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abstractarray.jl
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abstractarray.jl
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# This file is a part of Julia. License is MIT: http://julialang.org/license
## Type aliases for convenience ##
typealias AbstractVector{T} AbstractArray{T,1}
typealias AbstractMatrix{T} AbstractArray{T,2}
typealias AbstractVecOrMat{T} Union{AbstractVector{T}, AbstractMatrix{T}}
typealias RangeIndex Union{Int, Range{Int}, AbstractUnitRange{Int}, Colon}
typealias Indices{N} NTuple{N,AbstractUnitRange}
typealias IndicesOne{N} NTuple{N,OneTo}
typealias DimOrInd Union{Integer, AbstractUnitRange}
typealias DimsOrInds{N} NTuple{N,DimOrInd}
## Basic functions ##
vect() = Array{Any}(0)
vect{T}(X::T...) = T[ X[i] for i=1:length(X) ]
function vect(X...)
T = promote_typeof(X...)
#T[ X[i] for i=1:length(X) ]
# TODO: this is currently much faster. should figure out why. not clear.
copy!(Array{T}(length(X)), X)
end
size{T,N}(t::AbstractArray{T,N}, d) = d <= N ? size(t)[d] : 1
size{N}(x, d1::Integer, d2::Integer, dx::Vararg{Integer, N}) = (size(x, d1), size(x, d2), ntuple(k->size(x, dx[k]), Val{N})...)
"""
indices(A, d)
Returns the valid range of indices for array `A` along dimension `d`.
"""
function indices(A::AbstractArray, d)
@_inline_meta
OneTo(size(A,d))
end
"""
indices(A)
Returns the tuple of valid indices for array `A`.
"""
function indices{T,N}(A::AbstractArray{T,N})
@_inline_meta
_indices((), A)
end
_indices{T,N}(out::NTuple{N}, A::AbstractArray{T,N}) = out
function _indices(out, A::AbstractArray)
@_inline_meta
_indices((out..., indices(A, length(out)+1)), A)
end
# Note: a simpler implementation suffers from #16327
# function indices{T,N}(A::AbstractArray{T,N})
# @_inline_meta
# ntuple(d->indices(A, d), Val{N})
# end
indices1(A) = (@_inline_meta; indices(A, 1))
"""
linearindices(A)
Returns a `UnitRange` specifying the valid range of indices for `A[i]`
where `i` is an `Int`. For arrays with conventional indexing (indices
start at 1), or any multidimensional array, this is `1:length(A)`;
however, for one-dimensional arrays with unconventional indices, this
is `indices(A, 1)`.
Calling this function is the "safe" way to write algorithms that
exploit linear indexing.
"""
linearindices(A) = 1:length(A)
linearindices(A::AbstractVector) = indices1(A)
eltype{T}(::Type{AbstractArray{T}}) = T
eltype{T,N}(::Type{AbstractArray{T,N}}) = T
elsize{T}(::AbstractArray{T}) = sizeof(T)
ndims{T,N}(::AbstractArray{T,N}) = N
ndims{T,N}(::Type{AbstractArray{T,N}}) = N
ndims{T<:AbstractArray}(::Type{T}) = ndims(supertype(T))
length(t::AbstractArray) = prod(size(t))::Int
endof(a::AbstractArray) = length(a)
first(a::AbstractArray) = a[first(eachindex(a))]
function first(itr)
state = start(itr)
done(itr, state) && throw(ArgumentError("collection must be non-empty"))
next(itr, state)[1]
end
last(a) = a[end]
"""
stride(A, k)
Returns the distance in memory (in number of elements) between adjacent elements in dimension `k`.
"""
function stride(a::AbstractArray, i::Integer)
if i > ndims(a)
return length(a)
end
s = 1
for n=1:(i-1)
s *= size(a, n)
end
return s
end
strides{T}(A::AbstractArray{T,0}) = ()
"""
strides(A)
Returns a tuple of the memory strides in each dimension.
"""
strides(A::AbstractArray) = _strides((1,), A)
_strides{T,N}(out::NTuple{N}, A::AbstractArray{T,N}) = out
function _strides{M,T,N}(out::NTuple{M}, A::AbstractArray{T,N})
@_inline_meta
_strides((out..., out[M]*size(A, M)), A)
end
function isassigned(a::AbstractArray, i::Int...)
# TODO
try
a[i...]
true
catch
false
end
end
# used to compute "end" for last index
function trailingsize(A, n)
s = 1
for i=n:ndims(A)
s *= size(A,i)
end
return s
end
## Traits for array types ##
abstract LinearIndexing
immutable LinearFast <: LinearIndexing end
immutable LinearSlow <: LinearIndexing end
linearindexing(A::AbstractArray) = linearindexing(typeof(A))
linearindexing{T<:AbstractArray}(::Type{T}) = LinearSlow()
linearindexing{T<:Array}(::Type{T}) = LinearFast()
linearindexing{T<:Range}(::Type{T}) = LinearFast()
linearindexing(A::AbstractArray, B::AbstractArray) = linearindexing(linearindexing(A), linearindexing(B))
linearindexing(A::AbstractArray, B::AbstractArray...) = linearindexing(linearindexing(A), linearindexing(B...))
linearindexing(::LinearFast, ::LinearFast) = LinearFast()
linearindexing(::LinearIndexing, ::LinearIndexing) = LinearSlow()
abstract IndicesPerformance
immutable IndicesFast1D <: IndicesPerformance end # indices(A, d) is fast
immutable IndicesSlow1D <: IndicesPerformance end # indices(A) is better than indices(A,d)
indicesperformance(A::AbstractArray) = indicesperformance(typeof(A))
indicesperformance{T<:AbstractArray}(::Type{T}) = IndicesFast1D()
## Bounds checking ##
@generated function trailingsize{T,N,n}(A::AbstractArray{T,N}, ::Type{Val{n}})
(isa(n, Int) && isa(N, Int)) || error("Must have concrete type")
n > N && return 1
ex = :(size(A, $n))
for m = n+1:N
ex = :($ex * size(A, $m))
end
Expr(:block, Expr(:meta, :inline), ex)
end
# check along a single dimension
"""
checkindex(Bool, inds::UnitRange, index)
Return `true` if the given `index` is within the bounds of
`inds`. Custom types that would like to behave as indices for all
arrays can extend this method in order to provide a specialized bounds
checking implementation.
"""
checkindex(::Type{Bool}, inds::AbstractUnitRange, i) = throw(ArgumentError("unable to check bounds for indices of type $(typeof(i))"))
checkindex(::Type{Bool}, inds::AbstractUnitRange, i::Real) = (first(inds) <= i) & (i <= last(inds))
checkindex(::Type{Bool}, inds::AbstractUnitRange, ::Colon) = true
function checkindex(::Type{Bool}, inds::AbstractUnitRange, r::Range)
@_propagate_inbounds_meta
isempty(r) | (checkindex(Bool, inds, first(r)) & checkindex(Bool, inds, last(r)))
end
checkindex{N}(::Type{Bool}, indx::AbstractUnitRange, I::AbstractArray{Bool,N}) = N == 1 && indx == indices1(I)
function checkindex(::Type{Bool}, inds::AbstractUnitRange, I::AbstractArray)
@_inline_meta
b = true
for i in I
b &= checkindex(Bool, inds, i)
end
b
end
# check all indices/dimensions
# To make extension easier, avoid specializing checkbounds on index types
"""
checkbounds(Bool, array, indexes...)
Return `true` if the specified `indexes` are in bounds for the given `array`. Subtypes of
`AbstractArray` should specialize this method if they need to provide custom bounds checking
behaviors.
"""
function checkbounds(::Type{Bool}, A::AbstractArray, I...)
@_inline_meta
_checkbounds(Bool, indicesperformance(A), A, I...)
end
function _checkbounds(::Type{Bool}, ::IndicesSlow1D, A::AbstractArray, I...)
@_inline_meta
checkbounds_indices(indices(A), I)
end
_checkbounds(::Type{Bool}, ::IndicesSlow1D, A::AbstractArray, I::AbstractArray{Bool}) = _chkbnds(A, (true,), I)
# Bounds-checking for arrays for which indices(A) is faster than indices(A, d)
checkbounds_indices(::Tuple{}, ::Tuple{}) = true
checkbounds_indices(::Tuple{}, I::Tuple{Any}) = (@_inline_meta; checkindex(Bool, 1:1, I[1]))
checkbounds_indices(::Tuple{}, I::Tuple) = (@_inline_meta; checkindex(Bool, 1:1, I[1]) & checkbounds_indices((), tail(I)))
checkbounds_indices(inds::Tuple{Any}, I::Tuple{Any}) = (@_inline_meta; checkindex(Bool, inds[1], I[1]))
checkbounds_indices(inds::Tuple, I::Tuple{Any}) = (@_inline_meta; checkindex(Bool, 1:prod(map(dimlength, inds)), I[1]))
checkbounds_indices(inds::Tuple, I::Tuple) = (@_inline_meta; checkindex(Bool, inds[1], I[1]) & checkbounds_indices(tail(inds), tail(I)))
# Bounds-checking for arrays for which indices(A, d) is fast
function _checkbounds(::Type{Bool}, ::IndicesFast1D, A::AbstractArray, I...)
@_inline_meta
# checked::NTuple{M} means we have checked dimensions 1:M-1, now
# need to check dimension M. checked[M] indicates whether all the
# previous ones are in-bounds.
# By growing checked, it allows us to test whether we've processed
# the same number of dimensions as the array, even while
# supporting CartesianIndex
_chkbnds(A, (true,), I...)
end
checkbounds(::Type{Bool}, A::AbstractArray) = checkbounds(Bool, A, 1) # 0-d case
# Single logical array indexing:
_chkbnds(A::AbstractArray, ::NTuple{1,Bool}, I::AbstractArray{Bool}) = indices(A) == indices(I)
_chkbnds(A::AbstractArray, ::NTuple{1,Bool}, I::AbstractVector{Bool}) = length(A) == length(I)
_chkbnds(A::AbstractVector, ::NTuple{1,Bool}, I::AbstractArray{Bool}) = length(A) == length(I)
_chkbnds(A::AbstractVector, ::NTuple{1,Bool}, I::AbstractVector{Bool}) = indices(A) == indices(I)
# Linear indexing:
function _chkbnds(A::AbstractVector, ::NTuple{1,Bool}, I)
@_inline_meta
checkindex(Bool, indices1(A), I)
end
function _chkbnds(A::AbstractArray, ::NTuple{1,Bool}, I)
@_inline_meta
checkindex(Bool, 1:length(A), I)
end
# When all indices have been checked:
_chkbnds{M}(A, checked::NTuple{M,Bool}) = checked[M]
# When the number of indices matches the array dimensionality:
function _chkbnds{T,N}(A::AbstractArray{T,N}, checked::NTuple{N,Bool}, I1)
@_inline_meta
checked[N] & checkindex(Bool, indices(A, N), I1)
end
# When the last checked dimension is not equal to the array dimensionality:
# TODO: for #14770 (deprecating partial linear indexing), change to 1:trailingsize(...) to 1:1
function _chkbnds{T,N,M}(A::AbstractArray{T,N}, checked::NTuple{M,Bool}, I1)
@_inline_meta
checked[M] & checkindex(Bool, 1:trailingsize(A, Val{M}), I1)
end
# Checking an interior dimension:
function _chkbnds{T,N,M}(A::AbstractArray{T,N}, checked::NTuple{M,Bool}, I1, I...)
@_inline_meta
# grow checked by one
newchecked = (checked..., checked[M] & checkindex(Bool, indices(A, M), I1))
_chkbnds(A, newchecked, I...)
end
throw_boundserror(A, I) = (@_noinline_meta; throw(BoundsError(A, I)))
"""
checkbounds(array, indexes...)
Throw an error if the specified `indexes` are not in bounds for the given `array`.
"""
function checkbounds(A::AbstractArray, I...)
@_inline_meta
checkbounds(Bool, A, I...) || throw_boundserror(A, I)
end
checkbounds(A::AbstractArray) = checkbounds(A, 1) # 0-d case
# See also specializations in multidimensional
## Constructors ##
# default arguments to similar()
"""
similar(array, [element_type=eltype(array)], [dims=size(array)])
Create an uninitialized mutable array with the given element type and size, based upon the
given source array. The second and third arguments are both optional, defaulting to the
given array's `eltype` and `size`. The dimensions may be specified either as a single tuple
argument or as a series of integer arguments.
Custom AbstractArray subtypes may choose which specific array type is best-suited to return
for the given element type and dimensionality. If they do not specialize this method, the
default is an `Array{element_type}(dims...)`.
For example, `similar(1:10, 1, 4)` returns an uninitialized `Array{Int,2}` since ranges are
neither mutable nor support 2 dimensions:
julia> similar(1:10, 1, 4)
1×4 Array{Int64,2}:
4419743872 4374413872 4419743888 0
Conversely, `similar(trues(10,10), 2)` returns an uninitialized `BitVector` with two
elements since `BitArray`s are both mutable and can support 1-dimensional arrays:
julia> similar(trues(10,10), 2)
2-element BitArray{1}:
false
false
Since `BitArray`s can only store elements of type `Bool`, however, if you request a
different element type it will create a regular `Array` instead:
julia> similar(falses(10), Float64, 2, 4)
2×4 Array{Float64,2}:
2.18425e-314 2.18425e-314 2.18425e-314 2.18425e-314
2.18425e-314 2.18425e-314 2.18425e-314 2.18425e-314
"""
similar{T}(a::AbstractArray{T}) = similar(a, T)
similar( a::AbstractArray, T::Type) = similar(a, T, to_shape(indices(a)))
similar{T}(a::AbstractArray{T}, dims::Tuple) = similar(a, T, to_shape(dims))
similar{T}(a::AbstractArray{T}, dims::DimOrInd...) = similar(a, T, to_shape(dims))
similar( a::AbstractArray, T::Type, dims::DimOrInd...) = similar(a, T, to_shape(dims))
similar( a::AbstractArray, T::Type, dims) = similar(a, T, to_shape(dims))
# similar creates an Array by default
similar( a::AbstractArray, T::Type, dims::Dims) = Array{T}(dims)
to_shape(::Tuple{}) = ()
to_shape(dims::Dims) = dims
to_shape(dims::DimsOrInds) = map(to_shape, dims)
# each dimension
to_shape(i::Int) = i
to_shape(i::Integer) = Int(i)
to_shape(r::OneTo) = Int(last(r))
to_shape(r::UnitRange) = convert(UnitRange{Int}, r)
"""
similar(storagetype, indices)
Create an uninitialized mutable array analogous to that specified by
`storagetype`, but with `indices` specified by the last
argument. `storagetype` might be a type or a function.
**Examples**:
similar(Array{Int}, indices(A))
creates an array that "acts like" an `Array{Int}` (and might indeed be
backed by one), but which is indexed identically to `A`. If `A` has
conventional indexing, this will be identical to
`Array{Int}(size(A))`, but if `A` has unconventional indexing then the
indices of the result will match `A`.
similar(BitArray, (indices(A, 2),))
would create a 1-dimensional logical array whose indices match those
of the columns of `A`.
similar(dims->zeros(Int, dims), indices(A))
would create an array of `Int`, initialized to zero, matching the
indices of `A`.
"""
similar(f, shape::Tuple) = f(to_shape(shape))
similar(f, dims::DimOrInd...) = similar(f, dims)
## from general iterable to any array
function copy!(dest::AbstractArray, src)
destiter = eachindex(dest)
state = start(destiter)
for x in src
i, state = next(destiter, state)
dest[i] = x
end
return dest
end
function copy!(dest::AbstractArray, dstart::Integer, src)
i = Int(dstart)
for x in src
dest[i] = x
i += 1
end
return dest
end
# copy from an some iterable object into an AbstractArray
function copy!(dest::AbstractArray, dstart::Integer, src, sstart::Integer)
if (sstart < 1)
throw(ArgumentError(string("source start offset (",sstart,") is < 1")))
end
st = start(src)
for j = 1:(sstart-1)
if done(src, st)
throw(ArgumentError(string("source has fewer elements than required, ",
"expected at least ",sstart,", got ",j-1)))
end
_, st = next(src, st)
end
dn = done(src, st)
if dn
throw(ArgumentError(string("source has fewer elements than required, ",
"expected at least ",sstart,", got ",sstart-1)))
end
i = Int(dstart)
while !dn
val, st = next(src, st)
dest[i] = val
i += 1
dn = done(src, st)
end
return dest
end
# this method must be separate from the above since src might not have a length
function copy!(dest::AbstractArray, dstart::Integer, src, sstart::Integer, n::Integer)
n < 0 && throw(ArgumentError(string("tried to copy n=", n, " elements, but n should be nonnegative")))
n == 0 && return dest
dmax = dstart + n - 1
inds = linearindices(dest)
if (dstart ∉ inds || dmax ∉ inds) | (sstart < 1)
sstart < 1 && throw(ArgumentError(string("source start offset (",sstart,") is < 1")))
throw(BoundsError(dest, dstart:dmax))
end
st = start(src)
for j = 1:(sstart-1)
if done(src, st)
throw(ArgumentError(string("source has fewer elements than required, ",
"expected at least ",sstart,", got ",j-1)))
end
_, st = next(src, st)
end
i = Int(dstart)
while i <= dmax && !done(src, st)
val, st = next(src, st)
@inbounds dest[i] = val
i += 1
end
i <= dmax && throw(BoundsError(dest, i))
return dest
end
## copy between abstract arrays - generally more efficient
## since a single index variable can be used.
copy!(dest::AbstractArray, src::AbstractArray) =
copy!(linearindexing(dest), dest, linearindexing(src), src)
function copy!(::LinearIndexing, dest::AbstractArray, ::LinearIndexing, src::AbstractArray)
destinds, srcinds = linearindices(dest), linearindices(src)
isempty(srcinds) || (first(srcinds) ∈ destinds && last(srcinds) ∈ destinds) || throw(BoundsError(dest, srcinds))
@inbounds for i in srcinds
dest[i] = src[i]
end
return dest
end
function copy!(::LinearIndexing, dest::AbstractArray, ::LinearSlow, src::AbstractArray)
destinds, srcinds = linearindices(dest), linearindices(src)
isempty(srcinds) || (first(srcinds) ∈ destinds && last(srcinds) ∈ destinds) || throw(BoundsError(dest, srcinds))
i = 0
@inbounds for a in src
dest[i+=1] = a
end
return dest
end
function copy!(dest::AbstractArray, dstart::Integer, src::AbstractArray)
copy!(dest, dstart, src, first(linearindices(src)), length(src))
end
function copy!(dest::AbstractArray, dstart::Integer, src::AbstractArray, sstart::Integer)
srcinds = linearindices(src)
sstart ∈ srcinds || throw(BoundsError(src, sstart))
copy!(dest, dstart, src, sstart, last(srcinds)-sstart+1)
end
function copy!(dest::AbstractArray, dstart::Integer,
src::AbstractArray, sstart::Integer,
n::Integer)
n == 0 && return dest
n < 0 && throw(ArgumentError(string("tried to copy n=", n, " elements, but n should be nonnegative")))
destinds, srcinds = linearindices(dest), linearindices(src)
(dstart ∈ destinds && dstart+n-1 ∈ destinds) || throw(BoundsError(dest, dstart:dstart+n-1))
(sstart ∈ srcinds && sstart+n-1 ∈ srcinds) || throw(BoundsError(src, sstart:sstart+n-1))
@inbounds for i = 0:(n-1)
dest[dstart+i] = src[sstart+i]
end
return dest
end
function copy(a::AbstractArray)
@_propagate_inbounds_meta
copymutable(a)
end
function copy!{R,S}(B::AbstractVecOrMat{R}, ir_dest::Range{Int}, jr_dest::Range{Int},
A::AbstractVecOrMat{S}, ir_src::Range{Int}, jr_src::Range{Int})
if length(ir_dest) != length(ir_src)
throw(ArgumentError(string("source and destination must have same size (got ",
length(ir_src)," and ",length(ir_dest),")")))
end
if length(jr_dest) != length(jr_src)
throw(ArgumentError(string("source and destination must have same size (got ",
length(jr_src)," and ",length(jr_dest),")")))
end
@boundscheck checkbounds(B, ir_dest, jr_dest)
@boundscheck checkbounds(A, ir_src, jr_src)
jdest = first(jr_dest)
for jsrc in jr_src
idest = first(ir_dest)
for isrc in ir_src
B[idest,jdest] = A[isrc,jsrc]
idest += step(ir_dest)
end
jdest += step(jr_dest)
end
return B
end
function copy_transpose!{R,S}(B::AbstractVecOrMat{R}, ir_dest::Range{Int}, jr_dest::Range{Int},
A::AbstractVecOrMat{S}, ir_src::Range{Int}, jr_src::Range{Int})
if length(ir_dest) != length(jr_src)
throw(ArgumentError(string("source and destination must have same size (got ",
length(jr_src)," and ",length(ir_dest),")")))
end
if length(jr_dest) != length(ir_src)
throw(ArgumentError(string("source and destination must have same size (got ",
length(ir_src)," and ",length(jr_dest),")")))
end
@boundscheck checkbounds(B, ir_dest, jr_dest)
@boundscheck checkbounds(A, ir_src, jr_src)
idest = first(ir_dest)
for jsrc in jr_src
jdest = first(jr_dest)
for isrc in ir_src
B[idest,jdest] = A[isrc,jsrc]
jdest += step(jr_dest)
end
idest += step(ir_dest)
end
return B
end
function copymutable(a::AbstractArray)
@_propagate_inbounds_meta
copy!(similar(a), a)
end
copymutable(itr) = collect(itr)
"""
copymutable(a)
Make a mutable copy of an array or iterable `a`. For `a::Array`,
this is equivalent to `copy(a)`, but for other array types it may
differ depending on the type of `similar(a)`. For generic iterables
this is equivalent to `collect(a)`.
"""
copymutable
zero{T}(x::AbstractArray{T}) = fill!(similar(x), zero(T))
## iteration support for arrays by iterating over `eachindex` in the array ##
# Allows fast iteration by default for both LinearFast and LinearSlow arrays
# While the definitions for LinearFast are all simple enough to inline on their
# own, LinearSlow's CartesianRange is more complicated and requires explicit
# inlining.
start(A::AbstractArray) = (@_inline_meta; itr = eachindex(A); (itr, start(itr)))
next(A::AbstractArray,i) = (@_propagate_inbounds_meta; (idx, s) = next(i[1], i[2]); (A[idx], (i[1], s)))
done(A::AbstractArray,i) = (@_propagate_inbounds_meta; done(i[1], i[2]))
# eachindex iterates over all indices. LinearSlow definitions are later.
eachindex(A::AbstractVector) = (@_inline_meta(); indices1(A))
eachindex(A::AbstractArray) = (@_inline_meta(); eachindex(linearindexing(A), A))
function eachindex(A::AbstractArray, B::AbstractArray)
@_inline_meta
eachindex(linearindexing(A,B), A, B)
end
function eachindex(A::AbstractArray, B::AbstractArray...)
@_inline_meta
eachindex(linearindexing(A,B...), A, B...)
end
eachindex(::LinearFast, A::AbstractArray) = linearindices(A)
function eachindex(::LinearFast, A::AbstractArray, B::AbstractArray...)
@_inline_meta
1:_maxlength(A, B...)
end
_maxlength(A) = length(A)
function _maxlength(A, B, C...)
@_inline_meta
max(length(A), _maxlength(B, C...))
end
isempty(a::AbstractArray) = (length(a) == 0)
## Conversions ##
convert{T,N }(::Type{AbstractArray{T,N}}, A::AbstractArray{T,N}) = A
convert{T,S,N}(::Type{AbstractArray{T,N}}, A::AbstractArray{S,N}) = copy!(similar(A,T), A)
convert{T,S,N}(::Type{AbstractArray{T }}, A::AbstractArray{S,N}) = convert(AbstractArray{T,N}, A)
convert{T,N}(::Type{Array}, A::AbstractArray{T,N}) = convert(Array{T,N}, A)
full(x::AbstractArray) = x
map(::Type{Integer}, a::Array) = map!(Integer, similar(a,typeof(Integer(one(eltype(a))))), a)
map(::Type{Signed}, a::Array) = map!(Signed, similar(a,typeof(Signed(one(eltype(a))))), a)
map(::Type{Unsigned}, a::Array) = map!(Unsigned, similar(a,typeof(Unsigned(one(eltype(a))))), a)
## range conversions ##
map{T<:Real}(::Type{T}, r::StepRange) = T(r.start):T(r.step):T(last(r))
map{T<:Real}(::Type{T}, r::UnitRange) = T(r.start):T(last(r))
map{T<:AbstractFloat}(::Type{T}, r::FloatRange) = FloatRange(T(r.start), T(r.step), r.len, T(r.divisor))
function map{T<:AbstractFloat}(::Type{T}, r::LinSpace)
new_len = T(r.len)
new_len == r.len || error("$r: too long for $T")
LinSpace(T(r.start), T(r.stop), new_len, T(r.divisor))
end
## unsafe/pointer conversions ##
# note: the following type definitions don't mean any AbstractArray is convertible to
# a data Ref. they just map the array element type to the pointer type for
# convenience in cases that work.
pointer{T}(x::AbstractArray{T}) = unsafe_convert(Ptr{T}, x)
pointer{T}(x::AbstractArray{T}, i::Integer) = (@_inline_meta; unsafe_convert(Ptr{T},x) + (i-first(linearindices(x)))*elsize(x))
## Approach:
# We only define one fallback method on getindex for all argument types.
# That dispatches to an (inlined) internal _getindex function, where the goal is
# to transform the indices such that we can call the only getindex method that
# we require the type A{T,N} <: AbstractArray{T,N} to define; either:
# getindex(::A, ::Int) # if linearindexing(A) == LinearFast() OR
# getindex{T,N}(::A{T,N}, ::Vararg{Int, N}) # if LinearSlow()
# If the subtype hasn't defined the required method, it falls back to the
# _getindex function again where an error is thrown to prevent stack overflows.
function getindex(A::AbstractArray, I...)
@_propagate_inbounds_meta
_getindex(linearindexing(A), A, I...)
end
function unsafe_getindex(A::AbstractArray, I...)
@_inline_meta
@inbounds r = getindex(A, I...)
r
end
## Internal definitions
_getindex(::LinearIndexing, A::AbstractArray, I...) = error("indexing $(typeof(A)) with types $(typeof(I)) is not supported")
## LinearFast Scalar indexing: canonical method is one Int
_getindex(::LinearFast, A::AbstractVector, ::Int) = error("indexing not defined for ", typeof(A))
_getindex(::LinearFast, A::AbstractArray, ::Int) = error("indexing not defined for ", typeof(A))
_getindex{T}(::LinearFast, A::AbstractArray{T,0}) = A[1]
_getindex(::LinearFast, A::AbstractArray, i::Real) = (@_propagate_inbounds_meta; getindex(A, to_index(i)))
function _getindex{T,N}(::LinearFast, A::AbstractArray{T,N}, I::Vararg{Real,N})
# We must check bounds for sub2ind; so we can then use @inbounds
@_inline_meta
J = to_indexes(I...)
@boundscheck checkbounds(A, J...)
@inbounds r = getindex(A, sub2ind(A, J...))
r
end
function _getindex(::LinearFast, A::AbstractVector, I1::Real, I::Real...)
@_inline_meta
J = to_indexes(I1, I...)
@boundscheck checkbounds(A, J...)
@inbounds r = getindex(A, J[1])
r
end
function _getindex(::LinearFast, A::AbstractArray, I::Real...) # TODO: DEPRECATE FOR #14770
@_inline_meta
J = to_indexes(I...)
@boundscheck checkbounds(A, J...)
@inbounds r = getindex(A, sub2ind(A, J...))
r
end
## LinearSlow Scalar indexing: Canonical method is full dimensionality of Ints
_getindex{T,N}(::LinearSlow, A::AbstractArray{T,N}, ::Vararg{Int, N}) = error("indexing not defined for ", typeof(A))
_getindex{T,N}(::LinearSlow, A::AbstractArray{T,N}, I::Vararg{Real, N}) = (@_propagate_inbounds_meta; getindex(A, to_indexes(I...)...))
function _getindex(::LinearSlow, A::AbstractArray, i::Real)
# ind2sub requires all dimensions to be > 0; may as well just check bounds
@_inline_meta
@boundscheck checkbounds(A, i)
@inbounds r = getindex(A, ind2sub(A, to_index(i))...)
r
end
@generated function _getindex{T,AN}(::LinearSlow, A::AbstractArray{T,AN}, I::Real...) # TODO: DEPRECATE FOR #14770
N = length(I)
if N > AN
# Drop trailing ones
Isplat = Expr[:(I[$d]) for d = 1:AN]
Osplat = Expr[:(to_index(I[$d]) == 1) for d = AN+1:N]
quote
@_propagate_inbounds_meta
@boundscheck (&)($(Osplat...)) || throw_boundserror(A, I)
getindex(A, $(Isplat...))
end
else
# Expand the last index into the appropriate number of indices
Isplat = Expr[:(I[$d]) for d = 1:N-1]
sz = Expr(:tuple)
sz.args = Expr[:(size(A, $d)) for d=max(N,1):AN]
szcheck = Expr[:(size(A, $d) > 0) for d=max(N,1):AN]
last_idx = N > 0 ? :(to_index(I[$N])) : 1
quote
# ind2sub requires all dimensions to be > 0:
@_propagate_inbounds_meta
@boundscheck (&)($(szcheck...)) || throw_boundserror(A, I)
getindex(A, $(Isplat...), ind2sub($sz, $last_idx)...)
end
end
end
## Setindex! is defined similarly. We first dispatch to an internal _setindex!
# function that allows dispatch on array storage
function setindex!(A::AbstractArray, v, I...)
@_propagate_inbounds_meta
_setindex!(linearindexing(A), A, v, I...)
end
function unsafe_setindex!(A::AbstractArray, v, I...)
@_inline_meta
@inbounds r = setindex!(A, v, I...)
r
end
## Internal defitions
_setindex!(::LinearIndexing, A::AbstractArray, v, I...) = error("indexing $(typeof(A)) with types $(typeof(I)) is not supported")
## LinearFast Scalar indexing
_setindex!(::LinearFast, A::AbstractVector, v, ::Int) = error("indexed assignment not defined for ", typeof(A))
_setindex!(::LinearFast, A::AbstractArray, v, ::Int) = error("indexed assignment not defined for ", typeof(A))
_setindex!{T}(::LinearFast, A::AbstractArray{T,0}, v) = (@_propagate_inbounds_meta; setindex!(A, v, 1))
_setindex!(::LinearFast, A::AbstractArray, v, i::Real) = (@_propagate_inbounds_meta; setindex!(A, v, to_index(i)))
function _setindex!{T,N}(::LinearFast, A::AbstractArray{T,N}, v, I::Vararg{Real,N})
# We must check bounds for sub2ind; so we can then use @inbounds
@_inline_meta
J = to_indexes(I...)
@boundscheck checkbounds(A, J...)
@inbounds r = setindex!(A, v, sub2ind(A, J...))
r
end
function _setindex!(::LinearFast, A::AbstractVector, v, I1::Real, I::Real...)
@_inline_meta
J = to_indexes(I1, I...)
@boundscheck checkbounds(A, J...)
@inbounds r = setindex!(A, v, J[1])
r
end
function _setindex!(::LinearFast, A::AbstractArray, v, I::Real...) # TODO: DEPRECATE FOR #14770
@_inline_meta
J = to_indexes(I...)
@boundscheck checkbounds(A, J...)
@inbounds r = setindex!(A, v, sub2ind(A, J...))
r
end
# LinearSlow Scalar indexing
_setindex!{T,N}(::LinearSlow, A::AbstractArray{T,N}, v, ::Vararg{Int, N}) = error("indexed assignment not defined for ", typeof(A))
_setindex!{T,N}(::LinearSlow, A::AbstractArray{T,N}, v, I::Vararg{Real, N}) = (@_propagate_inbounds_meta; setindex!(A, v, to_indexes(I...)...))
function _setindex!(::LinearSlow, A::AbstractArray, v, i::Real)
# ind2sub requires all dimensions to be > 0; may as well just check bounds
@_inline_meta
@boundscheck checkbounds(A, i)
@inbounds r = setindex!(A, v, ind2sub(A, to_index(i))...)
r
end
@generated function _setindex!{T,AN}(::LinearSlow, A::AbstractArray{T,AN}, v, I::Real...) # TODO: DEPRECATE FOR #14770
N = length(I)
if N > AN
# Drop trailing ones
Isplat = Expr[:(I[$d]) for d = 1:AN]
Osplat = Expr[:(to_index(I[$d]) == 1) for d = AN+1:N]
quote
# We only check the trailing ones, so just propagate @inbounds state
@_propagate_inbounds_meta
@boundscheck (&)($(Osplat...)) || throw_boundserror(A, I)
setindex!(A, v, $(Isplat...))
end
else
# Expand the last index into the appropriate number of indices
Isplat = Expr[:(I[$d]) for d = 1:N-1]
sz = Expr(:tuple)
sz.args = Expr[:(size(A, $d)) for d=max(N,1):AN]
szcheck = Expr[:(size(A, $d) > 0) for d=max(N,1):AN]
last_idx = N > 0 ? :(to_index(I[$N])) : 1
quote
# ind2sub requires all dimensions to be > 0:
@_propagate_inbounds_meta
@boundscheck (&)($(szcheck...)) || throw_boundserror(A, I)
setindex!(A, v, $(Isplat...), ind2sub($sz, $last_idx)...)
end
end
end
## get (getindex with a default value) ##
typealias RangeVecIntList{A<:AbstractVector{Int}} Union{Tuple{Vararg{Union{Range, AbstractVector{Int}}}}, AbstractVector{UnitRange{Int}}, AbstractVector{Range{Int}}, AbstractVector{A}}
get(A::AbstractArray, i::Integer, default) = checkbounds(Bool, A, i) ? A[i] : default
get(A::AbstractArray, I::Tuple{}, default) = similar(A, typeof(default), 0)
get(A::AbstractArray, I::Dims, default) = checkbounds(Bool, A, I...) ? A[I...] : default
function get!{T}(X::AbstractVector{T}, A::AbstractVector, I::Union{Range, AbstractVector{Int}}, default::T)
# 1d is not linear indexing
ind = findin(I, indices1(A))
X[ind] = A[I[ind]]
Xind = indices1(X)
X[first(Xind):first(ind)-1] = default
X[last(ind)+1:last(Xind)] = default
X
end
function get!{T}(X::AbstractArray{T}, A::AbstractArray, I::Union{Range, AbstractVector{Int}}, default::T)
# Linear indexing
ind = findin(I, 1:length(A))
X[ind] = A[I[ind]]
X[1:first(ind)-1] = default
X[last(ind)+1:length(X)] = default
X
end
get(A::AbstractArray, I::Range, default) = get!(similar(A, typeof(default), index_shape(A, I)), A, I, default)
# TODO: DEPRECATE FOR #14770 (just the partial linear indexing part)
function get!{T}(X::AbstractArray{T}, A::AbstractArray, I::RangeVecIntList, default::T)
fill!(X, default)
dst, src = indcopy(size(A), I)
X[dst...] = A[src...]
X
end
get(A::AbstractArray, I::RangeVecIntList, default) = get!(similar(A, typeof(default), index_shape(A, I...)), A, I, default)
## structured matrix methods ##
replace_in_print_matrix(A::AbstractMatrix,i::Integer,j::Integer,s::AbstractString) = s
replace_in_print_matrix(A::AbstractVector,i::Integer,j::Integer,s::AbstractString) = s
## Concatenation ##
promote_eltype() = Bottom
promote_eltype(v1, vs...) = promote_type(eltype(v1), promote_eltype(vs...))
#TODO: ERROR CHECK
cat(catdim::Integer) = Array{Any}(0)
vcat() = Array{Any}(0)
hcat() = Array{Any}(0)
typed_vcat{T}(::Type{T}) = Array{T}(0)
typed_hcat{T}(::Type{T}) = Array{T}(0)
## cat: special cases
vcat{T}(X::T...) = T[ X[i] for i=1:length(X) ]
vcat{T<:Number}(X::T...) = T[ X[i] for i=1:length(X) ]
hcat{T}(X::T...) = T[ X[j] for i=1, j=1:length(X) ]
hcat{T<:Number}(X::T...) = T[ X[j] for i=1, j=1:length(X) ]
vcat(X::Number...) = hvcat_fill(Array{promote_typeof(X...)}(length(X)), X)
hcat(X::Number...) = hvcat_fill(Array{promote_typeof(X...)}(1,length(X)), X)
typed_vcat{T}(::Type{T}, X::Number...) = hvcat_fill(Array{T}(length(X)), X)
typed_hcat{T}(::Type{T}, X::Number...) = hvcat_fill(Array{T}(1,length(X)), X)
vcat(V::AbstractVector...) = typed_vcat(promote_eltype(V...), V...)
vcat{T}(V::AbstractVector{T}...) = typed_vcat(T, V...)
function typed_vcat{T}(::Type{T}, V::AbstractVector...)
n::Int = 0
for Vk in V
n += length(Vk)
end
a = similar(full(V[1]), T, n)
pos = 1
for k=1:length(V)
Vk = V[k]
p1 = pos+length(Vk)-1
a[pos:p1] = Vk
pos = p1+1
end
a
end
hcat(A::AbstractVecOrMat...) = typed_hcat(promote_eltype(A...), A...)
hcat{T}(A::AbstractVecOrMat{T}...) = typed_hcat(T, A...)
function typed_hcat{T}(::Type{T}, A::AbstractVecOrMat...)
nargs = length(A)
nrows = size(A[1], 1)
ncols = 0
dense = true
for j = 1:nargs
Aj = A[j]
if size(Aj, 1) != nrows
throw(ArgumentError("number of rows of each array must match (got $(map(x->size(x,1), A)))"))
end
dense &= isa(Aj,Array)
nd = ndims(Aj)
ncols += (nd==2 ? size(Aj,2) : 1)
end
B = similar(full(A[1]), T, nrows, ncols)
pos = 1
if dense
for k=1:nargs
Ak = A[k]
n = length(Ak)
copy!(B, pos, Ak, 1, n)
pos += n
end
else
for k=1:nargs
Ak = A[k]
p1 = pos+(isa(Ak,AbstractMatrix) ? size(Ak, 2) : 1)-1
B[:, pos:p1] = Ak
pos = p1+1
end
end
return B
end
vcat(A::AbstractMatrix...) = typed_vcat(promote_eltype(A...), A...)
vcat{T}(A::AbstractMatrix{T}...) = typed_vcat(T, A...)
function typed_vcat{T}(::Type{T}, A::AbstractMatrix...)
nargs = length(A)
nrows = sum(a->size(a, 1), A)::Int
ncols = size(A[1], 2)
for j = 2:nargs
if size(A[j], 2) != ncols
throw(ArgumentError("number of columns of each array must match (got $(map(x->size(x,2), A)))"))
end
end
B = similar(full(A[1]), T, nrows, ncols)
pos = 1
for k=1:nargs
Ak = A[k]
p1 = pos+size(Ak,1)-1
B[pos:p1, :] = Ak
pos = p1+1
end
return B
end
## cat: general case
function cat(catdims, X...)
T = promote_type(map(x->isa(x,AbstractArray) ? eltype(x) : typeof(x), X)...)
cat_t(catdims, T, X...)
end
function cat_t(catdims, typeC::Type, X...)
catdims = collect(catdims)
nargs = length(X)
ndimsX = Int[isa(a,AbstractArray) ? ndims(a) : 0 for a in X]
ndimsC = max(maximum(ndimsX), maximum(catdims))
catsizes = zeros(Int,(nargs,length(catdims)))
dims2cat = zeros(Int,ndimsC)
for k = 1:length(catdims)
dims2cat[catdims[k]]=k
end
dimsC = Int[d <= ndimsX[1] ? size(X[1],d) : 1 for d=1:ndimsC]
for k = 1:length(catdims)
catsizes[1,k] = dimsC[catdims[k]]
end
for i = 2:nargs
for d = 1:ndimsC
currentdim = (d <= ndimsX[i] ? size(X[i],d) : 1)
if dims2cat[d] != 0
dimsC[d] += currentdim
catsizes[i,dims2cat[d]] = currentdim
elseif dimsC[d] != currentdim
throw(DimensionMismatch(string("mismatch in dimension ",d,
" (expected ",dimsC[d],
" got ",currentdim,")")))
end
end
end
C = similar(isa(X[1],AbstractArray) ? full(X[1]) : [X[1]], typeC, tuple(dimsC...))
if length(catdims)>1
fill!(C,0)
end
offsets = zeros(Int,length(catdims))
for i=1:nargs
cat_one = [ dims2cat[d] == 0 ? (1:dimsC[d]) : (offsets[dims2cat[d]]+(1:catsizes[i,dims2cat[d]]))
for d=1:ndimsC ]
C[cat_one...] = X[i]
for k = 1:length(catdims)
offsets[k] += catsizes[i,k]
end
end
return C