Actual source code: linesearchl2.c

petsc-3.11.2 2019-05-18
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  1: #include <petsc/private/linesearchimpl.h>
  2: #include <petscsnes.h>

  4: static PetscErrorCode  SNESLineSearchApply_L2(SNESLineSearch linesearch)
  5: {
  6:   PetscBool      changed_y, changed_w;
  8:   Vec            X;
  9:   Vec            F;
 10:   Vec            Y;
 11:   Vec            W;
 12:   SNES           snes;
 13:   PetscReal      gnorm;
 14:   PetscReal      ynorm;
 15:   PetscReal      xnorm;
 16:   PetscReal      steptol, maxstep, rtol, atol, ltol;
 17:   PetscViewer    monitor;
 18:   PetscReal      lambda, lambda_old, lambda_mid, lambda_update, delLambda;
 19:   PetscReal      fnrm, fnrm_old, fnrm_mid;
 20:   PetscReal      delFnrm, delFnrm_old, del2Fnrm;
 21:   PetscInt       i, max_its;
 22:   PetscErrorCode (*objective)(SNES,Vec,PetscReal*,void*);

 25:   SNESLineSearchGetVecs(linesearch, &X, &F, &Y, &W, NULL);
 26:   SNESLineSearchGetNorms(linesearch, &xnorm, &gnorm, &ynorm);
 27:   SNESLineSearchGetLambda(linesearch, &lambda);
 28:   SNESLineSearchGetSNES(linesearch, &snes);
 29:   SNESLineSearchSetReason(linesearch, SNES_LINESEARCH_SUCCEEDED);
 30:   SNESLineSearchGetTolerances(linesearch, &steptol, &maxstep, &rtol, &atol, &ltol, &max_its);
 31:   SNESLineSearchGetDefaultMonitor(linesearch, &monitor);

 33:   SNESGetObjective(snes,&objective,NULL);

 35:   /* precheck */
 36:   SNESLineSearchPreCheck(linesearch,X,Y,&changed_y);
 37:   lambda_old = 0.0;
 38:   if (!objective) {
 39:     fnrm_old = gnorm*gnorm;
 40:   } else {
 41:     SNESComputeObjective(snes,X,&fnrm_old);
 42:   }
 43:   lambda_mid = 0.5*(lambda + lambda_old);

 45:   for (i = 0; i < max_its; i++) {

 47:     while (PETSC_TRUE) {
 48:       VecCopy(X, W);
 49:       VecAXPY(W, -lambda_mid, Y);
 50:       if (linesearch->ops->viproject) {
 51:         (*linesearch->ops->viproject)(snes, W);
 52:       }
 53:       if (!objective) {
 54:         /* compute the norm at the midpoint */
 55:         (*linesearch->ops->snesfunc)(snes, W, F);
 56:         if (linesearch->ops->vinorm) {
 57:           fnrm_mid = gnorm;
 58:           (*linesearch->ops->vinorm)(snes, F, W, &fnrm_mid);
 59:         } else {
 60:           VecNorm(F,NORM_2,&fnrm_mid);
 61:         }

 63:         /* compute the norm at the new endpoit */
 64:         VecCopy(X, W);
 65:         VecAXPY(W, -lambda, Y);
 66:         if (linesearch->ops->viproject) {
 67:           (*linesearch->ops->viproject)(snes, W);
 68:         }
 69:         (*linesearch->ops->snesfunc)(snes, W, F);
 70:         if (linesearch->ops->vinorm) {
 71:           fnrm = gnorm;
 72:           (*linesearch->ops->vinorm)(snes, F, W, &fnrm);
 73:         } else {
 74:           VecNorm(F,NORM_2,&fnrm);
 75:         }
 76:         fnrm_mid = fnrm_mid*fnrm_mid;
 77:         fnrm = fnrm*fnrm;
 78:       } else {
 79:         /* compute the objective at the midpoint */
 80:         VecCopy(X, W);
 81:         VecAXPY(W, -lambda_mid, Y);
 82:         SNESComputeObjective(snes,W,&fnrm_mid);

 84:         /* compute the objective at the new endpoint */
 85:         VecCopy(X, W);
 86:         VecAXPY(W, -lambda, Y);
 87:         SNESComputeObjective(snes,W,&fnrm);
 88:       }
 89:       if (!PetscIsInfOrNanReal(fnrm)) break;
 90:       if (monitor) {
 91:         PetscViewerASCIIAddTab(monitor,((PetscObject)linesearch)->tablevel);
 92:         PetscViewerASCIIPrintf(monitor,"    Line search: objective function at lambdas = %g is Inf or Nan, cutting lambda\n",(double)lambda);
 93:         PetscViewerASCIISubtractTab(monitor,((PetscObject)linesearch)->tablevel);
 94:       }
 95:       if (lambda <= steptol) {
 96:         SNESLineSearchSetReason(linesearch, SNES_LINESEARCH_FAILED_REDUCT);
 97:         return(0);
 98:       }
 99:       maxstep = .95*lambda; /* forbid the search from ever going back to the "failed" length that generates Nan or Inf */
100:       lambda  = .5*(lambda + lambda_old);
101:       lambda_mid = .5*(lambda + lambda_old);
102:     }

104:     delLambda   = lambda - lambda_old;
105:     /* compute f'() at the end points using second order one sided differencing */
106:     delFnrm     = (3.*fnrm - 4.*fnrm_mid + 1.*fnrm_old) / delLambda;
107:     delFnrm_old = (-3.*fnrm_old + 4.*fnrm_mid -1.*fnrm) / delLambda;
108:     /* compute f''() at the midpoint using centered differencing */
109:     del2Fnrm    = (delFnrm - delFnrm_old) / delLambda;

111:     if (monitor) {
112:       PetscViewerASCIIAddTab(monitor,((PetscObject)linesearch)->tablevel);
113:       if (!objective) {
114:         PetscViewerASCIIPrintf(monitor,"    Line search: lambdas = [%g, %g, %g], fnorms = [%g, %g, %g]\n",(double)lambda, (double)lambda_mid, (double)lambda_old, (double)PetscSqrtReal(fnrm), (double)PetscSqrtReal(fnrm_mid), (double)PetscSqrtReal(fnrm_old));
115:       } else {
116:         PetscViewerASCIIPrintf(monitor,"    Line search: lambdas = [%g, %g, %g], obj = [%g, %g, %g]\n",(double)lambda, (double)lambda_mid, (double)lambda_old, (double)fnrm, (double)fnrm_mid, (double)fnrm_old);
117:       }
118:       PetscViewerASCIISubtractTab(monitor,((PetscObject)linesearch)->tablevel);
119:     }

121:     /* compute the secant (Newton) update -- always go downhill */
122:     if (del2Fnrm > 0.) lambda_update = lambda - delFnrm / del2Fnrm;
123:     else if (del2Fnrm < 0.) lambda_update = lambda + delFnrm / del2Fnrm;
124:     else break;

126:     if (lambda_update < steptol) lambda_update = 0.5*(lambda + lambda_old);

128:     if (PetscIsInfOrNanReal(lambda_update)) break;

130:     if (lambda_update > maxstep) break;

132:     /* update the endpoints and the midpoint of the bracketed secant region */
133:     lambda_old = lambda;
134:     lambda     = lambda_update;
135:     fnrm_old   = fnrm;
136:     lambda_mid = 0.5*(lambda + lambda_old);
137:   }
138:   /* construct the solution */
139:   VecCopy(X, W);
140:   VecAXPY(W, -lambda, Y);
141:   if (linesearch->ops->viproject) {
142:     (*linesearch->ops->viproject)(snes, W);
143:   }

145:   /* postcheck */
146:   SNESLineSearchPostCheck(linesearch,X,Y,W,&changed_y,&changed_w);
147:   if (changed_y) {
148:     VecAXPY(X, -lambda, Y);
149:     if (linesearch->ops->viproject) {
150:       (*linesearch->ops->viproject)(snes, X);
151:     }
152:   } else {
153:     VecCopy(W, X);
154:   }
155:   (*linesearch->ops->snesfunc)(snes,X,F);

157:   SNESLineSearchSetLambda(linesearch, lambda);
158:   SNESLineSearchComputeNorms(linesearch);
159:   SNESLineSearchGetNorms(linesearch, &xnorm, &gnorm, &ynorm);

161:   if (monitor) {
162:     PetscViewerASCIIAddTab(monitor,((PetscObject)linesearch)->tablevel);
163:     PetscViewerASCIIPrintf(monitor,"    Line search terminated: lambda = %g, fnorms = %g\n", (double)lambda, (double)gnorm);
164:     PetscViewerASCIISubtractTab(monitor,((PetscObject)linesearch)->tablevel);
165:   }
166:   if (lambda <= steptol) {
167:     SNESLineSearchSetReason(linesearch, SNES_LINESEARCH_FAILED_REDUCT);
168:   }
169:   return(0);
170: }

172: /*MC
173:    SNESLINESEARCHL2 - Secant search in the L2 norm of the function or the objective function, if it is provided with SNESSetObjective().

175:    Attempts to solve min_lambda f(x + lambda y) using the secant method with the initial bracketing of lambda between [0,damping]. Differences of f()
176:    are used to approximate the first and second derivative of f() with respect to lambda, f'() and f''(). The secant method is run for maxit iterations.

178:    When an objective function is provided f(w) is the objective function otherwise f(w) = ||F(w)||^2. x is the current step and y is the search direction.

180:    This has no checks on whether the secant method is actually converging.

182:    Options Database Keys:
183: +  -snes_linesearch_max_it <maxit> - maximum number of iterations, default is 1
184: .  -snes_linesearch_maxstep <length> - the algorithm insures that a step length is never longer than this value
185: .  -snes_linesearch_damping <damping> - initial step is scaled back by this factor, default is 1.0
186: -  -snes_linesearch_minlambda <minlambda> - minimum allowable lambda

188:    Level: advanced

190:    Developer Notes:
191:     A better name for this method might be SNESLINESEARCHSECANT, L2 is not descriptive

193: .keywords: SNES, nonlinear, line search, norm, secant

195: .seealso: SNESLINESEARCHBT, SNESLINESEARCHCP, SNESLineSearch, SNESLineSearchCreate(), SNESLineSearchSetType()
196: M*/
197: PETSC_EXTERN PetscErrorCode SNESLineSearchCreate_L2(SNESLineSearch linesearch)
198: {
200:   linesearch->ops->apply          = SNESLineSearchApply_L2;
201:   linesearch->ops->destroy        = NULL;
202:   linesearch->ops->setfromoptions = NULL;
203:   linesearch->ops->reset          = NULL;
204:   linesearch->ops->view           = NULL;
205:   linesearch->ops->setup          = NULL;

207:   linesearch->max_its = 1;
208:   return(0);
209: }