https://github.com/JuliaLang/julia
Tip revision: 9c76c3e89a8c384f324c2e0b84ad28ceef9ab69d authored by Tony Kelman on 09 September 2016, 01:43:44 UTC
Tag v0.5.0-rc4
Tag v0.5.0-rc4
Tip revision: 9c76c3e
array.jl
# This file is a part of Julia. License is MIT: http://julialang.org/license
## array.jl: Dense arrays
typealias Vector{T} Array{T,1}
typealias Matrix{T} Array{T,2}
typealias VecOrMat{T} Union{Vector{T}, Matrix{T}}
typealias DenseVector{T} DenseArray{T,1}
typealias DenseMatrix{T} DenseArray{T,2}
typealias DenseVecOrMat{T} Union{DenseVector{T}, DenseMatrix{T}}
## Basic functions ##
import Core: arraysize, arrayset, arrayref
size(a::Array, d) = arraysize(a, d)
size(a::Vector) = (arraysize(a,1),)
size(a::Matrix) = (arraysize(a,1), arraysize(a,2))
size(a::Array) = (@_inline_meta; _size((), a))
_size{_,N}(out::NTuple{N}, A::Array{_,N}) = out
function _size{_,M,N}(out::NTuple{M}, A::Array{_,N})
@_inline_meta
_size((out..., size(A,M+1)), A)
end
asize_from(a::Array, n) = n > ndims(a) ? () : (arraysize(a,n), asize_from(a, n+1)...)
length(a::Array) = arraylen(a)
elsize{T}(a::Array{T}) = isbits(T) ? sizeof(T) : sizeof(Ptr)
sizeof(a::Array) = elsize(a) * length(a)
function isassigned{T}(a::Array{T}, i::Int...)
ii = sub2ind(size(a), i...)
1 <= ii <= length(a) || return false
ccall(:jl_array_isassigned, Cint, (Any, UInt), a, ii-1) == 1
end
## copy ##
function unsafe_copy!{T}(dest::Ptr{T}, src::Ptr{T}, n)
# Do not use this to copy data between pointer arrays.
# It can't be made safe no matter how carefully you checked.
ccall(:memmove, Ptr{Void}, (Ptr{Void}, Ptr{Void}, UInt),
dest, src, n*sizeof(T))
return dest
end
function unsafe_copy!{T}(dest::Array{T}, doffs, src::Array{T}, soffs, n)
if isbits(T)
unsafe_copy!(pointer(dest, doffs), pointer(src, soffs), n)
else
ccall(:jl_array_ptr_copy, Void, (Any, Ptr{Void}, Any, Ptr{Void}, Int),
dest, pointer(dest, doffs), src, pointer(src, soffs), n)
end
return dest
end
function copy!{T}(dest::Array{T}, doffs::Integer, src::Array{T}, soffs::Integer, n::Integer)
n == 0 && return dest
n > 0 || throw(ArgumentError(string("tried to copy n=", n, " elements, but n should be nonnegative")))
if soffs < 1 || doffs < 1 || soffs+n-1 > length(src) || doffs+n-1 > length(dest)
throw(BoundsError())
end
unsafe_copy!(dest, doffs, src, soffs, n)
end
copy!{T}(dest::Array{T}, src::Array{T}) = copy!(dest, 1, src, 1, length(src))
copy{T<:Array}(a::T) = ccall(:jl_array_copy, Ref{T}, (Any,), a)
function reinterpret{T,S}(::Type{T}, a::Array{S,1})
nel = Int(div(length(a)*sizeof(S),sizeof(T)))
# TODO: maybe check that remainder is zero?
return reinterpret(T, a, (nel,))
end
function reinterpret{T,S}(::Type{T}, a::Array{S})
if sizeof(S) != sizeof(T)
throw(ArgumentError("result shape not specified"))
end
reinterpret(T, a, size(a))
end
function reinterpret{T,S,N}(::Type{T}, a::Array{S}, dims::NTuple{N,Int})
if !isbits(T)
throw(ArgumentError("cannot reinterpret Array{$(S)} to ::Type{Array{$(T)}}, type $(T) is not a bitstype"))
end
if !isbits(S)
throw(ArgumentError("cannot reinterpret Array{$(S)} to ::Type{Array{$(T)}}, type $(S) is not a bitstype"))
end
nel = div(length(a)*sizeof(S),sizeof(T))
if prod(dims) != nel
throw(DimensionMismatch("new dimensions $(dims) must be consistent with array size $(nel)"))
end
ccall(:jl_reshape_array, Array{T,N}, (Any, Any, Any), Array{T,N}, a, dims)
end
# reshaping to same # of dimensions
function reshape{T,N}(a::Array{T,N}, dims::NTuple{N,Int})
if prod(dims) != length(a)
throw(DimensionMismatch("new dimensions $(dims) must be consistent with array size $(length(a))"))
end
if dims == size(a)
return a
end
ccall(:jl_reshape_array, Array{T,N}, (Any, Any, Any), Array{T,N}, a, dims)
end
# reshaping to different # of dimensions
function reshape{T,N}(a::Array{T}, dims::NTuple{N,Int})
if prod(dims) != length(a)
throw(DimensionMismatch("new dimensions $(dims) must be consistent with array size $(length(a))"))
end
ccall(:jl_reshape_array, Array{T,N}, (Any, Any, Any), Array{T,N}, a, dims)
end
## Constructors ##
similar{T}(a::Array{T,1}) = Array{T,1}(size(a,1))
similar{T}(a::Array{T,2}) = Array{T,2}(size(a,1), size(a,2))
similar{T}(a::Array{T,1}, S::Type) = Array{S,1}(size(a,1))
similar{T}(a::Array{T,2}, S::Type) = Array{S,2}(size(a,1), size(a,2))
similar{T}(a::Array{T}, m::Int) = Array{T,1}(m)
similar{N}(a::Array, T::Type, dims::Dims{N}) = Array{T,N}(dims)
similar{T,N}(a::Array{T}, dims::Dims{N}) = Array{T,N}(dims)
# T[x...] constructs Array{T,1}
function getindex{T}(::Type{T}, vals...)
a = Array{T,1}(length(vals))
@inbounds for i = 1:length(vals)
a[i] = vals[i]
end
return a
end
getindex{T}(::Type{T}) = (@_inline_meta; Array{T,1}(0))
getindex{T}(::Type{T}, x) = (@_inline_meta; a = Array{T,1}(1); @inbounds a[1] = x; a)
getindex{T}(::Type{T}, x, y) = (@_inline_meta; a = Array{T,1}(2); @inbounds (a[1] = x; a[2] = y); a)
getindex{T}(::Type{T}, x, y, z) = (@_inline_meta; a = Array{T,1}(3); @inbounds (a[1] = x; a[2] = y; a[3] = z); a)
function getindex(::Type{Any}, vals::ANY...)
a = Array{Any,1}(length(vals))
@inbounds for i = 1:length(vals)
a[i] = vals[i]
end
return a
end
getindex(::Type{Any}) = Array{Any,1}(0)
function fill!(a::Union{Array{UInt8}, Array{Int8}}, x::Integer)
ccall(:memset, Ptr{Void}, (Ptr{Void}, Cint, Csize_t), a, x, length(a))
return a
end
function fill!{T<:Union{Integer,AbstractFloat}}(a::Array{T}, x)
xT = convert(T, x)
for i in eachindex(a)
@inbounds a[i] = xT
end
return a
end
fill(v, dims::Dims) = fill!(Array{typeof(v)}(dims), v)
fill(v, dims::Integer...) = fill!(Array{typeof(v)}(dims...), v)
for (fname, felt) in ((:zeros,:zero), (:ones,:one))
@eval begin
($fname)(T::Type, dims...) = fill!(Array{T}(dims...), ($felt)(T))
($fname)(dims...) = fill!(Array{Float64}(dims...), ($felt)(Float64))
($fname){T}(A::AbstractArray{T}) = fill!(similar(A), ($felt)(T))
end
end
"""
eye([T::Type=Float64,] m::Integer, n::Integer)
`m`-by-`n` identity matrix.
The default element type is `Float64`.
"""
function eye(T::Type, m::Integer, n::Integer)
a = zeros(T,m,n)
for i = 1:min(m,n)
a[i,i] = one(T)
end
return a
end
eye(m::Integer, n::Integer) = eye(Float64, m, n)
eye(T::Type, n::Integer) = eye(T, n, n)
"""
eye([T::Type=Float64,] n::Integer)
`n`-by-`n` identity matrix.
The default element type is `Float64`.
"""
eye(n::Integer) = eye(Float64, n)
"""
eye(A)
Constructs an identity matrix of the same dimensions and type as `A`.
```jldoctest
julia> A = [1 2 3; 4 5 6; 7 8 9]
3×3 Array{Int64,2}:
1 2 3
4 5 6
7 8 9
julia> eye(A)
3×3 Array{Int64,2}:
1 0 0
0 1 0
0 0 1
```
Note the difference from [`ones`](:func:`ones`).
"""
eye{T}(x::AbstractMatrix{T}) = eye(T, size(x, 1), size(x, 2))
function one{T}(x::AbstractMatrix{T})
m,n = size(x)
m==n || throw(DimensionMismatch("multiplicative identity defined only for square matrices"))
eye(T, m)
end
## Conversions ##
convert{T}(::Type{Vector}, x::AbstractVector{T}) = convert(Vector{T}, x)
convert{T}(::Type{Matrix}, x::AbstractMatrix{T}) = convert(Matrix{T}, x)
convert{T,n}(::Type{Array{T}}, x::Array{T,n}) = x
convert{T,n}(::Type{Array{T,n}}, x::Array{T,n}) = x
convert{T,n,S}(::Type{Array{T}}, x::AbstractArray{S, n}) = convert(Array{T, n}, x)
convert{T,n,S}(::Type{Array{T,n}}, x::AbstractArray{S,n}) = copy!(Array{T,n}(size(x)), x)
promote_rule{T,n,S}(::Type{Array{T,n}}, ::Type{Array{S,n}}) = Array{promote_type(T,S),n}
## copying iterators to containers
"""
collect(element_type, collection)
Return an `Array` with the given element type of all items in a collection or iterable.
The result has the same shape and number of dimensions as `collection`.
"""
collect{T}(::Type{T}, itr) = _collect(T, itr, iteratorsize(itr))
_collect{T}(::Type{T}, itr, isz::HasLength) = copy!(Array{T,1}(Int(length(itr)::Integer)), itr)
_collect{T}(::Type{T}, itr, isz::HasShape) = copy!(similar(Array{T}, indices(itr)), itr)
function _collect{T}(::Type{T}, itr, isz::SizeUnknown)
a = Array{T,1}(0)
for x in itr
push!(a,x)
end
return a
end
# make a collection similar to `c` and appropriate for collecting `itr`
_similar_for(c::AbstractArray, T, itr, ::SizeUnknown) = similar(c, T, 0)
_similar_for(c::AbstractArray, T, itr, ::HasLength) = similar(c, T, Int(length(itr)::Integer))
_similar_for(c::AbstractArray, T, itr, ::HasShape) = similar(c, T, indices(itr))
_similar_for(c, T, itr, isz) = similar(c, T)
"""
collect(collection)
Return an `Array` of all items in a collection or iterator. For associative collections, returns
`Pair{KeyType, ValType}`. If the argument is array-like or is an iterator with the `HasShape()`
trait, the result will have the same shape and number of dimensions as the argument.
"""
collect(itr) = _collect(1:1 #= Array =#, itr, iteratoreltype(itr), iteratorsize(itr))
collect_similar(cont, itr) = _collect(cont, itr, iteratoreltype(itr), iteratorsize(itr))
_collect(cont, itr, ::HasEltype, isz::Union{HasLength,HasShape}) =
copy!(_similar_for(cont, eltype(itr), itr, isz), itr)
function _collect(cont, itr, ::HasEltype, isz::SizeUnknown)
a = _similar_for(cont, eltype(itr), itr, isz)
for x in itr
push!(a,x)
end
return a
end
if isdefined(Core, :Inference)
_default_eltype(itrt::ANY) = Core.Inference.return_type(first, Tuple{itrt})
else
_default_eltype(itr::ANY) = Any
end
_array_for{T}(::Type{T}, itr, ::HasLength) = Array{T,1}(Int(length(itr)::Integer))
_array_for{T}(::Type{T}, itr, ::HasShape) = similar(Array{T}, indices(itr))
function collect(itr::Generator)
isz = iteratorsize(itr.iter)
et = _default_eltype(typeof(itr))
if isa(isz, SizeUnknown)
return grow_to!(Array{et,1}(0), itr)
else
st = start(itr)
if done(itr,st)
return _array_for(et, itr.iter, isz)
end
v1, st = next(itr, st)
collect_to_with_first!(_array_for(typeof(v1), itr.iter, isz), v1, itr, st)
end
end
_collect(c, itr, ::EltypeUnknown, isz::SizeUnknown) =
grow_to!(_similar_for(c, _default_eltype(typeof(itr)), itr, isz), itr)
function _collect(c, itr, ::EltypeUnknown, isz::Union{HasLength,HasShape})
st = start(itr)
if done(itr,st)
return _similar_for(c, _default_eltype(typeof(itr)), itr, isz)
end
v1, st = next(itr, st)
collect_to_with_first!(_similar_for(c, typeof(v1), itr, isz), v1, itr, st)
end
function collect_to_with_first!(dest::AbstractArray, v1, itr, st)
i1 = first(linearindices(dest))
dest[i1] = v1
return collect_to!(dest, itr, i1+1, st)
end
function collect_to_with_first!(dest, v1, itr, st)
push!(dest, v1)
return grow_to!(dest, itr, st)
end
function collect_to!{T}(dest::AbstractArray{T}, itr, offs, st)
# collect to dest array, checking the type of each result. if a result does not
# match, widen the result type and re-dispatch.
i = offs
while !done(itr, st)
el, st = next(itr, st)
S = typeof(el)
if S === T || S <: T
@inbounds dest[i] = el::T
i += 1
else
R = typejoin(T, S)
new = similar(dest, R)
copy!(new,1, dest,1, i-1)
@inbounds new[i] = el
return collect_to!(new, itr, i+1, st)
end
end
return dest
end
function grow_to!(dest, itr)
out = grow_to!(similar(dest,Union{}), itr, start(itr))
return isempty(out) ? dest : out
end
function grow_to!(dest, itr, st)
T = eltype(dest)
while !done(itr, st)
el, st = next(itr, st)
S = typeof(el)
if S === T || S <: T
push!(dest, el::T)
else
new = similar(dest, typejoin(T, S))
copy!(new, dest)
push!(new, el)
return grow_to!(new, itr, st)
end
end
return dest
end
## Iteration ##
start(A::Array) = 1
next(a::Array,i) = (@_propagate_inbounds_meta; (a[i],i+1))
done(a::Array,i) = (@_inline_meta; i == length(a)+1)
## Indexing: getindex ##
# This is more complicated than it needs to be in order to get Win64 through bootstrap
getindex(A::Array, i1::Real) = arrayref(A, to_index(i1))
getindex(A::Array, i1::Real, i2::Real, I::Real...) = arrayref(A, to_index(i1), to_index(i2), to_indexes(I...)...) # TODO: REMOVE FOR #14770
# Faster contiguous indexing using copy! for UnitRange and Colon
function getindex(A::Array, I::UnitRange{Int})
@_inline_meta
@boundscheck checkbounds(A, I)
lI = length(I)
X = similar(A, lI)
if lI > 0
unsafe_copy!(X, 1, A, first(I), lI)
end
return X
end
function getindex(A::Array, c::Colon)
lI = length(A)
X = similar(A, lI)
if lI > 0
unsafe_copy!(X, 1, A, 1, lI)
end
return X
end
# This is redundant with the abstract fallbacks, but needed for bootstrap
function getindex{S,T<:Real}(A::Array{S}, I::Range{T})
return S[ A[to_index(i)] for i in I ]
end
## Indexing: setindex! ##
setindex!{T}(A::Array{T}, x, i1::Real) = arrayset(A, convert(T,x)::T, to_index(i1))
setindex!{T}(A::Array{T}, x, i1::Real, i2::Real, I::Real...) = arrayset(A, convert(T,x)::T, to_index(i1), to_index(i2), to_indexes(I...)...) # TODO: REMOVE FOR #14770
# These are redundant with the abstract fallbacks but needed for bootstrap
function setindex!(A::Array, x, I::AbstractVector{Int})
is(A, I) && (I = copy(I))
for i in I
A[i] = x
end
return A
end
function setindex!(A::Array, X::AbstractArray, I::AbstractVector{Int})
setindex_shape_check(X, length(I))
count = 1
if is(X,A)
X = copy(X)
is(I,A) && (I = X::typeof(I))
elseif is(I,A)
I = copy(I)
end
for i in I
A[i] = X[count]
count += 1
end
return A
end
# Faster contiguous setindex! with copy!
function setindex!{T}(A::Array{T}, X::Array{T}, I::UnitRange{Int})
@_inline_meta
@boundscheck checkbounds(A, I)
lI = length(I)
setindex_shape_check(X, lI)
if lI > 0
unsafe_copy!(A, first(I), X, 1, lI)
end
return A
end
function setindex!{T}(A::Array{T}, X::Array{T}, c::Colon)
lI = length(A)
setindex_shape_check(X, lI)
if lI > 0
unsafe_copy!(A, 1, X, 1, lI)
end
return A
end
setindex!(A::Array, x::Number, ::Colon) = fill!(A, x)
setindex!{T, N}(A::Array{T, N}, x::Number, ::Vararg{Colon, N}) = fill!(A, x)
# efficiently grow an array
_growat!(a::Vector, i::Integer, delta::Integer) =
ccall(:jl_array_grow_at, Void, (Any, Int, UInt), a, i - 1, delta)
# efficiently delete part of an array
_deleteat!(a::Vector, i::Integer, delta::Integer) =
ccall(:jl_array_del_at, Void, (Any, Int, UInt), a, i - 1, delta)
## Dequeue functionality ##
function push!{T}(a::Array{T,1}, item)
# convert first so we don't grow the array if the assignment won't work
itemT = convert(T, item)
ccall(:jl_array_grow_end, Void, (Any, UInt), a, 1)
a[end] = itemT
return a
end
function push!(a::Array{Any,1}, item::ANY)
ccall(:jl_array_grow_end, Void, (Any, UInt), a, 1)
arrayset(a, item, length(a))
return a
end
function append!{T}(a::Array{T,1}, items::AbstractVector)
n = length(items)
ccall(:jl_array_grow_end, Void, (Any, UInt), a, n)
copy!(a, length(a)-n+1, items, 1, n)
return a
end
function prepend!{T}(a::Array{T,1}, items::AbstractVector)
n = length(items)
ccall(:jl_array_grow_beg, Void, (Any, UInt), a, n)
if a === items
copy!(a, 1, items, n+1, n)
else
copy!(a, 1, items, 1, n)
end
return a
end
function resize!(a::Vector, nl::Integer)
l = length(a)
if nl > l
ccall(:jl_array_grow_end, Void, (Any, UInt), a, nl-l)
else
if nl < 0
throw(ArgumentError("new length must be ≥ 0"))
end
ccall(:jl_array_del_end, Void, (Any, UInt), a, l-nl)
end
return a
end
function sizehint!(a::Vector, sz::Integer)
ccall(:jl_array_sizehint, Void, (Any, UInt), a, sz)
a
end
function pop!(a::Vector)
if isempty(a)
throw(ArgumentError("array must be non-empty"))
end
item = a[end]
ccall(:jl_array_del_end, Void, (Any, UInt), a, 1)
return item
end
function unshift!{T}(a::Array{T,1}, item)
item = convert(T, item)
ccall(:jl_array_grow_beg, Void, (Any, UInt), a, 1)
a[1] = item
return a
end
function shift!(a::Vector)
if isempty(a)
throw(ArgumentError("array must be non-empty"))
end
item = a[1]
ccall(:jl_array_del_beg, Void, (Any, UInt), a, 1)
return item
end
function insert!{T}(a::Array{T,1}, i::Integer, item)
# Throw convert error before changing the shape of the array
_item = convert(T, item)
_growat!(a, i, 1)
# _growat! already did bound check
@inbounds a[i] = _item
return a
end
"""
deleteat!(a::Vector, i::Integer)
Remove the item at the given `i` and return the modified `a`. Subsequent items
are shifted to fill the resulting gap.
```jldoctest
julia> deleteat!([6, 5, 4, 3, 2, 1], 2)
5-element Array{Int64,1}:
6
4
3
2
1
```
"""
deleteat!(a::Vector, i::Integer) = (_deleteat!(a, i, 1); a)
function deleteat!{T<:Integer}(a::Vector, r::UnitRange{T})
n = length(a)
isempty(r) || _deleteat!(a, first(r), length(r))
return a
end
"""
deleteat!(a::Vector, inds)
Remove the items at the indices given by `inds`, and return the modified `a`.
Subsequent items are shifted to fill the resulting gap. `inds` must be sorted and unique.
```jldoctest
julia> deleteat!([6, 5, 4, 3, 2, 1], 1:2:5)
3-element Array{Int64,1}:
5
3
1
julia> deleteat!([6, 5, 4, 3, 2, 1], (2, 2))
ERROR: ArgumentError: indices must be unique and sorted
in deleteat!(::Array{Int64,1}, ::Tuple{Int64,Int64}) at ./array.jl:614
...
```
"""
function deleteat!(a::Vector, inds)
n = length(a)
s = start(inds)
done(inds, s) && return a
(p, s) = next(inds, s)
q = p+1
while !done(inds, s)
(i,s) = next(inds, s)
if !(q <= i <= n)
if i < q
throw(ArgumentError("indices must be unique and sorted"))
else
throw(BoundsError())
end
end
while q < i
@inbounds a[p] = a[q]
p += 1; q += 1
end
q = i+1
end
while q <= n
@inbounds a[p] = a[q]
p += 1; q += 1
end
ccall(:jl_array_del_end, Void, (Any, UInt), a, n-p+1)
return a
end
const _default_splice = []
function splice!(a::Vector, i::Integer, ins=_default_splice)
v = a[i]
m = length(ins)
if m == 0
_deleteat!(a, i, 1)
elseif m == 1
a[i] = ins[1]
else
_growat!(a, i, m-1)
k = 1
for x in ins
a[i+k-1] = x
k += 1
end
end
return v
end
function splice!{T<:Integer}(a::Vector, r::UnitRange{T}, ins=_default_splice)
v = a[r]
m = length(ins)
if m == 0
deleteat!(a, r)
return v
end
n = length(a)
f = first(r)
l = last(r)
d = length(r)
if m < d
delta = d - m
_deleteat!(a, (f - 1 < n - l) ? f : (l - delta + 1), delta)
elseif m > d
_growat!(a, (f - 1 < n - l) ? f : (l + 1), m - d)
end
k = 1
for x in ins
a[f+k-1] = x
k += 1
end
return v
end
function empty!(a::Vector)
ccall(:jl_array_del_end, Void, (Any, UInt), a, length(a))
return a
end
# use memcmp for lexcmp on byte arrays
function lexcmp(a::Array{UInt8,1}, b::Array{UInt8,1})
c = ccall(:memcmp, Int32, (Ptr{UInt8}, Ptr{UInt8}, UInt),
a, b, min(length(a),length(b)))
return c < 0 ? -1 : c > 0 ? +1 : cmp(length(a),length(b))
end
function reverse(A::AbstractVector, s=1, n=length(A))
B = similar(A)
for i = 1:s-1
B[i] = A[i]
end
for i = s:n
B[i] = A[n+s-i]
end
for i = n+1:length(A)
B[i] = A[i]
end
return B
end
reverseind(a::AbstractVector, i::Integer) = length(a) + 1 - i
function reverse!(v::AbstractVector, s=1, n=length(v))
if n <= s # empty case; ok
elseif !(1 ≤ s ≤ endof(v))
throw(BoundsError(v, s))
elseif !(1 ≤ n ≤ endof(v))
throw(BoundsError(v, n))
end
r = n
@inbounds for i in s:div(s+n-1, 2)
v[i], v[r] = v[r], v[i]
r -= 1
end
return v
end
# concatenations of combinations (homogeneous, heterogeneous) of dense matrices/vectors #
vcat{T}(A::Union{Vector{T},Matrix{T}}...) = typed_vcat(T, A...)
vcat(A::Union{Vector,Matrix}...) = typed_vcat(promote_eltype(A...), A...)
hcat{T}(A::Union{Vector{T},Matrix{T}}...) = typed_hcat(T, A...)
hcat(A::Union{Vector,Matrix}...) = typed_hcat(promote_eltype(A...), A...)
hvcat{T}(rows::Tuple{Vararg{Int}}, xs::Union{Vector{T},Matrix{T}}...) = typed_hvcat(T, rows, xs...)
hvcat(rows::Tuple{Vararg{Int}}, xs::Union{Vector,Matrix}...) = typed_hvcat(promote_eltype(xs...), rows, xs...)
cat{T}(catdims, xs::Union{Vector{T},Matrix{T}}...) = Base.cat_t(catdims, T, xs...)
cat(catdims, xs::Union{Vector,Matrix}...) = Base.cat_t(catdims, promote_eltype(xs...), xs...)
# concatenations of homogeneous combinations of vectors, horizontal and vertical
function hcat{T}(V::Vector{T}...)
height = length(V[1])
for j = 2:length(V)
if length(V[j]) != height
throw(DimensionMismatch("vectors must have same lengths"))
end
end
return [ V[j][i]::T for i=1:length(V[1]), j=1:length(V) ]
end
function vcat{T}(arrays::Vector{T}...)
n = 0
for a in arrays
n += length(a)
end
arr = Array{T,1}(n)
ptr = pointer(arr)
if isbits(T)
elsz = Core.sizeof(T)
else
elsz = Core.sizeof(Ptr{Void})
end
for a in arrays
na = length(a)
nba = na * elsz
if isbits(T)
ccall(:memcpy, Ptr{Void}, (Ptr{Void}, Ptr{Void}, UInt),
ptr, a, nba)
else
ccall(:jl_array_ptr_copy, Void, (Any, Ptr{Void}, Any, Ptr{Void}, Int),
arr, ptr, a, pointer(a), na)
end
ptr += nba
end
return arr
end
## find ##
"""
findnext(A, i::Integer)
Find the next linear index >= `i` of a non-zero element of `A`, or `0` if not found.
```jldoctest
julia> A = [0 0; 1 0]
2×2 Array{Int64,2}:
0 0
1 0
julia> findnext(A,1)
2
julia> findnext(A,3)
0
```
"""
function findnext(A, start::Integer)
for i = start:length(A)
if A[i] != 0
return i
end
end
return 0
end
"""
findfirst(A)
Return the linear index of the first non-zero value in `A` (determined by `A[i]!=0`).
Returns `0` if no such value is found.
```jldoctest
julia> A = [0 0; 1 0]
2×2 Array{Int64,2}:
0 0
1 0
julia> findfirst(A)
2
```
"""
findfirst(A) = findnext(A, 1)
"""
findnext(A, v, i::Integer)
Find the next linear index >= `i` of an element of `A` equal to `v` (using `==`), or `0` if not found.
```jldoctest
julia> A = [1 4; 2 2]
2×2 Array{Int64,2}:
1 4
2 2
julia> findnext(A,4,4)
0
julia> findnext(A,4,3)
3
```
"""
function findnext(A, v, start::Integer)
for i = start:length(A)
if A[i] == v
return i
end
end
return 0
end
"""
findfirst(A, v)
Return the linear index of the first element equal to `v` in `A`.
Returns `0` if `v` is not found.
```jldoctest
julia> A = [4 6; 2 2]
2×2 Array{Int64,2}:
4 6
2 2
julia> findfirst(A,2)
2
julia> findfirst(A,3)
0
```
"""
findfirst(A, v) = findnext(A, v, 1)
"""
findnext(predicate::Function, A, i::Integer)
Find the next linear index >= `i` of an element of `A` for which `predicate` returns `true`, or `0` if not found.
```jldoctest
julia> A = [1 4; 2 2]
2×2 Array{Int64,2}:
1 4
2 2
julia> findnext(isodd, A, 1)
1
julia> findnext(isodd, A, 2)
0
```
"""
function findnext(testf::Function, A, start::Integer)
for i = start:length(A)
if testf(A[i])
return i
end
end
return 0
end
"""
findfirst(predicate::Function, A)
Return the linear index of the first element of `A` for which `predicate` returns `true`.
Returns `0` if there is no such element.
```jldoctest
julia> A = [1 4; 2 2]
2×2 Array{Int64,2}:
1 4
2 2
julia> findfirst(iseven, A)
2
julia> findfirst(x -> x>10, A)
0
```
"""
findfirst(testf::Function, A) = findnext(testf, A, 1)
"""
findprev(A, i::Integer)
Find the previous linear index <= `i` of a non-zero element of `A`, or `0` if not found.
```jldoctest
julia> A = [0 0; 1 2]
2×2 Array{Int64,2}:
0 0
1 2
julia> findprev(A,2)
2
julia> findprev(A,1)
0
```
"""
function findprev(A, start::Integer)
for i = start:-1:1
A[i] != 0 && return i
end
return 0
end
"""
findlast(A)
Return the linear index of the last non-zero value in `A` (determined by `A[i]!=0`).
Returns `0` if there is no non-zero value in `A`.
```jldoctest
julia> A = [1 0; 1 0]
2×2 Array{Int64,2}:
1 0
1 0
julia> findlast(A)
2
julia> A = zeros(2,2)
2×2 Array{Float64,2}:
0.0 0.0
0.0 0.0
julia> findlast(A)
0
```
"""
findlast(A) = findprev(A, length(A))
"""
findprev(A, v, i::Integer)
Find the previous linear index <= `i` of an element of `A` equal to `v` (using `==`), or `0` if not found.
```jldoctest
julia> A = [0 0; 1 2]
2×2 Array{Int64,2}:
0 0
1 2
julia> findprev(A, 1, 4)
2
julia> findprev(A, 1, 1)
0
```
"""
function findprev(A, v, start::Integer)
for i = start:-1:1
A[i] == v && return i
end
return 0
end
"""
findlast(A, v)
Return the linear index of the last element equal to `v` in `A`.
Returns `0` if there is no element of `A` equal to `v`.
```jldoctest
julia> A = [1 2; 2 1]
2×2 Array{Int64,2}:
1 2
2 1
julia> findlast(A,1)
4
julia> findlast(A,2)
3
julia> findlast(A,3)
0
```
"""
findlast(A, v) = findprev(A, v, length(A))
"""
findprev(predicate::Function, A, i::Integer)
Find the previous linear index <= `i` of an element of `A` for which `predicate` returns `true`, or
`0` if not found.
```jldoctest
julia> A = [4 6; 1 2]
2×2 Array{Int64,2}:
4 6
1 2
julia> findprev(isodd, A, 1)
0
julia> findprev(isodd, A, 3)
2
```
"""
function findprev(testf::Function, A, start::Integer)
for i = start:-1:1
testf(A[i]) && return i
end
return 0
end
"""
findlast(predicate::Function, A)
Return the linear index of the last element of `A` for which `predicate` returns `true`.
Returns `0` if there is no such element.
```jldoctest
julia> A = [1 2; 3 4]
2×2 Array{Int64,2}:
1 2
3 4
julia> findlast(isodd, A)
2
julia> findlast(x -> x > 5, A)
0
```
"""
findlast(testf::Function, A) = findprev(testf, A, length(A))
"""
find(f::Function, A)
Return a vector `I` of the linear indexes of `A` where `f(A[I])` returns `true`.
If there are no such elements of `A`, find returns an empty array.
```jldoctest
julia> A = [1 2; 3 4]
2×2 Array{Int64,2}:
1 2
3 4
julia> find(isodd,A)
2-element Array{Int64,1}:
1
2
```
"""
function find(testf::Function, A)
# use a dynamic-length array to store the indexes, then copy to a non-padded
# array for the return
tmpI = Array{Int,1}(0)
inds = _index_remapper(A)
for (i,a) = enumerate(A)
if testf(a)
push!(tmpI, inds[i])
end
end
I = Array{Int,1}(length(tmpI))
copy!(I, tmpI)
return I
end
_index_remapper(A::AbstractArray) = linearindices(A)
_index_remapper(iter) = Colon() # safe for objects that don't implement length
"""
find(A)
Return a vector of the linear indexes of the non-zeros in `A` (determined by `A[i]!=0`). A
common use of this is to convert a boolean array to an array of indexes of the `true`
elements. If there are no non-zero elements of `A`, `find` returns an empty array.
```jldoctest
julia> A = [true false; false true]
2×2 Array{Bool,2}:
true false
false true
julia> find(A)
2-element Array{Int64,1}:
1
4
```
"""
function find(A)
nnzA = countnz(A)
I = Vector{Int}(nnzA)
count = 1
inds = _index_remapper(A)
for (i,a) in enumerate(A)
if a != 0
I[count] = inds[i]
count += 1
end
end
return I
end
find(x::Number) = x == 0 ? Array{Int,1}(0) : [1]
find(testf::Function, x::Number) = !testf(x) ? Array{Int,1}(0) : [1]
findn(A::AbstractVector) = find(A)
"""
findn(A)
Return a vector of indexes for each dimension giving the locations of the non-zeros in `A`
(determined by `A[i]!=0`).
If there are no non-zero elements of `A`, `findn` returns a 2-tuple of empty arrays.
```jldoctest
julia> A = [1 2 0; 0 0 3; 0 4 0]
3×3 Array{Int64,2}:
1 2 0
0 0 3
0 4 0
julia> findn(A)
([1,1,3,2],[1,2,2,3])
julia> A = zeros(2,2)
2×2 Array{Float64,2}:
0.0 0.0
0.0 0.0
julia> findn(A)
(Int64[],Int64[])
```
"""
function findn(A::AbstractMatrix)
nnzA = countnz(A)
I = similar(A, Int, nnzA)
J = similar(A, Int, nnzA)
count = 1
for j=indices(A,2), i=indices(A,1)
if A[i,j] != 0
I[count] = i
J[count] = j
count += 1
end
end
return (I, J)
end
"""
findnz(A)
Return a tuple `(I, J, V)` where `I` and `J` are the row and column indexes of the non-zero
values in matrix `A`, and `V` is a vector of the non-zero values.
```jldoctest
julia> A = [1 2 0; 0 0 3; 0 4 0]
3×3 Array{Int64,2}:
1 2 0
0 0 3
0 4 0
julia> findnz(A)
([1,1,3,2],[1,2,2,3],[1,2,4,3])
```
"""
function findnz{T}(A::AbstractMatrix{T})
nnzA = countnz(A)
I = zeros(Int, nnzA)
J = zeros(Int, nnzA)
NZs = Array{T,1}(nnzA)
count = 1
if nnzA > 0
for j=indices(A,2), i=indices(A,1)
Aij = A[i,j]
if Aij != 0
I[count] = i
J[count] = j
NZs[count] = Aij
count += 1
end
end
end
return (I, J, NZs)
end
"""
findmax(itr) -> (x, index)
Returns the maximum element and its index.
The collection must not be empty.
```jldoctest
julia> findmax([8,0.1,-9,pi])
(8.0,1)
```
"""
function findmax(a)
if isempty(a)
throw(ArgumentError("collection must be non-empty"))
end
s = start(a)
mi = i = 1
m, s = next(a, s)
while !done(a, s)
ai, s = next(a, s)
i += 1
if ai > m || m!=m
m = ai
mi = i
end
end
return (m, mi)
end
"""
findmin(itr) -> (x, index)
Returns the minimum element and its index.
The collection must not be empty.
```jldoctest
julia> findmin([8,0.1,-9,pi])
(-9.0,3)
```
"""
function findmin(a)
if isempty(a)
throw(ArgumentError("collection must be non-empty"))
end
s = start(a)
mi = i = 1
m, s = next(a, s)
while !done(a, s)
ai, s = next(a, s)
i += 1
if ai < m || m!=m
m = ai
mi = i
end
end
return (m, mi)
end
"""
indmax(itr) -> Integer
Returns the index of the maximum element in a collection.
The collection must not be empty.
```jldoctest
julia> indmax([8,0.1,-9,pi])
1
```
"""
indmax(a) = findmax(a)[2]
"""
indmin(itr) -> Integer
Returns the index of the minimum element in a collection.
The collection must not be empty.
```jldoctest
julia> indmin([8,0.1,-9,pi])
3
```
"""
indmin(a) = findmin(a)[2]
# similar to Matlab's ismember
"""
indexin(a, b)
Returns a vector containing the highest index in `b` for
each value in `a` that is a member of `b` . The output
vector contains 0 wherever `a` is not a member of `b`.
```jldoctest
julia> a = ['a', 'b', 'c', 'b', 'd', 'a'];
julia> b = ['a','b','c'];
julia> indexin(a,b)
6-element Array{Int64,1}:
1
2
3
2
0
1
julia> indexin(b,a)
3-element Array{Int64,1}:
6
4
3
```
"""
function indexin(a::AbstractArray, b::AbstractArray)
bdict = Dict(zip(b, 1:length(b)))
[get(bdict, i, 0) for i in a]
end
"""
findin(a, b)
Returns the indices of elements in collection `a` that appear in collection `b`.
```jldoctest
julia> a = collect(1:3:15)
5-element Array{Int64,1}:
1
4
7
10
13
julia> b = collect(2:4:10)
3-element Array{Int64,1}:
2
6
10
julia> findin(a,b) # 10 is the only common element
1-element Array{Int64,1}:
4
```
"""
function findin(a, b)
ind = Array{Int,1}(0)
bset = Set(b)
@inbounds for (i,ai) in enumerate(a)
ai in bset && push!(ind, i)
end
ind
end
# Copying subregions
# TODO: DEPRECATE FOR #14770
function indcopy(sz::Dims, I::Vector)
n = length(I)
s = sz[n]
for i = n+1:length(sz)
s *= sz[i]
end
dst = eltype(I)[findin(I[i], i < n ? (1:sz[i]) : (1:s)) for i = 1:n]
src = eltype(I)[I[i][findin(I[i], i < n ? (1:sz[i]) : (1:s))] for i = 1:n]
dst, src
end
function indcopy(sz::Dims, I::Tuple{Vararg{RangeIndex}})
n = length(I)
s = sz[n]
for i = n+1:length(sz)
s *= sz[i]
end
dst::typeof(I) = ntuple(i-> findin(I[i], i < n ? (1:sz[i]) : (1:s)), n)::typeof(I)
src::typeof(I) = ntuple(i-> I[i][findin(I[i], i < n ? (1:sz[i]) : (1:s))], n)::typeof(I)
dst, src
end
## Filter ##
# given a function returning a boolean and an array, return matching elements
filter(f, As::AbstractArray) = As[map(f, As)::AbstractArray{Bool}]
function filter!(f, a::Vector)
insrt = 1
for acurr in a
if f(acurr)
a[insrt] = acurr
insrt += 1
end
end
deleteat!(a, insrt:length(a))
return a
end
function filter(f, a::Vector)
r = Array{eltype(a)}(0)
for ai in a
if f(ai)
push!(r, ai)
end
end
return r
end
# set-like operators for vectors
# These are moderately efficient, preserve order, and remove dupes.
function intersect(v1, vs...)
ret = Array{promote_eltype(v1, vs...)}(0)
for v_elem in v1
inall = true
for vsi in vs
if !in(v_elem, vsi)
inall=false; break
end
end
if inall
push!(ret, v_elem)
end
end
ret
end
function union(vs...)
ret = Array{promote_eltype(vs...)}(0)
seen = Set()
for v in vs
for v_elem in v
if !in(v_elem, seen)
push!(ret, v_elem)
push!(seen, v_elem)
end
end
end
ret
end
# setdiff only accepts two args
"""
setdiff(a, b)
Construct the set of elements in `a` but not `b`. Maintains order with arrays. Note that
both arguments must be collections, and both will be iterated over. In particular,
`setdiff(set,element)` where `element` is a potential member of `set`, will not work in
general.
```jldoctest
julia> setdiff([1,2,3],[3,4,5])
2-element Array{Int64,1}:
1
2
```
"""
function setdiff(a, b)
args_type = promote_type(eltype(a), eltype(b))
bset = Set(b)
ret = Array{args_type,1}(0)
seen = Set{eltype(a)}()
for a_elem in a
if !in(a_elem, seen) && !in(a_elem, bset)
push!(ret, a_elem)
push!(seen, a_elem)
end
end
ret
end
# symdiff is associative, so a relatively clean
# way to implement this is by using setdiff and union, and
# recursing. Has the advantage of keeping order, too, but
# not as fast as other methods that make a single pass and
# store counts with a Dict.
symdiff(a) = a
symdiff(a, b) = union(setdiff(a,b), setdiff(b,a))
"""
symdiff(a, b, rest...)
Construct the symmetric difference of elements in the passed in sets or arrays.
Maintains order with arrays.
```jldoctest
julia> symdiff([1,2,3],[3,4,5],[4,5,6])
3-element Array{Int64,1}:
1
2
6
```
"""
symdiff(a, b, rest...) = symdiff(a, symdiff(b, rest...))