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// Copyright (c) 2005 INRIA Sophia-Antipolis (France).
// All rights reserved.
//
// This file is part of CGAL (www.cgal.org); you may redistribute it under
// the terms of the Q Public License version 1.0.
// See the file LICENSE.QPL distributed with CGAL.
//
// Licensees holding a valid commercial license may use this file in
// accordance with the commercial license agreement provided with the software.
//
// This file is provided AS IS with NO WARRANTY OF ANY KIND, INCLUDING THE
// WARRANTY OF DESIGN, MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE.
//
// $URL: svn+ssh://scm.gforge.inria.fr/svn/cgal/branches/CGAL-3.6-branch/Principal_component_analysis/include/CGAL/linear_least_squares_fitting_points_2.h $
// $Id: linear_least_squares_fitting_points_2.h 52628 2009-10-20 08:59:26Z lrineau $
//
// Author(s) : Pierre Alliez and Sylvain Pion and Ankit Gupta
#ifndef CGAL_LINEAR_LEAST_SQUARES_FITTING_POINTS_2_H
#define CGAL_LINEAR_LEAST_SQUARES_FITTING_POINTS_2_H
#include <CGAL/basic.h>
#include <CGAL/Object.h>
#include <CGAL/centroid.h>
#include <CGAL/eigen_2.h>
#include <iterator>
#include <cmath>
CGAL_BEGIN_NAMESPACE
namespace internal {
// Fits a line to a 2D point set.
// Returns a fitting quality (1 - lambda_min/lambda_max):
// 1 is best (zero variance orthogonally to the fitting line);
// 0 is worst (isotropic case, returns a line with horizontal
// direction by default).
template < typename InputIterator,
typename K >
typename K::FT
linear_least_squares_fitting_2(InputIterator first,
InputIterator beyond,
typename K::Line_2& line, // best fit line
typename K::Point_2& c, // centroid
const typename K::Point_2*,// used for indirection
const K&, // kernel
const CGAL::Dimension_tag<0>& tag)
{
// types
typedef typename K::FT FT;
typedef typename K::Line_2 Line;
typedef typename K::Point_2 Point;
typedef typename K::Vector_2 Vector;
// if internally double, declare a kernel
// precondition: at least one element in the container.
CGAL_precondition(first != beyond);
// compute centroid
c = centroid(first,beyond,K(),tag);
// assemble covariance matrix as a semi-definite matrix.
// Matrix numbering:
// 0
// 1 2
FT covariance[3] = {0,0,0};
for(InputIterator it = first;
it != beyond;
it++)
{
const Point& p = *it;
Vector d = p - c; // centered data point
covariance[0] += d.x() * d.x();
covariance[1] += d.x() * d.y();
covariance[2] += d.y() * d.y();
}
// solve for eigenvalues and eigenvectors.
// eigen values are sorted in descending order,
// eigen vectors are sorted in accordance.
std::pair<FT,FT> eigen_values;
std::pair<Vector,Vector> eigen_vectors;
internal::eigen_symmetric_2<K>(covariance, eigen_vectors, eigen_values);
// check unicity and build fitting line accordingly
if(eigen_values.first != eigen_values.second)
{
// regular case
line = Line(c, eigen_vectors.first);
return (FT)1.0 - eigen_values.second / eigen_values.first;
}
else
{
// isotropic case (infinite number of directions)
// by default: assemble a line that goes through
// the centroid and with a default horizontal vector.
line = Line(c, Vector(1.0, 0.0));
return (FT)0.0;
}
} // end linear_least_squares_fitting_2 for point set
} // end namespace internal
CGAL_END_NAMESPACE
#endif // CGAL_LINEAR_LEAST_SQUARES_FITTING_POINTS_2_H
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