SLATE 2024.05.31
Software for Linear Algebra Targeting Exascale
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\(Ax = \lambda x\) More...

Functions

template<typename scalar_t >
void slate::heev (HermitianMatrix< scalar_t > &A, std::vector< blas::real_type< scalar_t > > &Lambda, Matrix< scalar_t > &Z, Options const &opts)
 Distributed parallel Hermitian matrix eigen decomposition.
 

Detailed Description

\(Ax = \lambda x\)

Function Documentation

◆ heev()

template<typename scalar_t >
void slate::heev ( HermitianMatrix< scalar_t > &  A,
std::vector< blas::real_type< scalar_t > > &  Lambda,
Matrix< scalar_t > &  Z,
Options const &  opts 
)

Distributed parallel Hermitian matrix eigen decomposition.

heev Computes all eigenvalues and, optionally, eigenvectors of a Hermitian matrix A. The matrix A is preliminary reduced to tridiagonal form using a two-stage approach: First stage: reduction to band tridiagonal form (see he2hb); Second stage: reduction from band to tridiagonal form (see hb2st).

Template Parameters
scalar_tOne of float, double, std::complex<float>, std::complex<double>.
Parameters
[in]AOn entry, the n-by-n Hermitian matrix \(A\). On exit, contents are destroyed.
[out]LambdaThe vector Lambda of length n. If successful, the eigenvalues in ascending order.
[out]ZOn entry, if Z is empty, does not compute eigenvectors. Otherwise, the n-by-n matrix \(Z\) to store eigenvectors. On exit, orthonormal eigenvectors of the matrix A.
[in]optsAdditional options, as map of name = value pairs. Possible options:
  • Option::InnerBlocking: Inner blocking to use for panel. Default 16.
  • Option::MaxPanelThreads: Number of threads to use for panel. Default omp_get_max_threads()/2.
  • 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.