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, 234107 (2008).          
 * [4]  Kuang & Gezelter,  J. Chem. Phys. 133, 164101 (2010).
 * [5]  Vardeman, Stocker & Gezelter, J. Chem. Theory Comput. 7, 834 (2011).
 */
 
/**
 * @file SquareMatrix3.hpp
 * @author Teng Lin
 * @date 10/11/2004
 * @version 1.0
 */
#ifndef MATH_SQUAREMATRIX3_HPP
#define  MATH_SQUAREMATRIX3_HPP
#include "config.h"
#include <cmath>
#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
     * @param psi
     */
    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;

  const Mat3x3d M3Zero(0.0);


} //namespace OpenMD
#endif // MATH_SQUAREMATRIX_HPP

Revision:	2000
Committed:	Sat May 31 22:35:05 2014 UTC (10 years, 11 months ago) by gezelter
File size:	18721 byte(s)
Log Message:	Bug Fixes
#	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	gezelter	1879	* [3] Sun, Lin & Gezelter, J. Chem. Phys. 128, 234107 (2008).
39	gezelter	1782	* [4] Kuang & Gezelter, J. Chem. Phys. 133, 164101 (2010).
40			* [5] Vardeman, Stocker & Gezelter, J. Chem. Theory Comput. 7, 834 (2011).
41	tim	70	*/
42	gezelter	246
43	tim	70	/**
44			* @file SquareMatrix3.hpp
45			* @author Teng Lin
46			* @date 10/11/2004
47			* @version 1.0
48			*/
49	gezelter	507	#ifndef MATH_SQUAREMATRIX3_HPP
50	tim	99	#define MATH_SQUAREMATRIX3_HPP
51	gezelter	1782	#include "config.h"
52			#include <cmath>
53	tim	895	#include <vector>
54	tim	93	#include "Quaternion.hpp"
55	tim	70	#include "SquareMatrix.hpp"
56	tim	93	#include "Vector3.hpp"
57	tim	451	#include "utils/NumericConstant.hpp"
58	gezelter	1390	namespace OpenMD {
59	tim	70
60	gezelter	507	template<typename Real>
61			class SquareMatrix3 : public SquareMatrix<Real, 3> {
62			public:
63	tim	137
64	gezelter	507	typedef Real ElemType;
65			typedef Real* ElemPoinerType;
66	tim	70
67	gezelter	507	/** default constructor */
68			SquareMatrix3() : SquareMatrix<Real, 3>() {
69			}
70	tim	70
71	gezelter	507	/** Constructs and initializes every element of this matrix to a scalar */
72			SquareMatrix3(Real s) : SquareMatrix<Real,3>(s){
73			}
74	tim	151
75	gezelter	507	/** Constructs and initializes from an array */
76			SquareMatrix3(Real* array) : SquareMatrix<Real,3>(array){
77			}
78	tim	151
79
80	gezelter	507	/** copy constructor */
81			SquareMatrix3(const SquareMatrix<Real, 3>& m) : SquareMatrix<Real, 3>(m) {
82			}
83	gezelter	246
84	gezelter	507	SquareMatrix3( const Vector3<Real>& eulerAngles) {
85			setupRotMat(eulerAngles);
86			}
87	tim	93
88	gezelter	507	SquareMatrix3(Real phi, Real theta, Real psi) {
89			setupRotMat(phi, theta, psi);
90			}
91	tim	93
92	gezelter	507	SquareMatrix3(const Quaternion<Real>& q) {
93			setupRotMat(q);
94	tim	113
95	gezelter	507	}
96	tim	93
97	gezelter	507	SquareMatrix3(Real w, Real x, Real y, Real z) {
98			setupRotMat(w, x, y, z);
99			}
100	tim	93
101	gezelter	507	/** copy assignment operator */
102			SquareMatrix3<Real>& operator =(const SquareMatrix<Real, 3>& m) {
103			if (this == &m)
104			return *this;
105			SquareMatrix<Real, 3>::operator=(m);
106			return *this;
107			}
108	tim	76
109	gezelter	246
110	gezelter	507	SquareMatrix3<Real>& operator =(const Quaternion<Real>& q) {
111			this->setupRotMat(q);
112			return *this;
113			}
114	gezelter	246
115	gezelter	1782
116	gezelter	507	/**
117			* Sets this matrix to a rotation matrix by three euler angles
118			* @ param euler
119			*/
120			void setupRotMat(const Vector3<Real>& eulerAngles) {
121			setupRotMat(eulerAngles[0], eulerAngles[1], eulerAngles[2]);
122			}
123	tim	76
124	gezelter	507	/**
125			* Sets this matrix to a rotation matrix by three euler angles
126			* @param phi
127			* @param theta
128	gezelter	1879	* @param psi
129	gezelter	507	*/
130			void setupRotMat(Real phi, Real theta, Real psi) {
131			Real sphi, stheta, spsi;
132			Real cphi, ctheta, cpsi;
133	tim	76
134	gezelter	507	sphi = sin(phi);
135			stheta = sin(theta);
136			spsi = sin(psi);
137			cphi = cos(phi);
138			ctheta = cos(theta);
139			cpsi = cos(psi);
140	tim	76
141	gezelter	507	this->data_[0][0] = cpsi * cphi - ctheta * sphi * spsi;
142			this->data_[0][1] = cpsi * sphi + ctheta * cphi * spsi;
143			this->data_[0][2] = spsi * stheta;
144	tim	93
145	gezelter	507	this->data_[1][0] = -spsi * ctheta - ctheta * sphi * cpsi;
146			this->data_[1][1] = -spsi * stheta + ctheta * cphi * cpsi;
147			this->data_[1][2] = cpsi * stheta;
148	tim	93
149	gezelter	507	this->data_[2][0] = stheta * sphi;
150			this->data_[2][1] = -stheta * cphi;
151			this->data_[2][2] = ctheta;
152			}
153	tim	93
154
155	gezelter	507	/**
156			* Sets this matrix to a rotation matrix by quaternion
157			* @param quat
158			*/
159			void setupRotMat(const Quaternion<Real>& quat) {
160			setupRotMat(quat.w(), quat.x(), quat.y(), quat.z());
161			}
162	tim	76
163	gezelter	507	/**
164			* Sets this matrix to a rotation matrix by quaternion
165			* @param w the first element
166			* @param x the second element
167			* @param y the third element
168			* @param z the fourth element
169			*/
170			void setupRotMat(Real w, Real x, Real y, Real z) {
171			Quaternion<Real> q(w, x, y, z);
172			*this = q.toRotationMatrix3();
173			}
174	tim	76
175	tim	891	void setupSkewMat(Vector3<Real> v) {
176			setupSkewMat(v[0], v[1], v[2]);
177			}
178
179			void setupSkewMat(Real v1, Real v2, Real v3) {
180			this->data_[0][0] = 0;
181			this->data_[0][1] = -v3;
182			this->data_[0][2] = v2;
183			this->data_[1][0] = v3;
184			this->data_[1][1] = 0;
185			this->data_[1][2] = -v1;
186			this->data_[2][0] = -v2;
187			this->data_[2][1] = v1;
188			this->data_[2][2] = 0;
189
190
191			}
192
193
194	gezelter	507	/**
195			* Returns the quaternion from this rotation matrix
196			* @return the quaternion from this rotation matrix
197			* @exception invalid rotation matrix
198			*/
199			Quaternion<Real> toQuaternion() {
200			Quaternion<Real> q;
201			Real t, s;
202			Real ad1, ad2, ad3;
203			t = this->data_[0][0] + this->data_[1][1] + this->data_[2][2] + 1.0;
204	tim	76
205	tim	637	if( t > NumericConstant::epsilon ){
206	tim	93
207	gezelter	507	s = 0.5 / sqrt( t );
208			q[0] = 0.25 / s;
209			q[1] = (this->data_[1][2] - this->data_[2][1]) * s;
210			q[2] = (this->data_[2][0] - this->data_[0][2]) * s;
211			q[3] = (this->data_[0][1] - this->data_[1][0]) * s;
212			} else {
213	tim	93
214	tim	633	ad1 = this->data_[0][0];
215			ad2 = this->data_[1][1];
216			ad3 = this->data_[2][2];
217	tim	93
218	gezelter	507	if( ad1 >= ad2 && ad1 >= ad3 ){
219	tim	93
220	gezelter	507	s = 0.5 / sqrt( 1.0 + this->data_[0][0] - this->data_[1][1] - this->data_[2][2] );
221			q[0] = (this->data_[1][2] - this->data_[2][1]) * s;
222			q[1] = 0.25 / s;
223			q[2] = (this->data_[0][1] + this->data_[1][0]) * s;
224			q[3] = (this->data_[0][2] + this->data_[2][0]) * s;
225			} else if ( ad2 >= ad1 && ad2 >= ad3 ) {
226			s = 0.5 / sqrt( 1.0 + this->data_[1][1] - this->data_[0][0] - this->data_[2][2] );
227			q[0] = (this->data_[2][0] - this->data_[0][2] ) * s;
228			q[1] = (this->data_[0][1] + this->data_[1][0]) * s;
229			q[2] = 0.25 / s;
230			q[3] = (this->data_[1][2] + this->data_[2][1]) * s;
231			} else {
232	tim	93
233	gezelter	507	s = 0.5 / sqrt( 1.0 + this->data_[2][2] - this->data_[0][0] - this->data_[1][1] );
234			q[0] = (this->data_[0][1] - this->data_[1][0]) * s;
235			q[1] = (this->data_[0][2] + this->data_[2][0]) * s;
236			q[2] = (this->data_[1][2] + this->data_[2][1]) * s;
237			q[3] = 0.25 / s;
238			}
239			}
240	tim	93
241	gezelter	507	return q;
242	tim	93
243	gezelter	507	}
244	tim	93
245	gezelter	507	/**
246			* Returns the euler angles from this rotation matrix
247			* @return the euler angles in a vector
248			* @exception invalid rotation matrix
249			* We use so-called "x-convention", which is the most common definition.
250	cli2	1360	* In this convention, the rotation given by Euler angles (phi, theta,
251			* psi), where the first rotation is by an angle phi about the z-axis,
252			* the second is by an angle theta (0 <= theta <= 180) about the x-axis,
253			* and the third is by an angle psi about the z-axis (again).
254	gezelter	507	*/
255			Vector3<Real> toEulerAngles() {
256			Vector3<Real> myEuler;
257			Real phi;
258			Real theta;
259			Real psi;
260			Real ctheta;
261			Real stheta;
262	tim	93
263	gezelter	507	// set the tolerance for Euler angles and rotation elements
264	tim	93
265	tim	963	theta = acos(std::min((RealType)1.0, std::max((RealType)-1.0,this->data_[2][2])));
266	gezelter	507	ctheta = this->data_[2][2];
267			stheta = sqrt(1.0 - ctheta * ctheta);
268	tim	93
269	cli2	1360	// when sin(theta) is close to 0, we need to consider
270			// singularity In this case, we can assign an arbitary value to
271			// phi (or psi), and then determine the psi (or phi) or
272			// vice-versa. We'll assume that phi always gets the rotation,
273			// and psi is 0 in cases of singularity.
274	gezelter	507	// we use atan2 instead of atan, since atan2 will give us -Pi to Pi.
275	cli2	1360	// Since 0 <= theta <= 180, sin(theta) will be always
276			// non-negative. Therefore, it will never change the sign of both of
277			// the parameters passed to atan2.
278	tim	93
279	cli2	1360	if (fabs(stheta) < 1e-6){
280	gezelter	507	psi = 0.0;
281			phi = atan2(-this->data_[1][0], this->data_[0][0]);
282			}
283			// we only have one unique solution
284			else{
285			phi = atan2(this->data_[2][0], -this->data_[2][1]);
286			psi = atan2(this->data_[0][2], this->data_[1][2]);
287			}
288	tim	93
289	gezelter	507	//wrap phi and psi, make sure they are in the range from 0 to 2*Pi
290			if (phi < 0)
291	cli2	1360	phi += 2.0 * M_PI;
292	tim	93
293	gezelter	507	if (psi < 0)
294	cli2	1360	psi += 2.0 * M_PI;
295	tim	93
296	gezelter	507	myEuler[0] = phi;
297			myEuler[1] = theta;
298			myEuler[2] = psi;
299	tim	93
300	gezelter	507	return myEuler;
301			}
302	tim	70
303	gezelter	507	/** Returns the determinant of this matrix. */
304			Real determinant() const {
305			Real x,y,z;
306	tim	101
307	gezelter	507	x = this->data_[0][0] * (this->data_[1][1] * this->data_[2][2] - this->data_[1][2] * this->data_[2][1]);
308			y = this->data_[0][1] * (this->data_[1][2] * this->data_[2][0] - this->data_[1][0] * this->data_[2][2]);
309			z = this->data_[0][2] * (this->data_[1][0] * this->data_[2][1] - this->data_[1][1] * this->data_[2][0]);
310	tim	101
311	gezelter	507	return(x + y + z);
312			}
313	gezelter	246
314	gezelter	507	/** Returns the trace of this matrix. */
315			Real trace() const {
316			return this->data_[0][0] + this->data_[1][1] + this->data_[2][2];
317			}
318	tim	101
319	gezelter	507	/**
320			* Sets the value of this matrix to the inversion of itself.
321			* @note since simple algorithm can be applied to inverse the 3 by 3 matrix, we hide the
322			* implementation of inverse in SquareMatrix class
323			*/
324			SquareMatrix3<Real> inverse() const {
325			SquareMatrix3<Real> m;
326	tim	963	RealType det = determinant();
327	gezelter	1390	if (fabs(det) <= OpenMD::epsilon) {
328	gezelter	507	//"The method was called on a matrix with \|determinant\| <= 1e-6.",
329			//"This is a runtime or a programming error in your application.");
330	tim	895	std::vector<int> zeroDiagElementIndex;
331			for (int i =0; i < 3; ++i) {
332	gezelter	1390	if (fabs(this->data_[i][i]) <= OpenMD::epsilon) {
333	tim	895	zeroDiagElementIndex.push_back(i);
334			}
335			}
336	tim	70
337	tim	895	if (zeroDiagElementIndex.size() == 2) {
338			int index = zeroDiagElementIndex[0];
339			m(index, index) = 1.0 / this->data_[index][index];
340			}else if (zeroDiagElementIndex.size() == 1) {
341	tim	101
342	tim	895	int a = (zeroDiagElementIndex[0] + 1) % 3;
343			int b = (zeroDiagElementIndex[0] + 2) %3;
344	tim	963	RealType denom = this->data_[a][a] * this->data_[b][b] - this->data_[b][a]*this->data_[a][b];
345	tim	895	m(a, a) = this->data_[b][b] /denom;
346			m(b, a) = -this->data_[b][a]/denom;
347
348			m(a,b) = -this->data_[a][b]/denom;
349			m(b, b) = this->data_[a][a]/denom;
350
351			}
352
353			/*
354			for(std::vector<int>::iterator iter = zeroDiagElementIndex.begin(); iter != zeroDiagElementIndex.end() ++iter) {
355	gezelter	1390	if (this->data_[iter][0] > OpenMD::epsilon \|\| this->data_[iter][1] \|\|this->data_[*iter][2] \|\|
356			this->data_[0][iter] > OpenMD::epsilon \|\| this->data_[1][iter] \|\|this->data_[2][*iter] ) {
357	tim	895	std::cout << "can not inverse matrix" << std::endl;
358			}
359			}
360			*/
361			} else {
362
363			m(0, 0) = this->data_[1][1]this->data_[2][2] - this->data_[1][2]this->data_[2][1];
364			m(1, 0) = this->data_[1][2]this->data_[2][0] - this->data_[1][0]this->data_[2][2];
365			m(2, 0) = this->data_[1][0]this->data_[2][1] - this->data_[1][1]this->data_[2][0];
366			m(0, 1) = this->data_[2][1]this->data_[0][2] - this->data_[2][2]this->data_[0][1];
367			m(1, 1) = this->data_[2][2]this->data_[0][0] - this->data_[2][0]this->data_[0][2];
368			m(2, 1) = this->data_[2][0]this->data_[0][1] - this->data_[2][1]this->data_[0][0];
369			m(0, 2) = this->data_[0][1]this->data_[1][2] - this->data_[0][2]this->data_[1][1];
370			m(1, 2) = this->data_[0][2]this->data_[1][0] - this->data_[0][0]this->data_[1][2];
371			m(2, 2) = this->data_[0][0]this->data_[1][1] - this->data_[0][1]this->data_[1][0];
372
373			m /= det;
374			}
375	gezelter	507	return m;
376			}
377	tim	883
378			SquareMatrix3<Real> transpose() const{
379			SquareMatrix3<Real> result;
380
381			for (unsigned int i = 0; i < 3; i++)
382			for (unsigned int j = 0; j < 3; j++)
383			result(j, i) = this->data_[i][j];
384
385			return result;
386			}
387	gezelter	507	/**
388			* Extract the eigenvalues and eigenvectors from a 3x3 matrix.
389			* The eigenvectors (the columns of V) will be normalized.
390			* The eigenvectors are aligned optimally with the x, y, and z
391			* axes respectively.
392			* @param a symmetric matrix whose eigenvectors are to be computed. On return, the matrix is
393			* overwritten
394			* @param w will contain the eigenvalues of the matrix On return of this function
395			* @param v the columns of this matrix will contain the eigenvectors. The eigenvectors are
396			* normalized and mutually orthogonal.
397			* @warning a will be overwritten
398			*/
399			static void diagonalize(SquareMatrix3<Real>& a, Vector3<Real>& w, SquareMatrix3<Real>& v);
400			};
401			/*=========================================================================
402	tim	76
403	tim	123	Program: Visualization Toolkit
404			Module: $RCSfile: SquareMatrix3.hpp,v $
405	tim	99
406	tim	123	Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen
407			All rights reserved.
408			See Copyright.txt or http://www.kitware.com/Copyright.htm for details.
409	tim	101
410	gezelter	507	This software is distributed WITHOUT ANY WARRANTY; without even
411			the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
412			PURPOSE. See the above copyright notice for more information.
413	tim	101
414	gezelter	507	=========================================================================*/
415			template<typename Real>
416			void SquareMatrix3<Real>::diagonalize(SquareMatrix3<Real>& a, Vector3<Real>& w,
417			SquareMatrix3<Real>& v) {
418			int i,j,k,maxI;
419			Real tmp, maxVal;
420			Vector3<Real> v_maxI, v_k, v_j;
421	tim	101
422	gezelter	507	// diagonalize using Jacobi
423	gezelter	1610	SquareMatrix3<Real>::jacobi(a, w, v);
424	gezelter	507	// if all the eigenvalues are the same, return identity matrix
425			if (w[0] == w[1] && w[0] == w[2] ) {
426			v = SquareMatrix3<Real>::identity();
427			return;
428			}
429	tim	101
430	gezelter	507	// transpose temporarily, it makes it easier to sort the eigenvectors
431			v = v.transpose();
432	tim	123
433	gezelter	507	// if two eigenvalues are the same, re-orthogonalize to optimally line
434			// up the eigenvectors with the x, y, and z axes
435			for (i = 0; i < 3; i++) {
436			if (w((i+1)%3) == w((i+2)%3)) {// two eigenvalues are the same
437			// find maximum element of the independant eigenvector
438			maxVal = fabs(v(i, 0));
439			maxI = 0;
440			for (j = 1; j < 3; j++) {
441			if (maxVal < (tmp = fabs(v(i, j)))){
442			maxVal = tmp;
443			maxI = j;
444			}
445			}
446	tim	123
447	gezelter	507	// swap the eigenvector into its proper position
448			if (maxI != i) {
449			tmp = w(maxI);
450			w(maxI) = w(i);
451			w(i) = tmp;
452	tim	101
453	gezelter	507	v.swapRow(i, maxI);
454			}
455			// maximum element of eigenvector should be positive
456			if (v(maxI, maxI) < 0) {
457			v(maxI, 0) = -v(maxI, 0);
458			v(maxI, 1) = -v(maxI, 1);
459			v(maxI, 2) = -v(maxI, 2);
460			}
461	tim	101
462	gezelter	507	// re-orthogonalize the other two eigenvectors
463			j = (maxI+1)%3;
464			k = (maxI+2)%3;
465	tim	101
466	gezelter	507	v(j, 0) = 0.0;
467			v(j, 1) = 0.0;
468			v(j, 2) = 0.0;
469			v(j, j) = 1.0;
470	tim	101
471	gezelter	507	/** @todo */
472			v_maxI = v.getRow(maxI);
473			v_j = v.getRow(j);
474			v_k = cross(v_maxI, v_j);
475			v_k.normalize();
476			v_j = cross(v_k, v_maxI);
477			v.setRow(j, v_j);
478			v.setRow(k, v_k);
479	tim	101
480
481	gezelter	507	// transpose vectors back to columns
482			v = v.transpose();
483			return;
484			}
485			}
486	tim	101
487	gezelter	507	// the three eigenvalues are different, just sort the eigenvectors
488			// to align them with the x, y, and z axes
489	tim	101
490	gezelter	507	// find the vector with the largest x element, make that vector
491			// the first vector
492			maxVal = fabs(v(0, 0));
493			maxI = 0;
494			for (i = 1; i < 3; i++) {
495			if (maxVal < (tmp = fabs(v(i, 0)))) {
496			maxVal = tmp;
497			maxI = i;
498			}
499			}
500	tim	101
501	gezelter	507	// swap eigenvalue and eigenvector
502			if (maxI != 0) {
503			tmp = w(maxI);
504			w(maxI) = w(0);
505			w(0) = tmp;
506			v.swapRow(maxI, 0);
507			}
508			// do the same for the y element
509			if (fabs(v(1, 1)) < fabs(v(2, 1))) {
510			tmp = w(2);
511			w(2) = w(1);
512			w(1) = tmp;
513			v.swapRow(2, 1);
514			}
515	tim	101
516	gezelter	507	// ensure that the sign of the eigenvectors is correct
517			for (i = 0; i < 2; i++) {
518			if (v(i, i) < 0) {
519			v(i, 0) = -v(i, 0);
520			v(i, 1) = -v(i, 1);
521			v(i, 2) = -v(i, 2);
522			}
523			}
524	tim	70
525	gezelter	507	// set sign of final eigenvector to ensure that determinant is positive
526			if (v.determinant() < 0) {
527			v(2, 0) = -v(2, 0);
528			v(2, 1) = -v(2, 1);
529			v(2, 2) = -v(2, 2);
530	tim	123	}
531	gezelter	246
532	gezelter	507	// transpose the eigenvectors back again
533			v = v.transpose();
534			return ;
535			}
536	gezelter	246
537	gezelter	507	/**
538			* Return the multiplication of two matrixes (m1 * m2).
539			* @return the multiplication of two matrixes
540			* @param m1 the first matrix
541			* @param m2 the second matrix
542			*/
543			template<typename Real>
544			inline SquareMatrix3<Real> operator *(const SquareMatrix3<Real>& m1, const SquareMatrix3<Real>& m2) {
545			SquareMatrix3<Real> result;
546	gezelter	246
547	gezelter	507	for (unsigned int i = 0; i < 3; i++)
548			for (unsigned int j = 0; j < 3; j++)
549			for (unsigned int k = 0; k < 3; k++)
550			result(i, j) += m1(i, k) * m2(k, j);
551	gezelter	246
552	gezelter	507	return result;
553			}
554	gezelter	246
555	gezelter	507	template<typename Real>
556			inline SquareMatrix3<Real> outProduct(const Vector3<Real>& v1, const Vector3<Real>& v2) {
557			SquareMatrix3<Real> result;
558
559			for (unsigned int i = 0; i < 3; i++) {
560			for (unsigned int j = 0; j < 3; j++) {
561			result(i, j) = v1[i] * v2[j];
562			}
563			}
564	gezelter	246
565	gezelter	507	return result;
566			}
567	gezelter	246
568
569	tim	963	typedef SquareMatrix3<RealType> Mat3x3d;
570			typedef SquareMatrix3<RealType> RotMat3x3d;
571	tim	93
572	gezelter	2000	const Mat3x3d M3Zero(0.0);
573
574
575	gezelter	1390	} //namespace OpenMD
576	tim	93	#endif // MATH_SQUAREMATRIX_HPP
577	tim	123