Driver

Solve \(AX = B\). More...

Functions
template<typename scalar_t >
int64_t	slate::pbsv (HermitianBandMatrix< scalar_t > &A, Matrix< scalar_t > &B, Options const &opts)
	Distributed parallel Cholesky factorization and solve.

Detailed Description

Solve \(AX = B\).

Function Documentation

pbsv()

template<typename scalar_t >

int64_t slate::pbsv	(	HermitianBandMatrix< scalar_t > &	A,
		Matrix< scalar_t > &	B,
		Options const &	opts
	)

Distributed parallel Cholesky factorization and solve.

Computes the solution to a system of linear equations

\[ A X = B, \]

where \(A\) is an n-by-n Hermitian positive definite band matrix and \(X\) and \(B\) are n-by-nrhs matrices. The Cholesky decomposition is used to factor \(A\) as

\[ A = L L^H, \]

if \(A\) is stored lower, where \(L\) is a lower triangular band matrix, or

\[ A = U^H U, \]

if \(A\) is stored upper, where \(U\) is an upper triangular band matrix. The factored form of \(A\) is then used to solve the system of equations \(A X = B\).

Template Parameters

scalar_t

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

Parameters

[in,out]	A	On entry, the n-by-n Hermitian positive definite band matrix \(A\). On exit, if return value = 0, overwritten by the factor \(U\) or \(L\) from the Cholesky factorization \(A = U^H U\) or \(A = L L^H\). If scalar_t is real, \(A\) can be a SymmetricMatrix object.
[in,out]	B	On entry, the n-by-nrhs right hand side matrix \(B\). On exit, if return value = 0, the n-by-nrhs solution matrix \(X\).
[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.

Returns

0: successful exit

i > 0: the leading minor of order \(i\) of \(A\) is not positive definite, so the factorization could not be completed, and the solution has not been computed.