.. _unmrq:

unmrq
=====

Multiplies a complex matrix by the unitary matrix Q of the RQ
factorization formed by ``gerqf``. This routine belongs to the
``oneapi::mkl::lapack`` namespace.


.. contents::
    :local:
    :depth: 1

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

The routine multiplies a complex ``m``-by-``n`` matrix ``C`` by ``Q``
or ``Q``\ :sup:`H`, where ``Q`` is the complex unitary matrix defined
as a product of ``k`` elementary reflectors ``H(i)`` of order ``n``:
``Q = H(1)H* H(2)``\ :sup:`H`\ \*...\*\ ``H(k)H``\ as returned by the
``RQ`` factorization routine
:ref:`gerqf`
.


Depending on the parameters ``side`` and ``trans``, the routine can
form one of the matrix products ``Q*C``, ``Q``\ :sup:`H`\ ``*C``,
``C*Q``, or ``C*Q``\ :sup:`H` (overwriting the result over ``C``).


API
***


Syntax
------

.. code-block:: cpp

   namespace oneapi::mkl::lapack {
     void unmrq(cl::sycl::queue &queue,
     mkl::side side,
     mkl::transpose trans,
     std::int64_t m,
     std::int64_t n,
     std::int64_t k,
     cl::sycl::buffer<T> &a,
     std::int64_t lda,
     cl::sycl::buffer<T> &tau,
     cl::sycl::buffer<T> &c,
     std::int64_t ldc,
     cl::sycl::buffer<T> &scratchpad,
     std::int64_t scratchpad_size)
   }

``unmrq`` supports the following precisions and devices:

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

   * -  T
     -  Devices supported
   * -  ``std::complex<float>``
     -  Host and CPU
   * -  ``std::complex<double>``
     -  Host and CPU


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

queue
   Device queue where calculations will be performed.


side
   If ``side`` = ``mkl::side::left``, ``Q`` or ``Q``\ :sup:`T` is
   applied to ``C`` from the left. If ``side`` =
   ``mkl::side::right``, ``Q`` or ``Q``\ :sup:`T` is applied to ``C``
   from the right.

trans
   If ``trans=mkl::transpose::trans``, the routine multiplies ``C``
   by ``Q``.


   If ``trans=mkl::transpose::nontrans``, the routine multiplies
   ``C`` by ``Q``\ :sup:`T`.


m
   The number of rows in the matrix ``A`` (``0≤m``).


n
   The number of columns in the matrix ``A`` (``0≤n≤m``).


k
   The number of elementary reflectors whose product defines the
   matrix ``Q`` (``0≤k≤n``).


a
   Buffer holding the result of the
   :ref:`gerqf`
   function. The second dimension of ``a`` must be at least
   ``max(1,k)``.


lda
   The leading dimension of a.


tau
   Buffer holding tau returned by the
   `:ref:`gerqf`
   function.


c
   Buffer holding the matrix ``C``. The second dimension of c must be
   at least ``max(1,n)``.


ldc
   The leading dimension of c.


scratchpad
   Buffer holding scratchpad memory to be used by the routine for
   storing intermediate results.


scratchpad_size
   Size of scratchpad memory as a number of floating point elements
   of type ``T``. Size should not be less than the value returned by
   the
   :ref:`unmrq_scratchpad_size`
   function.


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

c
   Overwritten by the product ``Q``\ \*\ ``C``,
   ``Q``\ :sup:`T`\ \*\ ``C``, ``C``\ \*\ ``Q``, or
   ``C``\ \*\ ``Q``\ :sup:`T` (as specified by side and trans).


Exceptions
----------

.. tabularcolumns:: |\Y{0.3}|\Y{0.7}|

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

   * - Exception
     - Description

   * -     ``mkl::lapack::exception``
     -     This exception is thrown when problems occur during    calculations. You can obtain the info code of the problem using the   info() method of the exception object:

           If   ``info = -i``, the ``i``-th parameter had an illegal   value.

           If ``info`` is equal to the value passed as   scratchpad size, and detail() returns non zero, then the passed   scratchpad has an insufficient size, and the required size should not   be less than the value returned by the detail() method of the   exception object.