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Batch and Online Processing
===========================

Online processing computation mode assumes that the data arrives in blocks :math:`i = 1, 2, 3, \ldots \text{nblocks}`.

Algorithm Input
---------------

QR decomposition accepts the input described below.
Pass the ``Input ID`` as a parameter to the methods that provide input for your algorithm.
For more details, see :ref:`algorithms`.

.. tabularcolumns::  |\Y{0.2}|\Y{0.8}|

.. list-table:: Algorithm Input for QR Decomposition without Pivoting (Batch and Online Processing)
   :widths: 10 60
   :header-rows: 1

   * - Input ID
     - Input
   * - ``data``
     - Pointer to the numeric table that represents:

       - For batch processing: the entire :math:`n \times p` matrix :math:`X` to be factorized.
       - For online processing: the :math:`n_i \times p` submatrix of :math:`X` that represents
         the current data block in the online processing mode.
         Note that each current data block must have sufficient size: :math:`n_i > p`.

       The input can be an object of any class derived from ``NumericTable``.

Algorithm Parameters
--------------------

QR decomposition has the following parameters:

.. tabularcolumns::  |\Y{0.15}|\Y{0.15}|\Y{0.7}|

.. list-table:: Algorithm Parameters for QR Decomposition without Pivoting (Batch and Online Processing)
   :header-rows: 1
   :widths: 10 10 60
   :align: left
   :class: longtable

   * - Parameter
     - Default Value
     - Description
   * - ``algorithmFPType``
     - ``float``
     - The floating-point type that the algorithm uses for intermediate computations. Can be ``float`` or ``double``.
   * - ``method``
     - ``defaultDense``
     - Performance-oriented computation method, the only method supported by the algorithm.

Algorithm Output
----------------

QR decomposition calculates the results described below.
Pass the ``Result ID`` as a parameter to the methods that access the results of your algorithm.
For more details, see :ref:`algorithms`.

.. tabularcolumns::  |\Y{0.2}|\Y{0.8}|

.. list-table:: Algorithm Output for QR Decomposition without Pivoting (Batch and Online Processing)
   :widths: 10 60
   :header-rows: 1
   :class: longtable

   * - Result ID
     - Result
   * - ``matrixQ``
     - Pointer to the numeric table with the :math:`n \times p` matrix :math:`Q_1`.

       .. note::
           By default, this result is an object of the ``HomogenNumericTable`` class, but you can define the result as an object of any class
           derived from ``NumericTable`` except ``PackedSymmetricMatrix``, ``PackedTriangularMatrix``, and ``CSRNumericTable``.

   * - ``matrixR``
     - Pointer to the numeric table with the :math:`p \times p` upper triangular matrix :math:`R_1`.

       .. note::
           By default, this result is an object of the ``HomogenNumericTable`` class, but you can define the result as an object of any class
           derived from ``NumericTable`` except the ``PackedSymmetricMatrix`` class, ``CSRNumericTable`` class,
           and ``PackedTriangularMatrix`` class with the ``lowerPackedTriangularMatrix`` layout.