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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:
LaTex Math image.
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.

Product and Performance Information

1

Performance varies by use, configuration and other factors. Learn more at www.Intel.com/PerformanceIndex.