DualityDiagram.cpp

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//
// File: DualityDiagram.cpp
// Created by: Mathieu Groussin
//

/*
   Copyright or © or Copr. Bio++ Development Tools, (November 16, 2004)

   This software is a computer program whose purpose is to provide classes
   for phylogenetic data analysis.

   This software is governed by the CeCILL  license under French law and
   abiding by the rules of distribution of free software.  You can  use,
   modify and/ or redistribute the software under the terms of the CeCILL
   license as circulated by CEA, CNRS and INRIA at the following URL
   "http://www.cecill.info".

   As a counterpart to the access to the source code and  rights to copy,
   modify and redistribute granted by the license, users are provided only
   with a limited warranty  and the software's author,  the holder of the
   economic rights,  and the successive licensors  have only  limited
   liability.

   In this respect, the user's attention is drawn to the risks associated
   with loading,  using,  modifying and/or developing or reproducing the
   software by the user in light of its specific status of free software,
   that may mean  that it is complicated to manipulate,  and  that  also
   therefore means  that it is reserved for developers  and  experienced
   professionals having in-depth computer knowledge. Users are therefore
   encouraged to load and test the software's suitability as regards their
   requirements in conditions enabling the security of their systems and/or
   data to be ensured and,  more generally, to use and operate it in the
   same conditions as regards security.

   The fact that you are presently reading this means that you have had
   knowledge of the CeCILL license and that you accept its terms.
 */

#include "DualityDiagram.h"
#include "../../Matrix/Matrix.h"
#include "../../Matrix/MatrixTools.h"
#include "../../Matrix/EigenValue.h"
#include "../../../App/ApplicationTools.h"

#include <cmath>

using namespace bpp;
using namespace std;

DualityDiagram::DualityDiagram(
  const Matrix<double>& matrix,
  const vector<double>& rowWeights,
  const vector<double>& colWeights,
  unsigned int nbAxes,
  double tol, bool verbose) throw (Exception) :
  rowWeights_(rowWeights),
  colWeights_(colWeights),
  nbAxes_(nbAxes),
  eigenValues_(),
  eigenVectors_(),
  rowCoord_(),
  colCoord_(),
  ppalAxes_(),
  ppalComponents_()
{
  check_(matrix, rowWeights, colWeights, verbose);
  compute_(matrix, tol, verbose);
}

void DualityDiagram::check_(
  const Matrix<double>& matrix,
  const vector<double>& rowWeights,
  const vector<double>& colWeights,
  unsigned int nbAxes) throw (Exception)
{
  size_t rowNb = matrix.getNumberOfRows();
  size_t colNb = matrix.getNumberOfColumns();

  if (rowWeights.size() != rowNb)
    throw Exception("DualityDiagram::check_. The number of row weigths has to be equal to the number of rows!");
  if (colWeights.size() != colNb)
    throw Exception("DualityDiagram::check_. The number of column weigths has to be equal to the number of columns!");

  // All row weigths have to be positive
  for (vector<double>::const_iterator it = rowWeights.begin(); it != rowWeights.end(); it++)
  {
    if (*it < 0.)
      throw Exception("DualityDiagram::check_. All row weights have to be positive");
  }

  // All column weigths have to be positive
  for (vector<double>::const_iterator it = colWeights.begin(); it != colWeights.end(); it++)
  {
    if (*it < 0.)
      throw Exception("DualityDiagram::check_. All column weights have to be positive");
  }
}


void DualityDiagram::setData(
  const Matrix<double>& matrix,
  const vector<double>& rowWeights,
  const vector<double>& colWeights,
  unsigned int nbAxes,
  double tol, bool verbose) throw (Exception)
{
  check_(matrix, rowWeights, colWeights, verbose);
  rowWeights_ = rowWeights;
  colWeights_ = colWeights;
  nbAxes_     = nbAxes;
  compute_(matrix, tol, verbose);
}

void DualityDiagram::compute_(const Matrix<double>& matrix,
    double tol, bool verbose)
{
  size_t rowNb = matrix.getNumberOfRows();
  size_t colNb = matrix.getNumberOfColumns();
  
  // If there are less rows than columns, the variance-covariance or correlation matrix is obtain differently (see below)
  bool transpose = (rowNb < colNb);

  // The initial matrix is multiplied by the square root of the row weigths.
  vector<double> rW(rowWeights_);
  for (unsigned int i = 0; i < rowWeights_.size(); i++)
  {
    rW[i] = sqrt(rowWeights_[i]);
  }

  RowMatrix<double> M1(rowNb, colNb);
  MatrixTools::hadamardMult(matrix, rW, M1, true);

  // The resulting matrix is then multiplied by the square root of the column weigths.
  vector<double> cW(colWeights_);
  for (unsigned int i = 0; i < colWeights_.size(); i++)
  {
    cW[i] = sqrt(colWeights_[i]);
  }

  RowMatrix<double> M2;
  MatrixTools::hadamardMult(M1, cW, M2, false);

  // The variance-covariance (if the data is centered) or the correlation (if the data is centered and normalized) matrix is calculated
  RowMatrix<double> tM2;
  MatrixTools::transpose(M2, tM2);
  RowMatrix<double> M3;
  if (!transpose)
    MatrixTools::mult(tM2, M2, M3);
  else
    MatrixTools::mult(M2, tM2, M3);
  
  EigenValue<double> eigen(M3);
  if (!eigen.isSymmetric())
    throw Exception("DualityDiagram (constructor). The variance-covariance or correlation matrix should be symmetric...");

  eigenValues_ = eigen.getRealEigenValues();
  eigenVectors_ = eigen.getV();

  // How many significant axes have to be conserved?
  size_t rank = 0;
  for (size_t i = eigenValues_.size(); i > 0; i--)
  {
    if ((eigenValues_[i - 1] / eigenValues_[eigenValues_.size() - 1]) > tol)
      rank++;
  }

  if (nbAxes_ <=0)
  {
    throw Exception("DualityDiagram (constructor). The number of axes to keep must be positive.");
  }
  if (nbAxes_ > rank)
  {
    if (verbose)
      ApplicationTools::displayWarning("The number of axes to kept has been reduced to conserve only significant axes");
    nbAxes_ = rank;
  }

  /*The eigen values are initially sorted into ascending order by the 'eigen' function. Here the significant values are sorted
     in the other way around.*/
  vector<double> tmpEigenValues(nbAxes_);
  size_t cpt = 0;
  for (size_t i = eigenValues_.size(); i > (eigenValues_.size() - nbAxes_); i--)
  {
    tmpEigenValues[cpt] = eigenValues_[i-1];
    cpt++;
  }
  eigenValues_ = tmpEigenValues;

  for (vector<double>::iterator it = rowWeights_.begin(); it != rowWeights_.end(); it++)
  {
    if (*it == 0.)
      *it = 1.;
  }

  for (vector<double>::iterator it = colWeights_.begin(); it != colWeights_.end(); it++)
  {
    if (*it == 0.)
      *it = 1.;
  }

  vector<double> dval(nbAxes_);
  for (size_t i = 0; i < dval.size(); i++)
  {
    dval[i] = sqrt(eigenValues_[i]);
  }

  vector<double> invDval(nbAxes_);
  for (size_t i = 0; i < invDval.size(); i++)
  {
    invDval[i] = 1. / sqrt(eigenValues_[i]);
  }

  // Calculation of the row and column coordinates as well as the principal axes and components:
  if (!transpose)
  {
    vector<double> tmpColWeights(colNb);
    for (unsigned int i = 0; i < colWeights_.size(); i++)
    {
      tmpColWeights[i] = 1. / sqrt(colWeights_[i]);
    }

    // The eigen vectors are placed in the same order as their corresponding eigen value in eigenValues_.
    RowMatrix<double> tmpEigenVectors;
    tmpEigenVectors.resize(eigenVectors_.getNumberOfRows(), nbAxes_);
    size_t cpt2 = 0;
    for (size_t i = eigenVectors_.getNumberOfColumns(); i > (eigenVectors_.getNumberOfColumns() - nbAxes_); i--)
    {
      for (unsigned int j = 0; j < eigenVectors_.getNumberOfRows(); j++)
      {
        tmpEigenVectors(j, cpt2) = eigenVectors_(j, i-1);
      }
      cpt2++;
    }
    
    // matrix of principal axes
    MatrixTools::hadamardMult(tmpEigenVectors, tmpColWeights, ppalAxes_, true);
    // matrix of row coordinates
    RowMatrix<double> tmpRowCoord_;
    tmpRowCoord_.resize(rowNb, nbAxes_);
    MatrixTools::hadamardMult(matrix, colWeights_, tmpRowCoord_, false);
    MatrixTools::mult(tmpRowCoord_, ppalAxes_, rowCoord_);

    // matrix of column coordinates
    MatrixTools::hadamardMult(ppalAxes_, dval, colCoord_, false);
    // matrix of principal components
    MatrixTools::hadamardMult(rowCoord_, invDval, ppalComponents_, false);
  }
  else
  {
    vector<double> tmpRowWeights(rowNb);
    for (unsigned int i = 0; i < rowWeights_.size(); i++)
    {
      tmpRowWeights[i] = 1. / sqrt(rowWeights_[i]);
    }

    // The eigen vectors are placed in the same order as their corresponding eigen value in eigenValues_.
    RowMatrix<double> tmpEigenVectors;
    tmpEigenVectors.resize(eigenVectors_.getNumberOfRows(), nbAxes_);
    size_t cpt2 = 0;
    for (size_t i = eigenVectors_.getNumberOfColumns(); i > (eigenVectors_.getNumberOfColumns() - nbAxes_); i--)
    {
      for (size_t j = 0; j < eigenVectors_.getNumberOfRows(); j++)
      {
        tmpEigenVectors(j, cpt2) = eigenVectors_(j, i-1);
      }
      cpt2++;
    }

    // matrix of principal components
    MatrixTools::hadamardMult(tmpEigenVectors, tmpRowWeights, ppalComponents_, true);
    // matrix of column coordinates
    RowMatrix<double> tmpColCoord_;
    tmpColCoord_.resize(colNb, nbAxes_);
    MatrixTools::hadamardMult(matrix, rowWeights_, tmpColCoord_, true);
    RowMatrix<double> tTmpColCoord_;
    MatrixTools::transpose(tmpColCoord_, tTmpColCoord_);
    MatrixTools::mult(tTmpColCoord_, ppalComponents_, colCoord_);

    // matrix of row coordinates
    MatrixTools::hadamardMult(ppalComponents_, dval, rowCoord_, false);
    // matrix of principal axes
    MatrixTools::hadamardMult(colCoord_, invDval, ppalAxes_, false);
  }
}

/******************************************************************************/

DualityDiagram::~DualityDiagram() {}

/******************************************************************************/