.. _potrf_batch-buffer-strided-version:

potrf_batch (Buffer Strided Version)
====================================


Computes the Cholesky factorizations of a batch of symmetric (or
Hermitian, for complex data) positive-definite matrices. This routine
belongs to the ``oneapi::mkl::lapack`` namespace.


.. contents::
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Description
***********

The routine forms the Cholesky factorizations of a symmetric
positive-definite or, for complex data, Hermitian positive-definite
matrices ``A``\ :sub:`i`, ``i``\ ``ϵ{1...batch_size}``:

- ``A``\ :sub:`i` = ``U``\ :sub:`i`\ :sup:`T` \* ``U``\ :sub:`i` for real data, ``A``\ :sub:`i` = ``U``\ :sub:`i`\ :sup:`H` \* ``U``\ :sub:`i` for complex data. if ``uplo = mkl::uplo::upper``,

- ``A``\ :sub:`i` = ``L``\ :sub:`i`\ :sup:`T` \* ``L``\ :sub:`i` for real data, ``A``\ :sub:`i` = ``L``\ :sub:`i`\ :sup:`H` \* ``L``\ :sub:`i` for complex data if ``uplo = mkl::uplo::lower``


Where ``L``\ :sub:`i` is a lower triangular matrix and
``U``\ :sub:`i` is an upper triangular matrix.


API
***


Syntax
------

.. code-block:: cpp

   namespace oneapi::mkl::lapack {
     void potrf_batch(cl::sycl::queue &queue,
     mkl::uplo uplo,
     std::int64_t n,
     cl::sycl::buffer<T> &a,
     std::int64_t lda,
     std::int64_t stride_a,
     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.


uplo
   Indicates whether the upper or lower triangular part of
   ``A``\ :sub:`i` is stored and how ``A``\ :sub:`i` is factored:


   If uplo = mkl::uplo::upper, the array ``a`` stores the upper
   triangular parts of the matrices ``A``\ :sub:`i`.


   If uplo = mkl::uplo::lower, the array ``a`` stores the lower
   triangular parts of the matrices ``A``\ :sub:`i`.


n
   Specifies the order of the matrices ``A``\ :sub:`i`, (``0 ≤ n``).


a
   Array containing a batch of input matrices ``A``\ :sub:`i`, each
   of ``A``\ :sub:`i` being of size ``lda``\ \*\ ``n`` and holding
   either uppoer or lower triangular parts of the matrices
   ``A``\ :sub:`i` (see uplo).


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


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


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
   :ref:`potrf_batch_scratchpad_size-strided-version`.


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

a
   The batch array ``a`` is overwritten by the Cholesky factor
   ``U``\ :sub:`i` or ``L``\ :sub:`i`, as specified by uplo .


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.