.. _orgtr:

orgtr
=====

Generates the real orthogonal matrix Q determined by :ref:`sytrd <sytrd>`. This routine belongs to the ``oneapi::mkl::lapack`` namespace.


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

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

The routine explicitly generates the ``n``-by-``n`` orthogonal matrix
``Q`` formed by :ref:`sytrd` when reducing a real symmetric matrix ``A`` to tridiagonal form: ``A = Q*T*QT``. Use this routine after a call to :ref:`sytrd`.


API
***


Syntax
------

.. code-block:: cpp

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

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

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

   * -  T
     -  Devices supported
   * -  ``float``
     -  Host and CPU
   * -  ``double``
     -  Host and CPU


Input Parameters
----------------

queue
   Device queue where calculations will be performed.


uplo
   Must be uplo::upper or uplo::lower. Uses the same uplo as supplied
   to the :ref:`sytrd`
   function


n
   The order of matrix ``Q`` (``0≤n``).


a
   The buffer ``a`` returned by the
   :ref:`sytrd`
   function. The second dimension of ``a`` must be at least
   ``max(1, n)``.


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


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:`orgtr_scratchpad_size`
   function.


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

a
   Overwritten by the orthogonal matrix ``Q``.


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.