--- trunk/src/math/SquareMatrix3.hpp 2004/10/19 23:01:03 113 +++ trunk/src/math/SquareMatrix3.hpp 2005/03/01 20:10:14 385 @@ -1,35 +1,51 @@ -/* - * Copyright (C) 2000-2004 Object Oriented Parallel Simulation Engine (OOPSE) project - * - * Contact: oopse@oopse.org - * - * This program is free software; you can redistribute it and/or - * modify it under the terms of the GNU Lesser General Public License - * as published by the Free Software Foundation; either version 2.1 - * of the License, or (at your option) any later version. - * All we ask is that proper credit is given for our work, which includes - * - but is not limited to - adding the above copyright notice to the beginning - * of your source code files, and to any copyright notice that you may distribute - * with programs based on this work. - * - * This program is distributed in the hope that it will be useful, - * but WITHOUT ANY WARRANTY; without even the implied warranty of - * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the - * GNU Lesser General Public License for more details. - * - * You should have received a copy of the GNU Lesser General Public License - * along with this program; if not, write to the Free Software - * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. + /* + * 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. Acknowledgement of the program authors must be made in any + * publication of scientific results based in part on use of the + * program. An acceptable form of acknowledgement is citation of + * the article in which the program was described (Matthew + * A. Meineke, Charles F. Vardeman II, Teng Lin, Christopher + * J. Fennell and J. Daniel Gezelter, "OOPSE: An Object-Oriented + * Parallel Simulation Engine for Molecular Dynamics," + * J. Comput. Chem. 26, pp. 252-271 (2005)) + * + * 2. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * + * 3. 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. */ - + /** * @file SquareMatrix3.hpp * @author Teng Lin * @date 10/11/2004 * @version 1.0 */ -#ifndef MATH_SQUAREMATRIX3_HPP + #ifndef MATH_SQUAREMATRIX3_HPP #define MATH_SQUAREMATRIX3_HPP #include "Quaternion.hpp" @@ -41,15 +57,27 @@ namespace oopse { template class SquareMatrix3 : public SquareMatrix { public: + + typedef Real ElemType; + typedef Real* ElemPoinerType; /** default constructor */ SquareMatrix3() : SquareMatrix() { } + /** Constructs and initializes every element of this matrix to a scalar */ + SquareMatrix3(Real s) : SquareMatrix(s){ + } + + /** Constructs and initializes from an array */ + SquareMatrix3(Real* array) : SquareMatrix(array){ + } + + /** copy constructor */ SquareMatrix3(const SquareMatrix& m) : SquareMatrix(m) { } - + SquareMatrix3( const Vector3& eulerAngles) { setupRotMat(eulerAngles); } @@ -75,6 +103,12 @@ namespace oopse { return *this; } + + SquareMatrix3& operator =(const Quaternion& q) { + this->setupRotMat(q); + return *this; + } + /** * Sets this matrix to a rotation matrix by three euler angles * @ param euler @@ -100,17 +134,17 @@ namespace oopse { ctheta = cos(theta); cpsi = cos(psi); - data_[0][0] = cpsi * cphi - ctheta * sphi * spsi; - data_[0][1] = cpsi * sphi + ctheta * cphi * spsi; - data_[0][2] = spsi * stheta; + this->data_[0][0] = cpsi * cphi - ctheta * sphi * spsi; + this->data_[0][1] = cpsi * sphi + ctheta * cphi * spsi; + this->data_[0][2] = spsi * stheta; - data_[1][0] = -spsi * ctheta - ctheta * sphi * cpsi; - data_[1][1] = -spsi * stheta + ctheta * cphi * cpsi; - data_[1][2] = cpsi * 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; - data_[2][0] = stheta * sphi; - data_[2][1] = -stheta * cphi; - data_[2][2] = ctheta; + this->data_[2][0] = stheta * sphi; + this->data_[2][1] = -stheta * cphi; + this->data_[2][2] = ctheta; } @@ -143,40 +177,40 @@ namespace oopse { Quaternion q; Real t, s; Real ad1, ad2, ad3; - t = data_[0][0] + data_[1][1] + data_[2][2] + 1.0; + t = this->data_[0][0] + this->data_[1][1] + this->data_[2][2] + 1.0; if( t > 0.0 ){ s = 0.5 / sqrt( t ); q[0] = 0.25 / s; - q[1] = (data_[1][2] - data_[2][1]) * s; - q[2] = (data_[2][0] - data_[0][2]) * s; - q[3] = (data_[0][1] - data_[1][0]) * 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 = fabs( data_[0][0] ); - ad2 = fabs( data_[1][1] ); - ad3 = fabs( data_[2][2] ); + ad1 = fabs( this->data_[0][0] ); + ad2 = fabs( this->data_[1][1] ); + ad3 = fabs( this->data_[2][2] ); if( ad1 >= ad2 && ad1 >= ad3 ){ - s = 2.0 * sqrt( 1.0 + data_[0][0] - data_[1][1] - data_[2][2] ); - q[0] = (data_[1][2] + data_[2][1]) / s; + s = 2.0 * 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] = 0.5 / s; - q[2] = (data_[0][1] + data_[1][0]) / s; - q[3] = (data_[0][2] + data_[2][0]) / 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 = sqrt( 1.0 + data_[1][1] - data_[0][0] - data_[2][2] ) * 2.0; - q[0] = (data_[0][2] + data_[2][0]) / s; - q[1] = (data_[0][1] + data_[1][0]) / s; + s = sqrt( 1.0 + this->data_[1][1] - this->data_[0][0] - this->data_[2][2] ) * 2.0; + q[0] = (this->data_[0][2] + this->data_[2][0]) / s; + q[1] = (this->data_[0][1] + this->data_[1][0]) / s; q[2] = 0.5 / s; - q[3] = (data_[1][2] + data_[2][1]) / s; + q[3] = (this->data_[1][2] + this->data_[2][1]) / s; } else { - s = sqrt( 1.0 + data_[2][2] - data_[0][0] - data_[1][1] ) * 2.0; - q[0] = (data_[0][1] + data_[1][0]) / s; - q[1] = (data_[0][2] + data_[2][0]) / s; - q[2] = (data_[1][2] + data_[2][1]) / s; + s = sqrt( 1.0 + this->data_[2][2] - this->data_[0][0] - this->data_[1][1] ) * 2.0; + 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] = 0.5 / s; } } @@ -197,13 +231,16 @@ namespace oopse { */ Vector3 toEulerAngles() { Vector3 myEuler; - Real phi,theta,psi,eps; - Real ctheta,stheta; + Real phi; + Real theta; + Real psi; + Real ctheta; + Real stheta; // set the tolerance for Euler angles and rotation elements - theta = acos(std::min(1.0, std::max(-1.0,data_[2][2]))); - ctheta = data_[2][2]; + theta = acos(std::min(1.0, std::max(-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 @@ -216,12 +253,12 @@ namespace oopse { if (fabs(stheta) <= oopse::epsilon){ psi = 0.0; - phi = atan2(-data_[1][0], data_[0][0]); + phi = atan2(-this->data_[1][0], this->data_[0][0]); } // we only have one unique solution else{ - phi = atan2(data_[2][0], -data_[2][1]); - psi = atan2(data_[0][2], data_[1][2]); + 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 @@ -242,19 +279,24 @@ namespace oopse { Real determinant() const { Real x,y,z; - x = data_[0][0] * (data_[1][1] * data_[2][2] - data_[1][2] * data_[2][1]); - y = data_[0][1] * (data_[1][2] * data_[2][0] - data_[1][0] * data_[2][2]); - z = data_[0][2] * (data_[1][0] * data_[2][1] - data_[1][1] * data_[2][0]); + 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 inverse() { + SquareMatrix3 inverse() const { SquareMatrix3 m; double det = determinant(); if (fabs(det) <= oopse::epsilon) { @@ -262,144 +304,204 @@ namespace oopse { //"This is a runtime or a programming error in your application."); } - m(0, 0) = data_[1][1]*data_[2][2] - data_[1][2]*data_[2][1]; - m(1, 0) = data_[1][2]*data_[2][0] - data_[1][0]*data_[2][2]; - m(2, 0) = data_[1][0]*data_[2][1] - data_[1][1]*data_[2][0]; - m(0, 1) = data_[2][1]*data_[0][2] - data_[2][2]*data_[0][1]; - m(1, 1) = data_[2][2]*data_[0][0] - data_[2][0]*data_[0][2]; - m(2, 1) = data_[2][0]*data_[0][1] - data_[2][1]*data_[0][0]; - m(0, 2) = data_[0][1]*data_[1][2] - data_[0][2]*data_[1][1]; - m(1, 2) = data_[0][2]*data_[1][0] - data_[0][0]*data_[1][2]; - m(2, 2) = data_[0][0]*data_[1][1] - data_[0][1]*data_[1][0]; + 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; } + /** + * 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& a, Vector3& w, SquareMatrix3& v); + }; +/*========================================================================= - void diagonalize(SquareMatrix3& a, Vector3& w, SquareMatrix3& v) { - int i,j,k,maxI; - Real tmp, maxVal; - Vector3 v_maxI, v_k, v_j; + Program: Visualization Toolkit + Module: $RCSfile: SquareMatrix3.hpp,v $ - // diagonalize using Jacobi - jacobi(a, w, v); + Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen + All rights reserved. + See Copyright.txt or http://www.kitware.com/Copyright.htm for details. - // if all the eigenvalues are the same, return identity matrix - if (w[0] == w[1] && w[0] == w[2] ) { - v = SquareMatrix3::identity(); - return; + 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 + void SquareMatrix3::diagonalize(SquareMatrix3& a, Vector3& w, + SquareMatrix3& v) { + int i,j,k,maxI; + Real tmp, maxVal; + Vector3 v_maxI, v_k, v_j; + + // diagonalize using Jacobi + jacobi(a, w, v); + // if all the eigenvalues are the same, return identity matrix + if (w[0] == w[1] && w[0] == w[2] ) { + v = SquareMatrix3::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; - // 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); + } - 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; - // 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; - 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); - /** @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; + } + } - // 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 - // 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; + } + } - // 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); + } - // 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); + } + } - // 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); + } - // 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 ; + } - // 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 + inline SquareMatrix3 operator *(const SquareMatrix3& m1, const SquareMatrix3& m2) { + SquareMatrix3 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 + inline SquareMatrix3 outProduct(const Vector3& v1, const Vector3& v2) { + SquareMatrix3 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 Mat3x3d; typedef SquareMatrix3 RotMat3x3d; } //namespace oopse #endif // MATH_SQUAREMATRIX_HPP +