/*$Id: ls.c,v 1.172 2001/08/07 03:04:11 balay Exp $*/ #include "src/snes/impls/ls/ls.h" /* Checks if J^T F = 0 which implies we've found a local minimum of the function, but not a zero. In the case when one cannot compute J^T F we use the fact that 0 = (J^T F)^T W = F^T J W iff W not in the null space of J. Thanks for Jorge More for this trick. */ #undef __FUNCT__ #define __FUNCT__ "SNESLSCheckLocalMin_Private" int SNESLSCheckLocalMin_Private(Mat A,Vec F,Vec W,PetscReal fnorm,PetscTruth *ismin) { PetscReal a1; int ierr; PetscTruth hastranspose; PetscFunctionBegin; *ismin = PETSC_FALSE; ierr = MatHasOperation(A,MATOP_MULT_TRANSPOSE,&hastranspose);CHKERRQ(ierr); if (hastranspose) { /* Compute || J^T F|| */ ierr = MatMultTranspose(A,F,W);CHKERRQ(ierr); ierr = VecNorm(W,NORM_2,&a1);CHKERRQ(ierr); PetscLogInfo(0,"SNESSolve_LS: || J^T F|| %g near zero implies found a local minimum\n",a1/fnorm); if (a1/fnorm < 1.e-4) *ismin = PETSC_TRUE; } else { Vec work; PetscScalar result; PetscReal wnorm; ierr = VecSetRandom(PETSC_NULL,W);CHKERRQ(ierr); ierr = VecNorm(W,NORM_2,&wnorm);CHKERRQ(ierr); ierr = VecDuplicate(W,&work);CHKERRQ(ierr); ierr = MatMult(A,W,work);CHKERRQ(ierr); ierr = VecDot(F,work,&result);CHKERRQ(ierr); ierr = VecDestroy(work);CHKERRQ(ierr); a1 = PetscAbsScalar(result)/(fnorm*wnorm); PetscLogInfo(0,"SNESSolve_LS: (F^T J random)/(|| F ||*||random|| %g near zero implies found a local minimum\n",a1); if (a1 < 1.e-4) *ismin = PETSC_TRUE; } PetscFunctionReturn(0); } /* Checks if J^T(F - J*X) = 0 */ #undef __FUNCT__ #define __FUNCT__ "SNESLSCheckResidual_Private" int SNESLSCheckResidual_Private(Mat A,Vec F,Vec X,Vec W1,Vec W2) { PetscReal a1,a2; int ierr; PetscTruth hastranspose; PetscScalar mone = -1.0; PetscFunctionBegin; ierr = MatHasOperation(A,MATOP_MULT_TRANSPOSE,&hastranspose);CHKERRQ(ierr); if (hastranspose) { ierr = MatMult(A,X,W1);CHKERRQ(ierr); ierr = VecAXPY(&mone,F,W1);CHKERRQ(ierr); /* Compute || J^T W|| */ ierr = MatMultTranspose(A,W1,W2);CHKERRQ(ierr); ierr = VecNorm(W1,NORM_2,&a1);CHKERRQ(ierr); ierr = VecNorm(W2,NORM_2,&a2);CHKERRQ(ierr); if (a1 != 0) { PetscLogInfo(0,"SNESSolve_LS: ||J^T(F-Ax)||/||F-AX|| %g near zero implies inconsistent rhs\n",a2/a1); } } PetscFunctionReturn(0); } /* -------------------------------------------------------------------- This file implements a truncated Newton method with a line search, for solving a system of nonlinear equations, using the SLES, Vec, and Mat interfaces for linear solvers, vectors, and matrices, respectively. The following basic routines are required for each nonlinear solver: SNESCreate_XXX() - Creates a nonlinear solver context SNESSetFromOptions_XXX() - Sets runtime options SNESSolve_XXX() - Solves the nonlinear system SNESDestroy_XXX() - Destroys the nonlinear solver context The suffix "_XXX" denotes a particular implementation, in this case we use _LS (e.g., SNESCreate_LS, SNESSolve_LS) for solving systems of nonlinear equations with a line search (LS) method. These routines are actually called via the common user interface routines SNESCreate(), SNESSetFromOptions(), SNESSolve(), and SNESDestroy(), so the application code interface remains identical for all nonlinear solvers. Another key routine is: SNESSetUp_XXX() - Prepares for the use of a nonlinear solver by setting data structures and options. The interface routine SNESSetUp() is not usually called directly by the user, but instead is called by SNESSolve() if necessary. Additional basic routines are: SNESView_XXX() - Prints details of runtime options that have actually been used. These are called by application codes via the interface routines SNESView(). The various types of solvers (preconditioners, Krylov subspace methods, nonlinear solvers, timesteppers) are all organized similarly, so the above description applies to these categories also. -------------------------------------------------------------------- */ /* SNESSolve_LS - Solves a nonlinear system with a truncated Newton method with a line search. Input Parameters: . snes - the SNES context Output Parameter: . outits - number of iterations until termination Application Interface Routine: SNESSolve() Notes: This implements essentially a truncated Newton method with a line search. By default a cubic backtracking line search is employed, as described in the text "Numerical Methods for Unconstrained Optimization and Nonlinear Equations" by Dennis and Schnabel. */ #undef __FUNCT__ #define __FUNCT__ "SNESSolve_LS" int SNESSolve_LS(SNES snes,int *outits) { SNES_LS *neP = (SNES_LS*)snes->data; int maxits,i,ierr,lits,lsfail; MatStructure flg = DIFFERENT_NONZERO_PATTERN; PetscReal fnorm,gnorm,xnorm,ynorm; Vec Y,X,F,G,W,TMP; PetscFunctionBegin; snes->reason = SNES_CONVERGED_ITERATING; maxits = snes->max_its; /* maximum number of iterations */ X = snes->vec_sol; /* solution vector */ F = snes->vec_func; /* residual vector */ Y = snes->work[0]; /* work vectors */ G = snes->work[1]; W = snes->work[2]; ierr = PetscObjectTakeAccess(snes);CHKERRQ(ierr); snes->iter = 0; ierr = PetscObjectGrantAccess(snes);CHKERRQ(ierr); ierr = SNESComputeFunction(snes,X,F);CHKERRQ(ierr); /* F(X) */ ierr = VecNorm(F,NORM_2,&fnorm);CHKERRQ(ierr); /* fnorm <- ||F|| */ ierr = PetscObjectTakeAccess(snes);CHKERRQ(ierr); snes->norm = fnorm; ierr = PetscObjectGrantAccess(snes);CHKERRQ(ierr); SNESLogConvHistory(snes,fnorm,0); SNESMonitor(snes,0,fnorm); if (fnorm < snes->atol) {*outits = 0; snes->reason = SNES_CONVERGED_FNORM_ABS; PetscFunctionReturn(0);} /* set parameter for default relative tolerance convergence test */ snes->ttol = fnorm*snes->rtol; for (i=0; iupdate != PETSC_NULL) { ierr = (*snes->update)(snes, snes->iter);CHKERRQ(ierr); } /* Solve J Y = F, where J is Jacobian matrix */ ierr = SNESComputeJacobian(snes,X,&snes->jacobian,&snes->jacobian_pre,&flg);CHKERRQ(ierr); ierr = SLESSetOperators(snes->sles,snes->jacobian,snes->jacobian_pre,flg);CHKERRQ(ierr); ierr = SLESSolve(snes->sles,F,Y,&lits);CHKERRQ(ierr); if (PetscLogPrintInfo){ ierr = SNESLSCheckResidual_Private(snes->jacobian,F,Y,G,W);CHKERRQ(ierr); } /* should check what happened to the linear solve? */ snes->linear_its += lits; PetscLogInfo(snes,"SNESSolve_LS: iter=%d, linear solve iterations=%d\n",snes->iter,lits); /* Compute a (scaled) negative update in the line search routine: Y <- X - lambda*Y and evaluate G(Y) = function(Y)) */ ierr = VecCopy(Y,snes->vec_sol_update_always);CHKERRQ(ierr); ierr = (*neP->LineSearch)(snes,neP->lsP,X,F,G,Y,W,fnorm,&ynorm,&gnorm,&lsfail);CHKERRQ(ierr); PetscLogInfo(snes,"SNESSolve_LS: fnorm=%18.16e, gnorm=%18.16e, ynorm=%18.16e, lsfail=%d\n",fnorm,gnorm,ynorm,lsfail); TMP = F; F = G; snes->vec_func_always = F; G = TMP; TMP = X; X = Y; snes->vec_sol_always = X; Y = TMP; fnorm = gnorm; ierr = PetscObjectTakeAccess(snes);CHKERRQ(ierr); snes->iter = i+1; snes->norm = fnorm; ierr = PetscObjectGrantAccess(snes);CHKERRQ(ierr); SNESLogConvHistory(snes,fnorm,lits); SNESMonitor(snes,i+1,fnorm); if (lsfail) { PetscTruth ismin; if (++snes->numFailures >= snes->maxFailures) { snes->reason = SNES_DIVERGED_LS_FAILURE; ierr = SNESLSCheckLocalMin_Private(snes->jacobian,F,W,fnorm,&ismin);CHKERRQ(ierr); if (ismin) snes->reason = SNES_DIVERGED_LOCAL_MIN; break; } } /* Test for convergence */ if (snes->converged) { ierr = VecNorm(X,NORM_2,&xnorm);CHKERRQ(ierr); /* xnorm = || X || */ ierr = (*snes->converged)(snes,xnorm,ynorm,fnorm,&snes->reason,snes->cnvP);CHKERRQ(ierr); if (snes->reason) { break; } } } if (X != snes->vec_sol) { ierr = VecCopy(X,snes->vec_sol);CHKERRQ(ierr); } if (F != snes->vec_func) { ierr = VecCopy(F,snes->vec_func);CHKERRQ(ierr); } snes->vec_sol_always = snes->vec_sol; snes->vec_func_always = snes->vec_func; if (i == maxits) { PetscLogInfo(snes,"SNESSolve_LS: Maximum number of iterations has been reached: %d\n",maxits); i--; snes->reason = SNES_DIVERGED_MAX_IT; } ierr = PetscObjectTakeAccess(snes);CHKERRQ(ierr); ierr = PetscObjectGrantAccess(snes);CHKERRQ(ierr); *outits = i+1; PetscFunctionReturn(0); } /* -------------------------------------------------------------------------- */ /* SNESSetUp_LS - Sets up the internal data structures for the later use of the SNESLS nonlinear solver. Input Parameter: . snes - the SNES context . x - the solution vector Application Interface Routine: SNESSetUp() Notes: For basic use of the SNES solvers, the user need not explicitly call SNESSetUp(), since these actions will automatically occur during the call to SNESSolve(). */ #undef __FUNCT__ #define __FUNCT__ "SNESSetUp_LS" int SNESSetUp_LS(SNES snes) { int ierr; PetscFunctionBegin; snes->nwork = 4; ierr = VecDuplicateVecs(snes->vec_sol,snes->nwork,&snes->work);CHKERRQ(ierr); PetscLogObjectParents(snes,snes->nwork,snes->work); snes->vec_sol_update_always = snes->work[3]; PetscFunctionReturn(0); } /* -------------------------------------------------------------------------- */ /* SNESDestroy_LS - Destroys the private SNES_LS context that was created with SNESCreate_LS(). Input Parameter: . snes - the SNES context Application Interface Routine: SNESDestroy() */ #undef __FUNCT__ #define __FUNCT__ "SNESDestroy_LS" int SNESDestroy_LS(SNES snes) { int ierr; PetscFunctionBegin; if (snes->nwork) { ierr = VecDestroyVecs(snes->work,snes->nwork);CHKERRQ(ierr); } ierr = PetscFree(snes->data);CHKERRQ(ierr); PetscFunctionReturn(0); } /* -------------------------------------------------------------------------- */ #undef __FUNCT__ #define __FUNCT__ "SNESNoLineSearch" /*@C SNESNoLineSearch - This routine is not a line search at all; it simply uses the full Newton step. Thus, this routine is intended to serve as a template and is not recommended for general use. Collective on SNES and Vec Input Parameters: + snes - nonlinear context . lsctx - optional context for line search (not used here) . x - current iterate . f - residual evaluated at x . y - search direction (contains new iterate on output) . w - work vector - fnorm - 2-norm of f Output Parameters: + g - residual evaluated at new iterate y . y - new iterate (contains search direction on input) . gnorm - 2-norm of g . ynorm - 2-norm of search length - flag - set to 0, indicating a successful line search Options Database Key: . -snes_ls basic - Activates SNESNoLineSearch() Level: advanced .keywords: SNES, nonlinear, line search, cubic .seealso: SNESCubicLineSearch(), SNESQuadraticLineSearch(), SNESSetLineSearch(), SNESNoLineSearchNoNorms() @*/ int SNESNoLineSearch(SNES snes,void *lsctx,Vec x,Vec f,Vec g,Vec y,Vec w,PetscReal fnorm,PetscReal *ynorm,PetscReal *gnorm,int *flag) { int ierr; PetscScalar mone = -1.0; SNES_LS *neP = (SNES_LS*)snes->data; PetscTruth change_y = PETSC_FALSE; PetscFunctionBegin; *flag = 0; ierr = PetscLogEventBegin(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr); ierr = VecNorm(y,NORM_2,ynorm);CHKERRQ(ierr); /* ynorm = || y || */ ierr = VecAYPX(&mone,x,y);CHKERRQ(ierr); /* y <- y - x */ if (neP->CheckStep) { ierr = (*neP->CheckStep)(snes,neP->checkP,y,&change_y);CHKERRQ(ierr); } ierr = SNESComputeFunction(snes,y,g);CHKERRQ(ierr); /* Compute F(y) */ ierr = VecNorm(g,NORM_2,gnorm);CHKERRQ(ierr); /* gnorm = || g || */ ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr); PetscFunctionReturn(0); } /* -------------------------------------------------------------------------- */ #undef __FUNCT__ #define __FUNCT__ "SNESNoLineSearchNoNorms" /*@C SNESNoLineSearchNoNorms - This routine is not a line search at all; it simply uses the full Newton step. This version does not even compute the norm of the function or search direction; this is intended only when you know the full step is fine and are not checking for convergence of the nonlinear iteration (for example, you are running always for a fixed number of Newton steps). Collective on SNES and Vec Input Parameters: + snes - nonlinear context . lsctx - optional context for line search (not used here) . x - current iterate . f - residual evaluated at x . y - search direction (contains new iterate on output) . w - work vector - fnorm - 2-norm of f Output Parameters: + g - residual evaluated at new iterate y . gnorm - not changed . ynorm - not changed - flag - set to 0, indicating a successful line search Options Database Key: . -snes_ls basicnonorms - Activates SNESNoLineSearchNoNorms() Notes: SNESNoLineSearchNoNorms() must be used in conjunction with either the options $ -snes_no_convergence_test -snes_max_it or alternatively a user-defined custom test set via SNESSetConvergenceTest(); or a -snes_max_it of 1, otherwise, the SNES solver will generate an error. During the final iteration this will not evaluate the function at the solution point. This is to save a function evaluation while using pseudo-timestepping. The residual norms printed by monitoring routines such as SNESDefaultMonitor() (as activated via -snes_monitor) will not be correct, since they are not computed. Level: advanced .keywords: SNES, nonlinear, line search, cubic .seealso: SNESCubicLineSearch(), SNESQuadraticLineSearch(), SNESSetLineSearch(), SNESNoLineSearch() @*/ int SNESNoLineSearchNoNorms(SNES snes,void *lsctx,Vec x,Vec f,Vec g,Vec y,Vec w,PetscReal fnorm,PetscReal *ynorm,PetscReal *gnorm,int *flag) { int ierr; PetscScalar mone = -1.0; SNES_LS *neP = (SNES_LS*)snes->data; PetscTruth change_y = PETSC_FALSE; PetscFunctionBegin; *flag = 0; ierr = PetscLogEventBegin(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr); ierr = VecAYPX(&mone,x,y);CHKERRQ(ierr); /* y <- y - x */ if (neP->CheckStep) { ierr = (*neP->CheckStep)(snes,neP->checkP,y,&change_y);CHKERRQ(ierr); } /* don't evaluate function the last time through */ if (snes->iter < snes->max_its-1) { ierr = SNESComputeFunction(snes,y,g);CHKERRQ(ierr); /* Compute F(y) */ } ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr); PetscFunctionReturn(0); } /* -------------------------------------------------------------------------- */ #undef __FUNCT__ #define __FUNCT__ "SNESCubicLineSearch" /*@C SNESCubicLineSearch - Performs a cubic line search (default line search method). Collective on SNES Input Parameters: + snes - nonlinear context . lsctx - optional context for line search (not used here) . x - current iterate . f - residual evaluated at x . y - search direction (contains new iterate on output) . w - work vector - fnorm - 2-norm of f Output Parameters: + g - residual evaluated at new iterate y . y - new iterate (contains search direction on input) . gnorm - 2-norm of g . ynorm - 2-norm of search length - flag - 0 if line search succeeds; -1 on failure. Options Database Key: $ -snes_ls cubic - Activates SNESCubicLineSearch() Notes: This line search is taken from "Numerical Methods for Unconstrained Optimization and Nonlinear Equations" by Dennis and Schnabel, page 325. Level: advanced .keywords: SNES, nonlinear, line search, cubic .seealso: SNESQuadraticLineSearch(), SNESNoLineSearch(), SNESSetLineSearch(), SNESNoLineSearchNoNorms() @*/ int SNESCubicLineSearch(SNES snes,void *lsctx,Vec x,Vec f,Vec g,Vec y,Vec w,PetscReal fnorm,PetscReal *ynorm,PetscReal *gnorm,int *flag) { /* Note that for line search purposes we work with with the related minimization problem: min z(x): R^n -> R, where z(x) = .5 * fnorm*fnorm, and fnorm = || f ||_2. */ PetscReal steptol,initslope,lambdaprev,gnormprev,a,b,d,t1,t2,rellength; PetscReal maxstep,minlambda,alpha,lambda,lambdatemp,lambdaneg; #if defined(PETSC_USE_COMPLEX) PetscScalar cinitslope,clambda; #endif int ierr,count; SNES_LS *neP = (SNES_LS*)snes->data; PetscScalar mone = -1.0,scale; PetscTruth change_y = PETSC_FALSE; PetscFunctionBegin; ierr = PetscLogEventBegin(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr); *flag = 0; alpha = neP->alpha; maxstep = neP->maxstep; steptol = neP->steptol; ierr = VecNorm(y,NORM_2,ynorm);CHKERRQ(ierr); if (*ynorm < snes->atol) { PetscLogInfo(snes,"SNESCubicLineSearch: Search direction and size are nearly 0\n"); *gnorm = fnorm; ierr = VecCopy(x,y);CHKERRQ(ierr); ierr = VecCopy(f,g);CHKERRQ(ierr); goto theend1; } if (*ynorm > maxstep) { /* Step too big, so scale back */ scale = maxstep/(*ynorm); #if defined(PETSC_USE_COMPLEX) PetscLogInfo(snes,"SNESCubicLineSearch: Scaling step by %g old ynorm %g\n",PetscRealPart(scale),*ynorm); #else PetscLogInfo(snes,"SNESCubicLineSearch: Scaling step by %g old ynorm %g\n",scale,*ynorm); #endif ierr = VecScale(&scale,y);CHKERRQ(ierr); *ynorm = maxstep; } ierr = VecMaxPointwiseDivide(y,x,&rellength);CHKERRQ(ierr); minlambda = steptol/rellength; ierr = MatMult(snes->jacobian,y,w);CHKERRQ(ierr); #if defined(PETSC_USE_COMPLEX) ierr = VecDot(f,w,&cinitslope);CHKERRQ(ierr); initslope = PetscRealPart(cinitslope); #else ierr = VecDot(f,w,&initslope);CHKERRQ(ierr); #endif if (initslope > 0.0) initslope = -initslope; if (initslope == 0.0) initslope = -1.0; ierr = VecCopy(y,w);CHKERRQ(ierr); ierr = VecAYPX(&mone,x,w);CHKERRQ(ierr); ierr = SNESComputeFunction(snes,w,g);CHKERRQ(ierr); ierr = VecNorm(g,NORM_2,gnorm);CHKERRQ(ierr); if (.5*(*gnorm)*(*gnorm) <= .5*fnorm*fnorm + alpha*initslope) { /* Sufficient reduction */ ierr = VecCopy(w,y);CHKERRQ(ierr); PetscLogInfo(snes,"SNESCubicLineSearch: Using full step\n"); goto theend1; } /* Fit points with quadratic */ lambda = 1.0; lambdatemp = -initslope/((*gnorm)*(*gnorm) - fnorm*fnorm - 2.0*initslope); lambdaprev = lambda; gnormprev = *gnorm; if (lambdatemp > .5*lambda) lambdatemp = .5*lambda; if (lambdatemp <= .1*lambda) lambda = .1*lambda; else lambda = lambdatemp; ierr = VecCopy(x,w);CHKERRQ(ierr); lambdaneg = -lambda; #if defined(PETSC_USE_COMPLEX) clambda = lambdaneg; ierr = VecAXPY(&clambda,y,w);CHKERRQ(ierr); #else ierr = VecAXPY(&lambdaneg,y,w);CHKERRQ(ierr); #endif ierr = SNESComputeFunction(snes,w,g);CHKERRQ(ierr); ierr = VecNorm(g,NORM_2,gnorm);CHKERRQ(ierr); if (.5*(*gnorm)*(*gnorm) < .5*fnorm*fnorm + lambda*alpha*initslope) { /* sufficient reduction */ ierr = VecCopy(w,y);CHKERRQ(ierr); PetscLogInfo(snes,"SNESCubicLineSearch: Quadratically determined step, lambda=%18.16e\n",lambda); goto theend1; } /* Fit points with cubic */ count = 1; while (PETSC_TRUE) { if (lambda <= minlambda) { /* bad luck; use full step */ PetscLogInfo(snes,"SNESCubicLineSearch:Unable to find good step length! %d \n",count); 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); ierr = VecCopy(x,y);CHKERRQ(ierr); *flag = -1; break; } t1 = .5*((*gnorm)*(*gnorm) - fnorm*fnorm) - lambda*initslope; t2 = .5*(gnormprev*gnormprev - fnorm*fnorm) - lambdaprev*initslope; a = (t1/(lambda*lambda) - t2/(lambdaprev*lambdaprev))/(lambda-lambdaprev); b = (-lambdaprev*t1/(lambda*lambda) + lambda*t2/(lambdaprev*lambdaprev))/(lambda-lambdaprev); d = b*b - 3*a*initslope; if (d < 0.0) d = 0.0; if (a == 0.0) { lambdatemp = -initslope/(2.0*b); } else { lambdatemp = (-b + sqrt(d))/(3.0*a); } lambdaprev = lambda; gnormprev = *gnorm; if (lambdatemp > .5*lambda) lambdatemp = .5*lambda; if (lambdatemp <= .1*lambda) lambda = .1*lambda; else lambda = lambdatemp; ierr = VecCopy(x,w);CHKERRQ(ierr); lambdaneg = -lambda; #if defined(PETSC_USE_COMPLEX) clambda = lambdaneg; ierr = VecAXPY(&clambda,y,w);CHKERRQ(ierr); #else ierr = VecAXPY(&lambdaneg,y,w);CHKERRQ(ierr); #endif ierr = SNESComputeFunction(snes,w,g);CHKERRQ(ierr); ierr = VecNorm(g,NORM_2,gnorm);CHKERRQ(ierr); if (.5*(*gnorm)*(*gnorm) < .5*fnorm*fnorm + lambda*alpha*initslope) { /* is reduction enough? */ ierr = VecCopy(w,y);CHKERRQ(ierr); PetscLogInfo(snes,"SNESCubicLineSearch: Cubically determined step, lambda=%18.16e\n",lambda); goto theend1; } else { PetscLogInfo(snes,"SNESCubicLineSearch: Cubic step no good, shrinking lambda, lambda=%18.16e\n",lambda); } count++; } theend1: /* Optional user-defined check for line search step validity */ if (neP->CheckStep) { ierr = (*neP->CheckStep)(snes,neP->checkP,y,&change_y);CHKERRQ(ierr); if (change_y == PETSC_TRUE) { /* recompute the function if the step has changed */ ierr = SNESComputeFunction(snes,y,g);CHKERRQ(ierr); ierr = VecNormBegin(y,NORM_2,ynorm);CHKERRQ(ierr); ierr = VecNormBegin(g,NORM_2,gnorm);CHKERRQ(ierr); ierr = VecNormEnd(y,NORM_2,ynorm);CHKERRQ(ierr); ierr = VecNormEnd(g,NORM_2,gnorm);CHKERRQ(ierr); } } ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr); PetscFunctionReturn(0); } /* -------------------------------------------------------------------------- */ #undef __FUNCT__ #define __FUNCT__ "SNESQuadraticLineSearch" /*@C SNESQuadraticLineSearch - Performs a quadratic line search. Collective on SNES and Vec Input Parameters: + snes - the SNES context . lsctx - optional context for line search (not used here) . x - current iterate . f - residual evaluated at x . y - search direction (contains new iterate on output) . w - work vector - fnorm - 2-norm of f Output Parameters: + g - residual evaluated at new iterate y . y - new iterate (contains search direction on input) . gnorm - 2-norm of g . ynorm - 2-norm of search length - flag - 0 if line search succeeds; -1 on failure. Options Database Key: . -snes_ls quadratic - Activates SNESQuadraticLineSearch() Notes: Use SNESSetLineSearch() to set this routine within the SNESLS method. Level: advanced .keywords: SNES, nonlinear, quadratic, line search .seealso: SNESCubicLineSearch(), SNESNoLineSearch(), SNESSetLineSearch(), SNESNoLineSearchNoNorms() @*/ int SNESQuadraticLineSearch(SNES snes,void *lsctx,Vec x,Vec f,Vec g,Vec y,Vec w,PetscReal fnorm,PetscReal *ynorm,PetscReal *gnorm,int *flag) { /* Note that for line search purposes we work with with the related minimization problem: min z(x): R^n -> R, where z(x) = .5 * fnorm*fnorm,and fnorm = || f ||_2. */ PetscReal steptol,initslope,maxstep,minlambda,alpha,lambda,lambdatemp,lambdaneg,rellength; #if defined(PETSC_USE_COMPLEX) PetscScalar cinitslope,clambda; #endif int ierr,count; SNES_LS *neP = (SNES_LS*)snes->data; PetscScalar mone = -1.0,scale; PetscTruth change_y = PETSC_FALSE; PetscFunctionBegin; ierr = PetscLogEventBegin(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr); *flag = 0; alpha = neP->alpha; maxstep = neP->maxstep; steptol = neP->steptol; ierr = VecNorm(y,NORM_2,ynorm);CHKERRQ(ierr); if (*ynorm < snes->atol) { PetscLogInfo(snes,"SNESQuadraticLineSearch: Search direction and size is 0\n"); *gnorm = fnorm; ierr = VecCopy(x,y);CHKERRQ(ierr); ierr = VecCopy(f,g);CHKERRQ(ierr); goto theend2; } if (*ynorm > maxstep) { /* Step too big, so scale back */ scale = maxstep/(*ynorm); ierr = VecScale(&scale,y);CHKERRQ(ierr); *ynorm = maxstep; } ierr = VecMaxPointwiseDivide(y,x,&rellength);CHKERRQ(ierr); minlambda = steptol/rellength; ierr = MatMult(snes->jacobian,y,w);CHKERRQ(ierr); #if defined(PETSC_USE_COMPLEX) ierr = VecDot(f,w,&cinitslope);CHKERRQ(ierr); initslope = PetscRealPart(cinitslope); #else ierr = VecDot(f,w,&initslope);CHKERRQ(ierr); #endif if (initslope > 0.0) initslope = -initslope; if (initslope == 0.0) initslope = -1.0; ierr = VecCopy(y,w);CHKERRQ(ierr); ierr = VecAYPX(&mone,x,w);CHKERRQ(ierr); ierr = SNESComputeFunction(snes,w,g);CHKERRQ(ierr); ierr = VecNorm(g,NORM_2,gnorm);CHKERRQ(ierr); if (.5*(*gnorm)*(*gnorm) <= .5*fnorm*fnorm + alpha*initslope) { /* Sufficient reduction */ ierr = VecCopy(w,y);CHKERRQ(ierr); PetscLogInfo(snes,"SNESQuadraticLineSearch: Using full step\n"); goto theend2; } /* Fit points with quadratic */ lambda = 1.0; count = 1; while (PETSC_TRUE) { if (lambda <= minlambda) { /* bad luck; use full step */ PetscLogInfo(snes,"SNESQuadraticLineSearch:Unable to find good step length! %d \n",count); PetscLogInfo(snes,"SNESQuadraticLineSearch:fnorm=%g, gnorm=%g, ynorm=%g, lambda=%g, initial slope=%g\n",fnorm,*gnorm,*ynorm,lambda,initslope); ierr = VecCopy(x,y);CHKERRQ(ierr); *flag = -1; break; } lambdatemp = -initslope/((*gnorm)*(*gnorm) - fnorm*fnorm - 2.0*initslope); if (lambdatemp > .5*lambda) lambdatemp = .5*lambda; if (lambdatemp <= .1*lambda) lambda = .1*lambda; else lambda = lambdatemp; ierr = VecCopy(x,w);CHKERRQ(ierr); lambdaneg = -lambda; #if defined(PETSC_USE_COMPLEX) clambda = lambdaneg; ierr = VecAXPY(&clambda,y,w);CHKERRQ(ierr); #else ierr = VecAXPY(&lambdaneg,y,w);CHKERRQ(ierr); #endif ierr = SNESComputeFunction(snes,w,g);CHKERRQ(ierr); ierr = VecNorm(g,NORM_2,gnorm);CHKERRQ(ierr); if (.5*(*gnorm)*(*gnorm) < .5*fnorm*fnorm + lambda*alpha*initslope) { /* sufficient reduction */ ierr = VecCopy(w,y);CHKERRQ(ierr); PetscLogInfo(snes,"SNESQuadraticLineSearch:Quadratically determined step, lambda=%g\n",lambda); break; } count++; } theend2: /* Optional user-defined check for line search step validity */ if (neP->CheckStep) { ierr = (*neP->CheckStep)(snes,neP->checkP,y,&change_y);CHKERRQ(ierr); if (change_y == PETSC_TRUE) { /* recompute the function if the step has changed */ ierr = SNESComputeFunction(snes,y,g);CHKERRQ(ierr); ierr = VecNormBegin(y,NORM_2,ynorm);CHKERRQ(ierr); ierr = VecNormBegin(g,NORM_2,gnorm);CHKERRQ(ierr); ierr = VecNormEnd(y,NORM_2,ynorm);CHKERRQ(ierr); ierr = VecNormEnd(g,NORM_2,gnorm);CHKERRQ(ierr); } } ierr = PetscLogEventEnd(SNES_LineSearch,snes,x,f,g);CHKERRQ(ierr); PetscFunctionReturn(0); } /* -------------------------------------------------------------------------- */ #undef __FUNCT__ #define __FUNCT__ "SNESSetLineSearch" /*@C SNESSetLineSearch - Sets the line search routine to be used by the method SNESLS. Input Parameters: + snes - nonlinear context obtained from SNESCreate() . lsctx - optional user-defined context for use by line search - func - pointer to int function Collective on SNES Available Routines: + SNESCubicLineSearch() - default line search . SNESQuadraticLineSearch() - quadratic line search . SNESNoLineSearch() - the full Newton step (actually not a line search) - SNESNoLineSearchNoNorms() - the full Newton step (calculating no norms; faster in parallel) Options Database Keys: + -snes_ls [cubic,quadratic,basic,basicnonorms] - Selects line search . -snes_ls_alpha - Sets alpha . -snes_ls_maxstep - Sets maxstep - -snes_ls_steptol - Sets steptol, this is the minimum step size that the line search code will accept; min p[i]/x[i] < steptol. The -snes_stol is the minimum step length the default convergence test will use and is based on 2-norm(p) < stol*2-norm(x) Calling sequence of func: .vb func (SNES snes,void *lsctx,Vec x,Vec f,Vec g,Vec y,Vec w, PetscReal fnorm,PetscReal *ynorm,PetscReal *gnorm,*flag) .ve Input parameters for func: + snes - nonlinear context . lsctx - optional user-defined context for line search . x - current iterate . f - residual evaluated at x . y - search direction (contains new iterate on output) . w - work vector - fnorm - 2-norm of f Output parameters for func: + g - residual evaluated at new iterate y . y - new iterate (contains search direction on input) . gnorm - 2-norm of g . ynorm - 2-norm of search length - flag - set to 0 if the line search succeeds; a nonzero integer on failure. Level: advanced .keywords: SNES, nonlinear, set, line search, routine .seealso: SNESCubicLineSearch(), SNESQuadraticLineSearch(), SNESNoLineSearch(), SNESNoLineSearchNoNorms(), SNESSetLineSearchCheck(), SNESSetLineSearchParams(), SNESGetLineSearchParams() @*/ int SNESSetLineSearch(SNES snes,int (*func)(SNES,void*,Vec,Vec,Vec,Vec,Vec,PetscReal,PetscReal*,PetscReal*,int*),void *lsctx) { int ierr,(*f)(SNES,int (*)(SNES,void*,Vec,Vec,Vec,Vec,Vec,PetscReal,PetscReal*,PetscReal*,int*),void*); PetscFunctionBegin; ierr = PetscObjectQueryFunction((PetscObject)snes,"SNESSetLineSearch_C",(void (**)(void))&f);CHKERRQ(ierr); if (f) { ierr = (*f)(snes,func,lsctx);CHKERRQ(ierr); } PetscFunctionReturn(0); } /* -------------------------------------------------------------------------- */ EXTERN_C_BEGIN #undef __FUNCT__ #define __FUNCT__ "SNESSetLineSearch_LS" int SNESSetLineSearch_LS(SNES snes,int (*func)(SNES,void*,Vec,Vec,Vec,Vec,Vec, PetscReal,PetscReal*,PetscReal*,int*),void *lsctx) { PetscFunctionBegin; ((SNES_LS *)(snes->data))->LineSearch = func; ((SNES_LS *)(snes->data))->lsP = lsctx; PetscFunctionReturn(0); } EXTERN_C_END /* -------------------------------------------------------------------------- */ #undef __FUNCT__ #define __FUNCT__ "SNESSetLineSearchCheck" /*@C SNESSetLineSearchCheck - Sets a routine to check the validity of new iterate computed by the line search routine in the Newton-based method SNESLS. Input Parameters: + snes - nonlinear context obtained from SNESCreate() . func - pointer to int function - checkctx - optional user-defined context for use by step checking routine Collective on SNES Calling sequence of func: .vb int func (SNES snes, void *checkctx, Vec x, PetscTruth *flag) .ve where func returns an error code of 0 on success and a nonzero on failure. Input parameters for func: + snes - nonlinear context . checkctx - optional user-defined context for use by step checking routine - x - current candidate iterate Output parameters for func: + x - current iterate (possibly modified) - flag - flag indicating whether x has been modified (either PETSC_TRUE of PETSC_FALSE) Level: advanced Notes: SNESNoLineSearch() and SNESNoLineSearchNoNorms() accept the new iterate computed by the line search checking routine. In particular, these routines (1) compute a candidate iterate u_{i+1}, (2) pass control to the checking routine, and then (3) compute the corresponding nonlinear function f(u_{i+1}) with the (possibly altered) iterate u_{i+1}. SNESQuadraticLineSearch() and SNESCubicLineSearch() also accept the new iterate computed by the line search checking routine. In particular, these routines (1) compute a candidate iterate u_{i+1} as well as a candidate nonlinear function f(u_{i+1}), (2) pass control to the checking routine, and then (3) force a re-evaluation of f(u_{i+1}) if any changes were made to the candidate iterate in the checking routine (as indicated by flag=PETSC_TRUE). The overhead of this function re-evaluation can be very costly, so use this feature with caution! .keywords: SNES, nonlinear, set, line search check, step check, routine .seealso: SNESSetLineSearch() @*/ int SNESSetLineSearchCheck(SNES snes,int (*func)(SNES,void*,Vec,PetscTruth*),void *checkctx) { int ierr,(*f)(SNES,int (*)(SNES,void*,Vec,PetscTruth*),void*); PetscFunctionBegin; ierr = PetscObjectQueryFunction((PetscObject)snes,"SNESSetLineSearchCheck_C",(void (**)(void))&f);CHKERRQ(ierr); if (f) { ierr = (*f)(snes,func,checkctx);CHKERRQ(ierr); } PetscFunctionReturn(0); } /* -------------------------------------------------------------------------- */ EXTERN_C_BEGIN #undef __FUNCT__ #define __FUNCT__ "SNESSetLineSearchCheck_LS" int SNESSetLineSearchCheck_LS(SNES snes,int (*func)(SNES,void*,Vec,PetscTruth*),void *checkctx) { PetscFunctionBegin; ((SNES_LS *)(snes->data))->CheckStep = func; ((SNES_LS *)(snes->data))->checkP = checkctx; PetscFunctionReturn(0); } EXTERN_C_END /* -------------------------------------------------------------------------- */ /* SNESPrintHelp_LS - Prints all options for the SNES_LS method. Input Parameter: . snes - the SNES context Application Interface Routine: SNESPrintHelp() */ #undef __FUNCT__ #define __FUNCT__ "SNESPrintHelp_LS" static int SNESPrintHelp_LS(SNES snes,char *p) { SNES_LS *ls = (SNES_LS *)snes->data; PetscFunctionBegin; (*PetscHelpPrintf)(snes->comm," method SNES_LS (ls) for systems of nonlinear equations:\n"); (*PetscHelpPrintf)(snes->comm," %ssnes_ls [cubic,quadratic,basic,basicnonorms,...]\n",p); (*PetscHelpPrintf)(snes->comm," %ssnes_ls_alpha (default %g)\n",p,ls->alpha); (*PetscHelpPrintf)(snes->comm," %ssnes_ls_maxstep (default %g)\n",p,ls->maxstep); (*PetscHelpPrintf)(snes->comm," %ssnes_ls_steptol (default %g)\n",p,ls->steptol); PetscFunctionReturn(0); } /* SNESView_LS - Prints info from the SNESLS data structure. Input Parameters: . SNES - the SNES context . viewer - visualization context Application Interface Routine: SNESView() */ #undef __FUNCT__ #define __FUNCT__ "SNESView_LS" static int SNESView_LS(SNES snes,PetscViewer viewer) { SNES_LS *ls = (SNES_LS *)snes->data; char *cstr; int ierr; PetscTruth isascii; PetscFunctionBegin; ierr = PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_ASCII,&isascii);CHKERRQ(ierr); if (isascii) { if (ls->LineSearch == SNESNoLineSearch) cstr = "SNESNoLineSearch"; else if (ls->LineSearch == SNESQuadraticLineSearch) cstr = "SNESQuadraticLineSearch"; else if (ls->LineSearch == SNESCubicLineSearch) cstr = "SNESCubicLineSearch"; else cstr = "unknown"; ierr = PetscViewerASCIIPrintf(viewer," line search variant: %s\n",cstr);CHKERRQ(ierr); ierr = PetscViewerASCIIPrintf(viewer," alpha=%g, maxstep=%g, steptol=%g\n",ls->alpha,ls->maxstep,ls->steptol);CHKERRQ(ierr); } else { SETERRQ1(1,"Viewer type %s not supported for SNES EQ LS",((PetscObject)viewer)->type_name); } PetscFunctionReturn(0); } /* -------------------------------------------------------------------------- */ /* SNESSetFromOptions_LS - Sets various parameters for the SNESLS method. Input Parameter: . snes - the SNES context Application Interface Routine: SNESSetFromOptions() */ #undef __FUNCT__ #define __FUNCT__ "SNESSetFromOptions_LS" static int SNESSetFromOptions_LS(SNES snes) { SNES_LS *ls = (SNES_LS *)snes->data; char ver[16],*lses[] = {"basic","basicnonorms","quadratic","cubic"}; int ierr; PetscTruth flg; PetscFunctionBegin; ierr = PetscOptionsHead("SNES Line search options");CHKERRQ(ierr); ierr = PetscOptionsReal("-snes_ls_alpha","Function norm must decrease by","None",ls->alpha,&ls->alpha,0);CHKERRQ(ierr); ierr = PetscOptionsReal("-snes_ls_maxstep","Step must be less than","None",ls->maxstep,&ls->maxstep,0);CHKERRQ(ierr); ierr = PetscOptionsReal("-snes_ls_steptol","Step must be greater than","None",ls->steptol,&ls->steptol,0);CHKERRQ(ierr); ierr = PetscOptionsEList("-snes_ls","Line search used","SNESSetLineSearch",lses,4,"cubic",ver,16,&flg);CHKERRQ(ierr); if (flg) { PetscTruth isbasic,isnonorms,isquad,iscubic; ierr = PetscStrcmp(ver,lses[0],&isbasic);CHKERRQ(ierr); ierr = PetscStrcmp(ver,lses[1],&isnonorms);CHKERRQ(ierr); ierr = PetscStrcmp(ver,lses[2],&isquad);CHKERRQ(ierr); ierr = PetscStrcmp(ver,lses[3],&iscubic);CHKERRQ(ierr); if (isbasic) { ierr = SNESSetLineSearch(snes,SNESNoLineSearch,PETSC_NULL);CHKERRQ(ierr); } else if (isnonorms) { ierr = SNESSetLineSearch(snes,SNESNoLineSearchNoNorms,PETSC_NULL);CHKERRQ(ierr); } else if (isquad) { ierr = SNESSetLineSearch(snes,SNESQuadraticLineSearch,PETSC_NULL);CHKERRQ(ierr); } else if (iscubic) { ierr = SNESSetLineSearch(snes,SNESCubicLineSearch,PETSC_NULL);CHKERRQ(ierr); } else {SETERRQ(PETSC_ERR_ARG_OUTOFRANGE,"Unknown line search");} } ierr = PetscOptionsTail();CHKERRQ(ierr); PetscFunctionReturn(0); } /* -------------------------------------------------------------------------- */ /* SNESCreate_LS - Creates a nonlinear solver context for the SNESLS method, SNES_LS, and sets this as the private data within the generic nonlinear solver context, SNES, that was created within SNESCreate(). Input Parameter: . snes - the SNES context Application Interface Routine: SNESCreate() */ EXTERN_C_BEGIN #undef __FUNCT__ #define __FUNCT__ "SNESCreate_LS" int SNESCreate_LS(SNES snes) { int ierr; SNES_LS *neP; PetscFunctionBegin; snes->setup = SNESSetUp_LS; snes->solve = SNESSolve_LS; snes->destroy = SNESDestroy_LS; snes->converged = SNESConverged_LS; snes->printhelp = SNESPrintHelp_LS; snes->setfromoptions = SNESSetFromOptions_LS; snes->view = SNESView_LS; snes->nwork = 0; ierr = PetscNew(SNES_LS,&neP);CHKERRQ(ierr); PetscLogObjectMemory(snes,sizeof(SNES_LS)); snes->data = (void*)neP; neP->alpha = 1.e-4; neP->maxstep = 1.e8; neP->steptol = 1.e-12; neP->LineSearch = SNESCubicLineSearch; neP->lsP = PETSC_NULL; neP->CheckStep = PETSC_NULL; neP->checkP = PETSC_NULL; ierr = PetscObjectComposeFunctionDynamic((PetscObject)snes,"SNESSetLineSearch_C","SNESSetLineSearch_LS",SNESSetLineSearch_LS);CHKERRQ(ierr); ierr = PetscObjectComposeFunctionDynamic((PetscObject)snes,"SNESSetLineSearchCheck_C","SNESSetLineSearchCheck_LS",SNESSetLineSearchCheck_LS);CHKERRQ(ierr); PetscFunctionReturn(0); } EXTERN_C_END