78 |
|
return m; |
79 |
|
} |
80 |
|
|
81 |
< |
/** Retunrs the inversion of this matrix. */ |
81 |
> |
/** |
82 |
> |
* Retunrs the inversion of this matrix. |
83 |
> |
* @todo |
84 |
> |
*/ |
85 |
|
SquareMatrix<Real, Dim> inverse() { |
86 |
|
SquareMatrix<Real, Dim> result; |
87 |
|
|
88 |
|
return result; |
89 |
|
} |
90 |
|
|
91 |
< |
/** Returns the determinant of this matrix. */ |
91 |
> |
/** |
92 |
> |
* Returns the determinant of this matrix. |
93 |
> |
* @todo |
94 |
> |
*/ |
95 |
|
double determinant() const { |
96 |
|
double det; |
97 |
|
return det; |
148 |
|
return true; |
149 |
|
} |
150 |
|
|
151 |
+ |
/** @todo need implement */ |
152 |
|
void diagonalize() { |
153 |
< |
jacobi(m, eigenValues, ortMat); |
153 |
> |
//jacobi(m, eigenValues, ortMat); |
154 |
|
} |
155 |
|
|
156 |
|
/** |
182 |
|
* @param w output eigenvalues |
183 |
|
* @param v output eigenvectors |
184 |
|
*/ |
185 |
< |
void jacobi(const SquareMatrix<Real, Dim>& a, |
179 |
< |
Vector<Real, Dim>& w, |
185 |
> |
bool jacobi(const SquareMatrix<Real, Dim>& a, Vector<Real, Dim>& w, |
186 |
|
SquareMatrix<Real, Dim>& v); |
187 |
|
};//end SquareMatrix |
188 |
|
|
190 |
|
#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 |
192 |
|
|
193 |
< |
template<Real, int Dim> |
194 |
< |
void SquareMatrix<Real, int Dim>::jacobi(SquareMatrix<Real, Dim>& a, |
195 |
< |
Vector<Real, Dim>& w, |
190 |
< |
SquareMatrix<Real, Dim>& v) { |
193 |
> |
template<typename Real, int Dim> |
194 |
> |
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; |
200 |
|
Vector<Real, Dim> b, z; |
201 |
|
|
202 |
|
// initialize |
203 |
< |
for (ip=0; ip<N; ip++) |
204 |
< |
{ |
205 |
< |
for (iq=0; iq<N; iq++) v(ip, iq) = 0.0; |
206 |
< |
v(ip, ip) = 1.0; |
203 |
> |
for (ip=0; ip<N; ip++) { |
204 |
> |
for (iq=0; iq<N; iq++) |
205 |
> |
v(ip, iq) = 0.0; |
206 |
> |
v(ip, ip) = 1.0; |
207 |
|
} |
208 |
< |
for (ip=0; ip<N; ip++) |
209 |
< |
{ |
210 |
< |
b(ip) = w(ip) = a(ip, ip); |
211 |
< |
z(ip) = 0.0; |
208 |
> |
|
209 |
> |
for (ip=0; ip<N; ip++) { |
210 |
> |
b(ip) = w(ip) = a(ip, ip); |
211 |
> |
z(ip) = 0.0; |
212 |
|
} |
213 |
|
|
214 |
|
// begin rotation sequence |
215 |
< |
for (i=0; i<MAX_ROTATIONS; i++) |
216 |
< |
{ |
217 |
< |
sm = 0.0; |
218 |
< |
for (ip=0; ip<2; ip++) |
219 |
< |
{ |
220 |
< |
for (iq=ip+1; iq<N; iq++) sm += fabs(a(ip, iq)); |
221 |
< |
} |
222 |
< |
if (sm == 0.0) break; |
215 |
> |
for (i=0; i<MAX_ROTATIONS; i++) { |
216 |
> |
sm = 0.0; |
217 |
> |
for (ip=0; ip<2; ip++) { |
218 |
> |
for (iq=ip+1; iq<N; iq++) |
219 |
> |
sm += fabs(a(ip, iq)); |
220 |
> |
} |
221 |
> |
|
222 |
> |
if (sm == 0.0) |
223 |
> |
break; |
224 |
|
|
225 |
< |
if (i < 4) tresh = 0.2*sm/(9); |
226 |
< |
else tresh = 0.0; |
225 |
> |
if (i < 4) |
226 |
> |
tresh = 0.2*sm/(9); |
227 |
> |
else |
228 |
> |
tresh = 0.0; |
229 |
|
|
230 |
< |
for (ip=0; ip<2; ip++) |
231 |
< |
{ |
232 |
< |
for (iq=ip+1; iq<N; iq++) |
233 |
< |
{ |
234 |
< |
g = 100.0*fabs(a(ip, iq)); |
235 |
< |
if (i > 4 && (fabs(w(ip))+g) == fabs(w(ip)) |
236 |
< |
&& (fabs(w(iq))+g) == fabs(w(iq))) |
237 |
< |
{ |
238 |
< |
a(ip, iq) = 0.0; |
239 |
< |
} |
240 |
< |
else if (fabs(a(ip, iq)) > tresh) |
241 |
< |
{ |
242 |
< |
h = w(iq) - w(ip); |
235 |
< |
if ( (fabs(h)+g) == fabs(h)) t = (a(ip, iq)) / h; |
236 |
< |
else |
237 |
< |
{ |
238 |
< |
theta = 0.5*h / (a(ip, iq)); |
239 |
< |
t = 1.0 / (fabs(theta)+sqrt(1.0+theta*theta)); |
240 |
< |
if (theta < 0.0) t = -t; |
241 |
< |
} |
242 |
< |
c = 1.0 / sqrt(1+t*t); |
243 |
< |
s = t*c; |
244 |
< |
tau = s/(1.0+c); |
245 |
< |
h = t*a(ip, iq); |
246 |
< |
z(ip) -= h; |
247 |
< |
z(iq) += h; |
248 |
< |
w(ip) -= h; |
249 |
< |
w(iq) += h; |
250 |
< |
a(ip, iq)=0.0; |
251 |
< |
for (j=0;j<ip-1;j++) |
252 |
< |
{ |
253 |
< |
ROT(a,j,ip,j,iq); |
254 |
< |
} |
255 |
< |
for (j=ip+1;j<iq-1;j++) |
256 |
< |
{ |
257 |
< |
ROT(a,ip,j,j,iq); |
258 |
< |
} |
259 |
< |
for (j=iq+1; j<N; j++) |
260 |
< |
{ |
261 |
< |
ROT(a,ip,j,iq,j); |
262 |
< |
} |
263 |
< |
for (j=0; j<N; j++) |
264 |
< |
{ |
265 |
< |
ROT(v,j,ip,j,iq); |
266 |
< |
} |
267 |
< |
} |
268 |
< |
} |
269 |
< |
} |
230 |
> |
for (ip=0; ip<2; ip++) { |
231 |
> |
for (iq=ip+1; iq<N; iq++) { |
232 |
> |
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)); |
243 |
|
|
244 |
< |
for (ip=0; ip<N; ip++) |
245 |
< |
{ |
246 |
< |
b(ip) += z(ip); |
274 |
< |
w(ip) = b(ip); |
275 |
< |
z(ip) = 0.0; |
276 |
< |
} |
277 |
< |
} |
244 |
> |
if (theta < 0.0) |
245 |
> |
t = -t; |
246 |
> |
} |
247 |
|
|
248 |
+ |
c = 1.0 / sqrt(1+t*t); |
249 |
+ |
s = t*c; |
250 |
+ |
tau = s/(1.0+c); |
251 |
+ |
h = t*a(ip, iq); |
252 |
+ |
z(ip) -= h; |
253 |
+ |
z(iq) += h; |
254 |
+ |
w(ip) -= h; |
255 |
+ |
w(iq) += h; |
256 |
+ |
a(ip, iq)=0.0; |
257 |
+ |
|
258 |
+ |
for (j=0;j<ip-1;j++) |
259 |
+ |
ROT(a,j,ip,j,iq); |
260 |
+ |
|
261 |
+ |
for (j=ip+1;j<iq-1;j++) |
262 |
+ |
ROT(a,ip,j,j,iq); |
263 |
+ |
|
264 |
+ |
for (j=iq+1; j<N; j++) |
265 |
+ |
ROT(a,ip,j,iq,j); |
266 |
+ |
|
267 |
+ |
for (j=0; j<N; j++) |
268 |
+ |
ROT(v,j,ip,j,iq); |
269 |
+ |
} |
270 |
+ |
} |
271 |
+ |
}//for (ip=0; ip<2; ip++) |
272 |
+ |
|
273 |
+ |
for (ip=0; ip<N; ip++) { |
274 |
+ |
b(ip) += z(ip); |
275 |
+ |
w(ip) = b(ip); |
276 |
+ |
z(ip) = 0.0; |
277 |
+ |
} |
278 |
+ |
|
279 |
+ |
} // end for (i=0; i<MAX_ROTATIONS; i++) |
280 |
+ |
|
281 |
|
if ( i >= MAX_ROTATIONS ) |
282 |
< |
return false; |
282 |
> |
return false; |
283 |
|
|
284 |
|
// sort eigenfunctions |
285 |
< |
for (j=0; j<N; j++) |
286 |
< |
{ |
287 |
< |
k = j; |
288 |
< |
tmp = w(k); |
289 |
< |
for (i=j; i<N; i++) |
290 |
< |
{ |
291 |
< |
if (w(i) >= tmp) |
292 |
< |
{ |
293 |
< |
k = i; |
294 |
< |
tmp = w(k); |
295 |
< |
} |
296 |
< |
} |
297 |
< |
if (k != j) |
298 |
< |
{ |
299 |
< |
w(k) = w(j); |
300 |
< |
w(j) = tmp; |
301 |
< |
for (i=0; i<N; i++) |
302 |
< |
{ |
303 |
< |
tmp = v(i, j); |
302 |
< |
v(i, j) = v(i, k); |
303 |
< |
v(i, k) = tmp; |
304 |
< |
} |
305 |
< |
} |
285 |
> |
for (j=0; j<N; j++) { |
286 |
> |
k = j; |
287 |
> |
tmp = w(k); |
288 |
> |
for (i=j; i<N; i++) { |
289 |
> |
if (w(i) >= tmp) { |
290 |
> |
k = i; |
291 |
> |
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 |
> |
} |
304 |
|
} |
305 |
|
|
306 |
|
// insure eigenvector consistency (i.e., Jacobi can compute |
309 |
|
// hyperstreamline/other stuff. We will select the most |
310 |
|
// positive eigenvector. |
311 |
|
int numPos; |
312 |
< |
for (j=0; j<N; j++) |
313 |
< |
{ |
314 |
< |
for (numPos=0, i=0; i<N; i++) if ( v(i, j) >= 0.0 ) numPos++; |
317 |
< |
if ( numPos < 2 ) for(i=0; i<N; i++) v(i, j) *= -1.0; |
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; |
315 |
|
} |
316 |
|
|
317 |
|
return true; |
322 |
|
|
323 |
|
} |
324 |
|
|
328 |
– |
|
329 |
– |
} |
325 |
|
#endif //MATH_SQUAREMATRIX_HPP |