.. _unmqr-usm-version:

unmqr (USM Version)
===================

Multiplies a complex matrix by the unitary matrix Q of the QR
factorization formed by the ``geqrf`` (USM Version) function. This routine
belongs to the ``oneapi::mkl::lapack`` namespace.


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

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

The routine multiplies a complex matrix ``C`` by ``Q`` or
``Q``\ :sup:`T`, where ``Q`` is the orthogonal matrix ``Q`` of the
``QR`` factorization formed by the routine :ref:`geqrf-usm-version`.


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


API
***


Syntax
------

.. code-block:: cpp

   namespace oneapi::mkl::lapack {
     cl::sycl::event unmqr(cl::sycl::queue &queue,
     mkl::side side,
     mkl::transpose trans,
     std::int64_t m,
     std::int64_t n,
     std::int64_t k,
     T *a,
     std::int64_t lda,
     T *tau,
     T *c,
     std::int64_t ldc,
     T *scratchpad,
     std::int64_t scratchpad_size,
     const std::vector<cl::sycl::event> &events = {})
   }

``ormqr`` (USM version) supports the following precisions and
devices:


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

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


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
   The pointer to the result of the :ref:`geqrf-usm-version`
   function. The second dimension of ``a`` must be at least
   ``max(1,k)``.


lda
   The leading dimension of a.


tau
   The pointer to tau returned by the :ref:`geqrf-usm-version`
   function.


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


ldc
   The leading dimension of c.


scratchpad
   Pointer to 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:`unmqr_scratchpad_size`
   function.


events
   List of events to wait for before starting computation. Defaults
   to empty list.


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.


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

Output event to wait on to ensure computation is complete.