hpr2

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

Description

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

A \leftarrow 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.

API

Syntax

namespace oneapi::mkl::blas::column_major {
    void hpr2(sycl::queue &queue,
              onemkl::uplo upper_lower,
              std::int64_t n,
              T alpha,
              sycl::buffer<T,1> &x,
              std::int64_t incx,
              sycl::buffer<T,1> &y,
              std::int64_t incy,
              sycl::buffer<T,1> &a)
}
namespace oneapi::mkl::blas::row_major {
    void hpr2(sycl::queue &queue,
              onemkl::uplo upper_lower,
              std::int64_t n,
              T alpha,
              sycl::buffer<T,1> &x,
              std::int64_t incx,
              sycl::buffer<T,1> &y,
              std::int64_t incy,
              sycl::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

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

a

Buffer holding the updated upper triangular part 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 to zero.