Sturm.hpp

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/******************************************************************************
 * Author:   Laurent Kneip                                                    *
 * Contact:  kneip.laurent@gmail.com                                          *
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#ifndef OPENGV_STURM_HPP_
#define OPENGV_STURM_HPP_

#include <memory>
#include <stdlib.h>
#include <vector>
#include <list>
#include <Eigen/Eigen>
#include <Eigen/src/Core/util/DisableStupidWarnings.h>

namespace opengv
{
namespace math
{

class Bracket
{
public:
  typedef std::shared_ptr<Bracket> Ptr;
  typedef std::shared_ptr<const Bracket> ConstPtr;

  Bracket( double lowerBound, double upperBound );
  Bracket( double lowerBound, double upperBound, size_t changes, bool setUpperBoundChanges );
  virtual ~Bracket();

  bool dividable( double eps ) const;
  void divide( std::list<Ptr> & brackets ) const;
  double lowerBound() const;
  double upperBound() const;
  bool lowerBoundChangesComputed() const;
  bool upperBoundChangesComputed() const;
  void setLowerBoundChanges( size_t changes );
  void setUpperBoundChanges( size_t changes );
  size_t numberRoots() const;

private:
  double _lowerBound;
  double _upperBound;
  bool _lowerBoundChangesComputed;
  bool _upperBoundChangesComputed;
  size_t _lowerBoundChanges;
  size_t _upperBoundChanges;
};

class Sturm
{

public:
  EIGEN_MAKE_ALIGNED_OPERATOR_NEW
  typedef std::pair<double,double> bracket_t;

  Sturm( const Eigen::MatrixXd & p );
  Sturm( const std::vector<double> & p );
  virtual ~Sturm();

  void findRoots2( std::vector<double> & roots, double eps_x = 0.001, double eps_val = 0.001 );
  std::vector<double> findRoots();
  void bracketRoots( std::vector<double> & roots, double eps = -1.0 );
  size_t evaluateChain( double bound );
  size_t evaluateChain2( double bound );
  double computeLagrangianBound();

private:
  void computeNegatedRemainder(
      const Eigen::MatrixXd & p1,
      const Eigen::MatrixXd & p2,
      Eigen::MatrixXd & r );

  Eigen::MatrixXd _C;
  size_t _dimension;
};

}
}

#endif /* OPENGV_STURM_HPP_ */