.. _potri:

potri
=====

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


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

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

The routine computes the inverse ``inv(A)`` of a symmetric positive definite or, for complex flavors, Hermitian positive-definite matrix ``A``. Before calling this routine, call :ref:`potrf` to factorize ``A``.


API
***


Syntax
------

.. code-block:: cpp

   namespace oneapi::mkl::lapack {
     void potri(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)
   }

``potri`` 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 how the input matrix A has been factored:


   If ``uplo = mkl::uplo::upper``, the upper triangle of ``A`` is
   stored.


   If ``uplo = mkl::uplo::lower``, the lower triangle of ``A`` is
   stored.

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


a
   Contains the factorization of the matrix ``A``, as returned by
   :ref:`potrf-usm-version`. 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:`potri_scratchpad_size`
   function.


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

a
   Overwritten by the upper or lower triangle of the inverse of
   ``A``. Specified by ``uplo``.


Exceptions
----------

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

.. list-table::
   :header-rows: 1

   * - 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``, the ``i``-th diagonal element   of the Cholesky factor (and therefore the factor itself) is zero, and   the inversion could not be completed.

           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.