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
    SquareMatrix3<Real>::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:	1610
Committed:	Fri Aug 12 14:37:25 2011 UTC (13 years, 8 months ago) by gezelter
File size:	18582 byte(s)
Log Message:	Fixed a clang compilation problem, added the ability to output particle potential in the dump files.
#	Content
1	/*
2	* Copyright (c) 2005 The University of Notre Dame. All Rights Reserved.
3	*
4	* 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	* 1. Redistributions of source code must retain the above copyright
10	* notice, this list of conditions and the following disclaimer.
11	*
12	* 2. Redistributions in binary form must reproduce the above copyright
13	* 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	*
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	*/
41
42	/**
43	* @file SquareMatrix3.hpp
44	* @author Teng Lin
45	* @date 10/11/2004
46	* @version 1.0
47	*/
48	#ifndef MATH_SQUAREMATRIX3_HPP
49	#define MATH_SQUAREMATRIX3_HPP
50	#include <vector>
51	#include "Quaternion.hpp"
52	#include "SquareMatrix.hpp"
53	#include "Vector3.hpp"
54	#include "utils/NumericConstant.hpp"
55	namespace OpenMD {
56
57	template<typename Real>
58	class SquareMatrix3 : public SquareMatrix<Real, 3> {
59	public:
60
61	typedef Real ElemType;
62	typedef Real* ElemPoinerType;
63
64	/** default constructor */
65	SquareMatrix3() : SquareMatrix<Real, 3>() {
66	}
67
68	/** Constructs and initializes every element of this matrix to a scalar */
69	SquareMatrix3(Real s) : SquareMatrix<Real,3>(s){
70	}
71
72	/** Constructs and initializes from an array */
73	SquareMatrix3(Real* array) : SquareMatrix<Real,3>(array){
74	}
75
76
77	/** copy constructor */
78	SquareMatrix3(const SquareMatrix<Real, 3>& m) : SquareMatrix<Real, 3>(m) {
79	}
80
81	SquareMatrix3( const Vector3<Real>& eulerAngles) {
82	setupRotMat(eulerAngles);
83	}
84
85	SquareMatrix3(Real phi, Real theta, Real psi) {
86	setupRotMat(phi, theta, psi);
87	}
88
89	SquareMatrix3(const Quaternion<Real>& q) {
90	setupRotMat(q);
91
92	}
93
94	SquareMatrix3(Real w, Real x, Real y, Real z) {
95	setupRotMat(w, x, y, z);
96	}
97
98	/** 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
106
107	SquareMatrix3<Real>& operator =(const Quaternion<Real>& q) {
108	this->setupRotMat(q);
109	return *this;
110	}
111
112	/**
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
120	/**
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
130	sphi = sin(phi);
131	stheta = sin(theta);
132	spsi = sin(psi);
133	cphi = cos(phi);
134	ctheta = cos(theta);
135	cpsi = cos(psi);
136
137	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
141	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
145	this->data_[2][0] = stheta * sphi;
146	this->data_[2][1] = -stheta * cphi;
147	this->data_[2][2] = ctheta;
148	}
149
150
151	/**
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
159	/**
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
171	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	/**
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
202	if( t > NumericConstant::epsilon ){
203
204	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
211	ad1 = this->data_[0][0];
212	ad2 = this->data_[1][1];
213	ad3 = this->data_[2][2];
214
215	if( ad1 >= ad2 && ad1 >= ad3 ){
216
217	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
230	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
238	return q;
239
240	}
241
242	/**
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	* 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	*/
252	Vector3<Real> toEulerAngles() {
253	Vector3<Real> myEuler;
254	Real phi;
255	Real theta;
256	Real psi;
257	Real ctheta;
258	Real stheta;
259
260	// set the tolerance for Euler angles and rotation elements
261
262	theta = acos(std::min((RealType)1.0, std::max((RealType)-1.0,this->data_[2][2])));
263	ctheta = this->data_[2][2];
264	stheta = sqrt(1.0 - ctheta * ctheta);
265
266	// 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	// we use atan2 instead of atan, since atan2 will give us -Pi to Pi.
272	// 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
276	if (fabs(stheta) < 1e-6){
277	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
286	//wrap phi and psi, make sure they are in the range from 0 to 2*Pi
287	if (phi < 0)
288	phi += 2.0 * M_PI;
289
290	if (psi < 0)
291	psi += 2.0 * M_PI;
292
293	myEuler[0] = phi;
294	myEuler[1] = theta;
295	myEuler[2] = psi;
296
297	return myEuler;
298	}
299
300	/** Returns the determinant of this matrix. */
301	Real determinant() const {
302	Real x,y,z;
303
304	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
308	return(x + y + z);
309	}
310
311	/** 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
316	/**
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	RealType det = determinant();
324	if (fabs(det) <= OpenMD::epsilon) {
325	//"The method was called on a matrix with \|determinant\| <= 1e-6.",
326	//"This is a runtime or a programming error in your application.");
327	std::vector<int> zeroDiagElementIndex;
328	for (int i =0; i < 3; ++i) {
329	if (fabs(this->data_[i][i]) <= OpenMD::epsilon) {
330	zeroDiagElementIndex.push_back(i);
331	}
332	}
333
334	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
339	int a = (zeroDiagElementIndex[0] + 1) % 3;
340	int b = (zeroDiagElementIndex[0] + 2) %3;
341	RealType denom = this->data_[a][a] * this->data_[b][b] - this->data_[b][a]*this->data_[a][b];
342	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	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	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	return m;
373	}
374
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	/**
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
400	Program: Visualization Toolkit
401	Module: $RCSfile: SquareMatrix3.hpp,v $
402
403	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
407	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
411	=========================================================================*/
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
419	// diagonalize using Jacobi
420	SquareMatrix3<Real>::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
427	// transpose temporarily, it makes it easier to sort the eigenvectors
428	v = v.transpose();
429
430	// 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
444	// 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
450	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
459	// re-orthogonalize the other two eigenvectors
460	j = (maxI+1)%3;
461	k = (maxI+2)%3;
462
463	v(j, 0) = 0.0;
464	v(j, 1) = 0.0;
465	v(j, 2) = 0.0;
466	v(j, j) = 1.0;
467
468	/** @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
477
478	// transpose vectors back to columns
479	v = v.transpose();
480	return;
481	}
482	}
483
484	// the three eigenvalues are different, just sort the eigenvectors
485	// to align them with the x, y, and z axes
486
487	// 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
498	// 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
513	// 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
522	// 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	}
528
529	// transpose the eigenvectors back again
530	v = v.transpose();
531	return ;
532	}
533
534	/**
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
544	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
549	return result;
550	}
551
552	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
562	return result;
563	}
564
565
566	typedef SquareMatrix3<RealType> Mat3x3d;
567	typedef SquareMatrix3<RealType> RotMat3x3d;
568
569	} //namespace OpenMD
570	#endif // MATH_SQUAREMATRIX_HPP
571