.. _potrf:

potrf
=====


Computes the Cholesky factorization of a symmetric (Hermitian)
positive-definite matrix.This routine belongs to the
``oneapi::mkl::lapack`` namespace.


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

The routine forms the Cholesky factorization of a symmetric
positive-definite or, for complex data, Hermitian positive-definite
matrix ``A``:


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

where ``L`` is a lower triangular matrix and ``U`` is upper
triangular.


API
***


Syntax
------

.. code-block:: cpp

   namespace oneapi::mkl::lapack {
     void potrf(cl::sycl::queue &queue,
     mkl::uplo uplo,
     std::int64_t n,
     cl::sycl::buffer<T> &a,
     std::int64_t lda,
     cl::sycl::buffer<T> &scratchpad,
     std::int64_t scratchpad_size)
   }

``potrf`` supports the following precisions and devices:

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   * -  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`` is
   stored and how ``A`` is factored:


   If uplo=\ ``mkl::uplo::upper``, the array ``a`` stores the upper
   triangular part of the matrix ``A``, and the strictly lower
   triangular part of the matrix is not referenced.


   If uplo=\ ``mkl::uplo::lower``, the array ``a`` stores the lower
   triangular part of the matrix ``A``, and the strictly upper
   triangular part of the matrix is not referenced.


n
   Specifies the order of the matrix ``A`` (``0≤n``).


a
   Buffer holding input matrix ``A``. The array holding input matrix
   a contains either the upper or the lower triangular part of the
   matrix ``A`` (see uplo). The second dimension of a must be at
   least ``max(1, n)``.


lda
   The leading dimension of a.


scratchpad
   Buffer holding scratchpad memory to be used by the 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
   the
   :ref:`potrf_scratchpad_size`
   function.


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

a
   The buffer a is overwritten by the Cholesky factor ``U`` or ``L``,
   as specified by uplo.


Exceptions
----------

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

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   * - Exception
     - Description

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

           If ``info = i``, and detail() returns 0, the   leading minor of order ``i`` (and therefore the matrix ``A`` itself)   is not positive-definite, and the factorization could not be   completed. This may indicate an error in forming the matrix   ``A``.

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



Known Limitations
------------------

- GPU support is for only real precisions.

- GPU support for this function does not include error reporting through the ``info`` parameter.