herk#

Performs a Hermitian rank-k update.

Description

The herk routines compute a rank-k update of a Hermitian matrix C by a general matrix A. The operation is defined as:

\[C \leftarrow alpha*op(A)*op(A)^H + beta*C\]

where:

op(X) is one of op(X) = X or op(X) = X^H,

alpha and beta are real scalars,

C is a Hermitian matrix and A is a general matrix.

Here op(A) is n x k, and C is n x n.

herk supports the following precisions:

T

T_real

std::complex<float>

float

std::complex<double>

double

T	T_real
`std::complex<float>`	`float`
`std::complex<double>`	`double`

herk (Buffer Version)#

Syntax

namespace oneapi::mkl::blas::column_major {
    void herk(sycl::queue &queue,
              onemkl::uplo upper_lower,
              onemkl::transpose trans,
              std::int64_t n,
              std::int64_t k,
              T_real alpha,
              sycl::buffer<T,1> &a,
              std::int64_t lda,
              T_real beta,
              sycl::buffer<T,1> &c,
              std::int64_t ldc)
}

namespace oneapi::mkl::blas::row_major {
    void herk(sycl::queue &queue,
              onemkl::uplo upper_lower,
              onemkl::transpose trans,
              std::int64_t n,
              std::int64_t k,
              T_real alpha,
              sycl::buffer<T,1> &a,
              std::int64_t lda,
              T_real beta,
              sycl::buffer<T,1> &c,
              std::int64_t ldc)
}

Input Parameters

queue

The queue where the routine should be executed.

upper_lower

Specifies whether A’s data is stored in its upper or lower triangle. See oneMKL defined datatypes for more details.

trans

Specifies op(A), the transposition operation applied to A. See oneMKL defined datatypes for more details. Supported operations are transpose::nontrans and transpose::conjtrans.

n

The number of rows and columns in C.The value of n must be at least zero.

k

Number of columns in op(A).

The value of k must be at least zero.

alpha

Real scaling factor for the rank-k update.

a

Buffer holding input matrix A.

	`trans` = `transpose::nontrans`	`trans` = `transpose::trans` or `transpose::conjtrans`
Column major	`A` is an `n`-by-`k` matrix so the array `a` must have size at least `lda`*`k`.	`A` is an `k`-by-`n` matrix so the array `a` must have size at least `lda`*`n`
Row major	`A` is an `n`-by-`k` matrix so the array `a` must have size at least `lda`*`n`.	`A` is an `k`-by-`n` matrix so the array `a` must have size at least `lda`*`k`.

See Matrix Storage for more details.

lda

The leading dimension of A. It must be positive.

	`trans` = `transpose::nontrans`	`trans` = `transpose::trans` or `transpose::conjtrans`
Column major	`lda` must be at least `n`.	`lda` must be at least `k`.
Row major	`lda` must be at least `k`.	`lda` must be at least `n`.

beta

Real scaling factor for matrix C.

c

Buffer holding input/output matrix C. Must have size at least ldc*n. See Matrix Storage for more details.

ldc

Leading dimension of C. Must be positive and at least n.

Output Parameters

c: The output buffer, overwritten by alpha*op(A)*op(A)^T + beta*C. 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::host_bad_alloc

oneapi::mkl::device_bad_alloc

oneapi::mkl::unimplemented

herk (USM Version)#