her2

Computes a rank-2 update of a Hermitian matrix.

Description

The her2 routines compute two scalar-vector-vector products and add them to a Hermitian 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,

x and y are vectors or length n.

her2 supports the following precisions.

T

std::complex<float>

std::complex<double>

her2 (Buffer Version)

Syntax

namespace oneapi::mkl::blas::column_major {
    void her2(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,
              std::int64_t lda)
}
namespace oneapi::mkl::blas::row_major {
    void her2(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,
              std::int64_t lda)
}

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 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 lda*n. See Matrix Storage for more details.

lda

Leading dimension of matrix A. Must be at least n, and positive.

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.

her2 (USM Version)

Syntax

namespace oneapi::mkl::blas::column_major {
    sycl::event her2(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,
                     std::int64_t lda,
                     const std::vector<sycl::event> &dependencies = {})
}
namespace oneapi::mkl::blas::row_major {
    sycl::event her2(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,
                     std::int64_t lda,
                     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 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 lda*n. See Matrix Storage for more details.

lda

Leading dimension of matrix A. Must be at least n, and positive.

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.

Parent topic: BLAS Level 2 Routines