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1 < /*
2 < * Copyright (C) 2000-2004  Object Oriented Parallel Simulation Engine (OOPSE) project
3 < *
4 < * Contact: oopse@oopse.org
5 < *
6 < * This program is free software; you can redistribute it and/or
7 < * modify it under the terms of the GNU Lesser General Public License
8 < * as published by the Free Software Foundation; either version 2.1
9 < * of the License, or (at your option) any later version.
10 < * All we ask is that proper credit is given for our work, which includes
11 < * - but is not limited to - adding the above copyright notice to the beginning
12 < * of your source code files, and to any copyright notice that you may distribute
13 < * with programs based on this work.
14 < *
15 < * This program is distributed in the hope that it will be useful,
16 < * but WITHOUT ANY WARRANTY; without even the implied warranty of
17 < * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
18 < * GNU Lesser General Public License for more details.
19 < *
20 < * You should have received a copy of the GNU Lesser General Public License
21 < * along with this program; if not, write to the Free Software
22 < * Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA  02111-1307, USA.
1 > /*
2 > * Copyright (c) 2005 The University of Notre Dame. All Rights Reserved.
3   *
4 + * 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 + * 1. Acknowledgement of the program authors must be made in any
10 + *    publication of scientific results based in part on use of the
11 + *    program.  An acceptable form of acknowledgement is citation of
12 + *    the article in which the program was described (Matthew
13 + *    A. Meineke, Charles F. Vardeman II, Teng Lin, Christopher
14 + *    J. Fennell and J. Daniel Gezelter, "OOPSE: An Object-Oriented
15 + *    Parallel Simulation Engine for Molecular Dynamics,"
16 + *    J. Comput. Chem. 26, pp. 252-271 (2005))
17 + *
18 + * 2. Redistributions of source code must retain the above copyright
19 + *    notice, this list of conditions and the following disclaimer.
20 + *
21 + * 3. Redistributions in binary form must reproduce the above copyright
22 + *    notice, this list of conditions and the following disclaimer in the
23 + *    documentation and/or other materials provided with the
24 + *    distribution.
25 + *
26 + * This software is provided "AS IS," without a warranty of any
27 + * kind. All express or implied conditions, representations and
28 + * warranties, including any implied warranty of merchantability,
29 + * fitness for a particular purpose or non-infringement, are hereby
30 + * excluded.  The University of Notre Dame and its licensors shall not
31 + * be liable for any damages suffered by licensee as a result of
32 + * using, modifying or distributing the software or its
33 + * derivatives. In no event will the University of Notre Dame or its
34 + * licensors be liable for any lost revenue, profit or data, or for
35 + * direct, indirect, special, consequential, incidental or punitive
36 + * damages, however caused and regardless of the theory of liability,
37 + * arising out of the use of or inability to use software, even if the
38 + * University of Notre Dame has been advised of the possibility of
39 + * such damages.
40   */
41 <
41 >
42   /**
43   * @file SquareMatrix.hpp
44   * @author Teng Lin
45   * @date 10/11/2004
46   * @version 1.0
47   */
48 < #ifndef MATH_SQUAREMATRIX_HPP
48 > #ifndef MATH_SQUAREMATRIX_HPP
49   #define MATH_SQUAREMATRIX_HPP
50  
51 < #include "Vector3d.hpp"
51 > #include "math/RectMatrix.hpp"
52  
53   namespace oopse {
54  
# Line 43 | Line 59 | namespace oopse {
59       * @template Dim the dimension of the square matrix
60       */
61      template<typename Real, int Dim>
62 <    class SquareMatrix{
62 >    class SquareMatrix : public RectMatrix<Real, Dim, Dim> {
63          public:
64 +            typedef Real ElemType;
65 +            typedef Real* ElemPoinerType;
66  
67 <        /** default constructor */
68 <        SquareMatrix() {
69 <            for (unsigned int i = 0; i < Dim; i++)
70 <                for (unsigned int j = 0; j < Dim; j++)
71 <                    data_[i][j] = 0.0;
72 <         }
67 >            /** default constructor */
68 >            SquareMatrix() {
69 >                for (unsigned int i = 0; i < Dim; i++)
70 >                    for (unsigned int j = 0; j < Dim; j++)
71 >                        this->data_[i][j] = 0.0;
72 >             }
73  
74 <        /** Constructs and initializes every element of this matrix to a scalar */
75 <        SquareMatrix(double s) {
76 <            for (unsigned int i = 0; i < Dim; i++)
59 <                for (unsigned int j = 0; j < Dim; j++)
60 <                    data_[i][j] = s;
61 <        }
74 >            /** Constructs and initializes every element of this matrix to a scalar */
75 >            SquareMatrix(Real s) : RectMatrix<Real, Dim, Dim>(s){
76 >            }
77  
78 <        /** copy constructor */
79 <        SquareMatrix(const SquareMatrix<Real, Dim>& m) {
80 <            *this = m;
66 <        }
67 <        
68 <        /** destructor*/
69 <        ~SquareMatrix() {}
78 >            /** Constructs and initializes from an array */
79 >            SquareMatrix(Real* array) : RectMatrix<Real, Dim, Dim>(array){
80 >            }
81  
71 –        /** copy assignment operator */
72 –        SquareMatrix<Real, Dim>& operator =(const SquareMatrix<Real, Dim>& m) {
73 –            for (unsigned int i = 0; i < Dim; i++)
74 –                for (unsigned int j = 0; j < Dim; j++)
75 –                    data_[i][j] = m.data_[i][j];
76 –        }
77 –        
78 –        /**
79 –         * Return the reference of a single element of this matrix.
80 –         * @return the reference of a single element of this matrix
81 –         * @param i row index
82 –         * @param j colum index
83 –         */
84 –        double& operator()(unsigned int i, unsigned int j) {
85 –            return data_[i][j];
86 –        }
82  
83 <        /**
84 <         * Return the value of a single element of this matrix.
85 <         * @return the value of a single element of this matrix
86 <         * @param i row index
87 <         * @param j colum index
88 <         */        
89 <        double operator()(unsigned int i, unsigned int j) const  {
90 <            return data_[i][j];  
91 <        }
83 >            /** copy constructor */
84 >            SquareMatrix(const RectMatrix<Real, Dim, Dim>& m) : RectMatrix<Real, Dim, Dim>(m) {
85 >            }
86 >            
87 >            /** copy assignment operator */
88 >            SquareMatrix<Real, Dim>& operator =(const RectMatrix<Real, Dim, Dim>& m) {
89 >                RectMatrix<Real, Dim, Dim>::operator=(m);
90 >                return *this;
91 >            }
92 >                                  
93 >            /** Retunrs  an identity matrix*/
94  
95 <        /**
96 <         * Returns a row of  this matrix as a vector.
97 <         * @return a row of  this matrix as a vector
98 <         * @param row the row index
99 <         */                
100 <        Vector<Real, Dim> getRow(unsigned int row) {
101 <            Vector<Real, Dim> v;
95 >           static SquareMatrix<Real, Dim> identity() {
96 >                SquareMatrix<Real, Dim> m;
97 >                
98 >                for (unsigned int i = 0; i < Dim; i++)
99 >                    for (unsigned int j = 0; j < Dim; j++)
100 >                        if (i == j)
101 >                            m(i, j) = 1.0;
102 >                        else
103 >                            m(i, j) = 0.0;
104  
105 <            for (unsigned int i = 0; i < Dim; i++)
106 <                v[i] = data_[row][i];
105 >                return m;
106 >            }
107  
108 <            return v;
109 <        }
108 >            /**
109 >             * Retunrs  the inversion of this matrix.
110 >             * @todo need implementation
111 >             */
112 >             SquareMatrix<Real, Dim>  inverse() {
113 >                 SquareMatrix<Real, Dim> result;
114  
115 <        /**
116 <         * Sets a row of  this matrix
114 <         * @param row the row index
115 <         * @param v the vector to be set
116 <         */                
117 <         void setRow(unsigned int row, const Vector<Real, Dim>& v) {
118 <            Vector<Real, Dim> v;
115 >                 return result;
116 >            }        
117  
118 <            for (unsigned int i = 0; i < Dim; i++)
119 <                data_[row][i] = v[i];
120 <         }
118 >            /**
119 >             * Returns the determinant of this matrix.
120 >             * @todo need implementation
121 >             */
122 >            Real determinant() const {
123 >                Real det;
124 >                return det;
125 >            }
126  
127 <        /**
128 <         * Returns a column of  this matrix as a vector.
129 <         * @return a column of  this matrix as a vector
130 <         * @param col the column index
131 <         */                
132 <        Vector<Real, Dim> getColum(unsigned int col) {
130 <            Vector<Real, Dim> v;
127 >            /** Returns the trace of this matrix. */
128 >            Real trace() const {
129 >               Real tmp = 0;
130 >              
131 >                for (unsigned int i = 0; i < Dim ; i++)
132 >                    tmp += this->data_[i][i];
133  
134 <            for (unsigned int i = 0; i < Dim; i++)
135 <                v[i] = data_[i][col];
134 >                return tmp;
135 >            }
136  
137 <            return v;
138 <        }
137 >            /** Tests if this matrix is symmetrix. */            
138 >            bool isSymmetric() const {
139 >                for (unsigned int i = 0; i < Dim - 1; i++)
140 >                    for (unsigned int j = i; j < Dim; j++)
141 >                        if (fabs(this->data_[i][j] - this->data_[j][i]) > oopse::epsilon)
142 >                            return false;
143 >                        
144 >                return true;
145 >            }
146  
147 <        /**
148 <         * Sets a column of  this matrix
149 <         * @param col the column index
141 <         * @param v the vector to be set
142 <         */                
143 <         void setColum(unsigned int col, const Vector<Real, Dim>& v){
144 <            Vector<Real, Dim> v;
147 >            /** Tests if this matrix is orthogonal. */            
148 >            bool isOrthogonal() {
149 >                SquareMatrix<Real, Dim> tmp;
150  
151 <            for (unsigned int i = 0; i < Dim; i++)
147 <                data_[i][col] = v[i];
148 <         }        
151 >                tmp = *this * transpose();
152  
153 <        /** Negates the value of this matrix in place. */          
151 <        inline void negate() {
152 <            for (unsigned int i = 0; i < Dim; i++)
153 <                for (unsigned int j = 0; j < Dim; j++)
154 <                    data_[i][j] = -data_[i][j];
155 <        }
156 <        
157 <        /**
158 <        * Sets the value of this matrix to the negation of matrix m.
159 <        * @param m the source matrix
160 <        */
161 <        inline void negate(const SquareMatrix<Real, Dim>& m) {
162 <            for (unsigned int i = 0; i < Dim; i++)
163 <                for (unsigned int j = 0; j < Dim; j++)
164 <                    data_[i][j] = -m.data_[i][j];        
165 <        }
166 <        
167 <        /**
168 <        * Sets the value of this matrix to the sum of itself and m (*this += m).
169 <        * @param m the other matrix
170 <        */
171 <        inline void add( const SquareMatrix<Real, Dim>& m ) {
172 <            for (unsigned int i = 0; i < Dim; i++)
173 <                for (unsigned int j = 0; j < Dim; j++)        
174 <                data_[i][j] += m.data_[i][j];
153 >                return tmp.isDiagonal();
154              }
176 –        
177 –        /**
178 –        * Sets the value of this matrix to the sum of m1 and m2 (*this = m1 + m2).
179 –        * @param m1 the first matrix
180 –        * @param m2 the second matrix
181 –        */
182 –        inline void add( const SquareMatrix<Real, Dim>& m1, const SquareMatrix<Real, Dim>& m2 ) {
183 –            for (unsigned int i = 0; i < Dim; i++)
184 –                for (unsigned int j = 0; j < Dim; j++)        
185 –                data_[i][j] = m1.data_[i][j] + m2.data_[i][j];
186 –        }
187 –        
188 –        /**
189 –        * Sets the value of this matrix to the difference  of itself and m (*this -= m).
190 –        * @param m the other matrix
191 –        */
192 –        inline void sub( const SquareMatrix<Real, Dim>& m ) {
193 –            for (unsigned int i = 0; i < Dim; i++)
194 –                for (unsigned int j = 0; j < Dim; j++)        
195 –                data_[i][j] -= m.data_[i][j];
196 –        }
197 –        
198 –        /**
199 –        * Sets the value of this matrix to the difference of matrix m1 and m2 (*this = m1 - m2).
200 –        * @param m1 the first matrix
201 –        * @param m2 the second matrix
202 –        */
203 –        inline void sub( const SquareMatrix<Real, Dim>& m1, const Vector  &m2){
204 –            for (unsigned int i = 0; i < Dim; i++)
205 –                for (unsigned int j = 0; j < Dim; j++)        
206 –                data_[i][j] = m1.data_[i][j] - m2.data_[i][j];
207 –        }
208 –        
209 –        /**
210 –        * Sets the value of this matrix to the scalar multiplication of itself (*this *= s).
211 –        * @param s the scalar value
212 –        */
213 –        inline void mul( double s ) {
214 –            for (unsigned int i = 0; i < Dim; i++)
215 –                for (unsigned int j = 0; j < Dim; j++)  
216 –                    data_[i][j] *= s;
217 –        }
155  
156 <        /**
157 <        * Sets the value of this matrix to the scalar multiplication of matrix m  (*this = s * m).
158 <        * @param s the scalar value
159 <        * @param m the matrix
160 <        */
161 <        inline void mul( double s, const SquareMatrix<Real, Dim>& m ) {
162 <            for (unsigned int i = 0; i < Dim; i++)
163 <                for (unsigned int j = 0; j < Dim; j++)  
164 <                    data_[i][j] = s * m.data_[i][j];
228 <        }
156 >            /** Tests if this matrix is diagonal. */
157 >            bool isDiagonal() const {
158 >                for (unsigned int i = 0; i < Dim ; i++)
159 >                    for (unsigned int j = 0; j < Dim; j++)
160 >                        if (i !=j && fabs(this->data_[i][j]) > oopse::epsilon)
161 >                            return false;
162 >                        
163 >                return true;
164 >            }
165  
166 <        /**
167 <        * Sets the value of this matrix to the  multiplication of this matrix and matrix m
168 <        * (*this = *this * m).
169 <        * @param m the matrix
170 <        */
171 <        inline void mul(const SquareMatrix<Real, Dim>& m ) {
172 <            SquareMatrix<Real, Dim> tmp(*this);
173 <            
238 <            for (unsigned int i = 0; i < Dim; i++)
239 <                for (unsigned int j = 0; j < Dim; j++) {  
166 >            /** Tests if this matrix is the unit matrix. */
167 >            bool isUnitMatrix() const {
168 >                if (!isDiagonal())
169 >                    return false;
170 >                
171 >                for (unsigned int i = 0; i < Dim ; i++)
172 >                    if (fabs(this->data_[i][i] - 1) > oopse::epsilon)
173 >                        return false;
174                      
175 <                    data_[i][j] = 0.0;
176 <                    for (unsigned int k = 0; k < Dim; k++)
177 <                        data_[i][j]  = tmp.data_[i][k] * m.data_[k][j]
178 <                }
179 <        }
180 <        
181 <        /**
182 <        * Sets the value of this matrix to the  left multiplication of matrix m into itself
183 <        * (*this = m *  *this).
184 <        * @param m the matrix
185 <        */
186 <        inline void leftmul(const SquareMatrix<Real, Dim>& m ) {
187 <            SquareMatrix<Real, Dim> tmp(*this);
175 >                return true;
176 >            }        
177 >
178 >            /** Return the transpose of this matrix */
179 >            SquareMatrix<Real,  Dim> transpose() const{
180 >                SquareMatrix<Real,  Dim> result;
181 >                
182 >                for (unsigned int i = 0; i < Dim; i++)
183 >                    for (unsigned int j = 0; j < Dim; j++)              
184 >                        result(j, i) = this->data_[i][j];
185 >
186 >                return result;
187 >            }
188              
189 <            for (unsigned int i = 0; i < Dim; i++)
190 <                for (unsigned int j = 0; j < Dim; j++) {  
191 <                    
192 <                    data_[i][j] = 0.0;
259 <                    for (unsigned int k = 0; k < Dim; k++)
260 <                        data_[i][j]  = m.data_[i][k] * tmp.data_[k][j]
261 <                }
262 <        }
189 >            /** @todo need implementation */
190 >            void diagonalize() {
191 >                //jacobi(m, eigenValues, ortMat);
192 >            }
193  
194 <        /**
195 <        * Sets the value of this matrix to the  multiplication of matrix m1 and matrix m2
196 <        * (*this = m1 * m2).
197 <        * @param m1 the first  matrix
198 <        * @param m2 the second matrix
199 <        */
200 <        inline void mul(const SquareMatrix<Real, Dim>& m1,
201 <                                  const SquareMatrix<Real, Dim>& m2 ) {
202 <            for (unsigned int i = 0; i < Dim; i++)
203 <                for (unsigned int j = 0; j < Dim; j++) {  
204 <                    
205 <                    data_[i][j] = 0.0;
206 <                    for (unsigned int k = 0; k < Dim; k++)
207 <                        data_[i][j]  = m1.data_[i][k] * m2.data_[k][j]
208 <                }
194 >            /**
195 >             * Jacobi iteration routines for computing eigenvalues/eigenvectors of
196 >             * real symmetric matrix
197 >             *
198 >             * @return true if success, otherwise return false
199 >             * @param a symmetric matrix whose eigenvectors are to be computed. On return, the matrix is
200 >             *     overwritten
201 >             * @param w will contain the eigenvalues of the matrix On return of this function
202 >             * @param v the columns of this matrix will contain the eigenvectors. The eigenvectors are
203 >             *    normalized and mutually orthogonal.
204 >             */
205 >          
206 >            static int jacobi(SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& d,
207 >                                  SquareMatrix<Real, Dim>& v);
208 >    };//end SquareMatrix
209 >
210 >
211 > /*=========================================================================
212 >
213 >  Program:   Visualization Toolkit
214 >  Module:    $RCSfile: SquareMatrix.hpp,v $
215 >
216 >  Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen
217 >  All rights reserved.
218 >  See Copyright.txt or http://www.kitware.com/Copyright.htm for details.
219  
220 <        }
221 <        
222 <        /**
283 <        * Sets the value of this matrix to the scalar division of itself  (*this /= s ).
284 <        * @param s the scalar value
285 <        */            
286 <        inline void div( double s) {
287 <            for (unsigned int i = 0; i < Dim; i++)
288 <                for (unsigned int j = 0; j < Dim; j++)  
289 <                    data_[i][j] /= s;
290 <        }
291 <        
292 <        inline SquareMatrix<Real, Dim>& operator=(const SquareMatrix<Real, Dim>& v) {
293 <            if (this == &v)
294 <                return *this;
295 <            
296 <            for (unsigned int i = 0; i < Dim; i++)            
297 <                data_[i] = v[i];
298 <            
299 <            return *this;
300 <        }
301 <        
302 <        /**
303 <        * Sets the value of this matrix to the scalar division of matrix v1  (*this = v1 / s ).
304 <        * @paran v1 the source matrix
305 <        * @param s the scalar value
306 <        */                        
307 <        inline void div( const SquareMatrix<Real, Dim>& v1, double s ) {
308 <            for (unsigned int i = 0; i < Dim; i++)
309 <                data_[i] = v1.data_[i] / s;
310 <        }
220 >     This software is distributed WITHOUT ANY WARRANTY; without even
221 >     the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
222 >     PURPOSE.  See the above copyright notice for more information.
223  
224 <        /**
313 <         *  Multiples a scalar into every element of this matrix.
314 <         * @param s the scalar value
315 <         */
316 <        SquareMatrix<Real, Dim>& operator *=(const double s) {
317 <            this->mul(s);
318 <            return *this;
319 <        }
224 > =========================================================================*/
225  
226 <        /**
227 <         *  Divides every element of this matrix by a scalar.
323 <         * @param s the scalar value
324 <         */
325 <        SquareMatrix<Real, Dim>& operator /=(const double s) {
326 <            this->div(s);
327 <            return *this;
328 <        }
226 > #define VTK_ROTATE(a,i,j,k,l) g=a(i, j);h=a(k, l);a(i, j)=g-s*(h+g*tau);\
227 >        a(k, l)=h+s*(g-h*tau)
228  
229 <        /**
331 <         * Sets the value of this matrix to the sum of the other matrix and itself (*this += m).
332 <         * @param m the other matrix
333 <         */
334 <        SquareMatrix<Real, Dim>& operator += (const SquareMatrix<Real, Dim>& m) {
335 <            add(m);
336 <            return *this;
337 <         }
229 > #define VTK_MAX_ROTATIONS 20
230  
231 <        /**
232 <         * Sets the value of this matrix to the differerence of itself and the other matrix (*this -= m)
233 <         * @param m the other matrix
234 <         */
235 <        SquareMatrix<Real, Dim>& operator -= (const SquareMatrix<Real, Dim>& m){
236 <            sub(m);
237 <            return *this;
238 <        }
231 >    // Jacobi iteration for the solution of eigenvectors/eigenvalues of a nxn
232 >    // real symmetric matrix. Square nxn matrix a; size of matrix in n;
233 >    // output eigenvalues in w; and output eigenvectors in v. Resulting
234 >    // eigenvalues/vectors are sorted in decreasing order; eigenvectors are
235 >    // normalized.
236 >    template<typename Real, int Dim>
237 >    int SquareMatrix<Real, Dim>::jacobi(SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& w,
238 >                                        SquareMatrix<Real, Dim>& v) {
239 >        const int n = Dim;  
240 >        int i, j, k, iq, ip, numPos;
241 >        Real tresh, theta, tau, t, sm, s, h, g, c, tmp;
242 >        Real bspace[4], zspace[4];
243 >        Real *b = bspace;
244 >        Real *z = zspace;
245  
246 <        /** set this matrix to an identity matrix*/
247 <
248 <       void identity() {
249 <            for (unsigned int i = 0; i < Dim; i++)
352 <                for (unsigned int i = 0; i < Dim; i++)
353 <                    if (i == j)
354 <                        data_[i][j] = 1.0;
355 <                    else
356 <                        data_[i][j] = 0.0;
246 >        // only allocate memory if the matrix is large
247 >        if (n > 4) {
248 >            b = new Real[n];
249 >            z = new Real[n];
250          }
251  
252 <        /** Sets the value of this matrix to  the inversion of itself. */
253 <        void  inverse() {
254 <            inverse(*this);
252 >        // initialize
253 >        for (ip=0; ip<n; ip++) {
254 >            for (iq=0; iq<n; iq++) {
255 >                v(ip, iq) = 0.0;
256 >            }
257 >            v(ip, ip) = 1.0;
258          }
259 <
260 <        /**
261 <         * Sets the value of this matrix to  the inversion of other matrix.
366 <         * @ param m the source matrix
367 <         */        
368 <        void inverse(const SquareMatrix<Real, Dim>& m);
369 <        
370 <        /** Sets the value of this matrix to  the transpose of itself. */
371 <        void transpose() {
372 <            for (unsigned int i = 0; i < Dim - 1; i++)
373 <                for (unsigned int j = i; j < Dim; j++)
374 <                    std::swap(data_[i][j], data_[j][i]);
259 >        for (ip=0; ip<n; ip++) {
260 >            b[ip] = w[ip] = a(ip, ip);
261 >            z[ip] = 0.0;
262          }
263  
264 <        /**
265 <         * Sets the value of this matrix to  the transpose of other matrix.
266 <         * @ param m the source matrix
267 <         */        
268 <        void transpose(const SquareMatrix<Real, Dim>& m) {
269 <            
270 <            if (this == &m) {
271 <                transpose();
264 >        // begin rotation sequence
265 >        for (i=0; i<VTK_MAX_ROTATIONS; i++) {
266 >            sm = 0.0;
267 >            for (ip=0; ip<n-1; ip++) {
268 >                for (iq=ip+1; iq<n; iq++) {
269 >                    sm += fabs(a(ip, iq));
270 >                }
271 >            }
272 >            if (sm == 0.0) {
273 >                break;
274 >            }
275 >
276 >            if (i < 3) {                                // first 3 sweeps
277 >                tresh = 0.2*sm/(n*n);
278              } else {
279 <                for (unsigned int i = 0; i < Dim; i++)
387 <                    for (unsigned int j =0; j < Dim; j++)
388 <                        data_[i][j] = m.data_[i][j];
279 >                tresh = 0.0;
280              }
390 –        }
281  
282 <        /** Returns the determinant of this matrix. */
283 <        double determinant() const {
282 >            for (ip=0; ip<n-1; ip++) {
283 >                for (iq=ip+1; iq<n; iq++) {
284 >                    g = 100.0*fabs(a(ip, iq));
285  
286 <        }
286 >                    // after 4 sweeps
287 >                    if (i > 3 && (fabs(w[ip])+g) == fabs(w[ip])
288 >                        && (fabs(w[iq])+g) == fabs(w[iq])) {
289 >                        a(ip, iq) = 0.0;
290 >                    } else if (fabs(a(ip, iq)) > tresh) {
291 >                        h = w[iq] - w[ip];
292 >                        if ( (fabs(h)+g) == fabs(h)) {
293 >                            t = (a(ip, iq)) / h;
294 >                        } else {
295 >                            theta = 0.5*h / (a(ip, iq));
296 >                            t = 1.0 / (fabs(theta)+sqrt(1.0+theta*theta));
297 >                            if (theta < 0.0) {
298 >                                t = -t;
299 >                            }
300 >                        }
301 >                        c = 1.0 / sqrt(1+t*t);
302 >                        s = t*c;
303 >                        tau = s/(1.0+c);
304 >                        h = t*a(ip, iq);
305 >                        z[ip] -= h;
306 >                        z[iq] += h;
307 >                        w[ip] -= h;
308 >                        w[iq] += h;
309 >                        a(ip, iq)=0.0;
310  
311 <        /** Returns the trace of this matrix. */
312 <        double trace() const {
313 <           double tmp = 0;
314 <          
315 <            for (unsigned int i = 0; i < Dim ; i++)
316 <                tmp += data_[i][i];
311 >                        // ip already shifted left by 1 unit
312 >                        for (j = 0;j <= ip-1;j++) {
313 >                            VTK_ROTATE(a,j,ip,j,iq);
314 >                        }
315 >                        // ip and iq already shifted left by 1 unit
316 >                        for (j = ip+1;j <= iq-1;j++) {
317 >                            VTK_ROTATE(a,ip,j,j,iq);
318 >                        }
319 >                        // iq already shifted left by 1 unit
320 >                        for (j=iq+1; j<n; j++) {
321 >                            VTK_ROTATE(a,ip,j,iq,j);
322 >                        }
323 >                        for (j=0; j<n; j++) {
324 >                            VTK_ROTATE(v,j,ip,j,iq);
325 >                        }
326 >                    }
327 >                }
328 >            }
329  
330 <            return tmp;
330 >            for (ip=0; ip<n; ip++) {
331 >                b[ip] += z[ip];
332 >                w[ip] = b[ip];
333 >                z[ip] = 0.0;
334 >            }
335          }
336  
337 <        /** Tests if this matrix is symmetrix. */            
338 <        bool isSymmetric() const {
339 <            for (unsigned int i = 0; i < Dim - 1; i++)
340 <                for (unsigned int j = i; j < Dim; j++)
411 <                    if (fabs(data_[i][j] - data_[j][i]) > epsilon)
412 <                        return false;
413 <                    
414 <            return true;
337 >        //// this is NEVER called
338 >        if ( i >= VTK_MAX_ROTATIONS ) {
339 >            std::cout << "vtkMath::Jacobi: Error extracting eigenfunctions" << std::endl;
340 >            return 0;
341          }
342  
343 <        /** Tests if this matrix is orthogona. */            
344 <        bool isOrthogonal() const {
345 <            SquareMatrix<Real, Dim> t(*this);
346 <
347 <            t.transpose();
348 <
349 <            return isUnitMatrix(*this * t);
343 >        // sort eigenfunctions                 these changes do not affect accuracy
344 >        for (j=0; j<n-1; j++) {                  // boundary incorrect
345 >            k = j;
346 >            tmp = w[k];
347 >            for (i=j+1; i<n; i++) {                // boundary incorrect, shifted already
348 >                if (w[i] >= tmp) {                   // why exchage if same?
349 >                    k = i;
350 >                    tmp = w[k];
351 >                }
352 >            }
353 >            if (k != j) {
354 >                w[k] = w[j];
355 >                w[j] = tmp;
356 >                for (i=0; i<n; i++) {
357 >                    tmp = v(i, j);
358 >                    v(i, j) = v(i, k);
359 >                    v(i, k) = tmp;
360 >                }
361 >            }
362          }
363 <
364 <        /** Tests if this matrix is diagonal. */
365 <        bool isDiagonal() const {
366 <            for (unsigned int i = 0; i < Dim ; i++)
367 <                for (unsigned int j = 0; j < Dim; j++)
368 <                    if (i !=j && fabs(data_[i][j]) > epsilon)
369 <                        return false;
370 <                    
371 <            return true;
363 >        // insure eigenvector consistency (i.e., Jacobi can compute vectors that
364 >        // are negative of one another (.707,.707,0) and (-.707,-.707,0). This can
365 >        // reek havoc in hyperstreamline/other stuff. We will select the most
366 >        // positive eigenvector.
367 >        int ceil_half_n = (n >> 1) + (n & 1);
368 >        for (j=0; j<n; j++) {
369 >            for (numPos=0, i=0; i<n; i++) {
370 >                if ( v(i, j) >= 0.0 ) {
371 >                    numPos++;
372 >                }
373 >            }
374 >            //    if ( numPos < ceil(double(n)/double(2.0)) )
375 >            if ( numPos < ceil_half_n) {
376 >                for (i=0; i<n; i++) {
377 >                    v(i, j) *= -1.0;
378 >                }
379 >            }
380          }
381  
382 <        /** Tests if this matrix is the unit matrix. */
383 <        bool isUnitMatrix() const {
384 <            if (!isDiagonal())
439 <                return false;
440 <            
441 <            for (unsigned int i = 0; i < Dim ; i++)
442 <                if (fabs(data_[i][i] - 1) > epsilon)
443 <                    return false;
444 <                
445 <            return true;
382 >        if (n > 4) {
383 >            delete [] b;
384 >            delete [] z;
385          }
386 <        
448 <        protected:
449 <            double data_[Dim][Dim]; /**< matrix element */            
450 <
451 <    };//end SquareMatrix
452 <
453 <    
454 <    /** Negate the value of every element of this matrix. */
455 <    template<typename Real, int Dim>
456 <    inline SquareMatrix<Real, Dim> operator -(const SquareMatrix& m) {
457 <        SquareMatrix<Real, Dim> result(m);
458 <
459 <        result.negate();
460 <
461 <        return result;
386 >        return 1;
387      }
463 –    
464 –    /**
465 –    * Return the sum of two matrixes  (m1 + m2).
466 –    * @return the sum of two matrixes
467 –    * @param m1 the first matrix
468 –    * @param m2 the second matrix
469 –    */
470 –    template<typename Real, int Dim>
471 –    inline SquareMatrix<Real, Dim> operator + (const SquareMatrix<Real, Dim>& m1,
472 –                                                                                         const SquareMatrix<Real, Dim>& m2) {
473 –        SquareMatrix<Real, Dim>result;
388  
475 –        result.add(m1, m2);
389  
477 –        return result;
478 –    }
479 –    
480 –    /**
481 –    * Return the difference of two matrixes  (m1 - m2).
482 –    * @return the sum of two matrixes
483 –    * @param m1 the first matrix
484 –    * @param m2 the second matrix
485 –    */
486 –    template<typename Real, int Dim>
487 –    inline SquareMatrix<Real, Dim> operator - (const SquareMatrix<Real, Dim>& m1,
488 –                                                                                        const SquareMatrix<Real, Dim>& m2) {
489 –        SquareMatrix<Real, Dim>result;
490 –
491 –        result.sub(m1, m2);
492 –
493 –        return result;
494 –    }
495 –    
496 –    /**
497 –    * Return the multiplication of two matrixes  (m1 * m2).
498 –    * @return the multiplication of two matrixes
499 –    * @param m1 the first matrix
500 –    * @param m2 the second matrix
501 –    */
502 –    template<typename Real, int Dim>
503 –    inline SquareMatrix<Real, Dim> operator *(const SquareMatrix<Real, Dim>& m1,
504 –                                                                                       const SquareMatrix<Real, Dim>& m2) {
505 –        SquareMatrix<Real, Dim> result;
506 –
507 –        result.mul(m1, m2);
508 –
509 –        return result;
510 –    }
511 –    
512 –    /**
513 –    * Return the multiplication of  matrixes m  and vector v (m * v).
514 –    * @return the multiplication of matrixes and vector
515 –    * @param m the matrix
516 –    * @param v the vector
517 –    */
518 –    template<typename Real, int Dim>
519 –    inline Vector<Real, Dim> operator *(const SquareMatrix<Real, Dim>& m,
520 –                                                                 const SquareMatrix<Real, Dim>& v) {
521 –        Vector<Real, Dim> result;
522 –
523 –        for (unsigned int i = 0; i < Dim ; i++)
524 –            for (unsigned int j = 0; j < Dim ; j++)            
525 –                result[i] += m(i, j) * v[j];
526 –            
527 –        return result;                                                                
528 –    }
390   }
391   #endif //MATH_SQUAREMATRIX_HPP
392 +

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