.. _onemkl_blas_syr2k:
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``,
.. math::
C \leftarrow alpha*(A*B^T + B*A^T) + beta*C
where ``A`` is ``n`` x ``k`` and ``B`` is ``k`` x ``n``.
If ``trans`` = ``transpose::trans``,
.. math::
C \leftarrow alpha*(A^T*B + B^T*A) + beta*C
where ``A`` is ``k`` x ``n`` and ``B`` is ``n`` x ``k``.
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:
.. list-table::
:header-rows: 1
* - T
* - ``float``
* - ``double``
* - ``std::complex<float>``
* - ``std::complex<double>``
syr2k (Buffer Version)
**********************
Syntax
------
.. code-block:: cpp
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)
}
.. code-block:: cpp
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 :ref:`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 :ref:`matrix-storage` for more details.
.. list-table::
:header-rows: 1
* -
- ``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.
.. list-table::
:header-rows: 1
* -
- ``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 :ref:`matrix-storage` for more details.
.. list-table::
:header-rows: 1
* -
- ``trans`` = ``transpose::nontrans``
- ``trans`` = ``transpose::trans`` or ``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
Leading dimension of matrix ``B``. Must be positive.
.. list-table::
:header-rows: 1
* -
- ``trans`` = ``transpose::nontrans``
- ``trans`` = ``transpose::trans`` or ``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 :ref:`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
------
.. code-block:: cpp
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 = {})
}
.. code-block:: cpp
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 :ref:`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 :ref:`matrix-storage` for more details.
.. list-table::
:header-rows: 1
* -
- ``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.
.. list-table::
:header-rows: 1
* -
- ``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 :ref:`matrix-storage` for more details.
.. list-table::
:header-rows: 1
* -
- ``trans`` = ``transpose::nontrans``
- ``trans`` = ``transpose::trans`` or ``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
Leading dimension of matrix ``B``. Must be positive.
.. list-table::
:header-rows: 1
* -
- ``trans`` = ``transpose::nontrans``
- ``trans`` = ``transpose::trans`` or ``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 :ref:`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.