https://github.com/JuliaLang/julia
Tip revision: cb62824794724ed443c8e7d493d95a60c12ae94d authored by Rafael Fourquet on 23 June 2017, 14:43:58 UTC
add doc for iteratoraccess
add doc for iteratoraccess
Tip revision: cb62824
subarray.jl
# This file is a part of Julia. License is MIT: https://julialang.org/license
abstract type AbstractCartesianIndex{N} end # This is a hacky forward declaration for CartesianIndex
const ViewIndex = Union{Real, AbstractArray}
const ScalarIndex = Real
# L is true if the view itself supports fast linear indexing
struct SubArray{T,N,P,I,L} <: AbstractArray{T,N}
parent::P
indexes::I
offset1::Int # for linear indexing and pointer, only valid when L==true
stride1::Int # used only for linear indexing
function SubArray{T,N,P,I,L}(parent, indexes, offset1, stride1) where {T,N,P,I,L}
@_inline_meta
check_parent_index_match(parent, indexes)
new(parent, indexes, offset1, stride1)
end
end
# Compute the linear indexability of the indices, and combine it with the linear indexing of the parent
function SubArray(parent::AbstractArray, indexes::Tuple)
@_inline_meta
SubArray(IndexStyle(viewindexing(indexes), IndexStyle(parent)), parent, ensure_indexable(indexes), index_dimsum(indexes...))
end
function SubArray(::IndexCartesian, parent::P, indexes::I, ::NTuple{N,Any}) where {P,I,N}
@_inline_meta
SubArray{eltype(P), N, P, I, false}(parent, indexes, 0, 0)
end
function SubArray(::IndexLinear, parent::P, indexes::I, ::NTuple{N,Any}) where {P,I,N}
@_inline_meta
# Compute the stride and offset
stride1 = compute_stride1(parent, indexes)
SubArray{eltype(P), N, P, I, true}(parent, indexes, compute_offset1(parent, stride1, indexes), stride1)
end
check_parent_index_match(parent, indexes) = check_parent_index_match(parent, index_ndims(indexes...))
check_parent_index_match(parent::AbstractArray{T,N}, ::NTuple{N, Bool}) where {T,N} = nothing
check_parent_index_match(parent, ::NTuple{N, Bool}) where {N} =
throw(ArgumentError("number of indices ($N) must match the parent dimensionality ($(ndims(parent)))"))
# This computes the linear indexing compatability for a given tuple of indices
viewindexing() = IndexLinear()
# Leading scalar indexes simply increase the stride
viewindexing(I::Tuple{ScalarIndex, Vararg{Any}}) = (@_inline_meta; viewindexing(tail(I)))
# Slices may begin a section which may be followed by any number of Slices
viewindexing(I::Tuple{Slice, Slice, Vararg{Any}}) = (@_inline_meta; viewindexing(tail(I)))
# A UnitRange can follow Slices, but only if all other indices are scalar
viewindexing(I::Tuple{Slice, UnitRange, Vararg{ScalarIndex}}) = IndexLinear()
# In general, ranges are only fast if all other indices are scalar
viewindexing(I::Tuple{Union{Range, Slice}, Vararg{ScalarIndex}}) = IndexLinear()
# All other index combinations are slow
viewindexing(I::Tuple{Vararg{Any}}) = IndexCartesian()
# Of course, all other array types are slow
viewindexing(I::Tuple{AbstractArray, Vararg{Any}}) = IndexCartesian()
# Simple utilities
size(V::SubArray) = (@_inline_meta; map(n->Int(unsafe_length(n)), indices(V)))
similar(V::SubArray, T::Type, dims::Dims) = similar(V.parent, T, dims)
parent(V::SubArray) = V.parent
parentindexes(V::SubArray) = V.indexes
parent(a::AbstractArray) = a
"""
parentindexes(A)
From an array view `A`, returns the corresponding indexes in the parent.
"""
parentindexes(a::AbstractArray) = ntuple(i->OneTo(size(a,i)), ndims(a))
## SubArray creation
# We always assume that the dimensionality of the parent matches the number of
# indices that end up getting passed to it, so we store the parent as a
# ReshapedArray view if necessary. The trouble is that arrays of `CartesianIndex`
# can make the number of effective indices not equal to length(I).
_maybe_reshape_parent(A::AbstractArray, ::NTuple{1, Bool}) = reshape(A, Val{1})
_maybe_reshape_parent(A::AbstractArray{<:Any,1}, ::NTuple{1, Bool}) = reshape(A, Val{1})
_maybe_reshape_parent(A::AbstractArray{<:Any,N}, ::NTuple{N, Bool}) where {N} = A
_maybe_reshape_parent(A::AbstractArray, ::NTuple{N, Bool}) where {N} = reshape(A, Val{N}) # TODO: DEPRECATE FOR #14770
"""
view(A, inds...)
Like [`getindex`](@ref), but returns a view into the parent array `A` with the
given indices instead of making a copy. Calling [`getindex`](@ref) or
[`setindex!`](@ref) on the returned `SubArray` computes the
indices to the parent array on the fly without checking bounds.
```jldoctest
julia> A = [1 2; 3 4]
2×2 Array{Int64,2}:
1 2
3 4
julia> b = view(A, :, 1)
2-element SubArray{Int64,1,Array{Int64,2},Tuple{Base.Slice{Base.OneTo{Int64}},Int64},true}:
1
3
julia> fill!(b, 0)
2-element SubArray{Int64,1,Array{Int64,2},Tuple{Base.Slice{Base.OneTo{Int64}},Int64},true}:
0
0
julia> A # Note A has changed even though we modified b
2×2 Array{Int64,2}:
0 2
0 4
```
"""
function view(A::AbstractArray, I...)
@_inline_meta
J = to_indices(A, I)
@boundscheck checkbounds(A, J...)
unsafe_view(_maybe_reshape_parent(A, index_ndims(J...)), J...)
end
function unsafe_view(A::AbstractArray, I::ViewIndex...)
@_inline_meta
SubArray(A, I)
end
# When we take the view of a view, it's often possible to "reindex" the parent
# view's indices such that we can "pop" the parent view and keep just one layer
# of indirection. But we can't always do this because arrays of `CartesianIndex`
# might span multiple parent indices, making the reindex calculation very hard.
# So we use _maybe_reindex to figure out if there are any arrays of
# `CartesianIndex`, and if so, we punt and keep two layers of indirection.
unsafe_view(V::SubArray, I::ViewIndex...) = (@_inline_meta; _maybe_reindex(V, I))
_maybe_reindex(V, I) = (@_inline_meta; _maybe_reindex(V, I, I))
_maybe_reindex(V, I, ::Tuple{AbstractArray{<:AbstractCartesianIndex}, Vararg{Any}}) =
(@_inline_meta; SubArray(V, I))
# But allow arrays of CartesianIndex{1}; they behave just like arrays of Ints
_maybe_reindex(V, I, A::Tuple{AbstractArray{<:AbstractCartesianIndex{1}}, Vararg{Any}}) =
(@_inline_meta; _maybe_reindex(V, I, tail(A)))
_maybe_reindex(V, I, A::Tuple{Any, Vararg{Any}}) = (@_inline_meta; _maybe_reindex(V, I, tail(A)))
function _maybe_reindex(V, I, ::Tuple{})
@_inline_meta
@inbounds idxs = to_indices(V.parent, reindex(V, V.indexes, I))
SubArray(V.parent, idxs)
end
## Re-indexing is the heart of a view, transforming A[i, j][x, y] to A[i[x], j[y]]
#
# Recursively look through the heads of the parent- and sub-indexes, considering
# the following cases:
# * Parent index is array -> re-index that with one or more sub-indexes (one per dimension)
# * Parent index is Colon -> just use the sub-index as provided
# * Parent index is scalar -> that dimension was dropped, so skip the sub-index and use the index as is
AbstractZeroDimArray{T} = AbstractArray{T, 0}
reindex(V, ::Tuple{}, ::Tuple{}) = ()
# Skip dropped scalars, so simply peel them off the parent indices and continue
reindex(V, idxs::Tuple{ScalarIndex, Vararg{Any}}, subidxs::Tuple{Vararg{Any}}) =
(@_propagate_inbounds_meta; (idxs[1], reindex(V, tail(idxs), subidxs)...))
# Slices simply pass their subindexes straight through
reindex(V, idxs::Tuple{Slice, Vararg{Any}}, subidxs::Tuple{Any, Vararg{Any}}) =
(@_propagate_inbounds_meta; (subidxs[1], reindex(V, tail(idxs), tail(subidxs))...))
# Re-index into parent vectors with one subindex
reindex(V, idxs::Tuple{AbstractVector, Vararg{Any}}, subidxs::Tuple{Any, Vararg{Any}}) =
(@_propagate_inbounds_meta; (idxs[1][subidxs[1]], reindex(V, tail(idxs), tail(subidxs))...))
# Parent matrices are re-indexed with two sub-indices
reindex(V, idxs::Tuple{AbstractMatrix, Vararg{Any}}, subidxs::Tuple{Any, Any, Vararg{Any}}) =
(@_propagate_inbounds_meta; (idxs[1][subidxs[1], subidxs[2]], reindex(V, tail(idxs), tail(tail(subidxs)))...))
# In general, we index N-dimensional parent arrays with N indices
@generated function reindex(V, idxs::Tuple{AbstractArray{T,N}, Vararg{Any}}, subidxs::Tuple{Vararg{Any}}) where {T,N}
if length(subidxs.parameters) >= N
subs = [:(subidxs[$d]) for d in 1:N]
tail = [:(subidxs[$d]) for d in N+1:length(subidxs.parameters)]
:(@_propagate_inbounds_meta; (idxs[1][$(subs...)], reindex(V, tail(idxs), ($(tail...),))...))
else
:(throw(ArgumentError("cannot re-index $(ndims(V)) dimensional SubArray with fewer than $(ndims(V)) indices\nThis should not occur; please submit a bug report.")))
end
end
# In general, we simply re-index the parent indices by the provided ones
SlowSubArray{T,N,P,I} = SubArray{T,N,P,I,false}
function getindex(V::SlowSubArray{T,N}, I::Vararg{Int,N}) where {T,N}
@_inline_meta
@boundscheck checkbounds(V, I...)
@inbounds r = V.parent[reindex(V, V.indexes, I)...]
r
end
FastSubArray{T,N,P,I} = SubArray{T,N,P,I,true}
function getindex(V::FastSubArray, i::Int)
@_inline_meta
@boundscheck checkbounds(V, i)
@inbounds r = V.parent[V.offset1 + V.stride1*i]
r
end
# We can avoid a multiplication if the first parent index is a Colon or UnitRange
FastContiguousSubArray{T,N,P,I<:Tuple{Union{Slice, UnitRange}, Vararg{Any}}} = SubArray{T,N,P,I,true}
function getindex(V::FastContiguousSubArray, i::Int)
@_inline_meta
@boundscheck checkbounds(V, i)
@inbounds r = V.parent[V.offset1 + i]
r
end
function setindex!(V::SlowSubArray{T,N}, x, I::Vararg{Int,N}) where {T,N}
@_inline_meta
@boundscheck checkbounds(V, I...)
@inbounds V.parent[reindex(V, V.indexes, I)...] = x
V
end
function setindex!(V::FastSubArray, x, i::Int)
@_inline_meta
@boundscheck checkbounds(V, i)
@inbounds V.parent[V.offset1 + V.stride1*i] = x
V
end
function setindex!(V::FastContiguousSubArray, x, i::Int)
@_inline_meta
@boundscheck checkbounds(V, i)
@inbounds V.parent[V.offset1 + i] = x
V
end
IndexStyle(::Type{<:FastSubArray}) = IndexLinear()
IndexStyle(::Type{<:SubArray}) = IndexCartesian()
# Strides are the distance between adjacent elements in a given dimension,
# so they are well-defined even for non-linear memory layouts
strides(V::SubArray) = substrides(V.parent, V.indexes)
substrides(parent, I::Tuple) = substrides(1, parent, 1, I)
substrides(s, parent, dim, ::Tuple{}) = ()
substrides(s, parent, dim, I::Tuple{ScalarIndex, Vararg{Any}}) = (substrides(s*size(parent, dim), parent, dim+1, tail(I))...)
substrides(s, parent, dim, I::Tuple{Slice, Vararg{Any}}) = (s, substrides(s*size(parent, dim), parent, dim+1, tail(I))...)
substrides(s, parent, dim, I::Tuple{Range, Vararg{Any}}) = (s*step(I[1]), substrides(s*size(parent, dim), parent, dim+1, tail(I))...)
substrides(s, parent, dim, I::Tuple{Any, Vararg{Any}}) = throw(ArgumentError("strides is invalid for SubArrays with indices of type $(typeof(I[1]))"))
stride(V::SubArray, d::Integer) = d <= ndims(V) ? strides(V)[d] : strides(V)[end] * size(V)[end]
compute_stride1(parent::AbstractArray, I::NTuple{N,Any}) where {N} =
(@_inline_meta; compute_stride1(1, fill_to_length(indices(parent), OneTo(1), Val{N}), I))
compute_stride1(s, inds, I::Tuple{}) = s
compute_stride1(s, inds, I::Tuple{ScalarIndex, Vararg{Any}}) =
(@_inline_meta; compute_stride1(s*unsafe_length(inds[1]), tail(inds), tail(I)))
compute_stride1(s, inds, I::Tuple{Range, Vararg{Any}}) = s*step(I[1])
compute_stride1(s, inds, I::Tuple{Slice, Vararg{Any}}) = s
compute_stride1(s, inds, I::Tuple{Any, Vararg{Any}}) = throw(ArgumentError("invalid strided index type $(typeof(I[1]))"))
iscontiguous(A::SubArray) = iscontiguous(typeof(A))
iscontiguous(::Type{<:SubArray}) = false
iscontiguous(::Type{<:FastContiguousSubArray}) = true
first_index(V::FastSubArray) = V.offset1 + V.stride1 # cached for fast linear SubArrays
function first_index(V::SubArray)
P, I = parent(V), V.indexes
s1 = compute_stride1(P, I)
s1 + compute_offset1(P, s1, I)
end
# Computing the first index simply steps through the indices, accumulating the
# sum of index each multiplied by the parent's stride.
# The running sum is `f`; the cumulative stride product is `s`.
# If the result is one-dimensional and it's a Colon, then linear
# indexing uses the indices along the given dimension. Otherwise
# linear indexing always starts with 1.
compute_offset1(parent, stride1::Integer, I::Tuple) =
(@_inline_meta; compute_offset1(parent, stride1, find_extended_dims(1, I...), find_extended_inds(I...), I))
compute_offset1(parent, stride1::Integer, dims::Tuple{Int}, inds::Tuple{Slice}, I::Tuple) =
(@_inline_meta; compute_linindex(parent, I) - stride1*first(indices(parent, dims[1]))) # index-preserving case
compute_offset1(parent, stride1::Integer, dims, inds, I::Tuple) =
(@_inline_meta; compute_linindex(parent, I) - stride1) # linear indexing starts with 1
function compute_linindex(parent, I::NTuple{N,Any}) where N
@_inline_meta
IP = fill_to_length(indices(parent), OneTo(1), Val{N})
compute_linindex(1, 1, IP, I)
end
function compute_linindex(f, s, IP::Tuple, I::Tuple{ScalarIndex, Vararg{Any}})
@_inline_meta
Δi = I[1]-first(IP[1])
compute_linindex(f + Δi*s, s*unsafe_length(IP[1]), tail(IP), tail(I))
end
function compute_linindex(f, s, IP::Tuple, I::Tuple{Any, Vararg{Any}})
@_inline_meta
Δi = first(I[1])-first(IP[1])
compute_linindex(f + Δi*s, s*unsafe_length(IP[1]), tail(IP), tail(I))
end
compute_linindex(f, s, IP::Tuple, I::Tuple{}) = f
find_extended_dims(dim, ::ScalarIndex, I...) = (@_inline_meta; find_extended_dims(dim + 1, I...))
find_extended_dims(dim, i1, I...) = (@_inline_meta; (dim, find_extended_dims(dim + 1, I...)...))
find_extended_dims(dim) = ()
find_extended_inds(::ScalarIndex, I...) = (@_inline_meta; find_extended_inds(I...))
find_extended_inds(i1, I...) = (@_inline_meta; (i1, find_extended_inds(I...)...))
find_extended_inds() = ()
unsafe_convert(::Type{Ptr{T}}, V::SubArray{T,N,P,<:Tuple{Vararg{RangeIndex}}}) where {T,N,P} =
unsafe_convert(Ptr{T}, V.parent) + (first_index(V)-1)*sizeof(T)
pointer(V::FastSubArray, i::Int) = pointer(V.parent, V.offset1 + V.stride1*i)
pointer(V::FastContiguousSubArray, i::Int) = pointer(V.parent, V.offset1 + i)
pointer(V::SubArray, i::Int) = _pointer(V, i)
_pointer(V::SubArray{<:Any,1}, i::Int) = pointer(V, (i,))
_pointer(V::SubArray, i::Int) = pointer(V, ind2sub(indices(V), i))
function pointer(V::SubArray{T,N,<:Array,<:Tuple{Vararg{RangeIndex}}}, is::Tuple{Vararg{Int}}) where {T,N}
index = first_index(V)
strds = strides(V)
for d = 1:length(is)
index += (is[d]-1)*strds[d]
end
return pointer(V.parent, index)
end
# indices are taken from the range/vector
# Since bounds-checking is performance-critical and uses
# indices, it's worth optimizing these implementations thoroughly
indices(S::SubArray) = (@_inline_meta; _indices_sub(S, S.indexes...))
_indices_sub(S::SubArray) = ()
_indices_sub(S::SubArray, ::Real, I...) = (@_inline_meta; _indices_sub(S, I...))
function _indices_sub(S::SubArray, i1::AbstractArray, I...)
@_inline_meta
(unsafe_indices(i1)..., _indices_sub(S, I...)...)
end
## Compatability
# deprecate?
function parentdims(s::SubArray)
nd = ndims(s)
dimindex = Vector{Int}(nd)
sp = strides(s.parent)
sv = strides(s)
j = 1
for i = 1:ndims(s.parent)
r = s.indexes[i]
if j <= nd && (isa(r,Union{Slice,Range}) ? sp[i]*step(r) : sp[i]) == sv[j]
dimindex[j] = i
j += 1
end
end
dimindex
end
"""
replace_ref_end!(ex)
Recursively replace occurrences of the symbol :end in a "ref" expression (i.e. A[...]) `ex`
with the appropriate function calls (`endof`, `size` or `trailingsize`). Replacement uses
the closest enclosing ref, so
A[B[end]]
should transform to
A[B[endof(B)]]
"""
replace_ref_end!(ex) = replace_ref_end_!(ex, nothing)[1]
# replace_ref_end_!(ex,withex) returns (new ex, whether withex was used)
function replace_ref_end_!(ex, withex)
used_withex = false
if isa(ex,Symbol) && ex == :end
withex === nothing && error("Invalid use of end")
return withex, true
elseif isa(ex,Expr)
if ex.head == :ref
ex.args[1], used_withex = replace_ref_end_!(ex.args[1],withex)
S = isa(ex.args[1],Symbol) ? ex.args[1]::Symbol : gensym(:S) # temp var to cache ex.args[1] if needed
used_S = false # whether we actually need S
# new :ref, so redefine withex
nargs = length(ex.args)-1
if nargs == 0
return ex, used_withex
elseif nargs == 1
# replace with endof(S)
ex.args[2], used_S = replace_ref_end_!(ex.args[2],:($endof($S)))
else
n = 1
J = endof(ex.args)
for j = 2:J-1
exj, used = replace_ref_end_!(ex.args[j],:($size($S,$n)))
used_S |= used
ex.args[j] = exj
if isa(exj,Expr) && exj.head == :...
# splatted object
exjs = exj.args[1]
n = :($n + length($exjs))
elseif isa(n, Expr)
# previous expression splatted
n = :($n + 1)
else
# an integer
n += 1
end
end
ex.args[J], used = replace_ref_end_!(ex.args[J],:($trailingsize($S,$n)))
used_S |= used
end
if used_S && S !== ex.args[1]
S0 = ex.args[1]
ex.args[1] = S
ex = Expr(:let, ex, :($S = $S0))
end
else
# recursive search
for i = eachindex(ex.args)
ex.args[i], used = replace_ref_end_!(ex.args[i],withex)
used_withex |= used
end
end
end
ex, used_withex
end
"""
@view A[inds...]
Creates a `SubArray` from an indexing expression. This can only be applied directly to a
reference expression (e.g. `@view A[1,2:end]`), and should *not* be used as the target of
an assignment (e.g. `@view(A[1,2:end]) = ...`). See also [`@views`](@ref)
to switch an entire block of code to use views for slicing.
```jldoctest
julia> A = [1 2; 3 4]
2×2 Array{Int64,2}:
1 2
3 4
julia> b = @view A[:, 1]
2-element SubArray{Int64,1,Array{Int64,2},Tuple{Base.Slice{Base.OneTo{Int64}},Int64},true}:
1
3
julia> fill!(b, 0)
2-element SubArray{Int64,1,Array{Int64,2},Tuple{Base.Slice{Base.OneTo{Int64}},Int64},true}:
0
0
julia> A
2×2 Array{Int64,2}:
0 2
0 4
```
"""
macro view(ex)
if Meta.isexpr(ex, :ref)
ex = replace_ref_end!(ex)
if Meta.isexpr(ex, :ref)
ex = Expr(:call, view, ex.args...)
else # ex replaced by let ...; foo[...]; end
assert(Meta.isexpr(ex, :let) && Meta.isexpr(ex.args[1], :ref))
ex.args[1] = Expr(:call, view, ex.args[1].args...)
end
Expr(:&&, true, esc(ex))
else
throw(ArgumentError("Invalid use of @view macro: argument must be a reference expression A[...]."))
end
end
############################################################################
# @views macro code:
# maybeview is like getindex, but returns a view for slicing operations
# (while remaining equivalent to getindex for scalar indices and non-array types)
@propagate_inbounds maybeview(A, args...) = getindex(A, args...)
@propagate_inbounds maybeview(A::AbstractArray, args...) = view(A, args...)
@propagate_inbounds maybeview(A::AbstractArray, args::Number...) = getindex(A, args...)
@propagate_inbounds maybeview(A) = getindex(A)
@propagate_inbounds maybeview(A::AbstractArray) = getindex(A)
# _views implements the transformation for the @views macro.
# @views calls esc(_views(...)) to work around #20241,
# so any function calls we insert (to maybeview, or to
# size and endof in replace_ref_end!) must be interpolated
# as values rather than as symbols to ensure that they are called
# from Base rather than from the caller's scope.
_views(x) = x
function _views(ex::Expr)
if ex.head in (:(=), :(.=))
# don't use view for ref on the lhs of an assignment,
# but still use views for the args of the ref:
lhs = ex.args[1]
Expr(ex.head, Meta.isexpr(lhs, :ref) ?
Expr(:ref, _views.(lhs.args)...) : _views(lhs),
_views(ex.args[2]))
elseif ex.head == :ref
Expr(:call, maybeview, _views.(ex.args)...)
else
h = string(ex.head)
# don't use view on the lhs of an op-assignment a[i...] += ...
if last(h) == '=' && Meta.isexpr(ex.args[1], :ref)
lhs = ex.args[1]
# temp vars to avoid recomputing a and i,
# which will be assigned in a let block:
a = gensym(:a)
i = [gensym(:i) for k = 1:length(lhs.args)-1]
# for splatted indices like a[i, j...], we need to
# splat the corresponding temp var.
I = similar(i, Any)
for k = 1:length(i)
if Meta.isexpr(lhs.args[k+1], :...)
I[k] = Expr(:..., i[k])
lhs.args[k+1] = lhs.args[k+1].args[1] # unsplat
else
I[k] = i[k]
end
end
Expr(:let,
Expr(first(h) == '.' ? :(.=) : :(=), :($a[$(I...)]),
Expr(:call, Symbol(h[1:end-1]),
:($maybeview($a, $(I...))),
_views.(ex.args[2:end])...)),
:($a = $(_views(lhs.args[1]))),
[:($(i[k]) = $(_views(lhs.args[k+1]))) for k=1:length(i)]...)
else
Expr(ex.head, _views.(ex.args)...)
end
end
end
"""
@views expression
Convert every array-slicing operation in the given expression
(which may be a `begin`/`end` block, loop, function, etc.)
to return a view. Scalar indices, non-array types, and
explicit `getindex` calls (as opposed to `array[...]`) are
unaffected.
Note that the `@views` macro only affects `array[...]` expressions
that appear explicitly in the given `expression`, not array slicing that
occurs in functions called by that code.
"""
macro views(x)
esc(_views(replace_ref_end!(x)))
end