193 |
|
Vector<Real, Dim> b, z; |
194 |
|
|
195 |
|
// initialize |
196 |
< |
for (ip=0; ip<N; ip++) |
197 |
< |
{ |
198 |
< |
for (iq=0; iq<N; iq++) v(ip, iq) = 0.0; |
199 |
< |
v(ip, ip) = 1.0; |
196 |
> |
for (ip=0; ip<N; ip++) { |
197 |
> |
for (iq=0; iq<N; iq++) |
198 |
> |
v(ip, iq) = 0.0; |
199 |
> |
v(ip, ip) = 1.0; |
200 |
|
} |
201 |
< |
for (ip=0; ip<N; ip++) |
202 |
< |
{ |
203 |
< |
b(ip) = w(ip) = a(ip, ip); |
204 |
< |
z(ip) = 0.0; |
201 |
> |
|
202 |
> |
for (ip=0; ip<N; ip++) { |
203 |
> |
b(ip) = w(ip) = a(ip, ip); |
204 |
> |
z(ip) = 0.0; |
205 |
|
} |
206 |
|
|
207 |
|
// begin rotation sequence |
208 |
< |
for (i=0; i<MAX_ROTATIONS; i++) |
209 |
< |
{ |
210 |
< |
sm = 0.0; |
211 |
< |
for (ip=0; ip<2; ip++) |
212 |
< |
{ |
213 |
< |
for (iq=ip+1; iq<N; iq++) sm += fabs(a(ip, iq)); |
214 |
< |
} |
215 |
< |
if (sm == 0.0) break; |
208 |
> |
for (i=0; i<MAX_ROTATIONS; i++) { |
209 |
> |
sm = 0.0; |
210 |
> |
for (ip=0; ip<2; ip++) { |
211 |
> |
for (iq=ip+1; iq<N; iq++) |
212 |
> |
sm += fabs(a(ip, iq)); |
213 |
> |
} |
214 |
> |
|
215 |
> |
if (sm == 0.0) |
216 |
> |
break; |
217 |
|
|
218 |
< |
if (i < 4) tresh = 0.2*sm/(9); |
219 |
< |
else tresh = 0.0; |
218 |
> |
if (i < 4) |
219 |
> |
tresh = 0.2*sm/(9); |
220 |
> |
else |
221 |
> |
tresh = 0.0; |
222 |
|
|
223 |
< |
for (ip=0; ip<2; ip++) |
224 |
< |
{ |
225 |
< |
for (iq=ip+1; iq<N; iq++) |
226 |
< |
{ |
227 |
< |
g = 100.0*fabs(a(ip, iq)); |
228 |
< |
if (i > 4 && (fabs(w(ip))+g) == fabs(w(ip)) |
229 |
< |
&& (fabs(w(iq))+g) == fabs(w(iq))) |
230 |
< |
{ |
231 |
< |
a(ip, iq) = 0.0; |
232 |
< |
} |
233 |
< |
else if (fabs(a(ip, iq)) > tresh) |
234 |
< |
{ |
235 |
< |
h = w(iq) - w(ip); |
233 |
< |
if ( (fabs(h)+g) == fabs(h)) t = (a(ip, iq)) / h; |
234 |
< |
else |
235 |
< |
{ |
236 |
< |
theta = 0.5*h / (a(ip, iq)); |
237 |
< |
t = 1.0 / (fabs(theta)+sqrt(1.0+theta*theta)); |
238 |
< |
if (theta < 0.0) t = -t; |
239 |
< |
} |
240 |
< |
c = 1.0 / sqrt(1+t*t); |
241 |
< |
s = t*c; |
242 |
< |
tau = s/(1.0+c); |
243 |
< |
h = t*a(ip, iq); |
244 |
< |
z(ip) -= h; |
245 |
< |
z(iq) += h; |
246 |
< |
w(ip) -= h; |
247 |
< |
w(iq) += h; |
248 |
< |
a(ip, iq)=0.0; |
249 |
< |
for (j=0;j<ip-1;j++) |
250 |
< |
{ |
251 |
< |
ROT(a,j,ip,j,iq); |
252 |
< |
} |
253 |
< |
for (j=ip+1;j<iq-1;j++) |
254 |
< |
{ |
255 |
< |
ROT(a,ip,j,j,iq); |
256 |
< |
} |
257 |
< |
for (j=iq+1; j<N; j++) |
258 |
< |
{ |
259 |
< |
ROT(a,ip,j,iq,j); |
260 |
< |
} |
261 |
< |
for (j=0; j<N; j++) |
262 |
< |
{ |
263 |
< |
ROT(v,j,ip,j,iq); |
264 |
< |
} |
265 |
< |
} |
266 |
< |
} |
267 |
< |
} |
223 |
> |
for (ip=0; ip<2; ip++) { |
224 |
> |
for (iq=ip+1; iq<N; iq++) { |
225 |
> |
g = 100.0*fabs(a(ip, iq)); |
226 |
> |
if (i > 4 && (fabs(w(ip))+g) == fabs(w(ip)) |
227 |
> |
&& (fabs(w(iq))+g) == fabs(w(iq))) { |
228 |
> |
a(ip, iq) = 0.0; |
229 |
> |
} else if (fabs(a(ip, iq)) > tresh) { |
230 |
> |
h = w(iq) - w(ip); |
231 |
> |
if ( (fabs(h)+g) == fabs(h)) { |
232 |
> |
t = (a(ip, iq)) / h; |
233 |
> |
} else { |
234 |
> |
theta = 0.5*h / (a(ip, iq)); |
235 |
> |
t = 1.0 / (fabs(theta)+sqrt(1.0+theta*theta)); |
236 |
|
|
237 |
< |
for (ip=0; ip<N; ip++) |
238 |
< |
{ |
239 |
< |
b(ip) += z(ip); |
272 |
< |
w(ip) = b(ip); |
273 |
< |
z(ip) = 0.0; |
274 |
< |
} |
275 |
< |
} |
237 |
> |
if (theta < 0.0) |
238 |
> |
t = -t; |
239 |
> |
} |
240 |
|
|
241 |
+ |
c = 1.0 / sqrt(1+t*t); |
242 |
+ |
s = t*c; |
243 |
+ |
tau = s/(1.0+c); |
244 |
+ |
h = t*a(ip, iq); |
245 |
+ |
z(ip) -= h; |
246 |
+ |
z(iq) += h; |
247 |
+ |
w(ip) -= h; |
248 |
+ |
w(iq) += h; |
249 |
+ |
a(ip, iq)=0.0; |
250 |
+ |
|
251 |
+ |
for (j=0;j<ip-1;j++) |
252 |
+ |
ROT(a,j,ip,j,iq); |
253 |
+ |
|
254 |
+ |
for (j=ip+1;j<iq-1;j++) |
255 |
+ |
ROT(a,ip,j,j,iq); |
256 |
+ |
|
257 |
+ |
for (j=iq+1; j<N; j++) |
258 |
+ |
ROT(a,ip,j,iq,j); |
259 |
+ |
for (j=0; j<N; j++) |
260 |
+ |
ROT(v,j,ip,j,iq); |
261 |
+ |
} |
262 |
+ |
} |
263 |
+ |
}//for (ip=0; ip<2; ip++) |
264 |
+ |
|
265 |
+ |
for (ip=0; ip<N; ip++) { |
266 |
+ |
b(ip) += z(ip); |
267 |
+ |
w(ip) = b(ip); |
268 |
+ |
z(ip) = 0.0; |
269 |
+ |
} |
270 |
+ |
|
271 |
+ |
} // end for (i=0; i<MAX_ROTATIONS; i++) |
272 |
+ |
|
273 |
|
if ( i >= MAX_ROTATIONS ) |
274 |
< |
return false; |
274 |
> |
return false; |
275 |
|
|
276 |
|
// sort eigenfunctions |
277 |
< |
for (j=0; j<N; j++) |
278 |
< |
{ |
279 |
< |
k = j; |
280 |
< |
tmp = w(k); |
281 |
< |
for (i=j; i<N; i++) |
282 |
< |
{ |
283 |
< |
if (w(i) >= tmp) |
284 |
< |
{ |
285 |
< |
k = i; |
286 |
< |
tmp = w(k); |
287 |
< |
} |
288 |
< |
} |
289 |
< |
if (k != j) |
290 |
< |
{ |
291 |
< |
w(k) = w(j); |
292 |
< |
w(j) = tmp; |
293 |
< |
for (i=0; i<N; i++) |
294 |
< |
{ |
295 |
< |
tmp = v(i, j); |
300 |
< |
v(i, j) = v(i, k); |
301 |
< |
v(i, k) = tmp; |
302 |
< |
} |
303 |
< |
} |
277 |
> |
for (j=0; j<N; j++) { |
278 |
> |
k = j; |
279 |
> |
tmp = w(k); |
280 |
> |
for (i=j; i<N; i++) { |
281 |
> |
if (w(i) >= tmp) { |
282 |
> |
k = i; |
283 |
> |
tmp = w(k); |
284 |
> |
} |
285 |
> |
} |
286 |
> |
|
287 |
> |
if (k != j) { |
288 |
> |
w(k) = w(j); |
289 |
> |
w(j) = tmp; |
290 |
> |
for (i=0; i<N; i++) { |
291 |
> |
tmp = v(i, j); |
292 |
> |
v(i, j) = v(i, k); |
293 |
> |
v(i, k) = tmp; |
294 |
> |
} |
295 |
> |
} |
296 |
|
} |
297 |
|
|
298 |
|
// insure eigenvector consistency (i.e., Jacobi can compute |
301 |
|
// hyperstreamline/other stuff. We will select the most |
302 |
|
// positive eigenvector. |
303 |
|
int numPos; |
304 |
< |
for (j=0; j<N; j++) |
305 |
< |
{ |
306 |
< |
for (numPos=0, i=0; i<N; i++) if ( v(i, j) >= 0.0 ) numPos++; |
315 |
< |
if ( numPos < 2 ) for(i=0; i<N; i++) v(i, j) *= -1.0; |
304 |
> |
for (j=0; j<N; j++) { |
305 |
> |
for (numPos=0, i=0; i<N; i++) if ( v(i, j) >= 0.0 ) numPos++; |
306 |
> |
if ( numPos < 2 ) for(i=0; i<N; i++) v(i, j) *= -1.0; |
307 |
|
} |
308 |
|
|
309 |
|
return true; |