Contents

# her2k

Performs a hermitian rank-2k update.

## Description

The
her2k
routines perform a rank-2k update of an
n
x
n
hermitian matrix
C
by general matrices
A
and
B
. The operation is defined as:
If
trans
=
transpose::nontrans
,
where:
• A
is
n
x
k
and
B
is
k
x
n
.
If
trans
=
transpose::conjtrans
,
where:
• A
is
k
x
n
and
B
is
n
x
k
.
In both cases:
• alpha
is a complex scalar and
beta
is a real scalar
• C
is hermitian matrix,
A
and
B
are general matrices
• The inner dimension of both matrix multiplications is
k
her2k
supports the following precisions:
T
T_real
std::complex<float>
float
std::complex<double>
double

## her2k (Buffer Version)

Syntax
``````namespace oneapi::mkl::blas::column_major {
void her2k(sycl::queue &queue,
oneapi::mkl::uplo upper_lower,
oneapi::mkl::transpose trans,
std::int64_t n,
std::int64_t k,
T alpha,
sycl::buffer<T,1> &a,
std::int64_t lda,
sycl::buffer<T,1> &b,
std::int64_t ldb,
T_real beta,
sycl::buffer<T,1> &c,
std::int64_t ldc)
}``````
``````namespace oneapi::mkl::blas::row_major {
void her2k(sycl::queue &queue,
oneapi::mkl::uplo upper_lower,
oneapi::mkl::transpose trans,
std::int64_t n,
std::int64_t k,
T alpha,
sycl::buffer<T,1> &a,
std::int64_t lda,
sycl::buffer<T,1> &b,
std::int64_t ldb,
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 the transposition operation applied as described above. Supported operations are
transpose::nontrans
and
transpose::conjtrans
.
n
Number of rows and columns of matrix
C
. Must be at least zero.
k
Inner dimension of matrix multiplications. Must be at least zero.
alpha
Complex scaling factor for the rank-2k 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
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
.
b
Buffer holding input matrix
B
. See Matrix Storage for more details.
trans
=
transpose::nontrans
trans
=
transpose::conjtrans
Column major
B
is
k
x
n
matrix. Size of array
b
must be at least
ldb
*
n
B
is
n
x
k
matrix. Size of array
b
must be at least
ldb
*
k
Row major
B
is
k
x
n
matrix. Size of array
b
must be at least
ldb
*
k
B
is
n
x
k
matrix. Size of array
b
must be at least
ldb
*
n
ldb
B
. Must be positive.
trans
=
transpose::nontrans
trans
=
transpose::conjtrans
Column major
Must be at least
k
Must be at least
n
Row major
Must be at least
n
Must be at least
k
c
Buffer holding input/output matrix
C
. Size of the buffer must be at least
ldc
*
n
. See Matrix Storage for more details.
ldc
C
. Must be positive and at least
n
.
Output Parameters
c
Output buffer overwritten by updated
C
matrix.

## her2k (USM Version)

Syntax
``````namespace oneapi::mkl::blas::column_major {
sycl::event her2k(sycl::queue &queue,
oneapi::mkl::uplo upper_lower,
oneapi::mkl::transpose trans,
std::int64_t n,
std::int64_t k,
T alpha,
const T* a,
std::int64_t lda,
const T* b,
std::int64_t ldb,
T_real beta,
T* c,
std::int64_t ldc,
const std::vector<sycl::event> &dependencies = {})
}``````
``````namespace oneapi::mkl::blas::row_major {
sycl::event her2k(sycl::queue &queue,
oneapi::mkl::uplo upper_lower,
oneapi::mkl::transpose trans,
std::int64_t n,
std::int64_t k,
T alpha,
const T* a,
std::int64_t lda,
const T* b,
std::int64_t ldb,
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 the transposition operation applied as described above. Supported operations are
transpose::nontrans
and
transpose::conjtrans
.
n
Number of rows and columns of matrix
C
. Must be at least zero.
k
Inner dimension of matrix multiplications. Must be at least zero.
alpha
Complex scaling factor for the rank-2k 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
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
.
b
Pointer to input matrix
B
. See Matrix Storage for more details.
trans
=
transpose::nontrans
trans
=
transpose::conjtrans
Column major
B
is
k
x
n
matrix. Size of array
b
must be at least
ldb
*
n
B
is
n
x
k
matrix. Size of array
b
must be at least
ldb
*
k
Row major
B
is
k
x
n
matrix. Size of array
b
must be at least
ldb
*
k
B
is
n
x
k
matrix. Size of array
b
must be at least
ldb
*
n
ldb
B
. Must be positive.
trans
=
transpose::nontrans
trans
=
transpose::conjtrans
Column major
Must be at least
k
Must be at least
n
Row major
Must be at least
n
Must be at least
k
c
Pointer to input/output matrix
C
. Size of the array must be at least
ldc
*
n
. See Matrix Storage for more details.
ldc
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 updated
C
matrix.
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.