herk

Performs a Hermitian rank-k update.

Syntax

void herk(queue &exec_queue, uplo upper_lower, transpose trans, std::int64_t n, std::int64_t k, T_real alpha, buffer<T, 1> &a, std::int64_t lda, T_real beta, buffer<T, 1> &c, std::int64_t ldc)

her2k supports the following precisions and devices:

T

T_real

Devices Supported

std::complex<float>

float

Host, CPU, and GPU

std::complex<double>

double

Host, CPU, and GPU

Description

The herk routines compute a rank-k update of a Hermitian matrix C by a general matrix A. The operation is defined as:

C <- alpha*op(A)*op(A)H + beta*C

where:

op(X) is one of op(X) = X or op(X) = XH,

alpha and beta are real scalars,

C is a Hermitian matrix and A is a general matrix.

Here op(A) is n x k, and C is n x n.

Input Parameters

exec_queue

The queue where the routine should be executed.

upper_lower

Specifies whether A’s data is stored in its upper or lower triangle. See Data Types for more details.

trans

Specifies op(A), the transposition operation applied to A. See Data Types for more details. Supported operations are transpose::nontrans and transpose::conjtrans.

n

The number of rows and columns in C.The value of n must be at least zero.

k

Number of columns in op(A).

The value of k must be at least zero.

alpha

Real scaling factor for the rank-k update.

a

Buffer holding input matrix A. If trans = transpose::nontrans, A is an n-by-k matrix so the array a must have size at least lda*k (respectively, lda*n) if column (respectively, row) major layout is used to store matrices. Otherwise, A is an k-by-n matrix so the array a must have size at least lda*n (respectively, lda*k) if column (respectively, row) major layout is used to store matrices. See Matrix and Vector Storage for more details.

lda

Leading dimension of A. If matrices are stored using column major layout, lda must be at least n if trans=transpose::nontrans, and at least k otherwise. If matrices are stored using row major layout, lda must be at least k if trans=transpose::nontrans, and at least n otherwise. Must be positive.

beta

Real scaling factor for matrix C.

c

Buffer holding input/output matrix C. Must have size at least ldc*n. See Matrix and Vector Storage for more details.

ldc

Leading dimension of C. Must be positive and at least n.

Output Parameters

c

The output buffer, overwritten by alpha*op(A)*op(A)T + beta*C. The imaginary parts of the diagonal elements are set to zero.