.. _getrf_batch-group-version:

getrf_batch (Group 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`, (``iϵ{1...batch_size}``) 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.


Total number of problems to solve, ``batch_size``, is a sum of sizes
of all of the groups of parameters as provided by
``group_sizes`` array.


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 **ipiv,
      std::int64_t group_count,
      std::int64_t *group_sizes,
      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
   Array of ``group_count`` parameters m\ :sub:`g` specifying the
   number of rows in the matrices ``A``\ :sub:`i` (``0 ≤ mg``)
   belonging to group ``g``.


n
   Array of ``group_count`` parameters n\ :sub:`g` specifying the
   number of columns in the matrices ``A``\ :sub:`i` (``0 ≤ ng``)
   belonging to group ``g``.


a
   Array of ``batch_size`` pointers to input
   matrices\ ``A``\ :sub:`i`.


lda
   Array of ``group_count`` parameters lda\ :sub:`g` specifying the
   leading dimension of ``A``\ :sub:`i` belonging to group ``g``.


group_count
   Specifies the number of groups of parameters. Must be at least 0.


group_sizes
   Array of group_count integers. Array element with index ``g``
   specifies the number of problems to solve for each of the groups
   of parameters ``g``. So the total number of problems to solve,
   ``batch_size``, is a sum of all parameter group sizes.


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 then the value returned by
   :ref:`getrf_batch_scratchpad_size-group-version`.


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


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

a
   Matrices pointed to by array ``a`` are overwritten by
   ``L``\ :sub:`i` and ``U``\ :sub:`i`. The unit diagnonal elements
   of ``L``\ :sub:`i` are not stored.


ipiv
   Arrays of batch_size pointers to arrays containing pivot indices
   ``ipiv``\ :sub:`i` each of size at least ``max(1,min(mg,ng))``;
   for 1 ≤ ``k`` ≤ ``min(mg,ng)``, 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.