.. _getrs_batch-buffer-strided-version:

getrs_batch (Buffer Strided Version)
====================================


Solves a batch of linear equations with an LU-factored square
coefficient matrices, with multiple right-hand sides. This routine
belongs to the ``oneapi::mkl::lapack`` namespace.


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

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

The routine solves for ``X``\ :sub:`i` the following systems of
linear equations:

- ``A``\ :sub:`i` \* ``X``\ :sub:`i` = ``B``\ :sub:`i` If ``trans = mkl::transpose::notrans``

- ``A``\ :sub:`i`\ :sup:`T` \* ``X``\ :sub:`i` = ``B``\ :sub:`i` If ``trans = mkl::transpose::trans``

- ``A``\ :sub:`i`\ :sup:`H` \* ``X``\ :sub:`i` = ``B``\ :sub:`i` If ``trans = mkl::transpose::conjtrans``


Before calling this routine you must call :ref:`getrf_batch-buffer-strided-version`
to compute the LU factorization of ``A``\ :sub:`1`.



API
***


Syntax
------

.. code-block:: cpp

    namespace oneapi::mkl::lapack {
      void getrs_batch(cl::sycl::queue &queue,
      mkl::transpose trans,
      std::int64_t n,
      std::int64_t nrhs,
      cl::sycl::buffer<T> &a,
      std::int64_t lda,
      std::int64_t stride_a,
      cl::sycl::buffer<std::int64_t> &ipiv,
      std::int64_t stride_ipiv,
      cl::sycl::buffer<T> &b,
      std::int64_t ldb,
      std::int64_t stride_b,
      std::int64_t batch_size,
      cl::sycl::buffer<T> &scratchpad,
      std::int64_t scratchpad_size)
   }

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.


trans
   Indicates the form of the equations:


   If trans = mkl::transpose::nontrans, then
   ``A``\ :sub:`i`\ \*\ ``X``\ :sub:`i` = ``B``\ :sub:`i` is solved
   for ``X``\ :sub:`i`.


   If trans = mkl::transpose::trans, then
   ``A``\ :sub:`i`\ :sup:`T`\ \*\ ``X``\ :sub:`i` = ``B``\ :sub:`i`
   is solved for ``X``\ :sub:`i`.


   If trans = mkl::transpose::conjtrans, then
   ``A``\ :sub:`i`\ :sup:`H`\ \*\ ``X``\ :sub:`i` = ``B``\ :sub:`i`
   is solved for ``X``\ :sub:`i`.


n
   The order of the matrices ``A``\ :sub:`i` and the number of rows
   in matrices ``B``\ :sub:`i` (``0 ≤ n``).


nrhs
   The number of right hand sides ``(0≤nrhs)``.


a
   Array containing the factorizations of the matrices
   ``A``\ :sub:`i`, as returned by :ref:`getrf_batch-buffer-strided-version`.


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


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


ipiv
   The ipiv array, as returned by :ref:`getrf_batch-buffer-strided-version`.


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


b
   The array containing the matrices ``B``\ :sub:`i` whose columns
   are the right-hand sides for the systems of equations.


ldb
   The leading dimensions of ``B``\ :sub:`i`.


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 then the value returned by
   stride version of :ref:`getrs_batch_scratchpad_size-strided-version`
   function.


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

b
   Overwritten by the solution matrices ``X``\ :sub:`i`.


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.