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higherorderfns.jl
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higherorderfns.jl
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# This file is a part of Julia. License is MIT: https://julialang.org/license
module HigherOrderFns
# This module provides higher order functions specialized for sparse arrays,
# particularly map[!]/broadcast[!] for SparseVectors and SparseMatrixCSCs at present.
import Base: map, map!, broadcast, broadcast!
using Base: front, tail, to_shape
using ..SparseArrays: SparseVector, SparseMatrixCSC, AbstractSparseVector,
AbstractSparseMatrix, AbstractSparseArray, indtype, nnz, nzrange
using Base.Broadcast: BroadcastStyle
# This module is organized as follows:
# (1) Define a common interface to SparseVectors and SparseMatrixCSCs sufficient for
# map[!]/broadcast[!]'s purposes. The methods below are written against this interface.
# (2) Define entry points for map[!] (short children of _map_[not]zeropres!).
# (3) Define entry points for broadcast[!] (short children of _broadcast_[not]zeropres!).
# (4) Define _map_[not]zeropres! specialized for a single (input) sparse vector/matrix.
# (5) Define _map_[not]zeropres! specialized for a pair of (input) sparse vectors/matrices.
# (6) Define general _map_[not]zeropres! capable of handling >2 (input) sparse vectors/matrices.
# (7) Define _broadcast_[not]zeropres! specialized for a single (input) sparse vector/matrix.
# (8) Define _broadcast_[not]zeropres! specialized for a pair of (input) sparse vectors/matrices.
# (9) Define general _broadcast_[not]zeropres! capable of handling >2 (input) sparse vectors/matrices.
# (10) Define broadcast methods handling combinations of broadcast scalars and sparse vectors/matrices.
# (11) Define broadcast[!] methods handling combinations of scalars, sparse vectors/matrices,
# structured matrices, and one- and two-dimensional Arrays.
# (12) Define map[!] methods handling combinations of sparse and structured matrices.
# (1) The definitions below provide a common interface to sparse vectors and matrices
# sufficient for the purposes of map[!]/broadcast[!]. This interface treats sparse vectors
# as n-by-one sparse matrices which, though technically incorrect, is how broacast[!] views
# sparse vectors in practice.
SparseVecOrMat = Union{SparseVector,SparseMatrixCSC}
@inline numrows(A::SparseVector) = A.n
@inline numrows(A::SparseMatrixCSC) = A.m
@inline numcols(A::SparseVector) = 1
@inline numcols(A::SparseMatrixCSC) = A.n
# numrows and numcols respectively yield size(A, 1) and size(A, 2), but avoid a branch
@inline columns(A::SparseVector) = 1
@inline columns(A::SparseMatrixCSC) = 1:A.n
@inline colrange(A::SparseVector, j) = 1:length(A.nzind)
@inline colrange(A::SparseMatrixCSC, j) = nzrange(A, j)
@inline colstartind(A::SparseVector, j) = one(indtype(A))
@inline colboundind(A::SparseVector, j) = convert(indtype(A), length(A.nzind) + 1)
@inline colstartind(A::SparseMatrixCSC, j) = A.colptr[j]
@inline colboundind(A::SparseMatrixCSC, j) = A.colptr[j + 1]
@inline storedinds(A::SparseVector) = A.nzind
@inline storedinds(A::SparseMatrixCSC) = A.rowval
@inline storedvals(A::SparseVecOrMat) = A.nzval
@inline setcolptr!(A::SparseVector, j, val) = val
@inline setcolptr!(A::SparseMatrixCSC, j, val) = A.colptr[j] = val
function trimstorage!(A::SparseVecOrMat, maxstored)
resize!(storedinds(A), maxstored)
resize!(storedvals(A), maxstored)
return maxstored
end
function expandstorage!(A::SparseVecOrMat, maxstored)
length(storedinds(A)) < maxstored && resize!(storedinds(A), maxstored)
length(storedvals(A)) < maxstored && resize!(storedvals(A), maxstored)
return maxstored
end
# (2) map[!] entry points
map(f::Tf, A::SparseVector) where {Tf} = _noshapecheck_map(f, A)
map(f::Tf, A::SparseMatrixCSC) where {Tf} = _noshapecheck_map(f, A)
map(f::Tf, A::SparseMatrixCSC, Bs::Vararg{SparseMatrixCSC,N}) where {Tf,N} =
(_checksameshape(A, Bs...); _noshapecheck_map(f, A, Bs...))
map(f::Tf, A::SparseVecOrMat, Bs::Vararg{SparseVecOrMat,N}) where {Tf,N} =
(_checksameshape(A, Bs...); _noshapecheck_map(f, A, Bs...))
map!(f::Tf, C::SparseMatrixCSC, A::SparseMatrixCSC, Bs::Vararg{SparseMatrixCSC,N}) where {Tf,N} =
(_checksameshape(C, A, Bs...); _noshapecheck_map!(f, C, A, Bs...))
map!(f::Tf, C::SparseVecOrMat, A::SparseVecOrMat, Bs::Vararg{SparseVecOrMat,N}) where {Tf,N} =
(_checksameshape(C, A, Bs...); _noshapecheck_map!(f, C, A, Bs...))
function _noshapecheck_map!(f::Tf, C::SparseVecOrMat, A::SparseVecOrMat, Bs::Vararg{SparseVecOrMat,N}) where {Tf,N}
fofzeros = f(_zeros_eltypes(A, Bs...)...)
fpreszeros = _iszero(fofzeros)
return fpreszeros ? _map_zeropres!(f, C, A, Bs...) :
_map_notzeropres!(f, fofzeros, C, A, Bs...)
end
function _noshapecheck_map(f::Tf, A::SparseVecOrMat, Bs::Vararg{SparseVecOrMat,N}) where {Tf,N}
fofzeros = f(_zeros_eltypes(A, Bs...)...)
fpreszeros = _iszero(fofzeros)
maxnnzC = fpreszeros ? min(length(A), _sumnnzs(A, Bs...)) : length(A)
entrytypeC = Base.Broadcast.combine_eltypes(f, A, Bs...)
indextypeC = _promote_indtype(A, Bs...)
C = _allocres(size(A), indextypeC, entrytypeC, maxnnzC)
return fpreszeros ? _map_zeropres!(f, C, A, Bs...) :
_map_notzeropres!(f, fofzeros, C, A, Bs...)
end
# (3) broadcast[!] entry points
broadcast(f::Tf, A::SparseVector) where {Tf} = _noshapecheck_map(f, A)
broadcast(f::Tf, A::SparseMatrixCSC) where {Tf} = _noshapecheck_map(f, A)
function broadcast!(f::Tf, C::SparseVecOrMat) where Tf
isempty(C) && return _finishempty!(C)
fofnoargs = f()
if _iszero(fofnoargs) # f() is zero, so empty C
trimstorage!(C, 0)
_finishempty!(C)
else # f() is nonzero, so densify C and fill with independent calls to f()
_densestructure!(C)
storedvals(C)[1] = fofnoargs
broadcast!(f, view(storedvals(C), 2:length(storedvals(C))))
end
return C
end
function broadcast!(f::Tf, C::SparseVecOrMat, A::SparseVecOrMat, Bs::Vararg{SparseVecOrMat,N}) where {Tf,N}
_aresameshape(C, A, Bs...) && return _noshapecheck_map!(f, C, A, Bs...)
Base.Broadcast.check_broadcast_indices(axes(C), A, Bs...)
fofzeros = f(_zeros_eltypes(A, Bs...)...)
fpreszeros = _iszero(fofzeros)
return fpreszeros ? _broadcast_zeropres!(f, C, A, Bs...) :
_broadcast_notzeropres!(f, fofzeros, C, A, Bs...)
end
# the following three similar defs are necessary for type stability in the mixed vector/matrix case
broadcast(f::Tf, A::SparseVector, Bs::Vararg{SparseVector,N}) where {Tf,N} =
_aresameshape(A, Bs...) ? _noshapecheck_map(f, A, Bs...) : _diffshape_broadcast(f, A, Bs...)
broadcast(f::Tf, A::SparseMatrixCSC, Bs::Vararg{SparseMatrixCSC,N}) where {Tf,N} =
_aresameshape(A, Bs...) ? _noshapecheck_map(f, A, Bs...) : _diffshape_broadcast(f, A, Bs...)
broadcast(f::Tf, A::SparseVecOrMat, Bs::Vararg{SparseVecOrMat,N}) where {Tf,N} =
_diffshape_broadcast(f, A, Bs...)
function _diffshape_broadcast(f::Tf, A::SparseVecOrMat, Bs::Vararg{SparseVecOrMat,N}) where {Tf,N}
fofzeros = f(_zeros_eltypes(A, Bs...)...)
fpreszeros = _iszero(fofzeros)
indextypeC = _promote_indtype(A, Bs...)
entrytypeC = Base.Broadcast.combine_eltypes(f, A, Bs...)
shapeC = to_shape(Base.Broadcast.combine_indices(A, Bs...))
maxnnzC = fpreszeros ? _checked_maxnnzbcres(shapeC, A, Bs...) : _densennz(shapeC)
C = _allocres(shapeC, indextypeC, entrytypeC, maxnnzC)
return fpreszeros ? _broadcast_zeropres!(f, C, A, Bs...) :
_broadcast_notzeropres!(f, fofzeros, C, A, Bs...)
end
# helper functions for map[!]/broadcast[!] entry points (and related methods below)
@inline _sumnnzs(A) = nnz(A)
@inline _sumnnzs(A, Bs...) = nnz(A) + _sumnnzs(Bs...)
@inline _iszero(x) = x == 0
@inline _iszero(x::Number) = Base.iszero(x)
@inline _iszero(x::AbstractArray) = Base.iszero(x)
@inline _zeros_eltypes(A) = (zero(eltype(A)),)
@inline _zeros_eltypes(A, Bs...) = (zero(eltype(A)), _zeros_eltypes(Bs...)...)
@inline _promote_indtype(A) = indtype(A)
@inline _promote_indtype(A, Bs...) = promote_type(indtype(A), _promote_indtype(Bs...))
@inline _aresameshape(A) = true
@inline _aresameshape(A, B) = size(A) == size(B)
@inline _aresameshape(A, B, Cs...) = _aresameshape(A, B) ? _aresameshape(B, Cs...) : false
@inline _checksameshape(As...) = _aresameshape(As...) || throw(DimensionMismatch("argument shapes must match"))
@inline _densennz(shape::NTuple{1}) = shape[1]
@inline _densennz(shape::NTuple{2}) = shape[1] * shape[2]
_maxnnzfrom(shape::NTuple{1}, A) = nnz(A) * div(shape[1], A.n)
_maxnnzfrom(shape::NTuple{2}, A::SparseVector) = nnz(A) * div(shape[1], A.n) * shape[2]
_maxnnzfrom(shape::NTuple{2}, A::SparseMatrixCSC) = nnz(A) * div(shape[1], A.m) * div(shape[2], A.n)
@inline _maxnnzfrom_each(shape, ::Tuple{}) = ()
@inline _maxnnzfrom_each(shape, As) = (_maxnnzfrom(shape, first(As)), _maxnnzfrom_each(shape, tail(As))...)
@inline _unchecked_maxnnzbcres(shape, As::Tuple) = min(_densennz(shape), sum(_maxnnzfrom_each(shape, As)))
@inline _unchecked_maxnnzbcres(shape, As...) = _unchecked_maxnnzbcres(shape, As)
@inline _checked_maxnnzbcres(shape::NTuple{1}, As...) = shape[1] != 0 ? _unchecked_maxnnzbcres(shape, As) : 0
@inline _checked_maxnnzbcres(shape::NTuple{2}, As...) = shape[1] != 0 && shape[2] != 0 ? _unchecked_maxnnzbcres(shape, As) : 0
@inline function _allocres(shape::NTuple{1}, indextype, entrytype, maxnnz)
storedinds = Vector{indextype}(uninitialized, maxnnz)
storedvals = Vector{entrytype}(uninitialized, maxnnz)
return SparseVector(shape..., storedinds, storedvals)
end
@inline function _allocres(shape::NTuple{2}, indextype, entrytype, maxnnz)
pointers = Vector{indextype}(uninitialized, shape[2] + 1)
storedinds = Vector{indextype}(uninitialized, maxnnz)
storedvals = Vector{entrytype}(uninitialized, maxnnz)
return SparseMatrixCSC(shape..., pointers, storedinds, storedvals)
end
# Ambiguity killers, TODO: nix conflicting specializations
ambiguityfunnel(f::Tf, x, y) where {Tf} = _aresameshape(x, y) ? _noshapecheck_map(f, x, y) : _diffshape_broadcast(f, x, y)
broadcast(::typeof(+), x::SparseVector, y::SparseVector) = ambiguityfunnel(+, x, y) # base/sparse/sparsevectors.jl:1266
broadcast(::typeof(-), x::SparseVector, y::SparseVector) = ambiguityfunnel(-, x, y) # base/sparse/sparsevectors.jl:1266
broadcast(::typeof(*), x::SparseVector, y::SparseVector) = ambiguityfunnel(*, x, y) # base/sparse/sparsevectors.jl:1266
# (4) _map_zeropres!/_map_notzeropres! specialized for a single sparse vector/matrix
"Stores only the nonzero entries of `map(f, Array(A))` in `C`."
function _map_zeropres!(f::Tf, C::SparseVecOrMat, A::SparseVecOrMat) where Tf
spaceC::Int = min(length(storedinds(C)), length(storedvals(C)))
Ck = 1
@inbounds for j in columns(C)
setcolptr!(C, j, Ck)
for Ak in colrange(A, j)
Cx = f(storedvals(A)[Ak])
if !_iszero(Cx)
Ck > spaceC && (spaceC = expandstorage!(C, Ck + nnz(A) - (Ak - 1)))
storedinds(C)[Ck] = storedinds(A)[Ak]
storedvals(C)[Ck] = Cx
Ck += 1
end
end
end
@inbounds setcolptr!(C, numcols(C) + 1, Ck)
trimstorage!(C, Ck - 1)
return C
end
"""
Densifies `C`, storing `fillvalue` in place of each unstored entry in `A` and
`f(A[i])`/`f(A[i,j])` in place of each stored entry `A[i]`/`A[i,j]` in `A`.
"""
function _map_notzeropres!(f::Tf, fillvalue, C::SparseVecOrMat, A::SparseVecOrMat) where Tf
# Build dense matrix structure in C, expanding storage if necessary
_densestructure!(C)
# Populate values
fill!(storedvals(C), fillvalue)
@inbounds for (j, jo) in zip(columns(C), _densecoloffsets(C))
for Ak in colrange(A, j)
Cx = f(storedvals(A)[Ak])
Cx != fillvalue && (storedvals(C)[jo + storedinds(A)[Ak]] = Cx)
end
end
# NOTE: Combining the fill! above into the loop above to avoid multiple sweeps over /
# nonsequential access of storedvals(C) does not appear to improve performance.
return C
end
# helper functions for these methods and some of those below
@inline _densecoloffsets(A::SparseVector) = 0
@inline _densecoloffsets(A::SparseMatrixCSC) = 0:A.m:(A.m*(A.n - 1))
function _densestructure!(A::SparseVector)
expandstorage!(A, A.n)
copyto!(A.nzind, 1:A.n)
return A
end
function _densestructure!(A::SparseMatrixCSC)
nnzA = A.m * A.n
expandstorage!(A, nnzA)
copyto!(A.colptr, 1:A.m:(nnzA + 1))
for k in _densecoloffsets(A)
copyto!(A.rowval, k + 1, 1:A.m)
end
return A
end
# (5) _map_zeropres!/_map_notzeropres! specialized for a pair of sparse vectors/matrices
function _map_zeropres!(f::Tf, C::SparseVecOrMat, A::SparseVecOrMat, B::SparseVecOrMat) where Tf
spaceC::Int = min(length(storedinds(C)), length(storedvals(C)))
rowsentinelA = convert(indtype(A), numrows(C) + 1)
rowsentinelB = convert(indtype(B), numrows(C) + 1)
Ck = 1
@inbounds for j in columns(C)
setcolptr!(C, j, Ck)
Ak, stopAk = colstartind(A, j), colboundind(A, j)
Bk, stopBk = colstartind(B, j), colboundind(B, j)
Ai = Ak < stopAk ? storedinds(A)[Ak] : rowsentinelA
Bi = Bk < stopBk ? storedinds(B)[Bk] : rowsentinelB
while true
if Ai == Bi
Ai == rowsentinelA && break # column complete
Cx, Ci::indtype(C) = f(storedvals(A)[Ak], storedvals(B)[Bk]), Ai
Ak += oneunit(Ak); Ai = Ak < stopAk ? storedinds(A)[Ak] : rowsentinelA
Bk += oneunit(Bk); Bi = Bk < stopBk ? storedinds(B)[Bk] : rowsentinelB
elseif Ai < Bi
Cx, Ci = f(storedvals(A)[Ak], zero(eltype(B))), Ai
Ak += oneunit(Ak); Ai = Ak < stopAk ? storedinds(A)[Ak] : rowsentinelA
else # Bi < Ai
Cx, Ci = f(zero(eltype(A)), storedvals(B)[Bk]), Bi
Bk += oneunit(Bk); Bi = Bk < stopBk ? storedinds(B)[Bk] : rowsentinelB
end
# NOTE: The ordering of the conditional chain above impacts which matrices this
# method performs best for. In the map situation (arguments have same shape, and
# likely same or similar stored entry pattern), the Ai == Bi and termination
# cases are equally or more likely than the Ai < Bi and Bi < Ai cases. Hence
# the ordering of the conditional chain above differs from that in the
# corresponding broadcast code (below).
if !_iszero(Cx)
Ck > spaceC && (spaceC = expandstorage!(C, Ck + (nnz(A) - (Ak - 1)) + (nnz(B) - (Bk - 1))))
storedinds(C)[Ck] = Ci
storedvals(C)[Ck] = Cx
Ck += 1
end
end
end
@inbounds setcolptr!(C, numcols(C) + 1, Ck)
trimstorage!(C, Ck - 1)
return C
end
function _map_notzeropres!(f::Tf, fillvalue, C::SparseVecOrMat, A::SparseVecOrMat, B::SparseVecOrMat) where Tf
# Build dense matrix structure in C, expanding storage if necessary
_densestructure!(C)
# Populate values
fill!(storedvals(C), fillvalue)
# NOTE: Combining this fill! into the loop below to avoid multiple sweeps over /
# nonsequential access of storedvals(C) does not appear to improve performance.
rowsentinelA = convert(indtype(A), numrows(A) + 1)
rowsentinelB = convert(indtype(B), numrows(B) + 1)
@inbounds for (j, jo) in zip(columns(C), _densecoloffsets(C))
Ak, stopAk = colstartind(A, j), colboundind(A, j)
Bk, stopBk = colstartind(B, j), colboundind(B, j)
Ai = Ak < stopAk ? storedinds(A)[Ak] : rowsentinelA
Bi = Bk < stopBk ? storedinds(B)[Bk] : rowsentinelB
while true
if Ai == Bi
Ai == rowsentinelA && break # column complete
Cx, Ci::indtype(C) = f(storedvals(A)[Ak], storedvals(B)[Bk]), Ai
Ak += oneunit(Ak); Ai = Ak < stopAk ? storedinds(A)[Ak] : rowsentinelA
Bk += oneunit(Bk); Bi = Bk < stopBk ? storedinds(B)[Bk] : rowsentinelB
elseif Ai < Bi
Cx, Ci = f(storedvals(A)[Ak], zero(eltype(B))), Ai
Ak += oneunit(Ak); Ai = Ak < stopAk ? storedinds(A)[Ak] : rowsentinelA
else # Bi < Ai
Cx, Ci = f(zero(eltype(A)), storedvals(B)[Bk]), Bi
Bk += oneunit(Bk); Bi = Bk < stopBk ? storedinds(B)[Bk] : rowsentinelB
end
Cx != fillvalue && (storedvals(C)[jo + Ci] = Cx)
end
end
return C
end
# (6) _map_zeropres!/_map_notzeropres! for more than two sparse matrices / vectors
function _map_zeropres!(f::Tf, C::SparseVecOrMat, As::Vararg{SparseVecOrMat,N}) where {Tf,N}
spaceC::Int = min(length(storedinds(C)), length(storedvals(C)))
rowsentinel = numrows(C) + 1
Ck = 1
stopks = _colstartind_all(1, As)
@inbounds for j in columns(C)
setcolptr!(C, j, Ck)
ks = stopks
stopks = _colboundind_all(j, As)
rows = _rowforind_all(rowsentinel, ks, stopks, As)
activerow = min(rows...)
while activerow < rowsentinel
vals, ks, rows = _fusedupdate_all(rowsentinel, activerow, rows, ks, stopks, As)
Cx = f(vals...)
if !_iszero(Cx)
Ck > spaceC && (spaceC = expandstorage!(C, Ck + min(length(C), _sumnnzs(As...)) - (sum(ks) - N)))
storedinds(C)[Ck] = activerow
storedvals(C)[Ck] = Cx
Ck += 1
end
activerow = min(rows...)
end
end
@inbounds setcolptr!(C, numcols(C) + 1, Ck)
trimstorage!(C, Ck - 1)
return C
end
function _map_notzeropres!(f::Tf, fillvalue, C::SparseVecOrMat, As::Vararg{SparseVecOrMat,N}) where {Tf,N}
# Build dense matrix structure in C, expanding storage if necessary
_densestructure!(C)
# Populate values
fill!(storedvals(C), fillvalue)
# NOTE: Combining this fill! into the loop below to avoid multiple sweeps over /
# nonsequential access of C.nzval does not appear to improve performance.
rowsentinel = numrows(C) + 1
stopks = _colstartind_all(1, As)
@inbounds for (j, jo) in zip(columns(C), _densecoloffsets(C))
ks = stopks
stopks = _colboundind_all(j, As)
rows = _rowforind_all(rowsentinel, ks, stopks, As)
activerow = min(rows...)
while activerow < rowsentinel
vals, ks, rows = _fusedupdate_all(rowsentinel, activerow, rows, ks, stopks, As)
Cx = f(vals...)
Cx != fillvalue && (storedvals(C)[jo + activerow] = Cx)
activerow = min(rows...)
end
end
return C
end
# helper methods for map/map! methods just above
@inline _colstartind(j, A) = colstartind(A, j)
@inline _colstartind_all(j, ::Tuple{}) = ()
@inline _colstartind_all(j, As) = (
_colstartind(j, first(As)),
_colstartind_all(j, tail(As))...)
@inline _colboundind(j, A) = colboundind(A, j)
@inline _colboundind_all(j, ::Tuple{}) = ()
@inline _colboundind_all(j, As) = (
_colboundind(j, first(As)),
_colboundind_all(j, tail(As))...)
@inline _rowforind(rowsentinel, k, stopk, A) =
k < stopk ? storedinds(A)[k] : convert(indtype(A), rowsentinel)
@inline _rowforind_all(rowsentinel, ::Tuple{}, ::Tuple{}, ::Tuple{}) = ()
@inline _rowforind_all(rowsentinel, ks, stopks, As) = (
_rowforind(rowsentinel, first(ks), first(stopks), first(As)),
_rowforind_all(rowsentinel, tail(ks), tail(stopks), tail(As))...)
@inline function _fusedupdate(rowsentinel, activerow, row, k, stopk, A)
# returns (val, nextk, nextrow)
if row == activerow
nextk = k + oneunit(k)
(storedvals(A)[k], nextk, (nextk < stopk ? storedinds(A)[nextk] : oftype(row, rowsentinel)))
else
(zero(eltype(A)), k, row)
end
end
@inline _fusedupdate_all(rowsentinel, activerow, ::Tuple{}, ::Tuple{}, ::Tuple{}, ::Tuple{}) = ((#=vals=#), (#=nextks=#), (#=nextrows=#))
@inline function _fusedupdate_all(rowsentinel, activerow, rows, ks, stopks, As)
val, nextk, nextrow = _fusedupdate(rowsentinel, activerow, first(rows), first(ks), first(stopks), first(As))
vals, nextks, nextrows = _fusedupdate_all(rowsentinel, activerow, tail(rows), tail(ks), tail(stopks), tail(As))
return ((val, vals...), (nextk, nextks...), (nextrow, nextrows...))
end
# (7) _broadcast_zeropres!/_broadcast_notzeropres! specialized for a single (input) sparse vector/matrix
function _broadcast_zeropres!(f::Tf, C::SparseVecOrMat, A::SparseVecOrMat) where Tf
isempty(C) && return _finishempty!(C)
spaceC::Int = min(length(storedinds(C)), length(storedvals(C)))
# C and A cannot have the same shape, as we directed that case to map in broadcast's
# entry point; here we need efficiently handle only heterogeneous C-A combinations where
# one or both of C and A has at least one singleton dimension.
#
# We first divide the cases into two groups: those in which the input argument does not
# expand vertically, and those in which the input argument expands vertically.
#
# Cases without vertical expansion
Ck = 1
if numrows(A) == numrows(C)
@inbounds for j in columns(C)
setcolptr!(C, j, Ck)
bccolrangejA = numcols(A) == 1 ? colrange(A, 1) : colrange(A, j)
for Ak in bccolrangejA
Cx = f(storedvals(A)[Ak])
if !_iszero(Cx)
Ck > spaceC && (spaceC = expandstorage!(C, _unchecked_maxnnzbcres(size(C), A)))
storedinds(C)[Ck] = storedinds(A)[Ak]
storedvals(C)[Ck] = Cx
Ck += 1
end
end
end
# Cases with vertical expansion
else # numrows(A) != numrows(C) (=> numrows(A) == 1)
@inbounds for j in columns(C)
setcolptr!(C, j, Ck)
Ak, stopAk = numcols(A) == 1 ? (colstartind(A, 1), colboundind(A, 1)) : (colstartind(A, j), colboundind(A, j))
Ax = Ak < stopAk ? storedvals(A)[Ak] : zero(eltype(A))
fofAx = f(Ax)
# if fofAx is zero, then either A's jth column is empty, or A's jth column
# contains a nonzero value x but f(Ax) is nonetheless zero, so we need store
# nothing in C's jth column. if to the contrary fofAx is nonzero, then we must
# densely populate C's jth column with fofAx.
if !_iszero(fofAx)
for Ci::indtype(C) in 1:numrows(C)
Ck > spaceC && (spaceC = expandstorage!(C, _unchecked_maxnnzbcres(size(C), A)))
storedinds(C)[Ck] = Ci
storedvals(C)[Ck] = fofAx
Ck += 1
end
end
end
end
@inbounds setcolptr!(C, numcols(C) + 1, Ck)
trimstorage!(C, Ck - 1)
return C
end
function _broadcast_notzeropres!(f::Tf, fillvalue, C::SparseVecOrMat, A::SparseVecOrMat) where Tf
# For information on this code, see comments in similar code in _broadcast_zeropres! above
# Build dense matrix structure in C, expanding storage if necessary
_densestructure!(C)
# Populate values
fill!(storedvals(C), fillvalue)
# Cases without vertical expansion
if numrows(A) == numrows(C)
@inbounds for (j, jo) in zip(columns(C), _densecoloffsets(C))
bccolrangejA = numcols(A) == 1 ? colrange(A, 1) : colrange(A, j)
for Ak in bccolrangejA
Cx, Ci = f(storedvals(A)[Ak]), storedinds(A)[Ak]
Cx != fillvalue && (storedvals(C)[jo + Ci] = Cx)
end
end
# Cases with vertical expansion
else # numrows(A) != numrows(C) (=> numrows(A) == 1)
@inbounds for (j, jo) in zip(columns(C), _densecoloffsets(C))
Ak, stopAk = numcols(A) == 1 ? (colstartind(A, 1), colboundind(A, 1)) : (colstartind(A, j), colboundind(A, j))
Ax = Ak < stopAk ? storedvals(A)[Ak] : zero(eltype(A))
fofAx = f(Ax)
fofAx != fillvalue && (storedvals(C)[(jo + 1):(jo + numrows(C))] = fofAx)
end
end
return C
end
# (8) _broadcast_zeropres!/_broadcast_notzeropres! specialized for a pair of (input) sparse vectors/matrices
function _broadcast_zeropres!(f::Tf, C::SparseVecOrMat, A::SparseVecOrMat, B::SparseVecOrMat) where Tf
isempty(C) && return _finishempty!(C)
spaceC::Int = min(length(storedinds(C)), length(storedvals(C)))
rowsentinelA = convert(indtype(A), numrows(C) + 1)
rowsentinelB = convert(indtype(B), numrows(C) + 1)
# C, A, and B cannot all have the same shape, as we directed that case to map in broadcast's
# entry point; here we need efficiently handle only heterogeneous combinations of mats/vecs
# with no singleton dimensions, one singleton dimension, and two singleton dimensions.
# Cases involving objects with two singleton dimensions should be rare and optimizing
# that case complicates the code appreciably, so we largely ignore that case's
# performance below.
#
# We first divide the cases into two groups: those in which neither input argument
# expands vertically, and those in which at least one argument expands vertically.
#
# NOTE: Placing the loops over columns outside the conditional chain segregating
# argument shape combinations eliminates some code replication but unfortunately
# hurts performance appreciably in some cases.
#
# Cases without vertical expansion
Ck = 1
if numrows(A) == numrows(B) == numrows(C)
@inbounds for j in columns(C)
setcolptr!(C, j, Ck)
Ak, stopAk = numcols(A) == 1 ? (colstartind(A, 1), colboundind(A, 1)) : (colstartind(A, j), colboundind(A, j))
Bk, stopBk = numcols(B) == 1 ? (colstartind(B, 1), colboundind(B, 1)) : (colstartind(B, j), colboundind(B, j))
# Restructuring this k/stopk code to avoid unnecessary colptr retrievals does
# not improve performance signicantly. Leave in this less complex form.
Ai = Ak < stopAk ? storedinds(A)[Ak] : rowsentinelA
Bi = Bk < stopBk ? storedinds(B)[Bk] : rowsentinelB
while true
if Ai != Bi
if Ai < Bi
Cx, Ci = f(storedvals(A)[Ak], zero(eltype(B))), Ai
Ak += oneunit(Ak); Ai = Ak < stopAk ? storedinds(A)[Ak] : rowsentinelA
else # Ai > Bi
Cx, Ci = f(zero(eltype(A)), storedvals(B)[Bk]), Bi
Bk += oneunit(Bk); Bi = Bk < stopBk ? storedinds(B)[Bk] : rowsentinelB
end
elseif #= Ai == Bi && =# Ai == rowsentinelA
break # column complete
else #= Ai == Bi != rowsentinel =#
Cx, Ci::indtype(C) = f(storedvals(A)[Ak], storedvals(B)[Bk]), Ai
Ak += oneunit(Ak); Ai = Ak < stopAk ? storedinds(A)[Ak] : rowsentinelA
Bk += oneunit(Bk); Bi = Bk < stopBk ? storedinds(B)[Bk] : rowsentinelB
end
# NOTE: The ordering of the conditional chain above impacts which matrices
# this method perform best for. In contrast to the map situation (arguments
# have same shape, and likely same or similar stored entry pattern), where
# the Ai == Bi and termination cases are equally or more likely than the
# Ai < Bi and Bi < Ai cases, in the broadcast situation (arguments have
# different shape, and likely largely disjoint expanded stored entry
# pattern) the Ai < Bi and Bi < Ai cases are equally or more likely than the
# Ai == Bi and termination cases. Hence the ordering of the conditional
# chain above differs from that in the corresponding map code.
if !_iszero(Cx)
Ck > spaceC && (spaceC = expandstorage!(C, _unchecked_maxnnzbcres(size(C), A, B)))
storedinds(C)[Ck] = Ci
storedvals(C)[Ck] = Cx
Ck += 1
end
end
end
# Cases with vertical expansion
elseif numrows(A) == numrows(B) == 1 # && numrows(C) != 1, vertically expand both A and B
@inbounds for j in columns(C)
setcolptr!(C, j, Ck)
Ak, stopAk = numcols(A) == 1 ? (colstartind(A, 1), colboundind(A, 1)) : (colstartind(A, j), colboundind(A, j))
Bk, stopBk = numcols(B) == 1 ? (colstartind(B, 1), colboundind(B, 1)) : (colstartind(B, j), colboundind(B, j))
Ax = Ak < stopAk ? storedvals(A)[Ak] : zero(eltype(A))
Bx = Bk < stopBk ? storedvals(B)[Bk] : zero(eltype(B))
Cx = f(Ax, Bx)
if !_iszero(Cx)
for Ci::indtype(C) in 1:numrows(C)
Ck > spaceC && (spaceC = expandstorage!(C, _unchecked_maxnnzbcres(size(C), A, B)))
storedinds(C)[Ck] = Ci
storedvals(C)[Ck] = Cx
Ck += 1
end
end
end
elseif numrows(A) == 1 # && numrows(B) == numrows(C) != 1 , vertically expand only A
@inbounds for j in columns(C)
setcolptr!(C, j, Ck)
Ak, stopAk = numcols(A) == 1 ? (colstartind(A, 1), colboundind(A, 1)) : (colstartind(A, j), colboundind(A, j))
Bk, stopBk = numcols(B) == 1 ? (colstartind(B, 1), colboundind(B, 1)) : (colstartind(B, j), colboundind(B, j))
Ax = Ak < stopAk ? storedvals(A)[Ak] : zero(eltype(A))
fvAzB = f(Ax, zero(eltype(B)))
if _iszero(fvAzB)
# either A's jth column is empty, or A's jth column contains a nonzero value
# Ax but f(Ax, zero(eltype(B))) is nonetheless zero, so we can scan through
# B's jth column without storing every entry in C's jth column
while Bk < stopBk
Cx = f(Ax, storedvals(B)[Bk])
if !_iszero(Cx)
Ck > spaceC && (spaceC = expandstorage!(C, _unchecked_maxnnzbcres(size(C), A, B)))
storedinds(C)[Ck] = storedinds(B)[Bk]
storedvals(C)[Ck] = Cx
Ck += 1
end
Bk += oneunit(Bk)
end
else
# A's jth column is nonempty and f(Ax, zero(eltype(B))) is not zero, so
# we must store (likely) every entry in C's jth column
Bi = Bk < stopBk ? storedinds(B)[Bk] : rowsentinelB
for Ci::indtype(C) in 1:numrows(C)
if Bi == Ci
Cx = f(Ax, storedvals(B)[Bk])
Bk += oneunit(Bk); Bi = Bk < stopBk ? storedinds(B)[Bk] : rowsentinelB
else
Cx = fvAzB
end
if !_iszero(Cx)
Ck > spaceC && (spaceC = expandstorage!(C, _unchecked_maxnnzbcres(size(C), A, B)))
storedinds(C)[Ck] = Ci
storedvals(C)[Ck] = Cx
Ck += 1
end
end
end
end
else # numrows(B) == 1 && numrows(A) == numrows(C) != 1, vertically expand only B
@inbounds for j in columns(C)
setcolptr!(C, j, Ck)
Ak, stopAk = numcols(A) == 1 ? (colstartind(A, 1), colboundind(A, 1)) : (colstartind(A, j), colboundind(A, j))
Bk, stopBk = numcols(B) == 1 ? (colstartind(B, 1), colboundind(B, 1)) : (colstartind(B, j), colboundind(B, j))
Bx = Bk < stopBk ? storedvals(B)[Bk] : zero(eltype(B))
fzAvB = f(zero(eltype(A)), Bx)
if _iszero(fzAvB)
# either B's jth column is empty, or B's jth column contains a nonzero value
# Bx but f(zero(eltype(A)), Bx) is nonetheless zero, so we can scan through
# A's jth column without storing every entry in C's jth column
while Ak < stopAk
Cx = f(storedvals(A)[Ak], Bx)
if !_iszero(Cx)
Ck > spaceC && (spaceC = expandstorage!(C, _unchecked_maxnnzbcres(size(C), A, B)))
storedinds(C)[Ck] = storedinds(A)[Ak]
storedvals(C)[Ck] = Cx
Ck += 1
end
Ak += oneunit(Ak)
end
else
# B's jth column is nonempty and f(zero(eltype(A)), Bx) is not zero, so
# we must store (likely) every entry in C's jth column
Ai = Ak < stopAk ? storedinds(A)[Ak] : rowsentinelA
for Ci::indtype(C) in 1:numrows(C)
if Ai == Ci
Cx = f(storedvals(A)[Ak], Bx)
Ak += oneunit(Ak); Ai = Ak < stopAk ? storedinds(A)[Ak] : rowsentinelA
else
Cx = fzAvB
end
if !_iszero(Cx)
Ck > spaceC && (spaceC = expandstorage!(C, _unchecked_maxnnzbcres(size(C), A, B)))
storedinds(C)[Ck] = Ci
storedvals(C)[Ck] = Cx
Ck += 1
end
end
end
end
end
@inbounds setcolptr!(C, numcols(C) + 1, Ck)
trimstorage!(C, Ck - 1)
return C
end
function _broadcast_notzeropres!(f::Tf, fillvalue, C::SparseVecOrMat, A::SparseVecOrMat, B::SparseVecOrMat) where Tf
# For information on this code, see comments in similar code in _broadcast_zeropres! above
# Build dense matrix structure in C, expanding storage if necessary
_densestructure!(C)
# Populate values
fill!(storedvals(C), fillvalue)
rowsentinelA = convert(indtype(A), numrows(C) + 1)
rowsentinelB = convert(indtype(B), numrows(C) + 1)
# Cases without vertical expansion
if numrows(A) == numrows(B) == numrows(C)
@inbounds for (j, jo) in zip(columns(C), _densecoloffsets(C))
Ak, stopAk = numcols(A) == 1 ? (colstartind(A, 1), colboundind(A, 1)) : (colstartind(A, j), colboundind(A, j))
Bk, stopBk = numcols(B) == 1 ? (colstartind(B, 1), colboundind(B, 1)) : (colstartind(B, j), colboundind(B, j))
Ai = Ak < stopAk ? storedinds(A)[Ak] : rowsentinelA
Bi = Bk < stopBk ? storedinds(B)[Bk] : rowsentinelB
while true
if Ai < Bi
Cx, Ci = f(storedvals(A)[Ak], zero(eltype(B))), Ai
Ak += oneunit(Ak); Ai = Ak < stopAk ? storedinds(A)[Ak] : rowsentinelA
elseif Ai > Bi
Cx, Ci = f(zero(eltype(A)), storedvals(B)[Bk]), Bi
Bk += oneunit(Bk); Bi = Bk < stopBk ? storedinds(B)[Bk] : rowsentinelB
elseif #= Ai == Bi && =# Ai == rowsentinelA
break # column complete
else #= Ai == Bi != rowsentinel =#
Cx, Ci::indtype(C) = f(storedvals(A)[Ak], storedvals(B)[Bk]), Ai
Ak += oneunit(Ak); Ai = Ak < stopAk ? storedinds(A)[Ak] : rowsentinelA
Bk += oneunit(Bk); Bi = Bk < stopBk ? storedinds(B)[Bk] : rowsentinelB
end
Cx != fillvalue && (storedvals(C)[jo + Ci] = Cx)
end
end
# Cases with vertical expansion
elseif numrows(A) == numrows(B) == 1 # && numrows(C) != 1, vertically expand both A and B
@inbounds for (j, jo) in zip(columns(C), _densecoloffsets(C))
Ak, stopAk = numcols(A) == 1 ? (colstartind(A, 1), colboundind(A, 1)) : (colstartind(A, j), colboundind(A, j))
Bk, stopBk = numcols(B) == 1 ? (colstartind(B, 1), colboundind(B, 1)) : (colstartind(B, j), colboundind(B, j))
Ax = Ak < stopAk ? storedvals(A)[Ak] : zero(eltype(A))
Bx = Bk < stopBk ? storedvals(B)[Bk] : zero(eltype(B))
Cx = f(Ax, Bx)
if Cx != fillvalue
for Ck::Int in (jo + 1):(jo + numrows(C))
storedvals(C)[Ck] = Cx
end
end
end
elseif numrows(A) == 1 # && numrows(B) == numrows(C) != 1, vertically expand only A
@inbounds for (j, jo) in zip(columns(C), _densecoloffsets(C))
Ak, stopAk = numcols(A) == 1 ? (colstartind(A, 1), colboundind(A, 1)) : (colstartind(A, j), colboundind(A, j))
Bk, stopBk = numcols(B) == 1 ? (colstartind(B, 1), colboundind(B, 1)) : (colstartind(B, j), colboundind(B, j))
Ax = Ak < stopAk ? storedvals(A)[Ak] : zero(eltype(A))
fvAzB = f(Ax, zero(eltype(B)))
if _iszero(fvAzB)
while Bk < stopBk
Cx = f(Ax, storedvals(B)[Bk])
Cx != fillvalue && (storedvals(C)[jo + storedinds(B)[Bk]] = Cx)
Bk += oneunit(Bk)
end
else
Bi = Bk < stopBk ? storedinds(B)[Bk] : rowsentinelB
for Ci::indtype(C) in 1:numrows(C)
if Bi == Ci
Cx = f(Ax, storedvals(B)[Bk])
Bk += oneunit(Bk); Bi = Bk < stopBk ? storedinds(B)[Bk] : rowsentinelB
else
Cx = fvAzB
end
Cx != fillvalue && (storedvals(C)[jo + Ci] = Cx)
end
end
end
else # numrows(B) == 1 && numrows(A) == numrows(C) != 1, vertically expand only B
@inbounds for (j, jo) in zip(columns(C), _densecoloffsets(C))
Ak, stopAk = numcols(A) == 1 ? (colstartind(A, 1), colboundind(A, 1)) : (colstartind(A, j), colboundind(A, j))
Bk, stopBk = numcols(B) == 1 ? (colstartind(B, 1), colboundind(B, 1)) : (colstartind(B, j), colboundind(B, j))
Bx = Bk < stopBk ? storedvals(B)[Bk] : zero(eltype(B))
fzAvB = f(zero(eltype(A)), Bx)
if _iszero(fzAvB)
while Ak < stopAk
Cx = f(storedvals(A)[Ak], Bx)
Cx != fillvalue && (storedvals(C)[jo + storedinds(A)[Ak]] = Cx)
Ak += oneunit(Ak)
end
else
Ai = Ak < stopAk ? storedinds(A)[Ak] : rowsentinelA
for Ci::indtype(C) in 1:numrows(C)
if Ai == Ci
Cx = f(storedvals(A)[Ak], Bx)
Ak += oneunit(Ak); Ai = Ak < stopAk ? storedinds(A)[Ak] : rowsentinelA
else
Cx = fzAvB
end
Cx != fillvalue && (storedvals(C)[jo + Ci] = Cx)
end
end
end
end
return C
end
_finishempty!(C::SparseVector) = C
_finishempty!(C::SparseMatrixCSC) = (fill!(C.colptr, 1); C)
# (9) _broadcast_zeropres!/_broadcast_notzeropres! for more than two (input) sparse vectors/matrices
function _broadcast_zeropres!(f::Tf, C::SparseVecOrMat, As::Vararg{SparseVecOrMat,N}) where {Tf,N}
isempty(C) && return _finishempty!(C)
spaceC::Int = min(length(storedinds(C)), length(storedvals(C)))
expandsverts = _expandsvert_all(C, As)
expandshorzs = _expandshorz_all(C, As)
rowsentinel = numrows(C) + 1
Ck = 1
@inbounds for j in columns(C)
setcolptr!(C, j, Ck)
ks = _startindforbccol_all(j, expandshorzs, As)
stopks = _stopindforbccol_all(j, expandshorzs, As)
# Neither fusing ks and stopks construction, nor restructuring them to avoid repeated
# colptr lookups, improves performance significantly. So keep the less complex approach here.
isemptys = _isemptycol_all(ks, stopks)
defargs = _defargforcol_all(j, isemptys, expandsverts, ks, As)
rows = _initrowforcol_all(j, rowsentinel, isemptys, expandsverts, ks, As)
defaultCx = f(defargs...)
activerow = min(rows...)
if _iszero(defaultCx) # zero-preserving column scan
while activerow < rowsentinel
args, ks, rows = _fusedupdatebc_all(rowsentinel, activerow, rows, defargs, ks, stopks, As)
Cx = f(args...)
if !_iszero(Cx)
Ck > spaceC && (spaceC = expandstorage!(C, _unchecked_maxnnzbcres(size(C), As)))
storedinds(C)[Ck] = activerow
storedvals(C)[Ck] = Cx
Ck += 1
end
activerow = min(rows...)
end
else # zero-non-preserving column scan
for Ci in 1:numrows(C)
if Ci == activerow
args, ks, rows = _fusedupdatebc_all(rowsentinel, activerow, rows, defargs, ks, stopks, As)
Cx = f(args...)
activerow = min(rows...)
else
Cx = defaultCx
end
if !_iszero(Cx)
Ck > spaceC && (spaceC = expandstorage!(C, _unchecked_maxnnzbcres(size(C), As)))
storedinds(C)[Ck] = Ci
storedvals(C)[Ck] = Cx
Ck += 1
end
end
end
end
@inbounds setcolptr!(C, numcols(C) + 1, Ck)
trimstorage!(C, Ck - 1)
return C
end
function _broadcast_notzeropres!(f::Tf, fillvalue, C::SparseVecOrMat, As::Vararg{SparseVecOrMat,N}) where {Tf,N}
isempty(C) && return _finishempty!(C)
# Build dense matrix structure in C, expanding storage if necessary
_densestructure!(C)
# Populate values
fill!(storedvals(C), fillvalue)
expandsverts = _expandsvert_all(C, As)
expandshorzs = _expandshorz_all(C, As)
rowsentinel = numrows(C) + 1
@inbounds for (j, jo) in zip(columns(C), _densecoloffsets(C))
ks = _startindforbccol_all(j, expandshorzs, As)
stopks = _stopindforbccol_all(j, expandshorzs, As)
# Neither fusing ks and stopks construction, nor restructuring them to avoid repeated
# colptr lookups, improves performance significantly. So keep the less complex approach here.
isemptys = _isemptycol_all(ks, stopks)
defargs = _defargforcol_all(j, isemptys, expandsverts, ks, As)
rows = _initrowforcol_all(j, rowsentinel, isemptys, expandsverts, ks, As)
defaultCx = f(defargs...)
activerow = min(rows...)
if defaultCx == fillvalue # fillvalue-preserving column scan
while activerow < rowsentinel
args, ks, rows = _fusedupdatebc_all(rowsentinel, activerow, rows, defargs, ks, stopks, As)
Cx = f(args...)
Cx != fillvalue && (storedvals(C)[jo + activerow] = Cx)
activerow = min(rows...)
end
else # fillvalue-non-preserving column scan
for Ci in 1:numrows(C)
if Ci == activerow
args, ks, rows = _fusedupdatebc_all(rowsentinel, activerow, rows, defargs, ks, stopks, As)
Cx = f(args...)
activerow = min(rows...)
else
Cx = defaultCx
end
Cx != fillvalue && (storedvals(C)[jo + Ci] = Cx)
end
end
end
return C
end
# helper method for broadcast/broadcast! methods just above
@inline _expandsvert(C, A) = numrows(A) != numrows(C)
@inline _expandsvert_all(C, ::Tuple{}) = ()
@inline _expandsvert_all(C, As) = (_expandsvert(C, first(As)), _expandsvert_all(C, tail(As))...)
@inline _expandshorz(C, A) = numcols(A) != numcols(C)
@inline _expandshorz_all(C, ::Tuple{}) = ()
@inline _expandshorz_all(C, As) = (_expandshorz(C, first(As)), _expandshorz_all(C, tail(As))...)
@inline _startindforbccol(j, expandshorz, A) = expandshorz ? colstartind(A, 1) : colstartind(A, j)
@inline _startindforbccol_all(j, ::Tuple{}, ::Tuple{}) = ()
@inline _startindforbccol_all(j, expandshorzs, As) = (
_startindforbccol(j, first(expandshorzs), first(As)),
_startindforbccol_all(j, tail(expandshorzs), tail(As))...)
@inline _stopindforbccol(j, expandshorz, A) = expandshorz ? colboundind(A, 1) : colboundind(A, j)
@inline _stopindforbccol_all(j, ::Tuple{}, ::Tuple{}) = ()
@inline _stopindforbccol_all(j, expandshorzs, As) = (
_stopindforbccol(j, first(expandshorzs), first(As)),
_stopindforbccol_all(j, tail(expandshorzs), tail(As))...)
@inline _isemptycol(k, stopk) = k == stopk
@inline _isemptycol_all(::Tuple{}, ::Tuple{}) = ()
@inline _isemptycol_all(ks, stopks) = (
_isemptycol(first(ks), first(stopks)),
_isemptycol_all(tail(ks), tail(stopks))...)
@inline _initrowforcol(j, rowsentinel, isempty, expandsvert, k, A) =
expandsvert || isempty ? convert(indtype(A), rowsentinel) : storedinds(A)[k]
@inline _initrowforcol_all(j, rowsentinel, ::Tuple{}, ::Tuple{}, ::Tuple{}, ::Tuple{}) = ()
@inline _initrowforcol_all(j, rowsentinel, isemptys, expandsverts, ks, As) = (
_initrowforcol(j, rowsentinel, first(isemptys), first(expandsverts), first(ks), first(As)),
_initrowforcol_all(j, rowsentinel, tail(isemptys), tail(expandsverts), tail(ks), tail(As))...)
@inline _defargforcol(j, isempty, expandsvert, k, A) =
expandsvert && !isempty ? storedvals(A)[k] : zero(eltype(A))
@inline _defargforcol_all(j, ::Tuple{}, ::Tuple{}, ::Tuple{}, ::Tuple{}) = ()
@inline _defargforcol_all(j, isemptys, expandsverts, ks, As) = (
_defargforcol(j, first(isemptys), first(expandsverts), first(ks), first(As)),
_defargforcol_all(j, tail(isemptys), tail(expandsverts), tail(ks), tail(As))...)
@inline function _fusedupdatebc(rowsentinel, activerow, row, defarg, k, stopk, A)
# returns (val, nextk, nextrow)
if row == activerow
nextk = k + oneunit(k)
(storedvals(A)[k], nextk, (nextk < stopk ? storedinds(A)[nextk] : oftype(row, rowsentinel)))
else
(defarg, k, row)
end
end
@inline _fusedupdatebc_all(rowsent, activerow, ::Tuple{}, ::Tuple{}, ::Tuple{}, ::Tuple{}, ::Tuple{}) = ((#=vals=#), (#=nextks=#), (#=nextrows=#))
@inline function _fusedupdatebc_all(rowsentinel, activerow, rows, defargs, ks, stopks, As)
val, nextk, nextrow = _fusedupdatebc(rowsentinel, activerow, first(rows), first(defargs), first(ks), first(stopks), first(As))
vals, nextks, nextrows = _fusedupdatebc_all(rowsentinel, activerow, tail(rows), tail(defargs), tail(ks), tail(stopks), tail(As))
return ((val, vals...), (nextk, nextks...), (nextrow, nextrows...))
end
# (10) broadcast over combinations of broadcast scalars and sparse vectors/matrices
# broadcast container type promotion for combinations of sparse arrays and other types
struct SparseVecStyle <: Broadcast.AbstractArrayStyle{1} end
struct SparseMatStyle <: Broadcast.AbstractArrayStyle{2} end
Broadcast.BroadcastStyle(::Type{<:SparseVector}) = SparseVecStyle()
Broadcast.BroadcastStyle(::Type{<:SparseMatrixCSC}) = SparseMatStyle()
const SPVM = Union{SparseVecStyle,SparseMatStyle}
# SparseVecStyle handles 0-1 dimensions, SparseMatStyle 0-2 dimensions.
# SparseVecStyle promotes to SparseMatStyle for 2 dimensions.
# Fall back to DefaultArrayStyle for higher dimensionality.
SparseVecStyle(::Val{0}) = SparseVecStyle()
SparseVecStyle(::Val{1}) = SparseVecStyle()
SparseVecStyle(::Val{2}) = SparseMatStyle()
SparseVecStyle(::Val{N}) where N = Broadcast.DefaultArrayStyle{N}()
SparseMatStyle(::Val{0}) = SparseMatStyle()
SparseMatStyle(::Val{1}) = SparseMatStyle()
SparseMatStyle(::Val{2}) = SparseMatStyle()
SparseMatStyle(::Val{N}) where N = Broadcast.DefaultArrayStyle{N}()
Broadcast.BroadcastStyle(::SparseMatStyle, ::SparseVecStyle) = SparseMatStyle()
# Tuples promote to dense
Broadcast.BroadcastStyle(::SparseVecStyle, ::Broadcast.Style{Tuple}) = Broadcast.DefaultArrayStyle{1}()
Broadcast.BroadcastStyle(::SparseMatStyle, ::Broadcast.Style{Tuple}) = Broadcast.DefaultArrayStyle{2}()
# broadcast entry points for combinations of sparse arrays and other (scalar) types
function broadcast(f, ::SPVM, ::Void, ::Void, mixedargs::Vararg{Any,N}) where N
parevalf, passedargstup = capturescalars(f, mixedargs)
return broadcast(parevalf, passedargstup...)
end
# for broadcast! see (11)
# capturescalars takes a function (f) and a tuple of mixed sparse vectors/matrices and
# broadcast scalar arguments (mixedargs), and returns a function (parevalf, i.e. partially
# evaluated f) and a reduced argument tuple (passedargstup) containing only the sparse
# vectors/matrices in mixedargs in their orginal order, and such that the result of
# broadcast(parevalf, passedargstup...) is broadcast(f, mixedargs...)
@inline function capturescalars(f, mixedargs)
let (passedsrcargstup, makeargs) = _capturescalars(mixedargs...)
parevalf = (passed...) -> f(makeargs(passed...)...)
return (parevalf, passedsrcargstup)
end
end
nonscalararg(::SparseVecOrMat) = true
nonscalararg(::Any) = false
@inline function _capturescalars()
return (), () -> ()
end
@inline function _capturescalars(arg, mixedargs...)
let (rest, f) = _capturescalars(mixedargs...)
if nonscalararg(arg)
return (arg, rest...), (head, tail...) -> (head, f(tail...)...) # pass-through to broadcast
else
return rest, (tail...) -> (arg, f(tail...)...) # add back scalararg after (in makeargs)
end
end
end
@inline function _capturescalars(arg) # this definition is just an optimization (to bottom out the recursion slightly sooner)
if nonscalararg(arg)
return (arg,), (head,) -> (head,) # pass-through
else
return (), () -> (arg,) # add scalararg
end
end
# NOTE: The following two method definitions work around #19096.
broadcast(f::Tf, ::Type{T}, A::SparseMatrixCSC) where {Tf,T} = broadcast(y -> f(T, y), A)
broadcast(f::Tf, A::SparseMatrixCSC, ::Type{T}) where {Tf,T} = broadcast(x -> f(x, T), A)
# (11) broadcast[!] over combinations of scalars, sparse vectors/matrices, structured matrices,
# and one- and two-dimensional Arrays (via promotion of structured matrices and Arrays)
#
# for combinations involving only scalars, sparse arrays, structured matrices, and dense
# vectors/matrices, promote all structured matrices and dense vectors/matrices to sparse
# and rebroadcast. otherwise, divert to generic AbstractArray broadcast code.
struct PromoteToSparse <: Broadcast.AbstractArrayStyle{2} end
StructuredMatrix = Union{Diagonal,Bidiagonal,Tridiagonal,SymTridiagonal}
Broadcast.BroadcastStyle(::Type{<:StructuredMatrix}) = PromoteToSparse()
PromoteToSparse(::Val{0}) = PromoteToSparse()
PromoteToSparse(::Val{1}) = PromoteToSparse()
PromoteToSparse(::Val{2}) = PromoteToSparse()
PromoteToSparse(::Val{N}) where N = Broadcast.DefaultArrayStyle{N}()
Broadcast.BroadcastStyle(::PromoteToSparse, ::SPVM) = PromoteToSparse()
Broadcast.BroadcastStyle(::PromoteToSparse, ::Broadcast.Style{Tuple}) = Broadcast.DefaultArrayStyle{2}()
# FIXME: switch to DefaultArrayStyle once we can delete VectorStyle and MatrixStyle
# Broadcast.BroadcastStyle(::SPVM, ::Broadcast.DefaultArrayStyle{0}) = PromoteToSparse()
# Broadcast.BroadcastStyle(::SPVM, ::Broadcast.DefaultArrayStyle{1}) = PromoteToSparse()
# Broadcast.BroadcastStyle(::SPVM, ::Broadcast.DefaultArrayStyle{2}) = PromoteToSparse()
BroadcastStyle(::Type{<:Base.Adjoint{T,<:Vector}}) where T = Broadcast.MatrixStyle() # Adjoint not yet defined when broadcast.jl loaded
BroadcastStyle(::Type{<:Base.Transpose{T,<:Vector}}) where T = Broadcast.MatrixStyle() # Transpose not yet defined when broadcast.jl loaded
Broadcast.BroadcastStyle(::SPVM, ::Broadcast.VectorStyle) = PromoteToSparse()
Broadcast.BroadcastStyle(::SPVM, ::Broadcast.MatrixStyle) = PromoteToSparse()
Broadcast.BroadcastStyle(::SparseVecStyle, ::Broadcast.DefaultArrayStyle{N}) where N =