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Oct 10, 2018
Merged

add specialized methods for Triangular * Triangular #511

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059c66e
add specialized methods for Triangular*Triangular
kleinschmidt Oct 3, 2018
bad957d
tests for Triangular*Triangular
kleinschmidt Oct 3, 2018
c90c055
replace top level `quote end` with `Expr(:block)` in generated
kleinschmidt Oct 8, 2018
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167 changes: 148 additions & 19 deletions src/triangular.jl
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Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -17,9 +17,12 @@
@inline Base.:*(A::LinearAlgebra.AbstractTriangular{<:Any,<:StaticMatrix}, B::Transpose{<:Any,<:StaticVecOrMat}) =
transpose(transpose(B) * transpose(A))

const StaticULT = Union{UpperTriangular{<:Any,<:StaticMatrix},LowerTriangular{<:Any,<:StaticMatrix}}

@inline Base.:*(A::LinearAlgebra.AbstractTriangular{<:Any,<:StaticMatrix}, B::StaticVecOrMat) = _A_mul_B(Size(A), Size(B), A, B)
@inline Base.:*(A::StaticVecOrMat, B::LinearAlgebra.AbstractTriangular{<:Any,<:StaticMatrix}) = _A_mul_B(Size(A), Size(B), A, B)
@inline Base.:\(A::Union{UpperTriangular{<:Any,<:StaticMatrix},LowerTriangular{<:Any,<:StaticMatrix}}, B::StaticVecOrMat) = _A_ldiv_B(Size(A), Size(B), A, B)
@inline Base.:*(A::StaticULT, B::StaticULT) = _A_mul_B(Size(A), Size(B), A, B)
@inline Base.:\(A::StaticULT, B::StaticVecOrMat) = _A_ldiv_B(Size(A), Size(B), A, B)


@generated function _A_mul_B(::Size{sa}, ::Size{sb}, A::UpperTriangular{TA,<:StaticMatrix}, B::StaticVecOrMat{TB}) where {sa,sb,TA,TB}
Expand All @@ -31,7 +34,7 @@

X = [Symbol("X_$(i)_$(j)") for i = 1:m, j = 1:n]

code = quote end
code = Expr(:block)
for j = 1:n
for i = 1:m
ex = :(A.data[$(LinearIndices(sa)[i, i])]*B[$(LinearIndices(sb)[i, j])])
Expand Down Expand Up @@ -59,7 +62,7 @@ end

X = [Symbol("X_$(i)_$(j)") for i = 1:m, j = 1:n]

code = quote end
code = Expr(:block)
for j = 1:n
for i = m:-1:1
ex = :(A.data[$(LinearIndices(sa)[i, i])]'*B[$(LinearIndices(sb)[i, j])])
Expand Down Expand Up @@ -87,7 +90,7 @@ end

X = [Symbol("X_$(i)_$(j)") for i = 1:m, j = 1:n]

code = quote end
code = Expr(:block)
for j = 1:n
for i = m:-1:1
ex = :(transpose(A.data[$(LinearIndices(sa)[i, i])])*B[$(LinearIndices(sb)[i, j])])
Expand Down Expand Up @@ -115,7 +118,7 @@ end

X = [Symbol("X_$(i)_$(j)") for i = 1:m, j = 1:n]

code = quote end
code = Expr(:block)
for j = 1:n
for i = m:-1:1
ex = :(A.data[$(LinearIndices(sa)[i, i])]*B[$(LinearIndices(sb)[i, j])])
Expand Down Expand Up @@ -143,7 +146,7 @@ end

X = [Symbol("X_$(i)_$(j)") for i = 1:m, j = 1:n]

code = quote end
code = Expr(:block)
for j = 1:n
for i = 1:m
ex = :(A.data[$(LinearIndices(sa)[i, i])]'*B[$(LinearIndices(sb)[i, j])])
Expand Down Expand Up @@ -171,7 +174,7 @@ end

X = [Symbol("X_$(i)_$(j)") for i = 1:m, j = 1:n]

code = quote end
code = Expr(:block)
for j = 1:n
for i = 1:m
ex = :(transpose(A.data[$(LinearIndices(sa)[i, i])])*B[$(LinearIndices(sb)[i, j])])
Expand Down Expand Up @@ -203,7 +206,7 @@ end

X = [Symbol("X_$(i)_$(j)") for i = 1:m, j = 1:n]

code = quote end
code = Expr(:block)
for i = 1:m
for j = n:-1:1
ex = :(A[$(LinearIndices(sa)[i, j])]*B[$(LinearIndices(sb)[j, j])])
Expand Down Expand Up @@ -235,7 +238,7 @@ end

X = [Symbol("X_$(i)_$(j)") for i = 1:m, j = 1:n]

code = quote end
code = Expr(:block)
for i = 1:m
for j = 1:n
ex = :(A[$(LinearIndices(sa)[i, j])]*B[$(LinearIndices(sb)[j, j])]')
Expand All @@ -262,7 +265,7 @@ end

X = [Symbol("X_$(i)_$(j)") for i = 1:m, j = 1:n]

code = quote end
code = Expr(:block)
for i = 1:m
for j = 1:n
ex = :(A[$(LinearIndices(sa)[i, j])]*transpose(B[$(LinearIndices(sb)[j, j])]))
Expand Down Expand Up @@ -294,7 +297,7 @@ end

X = [Symbol("X_$(i)_$(j)") for i = 1:m, j = 1:n]

code = quote end
code = Expr(:block)
for i = 1:m
for j = 1:n
ex = :(A[$(LinearIndices(sa)[i, j])]*B[$(LinearIndices(sb)[j, j])])
Expand Down Expand Up @@ -326,7 +329,7 @@ end

X = [Symbol("X_$(i)_$(j)") for i = 1:m, j = 1:n]

code = quote end
code = Expr(:block)
for i = 1:m
for j = n:-1:1
ex = :(A[$(LinearIndices(sa)[i, j])]*B[$(LinearIndices(sb)[j, j])]')
Expand All @@ -353,7 +356,7 @@ end

X = [Symbol("X_$(i)_$(j)") for i = 1:m, j = 1:n]

code = quote end
code = Expr(:block)
for i = 1:m
for j = n:-1:1
ex = :(A[$(LinearIndices(sa)[i, j])]*transpose(B[$(LinearIndices(sb)[j, j])]))
Expand Down Expand Up @@ -382,7 +385,7 @@ end
X = [Symbol("X_$(i)_$(j)") for i = 1:m, j = 1:n]
init = [:($(X[i,j]) = B[$(LinearIndices(sb)[i, j])]) for i = 1:m, j = 1:n]

code = quote end
code = Expr(:block)
for k = 1:n
for j = m:-1:1
if k == 1
Expand Down Expand Up @@ -414,7 +417,7 @@ end
X = [Symbol("X_$(i)_$(j)") for i = 1:m, j = 1:n]
init = [:($(X[i,j]) = B[$(LinearIndices(sb)[i, j])]) for i = 1:m, j = 1:n]

code = quote end
code = Expr(:block)
for k = 1:n
for j = 1:m
if k == 1
Expand Down Expand Up @@ -445,7 +448,7 @@ end

X = [Symbol("X_$(i)_$(j)") for i = 1:m, j = 1:n]

code = quote end
code = Expr(:block)
for k = 1:n
for j = 1:m
ex = :(B[$(LinearIndices(sb)[j, k])])
Expand Down Expand Up @@ -476,7 +479,7 @@ end

X = [Symbol("X_$(i)_$(j)") for i = 1:m, j = 1:n]

code = quote end
code = Expr(:block)
for k = 1:n
for j = 1:m
ex = :(B[$(LinearIndices(sb)[j, k])])
Expand Down Expand Up @@ -507,7 +510,7 @@ end

X = [Symbol("X_$(i)_$(j)") for i = 1:m, j = 1:n]

code = quote end
code = Expr(:block)
for k = 1:n
for j = m:-1:1
ex = :(B[$(LinearIndices(sb)[j, k])])
Expand Down Expand Up @@ -538,7 +541,7 @@ end

X = [Symbol("X_$(i)_$(j)") for i = 1:m, j = 1:n]

code = quote end
code = Expr(:block)
for k = 1:n
for j = m:-1:1
ex = :(B[$(LinearIndices(sb)[j, k])])
Expand All @@ -559,3 +562,129 @@ end
@inbounds return similar_type(B, TAB)(tuple($(X...)))
end
end

@generated function _A_mul_B(::Size{sa}, ::Size{sb}, A::UpperTriangular{<:TA,<:StaticMatrix}, B::UpperTriangular{<:TB,<:StaticMatrix}) where {sa,sb,TA,TB}
n = sa[1]
if n != sb[1]
throw(DimensionMismatch("left and right-hand must have same sizes, got $(n) and $(sb[1])"))
end

X = [Symbol("X_$(i)_$(j)") for i = 1:n, j = 1:n]

TAB = promote_op(*, eltype(TA), eltype(TB))
z = zero(TAB)

code = Expr(:block)
for j = 1:n
for i = 1:n
if i > j
push!(code.args, :($(X[i,j]) = $z))
else
ex = :(A.data[$(LinearIndices(sa)[i,i])] * B.data[$(LinearIndices(sb)[i,j])])
for k = i+1:j
ex = :($ex + A.data[$(LinearIndices(sa)[i,k])] * B.data[$(LinearIndices(sb)[k,j])])
end
push!(code.args, :($(X[i,j]) = $ex))
end
end
end

return quote
@_inline_meta
@inbounds $code
return UpperTriangular(similar_type(B.data, $TAB)(tuple($(X...))))
end

end

@generated function _A_mul_B(::Size{sa}, ::Size{sb}, A::LowerTriangular{<:TA,<:StaticMatrix}, B::LowerTriangular{<:TB,<:StaticMatrix}) where {sa,sb,TA,TB}
n = sa[1]
if n != sb[1]
throw(DimensionMismatch("left and right-hand must have same sizes, got $(n) and $(sb[1])"))
end

X = [Symbol("X_$(i)_$(j)") for i = 1:n, j = 1:n]

TAB = promote_op(*, eltype(TA), eltype(TB))
z = zero(TAB)

code = Expr(:block)
for j = 1:n
for i = 1:n
if i < j
push!(code.args, :($(X[i,j]) = $z))
else
ex = :(A.data[$(LinearIndices(sa)[i,j])] * B.data[$(LinearIndices(sb)[j,j])])
for k = j+1:i
ex = :($ex + A.data[$(LinearIndices(sa)[i,k])] * B.data[$(LinearIndices(sb)[k,j])])
end
push!(code.args, :($(X[i,j]) = $ex))
end
end
end

return quote
@_inline_meta
@inbounds $code
return LowerTriangular(similar_type(B.data, $TAB)(tuple($(X...))))
end

end


@generated function _A_mul_B(::Size{sa}, ::Size{sb}, A::UpperTriangular{<:TA,<:StaticMatrix}, B::LowerTriangular{<:TB,<:StaticMatrix}) where {sa,sb,TA,TB}
n = sa[1]
if n != sb[1]
throw(DimensionMismatch("left and right-hand must have same sizes, got $(n) and $(sb[1])"))
end

X = [Symbol("X_$(i)_$(j)") for i = 1:n, j = 1:n]

code = Expr(:block)
for j = 1:n
for i = 1:n
k1 = max(i,j)
ex = :(A.data[$(LinearIndices(sa)[i,k1])] * B.data[$(LinearIndices(sb)[k1,j])])
for k = k1+1:n
ex = :($ex + A.data[$(LinearIndices(sa)[i,k])] * B.data[$(LinearIndices(sb)[k,j])])
end
push!(code.args, :($(X[i,j]) = $ex))
end
end

return quote
@_inline_meta
@inbounds $code
TAB = promote_op(*, eltype(TA), eltype(TB))
return similar_type(B.data, TAB)(tuple($(X...)))
end

end

@generated function _A_mul_B(::Size{sa}, ::Size{sb}, A::LowerTriangular{<:TA,<:StaticMatrix}, B::UpperTriangular{<:TB,<:StaticMatrix}) where {sa,sb,TA,TB}
n = sa[1]
if n != sb[1]
throw(DimensionMismatch("left and right-hand must have same sizes, got $(n) and $(sb[1])"))
end

X = [Symbol("X_$(i)_$(j)") for i = 1:n, j = 1:n]

code = Expr(:block)
for j = 1:n
for i = 1:n
ex = :(A.data[$(LinearIndices(sa)[i,1])] * B.data[$(LinearIndices(sb)[1,j])])
for k = 2:min(i,j)
ex = :($ex + A.data[$(LinearIndices(sa)[i,k])] * B.data[$(LinearIndices(sb)[k,j])])
end
push!(code.args, :($(X[i,j]) = $ex))
end
end

return quote
@_inline_meta
@inbounds $code
TAB = promote_op(*, eltype(TA), eltype(TB))
return similar_type(B.data, TAB)(tuple($(X...)))
end

end
23 changes: 23 additions & 0 deletions test/triangular.jl
View file
Open in desktop
Original file line number Diff line number Diff line change
Expand Up @@ -82,6 +82,29 @@ end
end
end

@testset "Triangular-triangular multiplication" begin
for n in (1, 2, 3, 4),
eltyA in (Float64, ComplexF64, Int),
eltyB in (Float64, ComplexF64, Int),
(ta, uploa) in ((UpperTriangular, :U), (LowerTriangular, :L)),
(tb, uplob) in ((UpperTriangular, :U), (LowerTriangular, :L))

A = ta(eltyA == Int ? rand(1:7, n, n) : rand(eltyA, n, n))
B = tb(eltyB == Int ? rand(1:7, n, n) : rand(eltyB, n, n))

SA = ta(SMatrix{n,n}(A.data))
SB = tb(SMatrix{n,n}(B.data))

eltyAB = Base.promote_op(*, eltyA, eltyB)

@test SA*SB ≈ A*B
@test eltype(SA*SB) == eltyAB
@test SA*SB isa (ta===tb ? ta : SMatrix)

end

end

@testset "Triangular-matrix division" begin
for n in (1, 2, 3, 4),
eltyA in (Float64, ComplexF64, Int),
Expand Down