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Revision 1644 by tim, Mon Oct 25 22:46:19 2004 UTC vs.
Revision 2204 by gezelter, Fri Apr 15 22:04:00 2005 UTC

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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.
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 "math/RectMatrix.hpp"
52  
53   namespace oopse {
54  
55 <    /**
56 <     * @class SquareMatrix SquareMatrix.hpp "math/SquareMatrix.hpp"
57 <     * @brief A square matrix class
58 <     * @template Real the element type
59 <     * @template Dim the dimension of the square matrix
60 <     */
61 <    template<typename Real, int Dim>
62 <    class SquareMatrix : public RectMatrix<Real, Dim, Dim> {
63 <        public:
64 <            typedef Real ElemType;
65 <            typedef Real* ElemPoinerType;
55 >  /**
56 >   * @class SquareMatrix SquareMatrix.hpp "math/SquareMatrix.hpp"
57 >   * @brief A square matrix class
58 >   * @template Real the element type
59 >   * @template Dim the dimension of the square matrix
60 >   */
61 >  template<typename Real, int Dim>
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(Real s) : RectMatrix<Real, Dim, Dim>(s){
76 <            }
74 >    /** Constructs and initializes every element of this matrix to a scalar */
75 >    SquareMatrix(Real s) : RectMatrix<Real, Dim, Dim>(s){
76 >    }
77  
78 <            /** Constructs and initializes from an array */
79 <            SquareMatrix(Real* array) : RectMatrix<Real, Dim, Dim>(array){
80 <            }
78 >    /** Constructs and initializes from an array */
79 >    SquareMatrix(Real* array) : RectMatrix<Real, Dim, Dim>(array){
80 >    }
81  
82  
83 <            /** copy constructor */
84 <            SquareMatrix(const RectMatrix<Real, Dim, Dim>& m) : RectMatrix<Real, Dim, Dim>(m) {
85 <            }
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 <            }
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*/
93 >    /** Retunrs  an identity matrix*/
94  
95 <           static SquareMatrix<Real, Dim> identity() {
96 <                SquareMatrix<Real, Dim> m;
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;
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 <                return m;
106 <            }
105 >      return m;
106 >    }
107  
108 <            /**
109 <             * Retunrs  the inversion of this matrix.
110 <             * @todo need implementation
111 <             */
112 <             SquareMatrix<Real, Dim>  inverse() {
113 <                 SquareMatrix<Real, Dim> result;
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 <                 return result;
116 <            }        
115 >      return result;
116 >    }        
117  
118 <            /**
119 <             * Returns the determinant of this matrix.
120 <             * @todo need implementation
121 <             */
122 <            Real determinant() const {
123 <                Real det;
124 <                return det;
125 <            }
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 <            /** Returns the trace of this matrix. */
128 <            Real trace() const {
129 <               Real tmp = 0;
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 += data_[i][i];
131 >      for (unsigned int i = 0; i < Dim ; i++)
132 >        tmp += this->data_[i][i];
133  
134 <                return tmp;
135 <            }
134 >      return tmp;
135 >    }
136  
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(data_[i][j] - data_[j][i]) > oopse::epsilon)
142 <                            return false;
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 <            }
144 >      return true;
145 >    }
146  
147 <            /** Tests if this matrix is orthogonal. */            
148 <            bool isOrthogonal() {
149 <                SquareMatrix<Real, Dim> tmp;
147 >    /** Tests if this matrix is orthogonal. */            
148 >    bool isOrthogonal() {
149 >      SquareMatrix<Real, Dim> tmp;
150  
151 <                tmp = *this * transpose();
151 >      tmp = *this * transpose();
152  
153 <                return tmp.isDiagonal();
154 <            }
153 >      return tmp.isDiagonal();
154 >    }
155  
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(data_[i][j]) > oopse::epsilon)
161 <                            return false;
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 <            }
163 >      return true;
164 >    }
165  
166 <            /** Tests if this matrix is the unit matrix. */
167 <            bool isUnitMatrix() const {
168 <                if (!isDiagonal())
169 <                    return false;
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(data_[i][i] - 1) > oopse::epsilon)
173 <                        return false;
171 >      for (unsigned int i = 0; i < Dim ; i++)
172 >        if (fabs(this->data_[i][i] - 1) > oopse::epsilon)
173 >          return false;
174                      
175 <                return true;
176 <            }        
175 >      return true;
176 >    }        
177  
178 <            /** @todo need implementation */
179 <            void diagonalize() {
180 <                //jacobi(m, eigenValues, ortMat);
181 <            }
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 <            /**
187 <             * Jacobi iteration routines for computing eigenvalues/eigenvectors of
188 <             * real symmetric matrix
189 <             *
190 <             * @return true if success, otherwise return false
191 <             * @param a symmetric matrix whose eigenvectors are to be computed. On return, the matrix is
192 <             *     overwritten
193 <             * @param w will contain the eigenvalues of the matrix On return of this function
194 <             * @param v the columns of this matrix will contain the eigenvectors. The eigenvectors are
195 <             *    normalized and mutually orthogonal.
196 <             */
186 >      return result;
187 >    }
188 >            
189 >    /** @todo need implementation */
190 >    void diagonalize() {
191 >      //jacobi(m, eigenValues, ortMat);
192 >    }
193 >
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
206 >    static int jacobi(SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& d,
207 >                      SquareMatrix<Real, Dim>& v);
208 >  };//end SquareMatrix
209  
210  
211 < /*=========================================================================
211 >  /*=========================================================================
212  
213    Program:   Visualization Toolkit
214    Module:    $RCSfile: SquareMatrix.hpp,v $
# Line 190 | Line 217 | namespace oopse {
217    All rights reserved.
218    See Copyright.txt or http://www.kitware.com/Copyright.htm for details.
219  
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.
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 < =========================================================================*/
224 >  =========================================================================*/
225  
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)
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   #define VTK_MAX_ROTATIONS 20
230  
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;
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 <        // only allocate memory if the matrix is large
247 <        if (n > 4) {
248 <            b = new Real[n];
249 <            z = new Real[n];
250 <        }
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 <        // 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 <        for (ip=0; ip<n; ip++) {
260 <            b[ip] = w[ip] = a(ip, ip);
261 <            z[ip] = 0.0;
262 <        }
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 >    for (ip=0; ip<n; ip++) {
260 >      b[ip] = w[ip] = a(ip, ip);
261 >      z[ip] = 0.0;
262 >    }
263  
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 <            }
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 <                tresh = 0.0;
280 <            }
276 >      if (i < 3) {                                // first 3 sweeps
277 >        tresh = 0.2*sm/(n*n);
278 >      } else {
279 >        tresh = 0.0;
280 >      }
281  
282 <            for (ip=0; ip<n-1; ip++) {
283 <                for (iq=ip+1; iq<n; iq++) {
284 <                    g = 100.0*fabs(a(ip, iq));
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 <                    // 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;
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 <                        // 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 <            }
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 <            for (ip=0; ip<n; ip++) {
331 <                b[ip] += z[ip];
332 <                w[ip] = b[ip];
333 <                z[ip] = 0.0;
334 <            }
335 <        }
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 <        //// this is NEVER called
338 <        if ( i >= VTK_MAX_ROTATIONS ) {
339 <            std::cout << "vtkMath::Jacobi: Error extracting eigenfunctions" << std::endl;
340 <            return 0;
341 <        }
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 <        // 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 <        // 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 <        }
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 >    // 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 <        if (n > 4) {
383 <            delete [] b;
384 <            delete [] z;
358 <        }
359 <        return 1;
382 >    if (n > 4) {
383 >      delete [] b;
384 >      delete [] z;
385      }
386 +    return 1;
387 +  }
388  
389  
390   }

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