| 1 |
#define EXTERN extern |
| 2 |
|
| 3 |
// mode |
| 4 |
#define NONE 0 |
| 5 |
#define NEWTON 1 |
| 6 |
#define TNCG 2 |
| 7 |
#define DTNCG 3 |
| 8 |
#define AUTO 4 |
| 9 |
// method |
| 10 |
#define DIAG 5 |
| 11 |
#define SSOR 6 |
| 12 |
#define ICCG 7 |
| 13 |
#define BLOCK 8 |
| 14 |
|
| 15 |
|
| 16 |
#include "pcwin.h" |
| 17 |
#include "pcmod.h" |
| 18 |
|
| 19 |
#include "energies.h" |
| 20 |
#include "derivs.h" |
| 21 |
#include "utility.h" |
| 22 |
|
| 23 |
//#define min(a,b) (((a) < (b) ? (a) : (b)) |
| 24 |
|
| 25 |
EXTERN struct t_minvar{ |
| 26 |
double cappa, stpmin, stpmax, angmax; |
| 27 |
int intmax; |
| 28 |
} minvar; |
| 29 |
|
| 30 |
void solve(int,int,int,int, double *,double *,double *,double *,int *, |
| 31 |
int *,int *,double *,int *,int *,int *, double (*)()); |
| 32 |
|
| 33 |
|
| 34 |
static void precond(int,int ,int ,double *,double *,double *,int *,int *,int *,double *); |
| 35 |
static void cholesky(int , double *, double *); |
| 36 |
static void column(int, int *, int *,int *,int *,int *,int *, int *); |
| 37 |
|
| 38 |
int stable; |
| 39 |
double *f, *f_diag; |
| 40 |
int *c_index, *c_value; |
| 41 |
|
| 42 |
void solve(int mode,int method,int negtest,int nvar,double *p,double *x, |
| 43 |
double *g, double *h, int *h_init, int *h_stop, int *h_index, |
| 44 |
double *h_diag,int *icycle,int *iter_cg,int *fg_call,double (*fgvalue) ()) |
| 45 |
{ |
| 46 |
int i,j,k, iter,maxiter,maxhess; |
| 47 |
double *m, *d, *si, *r, *q; // |
| 48 |
double alpha,beta,delta,sigma; |
| 49 |
double f_sigma; |
| 50 |
double *x_sigma; |
| 51 |
double *g_sigma; |
| 52 |
double g_norm,g_rms,eps,converge; |
| 53 |
double hj,gg,dq,rr,dd,rs,rs_new,r_norm; |
| 54 |
int maxvar = 3*natom; |
| 55 |
|
| 56 |
if (natom < 300) |
| 57 |
maxhess = (3*natom*(3*natom-1))/2; |
| 58 |
else if (natom < 800) |
| 59 |
maxhess = (3*natom*(3*natom-1))/3; |
| 60 |
else |
| 61 |
maxhess = (3*natom*(3*natom-1))/20; |
| 62 |
|
| 63 |
|
| 64 |
m = dvector(0,maxvar); |
| 65 |
r = dvector(0,maxvar); |
| 66 |
si = dvector(0,maxvar); |
| 67 |
d = dvector(0,maxvar); |
| 68 |
q = dvector(0,maxvar); |
| 69 |
x_sigma = dvector(0,maxvar); |
| 70 |
g_sigma = dvector(0,maxvar); |
| 71 |
f_diag = dvector(0,maxvar); |
| 72 |
f = dvector(0,maxhess); |
| 73 |
c_index = ivector(0,maxhess); |
| 74 |
c_value = ivector(0,maxhess); |
| 75 |
|
| 76 |
if (mode != DTNCG && method != NONE) |
| 77 |
{ |
| 78 |
for (i=0; i < nvar; i++) |
| 79 |
m[i] = 1.0 / sqrt(fabs(h_diag[i])); |
| 80 |
|
| 81 |
for (i=0; i < nvar; i++) |
| 82 |
{ |
| 83 |
g[i] = g[i] * m[i]; |
| 84 |
h_diag[i] *= m[i] * m[i]; |
| 85 |
for (j = h_init[i]; j < h_stop[i]; j++) |
| 86 |
{ |
| 87 |
k = h_index[j]; |
| 88 |
h[j] *= m[i] * m[k]; |
| 89 |
} |
| 90 |
} |
| 91 |
} |
| 92 |
|
| 93 |
iter = 0; |
| 94 |
gg = 0.0; |
| 95 |
for (i=0; i < nvar; i++) |
| 96 |
{ |
| 97 |
p[i] = 0.0; |
| 98 |
r[i] = -g[i]; |
| 99 |
gg += g[i]*g[i]; |
| 100 |
} |
| 101 |
g_norm = sqrt(gg); |
| 102 |
precond(method, iter,nvar, si, r, h, h_init, h_stop, h_index, h_diag); |
| 103 |
rs = 0.0; |
| 104 |
for (i=0; i < nvar; i++) |
| 105 |
{ |
| 106 |
d[i] = si[i]; |
| 107 |
rs += r[i]*si[i]; |
| 108 |
} |
| 109 |
|
| 110 |
if (mode == NEWTON) |
| 111 |
{ |
| 112 |
eps = 1.0e-10; |
| 113 |
maxiter = nvar; |
| 114 |
} else if (mode == TNCG || mode == DTNCG) |
| 115 |
{ |
| 116 |
delta = 1.0; |
| 117 |
eps = delta/(double) *icycle; |
| 118 |
g_rms = g_norm/sqrt((double) nvar); |
| 119 |
eps = MinFun(eps,g_rms); |
| 120 |
converge = 1.0; |
| 121 |
maxiter = (int) (10.0*sqrt((double)nvar)); |
| 122 |
} |
| 123 |
iter = 1; |
| 124 |
|
| 125 |
// evaluate the matrix vector product |
| 126 |
while (TRUE) |
| 127 |
{ |
| 128 |
if (mode == TNCG || mode == NEWTON) |
| 129 |
{ |
| 130 |
for (i=0; i < nvar; i++) |
| 131 |
q[i] = 0.0; |
| 132 |
for (i=0; i < nvar; i++) |
| 133 |
{ |
| 134 |
q[i] += h_diag[i]*d[i]; |
| 135 |
for(j= h_init[i]; j < h_stop[i]; j++) |
| 136 |
{ |
| 137 |
k = h_index[j]; |
| 138 |
hj = h[j]; |
| 139 |
q[i] += hj*d[k]; |
| 140 |
q[k] += hj*d[i]; |
| 141 |
} |
| 142 |
} |
| 143 |
}else if (mode == DTNCG) |
| 144 |
{ |
| 145 |
dd = 0.0; |
| 146 |
for (i=0; i < nvar; i++) |
| 147 |
dd += d[i]*d[i]; |
| 148 |
|
| 149 |
sigma = 1.0e-7 / sqrt(dd); |
| 150 |
|
| 151 |
for (i=0; i < nvar; i++) |
| 152 |
x_sigma[i] = x[i] + sigma*d[i]; |
| 153 |
|
| 154 |
fg_call = fg_call + 1; |
| 155 |
f_sigma = fgvalue (x_sigma,g_sigma); |
| 156 |
|
| 157 |
for (i=0; i < nvar; i++) |
| 158 |
q[i] = (g_sigma[i]-g[i]) / sigma; |
| 159 |
} |
| 160 |
|
| 161 |
// test for direction of negative curvature |
| 162 |
dq = 0.0; |
| 163 |
for (i=0; i < nvar; i++) |
| 164 |
dq += d[i]*q[i]; |
| 165 |
|
| 166 |
if (negtest) |
| 167 |
{ |
| 168 |
if (dq <= 0.0) |
| 169 |
{ |
| 170 |
if (iter == 1) |
| 171 |
{ |
| 172 |
for (i=0; i < nvar; i++) |
| 173 |
p[i] = d[i]; |
| 174 |
} |
| 175 |
goto L_10; |
| 176 |
} |
| 177 |
} |
| 178 |
|
| 179 |
// test truncated Newton termination criterion |
| 180 |
alpha = rs / dq; |
| 181 |
rr = 0.0; |
| 182 |
for (i=0; i < nvar; i++) |
| 183 |
{ |
| 184 |
p[i] += alpha*d[i]; |
| 185 |
r[i] -= alpha*q[i]; |
| 186 |
rr += r[i]*r[i]; |
| 187 |
} |
| 188 |
r_norm = sqrt(rr); |
| 189 |
if (r_norm/g_norm <= eps) |
| 190 |
goto L_10; |
| 191 |
|
| 192 |
// precondition |
| 193 |
precond(method,iter,nvar, si, r,h,h_init,h_stop, |
| 194 |
h_index,h_diag); |
| 195 |
|
| 196 |
// update direction |
| 197 |
rs_new = 0.0; |
| 198 |
for (i=0; i < nvar; i++) |
| 199 |
rs_new += r[i]*si[i]; |
| 200 |
|
| 201 |
beta = rs_new/rs; |
| 202 |
rs = rs_new; |
| 203 |
|
| 204 |
for (i=0; i < nvar; i++) |
| 205 |
d[i] = si[i] + beta*d[i]; |
| 206 |
|
| 207 |
// check for overlimit next iteration |
| 208 |
if (iter >= maxiter) |
| 209 |
goto L_10; |
| 210 |
|
| 211 |
iter++; |
| 212 |
} |
| 213 |
|
| 214 |
// termination |
| 215 |
|
| 216 |
L_10: |
| 217 |
if (mode != DTNCG && method != NONE) |
| 218 |
{ |
| 219 |
for (i=0; i < nvar; i++) |
| 220 |
{ |
| 221 |
p[i] *= m[i]; |
| 222 |
g[i] /= m[i]; |
| 223 |
} |
| 224 |
} |
| 225 |
iter_cg += iter; |
| 226 |
free_dvector( m ,0,maxvar); |
| 227 |
free_dvector( r ,0,maxvar); |
| 228 |
free_dvector( si ,0,maxvar); |
| 229 |
free_dvector( d ,0,maxvar); |
| 230 |
free_dvector( q ,0,maxvar); |
| 231 |
free_dvector( x_sigma ,0,maxvar); |
| 232 |
free_dvector( g_sigma ,0,maxvar); |
| 233 |
free_dvector( f_diag ,0,maxvar); |
| 234 |
free_dvector( f ,0,maxhess); |
| 235 |
free_ivector( c_index ,0,maxhess); |
| 236 |
free_ivector( c_value ,0,maxhess); |
| 237 |
} |
| 238 |
//================================ |
| 239 |
// ============================== |
| 240 |
void column(int nvar, int *h_init, int *h_stop,int *h_index, |
| 241 |
int *c_init,int *c_stop,int *c_index, int *c_value) |
| 242 |
{ |
| 243 |
int i,j,k,m; |
| 244 |
|
| 245 |
for (i=0; i < nvar; i++) |
| 246 |
{ |
| 247 |
c_init[i] = 0; |
| 248 |
c_stop[i] = 0; |
| 249 |
} |
| 250 |
// count number of elements in each column |
| 251 |
for (i=0; i < nvar; i++) |
| 252 |
{ |
| 253 |
for (j=h_init[i]; j < h_stop[i]; j++) |
| 254 |
{ |
| 255 |
k = h_index[j]; |
| 256 |
c_stop[k]++; |
| 257 |
} |
| 258 |
} |
| 259 |
// set each beginning marker past the last element for its column |
| 260 |
c_init[0] = c_stop[0] + 1; |
| 261 |
for (i=1; i <nvar; i++) |
| 262 |
{ |
| 263 |
c_init[i] = c_init[i-1] + c_stop[i]; |
| 264 |
} |
| 265 |
// set column index scanning rows in reverse order |
| 266 |
for (i = nvar-1; i >= 0; i--) |
| 267 |
{ |
| 268 |
for (j=h_init[i]; j < h_stop[i]; j++) |
| 269 |
{ |
| 270 |
k = h_index[j]; |
| 271 |
m = c_init[k]-1; |
| 272 |
c_init[k] = m; |
| 273 |
c_index[m] = i; |
| 274 |
c_value[m] = j; |
| 275 |
} |
| 276 |
} |
| 277 |
for(i=0; i < nvar; i++) |
| 278 |
{ |
| 279 |
c_stop[i] = c_init[i] + c_stop[i]-1; |
| 280 |
} |
| 281 |
} |
| 282 |
// ============================== |
| 283 |
void precond(int method, int iter, int nvar, double *s, double *r, |
| 284 |
double *h, int *h_init, int *h_stop,int *h_index, |
| 285 |
double *h_diag) |
| 286 |
{ |
| 287 |
int i,j,k,ii,kk,iii,kkk,nblock,ix,iy,iz,icount; |
| 288 |
int *c_init, *c_stop; // c_init[maxvar],c_stop[maxvar]; |
| 289 |
double a[6],b[3]; |
| 290 |
double omega,factor,*diag; // diag[maxvar]; |
| 291 |
double maxalpha, alpha, f_i, f_k; |
| 292 |
int maxvar; |
| 293 |
|
| 294 |
maxvar = 3*natom; |
| 295 |
c_init = ivector(0,maxvar); |
| 296 |
c_stop = ivector(0,maxvar); |
| 297 |
diag = dvector(0,maxvar); |
| 298 |
|
| 299 |
|
| 300 |
// no preconditioning |
| 301 |
if (method == NONE) |
| 302 |
{ |
| 303 |
for (i=0; i < nvar; i++) |
| 304 |
s[i] = r[i]; |
| 305 |
} |
| 306 |
// diagonal |
| 307 |
if (method == DIAG) |
| 308 |
{ |
| 309 |
for (i=0; i < nvar; i++) |
| 310 |
s[i] = r[i]/ fabs(h_diag[i]); |
| 311 |
} |
| 312 |
// block diagonal |
| 313 |
if (method == BLOCK) |
| 314 |
{ |
| 315 |
nblock = 3; |
| 316 |
for (i=1; i <= natom; i++) |
| 317 |
{ |
| 318 |
iz = (i-1)*3+2; |
| 319 |
iy = (i-1)*3+1; |
| 320 |
ix = (i-1)*3; |
| 321 |
a[0] = h_diag[ix]; |
| 322 |
if (h_index[h_init[ix]] == iy) |
| 323 |
a[1] = h[h_init[ix]]; |
| 324 |
else |
| 325 |
a[1] = 0.0; |
| 326 |
|
| 327 |
if (h_index[h_init[ix]+1] == iz) |
| 328 |
a[2] = h[h_init[ix]+1]; |
| 329 |
else |
| 330 |
a[2] = 0.0; |
| 331 |
|
| 332 |
a[3] = h_diag[iy]; |
| 333 |
if (h_index[h_init[iy]] == iz) |
| 334 |
a[4] = h[h_init[iy]]; |
| 335 |
else |
| 336 |
a[4] = 0.0; |
| 337 |
|
| 338 |
a[5] = h_diag[iz]; |
| 339 |
b[0] = r[ix]; |
| 340 |
b[1] = r[iy]; |
| 341 |
b[2] = r[iz]; |
| 342 |
cholesky (nblock,a,b); |
| 343 |
s[ix] = b[0]; |
| 344 |
s[iy] = b[1]; |
| 345 |
s[iz] = b[2]; |
| 346 |
} |
| 347 |
} |
| 348 |
|
| 349 |
// SSOR |
| 350 |
if (method == SSOR) |
| 351 |
{ |
| 352 |
omega = 1.0; |
| 353 |
factor = 2.0 - omega; |
| 354 |
for (i=0; i < nvar; i++) |
| 355 |
{ |
| 356 |
s[i] = r[i] * factor; |
| 357 |
diag[i] = h_diag[i] / omega; |
| 358 |
} |
| 359 |
for (i=0; i < nvar; i++) |
| 360 |
{ |
| 361 |
s[i] = s[i] / diag[i]; |
| 362 |
for (j=h_init[i]; j< h_stop[i]; j++) |
| 363 |
{ |
| 364 |
k = h_index[j]; |
| 365 |
s[k] = s[k] - h[j]*s[i]; |
| 366 |
} |
| 367 |
} |
| 368 |
for (i=nvar-1; i >= 0; i--) |
| 369 |
{ |
| 370 |
s[i] = s[i] * diag[i]; |
| 371 |
for (j=h_init[i]; j< h_stop[i]; j++) |
| 372 |
{ |
| 373 |
k = h_index[j]; |
| 374 |
s[i] = s[i] - h[j]*s[k]; |
| 375 |
} |
| 376 |
s[i] = s[i] / diag[i]; |
| 377 |
} |
| 378 |
} |
| 379 |
// incomplete cholesky preconditioning |
| 380 |
if (method == ICCG && iter == 0) |
| 381 |
{ |
| 382 |
column (nvar,h_init,h_stop,h_index, |
| 383 |
c_init,c_stop,c_index,c_value); |
| 384 |
stable = TRUE; |
| 385 |
icount = 0; |
| 386 |
maxalpha = 2.1; |
| 387 |
alpha = -0.001; |
| 388 |
L_10: |
| 389 |
if (alpha <= 0.0) |
| 390 |
alpha = alpha + 0.001; |
| 391 |
else |
| 392 |
alpha = 2.0 * alpha; |
| 393 |
|
| 394 |
if (alpha > maxalpha) |
| 395 |
{ |
| 396 |
stable = FALSE; |
| 397 |
fprintf(pcmlogfile,"Precond - Incomplete Cholesky is Unstable\n"); |
| 398 |
} else |
| 399 |
{ |
| 400 |
factor = 1.0 + alpha; |
| 401 |
for (i=0; i < nvar; i++) |
| 402 |
{ |
| 403 |
f_diag[i] = factor * h_diag[i]; |
| 404 |
for(j = c_init[i]; j<= c_stop[i]; j++) |
| 405 |
{ |
| 406 |
k = c_index[j]; |
| 407 |
f_i = f[c_value[j]]; |
| 408 |
f_diag[i] = f_diag[i] - (f_i*f_i*f_diag[k]); |
| 409 |
icount++; |
| 410 |
} |
| 411 |
if (f_diag[i] <= 0.0) goto L_10; |
| 412 |
if (f_diag[i] < 1.0e-7) f_diag[i] = 1.0e-7; |
| 413 |
f_diag[i] = 1.0 / f_diag[i]; |
| 414 |
for( j = h_init[i]; j < h_stop[i]; j++) |
| 415 |
{ |
| 416 |
k = h_index[j]; |
| 417 |
f[j] = h[j]; |
| 418 |
ii = c_init[i]; |
| 419 |
kk = c_init[k]; |
| 420 |
while (ii <= c_stop[i] && kk <= c_stop[k]) |
| 421 |
{ |
| 422 |
iii = c_index[ii]; |
| 423 |
kkk = c_index[kk]; |
| 424 |
if (iii < kkk) |
| 425 |
ii = ii + 1; |
| 426 |
else if (kkk < iii) |
| 427 |
kk = kk + 1; |
| 428 |
else |
| 429 |
{ |
| 430 |
f_i = f[c_value[ii]]; |
| 431 |
f_k = f[c_value[kk]]; |
| 432 |
f[j] = f[j] - (f_i*f_k*f_diag[iii]); |
| 433 |
ii = ii + 1; |
| 434 |
kk = kk + 1; |
| 435 |
icount = icount + 1; |
| 436 |
} |
| 437 |
} |
| 438 |
} |
| 439 |
} |
| 440 |
} |
| 441 |
} |
| 442 |
// incomplete cholesky preconditioning (solution phase) |
| 443 |
|
| 444 |
if (method == ICCG) |
| 445 |
{ |
| 446 |
if (stable) |
| 447 |
{ |
| 448 |
for (i=0; i < nvar; i++) |
| 449 |
s[i] = r[i]; |
| 450 |
|
| 451 |
for (i=0; i < nvar; i++) |
| 452 |
{ |
| 453 |
s[i] = s[i] * f_diag[i]; |
| 454 |
for( j = h_init[i]; j < h_stop[i]; j++) |
| 455 |
{ |
| 456 |
k = h_index[j]; |
| 457 |
s[k] = s[k] - f[j]*s[i]; |
| 458 |
} |
| 459 |
} |
| 460 |
for (i = nvar-1; i >= 0; i--) |
| 461 |
{ |
| 462 |
s[i] = s[i] / f_diag[i]; |
| 463 |
for( j = h_init[i]; j < h_stop[i]; j++) |
| 464 |
{ |
| 465 |
k = h_index[j]; |
| 466 |
s[i] = s[i] - f[j]*s[k]; |
| 467 |
} |
| 468 |
s[i] = s[i] * f_diag[i]; |
| 469 |
} |
| 470 |
} else |
| 471 |
{ |
| 472 |
for (i=0; i < nvar; i++) |
| 473 |
s[i] = r[i] / fabs(h_diag[i]); |
| 474 |
} |
| 475 |
} |
| 476 |
free_ivector(c_init ,0,maxvar); |
| 477 |
free_ivector(c_stop ,0,maxvar); |
| 478 |
free_dvector(diag ,0,maxvar); |
| 479 |
} |
| 480 |
|
| 481 |
void cholesky(int nvar, double *a, double *b) |
| 482 |
{ |
| 483 |
int i,j,k,ii,ij,ik,im,jk,jm,ki,kk; |
| 484 |
double r,sa,t; |
| 485 |
|
| 486 |
ii = 0; |
| 487 |
for (i=0; i < nvar; i++) |
| 488 |
{ |
| 489 |
im = i - 1; |
| 490 |
if (i != 0) |
| 491 |
{ |
| 492 |
ij = i; |
| 493 |
for( j = 0; j < im; j++) |
| 494 |
{ |
| 495 |
r = a[ij]; |
| 496 |
if (j != 0) |
| 497 |
{ |
| 498 |
ik = i; |
| 499 |
jk = j; |
| 500 |
jm = j - 1; |
| 501 |
for ( k = 0; k < jm; k++) |
| 502 |
{ |
| 503 |
r = r - a[ik]*a[jk]; |
| 504 |
ik = nvar-1 - k + ik; |
| 505 |
jk = nvar-1 - k + jk; |
| 506 |
} |
| 507 |
} |
| 508 |
a[ij] = r; |
| 509 |
ij = nvar-1 - j + ij; |
| 510 |
} |
| 511 |
} |
| 512 |
r = a[ii]; |
| 513 |
if (i != 0) |
| 514 |
{ |
| 515 |
kk = 0; |
| 516 |
ik = i; |
| 517 |
for (k = 0; k < im; k++) |
| 518 |
{ |
| 519 |
sa = a[ik]; |
| 520 |
t = sa * a[kk]; |
| 521 |
a[ik] = t; |
| 522 |
r = r - sa*t; |
| 523 |
ik = nvar-1 - k + ik; |
| 524 |
kk = nvar-1 - k +1 + kk; |
| 525 |
} |
| 526 |
} |
| 527 |
a[ii] = 1.0/ r; |
| 528 |
ii = nvar-1 - i + 1 + ii; |
| 529 |
} |
| 530 |
|
| 531 |
// solve linear equations; first solve Ly = b for y |
| 532 |
|
| 533 |
for (i=0; i < nvar; i++) |
| 534 |
{ |
| 535 |
if (i != 0) |
| 536 |
{ |
| 537 |
ik = i; |
| 538 |
im = i - 1; |
| 539 |
r = b[i]; |
| 540 |
for (k = 0; k < im; k++) |
| 541 |
{ |
| 542 |
r = r - b[k]*a[ik]; |
| 543 |
ik = nvar-1 - k + ik; |
| 544 |
} |
| 545 |
b[i] = r; |
| 546 |
} |
| 547 |
} |
| 548 |
|
| 549 |
// now, solve (D)(L transpose)(x) = y for x |
| 550 |
|
| 551 |
ii = (nvar*(nvar+1)/2)-1; |
| 552 |
for ( j = 0; j < nvar; j++) |
| 553 |
{ |
| 554 |
i = nvar-1 - j; |
| 555 |
r = b[i] * a[ii]; |
| 556 |
if (j != 0) |
| 557 |
{ |
| 558 |
im = i + 1; |
| 559 |
ki = ii + 1; |
| 560 |
for( k = im; k < nvar; k++) |
| 561 |
{ |
| 562 |
r = r - a[ki]*b[k]; |
| 563 |
ki++; |
| 564 |
} |
| 565 |
} |
| 566 |
b[i] = r; |
| 567 |
ii = ii - j - 2; |
| 568 |
} |
| 569 |
} |
