--- trunk/src/math/SquareMatrix.hpp 2004/10/22 23:09:57 146 +++ branches/development/src/math/SquareMatrix.hpp 2010/07/09 23:08:25 1465 @@ -1,178 +1,215 @@ /* - * 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. Redistributions of source code must retain the above copyright + * notice, this list of conditions and the following disclaimer. + * + * 2. Redistributions in binary form must reproduce the above copyright + * notice, this list of conditions and the following disclaimer in the + * documentation and/or other materials provided with the + * distribution. + * + * This software is provided "AS IS," without a warranty of any + * kind. All express or implied conditions, representations and + * warranties, including any implied warranty of merchantability, + * fitness for a particular purpose or non-infringement, are hereby + * excluded. The University of Notre Dame and its licensors shall not + * be liable for any damages suffered by licensee as a result of + * using, modifying or distributing the software or its + * derivatives. In no event will the University of Notre Dame or its + * licensors be liable for any lost revenue, profit or data, or for + * direct, indirect, special, consequential, incidental or punitive + * damages, however caused and regardless of the theory of liability, + * arising out of the use of or inability to use software, even if the + * University of Notre Dame has been advised of the possibility of + * such damages. + * + * SUPPORT OPEN SCIENCE! If you use OpenMD or its source code in your + * research, please cite the appropriate papers when you publish your + * work. Good starting points are: + * + * [1] Meineke, et al., J. Comp. Chem. 26, 252-271 (2005). + * [2] Fennell & Gezelter, J. Chem. Phys. 124, 234104 (2006). + * [3] Sun, Lin & Gezelter, J. Chem. Phys. 128, 24107 (2008). + * [4] Vardeman & Gezelter, in progress (2009). */ - + /** * @file SquareMatrix.hpp * @author Teng Lin * @date 10/11/2004 * @version 1.0 */ - #ifndef MATH_SQUAREMATRIX_HPP +#ifndef MATH_SQUAREMATRIX_HPP #define MATH_SQUAREMATRIX_HPP #include "math/RectMatrix.hpp" +#include "utils/NumericConstant.hpp" -namespace oopse { +namespace OpenMD { - /** - * @class SquareMatrix SquareMatrix.hpp "math/SquareMatrix.hpp" - * @brief A square matrix class - * @template Real the element type - * @template Dim the dimension of the square matrix - */ - template - class SquareMatrix : public RectMatrix { - public: - typedef Real ElemType; - typedef Real* ElemPoinerType; + /** + * @class SquareMatrix SquareMatrix.hpp "math/SquareMatrix.hpp" + * @brief A square matrix class + * @template Real the element type + * @template Dim the dimension of the square matrix + */ + template + class SquareMatrix : public RectMatrix { + public: + typedef Real ElemType; + typedef Real* ElemPoinerType; - /** default constructor */ - SquareMatrix() { - for (unsigned int i = 0; i < Dim; i++) - for (unsigned int j = 0; j < Dim; j++) - data_[i][j] = 0.0; - } + /** default constructor */ + SquareMatrix() { + for (unsigned int i = 0; i < Dim; i++) + for (unsigned int j = 0; j < Dim; j++) + this->data_[i][j] = 0.0; + } - /** copy constructor */ - SquareMatrix(const RectMatrix& m) : RectMatrix(m) { - } + /** Constructs and initializes every element of this matrix to a scalar */ + SquareMatrix(Real s) : RectMatrix(s){ + } + + /** Constructs and initializes from an array */ + SquareMatrix(Real* array) : RectMatrix(array){ + } + + + /** copy constructor */ + SquareMatrix(const RectMatrix& m) : RectMatrix(m) { + } - /** copy assignment operator */ - SquareMatrix& operator =(const RectMatrix& m) { - RectMatrix::operator=(m); - return *this; - } + /** copy assignment operator */ + SquareMatrix& operator =(const RectMatrix& m) { + RectMatrix::operator=(m); + return *this; + } - /** Retunrs an identity matrix*/ + /** Retunrs an identity matrix*/ - static SquareMatrix identity() { - SquareMatrix m; + static SquareMatrix identity() { + SquareMatrix m; - for (unsigned int i = 0; i < Dim; i++) - for (unsigned int j = 0; j < Dim; j++) - if (i == j) - m(i, j) = 1.0; - else - m(i, j) = 0.0; + for (unsigned int i = 0; i < Dim; i++) + for (unsigned int j = 0; j < Dim; j++) + if (i == j) + m(i, j) = 1.0; + else + m(i, j) = 0.0; - return m; - } + return m; + } - /** - * Retunrs the inversion of this matrix. - * @todo need implementation - */ - SquareMatrix inverse() { - SquareMatrix result; + /** + * Retunrs the inversion of this matrix. + * @todo need implementation + */ + SquareMatrix inverse() { + SquareMatrix result; - return result; - } + return result; + } - /** - * Returns the determinant of this matrix. - * @todo need implementation - */ - Real determinant() const { - Real det; - return det; - } + /** + * Returns the determinant of this matrix. + * @todo need implementation + */ + Real determinant() const { + Real det; + return det; + } - /** Returns the trace of this matrix. */ - Real trace() const { - Real tmp = 0; + /** Returns the trace of this matrix. */ + Real trace() const { + Real tmp = 0; - for (unsigned int i = 0; i < Dim ; i++) - tmp += data_[i][i]; + for (unsigned int i = 0; i < Dim ; i++) + tmp += this->data_[i][i]; - return tmp; - } + return tmp; + } - /** Tests if this matrix is symmetrix. */ - bool isSymmetric() const { - for (unsigned int i = 0; i < Dim - 1; i++) - for (unsigned int j = i; j < Dim; j++) - if (fabs(data_[i][j] - data_[j][i]) > oopse::epsilon) - return false; + /** Tests if this matrix is symmetrix. */ + bool isSymmetric() const { + for (unsigned int i = 0; i < Dim - 1; i++) + for (unsigned int j = i; j < Dim; j++) + if (fabs(this->data_[i][j] - this->data_[j][i]) > epsilon) + return false; - return true; - } + return true; + } - /** Tests if this matrix is orthogonal. */ - bool isOrthogonal() { - SquareMatrix tmp; + /** Tests if this matrix is orthogonal. */ + bool isOrthogonal() { + SquareMatrix tmp; - tmp = *this * transpose(); + tmp = *this * transpose(); - return tmp.isDiagonal(); - } + return tmp.isDiagonal(); + } - /** Tests if this matrix is diagonal. */ - bool isDiagonal() const { - for (unsigned int i = 0; i < Dim ; i++) - for (unsigned int j = 0; j < Dim; j++) - if (i !=j && fabs(data_[i][j]) > oopse::epsilon) - return false; + /** Tests if this matrix is diagonal. */ + bool isDiagonal() const { + for (unsigned int i = 0; i < Dim ; i++) + for (unsigned int j = 0; j < Dim; j++) + if (i !=j && fabs(this->data_[i][j]) > epsilon) + return false; - return true; - } + return true; + } - /** Tests if this matrix is the unit matrix. */ - bool isUnitMatrix() const { - if (!isDiagonal()) - return false; + /** Tests if this matrix is the unit matrix. */ + bool isUnitMatrix() const { + if (!isDiagonal()) + return false; - for (unsigned int i = 0; i < Dim ; i++) - if (fabs(data_[i][i] - 1) > oopse::epsilon) - return false; + for (unsigned int i = 0; i < Dim ; i++) + if (fabs(this->data_[i][i] - 1) > epsilon) + return false; - return true; - } + return true; + } - /** @todo need implementation */ - void diagonalize() { - //jacobi(m, eigenValues, ortMat); - } + /** Return the transpose of this matrix */ + SquareMatrix transpose() const{ + SquareMatrix result; + + for (unsigned int i = 0; i < Dim; i++) + for (unsigned int j = 0; j < Dim; j++) + result(j, i) = this->data_[i][j]; - /** - * Jacobi iteration routines for computing eigenvalues/eigenvectors of - * real symmetric matrix - * - * @return true if success, otherwise return false - * @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. - */ + return result; + } + + /** @todo need implementation */ + void diagonalize() { + //jacobi(m, eigenValues, ortMat); + } + + /** + * Jacobi iteration routines for computing eigenvalues/eigenvectors of + * real symmetric matrix + * + * @return true if success, otherwise return false + * @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. + */ - static int jacobi(SquareMatrix& a, Vector& d, - SquareMatrix& v); - };//end SquareMatrix + static int jacobi(SquareMatrix& a, Vector& d, + SquareMatrix& v); + };//end SquareMatrix -/*========================================================================= + /*========================================================================= Program: Visualization Toolkit Module: $RCSfile: SquareMatrix.hpp,v $ @@ -181,176 +218,177 @@ namespace oopse { 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. + 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. -=========================================================================*/ + =========================================================================*/ -#define VTK_ROTATE(a,i,j,k,l) g=a(i, j);h=a(k, l);a(i, j)=g-s*(h+g*tau);\ - a(k, l)=h+s*(g-h*tau) +#define VTK_ROTATE(a,i,j,k,l) g=a(i, j);h=a(k, l);a(i, j)=g-s*(h+g*tau); \ + a(k, l)=h+s*(g-h*tau) #define VTK_MAX_ROTATIONS 20 - // Jacobi iteration for the solution of eigenvectors/eigenvalues of a nxn - // real symmetric matrix. Square nxn matrix a; size of matrix in n; - // output eigenvalues in w; and output eigenvectors in v. Resulting - // eigenvalues/vectors are sorted in decreasing order; eigenvectors are - // normalized. - template - int SquareMatrix::jacobi(SquareMatrix& a, Vector& w, - SquareMatrix& v) { - const int n = Dim; - int i, j, k, iq, ip, numPos; - Real tresh, theta, tau, t, sm, s, h, g, c, tmp; - Real bspace[4], zspace[4]; - Real *b = bspace; - Real *z = zspace; + // Jacobi iteration for the solution of eigenvectors/eigenvalues of a nxn + // real symmetric matrix. Square nxn matrix a; size of matrix in n; + // output eigenvalues in w; and output eigenvectors in v. Resulting + // eigenvalues/vectors are sorted in decreasing order; eigenvectors are + // normalized. + template + int SquareMatrix::jacobi(SquareMatrix& a, Vector& w, + SquareMatrix& v) { + const int n = Dim; + int i, j, k, iq, ip, numPos; + Real tresh, theta, tau, t, sm, s, h, g, c, tmp; + Real bspace[4], zspace[4]; + Real *b = bspace; + Real *z = zspace; - // only allocate memory if the matrix is large - if (n > 4) { - b = new Real[n]; - z = new Real[n]; - } + // only allocate memory if the matrix is large + if (n > 4) { + b = new Real[n]; + z = new Real[n]; + } - // initialize - for (ip=0; ip 3 && (fabs(w[ip])+g) == fabs(w[ip]) - && (fabs(w[iq])+g) == fabs(w[iq])) { - a(ip, iq) = 0.0; - } else if (fabs(a(ip, iq)) > tresh) { - h = w[iq] - w[ip]; - if ( (fabs(h)+g) == fabs(h)) { - t = (a(ip, iq)) / h; - } else { - theta = 0.5*h / (a(ip, iq)); - t = 1.0 / (fabs(theta)+sqrt(1.0+theta*theta)); - if (theta < 0.0) { - t = -t; - } - } - c = 1.0 / sqrt(1+t*t); - s = t*c; - tau = s/(1.0+c); - h = t*a(ip, iq); - z[ip] -= h; - z[iq] += h; - w[ip] -= h; - w[iq] += h; - a(ip, iq)=0.0; + // after 4 sweeps + if (i > 3 && (fabs(w[ip])+g) == fabs(w[ip]) + && (fabs(w[iq])+g) == fabs(w[iq])) { + a(ip, iq) = 0.0; + } else if (fabs(a(ip, iq)) > tresh) { + h = w[iq] - w[ip]; + if ( (fabs(h)+g) == fabs(h)) { + t = (a(ip, iq)) / h; + } else { + theta = 0.5*h / (a(ip, iq)); + t = 1.0 / (fabs(theta)+sqrt(1.0+theta*theta)); + if (theta < 0.0) { + t = -t; + } + } + c = 1.0 / sqrt(1+t*t); + s = t*c; + tau = s/(1.0+c); + h = t*a(ip, iq); + z[ip] -= h; + z[iq] += h; + w[ip] -= h; + w[iq] += h; + a(ip, iq)=0.0; - // ip already shifted left by 1 unit - for (j = 0;j <= ip-1;j++) { - VTK_ROTATE(a,j,ip,j,iq); - } - // ip and iq already shifted left by 1 unit - for (j = ip+1;j <= iq-1;j++) { - VTK_ROTATE(a,ip,j,j,iq); - } - // iq already shifted left by 1 unit - for (j=iq+1; j= VTK_MAX_ROTATIONS ) { - std::cout << "vtkMath::Jacobi: Error extracting eigenfunctions" << std::endl; - return 0; - } + //// this is NEVER called + if ( i >= VTK_MAX_ROTATIONS ) { + std::cout << "vtkMath::Jacobi: Error extracting eigenfunctions" << std::endl; + return 0; + } - // sort eigenfunctions these changes do not affect accuracy - for (j=0; j= tmp) { // why exchage if same? - k = i; - tmp = w[k]; - } - } - if (k != j) { - w[k] = w[j]; - w[j] = tmp; - for (i=0; i> 1) + (n & 1); - for (j=0; j= 0.0 ) { - numPos++; - } - } - // if ( numPos < ceil(double(n)/double(2.0)) ) - if ( numPos < ceil_half_n) { - for (i=0; i= tmp) { // why exchage if same? + k = i; + tmp = w[k]; + } + } + if (k != j) { + w[k] = w[j]; + w[j] = tmp; + for (i=0; i> 1) + (n & 1); + for (j=0; j= 0.0 ) { + numPos++; + } + } + // if ( numPos < ceil(RealType(n)/RealType(2.0)) ) + if ( numPos < ceil_half_n) { + for (i=0; i 4) { - delete [] b; - delete [] z; - } - return 1; + if (n > 4) { + delete [] b; + delete [] z; } + return 1; + } + typedef SquareMatrix Mat6x6d; } #endif //MATH_SQUAREMATRIX_HPP