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syr2k

Performs a symmetric rank-2k update.

Description

The
syr2k
routines perform a rank-2k update of an
n
x
n
symmetric matrix
C
by general matrices
A
and
B
. The operation is defined as:
If
trans
=
transpose::nontrans
,
LaTex Math image.
where
A
and
B
are
n
x
k
matrices.
If
trans
=
transpose::trans
,
LaTex Math image.
where
A
and
B
are
k
x
n
matrices.
In both cases:
  • alpha
    and
    beta
    are scalars
  • C
    is symmetric matrix,
    A
    and
    B
    are general matrices
  • The inner dimension of both matrix multiplications is
    k
syr2k
supports the following precisions:
T
float
double
std::complex<float>
std::complex<double>

syr2k (Buffer Version)

Syntax
namespace oneapi::mkl::blas::column_major { void syr2k(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 beta, sycl::buffer<T,1> &c, std::int64_t ldc) }
namespace oneapi::mkl::blas::row_major { void syr2k(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 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. Conjugation is never performed even if
trans
=
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::trans
or
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::trans
or
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
b
Buffer holding input matrix
B
. See Matrix Storage for more details.
trans
=
transpose::nontrans
trans
=
transpose::trans
or
trans
=
transpose::conjtrans
Column major
B
is
n
x
k
matrix. Size of array
b
must be at least
ldb
*
k
B
is
k
x
n
matrix. Size of array
b
must be at least
ldb
*
n
Row major
B
is
n
x
k
matrix. Size of array
b
must be at least
ldb
*
n
B
is
k
x
n
matrix. Size of array
b
must be at least
ldb
*
k
ldb
Leading dimension of matrix
B
. Must be positive.
trans
=
transpose::nontrans
trans
=
transpose::trans
or
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
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 updated
C
matrix.

syr2k (USM Version)

Syntax
namespace oneapi::mkl::blas::column_major { sycl::event syr2k(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 beta, T* c, std::int64_t ldc, const std::vector<sycl::event> &dependencies = {}) }
namespace oneapi::mkl::blas::row_major { sycl::event syr2k(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 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. Conjugation is never performed even if
trans
=
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::trans
or
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::trans
or
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
b
Pointer to input matrix
B
. See Matrix Storage for more details.
trans
=
transpose::nontrans
trans
=
transpose::trans
or
trans
=
transpose::conjtrans
Column major
B
is
n
x
k
matrix. Size of array
b
must be at least
ldb
*
k
B
is
k
x
n
matrix. Size of array
b
must be at least
ldb
*
n
Row major
B
is
n
x
k
matrix. Size of array
b
must be at least
ldb
*
n
B
is
k
x
n
matrix. Size of array
b
must be at least
ldb
*
k
ldb
Leading dimension of matrix
B
. Must be positive.
trans
=
transpose::nontrans
trans
=
transpose::trans
or
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
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 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.