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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:

where:

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

• alpha and beta are real scalars

• C is n x n hermitian matrix

• op(A) is n x k general matrix

herk supports the following precisions:

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,
              oneapi::mkl::uplo upper_lower,
              oneapi::mkl::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,
              oneapi::mkl::uplo upper_lower,
              oneapi::mkl::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 matrix C is upper or lower triangular. See Data Types for more details.

trans

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

n

Number of rows and columns of matrix C. Must be at least zero.

k

Number of columns of matrix op(A). Must be at least zero.

alpha

Complex scaling factor for the rank-k update.

a

Buffer holding input matrix A. See Matrix Storage for more details.

	trans = transpose::nontrans	trans = transpose::conjtrans
Column major	A is n x k matrix. Size of array a must be at least lda * k	A is k x n matrix. Size of array a must be at least lda * n
Row major	A is n x k matrix. Size of array a must be at least lda * n	A is k x n matrix. Size of array a must be at least lda * k

lda

Leading dimension of matrix A. Must be positive.

	trans = transpose::nontrans	trans = transpose::conjtrans
Column major	Must be at least n	Must be at least k
Row major	Must be at least k	Must be at least n

beta

Real scaling factor for matrix C.

c

Buffer holding input/output matrix C. Size of the buffer must be at least ldc * n. See Matrix Storage for more details.

ldc

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

Output Parameters

c

Output buffer overwritten by alpha * op(A) * op(A)^H + beta * C. The imaginary parts of the diagonal elements are set to zero.

herk (USM Version)

Syntax

namespace oneapi::mkl::blas::column_major {
    sycl::event herk(sycl::queue &queue,
                     oneapi::mkl::uplo upper_lower,
                     oneapi::mkl::transpose trans,
                     std::int64_t n,
                     std::int64_t k,
                     T_real alpha,
                     const T* a,
                     std::int64_t lda,
                     T_real beta,
                     T* c,
                     std::int64_t ldc,
                     const std::vector<sycl::event> &dependencies = {})
}

namespace oneapi::mkl::blas::row_major {
    sycl::event herk(sycl::queue &queue,
                     oneapi::mkl::uplo upper_lower,
                     oneapi::mkl::transpose trans,
                     std::int64_t n,
                     std::int64_t k,
                     T_real alpha,
                     const T* a,
                     std::int64_t lda,
                     T_real beta,
                     T* c,
                     std::int64_t ldc,
                     const std::vector<sycl::event> &dependencies = {})
}

Input Parameters

queue

The queue where the routine should be executed.

upper_lower

Specifies whether matrix C is upper or lower triangular. See Data Types for more details.

trans

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

n

Number of rows and columns of matrix C. Must be at least zero.

k

Number of columns of matrix op(A). Must be at least zero.

alpha

Complex scaling factor for the rank-k update.

a

Pointer to input matrix A. See Matrix Storage for more details.

	trans = transpose::nontrans	trans = transpose::conjtrans
Column major	A is n x k matrix. Size of array a must be at least lda * k	A is k x n matrix. Size of array a must be at least lda * n
Row major	A is n x k matrix. Size of array a must be at least lda * n	A is k x n matrix. Size of array a must be at least lda * k

lda

Leading dimension of matrix A. Must be positive.

	trans = transpose::nontrans	trans = transpose::conjtrans
Column major	Must be at least n	Must be at least k
Row major	Must be at least k	Must be at least n

beta

Real scaling factor for matrix C.

c

Pointer to input/output matrix C. Size of the array must be at least ldc * n. See Matrix Storage for more details.

ldc

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

dependencies

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

Output Parameters

c

Pointer to output matrix overwritten by alpha * op(A) * op(A)^H + beta * C. The imaginary parts of the diagonal elements are set to zero.

Return Values

Output event to wait on to ensure computation is complete.

her2k symm