Actual source code: linesearchl2.c

petsc-3.7.4 2016-10-02
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  1: #include <petsc/private/linesearchimpl.h>
  2: #include <petscsnes.h>

  6: static PetscErrorCode  SNESLineSearchApply_L2(SNESLineSearch linesearch)
  7: {

  9:   PetscBool      changed_y, changed_w;
 11:   Vec            X;
 12:   Vec            F;
 13:   Vec            Y;
 14:   Vec            W;
 15:   SNES           snes;
 16:   PetscReal      gnorm;
 17:   PetscReal      ynorm;
 18:   PetscReal      xnorm;
 19:   PetscReal      steptol, maxstep, rtol, atol, ltol;

 21:   PetscViewer monitor;
 22:   PetscReal   lambda, lambda_old, lambda_mid, lambda_update, delLambda;
 23:   PetscReal   fnrm, fnrm_old, fnrm_mid;
 24:   PetscReal   delFnrm, delFnrm_old, del2Fnrm;
 25:   PetscInt    i, max_its;

 27:   PetscErrorCode (*objective)(SNES,Vec,PetscReal*,void*);

 30:   SNESLineSearchGetVecs(linesearch, &X, &F, &Y, &W, NULL);
 31:   SNESLineSearchGetNorms(linesearch, &xnorm, &gnorm, &ynorm);
 32:   SNESLineSearchGetLambda(linesearch, &lambda);
 33:   SNESLineSearchGetSNES(linesearch, &snes);
 34:   SNESLineSearchSetReason(linesearch, SNES_LINESEARCH_SUCCEEDED);
 35:   SNESLineSearchGetTolerances(linesearch, &steptol, &maxstep, &rtol, &atol, &ltol, &max_its);
 36:   SNESLineSearchGetDefaultMonitor(linesearch, &monitor);

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

 40:   /* precheck */
 41:   SNESLineSearchPreCheck(linesearch,X,Y,&changed_y);
 42:   lambda_old = 0.0;
 43:   if (!objective) {
 44:     fnrm_old = gnorm*gnorm;
 45:   } else {
 46:     SNESComputeObjective(snes,X,&fnrm_old);
 47:   }
 48:   lambda_mid = 0.5*(lambda + lambda_old);

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

 52:     VecCopy(X, W);
 53:     VecAXPY(W, -lambda_mid, Y);
 54:     if (linesearch->ops->viproject) {
 55:       (*linesearch->ops->viproject)(snes, W);
 56:     }
 57:     if (!objective) {
 58:       /* compute the norm at the midpoint */
 59:       (*linesearch->ops->snesfunc)(snes, W, F);
 60:       if (linesearch->ops->vinorm) {
 61:         fnrm_mid = gnorm;
 62:         (*linesearch->ops->vinorm)(snes, F, W, &fnrm_mid);
 63:       } else {
 64:         VecNorm(F,NORM_2,&fnrm_mid);
 65:       }

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

 88:       /* compute the objective at the new endpoint */
 89:       VecCopy(X, W);
 90:       VecAXPY(W, -lambda, Y);
 91:       SNESComputeObjective(snes,W,&fnrm);
 92:     }

 94:     delLambda   = lambda - lambda_old;
 95:     /* compute f'() at the end points using second order one sided differencing */
 96:     delFnrm     = (3.*fnrm - 4.*fnrm_mid + 1.*fnrm_old) / delLambda;
 97:     delFnrm_old = (-3.*fnrm_old + 4.*fnrm_mid -1.*fnrm) / delLambda;
 98:     /* compute f''() at the midpoint using centered differencing */
 99:     del2Fnrm    = (delFnrm - delFnrm_old) / delLambda;

101:     if (monitor) {
102:       PetscViewerASCIIAddTab(monitor,((PetscObject)linesearch)->tablevel);
103:       if (!objective) {
104:         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));
105:       } else {
106:         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);
107:       }
108:       PetscViewerASCIISubtractTab(monitor,((PetscObject)linesearch)->tablevel);
109:     }

111:     /* compute the secant (Newton) update -- always go downhill */
112:     if (del2Fnrm > 0.) lambda_update = lambda - delFnrm / del2Fnrm;
113:     else lambda_update = lambda + delFnrm / del2Fnrm;

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

117:     if (PetscIsInfOrNanReal(lambda_update)) break;

119:     if (lambda_update > maxstep) break;

121:     /* update the endpoints and the midpoint of the bracketed secant region */
122:     lambda_old = lambda;
123:     lambda     = lambda_update;
124:     fnrm_old   = fnrm;
125:     lambda_mid = 0.5*(lambda + lambda_old);
126:   }
127:   /* construct the solution */
128:   VecCopy(X, W);
129:   VecAXPY(W, -lambda, Y);
130:   if (linesearch->ops->viproject) {
131:     (*linesearch->ops->viproject)(snes, W);
132:   }

134:   /* postcheck */
135:   SNESLineSearchPostCheck(linesearch,X,Y,W,&changed_y,&changed_w);
136:   if (changed_y) {
137:     VecAXPY(X, -lambda, Y);
138:     if (linesearch->ops->viproject) {
139:       (*linesearch->ops->viproject)(snes, X);
140:     }
141:   } else {
142:     VecCopy(W, X);
143:   }
144:   (*linesearch->ops->snesfunc)(snes,X,F);

146:   SNESLineSearchSetLambda(linesearch, lambda);
147:   SNESLineSearchComputeNorms(linesearch);
148:   SNESLineSearchGetNorms(linesearch, &xnorm, &gnorm, &ynorm);

150:   if (monitor) {
151:     PetscViewerASCIIAddTab(monitor,((PetscObject)linesearch)->tablevel);
152:     PetscViewerASCIIPrintf(monitor,"    Line search terminated: lambda = %g, fnorms = %g\n", (double)lambda, (double)gnorm);
153:     PetscViewerASCIISubtractTab(monitor,((PetscObject)linesearch)->tablevel);
154:   }
155:   if (lambda <= steptol) {
156:     SNESLineSearchSetReason(linesearch, SNES_LINESEARCH_FAILED_REDUCT);
157:   }
158:   return(0);
159: }

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

166:    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()
167:    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.

169:    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.

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

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

179:    Level: advanced

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

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

185: .seealso: SNESLINESEARCHBT, SNESLINESEARCHCP, SNESLineSearch, SNESLineSearchCreate(), SNESLineSearchSetType()
186: M*/
187: PETSC_EXTERN PetscErrorCode SNESLineSearchCreate_L2(SNESLineSearch linesearch)
188: {
190:   linesearch->ops->apply          = SNESLineSearchApply_L2;
191:   linesearch->ops->destroy        = NULL;
192:   linesearch->ops->setfromoptions = NULL;
193:   linesearch->ops->reset          = NULL;
194:   linesearch->ops->view           = NULL;
195:   linesearch->ops->setup          = NULL;

197:   linesearch->max_its = 1;
198:   return(0);
199: }