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. |
23 |
* |
24 |
*/ |
25 |
|
26 |
/** |
27 |
* @file SquareMatrix.hpp |
28 |
* @author Teng Lin |
29 |
* @date 10/11/2004 |
30 |
* @version 1.0 |
31 |
*/ |
32 |
#ifndef MATH_SQUAREMATRIX_HPP |
33 |
#define MATH_SQUAREMATRIX_HPP |
34 |
|
35 |
#include "math/RectMatrix.hpp" |
36 |
|
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 |
class SquareMatrix : public RectMatrix<Real, Dim, Dim> { |
47 |
public: |
48 |
typedef Real ElemType; |
49 |
typedef Real* ElemPoinerType; |
50 |
|
51 |
/** 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 |
|
58 |
/** copy constructor */ |
59 |
SquareMatrix(const RectMatrix<Real, Dim, Dim>& m) : RectMatrix<Real, Dim, Dim>(m) { |
60 |
} |
61 |
|
62 |
/** 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 |
|
70 |
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 |
|
80 |
return m; |
81 |
} |
82 |
|
83 |
/** |
84 |
* Retunrs the inversion of this matrix. |
85 |
* @todo need implementation |
86 |
*/ |
87 |
SquareMatrix<Real, Dim> inverse() { |
88 |
SquareMatrix<Real, Dim> result; |
89 |
|
90 |
return result; |
91 |
} |
92 |
|
93 |
/** |
94 |
* Returns the determinant of this matrix. |
95 |
* @todo need implementation |
96 |
*/ |
97 |
Real determinant() const { |
98 |
Real det; |
99 |
return det; |
100 |
} |
101 |
|
102 |
/** 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 |
|
109 |
return tmp; |
110 |
} |
111 |
|
112 |
/** 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 |
|
122 |
/** Tests if this matrix is orthogonal. */ |
123 |
bool isOrthogonal() { |
124 |
SquareMatrix<Real, Dim> tmp; |
125 |
|
126 |
tmp = *this * transpose(); |
127 |
|
128 |
return tmp.isDiagonal(); |
129 |
} |
130 |
|
131 |
/** 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 |
return false; |
145 |
|
146 |
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 |
|
153 |
/** @todo need implementation */ |
154 |
void diagonalize() { |
155 |
//jacobi(m, eigenValues, ortMat); |
156 |
} |
157 |
|
158 |
/** |
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 |
};//end SquareMatrix |
173 |
|
174 |
|
175 |
/*========================================================================= |
176 |
|
177 |
Program: Visualization Toolkit |
178 |
Module: $RCSfile: SquareMatrix.hpp,v $ |
179 |
|
180 |
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 |
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 |
|
210 |
// only allocate memory if the matrix is large |
211 |
if (n > 4) { |
212 |
b = new Real[n]; |
213 |
z = new Real[n]; |
214 |
} |
215 |
|
216 |
// 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 |
} |
223 |
for (ip=0; ip<n; ip++) { |
224 |
b[ip] = w[ip] = a(ip, ip); |
225 |
z[ip] = 0.0; |
226 |
} |
227 |
|
228 |
// 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 |
} |
236 |
if (sm == 0.0) { |
237 |
break; |
238 |
} |
239 |
|
240 |
if (i < 3) { // first 3 sweeps |
241 |
tresh = 0.2*sm/(n*n); |
242 |
} else { |
243 |
tresh = 0.0; |
244 |
} |
245 |
|
246 |
for (ip=0; ip<n-1; ip++) { |
247 |
for (iq=ip+1; iq<n; iq++) { |
248 |
g = 100.0*fabs(a(ip, iq)); |
249 |
|
250 |
// 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 |
|
275 |
// 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 |
} |
292 |
} |
293 |
|
294 |
for (ip=0; ip<n; ip++) { |
295 |
b[ip] += z[ip]; |
296 |
w[ip] = b[ip]; |
297 |
z[ip] = 0.0; |
298 |
} |
299 |
} |
300 |
|
301 |
//// this is NEVER called |
302 |
if ( i >= VTK_MAX_ROTATIONS ) { |
303 |
std::cout << "vtkMath::Jacobi: Error extracting eigenfunctions" << std::endl; |
304 |
return 0; |
305 |
} |
306 |
|
307 |
// sort eigenfunctions these changes do not affect accuracy |
308 |
for (j=0; j<n-1; j++) { // boundary incorrect |
309 |
k = j; |
310 |
tmp = w[k]; |
311 |
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 |
} |
317 |
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 |
} |
326 |
} |
327 |
// 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 |
} |
338 |
// 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 |
} |
344 |
} |
345 |
|
346 |
if (n > 4) { |
347 |
delete [] b; |
348 |
delete [] z; |
349 |
} |
350 |
return 1; |
351 |
} |
352 |
|
353 |
|
354 |
} |
355 |
#endif //MATH_SQUAREMATRIX_HPP |
356 |
|