| 199 |
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// normalized. |
| 200 |
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template<typename Real, int Dim> |
| 201 |
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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 |
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Real tresh, theta, tau, t, sm, s, h, g, c, tmp; |
| 206 |
< |
Real bspace[4], zspace[4]; |
| 207 |
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Real *b = bspace; |
| 208 |
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Real *z = zspace; |
| 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 |
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|
| 210 |
< |
// only allocate memory if the matrix is large |
| 211 |
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if (n > 4) |
| 212 |
< |
{ |
| 213 |
< |
b = new Real[n]; |
| 214 |
< |
z = new Real[n]; |
| 210 |
> |
// only allocate memory if the matrix is large |
| 211 |
> |
if (n > 4) { |
| 212 |
> |
b = new Real[n]; |
| 213 |
> |
z = new Real[n]; |
| 214 |
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} |
| 215 |
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|
| 216 |
< |
// initialize |
| 217 |
< |
for (ip=0; ip<n; ip++) |
| 218 |
< |
{ |
| 219 |
< |
for (iq=0; iq<n; iq++) |
| 220 |
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{ |
| 221 |
< |
v(ip, iq) = 0.0; |
| 223 |
< |
} |
| 224 |
< |
v(ip, ip) = 1.0; |
| 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 |
< |
{ |
| 225 |
< |
b[ip] = w[ip] = a(ip, ip); |
| 229 |
< |
z[ip] = 0.0; |
| 223 |
> |
for (ip=0; ip<n; ip++) { |
| 224 |
> |
b[ip] = w[ip] = a(ip, ip); |
| 225 |
> |
z[ip] = 0.0; |
| 226 |
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} |
| 227 |
|
|
| 228 |
< |
// begin rotation sequence |
| 229 |
< |
for (i=0; i<VTK_MAX_ROTATIONS; i++) |
| 230 |
< |
{ |
| 231 |
< |
sm = 0.0; |
| 232 |
< |
for (ip=0; ip<n-1; ip++) |
| 233 |
< |
{ |
| 234 |
< |
for (iq=ip+1; iq<n; iq++) |
| 239 |
< |
{ |
| 240 |
< |
sm += fabs(a(ip, iq)); |
| 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 |
< |
} |
| 237 |
< |
if (sm == 0.0) |
| 238 |
< |
{ |
| 245 |
< |
break; |
| 246 |
< |
} |
| 247 |
< |
|
| 248 |
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if (i < 3) // first 3 sweeps |
| 249 |
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{ |
| 250 |
< |
tresh = 0.2*sm/(n*n); |
| 251 |
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} |
| 252 |
< |
else |
| 253 |
< |
{ |
| 254 |
< |
tresh = 0.0; |
| 255 |
< |
} |
| 236 |
> |
if (sm == 0.0) { |
| 237 |
> |
break; |
| 238 |
> |
} |
| 239 |
|
|
| 240 |
< |
for (ip=0; ip<n-1; ip++) |
| 241 |
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{ |
| 242 |
< |
for (iq=ip+1; iq<n; iq++) |
| 243 |
< |
{ |
| 244 |
< |
g = 100.0*fabs(a(ip, iq)); |
| 240 |
> |
if (i < 3) { // first 3 sweeps |
| 241 |
> |
tresh = 0.2*sm/(n*n); |
| 242 |
> |
} else { |
| 243 |
> |
tresh = 0.0; |
| 244 |
> |
} |
| 245 |
|
|
| 246 |
< |
// after 4 sweeps |
| 247 |
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if (i > 3 && (fabs(w[ip])+g) == fabs(w[ip]) |
| 248 |
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&& (fabs(w[iq])+g) == fabs(w[iq])) |
| 266 |
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{ |
| 267 |
< |
a(ip, iq) = 0.0; |
| 268 |
< |
} |
| 269 |
< |
else if (fabs(a(ip, iq)) > tresh) |
| 270 |
< |
{ |
| 271 |
< |
h = w[iq] - w[ip]; |
| 272 |
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if ( (fabs(h)+g) == fabs(h)) |
| 273 |
< |
{ |
| 274 |
< |
t = (a(ip, iq)) / h; |
| 275 |
< |
} |
| 276 |
< |
else |
| 277 |
< |
{ |
| 278 |
< |
theta = 0.5*h / (a(ip, iq)); |
| 279 |
< |
t = 1.0 / (fabs(theta)+sqrt(1.0+theta*theta)); |
| 280 |
< |
if (theta < 0.0) |
| 281 |
< |
{ |
| 282 |
< |
t = -t; |
| 283 |
< |
} |
| 284 |
< |
} |
| 285 |
< |
c = 1.0 / sqrt(1+t*t); |
| 286 |
< |
s = t*c; |
| 287 |
< |
tau = s/(1.0+c); |
| 288 |
< |
h = t*a(ip, iq); |
| 289 |
< |
z[ip] -= h; |
| 290 |
< |
z[iq] += h; |
| 291 |
< |
w[ip] -= h; |
| 292 |
< |
w[iq] += h; |
| 293 |
< |
a(ip, iq)=0.0; |
| 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 |
< |
// ip already shifted left by 1 unit |
| 251 |
< |
for (j = 0;j <= ip-1;j++) |
| 252 |
< |
{ |
| 253 |
< |
VTK_ROTATE(a,j,ip,j,iq); |
| 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 |
|
} |
| 300 |
– |
// ip and iq already shifted left by 1 unit |
| 301 |
– |
for (j = ip+1;j <= iq-1;j++) |
| 302 |
– |
{ |
| 303 |
– |
VTK_ROTATE(a,ip,j,j,iq); |
| 304 |
– |
} |
| 305 |
– |
// iq already shifted left by 1 unit |
| 306 |
– |
for (j=iq+1; j<n; j++) |
| 307 |
– |
{ |
| 308 |
– |
VTK_ROTATE(a,ip,j,iq,j); |
| 309 |
– |
} |
| 310 |
– |
for (j=0; j<n; j++) |
| 311 |
– |
{ |
| 312 |
– |
VTK_ROTATE(v,j,ip,j,iq); |
| 313 |
– |
} |
| 314 |
– |
} |
| 292 |
|
} |
| 316 |
– |
} |
| 293 |
|
|
| 294 |
< |
for (ip=0; ip<n; ip++) |
| 295 |
< |
{ |
| 296 |
< |
b[ip] += z[ip]; |
| 297 |
< |
w[ip] = b[ip]; |
| 298 |
< |
z[ip] = 0.0; |
| 323 |
< |
} |
| 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 |
< |
{ |
| 304 |
< |
std::cout << "vtkMath::Jacobi: Error extracting eigenfunctions" << std::endl; |
| 330 |
< |
return 0; |
| 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 |
< |
{ |
| 336 |
< |
k = j; |
| 337 |
< |
tmp = w[k]; |
| 338 |
< |
for (i=j+1; i<n; i++) // boundary incorrect, shifted already |
| 339 |
< |
{ |
| 340 |
< |
if (w[i] >= tmp) // why exchage if same? |
| 341 |
< |
{ |
| 342 |
< |
k = i; |
| 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 |
< |
} |
| 318 |
< |
if (k != j) |
| 319 |
< |
{ |
| 320 |
< |
w[k] = w[j]; |
| 321 |
< |
w[j] = tmp; |
| 322 |
< |
for (i=0; i<n; i++) |
| 323 |
< |
{ |
| 324 |
< |
tmp = v(i, j); |
| 353 |
< |
v(i, j) = v(i, k); |
| 354 |
< |
v(i, k) = tmp; |
| 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 |
|
} |
| 356 |
– |
} |
| 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 |
< |
{ |
| 334 |
< |
for (numPos=0, i=0; i<n; i++) |
| 335 |
< |
{ |
| 336 |
< |
if ( v(i, j) >= 0.0 ) |
| 368 |
< |
{ |
| 369 |
< |
numPos++; |
| 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 |
< |
} |
| 339 |
< |
// if ( numPos < ceil(double(n)/double(2.0)) ) |
| 340 |
< |
if ( numPos < ceil_half_n) |
| 341 |
< |
{ |
| 342 |
< |
for(i=0; i<n; i++) |
| 376 |
< |
{ |
| 377 |
< |
v(i, j) *= -1.0; |
| 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 |
|
} |
| 379 |
– |
} |
| 344 |
|
} |
| 345 |
|
|
| 346 |
< |
if (n > 4) |
| 347 |
< |
{ |
| 348 |
< |
delete [] b; |
| 385 |
< |
delete [] z; |
| 346 |
> |
if (n > 4) { |
| 347 |
> |
delete [] b; |
| 348 |
> |
delete [] z; |
| 349 |
|
} |
| 350 |
< |
return 1; |
| 350 |
> |
return 1; |
| 351 |
|
} |
| 352 |
|
|
| 353 |
|
|
