arraymath.jl
# This file is a part of Julia. License is MIT: https://julialang.org/license
## 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 Array{Complex{Int64},2}:
1+1im 2-1im
2+2im 3+1im
julia> conj!(A);
julia> A
2×2 Array{Complex{Int64},2}:
1-1im 2+1im
2-2im 3-1im
```
"""
conj!(A::AbstractArray{<:Number}) = (@inbounds broadcast!(conj, A, A); A)
for f in (:-, :conj, :real, :imag)
@eval ($f)(A::AbstractArray) = broadcast($f, A)
end
## Binary arithmetic operators ##
for f in (:+, :-)
@eval function ($f)(A::AbstractArray, B::AbstractArray)
promote_shape(A, B) # check size compatibility
broadcast($f, A, B)
end
end
function +(A::Array, Bs::Array...)
for B in Bs
promote_shape(A, B) # check size compatibility
end
broadcast(+, A, Bs...)
end
for f in (:/, :\, :*)
if f != :/
@eval ($f)(A::Number, B::AbstractArray) = broadcast($f, A, B)
end
if f != :\
@eval ($f)(A::AbstractArray, B::Number) = broadcast($f, A, B)
end
end
## data movement ##
function reverse(A::Array{T}; dims::Integer) where T
nd = ndims(A); d = dims
1 ≤ d ≤ nd || throw(ArgumentError("dimension $d is not 1 ≤ $d ≤ $nd"))
sd = 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
# reverse along the only non-singleton dimension
for i = 1:sd
B[i] = A[sd+1-i]
end
return B
end
d_in = size(A)
leading = d_in[1:(d-1)]
M = prod(leading)
N = length(A)
stride = M * sd
if M==1
for j = 0:stride:(N-stride)
for i = 1:sd
ri = sd+1-i
B[j + ri] = A[j + i]
end
end
else
if isbitstype(T) && M>200
for i = 1:sd
ri = sd+1-i
for j=0:stride:(N-stride)
offs = j + 1 + (i-1)*M
boffs = j + 1 + (ri-1)*M
copyto!(B, boffs, A, offs, M)
end
end
else
for i = 1:sd
ri = sd+1-i
for j=0:stride:(N-stride)
offs = j + 1 + (i-1)*M
boffs = j + 1 + (ri-1)*M
for k=0:(M-1)
B[boffs + k] = A[offs + k]
end
end
end
end
end
return B
end
"""
rotl90(A)
Rotate matrix `A` left 90 degrees.
# Examples
```jldoctest
julia> a = [1 2; 3 4]
2×2 Array{Int64,2}:
1 2
3 4
julia> rotl90(a)
2×2 Array{Int64,2}:
2 4
1 3
```
"""
function rotl90(A::AbstractMatrix)
ind1, ind2 = axes(A)
B = similar(A, (ind2,ind1))
n = first(ind2)+last(ind2)
for i=axes(A,1), j=ind2
B[n-j,i] = A[i,j]
end
return B
end
"""
rotr90(A)
Rotate matrix `A` right 90 degrees.
# Examples
```jldoctest
julia> a = [1 2; 3 4]
2×2 Array{Int64,2}:
1 2
3 4
julia> rotr90(a)
2×2 Array{Int64,2}:
3 1
4 2
```
"""
function rotr90(A::AbstractMatrix)
ind1, ind2 = axes(A)
B = similar(A, (ind2,ind1))
m = first(ind1)+last(ind1)
for i=ind1, j=axes(A,2)
B[j,m-i] = A[i,j]
end
return B
end
"""
rot180(A)
Rotate matrix `A` 180 degrees.
# Examples
```jldoctest
julia> a = [1 2; 3 4]
2×2 Array{Int64,2}:
1 2
3 4
julia> rot180(a)
2×2 Array{Int64,2}:
4 3
2 1
```
"""
function rot180(A::AbstractMatrix)
B = similar(A)
ind1, ind2 = axes(A,1), axes(A,2)
m, n = first(ind1)+last(ind1), first(ind2)+last(ind2)
for j=ind2, i=ind1
B[m-i,n-j] = A[i,j]
end
return B
end
"""
rotl90(A, k)
Left-rotate matrix `A` 90 degrees counterclockwise an integer `k` number of times.
If `k` is a multiple of four (including zero), this is equivalent to a `copy`.
# Examples
```jldoctest
julia> a = [1 2; 3 4]
2×2 Array{Int64,2}:
1 2
3 4
julia> rotl90(a,1)
2×2 Array{Int64,2}:
2 4
1 3
julia> rotl90(a,2)
2×2 Array{Int64,2}:
4 3
2 1
julia> rotl90(a,3)
2×2 Array{Int64,2}:
3 1
4 2
julia> rotl90(a,4)
2×2 Array{Int64,2}:
1 2
3 4
```
"""
function rotl90(A::AbstractMatrix, k::Integer)
k = mod(k, 4)
k == 1 ? rotl90(A) :
k == 2 ? rot180(A) :
k == 3 ? rotr90(A) : copy(A)
end
"""
rotr90(A, k)
Right-rotate matrix `A` 90 degrees clockwise an integer `k` number of times.
If `k` is a multiple of four (including zero), this is equivalent to a `copy`.
# Examples
```jldoctest
julia> a = [1 2; 3 4]
2×2 Array{Int64,2}:
1 2
3 4
julia> rotr90(a,1)
2×2 Array{Int64,2}:
3 1
4 2
julia> rotr90(a,2)
2×2 Array{Int64,2}:
4 3
2 1
julia> rotr90(a,3)
2×2 Array{Int64,2}:
2 4
1 3
julia> rotr90(a,4)
2×2 Array{Int64,2}:
1 2
3 4
```
"""
rotr90(A::AbstractMatrix, k::Integer) = rotl90(A,-k)
"""
rot180(A, k)
Rotate matrix `A` 180 degrees an integer `k` number of times.
If `k` is even, this is equivalent to a `copy`.
# Examples
```jldoctest
julia> a = [1 2; 3 4]
2×2 Array{Int64,2}:
1 2
3 4
julia> rot180(a,1)
2×2 Array{Int64,2}:
4 3
2 1
julia> rot180(a,2)
2×2 Array{Int64,2}:
1 2
3 4
```
"""
rot180(A::AbstractMatrix, k::Integer) = mod(k, 2) == 1 ? rot180(A) : copy(A)