src/math/SquareMatrix3.hpp

/*
 * Copyright (c) 2005 The University of Notre Dame. All Rights Reserved.
 *
 * The University of Notre Dame grants you ("Licensee") a
 * non-exclusive, royalty free, license to use, modify and
 * redistribute this software in source and binary code form, provided
 * that the following conditions are met:
 *
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 *
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the
 *    distribution.
 *
 * This software is provided "AS IS," without a warranty of any
 * kind. All express or implied conditions, representations and
 * warranties, including any implied warranty of merchantability,
 * fitness for a particular purpose or non-infringement, are hereby
 * excluded.  The University of Notre Dame and its licensors shall not
 * be liable for any damages suffered by licensee as a result of
 * using, modifying or distributing the software or its
 * derivatives. In no event will the University of Notre Dame or its
 * licensors be liable for any lost revenue, profit or data, or for
 * direct, indirect, special, consequential, incidental or punitive
 * damages, however caused and regardless of the theory of liability,
 * arising out of the use of or inability to use software, even if the
 * University of Notre Dame has been advised of the possibility of
 * such damages.
 *
 * SUPPORT OPEN SCIENCE!  If you use OpenMD or its source code in your
 * research, please cite the appropriate papers when you publish your
 * work.  Good starting points are:
 *                                                                      
 * [1]  Meineke, et al., J. Comp. Chem. 26, 252-271 (2005).             
 * [2]  Fennell & Gezelter, J. Chem. Phys. 124, 234104 (2006).          
 * [3]  Sun, Lin & Gezelter, J. Chem. Phys. 128, 24107 (2008).          
 * [4]  Vardeman & Gezelter, in progress (2009).                        
 */
 
/**
 * @file SquareMatrix3.hpp
 * @author Teng Lin
 * @date 10/11/2004
 * @version 1.0
 */
#ifndef MATH_SQUAREMATRIX3_HPP
#define  MATH_SQUAREMATRIX3_HPP
#include <vector>
#include "Quaternion.hpp"
#include "SquareMatrix.hpp"
#include "Vector3.hpp"
#include "utils/NumericConstant.hpp"
namespace OpenMD {

  template<typename Real>
  class SquareMatrix3 : public SquareMatrix<Real, 3> {
  public:

    typedef Real ElemType;
    typedef Real* ElemPoinerType;
            
    /** default constructor */
    SquareMatrix3() : SquareMatrix<Real, 3>() {
    }

    /** Constructs and initializes every element of this matrix to a scalar */ 
    SquareMatrix3(Real s) : SquareMatrix<Real,3>(s){
    }

    /** Constructs and initializes from an array */ 
    SquareMatrix3(Real* array) : SquareMatrix<Real,3>(array){
    }


    /** copy  constructor */
    SquareMatrix3(const SquareMatrix<Real, 3>& m)  : SquareMatrix<Real, 3>(m) {
    }
            
    SquareMatrix3( const Vector3<Real>& eulerAngles) {
      setupRotMat(eulerAngles);
    }
            
    SquareMatrix3(Real phi, Real theta, Real psi) {
      setupRotMat(phi, theta, psi);
    }

    SquareMatrix3(const Quaternion<Real>& q) {
      setupRotMat(q);

    }

    SquareMatrix3(Real w, Real x, Real y, Real z) {
      setupRotMat(w, x, y, z);
    }
            
    /** copy assignment operator */
    SquareMatrix3<Real>& operator =(const SquareMatrix<Real, 3>& m) {
      if (this == &m)
        return *this;
      SquareMatrix<Real, 3>::operator=(m);
      return *this;
    }


    SquareMatrix3<Real>& operator =(const Quaternion<Real>& q) {
      this->setupRotMat(q);
      return *this;
    }

    /**
     * Sets this matrix to a rotation matrix by three euler angles
     * @ param euler
     */
    void setupRotMat(const Vector3<Real>& eulerAngles) {
      setupRotMat(eulerAngles[0], eulerAngles[1], eulerAngles[2]);
    }

    /**
     * Sets this matrix to a rotation matrix by three euler angles
     * @param phi
     * @param theta
     * @psi theta
     */
    void setupRotMat(Real phi, Real theta, Real psi) {
      Real sphi, stheta, spsi;
      Real cphi, ctheta, cpsi;

      sphi = sin(phi);
      stheta = sin(theta);
      spsi = sin(psi);
      cphi = cos(phi);
      ctheta = cos(theta);
      cpsi = cos(psi);

      this->data_[0][0] = cpsi * cphi - ctheta * sphi * spsi;
      this->data_[0][1] = cpsi * sphi + ctheta * cphi * spsi;
      this->data_[0][2] = spsi * stheta;
                
      this->data_[1][0] = -spsi * ctheta - ctheta * sphi * cpsi;
      this->data_[1][1] = -spsi * stheta + ctheta * cphi * cpsi;
      this->data_[1][2] = cpsi * stheta;

      this->data_[2][0] = stheta * sphi;
      this->data_[2][1] = -stheta * cphi;
      this->data_[2][2] = ctheta;
    }


    /**
     * Sets this matrix to a rotation matrix by quaternion
     * @param quat
     */
    void setupRotMat(const Quaternion<Real>& quat) {
      setupRotMat(quat.w(), quat.x(), quat.y(), quat.z());
    }

    /**
     * Sets this matrix to a rotation matrix by quaternion
     * @param w the first element 
     * @param x the second element
     * @param y the third element
     * @param z the fourth element
     */
    void setupRotMat(Real w, Real x, Real y, Real z) {
      Quaternion<Real> q(w, x, y, z);
      *this = q.toRotationMatrix3();
    }

    void setupSkewMat(Vector3<Real> v) {
        setupSkewMat(v[0], v[1], v[2]);
    }

    void setupSkewMat(Real v1, Real v2, Real v3) {
        this->data_[0][0] = 0;
        this->data_[0][1] = -v3;
        this->data_[0][2] = v2;
        this->data_[1][0] = v3;
        this->data_[1][1] = 0;
        this->data_[1][2] = -v1;
        this->data_[2][0] = -v2;
        this->data_[2][1] = v1;
        this->data_[2][2] = 0;
        
        
    }


    /**
     * Returns the quaternion from this rotation matrix
     * @return the quaternion from this rotation matrix
     * @exception invalid rotation matrix
     */            
    Quaternion<Real> toQuaternion() {
      Quaternion<Real> q;
      Real t, s;
      Real ad1, ad2, ad3;    
      t = this->data_[0][0] + this->data_[1][1] + this->data_[2][2] + 1.0;

      if( t > NumericConstant::epsilon ){

        s = 0.5 / sqrt( t );
        q[0] = 0.25 / s;
        q[1] = (this->data_[1][2] - this->data_[2][1]) * s;
        q[2] = (this->data_[2][0] - this->data_[0][2]) * s;
        q[3] = (this->data_[0][1] - this->data_[1][0]) * s;
      } else {

        ad1 = this->data_[0][0];
        ad2 = this->data_[1][1];
        ad3 = this->data_[2][2];

        if( ad1 >= ad2 && ad1 >= ad3 ){

          s = 0.5 / sqrt( 1.0 + this->data_[0][0] - this->data_[1][1] - this->data_[2][2] );
          q[0] = (this->data_[1][2] - this->data_[2][1]) * s;
          q[1] = 0.25 / s;
          q[2] = (this->data_[0][1] + this->data_[1][0]) * s;
          q[3] = (this->data_[0][2] + this->data_[2][0]) * s;
        } else if ( ad2 >= ad1 && ad2 >= ad3 ) {
          s = 0.5 / sqrt( 1.0 + this->data_[1][1] - this->data_[0][0] - this->data_[2][2] );
          q[0] = (this->data_[2][0] - this->data_[0][2] ) * s;
          q[1] = (this->data_[0][1] + this->data_[1][0]) * s;
          q[2] = 0.25 / s;
          q[3] = (this->data_[1][2] + this->data_[2][1]) * s;
        } else {

          s = 0.5 / sqrt( 1.0 + this->data_[2][2] - this->data_[0][0] - this->data_[1][1] );
          q[0] = (this->data_[0][1] - this->data_[1][0]) * s;
          q[1] = (this->data_[0][2] + this->data_[2][0]) * s;
          q[2] = (this->data_[1][2] + this->data_[2][1]) * s;
          q[3] = 0.25 / s;
        }
      }             

      return q;
                
    }

    /**
     * Returns the euler angles from this rotation matrix
     * @return the euler angles in a vector 
     * @exception invalid rotation matrix
     * We use so-called "x-convention", which is the most common definition. 
     * In this convention, the rotation given by Euler angles (phi, theta, 
     * psi), where the first rotation is by an angle phi about the z-axis, 
     * the second is by an angle theta (0 <= theta <= 180) about the x-axis, 
     * and the third is by an angle psi about the z-axis (again). 
     */            
    Vector3<Real> toEulerAngles() {
      Vector3<Real> myEuler;
      Real phi;
      Real theta;
      Real psi;
      Real ctheta;
      Real stheta;
                
      // set the tolerance for Euler angles and rotation elements

      theta = acos(std::min((RealType)1.0, std::max((RealType)-1.0,this->data_[2][2])));
      ctheta = this->data_[2][2]; 
      stheta = sqrt(1.0 - ctheta * ctheta);

      // when sin(theta) is close to 0, we need to consider
      // singularity In this case, we can assign an arbitary value to
      // phi (or psi), and then determine the psi (or phi) or
      // vice-versa. We'll assume that phi always gets the rotation,
      // and psi is 0 in cases of singularity.
      // we use atan2 instead of atan, since atan2 will give us -Pi to Pi. 
      // Since 0 <= theta <= 180, sin(theta) will be always
      // non-negative. Therefore, it will never change the sign of both of
      // the parameters passed to atan2.

      if (fabs(stheta) < 1e-6){
        psi = 0.0;
        phi = atan2(-this->data_[1][0], this->data_[0][0]);  
      }
      // we only have one unique solution
      else{    
        phi = atan2(this->data_[2][0], -this->data_[2][1]);
        psi = atan2(this->data_[0][2], this->data_[1][2]);
      }

      //wrap phi and psi, make sure they are in the range from 0 to 2*Pi
      if (phi < 0)
        phi += 2.0 * M_PI;

      if (psi < 0)
        psi += 2.0 * M_PI;

      myEuler[0] = phi;
      myEuler[1] = theta;
      myEuler[2] = psi;

      return myEuler;
    }
            
    /** Returns the determinant of this matrix. */
    Real determinant() const {
      Real x,y,z;

      x = this->data_[0][0] * (this->data_[1][1] * this->data_[2][2] - this->data_[1][2] * this->data_[2][1]);
      y = this->data_[0][1] * (this->data_[1][2] * this->data_[2][0] - this->data_[1][0] * this->data_[2][2]);
      z = this->data_[0][2] * (this->data_[1][0] * this->data_[2][1] - this->data_[1][1] * this->data_[2][0]);

      return(x + y + z);
    }            

    /** Returns the trace of this matrix. */
    Real trace() const {
      return this->data_[0][0] + this->data_[1][1] + this->data_[2][2];
    }
            
    /**
     * Sets the value of this matrix to  the inversion of itself. 
     * @note since simple algorithm can be applied to inverse the 3 by 3 matrix, we hide the 
     * implementation of inverse in SquareMatrix class
     */
    SquareMatrix3<Real>  inverse() const {
      SquareMatrix3<Real> m;
      RealType det = determinant();
      if (fabs(det) <= OpenMD::epsilon) {
        //"The method was called on a matrix with |determinant| <= 1e-6.",
        //"This is a runtime or a programming error in your application.");
        std::vector<int> zeroDiagElementIndex;
        for (int i =0; i < 3; ++i) {
            if (fabs(this->data_[i][i]) <= OpenMD::epsilon) {
                zeroDiagElementIndex.push_back(i);
            }
        }

        if (zeroDiagElementIndex.size() == 2) {
            int index = zeroDiagElementIndex[0];
            m(index, index) = 1.0 / this->data_[index][index];
        }else if (zeroDiagElementIndex.size() == 1) {

            int a = (zeroDiagElementIndex[0] + 1) % 3;
            int b = (zeroDiagElementIndex[0] + 2) %3;
            RealType denom = this->data_[a][a] * this->data_[b][b] - this->data_[b][a]*this->data_[a][b];
            m(a, a) = this->data_[b][b] /denom;
            m(b, a) = -this->data_[b][a]/denom;

            m(a,b) = -this->data_[a][b]/denom;
            m(b, b) = this->data_[a][a]/denom;
                
        }
      
/*
        for(std::vector<int>::iterator iter = zeroDiagElementIndex.begin(); iter != zeroDiagElementIndex.end() ++iter) {
            if (this->data_[*iter][0] > OpenMD::epsilon || this->data_[*iter][1] ||this->data_[*iter][2] ||
                this->data_[0][*iter] > OpenMD::epsilon || this->data_[1][*iter] ||this->data_[2][*iter] ) {
                std::cout << "can not inverse matrix" << std::endl;
            }
        }
*/
      } else {

          m(0, 0) = this->data_[1][1]*this->data_[2][2] - this->data_[1][2]*this->data_[2][1];
          m(1, 0) = this->data_[1][2]*this->data_[2][0] - this->data_[1][0]*this->data_[2][2];
          m(2, 0) = this->data_[1][0]*this->data_[2][1] - this->data_[1][1]*this->data_[2][0];
          m(0, 1) = this->data_[2][1]*this->data_[0][2] - this->data_[2][2]*this->data_[0][1];
          m(1, 1) = this->data_[2][2]*this->data_[0][0] - this->data_[2][0]*this->data_[0][2];
          m(2, 1) = this->data_[2][0]*this->data_[0][1] - this->data_[2][1]*this->data_[0][0];
          m(0, 2) = this->data_[0][1]*this->data_[1][2] - this->data_[0][2]*this->data_[1][1];
          m(1, 2) = this->data_[0][2]*this->data_[1][0] - this->data_[0][0]*this->data_[1][2];
          m(2, 2) = this->data_[0][0]*this->data_[1][1] - this->data_[0][1]*this->data_[1][0];

          m /= det;
        }
      return m;
    }

    SquareMatrix3<Real> transpose() const{
      SquareMatrix3<Real> result;
                
      for (unsigned int i = 0; i < 3; i++)
        for (unsigned int j = 0; j < 3; j++)              
          result(j, i) = this->data_[i][j];

      return result;
    }
    /**
     * Extract the eigenvalues and eigenvectors from a 3x3 matrix.
     * The eigenvectors (the columns of V) will be normalized. 
     * The eigenvectors are aligned optimally with the x, y, and z
     * axes respectively.
     * @param a symmetric matrix whose eigenvectors are to be computed. On return, the matrix is
     *     overwritten             
     * @param w will contain the eigenvalues of the matrix On return of this function
     * @param v the columns of this matrix will contain the eigenvectors. The eigenvectors are 
     *    normalized and mutually orthogonal.              
     * @warning a will be overwritten
     */
    static void diagonalize(SquareMatrix3<Real>& a, Vector3<Real>& w, SquareMatrix3<Real>& v); 
  };
  /*=========================================================================

  Program:   Visualization Toolkit
  Module:    $RCSfile: SquareMatrix3.hpp,v $

  Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen
  All rights reserved.
  See Copyright.txt or http://www.kitware.com/Copyright.htm for details.

  This software is distributed WITHOUT ANY WARRANTY; without even
  the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
  PURPOSE.  See the above copyright notice for more information.

  =========================================================================*/
  template<typename Real>
  void SquareMatrix3<Real>::diagonalize(SquareMatrix3<Real>& a, Vector3<Real>& w, 
                                        SquareMatrix3<Real>& v) {
    int i,j,k,maxI;
    Real tmp, maxVal;
    Vector3<Real> v_maxI, v_k, v_j;

    // diagonalize using Jacobi
    jacobi(a, w, v);
    // if all the eigenvalues are the same, return identity matrix
    if (w[0] == w[1] && w[0] == w[2] ) {
      v = SquareMatrix3<Real>::identity();
      return;
    }

    // transpose temporarily, it makes it easier to sort the eigenvectors
    v = v.transpose(); 
        
    // if two eigenvalues are the same, re-orthogonalize to optimally line
    // up the eigenvectors with the x, y, and z axes
    for (i = 0; i < 3; i++) {
      if (w((i+1)%3) == w((i+2)%3)) {// two eigenvalues are the same
        // find maximum element of the independant eigenvector
        maxVal = fabs(v(i, 0));
        maxI = 0;
        for (j = 1; j < 3; j++) {
          if (maxVal < (tmp = fabs(v(i, j)))){
            maxVal = tmp;
            maxI = j;
          }
        }
            
        // swap the eigenvector into its proper position
        if (maxI != i) {
          tmp = w(maxI);
          w(maxI) = w(i);
          w(i) = tmp;

          v.swapRow(i, maxI);
        }
        // maximum element of eigenvector should be positive
        if (v(maxI, maxI) < 0) {
          v(maxI, 0) = -v(maxI, 0);
          v(maxI, 1) = -v(maxI, 1);
          v(maxI, 2) = -v(maxI, 2);
        }

        // re-orthogonalize the other two eigenvectors
        j = (maxI+1)%3;
        k = (maxI+2)%3;

        v(j, 0) = 0.0; 
        v(j, 1) = 0.0; 
        v(j, 2) = 0.0;
        v(j, j) = 1.0;

        /** @todo */
        v_maxI = v.getRow(maxI);
        v_j = v.getRow(j);
        v_k = cross(v_maxI, v_j);
        v_k.normalize();
        v_j = cross(v_k, v_maxI);
        v.setRow(j, v_j);
        v.setRow(k, v_k);


        // transpose vectors back to columns
        v = v.transpose();
        return;
      }
    }

    // the three eigenvalues are different, just sort the eigenvectors
    // to align them with the x, y, and z axes

    // find the vector with the largest x element, make that vector
    // the first vector
    maxVal = fabs(v(0, 0));
    maxI = 0;
    for (i = 1; i < 3; i++) {
      if (maxVal < (tmp = fabs(v(i, 0)))) {
        maxVal = tmp;
        maxI = i;
      }
    }

    // swap eigenvalue and eigenvector
    if (maxI != 0) {
      tmp = w(maxI);
      w(maxI) = w(0);
      w(0) = tmp;
      v.swapRow(maxI, 0);
    }
    // do the same for the y element
    if (fabs(v(1, 1)) < fabs(v(2, 1))) {
      tmp = w(2);
      w(2) = w(1);
      w(1) = tmp;
      v.swapRow(2, 1);
    }

    // ensure that the sign of the eigenvectors is correct
    for (i = 0; i < 2; i++) {
      if (v(i, i) < 0) {
        v(i, 0) = -v(i, 0);
        v(i, 1) = -v(i, 1);
        v(i, 2) = -v(i, 2);
      }
    }

    // set sign of final eigenvector to ensure that determinant is positive
    if (v.determinant() < 0) {
      v(2, 0) = -v(2, 0);
      v(2, 1) = -v(2, 1);
      v(2, 2) = -v(2, 2);
    }

    // transpose the eigenvectors back again
    v = v.transpose();
    return ;
  }

  /**
   * Return the multiplication of two matrixes  (m1 * m2). 
   * @return the multiplication of two matrixes
   * @param m1 the first matrix
   * @param m2 the second matrix
   */
  template<typename Real> 
  inline SquareMatrix3<Real> operator *(const SquareMatrix3<Real>& m1, const SquareMatrix3<Real>& m2) {
    SquareMatrix3<Real> result;

    for (unsigned int i = 0; i < 3; i++)
      for (unsigned int j = 0; j < 3; j++)
        for (unsigned int k = 0; k < 3; k++)
          result(i, j)  += m1(i, k) * m2(k, j);                

    return result;
  }

  template<typename Real> 
  inline SquareMatrix3<Real> outProduct(const Vector3<Real>& v1, const Vector3<Real>& v2) {
    SquareMatrix3<Real> result;

    for (unsigned int i = 0; i < 3; i++) {
      for (unsigned int j = 0; j < 3; j++) {
        result(i, j)  = v1[i] * v2[j];                
      }
    }
            
    return result;        
  }

    
  typedef SquareMatrix3<RealType> Mat3x3d;
  typedef SquareMatrix3<RealType> RotMat3x3d;

} //namespace OpenMD
#endif // MATH_SQUAREMATRIX_HPP

Revision:	1390
Committed:	Wed Nov 25 20:02:06 2009 UTC (15 years, 11 months ago) by gezelter
File size:	18561 byte(s)
Log Message:	Almost all of the changes necessary to create OpenMD out of our old project (OOPSE-4)
#	User	Rev	Content
1	gezelter	507	/*
2	gezelter	246	* Copyright (c) 2005 The University of Notre Dame. All Rights Reserved.
3	tim	70	*
4	gezelter	246	* The University of Notre Dame grants you ("Licensee") a
5			* non-exclusive, royalty free, license to use, modify and
6			* redistribute this software in source and binary code form, provided
7			* that the following conditions are met:
8			*
9	gezelter	1390	* 1. Redistributions of source code must retain the above copyright
10	gezelter	246	* notice, this list of conditions and the following disclaimer.
11			*
12	gezelter	1390	* 2. Redistributions in binary form must reproduce the above copyright
13	gezelter	246	* notice, this list of conditions and the following disclaimer in the
14			* documentation and/or other materials provided with the
15			* distribution.
16			*
17			* This software is provided "AS IS," without a warranty of any
18			* kind. All express or implied conditions, representations and
19			* warranties, including any implied warranty of merchantability,
20			* fitness for a particular purpose or non-infringement, are hereby
21			* excluded. The University of Notre Dame and its licensors shall not
22			* be liable for any damages suffered by licensee as a result of
23			* using, modifying or distributing the software or its
24			* derivatives. In no event will the University of Notre Dame or its
25			* licensors be liable for any lost revenue, profit or data, or for
26			* direct, indirect, special, consequential, incidental or punitive
27			* damages, however caused and regardless of the theory of liability,
28			* arising out of the use of or inability to use software, even if the
29			* University of Notre Dame has been advised of the possibility of
30			* such damages.
31	gezelter	1390	*
32			* SUPPORT OPEN SCIENCE! If you use OpenMD or its source code in your
33			* research, please cite the appropriate papers when you publish your
34			* work. Good starting points are:
35			*
36			* [1] Meineke, et al., J. Comp. Chem. 26, 252-271 (2005).
37			* [2] Fennell & Gezelter, J. Chem. Phys. 124, 234104 (2006).
38			* [3] Sun, Lin & Gezelter, J. Chem. Phys. 128, 24107 (2008).
39			* [4] Vardeman & Gezelter, in progress (2009).
40	tim	70	*/
41	gezelter	246
42	tim	70	/**
43			* @file SquareMatrix3.hpp
44			* @author Teng Lin
45			* @date 10/11/2004
46			* @version 1.0
47			*/
48	gezelter	507	#ifndef MATH_SQUAREMATRIX3_HPP
49	tim	99	#define MATH_SQUAREMATRIX3_HPP
50	tim	895	#include <vector>
51	tim	93	#include "Quaternion.hpp"
52	tim	70	#include "SquareMatrix.hpp"
53	tim	93	#include "Vector3.hpp"
54	tim	451	#include "utils/NumericConstant.hpp"
55	gezelter	1390	namespace OpenMD {
56	tim	70
57	gezelter	507	template<typename Real>
58			class SquareMatrix3 : public SquareMatrix<Real, 3> {
59			public:
60	tim	137
61	gezelter	507	typedef Real ElemType;
62			typedef Real* ElemPoinerType;
63	tim	70
64	gezelter	507	/** default constructor */
65			SquareMatrix3() : SquareMatrix<Real, 3>() {
66			}
67	tim	70
68	gezelter	507	/** Constructs and initializes every element of this matrix to a scalar */
69			SquareMatrix3(Real s) : SquareMatrix<Real,3>(s){
70			}
71	tim	151
72	gezelter	507	/** Constructs and initializes from an array */
73			SquareMatrix3(Real* array) : SquareMatrix<Real,3>(array){
74			}
75	tim	151
76
77	gezelter	507	/** copy constructor */
78			SquareMatrix3(const SquareMatrix<Real, 3>& m) : SquareMatrix<Real, 3>(m) {
79			}
80	gezelter	246
81	gezelter	507	SquareMatrix3( const Vector3<Real>& eulerAngles) {
82			setupRotMat(eulerAngles);
83			}
84	tim	93
85	gezelter	507	SquareMatrix3(Real phi, Real theta, Real psi) {
86			setupRotMat(phi, theta, psi);
87			}
88	tim	93
89	gezelter	507	SquareMatrix3(const Quaternion<Real>& q) {
90			setupRotMat(q);
91	tim	113
92	gezelter	507	}
93	tim	93
94	gezelter	507	SquareMatrix3(Real w, Real x, Real y, Real z) {
95			setupRotMat(w, x, y, z);
96			}
97	tim	93
98	gezelter	507	/** copy assignment operator */
99			SquareMatrix3<Real>& operator =(const SquareMatrix<Real, 3>& m) {
100			if (this == &m)
101			return *this;
102			SquareMatrix<Real, 3>::operator=(m);
103			return *this;
104			}
105	tim	76
106	gezelter	246
107	gezelter	507	SquareMatrix3<Real>& operator =(const Quaternion<Real>& q) {
108			this->setupRotMat(q);
109			return *this;
110			}
111	gezelter	246
112	gezelter	507	/**
113			* Sets this matrix to a rotation matrix by three euler angles
114			* @ param euler
115			*/
116			void setupRotMat(const Vector3<Real>& eulerAngles) {
117			setupRotMat(eulerAngles[0], eulerAngles[1], eulerAngles[2]);
118			}
119	tim	76
120	gezelter	507	/**
121			* Sets this matrix to a rotation matrix by three euler angles
122			* @param phi
123			* @param theta
124			* @psi theta
125			*/
126			void setupRotMat(Real phi, Real theta, Real psi) {
127			Real sphi, stheta, spsi;
128			Real cphi, ctheta, cpsi;
129	tim	76
130	gezelter	507	sphi = sin(phi);
131			stheta = sin(theta);
132			spsi = sin(psi);
133			cphi = cos(phi);
134			ctheta = cos(theta);
135			cpsi = cos(psi);
136	tim	76
137	gezelter	507	this->data_[0][0] = cpsi * cphi - ctheta * sphi * spsi;
138			this->data_[0][1] = cpsi * sphi + ctheta * cphi * spsi;
139			this->data_[0][2] = spsi * stheta;
140	tim	93
141	gezelter	507	this->data_[1][0] = -spsi * ctheta - ctheta * sphi * cpsi;
142			this->data_[1][1] = -spsi * stheta + ctheta * cphi * cpsi;
143			this->data_[1][2] = cpsi * stheta;
144	tim	93
145	gezelter	507	this->data_[2][0] = stheta * sphi;
146			this->data_[2][1] = -stheta * cphi;
147			this->data_[2][2] = ctheta;
148			}
149	tim	93
150
151	gezelter	507	/**
152			* Sets this matrix to a rotation matrix by quaternion
153			* @param quat
154			*/
155			void setupRotMat(const Quaternion<Real>& quat) {
156			setupRotMat(quat.w(), quat.x(), quat.y(), quat.z());
157			}
158	tim	76
159	gezelter	507	/**
160			* Sets this matrix to a rotation matrix by quaternion
161			* @param w the first element
162			* @param x the second element
163			* @param y the third element
164			* @param z the fourth element
165			*/
166			void setupRotMat(Real w, Real x, Real y, Real z) {
167			Quaternion<Real> q(w, x, y, z);
168			*this = q.toRotationMatrix3();
169			}
170	tim	76
171	tim	891	void setupSkewMat(Vector3<Real> v) {
172			setupSkewMat(v[0], v[1], v[2]);
173			}
174
175			void setupSkewMat(Real v1, Real v2, Real v3) {
176			this->data_[0][0] = 0;
177			this->data_[0][1] = -v3;
178			this->data_[0][2] = v2;
179			this->data_[1][0] = v3;
180			this->data_[1][1] = 0;
181			this->data_[1][2] = -v1;
182			this->data_[2][0] = -v2;
183			this->data_[2][1] = v1;
184			this->data_[2][2] = 0;
185
186
187			}
188
189
190
191	gezelter	507	/**
192			* Returns the quaternion from this rotation matrix
193			* @return the quaternion from this rotation matrix
194			* @exception invalid rotation matrix
195			*/
196			Quaternion<Real> toQuaternion() {
197			Quaternion<Real> q;
198			Real t, s;
199			Real ad1, ad2, ad3;
200			t = this->data_[0][0] + this->data_[1][1] + this->data_[2][2] + 1.0;
201	tim	76
202	tim	637	if( t > NumericConstant::epsilon ){
203	tim	93
204	gezelter	507	s = 0.5 / sqrt( t );
205			q[0] = 0.25 / s;
206			q[1] = (this->data_[1][2] - this->data_[2][1]) * s;
207			q[2] = (this->data_[2][0] - this->data_[0][2]) * s;
208			q[3] = (this->data_[0][1] - this->data_[1][0]) * s;
209			} else {
210	tim	93
211	tim	633	ad1 = this->data_[0][0];
212			ad2 = this->data_[1][1];
213			ad3 = this->data_[2][2];
214	tim	93
215	gezelter	507	if( ad1 >= ad2 && ad1 >= ad3 ){
216	tim	93
217	gezelter	507	s = 0.5 / sqrt( 1.0 + this->data_[0][0] - this->data_[1][1] - this->data_[2][2] );
218			q[0] = (this->data_[1][2] - this->data_[2][1]) * s;
219			q[1] = 0.25 / s;
220			q[2] = (this->data_[0][1] + this->data_[1][0]) * s;
221			q[3] = (this->data_[0][2] + this->data_[2][0]) * s;
222			} else if ( ad2 >= ad1 && ad2 >= ad3 ) {
223			s = 0.5 / sqrt( 1.0 + this->data_[1][1] - this->data_[0][0] - this->data_[2][2] );
224			q[0] = (this->data_[2][0] - this->data_[0][2] ) * s;
225			q[1] = (this->data_[0][1] + this->data_[1][0]) * s;
226			q[2] = 0.25 / s;
227			q[3] = (this->data_[1][2] + this->data_[2][1]) * s;
228			} else {
229	tim	93
230	gezelter	507	s = 0.5 / sqrt( 1.0 + this->data_[2][2] - this->data_[0][0] - this->data_[1][1] );
231			q[0] = (this->data_[0][1] - this->data_[1][0]) * s;
232			q[1] = (this->data_[0][2] + this->data_[2][0]) * s;
233			q[2] = (this->data_[1][2] + this->data_[2][1]) * s;
234			q[3] = 0.25 / s;
235			}
236			}
237	tim	93
238	gezelter	507	return q;
239	tim	93
240	gezelter	507	}
241	tim	93
242	gezelter	507	/**
243			* Returns the euler angles from this rotation matrix
244			* @return the euler angles in a vector
245			* @exception invalid rotation matrix
246			* We use so-called "x-convention", which is the most common definition.
247	cli2	1360	* In this convention, the rotation given by Euler angles (phi, theta,
248			* psi), where the first rotation is by an angle phi about the z-axis,
249			* the second is by an angle theta (0 <= theta <= 180) about the x-axis,
250			* and the third is by an angle psi about the z-axis (again).
251	gezelter	507	*/
252			Vector3<Real> toEulerAngles() {
253			Vector3<Real> myEuler;
254			Real phi;
255			Real theta;
256			Real psi;
257			Real ctheta;
258			Real stheta;
259	tim	93
260	gezelter	507	// set the tolerance for Euler angles and rotation elements
261	tim	93
262	tim	963	theta = acos(std::min((RealType)1.0, std::max((RealType)-1.0,this->data_[2][2])));
263	gezelter	507	ctheta = this->data_[2][2];
264			stheta = sqrt(1.0 - ctheta * ctheta);
265	tim	93
266	cli2	1360	// when sin(theta) is close to 0, we need to consider
267			// singularity In this case, we can assign an arbitary value to
268			// phi (or psi), and then determine the psi (or phi) or
269			// vice-versa. We'll assume that phi always gets the rotation,
270			// and psi is 0 in cases of singularity.
271	gezelter	507	// we use atan2 instead of atan, since atan2 will give us -Pi to Pi.
272	cli2	1360	// Since 0 <= theta <= 180, sin(theta) will be always
273			// non-negative. Therefore, it will never change the sign of both of
274			// the parameters passed to atan2.
275	tim	93
276	cli2	1360	if (fabs(stheta) < 1e-6){
277	gezelter	507	psi = 0.0;
278			phi = atan2(-this->data_[1][0], this->data_[0][0]);
279			}
280			// we only have one unique solution
281			else{
282			phi = atan2(this->data_[2][0], -this->data_[2][1]);
283			psi = atan2(this->data_[0][2], this->data_[1][2]);
284			}
285	tim	93
286	gezelter	507	//wrap phi and psi, make sure they are in the range from 0 to 2*Pi
287			if (phi < 0)
288	cli2	1360	phi += 2.0 * M_PI;
289	tim	93
290	gezelter	507	if (psi < 0)
291	cli2	1360	psi += 2.0 * M_PI;
292	tim	93
293	gezelter	507	myEuler[0] = phi;
294			myEuler[1] = theta;
295			myEuler[2] = psi;
296	tim	93
297	gezelter	507	return myEuler;
298			}
299	tim	70
300	gezelter	507	/** Returns the determinant of this matrix. */
301			Real determinant() const {
302			Real x,y,z;
303	tim	101
304	gezelter	507	x = this->data_[0][0] * (this->data_[1][1] * this->data_[2][2] - this->data_[1][2] * this->data_[2][1]);
305			y = this->data_[0][1] * (this->data_[1][2] * this->data_[2][0] - this->data_[1][0] * this->data_[2][2]);
306			z = this->data_[0][2] * (this->data_[1][0] * this->data_[2][1] - this->data_[1][1] * this->data_[2][0]);
307	tim	101
308	gezelter	507	return(x + y + z);
309			}
310	gezelter	246
311	gezelter	507	/** Returns the trace of this matrix. */
312			Real trace() const {
313			return this->data_[0][0] + this->data_[1][1] + this->data_[2][2];
314			}
315	tim	101
316	gezelter	507	/**
317			* Sets the value of this matrix to the inversion of itself.
318			* @note since simple algorithm can be applied to inverse the 3 by 3 matrix, we hide the
319			* implementation of inverse in SquareMatrix class
320			*/
321			SquareMatrix3<Real> inverse() const {
322			SquareMatrix3<Real> m;
323	tim	963	RealType det = determinant();
324	gezelter	1390	if (fabs(det) <= OpenMD::epsilon) {
325	gezelter	507	//"The method was called on a matrix with \|determinant\| <= 1e-6.",
326			//"This is a runtime or a programming error in your application.");
327	tim	895	std::vector<int> zeroDiagElementIndex;
328			for (int i =0; i < 3; ++i) {
329	gezelter	1390	if (fabs(this->data_[i][i]) <= OpenMD::epsilon) {
330	tim	895	zeroDiagElementIndex.push_back(i);
331			}
332			}
333	tim	70
334	tim	895	if (zeroDiagElementIndex.size() == 2) {
335			int index = zeroDiagElementIndex[0];
336			m(index, index) = 1.0 / this->data_[index][index];
337			}else if (zeroDiagElementIndex.size() == 1) {
338	tim	101
339	tim	895	int a = (zeroDiagElementIndex[0] + 1) % 3;
340			int b = (zeroDiagElementIndex[0] + 2) %3;
341	tim	963	RealType denom = this->data_[a][a] * this->data_[b][b] - this->data_[b][a]*this->data_[a][b];
342	tim	895	m(a, a) = this->data_[b][b] /denom;
343			m(b, a) = -this->data_[b][a]/denom;
344
345			m(a,b) = -this->data_[a][b]/denom;
346			m(b, b) = this->data_[a][a]/denom;
347
348			}
349
350			/*
351			for(std::vector<int>::iterator iter = zeroDiagElementIndex.begin(); iter != zeroDiagElementIndex.end() ++iter) {
352	gezelter	1390	if (this->data_[iter][0] > OpenMD::epsilon \|\| this->data_[iter][1] \|\|this->data_[*iter][2] \|\|
353			this->data_[0][iter] > OpenMD::epsilon \|\| this->data_[1][iter] \|\|this->data_[2][*iter] ) {
354	tim	895	std::cout << "can not inverse matrix" << std::endl;
355			}
356			}
357			*/
358			} else {
359
360			m(0, 0) = this->data_[1][1]this->data_[2][2] - this->data_[1][2]this->data_[2][1];
361			m(1, 0) = this->data_[1][2]this->data_[2][0] - this->data_[1][0]this->data_[2][2];
362			m(2, 0) = this->data_[1][0]this->data_[2][1] - this->data_[1][1]this->data_[2][0];
363			m(0, 1) = this->data_[2][1]this->data_[0][2] - this->data_[2][2]this->data_[0][1];
364			m(1, 1) = this->data_[2][2]this->data_[0][0] - this->data_[2][0]this->data_[0][2];
365			m(2, 1) = this->data_[2][0]this->data_[0][1] - this->data_[2][1]this->data_[0][0];
366			m(0, 2) = this->data_[0][1]this->data_[1][2] - this->data_[0][2]this->data_[1][1];
367			m(1, 2) = this->data_[0][2]this->data_[1][0] - this->data_[0][0]this->data_[1][2];
368			m(2, 2) = this->data_[0][0]this->data_[1][1] - this->data_[0][1]this->data_[1][0];
369
370			m /= det;
371			}
372	gezelter	507	return m;
373			}
374	tim	883
375			SquareMatrix3<Real> transpose() const{
376			SquareMatrix3<Real> result;
377
378			for (unsigned int i = 0; i < 3; i++)
379			for (unsigned int j = 0; j < 3; j++)
380			result(j, i) = this->data_[i][j];
381
382			return result;
383			}
384	gezelter	507	/**
385			* Extract the eigenvalues and eigenvectors from a 3x3 matrix.
386			* The eigenvectors (the columns of V) will be normalized.
387			* The eigenvectors are aligned optimally with the x, y, and z
388			* axes respectively.
389			* @param a symmetric matrix whose eigenvectors are to be computed. On return, the matrix is
390			* overwritten
391			* @param w will contain the eigenvalues of the matrix On return of this function
392			* @param v the columns of this matrix will contain the eigenvectors. The eigenvectors are
393			* normalized and mutually orthogonal.
394			* @warning a will be overwritten
395			*/
396			static void diagonalize(SquareMatrix3<Real>& a, Vector3<Real>& w, SquareMatrix3<Real>& v);
397			};
398			/*=========================================================================
399	tim	76
400	tim	123	Program: Visualization Toolkit
401			Module: $RCSfile: SquareMatrix3.hpp,v $
402	tim	99
403	tim	123	Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen
404			All rights reserved.
405			See Copyright.txt or http://www.kitware.com/Copyright.htm for details.
406	tim	101
407	gezelter	507	This software is distributed WITHOUT ANY WARRANTY; without even
408			the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
409			PURPOSE. See the above copyright notice for more information.
410	tim	101
411	gezelter	507	=========================================================================*/
412			template<typename Real>
413			void SquareMatrix3<Real>::diagonalize(SquareMatrix3<Real>& a, Vector3<Real>& w,
414			SquareMatrix3<Real>& v) {
415			int i,j,k,maxI;
416			Real tmp, maxVal;
417			Vector3<Real> v_maxI, v_k, v_j;
418	tim	101
419	gezelter	507	// diagonalize using Jacobi
420			jacobi(a, w, v);
421			// if all the eigenvalues are the same, return identity matrix
422			if (w[0] == w[1] && w[0] == w[2] ) {
423			v = SquareMatrix3<Real>::identity();
424			return;
425			}
426	tim	101
427	gezelter	507	// transpose temporarily, it makes it easier to sort the eigenvectors
428			v = v.transpose();
429	tim	123
430	gezelter	507	// if two eigenvalues are the same, re-orthogonalize to optimally line
431			// up the eigenvectors with the x, y, and z axes
432			for (i = 0; i < 3; i++) {
433			if (w((i+1)%3) == w((i+2)%3)) {// two eigenvalues are the same
434			// find maximum element of the independant eigenvector
435			maxVal = fabs(v(i, 0));
436			maxI = 0;
437			for (j = 1; j < 3; j++) {
438			if (maxVal < (tmp = fabs(v(i, j)))){
439			maxVal = tmp;
440			maxI = j;
441			}
442			}
443	tim	123
444	gezelter	507	// swap the eigenvector into its proper position
445			if (maxI != i) {
446			tmp = w(maxI);
447			w(maxI) = w(i);
448			w(i) = tmp;
449	tim	101
450	gezelter	507	v.swapRow(i, maxI);
451			}
452			// maximum element of eigenvector should be positive
453			if (v(maxI, maxI) < 0) {
454			v(maxI, 0) = -v(maxI, 0);
455			v(maxI, 1) = -v(maxI, 1);
456			v(maxI, 2) = -v(maxI, 2);
457			}
458	tim	101
459	gezelter	507	// re-orthogonalize the other two eigenvectors
460			j = (maxI+1)%3;
461			k = (maxI+2)%3;
462	tim	101
463	gezelter	507	v(j, 0) = 0.0;
464			v(j, 1) = 0.0;
465			v(j, 2) = 0.0;
466			v(j, j) = 1.0;
467	tim	101
468	gezelter	507	/** @todo */
469			v_maxI = v.getRow(maxI);
470			v_j = v.getRow(j);
471			v_k = cross(v_maxI, v_j);
472			v_k.normalize();
473			v_j = cross(v_k, v_maxI);
474			v.setRow(j, v_j);
475			v.setRow(k, v_k);
476	tim	101
477
478	gezelter	507	// transpose vectors back to columns
479			v = v.transpose();
480			return;
481			}
482			}
483	tim	101
484	gezelter	507	// the three eigenvalues are different, just sort the eigenvectors
485			// to align them with the x, y, and z axes
486	tim	101
487	gezelter	507	// find the vector with the largest x element, make that vector
488			// the first vector
489			maxVal = fabs(v(0, 0));
490			maxI = 0;
491			for (i = 1; i < 3; i++) {
492			if (maxVal < (tmp = fabs(v(i, 0)))) {
493			maxVal = tmp;
494			maxI = i;
495			}
496			}
497	tim	101
498	gezelter	507	// swap eigenvalue and eigenvector
499			if (maxI != 0) {
500			tmp = w(maxI);
501			w(maxI) = w(0);
502			w(0) = tmp;
503			v.swapRow(maxI, 0);
504			}
505			// do the same for the y element
506			if (fabs(v(1, 1)) < fabs(v(2, 1))) {
507			tmp = w(2);
508			w(2) = w(1);
509			w(1) = tmp;
510			v.swapRow(2, 1);
511			}
512	tim	101
513	gezelter	507	// ensure that the sign of the eigenvectors is correct
514			for (i = 0; i < 2; i++) {
515			if (v(i, i) < 0) {
516			v(i, 0) = -v(i, 0);
517			v(i, 1) = -v(i, 1);
518			v(i, 2) = -v(i, 2);
519			}
520			}
521	tim	70
522	gezelter	507	// set sign of final eigenvector to ensure that determinant is positive
523			if (v.determinant() < 0) {
524			v(2, 0) = -v(2, 0);
525			v(2, 1) = -v(2, 1);
526			v(2, 2) = -v(2, 2);
527	tim	123	}
528	gezelter	246
529	gezelter	507	// transpose the eigenvectors back again
530			v = v.transpose();
531			return ;
532			}
533	gezelter	246
534	gezelter	507	/**
535			* Return the multiplication of two matrixes (m1 * m2).
536			* @return the multiplication of two matrixes
537			* @param m1 the first matrix
538			* @param m2 the second matrix
539			*/
540			template<typename Real>
541			inline SquareMatrix3<Real> operator *(const SquareMatrix3<Real>& m1, const SquareMatrix3<Real>& m2) {
542			SquareMatrix3<Real> result;
543	gezelter	246
544	gezelter	507	for (unsigned int i = 0; i < 3; i++)
545			for (unsigned int j = 0; j < 3; j++)
546			for (unsigned int k = 0; k < 3; k++)
547			result(i, j) += m1(i, k) * m2(k, j);
548	gezelter	246
549	gezelter	507	return result;
550			}
551	gezelter	246
552	gezelter	507	template<typename Real>
553			inline SquareMatrix3<Real> outProduct(const Vector3<Real>& v1, const Vector3<Real>& v2) {
554			SquareMatrix3<Real> result;
555
556			for (unsigned int i = 0; i < 3; i++) {
557			for (unsigned int j = 0; j < 3; j++) {
558			result(i, j) = v1[i] * v2[j];
559			}
560			}
561	gezelter	246
562	gezelter	507	return result;
563			}
564	gezelter	246
565
566	tim	963	typedef SquareMatrix3<RealType> Mat3x3d;
567			typedef SquareMatrix3<RealType> RotMat3x3d;
568	tim	93
569	gezelter	1390	} //namespace OpenMD
570	tim	93	#endif // MATH_SQUAREMATRIX_HPP
571	tim	123