her2k: Hermitian rank 2k update

\(C = \alpha A B^H + \alpha B A^H + \beta C\) where \(C\) is Hermitian More...

Functions
template<typename scalar_t >
void	slate::her2k (scalar_t alpha, Matrix< scalar_t > &A, Matrix< scalar_t > &B, blas::real_type< scalar_t > beta, HermitianMatrix< scalar_t > &C, Options const &opts)
	Distributed parallel Hermitian rank 2k update.

Detailed Description

\(C = \alpha A B^H + \alpha B A^H + \beta C\) where \(C\) is Hermitian

Function Documentation

her2k()

template<typename scalar_t >

void slate::her2k	(	scalar_t	alpha,
		Matrix< scalar_t > &	A,
		Matrix< scalar_t > &	B,
		blas::real_type< scalar_t >	beta,
		HermitianMatrix< scalar_t > &	C,
		Options const &	opts
	)

Distributed parallel Hermitian rank 2k update.

Performs the Hermitian rank 2k operation

\[ C = \alpha A B^H + \alpha B A^H + \beta C, \]

where alpha and beta are scalars, C is an n-by-n Hermitian matrix, and A and B are an n-by-k matrices. The matrices can be conjugate-transposed beforehand, e.g.,

auto AT = slate::conj_transpose( A );
auto BT = slate::conj_transpose( B );
slate::her2k( alpha, AT, BT, beta, C );

Complexity (in real): \(\approx 2 k n^{2}\) flops.

Template Parameters

scalar_t

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

Parameters

[in]	alpha	The scalar alpha.
[in]	A	The n-by-k matrix A.
[in]	B	The n-by-k matrix B.
[in]	beta	The real scalar beta.
[in,out]	C	On entry, the n-by-n Hermitian matrix C. On exit, overwritten by the result \(C = \alpha A B^H + \alpha B A^H + \beta C\).
[in]	opts	Additional options, as map of name = value pairs. Possible options: Option::Lookahead: Number of blocks to overlap communication and computation. 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.