static PetscErrorCode SNESLineSearchApply_BT(SNESLineSearch linesearch)
{
PetscBool changed_y,changed_w;
PetscErrorCode ierr;
Vec X,F,Y,W,G;
SNES snes;
PetscReal fnorm, xnorm, ynorm, gnorm;
PetscReal lambda,lambdatemp,lambdaprev,minlambda,maxstep,initslope,alpha,stol;
PetscReal t1,t2,a,b,d;
PetscReal f;
PetscReal g,gprev;
PetscBool domainerror;
PetscViewer monitor;
PetscInt max_its,count;
SNESLineSearch_BT *bt;
Mat jac;
PetscErrorCode (*objective)(SNES,Vec,PetscReal*,void*);
PetscFunctionBegin;
ierr = SNESLineSearchGetVecs(linesearch, &X, &F, &Y, &W, &G);CHKERRQ(ierr);
ierr = SNESLineSearchGetNorms(linesearch, &xnorm, &fnorm, &ynorm);CHKERRQ(ierr);
ierr = SNESLineSearchGetLambda(linesearch, &lambda);CHKERRQ(ierr);
ierr = SNESLineSearchGetSNES(linesearch, &snes);CHKERRQ(ierr);
ierr = SNESLineSearchGetMonitor(linesearch, &monitor);CHKERRQ(ierr);
ierr = SNESLineSearchGetTolerances(linesearch,&minlambda,&maxstep,NULL,NULL,NULL,&max_its);CHKERRQ(ierr);
ierr = SNESGetTolerances(snes,NULL,NULL,&stol,NULL,NULL);CHKERRQ(ierr);
ierr = SNESGetObjective(snes,&objective,NULL);CHKERRQ(ierr);
bt = (SNESLineSearch_BT*)linesearch->data;
alpha = bt->alpha;
ierr = SNESGetJacobian(snes, &jac, NULL, NULL, NULL);CHKERRQ(ierr);
if (!jac && !objective) SETERRQ(PetscObjectComm((PetscObject)linesearch), PETSC_ERR_USER, "SNESLineSearchBT requires a Jacobian matrix");
/* precheck */
ierr = SNESLineSearchPreCheck(linesearch,X,Y,&changed_y);CHKERRQ(ierr);
ierr = SNESLineSearchSetSuccess(linesearch, PETSC_TRUE);CHKERRQ(ierr);
ierr = VecNormBegin(Y, NORM_2, &ynorm);CHKERRQ(ierr);
ierr = VecNormBegin(X, NORM_2, &xnorm);CHKERRQ(ierr);
ierr = VecNormEnd(Y, NORM_2, &ynorm);CHKERRQ(ierr);
ierr = VecNormEnd(X, NORM_2, &xnorm);CHKERRQ(ierr);
if (ynorm == 0.0) {
if (monitor) {
ierr = PetscViewerASCIIAddTab(monitor,((PetscObject)linesearch)->tablevel);CHKERRQ(ierr);
ierr = PetscViewerASCIIPrintf(monitor," Line search: Initial direction and size is 0\n");CHKERRQ(ierr);
ierr = PetscViewerASCIISubtractTab(monitor,((PetscObject)linesearch)->tablevel);CHKERRQ(ierr);
}
ierr = VecCopy(X,W);CHKERRQ(ierr);
ierr = VecCopy(F,G);CHKERRQ(ierr);
ierr = SNESLineSearchSetSuccess(linesearch, PETSC_FALSE);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
if (ynorm > maxstep) { /* Step too big, so scale back */
if (monitor) {
ierr = PetscViewerASCIIAddTab(monitor,((PetscObject)linesearch)->tablevel);CHKERRQ(ierr);
ierr = PetscViewerASCIIPrintf(monitor," Line search: Scaling step by %14.12e old ynorm %14.12e\n", (double)(maxstep/ynorm),(double)ynorm);CHKERRQ(ierr);
ierr = PetscViewerASCIISubtractTab(monitor,((PetscObject)linesearch)->tablevel);CHKERRQ(ierr);
}
ierr = VecScale(Y,maxstep/(ynorm));CHKERRQ(ierr);
ynorm = maxstep;
}
/* if the SNES has an objective set, use that instead of the function value */
if (objective) {
ierr = SNESComputeObjective(snes,X,&f);CHKERRQ(ierr);
} else {
f = fnorm*fnorm;
}
/* compute the initial slope */
if (objective) {
/* slope comes from the function (assumed to be the gradient of the objective */
ierr = VecDotRealPart(Y,F,&initslope);CHKERRQ(ierr);
} else {
/* slope comes from the normal equations */
ierr = MatMult(jac,Y,W);CHKERRQ(ierr);
ierr = VecDotRealPart(F,W,&initslope);CHKERRQ(ierr);
if (initslope > 0.0) initslope = -initslope;
if (initslope == 0.0) initslope = -1.0;
}
ierr = VecWAXPY(W,-lambda,Y,X);CHKERRQ(ierr);
if (linesearch->ops->viproject) {
ierr = (*linesearch->ops->viproject)(snes, W);CHKERRQ(ierr);
}
if (snes->nfuncs >= snes->max_funcs) {
ierr = PetscInfo(snes,"Exceeded maximum function evaluations, while checking full step length!\n");CHKERRQ(ierr);
snes->reason = SNES_DIVERGED_FUNCTION_COUNT;
ierr = SNESLineSearchSetSuccess(linesearch, PETSC_FALSE);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
if (objective) {
ierr = SNESComputeObjective(snes,W,&g);CHKERRQ(ierr);
} else {
ierr = (*linesearch->ops->snesfunc)(snes,W,G);CHKERRQ(ierr);
ierr = SNESGetFunctionDomainError(snes, &domainerror);CHKERRQ(ierr);
if (domainerror) {
ierr = SNESLineSearchSetSuccess(linesearch, PETSC_FALSE);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
if (linesearch->ops->vinorm) {
gnorm = fnorm;
ierr = (*linesearch->ops->vinorm)(snes, G, W, &gnorm);CHKERRQ(ierr);
} else {
ierr = VecNorm(G,NORM_2,&gnorm);CHKERRQ(ierr);
}
g = PetscSqr(gnorm);
}
if (PetscIsInfOrNanReal(g)) {
ierr = SNESLineSearchSetSuccess(linesearch, PETSC_FALSE);CHKERRQ(ierr);
ierr = PetscInfo(monitor,"Aborted due to Nan or Inf in function evaluation\n");CHKERRQ(ierr);
PetscFunctionReturn(0);
}
if (!objective) {
ierr = PetscInfo2(snes,"Initial fnorm %14.12e gnorm %14.12e\n", (double)fnorm, (double)gnorm);CHKERRQ(ierr);
}
if (.5*g <= .5*f + lambda*alpha*initslope) { /* Sufficient reduction or step tolerance convergence */
if (monitor) {
ierr = PetscViewerASCIIAddTab(monitor,((PetscObject)linesearch)->tablevel);CHKERRQ(ierr);
if (!objective) {
ierr = PetscViewerASCIIPrintf(monitor," Line search: Using full step: fnorm %14.12e gnorm %14.12e\n", (double)fnorm, (double)gnorm);CHKERRQ(ierr);
} else {
ierr = PetscViewerASCIIPrintf(monitor," Line search: Using full step: obj0 %14.12e obj %14.12e\n", (double)f, (double)g);CHKERRQ(ierr);
}
ierr = PetscViewerASCIISubtractTab(monitor,((PetscObject)linesearch)->tablevel);CHKERRQ(ierr);
}
} else {
/* Since the full step didn't work and the step is tiny, quit */
if (stol*xnorm > ynorm) {
ierr = SNESLineSearchSetSuccess(linesearch, PETSC_FALSE);CHKERRQ(ierr);
ierr = PetscInfo2(monitor,"Aborted due to ynorm < stol*xnorm (%14.12e < %14.12e) and inadequate full step.\n",ynorm,stol*xnorm);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/* Fit points with quadratic */
lambdatemp = -initslope/(g - f - 2.0*lambda*initslope);
lambdaprev = lambda;
gprev = g;
if (lambdatemp > .5*lambda) lambdatemp = .5*lambda;
if (lambdatemp <= .1*lambda) lambda = .1*lambda;
else lambda = lambdatemp;
ierr = VecWAXPY(W,-lambda,Y,X);CHKERRQ(ierr);
if (linesearch->ops->viproject) {
ierr = (*linesearch->ops->viproject)(snes, W);CHKERRQ(ierr);
}
if (snes->nfuncs >= snes->max_funcs) {
ierr = PetscInfo1(snes,"Exceeded maximum function evaluations, while attempting quadratic backtracking! %D \n",snes->nfuncs);CHKERRQ(ierr);
snes->reason = SNES_DIVERGED_FUNCTION_COUNT;
ierr = SNESLineSearchSetSuccess(linesearch, PETSC_FALSE);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
if (objective) {
ierr = SNESComputeObjective(snes,W,&g);CHKERRQ(ierr);
} else {
ierr = (*linesearch->ops->snesfunc)(snes,W,G);CHKERRQ(ierr);
ierr = SNESGetFunctionDomainError(snes, &domainerror);CHKERRQ(ierr);
if (domainerror) PetscFunctionReturn(0);
if (linesearch->ops->vinorm) {
gnorm = fnorm;
ierr = (*linesearch->ops->vinorm)(snes, G, W, &gnorm);CHKERRQ(ierr);
} else {
ierr = VecNorm(G,NORM_2,&gnorm);CHKERRQ(ierr);
g = gnorm*gnorm;
}
}
if (PetscIsInfOrNanReal(g)) {
ierr = SNESLineSearchSetSuccess(linesearch, PETSC_FALSE);CHKERRQ(ierr);
ierr = PetscInfo(monitor,"Aborted due to Nan or Inf in function evaluation\n");CHKERRQ(ierr);
PetscFunctionReturn(0);
}
if (monitor) {
ierr = PetscViewerASCIIAddTab(monitor,((PetscObject)linesearch)->tablevel);CHKERRQ(ierr);
if (!objective) {
ierr = PetscViewerASCIIPrintf(monitor," Line search: gnorm after quadratic fit %14.12e\n",(double)gnorm);CHKERRQ(ierr);
} else {
ierr = PetscViewerASCIIPrintf(monitor," Line search: obj after quadratic fit %14.12e\n",(double)g);CHKERRQ(ierr);
}
ierr = PetscViewerASCIISubtractTab(monitor,((PetscObject)linesearch)->tablevel);CHKERRQ(ierr);
}
if (.5*g < .5*f + lambda*alpha*initslope) { /* sufficient reduction */
if (monitor) {
ierr = PetscViewerASCIIAddTab(monitor,((PetscObject)linesearch)->tablevel);CHKERRQ(ierr);
ierr = PetscViewerASCIIPrintf(monitor," Line search: Quadratically determined step, lambda=%18.16e\n",(double)lambda);CHKERRQ(ierr);
ierr = PetscViewerASCIISubtractTab(monitor,((PetscObject)linesearch)->tablevel);CHKERRQ(ierr);
}
} else {
/* Fit points with cubic */
for (count = 0; count < max_its; count++) {
if (lambda <= minlambda) {
if (monitor) {
ierr = PetscViewerASCIIAddTab(monitor,((PetscObject)linesearch)->tablevel);CHKERRQ(ierr);
ierr = PetscViewerASCIIPrintf(monitor," Line search: unable to find good step length! After %D tries \n",count);CHKERRQ(ierr);
if (!objective) {
ierr = PetscViewerASCIIPrintf(monitor,
" Line search: fnorm=%18.16e, gnorm=%18.16e, ynorm=%18.16e, minlambda=%18.16e, lambda=%18.16e, initial slope=%18.16e\n",
(double)fnorm, (double)gnorm, (double)ynorm, (double)minlambda, (double)lambda, (double)initslope);CHKERRQ(ierr);
} else {
ierr = PetscViewerASCIIPrintf(monitor,
" Line search: obj(0)=%18.16e, obj=%18.16e, ynorm=%18.16e, minlambda=%18.16e, lambda=%18.16e, initial slope=%18.16e\n",
(double)f, (double)g, (double)ynorm, (double)minlambda, (double)lambda, (double)initslope);CHKERRQ(ierr);
}
ierr = PetscViewerASCIISubtractTab(monitor,((PetscObject)linesearch)->tablevel);CHKERRQ(ierr);
}
ierr = SNESLineSearchSetSuccess(linesearch, PETSC_FALSE);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
if (linesearch->order == SNES_LINESEARCH_ORDER_CUBIC) {
t1 = .5*(g - f) - lambda*initslope;
t2 = .5*(gprev - f) - 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 + PetscSqrtReal(d))/(3.0*a);
} else if (linesearch->order == SNES_LINESEARCH_ORDER_QUADRATIC) {
lambdatemp = -initslope/(g - f - 2.0*initslope);
} else SETERRQ(PetscObjectComm((PetscObject)linesearch), PETSC_ERR_SUP, "unsupported line search order for type bt");
lambdaprev = lambda;
gprev = g;
if (lambdatemp > .5*lambda) lambdatemp = .5*lambda;
if (lambdatemp <= .1*lambda) lambda = .1*lambda;
else lambda = lambdatemp;
ierr = VecWAXPY(W,-lambda,Y,X);CHKERRQ(ierr);
if (linesearch->ops->viproject) {
ierr = (*linesearch->ops->viproject)(snes,W);CHKERRQ(ierr);
}
if (snes->nfuncs >= snes->max_funcs) {
ierr = PetscInfo1(snes,"Exceeded maximum function evaluations, while looking for good step length! %D \n",count);CHKERRQ(ierr);
if (!objective) {
ierr = PetscInfo5(snes,"fnorm=%18.16e, gnorm=%18.16e, ynorm=%18.16e, lambda=%18.16e, initial slope=%18.16e\n",
(double)fnorm,(double)gnorm,(double)ynorm,(double)lambda,(double)initslope);CHKERRQ(ierr);
}
ierr = SNESLineSearchSetSuccess(linesearch, PETSC_FALSE);CHKERRQ(ierr);
snes->reason = SNES_DIVERGED_FUNCTION_COUNT;
PetscFunctionReturn(0);
}
if (objective) {
ierr = SNESComputeObjective(snes,W,&g);CHKERRQ(ierr);
} else {
ierr = (*linesearch->ops->snesfunc)(snes,W,G);CHKERRQ(ierr);
ierr = SNESGetFunctionDomainError(snes, &domainerror);CHKERRQ(ierr);
if (domainerror) {
ierr = SNESLineSearchSetSuccess(linesearch, PETSC_FALSE);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
if (linesearch->ops->vinorm) {
gnorm = fnorm;
ierr = (*linesearch->ops->vinorm)(snes, G, W, &gnorm);CHKERRQ(ierr);
} else {
ierr = VecNorm(G,NORM_2,&gnorm);CHKERRQ(ierr);
g = gnorm*gnorm;
}
}
if (PetscIsInfOrNanReal(gnorm)) {
ierr = SNESLineSearchSetSuccess(linesearch, PETSC_FALSE);CHKERRQ(ierr);
ierr = PetscInfo(monitor,"Aborted due to Nan or Inf in function evaluation\n");CHKERRQ(ierr);
PetscFunctionReturn(0);
}
if (.5*g < .5*f + lambda*alpha*initslope) { /* is reduction enough? */
if (monitor) {
ierr = PetscViewerASCIIAddTab(monitor,((PetscObject)linesearch)->tablevel);CHKERRQ(ierr);
if (!objective) {
if (linesearch->order == SNES_LINESEARCH_ORDER_CUBIC) {
ierr = PetscViewerASCIIPrintf(monitor," Line search: Cubically determined step, current gnorm %14.12e lambda=%18.16e\n",(double)gnorm,(double)lambda);CHKERRQ(ierr);
} else {
ierr = PetscViewerASCIIPrintf(monitor," Line search: Quadratically determined step, current gnorm %14.12e lambda=%18.16e\n",(double)gnorm,(double)lambda);CHKERRQ(ierr);
}
ierr = PetscViewerASCIISubtractTab(monitor,((PetscObject)linesearch)->tablevel);CHKERRQ(ierr);
} else {
if (linesearch->order == SNES_LINESEARCH_ORDER_CUBIC) {
ierr = PetscViewerASCIIPrintf(monitor," Line search: Cubically determined step, obj %14.12e lambda=%18.16e\n",(double)g,(double)lambda);CHKERRQ(ierr);
} else {
ierr = PetscViewerASCIIPrintf(monitor," Line search: Quadratically determined step, obj %14.12e lambda=%18.16e\n",(double)g,(double)lambda);CHKERRQ(ierr);
}
ierr = PetscViewerASCIISubtractTab(monitor,((PetscObject)linesearch)->tablevel);CHKERRQ(ierr);
}
}
break;
} else if (monitor) {
ierr = PetscViewerASCIIAddTab(monitor,((PetscObject)linesearch)->tablevel);CHKERRQ(ierr);
if (!objective) {
if (linesearch->order == SNES_LINESEARCH_ORDER_CUBIC) {
ierr = PetscViewerASCIIPrintf(monitor," Line search: Cubic step no good, shrinking lambda, current gnorm %12.12e lambda=%18.16e\n",(double)gnorm,(double)lambda);CHKERRQ(ierr);
} else {
ierr = PetscViewerASCIIPrintf(monitor," Line search: Quadratic step no good, shrinking lambda, current gnorm %12.12e lambda=%18.16e\n",(double)gnorm,(double)lambda);CHKERRQ(ierr);
}
ierr = PetscViewerASCIISubtractTab(monitor,((PetscObject)linesearch)->tablevel);CHKERRQ(ierr);
} else {
if (linesearch->order == SNES_LINESEARCH_ORDER_CUBIC) {
ierr = PetscViewerASCIIPrintf(monitor," Line search: Cubic step no good, shrinking lambda, obj %12.12e lambda=%18.16e\n",(double)g,(double)lambda);CHKERRQ(ierr);
} else {
ierr = PetscViewerASCIIPrintf(monitor," Line search: Quadratic step no good, shrinking lambda, obj %12.12e lambda=%18.16e\n",(double)g,(double)lambda);CHKERRQ(ierr);
}
ierr = PetscViewerASCIISubtractTab(monitor,((PetscObject)linesearch)->tablevel);CHKERRQ(ierr);
}
}
}
}
}
/* postcheck */
ierr = SNESLineSearchPostCheck(linesearch,X,Y,W,&changed_y,&changed_w);CHKERRQ(ierr);
if (changed_y) {
ierr = VecWAXPY(W,-lambda,Y,X);CHKERRQ(ierr);
if (linesearch->ops->viproject) {
ierr = (*linesearch->ops->viproject)(snes, W);CHKERRQ(ierr);
}
}
if (changed_y || changed_w || objective) { /* recompute the function norm if the step has changed or the objective isn't the norm */
ierr = (*linesearch->ops->snesfunc)(snes,W,G);CHKERRQ(ierr);
ierr = SNESGetFunctionDomainError(snes, &domainerror);CHKERRQ(ierr);
if (domainerror) {
ierr = SNESLineSearchSetSuccess(linesearch, PETSC_FALSE);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
if (linesearch->ops->vinorm) {
gnorm = fnorm;
ierr = (*linesearch->ops->vinorm)(snes, G, W, &gnorm);CHKERRQ(ierr);
} else {
ierr = VecNorm(G,NORM_2,&gnorm);CHKERRQ(ierr);
}
ierr = VecNorm(Y,NORM_2,&ynorm);CHKERRQ(ierr);
if (PetscIsInfOrNanReal(gnorm)) {
ierr = SNESLineSearchSetSuccess(linesearch, PETSC_FALSE);CHKERRQ(ierr);
ierr = PetscInfo(monitor,"Aborted due to Nan or Inf in function evaluation\n");CHKERRQ(ierr);
PetscFunctionReturn(0);
}
}
/* copy the solution over */
ierr = VecCopy(W, X);CHKERRQ(ierr);
ierr = VecCopy(G, F);CHKERRQ(ierr);
ierr = VecNorm(X, NORM_2, &xnorm);CHKERRQ(ierr);
ierr = SNESLineSearchSetLambda(linesearch, lambda);CHKERRQ(ierr);
ierr = SNESLineSearchSetNorms(linesearch, xnorm, gnorm, ynorm);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/*@C
SNESObjectiveComputeFunctionDefaultFD - Computes the gradient of a user provided objective
Collective on SNES
Input Parameter:
+ snes - the SNES context
. X - the state vector
- ctx - the (ignored) function context
Output Parameter:
. F - the function value
Options Database Key:
+ -snes_fd_function_eps - The differencing parameter
- -snes_fd_function - Compute function from user provided objective with finite difference
Notes:
SNESObjectiveComputeFunctionDefaultFD is similar in character to SNESComputeJacobianDefault.
Therefore, it should be used for debugging purposes only. Using it in conjunction with
SNESComputeJacobianDefault is excessively costly and produces a Jacobian that is quite
noisy. This is often necessary, but should be done with a grain of salt, even when debugging
small problems.
Note that this uses quadratic interpolation of the objective to form each value in the function.
Level: advanced
.keywords: SNES, objective, debugging, finite differences, function
.seealso: SNESSetFunction(), SNESComputeObjective(), SNESComputeJacobianDefault()
@*/
PetscErrorCode SNESObjectiveComputeFunctionDefaultFD(SNES snes,Vec X,Vec F,void *ctx)
{
Vec Xh;
PetscErrorCode ierr;
PetscInt i,N,start,end;
PetscReal ob,ob1,ob2,ob3,fob,dx,eps=1e-6;
PetscScalar fv,xv;
PetscFunctionBegin;
ierr = VecDuplicate(X,&Xh);CHKERRQ(ierr);
ierr = PetscOptionsReal("-snes_fd_function_eps","Tolerance for nonzero entries in fd function","None",eps,&eps,NULL);CHKERRQ(ierr);
ierr = VecSet(F,0.);CHKERRQ(ierr);
ierr = VecNorm(X,NORM_2,&fob);CHKERRQ(ierr);
ierr = VecGetSize(X,&N);CHKERRQ(ierr);
ierr = VecGetOwnershipRange(X,&start,&end);CHKERRQ(ierr);
ierr = SNESComputeObjective(snes,X,&ob);CHKERRQ(ierr);
if (fob > 0.) dx =1e-6*fob;
else dx = 1e-6;
for (i=0; i<N; i++) {
/* compute the 1st value */
ierr = VecCopy(X,Xh);CHKERRQ(ierr);
if (i>= start && i<end) {
xv = dx;
ierr = VecSetValues(Xh,1,&i,&xv,ADD_VALUES);CHKERRQ(ierr);
}
ierr = VecAssemblyBegin(Xh);CHKERRQ(ierr);
ierr = VecAssemblyEnd(Xh);CHKERRQ(ierr);
ierr = SNESComputeObjective(snes,Xh,&ob1);CHKERRQ(ierr);
/* compute the 2nd value */
ierr = VecCopy(X,Xh);CHKERRQ(ierr);
if (i>= start && i<end) {
xv = 2.*dx;
ierr = VecSetValues(Xh,1,&i,&xv,ADD_VALUES);CHKERRQ(ierr);
}
ierr = VecAssemblyBegin(Xh);CHKERRQ(ierr);
ierr = VecAssemblyEnd(Xh);CHKERRQ(ierr);
ierr = SNESComputeObjective(snes,Xh,&ob2);CHKERRQ(ierr);
/* compute the 3rd value */
ierr = VecCopy(X,Xh);CHKERRQ(ierr);
if (i>= start && i<end) {
xv = -dx;
ierr = VecSetValues(Xh,1,&i,&xv,ADD_VALUES);CHKERRQ(ierr);
}
ierr = VecAssemblyBegin(Xh);CHKERRQ(ierr);
ierr = VecAssemblyEnd(Xh);CHKERRQ(ierr);
ierr = SNESComputeObjective(snes,Xh,&ob3);CHKERRQ(ierr);
if (i >= start && i<end) {
/* set this entry to be the gradient of the objective */
fv = (-ob2 + 6.*ob1 - 3.*ob -2.*ob3) / (6.*dx);
if (PetscAbsScalar(fv) > eps) {
ierr = VecSetValues(F,1,&i,&fv,INSERT_VALUES);CHKERRQ(ierr);
} else {
fv = 0.;
ierr = VecSetValues(F,1,&i,&fv,INSERT_VALUES);CHKERRQ(ierr);
}
}
}
ierr = VecDestroy(&Xh);CHKERRQ(ierr);
ierr = VecAssemblyBegin(F);CHKERRQ(ierr);
ierr = VecAssemblyEnd(F);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
static PetscErrorCode SNESLineSearchApply_L2(SNESLineSearch linesearch)
{
PetscBool changed_y, changed_w;
PetscErrorCode ierr;
Vec X;
Vec F;
Vec Y;
Vec W;
SNES snes;
PetscReal gnorm;
PetscReal ynorm;
PetscReal xnorm;
PetscReal steptol, maxstep, rtol, atol, ltol;
PetscViewer monitor;
PetscBool domainerror;
PetscReal lambda, lambda_old, lambda_mid, lambda_update, delLambda;
PetscReal fnrm, fnrm_old, fnrm_mid;
PetscReal delFnrm, delFnrm_old, del2Fnrm;
PetscInt i, max_its;
PetscErrorCode (*objective)(SNES,Vec,PetscReal*,void*);
PetscFunctionBegin;
ierr = SNESLineSearchGetVecs(linesearch, &X, &F, &Y, &W, NULL);CHKERRQ(ierr);
ierr = SNESLineSearchGetNorms(linesearch, &xnorm, &gnorm, &ynorm);CHKERRQ(ierr);
ierr = SNESLineSearchGetLambda(linesearch, &lambda);CHKERRQ(ierr);
ierr = SNESLineSearchGetSNES(linesearch, &snes);CHKERRQ(ierr);
ierr = SNESLineSearchSetSuccess(linesearch, PETSC_TRUE);CHKERRQ(ierr);
ierr = SNESLineSearchGetTolerances(linesearch, &steptol, &maxstep, &rtol, &atol, <ol, &max_its);CHKERRQ(ierr);
ierr = SNESLineSearchGetMonitor(linesearch, &monitor);CHKERRQ(ierr);
ierr = SNESGetObjective(snes,&objective,NULL);CHKERRQ(ierr);
/* precheck */
ierr = SNESLineSearchPreCheck(linesearch,X,Y,&changed_y);CHKERRQ(ierr);
lambda_old = 0.0;
if (!objective) {
fnrm_old = gnorm*gnorm;
} else {
ierr = SNESComputeObjective(snes,X,&fnrm_old);CHKERRQ(ierr);
}
lambda_mid = 0.5*(lambda + lambda_old);
for (i = 0; i < max_its; i++) {
/* compute the norm at the midpoint */
ierr = VecCopy(X, W);CHKERRQ(ierr);
ierr = VecAXPY(W, -lambda_mid, Y);CHKERRQ(ierr);
if (linesearch->ops->viproject) {
ierr = (*linesearch->ops->viproject)(snes, W);CHKERRQ(ierr);
}
if (!objective) {
ierr = (*linesearch->ops->snesfunc)(snes, W, F);CHKERRQ(ierr);
if (linesearch->ops->vinorm) {
fnrm_mid = gnorm;
ierr = (*linesearch->ops->vinorm)(snes, F, W, &fnrm_mid);CHKERRQ(ierr);
} else {
ierr = VecNorm(F,NORM_2,&fnrm_mid);CHKERRQ(ierr);
}
/* compute the norm at lambda */
ierr = VecCopy(X, W);CHKERRQ(ierr);
ierr = VecAXPY(W, -lambda, Y);CHKERRQ(ierr);
if (linesearch->ops->viproject) {
ierr = (*linesearch->ops->viproject)(snes, W);CHKERRQ(ierr);
}
ierr = (*linesearch->ops->snesfunc)(snes, W, F);CHKERRQ(ierr);
if (linesearch->ops->vinorm) {
fnrm = gnorm;
ierr = (*linesearch->ops->vinorm)(snes, F, W, &fnrm);CHKERRQ(ierr);
} else {
ierr = VecNorm(F,NORM_2,&fnrm);CHKERRQ(ierr);
}
fnrm_mid = fnrm_mid*fnrm_mid;
fnrm = fnrm*fnrm;
} else {
/* compute the objective at the midpoint */
ierr = VecCopy(X, W);CHKERRQ(ierr);
ierr = VecAXPY(W, -lambda_mid, Y);CHKERRQ(ierr);
ierr = SNESComputeObjective(snes,W,&fnrm_mid);CHKERRQ(ierr);
/* compute the objective at the midpoint */
ierr = VecCopy(X, W);CHKERRQ(ierr);
ierr = VecAXPY(W, -lambda, Y);CHKERRQ(ierr);
ierr = SNESComputeObjective(snes,W,&fnrm);CHKERRQ(ierr);
}
/* this gives us the derivatives at the endpoints -- compute them from here
a = x - a0
p_0(x) = (x / dA - 1)(2x / dA - 1)
p_1(x) = 4(x / dA)(1 - x / dA)
p_2(x) = (x / dA)(2x / dA - 1)
dp_0[0] / dx = 3 / dA
dp_1[0] / dx = -4 / dA
dp_2[0] / dx = 1 / dA
dp_0[dA] / dx = -1 / dA
dp_1[dA] / dx = 4 / dA
dp_2[dA] / dx = -3 / dA
d^2p_0[0] / dx^2 = 4 / dA^2
d^2p_1[0] / dx^2 = -8 / dA^2
d^2p_2[0] / dx^2 = 4 / dA^2
*/
delLambda = lambda - lambda_old;
delFnrm = (3.*fnrm - 4.*fnrm_mid + 1.*fnrm_old) / delLambda;
delFnrm_old = (-3.*fnrm_old + 4.*fnrm_mid -1.*fnrm) / delLambda;
del2Fnrm = (delFnrm - delFnrm_old) / delLambda;
if (monitor) {
ierr = PetscViewerASCIIAddTab(monitor,((PetscObject)linesearch)->tablevel);CHKERRQ(ierr);
if (!objective) {
ierr = 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));CHKERRQ(ierr);
} else {
ierr = 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);CHKERRQ(ierr);
}
ierr = PetscViewerASCIISubtractTab(monitor,((PetscObject)linesearch)->tablevel);CHKERRQ(ierr);
}
/* compute the search direction -- always go downhill */
if (del2Fnrm > 0.) lambda_update = lambda - delFnrm / del2Fnrm;
else lambda_update = lambda + delFnrm / del2Fnrm;
if (lambda_update < steptol) lambda_update = 0.5*(lambda + lambda_old);
if (PetscIsInfOrNanScalar(lambda_update)) break;
if (lambda_update > maxstep) break;
/* compute the new state of the line search */
lambda_old = lambda;
lambda = lambda_update;
fnrm_old = fnrm;
lambda_mid = 0.5*(lambda + lambda_old);
}
/* construct the solution */
ierr = VecCopy(X, W);CHKERRQ(ierr);
ierr = VecAXPY(W, -lambda, Y);CHKERRQ(ierr);
if (linesearch->ops->viproject) {
ierr = (*linesearch->ops->viproject)(snes, W);CHKERRQ(ierr);
}
/* postcheck */
ierr = SNESLineSearchPostCheck(linesearch,X,Y,W,&changed_y,&changed_w);CHKERRQ(ierr);
if (changed_y) {
ierr = VecAXPY(X, -lambda, Y);CHKERRQ(ierr);
if (linesearch->ops->viproject) {
ierr = (*linesearch->ops->viproject)(snes, X);CHKERRQ(ierr);
}
} else {
ierr = VecCopy(W, X);CHKERRQ(ierr);
}
ierr = (*linesearch->ops->snesfunc)(snes,X,F);CHKERRQ(ierr);
ierr = SNESGetFunctionDomainError(snes, &domainerror);CHKERRQ(ierr);
if (domainerror) {
ierr = SNESLineSearchSetSuccess(linesearch, PETSC_FALSE);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
ierr = SNESLineSearchSetLambda(linesearch, lambda);CHKERRQ(ierr);
ierr = SNESLineSearchComputeNorms(linesearch);CHKERRQ(ierr);
ierr = SNESLineSearchGetNorms(linesearch, &xnorm, &gnorm, &ynorm);CHKERRQ(ierr);
if (monitor) {
ierr = PetscViewerASCIIAddTab(monitor,((PetscObject)linesearch)->tablevel);CHKERRQ(ierr);
ierr = PetscViewerASCIIPrintf(monitor," Line search terminated: lambda = %g, fnorms = %g\n", (double)lambda, (double)gnorm);CHKERRQ(ierr);
ierr = PetscViewerASCIISubtractTab(monitor,((PetscObject)linesearch)->tablevel);CHKERRQ(ierr);
}
if (lambda <= steptol) {
ierr = SNESLineSearchSetSuccess(linesearch, PETSC_FALSE);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}