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.. _cor_cov_online:

Online Processing
=================

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

Computation of correlation and variance-covariance matrices in the online processing mode follows
the general computation schema for online processing described in :ref:`algorithms`.

Algorithm Input
***************

The correlation and variance-covariance matrices algorithm in the online processing mode 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 Correlation and Variance-Covariance Matrices Algorithm (Online Processing)
   :widths: 10 60
   :header-rows: 1

   * - Input ID
     - Input
   * - ``data``
     - Pointer to the numeric table of size :math:`n_i \times p` that represents the current data block.

       While the input for ``defaultDense``, ``singlePassDense``, or ``sumDense`` method can be an object of any class derived
       from ``NumericTable``, the input for ``fastCSR``, ``singlePassCSR``, or ``sumCSR`` method can only be an object of
       the ``CSRNumericTable`` class.

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

The correlation and variance-covariance matrices algorithm has the following parameters in the online processing mode:

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

.. list-table:: Algorithm Parameters for for Correlation and Variance-Covariance Matrices Algorithm (Online Processing)
   :widths: 10 10 60
   :header-rows: 1
   :class: longtable

   * - Parameter
     - Default Valude
     - Description
   * - ``algorithmFPType``
     - ``float``
     - The floating-point type that the algorithm uses for intermediate computations. Can be ``float`` or ``double``.
   * - ``method``
     - ``defaultDense``
     - Available methods for computation of correlation and variance-covariance matrices:

       defaultDense
           default performance-oriented method

       singlePassDense
           implementation of the single-pass algorithm proposed by D.H.D. West

       sumDense
           implementation of the algorithm in the cases where the basic statistics associated with
           the numeric table are pre-computed sums; returns an error if pre-computed sums are not defined

       fastCSR
           performance-oriented method for CSR numeric tables

       singlePassCSR
           implementation of the single-pass algorithm proposed by D.H.D. West; optimized for CSR numeric tables

       sumCSR
           implementation of the algorithm in the cases where the basic statistics associated with
           the numeric table are pre-computed sums; optimized for CSR numeric tables;
           returns an error if pre-computed sums are not defined

   * - ``outputMatrixType``
     - ``covarianceMatrix``
     - The type of the output matrix. Can be:

       - ``covarianceMatrix`` - variance-covariance matrix
       - ``correlationMatrix`` - correlation matrix

   * - ``initializationProcedure``
     - Not applicable
     - The procedure for setting initial parameters of the algorithm in the online processing mode.
       By default, the algorithm sets the ``nObservations``, ``sum``, and ``crossProduct`` parameters to zero.

Partial Results
***************

The correlation and variance-covariance matrices algorithm in the online processing mode calculates partial 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:: Partial Results for Correlation and Variance-Covariance Matrices Algorithm (Online Processing)
   :widths: 10 60
   :header-rows: 1
   :class: longtable

   * - Result ID
     - Result
   * - ``nObservations``
     - Pointer to the :math:`1 \times 1` numeric table that contains the number of observations processed so far.

       .. 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 ``CSRNumericTable``.
   * - ``crossProduct``
     - Pointer to :math:`p \times p` numeric table with the cross-product matrix computed so far.

       .. note::

          By default, this table 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``.
   * - ``sum``
     - Pointer to :math:`1 \times p` numeric table with partial sums computed so far.

       .. note::

          By default, this table 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``.

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

The correlation and variance-covariance matrices algorithm calculates the result 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 Correlation and Variance-Covariance Matrices Algorithm (Online Processing)
   :widths: 10 60
   :header-rows: 1
   :class: longtable

   * - Result ID
     - Result
   * - ``covariance``
     - Use when ``outputMatrixType``=``covarianceMatrix``. Pointer to the numeric table with the :math:`p \times p` variance-covariance matrix.

       .. 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 ``PackedTriangularMatrix`` and ``CSRNumericTable``.
   * - ``correlation``
     - Use when ``outputMatrixType``=``correlationMatrix``. Pointer to the numeric table with the :math:`p \times p` correlation matrix.

       .. 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 ``PackedTriangularMatrix`` and ``CSRNumericTable``.
   * - ``mean``
     - Pointer to the :math:`1 \times p` numeric table with means.

       .. 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 ``PackedTriangularMatrix``, ``PackedSymmetricMatrix``, and ``CSRNumericTable``.


.. include:: ../../../opt-notice.rst