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# This file is a part of Julia. License is MIT: http://julialang.org/license
## Functions to compute the reduced shape
# for reductions that expand 0 dims to 1
reduced_dims(a::AbstractArray, region) = reduced_dims(size(a), region)
# for reductions that keep 0 dims as 0
reduced_dims0(a::AbstractArray, region) = reduced_dims0(size(a), region)
function reduced_dims{N}(siz::NTuple{N,Int}, d::Int, rd::Int)
if d < 1
throw(ArgumentError("dimension must be ≥ 1, got $d"))
elseif d == 1
return tuple(rd, siz[d+1:N]...)::typeof(siz)
elseif 1 < d < N
return tuple(siz[1:d-1]..., rd, siz[d+1:N]...)::typeof(siz)
elseif d == N
return tuple(siz[1:N-1]..., rd)::typeof(siz)
else
return siz
end
end
reduced_dims{N}(siz::NTuple{N,Int}, d::Int) = reduced_dims(siz, d, 1)
function reduced_dims0{N}(siz::NTuple{N,Int}, d::Int)
if d < 1
throw(ArgumentError("dimension must be ≥ 1, got $d"))
elseif d <= N
return reduced_dims(siz, d, (siz[d] == 0 ? 0 : 1))
else
return siz
end
end
function reduced_dims{N}(siz::NTuple{N,Int}, region)
rsiz = [siz...]
for i in region
isa(i, Integer) || throw(ArgumentError("reduced dimension(s) must be integers"))
d = convert(Int, i)::Int
if d < 1
throw(ArgumentError("region dimension(s) must be ≥ 1, got $d"))
elseif d <= N
rsiz[d] = 1
end
end
tuple(rsiz...)::typeof(siz)
end
function reduced_dims0{N}(siz::NTuple{N,Int}, region)
rsiz = [siz...]
for i in region
isa(i, Integer) || throw(ArgumentError("reduced dimension(s) must be integers"))
d = convert(Int, i)::Int
if d < 1
throw(ArgumentError("region dimension(s) must be ≥ 1, got $d"))
elseif d <= N
rsiz[d] = (rsiz[d] == 0 ? 0 : 1)
end
end
tuple(rsiz...)::typeof(siz)
end
function regionsize(a, region)
s = 1
for d in region
s *= size(a,d)
end
s
end
###### Generic reduction functions #####
## initialization
for (Op, initfun) in ((:AddFun, :zero), (:MulFun, :one), (:MaxFun, :typemin), (:MinFun, :typemax))
@eval initarray!{T}(a::AbstractArray{T}, ::$(Op), init::Bool) = (init && fill!(a, $(initfun)(T)); a)
end
for (Op, initval) in ((:AndFun, true), (:OrFun, false))
@eval initarray!(a::AbstractArray, ::$(Op), init::Bool) = (init && fill!(a, $initval); a)
end
reducedim_initarray{R}(A::AbstractArray, region, v0, ::Type{R}) = fill!(similar(A,R,reduced_dims(A,region)), v0)
reducedim_initarray{T}(A::AbstractArray, region, v0::T) = reducedim_initarray(A, region, v0, T)
reducedim_initarray0{R}(A::AbstractArray, region, v0, ::Type{R}) = fill!(similar(A,R,reduced_dims0(A,region)), v0)
reducedim_initarray0{T}(A::AbstractArray, region, v0::T) = reducedim_initarray0(A, region, v0, T)
# TODO: better way to handle reducedim initialization
#
# The current scheme is basically following Steven G. Johnson's original implementation
#
promote_union(T::UnionType) = promote_type(T.types...)
promote_union(T) = T
function reducedim_init{S}(f, op::AddFun, A::AbstractArray{S}, region)
T = promote_union(S)
if method_exists(zero, Tuple{Type{T}})
x = f(zero(T))
z = zero(x) + zero(x)
Tr = typeof(z) == typeof(x) && !isbits(T) ? T : typeof(z)
else
z = zero(sum(f, A))
Tr = typeof(z)
end
return reducedim_initarray(A, region, z, Tr)
end
function reducedim_init{S}(f, op::MulFun, A::AbstractArray{S}, region)
T = promote_union(S)
if method_exists(zero, Tuple{Type{T}})
x = f(zero(T))
z = one(x) * one(x)
Tr = typeof(z) == typeof(x) && !isbits(T) ? T : typeof(z)
else
z = one(prod(f, A))
Tr = typeof(z)
end
return reducedim_initarray(A, region, z, Tr)
end
reducedim_init{T}(f, op::MaxFun, A::AbstractArray{T}, region) = reducedim_initarray0(A, region, typemin(f(zero(T))))
reducedim_init{T}(f, op::MinFun, A::AbstractArray{T}, region) = reducedim_initarray0(A, region, typemax(f(zero(T))))
reducedim_init{T}(f::Union(AbsFun,Abs2Fun), op::MaxFun, A::AbstractArray{T}, region) =
reducedim_initarray(A, region, zero(f(zero(T))))
reducedim_init(f, op::AndFun, A::AbstractArray, region) = reducedim_initarray(A, region, true)
reducedim_init(f, op::OrFun, A::AbstractArray, region) = reducedim_initarray(A, region, false)
# specialize to make initialization more efficient for common cases
for (IT, RT) in ((CommonReduceResult, :(eltype(A))), (SmallSigned, :Int), (SmallUnsigned, :UInt))
T = Union([AbstractArray{t} for t in IT.types]..., [AbstractArray{Complex{t}} for t in IT.types]...)
@eval begin
reducedim_init(f::IdFun, op::AddFun, A::$T, region) =
reducedim_initarray(A, region, zero($RT))
reducedim_init(f::IdFun, op::MulFun, A::$T, region) =
reducedim_initarray(A, region, one($RT))
reducedim_init(f::Union(AbsFun,Abs2Fun), op::AddFun, A::$T, region) =
reducedim_initarray(A, region, real(zero($RT)))
reducedim_init(f::Union(AbsFun,Abs2Fun), op::MulFun, A::$T, region) =
reducedim_initarray(A, region, real(one($RT)))
end
end
reducedim_init(f::Union(IdFun,AbsFun,Abs2Fun), op::AddFun, A::AbstractArray{Bool}, region) =
reducedim_initarray(A, region, 0)
## generic (map)reduction
has_fast_linear_indexing(a::AbstractArray) = false
has_fast_linear_indexing(a::Array) = true
function check_reducedims(R, A)
# Check whether R has compatible dimensions w.r.t. A for reduction
#
# It returns an integer value (useful for choosing implementation)
# - If it reduces only along leading dimensions, e.g. sum(A, 1) or sum(A, (1, 2)),
# it returns the length of the leading slice. For the two examples above,
# it will be size(A, 1) or size(A, 1) * size(A, 2).
# - Otherwise, e.g. sum(A, 2) or sum(A, (1, 3)), it returns 0.
#
ndims(R) <= ndims(A) || throw(DimensionMismatch("Cannot reduce $(ndims(A))-dimensional array to $(ndims(R)) dimensions"))
lsiz = 1
had_nonreduc = false
for i = 1:ndims(A)
sRi = size(R, i)
sAi = size(A, i)
if sRi == 1
if sAi > 1
if had_nonreduc
lsiz = 0 # to reduce along i, but some previous dimensions were non-reducing
else
lsiz *= sAi # if lsiz was set to zero, it will stay to be zero
end
end
else
sRi == sAi ||
throw(DimensionMismatch("Reduction on array of size $(size(A)) with output of size $(size(R))"))
had_nonreduc = true
end
end
return lsiz
end
function _mapreducedim!{T,N}(f, op, R::AbstractArray, A::AbstractArray{T,N})
lsiz = check_reducedims(R,A)
isempty(A) && return R
sizA1 = size(A, 1)
if has_fast_linear_indexing(A) && lsiz > 16
# use mapreduce_impl, which is probably better tuned to achieve higher performance
nslices = div(length(A), lsiz)
ibase = 0
for i = 1:nslices
@inbounds R[i] = op(R[i], mapreduce_impl(f, op, A, ibase+1, ibase+lsiz))
ibase += lsiz
end
elseif size(R, 1) == 1 && sizA1 > 1
# keep the accumulator as a local variable when reducing along the first dimension
sizeR1 = size_skip1(size(R), A)
sizeA1 = size_skip1(size(A), A)
@inbounds for IA in CartesianRange(sizeA1)
IR = min(sizeR1, IA)
r = R[1,IR]
@simd for i = 1:size(A, 1)
r = op(r, f(A[i, IA]))
end
R[1,IR] = r
end
else
sizeR = CartesianIndex{N}(size(R))
@inbounds @simd for IA in CartesianRange(size(A))
IR = min(IA, sizeR)
R[IR] = op(R[IR], f(A[IA]))
end
end
return R
end
mapreducedim!(f, op, R::AbstractArray, A::AbstractArray) = (_mapreducedim!(f, op, R, A); R)
to_op(op) = op
function to_op(op::Function)
is(op, +) ? AddFun() :
is(op, *) ? MulFun() :
is(op, &) ? AndFun() :
is(op, |) ? OrFun() : op
end
mapreducedim!(f, op, R::AbstractArray, A::AbstractArray) =
(_mapreducedim!(f, to_op(op), R, A); R)
reducedim!{RT}(op, R::AbstractArray{RT}, A::AbstractArray) =
mapreducedim!(IdFun(), op, R, A, zero(RT))
mapreducedim(f, op, A::AbstractArray, region, v0) =
mapreducedim!(f, op, reducedim_initarray(A, region, v0), A)
mapreducedim{T}(f, op, A::AbstractArray{T}, region) =
mapreducedim!(f, op, reducedim_init(f, to_op(op), A, region), A)
reducedim(op, A::AbstractArray, region, v0) = mapreducedim(IdFun(), op, A, region, v0)
reducedim(op, A::AbstractArray, region) = mapreducedim(IdFun(), op, A, region)
##### Specific reduction functions #####
for (fname, Op) in [(:sum, :AddFun), (:prod, :MulFun),
(:maximum, :MaxFun), (:minimum, :MinFun),
(:all, :AndFun), (:any, :OrFun)]
fname! = symbol(fname, '!')
@eval begin
$(fname!)(f::Union(Function,Func{1}), r::AbstractArray, A::AbstractArray; init::Bool=true) =
mapreducedim!(f, $(Op)(), initarray!(r, $(Op)(), init), A)
$(fname!)(r::AbstractArray, A::AbstractArray; init::Bool=true) = $(fname!)(IdFun(), r, A; init=init)
$(fname)(f::Union(Function,Func{1}), A::AbstractArray, region) =
mapreducedim(f, $(Op)(), A, region)
$(fname)(A::AbstractArray, region) = $(fname)(IdFun(), A, region)
end
end
for (fname, fbase, Fun) in [(:sumabs, :sum, :AbsFun),
(:sumabs2, :sum, :Abs2Fun),
(:maxabs, :maximum, :AbsFun),
(:minabs, :minimum, :AbsFun)]
fname! = symbol(fname, '!')
fbase! = symbol(fbase, '!')
@eval begin
$(fname!)(r::AbstractArray, A::AbstractArray; init::Bool=true) =
$(fbase!)($(Fun)(), r, A; init=init)
$(fname)(A::AbstractArray, region) = $(fbase)($(Fun)(), A, region)
end
end
##### findmin & findmax #####
function findminmax!{T,N}(f, Rval, Rind, A::AbstractArray{T,N})
(isempty(Rval) || isempty(A)) && return Rval, Rind
(ndims(Rval) <= N && ndims(Rind) <= N) || throw(DimensionMismatch("Cannot find-reduce $(ndims(A))-dimensional array to $(ndims(Rval)),$(ndims(Rind)) dimensions"))
for i = 1:N
(size(Rval, i) == size(A, i) || size(Rval, i) == 1) || throw(DimensionMismatch("Find-reduction on array of size $(size(A)) with output of size $(size(Rval))"))
size(Rval, i) == size(Rind, i) || throw(DimensionMismatch("Find-reduction: outputs must be of the same size"))
end
# If we're reducing along dimension 1, for efficiency we can make use of a temporary.
# Otherwise, keep the result in Rval/Rind so that we traverse A in storage order.
k = 0
if size(Rval, 1) < size(A, 1)
sizeR1 = size_skip1(size(Rval), A)
sizeA1 = size_skip1(size(A), A)
@inbounds for IA in CartesianRange(sizeA1)
IR = min(sizeR1, IA)
tmpRv = Rval[1,IR]
tmpRi = Rind[1,IR]
for i = 1:size(A,1)
k += 1
tmpAv = A[i,IA]
if f(tmpAv, tmpRv)
tmpRv = tmpAv
tmpRi = k
end
end
Rval[1,IR] = tmpRv
Rind[1,IR] = tmpRi
end
else
sizeR = CartesianIndex(size(Rval))
@inbounds for IA in CartesianRange(size(A))
IR = min(sizeR, IA)
k += 1
tmpAv = A[IA]
if f(tmpAv, Rval[IR])
Rval[IR] = tmpAv
Rind[IR] = k
end
end
end
Rval, Rind
end
# findmin
function findmin!{R}(rval::AbstractArray{R},
rind::AbstractArray,
A::AbstractArray;
init::Bool=true)
findminmax!(LessFun(), initarray!(rval, typemax(R), init), rind, A)
end
function findmin{T}(A::AbstractArray{T}, region)
if isempty(A)
return (similar(A, reduced_dims0(A, region)),
zeros(Int, reduced_dims0(A, region)))
end
return findminmax!(LessFun(), reducedim_initarray0(A, region, typemax(T)),
zeros(Int, reduced_dims0(A, region)), A)
end
# findmax
function findmax!{R}(rval::AbstractArray{R},
rind::AbstractArray,
A::AbstractArray;
init::Bool=true)
findminmax!(MoreFun(), initarray!(rval, typemin(R), init), rind, A)
end
function findmax{T}(A::AbstractArray{T}, region)
if isempty(A)
return (similar(A, reduced_dims0(A,region)),
zeros(Int, reduced_dims0(A,region)))
end
return findminmax!(MoreFun(), reducedim_initarray0(A, region, typemin(T)),
zeros(Int, reduced_dims0(A, region)), A)
end
size_skip1{T}(dims::Tuple{}, Aref::AbstractArray{T,0}) = CartesianIndex(())
size_skip1{T,N}(dims::NTuple{N,Int}, Aref::AbstractArray{T,N}) = CartesianIndex(skip1(dims...))
@inline size_skip1{T,M,N}(dims::NTuple{M,Int}, Aref::AbstractArray{T,N}) = size_skip1(tuple(dims..., 1), Aref)
skip1(x, t...) = t
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