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Comparing trunk/src/math/SquareMatrix.hpp (file contents):
Revision 74 by tim, Wed Oct 13 23:53:40 2004 UTC vs.
Revision 906 by tim, Fri Mar 17 23:20:35 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
# 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;
80 <            
71 <            for (unsigned int i = 0; i < Dim; i++)
72 <                for (unsigned int j = 0; j < Dim; j++)
73 <                    if (i == j)
74 <                        m(i, j) = 1.0;
75 <                    else
76 <                        m(i, j) = 0.0;
78 >    /** Constructs and initializes from an array */
79 >    SquareMatrix(Real* array) : RectMatrix<Real, Dim, Dim>(array){
80 >    }
81  
78 –            return m;
79 –        }
82  
83 <        /** Retunrs  the inversion of this matrix. */
84 <         SquareMatrix<Real, Dim>  inverse() {
85 <             SquareMatrix<Real, Dim> result;
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 <             return result;
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 <        
105 >      return m;
106 >    }
107  
108 <        /** Returns the determinant of this matrix. */
109 <        double determinant() const {
110 <            double det;
111 <            return det;
112 <        }
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 <        /** Returns the trace of this matrix. */
116 <        double trace() const {
98 <           double tmp = 0;
99 <          
100 <            for (unsigned int i = 0; i < Dim ; i++)
101 <                tmp += data_[i][i];
115 >      return result;
116 >    }        
117  
118 <            return tmp;
119 <        }
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 <        /** Tests if this matrix is symmetrix. */            
128 <        bool isSymmetric() const {
129 <            for (unsigned int i = 0; i < Dim - 1; i++)
130 <                for (unsigned int j = i; j < Dim; j++)
131 <                    if (fabs(data_[i][j] - data_[j][i]) > oopse::epsilon)
132 <                        return false;
112 <                    
113 <            return true;
114 <        }
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 orthogona. */            
135 <        bool isOrthogonal() {
118 <            SquareMatrix<Real, Dim> tmp;
134 >      return tmp;
135 >    }
136  
137 <            tmp = *this * transpose();
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 <            return tmp.isUnitMatrix();
148 <        }
147 >    /** Tests if this matrix is orthogonal. */            
148 >    bool isOrthogonal() {
149 >      SquareMatrix<Real, Dim> tmp;
150  
151 <        /** Tests if this matrix is diagonal. */
126 <        bool isDiagonal() const {
127 <            for (unsigned int i = 0; i < Dim ; i++)
128 <                for (unsigned int j = 0; j < Dim; j++)
129 <                    if (i !=j && fabs(data_[i][j]) > oopse::epsilon)
130 <                        return false;
131 <                    
132 <            return true;
133 <        }
151 >      tmp = *this * transpose();
152  
153 <        /** Tests if this matrix is the unit matrix. */
154 <        bool isUnitMatrix() const {
137 <            if (!isDiagonal())
138 <                return false;
139 <            
140 <            for (unsigned int i = 0; i < Dim ; i++)
141 <                if (fabs(data_[i][i] - 1) > oopse::epsilon)
142 <                    return false;
143 <                
144 <            return true;
145 <        }        
153 >      return tmp.isDiagonal();
154 >    }
155  
156 <    };//end SquareMatrix
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 +    }        
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 +    /** @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
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 +  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 +      }
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 +      }
275 +
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));
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;
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 +      }
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 +    }
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 +    }
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 +    }
381 +
382 +    if (n > 4) {
383 +      delete [] b;
384 +      delete [] z;
385 +    }
386 +    return 1;
387 +  }
388 +
389 +
390 +  typedef SquareMatrix<double, 6> Mat6x6d;
391   }
392   #endif //MATH_SQUAREMATRIX_HPP
393 +

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