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Revision 74 by tim, Wed Oct 13 23:53:40 2004 UTC vs.
Revision 963 by tim, Wed May 17 21:51:42 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 33 | Line 49
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:
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 <        }
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*/
75 >    /** Constructs and initializes every element of this matrix to a scalar */
76 >    SquareMatrix(Real s) : RectMatrix<Real, Dim, Dim>(s){
77 >    }
78  
79 <       static SquareMatrix<Real, Dim> identity() {
80 <            SquareMatrix<Real, Dim> m;
81 <            
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;
79 >    /** Constructs and initializes from an array */
80 >    SquareMatrix(Real* array) : RectMatrix<Real, Dim, Dim>(array){
81 >    }
82  
78 –            return m;
79 –        }
83  
84 <        /** Retunrs  the inversion of this matrix. */
85 <         SquareMatrix<Real, Dim>  inverse() {
86 <             SquareMatrix<Real, Dim> result;
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 >    }
93 >                                  
94 >    /** Retunrs  an identity matrix*/
95  
96 <             return result;
97 <        }
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;
105  
106 <        
106 >      return m;
107 >    }
108  
109 <        /** Returns the determinant of this matrix. */
110 <        double determinant() const {
111 <            double det;
112 <            return det;
113 <        }
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 <        /** Returns the trace of this matrix. */
117 <        double trace() const {
98 <           double tmp = 0;
99 <          
100 <            for (unsigned int i = 0; i < Dim ; i++)
101 <                tmp += data_[i][i];
116 >      return result;
117 >    }        
118  
119 <            return tmp;
120 <        }
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 <        /** Tests if this matrix is symmetrix. */            
129 <        bool isSymmetric() const {
130 <            for (unsigned int i = 0; i < Dim - 1; i++)
131 <                for (unsigned int j = i; j < Dim; j++)
132 <                    if (fabs(data_[i][j] - data_[j][i]) > oopse::epsilon)
133 <                        return false;
112 <                    
113 <            return true;
114 <        }
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 += this->data_[i][i];
134  
135 <        /** Tests if this matrix is orthogona. */            
136 <        bool isOrthogonal() {
118 <            SquareMatrix<Real, Dim> tmp;
135 >      return tmp;
136 >    }
137  
138 <            tmp = *this * transpose();
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 >    }
147  
148 <            return tmp.isUnitMatrix();
149 <        }
148 >    /** Tests if this matrix is orthogonal. */            
149 >    bool isOrthogonal() {
150 >      SquareMatrix<Real, Dim> tmp;
151  
152 <        /** 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 <        }
152 >      tmp = *this * transpose();
153  
154 <        /** Tests if this matrix is the unit matrix. */
155 <        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 <        }        
146 <
147 <    };//end SquareMatrix
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(this->data_[i][j]) > epsilon)
162 +            return false;
163 +                        
164 +      return true;
165 +    }
166 +
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(this->data_[i][i] - 1) > epsilon)
174 +          return false;
175 +                    
176 +      return true;
177 +    }        
178 +
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 +      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
210 +
211 +
212 +  /*=========================================================================
213 +
214 +  Program:   Visualization Toolkit
215 +  Module:    $RCSfile: SquareMatrix.hpp,v $
216 +
217 +  Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen
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.
224 +
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)
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;
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 +    }
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 +    }
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 +      }
276 +
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));
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;
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 +      }
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 +    }
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 +    }
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(RealType(n)/RealType(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;
386 +    }
387 +    return 1;
388 +  }
389 +
390 +
391 +  typedef SquareMatrix<RealType, 6> Mat6x6d;
392   }
393   #endif //MATH_SQUAREMATRIX_HPP
394 +

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