| 78 |
|
return m; |
| 79 |
|
} |
| 80 |
|
|
| 81 |
< |
/** Retunrs the inversion of this matrix. */ |
| 81 |
> |
/** |
| 82 |
> |
* Retunrs the inversion of this matrix. |
| 83 |
> |
* @todo need implementation |
| 84 |
> |
*/ |
| 85 |
|
SquareMatrix<Real, Dim> inverse() { |
| 86 |
|
SquareMatrix<Real, Dim> result; |
| 87 |
|
|
| 88 |
|
return result; |
| 89 |
|
} |
| 90 |
|
|
| 91 |
< |
/** Returns the determinant of this matrix. */ |
| 92 |
< |
double determinant() const { |
| 93 |
< |
double det; |
| 91 |
> |
/** |
| 92 |
> |
* Returns the determinant of this matrix. |
| 93 |
> |
* @todo need implementation |
| 94 |
> |
*/ |
| 95 |
> |
Real determinant() const { |
| 96 |
> |
Real det; |
| 97 |
|
return det; |
| 98 |
|
} |
| 99 |
|
|
| 100 |
|
/** Returns the trace of this matrix. */ |
| 101 |
< |
double trace() const { |
| 102 |
< |
double tmp = 0; |
| 101 |
> |
Real trace() const { |
| 102 |
> |
Real tmp = 0; |
| 103 |
|
|
| 104 |
|
for (unsigned int i = 0; i < Dim ; i++) |
| 105 |
|
tmp += data_[i][i]; |
| 148 |
|
return true; |
| 149 |
|
} |
| 150 |
|
|
| 151 |
+ |
/** @todo need implementation */ |
| 152 |
|
void diagonalize() { |
| 153 |
< |
jacobi(m, eigenValues, ortMat); |
| 153 |
> |
//jacobi(m, eigenValues, ortMat); |
| 154 |
|
} |
| 155 |
|
|
| 156 |
|
/** |
| 165 |
|
SquareMatrix<Real, Dim> ortMat; |
| 166 |
|
|
| 167 |
|
if ( !isSymmetric()){ |
| 168 |
< |
throw(); |
| 168 |
> |
//throw(); |
| 169 |
|
} |
| 170 |
|
|
| 171 |
|
SquareMatrix<Real, Dim> m(*this); |
| 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(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(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; |
| 199 |
< |
double tmp; |
| 198 |
> |
Real tresh, theta, tau, t, sm, s, h, g, c; |
| 199 |
> |
Real tmp; |
| 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 |
