.. _getrf_batch-usm-strided-version:

getrf_batch (USM Strided Version)
=================================


Computes the batch of LU factorizations of a general m-by-n matrices.
This routine belongs to the ``oneapi::mkl::lapack`` namespace.


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

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

The routine computes the LU factorizations of a batch of general
``m``-by-``n`` matrices ``A``\ :sub:`i`, as


.. math::

   A_i = P_i \times L_i \times U_i

Where ``P``\ :sub:`i` is a permutation matrix, ``L``\ :sub:`i` is
lower triangular with unit diagonal elements (lower trapezoidal if
``m > n``) and ``U``\ :sub:`i` is upper triangular (upper trapezoidal
if ``m < n``). The routine uses partial pivoting with row
interchanges.


API
***


Syntax
------

.. code-block:: cpp

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

Function 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 matrices ``A``\ :sub:`i` (``0 ≤ m``).


n
   The number of columns in the matrices ``A``\ :sub:`i` (``0 ≤ n``).


a
   Array holding input matrices ``A``\ :sub:`i`.


lda
   The leading dimension of ``A``\ :sub:`i` .


stride_a
   The stride between the beginnings of matrices ``A``\ :sub:`i`
   inside the batch array ``a``.


stride_ipiv
   The stride between the beginnings of arrays ``ipiv``\ :sub:`i`
   inside the array ``ipiv``.


batch_size
   Specifies the number of problems in a batch.


scratchpad
   Scratchpad memory to be used by 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
   :ref:`getrf_batch_scratchpad_size-strided-version`.


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


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

a
   Overwritten by ``L``\ :sub:`i` and ``U``\ :sub:`i`. The unit
   diagnonal elements of ``L``\ :sub:`i` are not stored.


ipiv
   Array containing the batch of the pivot indices ``ipiv``\ :sub:`i`
   each of size at least ``max(1,min(m,n))``; for 1 ≤ ``k`` ≤
   ``min(m,n)``, row ``k`` of ``A``\ :sub:`i` was interchanged with
   row ``ipiv``\ :sub:`i`\ (``k``).


Exceptions
----------

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

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

   * - Exception
     - Description

   * -     ``mkl::lapack::batch_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 = -n``, the ``n``-th parameter had an illegal   value.

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

           If ``info`` is zero, then the diagonal   element of some of ``U``\ :sub:`i` is zero, and the solve could not   be completed. The indexes of such matrices in the batch can be   obtained with the ids() method of the exception object. You can   obtain the indexes of the first zero diagonal elements in these   ``U``\ :sub:`i` matrices using the infos() method of the exception   object.





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

Output event to wait on to ensure computation is complete.