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) = XH,

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

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.

herk (USM Version)

Syntax

namespace oneapi::mkl::blas::column_major {
    sycl::event herk(sycl::queue &queue,
                     onemkl::uplo upper_lower,
                     onemkl::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,
                     onemkl::uplo upper_lower,
                     onemkl::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 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

Pointer to 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

Pointer to 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.

dependencies

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

Output Parameters

c

Pointer to the output matrix, overwritten by alpha*op(A)*op(A)T + 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.

Parent topic: BLAS Level 3 Routines