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Distributed Processing
======================

This mode assumes that the data set is split into ``nblocks`` blocks across computation nodes.

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

The low order moments algorithm in the distributed processing mode has the following parameters:

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

.. list-table:: Algorithm Parameters for Low Order Moments (Distributed Processing)
   :widths: 10 10 60
   :header-rows: 1
   :class: longtable

   * - Parameter
     - Default Valude
     - Description
   * - ``computeStep``
     - Not applicable
     - The parameter required to initialize the algorithm. Can be:

       - ``step1Local`` - the first step, performed on local nodes
       - ``step2Master`` - the second step, performed on a master node

   * - ``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 low order moments:

       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

   * - ``estimatesToCompute``
     - ``estimatesAll``
     - Estimates to be computed by the algorithm:

       - ``estimatesAll`` - all supported moments
       - ``estimatesMinMax`` - minimum and maximum
       - ``estimatesMeanVariance`` - mean and variance

Computation of low order moments follows the general schema described in :ref:`algorithms`:

.. _moments_step_1:

Step 1 - on Local Nodes
***********************

In this step, the low order moments algorithm 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 Low Order Moments (Distributed Processing, Step 1)
   :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 :math:`i`-th data block on the local node.

       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.

In this step, the low order moments algorithm 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 Low Order Moments (Distributed Processing, Step 1)
   :widths: 10 60
   :header-rows: 1

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

       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``.

Partial characteristics computed so far on the local node, each in a :math:`1 \times p` numeric table.
By default, each table is an object of the ``HomogenNumericTable`` class, but you can define the tables as objects
of any class derived from ``NumericTable`` except ``PackedSymmetricMatrix``, ``PackedTriangularMatrix``, and ``CSRNumericTable``.

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

.. list-table:: Partial Characteristics for Low Order Moments (Distributed Processing, Step 1)
   :widths: 10 60
   :header-rows: 1
   :class: longtable

   * - Result ID
     - Result
   * - ``partialMinimum``
     - Partial minimums
   * - ``partialMaximum``
     - Partial maximums
   * - ``partialSum``
     - Partial sums
   * - ``partialSumSquares``
     - Partial sums of squares
   * - ``partialSumSquaresCentered``
     - Partial sums of squared differences from the means

.. _moments_step_2:

Step 2 - on Master Node
***********************

In this step, the low order moments algorithm 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 Low Order Moments (Distributed Processing, Step 2)
   :widths: 10 60
   :header-rows: 1

   * - Input ID
     - Input
   * - ``partialResults``
     - A collection that contains numeric tables with partial results computed in :ref:`Step 1 <moments_step_1>` on local nodes (six numeric tables from each local node).
       These numeric tables can be objects of any class derived from the ``NumericTable`` class except ``PackedSymmetricMatrix`` and ``PackedTriangularMatrix``.

In this step, the low order moments algorithm calculates the results described in the following table.
Pass the ``Result ID`` as a parameter to the methods that access the results of your algorithm.
For more details, see :ref:`algorithms`.

.. note::

    Each result is a pointer to the :math:`1 \times p` numeric table that contains characteristics for each feature in the data set.
    By default, the tables are objects of the ``HomogenNumericTable`` class,
    but you can define each table as an object of any class derived from ``NumericTable``
    except ``PackedSymmetricMatrix``, ``PackedTriangularMatrix``, and ``CSRNumericTable``.

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

.. list-table:: Algorithm Output for Low Order Moments (Distributed Processing, Step 2)
   :widths: 10 60
   :header-rows: 1
   :class: longtable

   * - Result ID
     - Characteristic
   * - ``minimum``
     - Minimums
   * - ``maximum``
     - Maximums
   * - ``sum``
     - Sums
   * - ``sumSquares``
     - Sums of squares
   * - ``sumSquaresCentered``
     - Sums of squared differences from the means
   * - ``mean``
     - Estimates for the means
   * - ``secondOrderRawMoment``
     - Estimates for the second order raw moments
   * - ``variance``
     - Estimates for the variances
   * - ``standardDeviation``
     - Estimates for the standard deviations
   * - ``variation``
     - Estimates for the variations

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