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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
***************

The SVD algorithm accepts the input described below.
Pass the ``Input ID`` as a parameter to the methods that provide input for your algorithm.

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

.. list-table:: Algorithm Input for Singular Value Decomposition (Batch and Online Processing)
   :header-rows: 1
   :align: left
   :widths: 10 60

   * - 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.

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


Algorithm Parameters
********************

The SVD algorithm has the following parameters:

.. tabularcolumns::  |\Y{0.2}|\Y{0.2}|\Y{0.6}|

.. list-table:: Algorithm Parameters for Singular Value Decomposition (Batch and Online Processing)
   :header-rows: 1
   :align: left
   :widths: 10 20 30
   :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.
   * - ``leftSingularMatrix``
     - ``requiredInPackedForm``
     - Specifies whether the matrix of left singular vectors is required. Can be:

       - ``notRequired`` - the matrix is not required
       - ``requiredInPackedForm`` - the matrix in the packed format is required

   * - ``rightSingularMatrix``
     - ``requiredInPackedForm``
     - Specifies whether the matrix of left singular vectors is required. Can be:

       - ``notRequired`` - the matrix is not required
       - ``requiredInPackedForm`` - the matrix in the packed format is required

Algorithm Output
****************

The SVD algorithm calculates the results described below.
Pass the ``Result ID`` as a parameter to the methods that access the results of your algorithm.

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

.. list-table:: Algorithm Output for Singular Value Decomposition (Batch and Online Processing)
   :header-rows: 1
   :align: left
   :widths: 10 60
   :class: longtable

   * - Result ID
     - Result
   * - ``singularValues``
     - Pointer to the :math:`1 \times p` numeric table with singular values (the diagonal of the matrix :math:`\Sigma`).
   * - ``leftSingularMatrix``
     - Pointer to the :math:`n \times p` numeric table with left singular vectors (matrix :math:`U`).
       Pass ``NULL`` if left singular vectors are not required.
   * - ``rightSingularMatrix``
     - Pointer to the :math:`p \times p` numeric table with right singular vectors (matrix :math:`V`).
       Pass ``NULL`` if right singular vectors are not required.

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