hpr2

Performs a rank-2 update of a Hermitian packed matrix.

Syntax

void hpr2(queue &exec_queue, uplo upper_lower, std::int64_t n, T alpha, buffer<T, 1> &x, std::int64_t incx, buffer<T, 1> &y, std::int64_t incy, buffer<T, 1> &a)

hpr2 supports the following precisions and devices.

T

Devices Supported

std::complex<float>

Host, CPU, and GPU

std::complex<double>

Host, CPU, and GPU

Description

The hpr2 routines compute two scalar-vector-vector products and add them to a Hermitian packed matrix. The operation is defined as

A <- alpha*x*yH + conjg(alpha)*y*xH + A

where:

alpha is a scalar,

A is an n-by-n Hermitian matrix, supplied in packed form,

x and y are vectors of length n.

Input Parameters

exec_queue

The queue where the routine should be executed.

upper_lower

Specifies whether A is upper or lower triangular. See Data Types for more details.

n

Number of rows and columns of A. Must be at least zero.

alpha

Scaling factor for the matrix-vector product.

x

Buffer holding input vector x. The buffer must be of size at least (1 + (n - 1)*abs(incx)). See Matrix and Vector Storage for more details.

incx

Stride of vector x.

y

Buffer holding input/output vector y. The buffer must be of size at least (1 + (n - 1)*abs(incy)). See Matrix and Vector Storage for more details.

incy

Stride of vector y.

a

Buffer holding input matrix A. Must have size at least (n*(n-1))/2. See Matrix and Vector Storage for more details.

The imaginary parts of the diagonal elements need not be set and are assumed to be zero.

Output Parameters

sycl:

a

Buffer holding the updated upper triangularpart of the Hermitian matrix A if upper_lower =upper, or the updated lower triangular part of theHermitian matrix A if upper_lower =lower.

The imaginary parts of the diagonal elements are set tozero.