Actual source code: ls.c

  1: /*$Id: ls.c,v 1.172 2001/08/07 03:04:11 balay Exp $*/

 3:  #include src/snes/impls/ls/ls.h

  5: /*
  6:      Checks if J^T F = 0 which implies we've found a local minimum of the function,
  7:     but not a zero. In the case when one cannot compute J^T F we use the fact that
  8:     0 = (J^T F)^T W = F^T J W iff W not in the null space of J. Thanks for Jorge More 
  9:     for this trick.
 10: */
 13: int SNESLSCheckLocalMin_Private(Mat A,Vec F,Vec W,PetscReal fnorm,PetscTruth *ismin)
 14: {
 15:   PetscReal  a1;
 16:   int        ierr;
 17:   PetscTruth hastranspose;

 20:   *ismin = PETSC_FALSE;
 21:   MatHasOperation(A,MATOP_MULT_TRANSPOSE,&hastranspose);
 22:   if (hastranspose) {
 23:     /* Compute || J^T F|| */
 24:     MatMultTranspose(A,F,W);
 25:     VecNorm(W,NORM_2,&a1);
 26:     PetscLogInfo(0,"SNESSolve_LS: || J^T F|| %g near zero implies found a local minimum\n",a1/fnorm);
 27:     if (a1/fnorm < 1.e-4) *ismin = PETSC_TRUE;
 28:   } else {
 29:     Vec       work;
 30:     PetscScalar    result;
 31:     PetscReal wnorm;

 33:     VecSetRandom(PETSC_NULL,W);
 34:     VecNorm(W,NORM_2,&wnorm);
 35:     VecDuplicate(W,&work);
 36:     MatMult(A,W,work);
 37:     VecDot(F,work,&result);
 38:     VecDestroy(work);
 39:     a1   = PetscAbsScalar(result)/(fnorm*wnorm);
 40:     PetscLogInfo(0,"SNESSolve_LS: (F^T J random)/(|| F ||*||random|| %g near zero implies found a local minimum\n",a1);
 41:     if (a1 < 1.e-4) *ismin = PETSC_TRUE;
 42:   }
 43:   return(0);
 44: }

 46: /*
 47:      Checks if J^T(F - J*X) = 0 
 48: */
 51: int SNESLSCheckResidual_Private(Mat A,Vec F,Vec X,Vec W1,Vec W2)
 52: {
 53:   PetscReal     a1,a2;
 54:   int           ierr;
 55:   PetscTruth    hastranspose;
 56:   PetscScalar   mone = -1.0;

 59:   MatHasOperation(A,MATOP_MULT_TRANSPOSE,&hastranspose);
 60:   if (hastranspose) {
 61:     MatMult(A,X,W1);
 62:     VecAXPY(&mone,F,W1);

 64:     /* Compute || J^T W|| */
 65:     MatMultTranspose(A,W1,W2);
 66:     VecNorm(W1,NORM_2,&a1);
 67:     VecNorm(W2,NORM_2,&a2);
 68:     if (a1 != 0) {
 69:       PetscLogInfo(0,"SNESSolve_LS: ||J^T(F-Ax)||/||F-AX|| %g near zero implies inconsistent rhs\n",a2/a1);
 70:     }
 71:   }
 72:   return(0);
 73: }

 75: /*  -------------------------------------------------------------------- 

 77:      This file implements a truncated Newton method with a line search,
 78:      for solving a system of nonlinear equations, using the SLES, Vec, 
 79:      and Mat interfaces for linear solvers, vectors, and matrices, 
 80:      respectively.

 82:      The following basic routines are required for each nonlinear solver:
 83:           SNESCreate_XXX()          - Creates a nonlinear solver context
 84:           SNESSetFromOptions_XXX()  - Sets runtime options
 85:           SNESSolve_XXX()           - Solves the nonlinear system
 86:           SNESDestroy_XXX()         - Destroys the nonlinear solver context
 87:      The suffix "_XXX" denotes a particular implementation, in this case
 88:      we use _LS (e.g., SNESCreate_LS, SNESSolve_LS) for solving
 89:      systems of nonlinear equations with a line search (LS) method.
 90:      These routines are actually called via the common user interface
 91:      routines SNESCreate(), SNESSetFromOptions(), SNESSolve(), and 
 92:      SNESDestroy(), so the application code interface remains identical 
 93:      for all nonlinear solvers.

 95:      Another key routine is:
 96:           SNESSetUp_XXX()           - Prepares for the use of a nonlinear solver
 97:      by setting data structures and options.   The interface routine SNESSetUp()
 98:      is not usually called directly by the user, but instead is called by
 99:      SNESSolve() if necessary.

101:      Additional basic routines are:
102:           SNESView_XXX()            - Prints details of runtime options that
103:                                       have actually been used.
104:      These are called by application codes via the interface routines
105:      SNESView().

107:      The various types of solvers (preconditioners, Krylov subspace methods,
108:      nonlinear solvers, timesteppers) are all organized similarly, so the
109:      above description applies to these categories also.  

111:     -------------------------------------------------------------------- */
112: /*
113:    SNESSolve_LS - Solves a nonlinear system with a truncated Newton
114:    method with a line search.

116:    Input Parameters:
117: .  snes - the SNES context

119:    Output Parameter:
120: .  outits - number of iterations until termination

122:    Application Interface Routine: SNESSolve()

124:    Notes:
125:    This implements essentially a truncated Newton method with a
126:    line search.  By default a cubic backtracking line search 
127:    is employed, as described in the text "Numerical Methods for
128:    Unconstrained Optimization and Nonlinear Equations" by Dennis 
129:    and Schnabel.
130: */
133: int SNESSolve_LS(SNES snes,int *outits)
134: {
135:   SNES_LS      *neP = (SNES_LS*)snes->data;
136:   int          maxits,i,ierr,lits,lsfail;
137:   MatStructure flg = DIFFERENT_NONZERO_PATTERN;
138:   PetscReal    fnorm,gnorm,xnorm,ynorm;
139:   Vec          Y,X,F,G,W,TMP;

142:   snes->reason  = SNES_CONVERGED_ITERATING;

144:   maxits        = snes->max_its;        /* maximum number of iterations */
145:   X                = snes->vec_sol;        /* solution vector */
146:   F                = snes->vec_func;        /* residual vector */
147:   Y                = snes->work[0];        /* work vectors */
148:   G                = snes->work[1];
149:   W                = snes->work[2];

151:   PetscObjectTakeAccess(snes);
152:   snes->iter = 0;
153:   PetscObjectGrantAccess(snes);
154:   SNESComputeFunction(snes,X,F);  /*  F(X)      */
155:   VecNorm(F,NORM_2,&fnorm);        /* fnorm <- ||F||  */
156:   PetscObjectTakeAccess(snes);
157:   snes->norm = fnorm;
158:   PetscObjectGrantAccess(snes);
159:   SNESLogConvHistory(snes,fnorm,0);
160:   SNESMonitor(snes,0,fnorm);

162:   if (fnorm < snes->atol) {*outits = 0; snes->reason = SNES_CONVERGED_FNORM_ABS; return(0);}

164:   /* set parameter for default relative tolerance convergence test */
165:   snes->ttol = fnorm*snes->rtol;

167:   for (i=0; i<maxits; i++) {

169:     /* Call general purpose update function */
170:     if (snes->update != PETSC_NULL) {
171:       (*snes->update)(snes, snes->iter);
172:     }

174:     /* Solve J Y = F, where J is Jacobian matrix */
175:     SNESComputeJacobian(snes,X,&snes->jacobian,&snes->jacobian_pre,&flg);
176:     SLESSetOperators(snes->sles,snes->jacobian,snes->jacobian_pre,flg);
177:     SLESSolve(snes->sles,F,Y,&lits);

179:     if (PetscLogPrintInfo){
180:       SNESLSCheckResidual_Private(snes->jacobian,F,Y,G,W);
181:     }

183:     /* should check what happened to the linear solve? */
184:     snes->linear_its += lits;
185:     PetscLogInfo(snes,"SNESSolve_LS: iter=%d, linear solve iterations=%d\n",snes->iter,lits);

187:     /* Compute a (scaled) negative update in the line search routine: 
188:          Y <- X - lambda*Y 
189:        and evaluate G(Y) = function(Y)) 
190:     */
191:     VecCopy(Y,snes->vec_sol_update_always);
192:     (*neP->LineSearch)(snes,neP->lsP,X,F,G,Y,W,fnorm,&ynorm,&gnorm,&lsfail);
193:     PetscLogInfo(snes,"SNESSolve_LS: fnorm=%18.16e, gnorm=%18.16e, ynorm=%18.16e, lsfail=%d\n",fnorm,gnorm,ynorm,lsfail);

195:     TMP = F; F = G; snes->vec_func_always = F; G = TMP;
196:     TMP = X; X = Y; snes->vec_sol_always = X;  Y = TMP;
197:     fnorm = gnorm;

199:     PetscObjectTakeAccess(snes);
200:     snes->iter = i+1;
201:     snes->norm = fnorm;
202:     PetscObjectGrantAccess(snes);
203:     SNESLogConvHistory(snes,fnorm,lits);
204:     SNESMonitor(snes,i+1,fnorm);

206:     if (lsfail) {
207:       PetscTruth ismin;

209:       if (++snes->numFailures >= snes->maxFailures) {
210:         snes->reason = SNES_DIVERGED_LS_FAILURE;
211:         SNESLSCheckLocalMin_Private(snes->jacobian,F,W,fnorm,&ismin);
212:         if (ismin) snes->reason = SNES_DIVERGED_LOCAL_MIN;
213:         break;
214:       }
215:     }

217:     /* Test for convergence */
218:     if (snes->converged) {
219:       VecNorm(X,NORM_2,&xnorm);        /* xnorm = || X || */
220:       (*snes->converged)(snes,xnorm,ynorm,fnorm,&snes->reason,snes->cnvP);
221:       if (snes->reason) {
222:         break;
223:       }
224:     }
225:   }
226:   if (X != snes->vec_sol) {
227:     VecCopy(X,snes->vec_sol);
228:   }
229:   if (F != snes->vec_func) {
230:     VecCopy(F,snes->vec_func);
231:   }
232:   snes->vec_sol_always  = snes->vec_sol;
233:   snes->vec_func_always = snes->vec_func;
234:   if (i == maxits) {
235:     PetscLogInfo(snes,"SNESSolve_LS: Maximum number of iterations has been reached: %d\n",maxits);
236:     i--;
237:     snes->reason = SNES_DIVERGED_MAX_IT;
238:   }
239:   PetscObjectTakeAccess(snes);
240:   PetscObjectGrantAccess(snes);
241:   *outits = i+1;
242:   return(0);
243: }
244: /* -------------------------------------------------------------------------- */
245: /*
246:    SNESSetUp_LS - Sets up the internal data structures for the later use
247:    of the SNESLS nonlinear solver.

249:    Input Parameter:
250: .  snes - the SNES context
251: .  x - the solution vector

253:    Application Interface Routine: SNESSetUp()

255:    Notes:
256:    For basic use of the SNES solvers, the user need not explicitly call
257:    SNESSetUp(), since these actions will automatically occur during
258:    the call to SNESSolve().
259:  */
262: int SNESSetUp_LS(SNES snes)
263: {

267:   snes->nwork = 4;
268:   VecDuplicateVecs(snes->vec_sol,snes->nwork,&snes->work);
269:   PetscLogObjectParents(snes,snes->nwork,snes->work);
270:   snes->vec_sol_update_always = snes->work[3];
271:   return(0);
272: }
273: /* -------------------------------------------------------------------------- */
274: /*
275:    SNESDestroy_LS - Destroys the private SNES_LS context that was created
276:    with SNESCreate_LS().

278:    Input Parameter:
279: .  snes - the SNES context

281:    Application Interface Routine: SNESDestroy()
282:  */
285: int SNESDestroy_LS(SNES snes)
286: {
287:   int  ierr;

290:   if (snes->nwork) {
291:     VecDestroyVecs(snes->work,snes->nwork);
292:   }
293:   PetscFree(snes->data);
294:   return(0);
295: }
296: /* -------------------------------------------------------------------------- */

300: /*@C
301:    SNESNoLineSearch - This routine is not a line search at all; 
302:    it simply uses the full Newton step.  Thus, this routine is intended 
303:    to serve as a template and is not recommended for general use.  

305:    Collective on SNES and Vec

307:    Input Parameters:
308: +  snes - nonlinear context
309: .  lsctx - optional context for line search (not used here)
310: .  x - current iterate
311: .  f - residual evaluated at x
312: .  y - search direction (contains new iterate on output)
313: .  w - work vector
314: -  fnorm - 2-norm of f

316:    Output Parameters:
317: +  g - residual evaluated at new iterate y
318: .  y - new iterate (contains search direction on input)
319: .  gnorm - 2-norm of g
320: .  ynorm - 2-norm of search length
321: -  flag - set to 0, indicating a successful line search

323:    Options Database Key:
324: .  -snes_ls basic - Activates SNESNoLineSearch()

326:    Level: advanced

328: .keywords: SNES, nonlinear, line search, cubic

330: .seealso: SNESCubicLineSearch(), SNESQuadraticLineSearch(), 
331:           SNESSetLineSearch(), SNESNoLineSearchNoNorms()
332: @*/
333: int SNESNoLineSearch(SNES snes,void *lsctx,Vec x,Vec f,Vec g,Vec y,Vec w,PetscReal fnorm,PetscReal *ynorm,PetscReal *gnorm,int *flag)
334: {
335:   int         ierr;
336:   PetscScalar mone = -1.0;
337:   SNES_LS     *neP = (SNES_LS*)snes->data;
338:   PetscTruth  change_y = PETSC_FALSE;

341:   *flag = 0;
342:   PetscLogEventBegin(SNES_LineSearch,snes,x,f,g);
343:   VecNorm(y,NORM_2,ynorm);  /* ynorm = || y || */
344:   VecAYPX(&mone,x,y);            /* y <- y - x      */
345:   if (neP->CheckStep) {
346:    (*neP->CheckStep)(snes,neP->checkP,y,&change_y);
347:   }
348:   SNESComputeFunction(snes,y,g); /* Compute F(y)    */
349:   VecNorm(g,NORM_2,gnorm);  /* gnorm = || g || */
350:   PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);
351:   return(0);
352: }
353: /* -------------------------------------------------------------------------- */

357: /*@C
358:    SNESNoLineSearchNoNorms - This routine is not a line search at 
359:    all; it simply uses the full Newton step. This version does not
360:    even compute the norm of the function or search direction; this
361:    is intended only when you know the full step is fine and are
362:    not checking for convergence of the nonlinear iteration (for
363:    example, you are running always for a fixed number of Newton steps).

365:    Collective on SNES and Vec

367:    Input Parameters:
368: +  snes - nonlinear context
369: .  lsctx - optional context for line search (not used here)
370: .  x - current iterate
371: .  f - residual evaluated at x
372: .  y - search direction (contains new iterate on output)
373: .  w - work vector
374: -  fnorm - 2-norm of f

376:    Output Parameters:
377: +  g - residual evaluated at new iterate y
378: .  gnorm - not changed
379: .  ynorm - not changed
380: -  flag - set to 0, indicating a successful line search

382:    Options Database Key:
383: .  -snes_ls basicnonorms - Activates SNESNoLineSearchNoNorms()

385:    Notes:
386:    SNESNoLineSearchNoNorms() must be used in conjunction with
387:    either the options
388: $     -snes_no_convergence_test -snes_max_it <its>
389:    or alternatively a user-defined custom test set via
390:    SNESSetConvergenceTest(); or a -snes_max_it of 1, 
391:    otherwise, the SNES solver will generate an error.

393:    During the final iteration this will not evaluate the function at
394:    the solution point. This is to save a function evaluation while
395:    using pseudo-timestepping.

397:    The residual norms printed by monitoring routines such as
398:    SNESDefaultMonitor() (as activated via -snes_monitor) will not be 
399:    correct, since they are not computed.

401:    Level: advanced

403: .keywords: SNES, nonlinear, line search, cubic

405: .seealso: SNESCubicLineSearch(), SNESQuadraticLineSearch(), 
406:           SNESSetLineSearch(), SNESNoLineSearch()
407: @*/
408: int SNESNoLineSearchNoNorms(SNES snes,void *lsctx,Vec x,Vec f,Vec g,Vec y,Vec w,PetscReal fnorm,PetscReal *ynorm,PetscReal *gnorm,int *flag)
409: {
410:   int         ierr;
411:   PetscScalar mone = -1.0;
412:   SNES_LS     *neP = (SNES_LS*)snes->data;
413:   PetscTruth  change_y = PETSC_FALSE;

416:   *flag = 0;
417:   PetscLogEventBegin(SNES_LineSearch,snes,x,f,g);
418:   VecAYPX(&mone,x,y);            /* y <- y - x      */
419:   if (neP->CheckStep) {
420:    (*neP->CheckStep)(snes,neP->checkP,y,&change_y);
421:   }
422: 
423:   /* don't evaluate function the last time through */
424:   if (snes->iter < snes->max_its-1) {
425:     SNESComputeFunction(snes,y,g); /* Compute F(y)    */
426:   }
427:   PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);
428:   return(0);
429: }
430: /* -------------------------------------------------------------------------- */
433: /*@C
434:    SNESCubicLineSearch - Performs a cubic line search (default line search method).

436:    Collective on SNES

438:    Input Parameters:
439: +  snes - nonlinear context
440: .  lsctx - optional context for line search (not used here)
441: .  x - current iterate
442: .  f - residual evaluated at x
443: .  y - search direction (contains new iterate on output)
444: .  w - work vector
445: -  fnorm - 2-norm of f

447:    Output Parameters:
448: +  g - residual evaluated at new iterate y
449: .  y - new iterate (contains search direction on input)
450: .  gnorm - 2-norm of g
451: .  ynorm - 2-norm of search length
452: -  flag - 0 if line search succeeds; -1 on failure.

454:    Options Database Key:
455: $  -snes_ls cubic - Activates SNESCubicLineSearch()

457:    Notes:
458:    This line search is taken from "Numerical Methods for Unconstrained 
459:    Optimization and Nonlinear Equations" by Dennis and Schnabel, page 325.

461:    Level: advanced

463: .keywords: SNES, nonlinear, line search, cubic

465: .seealso: SNESQuadraticLineSearch(), SNESNoLineSearch(), SNESSetLineSearch(), SNESNoLineSearchNoNorms()
466: @*/
467: int SNESCubicLineSearch(SNES snes,void *lsctx,Vec x,Vec f,Vec g,Vec y,Vec w,PetscReal fnorm,PetscReal *ynorm,PetscReal *gnorm,int *flag)
468: {
469:   /* 
470:      Note that for line search purposes we work with with the related
471:      minimization problem:
472:         min  z(x):  R^n -> R,
473:      where z(x) = .5 * fnorm*fnorm, and fnorm = || f ||_2.
474:    */
475: 
476:   PetscReal   steptol,initslope,lambdaprev,gnormprev,a,b,d,t1,t2,rellength;
477:   PetscReal   maxstep,minlambda,alpha,lambda,lambdatemp,lambdaneg;
478: #if defined(PETSC_USE_COMPLEX)
479:   PetscScalar cinitslope,clambda;
480: #endif
481:   int         ierr,count;
482:   SNES_LS     *neP = (SNES_LS*)snes->data;
483:   PetscScalar mone = -1.0,scale;
484:   PetscTruth  change_y = PETSC_FALSE;

487:   PetscLogEventBegin(SNES_LineSearch,snes,x,f,g);
488:   *flag   = 0;
489:   alpha   = neP->alpha;
490:   maxstep = neP->maxstep;
491:   steptol = neP->steptol;

493:   VecNorm(y,NORM_2,ynorm);
494:   if (*ynorm == 0.0) {
495:     PetscLogInfo(snes,"SNESCubicLineSearch: Search direction and size is 0\n");
496:     *gnorm = fnorm;
497:     VecCopy(x,y);
498:     VecCopy(f,g);
499:     *flag  = -1;
500:     goto theend1;
501:   }
502:   if (*ynorm > maxstep) {        /* Step too big, so scale back */
503:     scale = maxstep/(*ynorm);
504: #if defined(PETSC_USE_COMPLEX)
505:     PetscLogInfo(snes,"SNESCubicLineSearch: Scaling step by %g old ynorm %g\n",PetscRealPart(scale),*ynorm);
506: #else
507:     PetscLogInfo(snes,"SNESCubicLineSearch: Scaling step by %g old ynorm %g\n",scale,*ynorm);
508: #endif
509:     VecScale(&scale,y);
510:     *ynorm = maxstep;
511:   }
512:   VecMaxPointwiseDivide(y,x,&rellength);
513:   minlambda = steptol/rellength;
514:   MatMult(snes->jacobian,y,w);
515: #if defined(PETSC_USE_COMPLEX)
516:   VecDot(f,w,&cinitslope);
517:   initslope = PetscRealPart(cinitslope);
518: #else
519:   VecDot(f,w,&initslope);
520: #endif
521:   if (initslope > 0.0) initslope = -initslope;
522:   if (initslope == 0.0) initslope = -1.0;

524:   VecCopy(y,w);
525:   VecAYPX(&mone,x,w);
526:   SNESComputeFunction(snes,w,g);
527:   VecNorm(g,NORM_2,gnorm);
528:   if (.5*(*gnorm)*(*gnorm) <= .5*fnorm*fnorm + alpha*initslope) { /* Sufficient reduction */
529:     VecCopy(w,y);
530:     PetscLogInfo(snes,"SNESCubicLineSearch: Using full step\n");
531:     goto theend1;
532:   }

534:   /* Fit points with quadratic */
535:   lambda = 1.0;
536:   lambdatemp = -initslope/((*gnorm)*(*gnorm) - fnorm*fnorm - 2.0*initslope);
537:   lambdaprev = lambda;
538:   gnormprev = *gnorm;
539:   if (lambdatemp > .5*lambda)  lambdatemp = .5*lambda;
540:   if (lambdatemp <= .1*lambda) lambda = .1*lambda;
541:   else                         lambda = lambdatemp;
542:   VecCopy(x,w);
543:   lambdaneg = -lambda;
544: #if defined(PETSC_USE_COMPLEX)
545:   clambda = lambdaneg; VecAXPY(&clambda,y,w);
546: #else
547:   VecAXPY(&lambdaneg,y,w);
548: #endif
549:   SNESComputeFunction(snes,w,g);
550:   VecNorm(g,NORM_2,gnorm);
551:   if (.5*(*gnorm)*(*gnorm) < .5*fnorm*fnorm + lambda*alpha*initslope) { /* sufficient reduction */
552:     VecCopy(w,y);
553:     PetscLogInfo(snes,"SNESCubicLineSearch: Quadratically determined step, lambda=%18.16e\n",lambda);
554:     goto theend1;
555:   }

557:   /* Fit points with cubic */
558:   count = 1;
559:   while (count < 10000) {
560:     if (lambda <= minlambda) { /* bad luck; use full step */
561:       PetscLogInfo(snes,"SNESCubicLineSearch:Unable to find good step length! %d \n",count);
562:       PetscLogInfo(snes,"SNESCubicLineSearch:fnorm=%18.16e, gnorm=%18.16e, ynorm=%18.16e, lambda=%18.16e, initial slope=%18.16e\n",fnorm,*gnorm,*ynorm,lambda,initslope);
563:       VecCopy(x,y);
564:       *flag = -1; break;
565:     }
566:     t1 = .5*((*gnorm)*(*gnorm) - fnorm*fnorm) - lambda*initslope;
567:     t2 = .5*(gnormprev*gnormprev  - fnorm*fnorm) - lambdaprev*initslope;
568:     a  = (t1/(lambda*lambda) - t2/(lambdaprev*lambdaprev))/(lambda-lambdaprev);
569:     b  = (-lambdaprev*t1/(lambda*lambda) + lambda*t2/(lambdaprev*lambdaprev))/(lambda-lambdaprev);
570:     d  = b*b - 3*a*initslope;
571:     if (d < 0.0) d = 0.0;
572:     if (a == 0.0) {
573:       lambdatemp = -initslope/(2.0*b);
574:     } else {
575:       lambdatemp = (-b + sqrt(d))/(3.0*a);
576:     }
577:     lambdaprev = lambda;
578:     gnormprev  = *gnorm;
579:     if (lambdatemp > .5*lambda)  lambdatemp = .5*lambda;
580:     if (lambdatemp <= .1*lambda) lambda     = .1*lambda;
581:     else                         lambda     = lambdatemp;
582:     VecCopy(x,w);
583:     lambdaneg = -lambda;
584: #if defined(PETSC_USE_COMPLEX)
585:     clambda = lambdaneg;
586:     VecAXPY(&clambda,y,w);
587: #else
588:     VecAXPY(&lambdaneg,y,w);
589: #endif
590:     SNESComputeFunction(snes,w,g);
591:     VecNorm(g,NORM_2,gnorm);
592:     if (.5*(*gnorm)*(*gnorm) < .5*fnorm*fnorm + lambda*alpha*initslope) { /* is reduction enough? */
593:       VecCopy(w,y);
594:       PetscLogInfo(snes,"SNESCubicLineSearch: Cubically determined step, lambda=%18.16e\n",lambda);
595:       goto theend1;
596:     } else {
597:       PetscLogInfo(snes,"SNESCubicLineSearch: Cubic step no good, shrinking lambda,  lambda=%18.16e\n",lambda);
598:     }
599:     count++;
600:   }
601:   if (count >= 10000) {
602:     SETERRQ(PETSC_ERR_LIB, "Lambda was decreased more than 10,000 times, so something is probably wrong with the function evaluation");
603:   }
604:   theend1:
605:   /* Optional user-defined check for line search step validity */
606:   if (neP->CheckStep) {
607:     (*neP->CheckStep)(snes,neP->checkP,y,&change_y);
608:     if (change_y == PETSC_TRUE) { /* recompute the function if the step has changed */
609:       SNESComputeFunction(snes,y,g);
610:       VecNormBegin(y,NORM_2,ynorm);
611:       VecNormBegin(g,NORM_2,gnorm);
612:       VecNormEnd(y,NORM_2,ynorm);
613:       VecNormEnd(g,NORM_2,gnorm);
614:     }
615:   }
616:   PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);
617:   return(0);
618: }
619: /* -------------------------------------------------------------------------- */
622: /*@C
623:    SNESQuadraticLineSearch - Performs a quadratic line search.

625:    Collective on SNES and Vec

627:    Input Parameters:
628: +  snes - the SNES context
629: .  lsctx - optional context for line search (not used here)
630: .  x - current iterate
631: .  f - residual evaluated at x
632: .  y - search direction (contains new iterate on output)
633: .  w - work vector
634: -  fnorm - 2-norm of f

636:    Output Parameters:
637: +  g - residual evaluated at new iterate y
638: .  y - new iterate (contains search direction on input)
639: .  gnorm - 2-norm of g
640: .  ynorm - 2-norm of search length
641: -  flag - 0 if line search succeeds; -1 on failure.

643:    Options Database Key:
644: .  -snes_ls quadratic - Activates SNESQuadraticLineSearch()

646:    Notes:
647:    Use SNESSetLineSearch() to set this routine within the SNESLS method.  

649:    Level: advanced

651: .keywords: SNES, nonlinear, quadratic, line search

653: .seealso: SNESCubicLineSearch(), SNESNoLineSearch(), SNESSetLineSearch(), SNESNoLineSearchNoNorms()
654: @*/
655: int SNESQuadraticLineSearch(SNES snes,void *lsctx,Vec x,Vec f,Vec g,Vec y,Vec w,PetscReal fnorm,PetscReal *ynorm,PetscReal *gnorm,int *flag)
656: {
657:   /* 
658:      Note that for line search purposes we work with with the related
659:      minimization problem:
660:         min  z(x):  R^n -> R,
661:      where z(x) = .5 * fnorm*fnorm,and fnorm = || f ||_2.
662:    */
663:   PetscReal   steptol,initslope,maxstep,minlambda,alpha,lambda,lambdatemp,lambdaneg,rellength;
664: #if defined(PETSC_USE_COMPLEX)
665:   PetscScalar cinitslope,clambda;
666: #endif
667:   int         ierr,count;
668:   SNES_LS     *neP = (SNES_LS*)snes->data;
669:   PetscScalar mone = -1.0,scale;
670:   PetscTruth  change_y = PETSC_FALSE;

673:   PetscLogEventBegin(SNES_LineSearch,snes,x,f,g);
674:   *flag   = 0;
675:   alpha   = neP->alpha;
676:   maxstep = neP->maxstep;
677:   steptol = neP->steptol;

679:   VecNorm(y,NORM_2,ynorm);
680:   if (*ynorm == 0.0) {
681:     PetscLogInfo(snes,"SNESQuadraticLineSearch: Search direction and size is 0\n");
682:     *gnorm = fnorm;
683:     VecCopy(x,y);
684:     VecCopy(f,g);
685:     *flag  = -1;
686:     goto theend2;
687:   }
688:   if (*ynorm > maxstep) {        /* Step too big, so scale back */
689:     scale = maxstep/(*ynorm);
690:     VecScale(&scale,y);
691:     *ynorm = maxstep;
692:   }
693:   VecMaxPointwiseDivide(y,x,&rellength);
694:   minlambda = steptol/rellength;
695:   MatMult(snes->jacobian,y,w);
696: #if defined(PETSC_USE_COMPLEX)
697:   VecDot(f,w,&cinitslope);
698:   initslope = PetscRealPart(cinitslope);
699: #else
700:   VecDot(f,w,&initslope);
701: #endif
702:   if (initslope > 0.0) initslope = -initslope;
703:   if (initslope == 0.0) initslope = -1.0;

705:   VecCopy(y,w);
706:   VecAYPX(&mone,x,w);
707:   SNESComputeFunction(snes,w,g);
708:   VecNorm(g,NORM_2,gnorm);
709:   if (.5*(*gnorm)*(*gnorm) <= .5*fnorm*fnorm + alpha*initslope) { /* Sufficient reduction */
710:     VecCopy(w,y);
711:     PetscLogInfo(snes,"SNESQuadraticLineSearch: Using full step\n");
712:     goto theend2;
713:   }

715:   /* Fit points with quadratic */
716:   lambda = 1.0;
717:   count = 1;
718:   while (PETSC_TRUE) {
719:     if (lambda <= minlambda) { /* bad luck; use full step */
720:       PetscLogInfo(snes,"SNESQuadraticLineSearch:Unable to find good step length! %d \n",count);
721:       PetscLogInfo(snes,"SNESQuadraticLineSearch:fnorm=%g, gnorm=%g, ynorm=%g, lambda=%g, initial slope=%g\n",fnorm,*gnorm,*ynorm,lambda,initslope);
722:       VecCopy(x,y);
723:       *flag = -1; break;
724:     }
725:     lambdatemp = -initslope/((*gnorm)*(*gnorm) - fnorm*fnorm - 2.0*initslope);
726:     if (lambdatemp > .5*lambda)  lambdatemp = .5*lambda;
727:     if (lambdatemp <= .1*lambda) lambda     = .1*lambda;
728:     else                         lambda     = lambdatemp;
729:     VecCopy(x,w);
730:     lambdaneg = -lambda;
731: #if defined(PETSC_USE_COMPLEX)
732:     clambda = lambdaneg; VecAXPY(&clambda,y,w);
733: #else
734:     VecAXPY(&lambdaneg,y,w);
735: #endif
736:     SNESComputeFunction(snes,w,g);
737:     VecNorm(g,NORM_2,gnorm);
738:     if (.5*(*gnorm)*(*gnorm) < .5*fnorm*fnorm + lambda*alpha*initslope) { /* sufficient reduction */
739:       VecCopy(w,y);
740:       PetscLogInfo(snes,"SNESQuadraticLineSearch:Quadratically determined step, lambda=%g\n",lambda);
741:       break;
742:     }
743:     count++;
744:   }
745:   theend2:
746:   /* Optional user-defined check for line search step validity */
747:   if (neP->CheckStep) {
748:     (*neP->CheckStep)(snes,neP->checkP,y,&change_y);
749:     if (change_y == PETSC_TRUE) { /* recompute the function if the step has changed */
750:       SNESComputeFunction(snes,y,g);
751:       VecNormBegin(y,NORM_2,ynorm);
752:       VecNormBegin(g,NORM_2,gnorm);
753:       VecNormEnd(y,NORM_2,ynorm);
754:       VecNormEnd(g,NORM_2,gnorm);
755:     }
756:   }
757:   PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);
758:   return(0);
759: }
760: /* -------------------------------------------------------------------------- */
763: /*@C
764:    SNESSetLineSearch - Sets the line search routine to be used
765:    by the method SNESLS.

767:    Input Parameters:
768: +  snes - nonlinear context obtained from SNESCreate()
769: .  lsctx - optional user-defined context for use by line search 
770: -  func - pointer to int function

772:    Collective on SNES

774:    Available Routines:
775: +  SNESCubicLineSearch() - default line search
776: .  SNESQuadraticLineSearch() - quadratic line search
777: .  SNESNoLineSearch() - the full Newton step (actually not a line search)
778: -  SNESNoLineSearchNoNorms() - the full Newton step (calculating no norms; faster in parallel)

780:     Options Database Keys:
781: +   -snes_ls [cubic,quadratic,basic,basicnonorms] - Selects line search
782: .   -snes_ls_alpha <alpha> - Sets alpha
783: .   -snes_ls_maxstep <max> - Sets maxstep
784: -   -snes_ls_steptol <steptol> - Sets steptol, this is the minimum step size that the line search code
785:                    will accept; min p[i]/x[i] < steptol. The -snes_stol <stol> is the minimum step length
786:                    the default convergence test will use and is based on 2-norm(p) < stol*2-norm(x)

788:    Calling sequence of func:
789: .vb
790:    func (SNES snes,void *lsctx,Vec x,Vec f,Vec g,Vec y,Vec w,
791:          PetscReal fnorm,PetscReal *ynorm,PetscReal *gnorm,*flag)
792: .ve

794:     Input parameters for func:
795: +   snes - nonlinear context
796: .   lsctx - optional user-defined context for line search
797: .   x - current iterate
798: .   f - residual evaluated at x
799: .   y - search direction (contains new iterate on output)
800: .   w - work vector
801: -   fnorm - 2-norm of f

803:     Output parameters for func:
804: +   g - residual evaluated at new iterate y
805: .   y - new iterate (contains search direction on input)
806: .   gnorm - 2-norm of g
807: .   ynorm - 2-norm of search length
808: -   flag - set to 0 if the line search succeeds; a nonzero integer 
809:            on failure.

811:     Level: advanced

813: .keywords: SNES, nonlinear, set, line search, routine

815: .seealso: SNESCubicLineSearch(), SNESQuadraticLineSearch(), SNESNoLineSearch(), SNESNoLineSearchNoNorms(), 
816:           SNESSetLineSearchCheck(), SNESSetLineSearchParams(), SNESGetLineSearchParams()
817: @*/
818: int SNESSetLineSearch(SNES snes,int (*func)(SNES,void*,Vec,Vec,Vec,Vec,Vec,PetscReal,PetscReal*,PetscReal*,int*),void *lsctx)
819: {
820:   int ierr,(*f)(SNES,int (*)(SNES,void*,Vec,Vec,Vec,Vec,Vec,PetscReal,PetscReal*,PetscReal*,int*),void*);

823:   PetscObjectQueryFunction((PetscObject)snes,"SNESSetLineSearch_C",(void (**)(void))&f);
824:   if (f) {
825:     (*f)(snes,func,lsctx);
826:   }
827:   return(0);
828: }
829: /* -------------------------------------------------------------------------- */
830: EXTERN_C_BEGIN
833: int SNESSetLineSearch_LS(SNES snes,int (*func)(SNES,void*,Vec,Vec,Vec,Vec,Vec,
834:                          PetscReal,PetscReal*,PetscReal*,int*),void *lsctx)
835: {
837:   ((SNES_LS *)(snes->data))->LineSearch = func;
838:   ((SNES_LS *)(snes->data))->lsP        = lsctx;
839:   return(0);
840: }
841: EXTERN_C_END
842: /* -------------------------------------------------------------------------- */
845: /*@C
846:    SNESSetLineSearchCheck - Sets a routine to check the validity of new iterate computed
847:    by the line search routine in the Newton-based method SNESLS.

849:    Input Parameters:
850: +  snes - nonlinear context obtained from SNESCreate()
851: .  func - pointer to int function
852: -  checkctx - optional user-defined context for use by step checking routine 

854:    Collective on SNES

856:    Calling sequence of func:
857: .vb
858:    int func (SNES snes, void *checkctx, Vec x, PetscTruth *flag)
859: .ve
860:    where func returns an error code of 0 on success and a nonzero
861:    on failure.

863:    Input parameters for func:
864: +  snes - nonlinear context
865: .  checkctx - optional user-defined context for use by step checking routine 
866: -  x - current candidate iterate

868:    Output parameters for func:
869: +  x - current iterate (possibly modified)
870: -  flag - flag indicating whether x has been modified (either
871:            PETSC_TRUE of PETSC_FALSE)

873:    Level: advanced

875:    Notes:
876:    SNESNoLineSearch() and SNESNoLineSearchNoNorms() accept the new
877:    iterate computed by the line search checking routine.  In particular,
878:    these routines (1) compute a candidate iterate u_{i+1}, (2) pass control 
879:    to the checking routine, and then (3) compute the corresponding nonlinear
880:    function f(u_{i+1}) with the (possibly altered) iterate u_{i+1}.

882:    SNESQuadraticLineSearch() and SNESCubicLineSearch() also accept the
883:    new iterate computed by the line search checking routine.  In particular,
884:    these routines (1) compute a candidate iterate u_{i+1} as well as a
885:    candidate nonlinear function f(u_{i+1}), (2) pass control to the checking 
886:    routine, and then (3) force a re-evaluation of f(u_{i+1}) if any changes 
887:    were made to the candidate iterate in the checking routine (as indicated 
888:    by flag=PETSC_TRUE).  The overhead of this function re-evaluation can be
889:    very costly, so use this feature with caution!

891: .keywords: SNES, nonlinear, set, line search check, step check, routine

893: .seealso: SNESSetLineSearch()
894: @*/
895: int SNESSetLineSearchCheck(SNES snes,int (*func)(SNES,void*,Vec,PetscTruth*),void *checkctx)
896: {
897:   int ierr,(*f)(SNES,int (*)(SNES,void*,Vec,PetscTruth*),void*);

900:   PetscObjectQueryFunction((PetscObject)snes,"SNESSetLineSearchCheck_C",(void (**)(void))&f);
901:   if (f) {
902:     (*f)(snes,func,checkctx);
903:   }
904:   return(0);
905: }
906: /* -------------------------------------------------------------------------- */
907: EXTERN_C_BEGIN
910: int SNESSetLineSearchCheck_LS(SNES snes,int (*func)(SNES,void*,Vec,PetscTruth*),void *checkctx)
911: {
913:   ((SNES_LS *)(snes->data))->CheckStep = func;
914:   ((SNES_LS *)(snes->data))->checkP    = checkctx;
915:   return(0);
916: }
917: EXTERN_C_END
918: /* -------------------------------------------------------------------------- */
919: /*
920:    SNESPrintHelp_LS - Prints all options for the SNES_LS method.

922:    Input Parameter:
923: .  snes - the SNES context

925:    Application Interface Routine: SNESPrintHelp()
926: */
929: static int SNESPrintHelp_LS(SNES snes,char *p)
930: {
931:   SNES_LS *ls = (SNES_LS *)snes->data;

934:   (*PetscHelpPrintf)(snes->comm," method SNES_LS (ls) for systems of nonlinear equations:\n");
935:   (*PetscHelpPrintf)(snes->comm,"   %ssnes_ls [cubic,quadratic,basic,basicnonorms,...]\n",p);
936:   (*PetscHelpPrintf)(snes->comm,"   %ssnes_ls_alpha <alpha> (default %g)\n",p,ls->alpha);
937:   (*PetscHelpPrintf)(snes->comm,"   %ssnes_ls_maxstep <max> (default %g)\n",p,ls->maxstep);
938:   (*PetscHelpPrintf)(snes->comm,"   %ssnes_ls_steptol <tol> (default %g)\n",p,ls->steptol);
939:   return(0);
940: }

942: /*
943:    SNESView_LS - Prints info from the SNESLS data structure.

945:    Input Parameters:
946: .  SNES - the SNES context
947: .  viewer - visualization context

949:    Application Interface Routine: SNESView()
950: */
953: static int SNESView_LS(SNES snes,PetscViewer viewer)
954: {
955:   SNES_LS    *ls = (SNES_LS *)snes->data;
956:   char       *cstr;
957:   int        ierr;
958:   PetscTruth isascii;

961:   PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_ASCII,&isascii);
962:   if (isascii) {
963:     if (ls->LineSearch == SNESNoLineSearch)             cstr = "SNESNoLineSearch";
964:     else if (ls->LineSearch == SNESQuadraticLineSearch) cstr = "SNESQuadraticLineSearch";
965:     else if (ls->LineSearch == SNESCubicLineSearch)     cstr = "SNESCubicLineSearch";
966:     else                                                cstr = "unknown";
967:     PetscViewerASCIIPrintf(viewer,"  line search variant: %s\n",cstr);
968:     PetscViewerASCIIPrintf(viewer,"  alpha=%g, maxstep=%g, steptol=%g\n",ls->alpha,ls->maxstep,ls->steptol);
969:   } else {
970:     SETERRQ1(1,"Viewer type %s not supported for SNES EQ LS",((PetscObject)viewer)->type_name);
971:   }
972:   return(0);
973: }
974: /* -------------------------------------------------------------------------- */
975: /*
976:    SNESSetFromOptions_LS - Sets various parameters for the SNESLS method.

978:    Input Parameter:
979: .  snes - the SNES context

981:    Application Interface Routine: SNESSetFromOptions()
982: */
985: static int SNESSetFromOptions_LS(SNES snes)
986: {
987:   SNES_LS    *ls = (SNES_LS *)snes->data;
988:   char       ver[16],*lses[] = {"basic","basicnonorms","quadratic","cubic"};
989:   int        ierr;
990:   PetscTruth flg;

993:   PetscOptionsHead("SNES Line search options");
994:     PetscOptionsReal("-snes_ls_alpha","Function norm must decrease by","None",ls->alpha,&ls->alpha,0);
995:     PetscOptionsReal("-snes_ls_maxstep","Step must be less than","None",ls->maxstep,&ls->maxstep,0);
996:     PetscOptionsReal("-snes_ls_steptol","Step must be greater than","None",ls->steptol,&ls->steptol,0);

998:     PetscOptionsEList("-snes_ls","Line search used","SNESSetLineSearch",lses,4,"cubic",ver,16,&flg);
999:     if (flg) {
1000:       PetscTruth isbasic,isnonorms,isquad,iscubic;

1002:       PetscStrcmp(ver,lses[0],&isbasic);
1003:       PetscStrcmp(ver,lses[1],&isnonorms);
1004:       PetscStrcmp(ver,lses[2],&isquad);
1005:       PetscStrcmp(ver,lses[3],&iscubic);

1007:       if (isbasic) {
1008:         SNESSetLineSearch(snes,SNESNoLineSearch,PETSC_NULL);
1009:       } else if (isnonorms) {
1010:         SNESSetLineSearch(snes,SNESNoLineSearchNoNorms,PETSC_NULL);
1011:       } else if (isquad) {
1012:         SNESSetLineSearch(snes,SNESQuadraticLineSearch,PETSC_NULL);
1013:       } else if (iscubic) {
1014:         SNESSetLineSearch(snes,SNESCubicLineSearch,PETSC_NULL);
1015:       }
1016:       else {SETERRQ(PETSC_ERR_ARG_OUTOFRANGE,"Unknown line search");}
1017:     }
1018:   PetscOptionsTail();
1019:   return(0);
1020: }
1021: /* -------------------------------------------------------------------------- */
1022: /*
1023:    SNESCreate_LS - Creates a nonlinear solver context for the SNESLS method,
1024:    SNES_LS, and sets this as the private data within the generic nonlinear solver
1025:    context, SNES, that was created within SNESCreate().


1028:    Input Parameter:
1029: .  snes - the SNES context

1031:    Application Interface Routine: SNESCreate()
1032:  */
1033: EXTERN_C_BEGIN
1036: int SNESCreate_LS(SNES snes)
1037: {
1038:   int     ierr;
1039:   SNES_LS *neP;

1042:   snes->setup                = SNESSetUp_LS;
1043:   snes->solve                = SNESSolve_LS;
1044:   snes->destroy                = SNESDestroy_LS;
1045:   snes->converged        = SNESConverged_LS;
1046:   snes->printhelp       = SNESPrintHelp_LS;
1047:   snes->setfromoptions  = SNESSetFromOptions_LS;
1048:   snes->view            = SNESView_LS;
1049:   snes->nwork           = 0;

1051:   PetscNew(SNES_LS,&neP);
1052:   PetscLogObjectMemory(snes,sizeof(SNES_LS));
1053:   snes->data            = (void*)neP;
1054:   neP->alpha                = 1.e-4;
1055:   neP->maxstep                = 1.e8;
1056:   neP->steptol                = 1.e-12;
1057:   neP->LineSearch       = SNESCubicLineSearch;
1058:   neP->lsP              = PETSC_NULL;
1059:   neP->CheckStep        = PETSC_NULL;
1060:   neP->checkP           = PETSC_NULL;

1062:   PetscObjectComposeFunctionDynamic((PetscObject)snes,"SNESSetLineSearch_C","SNESSetLineSearch_LS",SNESSetLineSearch_LS);
1063:   PetscObjectComposeFunctionDynamic((PetscObject)snes,"SNESSetLineSearchCheck_C","SNESSetLineSearchCheck_LS",SNESSetLineSearchCheck_LS);

1065:   return(0);
1066: }
1067: EXTERN_C_END