.. _getri-usm-version:

getri (USM Version)
===================


Computes the inverse of an LU-factored general matrix determined by
``getrf`` (USM Version). This routine belongs to the
``oneapi::mkl::lapack`` namespace.


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

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

The routine computes the inverse ``inv(A)`` of a general matrix
``A``. Before calling this routine, call :ref:`getrf-usm-version` to
factorize ``A``.


API
***


Syntax
------

.. code-block:: cpp

    namespace oneapi::mkl::lapack {
      cl::sycl::event getri(cl::sycl::queue &queue,
      std::int64_t n,
      T *a,
      std::int64_t lda,
      std::int64_t *ipiv,
      T *scratchpad,
      std::int64_t scratchpad_size,
      const std::vector<cl::sycl::event> &events = {})
   }

``getri`` (USM version) 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.


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


a
   The pointer returned by :ref:`getrf-usm-version`. Must
   be of size at least ``lda*max(1,n)``.


lda
   The leading dimension of a\ ``(n≤lda)``.


ipiv
   The array as returned by :ref:`getrf-usm-version`. The
   dimension of ipiv must be at least ``max(1, n)``.


scratchpad
   Pointer to 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:`getri_scratchpad_size`
   function.


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


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

a
   Overwritten by the n-by-n matrix ``inv(A)``.


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`` 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.


Return Values
-------------

Output event to wait on to ensure computation is complete.