/*=========================================================================

Program:   Visualization Toolkit
Module:    vtkPCAStatistics.h

Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen
All rights reserved.
See Copyright.txt or http://www.kitware.com/Copyright.htm for details.

This software is distributed WITHOUT ANY WARRANTY; without even
the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
PURPOSE.  See the above copyright notice for more information.

=========================================================================*/
/*-------------------------------------------------------------------------
  Copyright 2010 Sandia Corporation.
  Under the terms of Contract DE-AC04-94AL85000 with Sandia Corporation,
  the U.S. Government retains certain rights in this software.
  -------------------------------------------------------------------------*/
/**
 * @class   vtkPCAStatistics
 * @brief   A class for multivariate principal component analysis
 *
 *
 * This class derives from the multi-correlative statistics algorithm and
 * uses the covariance matrix and Cholesky decomposition computed by it.
 * However, when it finalizes the statistics in learn operation, the PCA class
 * computes the SVD of the covariance matrix in order to obtain its eigenvectors.
 *
 * In the assess operation, the input data are
 * - projected into the basis defined by the eigenvectors,
 * - the energy associated with each datum is computed,
 * - or some combination thereof.
 * Additionally, the user may specify some threshold energy or
 * eigenvector entry below which the basis is truncated. This allows
 * projection into a lower-dimensional state while minimizing (in a
 * least squares sense) the projection error.
 *
 * In the test operation, a Jarque-Bera-Srivastava test of n-d normality is performed.
 *
 * The Robust PCA can be computed by using the median instead of the mean,
 * and the MAD matrix (Median Absolute Deviation) instead of the covariance matrix.
 * This can be done by activating the MedianAbsoluteDeviation boolean (declared in
 * the superclass).
 *
 * @par Thanks:
 * Thanks to David Thompson, Philippe Pebay and Jackson Mayo from
 * Sandia National Laboratories for implementing this class.
 * Updated by Philippe Pebay, Kitware SAS 2012
 * Updated by Tristan Coulange and Joachim Pouderoux, Kitware SAS 2013
*/

#ifndef vtkPCAStatistics_h
#define vtkPCAStatistics_h

#include "vtkFiltersStatisticsModule.h" // For export macro
#include "vtkMultiCorrelativeStatistics.h"

class vtkDoubleArray;
class vtkIdTypeArray;

class VTKFILTERSSTATISTICS_EXPORT vtkPCAStatistics : public vtkMultiCorrelativeStatistics
{
public:
  vtkTypeMacro(vtkPCAStatistics,vtkMultiCorrelativeStatistics);
  void PrintSelf( ostream& os, vtkIndent indent ) override;
  static vtkPCAStatistics* New();

  /**
   * Methods by which the covariance matrix may be normalized.
   */
  enum NormalizationType
  {
    NONE,               //!< The covariance matrix should be used as computed.
    TRIANGLE_SPECIFIED, //!< Normalize cov(i,j) by V(i,j) where V is supplied by the user.
    DIAGONAL_SPECIFIED, //!< Normalize cov(i,j) by sqrt(V(i)*V(j)) where V is supplied by the user.
    DIAGONAL_VARIANCE,  //!< Normalize cov(i,j) by sqrt(cov(i,i)*cov(j,j)).
    NUM_NORMALIZATION_SCHEMES //!< The number of normalization schemes.
  };

  /**
   * These are the enumeration values that SetBasisScheme() accepts and GetBasisScheme returns.
   */
  enum ProjectionType
  {
    FULL_BASIS,         //!< Use all entries in the basis matrix
    FIXED_BASIS_SIZE,   //!< Use the first N entries in the basis matrix
    FIXED_BASIS_ENERGY, //!< Use consecutive basis matrix entries whose energies sum to at least T
    NUM_BASIS_SCHEMES   //!< The number of schemes (not a valid scheme).
  };

  //@{
  /**
   * This determines how (or if) the covariance matrix \a cov is normalized before PCA.

   * When set to NONE, no normalization is performed. This is the default.

   * When set to TRIANGLE_SPECIFIED, each entry cov(i,j) is divided by V(i,j).
   * The list V of normalization factors must be set using the SetNormalization method
   * before the filter is executed.

   * When set to DIAGONAL_SPECIFIED, each entry cov(i,j) is divided by sqrt(V(i)*V(j)).
   * The list V of normalization factors must be set using the SetNormalization method
   * before the filter is executed.

   * When set to DIAGONAL_VARIANCE, each entry cov(i,j) is divided by sqrt(cov(i,i)*cov(j,j)).
   * <b>Warning</b>: Although this is accepted practice in some fields,
   * some people think you should not turn this option on unless there
   * is a good physically-based reason for doing so. Much better instead
   * to determine how component magnitudes should be compared using
   * physical reasoning and use DIAGONAL_SPECIFIED, TRIANGLE_SPECIFIED, or
   * perform some pre-processing to shift and scale input data columns
   * appropriately than to expect magical results from a shady normalization hack.
   */
  vtkSetMacro(NormalizationScheme,int);
  vtkGetMacro(NormalizationScheme,int);
  virtual void SetNormalizationSchemeByName( const char* sname );
  virtual const char* GetNormalizationSchemeName( int scheme );
  //@}

  //@{
  /**
   * These methods allow you to set/get values used to normalize the covariance matrix before PCA.
   * The normalization values apply to all requests, so you do not specify a single
   * vector but a 3-column table.

   * The first two columns contain the names of columns from input 0 and the third column contains
   * the value to normalize the corresponding entry in the covariance matrix.
   * The table must always have 3 columns even when the NormalizationScheme is DIAGONAL_SPECIFIED.
   * When only diagonal entries are to be used, only table rows where the first two columns are
   * identical to one another will be employed.
   * If there are multiple rows specifying different values for the same pair of columns,
   * the entry nearest the bottom of the table takes precedence.

   * These functions are actually convenience methods that set/get the third input of the filter.
   * Because the table is the third input, you may use other filters to produce a table of
   * normalizations and have the pipeline take care of updates.

   * Any missing entries will be set to 1.0 and a warning issued.
   * An error will occur if the third input to the filter is not set and the
   * NormalizationScheme is DIAGONAL_SPECIFIED or TRIANGLE_SPECIFIED.

   * NOTE: SetSpecifiedNormalization( table ) is equivalent to SetInputData(3, table)
   * and therefore does not make a pipeline connection.
   */
  virtual vtkTable* GetSpecifiedNormalization();
  virtual void SetSpecifiedNormalization( vtkTable* );
  //@}

  //@{
  /**
   * Get the eigenvalues. The eigenvalues are ordered according from largest to smallest.
   * This function:
   * void GetEigenvalues(int request, int i, vtkDoubleArray*);
   * does all of the work. The other functions simply call this function with the appropriate
   * parameters. These functions are not valid unless Update() has been called and the Derive
   * option is turned on.
   */
  void GetEigenvalues(int request, vtkDoubleArray*);
  void GetEigenvalues(vtkDoubleArray*);
  double GetEigenvalue(int request, int i);
  double GetEigenvalue(int i);
  //@}

  //@{
  /**
   * Get the eigenvectors. The eigenvectors are ordered according to the magnitude of their
   * associated eigenvalues, sorted from largest to smallest. That is, eigenvector 0 corresponds
   * to the largest eigenvalue.
   * This function:
   * void GetEigenvectors(int request, vtkDoubleArray* eigenvectors)
   * does all of the work. The other functions are convenience functions that call this function
   * with default arguments. These functions are not valid unless Update() has been called and the Derive
   * option is turned on.
   */
  void GetEigenvectors(int request, vtkDoubleArray* eigenvectors);
  void GetEigenvectors(vtkDoubleArray* eigenvectors);
  void GetEigenvector(int i, vtkDoubleArray* eigenvector);
  void GetEigenvector(int request, int i, vtkDoubleArray* eigenvector);
  //@}

  //@{
  /**
   * This variable controls the dimensionality of output tuples in Assess operation.
   * Consider the case where you have requested a PCA on D columns.

   * When set to vtkPCAStatistics::FULL_BASIS, the entire set of basis vectors
   * is used to derive new coordinates for each tuple being assessed.
   * In this mode, you are guaranteed to have output tuples of the same dimension
   * as the input tuples. (That dimension is D, so there will be D additional
   * columns added to the table for the request.)

   * When set to vtkPCAStatistics::FIXED_BASIS_SIZE, only the first N basis vectors
   * are used to derive new coordinates for each tuple being assessed.
   * In this mode, you are guaranteed to have output tuples of dimension min(N,D).
   * You must set N prior to assessing data using the SetFixedBasisSize() method.
   * When N < D, this turns the PCA into a projection (instead of change of basis).

   * When set to vtkPCAStatistics::FIXED_BASIS_ENERGY, the number of basis vectors
   * used to derive new coordinates for each tuple will be the minimum number
   * of columns N that satisfy
   * \f[
   * \frac{\sum_{i=1}^{N} \lambda_i}{\sum_{i=1}^{D} \lambda_i} < T
   * \f]
   * You must set T prior to assessing data using the SetFixedBasisEnergy() method.
   * When T < 1, this turns the PCA into a projection (instead of change of basis).

   * By default BasisScheme is set to vtkPCAStatistics::FULL_BASIS.
   */
  vtkSetMacro(BasisScheme,int);
  vtkGetMacro(BasisScheme,int);
  virtual const char* GetBasisSchemeName( int schemeIndex );
  virtual void SetBasisSchemeByName( const char* schemeName );
  //@}

  //@{
  /**
   * The number of basis vectors to use. See SetBasisScheme() for more information.
   * When FixedBasisSize <= 0 (the default), the fixed basis size scheme is equivalent to the full basis scheme.
   */
  vtkSetMacro(FixedBasisSize,int);
  vtkGetMacro(FixedBasisSize,int);
  //@}

  //@{
  /**
   * The minimum energy the new basis should use, as a fraction. See SetBasisScheme() for more information.
   * When FixedBasisEnergy >= 1 (the default), the fixed basis energy scheme is equivalent to the full basis scheme.
   */
  vtkSetClampMacro(FixedBasisEnergy,double,0.,1.);
  vtkGetMacro(FixedBasisEnergy,double);
  //@}

  /**
   * A convenience method (in particular for access from other applications) to
   * set parameter values.
   * Return true if setting of requested parameter name was executed, false otherwise.
   */
  bool SetParameter( const char* parameter,
                     int index,
                     vtkVariant value ) override;

protected:
  vtkPCAStatistics();
  ~vtkPCAStatistics() override;

  /**
   * This algorithm accepts a vtkTable containing normalization values for
   * its fourth input (port 3).
   * We override FillInputPortInformation to indicate this.
   */
  int FillInputPortInformation( int port, vtkInformation* info ) override;

  /**
   * Execute the calculations required by the Derive option.
   */
  void Derive( vtkMultiBlockDataSet* ) override;

  /**
   * Execute the calculations required by the Test option.
   */
  void Test( vtkTable*,
             vtkMultiBlockDataSet*,
             vtkTable* ) override;

  /**
   * Execute the calculations required by the Assess option.
   */
  void Assess( vtkTable*,
               vtkMultiBlockDataSet*,
               vtkTable* ) override;

  /**
   * Calculate p-value. This will be overridden using the object factory with an
   * R implementation if R is present.
   */
  virtual vtkDoubleArray* CalculatePValues(vtkIdTypeArray*, vtkDoubleArray*);

  /**
   * Provide the appropriate assessment functor.
   */
  void SelectAssessFunctor( vtkTable* inData,
                            vtkDataObject* inMeta,
                            vtkStringArray* rowNames,
                            AssessFunctor*& dfunc ) override;

  int NormalizationScheme;
  int BasisScheme;
  int FixedBasisSize;
  double FixedBasisEnergy;

  static const char* BasisSchemeEnumNames[NUM_BASIS_SCHEMES + 1];
  static const char* NormalizationSchemeEnumNames[NUM_NORMALIZATION_SCHEMES + 1];

private:
  vtkPCAStatistics( const vtkPCAStatistics& ) = delete;
  void operator = ( const vtkPCAStatistics& ) = delete;
};

#endif // vtkPCAStatistics_h

