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Comparing trunk/OOPSE-3.0/src/math/SquareMatrix.hpp (file contents):
Revision 1594 by tim, Mon Oct 18 23:13:23 2004 UTC vs.
Revision 2204 by gezelter, Fri Apr 15 22:04:00 2005 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
# Line 36 | Line 52 | namespace oopse {
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:
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 <        /** copy constructor */
75 <        SquareMatrix(const RectMatrix<Real, Dim, Dim>& m)  : RectMatrix<Real, Dim, Dim>(m) {
76 <        }
59 <        
60 <        /** copy assignment operator */
61 <        SquareMatrix<Real, Dim>& operator =(const RectMatrix<Real, Dim, Dim>& m) {
62 <            RectMatrix<Real, Dim, Dim>::operator=(m);
63 <            return *this;
64 <        }
65 <                              
66 <        /** Retunrs  an identity matrix*/
74 >    /** Constructs and initializes every element of this matrix to a scalar */
75 >    SquareMatrix(Real s) : RectMatrix<Real, Dim, Dim>(s){
76 >    }
77  
78 <       static SquareMatrix<Real, Dim> identity() {
79 <            SquareMatrix<Real, Dim> m;
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 >    }
86              
87 <            for (unsigned int i = 0; i < Dim; i++)
88 <                for (unsigned int j = 0; j < Dim; j++)
89 <                    if (i == j)
90 <                        m(i, j) = 1.0;
91 <                    else
92 <                        m(i, j) = 0.0;
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 <            return m;
96 <        }
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 <        /**
106 <         * Retunrs  the inversion of this matrix.
83 <         * @todo
84 <         */
85 <         SquareMatrix<Real, Dim>  inverse() {
86 <             SquareMatrix<Real, Dim> result;
105 >      return m;
106 >    }
107  
108 <             return result;
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 <         * Returns the determinant of this matrix.
93 <         * @todo
94 <         */
95 <        double determinant() const {
96 <            double det;
97 <            return det;
98 <        }
115 >      return result;
116 >    }        
117  
118 <        /** Returns the trace of this matrix. */
119 <        double trace() const {
120 <           double tmp = 0;
121 <          
122 <            for (unsigned int i = 0; i < Dim ; i++)
123 <                tmp += data_[i][i];
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 <            return tmp;
128 <        }
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 <        /** Tests if this matrix is symmetrix. */            
135 <        bool isSymmetric() const {
112 <            for (unsigned int i = 0; i < Dim - 1; i++)
113 <                for (unsigned int j = i; j < Dim; j++)
114 <                    if (fabs(data_[i][j] - data_[j][i]) > oopse::epsilon)
115 <                        return false;
116 <                    
117 <            return true;
118 <        }
134 >      return tmp;
135 >    }
136  
137 <        /** Tests if this matrix is orthogonal. */            
138 <        bool isOrthogonal() {
139 <            SquareMatrix<Real, Dim> tmp;
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 <            tmp = *this * transpose();
147 >    /** Tests if this matrix is orthogonal. */            
148 >    bool isOrthogonal() {
149 >      SquareMatrix<Real, Dim> tmp;
150  
151 <            return tmp.isDiagonal();
127 <        }
151 >      tmp = *this * transpose();
152  
153 <        /** Tests if this matrix is diagonal. */
154 <        bool isDiagonal() const {
155 <            for (unsigned int i = 0; i < Dim ; i++)
156 <                for (unsigned int j = 0; j < Dim; j++)
157 <                    if (i !=j && fabs(data_[i][j]) > oopse::epsilon)
158 <                        return false;
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(this->data_[i][j]) > oopse::epsilon)
161 >            return false;
162 >                        
163 >      return true;
164 >    }
165 >
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 <            return true;
176 <        }
175 >      return true;
176 >    }        
177  
178 <        /** Tests if this matrix is the unit matrix. */
179 <        bool isUnitMatrix() const {
180 <            if (!isDiagonal())
142 <                return false;
143 <            
144 <            for (unsigned int i = 0; i < Dim ; i++)
145 <                if (fabs(data_[i][i] - 1) > oopse::epsilon)
146 <                    return false;
178 >    /** Return the transpose of this matrix */
179 >    SquareMatrix<Real,  Dim> transpose() const{
180 >      SquareMatrix<Real,  Dim> result;
181                  
182 <            return true;
183 <        }        
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 <        /** @todo need implement */
187 <        void diagonalize() {
153 <            //jacobi(m, eigenValues, ortMat);
154 <        }
155 <
156 <        /**
157 <         * Finds the eigenvalues and eigenvectors of a symmetric matrix
158 <         * @param eigenvals a reference to a vector3 where the
159 <         * eigenvalues will be stored. The eigenvalues are ordered so
160 <         * that eigenvals[0] <= eigenvals[1] <= eigenvals[2].
161 <         * @return an orthogonal matrix whose ith column is an
162 <         * eigenvector for the eigenvalue eigenvals[i]
163 <         */
164 <        SquareMatrix<Real, Dim>  findEigenvectors(Vector<Real, Dim>& eigenValues) {
165 <            SquareMatrix<Real, Dim> ortMat;
186 >      return result;
187 >    }
188              
189 <            if ( !isSymmetric()){
190 <                throw();
191 <            }
192 <            
171 <            SquareMatrix<Real, Dim> m(*this);
172 <            jacobi(m, eigenValues, ortMat);
189 >    /** @todo need implementation */
190 >    void diagonalize() {
191 >      //jacobi(m, eigenValues, ortMat);
192 >    }
193  
194 <            return ortMat;
195 <        }
196 <        /**
197 <         * Jacobi iteration routines for computing eigenvalues/eigenvectors of
198 <         * real symmetric matrix
199 <         *
200 <         * @return true if success, otherwise return false
201 <         * @param a source matrix
202 <         * @param w output eigenvalues
203 <         * @param v output eigenvectors
204 <         */
205 <        bool jacobi(const SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& w,
206 <                              SquareMatrix<Real, Dim>& v);
207 <    };//end SquareMatrix
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 < #define ROT(a,i,j,k,l) g=a(i, j);h=a(k, l);a(i, j)=g-s*(h+g*tau);a(k, l)=h+s*(g-h*tau)
191 < #define MAX_ROTATIONS 60
211 >  /*=========================================================================
212  
213 < template<typename Real, int Dim>
214 < bool SquareMatrix<Real, Dim>::jacobi(const SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& w,
195 <                              SquareMatrix<Real, Dim>& v) {
196 <    const int N = Dim;                                                                      
197 <    int i, j, k, iq, ip;
198 <    double tresh, theta, tau, t, sm, s, h, g, c;
199 <    double tmp;
200 <    Vector<Real, Dim> b, z;
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 +  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 +  =========================================================================*/
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)
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;
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 +    }
251 +
252      // initialize
253 <    for (ip=0; ip<N; ip++) {
254 <        for (iq=0; iq<N; iq++)
255 <            v(ip, iq) = 0.0;
256 <        v(ip, ip) = 1.0;
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 <    for (ip=0; ip<N; ip++) {
261 <        b(ip) = w(ip) = a(ip, ip);
211 <        z(ip) = 0.0;
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<MAX_ROTATIONS; i++) {
266 <        sm = 0.0;
267 <        for (ip=0; ip<2; ip++) {
268 <            for (iq=ip+1; iq<N; iq++)
269 <                sm += fabs(a(ip, iq));
270 <        }
271 <        
272 <        if (sm == 0.0)
273 <            break;
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 < 4)
277 <            tresh = 0.2*sm/(9);
278 <        else
279 <            tresh = 0.0;
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<2; ip++) {
283 <            for (iq=ip+1; iq<N; iq++) {
284 <                g = 100.0*fabs(a(ip, iq));
233 <                if (i > 4 && (fabs(w(ip))+g) == fabs(w(ip))
234 <                    && (fabs(w(iq))+g) == fabs(w(iq))) {
235 <                    a(ip, iq) = 0.0;
236 <                } else if (fabs(a(ip, iq)) > tresh) {
237 <                    h = w(iq) - w(ip);
238 <                    if ( (fabs(h)+g) == fabs(h)) {
239 <                        t = (a(ip, iq)) / h;
240 <                    } else {
241 <                        theta = 0.5*h / (a(ip, iq));
242 <                        t = 1.0 / (fabs(theta)+sqrt(1.0+theta*theta));
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 <                        if (theta < 0.0)
287 <                            t = -t;
288 <                    }
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 <                    c = 1.0 / sqrt(1+t*t);
312 <                    s = t*c;
313 <                    tau = s/(1.0+c);
314 <                    h = t*a(ip, iq);
315 <                    z(ip) -= h;
316 <                    z(iq) += h;
317 <                    w(ip) -= h;
318 <                    w(iq) += h;
319 <                    a(ip, iq)=0.0;
320 <                    
321 <                    for (j=0;j<ip-1;j++)
322 <                        ROT(a,j,ip,j,iq);
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 (j=ip+1;j<iq-1;j++)
331 <                        ROT(a,ip,j,j,iq);
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 <                    for (j=iq+1; j<N; j++)
338 <                        ROT(a,ip,j,iq,j);
339 <                    
340 <                    for (j=0; j<N; j++)
341 <                        ROT(v,j,ip,j,iq);
269 <                }
270 <            }
271 <        }//for (ip=0; ip<2; ip++)
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 <        for (ip=0; ip<N; ip++) {
344 <            b(ip) += z(ip);
345 <            w(ip) = b(ip);
346 <            z(ip) = 0.0;
347 <        }
348 <        
349 <    } // end for (i=0; i<MAX_ROTATIONS; i++)
350 <
351 <    if ( i >= MAX_ROTATIONS )
352 <        return false;
353 <
354 <    // sort eigenfunctions
355 <    for (j=0; j<N; j++) {
356 <        k = j;
357 <        tmp = w(k);
358 <        for (i=j; i<N; i++) {
359 <            if (w(i) >= tmp) {
360 <            k = i;
361 <            tmp = w(k);
292 <            }
293 <        }
294 <    
295 <        if (k != j) {
296 <            w(k) = w(j);
297 <            w(j) = tmp;
298 <            for (i=0; i<N; i++)  {
299 <                tmp = v(i, j);
300 <                v(i, j) = v(i, k);
301 <                v(i, k) = tmp;
302 <            }
303 <        }
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 <    //    insure eigenvector consistency (i.e., Jacobi can compute
383 <    //    vectors that are negative of one another (.707,.707,0) and
384 <    //    (-.707,-.707,0). This can reek havoc in
309 <    //    hyperstreamline/other stuff. We will select the most
310 <    //    positive eigenvector.
311 <    int numPos;
312 <    for (j=0; j<N; j++) {
313 <        for (numPos=0, i=0; i<N; i++) if ( v(i, j) >= 0.0 ) numPos++;
314 <        if ( numPos < 2 ) for(i=0; i<N; i++) v(i, j) *= -1.0;
382 >    if (n > 4) {
383 >      delete [] b;
384 >      delete [] z;
385      }
386 +    return 1;
387 +  }
388  
317 –    return true;
318 – }
389  
320 – #undef ROT
321 – #undef MAX_ROTATIONS
322 –
390   }
324 –
391   #endif //MATH_SQUAREMATRIX_HPP
392 +

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