.. _potrf_batch-group-version:

potrf_batch (Group 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::
    :local:
    :depth: 1

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 ``uplog = 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 ``uplog = mkl::uplo::lower``

Where ``L``\ :sub:`i` is a lower triangular matrix and
``U``\ :sub:`i` is an upper triangular matrix, ``g`` is an index of
group of parameters corresponding to ``A``\ :sub:`i`, and the total
number of problems to solve, ``batch_size``, is a sum of sizes for
all of the groups of parameters as provided by the ``group_sizes``
array.


API
***


Syntax
------

.. code-block:: cpp

   namespace oneapi::mkl::lapack {
     cl::sycl::event potrf_batch(cl::sycl::queue &queue,
     mkl::uplo *uplo,
     std::int64_t *n,
     T **a,
     std::int64_t *lda,
     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.


uplo
   Array of ``group_count``\ uplo\ :sub:`g` parameters.


   Each of uplo\ :sub:`g` indicates whether the upper or lower
   triangular parts of the input matrices are provided:


   If uplo\ :sub:`g`\ =\ ``mkl::uplo::upper``, input matrices from
   array ``a`` belonging to group ``g`` store the upper triangular
   parts.


   If uplo\ :sub:`g`\ =\ ``mkl::uplo::lower``, input matrices from
   array ``a`` belonging to group ``g`` store the lower triangular
   parts.


n
   Array of ``group_count`` parameters ``n``\ :sub:`g`.


   Each ``n``\ :sub:`g` specifies the order of the input matrices
   from array ``a`` belonging to group ``g``.


a
   Array of ``batch_size`` pointers to input matrices
   ``A``\ :sub:`i`, each being of size
   ``lda``\ :sub:`g`\ \*\ ``n``\ :sub:`g` (``g`` is an index of the
   group to which ``A``\ :sub:`i` belongs) and holding either upper
   or lower triangular part as specified by uplo\ :sub:`g`.


lda
   Array of ``group_count`` parameters lda\ :sub:`g`.


   Each lda\ :sub:`g` specifies the leading dimension of matrices
   from ``a`` 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:`potrf_batch_scratchpad_size-group-version`.


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


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

a
   The matrices pointed to by array a are overwritten by the Cholesky
   factors ``U``\ :sub:`i` or ``L``\ :sub:`i`, as specified by
   uplo\ :sub:`g` from the corresponding group of parameters.


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.