.. _onemkl_blas_rot:

rot
===

Performs rotation of points in the plane.

Description
***********

Given two vectors ``x`` and ``y`` of ``n`` elements, the ``rot`` routines
compute four scalar-vector products and update the input vectors with
the sum of two of these scalar-vector products. The operation is defined as: 

.. math::

   \left[\begin{array}{c}
      x\\y
   \end{array}\right]
   \leftarrow
   \left[\begin{array}{c}
       \phantom{-}c*x + s*y\\
       -s*x + c*y
   \end{array}\right]

``rot`` supports the following precisions:

.. list-table::
   :header-rows: 1

   * -  T
     -  T_scalar
   * -  ``float``
     -  ``float``
   * -  ``double``
     -  ``double``
   * -  ``std::complex<float>``
     -  ``float``
   * -  ``std::complex<double>``
     -  ``double``


rot (Buffer Version)
********************

Syntax
------

.. code-block:: cpp

   namespace oneapi::mkl::blas::column_major {
       void rot(sycl::queue &queue,
                std::int64_t n,
                sycl::buffer<T,1> &x,
                std::int64_t incx,
                sycl::buffer<T,1> &y,
                std::int64_t incy,
                T_scalar c,
                T_scalar s)
   }

.. code-block:: cpp

   namespace oneapi::mkl::blas::row_major {
       void rot(sycl::queue &queue,
                std::int64_t n,
                sycl::buffer<T,1> &x,
                std::int64_t incx,
                sycl::buffer<T,1> &y,
                std::int64_t incy,
                T_scalar c,
                T_scalar s)
   }

Input Parameters
----------------

queue
   The queue where the routine should be executed.

n
   Number of elements in vector ``x``.

x
   Buffer holding input vector ``x``. Size of the buffer must be at
   least (1 + (``n`` - 1)*abs(``incx``)). See :ref:`matrix-storage` for
   more details.

incx
   Stride of vector ``x``.

y
   Buffer holding input vector ``y``. Size of the buffer must be at
   least (1 + (``n`` - 1)*abs(``incy``)). See :ref:`matrix-storage` for
   more details.

incy
   Stride of vector ``y``.

c
   Scaling factor.

s
   Scaling factor.

Output Parameters
-----------------

x
   Buffer holding updated buffer ``x``.

y
   Buffer holding updated buffer ``y``.


rot (USM Version)
********************

Syntax
------

.. code-block:: cpp

   namespace oneapi::mkl::blas::column_major {
       sycl::event rot(sycl::queue &queue,
                       std::int64_t n,
                       T *x,
                       std::int64_t incx,
                       T *y,
                       std::int64_t incy,
                       T_scalar c,
                       T_scalar s,
                       const std::vector<sycl::event> &dependencies = {})
   }

.. code-block:: cpp

   namespace oneapi::mkl::blas::row_major {
       sycl::event rot(sycl::queue &queue,
                       std::int64_t n,
                       T *x,
                       std::int64_t incx,
                       T *y,
                       std::int64_t incy,
                       T_scalar c,
                       T_scalar s,
                       const std::vector<sycl::event> &dependencies = {})
   }

Input Parameters
----------------

queue
   The queue where the routine should be executed.

n
   Number of elements in vector ``x``.

x
   Pointer to input vector ``x``. Size of the array holding input vector
   ``x`` must be at least (1 + (``n`` - 1)*abs(``incx``)).
   See :ref:`matrix-storage` for more details.

incx
   Stride of vector ``x``.

y
   Pointer to input vector ``y``. Size of the array holding input vector
   ``y`` must be at least (1 + (``n`` - 1)*abs(``incy``)).
   See :ref:`matrix-storage` for more details.

incy
   Stride of vector ``y``.

c
   Scaling factor.

s
   Scaling factor.

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

Output Parameters
-----------------

x
   Pointer to updated vector ``x``.

y
   Pointer to updated vector ``y``.

Return Values
-------------

Output event to wait on to ensure computation is complete.