
julia> dropdims(a; dims=3)
2×2×1 Array{Int64,3}:
[:, :, 1] =
1 3
2 4
```
"""
dropdims(A; dims) = _dropdims(A, dims)
function _dropdims(A::AbstractArray, dims::Dims)
for i in 1:length(dims)
1 <= dims[i] <= ndims(A) || throw(ArgumentError("dropped dims must be in range 1:ndims(A)"))
length(axes(A, dims[i])) == 1 || throw(ArgumentError("dropped dims must all be size 1"))
for j = 1:i-1
dims[j] == dims[i] && throw(ArgumentError("dropped dims must be unique"))
end
end
d = ()
for i = 1:ndims(A)
if !in(i, dims)
d = tuple(d..., axes(A, i))
end
end
reshape(A, d::typeof(_sub(axes(A), dims)))
end
_dropdims(A::AbstractArray, dim::Integer) = _dropdims(A, (Int(dim),))
## Unary operators ##
conj(x::AbstractArray{<:Real}) = x
conj!(x::AbstractArray{<:Real}) = x
real(x::AbstractArray{<:Real}) = x
imag(x::AbstractArray{<:Real}) = zero(x)
+(x::AbstractArray{<:Number}) = x
*(x::AbstractArray{<:Number,2}) = x
# index A[:,:,...,i,:,:,...] where "i" is in dimension "d"
"""
selectdim(A, d::Integer, i)
Return a view of all the data of `A` where the index for dimension `d` equals `i`.
Equivalent to `view(A,:,:,...,i,:,:,...)` where `i` is in position `d`.
# Examples
```jldoctest
julia> A = [1 2 3 4; 5 6 7 8]
2×4 Array{Int64,2}:
1 2 3 4
5 6 7 8
julia> selectdim(A, 2, 3)
2-element view(::Array{Int64,2}, :, 3) with eltype Int64:
3
7
```
"""
@inline selectdim(A::AbstractArray, d::Integer, i) = _selectdim(A, d, i, setindex(map(Slice, axes(A)), i, d))
@noinline function _selectdim(A, d, i, idxs)
d >= 1 || throw(ArgumentError("dimension must be ≥ 1, got $d"))
nd = ndims(A)
d > nd && (i == 1 || throw(BoundsError(A, (ntuple(k->Colon(),d-1)..., i))))
return view(A, idxs...)
end
"""
reverse(A; dims::Integer)
Reverse `A` in dimension `dims`.
# Examples
```jldoctest
julia> b = [1 2; 3 4]
2×2 Array{Int64,2}:
1 2
3 4
julia> reverse(b, dims=2)
2×2 Array{Int64,2}:
2 1
4 3
```
"""
function reverse(A::AbstractArray; dims::Integer)
nd = ndims(A); d = dims
1 ≤ d ≤ nd || throw(ArgumentError("dimension $d is not 1 ≤ $d ≤ $nd"))
if isempty(A)
return copy(A)
elseif nd == 1
return reverse(A)
end
inds = axes(A)
B = similar(A)
nnd = 0
for i = 1:nd
nnd += Int(length(inds[i])==1 || i==d)
end
indsd = inds[d]
sd = first(indsd)+last(indsd)
if nnd==nd
# reverse along the only non-singleton dimension
for i in indsd
B[i] = A[sd-i]
end
return B
end
let B=B # workaround #15276
alli = [ axes(B,n) for n in 1:nd ]
for i in indsd
B[[ n==d ? sd-i : alli[n] for n in 1:nd ]...] = selectdim(A, d, i)
end
end
return B
end
function circshift(a::AbstractArray, shiftamt::Real)
circshift!(similar(a), a, (Integer(shiftamt),))
end
circshift(a::AbstractArray, shiftamt::DimsInteger) = circshift!(similar(a), a, shiftamt)
"""
circshift(A, shifts)
Circularly shift, i.e. rotate, the data in an array. The second argument is a tuple or
vector giving the amount to shift in each dimension, or an integer to shift only in the
first dimension.
# Examples
```jldoctest
julia> b = reshape(Vector(1:16), (4,4))
4×4 Array{Int64,2}:
1 5 9 13
2 6 10 14
3 7 11 15
4 8 12 16
julia> circshift(b, (0,2))
4×4 Array{Int64,2}:
9 13 1 5
10 14 2 6
11 15 3 7
12 16 4 8
julia> circshift(b, (-1,0))
4×4 Array{Int64,2}:
2 6 10 14
3 7 11 15
4 8 12 16
1 5 9 13
julia> a = BitArray([true, true, false, false, true])
5-element BitArray{1}:
1
1
0
0
1
julia> circshift(a, 1)
5-element BitArray{1}:
1
1
1
0
0
julia> circshift(a, -1)
5-element BitArray{1}:
1
0
0
1
1
```
See also [`circshift!`](@ref).
"""
function circshift(a::AbstractArray, shiftamt)
circshift!(similar(a), a, map(Integer, (shiftamt...,)))
end
## Other array functions ##
"""
repeat(A::AbstractArray, counts::Integer...)
Construct an array by repeating array `A` a given number of times in each dimension, specified by `counts`.
# Examples
```jldoctest
julia> repeat([1, 2, 3], 2)
6-element Array{Int64,1}:
1
2
3
1
2
3
julia> repeat([1, 2, 3], 2, 3)
6×3 Array{Int64,2}:
1 1 1
2 2 2
3 3 3
1 1 1
2 2 2
3 3 3
```
"""
repeat(a::AbstractArray, counts::Integer...) = repeat(a, outer = counts)
function repeat(a::AbstractVecOrMat, m::Integer, n::Integer=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 repeat(a::AbstractVector, m::Integer)
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
"""
repeat(A::AbstractArray; inner=ntuple(x->1, ndims(A)), outer=ntuple(x->1, ndims(A)))
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. If `inner` or `outer` are omitted, no repetition
is performed.
# Examples
```jldoctest
julia> repeat(1:2, inner=2)
4-element Array{Int64,1}:
1
1
2
2
julia> repeat(1:2, outer=2)
4-element Array{Int64,1}:
1
2
1
2
julia> repeat([1 2; 3 4], inner=(2, 1), outer=(1, 3))
4×6 Array{Int64,2}:
1 2 1 2 1 2
1 2 1 2 1 2
3 4 3 4 3 4
3 4 3 4 3 4
```
"""
function repeat(A::AbstractArray; inner = nothing, outer = nothing)
return _repeat_inner_outer(A, inner, outer)
end
# we have optimized implementations of these cases above
_repeat_inner_outer(A::AbstractVecOrMat, ::Nothing, r::Union{Tuple{Integer},Tuple{Integer,Integer}}) = repeat(A, r...)
_repeat_inner_outer(A::AbstractVecOrMat, ::Nothing, r::Integer) = repeat(A, r)
_repeat_inner_outer(A, ::Nothing, ::Nothing) = A
_repeat_inner_outer(A, ::Nothing, outer) = _repeat(A, ntuple(n->1, Val(ndims(A))), rep_kw2tup(outer))
_repeat_inner_outer(A, inner, ::Nothing) = _repeat(A, rep_kw2tup(inner), ntuple(n->1, Val(ndims(A))))
_repeat_inner_outer(A, inner, outer) = _repeat(A, rep_kw2tup(inner), rep_kw2tup(outer))
rep_kw2tup(n::Integer) = (n,)
rep_kw2tup(v::AbstractArray{<:Integer}) = (v...,)
rep_kw2tup(t::Tuple) = t
rep_shapes(A, i, o) = _rshps((), (), size(A), i, o)
_rshps(shp, shp_i, ::Tuple{}, ::Tuple{}, ::Tuple{}) = (shp, shp_i)
@inline _rshps(shp, shp_i, ::Tuple{}, ::Tuple{}, o) =
_rshps((shp..., o[1]), (shp_i..., 1), (), (), tail(o))
@inline _rshps(shp, shp_i, ::Tuple{}, i, ::Tuple{}) = (n = i[1];
_rshps((shp..., n), (shp_i..., n), (), tail(i), ()))
@inline _rshps(shp, shp_i, ::Tuple{}, i, o) = (n = i[1];
_rshps((shp..., n * o[1]), (shp_i..., n), (), tail(i), tail(o)))
@inline _rshps(shp, shp_i, sz, i, o) = (n = sz[1] * i[1];
_rshps((shp..., n * o[1]), (shp_i..., n), tail(sz), tail(i), tail(o)))
_rshps(shp, shp_i, sz, ::Tuple{}, ::Tuple{}) =
(n = length(shp); N = n + length(sz); _reperr("inner", n, N))
_rshps(shp, shp_i, sz, ::Tuple{}, o) =
(n = length(shp); N = n + length(sz); _reperr("inner", n, N))
_rshps(shp, shp_i, sz, i, ::Tuple{}) =
(n = length(shp); N = n + length(sz); _reperr("outer", n, N))
_reperr(s, n, N) = throw(ArgumentError("number of " * s * " repetitions " *
"($n) cannot be less than number of dimensions of input ($N)"))
@noinline function _repeat(A::AbstractArray, inner, outer)
shape, inner_shape = rep_shapes(A, inner, outer)
R = similar(A, shape)
if any(iszero, shape)
return R
end
# fill the first inner block
if all(x -> x == 1, inner)
idxs = (axes(A)..., ntuple(n->OneTo(1), ndims(R)-ndims(A))...) # keep dimension consistent
R[idxs...] = A
else
inner_indices = [1:n for n in inner]
for c in CartesianIndices(axes(A))
for i in 1:ndims(A)
n = inner[i]
inner_indices[i] = (1:n) .+ ((c[i] - 1) * n)
end
fill!(view(R, inner_indices...), A[c])
end
end
# fill the outer blocks along each dimension
if all(x -> x == 1, outer)
return R
end
src_indices = [1:n for n in inner_shape]
dest_indices = copy(src_indices)
for i in 1:length(outer)
B = view(R, src_indices...)
for j in 2:outer[i]
dest_indices[i] = dest_indices[i] .+ inner_shape[i]
R[dest_indices...] = B
end
src_indices[i] = dest_indices[i] = 1:shape[i]
end
return R
end
"""
eachrow(A::AbstractVecOrMat)
Create a generator that iterates over the first dimension of vector or matrix `A`,
returning the rows as views.
See also [`eachcol`](@ref) and [`eachslice`](@ref).
!!! compat "Julia 1.1"
This function requires at least Julia 1.1.
"""
eachrow(A::AbstractVecOrMat) = (view(A, i, :) for i in axes(A, 1))
"""
eachcol(A::AbstractVecOrMat)
Create a generator that iterates over the second dimension of matrix `A`, returning the
columns as views.
See also [`eachrow`](@ref) and [`eachslice`](@ref).
!!! compat "Julia 1.1"
This function requires at least Julia 1.1.
"""
eachcol(A::AbstractVecOrMat) = (view(A, :, i) for i in axes(A, 2))
"""
eachslice(A::AbstractArray; dims)
Create a generator that iterates over dimensions `dims` of `A`, returning views that select all
the data from the other dimensions in `A`.
Only a single dimension in `dims` is currently supported. Equivalent to `(view(A,:,:,...,i,:,:
...)) for i in axes(A, dims))`, where `i` is in position `dims`.
See also [`eachrow`](@ref), [`eachcol`](@ref), and [`selectdim`](@ref).
!!! compat "Julia 1.1"
This function requires at least Julia 1.1.
"""
@inline function eachslice(A::AbstractArray; dims)
length(dims) == 1 || throw(ArgumentError("only single dimensions are supported"))
dim = first(dims)
dim <= ndims(A) || throw(DimensionMismatch("A doesn't have $dim dimensions"))
idx1, idx2 = ntuple(d->(:), dim-1), ntuple(d->(:), ndims(A)-dim)
return (view(A, idx1..., i, idx2...) for i in axes(A, dim))
end