/*@
TaoLineSearchComputeGradient - Computes the gradient of the objective function
Collective on TaoLineSearch
Input Parameters:
+ ls - the TaoLineSearch context
- x - input vector
Output Parameter:
. g - gradient vector
Notes: TaoComputeGradient() is typically used within line searches
so most users would not generally call this routine themselves.
Level: developer
.seealso: TaoLineSearchComputeObjective(), TaoLineSearchComputeObjectiveAndGradient(), TaoLineSearchSetGradient()
@*/
PetscErrorCode TaoLineSearchComputeGradient(TaoLineSearch ls, Vec x, Vec g)
{
PetscErrorCode ierr;
PetscReal fdummy;
PetscFunctionBegin;
PetscValidHeaderSpecific(ls,TAOLINESEARCH_CLASSID,1);
PetscValidHeaderSpecific(x,VEC_CLASSID,2);
PetscValidHeaderSpecific(g,VEC_CLASSID,3);
PetscCheckSameComm(ls,1,x,2);
PetscCheckSameComm(ls,1,g,3);
if (ls->usetaoroutines) {
ierr = TaoComputeGradient(ls->tao,x,g);CHKERRQ(ierr);
} else {
ierr = PetscLogEventBegin(TaoLineSearch_EvalEvent,ls,0,0,0);CHKERRQ(ierr);
if (!ls->ops->computegradient && !ls->ops->computeobjectiveandgradient) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Line Search does not have gradient functions set");
PetscStackPush("TaoLineSearch user gradient routine");
if (ls->ops->computegradient) {
ierr = (*ls->ops->computegradient)(ls,x,g,ls->userctx_grad);CHKERRQ(ierr);
} else {
ierr = (*ls->ops->computeobjectiveandgradient)(ls,x,&fdummy,g,ls->userctx_funcgrad);CHKERRQ(ierr);
}
PetscStackPop;
ierr = PetscLogEventEnd(TaoLineSearch_EvalEvent,ls,0,0,0);CHKERRQ(ierr);
}
ls->ngeval++;
PetscFunctionReturn(0);
}
/*
For finited difference computations of the Hessian, we use PETSc's SNESComputeJacobianDefault
*/
static PetscErrorCode Fsnes(SNES snes,Vec X,Vec G,void* ctx)
{
PetscErrorCode ierr;
Tao tao = (Tao)ctx;
PetscFunctionBegin;
PetscValidHeaderSpecific(tao,TAO_CLASSID,4);
ierr = TaoComputeGradient(tao,X,G);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/*@C
TaoDefaultComputeHessian - Computes the Hessian using finite differences.
Collective on Tao
Input Parameters:
+ tao - the Tao context
. V - compute Hessian at this point
- dummy - not used
Output Parameters:
+ H - Hessian matrix (not altered in this routine)
- B - newly computed Hessian matrix to use with preconditioner (generally the same as H)
Options Database Key:
. -tao_fd_hessian - activates TaoDefaultComputeHessian()
Level: advanced
Notes:
This routine is slow and expensive, and is not currently optimized
to take advantage of sparsity in the problem. Although
TaoDefaultComputeHessian() is not recommended for general use
in large-scale applications, It can be useful in checking the
correctness of a user-provided Hessian.
.seealso: TaoSetHessianRoutine(), TaoDefaultComputeHessianColor(), SNESComputeJacobianDefault(), TaoSetGradientRoutine(), TaoDefaultComputeGradient()
@*/
PetscErrorCode TaoDefaultComputeHessian(Tao tao,Vec V,Mat H,Mat B,void *dummy)
{
PetscErrorCode ierr;
Vec G;
SNES snes;
DM dm;
PetscFunctionBegin;
ierr = VecDuplicate(V,&G);CHKERRQ(ierr);
ierr = PetscInfo(tao,"TAO Using finite differences w/o coloring to compute Hessian matrix\n");CHKERRQ(ierr);
ierr = TaoComputeGradient(tao,V,G);CHKERRQ(ierr);
ierr = SNESCreate(PetscObjectComm((PetscObject)H),&snes);CHKERRQ(ierr);
ierr = SNESSetFunction(snes,G,Fsnes,tao);CHKERRQ(ierr);
ierr = SNESGetDM(snes,&dm);CHKERRQ(ierr);
ierr = DMShellSetGlobalVector(dm,V);CHKERRQ(ierr);
ierr = SNESSetUp(snes);CHKERRQ(ierr);
if (H) {
PetscInt n,N;
ierr = VecGetSize(V,&N);CHKERRQ(ierr);
ierr = VecGetLocalSize(V,&n);CHKERRQ(ierr);
ierr = MatSetSizes(H,n,n,N,N);CHKERRQ(ierr);
ierr = MatSetUp(H);CHKERRQ(ierr);
}
if (B && B != H) {
PetscInt n,N;
ierr = VecGetSize(V,&N);CHKERRQ(ierr);
ierr = VecGetLocalSize(V,&n);CHKERRQ(ierr);
ierr = MatSetSizes(B,n,n,N,N);CHKERRQ(ierr);
ierr = MatSetUp(B);CHKERRQ(ierr);
}
ierr = SNESComputeJacobianDefault(snes,V,H,B,NULL);CHKERRQ(ierr);
ierr = SNESDestroy(&snes);CHKERRQ(ierr);
ierr = VecDestroy(&G);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/*@C
TaoDefaultComputeHessian - Computes the Hessian using finite differences.
Collective on Tao
Input Parameters:
+ tao - the Tao context
. V - compute Hessian at this point
- dummy - not used
Output Parameters:
+ H - Hessian matrix (not altered in this routine)
- B - newly computed Hessian matrix to use with preconditioner (generally the same as H)
Options Database Key:
+ -tao_fd - Activates TaoDefaultComputeHessian()
- -tao_view_hessian - view the hessian after each evaluation using PETSC_VIEWER_STDOUT_WORLD
Level: advanced
Notes:
This routine is slow and expensive, and is not currently optimized
to take advantage of sparsity in the problem. Although
TaoDefaultComputeHessian() is not recommended for general use
in large-scale applications, It can be useful in checking the
correctness of a user-provided Hessian.
.seealso: TaoSetHessianRoutine(), TaoDefaultComputeHessianColor(), SNESComputeJacobianDefault(), TaoSetGradientRoutine(), TaoDefaultComputeGradient()
@*/
PetscErrorCode TaoDefaultComputeHessian(Tao tao,Vec V,Mat H,Mat B,void *dummy)
{
PetscErrorCode ierr;
MPI_Comm comm;
Vec G;
SNES snes;
PetscFunctionBegin;
PetscValidHeaderSpecific(V,VEC_CLASSID,2);
ierr = VecDuplicate(V,&G);CHKERRQ(ierr);
ierr = PetscInfo(tao,"TAO Using finite differences w/o coloring to compute Hessian matrix\n");CHKERRQ(ierr);
ierr = TaoComputeGradient(tao,V,G);CHKERRQ(ierr);
ierr = PetscObjectGetComm((PetscObject)H,&comm);CHKERRQ(ierr);
ierr = SNESCreate(comm,&snes);CHKERRQ(ierr);
ierr = SNESSetFunction(snes,G,Fsnes,tao);CHKERRQ(ierr);
ierr = SNESComputeJacobianDefault(snes,V,H,B,tao);CHKERRQ(ierr);
ierr = SNESDestroy(&snes);CHKERRQ(ierr);
ierr = VecDestroy(&G);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode TaoSolve_Test(Tao tao)
{
Mat A = tao->hessian,B;
Vec x = tao->solution,g1,g2;
PetscErrorCode ierr;
PetscInt i;
PetscReal nrm,gnorm,hcnorm,fdnorm;
MPI_Comm comm;
Tao_Test *fd = (Tao_Test*)tao->data;
PetscFunctionBegin;
comm = ((PetscObject)tao)->comm;
if (fd->check_gradient) {
ierr = VecDuplicate(x,&g1);CHKERRQ(ierr);
ierr = VecDuplicate(x,&g2);CHKERRQ(ierr);
ierr = PetscPrintf(comm,"Testing hand-coded gradient (hc) against finite difference gradient (fd), if the ratio ||fd - hc|| / ||hc|| is\n");CHKERRQ(ierr);
ierr = PetscPrintf(comm,"0 (1.e-8), the hand-coded gradient is probably correct.\n");CHKERRQ(ierr);
if (!fd->complete_print) {
ierr = PetscPrintf(comm,"Run with -tao_test_display to show difference\n");CHKERRQ(ierr);
ierr = PetscPrintf(comm,"between hand-coded and finite difference gradient.\n");CHKERRQ(ierr);
}
for (i=0; i<3; i++) {
if (i == 1) {ierr = VecSet(x,-1.0);CHKERRQ(ierr);}
else if (i == 2) {ierr = VecSet(x,1.0);CHKERRQ(ierr);}
/* Compute both version of gradient */
ierr = TaoComputeGradient(tao,x,g1);CHKERRQ(ierr);
ierr = TaoDefaultComputeGradient(tao,x,g2,NULL);CHKERRQ(ierr);
if (fd->complete_print) {
MPI_Comm gcomm;
PetscViewer viewer;
ierr = PetscPrintf(comm,"Finite difference gradient\n");CHKERRQ(ierr);
ierr = PetscObjectGetComm((PetscObject)g2,&gcomm);CHKERRQ(ierr);
ierr = PetscViewerASCIIGetStdout(gcomm,&viewer);CHKERRQ(ierr);
ierr = VecView(g2,viewer);CHKERRQ(ierr);
ierr = PetscPrintf(comm,"Hand-coded gradient\n");CHKERRQ(ierr);
ierr = PetscObjectGetComm((PetscObject)g1,&gcomm);CHKERRQ(ierr);
ierr = PetscViewerASCIIGetStdout(gcomm,&viewer);CHKERRQ(ierr);
ierr = VecView(g1,viewer);CHKERRQ(ierr);
ierr = PetscPrintf(comm,"\n");CHKERRQ(ierr);
}
ierr = VecAXPY(g2,-1.0,g1);CHKERRQ(ierr);
ierr = VecNorm(g1,NORM_2,&hcnorm);CHKERRQ(ierr);
ierr = VecNorm(g2,NORM_2,&fdnorm);CHKERRQ(ierr);
if (!hcnorm) hcnorm=1.0e-20;
ierr = PetscPrintf(comm,"ratio ||fd-hc||/||hc|| = %g, difference ||fd-hc|| = %g\n", (double)(fdnorm/hcnorm), (double)fdnorm);CHKERRQ(ierr);
}
ierr = VecDestroy(&g1);CHKERRQ(ierr);
ierr = VecDestroy(&g2);CHKERRQ(ierr);
}
if (fd->check_hessian) {
if (A != tao->hessian_pre) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Cannot test with alternative preconditioner");
ierr = PetscPrintf(comm,"Testing hand-coded Hessian (hc) against finite difference Hessian (fd). If the ratio is\n");CHKERRQ(ierr);
ierr = PetscPrintf(comm,"O (1.e-8), the hand-coded Hessian is probably correct.\n");CHKERRQ(ierr);
if (!fd->complete_print) {
ierr = PetscPrintf(comm,"Run with -tao_test_display to show difference\n");CHKERRQ(ierr);
ierr = PetscPrintf(comm,"of hand-coded and finite difference Hessian.\n");CHKERRQ(ierr);
}
for (i=0;i<3;i++) {
/* compute both versions of Hessian */
ierr = TaoComputeHessian(tao,x,A,A);CHKERRQ(ierr);
if (!i) {ierr = MatConvert(A,MATSAME,MAT_INITIAL_MATRIX,&B);CHKERRQ(ierr);}
ierr = TaoDefaultComputeHessian(tao,x,B,B,tao->user_hessP);CHKERRQ(ierr);
if (fd->complete_print) {
MPI_Comm bcomm;
PetscViewer viewer;
ierr = PetscPrintf(comm,"Finite difference Hessian\n");CHKERRQ(ierr);
ierr = PetscObjectGetComm((PetscObject)B,&bcomm);CHKERRQ(ierr);
ierr = PetscViewerASCIIGetStdout(bcomm,&viewer);CHKERRQ(ierr);
ierr = MatView(B,viewer);CHKERRQ(ierr);
}
/* compare */
ierr = MatAYPX(B,-1.0,A,DIFFERENT_NONZERO_PATTERN);CHKERRQ(ierr);
ierr = MatNorm(B,NORM_FROBENIUS,&nrm);CHKERRQ(ierr);
ierr = MatNorm(A,NORM_FROBENIUS,&gnorm);CHKERRQ(ierr);
if (fd->complete_print) {
MPI_Comm hcomm;
PetscViewer viewer;
ierr = PetscPrintf(comm,"Hand-coded Hessian\n");CHKERRQ(ierr);
ierr = PetscObjectGetComm((PetscObject)B,&hcomm);CHKERRQ(ierr);
ierr = PetscViewerASCIIGetStdout(hcomm,&viewer);CHKERRQ(ierr);
ierr = MatView(A,viewer);CHKERRQ(ierr);
ierr = PetscPrintf(comm,"Hand-coded minus finite difference Hessian\n");CHKERRQ(ierr);
ierr = MatView(B,viewer);CHKERRQ(ierr);
}
if (!gnorm) gnorm = 1.0e-20;
ierr = PetscPrintf(comm,"ratio ||fd-hc||/||hc|| = %g, difference ||fd-hc|| = %g\n",(double)(nrm/gnorm),(double)nrm);CHKERRQ(ierr);
}
ierr = MatDestroy(&B);CHKERRQ(ierr);
}
tao->reason = TAO_CONVERGED_USER;
PetscFunctionReturn(0);
}
static PetscErrorCode TaoSolve_NTR(Tao tao)
{
TAO_NTR *tr = (TAO_NTR *)tao->data;
PC pc;
KSPConvergedReason ksp_reason;
TaoConvergedReason reason;
PetscReal fmin, ftrial, prered, actred, kappa, sigma, beta;
PetscReal tau, tau_1, tau_2, tau_max, tau_min, max_radius;
PetscReal f, gnorm;
PetscReal delta;
PetscReal norm_d;
PetscErrorCode ierr;
PetscInt iter = 0;
PetscInt bfgsUpdates = 0;
PetscInt needH;
PetscInt i_max = 5;
PetscInt j_max = 1;
PetscInt i, j, N, n, its;
PetscFunctionBegin;
if (tao->XL || tao->XU || tao->ops->computebounds) {
ierr = PetscPrintf(((PetscObject)tao)->comm,"WARNING: Variable bounds have been set but will be ignored by ntr algorithm\n");CHKERRQ(ierr);
}
tao->trust = tao->trust0;
/* Modify the radius if it is too large or small */
tao->trust = PetscMax(tao->trust, tr->min_radius);
tao->trust = PetscMin(tao->trust, tr->max_radius);
if (NTR_PC_BFGS == tr->pc_type && !tr->M) {
ierr = VecGetLocalSize(tao->solution,&n);CHKERRQ(ierr);
ierr = VecGetSize(tao->solution,&N);CHKERRQ(ierr);
ierr = MatCreateLMVM(((PetscObject)tao)->comm,n,N,&tr->M);CHKERRQ(ierr);
ierr = MatLMVMAllocateVectors(tr->M,tao->solution);CHKERRQ(ierr);
}
/* Check convergence criteria */
ierr = TaoComputeObjectiveAndGradient(tao, tao->solution, &f, tao->gradient);CHKERRQ(ierr);
ierr = VecNorm(tao->gradient,NORM_2,&gnorm);CHKERRQ(ierr);
if (PetscIsInfOrNanReal(f) || PetscIsInfOrNanReal(gnorm)) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN");
needH = 1;
ierr = TaoMonitor(tao, iter, f, gnorm, 0.0, 1.0, &reason);CHKERRQ(ierr);
if (reason != TAO_CONTINUE_ITERATING) PetscFunctionReturn(0);
/* Create vectors for the limited memory preconditioner */
if ((NTR_PC_BFGS == tr->pc_type) &&
(BFGS_SCALE_BFGS != tr->bfgs_scale_type)) {
if (!tr->Diag) {
ierr = VecDuplicate(tao->solution, &tr->Diag);CHKERRQ(ierr);
}
}
switch(tr->ksp_type) {
case NTR_KSP_NASH:
ierr = KSPSetType(tao->ksp, KSPNASH);CHKERRQ(ierr);
if (tao->ksp->ops->setfromoptions) {
(*tao->ksp->ops->setfromoptions)(tao->ksp);
}
break;
case NTR_KSP_STCG:
ierr = KSPSetType(tao->ksp, KSPSTCG);CHKERRQ(ierr);
if (tao->ksp->ops->setfromoptions) {
(*tao->ksp->ops->setfromoptions)(tao->ksp);
}
break;
default:
ierr = KSPSetType(tao->ksp, KSPGLTR);CHKERRQ(ierr);
if (tao->ksp->ops->setfromoptions) {
(*tao->ksp->ops->setfromoptions)(tao->ksp);
}
break;
}
/* Modify the preconditioner to use the bfgs approximation */
ierr = KSPGetPC(tao->ksp, &pc);CHKERRQ(ierr);
switch(tr->pc_type) {
case NTR_PC_NONE:
ierr = PCSetType(pc, PCNONE);CHKERRQ(ierr);
if (pc->ops->setfromoptions) {
(*pc->ops->setfromoptions)(pc);
}
break;
case NTR_PC_AHESS:
ierr = PCSetType(pc, PCJACOBI);CHKERRQ(ierr);
if (pc->ops->setfromoptions) {
(*pc->ops->setfromoptions)(pc);
}
ierr = PCJacobiSetUseAbs(pc);CHKERRQ(ierr);
break;
case NTR_PC_BFGS:
ierr = PCSetType(pc, PCSHELL);CHKERRQ(ierr);
if (pc->ops->setfromoptions) {
(*pc->ops->setfromoptions)(pc);
}
ierr = PCShellSetName(pc, "bfgs");CHKERRQ(ierr);
ierr = PCShellSetContext(pc, tr->M);CHKERRQ(ierr);
ierr = PCShellSetApply(pc, MatLMVMSolveShell);CHKERRQ(ierr);
break;
default:
/* Use the pc method set by pc_type */
break;
}
/* Initialize trust-region radius */
switch(tr->init_type) {
case NTR_INIT_CONSTANT:
/* Use the initial radius specified */
break;
case NTR_INIT_INTERPOLATION:
/* Use the initial radius specified */
max_radius = 0.0;
for (j = 0; j < j_max; ++j) {
fmin = f;
sigma = 0.0;
if (needH) {
ierr = TaoComputeHessian(tao,tao->solution,tao->hessian,tao->hessian_pre);CHKERRQ(ierr);
needH = 0;
}
for (i = 0; i < i_max; ++i) {
ierr = VecCopy(tao->solution, tr->W);CHKERRQ(ierr);
ierr = VecAXPY(tr->W, -tao->trust/gnorm, tao->gradient);CHKERRQ(ierr);
ierr = TaoComputeObjective(tao, tr->W, &ftrial);CHKERRQ(ierr);
if (PetscIsInfOrNanReal(ftrial)) {
tau = tr->gamma1_i;
}
else {
if (ftrial < fmin) {
fmin = ftrial;
sigma = -tao->trust / gnorm;
}
ierr = MatMult(tao->hessian, tao->gradient, tao->stepdirection);CHKERRQ(ierr);
ierr = VecDot(tao->gradient, tao->stepdirection, &prered);CHKERRQ(ierr);
prered = tao->trust * (gnorm - 0.5 * tao->trust * prered / (gnorm * gnorm));
actred = f - ftrial;
if ((PetscAbsScalar(actred) <= tr->epsilon) &&
(PetscAbsScalar(prered) <= tr->epsilon)) {
kappa = 1.0;
}
else {
kappa = actred / prered;
}
tau_1 = tr->theta_i * gnorm * tao->trust / (tr->theta_i * gnorm * tao->trust + (1.0 - tr->theta_i) * prered - actred);
tau_2 = tr->theta_i * gnorm * tao->trust / (tr->theta_i * gnorm * tao->trust - (1.0 + tr->theta_i) * prered + actred);
tau_min = PetscMin(tau_1, tau_2);
tau_max = PetscMax(tau_1, tau_2);
if (PetscAbsScalar(kappa - 1.0) <= tr->mu1_i) {
/* Great agreement */
max_radius = PetscMax(max_radius, tao->trust);
if (tau_max < 1.0) {
tau = tr->gamma3_i;
}
else if (tau_max > tr->gamma4_i) {
tau = tr->gamma4_i;
}
else {
tau = tau_max;
}
}
else if (PetscAbsScalar(kappa - 1.0) <= tr->mu2_i) {
/* Good agreement */
max_radius = PetscMax(max_radius, tao->trust);
if (tau_max < tr->gamma2_i) {
tau = tr->gamma2_i;
}
else if (tau_max > tr->gamma3_i) {
tau = tr->gamma3_i;
}
else {
tau = tau_max;
}
}
else {
/* Not good agreement */
if (tau_min > 1.0) {
tau = tr->gamma2_i;
}
else if (tau_max < tr->gamma1_i) {
tau = tr->gamma1_i;
}
else if ((tau_min < tr->gamma1_i) && (tau_max >= 1.0)) {
tau = tr->gamma1_i;
}
else if ((tau_1 >= tr->gamma1_i) && (tau_1 < 1.0) &&
((tau_2 < tr->gamma1_i) || (tau_2 >= 1.0))) {
tau = tau_1;
}
else if ((tau_2 >= tr->gamma1_i) && (tau_2 < 1.0) &&
((tau_1 < tr->gamma1_i) || (tau_2 >= 1.0))) {
tau = tau_2;
}
else {
tau = tau_max;
}
}
}
tao->trust = tau * tao->trust;
}
if (fmin < f) {
f = fmin;
ierr = VecAXPY(tao->solution, sigma, tao->gradient);CHKERRQ(ierr);
ierr = TaoComputeGradient(tao,tao->solution, tao->gradient);CHKERRQ(ierr);
ierr = VecNorm(tao->gradient, NORM_2, &gnorm);CHKERRQ(ierr);
if (PetscIsInfOrNanReal(f) || PetscIsInfOrNanReal(gnorm)) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN");
needH = 1;
ierr = TaoMonitor(tao, iter, f, gnorm, 0.0, 1.0, &reason);CHKERRQ(ierr);
if (reason != TAO_CONTINUE_ITERATING) {
PetscFunctionReturn(0);
}
}
}
tao->trust = PetscMax(tao->trust, max_radius);
/* Modify the radius if it is too large or small */
tao->trust = PetscMax(tao->trust, tr->min_radius);
tao->trust = PetscMin(tao->trust, tr->max_radius);
break;
default:
/* Norm of the first direction will initialize radius */
tao->trust = 0.0;
break;
}
/* Set initial scaling for the BFGS preconditioner
This step is done after computing the initial trust-region radius
since the function value may have decreased */
if (NTR_PC_BFGS == tr->pc_type) {
if (f != 0.0) {
delta = 2.0 * PetscAbsScalar(f) / (gnorm*gnorm);
}
else {
delta = 2.0 / (gnorm*gnorm);
}
ierr = MatLMVMSetDelta(tr->M,delta);CHKERRQ(ierr);
}
/* Have not converged; continue with Newton method */
while (reason == TAO_CONTINUE_ITERATING) {
++iter;
tao->ksp_its=0;
/* Compute the Hessian */
if (needH) {
ierr = TaoComputeHessian(tao,tao->solution,tao->hessian,tao->hessian_pre);CHKERRQ(ierr);
needH = 0;
}
if (NTR_PC_BFGS == tr->pc_type) {
if (BFGS_SCALE_AHESS == tr->bfgs_scale_type) {
/* Obtain diagonal for the bfgs preconditioner */
ierr = MatGetDiagonal(tao->hessian, tr->Diag);CHKERRQ(ierr);
ierr = VecAbs(tr->Diag);CHKERRQ(ierr);
ierr = VecReciprocal(tr->Diag);CHKERRQ(ierr);
ierr = MatLMVMSetScale(tr->M,tr->Diag);CHKERRQ(ierr);
}
/* Update the limited memory preconditioner */
ierr = MatLMVMUpdate(tr->M, tao->solution, tao->gradient);CHKERRQ(ierr);
++bfgsUpdates;
}
while (reason == TAO_CONTINUE_ITERATING) {
ierr = KSPSetOperators(tao->ksp, tao->hessian, tao->hessian_pre);CHKERRQ(ierr);
/* Solve the trust region subproblem */
if (NTR_KSP_NASH == tr->ksp_type) {
ierr = KSPNASHSetRadius(tao->ksp,tao->trust);CHKERRQ(ierr);
ierr = KSPSolve(tao->ksp, tao->gradient, tao->stepdirection);CHKERRQ(ierr);
ierr = KSPGetIterationNumber(tao->ksp,&its);CHKERRQ(ierr);
tao->ksp_its+=its;
tao->ksp_tot_its+=its;
ierr = KSPNASHGetNormD(tao->ksp, &norm_d);CHKERRQ(ierr);
} else if (NTR_KSP_STCG == tr->ksp_type) {
ierr = KSPSTCGSetRadius(tao->ksp,tao->trust);CHKERRQ(ierr);
ierr = KSPSolve(tao->ksp, tao->gradient, tao->stepdirection);CHKERRQ(ierr);
ierr = KSPGetIterationNumber(tao->ksp,&its);CHKERRQ(ierr);
tao->ksp_its+=its;
tao->ksp_tot_its+=its;
ierr = KSPSTCGGetNormD(tao->ksp, &norm_d);CHKERRQ(ierr);
} else { /* NTR_KSP_GLTR */
ierr = KSPGLTRSetRadius(tao->ksp,tao->trust);CHKERRQ(ierr);
ierr = KSPSolve(tao->ksp, tao->gradient, tao->stepdirection);CHKERRQ(ierr);
ierr = KSPGetIterationNumber(tao->ksp,&its);CHKERRQ(ierr);
tao->ksp_its+=its;
tao->ksp_tot_its+=its;
ierr = KSPGLTRGetNormD(tao->ksp, &norm_d);CHKERRQ(ierr);
}
if (0.0 == tao->trust) {
/* Radius was uninitialized; use the norm of the direction */
if (norm_d > 0.0) {
tao->trust = norm_d;
/* Modify the radius if it is too large or small */
tao->trust = PetscMax(tao->trust, tr->min_radius);
tao->trust = PetscMin(tao->trust, tr->max_radius);
}
else {
/* The direction was bad; set radius to default value and re-solve
the trust-region subproblem to get a direction */
tao->trust = tao->trust0;
/* Modify the radius if it is too large or small */
tao->trust = PetscMax(tao->trust, tr->min_radius);
tao->trust = PetscMin(tao->trust, tr->max_radius);
if (NTR_KSP_NASH == tr->ksp_type) {
ierr = KSPNASHSetRadius(tao->ksp,tao->trust);CHKERRQ(ierr);
ierr = KSPSolve(tao->ksp, tao->gradient, tao->stepdirection);CHKERRQ(ierr);
ierr = KSPGetIterationNumber(tao->ksp,&its);CHKERRQ(ierr);
tao->ksp_its+=its;
tao->ksp_tot_its+=its;
ierr = KSPNASHGetNormD(tao->ksp, &norm_d);CHKERRQ(ierr);
} else if (NTR_KSP_STCG == tr->ksp_type) {
ierr = KSPSTCGSetRadius(tao->ksp,tao->trust);CHKERRQ(ierr);
ierr = KSPSolve(tao->ksp, tao->gradient, tao->stepdirection);CHKERRQ(ierr);
ierr = KSPGetIterationNumber(tao->ksp,&its);CHKERRQ(ierr);
tao->ksp_its+=its;
tao->ksp_tot_its+=its;
ierr = KSPSTCGGetNormD(tao->ksp, &norm_d);CHKERRQ(ierr);
} else { /* NTR_KSP_GLTR */
ierr = KSPGLTRSetRadius(tao->ksp,tao->trust);CHKERRQ(ierr);
ierr = KSPSolve(tao->ksp, tao->gradient, tao->stepdirection);CHKERRQ(ierr);
ierr = KSPGetIterationNumber(tao->ksp,&its);CHKERRQ(ierr);
tao->ksp_its+=its;
tao->ksp_tot_its+=its;
ierr = KSPGLTRGetNormD(tao->ksp, &norm_d);CHKERRQ(ierr);
}
if (norm_d == 0.0) SETERRQ(PETSC_COMM_SELF,1, "Initial direction zero");
}
}
ierr = VecScale(tao->stepdirection, -1.0);CHKERRQ(ierr);
ierr = KSPGetConvergedReason(tao->ksp, &ksp_reason);CHKERRQ(ierr);
if ((KSP_DIVERGED_INDEFINITE_PC == ksp_reason) &&
(NTR_PC_BFGS == tr->pc_type) && (bfgsUpdates > 1)) {
/* Preconditioner is numerically indefinite; reset the
approximate if using BFGS preconditioning. */
if (f != 0.0) {
delta = 2.0 * PetscAbsScalar(f) / (gnorm*gnorm);
}
else {
delta = 2.0 / (gnorm*gnorm);
}
ierr = MatLMVMSetDelta(tr->M, delta);CHKERRQ(ierr);
ierr = MatLMVMReset(tr->M);CHKERRQ(ierr);
ierr = MatLMVMUpdate(tr->M, tao->solution, tao->gradient);CHKERRQ(ierr);
bfgsUpdates = 1;
}
if (NTR_UPDATE_REDUCTION == tr->update_type) {
/* Get predicted reduction */
if (NTR_KSP_NASH == tr->ksp_type) {
ierr = KSPNASHGetObjFcn(tao->ksp,&prered);CHKERRQ(ierr);
} else if (NTR_KSP_STCG == tr->ksp_type) {
ierr = KSPSTCGGetObjFcn(tao->ksp,&prered);CHKERRQ(ierr);
} else { /* gltr */
ierr = KSPGLTRGetObjFcn(tao->ksp,&prered);CHKERRQ(ierr);
}
if (prered >= 0.0) {
/* The predicted reduction has the wrong sign. This cannot
happen in infinite precision arithmetic. Step should
be rejected! */
tao->trust = tr->alpha1 * PetscMin(tao->trust, norm_d);
}
else {
/* Compute trial step and function value */
ierr = VecCopy(tao->solution,tr->W);CHKERRQ(ierr);
ierr = VecAXPY(tr->W, 1.0, tao->stepdirection);CHKERRQ(ierr);
ierr = TaoComputeObjective(tao, tr->W, &ftrial);CHKERRQ(ierr);
if (PetscIsInfOrNanReal(ftrial)) {
tao->trust = tr->alpha1 * PetscMin(tao->trust, norm_d);
} else {
/* Compute and actual reduction */
actred = f - ftrial;
prered = -prered;
if ((PetscAbsScalar(actred) <= tr->epsilon) &&
(PetscAbsScalar(prered) <= tr->epsilon)) {
kappa = 1.0;
}
else {
kappa = actred / prered;
}
/* Accept or reject the step and update radius */
if (kappa < tr->eta1) {
/* Reject the step */
tao->trust = tr->alpha1 * PetscMin(tao->trust, norm_d);
}
else {
/* Accept the step */
if (kappa < tr->eta2) {
/* Marginal bad step */
tao->trust = tr->alpha2 * PetscMin(tao->trust, norm_d);
}
else if (kappa < tr->eta3) {
/* Reasonable step */
tao->trust = tr->alpha3 * tao->trust;
}
else if (kappa < tr->eta4) {
/* Good step */
tao->trust = PetscMax(tr->alpha4 * norm_d, tao->trust);
}
else {
/* Very good step */
tao->trust = PetscMax(tr->alpha5 * norm_d, tao->trust);
}
break;
}
}
}
}
else {
/* Get predicted reduction */
if (NTR_KSP_NASH == tr->ksp_type) {
ierr = KSPNASHGetObjFcn(tao->ksp,&prered);CHKERRQ(ierr);
} else if (NTR_KSP_STCG == tr->ksp_type) {
ierr = KSPSTCGGetObjFcn(tao->ksp,&prered);CHKERRQ(ierr);
} else { /* gltr */
ierr = KSPGLTRGetObjFcn(tao->ksp,&prered);CHKERRQ(ierr);
}
if (prered >= 0.0) {
/* The predicted reduction has the wrong sign. This cannot
happen in infinite precision arithmetic. Step should
be rejected! */
tao->trust = tr->gamma1 * PetscMin(tao->trust, norm_d);
}
else {
ierr = VecCopy(tao->solution, tr->W);CHKERRQ(ierr);
ierr = VecAXPY(tr->W, 1.0, tao->stepdirection);CHKERRQ(ierr);
ierr = TaoComputeObjective(tao, tr->W, &ftrial);CHKERRQ(ierr);
if (PetscIsInfOrNanReal(ftrial)) {
tao->trust = tr->gamma1 * PetscMin(tao->trust, norm_d);
}
else {
ierr = VecDot(tao->gradient, tao->stepdirection, &beta);CHKERRQ(ierr);
actred = f - ftrial;
prered = -prered;
if ((PetscAbsScalar(actred) <= tr->epsilon) &&
(PetscAbsScalar(prered) <= tr->epsilon)) {
kappa = 1.0;
}
else {
kappa = actred / prered;
}
tau_1 = tr->theta * beta / (tr->theta * beta - (1.0 - tr->theta) * prered + actred);
tau_2 = tr->theta * beta / (tr->theta * beta + (1.0 + tr->theta) * prered - actred);
tau_min = PetscMin(tau_1, tau_2);
tau_max = PetscMax(tau_1, tau_2);
if (kappa >= 1.0 - tr->mu1) {
/* Great agreement; accept step and update radius */
if (tau_max < 1.0) {
tao->trust = PetscMax(tao->trust, tr->gamma3 * norm_d);
}
else if (tau_max > tr->gamma4) {
tao->trust = PetscMax(tao->trust, tr->gamma4 * norm_d);
}
else {
tao->trust = PetscMax(tao->trust, tau_max * norm_d);
}
break;
}
else if (kappa >= 1.0 - tr->mu2) {
/* Good agreement */
if (tau_max < tr->gamma2) {
tao->trust = tr->gamma2 * PetscMin(tao->trust, norm_d);
}
else if (tau_max > tr->gamma3) {
tao->trust = PetscMax(tao->trust, tr->gamma3 * norm_d);
}
else if (tau_max < 1.0) {
tao->trust = tau_max * PetscMin(tao->trust, norm_d);
}
else {
tao->trust = PetscMax(tao->trust, tau_max * norm_d);
}
break;
}
else {
/* Not good agreement */
if (tau_min > 1.0) {
tao->trust = tr->gamma2 * PetscMin(tao->trust, norm_d);
}
else if (tau_max < tr->gamma1) {
tao->trust = tr->gamma1 * PetscMin(tao->trust, norm_d);
}
else if ((tau_min < tr->gamma1) && (tau_max >= 1.0)) {
tao->trust = tr->gamma1 * PetscMin(tao->trust, norm_d);
}
else if ((tau_1 >= tr->gamma1) && (tau_1 < 1.0) &&
((tau_2 < tr->gamma1) || (tau_2 >= 1.0))) {
tao->trust = tau_1 * PetscMin(tao->trust, norm_d);
}
else if ((tau_2 >= tr->gamma1) && (tau_2 < 1.0) &&
((tau_1 < tr->gamma1) || (tau_2 >= 1.0))) {
tao->trust = tau_2 * PetscMin(tao->trust, norm_d);
}
else {
tao->trust = tau_max * PetscMin(tao->trust, norm_d);
}
}
}
}
}
/* The step computed was not good and the radius was decreased.
Monitor the radius to terminate. */
ierr = TaoMonitor(tao, iter, f, gnorm, 0.0, tao->trust, &reason);CHKERRQ(ierr);
}
/* The radius may have been increased; modify if it is too large */
tao->trust = PetscMin(tao->trust, tr->max_radius);
if (reason == TAO_CONTINUE_ITERATING) {
ierr = VecCopy(tr->W, tao->solution);CHKERRQ(ierr);
f = ftrial;
ierr = TaoComputeGradient(tao, tao->solution, tao->gradient);
ierr = VecNorm(tao->gradient, NORM_2, &gnorm);CHKERRQ(ierr);
if (PetscIsInfOrNanReal(f) || PetscIsInfOrNanReal(gnorm)) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN");
needH = 1;
ierr = TaoMonitor(tao, iter, f, gnorm, 0.0, tao->trust, &reason);CHKERRQ(ierr);
}
}
PetscFunctionReturn(0);
}
PetscErrorCode TaoSolve_BNTR(Tao tao)
{
PetscErrorCode ierr;
TAO_BNK *bnk = (TAO_BNK *)tao->data;
KSPConvergedReason ksp_reason;
PetscReal oldTrust, prered, actred, steplen, resnorm;
PetscBool cgTerminate, needH = PETSC_TRUE, stepAccepted, shift = PETSC_FALSE;
PetscInt stepType, nDiff;
PetscFunctionBegin;
/* Initialize the preconditioner, KSP solver and trust radius/line search */
tao->reason = TAO_CONTINUE_ITERATING;
ierr = TaoBNKInitialize(tao, bnk->init_type, &needH);CHKERRQ(ierr);
if (tao->reason != TAO_CONTINUE_ITERATING) PetscFunctionReturn(0);
/* Have not converged; continue with Newton method */
while (tao->reason == TAO_CONTINUE_ITERATING) {
/* Call general purpose update function */
if (tao->ops->update) {
ierr = (*tao->ops->update)(tao, tao->niter, tao->user_update);CHKERRQ(ierr);
}
++tao->niter;
if (needH && bnk->inactive_idx) {
/* Take BNCG steps (if enabled) to trade-off Hessian evaluations for more gradient evaluations */
ierr = TaoBNKTakeCGSteps(tao, &cgTerminate);CHKERRQ(ierr);
if (cgTerminate) {
tao->reason = bnk->bncg->reason;
PetscFunctionReturn(0);
}
/* Compute the hessian and update the BFGS preconditioner at the new iterate */
ierr = (*bnk->computehessian)(tao);CHKERRQ(ierr);
needH = PETSC_FALSE;
}
/* Store current solution before it changes */
bnk->fold = bnk->f;
ierr = VecCopy(tao->solution, bnk->Xold);CHKERRQ(ierr);
ierr = VecCopy(tao->gradient, bnk->Gold);CHKERRQ(ierr);
ierr = VecCopy(bnk->unprojected_gradient, bnk->unprojected_gradient_old);CHKERRQ(ierr);
/* Enter into trust region loops */
stepAccepted = PETSC_FALSE;
while (!stepAccepted && tao->reason == TAO_CONTINUE_ITERATING) {
tao->ksp_its=0;
/* Use the common BNK kernel to compute the Newton step (for inactive variables only) */
ierr = (*bnk->computestep)(tao, shift, &ksp_reason, &stepType);CHKERRQ(ierr);
/* Temporarily accept the step and project it into the bounds */
ierr = VecAXPY(tao->solution, 1.0, tao->stepdirection);CHKERRQ(ierr);
ierr = TaoBoundSolution(tao->solution, tao->XL,tao->XU, 0.0, &nDiff, tao->solution);CHKERRQ(ierr);
/* Check if the projection changed the step direction */
if (nDiff > 0) {
/* Projection changed the step, so we have to recompute the step and
the predicted reduction. Leave the trust radius unchanged. */
ierr = VecCopy(tao->solution, tao->stepdirection);CHKERRQ(ierr);
ierr = VecAXPY(tao->stepdirection, -1.0, bnk->Xold);CHKERRQ(ierr);
ierr = TaoBNKRecomputePred(tao, tao->stepdirection, &prered);CHKERRQ(ierr);
} else {
/* Step did not change, so we can just recover the pre-computed prediction */
ierr = KSPCGGetObjFcn(tao->ksp, &prered);CHKERRQ(ierr);
}
prered = -prered;
/* Compute the actual reduction and update the trust radius */
ierr = TaoComputeObjective(tao, tao->solution, &bnk->f);CHKERRQ(ierr);
if (PetscIsInfOrNanReal(bnk->f)) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN");
actred = bnk->fold - bnk->f;
oldTrust = tao->trust;
ierr = TaoBNKUpdateTrustRadius(tao, prered, actred, bnk->update_type, stepType, &stepAccepted);CHKERRQ(ierr);
if (stepAccepted) {
/* Step is good, evaluate the gradient and flip the need-Hessian switch */
steplen = 1.0;
needH = PETSC_TRUE;
++bnk->newt;
ierr = TaoComputeGradient(tao, tao->solution, bnk->unprojected_gradient);CHKERRQ(ierr);
ierr = TaoBNKEstimateActiveSet(tao, bnk->as_type);CHKERRQ(ierr);
ierr = VecCopy(bnk->unprojected_gradient, tao->gradient);CHKERRQ(ierr);
ierr = VecISSet(tao->gradient, bnk->active_idx, 0.0);CHKERRQ(ierr);
ierr = TaoGradientNorm(tao, tao->gradient, NORM_2, &bnk->gnorm);CHKERRQ(ierr);
} else {
/* Step is bad, revert old solution and re-solve with new radius*/
steplen = 0.0;
needH = PETSC_FALSE;
bnk->f = bnk->fold;
ierr = VecCopy(bnk->Xold, tao->solution);CHKERRQ(ierr);
ierr = VecCopy(bnk->Gold, tao->gradient);CHKERRQ(ierr);
ierr = VecCopy(bnk->unprojected_gradient_old, bnk->unprojected_gradient);CHKERRQ(ierr);
if (oldTrust == tao->trust) {
/* Can't change the radius anymore so just terminate */
tao->reason = TAO_DIVERGED_TR_REDUCTION;
}
}
/* Check for termination */
ierr = VecFischer(tao->solution, bnk->unprojected_gradient, tao->XL, tao->XU, bnk->W);CHKERRQ(ierr);
ierr = VecNorm(bnk->W, NORM_2, &resnorm);CHKERRQ(ierr);
if (PetscIsInfOrNanReal(resnorm)) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN");
ierr = TaoLogConvergenceHistory(tao, bnk->f, resnorm, 0.0, tao->ksp_its);CHKERRQ(ierr);
ierr = TaoMonitor(tao, tao->niter, bnk->f, resnorm, 0.0, steplen);CHKERRQ(ierr);
ierr = (*tao->ops->convergencetest)(tao, tao->cnvP);CHKERRQ(ierr);
}
}
PetscFunctionReturn(0);
}
