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

Functions
template<typename scalar_t >
void	slate::tbsm (Side side, scalar_t alpha, TriangularBandMatrix< scalar_t > &A, Matrix< scalar_t > &B, Options const &opts)
	Distributed parallel triangular band matrix-matrix solve.

template<typename scalar_t >
void	slate::tbsm (blas::Side side, scalar_t alpha, TriangularBandMatrix< scalar_t > &A, Pivots &pivots, Matrix< scalar_t > &B, Options const &opts)
	Distributed parallel triangular band matrix-matrix solve.

Detailed Description

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

Function Documentation

◆ tbsm() [1/2]

template<typename scalar_t >

void slate::tbsm	(	blas::Side	side,
		scalar_t	alpha,
		TriangularBandMatrix< scalar_t > &	A,
		Pivots &	pivots,
		Matrix< scalar_t > &	B,
		Options const &	opts
	)

Distributed parallel triangular band 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 band matrix. The matrix X overwrites B. Pivoting from tbtrf is applied during the solve. The matrices can be transposed or conjugate-transposed beforehand, e.g.,

auto AT = slate::transpose( A );
slate::tbsm( Side::Left, alpha, AT, pivots, 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]	pivots	Pivot information from gbtrf. If pivots is an empty vector, no pivoting is applied.
[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.

◆ tbsm() [2/2]