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root/group/trunk/OOPSE-3.0/src/math/SquareMatrix.hpp
Revision: 1639
Committed: Fri Oct 22 23:09:57 2004 UTC (19 years, 8 months ago) by tim
File size: 12399 byte(s)
Log Message:
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1 tim 1563 /*
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.
23     *
24     */
25    
26     /**
27     * @file SquareMatrix.hpp
28     * @author Teng Lin
29     * @date 10/11/2004
30     * @version 1.0
31     */
32 tim 1616 #ifndef MATH_SQUAREMATRIX_HPP
33 tim 1563 #define MATH_SQUAREMATRIX_HPP
34    
35 tim 1567 #include "math/RectMatrix.hpp"
36 tim 1563
37     namespace oopse {
38    
39     /**
40     * @class SquareMatrix SquareMatrix.hpp "math/SquareMatrix.hpp"
41     * @brief A square matrix class
42     * @template Real the element type
43     * @template Dim the dimension of the square matrix
44     */
45     template<typename Real, int Dim>
46 tim 1567 class SquareMatrix : public RectMatrix<Real, Dim, Dim> {
47 tim 1563 public:
48 tim 1630 typedef Real ElemType;
49     typedef Real* ElemPoinerType;
50 tim 1563
51 tim 1630 /** default constructor */
52     SquareMatrix() {
53     for (unsigned int i = 0; i < Dim; i++)
54     for (unsigned int j = 0; j < Dim; j++)
55     data_[i][j] = 0.0;
56     }
57 tim 1563
58 tim 1630 /** copy constructor */
59     SquareMatrix(const RectMatrix<Real, Dim, Dim>& m) : RectMatrix<Real, Dim, Dim>(m) {
60     }
61 tim 1563
62 tim 1630 /** copy assignment operator */
63     SquareMatrix<Real, Dim>& operator =(const RectMatrix<Real, Dim, Dim>& m) {
64     RectMatrix<Real, Dim, Dim>::operator=(m);
65     return *this;
66     }
67    
68     /** Retunrs an identity matrix*/
69 tim 1567
70 tim 1630 static SquareMatrix<Real, Dim> identity() {
71     SquareMatrix<Real, Dim> m;
72    
73     for (unsigned int i = 0; i < Dim; i++)
74     for (unsigned int j = 0; j < Dim; j++)
75     if (i == j)
76     m(i, j) = 1.0;
77     else
78     m(i, j) = 0.0;
79 tim 1563
80 tim 1630 return m;
81     }
82 tim 1567
83 tim 1630 /**
84     * Retunrs the inversion of this matrix.
85     * @todo need implementation
86     */
87     SquareMatrix<Real, Dim> inverse() {
88     SquareMatrix<Real, Dim> result;
89 tim 1563
90 tim 1630 return result;
91     }
92 tim 1563
93 tim 1630 /**
94     * Returns the determinant of this matrix.
95     * @todo need implementation
96     */
97     Real determinant() const {
98     Real det;
99     return det;
100     }
101 tim 1563
102 tim 1630 /** Returns the trace of this matrix. */
103     Real trace() const {
104     Real tmp = 0;
105    
106     for (unsigned int i = 0; i < Dim ; i++)
107     tmp += data_[i][i];
108 tim 1563
109 tim 1630 return tmp;
110     }
111 tim 1563
112 tim 1630 /** Tests if this matrix is symmetrix. */
113     bool isSymmetric() const {
114     for (unsigned int i = 0; i < Dim - 1; i++)
115     for (unsigned int j = i; j < Dim; j++)
116     if (fabs(data_[i][j] - data_[j][i]) > oopse::epsilon)
117     return false;
118    
119     return true;
120     }
121 tim 1563
122 tim 1630 /** Tests if this matrix is orthogonal. */
123     bool isOrthogonal() {
124     SquareMatrix<Real, Dim> tmp;
125 tim 1563
126 tim 1630 tmp = *this * transpose();
127 tim 1563
128 tim 1630 return tmp.isDiagonal();
129     }
130 tim 1563
131 tim 1630 /** Tests if this matrix is diagonal. */
132     bool isDiagonal() const {
133     for (unsigned int i = 0; i < Dim ; i++)
134     for (unsigned int j = 0; j < Dim; j++)
135     if (i !=j && fabs(data_[i][j]) > oopse::epsilon)
136     return false;
137    
138     return true;
139     }
140    
141     /** Tests if this matrix is the unit matrix. */
142     bool isUnitMatrix() const {
143     if (!isDiagonal())
144 tim 1563 return false;
145    
146 tim 1630 for (unsigned int i = 0; i < Dim ; i++)
147     if (fabs(data_[i][i] - 1) > oopse::epsilon)
148     return false;
149    
150     return true;
151     }
152 tim 1563
153 tim 1630 /** @todo need implementation */
154     void diagonalize() {
155     //jacobi(m, eigenValues, ortMat);
156     }
157 tim 1569
158 tim 1630 /**
159     * Jacobi iteration routines for computing eigenvalues/eigenvectors of
160     * real symmetric matrix
161     *
162     * @return true if success, otherwise return false
163     * @param a symmetric matrix whose eigenvectors are to be computed. On return, the matrix is
164     * overwritten
165     * @param w will contain the eigenvalues of the matrix On return of this function
166     * @param v the columns of this matrix will contain the eigenvectors. The eigenvectors are
167     * normalized and mutually orthogonal.
168     */
169    
170     static int jacobi(SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& d,
171     SquareMatrix<Real, Dim>& v);
172 tim 1563 };//end SquareMatrix
173    
174 tim 1569
175 tim 1616 /*=========================================================================
176 tim 1569
177 tim 1616 Program: Visualization Toolkit
178     Module: $RCSfile: SquareMatrix.hpp,v $
179 tim 1569
180 tim 1616 Copyright (c) Ken Martin, Will Schroeder, Bill Lorensen
181     All rights reserved.
182     See Copyright.txt or http://www.kitware.com/Copyright.htm for details.
183    
184     This software is distributed WITHOUT ANY WARRANTY; without even
185     the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR
186     PURPOSE. See the above copyright notice for more information.
187    
188     =========================================================================*/
189    
190     #define VTK_ROTATE(a,i,j,k,l) g=a(i, j);h=a(k, l);a(i, j)=g-s*(h+g*tau);\
191     a(k, l)=h+s*(g-h*tau)
192    
193     #define VTK_MAX_ROTATIONS 20
194    
195     // Jacobi iteration for the solution of eigenvectors/eigenvalues of a nxn
196     // real symmetric matrix. Square nxn matrix a; size of matrix in n;
197     // output eigenvalues in w; and output eigenvectors in v. Resulting
198     // eigenvalues/vectors are sorted in decreasing order; eigenvectors are
199     // normalized.
200     template<typename Real, int Dim>
201     int SquareMatrix<Real, Dim>::jacobi(SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& w,
202 tim 1639 SquareMatrix<Real, Dim>& v) {
203     const int n = Dim;
204     int i, j, k, iq, ip, numPos;
205     Real tresh, theta, tau, t, sm, s, h, g, c, tmp;
206     Real bspace[4], zspace[4];
207     Real *b = bspace;
208     Real *z = zspace;
209 tim 1616
210 tim 1639 // only allocate memory if the matrix is large
211     if (n > 4) {
212     b = new Real[n];
213     z = new Real[n];
214 tim 1616 }
215    
216 tim 1639 // initialize
217     for (ip=0; ip<n; ip++) {
218     for (iq=0; iq<n; iq++) {
219     v(ip, iq) = 0.0;
220     }
221     v(ip, ip) = 1.0;
222 tim 1616 }
223 tim 1639 for (ip=0; ip<n; ip++) {
224     b[ip] = w[ip] = a(ip, ip);
225     z[ip] = 0.0;
226 tim 1616 }
227 tim 1569
228 tim 1639 // begin rotation sequence
229     for (i=0; i<VTK_MAX_ROTATIONS; i++) {
230     sm = 0.0;
231     for (ip=0; ip<n-1; ip++) {
232     for (iq=ip+1; iq<n; iq++) {
233     sm += fabs(a(ip, iq));
234     }
235 tim 1616 }
236 tim 1639 if (sm == 0.0) {
237     break;
238     }
239 tim 1569
240 tim 1639 if (i < 3) { // first 3 sweeps
241     tresh = 0.2*sm/(n*n);
242     } else {
243     tresh = 0.0;
244     }
245 tim 1569
246 tim 1639 for (ip=0; ip<n-1; ip++) {
247     for (iq=ip+1; iq<n; iq++) {
248     g = 100.0*fabs(a(ip, iq));
249 tim 1569
250 tim 1639 // after 4 sweeps
251     if (i > 3 && (fabs(w[ip])+g) == fabs(w[ip])
252     && (fabs(w[iq])+g) == fabs(w[iq])) {
253     a(ip, iq) = 0.0;
254     } else if (fabs(a(ip, iq)) > tresh) {
255     h = w[iq] - w[ip];
256     if ( (fabs(h)+g) == fabs(h)) {
257     t = (a(ip, iq)) / h;
258     } else {
259     theta = 0.5*h / (a(ip, iq));
260     t = 1.0 / (fabs(theta)+sqrt(1.0+theta*theta));
261     if (theta < 0.0) {
262     t = -t;
263     }
264     }
265     c = 1.0 / sqrt(1+t*t);
266     s = t*c;
267     tau = s/(1.0+c);
268     h = t*a(ip, iq);
269     z[ip] -= h;
270     z[iq] += h;
271     w[ip] -= h;
272     w[iq] += h;
273     a(ip, iq)=0.0;
274 tim 1569
275 tim 1639 // ip already shifted left by 1 unit
276     for (j = 0;j <= ip-1;j++) {
277     VTK_ROTATE(a,j,ip,j,iq);
278     }
279     // ip and iq already shifted left by 1 unit
280     for (j = ip+1;j <= iq-1;j++) {
281     VTK_ROTATE(a,ip,j,j,iq);
282     }
283     // iq already shifted left by 1 unit
284     for (j=iq+1; j<n; j++) {
285     VTK_ROTATE(a,ip,j,iq,j);
286     }
287     for (j=0; j<n; j++) {
288     VTK_ROTATE(v,j,ip,j,iq);
289     }
290     }
291 tim 1586 }
292     }
293    
294 tim 1639 for (ip=0; ip<n; ip++) {
295     b[ip] += z[ip];
296     w[ip] = b[ip];
297     z[ip] = 0.0;
298     }
299 tim 1586 }
300    
301 tim 1639 //// this is NEVER called
302     if ( i >= VTK_MAX_ROTATIONS ) {
303     std::cout << "vtkMath::Jacobi: Error extracting eigenfunctions" << std::endl;
304     return 0;
305 tim 1616 }
306 tim 1569
307 tim 1639 // sort eigenfunctions these changes do not affect accuracy
308     for (j=0; j<n-1; j++) { // boundary incorrect
309     k = j;
310 tim 1616 tmp = w[k];
311 tim 1639 for (i=j+1; i<n; i++) { // boundary incorrect, shifted already
312     if (w[i] >= tmp) { // why exchage if same?
313     k = i;
314     tmp = w[k];
315     }
316 tim 1586 }
317 tim 1639 if (k != j) {
318     w[k] = w[j];
319     w[j] = tmp;
320     for (i=0; i<n; i++) {
321     tmp = v(i, j);
322     v(i, j) = v(i, k);
323     v(i, k) = tmp;
324     }
325 tim 1616 }
326 tim 1586 }
327 tim 1639 // insure eigenvector consistency (i.e., Jacobi can compute vectors that
328     // are negative of one another (.707,.707,0) and (-.707,-.707,0). This can
329     // reek havoc in hyperstreamline/other stuff. We will select the most
330     // positive eigenvector.
331     int ceil_half_n = (n >> 1) + (n & 1);
332     for (j=0; j<n; j++) {
333     for (numPos=0, i=0; i<n; i++) {
334     if ( v(i, j) >= 0.0 ) {
335     numPos++;
336     }
337 tim 1586 }
338 tim 1639 // if ( numPos < ceil(double(n)/double(2.0)) )
339     if ( numPos < ceil_half_n) {
340     for (i=0; i<n; i++) {
341     v(i, j) *= -1.0;
342     }
343 tim 1616 }
344 tim 1586 }
345 tim 1569
346 tim 1639 if (n > 4) {
347     delete [] b;
348     delete [] z;
349 tim 1616 }
350 tim 1639 return 1;
351 tim 1569 }
352    
353    
354     }
355 tim 1616 #endif //MATH_SQUAREMATRIX_HPP
356 tim 1569