Actual source code: tao_util.c

petsc-3.11.3 2019-06-26
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  1:  #include <petsc/private/petscimpl.h>
  2:  #include <petsctao.h>


  5: PETSC_STATIC_INLINE PetscReal Fischer(PetscReal a, PetscReal b)
  6: {
  7:   /* Method suggested by Bob Vanderbei */
  8:    if (a + b <= 0) {
  9:      return PetscSqrtReal(a*a + b*b) - (a + b);
 10:    }
 11:    return -2.0*a*b / (PetscSqrtReal(a*a + b*b) + (a + b));
 12: }

 14: /*@
 15:    VecFischer - Evaluates the Fischer-Burmeister function for complementarity
 16:    problems.

 18:    Logically Collective on vectors

 20:    Input Parameters:
 21: +  X - current point
 22: .  F - function evaluated at x
 23: .  L - lower bounds
 24: -  U - upper bounds

 26:    Output Parameters:
 27: .  FB - The Fischer-Burmeister function vector

 29:    Notes:
 30:    The Fischer-Burmeister function is defined as
 31: $        phi(a,b) := sqrt(a*a + b*b) - a - b
 32:    and is used reformulate a complementarity problem as a semismooth
 33:    system of equations.

 35:    The result of this function is done by cases:
 36: +  l[i] == -infinity, u[i] == infinity  -- fb[i] = -f[i]
 37: .  l[i] == -infinity, u[i] finite       -- fb[i] = phi(u[i]-x[i], -f[i])
 38: .  l[i] finite,       u[i] == infinity  -- fb[i] = phi(x[i]-l[i],  f[i])
 39: .  l[i] finite < u[i] finite -- fb[i] = phi(x[i]-l[i], phi(u[i]-x[i], -f[u]))
 40: -  otherwise l[i] == u[i] -- fb[i] = l[i] - x[i]

 42:    Level: developer

 44: @*/
 45: PetscErrorCode VecFischer(Vec X, Vec F, Vec L, Vec U, Vec FB)
 46: {
 47:   const PetscScalar *x, *f, *l, *u;
 48:   PetscScalar       *fb;
 49:   PetscReal         xval, fval, lval, uval;
 50:   PetscErrorCode    ierr;
 51:   PetscInt          low[5], high[5], n, i;


 60:   VecGetOwnershipRange(X, low, high);
 61:   VecGetOwnershipRange(F, low + 1, high + 1);
 62:   VecGetOwnershipRange(L, low + 2, high + 2);
 63:   VecGetOwnershipRange(U, low + 3, high + 3);
 64:   VecGetOwnershipRange(FB, low + 4, high + 4);

 66:   for (i = 1; i < 4; ++i) {
 67:     if (low[0] != low[i] || high[0] != high[i]) SETERRQ(PETSC_COMM_SELF,1,"Vectors must be identically loaded over processors");
 68:   }

 70:   VecGetArrayRead(X, &x);
 71:   VecGetArrayRead(F, &f);
 72:   VecGetArrayRead(L, &l);
 73:   VecGetArrayRead(U, &u);
 74:   VecGetArray(FB, &fb);

 76:   VecGetLocalSize(X, &n);

 78:   for (i = 0; i < n; ++i) {
 79:     xval = PetscRealPart(x[i]); fval = PetscRealPart(f[i]);
 80:     lval = PetscRealPart(l[i]); uval = PetscRealPart(u[i]);

 82:     if ((lval <= -PETSC_INFINITY) && (uval >= PETSC_INFINITY)) {
 83:       fb[i] = -fval;
 84:     } else if (lval <= -PETSC_INFINITY) {
 85:       fb[i] = -Fischer(uval - xval, -fval);
 86:     } else if (uval >=  PETSC_INFINITY) {
 87:       fb[i] =  Fischer(xval - lval,  fval);
 88:     } else if (lval == uval) {
 89:       fb[i] = lval - xval;
 90:     } else {
 91:       fval  =  Fischer(uval - xval, -fval);
 92:       fb[i] =  Fischer(xval - lval,  fval);
 93:     }
 94:   }

 96:   VecRestoreArrayRead(X, &x);
 97:   VecRestoreArrayRead(F, &f);
 98:   VecRestoreArrayRead(L, &l);
 99:   VecRestoreArrayRead(U, &u);
100:   VecRestoreArray(FB, &fb);
101:   return(0);
102: }

104: PETSC_STATIC_INLINE PetscReal SFischer(PetscReal a, PetscReal b, PetscReal c)
105: {
106:   /* Method suggested by Bob Vanderbei */
107:    if (a + b <= 0) {
108:      return PetscSqrtReal(a*a + b*b + 2.0*c*c) - (a + b);
109:    }
110:    return 2.0*(c*c - a*b) / (PetscSqrtReal(a*a + b*b + 2.0*c*c) + (a + b));
111: }

113: /*@
114:    VecSFischer - Evaluates the Smoothed Fischer-Burmeister function for
115:    complementarity problems.

117:    Logically Collective on vectors

119:    Input Parameters:
120: +  X - current point
121: .  F - function evaluated at x
122: .  L - lower bounds
123: .  U - upper bounds
124: -  mu - smoothing parameter

126:    Output Parameters:
127: .  FB - The Smoothed Fischer-Burmeister function vector

129:    Notes:
130:    The Smoothed Fischer-Burmeister function is defined as
131: $        phi(a,b) := sqrt(a*a + b*b + 2*mu*mu) - a - b
132:    and is used reformulate a complementarity problem as a semismooth
133:    system of equations.

135:    The result of this function is done by cases:
136: +  l[i] == -infinity, u[i] == infinity  -- fb[i] = -f[i] - 2*mu*x[i]
137: .  l[i] == -infinity, u[i] finite       -- fb[i] = phi(u[i]-x[i], -f[i], mu)
138: .  l[i] finite,       u[i] == infinity  -- fb[i] = phi(x[i]-l[i],  f[i], mu)
139: .  l[i] finite < u[i] finite -- fb[i] = phi(x[i]-l[i], phi(u[i]-x[i], -f[u], mu), mu)
140: -  otherwise l[i] == u[i] -- fb[i] = l[i] - x[i]

142:    Level: developer

144: .seealso  VecFischer()
145: @*/
146: PetscErrorCode VecSFischer(Vec X, Vec F, Vec L, Vec U, PetscReal mu, Vec FB)
147: {
148:   const PetscScalar *x, *f, *l, *u;
149:   PetscScalar       *fb;
150:   PetscReal         xval, fval, lval, uval;
151:   PetscErrorCode    ierr;
152:   PetscInt          low[5], high[5], n, i;


161:   VecGetOwnershipRange(X, low, high);
162:   VecGetOwnershipRange(F, low + 1, high + 1);
163:   VecGetOwnershipRange(L, low + 2, high + 2);
164:   VecGetOwnershipRange(U, low + 3, high + 3);
165:   VecGetOwnershipRange(FB, low + 4, high + 4);

167:   for (i = 1; i < 4; ++i) {
168:     if (low[0] != low[i] || high[0] != high[i]) SETERRQ(PETSC_COMM_SELF,1,"Vectors must be identically loaded over processors");
169:   }

171:   VecGetArrayRead(X, &x);
172:   VecGetArrayRead(F, &f);
173:   VecGetArrayRead(L, &l);
174:   VecGetArrayRead(U, &u);
175:   VecGetArray(FB, &fb);

177:   VecGetLocalSize(X, &n);

179:   for (i = 0; i < n; ++i) {
180:     xval = PetscRealPart(*x++); fval = PetscRealPart(*f++);
181:     lval = PetscRealPart(*l++); uval = PetscRealPart(*u++);

183:     if ((lval <= -PETSC_INFINITY) && (uval >= PETSC_INFINITY)) {
184:       (*fb++) = -fval - mu*xval;
185:     } else if (lval <= -PETSC_INFINITY) {
186:       (*fb++) = -SFischer(uval - xval, -fval, mu);
187:     } else if (uval >=  PETSC_INFINITY) {
188:       (*fb++) =  SFischer(xval - lval,  fval, mu);
189:     } else if (lval == uval) {
190:       (*fb++) = lval - xval;
191:     } else {
192:       fval    =  SFischer(uval - xval, -fval, mu);
193:       (*fb++) =  SFischer(xval - lval,  fval, mu);
194:     }
195:   }
196:   x -= n; f -= n; l -=n; u -= n; fb -= n;

198:   VecRestoreArrayRead(X, &x);
199:   VecRestoreArrayRead(F, &f);
200:   VecRestoreArrayRead(L, &l);
201:   VecRestoreArrayRead(U, &u);
202:   VecRestoreArray(FB, &fb);
203:   return(0);
204: }

206: PETSC_STATIC_INLINE PetscReal fischnorm(PetscReal a, PetscReal b)
207: {
208:   return PetscSqrtReal(a*a + b*b);
209: }

211: PETSC_STATIC_INLINE PetscReal fischsnorm(PetscReal a, PetscReal b, PetscReal c)
212: {
213:   return PetscSqrtReal(a*a + b*b + 2.0*c*c);
214: }

216: /*@
217:    MatDFischer - Calculates an element of the B-subdifferential of the
218:    Fischer-Burmeister function for complementarity problems.

220:    Collective on jac

222:    Input Parameters:
223: +  jac - the jacobian of f at X
224: .  X - current point
225: .  Con - constraints function evaluated at X
226: .  XL - lower bounds
227: .  XU - upper bounds
228: .  t1 - work vector
229: -  t2 - work vector

231:    Output Parameters:
232: +  Da - diagonal perturbation component of the result
233: -  Db - row scaling component of the result

235:    Level: developer

237: .seealso: VecFischer()
238: @*/
239: PetscErrorCode MatDFischer(Mat jac, Vec X, Vec Con, Vec XL, Vec XU, Vec T1, Vec T2, Vec Da, Vec Db)
240: {
241:   PetscErrorCode    ierr;
242:   PetscInt          i,nn;
243:   const PetscScalar *x,*f,*l,*u,*t2;
244:   PetscScalar       *da,*db,*t1;
245:   PetscReal          ai,bi,ci,di,ei;

248:   VecGetLocalSize(X,&nn);
249:   VecGetArrayRead(X,&x);
250:   VecGetArrayRead(Con,&f);
251:   VecGetArrayRead(XL,&l);
252:   VecGetArrayRead(XU,&u);
253:   VecGetArray(Da,&da);
254:   VecGetArray(Db,&db);
255:   VecGetArray(T1,&t1);
256:   VecGetArrayRead(T2,&t2);

258:   for (i = 0; i < nn; i++) {
259:     da[i] = 0.0;
260:     db[i] = 0.0;
261:     t1[i] = 0.0;

263:     if (PetscAbsScalar(f[i]) <= PETSC_MACHINE_EPSILON) {
264:       if (PetscRealPart(l[i]) > PETSC_NINFINITY && PetscAbsScalar(x[i] - l[i]) <= PETSC_MACHINE_EPSILON) {
265:         t1[i] = 1.0;
266:         da[i] = 1.0;
267:       }

269:       if (PetscRealPart(u[i]) <  PETSC_INFINITY && PetscAbsScalar(u[i] - x[i]) <= PETSC_MACHINE_EPSILON) {
270:         t1[i] = 1.0;
271:         db[i] = 1.0;
272:       }
273:     }
274:   }

276:   VecRestoreArray(T1,&t1);
277:   VecRestoreArrayRead(T2,&t2);
278:   MatMult(jac,T1,T2);
279:   VecGetArrayRead(T2,&t2);

281:   for (i = 0; i < nn; i++) {
282:     if ((PetscRealPart(l[i]) <= PETSC_NINFINITY) && (PetscRealPart(u[i]) >= PETSC_INFINITY)) {
283:       da[i] = 0.0;
284:       db[i] = -1.0;
285:     } else if (PetscRealPart(l[i]) <= PETSC_NINFINITY) {
286:       if (PetscRealPart(db[i]) >= 1) {
287:         ai = fischnorm(1.0, PetscRealPart(t2[i]));

289:         da[i] = -1.0 / ai - 1.0;
290:         db[i] = -t2[i] / ai - 1.0;
291:       } else {
292:         bi = PetscRealPart(u[i]) - PetscRealPart(x[i]);
293:         ai = fischnorm(bi, PetscRealPart(f[i]));
294:         ai = PetscMax(PETSC_MACHINE_EPSILON, ai);

296:         da[i] = bi / ai - 1.0;
297:         db[i] = -f[i] / ai - 1.0;
298:       }
299:     } else if (PetscRealPart(u[i]) >=  PETSC_INFINITY) {
300:       if (PetscRealPart(da[i]) >= 1) {
301:         ai = fischnorm(1.0, PetscRealPart(t2[i]));

303:         da[i] = 1.0 / ai - 1.0;
304:         db[i] = t2[i] / ai - 1.0;
305:       } else {
306:         bi = PetscRealPart(x[i]) - PetscRealPart(l[i]);
307:         ai = fischnorm(bi, PetscRealPart(f[i]));
308:         ai = PetscMax(PETSC_MACHINE_EPSILON, ai);

310:         da[i] = bi / ai - 1.0;
311:         db[i] = f[i] / ai - 1.0;
312:       }
313:     } else if (PetscRealPart(l[i]) == PetscRealPart(u[i])) {
314:       da[i] = -1.0;
315:       db[i] = 0.0;
316:     } else {
317:       if (PetscRealPart(db[i]) >= 1) {
318:         ai = fischnorm(1.0, PetscRealPart(t2[i]));

320:         ci = 1.0 / ai + 1.0;
321:         di = PetscRealPart(t2[i]) / ai + 1.0;
322:       } else {
323:         bi = PetscRealPart(x[i]) - PetscRealPart(u[i]);
324:         ai = fischnorm(bi, PetscRealPart(f[i]));
325:         ai = PetscMax(PETSC_MACHINE_EPSILON, ai);

327:         ci = bi / ai + 1.0;
328:         di = PetscRealPart(f[i]) / ai + 1.0;
329:       }

331:       if (PetscRealPart(da[i]) >= 1) {
332:         bi = ci + di*PetscRealPart(t2[i]);
333:         ai = fischnorm(1.0, bi);

335:         bi = bi / ai - 1.0;
336:         ai = 1.0 / ai - 1.0;
337:       } else {
338:         ei = Fischer(PetscRealPart(u[i]) - PetscRealPart(x[i]), -PetscRealPart(f[i]));
339:         ai = fischnorm(PetscRealPart(x[i]) - PetscRealPart(l[i]), ei);
340:         ai = PetscMax(PETSC_MACHINE_EPSILON, ai);

342:         bi = ei / ai - 1.0;
343:         ai = (PetscRealPart(x[i]) - PetscRealPart(l[i])) / ai - 1.0;
344:       }

346:       da[i] = ai + bi*ci;
347:       db[i] = bi*di;
348:     }
349:   }

351:   VecRestoreArray(Da,&da);
352:   VecRestoreArray(Db,&db);
353:   VecRestoreArrayRead(X,&x);
354:   VecRestoreArrayRead(Con,&f);
355:   VecRestoreArrayRead(XL,&l);
356:   VecRestoreArrayRead(XU,&u);
357:   VecRestoreArrayRead(T2,&t2);
358:   return(0);
359: }

361: /*@
362:    MatDSFischer - Calculates an element of the B-subdifferential of the
363:    smoothed Fischer-Burmeister function for complementarity problems.

365:    Collective on jac

367:    Input Parameters:
368: +  jac - the jacobian of f at X
369: .  X - current point
370: .  F - constraint function evaluated at X
371: .  XL - lower bounds
372: .  XU - upper bounds
373: .  mu - smoothing parameter
374: .  T1 - work vector
375: -  T2 - work vector

377:    Output Parameter:
378: +  Da - diagonal perturbation component of the result
379: .  Db - row scaling component of the result
380: -  Dm - derivative with respect to scaling parameter

382:    Level: developer

384: .seealso MatDFischer()
385: @*/
386: PetscErrorCode MatDSFischer(Mat jac, Vec X, Vec Con,Vec XL, Vec XU, PetscReal mu,Vec T1, Vec T2,Vec Da, Vec Db, Vec Dm)
387: {
388:   PetscErrorCode    ierr;
389:   PetscInt          i,nn;
390:   const PetscScalar *x, *f, *l, *u;
391:   PetscScalar       *da, *db, *dm;
392:   PetscReal         ai, bi, ci, di, ei, fi;

395:   if (PetscAbsReal(mu) <= PETSC_MACHINE_EPSILON) {
396:     VecZeroEntries(Dm);
397:     MatDFischer(jac, X, Con, XL, XU, T1, T2, Da, Db);
398:   } else {
399:     VecGetLocalSize(X,&nn);
400:     VecGetArrayRead(X,&x);
401:     VecGetArrayRead(Con,&f);
402:     VecGetArrayRead(XL,&l);
403:     VecGetArrayRead(XU,&u);
404:     VecGetArray(Da,&da);
405:     VecGetArray(Db,&db);
406:     VecGetArray(Dm,&dm);

408:     for (i = 0; i < nn; ++i) {
409:       if ((PetscRealPart(l[i]) <= PETSC_NINFINITY) && (PetscRealPart(u[i]) >= PETSC_INFINITY)) {
410:         da[i] = -mu;
411:         db[i] = -1.0;
412:         dm[i] = -x[i];
413:       } else if (PetscRealPart(l[i]) <= PETSC_NINFINITY) {
414:         bi = PetscRealPart(u[i]) - PetscRealPart(x[i]);
415:         ai = fischsnorm(bi, PetscRealPart(f[i]), mu);
416:         ai = PetscMax(PETSC_MACHINE_EPSILON, ai);

418:         da[i] = bi / ai - 1.0;
419:         db[i] = -PetscRealPart(f[i]) / ai - 1.0;
420:         dm[i] = 2.0 * mu / ai;
421:       } else if (PetscRealPart(u[i]) >=  PETSC_INFINITY) {
422:         bi = PetscRealPart(x[i]) - PetscRealPart(l[i]);
423:         ai = fischsnorm(bi, PetscRealPart(f[i]), mu);
424:         ai = PetscMax(PETSC_MACHINE_EPSILON, ai);

426:         da[i] = bi / ai - 1.0;
427:         db[i] = PetscRealPart(f[i]) / ai - 1.0;
428:         dm[i] = 2.0 * mu / ai;
429:       } else if (PetscRealPart(l[i]) == PetscRealPart(u[i])) {
430:         da[i] = -1.0;
431:         db[i] = 0.0;
432:         dm[i] = 0.0;
433:       } else {
434:         bi = PetscRealPart(x[i]) - PetscRealPart(u[i]);
435:         ai = fischsnorm(bi, PetscRealPart(f[i]), mu);
436:         ai = PetscMax(PETSC_MACHINE_EPSILON, ai);

438:         ci = bi / ai + 1.0;
439:         di = PetscRealPart(f[i]) / ai + 1.0;
440:         fi = 2.0 * mu / ai;

442:         ei = SFischer(PetscRealPart(u[i]) - PetscRealPart(x[i]), -PetscRealPart(f[i]), mu);
443:         ai = fischsnorm(PetscRealPart(x[i]) - PetscRealPart(l[i]), ei, mu);
444:         ai = PetscMax(PETSC_MACHINE_EPSILON, ai);

446:         bi = ei / ai - 1.0;
447:         ei = 2.0 * mu / ei;
448:         ai = (PetscRealPart(x[i]) - PetscRealPart(l[i])) / ai - 1.0;

450:         da[i] = ai + bi*ci;
451:         db[i] = bi*di;
452:         dm[i] = ei + bi*fi;
453:       }
454:     }

456:     VecRestoreArrayRead(X,&x);
457:     VecRestoreArrayRead(Con,&f);
458:     VecRestoreArrayRead(XL,&l);
459:     VecRestoreArrayRead(XU,&u);
460:     VecRestoreArray(Da,&da);
461:     VecRestoreArray(Db,&db);
462:     VecRestoreArray(Dm,&dm);
463:   }
464:   return(0);
465: }