Actual source code: linesearchl2.c

petsc-3.6.1 2015-07-22
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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:   SNESLineSearchGetMonitor(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:     /* compute the norm at the midpoint */
 53:     VecCopy(X, W);
 54:     VecAXPY(W, -lambda_mid, Y);
 55:     if (linesearch->ops->viproject) {
 56:       (*linesearch->ops->viproject)(snes, W);
 57:     }
 58:     if (!objective) {
 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 lambda */
 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 midpoint */
 89:       VecCopy(X, W);
 90:       VecAXPY(W, -lambda, Y);
 91:       SNESComputeObjective(snes,W,&fnrm);
 92:     }
 93:     /* this gives us the derivatives at the endpoints -- compute them from here

 95:      a = x - a0

 97:      p_0(x) = (x / dA - 1)(2x / dA - 1)
 98:      p_1(x) = 4(x / dA)(1 - x / dA)
 99:      p_2(x) = (x / dA)(2x / dA - 1)

101:      dp_0[0] / dx = 3 / dA
102:      dp_1[0] / dx = -4 / dA
103:      dp_2[0] / dx = 1 / dA

105:      dp_0[dA] / dx = -1 / dA
106:      dp_1[dA] / dx = 4 / dA
107:      dp_2[dA] / dx = -3 / dA

109:      d^2p_0[0] / dx^2 =  4 / dA^2
110:      d^2p_1[0] / dx^2 = -8 / dA^2
111:      d^2p_2[0] / dx^2 =  4 / dA^2
112:      */

114:     delLambda   = lambda - lambda_old;
115:     delFnrm     = (3.*fnrm - 4.*fnrm_mid + 1.*fnrm_old) / delLambda;
116:     delFnrm_old = (-3.*fnrm_old + 4.*fnrm_mid -1.*fnrm) / delLambda;
117:     del2Fnrm    = (delFnrm - delFnrm_old) / delLambda;

119:     if (monitor) {
120:       PetscViewerASCIIAddTab(monitor,((PetscObject)linesearch)->tablevel);
121:       if (!objective) {
122:         PetscViewerASCIIPrintf(monitor,"    Line search: lambdas = [%g, %g, %g], fnorms = [%g, %g, %g]\n",
123:                                       (double)lambda, (double)lambda_mid, (double)lambda_old, (double)PetscSqrtReal(fnrm), (double)PetscSqrtReal(fnrm_mid), (double)PetscSqrtReal(fnrm_old));
124:       } else {
125:         PetscViewerASCIIPrintf(monitor,"    Line search: lambdas = [%g, %g, %g], obj = [%g, %g, %g]\n",
126:                                       (double)lambda, (double)lambda_mid, (double)lambda_old, (double)fnrm, (double)fnrm_mid, (double)fnrm_old);

128:       }
129:       PetscViewerASCIISubtractTab(monitor,((PetscObject)linesearch)->tablevel);
130:     }

132:     /* compute the search direction -- always go downhill */
133:     if (del2Fnrm > 0.) lambda_update = lambda - delFnrm / del2Fnrm;
134:     else lambda_update = lambda + delFnrm / del2Fnrm;

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

138:     if (PetscIsInfOrNanReal(lambda_update)) break;

140:     if (lambda_update > maxstep) break;

142:     /* compute the new state of the line search */
143:     lambda_old = lambda;
144:     lambda     = lambda_update;
145:     fnrm_old   = fnrm;
146:     lambda_mid = 0.5*(lambda + lambda_old);
147:   }
148:   /* construct the solution */
149:   VecCopy(X, W);
150:   VecAXPY(W, -lambda, Y);
151:   if (linesearch->ops->viproject) {
152:     (*linesearch->ops->viproject)(snes, W);
153:   }

155:   /* postcheck */
156:   SNESLineSearchPostCheck(linesearch,X,Y,W,&changed_y,&changed_w);
157:   if (changed_y) {
158:     VecAXPY(X, -lambda, Y);
159:     if (linesearch->ops->viproject) {
160:       (*linesearch->ops->viproject)(snes, X);
161:     }
162:   } else {
163:     VecCopy(W, X);
164:   }
165:   (*linesearch->ops->snesfunc)(snes,X,F);

167:   SNESLineSearchSetLambda(linesearch, lambda);
168:   SNESLineSearchComputeNorms(linesearch);
169:   SNESLineSearchGetNorms(linesearch, &xnorm, &gnorm, &ynorm);

171:   if (monitor) {
172:     PetscViewerASCIIAddTab(monitor,((PetscObject)linesearch)->tablevel);
173:     PetscViewerASCIIPrintf(monitor,"    Line search terminated: lambda = %g, fnorms = %g\n", (double)lambda, (double)gnorm);
174:     PetscViewerASCIISubtractTab(monitor,((PetscObject)linesearch)->tablevel);
175:   }
176:   if (lambda <= steptol) {
177:     SNESLineSearchSetReason(linesearch, SNES_LINESEARCH_FAILED_REDUCT);
178:   }
179:   return(0);
180: }

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

187:    The function norm is evaluated at points in [0, damping] to construct
188:    a polynomial fitting.  This fitting is used to construct a new lambda
189:    based upon secant descent.  The process is repeated on the new
190:    interval, [lambda, lambda_old], max_it - 1 times.

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

198:    Level: advanced

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

202: .seealso: SNESLineSearchBT, SNESLineSearchCP, SNESLineSearch
203: M*/
204: PETSC_EXTERN PetscErrorCode SNESLineSearchCreate_L2(SNESLineSearch linesearch)
205: {
207:   linesearch->ops->apply          = SNESLineSearchApply_L2;
208:   linesearch->ops->destroy        = NULL;
209:   linesearch->ops->setfromoptions = NULL;
210:   linesearch->ops->reset          = NULL;
211:   linesearch->ops->view           = NULL;
212:   linesearch->ops->setup          = NULL;

214:   linesearch->max_its = 1;
215:   return(0);
216: }