SLATE 2024.05.31
Software for Linear Algebra Targeting Exascale
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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_tOne of float, double, std::complex<float>, std::complex<double>.
Parameters
[in,out]AOn 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]BOn entry, the n-by-nrhs right hand side matrix \(B\). On exit, if return value = 0, the n-by-nrhs solution matrix \(X\).
[in]optsAdditional 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.