source: code/branches/physics/src/ogreode/OgreOdeEigenSolver.h @ 1983

#ifndef _OGREODEEIGENSOLVER_H_
#define _OGREODEEIGENSOLVER_H_

#include "OgreOdePreReqs.h"

#include <OgreMatrix3.h>

namespace OgreOde 
{
        class _OgreOdeExport EigenSolver
        {
        public:
                EigenSolver(int iSize);
                ~EigenSolver();

                // set the matrix for eigensolving
                Ogre::Real& operator() (int iRow, int iCol);

                // Get the eigenresults (eigenvectors are columns of eigenmatrix).  The
                // GetEigenvector calls involving Vector2, Ogre::Vector3, and Vector4 should
                // only be called if you know that the eigenmatrix is of the appropriate
                // size.
            void GetEigenvector (int i, Ogre::Vector3& rkV) const;
                Ogre::Real GetEigenvalue (int i) const;

                // solve eigensystem, use decreasing sort on eigenvalues
            void DecrSortEigenStuff3 ();
                void IncrSortEigenStuff3 ();

                static void GenerateOrthonormalBasis (Ogre::Vector3& rkU, Ogre::Vector3& rkV, Ogre::Vector3& rkW, bool bUnitLengthW);
                static void orthogonalLineFit(unsigned int vertex_count, const Ogre::Vector3* vertices, Ogre::Vector3& origin, Ogre::Vector3& direction);
                static Ogre::Real SqrDistance(const Ogre::Vector3& rkPoint,const Ogre::Vector3& origin,const Ogre::Vector3& direction);
                static void GaussPointsFit(unsigned int iQuantity,const Ogre::Vector3* akPoint, Ogre::Vector3 &rkCenter, Ogre::Vector3 akAxis[3], Ogre::Real afExtent[3]);

        protected:
                int m_iSize;
                Ogre::Matrix3 m_kMat;
                Ogre::Real* m_afDiag;
                Ogre::Real* m_afSubd;

                // For odd size matrices, the Householder reduction involves an odd
                // number of reflections.  The product of these is a reflection.  The
                // QL algorithm uses rotations for further reductions.  The final
                // orthogonal matrix whose columns are the eigenvectors is a reflection,
                // so its determinant is -1.  For even size matrices, the Householder
                // reduction involves an even number of reflections whose product is a
                // rotation.  The final orthogonal matrix has determinant +1.  Many
                // algorithms that need an eigendecomposition want a rotation matrix.
                // We want to guarantee this is the case, so m_bRotation keeps track of
                // this.  The DecrSort and IncrSort further complicate the issue since
                // they swap columns of the orthogonal matrix, causing the matrix to
                // toggle between rotation and reflection.  The value m_bRotation must
                // be toggled accordingly.
                bool m_bIsRotation;
                void GuaranteeRotation ();

                // Householder reduction to tridiagonal form
            void Tridiagonal3 ();
  
                // QL algorithm with implicit shifting, applies to tridiagonal matrices
                bool QLAlgorithm ();

                // sort eigenvalues from largest to smallest
                void DecreasingSort ();

                void IncreasingSort ();
        };
}

#endif