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]  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 <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:	1753
Committed:	Tue Jun 12 13:20:28 2012 UTC (12 years, 10 months ago) by gezelter
File size:	18652 byte(s)
Log Message:	Added a double dot tensor contraction.
#	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	gezelter	1665	* [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	tim	895	#include <vector>
52	tim	93	#include "Quaternion.hpp"
53	tim	70	#include "SquareMatrix.hpp"
54	tim	93	#include "Vector3.hpp"
55	tim	451	#include "utils/NumericConstant.hpp"
56	gezelter	1390	namespace OpenMD {
57	tim	70
58	gezelter	507	template<typename Real>
59			class SquareMatrix3 : public SquareMatrix<Real, 3> {
60			public:
61	tim	137
62	gezelter	507	typedef Real ElemType;
63			typedef Real* ElemPoinerType;
64	tim	70
65	gezelter	507	/** default constructor */
66			SquareMatrix3() : SquareMatrix<Real, 3>() {
67			}
68	tim	70
69	gezelter	507	/** Constructs and initializes every element of this matrix to a scalar */
70			SquareMatrix3(Real s) : SquareMatrix<Real,3>(s){
71			}
72	tim	151
73	gezelter	507	/** Constructs and initializes from an array */
74			SquareMatrix3(Real* array) : SquareMatrix<Real,3>(array){
75			}
76	tim	151
77
78	gezelter	507	/** copy constructor */
79			SquareMatrix3(const SquareMatrix<Real, 3>& m) : SquareMatrix<Real, 3>(m) {
80			}
81	gezelter	246
82	gezelter	507	SquareMatrix3( const Vector3<Real>& eulerAngles) {
83			setupRotMat(eulerAngles);
84			}
85	tim	93
86	gezelter	507	SquareMatrix3(Real phi, Real theta, Real psi) {
87			setupRotMat(phi, theta, psi);
88			}
89	tim	93
90	gezelter	507	SquareMatrix3(const Quaternion<Real>& q) {
91			setupRotMat(q);
92	tim	113
93	gezelter	507	}
94	tim	93
95	gezelter	507	SquareMatrix3(Real w, Real x, Real y, Real z) {
96			setupRotMat(w, x, y, z);
97			}
98	tim	93
99	gezelter	507	/** copy assignment operator */
100			SquareMatrix3<Real>& operator =(const SquareMatrix<Real, 3>& m) {
101			if (this == &m)
102			return *this;
103			SquareMatrix<Real, 3>::operator=(m);
104			return *this;
105			}
106	tim	76
107	gezelter	246
108	gezelter	507	SquareMatrix3<Real>& operator =(const Quaternion<Real>& q) {
109			this->setupRotMat(q);
110			return *this;
111			}
112	gezelter	246
113	gezelter	1753
114	gezelter	507	/**
115			* Sets this matrix to a rotation matrix by three euler angles
116			* @ param euler
117			*/
118			void setupRotMat(const Vector3<Real>& eulerAngles) {
119			setupRotMat(eulerAngles[0], eulerAngles[1], eulerAngles[2]);
120			}
121	tim	76
122	gezelter	507	/**
123			* Sets this matrix to a rotation matrix by three euler angles
124			* @param phi
125			* @param theta
126			* @psi theta
127			*/
128			void setupRotMat(Real phi, Real theta, Real psi) {
129			Real sphi, stheta, spsi;
130			Real cphi, ctheta, cpsi;
131	tim	76
132	gezelter	507	sphi = sin(phi);
133			stheta = sin(theta);
134			spsi = sin(psi);
135			cphi = cos(phi);
136			ctheta = cos(theta);
137			cpsi = cos(psi);
138	tim	76
139	gezelter	507	this->data_[0][0] = cpsi * cphi - ctheta * sphi * spsi;
140			this->data_[0][1] = cpsi * sphi + ctheta * cphi * spsi;
141			this->data_[0][2] = spsi * stheta;
142	tim	93
143	gezelter	507	this->data_[1][0] = -spsi * ctheta - ctheta * sphi * cpsi;
144			this->data_[1][1] = -spsi * stheta + ctheta * cphi * cpsi;
145			this->data_[1][2] = cpsi * stheta;
146	tim	93
147	gezelter	507	this->data_[2][0] = stheta * sphi;
148			this->data_[2][1] = -stheta * cphi;
149			this->data_[2][2] = ctheta;
150			}
151	tim	93
152
153	gezelter	507	/**
154			* Sets this matrix to a rotation matrix by quaternion
155			* @param quat
156			*/
157			void setupRotMat(const Quaternion<Real>& quat) {
158			setupRotMat(quat.w(), quat.x(), quat.y(), quat.z());
159			}
160	tim	76
161	gezelter	507	/**
162			* Sets this matrix to a rotation matrix by quaternion
163			* @param w the first element
164			* @param x the second element
165			* @param y the third element
166			* @param z the fourth element
167			*/
168			void setupRotMat(Real w, Real x, Real y, Real z) {
169			Quaternion<Real> q(w, x, y, z);
170			*this = q.toRotationMatrix3();
171			}
172	tim	76
173	tim	891	void setupSkewMat(Vector3<Real> v) {
174			setupSkewMat(v[0], v[1], v[2]);
175			}
176
177			void setupSkewMat(Real v1, Real v2, Real v3) {
178			this->data_[0][0] = 0;
179			this->data_[0][1] = -v3;
180			this->data_[0][2] = v2;
181			this->data_[1][0] = v3;
182			this->data_[1][1] = 0;
183			this->data_[1][2] = -v1;
184			this->data_[2][0] = -v2;
185			this->data_[2][1] = v1;
186			this->data_[2][2] = 0;
187
188
189			}
190
191
192	gezelter	507	/**
193			* Returns the quaternion from this rotation matrix
194			* @return the quaternion from this rotation matrix
195			* @exception invalid rotation matrix
196			*/
197			Quaternion<Real> toQuaternion() {
198			Quaternion<Real> q;
199			Real t, s;
200			Real ad1, ad2, ad3;
201			t = this->data_[0][0] + this->data_[1][1] + this->data_[2][2] + 1.0;
202	tim	76
203	tim	637	if( t > NumericConstant::epsilon ){
204	tim	93
205	gezelter	507	s = 0.5 / sqrt( t );
206			q[0] = 0.25 / s;
207			q[1] = (this->data_[1][2] - this->data_[2][1]) * s;
208			q[2] = (this->data_[2][0] - this->data_[0][2]) * s;
209			q[3] = (this->data_[0][1] - this->data_[1][0]) * s;
210			} else {
211	tim	93
212	tim	633	ad1 = this->data_[0][0];
213			ad2 = this->data_[1][1];
214			ad3 = this->data_[2][2];
215	tim	93
216	gezelter	507	if( ad1 >= ad2 && ad1 >= ad3 ){
217	tim	93
218	gezelter	507	s = 0.5 / sqrt( 1.0 + this->data_[0][0] - this->data_[1][1] - this->data_[2][2] );
219			q[0] = (this->data_[1][2] - this->data_[2][1]) * s;
220			q[1] = 0.25 / s;
221			q[2] = (this->data_[0][1] + this->data_[1][0]) * s;
222			q[3] = (this->data_[0][2] + this->data_[2][0]) * s;
223			} else if ( ad2 >= ad1 && ad2 >= ad3 ) {
224			s = 0.5 / sqrt( 1.0 + this->data_[1][1] - this->data_[0][0] - this->data_[2][2] );
225			q[0] = (this->data_[2][0] - this->data_[0][2] ) * s;
226			q[1] = (this->data_[0][1] + this->data_[1][0]) * s;
227			q[2] = 0.25 / s;
228			q[3] = (this->data_[1][2] + this->data_[2][1]) * s;
229			} else {
230	tim	93
231	gezelter	507	s = 0.5 / sqrt( 1.0 + this->data_[2][2] - this->data_[0][0] - this->data_[1][1] );
232			q[0] = (this->data_[0][1] - this->data_[1][0]) * s;
233			q[1] = (this->data_[0][2] + this->data_[2][0]) * s;
234			q[2] = (this->data_[1][2] + this->data_[2][1]) * s;
235			q[3] = 0.25 / s;
236			}
237			}
238	tim	93
239	gezelter	507	return q;
240	tim	93
241	gezelter	507	}
242	tim	93
243	gezelter	507	/**
244			* Returns the euler angles from this rotation matrix
245			* @return the euler angles in a vector
246			* @exception invalid rotation matrix
247			* We use so-called "x-convention", which is the most common definition.
248	cli2	1360	* In this convention, the rotation given by Euler angles (phi, theta,
249			* psi), where the first rotation is by an angle phi about the z-axis,
250			* the second is by an angle theta (0 <= theta <= 180) about the x-axis,
251			* and the third is by an angle psi about the z-axis (again).
252	gezelter	507	*/
253			Vector3<Real> toEulerAngles() {
254			Vector3<Real> myEuler;
255			Real phi;
256			Real theta;
257			Real psi;
258			Real ctheta;
259			Real stheta;
260	tim	93
261	gezelter	507	// set the tolerance for Euler angles and rotation elements
262	tim	93
263	tim	963	theta = acos(std::min((RealType)1.0, std::max((RealType)-1.0,this->data_[2][2])));
264	gezelter	507	ctheta = this->data_[2][2];
265			stheta = sqrt(1.0 - ctheta * ctheta);
266	tim	93
267	cli2	1360	// when sin(theta) is close to 0, we need to consider
268			// singularity In this case, we can assign an arbitary value to
269			// phi (or psi), and then determine the psi (or phi) or
270			// vice-versa. We'll assume that phi always gets the rotation,
271			// and psi is 0 in cases of singularity.
272	gezelter	507	// we use atan2 instead of atan, since atan2 will give us -Pi to Pi.
273	cli2	1360	// Since 0 <= theta <= 180, sin(theta) will be always
274			// non-negative. Therefore, it will never change the sign of both of
275			// the parameters passed to atan2.
276	tim	93
277	cli2	1360	if (fabs(stheta) < 1e-6){
278	gezelter	507	psi = 0.0;
279			phi = atan2(-this->data_[1][0], this->data_[0][0]);
280			}
281			// we only have one unique solution
282			else{
283			phi = atan2(this->data_[2][0], -this->data_[2][1]);
284			psi = atan2(this->data_[0][2], this->data_[1][2]);
285			}
286	tim	93
287	gezelter	507	//wrap phi and psi, make sure they are in the range from 0 to 2*Pi
288			if (phi < 0)
289	cli2	1360	phi += 2.0 * M_PI;
290	tim	93
291	gezelter	507	if (psi < 0)
292	cli2	1360	psi += 2.0 * M_PI;
293	tim	93
294	gezelter	507	myEuler[0] = phi;
295			myEuler[1] = theta;
296			myEuler[2] = psi;
297	tim	93
298	gezelter	507	return myEuler;
299			}
300	tim	70
301	gezelter	507	/** Returns the determinant of this matrix. */
302			Real determinant() const {
303			Real x,y,z;
304	tim	101
305	gezelter	507	x = this->data_[0][0] * (this->data_[1][1] * this->data_[2][2] - this->data_[1][2] * this->data_[2][1]);
306			y = this->data_[0][1] * (this->data_[1][2] * this->data_[2][0] - this->data_[1][0] * this->data_[2][2]);
307			z = this->data_[0][2] * (this->data_[1][0] * this->data_[2][1] - this->data_[1][1] * this->data_[2][0]);
308	tim	101
309	gezelter	507	return(x + y + z);
310			}
311	gezelter	246
312	gezelter	507	/** Returns the trace of this matrix. */
313			Real trace() const {
314			return this->data_[0][0] + this->data_[1][1] + this->data_[2][2];
315			}
316	tim	101
317	gezelter	507	/**
318			* Sets the value of this matrix to the inversion of itself.
319			* @note since simple algorithm can be applied to inverse the 3 by 3 matrix, we hide the
320			* implementation of inverse in SquareMatrix class
321			*/
322			SquareMatrix3<Real> inverse() const {
323			SquareMatrix3<Real> m;
324	tim	963	RealType det = determinant();
325	gezelter	1390	if (fabs(det) <= OpenMD::epsilon) {
326	gezelter	507	//"The method was called on a matrix with \|determinant\| <= 1e-6.",
327			//"This is a runtime or a programming error in your application.");
328	tim	895	std::vector<int> zeroDiagElementIndex;
329			for (int i =0; i < 3; ++i) {
330	gezelter	1390	if (fabs(this->data_[i][i]) <= OpenMD::epsilon) {
331	tim	895	zeroDiagElementIndex.push_back(i);
332			}
333			}
334	tim	70
335	tim	895	if (zeroDiagElementIndex.size() == 2) {
336			int index = zeroDiagElementIndex[0];
337			m(index, index) = 1.0 / this->data_[index][index];
338			}else if (zeroDiagElementIndex.size() == 1) {
339	tim	101
340	tim	895	int a = (zeroDiagElementIndex[0] + 1) % 3;
341			int b = (zeroDiagElementIndex[0] + 2) %3;
342	tim	963	RealType denom = this->data_[a][a] * this->data_[b][b] - this->data_[b][a]*this->data_[a][b];
343	tim	895	m(a, a) = this->data_[b][b] /denom;
344			m(b, a) = -this->data_[b][a]/denom;
345
346			m(a,b) = -this->data_[a][b]/denom;
347			m(b, b) = this->data_[a][a]/denom;
348
349			}
350
351			/*
352			for(std::vector<int>::iterator iter = zeroDiagElementIndex.begin(); iter != zeroDiagElementIndex.end() ++iter) {
353	gezelter	1390	if (this->data_[iter][0] > OpenMD::epsilon \|\| this->data_[iter][1] \|\|this->data_[*iter][2] \|\|
354			this->data_[0][iter] > OpenMD::epsilon \|\| this->data_[1][iter] \|\|this->data_[2][*iter] ) {
355	tim	895	std::cout << "can not inverse matrix" << std::endl;
356			}
357			}
358			*/
359			} else {
360
361			m(0, 0) = this->data_[1][1]this->data_[2][2] - this->data_[1][2]this->data_[2][1];
362			m(1, 0) = this->data_[1][2]this->data_[2][0] - this->data_[1][0]this->data_[2][2];
363			m(2, 0) = this->data_[1][0]this->data_[2][1] - this->data_[1][1]this->data_[2][0];
364			m(0, 1) = this->data_[2][1]this->data_[0][2] - this->data_[2][2]this->data_[0][1];
365			m(1, 1) = this->data_[2][2]this->data_[0][0] - this->data_[2][0]this->data_[0][2];
366			m(2, 1) = this->data_[2][0]this->data_[0][1] - this->data_[2][1]this->data_[0][0];
367			m(0, 2) = this->data_[0][1]this->data_[1][2] - this->data_[0][2]this->data_[1][1];
368			m(1, 2) = this->data_[0][2]this->data_[1][0] - this->data_[0][0]this->data_[1][2];
369			m(2, 2) = this->data_[0][0]this->data_[1][1] - this->data_[0][1]this->data_[1][0];
370
371			m /= det;
372			}
373	gezelter	507	return m;
374			}
375	tim	883
376			SquareMatrix3<Real> transpose() const{
377			SquareMatrix3<Real> result;
378
379			for (unsigned int i = 0; i < 3; i++)
380			for (unsigned int j = 0; j < 3; j++)
381			result(j, i) = this->data_[i][j];
382
383			return result;
384			}
385	gezelter	507	/**
386			* Extract the eigenvalues and eigenvectors from a 3x3 matrix.
387			* The eigenvectors (the columns of V) will be normalized.
388			* The eigenvectors are aligned optimally with the x, y, and z
389			* axes respectively.
390			* @param a symmetric matrix whose eigenvectors are to be computed. On return, the matrix is
391			* overwritten
392			* @param w will contain the eigenvalues of the matrix On return of this function
393			* @param v the columns of this matrix will contain the eigenvectors. The eigenvectors are
394			* normalized and mutually orthogonal.
395			* @warning a will be overwritten
396			*/
397			static void diagonalize(SquareMatrix3<Real>& a, Vector3<Real>& w, SquareMatrix3<Real>& v);
398			};
399			/*=========================================================================
400	tim	76
401	tim	123	Program: Visualization Toolkit
402			Module: $RCSfile: SquareMatrix3.hpp,v $
403	tim	99
404	tim	123	Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen
405			All rights reserved.
406			See Copyright.txt or http://www.kitware.com/Copyright.htm for details.
407	tim	101
408	gezelter	507	This software is distributed WITHOUT ANY WARRANTY; without even
409			the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
410			PURPOSE. See the above copyright notice for more information.
411	tim	101
412	gezelter	507	=========================================================================*/
413			template<typename Real>
414			void SquareMatrix3<Real>::diagonalize(SquareMatrix3<Real>& a, Vector3<Real>& w,
415			SquareMatrix3<Real>& v) {
416			int i,j,k,maxI;
417			Real tmp, maxVal;
418			Vector3<Real> v_maxI, v_k, v_j;
419	tim	101
420	gezelter	507	// diagonalize using Jacobi
421	gezelter	1600	SquareMatrix3<Real>::jacobi(a, w, v);
422	gezelter	507	// if all the eigenvalues are the same, return identity matrix
423			if (w[0] == w[1] && w[0] == w[2] ) {
424			v = SquareMatrix3<Real>::identity();
425			return;
426			}
427	tim	101
428	gezelter	507	// transpose temporarily, it makes it easier to sort the eigenvectors
429			v = v.transpose();
430	tim	123
431	gezelter	507	// if two eigenvalues are the same, re-orthogonalize to optimally line
432			// up the eigenvectors with the x, y, and z axes
433			for (i = 0; i < 3; i++) {
434			if (w((i+1)%3) == w((i+2)%3)) {// two eigenvalues are the same
435			// find maximum element of the independant eigenvector
436			maxVal = fabs(v(i, 0));
437			maxI = 0;
438			for (j = 1; j < 3; j++) {
439			if (maxVal < (tmp = fabs(v(i, j)))){
440			maxVal = tmp;
441			maxI = j;
442			}
443			}
444	tim	123
445	gezelter	507	// swap the eigenvector into its proper position
446			if (maxI != i) {
447			tmp = w(maxI);
448			w(maxI) = w(i);
449			w(i) = tmp;
450	tim	101
451	gezelter	507	v.swapRow(i, maxI);
452			}
453			// maximum element of eigenvector should be positive
454			if (v(maxI, maxI) < 0) {
455			v(maxI, 0) = -v(maxI, 0);
456			v(maxI, 1) = -v(maxI, 1);
457			v(maxI, 2) = -v(maxI, 2);
458			}
459	tim	101
460	gezelter	507	// re-orthogonalize the other two eigenvectors
461			j = (maxI+1)%3;
462			k = (maxI+2)%3;
463	tim	101
464	gezelter	507	v(j, 0) = 0.0;
465			v(j, 1) = 0.0;
466			v(j, 2) = 0.0;
467			v(j, j) = 1.0;
468	tim	101
469	gezelter	507	/** @todo */
470			v_maxI = v.getRow(maxI);
471			v_j = v.getRow(j);
472			v_k = cross(v_maxI, v_j);
473			v_k.normalize();
474			v_j = cross(v_k, v_maxI);
475			v.setRow(j, v_j);
476			v.setRow(k, v_k);
477	tim	101
478
479	gezelter	507	// transpose vectors back to columns
480			v = v.transpose();
481			return;
482			}
483			}
484	tim	101
485	gezelter	507	// the three eigenvalues are different, just sort the eigenvectors
486			// to align them with the x, y, and z axes
487	tim	101
488	gezelter	507	// find the vector with the largest x element, make that vector
489			// the first vector
490			maxVal = fabs(v(0, 0));
491			maxI = 0;
492			for (i = 1; i < 3; i++) {
493			if (maxVal < (tmp = fabs(v(i, 0)))) {
494			maxVal = tmp;
495			maxI = i;
496			}
497			}
498	tim	101
499	gezelter	507	// swap eigenvalue and eigenvector
500			if (maxI != 0) {
501			tmp = w(maxI);
502			w(maxI) = w(0);
503			w(0) = tmp;
504			v.swapRow(maxI, 0);
505			}
506			// do the same for the y element
507			if (fabs(v(1, 1)) < fabs(v(2, 1))) {
508			tmp = w(2);
509			w(2) = w(1);
510			w(1) = tmp;
511			v.swapRow(2, 1);
512			}
513	tim	101
514	gezelter	507	// ensure that the sign of the eigenvectors is correct
515			for (i = 0; i < 2; i++) {
516			if (v(i, i) < 0) {
517			v(i, 0) = -v(i, 0);
518			v(i, 1) = -v(i, 1);
519			v(i, 2) = -v(i, 2);
520			}
521			}
522	tim	70
523	gezelter	507	// set sign of final eigenvector to ensure that determinant is positive
524			if (v.determinant() < 0) {
525			v(2, 0) = -v(2, 0);
526			v(2, 1) = -v(2, 1);
527			v(2, 2) = -v(2, 2);
528	tim	123	}
529	gezelter	246
530	gezelter	507	// transpose the eigenvectors back again
531			v = v.transpose();
532			return ;
533			}
534	gezelter	246
535	gezelter	507	/**
536			* Return the multiplication of two matrixes (m1 * m2).
537			* @return the multiplication of two matrixes
538			* @param m1 the first matrix
539			* @param m2 the second matrix
540			*/
541			template<typename Real>
542			inline SquareMatrix3<Real> operator *(const SquareMatrix3<Real>& m1, const SquareMatrix3<Real>& m2) {
543			SquareMatrix3<Real> result;
544	gezelter	246
545	gezelter	507	for (unsigned int i = 0; i < 3; i++)
546			for (unsigned int j = 0; j < 3; j++)
547			for (unsigned int k = 0; k < 3; k++)
548			result(i, j) += m1(i, k) * m2(k, j);
549	gezelter	246
550	gezelter	507	return result;
551			}
552	gezelter	246
553	gezelter	507	template<typename Real>
554			inline SquareMatrix3<Real> outProduct(const Vector3<Real>& v1, const Vector3<Real>& v2) {
555			SquareMatrix3<Real> result;
556
557			for (unsigned int i = 0; i < 3; i++) {
558			for (unsigned int j = 0; j < 3; j++) {
559			result(i, j) = v1[i] * v2[j];
560			}
561			}
562	gezelter	246
563	gezelter	507	return result;
564			}
565	gezelter	246
566
567	tim	963	typedef SquareMatrix3<RealType> Mat3x3d;
568			typedef SquareMatrix3<RealType> RotMat3x3d;
569	tim	93
570	gezelter	1390	} //namespace OpenMD
571	tim	93	#endif // MATH_SQUAREMATRIX_HPP
572	tim	123