.. _geqrf-usm-version:

geqrf (USM Version)
===================


Computes the QR factorization of a general m-by-n matrix. This routine belongs to the ``oneapi::mkl::lapack`` namespace.


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

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

The routine forms the ``QR`` factorization of a general
``m``-by-``n`` matrix ``A``. No pivoting is performed.


The routine does not form the matrix ``Q`` explicitly. Instead, ``Q``
is represented as a product of min(``m``, ``n``) elementary
reflectors. Routines are provided to work with ``Q`` in this
representation.


API
***


Syntax
------

.. code-block:: cpp

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

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

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

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


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

queue
   Device queue where calculations will be performed.


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


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


a
   Pointer to the memory holding input matrix ``A``. The second
   dimension of ``a`` must be at least ``max(1, n)``.


lda
   The leading dimension of ``a``, at least ``max(1, m)``.


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:`geqrf_scratchpad_size`
   function.


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


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

a
   Overwritten by the factorization data as follows:


   The elements on and above the diagonal of the array contain the
   ``min(m,n)``-by-``n`` upper trapezoidal matrix ``R`` (``R`` is
   upper triangular if ``m≥n``); the elements below the diagonal,
   with the array tau, present the orthogonal matrix ``Q`` as a
   product of ``min(m,n)`` elementary reflectors.


tau
   Array, size at least ``min(m,n)``.


   Contains scalars that define elementary reflectors for the matrix
   ``Q`` in its decomposition in a product of elementary reflectors.


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.