Revision 55f44179b9f9c75f8587c19f62cc17f031f5e3fd authored by Alexey Stukalov on 27 March 2017, 00:01:56 UTC, committed by Tony Kelman on 27 March 2017, 00:01:56 UTC
1 parent 2f02df9
abstractarraymath.jl
# This file is a part of Julia. License is MIT: http://julialang.org/license
## Basic functions ##
isreal(x::AbstractArray) = all(isreal,x)
iszero(x::AbstractArray) = all(iszero,x)
isreal(x::AbstractArray{<:Real}) = true
all(::typeof(isinteger), ::AbstractArray{<:Integer}) = true
## Constructors ##
"""
vec(a::AbstractArray) -> Vector
Reshape the array `a` as a one-dimensional column vector. The resulting array
shares the same underlying data as `a`, so modifying one will also modify the
other.
```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
```
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))
"""
squeeze(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`.
```jldoctest
julia> a = reshape(collect(1:4),(2,2,1,1))
2×2×1×1 Array{Int64,4}:
[:, :, 1, 1] =
1 3
2 4
julia> squeeze(a,3)
2×2×1 Array{Int64,3}:
[:, :, 1] =
1 3
2 4
```
"""
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(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"
"""
slicedim(A, d::Integer, i)
Return all the data of `A` where the index for dimension `d` equals `i`. Equivalent to
`A[:,:,...,i,:,:,...]` where `i` is in position `d`.
```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> slicedim(A,2,3)
2-element Array{Int64,1}:
3
7
```
"""
function slicedim(A::AbstractArray, d::Integer, i)
d >= 1 || throw(ArgumentError("dimension must be ≥ 1"))
nd = ndims(A)
d > nd && (i == 1 || throw_boundserror(A, (ntuple(k->Colon(),nd)..., ntuple(k->1,d-1-nd)..., i)))
A[setindex(indices(A), i, d)...]
end
function flipdim(A::AbstractVector, d::Integer)
d == 1 || throw(ArgumentError("dimension to flip must be 1"))
reverse(A)
end
"""
flipdim(A, d::Integer)
Reverse `A` in dimension `d`.
```jldoctest
julia> b = [1 2; 3 4]
2×2 Array{Int64,2}:
1 2
3 4
julia> flipdim(b,2)
2×2 Array{Int64,2}:
2 1
4 3
```
"""
function flipdim(A::AbstractArray, d::Integer)
nd = ndims(A)
1 ≤ d ≤ nd || throw(ArgumentError("dimension $d is not 1 ≤ $d ≤ $nd"))
if isempty(A)
return copy(A)
end
inds = indices(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
# flip along the only non-singleton dimension
for i in indsd
B[i] = A[sd-i]
end
return B
end
alli = [ indices(B,n) for n in 1:nd ]
for i in indsd
B[[ n==d ? sd-i : alli[n] for n in 1:nd ]...] = slicedim(A, d, i)
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 the data in an array. The second argument is a vector giving the amount to
shift in each dimension.
```jldoctest
julia> b = reshape(collect(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
```
See also [`circshift!`](@ref).
"""
function circshift(a::AbstractArray, shiftamt)
circshift!(similar(a), a, map(Integer, (shiftamt...,)))
end
# Uses K-B-N summation
function cumsum_kbn{T<:AbstractFloat}(v::AbstractVector{T})
r = similar(v)
if isempty(v); return r; end
inds = indices(v, 1)
i1 = first(inds)
s = r[i1] = v[i1]
c = zero(T)
for i=i1+1:last(inds)
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
# TODO: Needs a separate IndexCartesian method, this is only fast for IndexLinear
"""
cumsum_kbn(A, [dim::Integer=1])
Cumulative sum along a dimension, using the Kahan-Babuska-Neumaier compensated summation
algorithm for additional accuracy. The dimension defaults to 1.
"""
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
## Other array functions ##
"""
repmat(A, m::Integer, n::Integer=1)
Construct a matrix by repeating the given matrix (or vector) `m` times in dimension 1 and `n` times in
dimension 2.
```jldoctest
julia> repmat([1, 2, 3], 2)
6-element Array{Int64,1}:
1
2
3
1
2
3
julia> repmat([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
```
"""
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
@inline repmat(a::AbstractVecOrMat, m::Integer, n::Integer=1) = repmat(a, Int(m), Int(n))
@inline repmat(a::AbstractVector, m::Integer) = repmat(a, Int(m))
"""
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.
```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=ntuple(n->1, Val{ndims(A)}),
outer=ntuple(n->1, Val{ndims(A)}))
return _repeat(A, rep_kw2tup(inner), rep_kw2tup(outer))
end
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)"))
@propagate_inbounds 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)
R[indices(A)...] = A
else
inner_indices = [1:n for n in inner]
for c in CartesianRange(indices(A))
for i in 1:ndims(A)
n = inner[i]
inner_indices[i] = (1:n) + ((c[i] - 1) * n)
end
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] += inner_shape[i]
R[dest_indices...] = B
end
src_indices[i] = dest_indices[i] = 1:shape[i]
end
return R
end
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