subarray.jl
# import Base: ViewIndex, nextLD, dimsizeexpr, rangetype, merge_indexes, first_index, stride1expr, tailsize, subarray_linearindexing_dim
using Base.Cartesian
print_underestimates = false
######## Utilities ###########
# Generate an array similar to A[indx1, indx2, ...], but only call
# getindex with scalar-valued indexes. This will be safe even after
# getindex starts calling sub/slice.
# The "nodrop" variant is similar to current getindex/sub, except it
# doesn't drop any dimensions (not even trailing ones)
function Agen_nodrop(A::AbstractArray, I...)
irep = replace_colon(A, I)
_Agen(A, irep...)
end
# This does the same thing as slice
function Agen_slice(A::AbstractArray, I...)
irep = replace_colon(A, I)
B = _Agen(A, irep...)
sd = Int[]
for i = 1:length(I)
if isa(I[i], Real)
push!(sd, i)
end
end
squeeze(B, sd)
end
_Agen(A, i1) = [A[j1] for j1 in i1]
_Agen(A, i1, i2) = [A[j1,j2] for j1 in i1, j2 in i2]
_Agen(A, i1, i2, i3) = [A[j1,j2,j3] for j1 in i1, j2 in i2, j3 in i3]
_Agen(A, i1, i2, i3, i4) = [A[j1,j2,j3,j4] for j1 in i1, j2 in i2, j3 in i3, j4 in i4]
function replace_colon(A::AbstractArray, I)
Iout = Array(Any, length(I))
for d = 1:length(I)-1
Iout[d] = isa(I[d], Colon) ? (1:size(A,d)) : I[d]
end
d = length(I)
Iout[d] = isa(I[d], Colon) ? (1:prod(size(A)[d:end])) : I[d]
Iout
end
# To avoid getting confused by manipulations that are implemented for SubArrays,
# it's good to copy the contents to an Array. This version protects against
# `similar` ever changing its meaning.
function copy_to_array(A::AbstractArray)
Ac = Array(eltype(A), size(A))
copy!(Ac, A)
end
# Discover the highest dimension along which the values in A are
# separated by a single increment. If A was extracted via getindex
# from reshape(1:N, ...), this is equivalent to finding the highest
# dimension of the SubArray consistent with a single stride in the
# parent array.
function single_stride_dim(A::Array)
ld = 0
while ld < ndims(A)
# Collapse all dimensions up to & including ld+1 into the first dimension
shp = [prod(size(A)[1:ld+1])]
for j = ld+2:ndims(A)
push!(shp, size(A,j))
end
Ar = reshape(A, shp...)
# Compute the diff along dimension 1
if size(Ar, 1) > 1
indexes = map(d->1:size(Ar,d), [1:ndims(Ar)])
indexesp = copy(indexes); indexesp[1] = 2:size(Ar,1)
indexesm = copy(indexes); indexesm[1] = 1:size(Ar,1)-1
dA = Ar[indexesp...] - Ar[indexesm...]
ustride = unique(dA[:])
if length(ustride) == 1 # is it a single stride?
ld += 1
else
break
end
else
ld += 1
end
end
ld
end
single_stride_dim(A::AbstractArray) = single_stride_dim(copy_to_array(A))
# Extract the "linear indexing dimension" from a SubArray
getLD{T,N,P,I,LD}(::SubArray{T,N,P,I,LD}) = LD
# Compare the linear indexing dimension of a SubArray
# to a direct computation of strides
function cmpLD(Atest::SubArray, Acomp)
# Compute ld, skipping over dropped dimensions
LD = getLD(Atest)
ld = LD
for i = 1:LD
if isa(Atest.indexes[i], Real)
ld -= 1
end
end
ld, single_stride_dim(Acomp)
end
# Testing linear dimension inference for views-of-views
for N = 1:4
@eval begin
function test_viewview{T}(SB, A::Array{T,$N}, f, vindex)
local SSB
@nloops $N j d->(1:length(vindex)) d->(i_d = vindex[j_d]) begin
I = @ntuple $N d->i_d
try
SSB = f(SB, I...)
catch err
println(summary(SB))
println(I)
rethrow(err)
end
SA = f(A, I...)
ld, ldc = cmpLD(SSB, SA)
if ld == ldc
elseif ld <= ldc
if print_underestimates
println("Underestimate f = ", f, " on ", summary(SB), " with I = ", I, ", producing ", summary(SSB))
end
else
println(summary(SB))
println(summary(SSB))
error("failed on ", I)
end
end
end
end
end
# Testing equality of AbstractArrays, using several different methods to access values
function test_cartesian(A, B)
isgood = true
for (IA, IB) in zip(eachindex(A), eachindex(B))
if A[IA] != B[IB]
isgood = false
break
end
end
if !isgood
@show A
@show B
error("Mismatch")
end
end
function test_linear(A, B)
length(A) == length(B) || error("length mismatch")
isgood = true
for (iA, iB) in zip(1:length(A), 1:length(B))
if A[iA] != B[iB]
isgood = false
break
end
end
if !isgood
@show A
@show B
error("Mismatch")
end
end
# "mixed" means 2 indexes even for N-dimensional arrays
test_mixed{T}(A::AbstractArray{T,1}, B::Array) = nothing
test_mixed{T}(A::AbstractArray{T,2}, B::Array) = nothing
test_mixed(A, B::Array) = _test_mixed(A, reshape(B, size(A)))
function _test_mixed(A, B)
L = length(A)
m = size(A, 1)
n = div(L, m)
isgood = true
for j = 1:n, i = 1:m
if A[i,j] != B[i,j]
isgood = false
break
end
end
if !isgood
@show A
@show B
error("Mismatch")
end
end
function err_li(I::Tuple, ld::Int, ldc::Int)
@show I
@show ld, ldc
error("Linear indexing inference mismatch")
end
function err_li(S::SubArray, ldc::Int)
println(summary(S))
@show S.indexes
@show ldc
error("Linear indexing inference mismatch")
end
function runtests(A::Array, I...)
# Direct test of linear indexing inference
C = Agen_nodrop(A, I...)
ld = single_stride_dim(C)
ldc = Base.subarray_linearindexing_dim(typeof(A), typeof(I))
ld == ldc || err_li(I, ld, ldc)
# sub
S = sub(A, I...)
getLD(S) == ldc || err_li(S, ldc)
if Base.iscontiguous(S)
@test S.stride1 == 1
end
test_linear(S, C)
test_cartesian(S, C)
test_mixed(S, C)
# slice
S = slice(A, I...)
getLD(S) == ldc || err_li(S, ldc)
test_linear(S, C)
test_cartesian(S, C)
test_mixed(S, C)
end
function runtests(A::SubArray, I...)
AA = copy_to_array(A)
# Direct test of linear indexing inference
C = Agen_nodrop(AA, I...)
ld = single_stride_dim(C)
# sub
S = sub(A, I...)
ldc = getLD(S)
ldc <= ld || err_li(S, ld)
test_linear(S, C)
test_cartesian(S, C)
test_mixed(S, C)
# slice
S = slice(A, I...)
ldc = getLD(S)
ldc <= ld || err_li(S, ld)
test_linear(S, C)
test_cartesian(S, C)
test_mixed(S, C)
end
# indexN is a cartesian index, indexNN is a linear index for 2 dimensions, and indexNNN is a linear index for 3 dimensions
function runviews{T}(SB::AbstractArray{T,3}, indexN, indexNN, indexNNN)
for i3 in indexN, i2 in indexN, i1 in indexN
runtests(A, i1, i2, i3)
end
for i2 in indexNN, i1 in indexN
runtests(A, i1, i2)
end
for i1 in indexNNN
runtests(A, i1)
end
end
function runviews{T}(SB::AbstractArray{T,2}, indexN, indexNN, indexNNN)
for i2 in indexN, i1 in indexN
runtests(A, i1, i2)
end
for i1 in indexNN
runtests(A, i1)
end
end
function runviews{T}(SB::AbstractArray{T,1}, indexN, indexNN, indexNNN)
for i1 in indexN
runtests(A, i1)
end
end
runviews{T}(SB::AbstractArray{T,0}, indexN, indexNN, indexNNN) = nothing
######### Tests #########
### Views from Arrays ###
A = reshape(1:5*7*11, 11, 7, 5)
index5 = (2, :, 2:5, 1:2:5, [4,1,5]) # all work with at least size 5
index25 = (8, :, 2:11, 12:3:22, [4,1,5,9])
index125 = (113, :, 85:121, 2:15:92, [99,14,103])
runviews(A, index5, index25, index125)
### Views from views ###
B = reshape(1:13^3, 13, 13, 13)
# "outer" indexes create snips that have at least size 5 along each dimension, with the exception of Int-slicing
oindex = (:, 6, 3:7, 13:-2:1, [8,4,6,12,5,7])
for o3 in oindex, o2 in oindex, o1 in oindex
sliceB = slice(B, o1, o2, o3)
runviews(sliceB, index5, index25, index125)
end
####### "Classical" tests #######
# sub
A = reshape(1:120, 3, 5, 8)
sA = sub(A, 2, 1:5, :)
@test parent(sA) == A
@test parentindexes(sA) == (2:2, 1:5, :)
@test Base.parentdims(sA) == [1:3]
@test size(sA) == (1, 5, 8)
@test sA[1, 2, 1:8][:] == [5:15:120]
sA[2:5:end] = -1
@test all(sA[2:5:end] .== -1)
@test all(A[5:15:120] .== -1)
@test strides(sA) == (1,3,15)
@test stride(sA,3) == 15
@test stride(sA,4) == 120
sA = sub(A, 1:3, 1:5, 5)
@test Base.parentdims(sA) == [1:2]
sA[1:3,1:5] = -2
@test all(A[:,:,5] .== -2)
sA[:] = -3
@test all(A[:,:,5] .== -3)
@test strides(sA) == (1,3)
sA = sub(A, 1:3, 3, 2:5)
@test Base.parentdims(sA) == [1:3]
@test size(sA) == (3,1,4)
@test sA == A[1:3,3,2:5]
@test sA[:] == A[1:3,3,2:5][:]
sA = sub(A, 1:2:3, 1:3:5, 1:2:8)
@test Base.parentdims(sA) == [1:3]
@test strides(sA) == (2,9,30)
@test sA[:] == A[1:2:3, 1:3:5, 1:2:8][:]
# issue #8807
@test sub(sub([1:5], 1:5), 1:5) == [1:5]
# sub logical indexing #4763
A = sub([1:10], 5:8)
@test A[A.<7] == [5, 6]
B = reshape(1:16, 4, 4)
sB = sub(B, 2:3, 2:3)
@test sB[sB.>8] == [10, 11]
# slice
A = reshape(1:120, 3, 5, 8)
sA = slice(A, 2, :, 1:8)
@test parent(sA) == A
@test parentindexes(sA) == (2, :, 1:8)
@test Base.parentdims(sA) == [2:3]
@test size(sA) == (5, 8)
@test strides(sA) == (3,15)
@test sA[2, 1:8][:] == [5:15:120]
@test sA[:,1] == [2:3:14]
@test sA[2:5:end] == [5:15:110]
sA[2:5:end] = -1
@test all(sA[2:5:end] .== -1)
@test all(A[5:15:120] .== -1)
sA = slice(A, 1:3, 1:5, 5)
@test Base.parentdims(sA) == [1:2]
@test size(sA) == (3,5)
@test strides(sA) == (1,3)
sA = slice(A, 1:2:3, 3, 1:2:8)
@test Base.parentdims(sA) == [1,3]
@test size(sA) == (2,4)
@test strides(sA) == (2,30)
@test sA[:] == A[sA.indexes...][:]
a = [5:8]
@test parent(a) == a
@test parentindexes(a) == (1:4,)
# issue #6218 - logical indexing
A = rand(2, 2, 3)
msk = ones(Bool, 2, 2)
msk[2,1] = false
sA = sub(A, :, :, 1)
sA[msk] = 1.0
@test sA[msk] == ones(countnz(msk))