hpr

Computes a rank-1 update of a Hermitian packed matrix.

Description

The hpr routines compute a scalar-vector-vector product and add the result to a Hermitian packed matrix. The operation is defined as

\[A \leftarrow alpha*x*xH + A\]

where:

  • alpha is scalar,

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

  • x is a vector of length n.

API

Syntax

namespace oneapi::mkl::blas::column_major {
    void hpr(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> &a)
}
namespace oneapi::mkl::blas::row_major {
    void hpr(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> &a)
})

hpr 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.

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 part of the diagonal elements need not be set and are assumed to be zero

Output Parameters

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 to zero.