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Sorting
=======

In |short_name| sorting is an algorithm to sort the observations by each feature (column) in the ascending order.

The result of the sorting algorithm applied to the matrix
:math:`X = (x_{ij})_{n \times p}` is the matrix :math:`Y = (y_{ij})_{n \times p}`
where the :math:`j`-th column :math:`(Y)_j = ( y_{ij} )`, :math:`i = 1, \ldots, n`,
is the column :math:`(X)_j = ( x_{ij} )`, :math:`i = 1, \ldots, n`, sorted in the ascending order.

Batch Processing
****************

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

The sorting 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 Sorting (Batch Processing)
   :widths: 10 60
   :header-rows: 1

   * - Input ID
     - Input
   * - ``data``
     - Pointer to the :math:`n \times p` numeric table that contains the input data set.

       This table can be an object of any class derived from ``NumericTable`` except
       ``PackedSymmetricMatrix``, ``PackedTriangularMatrix``, and ``CSRNumericTable``.

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

The sorting algorithm has the following parameters:

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

.. list-table:: Algorithm Parameters for Sorting (Batch Processing)
   :header-rows: 1
   :align: left
   :widths: 10 10 60
   :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``
     - The radix method for sorting a data set, the only method supported by the algorithm.


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

The sorting algorithm function 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 Sorting (Batch Processing)
   :widths: 10 60
   :header-rows: 1

   * - Result ID
     - Result
   * - ``sortedData``
     - Pointer to the :math:`n \times p` numeric table that stores the results of sorting.

.. note::

    If the number of feature vectors is greater than or equal to :math:`2^{31}`,
    the library uses the quick sort method instead of radix sort.

Examples
********

.. tabs::

  .. tab:: C++ (CPU)

    Batch Processing:

    - :cpp_example:`sorting_dense_batch.cpp <sorting/sorting_dense_batch.cpp>`


  .. tab:: Python*

    Batch Processing:

    - :daal4py_example:`sorting.py`