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Revision 1639 by tim, Fri Oct 22 23:09:57 2004 UTC vs.
Revision 2752 by gezelter, Tue May 16 02:06:37 2006 UTC

# Line 1 | Line 1
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 + #include "utils/NumericConstant.hpp"
53  
54   namespace oopse {
55  
56 <    /**
57 <     * @class SquareMatrix SquareMatrix.hpp "math/SquareMatrix.hpp"
58 <     * @brief A square matrix class
59 <     * @template Real the element type
60 <     * @template Dim the dimension of the square matrix
61 <     */
62 <    template<typename Real, int Dim>
63 <    class SquareMatrix : public RectMatrix<Real, Dim, Dim> {
64 <        public:
65 <            typedef Real ElemType;
66 <            typedef Real* ElemPoinerType;
56 >  /**
57 >   * @class SquareMatrix SquareMatrix.hpp "math/SquareMatrix.hpp"
58 >   * @brief A square matrix class
59 >   * @template Real the element type
60 >   * @template Dim the dimension of the square matrix
61 >   */
62 >  template<typename Real, int Dim>
63 >  class SquareMatrix : public RectMatrix<Real, Dim, Dim> {
64 >  public:
65 >    typedef Real ElemType;
66 >    typedef Real* ElemPoinerType;
67  
68 <            /** default constructor */
69 <            SquareMatrix() {
70 <                for (unsigned int i = 0; i < Dim; i++)
71 <                    for (unsigned int j = 0; j < Dim; j++)
72 <                        data_[i][j] = 0.0;
73 <             }
68 >    /** default constructor */
69 >    SquareMatrix() {
70 >      for (unsigned int i = 0; i < Dim; i++)
71 >        for (unsigned int j = 0; j < Dim; j++)
72 >          this->data_[i][j] = 0.0;
73 >    }
74  
75 <            /** copy constructor */
76 <            SquareMatrix(const RectMatrix<Real, Dim, Dim>& m) : RectMatrix<Real, Dim, Dim>(m) {
77 <            }
75 >    /** Constructs and initializes every element of this matrix to a scalar */
76 >    SquareMatrix(Real s) : RectMatrix<Real, Dim, Dim>(s){
77 >    }
78 >
79 >    /** Constructs and initializes from an array */
80 >    SquareMatrix(Real* array) : RectMatrix<Real, Dim, Dim>(array){
81 >    }
82 >
83 >
84 >    /** copy constructor */
85 >    SquareMatrix(const RectMatrix<Real, Dim, Dim>& m) : RectMatrix<Real, Dim, Dim>(m) {
86 >    }
87              
88 <            /** copy assignment operator */
89 <            SquareMatrix<Real, Dim>& operator =(const RectMatrix<Real, Dim, Dim>& m) {
90 <                RectMatrix<Real, Dim, Dim>::operator=(m);
91 <                return *this;
92 <            }
88 >    /** copy assignment operator */
89 >    SquareMatrix<Real, Dim>& operator =(const RectMatrix<Real, Dim, Dim>& m) {
90 >      RectMatrix<Real, Dim, Dim>::operator=(m);
91 >      return *this;
92 >    }
93                                    
94 <            /** Retunrs  an identity matrix*/
94 >    /** Retunrs  an identity matrix*/
95  
96 <           static SquareMatrix<Real, Dim> identity() {
97 <                SquareMatrix<Real, Dim> m;
96 >    static SquareMatrix<Real, Dim> identity() {
97 >      SquareMatrix<Real, Dim> m;
98                  
99 <                for (unsigned int i = 0; i < Dim; i++)
100 <                    for (unsigned int j = 0; j < Dim; j++)
101 <                        if (i == j)
102 <                            m(i, j) = 1.0;
103 <                        else
104 <                            m(i, j) = 0.0;
99 >      for (unsigned int i = 0; i < Dim; i++)
100 >        for (unsigned int j = 0; j < Dim; j++)
101 >          if (i == j)
102 >            m(i, j) = 1.0;
103 >          else
104 >            m(i, j) = 0.0;
105  
106 <                return m;
107 <            }
106 >      return m;
107 >    }
108  
109 <            /**
110 <             * Retunrs  the inversion of this matrix.
111 <             * @todo need implementation
112 <             */
113 <             SquareMatrix<Real, Dim>  inverse() {
114 <                 SquareMatrix<Real, Dim> result;
109 >    /**
110 >     * Retunrs  the inversion of this matrix.
111 >     * @todo need implementation
112 >     */
113 >    SquareMatrix<Real, Dim>  inverse() {
114 >      SquareMatrix<Real, Dim> result;
115  
116 <                 return result;
117 <            }        
116 >      return result;
117 >    }        
118  
119 <            /**
120 <             * Returns the determinant of this matrix.
121 <             * @todo need implementation
122 <             */
123 <            Real determinant() const {
124 <                Real det;
125 <                return det;
126 <            }
119 >    /**
120 >     * Returns the determinant of this matrix.
121 >     * @todo need implementation
122 >     */
123 >    Real determinant() const {
124 >      Real det;
125 >      return det;
126 >    }
127  
128 <            /** Returns the trace of this matrix. */
129 <            Real trace() const {
130 <               Real tmp = 0;
128 >    /** Returns the trace of this matrix. */
129 >    Real trace() const {
130 >      Real tmp = 0;
131                
132 <                for (unsigned int i = 0; i < Dim ; i++)
133 <                    tmp += data_[i][i];
132 >      for (unsigned int i = 0; i < Dim ; i++)
133 >        tmp += this->data_[i][i];
134  
135 <                return tmp;
136 <            }
135 >      return tmp;
136 >    }
137  
138 <            /** Tests if this matrix is symmetrix. */            
139 <            bool isSymmetric() const {
140 <                for (unsigned int i = 0; i < Dim - 1; i++)
141 <                    for (unsigned int j = i; j < Dim; j++)
142 <                        if (fabs(data_[i][j] - data_[j][i]) > oopse::epsilon)
143 <                            return false;
138 >    /** Tests if this matrix is symmetrix. */            
139 >    bool isSymmetric() const {
140 >      for (unsigned int i = 0; i < Dim - 1; i++)
141 >        for (unsigned int j = i; j < Dim; j++)
142 >          if (fabs(this->data_[i][j] - this->data_[j][i]) > epsilon)
143 >            return false;
144                          
145 <                return true;
146 <            }
145 >      return true;
146 >    }
147  
148 <            /** Tests if this matrix is orthogonal. */            
149 <            bool isOrthogonal() {
150 <                SquareMatrix<Real, Dim> tmp;
148 >    /** Tests if this matrix is orthogonal. */            
149 >    bool isOrthogonal() {
150 >      SquareMatrix<Real, Dim> tmp;
151  
152 <                tmp = *this * transpose();
152 >      tmp = *this * transpose();
153  
154 <                return tmp.isDiagonal();
155 <            }
154 >      return tmp.isDiagonal();
155 >    }
156  
157 <            /** Tests if this matrix is diagonal. */
158 <            bool isDiagonal() const {
159 <                for (unsigned int i = 0; i < Dim ; i++)
160 <                    for (unsigned int j = 0; j < Dim; j++)
161 <                        if (i !=j && fabs(data_[i][j]) > oopse::epsilon)
162 <                            return false;
157 >    /** Tests if this matrix is diagonal. */
158 >    bool isDiagonal() const {
159 >      for (unsigned int i = 0; i < Dim ; i++)
160 >        for (unsigned int j = 0; j < Dim; j++)
161 >          if (i !=j && fabs(this->data_[i][j]) > epsilon)
162 >            return false;
163                          
164 <                return true;
165 <            }
164 >      return true;
165 >    }
166  
167 <            /** Tests if this matrix is the unit matrix. */
168 <            bool isUnitMatrix() const {
169 <                if (!isDiagonal())
170 <                    return false;
167 >    /** Tests if this matrix is the unit matrix. */
168 >    bool isUnitMatrix() const {
169 >      if (!isDiagonal())
170 >        return false;
171                  
172 <                for (unsigned int i = 0; i < Dim ; i++)
173 <                    if (fabs(data_[i][i] - 1) > oopse::epsilon)
174 <                        return false;
172 >      for (unsigned int i = 0; i < Dim ; i++)
173 >        if (fabs(this->data_[i][i] - 1) > epsilon)
174 >          return false;
175                      
176 <                return true;
177 <            }        
176 >      return true;
177 >    }        
178  
179 <            /** @todo need implementation */
180 <            void diagonalize() {
181 <                //jacobi(m, eigenValues, ortMat);
182 <            }
179 >    /** Return the transpose of this matrix */
180 >    SquareMatrix<Real,  Dim> transpose() const{
181 >      SquareMatrix<Real,  Dim> result;
182 >                
183 >      for (unsigned int i = 0; i < Dim; i++)
184 >        for (unsigned int j = 0; j < Dim; j++)              
185 >          result(j, i) = this->data_[i][j];
186  
187 <            /**
188 <             * Jacobi iteration routines for computing eigenvalues/eigenvectors of
189 <             * real symmetric matrix
190 <             *
191 <             * @return true if success, otherwise return false
192 <             * @param a symmetric matrix whose eigenvectors are to be computed. On return, the matrix is
193 <             *     overwritten
194 <             * @param w will contain the eigenvalues of the matrix On return of this function
195 <             * @param v the columns of this matrix will contain the eigenvectors. The eigenvectors are
196 <             *    normalized and mutually orthogonal.
197 <             */
187 >      return result;
188 >    }
189 >            
190 >    /** @todo need implementation */
191 >    void diagonalize() {
192 >      //jacobi(m, eigenValues, ortMat);
193 >    }
194 >
195 >    /**
196 >     * Jacobi iteration routines for computing eigenvalues/eigenvectors of
197 >     * real symmetric matrix
198 >     *
199 >     * @return true if success, otherwise return false
200 >     * @param a symmetric matrix whose eigenvectors are to be computed. On return, the matrix is
201 >     *     overwritten
202 >     * @param w will contain the eigenvalues of the matrix On return of this function
203 >     * @param v the columns of this matrix will contain the eigenvectors. The eigenvectors are
204 >     *    normalized and mutually orthogonal.
205 >     */
206            
207 <            static int jacobi(SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& d,
208 <                                  SquareMatrix<Real, Dim>& v);
209 <    };//end SquareMatrix
207 >    static int jacobi(SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& d,
208 >                      SquareMatrix<Real, Dim>& v);
209 >  };//end SquareMatrix
210  
211  
212 < /*=========================================================================
212 >  /*=========================================================================
213  
214    Program:   Visualization Toolkit
215    Module:    $RCSfile: SquareMatrix.hpp,v $
# Line 181 | Line 218 | namespace oopse {
218    All rights reserved.
219    See Copyright.txt or http://www.kitware.com/Copyright.htm for details.
220  
221 <     This software is distributed WITHOUT ANY WARRANTY; without even
222 <     the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
223 <     PURPOSE.  See the above copyright notice for more information.
221 >  This software is distributed WITHOUT ANY WARRANTY; without even
222 >  the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
223 >  PURPOSE.  See the above copyright notice for more information.
224  
225 < =========================================================================*/
225 >  =========================================================================*/
226  
227 < #define VTK_ROTATE(a,i,j,k,l) g=a(i, j);h=a(k, l);a(i, j)=g-s*(h+g*tau);\
228 <        a(k, l)=h+s*(g-h*tau)
227 > #define VTK_ROTATE(a,i,j,k,l) g=a(i, j);h=a(k, l);a(i, j)=g-s*(h+g*tau); \
228 >    a(k, l)=h+s*(g-h*tau)
229  
230   #define VTK_MAX_ROTATIONS 20
231  
232 <    // Jacobi iteration for the solution of eigenvectors/eigenvalues of a nxn
233 <    // real symmetric matrix. Square nxn matrix a; size of matrix in n;
234 <    // output eigenvalues in w; and output eigenvectors in v. Resulting
235 <    // eigenvalues/vectors are sorted in decreasing order; eigenvectors are
236 <    // normalized.
237 <    template<typename Real, int Dim>
238 <    int SquareMatrix<Real, Dim>::jacobi(SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& w,
239 <                                        SquareMatrix<Real, Dim>& v) {
240 <        const int n = Dim;  
241 <        int i, j, k, iq, ip, numPos;
242 <        Real tresh, theta, tau, t, sm, s, h, g, c, tmp;
243 <        Real bspace[4], zspace[4];
244 <        Real *b = bspace;
245 <        Real *z = zspace;
232 >  // Jacobi iteration for the solution of eigenvectors/eigenvalues of a nxn
233 >  // real symmetric matrix. Square nxn matrix a; size of matrix in n;
234 >  // output eigenvalues in w; and output eigenvectors in v. Resulting
235 >  // eigenvalues/vectors are sorted in decreasing order; eigenvectors are
236 >  // normalized.
237 >  template<typename Real, int Dim>
238 >  int SquareMatrix<Real, Dim>::jacobi(SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& w,
239 >                                      SquareMatrix<Real, Dim>& v) {
240 >    const int n = Dim;  
241 >    int i, j, k, iq, ip, numPos;
242 >    Real tresh, theta, tau, t, sm, s, h, g, c, tmp;
243 >    Real bspace[4], zspace[4];
244 >    Real *b = bspace;
245 >    Real *z = zspace;
246  
247 <        // only allocate memory if the matrix is large
248 <        if (n > 4) {
249 <            b = new Real[n];
250 <            z = new Real[n];
251 <        }
247 >    // only allocate memory if the matrix is large
248 >    if (n > 4) {
249 >      b = new Real[n];
250 >      z = new Real[n];
251 >    }
252  
253 <        // initialize
254 <        for (ip=0; ip<n; ip++) {
255 <            for (iq=0; iq<n; iq++) {
256 <                v(ip, iq) = 0.0;
257 <            }
258 <            v(ip, ip) = 1.0;
259 <        }
260 <        for (ip=0; ip<n; ip++) {
261 <            b[ip] = w[ip] = a(ip, ip);
262 <            z[ip] = 0.0;
263 <        }
253 >    // initialize
254 >    for (ip=0; ip<n; ip++) {
255 >      for (iq=0; iq<n; iq++) {
256 >        v(ip, iq) = 0.0;
257 >      }
258 >      v(ip, ip) = 1.0;
259 >    }
260 >    for (ip=0; ip<n; ip++) {
261 >      b[ip] = w[ip] = a(ip, ip);
262 >      z[ip] = 0.0;
263 >    }
264  
265 <        // begin rotation sequence
266 <        for (i=0; i<VTK_MAX_ROTATIONS; i++) {
267 <            sm = 0.0;
268 <            for (ip=0; ip<n-1; ip++) {
269 <                for (iq=ip+1; iq<n; iq++) {
270 <                    sm += fabs(a(ip, iq));
271 <                }
272 <            }
273 <            if (sm == 0.0) {
274 <                break;
275 <            }
265 >    // begin rotation sequence
266 >    for (i=0; i<VTK_MAX_ROTATIONS; i++) {
267 >      sm = 0.0;
268 >      for (ip=0; ip<n-1; ip++) {
269 >        for (iq=ip+1; iq<n; iq++) {
270 >          sm += fabs(a(ip, iq));
271 >        }
272 >      }
273 >      if (sm == 0.0) {
274 >        break;
275 >      }
276  
277 <            if (i < 3) {                                // first 3 sweeps
278 <                tresh = 0.2*sm/(n*n);
279 <            } else {
280 <                tresh = 0.0;
281 <            }
277 >      if (i < 3) {                                // first 3 sweeps
278 >        tresh = 0.2*sm/(n*n);
279 >      } else {
280 >        tresh = 0.0;
281 >      }
282  
283 <            for (ip=0; ip<n-1; ip++) {
284 <                for (iq=ip+1; iq<n; iq++) {
285 <                    g = 100.0*fabs(a(ip, iq));
283 >      for (ip=0; ip<n-1; ip++) {
284 >        for (iq=ip+1; iq<n; iq++) {
285 >          g = 100.0*fabs(a(ip, iq));
286  
287 <                    // after 4 sweeps
288 <                    if (i > 3 && (fabs(w[ip])+g) == fabs(w[ip])
289 <                        && (fabs(w[iq])+g) == fabs(w[iq])) {
290 <                        a(ip, iq) = 0.0;
291 <                    } else if (fabs(a(ip, iq)) > tresh) {
292 <                        h = w[iq] - w[ip];
293 <                        if ( (fabs(h)+g) == fabs(h)) {
294 <                            t = (a(ip, iq)) / h;
295 <                        } else {
296 <                            theta = 0.5*h / (a(ip, iq));
297 <                            t = 1.0 / (fabs(theta)+sqrt(1.0+theta*theta));
298 <                            if (theta < 0.0) {
299 <                                t = -t;
300 <                            }
301 <                        }
302 <                        c = 1.0 / sqrt(1+t*t);
303 <                        s = t*c;
304 <                        tau = s/(1.0+c);
305 <                        h = t*a(ip, iq);
306 <                        z[ip] -= h;
307 <                        z[iq] += h;
308 <                        w[ip] -= h;
309 <                        w[iq] += h;
310 <                        a(ip, iq)=0.0;
287 >          // after 4 sweeps
288 >          if (i > 3 && (fabs(w[ip])+g) == fabs(w[ip])
289 >              && (fabs(w[iq])+g) == fabs(w[iq])) {
290 >            a(ip, iq) = 0.0;
291 >          } else if (fabs(a(ip, iq)) > tresh) {
292 >            h = w[iq] - w[ip];
293 >            if ( (fabs(h)+g) == fabs(h)) {
294 >              t = (a(ip, iq)) / h;
295 >            } else {
296 >              theta = 0.5*h / (a(ip, iq));
297 >              t = 1.0 / (fabs(theta)+sqrt(1.0+theta*theta));
298 >              if (theta < 0.0) {
299 >                t = -t;
300 >              }
301 >            }
302 >            c = 1.0 / sqrt(1+t*t);
303 >            s = t*c;
304 >            tau = s/(1.0+c);
305 >            h = t*a(ip, iq);
306 >            z[ip] -= h;
307 >            z[iq] += h;
308 >            w[ip] -= h;
309 >            w[iq] += h;
310 >            a(ip, iq)=0.0;
311  
312 <                        // ip already shifted left by 1 unit
313 <                        for (j = 0;j <= ip-1;j++) {
314 <                            VTK_ROTATE(a,j,ip,j,iq);
315 <                        }
316 <                        // ip and iq already shifted left by 1 unit
317 <                        for (j = ip+1;j <= iq-1;j++) {
318 <                            VTK_ROTATE(a,ip,j,j,iq);
319 <                        }
320 <                        // iq already shifted left by 1 unit
321 <                        for (j=iq+1; j<n; j++) {
322 <                            VTK_ROTATE(a,ip,j,iq,j);
323 <                        }
324 <                        for (j=0; j<n; j++) {
325 <                            VTK_ROTATE(v,j,ip,j,iq);
326 <                        }
327 <                    }
328 <                }
329 <            }
312 >            // ip already shifted left by 1 unit
313 >            for (j = 0;j <= ip-1;j++) {
314 >              VTK_ROTATE(a,j,ip,j,iq);
315 >            }
316 >            // ip and iq already shifted left by 1 unit
317 >            for (j = ip+1;j <= iq-1;j++) {
318 >              VTK_ROTATE(a,ip,j,j,iq);
319 >            }
320 >            // iq already shifted left by 1 unit
321 >            for (j=iq+1; j<n; j++) {
322 >              VTK_ROTATE(a,ip,j,iq,j);
323 >            }
324 >            for (j=0; j<n; j++) {
325 >              VTK_ROTATE(v,j,ip,j,iq);
326 >            }
327 >          }
328 >        }
329 >      }
330  
331 <            for (ip=0; ip<n; ip++) {
332 <                b[ip] += z[ip];
333 <                w[ip] = b[ip];
334 <                z[ip] = 0.0;
335 <            }
336 <        }
331 >      for (ip=0; ip<n; ip++) {
332 >        b[ip] += z[ip];
333 >        w[ip] = b[ip];
334 >        z[ip] = 0.0;
335 >      }
336 >    }
337  
338 <        //// this is NEVER called
339 <        if ( i >= VTK_MAX_ROTATIONS ) {
340 <            std::cout << "vtkMath::Jacobi: Error extracting eigenfunctions" << std::endl;
341 <            return 0;
342 <        }
338 >    //// this is NEVER called
339 >    if ( i >= VTK_MAX_ROTATIONS ) {
340 >      std::cout << "vtkMath::Jacobi: Error extracting eigenfunctions" << std::endl;
341 >      return 0;
342 >    }
343  
344 <        // sort eigenfunctions                 these changes do not affect accuracy
345 <        for (j=0; j<n-1; j++) {                  // boundary incorrect
346 <            k = j;
347 <            tmp = w[k];
348 <            for (i=j+1; i<n; i++) {                // boundary incorrect, shifted already
349 <                if (w[i] >= tmp) {                   // why exchage if same?
350 <                    k = i;
351 <                    tmp = w[k];
352 <                }
353 <            }
354 <            if (k != j) {
355 <                w[k] = w[j];
356 <                w[j] = tmp;
357 <                for (i=0; i<n; i++) {
358 <                    tmp = v(i, j);
359 <                    v(i, j) = v(i, k);
360 <                    v(i, k) = tmp;
361 <                }
362 <            }
363 <        }
364 <        // insure eigenvector consistency (i.e., Jacobi can compute vectors that
365 <        // are negative of one another (.707,.707,0) and (-.707,-.707,0). This can
366 <        // reek havoc in hyperstreamline/other stuff. We will select the most
367 <        // positive eigenvector.
368 <        int ceil_half_n = (n >> 1) + (n & 1);
369 <        for (j=0; j<n; j++) {
370 <            for (numPos=0, i=0; i<n; i++) {
371 <                if ( v(i, j) >= 0.0 ) {
372 <                    numPos++;
373 <                }
374 <            }
375 <            //    if ( numPos < ceil(double(n)/double(2.0)) )
376 <            if ( numPos < ceil_half_n) {
377 <                for (i=0; i<n; i++) {
378 <                    v(i, j) *= -1.0;
379 <                }
380 <            }
381 <        }
344 >    // sort eigenfunctions                 these changes do not affect accuracy
345 >    for (j=0; j<n-1; j++) {                  // boundary incorrect
346 >      k = j;
347 >      tmp = w[k];
348 >      for (i=j+1; i<n; i++) {                // boundary incorrect, shifted already
349 >        if (w[i] >= tmp) {                   // why exchage if same?
350 >          k = i;
351 >          tmp = w[k];
352 >        }
353 >      }
354 >      if (k != j) {
355 >        w[k] = w[j];
356 >        w[j] = tmp;
357 >        for (i=0; i<n; i++) {
358 >          tmp = v(i, j);
359 >          v(i, j) = v(i, k);
360 >          v(i, k) = tmp;
361 >        }
362 >      }
363 >    }
364 >    // insure eigenvector consistency (i.e., Jacobi can compute vectors that
365 >    // are negative of one another (.707,.707,0) and (-.707,-.707,0). This can
366 >    // reek havoc in hyperstreamline/other stuff. We will select the most
367 >    // positive eigenvector.
368 >    int ceil_half_n = (n >> 1) + (n & 1);
369 >    for (j=0; j<n; j++) {
370 >      for (numPos=0, i=0; i<n; i++) {
371 >        if ( v(i, j) >= 0.0 ) {
372 >          numPos++;
373 >        }
374 >      }
375 >      //    if ( numPos < ceil(double(n)/double(2.0)) )
376 >      if ( numPos < ceil_half_n) {
377 >        for (i=0; i<n; i++) {
378 >          v(i, j) *= -1.0;
379 >        }
380 >      }
381 >    }
382  
383 <        if (n > 4) {
384 <            delete [] b;
385 <            delete [] z;
349 <        }
350 <        return 1;
383 >    if (n > 4) {
384 >      delete [] b;
385 >      delete [] z;
386      }
387 +    return 1;
388 +  }
389  
390  
391 +  typedef SquareMatrix<double, 6> Mat6x6d;
392   }
393   #endif //MATH_SQUAREMATRIX_HPP
394  

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