# 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

$A \leftarrow alpha*x*y^H + conjg(alpha)*y*x^H + A$

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.

hpr2 supports the following precisions.

T

std::complex<float>

std::complex<double>

## hpr2 (Buffer Version)#

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)
}


Input Parameters

queue

The queue where the routine should be executed.

upper_lower

Specifies whether A is upper or lower triangular. See oneMKL defined datatypes 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 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 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 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 the Hermitian matrix A if upper_lower=lower.

The imaginary parts of the diagonal elements are set to zero.

Throws

This routine shall throw the following exceptions if the associated condition is detected. An implementation may throw additional implementation-specific exception(s) in case of error conditions not covered here.

oneapi::mkl::invalid_argument

oneapi::mkl::unsupported_device

oneapi::mkl::unimplemented

## hpr2 (USM Version)#

Syntax

namespace oneapi::mkl::blas::column_major {
sycl::event hpr2(sycl::queue &queue,
onemkl::uplo upper_lower,
std::int64_t n,
T alpha,
const T *x,
std::int64_t incx,
const T *y,
std::int64_t incy,
T *a,
const std::vector<sycl::event> &dependencies = {})
}

namespace oneapi::mkl::blas::row_major {
sycl::event hpr2(sycl::queue &queue,
onemkl::uplo upper_lower,
std::int64_t n,
T alpha,
const T *x,
std::int64_t incx,
const T *y,
std::int64_t incy,
T *a,
const std::vector<sycl::event> &dependencies = {})
}


Input Parameters

queue

The queue where the routine should be executed.

upper_lower

Specifies whether A is upper or lower triangular. See oneMKL defined datatypes 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

Pointer to input vector x. The array holding input vector x must be of size at least (1 + (n - 1)*abs(incx)). See Matrix Storage for more details.

incx

Stride of vector x.

y

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

incy

Stride of vector y.

a

Pointer to input matrix A. The array holding input matrix A must have size at least (n*(n-1))/2. See Matrix Storage for more details.

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

dependencies

List of events to wait for before starting computation, if any. If omitted, defaults to no dependencies.

Output Parameters

a

Pointer to the updated upper triangular part of the Hermitian matrix A if upper_lower=upper, or the updated lower triangular part of the Hermitian matrix A if upper_lower=lower.

The imaginary parts of the diagonal elements are set to zero.

Return Values

Output event to wait on to ensure computation is complete.

Throws

This routine shall throw the following exceptions if the associated condition is detected. An implementation may throw additional implementation-specific exception(s) in case of error conditions not covered here.

oneapi::mkl::invalid_argument

oneapi::mkl::unsupported_device