.. ******************************************************************************
.. * Copyright 2021 Intel Corporation
.. *
.. * Licensed under the Apache License, Version 2.0 (the "License");
.. * you may not use this file except in compliance with the License.
.. * You may obtain a copy of the License at
.. *
.. *     http://www.apache.org/licenses/LICENSE-2.0
.. *
.. * Unless required by applicable law or agreed to in writing, software
.. * distributed under the License is distributed on an "AS IS" BASIS,
.. * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
.. * See the License for the specific language governing permissions and
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.. *******************************************************************************/

.. highlight:: cpp
.. default-domain:: cpp

.. _api_pca:

===================================
Principal Components Analysis (PCA)
===================================

.. include:: ../../../includes/decomposition/pca-introduction.rst

------------------------
Mathematical formulation
------------------------

Refer to :ref:`Developer Guide: Principal Components Analysis <alg_pca>`.

---------------------
Programming Interface
---------------------
All types and functions in this section are declared in the
``oneapi::dal::pca`` namespace and be available via inclusion of the
``oneapi/dal/algo/pca.hpp`` header file.

Descriptor
----------
.. onedal_class:: oneapi::dal::pca::descriptor

Method tags
~~~~~~~~~~~
.. onedal_tags_namespace:: oneapi::dal::pca::method

Task tags
~~~~~~~~~
.. onedal_tags_namespace:: oneapi::dal::pca::task

Model
-----
.. onedal_class:: oneapi::dal::pca::model


.. _pca_t_api:

Training :cpp:expr:`train(...)`
--------------------------------
.. _pca_t_api_input:

Input
~~~~~
.. onedal_class:: oneapi::dal::pca::train_input


.. _pca_t_api_result:

Result
~~~~~~
.. onedal_class:: oneapi::dal::pca::train_result

Operation
~~~~~~~~~

.. function:: template <typename Descriptor> \
              pca::train_result train(const Descriptor& desc, \
                                         const pca::train_input& input)

   :param desc: PCA algorithm descriptor :expr:`pca::descriptor`
   :param input: Input data for the training operation

   Preconditions
      | :expr:`input.data.has_data == true`
      | :expr:`input.data.column_count >= desc.component_count`
   Postconditions
      | :expr:`result.means.row_count == 1`
      | :expr:`result.means.column_count == desc.component_count`
      | :expr:`result.variances.row_count == 1`
      | :expr:`result.variances.column_count == desc.component_count`
      | :expr:`result.variances[i] >= 0.0`
      | :expr:`result.eigenvalues.row_count == 1`
      | :expr:`result.eigenvalues.column_count == desc.component_count`
      | :expr:`result.model.eigenvectors.row_count == 1`
      | :expr:`result.model.eigenvectors.column_count == desc.component_count`

.. _pca_i_api:

Inference :cpp:expr:`infer(...)`
---------------------------------
.. _pca_i_api_input:

Input
~~~~~
.. onedal_class:: oneapi::dal::pca::infer_input


.. _pca_i_api_result:

Result
~~~~~~
.. onedal_class:: oneapi::dal::pca::infer_result

Operation
~~~~~~~~~

.. function:: template <typename Descriptor> \
              pca::infer_result infer(const Descriptor& desc, \
                                         const pca::infer_input& input)

   :param desc: PCA algorithm descriptor :expr:`pca::descriptor`
   :param input: Input data for the inference operation

   Preconditions
      | :expr:`input.data.has_data == true`
      | :expr:`input.model.eigenvectors.row_count == desc.component_count`
      | :expr:`input.model.eigenvectors.column_count == input.data.column_count`
   Postconditions
      | :expr:`result.transformed_data.row_count == input.data.row_count`
      | :expr:`result.transformed_data.column_count == desc.component_count`

-------------
Usage example
-------------

.. include:: ../../../includes/decomposition/pca-usage-examples.rst

--------
Examples
--------

.. include:: ../../../includes/decomposition/pca-examples.rst