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linalg.jl
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linalg.jl
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# integration with LinearAlgebra stdlib
## transpose and adjoint
function transpose_f!(f, At::AbstractGPUArray{T, 2}, A::AbstractGPUArray{T, 2}) where T
gpu_call(At, A) do ctx, At, A
idx = @cartesianidx A
@inbounds At[idx[2], idx[1]] = f(A[idx[1], idx[2]])
return
end
At
end
LinearAlgebra.transpose!(At::AbstractGPUArray, A::AbstractGPUArray) = transpose_f!(transpose, At, A)
LinearAlgebra.adjoint!(At::AbstractGPUArray, A::AbstractGPUArray) = transpose_f!(adjoint, At, A)
function Base.copyto!(A::AbstractGPUArray{T,N}, B::Adjoint{T, <: AbstractGPUArray{T,N}}) where {T,N}
adjoint!(A, B.parent)
end
function Base.copyto!(A::AbstractGPUArray{T,N}, B::Transpose{T, <: AbstractGPUArray{T,N}}) where {T,N}
transpose!(A, B.parent)
end
function Base.copyto!(A::Array{T,N}, B::Adjoint{T, <:AbstractGPUArray{T,N}}) where {T,N}
copyto!(A, Adjoint(Array(parent(B))))
end
function Base.copyto!(A::Array{T,N}, B::Transpose{T, <:AbstractGPUArray{T,N}}) where {T,N}
copyto!(A, Transpose(Array(parent(B))))
end
## copy upper triangle to lower and vice versa
function LinearAlgebra.copytri!(A::AbstractGPUMatrix{T}, uplo::AbstractChar) where T
n = LinearAlgebra.checksquare(A)
if uplo == 'U'
gpu_call(A) do ctx, _A
I = @cartesianidx _A
i, j = Tuple(I)
if j > i
_A[j,i] = _A[i,j]
end
return
end
elseif uplo == 'L'
gpu_call(A) do ctx, _A
I = @cartesianidx _A
i, j = Tuple(I)
if j > i
_A[i,j] = _A[j,i]
end
return
end
else
throw(ArgumentError("uplo argument must be 'U' (upper) or 'L' (lower), got $uplo"))
end
A
end
## triangular
# mixed CPU/GPU: B -> A
Base.copyto!(A::Array{T,N}, B::UpperTriangular{T, <:AbstractGPUArray{T,N}}) where {T,N} = copyto!(A, UpperTriangular(Array(parent(B))))
Base.copyto!(A::Array{T,N}, B::LowerTriangular{T, <:AbstractGPUArray{T,N}}) where {T,N} = copyto!(A, LowerTriangular(Array(parent(B))))
# GPU/GPU: B -> A
Base.copyto!(A::AbstractGPUArray{T,N}, B::UpperTriangular{T, <:AbstractGPUArray{T,N}}) where {T,N} = LinearAlgebra.triu!(copyto!(A, parent(B)))
Base.copyto!(A::AbstractGPUArray{T,N}, B::LowerTriangular{T, <:AbstractGPUArray{T,N}}) where {T,N} = LinearAlgebra.tril!(copyto!(A, parent(B)))
for T in (UpperTriangular, LowerTriangular, UnitUpperTriangular, UnitLowerTriangular)
@eval Base.copyto!(A::$T{T, <:AbstractGPUArray{T,N}}, B::$T{T, <:AbstractGPUArray{T,N}}) where {T,N} = $T(copyto!(parent(A), parent(B)))
end
function LinearAlgebra.tril!(A::AbstractGPUMatrix{T}, d::Integer = 0) where T
gpu_call(A, d; name="tril!") do ctx, _A, _d
I = @cartesianidx _A
i, j = Tuple(I)
if i < j - _d
_A[i, j] = 0
end
return
end
return A
end
function LinearAlgebra.triu!(A::AbstractGPUMatrix{T}, d::Integer = 0) where T
gpu_call(A, d; name="triu!") do ctx, _A, _d
I = @cartesianidx _A
i, j = Tuple(I)
if j < i + _d
_A[i, j] = 0
end
return
end
return A
end
## matrix multiplication
function generic_matmatmul!(C::AnyGPUArray{R}, A::AnyGPUArray{T}, B::AnyGPUArray{S}, a::Number, b::Number) where {T,S,R}
if size(A,2) != size(B,1)
throw(DimensionMismatch("matrix A has dimensions $(size(A)), matrix B has dimensions $(size(B))"))
end
if size(C,1) != size(A,1) || size(C,2) != size(B,2)
throw(DimensionMismatch("result C has dimensions $(size(C)), needs $((size(A,1),size(B,2)))"))
end
if isempty(A) || isempty(B)
return fill!(C, zero(R))
end
gpu_call(C, A, B; name="matmatmul!") do ctx, C, A, B
idx = @linearidx C
i, j = @inbounds Tuple(CartesianIndices(C)[idx])..., 1
@inbounds if i <= size(A,1) && j <= size(B,2)
z2 = zero(A[i, 1]*B[1, j] + A[i, 1]*B[1, j])
Ctmp = convert(promote_type(R, typeof(z2)), z2)
for k in 1:size(A,2)
Ctmp += A[i, k]*B[k, j]
end
C[i,j] = Ctmp*a + C[i,j]*b
end
return
end
C
end
LinearAlgebra.mul!(C::AbstractGPUVecOrMat, A::AbstractGPUVecOrMat, B::AbstractGPUVecOrMat, a::Number, b::Number) = generic_matmatmul!(C, A, B, a, b)
LinearAlgebra.mul!(C::AbstractGPUVecOrMat, A::AbstractGPUVecOrMat, B::LinearAlgebra.Adjoint{<:Any, <:AbstractGPUVecOrMat}, a::Number, b::Number) = generic_matmatmul!(C, A, B, a, b)
LinearAlgebra.mul!(C::AbstractGPUVecOrMat, A::AbstractGPUVecOrMat, B::LinearAlgebra.Transpose{<:Any, <:AbstractGPUVecOrMat}, a::Number, b::Number) = generic_matmatmul!(C, A, B, a, b)
LinearAlgebra.mul!(C::AbstractGPUVecOrMat, A::LinearAlgebra.Adjoint{<:Any, <:AbstractGPUVecOrMat}, B::AbstractGPUVecOrMat, a::Number, b::Number) = generic_matmatmul!(C, A, B, a, b)
LinearAlgebra.mul!(C::AbstractGPUVecOrMat, A::LinearAlgebra.Transpose{<:Any, <:AbstractGPUVecOrMat}, B::AbstractGPUVecOrMat, a::Number, b::Number) = generic_matmatmul!(C, A, B, a, b)
LinearAlgebra.mul!(C::AbstractGPUVecOrMat, A::LinearAlgebra.Transpose{<:Any, <:AbstractGPUVecOrMat}, B::LinearAlgebra.Adjoint{<:Any, <:AbstractGPUVecOrMat}, a::Number, b::Number) = generic_matmatmul!(C, A, B, a, b)
LinearAlgebra.mul!(C::AbstractGPUVecOrMat, A::LinearAlgebra.Adjoint{<:Any, <:AbstractGPUVecOrMat}, B::LinearAlgebra.Transpose{<:Any, <:AbstractGPUVecOrMat}, a::Number, b::Number) = generic_matmatmul!(C, A, B, a, b)
LinearAlgebra.mul!(C::AbstractGPUVecOrMat, A::LinearAlgebra.Adjoint{<:Any, <:AbstractGPUVecOrMat}, B::LinearAlgebra.Adjoint{<:Any, <:AbstractGPUVecOrMat}, a::Number, b::Number) = generic_matmatmul!(C, A, B, a, b)
LinearAlgebra.mul!(C::AbstractGPUVecOrMat, A::LinearAlgebra.Transpose{<:Any, <:AbstractGPUVecOrMat}, B::LinearAlgebra.Transpose{<:Any, <:AbstractGPUVecOrMat}, a::Number, b::Number) = generic_matmatmul!(C, A, B, a, b)
# specificity hacks
LinearAlgebra.mul!(C::AbstractGPUVecOrMat, A::AbstractGPUVecOrMat, B::AbstractGPUVecOrMat, a::Real, b::Real) = generic_matmatmul!(C, A, B, a, b)
LinearAlgebra.mul!(C::AbstractGPUVecOrMat, A::AbstractGPUVecOrMat, B::LinearAlgebra.Adjoint{<:Any, <:AbstractGPUVecOrMat}, a::Real, b::Real) = generic_matmatmul!(C, A, B, a, b)
LinearAlgebra.mul!(C::AbstractGPUVecOrMat, A::AbstractGPUVecOrMat, B::LinearAlgebra.Transpose{<:Any, <:AbstractGPUVecOrMat}, a::Real, b::Real) = generic_matmatmul!(C, A, B, a, b)
LinearAlgebra.mul!(C::AbstractGPUVecOrMat, A::LinearAlgebra.Adjoint{<:Any, <:AbstractGPUVecOrMat}, B::AbstractGPUVecOrMat, a::Real, b::Real) = generic_matmatmul!(C, A, B, a, b)
LinearAlgebra.mul!(C::AbstractGPUVecOrMat, A::LinearAlgebra.Transpose{<:Any, <:AbstractGPUVecOrMat}, B::AbstractGPUVecOrMat, a::Real, b::Real) = generic_matmatmul!(C, A, B, a, b)
LinearAlgebra.mul!(C::AbstractGPUVecOrMat, A::LinearAlgebra.Transpose{<:Any, <:AbstractGPUVecOrMat}, B::LinearAlgebra.Adjoint{<:Any, <:AbstractGPUVecOrMat}, a::Real, b::Real) = generic_matmatmul!(C, A, B, a, b)
LinearAlgebra.mul!(C::AbstractGPUVecOrMat, A::LinearAlgebra.Adjoint{<:Any, <:AbstractGPUVecOrMat}, B::LinearAlgebra.Transpose{<:Any, <:AbstractGPUVecOrMat}, a::Real, b::Real) = generic_matmatmul!(C, A, B, a, b)
LinearAlgebra.mul!(C::AbstractGPUVecOrMat, A::LinearAlgebra.Adjoint{<:Any, <:AbstractGPUVecOrMat}, B::LinearAlgebra.Adjoint{<:Any, <:AbstractGPUVecOrMat}, a::Real, b::Real) = generic_matmatmul!(C, A, B, a, b)
LinearAlgebra.mul!(C::AbstractGPUVecOrMat, A::LinearAlgebra.Transpose{<:Any, <:AbstractGPUVecOrMat}, B::LinearAlgebra.Transpose{<:Any, <:AbstractGPUVecOrMat}, a::Real, b::Real) = generic_matmatmul!(C, A, B, a, b)
@static if v"1.3.0" <= VERSION <= v"1.3.1"
LinearAlgebra.mul!(C::AbstractGPUVecOrMat{T}, A::AbstractGPUVecOrMat{T}, B::AbstractGPUVecOrMat{T}, a::Union{Bool,T}, b::Union{Bool,T}) where {T<:LinearAlgebra.BLAS.BlasFloat} = generic_matmatmul!(C, A, B, a, b)
LinearAlgebra.mul!(C::AbstractGPUVecOrMat{T}, A::AbstractGPUVecOrMat{T}, B::LinearAlgebra.Adjoint{<:Any, <:AbstractGPUVecOrMat{T}}, a::Union{Bool,T}, b::Union{Bool,T}) where {T<:LinearAlgebra.BLAS.BlasReal} = generic_matmatmul!(C, A, B, a, b)
LinearAlgebra.mul!(C::AbstractGPUVecOrMat{T}, A::AbstractGPUVecOrMat{T}, B::LinearAlgebra.Adjoint{<:Any, <:AbstractGPUVecOrMat{T}}, a::Union{Bool,T}, b::Union{Bool,T}) where {T<:LinearAlgebra.BLAS.BlasComplex} = generic_matmatmul!(C, A, B, a, b)
LinearAlgebra.mul!(C::AbstractGPUVecOrMat{T}, A::AbstractGPUVecOrMat{T}, B::LinearAlgebra.Transpose{<:Any, <:AbstractGPUVecOrMat{T}}, a::Union{Bool,T}, b::Union{Bool,T}) where {T<:LinearAlgebra.BLAS.BlasFloat} = generic_matmatmul!(C, A, B, a, b)
LinearAlgebra.mul!(C::AbstractGPUVecOrMat{T}, A::LinearAlgebra.Adjoint{<:Any, <:AbstractGPUVecOrMat{T}}, B::AbstractGPUVecOrMat{T}, a::Union{Bool,T}, b::Union{Bool,T}) where {T<:LinearAlgebra.BLAS.BlasReal} = generic_matmatmul!(C, A, B, a, b)
LinearAlgebra.mul!(C::AbstractGPUVecOrMat{T}, A::LinearAlgebra.Adjoint{<:Any, <:AbstractGPUVecOrMat{T}}, B::AbstractGPUVecOrMat{T}, a::Union{Bool,T}, b::Union{Bool,T}) where {T<:LinearAlgebra.BLAS.BlasComplex} = generic_matmatmul!(C, A, B, a, b)
LinearAlgebra.mul!(C::AbstractGPUVecOrMat{T}, A::LinearAlgebra.Transpose{<:Any, <:AbstractGPUVecOrMat{T}}, B::AbstractGPUVecOrMat{T}, a::Union{Bool,T}, b::Union{Bool,T}) where {T<:LinearAlgebra.BLAS.BlasFloat} = generic_matmatmul!(C, A, B, a, b)
LinearAlgebra.mul!(C::AbstractGPUVecOrMat{T}, A::LinearAlgebra.Transpose{<:Any, <:AbstractGPUVecOrMat{T}}, B::LinearAlgebra.Adjoint{<:Any, <:AbstractGPUVecOrMat{T}}, a::Union{Bool,T}, b::Union{Bool,T}) where {T<:LinearAlgebra.BLAS.BlasReal} = generic_matmatmul!(C, A, B, a, b)
LinearAlgebra.mul!(C::AbstractGPUVecOrMat{T}, A::LinearAlgebra.Transpose{<:Any, <:AbstractGPUVecOrMat{T}}, B::LinearAlgebra.Adjoint{<:Any, <:AbstractGPUVecOrMat{T}}, a::Union{Bool,T}, b::Union{Bool,T}) where {T<:LinearAlgebra.BLAS.BlasComplex} = generic_matmatmul!(C, A, B, a, b)
LinearAlgebra.mul!(C::AbstractGPUVecOrMat{T}, A::LinearAlgebra.Adjoint{<:Any, <:AbstractGPUVecOrMat{T}}, B::LinearAlgebra.Transpose{<:Any, <:AbstractGPUVecOrMat{T}}, a::Union{Bool,T}, b::Union{Bool,T}) where {T<:LinearAlgebra.BLAS.BlasReal} = generic_matmatmul!(C, A, B, a, b)
LinearAlgebra.mul!(C::AbstractGPUVecOrMat{T}, A::LinearAlgebra.Adjoint{<:Any, <:AbstractGPUVecOrMat{T}}, B::LinearAlgebra.Transpose{<:Any, <:AbstractGPUVecOrMat{T}}, a::Union{Bool,T}, b::Union{Bool,T}) where {T<:LinearAlgebra.BLAS.BlasComplex} = generic_matmatmul!(C, A, B, a, b)
LinearAlgebra.mul!(C::AbstractGPUVecOrMat{T}, A::LinearAlgebra.Adjoint{<:Any, <:AbstractGPUVecOrMat{T}}, B::LinearAlgebra.Adjoint{<:Any, <:AbstractGPUVecOrMat{T}}, a::Union{Bool,T}, b::Union{Bool,T}) where {T<:LinearAlgebra.BLAS.BlasReal} = generic_matmatmul!(C, A, B, a, b)
LinearAlgebra.mul!(C::AbstractGPUVecOrMat{T}, A::LinearAlgebra.Adjoint{<:Any, <:AbstractGPUVecOrMat{T}}, B::LinearAlgebra.Adjoint{<:Any, <:AbstractGPUVecOrMat{T}}, a::Union{Bool,T}, b::Union{Bool,T}) where {T<:LinearAlgebra.BLAS.BlasComplex} = generic_matmatmul!(C, A, B, a, b)
LinearAlgebra.mul!(C::AbstractGPUVecOrMat{T}, A::LinearAlgebra.Transpose{<:Any, <:AbstractGPUVecOrMat{T}}, B::LinearAlgebra.Transpose{<:Any, <:AbstractGPUVecOrMat{T}}, a::Union{Bool,T}, b::Union{Bool,T}) where {T<:LinearAlgebra.BLAS.BlasFloat} = generic_matmatmul!(C, A, B, a, b)
end
function generic_rmul!(X::AbstractGPUArray, s::Number)
gpu_call(X, s; name="rmul!") do ctx, X, s
i = @linearidx X
@inbounds X[i] *= s
return
end
return X
end
LinearAlgebra.rmul!(A::AbstractGPUArray, b::Number) = generic_rmul!(A, b)
function generic_lmul!(s::Number, X::AbstractGPUArray)
gpu_call(X, s; name="lmul!") do ctx, X, s
i = @linearidx X
@inbounds X[i] = s*X[i]
return
end
return X
end
LinearAlgebra.lmul!(a::Number, B::AbstractGPUArray) = generic_lmul!(a, B)
## permutedims
function LinearAlgebra.permutedims!(dest::AbstractGPUArray, src::AbstractGPUArray,
perm::NTuple)
Base.checkdims_perm(dest, src, perm)
function permutedims_kernel(ctx, dest, src, ::Val{perm}) where {perm}
I = @cartesianidx src
@inbounds begin
J = CartesianIndex(map(i->I[i], perm))
dest[J] = src[I]
end
return
end
gpu_call(permutedims_kernel, dest, src, Val(perm))
return dest
end
# TODO: implementation without the memory copy
LinearAlgebra.permutedims!(dest::AbstractGPUArray, src::AbstractGPUArray, perm) =
permutedims!(dest, src, Tuple(perm))