trsm: Triangular solve matrix

\(C = A^{-1} B\) or \(C = B A^{-1}\) where \(A\) is triangular More...

Functions
template<typename scalar_t >
void	slate::trsm (blas::Side side, scalar_t alpha, TriangularMatrix< scalar_t > &A, Matrix< scalar_t > &B, Options const &opts)
	Distributed parallel triangular matrix-matrix solve.
template<typename scalar_t >
void	slate::trsmA (blas::Side side, scalar_t alpha, TriangularMatrix< scalar_t > &A, Matrix< scalar_t > &B, Options const &opts)
	Distributed parallel triangular matrix-matrix solve.
template<typename scalar_t >
void	slate::trsmB (blas::Side side, scalar_t alpha, TriangularMatrix< scalar_t > &A, Matrix< scalar_t > &B, Options const &opts)
	Distributed parallel triangular matrix-matrix solve.

Detailed Description

\(C = A^{-1} B\) or \(C = B A^{-1}\) where \(A\) is triangular

Function Documentation

trsm()

template<typename scalar_t >

void slate::trsm	(	blas::Side	side,
		scalar_t	alpha,
		TriangularMatrix< scalar_t > &	A,
		Matrix< scalar_t > &	B,
		Options const &	opts
	)

Distributed parallel triangular matrix-matrix solve.

Solves one of the triangular matrix equations

\[ A X = \alpha B, \]

or

\[ X A = \alpha B, \]

where alpha is a scalar, B is an m-by-n matrix and A is a unit or non-unit, upper or lower triangular matrix. The matrix X overwrites B. The matrices can be transposed or conjugate-transposed beforehand, e.g.,

auto AT = slate::transpose( A );
slate::trsm( Side::Left, alpha, AT, B );

Complexity (in real): \(m^{2} n\) flops.

Template Parameters

scalar_t

One of float, double, std::complex<float>, std::complex<double>.

Parameters

[in]	side	Whether A appears on the left or on the right of X: Side::Left: solve \(A X = \alpha B\) Side::Right: solve \(X A = \alpha B\)
[in]	alpha	The scalar alpha.
[in]	A	If side = left, the m-by-m triangular matrix A; if side = right, the n-by-n triangular matrix A.
[in,out]	B	On entry, the m-by-n matrix B. On exit, overwritten by the result X.
[in]	opts	Additional options, as map of name = value pairs. Possible options: Option::Lookahead: Number of panels to overlap with matrix updates. lookahead >= 0. Default 1. Option::MethodTrsm: Select the right routine to call. Possible values: Auto: let the routine decides [default] trsmA: select trsmA routine trsmB: select trsmB routine Option::Target: Implementation to target. Possible values: HostTask: OpenMP tasks on CPU host [default]. HostNest: nested OpenMP parallel for loop on CPU host. HostBatch: batched BLAS on CPU host. Devices: batched BLAS on GPU device.

trsmA()

template<typename scalar_t >

void slate::trsmA	(	blas::Side	side,
		scalar_t	alpha,
		TriangularMatrix< scalar_t > &	A,
		Matrix< scalar_t > &	B,
		Options const &	opts
	)

Distributed parallel triangular matrix-matrix solve.

Solves one of the triangular matrix equations

\[ A X = \alpha B, \]

or

\[ X A = \alpha B, \]

where alpha is a scalar, B is an m-by-n matrix and A is a unit or non-unit, upper or lower triangular matrix. The matrix X overwrites B. The matrices can be transposed or conjugate-transposed beforehand, e.g.,

auto AT = slate::transpose( A );
slate::trsmA( Side::Left, alpha, AT, B );

Note: The original trsm computes the solution where B is located. The trsmA is a variant of trsm where the computation is performed where A is located using temporary tiles to represent B, followed by a reduction to get the result into the given B. This approach is well suited in the case of a few right-hand side since it would require less communication.

Template Parameters

scalar_t

One of float, double, std::complex<float>, std::complex<double>.

Parameters

[in]	side	Whether A appears on the left or on the right of X: Side::Left: solve \(A X = \alpha B\) Side::Right: solve \(X A = \alpha B\)
[in]	alpha	The scalar alpha.
[in]	A	If side = left, the m-by-m triangular matrix A; if side = right, the n-by-n triangular matrix A.
[in,out]	B	On entry, the m-by-n matrix B. On exit, overwritten by the result X.
[in]	opts	Additional options, as map of name = value pairs. Possible options: Option::Lookahead: Number of panels to overlap with matrix updates. lookahead >= 0. Default 1. Option::Target: Implementation to target. Possible values: HostTask: OpenMP tasks on CPU host [default]. HostNest: nested OpenMP parallel for loop on CPU host. HostBatch: batched BLAS on CPU host. Devices: batched BLAS on GPU device.

trsmB()

template<typename scalar_t >

void slate::trsmB	(	blas::Side	side,
		scalar_t	alpha,
		TriangularMatrix< scalar_t > &	A,
		Matrix< scalar_t > &	B,
		Options const &	opts
	)

Distributed parallel triangular matrix-matrix solve.

Solves one of the triangular matrix equations

\[ A X = \alpha B, \]

or

\[ X A = \alpha B, \]

where alpha is a scalar, B is an m-by-n matrix and A is a unit or non-unit, upper or lower triangular matrix. The matrix X overwrites B. The matrices can be transposed or conjugate-transposed beforehand, e.g.,

auto AT = slate::transpose( A );
slate::trsm( Side::Left, alpha, AT, B );

Template Parameters

scalar_t

One of float, double, std::complex<float>, std::complex<double>.

Parameters

[in]	side	Whether A appears on the left or on the right of X: Side::Left: solve \(A X = \alpha B\) Side::Right: solve \(X A = \alpha B\)
[in]	alpha	The scalar alpha.
[in]	A	If side = left, the m-by-m triangular matrix A; if side = right, the n-by-n triangular matrix A.
[in,out]	B	On entry, the m-by-n matrix B. On exit, overwritten by the result X.
[in]	opts	Additional options, as map of name = value pairs. Possible options: Option::Lookahead: Number of panels to overlap with matrix updates. lookahead >= 0. Default 1. Option::Target: Implementation to target. Possible values: HostTask: OpenMP tasks on CPU host [default]. HostNest: nested OpenMP parallel for loop on CPU host. HostBatch: batched BLAS on CPU host. Devices: batched BLAS on GPU device.