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/* |
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* Copyright (C) 2000-2004 Object Oriented Parallel Simulation Engine (OOPSE) project |
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* |
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* Contact: oopse@oopse.org |
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* |
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* This program is free software; you can redistribute it and/or |
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* modify it under the terms of the GNU Lesser General Public License |
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* as published by the Free Software Foundation; either version 2.1 |
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* of the License, or (at your option) any later version. |
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* All we ask is that proper credit is given for our work, which includes |
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* - but is not limited to - adding the above copyright notice to the beginning |
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* of your source code files, and to any copyright notice that you may distribute |
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* with programs based on this work. |
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* |
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* This program is distributed in the hope that it will be useful, |
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* but WITHOUT ANY WARRANTY; without even the implied warranty of |
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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* GNU Lesser General Public License for more details. |
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* |
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* You should have received a copy of the GNU Lesser General Public License |
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* along with this program; if not, write to the Free Software |
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* Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA 02111-1307, USA. |
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/* |
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* Copyright (c) 2005 The University of Notre Dame. All Rights Reserved. |
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* |
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* The University of Notre Dame grants you ("Licensee") a |
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* non-exclusive, royalty free, license to use, modify and |
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* redistribute this software in source and binary code form, provided |
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* that the following conditions are met: |
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* |
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* 1. Acknowledgement of the program authors must be made in any |
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* publication of scientific results based in part on use of the |
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* program. An acceptable form of acknowledgement is citation of |
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* the article in which the program was described (Matthew |
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* A. Meineke, Charles F. Vardeman II, Teng Lin, Christopher |
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* J. Fennell and J. Daniel Gezelter, "OOPSE: An Object-Oriented |
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* Parallel Simulation Engine for Molecular Dynamics," |
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* J. Comput. Chem. 26, pp. 252-271 (2005)) |
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* |
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* 2. Redistributions of source code must retain the above copyright |
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* notice, this list of conditions and the following disclaimer. |
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* |
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* 3. Redistributions in binary form must reproduce the above copyright |
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* notice, this list of conditions and the following disclaimer in the |
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* documentation and/or other materials provided with the |
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* distribution. |
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* |
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* This software is provided "AS IS," without a warranty of any |
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* kind. All express or implied conditions, representations and |
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* warranties, including any implied warranty of merchantability, |
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* fitness for a particular purpose or non-infringement, are hereby |
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* excluded. The University of Notre Dame and its licensors shall not |
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* be liable for any damages suffered by licensee as a result of |
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* using, modifying or distributing the software or its |
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* derivatives. In no event will the University of Notre Dame or its |
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* licensors be liable for any lost revenue, profit or data, or for |
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* direct, indirect, special, consequential, incidental or punitive |
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* damages, however caused and regardless of the theory of liability, |
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* arising out of the use of or inability to use software, even if the |
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* University of Notre Dame has been advised of the possibility of |
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* such damages. |
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*/ |
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|
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/** |
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* @file SquareMatrix.hpp |
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* @author Teng Lin |
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* @date 10/11/2004 |
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* @version 1.0 |
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*/ |
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#ifndef MATH_SQUAREMATRIX_HPP |
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#ifndef MATH_SQUAREMATRIX_HPP |
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#define MATH_SQUAREMATRIX_HPP |
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#include "math/RectMatrix.hpp" |
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template<typename Real, int Dim> |
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class SquareMatrix : public RectMatrix<Real, Dim, Dim> { |
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public: |
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typedef Real ElemType; |
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typedef Real* ElemPoinerType; |
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|
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/** default constructor */ |
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SquareMatrix() { |
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for (unsigned int i = 0; i < Dim; i++) |
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for (unsigned int j = 0; j < Dim; j++) |
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data_[i][j] = 0.0; |
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} |
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/** default constructor */ |
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SquareMatrix() { |
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for (unsigned int i = 0; i < Dim; i++) |
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for (unsigned int j = 0; j < Dim; j++) |
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data_[i][j] = 0.0; |
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} |
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|
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/** copy constructor */ |
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SquareMatrix(const RectMatrix<Real, Dim, Dim>& m) : RectMatrix<Real, Dim, Dim>(m) { |
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} |
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|
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/** copy assignment operator */ |
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SquareMatrix<Real, Dim>& operator =(const RectMatrix<Real, Dim, Dim>& m) { |
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RectMatrix<Real, Dim, Dim>::operator=(m); |
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return *this; |
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} |
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|
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/** Retunrs an identity matrix*/ |
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/** Constructs and initializes every element of this matrix to a scalar */ |
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SquareMatrix(Real s) : RectMatrix<Real, Dim, Dim>(s){ |
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} |
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|
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static SquareMatrix<Real, Dim> identity() { |
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SquareMatrix<Real, Dim> m; |
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/** Constructs and initializes from an array */ |
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SquareMatrix(Real* array) : RectMatrix<Real, Dim, Dim>(array){ |
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} |
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|
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|
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/** copy constructor */ |
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SquareMatrix(const RectMatrix<Real, Dim, Dim>& m) : RectMatrix<Real, Dim, Dim>(m) { |
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} |
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|
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for (unsigned int i = 0; i < Dim; i++) |
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for (unsigned int j = 0; j < Dim; j++) |
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if (i == j) |
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m(i, j) = 1.0; |
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else |
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m(i, j) = 0.0; |
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/** copy assignment operator */ |
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SquareMatrix<Real, Dim>& operator =(const RectMatrix<Real, Dim, Dim>& m) { |
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RectMatrix<Real, Dim, Dim>::operator=(m); |
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return *this; |
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} |
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|
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/** Retunrs an identity matrix*/ |
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|
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return m; |
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} |
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static SquareMatrix<Real, Dim> identity() { |
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SquareMatrix<Real, Dim> m; |
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|
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for (unsigned int i = 0; i < Dim; i++) |
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for (unsigned int j = 0; j < Dim; j++) |
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if (i == j) |
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m(i, j) = 1.0; |
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else |
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m(i, j) = 0.0; |
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|
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/** Retunrs the inversion of this matrix. */ |
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SquareMatrix<Real, Dim> inverse() { |
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SquareMatrix<Real, Dim> result; |
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return m; |
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} |
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|
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return result; |
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} |
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/** |
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* Retunrs the inversion of this matrix. |
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* @todo need implementation |
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*/ |
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SquareMatrix<Real, Dim> inverse() { |
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SquareMatrix<Real, Dim> result; |
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|
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|
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return result; |
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} |
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|
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/** Returns the determinant of this matrix. */ |
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double determinant() const { |
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double det; |
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return det; |
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} |
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/** |
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* Returns the determinant of this matrix. |
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* @todo need implementation |
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*/ |
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Real determinant() const { |
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Real det; |
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return det; |
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} |
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|
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/** Returns the trace of this matrix. */ |
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double trace() const { |
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double tmp = 0; |
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|
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for (unsigned int i = 0; i < Dim ; i++) |
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tmp += data_[i][i]; |
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/** Returns the trace of this matrix. */ |
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Real trace() const { |
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Real tmp = 0; |
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|
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for (unsigned int i = 0; i < Dim ; i++) |
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tmp += data_[i][i]; |
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|
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return tmp; |
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} |
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return tmp; |
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} |
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|
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/** Tests if this matrix is symmetrix. */ |
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bool isSymmetric() const { |
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for (unsigned int i = 0; i < Dim - 1; i++) |
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for (unsigned int j = i; j < Dim; j++) |
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if (fabs(data_[i][j] - data_[j][i]) > oopse::epsilon) |
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return false; |
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|
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return true; |
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} |
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/** Tests if this matrix is symmetrix. */ |
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bool isSymmetric() const { |
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for (unsigned int i = 0; i < Dim - 1; i++) |
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for (unsigned int j = i; j < Dim; j++) |
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if (fabs(data_[i][j] - data_[j][i]) > oopse::epsilon) |
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return false; |
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|
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return true; |
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} |
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|
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/** Tests if this matrix is orthogona. */ |
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bool isOrthogonal() { |
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SquareMatrix<Real, Dim> tmp; |
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/** Tests if this matrix is orthogonal. */ |
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bool isOrthogonal() { |
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SquareMatrix<Real, Dim> tmp; |
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|
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tmp = *this * transpose(); |
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tmp = *this * transpose(); |
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|
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return tmp.isUnitMatrix(); |
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} |
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return tmp.isDiagonal(); |
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} |
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|
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/** Tests if this matrix is diagonal. */ |
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bool isDiagonal() const { |
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for (unsigned int i = 0; i < Dim ; i++) |
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for (unsigned int j = 0; j < Dim; j++) |
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if (i !=j && fabs(data_[i][j]) > oopse::epsilon) |
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return false; |
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|
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return true; |
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} |
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/** Tests if this matrix is diagonal. */ |
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bool isDiagonal() const { |
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for (unsigned int i = 0; i < Dim ; i++) |
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for (unsigned int j = 0; j < Dim; j++) |
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if (i !=j && fabs(data_[i][j]) > oopse::epsilon) |
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return false; |
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|
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return true; |
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} |
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|
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/** Tests if this matrix is the unit matrix. */ |
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bool isUnitMatrix() const { |
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if (!isDiagonal()) |
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return false; |
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|
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for (unsigned int i = 0; i < Dim ; i++) |
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if (fabs(data_[i][i] - 1) > oopse::epsilon) |
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/** Tests if this matrix is the unit matrix. */ |
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bool isUnitMatrix() const { |
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if (!isDiagonal()) |
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return false; |
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|
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return true; |
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} |
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for (unsigned int i = 0; i < Dim ; i++) |
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if (fabs(data_[i][i] - 1) > oopse::epsilon) |
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return false; |
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|
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return true; |
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} |
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|
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/** @todo need implementation */ |
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void diagonalize() { |
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//jacobi(m, eigenValues, ortMat); |
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} |
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|
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/** |
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* Jacobi iteration routines for computing eigenvalues/eigenvectors of |
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* real symmetric matrix |
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* |
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* @return true if success, otherwise return false |
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* @param a symmetric matrix whose eigenvectors are to be computed. On return, the matrix is |
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* overwritten |
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* @param w will contain the eigenvalues of the matrix On return of this function |
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* @param v the columns of this matrix will contain the eigenvectors. The eigenvectors are |
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* normalized and mutually orthogonal. |
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*/ |
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|
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static int jacobi(SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& d, |
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SquareMatrix<Real, Dim>& v); |
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};//end SquareMatrix |
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|
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|
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/*========================================================================= |
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|
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Program: Visualization Toolkit |
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Module: $RCSfile: SquareMatrix.hpp,v $ |
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|
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Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen |
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All rights reserved. |
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See Copyright.txt or http://www.kitware.com/Copyright.htm for details. |
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|
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This software is distributed WITHOUT ANY WARRANTY; without even |
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the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR |
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PURPOSE. See the above copyright notice for more information. |
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|
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=========================================================================*/ |
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|
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#define VTK_ROTATE(a,i,j,k,l) g=a(i, j);h=a(k, l);a(i, j)=g-s*(h+g*tau);\ |
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a(k, l)=h+s*(g-h*tau) |
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|
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#define VTK_MAX_ROTATIONS 20 |
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|
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// Jacobi iteration for the solution of eigenvectors/eigenvalues of a nxn |
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// real symmetric matrix. Square nxn matrix a; size of matrix in n; |
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// output eigenvalues in w; and output eigenvectors in v. Resulting |
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// eigenvalues/vectors are sorted in decreasing order; eigenvectors are |
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// normalized. |
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template<typename Real, int Dim> |
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int SquareMatrix<Real, Dim>::jacobi(SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& w, |
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SquareMatrix<Real, Dim>& v) { |
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const int n = Dim; |
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+ |
int i, j, k, iq, ip, numPos; |
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Real tresh, theta, tau, t, sm, s, h, g, c, tmp; |
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Real bspace[4], zspace[4]; |
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Real *b = bspace; |
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Real *z = zspace; |
| 234 |
+ |
|
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+ |
// only allocate memory if the matrix is large |
| 236 |
+ |
if (n > 4) { |
| 237 |
+ |
b = new Real[n]; |
| 238 |
+ |
z = new Real[n]; |
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+ |
} |
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+ |
|
| 241 |
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// initialize |
| 242 |
+ |
for (ip=0; ip<n; ip++) { |
| 243 |
+ |
for (iq=0; iq<n; iq++) { |
| 244 |
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v(ip, iq) = 0.0; |
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+ |
} |
| 246 |
+ |
v(ip, ip) = 1.0; |
| 247 |
+ |
} |
| 248 |
+ |
for (ip=0; ip<n; ip++) { |
| 249 |
+ |
b[ip] = w[ip] = a(ip, ip); |
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+ |
z[ip] = 0.0; |
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+ |
} |
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+ |
|
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// begin rotation sequence |
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+ |
for (i=0; i<VTK_MAX_ROTATIONS; i++) { |
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+ |
sm = 0.0; |
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+ |
for (ip=0; ip<n-1; ip++) { |
| 257 |
+ |
for (iq=ip+1; iq<n; iq++) { |
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+ |
sm += fabs(a(ip, iq)); |
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+ |
} |
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+ |
} |
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+ |
if (sm == 0.0) { |
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+ |
break; |
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+ |
} |
| 264 |
+ |
|
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+ |
if (i < 3) { // first 3 sweeps |
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+ |
tresh = 0.2*sm/(n*n); |
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+ |
} else { |
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+ |
tresh = 0.0; |
| 269 |
+ |
} |
| 270 |
+ |
|
| 271 |
+ |
for (ip=0; ip<n-1; ip++) { |
| 272 |
+ |
for (iq=ip+1; iq<n; iq++) { |
| 273 |
+ |
g = 100.0*fabs(a(ip, iq)); |
| 274 |
+ |
|
| 275 |
+ |
// after 4 sweeps |
| 276 |
+ |
if (i > 3 && (fabs(w[ip])+g) == fabs(w[ip]) |
| 277 |
+ |
&& (fabs(w[iq])+g) == fabs(w[iq])) { |
| 278 |
+ |
a(ip, iq) = 0.0; |
| 279 |
+ |
} else if (fabs(a(ip, iq)) > tresh) { |
| 280 |
+ |
h = w[iq] - w[ip]; |
| 281 |
+ |
if ( (fabs(h)+g) == fabs(h)) { |
| 282 |
+ |
t = (a(ip, iq)) / h; |
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+ |
} else { |
| 284 |
+ |
theta = 0.5*h / (a(ip, iq)); |
| 285 |
+ |
t = 1.0 / (fabs(theta)+sqrt(1.0+theta*theta)); |
| 286 |
+ |
if (theta < 0.0) { |
| 287 |
+ |
t = -t; |
| 288 |
+ |
} |
| 289 |
+ |
} |
| 290 |
+ |
c = 1.0 / sqrt(1+t*t); |
| 291 |
+ |
s = t*c; |
| 292 |
+ |
tau = s/(1.0+c); |
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+ |
h = t*a(ip, iq); |
| 294 |
+ |
z[ip] -= h; |
| 295 |
+ |
z[iq] += h; |
| 296 |
+ |
w[ip] -= h; |
| 297 |
+ |
w[iq] += h; |
| 298 |
+ |
a(ip, iq)=0.0; |
| 299 |
+ |
|
| 300 |
+ |
// ip already shifted left by 1 unit |
| 301 |
+ |
for (j = 0;j <= ip-1;j++) { |
| 302 |
+ |
VTK_ROTATE(a,j,ip,j,iq); |
| 303 |
+ |
} |
| 304 |
+ |
// ip and iq already shifted left by 1 unit |
| 305 |
+ |
for (j = ip+1;j <= iq-1;j++) { |
| 306 |
+ |
VTK_ROTATE(a,ip,j,j,iq); |
| 307 |
+ |
} |
| 308 |
+ |
// iq already shifted left by 1 unit |
| 309 |
+ |
for (j=iq+1; j<n; j++) { |
| 310 |
+ |
VTK_ROTATE(a,ip,j,iq,j); |
| 311 |
+ |
} |
| 312 |
+ |
for (j=0; j<n; j++) { |
| 313 |
+ |
VTK_ROTATE(v,j,ip,j,iq); |
| 314 |
+ |
} |
| 315 |
+ |
} |
| 316 |
+ |
} |
| 317 |
+ |
} |
| 318 |
+ |
|
| 319 |
+ |
for (ip=0; ip<n; ip++) { |
| 320 |
+ |
b[ip] += z[ip]; |
| 321 |
+ |
w[ip] = b[ip]; |
| 322 |
+ |
z[ip] = 0.0; |
| 323 |
+ |
} |
| 324 |
+ |
} |
| 325 |
+ |
|
| 326 |
+ |
//// this is NEVER called |
| 327 |
+ |
if ( i >= VTK_MAX_ROTATIONS ) { |
| 328 |
+ |
std::cout << "vtkMath::Jacobi: Error extracting eigenfunctions" << std::endl; |
| 329 |
+ |
return 0; |
| 330 |
+ |
} |
| 331 |
+ |
|
| 332 |
+ |
// sort eigenfunctions these changes do not affect accuracy |
| 333 |
+ |
for (j=0; j<n-1; j++) { // boundary incorrect |
| 334 |
+ |
k = j; |
| 335 |
+ |
tmp = w[k]; |
| 336 |
+ |
for (i=j+1; i<n; i++) { // boundary incorrect, shifted already |
| 337 |
+ |
if (w[i] >= tmp) { // why exchage if same? |
| 338 |
+ |
k = i; |
| 339 |
+ |
tmp = w[k]; |
| 340 |
+ |
} |
| 341 |
+ |
} |
| 342 |
+ |
if (k != j) { |
| 343 |
+ |
w[k] = w[j]; |
| 344 |
+ |
w[j] = tmp; |
| 345 |
+ |
for (i=0; i<n; i++) { |
| 346 |
+ |
tmp = v(i, j); |
| 347 |
+ |
v(i, j) = v(i, k); |
| 348 |
+ |
v(i, k) = tmp; |
| 349 |
+ |
} |
| 350 |
+ |
} |
| 351 |
+ |
} |
| 352 |
+ |
// insure eigenvector consistency (i.e., Jacobi can compute vectors that |
| 353 |
+ |
// are negative of one another (.707,.707,0) and (-.707,-.707,0). This can |
| 354 |
+ |
// reek havoc in hyperstreamline/other stuff. We will select the most |
| 355 |
+ |
// positive eigenvector. |
| 356 |
+ |
int ceil_half_n = (n >> 1) + (n & 1); |
| 357 |
+ |
for (j=0; j<n; j++) { |
| 358 |
+ |
for (numPos=0, i=0; i<n; i++) { |
| 359 |
+ |
if ( v(i, j) >= 0.0 ) { |
| 360 |
+ |
numPos++; |
| 361 |
+ |
} |
| 362 |
+ |
} |
| 363 |
+ |
// if ( numPos < ceil(double(n)/double(2.0)) ) |
| 364 |
+ |
if ( numPos < ceil_half_n) { |
| 365 |
+ |
for (i=0; i<n; i++) { |
| 366 |
+ |
v(i, j) *= -1.0; |
| 367 |
+ |
} |
| 368 |
+ |
} |
| 369 |
+ |
} |
| 370 |
+ |
|
| 371 |
+ |
if (n > 4) { |
| 372 |
+ |
delete [] b; |
| 373 |
+ |
delete [] z; |
| 374 |
+ |
} |
| 375 |
+ |
return 1; |
| 376 |
+ |
} |
| 377 |
+ |
|
| 378 |
+ |
|
| 379 |
|
} |
| 380 |
|
#endif //MATH_SQUAREMATRIX_HPP |
| 381 |
+ |
|
