| 1 |
gezelter |
1930 |
/* |
| 2 |
|
|
* Copyright (c) 2005 The University of Notre Dame. All Rights Reserved. |
| 3 |
|
|
* |
| 4 |
|
|
* The University of Notre Dame grants you ("Licensee") a |
| 5 |
|
|
* non-exclusive, royalty free, license to use, modify and |
| 6 |
|
|
* redistribute this software in source and binary code form, provided |
| 7 |
|
|
* that the following conditions are met: |
| 8 |
|
|
* |
| 9 |
|
|
* 1. Acknowledgement of the program authors must be made in any |
| 10 |
|
|
* publication of scientific results based in part on use of the |
| 11 |
|
|
* program. An acceptable form of acknowledgement is citation of |
| 12 |
|
|
* the article in which the program was described (Matthew |
| 13 |
|
|
* A. Meineke, Charles F. Vardeman II, Teng Lin, Christopher |
| 14 |
|
|
* J. Fennell and J. Daniel Gezelter, "OOPSE: An Object-Oriented |
| 15 |
|
|
* Parallel Simulation Engine for Molecular Dynamics," |
| 16 |
|
|
* J. Comput. Chem. 26, pp. 252-271 (2005)) |
| 17 |
|
|
* |
| 18 |
|
|
* 2. Redistributions of source code must retain the above copyright |
| 19 |
|
|
* notice, this list of conditions and the following disclaimer. |
| 20 |
|
|
* |
| 21 |
|
|
* 3. Redistributions in binary form must reproduce the above copyright |
| 22 |
|
|
* notice, this list of conditions and the following disclaimer in the |
| 23 |
|
|
* documentation and/or other materials provided with the |
| 24 |
|
|
* distribution. |
| 25 |
|
|
* |
| 26 |
|
|
* This software is provided "AS IS," without a warranty of any |
| 27 |
|
|
* kind. All express or implied conditions, representations and |
| 28 |
|
|
* warranties, including any implied warranty of merchantability, |
| 29 |
|
|
* fitness for a particular purpose or non-infringement, are hereby |
| 30 |
|
|
* excluded. The University of Notre Dame and its licensors shall not |
| 31 |
|
|
* be liable for any damages suffered by licensee as a result of |
| 32 |
|
|
* using, modifying or distributing the software or its |
| 33 |
|
|
* derivatives. In no event will the University of Notre Dame or its |
| 34 |
|
|
* licensors be liable for any lost revenue, profit or data, or for |
| 35 |
|
|
* direct, indirect, special, consequential, incidental or punitive |
| 36 |
|
|
* damages, however caused and regardless of the theory of liability, |
| 37 |
|
|
* arising out of the use of or inability to use software, even if the |
| 38 |
|
|
* University of Notre Dame has been advised of the possibility of |
| 39 |
|
|
* such damages. |
| 40 |
|
|
*/ |
| 41 |
|
|
|
| 42 |
gezelter |
1490 |
#include <stdio.h> |
| 43 |
|
|
#include <math.h> |
| 44 |
|
|
#include <stdlib.h> |
| 45 |
tim |
1492 |
#include "math/MatVec3.h" |
| 46 |
gezelter |
1490 |
|
| 47 |
|
|
/* |
| 48 |
|
|
* Contains various utilities for dealing with 3x3 matrices and |
| 49 |
|
|
* length 3 vectors |
| 50 |
|
|
*/ |
| 51 |
|
|
|
| 52 |
|
|
void identityMat3(double A[3][3]) { |
| 53 |
|
|
int i; |
| 54 |
|
|
for (i = 0; i < 3; i++) { |
| 55 |
|
|
A[i][0] = A[i][1] = A[i][2] = 0.0; |
| 56 |
|
|
A[i][i] = 1.0; |
| 57 |
|
|
} |
| 58 |
|
|
} |
| 59 |
|
|
|
| 60 |
|
|
void swapVectors3(double v1[3], double v2[3]) { |
| 61 |
|
|
int i; |
| 62 |
|
|
for (i = 0; i < 3; i++) { |
| 63 |
|
|
double tmp = v1[i]; |
| 64 |
|
|
v1[i] = v2[i]; |
| 65 |
|
|
v2[i] = tmp; |
| 66 |
|
|
} |
| 67 |
|
|
} |
| 68 |
|
|
|
| 69 |
|
|
double normalize3(double x[3]) { |
| 70 |
|
|
double den; |
| 71 |
|
|
int i; |
| 72 |
|
|
if ( (den = norm3(x)) != 0.0 ) { |
| 73 |
|
|
for (i=0; i < 3; i++) |
| 74 |
|
|
{ |
| 75 |
|
|
x[i] /= den; |
| 76 |
|
|
} |
| 77 |
|
|
} |
| 78 |
|
|
return den; |
| 79 |
|
|
} |
| 80 |
|
|
|
| 81 |
|
|
void matMul3(double a[3][3], double b[3][3], double c[3][3]) { |
| 82 |
|
|
double r00, r01, r02, r10, r11, r12, r20, r21, r22; |
| 83 |
|
|
|
| 84 |
|
|
r00 = a[0][0]*b[0][0] + a[0][1]*b[1][0] + a[0][2]*b[2][0]; |
| 85 |
|
|
r01 = a[0][0]*b[0][1] + a[0][1]*b[1][1] + a[0][2]*b[2][1]; |
| 86 |
|
|
r02 = a[0][0]*b[0][2] + a[0][1]*b[1][2] + a[0][2]*b[2][2]; |
| 87 |
|
|
|
| 88 |
|
|
r10 = a[1][0]*b[0][0] + a[1][1]*b[1][0] + a[1][2]*b[2][0]; |
| 89 |
|
|
r11 = a[1][0]*b[0][1] + a[1][1]*b[1][1] + a[1][2]*b[2][1]; |
| 90 |
|
|
r12 = a[1][0]*b[0][2] + a[1][1]*b[1][2] + a[1][2]*b[2][2]; |
| 91 |
|
|
|
| 92 |
|
|
r20 = a[2][0]*b[0][0] + a[2][1]*b[1][0] + a[2][2]*b[2][0]; |
| 93 |
|
|
r21 = a[2][0]*b[0][1] + a[2][1]*b[1][1] + a[2][2]*b[2][1]; |
| 94 |
|
|
r22 = a[2][0]*b[0][2] + a[2][1]*b[1][2] + a[2][2]*b[2][2]; |
| 95 |
|
|
|
| 96 |
|
|
c[0][0] = r00; c[0][1] = r01; c[0][2] = r02; |
| 97 |
|
|
c[1][0] = r10; c[1][1] = r11; c[1][2] = r12; |
| 98 |
|
|
c[2][0] = r20; c[2][1] = r21; c[2][2] = r22; |
| 99 |
|
|
} |
| 100 |
|
|
|
| 101 |
|
|
void matVecMul3(double m[3][3], double inVec[3], double outVec[3]) { |
| 102 |
|
|
double a0, a1, a2; |
| 103 |
|
|
|
| 104 |
|
|
a0 = inVec[0]; a1 = inVec[1]; a2 = inVec[2]; |
| 105 |
|
|
|
| 106 |
|
|
outVec[0] = m[0][0]*a0 + m[0][1]*a1 + m[0][2]*a2; |
| 107 |
|
|
outVec[1] = m[1][0]*a0 + m[1][1]*a1 + m[1][2]*a2; |
| 108 |
|
|
outVec[2] = m[2][0]*a0 + m[2][1]*a1 + m[2][2]*a2; |
| 109 |
|
|
} |
| 110 |
|
|
|
| 111 |
|
|
double matDet3(double a[3][3]) { |
| 112 |
|
|
int i, j, k; |
| 113 |
|
|
double determinant; |
| 114 |
|
|
|
| 115 |
|
|
determinant = 0.0; |
| 116 |
|
|
|
| 117 |
|
|
for(i = 0; i < 3; i++) { |
| 118 |
|
|
j = (i+1)%3; |
| 119 |
|
|
k = (i+2)%3; |
| 120 |
|
|
|
| 121 |
|
|
determinant += a[0][i] * (a[1][j]*a[2][k] - a[1][k]*a[2][j]); |
| 122 |
|
|
} |
| 123 |
|
|
|
| 124 |
|
|
return determinant; |
| 125 |
|
|
} |
| 126 |
|
|
|
| 127 |
|
|
void invertMat3(double a[3][3], double b[3][3]) { |
| 128 |
|
|
|
| 129 |
|
|
int i, j, k, l, m, n; |
| 130 |
|
|
double determinant; |
| 131 |
|
|
|
| 132 |
|
|
determinant = matDet3( a ); |
| 133 |
|
|
|
| 134 |
|
|
if (determinant == 0.0) { |
| 135 |
|
|
sprintf( painCave.errMsg, |
| 136 |
|
|
"Can't invert a matrix with a zero determinant!\n"); |
| 137 |
|
|
painCave.isFatal = 1; |
| 138 |
|
|
simError(); |
| 139 |
|
|
} |
| 140 |
|
|
|
| 141 |
|
|
for (i=0; i < 3; i++) { |
| 142 |
|
|
j = (i+1)%3; |
| 143 |
|
|
k = (i+2)%3; |
| 144 |
|
|
for(l = 0; l < 3; l++) { |
| 145 |
|
|
m = (l+1)%3; |
| 146 |
|
|
n = (l+2)%3; |
| 147 |
|
|
|
| 148 |
|
|
b[l][i] = (a[j][m]*a[k][n] - a[j][n]*a[k][m]) / determinant; |
| 149 |
|
|
} |
| 150 |
|
|
} |
| 151 |
|
|
} |
| 152 |
|
|
|
| 153 |
|
|
void transposeMat3(double in[3][3], double out[3][3]) { |
| 154 |
|
|
double temp[3][3]; |
| 155 |
|
|
int i, j; |
| 156 |
|
|
|
| 157 |
|
|
for (i = 0; i < 3; i++) { |
| 158 |
|
|
for (j = 0; j < 3; j++) { |
| 159 |
|
|
temp[j][i] = in[i][j]; |
| 160 |
|
|
} |
| 161 |
|
|
} |
| 162 |
|
|
for (i = 0; i < 3; i++) { |
| 163 |
|
|
for (j = 0; j < 3; j++) { |
| 164 |
|
|
out[i][j] = temp[i][j]; |
| 165 |
|
|
} |
| 166 |
|
|
} |
| 167 |
|
|
} |
| 168 |
|
|
|
| 169 |
|
|
void printMat3(double A[3][3] ){ |
| 170 |
|
|
|
| 171 |
|
|
fprintf(stderr, "[ %g, %g, %g ]\n[ %g, %g, %g ]\n[ %g, %g, %g ]\n", |
| 172 |
|
|
A[0][0] , A[0][1] , A[0][2], |
| 173 |
|
|
A[1][0] , A[1][1] , A[1][2], |
| 174 |
|
|
A[2][0] , A[2][1] , A[2][2]) ; |
| 175 |
|
|
} |
| 176 |
|
|
|
| 177 |
|
|
void printMat9(double A[9] ){ |
| 178 |
|
|
|
| 179 |
|
|
fprintf(stderr, "[ %g, %g, %g ]\n[ %g, %g, %g ]\n[ %g, %g, %g ]\n", |
| 180 |
|
|
A[0], A[1], A[2], |
| 181 |
|
|
A[3], A[4], A[5], |
| 182 |
|
|
A[6], A[7], A[8]); |
| 183 |
|
|
} |
| 184 |
|
|
|
| 185 |
|
|
double matTrace3(double m[3][3]){ |
| 186 |
|
|
double trace; |
| 187 |
|
|
trace = m[0][0] + m[1][1] + m[2][2]; |
| 188 |
|
|
|
| 189 |
|
|
return trace; |
| 190 |
|
|
} |
| 191 |
|
|
|
| 192 |
|
|
void crossProduct3(double a[3],double b[3], double out[3]){ |
| 193 |
|
|
|
| 194 |
|
|
out[0] = a[1] * b[2] - a[2] * b[1]; |
| 195 |
|
|
out[1] = a[2] * b[0] - a[0] * b[2] ; |
| 196 |
|
|
out[2] = a[0] * b[1] - a[1] * b[0]; |
| 197 |
|
|
|
| 198 |
|
|
} |
| 199 |
|
|
|
| 200 |
|
|
double dotProduct3(double a[3], double b[3]){ |
| 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. |
| 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 |
| 215 |
|
|
double C[3][3]; |
| 216 |
|
|
double *ATemp[3],*VTemp[3]; |
| 217 |
|
|
for (i = 0; i < 3; i++) |
| 218 |
|
|
{ |
| 219 |
|
|
C[i][0] = A[i][0]; |
| 220 |
|
|
C[i][1] = A[i][1]; |
| 221 |
|
|
C[i][2] = A[i][2]; |
| 222 |
|
|
ATemp[i] = C[i]; |
| 223 |
|
|
VTemp[i] = V[i]; |
| 224 |
|
|
} |
| 225 |
|
|
|
| 226 |
|
|
// diagonalize using Jacobi |
| 227 |
|
|
JacobiN(ATemp,3,w,VTemp); |
| 228 |
|
|
|
| 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 |
| 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 |
| 241 |
|
|
for (i = 0; i < 3; i++) |
| 242 |
|
|
{ |
| 243 |
|
|
if (w[(i+1)%3] == w[(i+2)%3]) // two eigenvalues are the same |
| 244 |
|
|
{ |
| 245 |
|
|
// find maximum element of the independant eigenvector |
| 246 |
|
|
maxVal = fabs(V[i][0]); |
| 247 |
|
|
maxI = 0; |
| 248 |
|
|
for (j = 1; j < 3; j++) |
| 249 |
|
|
{ |
| 250 |
|
|
if (maxVal < (tmp = fabs(V[i][j]))) |
| 251 |
|
|
{ |
| 252 |
|
|
maxVal = tmp; |
| 253 |
|
|
maxI = j; |
| 254 |
|
|
} |
| 255 |
|
|
} |
| 256 |
|
|
// swap the eigenvector into its proper position |
| 257 |
|
|
if (maxI != i) |
| 258 |
|
|
{ |
| 259 |
|
|
tmp = w[maxI]; |
| 260 |
|
|
w[maxI] = w[i]; |
| 261 |
|
|
w[i] = tmp; |
| 262 |
|
|
swapVectors3(V[i],V[maxI]); |
| 263 |
|
|
} |
| 264 |
|
|
// maximum element of eigenvector should be positive |
| 265 |
|
|
if (V[maxI][maxI] < 0) |
| 266 |
|
|
{ |
| 267 |
|
|
V[maxI][0] = -V[maxI][0]; |
| 268 |
|
|
V[maxI][1] = -V[maxI][1]; |
| 269 |
|
|
V[maxI][2] = -V[maxI][2]; |
| 270 |
|
|
} |
| 271 |
|
|
|
| 272 |
|
|
// re-orthogonalize the other two eigenvectors |
| 273 |
|
|
j = (maxI+1)%3; |
| 274 |
|
|
k = (maxI+2)%3; |
| 275 |
|
|
|
| 276 |
|
|
V[j][0] = 0.0; |
| 277 |
|
|
V[j][1] = 0.0; |
| 278 |
|
|
V[j][2] = 0.0; |
| 279 |
|
|
V[j][j] = 1.0; |
| 280 |
|
|
crossProduct3(V[maxI],V[j],V[k]); |
| 281 |
|
|
normalize3(V[k]); |
| 282 |
|
|
crossProduct3(V[k],V[maxI],V[j]); |
| 283 |
|
|
|
| 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 |
| 292 |
|
|
|
| 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++) |
| 298 |
|
|
{ |
| 299 |
|
|
if (maxVal < (tmp = fabs(V[i][0]))) |
| 300 |
|
|
{ |
| 301 |
|
|
maxVal = tmp; |
| 302 |
|
|
maxI = i; |
| 303 |
|
|
} |
| 304 |
|
|
} |
| 305 |
|
|
// swap eigenvalue and eigenvector |
| 306 |
|
|
if (maxI != 0) |
| 307 |
|
|
{ |
| 308 |
|
|
tmp = w[maxI]; |
| 309 |
|
|
w[maxI] = w[0]; |
| 310 |
|
|
w[0] = tmp; |
| 311 |
|
|
swapVectors3(V[maxI],V[0]); |
| 312 |
|
|
} |
| 313 |
|
|
// do the same for the y element |
| 314 |
|
|
if (fabs(V[1][1]) < fabs(V[2][1])) |
| 315 |
|
|
{ |
| 316 |
|
|
tmp = w[2]; |
| 317 |
|
|
w[2] = w[1]; |
| 318 |
|
|
w[1] = tmp; |
| 319 |
|
|
swapVectors3(V[2],V[1]); |
| 320 |
|
|
} |
| 321 |
|
|
|
| 322 |
|
|
// ensure that the sign of the eigenvectors is correct |
| 323 |
|
|
for (i = 0; i < 2; i++) |
| 324 |
|
|
{ |
| 325 |
|
|
if (V[i][i] < 0) |
| 326 |
|
|
{ |
| 327 |
|
|
V[i][0] = -V[i][0]; |
| 328 |
|
|
V[i][1] = -V[i][1]; |
| 329 |
|
|
V[i][2] = -V[i][2]; |
| 330 |
|
|
} |
| 331 |
|
|
} |
| 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]; |
| 336 |
|
|
V[2][1] = -V[2][1]; |
| 337 |
|
|
V[2][2] = -V[2][2]; |
| 338 |
|
|
} |
| 339 |
|
|
|
| 340 |
|
|
// transpose the eigenvectors back again |
| 341 |
|
|
transposeMat3(V,V); |
| 342 |
|
|
} |
| 343 |
|
|
|
| 344 |
|
|
|
| 345 |
|
|
#define MAT_ROTATE(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); |
| 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. |
| 354 |
|
|
int JacobiN(double **a, int n, double *w, double **v) { |
| 355 |
|
|
|
| 356 |
|
|
int i, j, k, iq, ip, numPos; |
| 357 |
|
|
int ceil_half_n; |
| 358 |
|
|
double tresh, theta, tau, t, sm, s, h, g, c, tmp; |
| 359 |
|
|
double bspace[4], zspace[4]; |
| 360 |
|
|
double *b = bspace; |
| 361 |
|
|
double *z = zspace; |
| 362 |
|
|
|
| 363 |
|
|
|
| 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 |
| 372 |
|
|
for (ip=0; ip<n; ip++) |
| 373 |
|
|
{ |
| 374 |
|
|
for (iq=0; iq<n; iq++) |
| 375 |
|
|
{ |
| 376 |
|
|
v[ip][iq] = 0.0; |
| 377 |
|
|
} |
| 378 |
|
|
v[ip][ip] = 1.0; |
| 379 |
|
|
} |
| 380 |
|
|
for (ip=0; ip<n; ip++) |
| 381 |
|
|
{ |
| 382 |
|
|
b[ip] = w[ip] = a[ip][ip]; |
| 383 |
|
|
z[ip] = 0.0; |
| 384 |
|
|
} |
| 385 |
|
|
|
| 386 |
|
|
// begin rotation sequence |
| 387 |
|
|
for (i=0; i<MAX_ROTATIONS; i++) |
| 388 |
|
|
{ |
| 389 |
|
|
sm = 0.0; |
| 390 |
|
|
for (ip=0; ip<n-1; ip++) |
| 391 |
|
|
{ |
| 392 |
|
|
for (iq=ip+1; iq<n; iq++) |
| 393 |
|
|
{ |
| 394 |
|
|
sm += fabs(a[ip][iq]); |
| 395 |
|
|
} |
| 396 |
|
|
} |
| 397 |
|
|
if (sm == 0.0) |
| 398 |
|
|
{ |
| 399 |
|
|
break; |
| 400 |
|
|
} |
| 401 |
|
|
|
| 402 |
|
|
if (i < 3) // first 3 sweeps |
| 403 |
|
|
{ |
| 404 |
|
|
tresh = 0.2*sm/(n*n); |
| 405 |
|
|
} |
| 406 |
|
|
else |
| 407 |
|
|
{ |
| 408 |
|
|
tresh = 0.0; |
| 409 |
|
|
} |
| 410 |
|
|
|
| 411 |
|
|
for (ip=0; ip<n-1; ip++) |
| 412 |
|
|
{ |
| 413 |
|
|
for (iq=ip+1; iq<n; iq++) |
| 414 |
|
|
{ |
| 415 |
|
|
g = 100.0*fabs(a[ip][iq]); |
| 416 |
|
|
|
| 417 |
|
|
// after 4 sweeps |
| 418 |
|
|
if (i > 3 && (fabs(w[ip])+g) == fabs(w[ip]) |
| 419 |
|
|
&& (fabs(w[iq])+g) == fabs(w[iq])) |
| 420 |
|
|
{ |
| 421 |
|
|
a[ip][iq] = 0.0; |
| 422 |
|
|
} |
| 423 |
|
|
else if (fabs(a[ip][iq]) > tresh) |
| 424 |
|
|
{ |
| 425 |
|
|
h = w[iq] - w[ip]; |
| 426 |
|
|
if ( (fabs(h)+g) == fabs(h)) |
| 427 |
|
|
{ |
| 428 |
|
|
t = (a[ip][iq]) / h; |
| 429 |
|
|
} |
| 430 |
|
|
else |
| 431 |
|
|
{ |
| 432 |
|
|
theta = 0.5*h / (a[ip][iq]); |
| 433 |
|
|
t = 1.0 / (fabs(theta)+sqrt(1.0+theta*theta)); |
| 434 |
|
|
if (theta < 0.0) |
| 435 |
|
|
{ |
| 436 |
|
|
t = -t; |
| 437 |
|
|
} |
| 438 |
|
|
} |
| 439 |
|
|
c = 1.0 / sqrt(1+t*t); |
| 440 |
|
|
s = t*c; |
| 441 |
|
|
tau = s/(1.0+c); |
| 442 |
|
|
h = t*a[ip][iq]; |
| 443 |
|
|
z[ip] -= h; |
| 444 |
|
|
z[iq] += h; |
| 445 |
|
|
w[ip] -= h; |
| 446 |
|
|
w[iq] += h; |
| 447 |
|
|
a[ip][iq]=0.0; |
| 448 |
|
|
|
| 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 |
| 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 |
| 460 |
|
|
for (j=iq+1; j<n; j++) |
| 461 |
|
|
{ |
| 462 |
|
|
MAT_ROTATE(a,ip,j,iq,j) |
| 463 |
|
|
} |
| 464 |
|
|
for (j=0; j<n; j++) |
| 465 |
|
|
{ |
| 466 |
|
|
MAT_ROTATE(v,j,ip,j,iq) |
| 467 |
|
|
} |
| 468 |
|
|
} |
| 469 |
|
|
} |
| 470 |
|
|
} |
| 471 |
|
|
|
| 472 |
|
|
for (ip=0; ip<n; ip++) |
| 473 |
|
|
{ |
| 474 |
|
|
b[ip] += z[ip]; |
| 475 |
|
|
w[ip] = b[ip]; |
| 476 |
|
|
z[ip] = 0.0; |
| 477 |
|
|
} |
| 478 |
|
|
} |
| 479 |
|
|
|
| 480 |
|
|
//// this is NEVER called |
| 481 |
|
|
if ( i >= MAX_ROTATIONS ) |
| 482 |
|
|
{ |
| 483 |
|
|
sprintf( painCave.errMsg, |
| 484 |
|
|
"Jacobi: Error extracting eigenfunctions!\n"); |
| 485 |
|
|
painCave.isFatal = 1; |
| 486 |
|
|
simError(); |
| 487 |
|
|
return 0; |
| 488 |
|
|
} |
| 489 |
|
|
|
| 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 |
| 496 |
|
|
{ |
| 497 |
|
|
if (w[i] >= tmp) // why exchage if same? |
| 498 |
|
|
{ |
| 499 |
|
|
k = i; |
| 500 |
|
|
tmp = w[k]; |
| 501 |
|
|
} |
| 502 |
|
|
} |
| 503 |
|
|
if (k != j) |
| 504 |
|
|
{ |
| 505 |
|
|
w[k] = w[j]; |
| 506 |
|
|
w[j] = tmp; |
| 507 |
|
|
for (i=0; i<n; i++) |
| 508 |
|
|
{ |
| 509 |
|
|
tmp = v[i][j]; |
| 510 |
|
|
v[i][j] = v[i][k]; |
| 511 |
|
|
v[i][k] = tmp; |
| 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. |
| 519 |
|
|
ceil_half_n = (n >> 1) + (n & 1); |
| 520 |
|
|
for (j=0; j<n; j++) |
| 521 |
|
|
{ |
| 522 |
|
|
for (numPos=0, i=0; i<n; i++) |
| 523 |
|
|
{ |
| 524 |
|
|
if ( v[i][j] >= 0.0 ) |
| 525 |
|
|
{ |
| 526 |
|
|
numPos++; |
| 527 |
|
|
} |
| 528 |
|
|
} |
| 529 |
|
|
// if ( numPos < ceil(double(n)/double(2.0)) ) |
| 530 |
|
|
if ( numPos < ceil_half_n) |
| 531 |
|
|
{ |
| 532 |
|
|
for(i=0; i<n; i++) |
| 533 |
|
|
{ |
| 534 |
|
|
v[i][j] *= -1.0; |
| 535 |
|
|
} |
| 536 |
|
|
} |
| 537 |
|
|
} |
| 538 |
|
|
|
| 539 |
|
|
if (n > 4) |
| 540 |
|
|
{ |
| 541 |
|
|
free(b); |
| 542 |
|
|
free(z); |
| 543 |
|
|
} |
| 544 |
|
|
return 1; |
| 545 |
|
|
} |
| 546 |
|
|
|
| 547 |
|
|
#undef MAT_ROTATE |
| 548 |
|
|
#undef MAX_ROTATIONS |
