| 201 |
|
return a[0]*b[0] + a[1]*b[1]+ a[2]*b[2]; |
| 202 |
|
} |
| 203 |
|
|
| 204 |
< |
//---------------------------------------------------------------------------- |
| 205 |
< |
// Extract the eigenvalues and eigenvectors from a 3x3 matrix. |
| 206 |
< |
// The eigenvectors (the columns of V) will be normalized. |
| 207 |
< |
// The eigenvectors are aligned optimally with the x, y, and z |
| 208 |
< |
// axes respectively. |
| 204 |
> |
/*----------------------------------------------------------------------------*/ |
| 205 |
> |
/* Extract the eigenvalues and eigenvectors from a 3x3 matrix.*/ |
| 206 |
> |
/* The eigenvectors (the columns of V) will be normalized. */ |
| 207 |
> |
/* The eigenvectors are aligned optimally with the x, y, and z*/ |
| 208 |
> |
/* axes respectively.*/ |
| 209 |
|
|
| 210 |
|
void diagonalize3x3(const double A[3][3], double w[3], double V[3][3]) { |
| 211 |
|
int i,j,k,maxI; |
| 212 |
|
double tmp, maxVal; |
| 213 |
|
|
| 214 |
< |
// do the matrix[3][3] to **matrix conversion for Jacobi |
| 214 |
> |
/* do the matrix[3][3] to **matrix conversion for Jacobi*/ |
| 215 |
|
double C[3][3]; |
| 216 |
|
double *ATemp[3],*VTemp[3]; |
| 217 |
|
for (i = 0; i < 3; i++) |
| 223 |
|
VTemp[i] = V[i]; |
| 224 |
|
} |
| 225 |
|
|
| 226 |
< |
// diagonalize using Jacobi |
| 226 |
> |
/* diagonalize using Jacobi*/ |
| 227 |
|
JacobiN(ATemp,3,w,VTemp); |
| 228 |
|
|
| 229 |
< |
// if all the eigenvalues are the same, return identity matrix |
| 229 |
> |
/* if all the eigenvalues are the same, return identity matrix*/ |
| 230 |
|
if (w[0] == w[1] && w[0] == w[2]) |
| 231 |
|
{ |
| 232 |
|
identityMat3(V); |
| 233 |
|
return; |
| 234 |
|
} |
| 235 |
|
|
| 236 |
< |
// transpose temporarily, it makes it easier to sort the eigenvectors |
| 236 |
> |
/* transpose temporarily, it makes it easier to sort the eigenvectors*/ |
| 237 |
|
transposeMat3(V,V); |
| 238 |
|
|
| 239 |
< |
// if two eigenvalues are the same, re-orthogonalize to optimally line |
| 240 |
< |
// up the eigenvectors with the x, y, and z axes |
| 239 |
> |
/* if two eigenvalues are the same, re-orthogonalize to optimally line*/ |
| 240 |
> |
/* up the eigenvectors with the x, y, and z axes*/ |
| 241 |
|
for (i = 0; i < 3; i++) |
| 242 |
|
{ |
| 243 |
< |
if (w[(i+1)%3] == w[(i+2)%3]) // two eigenvalues are the same |
| 243 |
> |
if (w[(i+1)%3] == w[(i+2)%3]) /* two eigenvalues are the same*/ |
| 244 |
|
{ |
| 245 |
< |
// find maximum element of the independant eigenvector |
| 245 |
> |
/* find maximum element of the independant eigenvector*/ |
| 246 |
|
maxVal = fabs(V[i][0]); |
| 247 |
|
maxI = 0; |
| 248 |
|
for (j = 1; j < 3; j++) |
| 253 |
|
maxI = j; |
| 254 |
|
} |
| 255 |
|
} |
| 256 |
< |
// swap the eigenvector into its proper position |
| 256 |
> |
/* swap the eigenvector into its proper position*/ |
| 257 |
|
if (maxI != i) |
| 258 |
|
{ |
| 259 |
|
tmp = w[maxI]; |
| 261 |
|
w[i] = tmp; |
| 262 |
|
swapVectors3(V[i],V[maxI]); |
| 263 |
|
} |
| 264 |
< |
// maximum element of eigenvector should be positive |
| 264 |
> |
/* maximum element of eigenvector should be positive*/ |
| 265 |
|
if (V[maxI][maxI] < 0) |
| 266 |
|
{ |
| 267 |
|
V[maxI][0] = -V[maxI][0]; |
| 269 |
|
V[maxI][2] = -V[maxI][2]; |
| 270 |
|
} |
| 271 |
|
|
| 272 |
< |
// re-orthogonalize the other two eigenvectors |
| 272 |
> |
/* re-orthogonalize the other two eigenvectors*/ |
| 273 |
|
j = (maxI+1)%3; |
| 274 |
|
k = (maxI+2)%3; |
| 275 |
|
|
| 281 |
|
normalize3(V[k]); |
| 282 |
|
crossProduct3(V[k],V[maxI],V[j]); |
| 283 |
|
|
| 284 |
< |
// transpose vectors back to columns |
| 284 |
> |
/* transpose vectors back to columns*/ |
| 285 |
|
transposeMat3(V,V); |
| 286 |
|
return; |
| 287 |
|
} |
| 288 |
|
} |
| 289 |
|
|
| 290 |
< |
// the three eigenvalues are different, just sort the eigenvectors |
| 291 |
< |
// to align them with the x, y, and z axes |
| 290 |
> |
/* the three eigenvalues are different, just sort the eigenvectors*/ |
| 291 |
> |
/* to align them with the x, y, and z axes*/ |
| 292 |
|
|
| 293 |
< |
// find the vector with the largest x element, make that vector |
| 294 |
< |
// the first vector |
| 293 |
> |
/* find the vector with the largest x element, make that vector*/ |
| 294 |
> |
/* the first vector*/ |
| 295 |
|
maxVal = fabs(V[0][0]); |
| 296 |
|
maxI = 0; |
| 297 |
|
for (i = 1; i < 3; i++) |
| 302 |
|
maxI = i; |
| 303 |
|
} |
| 304 |
|
} |
| 305 |
< |
// swap eigenvalue and eigenvector |
| 305 |
> |
/* swap eigenvalue and eigenvector*/ |
| 306 |
|
if (maxI != 0) |
| 307 |
|
{ |
| 308 |
|
tmp = w[maxI]; |
| 310 |
|
w[0] = tmp; |
| 311 |
|
swapVectors3(V[maxI],V[0]); |
| 312 |
|
} |
| 313 |
< |
// do the same for the y element |
| 313 |
> |
/* do the same for the y element*/ |
| 314 |
|
if (fabs(V[1][1]) < fabs(V[2][1])) |
| 315 |
|
{ |
| 316 |
|
tmp = w[2]; |
| 319 |
|
swapVectors3(V[2],V[1]); |
| 320 |
|
} |
| 321 |
|
|
| 322 |
< |
// ensure that the sign of the eigenvectors is correct |
| 322 |
> |
/* ensure that the sign of the eigenvectors is correct*/ |
| 323 |
|
for (i = 0; i < 2; i++) |
| 324 |
|
{ |
| 325 |
|
if (V[i][i] < 0) |
| 329 |
|
V[i][2] = -V[i][2]; |
| 330 |
|
} |
| 331 |
|
} |
| 332 |
< |
// set sign of final eigenvector to ensure that determinant is positive |
| 332 |
> |
/* set sign of final eigenvector to ensure that determinant is positive*/ |
| 333 |
|
if (matDet3(V) < 0) |
| 334 |
|
{ |
| 335 |
|
V[2][0] = -V[2][0]; |
| 337 |
|
V[2][2] = -V[2][2]; |
| 338 |
|
} |
| 339 |
|
|
| 340 |
< |
// transpose the eigenvectors back again |
| 340 |
> |
/* transpose the eigenvectors back again*/ |
| 341 |
|
transposeMat3(V,V); |
| 342 |
|
} |
| 343 |
|
|
| 346 |
|
|
| 347 |
|
#define MAX_ROTATIONS 20 |
| 348 |
|
|
| 349 |
< |
// Jacobi iteration for the solution of eigenvectors/eigenvalues of a nxn |
| 350 |
< |
// real symmetric matrix. Square nxn matrix a; size of matrix in n; |
| 351 |
< |
// output eigenvalues in w; and output eigenvectors in v. Resulting |
| 352 |
< |
// eigenvalues/vectors are sorted in decreasing order; eigenvectors are |
| 353 |
< |
// normalized. |
| 349 |
> |
/* Jacobi iteration for the solution of eigenvectors/eigenvalues of a nxn*/ |
| 350 |
> |
/* real symmetric matrix. Square nxn matrix a; size of matrix in n;*/ |
| 351 |
> |
/* output eigenvalues in w; and output eigenvectors in v. Resulting*/ |
| 352 |
> |
/* eigenvalues/vectors are sorted in decreasing order; eigenvectors are*/ |
| 353 |
> |
/* normalized.*/ |
| 354 |
|
int JacobiN(double **a, int n, double *w, double **v) { |
| 355 |
|
|
| 356 |
|
int i, j, k, iq, ip, numPos; |
| 361 |
|
double *z = zspace; |
| 362 |
|
|
| 363 |
|
|
| 364 |
< |
// only allocate memory if the matrix is large |
| 364 |
> |
/* only allocate memory if the matrix is large*/ |
| 365 |
|
if (n > 4) |
| 366 |
|
{ |
| 367 |
|
b = (double *) calloc(n, sizeof(double)); |
| 368 |
|
z = (double *) calloc(n, sizeof(double)); |
| 369 |
|
} |
| 370 |
|
|
| 371 |
< |
// initialize |
| 371 |
> |
/* initialize*/ |
| 372 |
|
for (ip=0; ip<n; ip++) |
| 373 |
|
{ |
| 374 |
|
for (iq=0; iq<n; iq++) |
| 383 |
|
z[ip] = 0.0; |
| 384 |
|
} |
| 385 |
|
|
| 386 |
< |
// begin rotation sequence |
| 386 |
> |
/* begin rotation sequence*/ |
| 387 |
|
for (i=0; i<MAX_ROTATIONS; i++) |
| 388 |
|
{ |
| 389 |
|
sm = 0.0; |
| 399 |
|
break; |
| 400 |
|
} |
| 401 |
|
|
| 402 |
< |
if (i < 3) // first 3 sweeps |
| 402 |
> |
if (i < 3) /* first 3 sweeps*/ |
| 403 |
|
{ |
| 404 |
|
tresh = 0.2*sm/(n*n); |
| 405 |
|
} |
| 414 |
|
{ |
| 415 |
|
g = 100.0*fabs(a[ip][iq]); |
| 416 |
|
|
| 417 |
< |
// after 4 sweeps |
| 417 |
> |
/* after 4 sweeps*/ |
| 418 |
|
if (i > 3 && (fabs(w[ip])+g) == fabs(w[ip]) |
| 419 |
|
&& (fabs(w[iq])+g) == fabs(w[iq])) |
| 420 |
|
{ |
| 446 |
|
w[iq] += h; |
| 447 |
|
a[ip][iq]=0.0; |
| 448 |
|
|
| 449 |
< |
// ip already shifted left by 1 unit |
| 449 |
> |
/* ip already shifted left by 1 unit*/ |
| 450 |
|
for (j = 0;j <= ip-1;j++) |
| 451 |
|
{ |
| 452 |
|
MAT_ROTATE(a,j,ip,j,iq) |
| 453 |
|
} |
| 454 |
< |
// ip and iq already shifted left by 1 unit |
| 454 |
> |
/* ip and iq already shifted left by 1 unit*/ |
| 455 |
|
for (j = ip+1;j <= iq-1;j++) |
| 456 |
|
{ |
| 457 |
|
MAT_ROTATE(a,ip,j,j,iq) |
| 458 |
|
} |
| 459 |
< |
// iq already shifted left by 1 unit |
| 459 |
> |
/* iq already shifted left by 1 unit*/ |
| 460 |
|
for (j=iq+1; j<n; j++) |
| 461 |
|
{ |
| 462 |
|
MAT_ROTATE(a,ip,j,iq,j) |
| 477 |
|
} |
| 478 |
|
} |
| 479 |
|
|
| 480 |
< |
//// this is NEVER called |
| 480 |
> |
/*// this is NEVER called*/ |
| 481 |
|
if ( i >= MAX_ROTATIONS ) |
| 482 |
|
{ |
| 483 |
|
sprintf( painCave.errMsg, |
| 487 |
|
return 0; |
| 488 |
|
} |
| 489 |
|
|
| 490 |
< |
// sort eigenfunctions these changes do not affect accuracy |
| 491 |
< |
for (j=0; j<n-1; j++) // boundary incorrect |
| 490 |
> |
/* sort eigenfunctions these changes do not affect accuracy */ |
| 491 |
> |
for (j=0; j<n-1; j++) /* boundary incorrect*/ |
| 492 |
|
{ |
| 493 |
|
k = j; |
| 494 |
|
tmp = w[k]; |
| 495 |
< |
for (i=j+1; i<n; i++) // boundary incorrect, shifted already |
| 495 |
> |
for (i=j+1; i<n; i++) /* boundary incorrect, shifted already*/ |
| 496 |
|
{ |
| 497 |
< |
if (w[i] >= tmp) // why exchage if same? |
| 497 |
> |
if (w[i] >= tmp) /* why exchage if same?*/ |
| 498 |
|
{ |
| 499 |
|
k = i; |
| 500 |
|
tmp = w[k]; |
| 512 |
|
} |
| 513 |
|
} |
| 514 |
|
} |
| 515 |
< |
// insure eigenvector consistency (i.e., Jacobi can compute vectors that |
| 516 |
< |
// are negative of one another (.707,.707,0) and (-.707,-.707,0). This can |
| 517 |
< |
// reek havoc in hyperstreamline/other stuff. We will select the most |
| 518 |
< |
// positive eigenvector. |
| 515 |
> |
/* insure eigenvector consistency (i.e., Jacobi can compute vectors that*/ |
| 516 |
> |
/* are negative of one another (.707,.707,0) and (-.707,-.707,0). This can*/ |
| 517 |
> |
/* reek havoc in hyperstreamline/other stuff. We will select the most*/ |
| 518 |
> |
/* positive eigenvector.*/ |
| 519 |
|
ceil_half_n = (n >> 1) + (n & 1); |
| 520 |
|
for (j=0; j<n; j++) |
| 521 |
|
{ |
| 526 |
|
numPos++; |
| 527 |
|
} |
| 528 |
|
} |
| 529 |
< |
// if ( numPos < ceil(double(n)/double(2.0)) ) |
| 529 |
> |
/* if ( numPos < ceil(double(n)/double(2.0)) )*/ |
| 530 |
|
if ( numPos < ceil_half_n) |
| 531 |
|
{ |
| 532 |
|
for(i=0; i<n; i++) |
