Computational

Functions
template<typename scalar_t >
void	slate::hegst (int64_t itype, HermitianMatrix< scalar_t > &A, HermitianMatrix< scalar_t > &B, Options const &opts)
	Distributed parallel reduction of a complex Hermitian positive-definite generalized eigenvalue problem to the standard form.

Detailed Description

Function Documentation

hegst()

template<typename scalar_t >

void slate::hegst	(	int64_t	itype,
		HermitianMatrix< scalar_t > &	A,
		HermitianMatrix< scalar_t > &	B,
		Options const &	opts
	)

Distributed parallel reduction of a complex Hermitian positive-definite generalized eigenvalue problem to the standard form.

Reduces a complex Hermitian positive-definite generalized eigenvalue problem to standard form, as follows:

itype	Problem
itype = 1	\(A x = \lambda B x\)
itype = 2	\(A B x = \lambda x\)
itype = 3	\(B A x = \lambda x\)

Before calling slate::hegst, you must call slate::potrf to compute the Cholesky factorization: \(B = L L^H\) or \(B = U^H U\).

Template Parameters

scalar_t

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

Parameters

[in]	itype	itype = 1: Compute \(A x = \lambda B x\); itype = 2: Compute \(A B x = \lambda x\); itype = 3: Compute \(B A x = \lambda x\).
[in,out]	A	On entry, the n-by-n Hermitian matrix \(A\). On exit, the upper or lower triangle is overwritten by the upper or lower triangle of C, as follows: itype = 1: A.uplo() = Uplo::Lower: \(C = L^{-1} A L^{-H}\); A.uplo() = Uplo::Upper: \(C = U^{-H} A U^{-1}\). itype = 2 or 3: A.uplo() = Uplo::Lower: \(C = L^H A L\); A.uplo() = Uplo::Upper: \(C = U A U^H\).
[in]	B	On entry, the triangular factor from the Cholesky factorization of \(B\), as returned by |slatepotrf|.
[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.

TODO: return value