#37940

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Remove NewPM pass exports. (#56269)

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54.11

/base/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 Matrix{Int64}:
 1  2  3
 4  5  6

julia> vec(a)
6-element Vector{Int64}:
 1
 4
 2
 5
 3
 6

julia> vec(1:3)
1:3
```

See also [`reshape`](@ref), [`dropdims`](@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)

Return an array with the same data as `A`, but with the dimensions specified by
`dims` removed. `size(A,d)` must equal 1 for every `d` in `dims`,
and repeated dimensions or numbers outside `1:ndims(A)` are forbidden.

The result shares the same underlying data as `A`, such that the
result is mutable if and only if `A` is mutable, and setting elements of one
alters the values of the other.

See also: [`reshape`](@ref), [`vec`](@ref).

# 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> b = dropdims(a; dims=3)
2×2×1 Array{Int64, 3}:
[:, :, 1] =
 1  3
 2  4

julia> b[1,1,1] = 5; a
2×2×1×1 Array{Int64, 4}:
[:, :, 1, 1] =
 5  3
 2  4
```
"""
dropdims(A; dims) = _dropdims(A, dims)
function _dropdims(A::AbstractArray, dims::Dims)
    for i in eachindex(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
    ax = _foldoneto((ds, d) -> d in dims ? ds : (ds..., axes(A,d)), (), Val(ndims(A)))
    reshape(A, ax::typeof(_sub(axes(A), dims)))
end
_dropdims(A::AbstractArray, dim::Integer) = _dropdims(A, (Int(dim),))


"""
    insertdims(A; dims)

Inverse of [`dropdims`](@ref); return an array with new singleton dimensions
at every dimension in `dims`.

Repeated dimensions are forbidden and the largest entry in `dims` must be
less than or equal than `ndims(A) + length(dims)`.

The result shares the same underlying data as `A`, such that the
result is mutable if and only if `A` is mutable, and setting elements of one
alters the values of the other.

See also: [`dropdims`](@ref), [`reshape`](@ref), [`vec`](@ref).
# Examples
```jldoctest
julia> x = [1 2 3; 4 5 6]
2×3 Matrix{Int64}:
 1  2  3
 4  5  6

julia> insertdims(x, dims=3)
2×3×1 Array{Int64, 3}:
[:, :, 1] =
 1  2  3
 4  5  6

julia> insertdims(x, dims=(1,2,5)) == reshape(x, 1, 1, 2, 3, 1)
true

julia> dropdims(insertdims(x, dims=(1,2,5)), dims=(1,2,5))
2×3 Matrix{Int64}:
 1  2  3
 4  5  6
```

!!! compat "Julia 1.12"
    Requires Julia 1.12 or later.
"""
insertdims(A; dims) = _insertdims(A, dims)
function _insertdims(A::AbstractArray{T, N}, dims::NTuple{M, Int}) where {T, N, M}
    for i in eachindex(dims)
        1 ≤ dims[i] || throw(ArgumentError("the smallest entry in dims must be ≥ 1."))
        dims[i] ≤ N+M || throw(ArgumentError("the largest entry in dims must be not larger than the dimension of the array and the length of dims added"))
        for j = 1:i-1
            dims[j] == dims[i] && throw(ArgumentError("inserted dims must be unique"))
        end
    end

    # acc is a tuple, where the first entry is the final shape
    # the second entry off acc is a counter for the axes of A
    inds= Base._foldoneto((acc, i) ->
                            i ∈ dims
                                ? ((acc[1]..., Base.OneTo(1)), acc[2])
                                : ((acc[1]..., axes(A, acc[2])), acc[2] + 1),
                            ((), 1), Val(N+M))
    new_shape = inds[1]
    return reshape(A, new_shape)
end
_insertdims(A::AbstractArray, dim::Integer) = _insertdims(A, (Int(dim),))



## Unary operators ##

"""
    conj!(A)

Transform an array to its complex conjugate in-place.

See also [`conj`](@ref).

# Examples
```jldoctest
julia> A = [1+im 2-im; 2+2im 3+im]
2×2 Matrix{Complex{Int64}}:
 1+1im  2-1im
 2+2im  3+1im

julia> conj!(A);

julia> A
2×2 Matrix{Complex{Int64}}:
 1-1im  2+1im
 2-2im  3-1im
```
"""
conj!(A::AbstractArray{<:Number}) = (@inbounds broadcast!(conj, A, A); A)
conj!(x::AbstractArray{<:Real}) = x
conj!(A::AbstractArray) = (foreach(conj!, A); A)

"""
    conj(A::AbstractArray)

Return an array containing the complex conjugate of each entry in array `A`.

Equivalent to `conj.(A)`, except that when `eltype(A) <: Real`
`A` is returned without copying, and that when `A` has zero dimensions,
a 0-dimensional array is returned (rather than a scalar).

# Examples
```jldoctest
julia> conj([1, 2im, 3 + 4im])
3-element Vector{Complex{Int64}}:
 1 + 0im
 0 - 2im
 3 - 4im

julia> conj(fill(2 - im))
0-dimensional Array{Complex{Int64}, 0}:
2 + 1im
```
"""
conj(A::AbstractArray) = broadcast_preserving_zero_d(conj, A)
conj(A::AbstractArray{<:Real}) = A

"""
    real(A::AbstractArray)

Return an array containing the real part of each entry in array `A`.

Equivalent to `real.(A)`, except that when `eltype(A) <: Real`
`A` is returned without copying, and that when `A` has zero dimensions,
a 0-dimensional array is returned (rather than a scalar).

# Examples
```jldoctest
julia> real([1, 2im, 3 + 4im])
3-element Vector{Int64}:
 1
 0
 3

julia> real(fill(2 - im))
0-dimensional Array{Int64, 0}:
2
```
"""
real(A::AbstractArray) = broadcast_preserving_zero_d(real, A)
real(A::AbstractArray{<:Real}) = A

"""
    imag(A::AbstractArray)

Return an array containing the imaginary part of each entry in array `A`.

Equivalent to `imag.(A)`, except that when `A` has zero dimensions,
a 0-dimensional array is returned (rather than a scalar).

# Examples
```jldoctest
julia> imag([1, 2im, 3 + 4im])
3-element Vector{Int64}:
 0
 2
 4

julia> imag(fill(2 - im))
0-dimensional Array{Int64, 0}:
-1
```
"""
imag(A::AbstractArray) = broadcast_preserving_zero_d(imag, A)
imag(A::AbstractArray{<:Real}) = zero(A)

"""
    reim(A::AbstractArray)

Return a tuple of two arrays containing respectively the real and the imaginary
part of each entry in `A`.

Equivalent to `(real.(A), imag.(A))`, except that when `eltype(A) <: Real`
`A` is returned without copying to represent the real part, and that when `A` has
zero dimensions, a 0-dimensional array is returned (rather than a scalar).

# Examples
```jldoctest
julia> reim([1, 2im, 3 + 4im])
([1, 0, 3], [0, 2, 4])

julia> reim(fill(2 - im))
(fill(2), fill(-1))
```
"""
reim(A::AbstractArray)

-(A::AbstractArray) = broadcast_preserving_zero_d(-, A)

+(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`.

See also: [`eachslice`](@ref).

# Examples
```jldoctest
julia> A = [1 2 3 4; 5 6 7 8]
2×4 Matrix{Int64}:
 1  2  3  4
 5  6  7  8

julia> selectdim(A, 2, 3)
2-element view(::Matrix{Int64}, :, 3) with eltype Int64:
 3
 7

julia> selectdim(A, 2, 3:4)
2×2 view(::Matrix{Int64}, :, 3:4) with eltype Int64:
 3  4
 7  8
```
"""
@inline selectdim(A::AbstractArray, d::Integer, i) = _selectdim(A, d, i, _setindex(i, d, map(Slice, axes(A))...))
@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(Returns(Colon()),d-1)..., i))))
    return view(A, idxs...)
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 `A`. 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.

The generated code is most efficient when the shift amounts are known at compile-time, i.e.,
compile-time constants.

See also: [`circshift!`](@ref), [`circcopy!`](@ref), [`bitrotate`](@ref), [`<<`](@ref).

# Examples
```jldoctest
julia> b = reshape(Vector(1:16), (4,4))
4×4 Matrix{Int64}:
 1  5   9  13
 2  6  10  14
 3  7  11  15
 4  8  12  16

julia> circshift(b, (0,2))
4×4 Matrix{Int64}:
  9  13  1  5
 10  14  2  6
 11  15  3  7
 12  16  4  8

julia> circshift(b, (-1,0))
4×4 Matrix{Int64}:
 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 BitVector:
 1
 1
 0
 0
 1

julia> circshift(a, 1)
5-element BitVector:
 1
 1
 1
 0
 0

julia> circshift(a, -1)
5-element BitVector:
 1
 0
 0
 1
 1

julia> x = (1, 2, 3, 4, 5)
(1, 2, 3, 4, 5)

julia> circshift(x, 4)
(2, 3, 4, 5, 1)

julia> z = (1, 'a', -7.0, 3)
(1, 'a', -7.0, 3)

julia> circshift(z, -1)
('a', -7.0, 3, 1)
```
"""
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`.

See also: [`fill`](@ref), [`Iterators.repeated`](@ref), [`Iterators.cycle`](@ref).

# Examples
```jldoctest
julia> repeat([1, 2, 3], 2)
6-element Vector{Int64}:
 1
 2
 3
 1
 2
 3

julia> repeat([1, 2, 3], 2, 3)
6×3 Matrix{Int64}:
 1  1  1
 2  2  2
 3  3  3
 1  1  1
 2  2  2
 3  3  3
```
"""
function repeat(A::AbstractArray, counts...)
    return repeat(A, outer=counts)
end

"""
    repeat(A::AbstractArray; inner=ntuple(Returns(1), ndims(A)), outer=ntuple(Returns(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 Vector{Int64}:
 1
 1
 2
 2

julia> repeat(1:2, outer=2)
4-element Vector{Int64}:
 1
 2
 1
 2

julia> repeat([1 2; 3 4], inner=(2, 1), outer=(1, 3))
4×6 Matrix{Int64}:
 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 _RepeatInnerOuter.repeat(A, inner=inner, outer=outer)
end

module _RepeatInnerOuter

function repeat(arr; inner=nothing, outer=nothing)
    check(arr, inner, outer)
    arr, inner, outer = resolve(arr, inner, outer)
    repeat_inner_outer(arr, inner, outer)
end

to_tuple(t::Tuple) = t
to_tuple(x::Integer) = (x,)
to_tuple(itr) = tuple(itr...)

function pad(a, b)
    N = max(length(a), length(b))
    Base.fill_to_length(a, 1, Val(N)), Base.fill_to_length(b, 1, Val(N))
end
function pad(a, b, c)
    N = max(max(length(a), length(b)), length(c))
    Base.fill_to_length(a, 1, Val(N)), Base.fill_to_length(b, 1, Val(N)), Base.fill_to_length(c, 1, Val(N))
end

function resolve(arr::AbstractArray{<:Any, N}, inner::NTuple{N, Any}, outer::NTuple{N,Any}) where {N}
    arr, inner, outer
end
function resolve(arr, inner, outer)
    dims, inner, outer = pad(size(arr), to_tuple(inner), to_tuple(outer))
    reshape(arr, dims), inner, outer
end
function resolve(arr, inner::Nothing, outer::Nothing)
    return arr, inner, outer
end
function resolve(arr, inner::Nothing, outer)
    dims, outer = pad(size(arr), to_tuple(outer))
    reshape(arr, dims), inner, outer
end
function resolve(arr, inner, outer::Nothing)
    dims, inner = pad(size(arr), to_tuple(inner))
    reshape(arr, dims), inner, outer
end

function check(arr, inner, outer)
    if inner !== nothing
        # TODO: Currently one based indexing is demanded for inner !== nothing,
        # but not for outer !== nothing. Decide for something consistent.
        Base.require_one_based_indexing(arr)
        if any(<(0), inner)
            throw(ArgumentError("no inner repetition count may be negative; got $inner"))
        end
        if length(inner) < ndims(arr)
            throw(ArgumentError("number of inner repetitions ($(length(inner))) cannot be less than number of dimensions of input array ($(ndims(arr)))"))
        end
    end
    if outer !== nothing
        if any(<(0), outer)
            throw(ArgumentError("no outer repetition count may be negative; got $outer"))
        end
        if (length(outer) < ndims(arr)) && (inner !== nothing)
            throw(ArgumentError("number of outer repetitions ($(length(outer))) cannot be less than number of dimensions of input array ($(ndims(arr)))"))
        end
    end
end

repeat_inner_outer(arr, inner::Nothing, outer::Nothing) = arr
repeat_inner_outer(arr, ::Nothing, outer) = repeat_outer(arr, outer)
repeat_inner_outer(arr, inner, ::Nothing) = repeat_inner(arr, inner)
repeat_inner_outer(arr, inner, outer) = repeat_outer(repeat_inner(arr, inner), outer)

function repeat_outer(a::AbstractMatrix, (m,n)::NTuple{2, Any})
    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
            @inbounds b[c:c+o-1, R] = a
        end
    end
    return b
end

function repeat_outer(a::AbstractVector, (m,)::Tuple{Any})
    o = length(a)
    b = similar(a, o*m)
    for i=1:m
        c = (i-1)*o+1
        @inbounds b[c:c+o-1] = a
    end
    return b
end

function repeat_outer(arr::AbstractArray{<:Any,N}, dims::NTuple{N,Any}) where {N}
    insize  = size(arr)
    outsize = map(*, insize, dims)
    out = similar(arr, outsize)
    for I in CartesianIndices(arr)
        for J in CartesianIndices(dims)
            TIJ = map(Tuple(I), Tuple(J), insize) do i, j, d
                i + d * (j-1)
            end
            IJ = CartesianIndex(TIJ)
            @inbounds out[IJ] = arr[I]
        end
    end
    return out
end

function repeat_inner(arr, inner)
    outsize = map(*, size(arr), inner)
    out = similar(arr, outsize)
    for I in CartesianIndices(arr)
        for J in CartesianIndices(inner)
            TIJ = map(Tuple(I), Tuple(J), inner) do i, j, d
                (i-1) * d + j
            end
            IJ = CartesianIndex(TIJ)
            @inbounds out[IJ] = arr[I]
        end
    end
    return out
end

end#module

1	# This file is a part of Julia. License is MIT: https://julialang.org/license
2
3	## Basic functions ##
4
5	isreal(x::AbstractArray) = all(isreal,x)	3,562✔
6	iszero(x::AbstractArray) = all(iszero,x)	4,232✔
7	isreal(x::AbstractArray{<:Real}) = true	×
8
9	## Constructors ##
10
11	"""
12	vec(a::AbstractArray) -> AbstractVector
13
14	Reshape the array `a` as a one-dimensional column vector. Return `a` if it is
15	already an `AbstractVector`. The resulting array
16	shares the same underlying data as `a`, so it will only be mutable if `a` is
17	mutable, in which case modifying one will also modify the other.
18
19	# Examples
20	```jldoctest
21	julia> a = [1 2 3; 4 5 6]
22	2×3 Matrix{Int64}:
23	1 2 3
24	4 5 6
25
26	julia> vec(a)
27	6-element Vector{Int64}:
28	1
29	4
30	2
31	5
32	3
33	6
34
35	julia> vec(1:3)
36	1:3
37	```
38
39	See also [`reshape`](@ref), [`dropdims`](@ref).
40	"""
41	vec(a::AbstractArray) = reshape(a,length(a))	3,168✔
42	vec(a::AbstractVector) = a	1,601✔
43
44	_sub(::Tuple{}, ::Tuple{}) = ()	×
45	_sub(t::Tuple, ::Tuple{}) = t	26✔
46	_sub(t::Tuple, s::Tuple) = _sub(tail(t), tail(s))	36✔
47
48	"""
49	dropdims(A; dims)
50
51	Return an array with the same data as `A`, but with the dimensions specified by
52	`dims` removed. `size(A,d)` must equal 1 for every `d` in `dims`,
53	and repeated dimensions or numbers outside `1:ndims(A)` are forbidden.
54
55	The result shares the same underlying data as `A`, such that the
56	result is mutable if and only if `A` is mutable, and setting elements of one
57	alters the values of the other.
58
59	See also: [`reshape`](@ref), [`vec`](@ref).
60
61	# Examples
62	```jldoctest
63	julia> a = reshape(Vector(1:4),(2,2,1,1))
64	2×2×1×1 Array{Int64, 4}:
65	[:, :, 1, 1] =
66	1 3
67	2 4
68
69	julia> b = dropdims(a; dims=3)
70	2×2×1 Array{Int64, 3}:
71	[:, :, 1] =
72	1 3
73	2 4
74
75	julia> b[1,1,1] = 5; a
76	2×2×1×1 Array{Int64, 4}:
77	[:, :, 1, 1] =
78	5 3
79	2 4
80	```
81	"""
82	dropdims(A; dims) = _dropdims(A, dims)	68✔
83	function _dropdims(A::AbstractArray, dims::Dims)	20✔
84	for i in eachindex(dims)	34✔
85	1 <= dims[i] <= ndims(A) \|\| throw(ArgumentError("dropped dims must be in range 1:ndims(A)"))	50✔
86	length(axes(A, dims[i])) == 1 \|\| throw(ArgumentError("dropped dims must all be size 1"))	49✔
87	for j = 1:i-1	43✔
88	dims[j] == dims[i] && throw(ArgumentError("dropped dims must be unique"))	16✔
89	end	15✔
90	end	54✔
91	ax = _foldoneto((ds, d) -> d in dims ? ds : (ds..., axes(A,d)), (), Val(ndims(A)))	150✔
92	reshape(A, ax::typeof(_sub(axes(A), dims)))	26✔
93	end
94	_dropdims(A::AbstractArray, dim::Integer) = _dropdims(A, (Int(dim),))	16✔
95
96
97	"""
98	insertdims(A; dims)
99
100	Inverse of [`dropdims`](@ref); return an array with new singleton dimensions
101	at every dimension in `dims`.
102
103	Repeated dimensions are forbidden and the largest entry in `dims` must be
104	less than or equal than `ndims(A) + length(dims)`.
105
106	The result shares the same underlying data as `A`, such that the
107	result is mutable if and only if `A` is mutable, and setting elements of one
108	alters the values of the other.
109
110	See also: [`dropdims`](@ref), [`reshape`](@ref), [`vec`](@ref).
111	# Examples
112	```jldoctest
113	julia> x = [1 2 3; 4 5 6]
114	2×3 Matrix{Int64}:
115	1 2 3
116	4 5 6
117
118	julia> insertdims(x, dims=3)
119	2×3×1 Array{Int64, 3}:
120	[:, :, 1] =
121	1 2 3
122	4 5 6
123
124	julia> insertdims(x, dims=(1,2,5)) == reshape(x, 1, 1, 2, 3, 1)
125	true
126
127	julia> dropdims(insertdims(x, dims=(1,2,5)), dims=(1,2,5))
128	2×3 Matrix{Int64}:
129	1 2 3
130	4 5 6
131	```
132
133	!!! compat "Julia 1.12"
134	Requires Julia 1.12 or later.
135	"""
136	insertdims(A; dims) = _insertdims(A, dims)	×
137	function _insertdims(A::AbstractArray{T, N}, dims::NTuple{M, Int}) where {T, N, M}	×
138	for i in eachindex(dims)	×
139	1 ≤ dims[i] \|\| throw(ArgumentError("the smallest entry in dims must be ≥ 1."))	×
140	dims[i] ≤ N+M \|\| throw(ArgumentError("the largest entry in dims must be not larger than the dimension of the array and the length of dims added"))	×
141	for j = 1:i-1	×
142	dims[j] == dims[i] && throw(ArgumentError("inserted dims must be unique"))	×
143	end	×
144	end	×
145
146	# acc is a tuple, where the first entry is the final shape
147	# the second entry off acc is a counter for the axes of A
148	inds= Base._foldoneto((acc, i) ->	×
149	i ∈ dims
150	? ((acc[1]..., Base.OneTo(1)), acc[2])
151	: ((acc[1]..., axes(A, acc[2])), acc[2] + 1),
152	((), 1), Val(N+M))
153	new_shape = inds[1]	×
154	return reshape(A, new_shape)	×
155	end
156	_insertdims(A::AbstractArray, dim::Integer) = _insertdims(A, (Int(dim),))	×
157
158
159
160	## Unary operators ##
161
162	"""
163	conj!(A)
164
165	Transform an array to its complex conjugate in-place.
166
167	See also [`conj`](@ref).
168
169	# Examples
170	```jldoctest
171	julia> A = [1+im 2-im; 2+2im 3+im]
172	2×2 Matrix{Complex{Int64}}:
173	1+1im 2-1im
174	2+2im 3+1im
175
176	julia> conj!(A);
177
178	julia> A
179	2×2 Matrix{Complex{Int64}}:
180	1-1im 2+1im
181	2-2im 3-1im
182	```
183	"""
184	conj!(A::AbstractArray{<:Number}) = (@inbounds broadcast!(conj, A, A); A)	120,373✔
185	conj!(x::AbstractArray{<:Real}) = x	2✔
186	conj!(A::AbstractArray) = (foreach(conj!, A); A)	×
187
188	"""
189	conj(A::AbstractArray)
190
191	Return an array containing the complex conjugate of each entry in array `A`.
192
193	Equivalent to `conj.(A)`, except that when `eltype(A) <: Real`
194	`A` is returned without copying, and that when `A` has zero dimensions,
195	a 0-dimensional array is returned (rather than a scalar).
196
197	# Examples
198	```jldoctest
199	julia> conj([1, 2im, 3 + 4im])
200	3-element Vector{Complex{Int64}}:
201	1 + 0im
202	0 - 2im
203	3 - 4im
204
205	julia> conj(fill(2 - im))
206	0-dimensional Array{Complex{Int64}, 0}:
207	2 + 1im
208	```
209	"""
210	conj(A::AbstractArray) = broadcast_preserving_zero_d(conj, A)	188✔
211	conj(A::AbstractArray{<:Real}) = A	168✔
212
213	"""
214	real(A::AbstractArray)
215
216	Return an array containing the real part of each entry in array `A`.
217
218	Equivalent to `real.(A)`, except that when `eltype(A) <: Real`
219	`A` is returned without copying, and that when `A` has zero dimensions,
220	a 0-dimensional array is returned (rather than a scalar).
221
222	# Examples
223	```jldoctest
224	julia> real([1, 2im, 3 + 4im])
225	3-element Vector{Int64}:
226	1
227	0
228	3
229
230	julia> real(fill(2 - im))
231	0-dimensional Array{Int64, 0}:
232	2
233	```
234	"""
235	real(A::AbstractArray) = broadcast_preserving_zero_d(real, A)	1,388✔
236	real(A::AbstractArray{<:Real}) = A	700✔
237
238	"""
239	imag(A::AbstractArray)
240
241	Return an array containing the imaginary part of each entry in array `A`.
242
243	Equivalent to `imag.(A)`, except that when `A` has zero dimensions,
244	a 0-dimensional array is returned (rather than a scalar).
245
246	# Examples
247	```jldoctest
248	julia> imag([1, 2im, 3 + 4im])
249	3-element Vector{Int64}:
250	0
251	2
252	4
253
254	julia> imag(fill(2 - im))
255	0-dimensional Array{Int64, 0}:
256	-1
257	```
258	"""
259	imag(A::AbstractArray) = broadcast_preserving_zero_d(imag, A)	865✔
260	imag(A::AbstractArray{<:Real}) = zero(A)	304✔
261
262	"""
263	reim(A::AbstractArray)
264
265	Return a tuple of two arrays containing respectively the real and the imaginary
266	part of each entry in `A`.
267
268	Equivalent to `(real.(A), imag.(A))`, except that when `eltype(A) <: Real`
269	`A` is returned without copying to represent the real part, and that when `A` has
270	zero dimensions, a 0-dimensional array is returned (rather than a scalar).
271
272	# Examples
273	```jldoctest
274	julia> reim([1, 2im, 3 + 4im])
275	([1, 0, 3], [0, 2, 4])
276
277	julia> reim(fill(2 - im))
278	(fill(2), fill(-1))
279	```
280	"""
281	reim(A::AbstractArray)
282
283	-(A::AbstractArray) = broadcast_preserving_zero_d(-, A)	2,494✔
284
285	+(x::AbstractArray{<:Number}) = x	3✔
286	*(x::AbstractArray{<:Number,2}) = x	1✔
287
288	# index A[:,:,...,i,:,:,...] where "i" is in dimension "d"
289
290	"""
291	selectdim(A, d::Integer, i)
292
293	Return a view of all the data of `A` where the index for dimension `d` equals `i`.
294
295	Equivalent to `view(A,:,:,...,i,:,:,...)` where `i` is in position `d`.
296
297	See also: [`eachslice`](@ref).
298
299	# Examples
300	```jldoctest
301	julia> A = [1 2 3 4; 5 6 7 8]
302	2×4 Matrix{Int64}:
303	1 2 3 4
304	5 6 7 8
305
306	julia> selectdim(A, 2, 3)
307	2-element view(::Matrix{Int64}, :, 3) with eltype Int64:
308	3
309	7
310
311	julia> selectdim(A, 2, 3:4)
312	2×2 view(::Matrix{Int64}, :, 3:4) with eltype Int64:
313	3 4
314	7 8
315	```
316	"""
317	@inline selectdim(A::AbstractArray, d::Integer, i) = _selectdim(A, d, i, _setindex(i, d, map(Slice, axes(A))...))	26✔
318	@noinline function _selectdim(A, d, i, idxs)	26✔
319	d >= 1 \|\| throw(ArgumentError("dimension must be ≥ 1, got $d"))	26✔
320	nd = ndims(A)	26✔
321	d > nd && (i == 1 \|\| throw(BoundsError(A, (ntuple(Returns(Colon()),d-1)..., i))))	26✔
322	return view(A, idxs...)	26✔
323	end
324
325	function circshift(a::AbstractArray, shiftamt::Real)	46✔
326	circshift!(similar(a), a, (Integer(shiftamt),))	206✔
327	end
328	circshift(a::AbstractArray, shiftamt::DimsInteger) = circshift!(similar(a), a, shiftamt)	51✔
329	"""
330	circshift(A, shifts)
331
332	Circularly shift, i.e. rotate, the data in `A`. The second argument is a tuple or
333	vector giving the amount to shift in each dimension, or an integer to shift only in the
334	first dimension.
335
336	The generated code is most efficient when the shift amounts are known at compile-time, i.e.,
337	compile-time constants.
338
339	See also: [`circshift!`](@ref), [`circcopy!`](@ref), [`bitrotate`](@ref), [`<<`](@ref).
340
341	# Examples
342	```jldoctest
343	julia> b = reshape(Vector(1:16), (4,4))
344	4×4 Matrix{Int64}:
345	1 5 9 13
346	2 6 10 14
347	3 7 11 15
348	4 8 12 16
349
350	julia> circshift(b, (0,2))
351	4×4 Matrix{Int64}:
352	9 13 1 5
353	10 14 2 6
354	11 15 3 7
355	12 16 4 8
356
357	julia> circshift(b, (-1,0))
358	4×4 Matrix{Int64}:
359	2 6 10 14
360	3 7 11 15
361	4 8 12 16
362	1 5 9 13
363
364	julia> a = BitArray([true, true, false, false, true])
365	5-element BitVector:
366	1
367	1
368	0
369	0
370	1
371
372	julia> circshift(a, 1)
373	5-element BitVector:
374	1
375	1
376	1
377	0
378	0
379
380	julia> circshift(a, -1)
381	5-element BitVector:
382	1
383	0
384	0
385	1
386	1
387
388	julia> x = (1, 2, 3, 4, 5)
389	(1, 2, 3, 4, 5)
390
391	julia> circshift(x, 4)
392	(2, 3, 4, 5, 1)
393
394	julia> z = (1, 'a', -7.0, 3)
395	(1, 'a', -7.0, 3)
396
397	julia> circshift(z, -1)
398	('a', -7.0, 3, 1)
399	```
400	"""
401	function circshift(a::AbstractArray, shiftamt)	×
402	circshift!(similar(a), a, map(Integer, (shiftamt...,)))	×
403	end
404
405	## Other array functions ##
406
407	"""
408	repeat(A::AbstractArray, counts::Integer...)
409
410	Construct an array by repeating array `A` a given number of times in each dimension, specified by `counts`.
411
412	See also: [`fill`](@ref), [`Iterators.repeated`](@ref), [`Iterators.cycle`](@ref).
413
414	# Examples
415	```jldoctest
416	julia> repeat([1, 2, 3], 2)
417	6-element Vector{Int64}:
418	1
419	2
420	3
421	1
422	2
423	3
424
425	julia> repeat([1, 2, 3], 2, 3)
426	6×3 Matrix{Int64}:
427	1 1 1
428	2 2 2
429	3 3 3
430	1 1 1
431	2 2 2
432	3 3 3
433	```
434	"""
435	function repeat(A::AbstractArray, counts...)	80✔
436	return repeat(A, outer=counts)	284✔
437	end
438
439	"""
440	repeat(A::AbstractArray; inner=ntuple(Returns(1), ndims(A)), outer=ntuple(Returns(1), ndims(A)))
441
442	Construct an array by repeating the entries of `A`. The i-th element of `inner` specifies
443	the number of times that the individual entries of the i-th dimension of `A` should be
444	repeated. The i-th element of `outer` specifies the number of times that a slice along the
445	i-th dimension of `A` should be repeated. If `inner` or `outer` are omitted, no repetition
446	is performed.
447
448	# Examples
449	```jldoctest
450	julia> repeat(1:2, inner=2)
451	4-element Vector{Int64}:
452	1
453	1
454	2
455	2
456
457	julia> repeat(1:2, outer=2)
458	4-element Vector{Int64}:
459	1
460	2
461	1
462	2
463
464	julia> repeat([1 2; 3 4], inner=(2, 1), outer=(1, 3))
465	4×6 Matrix{Int64}:
466	1 2 1 2 1 2
467	1 2 1 2 1 2
468	3 4 3 4 3 4
469	3 4 3 4 3 4
470	```
471	"""
472	function repeat(A::AbstractArray; inner = nothing, outer = nothing)	293✔
473	return _RepeatInnerOuter.repeat(A, inner=inner, outer=outer)	293✔
474	end
475
476	module _RepeatInnerOuter
477
478	function repeat(arr; inner=nothing, outer=nothing)	330✔
479	check(arr, inner, outer)	581✔
480	arr, inner, outer = resolve(arr, inner, outer)	281✔
481	repeat_inner_outer(arr, inner, outer)	281✔
482	end
483
484	to_tuple(t::Tuple) = t	279✔
485	to_tuple(x::Integer) = (x,)	×
486	to_tuple(itr) = tuple(itr...)	2✔
487
488	function pad(a, b)	2✔
489	N = max(length(a), length(b))	281✔
490	Base.fill_to_length(a, 1, Val(N)), Base.fill_to_length(b, 1, Val(N))	281✔
491	end
492	function pad(a, b, c)	×
493	N = max(max(length(a), length(b)), length(c))	×
494	Base.fill_to_length(a, 1, Val(N)), Base.fill_to_length(b, 1, Val(N)), Base.fill_to_length(c, 1, Val(N))	×
495	end
496
497	function resolve(arr::AbstractArray{<:Any, N}, inner::NTuple{N, Any}, outer::NTuple{N,Any}) where {N}	×
498	arr, inner, outer	×
499	end
500	function resolve(arr, inner, outer)	×
501	dims, inner, outer = pad(size(arr), to_tuple(inner), to_tuple(outer))	×
502	reshape(arr, dims), inner, outer	×
503	end
504	function resolve(arr, inner::Nothing, outer::Nothing)	×
505	return arr, inner, outer	×
506	end
507	function resolve(arr, inner::Nothing, outer)	2✔
508	dims, outer = pad(size(arr), to_tuple(outer))	281✔
509	reshape(arr, dims), inner, outer	281✔
510	end
511	function resolve(arr, inner, outer::Nothing)	×
512	dims, inner = pad(size(arr), to_tuple(inner))	×
513	reshape(arr, dims), inner, outer	×
514	end
515
516	function check(arr, inner, outer)
517	if inner !== nothing	281✔
518	# TODO: Currently one based indexing is demanded for inner !== nothing,
519	# but not for outer !== nothing. Decide for something consistent.
520	Base.require_one_based_indexing(arr)	×
521	if any(<(0), inner)	×
522	throw(ArgumentError("no inner repetition count may be negative; got $inner"))	×
523	end
524	if length(inner) < ndims(arr)	×
525	throw(ArgumentError("number of inner repetitions ($(length(inner))) cannot be less than number of dimensions of input array ($(ndims(arr)))"))	×
526	end
527	end
528	if outer !== nothing	281✔
529	if any(<(0), outer)	581✔
530	throw(ArgumentError("no outer repetition count may be negative; got $outer"))	×
531	end
532	if (length(outer) < ndims(arr)) && (inner !== nothing)	281✔
533	throw(ArgumentError("number of outer repetitions ($(length(outer))) cannot be less than number of dimensions of input array ($(ndims(arr)))"))	×
534	end
535	end
536	end
537
538	repeat_inner_outer(arr, inner::Nothing, outer::Nothing) = arr	×
539	repeat_inner_outer(arr, ::Nothing, outer) = repeat_outer(arr, outer)	281✔
540	repeat_inner_outer(arr, inner, ::Nothing) = repeat_inner(arr, inner)	×
541	repeat_inner_outer(arr, inner, outer) = repeat_outer(repeat_inner(arr, inner), outer)	×
542
543	function repeat_outer(a::AbstractMatrix, (m,n)::NTuple{2, Any})	38✔
544	o, p = size(a,1), size(a,2)	38✔
545	b = similar(a, om, pn)	61✔
546	for j=1:n	38✔
547	d = (j-1)*p+1	73✔
548	R = d:d+p-1	73✔
549	for i=1:m	73✔
550	c = (i-1)*o+1	99✔
551	@inbounds b[c:c+o-1, R] = a	99✔
552	end	138✔
553	end	116✔
554	return b	38✔
555	end
556
557	function repeat_outer(a::AbstractVector, (m,)::Tuple{Any})	243✔
558	o = length(a)	243✔
559	b = similar(a, o*m)	421✔
560	for i=1:m	243✔
561	c = (i-1)*o+1	1,011,177✔
562	@inbounds b[c:c+o-1] = a	2,020,029✔
563	end	2,022,152✔
564	return b	243✔
565	end
566
567	function repeat_outer(arr::AbstractArray{<:Any,N}, dims::NTuple{N,Any}) where {N}	×
568	insize = size(arr)	×
569	outsize = map(*, insize, dims)	×
570	out = similar(arr, outsize)	×
571	for I in CartesianIndices(arr)	×
572	for J in CartesianIndices(dims)	×
573	TIJ = map(Tuple(I), Tuple(J), insize) do i, j, d	×
574	i + d * (j-1)	×
575	end
576	IJ = CartesianIndex(TIJ)	×
577	@inbounds out[IJ] = arr[I]	×
578	end	×
579	end	×
580	return out	×
581	end
582
583	function repeat_inner(arr, inner)	×
584	outsize = map(*, size(arr), inner)	×
585	out = similar(arr, outsize)	×
586	for I in CartesianIndices(arr)	×
587	for J in CartesianIndices(inner)	×
588	TIJ = map(Tuple(I), Tuple(J), inner) do i, j, d	×
589	(i-1) * d + j	×
590	end
591	IJ = CartesianIndex(TIJ)	×
592	@inbounds out[IJ] = arr[I]	×
593	end	×
594	end	×
595	return out	×
596	end
597
598	end#module

JuliaLang / julia / #37940

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