SLATE 2024.05.31
Software for Linear Algebra Targeting Exascale
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Factor, forward and back solve. More...
Functions | |
template<typename scalar_t > | |
int64_t | slate::pbtrf (HermitianBandMatrix< scalar_t > &A, Options const &opts) |
Distributed parallel band Cholesky factorization. | |
template<typename scalar_t > | |
void | slate::pbtrs (HermitianBandMatrix< scalar_t > &A, Matrix< scalar_t > &B, Options const &opts) |
Distributed parallel Cholesky solve. | |
Factor, forward and back solve.
int64_t slate::pbtrf | ( | HermitianBandMatrix< scalar_t > & | A, |
Options const & | opts | ||
) |
Distributed parallel band Cholesky factorization.
Computes the Cholesky factorization of a Hermitian positive definite band matrix \(A\).
The factorization has the form
\[ A = L L^H, \]
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.
scalar_t | One of float, double, std::complex<float>, std::complex<double>. |
[in,out] | A | On entry, the Hermitian band matrix \(A\) to be factored. Tiles outside the bandwidth do not need to exist. For tiles that are partially outside the bandwidth, data outside the bandwidth should be explicitly set to zero. On exit, the factor \(L\) or \(U\) from the factorization \(A = L L^H\) or \(A = U^H U\). |
[in] | opts | Additional options, as map of name = value pairs. Possible options:
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void slate::pbtrs | ( | HermitianBandMatrix< scalar_t > & | A, |
Matrix< scalar_t > & | B, | ||
Options const & | opts | ||
) |
Distributed parallel Cholesky solve.
Solves a system of linear equations
\[ A X = B \]
with a Hermitian positive definite hermitian matrix \(A\) using the Cholesky factorization \(A = U^H U\) or \(A = L L^H\) computed by potrf.
scalar_t | One of float, double, std::complex<float>, std::complex<double>. |
[in] | A | The n-by-n triangular factor \(U\) or \(L\) from the Cholesky factorization \(A = U^H U\) or \(A = L L^H\), computed by potrf. 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, the n-by-nrhs solution matrix \(X\). |
[in] | opts | Additional options, as map of name = value pairs. Possible options:
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