pointset_eigen.h

// Description: Eigenvectors and eigenvalues of point-sets
// Detail: Eigenstructure of the covariance matrix of a point-set

#ifndef PASTELGEOMETRY_POINTSET_EIGEN_H
#define PASTELGEOMETRY_POINTSET_EIGEN_H

#include "pastel/sys/locator/locator_concept.h"

#include "pastel/sys/vector.h"
#include "pastel/sys/range.h"

#include "pastel/math/matrix/matrix.h"

namespace Pastel
{

    //! Computes an approximation of the largest eigenvector of a point-set.
    /*!
   Time complexity:
   O(pointSet.size() * dimension)
   */
    template <
        typename Point_ConstRange, 
        typename Locator>
    Vector<typename Locator::Real, Locator::N> 
    largestEigenVector(
        const Point_ConstRange& pointSet,
        const Locator& locator);

    //! Computes an approximation of the eigenstructure of a point-set.
    /*!
   Preconditions:
   eigenvectors > 0

   Time complexity:
   O(pointSet.size() * dimension * eigenvectors)
   
   pointSet:
   A set of vectors.

   eigenvectors:
   The number of dominant eigenvectors that is
   to be approximated.
   
   qOut:
   A matrix containing the approximated eigenvectors 
   as row vectors.

   dOut:
   A vector containing the approximated eigenvalues
   corresponding to the approximated eigenvectors
   in qOut.
   */
    template <typename Point_ConstRange, typename Locator>
    void approximateEigenstructure(
        const Point_ConstRange& pointSet,
        const Locator& locator,
        integer eigenvectors,
        Matrix<typename Locator::Real>& qOut,
        Vector<typename Locator::Real>& dOut);

}

#include "pastel/geometry/pointset_eigen.hpp"

#endif