static PetscErrorCode MatCopy_LMVM(Mat B, Mat M, MatStructure str)
{
Mat_LMVM *bctx = (Mat_LMVM*)B->data;
Mat_LMVM *mctx;
PetscErrorCode ierr;
PetscInt i;
PetscBool allocatedM;
PetscFunctionBegin;
if (str == DIFFERENT_NONZERO_PATTERN) {
ierr = MatLMVMReset(M, PETSC_TRUE);CHKERRQ(ierr);
ierr = MatLMVMAllocate(M, bctx->Xprev, bctx->Fprev);CHKERRQ(ierr);
} else {
ierr = MatLMVMIsAllocated(M, &allocatedM);CHKERRQ(ierr);
if (!allocatedM) SETERRQ(PetscObjectComm((PetscObject)B), PETSC_ERR_ARG_WRONGSTATE, "Target matrix must be allocated first");
MatCheckSameSize(B, 1, M, 2);
}
mctx = (Mat_LMVM*)M->data;
if (bctx->user_pc) {
ierr = MatLMVMSetJ0PC(M, bctx->J0pc);CHKERRQ(ierr);
} else if (bctx->user_ksp) {
ierr = MatLMVMSetJ0KSP(M, bctx->J0ksp);CHKERRQ(ierr);
} else if (bctx->J0) {
ierr = MatLMVMSetJ0(M, bctx->J0);CHKERRQ(ierr);
} else if (bctx->user_scale) {
if (bctx->J0diag) {
ierr = MatLMVMSetJ0Diag(M, bctx->J0diag);CHKERRQ(ierr);
} else {
ierr = MatLMVMSetJ0Scale(M, bctx->J0scalar);CHKERRQ(ierr);
}
}
mctx->nupdates = bctx->nupdates;
mctx->nrejects = bctx->nrejects;
mctx->k = bctx->k;
for (i=0; i<=bctx->k; ++i) {
ierr = VecCopy(bctx->S[i], mctx->S[i]);CHKERRQ(ierr);
ierr = VecCopy(bctx->Y[i], mctx->Y[i]);CHKERRQ(ierr);
ierr = VecCopy(bctx->Xprev, mctx->Xprev);CHKERRQ(ierr);
ierr = VecCopy(bctx->Fprev, mctx->Fprev);CHKERRQ(ierr);
}
if (bctx->ops->copy) {
ierr = (*bctx->ops->copy)(B, M, str);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
PetscErrorCode MatAllocate_LMVM(Mat B, Vec X, Vec F)
{
Mat_LMVM *lmvm = (Mat_LMVM*)B->data;
PetscErrorCode ierr;
PetscBool same, allocate = PETSC_FALSE;
PetscInt m, n, M, N;
VecType type;
PetscFunctionBegin;
if (lmvm->allocated) {
VecCheckMatCompatible(B, X, 2, F, 3);
ierr = VecGetType(X, &type);CHKERRQ(ierr);
ierr = PetscObjectTypeCompare((PetscObject)lmvm->Xprev, type, &same);CHKERRQ(ierr);
if (!same) {
/* Given X vector has a different type than allocated X-type data structures.
We need to destroy all of this and duplicate again out of the given vector. */
allocate = PETSC_TRUE;
ierr = MatLMVMReset(B, PETSC_TRUE);CHKERRQ(ierr);
}
} else {
allocate = PETSC_TRUE;
}
if (allocate) {
ierr = VecGetLocalSize(X, &n);CHKERRQ(ierr);
ierr = VecGetSize(X, &N);CHKERRQ(ierr);
ierr = VecGetLocalSize(F, &m);CHKERRQ(ierr);
ierr = VecGetSize(F, &M);CHKERRQ(ierr);
ierr = MatSetSizes(B, m, n, M, N);CHKERRQ(ierr);
ierr = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
ierr = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);
ierr = VecDuplicate(X, &lmvm->Xprev);CHKERRQ(ierr);
ierr = VecDuplicate(F, &lmvm->Fprev);CHKERRQ(ierr);
if (lmvm->m > 0) {
ierr = VecDuplicateVecs(lmvm->Xprev, lmvm->m, &lmvm->S);CHKERRQ(ierr);
ierr = VecDuplicateVecs(lmvm->Fprev, lmvm->m, &lmvm->Y);CHKERRQ(ierr);
}
lmvm->allocated = PETSC_TRUE;
B->preallocated = PETSC_TRUE;
B->assembled = PETSC_TRUE;
}
PetscFunctionReturn(0);
}
static PetscErrorCode TaoSolve_OWLQN(Tao tao)
{
TAO_OWLQN *lmP = (TAO_OWLQN *)tao->data;
PetscReal f, fold, gdx, gnorm;
PetscReal step = 1.0;
PetscReal delta;
PetscErrorCode ierr;
PetscInt stepType;
PetscInt iter = 0;
TaoConvergedReason reason = TAO_CONTINUE_ITERATING;
TaoLineSearchConvergedReason ls_status = TAOLINESEARCH_CONTINUE_ITERATING;
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 owlqn algorithm\n");CHKERRQ(ierr);
}
/* Check convergence criteria */
ierr = TaoComputeObjectiveAndGradient(tao, tao->solution, &f, tao->gradient);CHKERRQ(ierr);
ierr = VecCopy(tao->gradient, lmP->GV);CHKERRQ(ierr);
ierr = ComputePseudoGrad_OWLQN(tao->solution,lmP->GV,lmP->lambda);CHKERRQ(ierr);
ierr = VecNorm(lmP->GV,NORM_2,&gnorm);CHKERRQ(ierr);
if (PetscIsInfOrNanReal(f) || PetscIsInfOrNanReal(gnorm)) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf or NaN");
ierr = TaoMonitor(tao, iter, f, gnorm, 0.0, step, &reason);CHKERRQ(ierr);
if (reason != TAO_CONTINUE_ITERATING) PetscFunctionReturn(0);
/* Set initial scaling for the function */
if (f != 0.0) {
delta = 2.0 * PetscAbsScalar(f) / (gnorm*gnorm);
} else {
delta = 2.0 / (gnorm*gnorm);
}
ierr = MatLMVMSetDelta(lmP->M,delta);CHKERRQ(ierr);
/* Set counter for gradient/reset steps */
lmP->bfgs = 0;
lmP->sgrad = 0;
lmP->grad = 0;
/* Have not converged; continue with Newton method */
while (reason == TAO_CONTINUE_ITERATING) {
/* Compute direction */
ierr = MatLMVMUpdate(lmP->M,tao->solution,tao->gradient);CHKERRQ(ierr);
ierr = MatLMVMSolve(lmP->M, lmP->GV, lmP->D);CHKERRQ(ierr);
ierr = ProjDirect_OWLQN(lmP->D,lmP->GV);CHKERRQ(ierr);
++lmP->bfgs;
/* Check for success (descent direction) */
ierr = VecDot(lmP->D, lmP->GV , &gdx);CHKERRQ(ierr);
if ((gdx <= 0.0) || PetscIsInfOrNanReal(gdx)) {
/* Step is not descent or direction produced not a number
We can assert bfgsUpdates > 1 in this case because
the first solve produces the scaled gradient direction,
which is guaranteed to be descent
Use steepest descent direction (scaled) */
++lmP->grad;
if (f != 0.0) {
delta = 2.0 * PetscAbsScalar(f) / (gnorm*gnorm);
} else {
delta = 2.0 / (gnorm*gnorm);
}
ierr = MatLMVMSetDelta(lmP->M, delta);CHKERRQ(ierr);
ierr = MatLMVMReset(lmP->M);CHKERRQ(ierr);
ierr = MatLMVMUpdate(lmP->M, tao->solution, tao->gradient);CHKERRQ(ierr);
ierr = MatLMVMSolve(lmP->M,lmP->GV, lmP->D);CHKERRQ(ierr);
ierr = ProjDirect_OWLQN(lmP->D,lmP->GV);CHKERRQ(ierr);
lmP->bfgs = 1;
++lmP->sgrad;
stepType = OWLQN_SCALED_GRADIENT;
} else {
if (1 == lmP->bfgs) {
/* The first BFGS direction is always the scaled gradient */
++lmP->sgrad;
stepType = OWLQN_SCALED_GRADIENT;
} else {
++lmP->bfgs;
stepType = OWLQN_BFGS;
}
}
ierr = VecScale(lmP->D, -1.0);CHKERRQ(ierr);
/* Perform the linesearch */
fold = f;
ierr = VecCopy(tao->solution, lmP->Xold);CHKERRQ(ierr);
ierr = VecCopy(tao->gradient, lmP->Gold);CHKERRQ(ierr);
ierr = TaoLineSearchApply(tao->linesearch, tao->solution, &f, lmP->GV, lmP->D, &step,&ls_status);CHKERRQ(ierr);
ierr = TaoAddLineSearchCounts(tao);CHKERRQ(ierr);
while (((int)ls_status < 0) && (stepType != OWLQN_GRADIENT)) {
/* Reset factors and use scaled gradient step */
f = fold;
ierr = VecCopy(lmP->Xold, tao->solution);CHKERRQ(ierr);
ierr = VecCopy(lmP->Gold, tao->gradient);CHKERRQ(ierr);
ierr = VecCopy(tao->gradient, lmP->GV);CHKERRQ(ierr);
ierr = ComputePseudoGrad_OWLQN(tao->solution,lmP->GV,lmP->lambda);CHKERRQ(ierr);
switch(stepType) {
case OWLQN_BFGS:
/* Failed to obtain acceptable iterate with BFGS step
Attempt to use the scaled gradient direction */
if (f != 0.0) {
delta = 2.0 * PetscAbsScalar(f) / (gnorm*gnorm);
} else {
delta = 2.0 / (gnorm*gnorm);
}
ierr = MatLMVMSetDelta(lmP->M, delta);CHKERRQ(ierr);
ierr = MatLMVMReset(lmP->M);CHKERRQ(ierr);
ierr = MatLMVMUpdate(lmP->M, tao->solution, tao->gradient);CHKERRQ(ierr);
ierr = MatLMVMSolve(lmP->M, lmP->GV, lmP->D);CHKERRQ(ierr);
ierr = ProjDirect_OWLQN(lmP->D,lmP->GV);CHKERRQ(ierr);
lmP->bfgs = 1;
++lmP->sgrad;
stepType = OWLQN_SCALED_GRADIENT;
break;
case OWLQN_SCALED_GRADIENT:
/* The scaled gradient step did not produce a new iterate;
attempt to use the gradient direction.
Need to make sure we are not using a different diagonal scaling */
ierr = MatLMVMSetDelta(lmP->M, 1.0);CHKERRQ(ierr);
ierr = MatLMVMReset(lmP->M);CHKERRQ(ierr);
ierr = MatLMVMUpdate(lmP->M, tao->solution, tao->gradient);CHKERRQ(ierr);
ierr = MatLMVMSolve(lmP->M, lmP->GV, lmP->D);CHKERRQ(ierr);
ierr = ProjDirect_OWLQN(lmP->D,lmP->GV);CHKERRQ(ierr);
lmP->bfgs = 1;
++lmP->grad;
stepType = OWLQN_GRADIENT;
break;
}
ierr = VecScale(lmP->D, -1.0);CHKERRQ(ierr);
/* Perform the linesearch */
ierr = TaoLineSearchApply(tao->linesearch, tao->solution, &f, lmP->GV, lmP->D, &step, &ls_status);CHKERRQ(ierr);
ierr = TaoAddLineSearchCounts(tao);CHKERRQ(ierr);
}
if ((int)ls_status < 0) {
/* Failed to find an improving point*/
f = fold;
ierr = VecCopy(lmP->Xold, tao->solution);CHKERRQ(ierr);
ierr = VecCopy(lmP->Gold, tao->gradient);CHKERRQ(ierr);
ierr = VecCopy(tao->gradient, lmP->GV);CHKERRQ(ierr);
step = 0.0;
} else {
/* a little hack here, because that gv is used to store g */
ierr = VecCopy(lmP->GV, tao->gradient);CHKERRQ(ierr);
}
ierr = ComputePseudoGrad_OWLQN(tao->solution,lmP->GV,lmP->lambda);CHKERRQ(ierr);
/* Check for termination */
ierr = VecNorm(lmP->GV,NORM_2,&gnorm);CHKERRQ(ierr);
iter++;
ierr = TaoMonitor(tao,iter,f,gnorm,0.0,step,&reason);CHKERRQ(ierr);
if ((int)ls_status < 0) break;
}
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);
}
extern PetscErrorCode MatLMVMUpdate(Mat M, Vec x, Vec g)
{
MatLMVMCtx *ctx;
PetscReal rhotemp, rhotol;
PetscReal y0temp, s0temp;
PetscReal yDy, yDs, sDs;
PetscReal sigmanew, denom;
PetscErrorCode ierr;
PetscInt i;
PetscBool same;
PetscReal yy_sum=0.0, ys_sum=0.0, ss_sum=0.0;
PetscFunctionBegin;
PetscValidHeaderSpecific(x,VEC_CLASSID,2);
PetscValidHeaderSpecific(g,VEC_CLASSID,3);
ierr = PetscObjectTypeCompare((PetscObject)M,MATSHELL,&same);CHKERRQ(ierr);
if (!same) SETERRQ(PETSC_COMM_SELF,1,"Matrix M is not type MatLMVM");
ierr = MatShellGetContext(M,(void**)&ctx);CHKERRQ(ierr);
if (!ctx->allocated) {
ierr = MatLMVMAllocateVectors(M, x); CHKERRQ(ierr);
}
if (0 == ctx->iter) {
ierr = MatLMVMReset(M);CHKERRQ(ierr);
} else {
ierr = VecAYPX(ctx->Gprev,-1.0,g);CHKERRQ(ierr);
ierr = VecAYPX(ctx->Xprev,-1.0,x);CHKERRQ(ierr);
ierr = VecDot(ctx->Gprev,ctx->Xprev,&rhotemp);CHKERRQ(ierr);
ierr = VecDot(ctx->Gprev,ctx->Gprev,&y0temp);CHKERRQ(ierr);
rhotol = ctx->eps * y0temp;
if (rhotemp > rhotol) {
++ctx->nupdates;
ctx->lmnow = PetscMin(ctx->lmnow+1, ctx->lm);
ierr=PetscObjectDereference((PetscObject)ctx->S[ctx->lm]);CHKERRQ(ierr);
ierr=PetscObjectDereference((PetscObject)ctx->Y[ctx->lm]);CHKERRQ(ierr);
for (i = ctx->lm-1; i >= 0; --i) {
ctx->S[i+1] = ctx->S[i];
ctx->Y[i+1] = ctx->Y[i];
ctx->rho[i+1] = ctx->rho[i];
}
ctx->S[0] = ctx->Xprev;
ctx->Y[0] = ctx->Gprev;
PetscObjectReference((PetscObject)ctx->S[0]);
PetscObjectReference((PetscObject)ctx->Y[0]);
ctx->rho[0] = 1.0 / rhotemp;
/* Compute the scaling */
switch(ctx->scaleType) {
case MatLMVM_Scale_None:
break;
case MatLMVM_Scale_Scalar:
/* Compute s^T s */
ierr = VecDot(ctx->Xprev,ctx->Xprev,&s0temp);CHKERRQ(ierr);
/* Scalar is positive; safeguards are not required. */
/* Save information for scalar scaling */
ctx->yy_history[(ctx->nupdates - 1) % ctx->scalar_history] = y0temp;
ctx->ys_history[(ctx->nupdates - 1) % ctx->scalar_history] = rhotemp;
ctx->ss_history[(ctx->nupdates - 1) % ctx->scalar_history] = s0temp;
/* Compute summations for scalar scaling */
yy_sum = 0; /* No safeguard required; y^T y > 0 */
ys_sum = 0; /* No safeguard required; y^T s > 0 */
ss_sum = 0; /* No safeguard required; s^T s > 0 */
for (i = 0; i < PetscMin(ctx->nupdates, ctx->scalar_history); ++i) {
yy_sum += ctx->yy_history[i];
ys_sum += ctx->ys_history[i];
ss_sum += ctx->ss_history[i];
}
if (0.0 == ctx->s_alpha) {
/* Safeguard ys_sum */
if (0.0 == ys_sum) {
ys_sum = TAO_ZERO_SAFEGUARD;
}
sigmanew = ss_sum / ys_sum;
} else if (1.0 == ctx->s_alpha) {
/* Safeguard yy_sum */
if (0.0 == yy_sum) {
yy_sum = TAO_ZERO_SAFEGUARD;
}
sigmanew = ys_sum / yy_sum;
} else {
denom = 2*ctx->s_alpha*yy_sum;
/* Safeguard denom */
if (0.0 == denom) {
denom = TAO_ZERO_SAFEGUARD;
}
sigmanew = ((2*ctx->s_alpha-1)*ys_sum + PetscSqrtScalar((2*ctx->s_alpha-1)*(2*ctx->s_alpha-1)*ys_sum*ys_sum - 4*(ctx->s_alpha)*(ctx->s_alpha-1)*yy_sum*ss_sum)) / denom;
}
switch(ctx->limitType) {
case MatLMVM_Limit_Average:
if (1.0 == ctx->mu) {
ctx->sigma = sigmanew;
} else if (ctx->mu) {
ctx->sigma = ctx->mu * sigmanew + (1.0 - ctx->mu) * ctx->sigma;
}
break;
case MatLMVM_Limit_Relative:
if (ctx->mu) {
ctx->sigma = TaoMid((1.0 - ctx->mu) * ctx->sigma, sigmanew, (1.0 + ctx->mu) * ctx->sigma);
}
break;
case MatLMVM_Limit_Absolute:
if (ctx->nu) {
ctx->sigma = TaoMid(ctx->sigma - ctx->nu, sigmanew, ctx->sigma + ctx->nu);
}
break;
default:
ctx->sigma = sigmanew;
break;
}
break;
case MatLMVM_Scale_Broyden:
/* Original version */
/* Combine DFP and BFGS */
/* This code appears to be numerically unstable. We use the */
/* original version because this was used to generate all of */
/* the data and because it may be the least unstable of the */
/* bunch. */
/* P = Q = inv(D); */
ierr = VecCopy(ctx->D,ctx->P);CHKERRQ(ierr);
ierr = VecReciprocal(ctx->P);CHKERRQ(ierr);
ierr = VecCopy(ctx->P,ctx->Q);CHKERRQ(ierr);
/* V = y*y */
ierr = VecPointwiseMult(ctx->V,ctx->Gprev,ctx->Gprev);CHKERRQ(ierr);
/* W = inv(D)*s */
ierr = VecPointwiseMult(ctx->W,ctx->Xprev,ctx->P);CHKERRQ(ierr);
ierr = VecDot(ctx->W,ctx->Xprev,&sDs);CHKERRQ(ierr);
/* Safeguard rhotemp and sDs */
if (0.0 == rhotemp) {
rhotemp = TAO_ZERO_SAFEGUARD;
}
if (0.0 == sDs) {
sDs = TAO_ZERO_SAFEGUARD;
}
if (1.0 != ctx->phi) {
/* BFGS portion of the update */
/* U = (inv(D)*s)*(inv(D)*s) */
ierr = VecPointwiseMult(ctx->U,ctx->W,ctx->W);CHKERRQ(ierr);
/* Assemble */
ierr = VecAXPY(ctx->P,1.0/rhotemp,ctx->V);CHKERRQ(ierr);
ierr = VecAXPY(ctx->P,-1.0/sDs,ctx->U);CHKERRQ(ierr);
}
if (0.0 != ctx->phi) {
/* DFP portion of the update */
/* U = inv(D)*s*y */
ierr = VecPointwiseMult(ctx->U, ctx->W, ctx->Gprev);CHKERRQ(ierr);
/* Assemble */
ierr = VecAXPY(ctx->Q,1.0/rhotemp + sDs/(rhotemp*rhotemp), ctx->V);CHKERRQ(ierr);
ierr = VecAXPY(ctx->Q,-2.0/rhotemp,ctx->U);CHKERRQ(ierr);
}
if (0.0 == ctx->phi) {
ierr = VecCopy(ctx->P,ctx->U);CHKERRQ(ierr);
} else if (1.0 == ctx->phi) {
ierr = VecCopy(ctx->Q,ctx->U);CHKERRQ(ierr);
} else {
/* Broyden update U=(1-phi)*P + phi*Q */
ierr = VecCopy(ctx->Q,ctx->U);CHKERRQ(ierr);
ierr = VecAXPBY(ctx->U,1.0-ctx->phi, ctx->phi, ctx->P);CHKERRQ(ierr);
}
/* Obtain inverse and ensure positive definite */
ierr = VecReciprocal(ctx->U);CHKERRQ(ierr);
ierr = VecAbs(ctx->U);CHKERRQ(ierr);
switch(ctx->rScaleType) {
case MatLMVM_Rescale_None:
break;
case MatLMVM_Rescale_Scalar:
case MatLMVM_Rescale_GL:
if (ctx->rScaleType == MatLMVM_Rescale_GL) {
/* Gilbert and Lemarachal use the old diagonal */
ierr = VecCopy(ctx->D,ctx->P);CHKERRQ(ierr);
} else {
/* The default version uses the current diagonal */
ierr = VecCopy(ctx->U,ctx->P);CHKERRQ(ierr);
}
/* Compute s^T s */
ierr = VecDot(ctx->Xprev,ctx->Xprev,&s0temp);CHKERRQ(ierr);
/* Save information for special cases of scalar rescaling */
ctx->yy_rhistory[(ctx->nupdates - 1) % ctx->rescale_history] = y0temp;
ctx->ys_rhistory[(ctx->nupdates - 1) % ctx->rescale_history] = rhotemp;
ctx->ss_rhistory[(ctx->nupdates - 1) % ctx->rescale_history] = s0temp;
if (0.5 == ctx->r_beta) {
if (1 == PetscMin(ctx->nupdates, ctx->rescale_history)) {
ierr = VecPointwiseMult(ctx->V,ctx->Y[0],ctx->P);CHKERRQ(ierr);
ierr = VecDot(ctx->V,ctx->Y[0],&yy_sum);CHKERRQ(ierr);
ierr = VecPointwiseDivide(ctx->W,ctx->S[0],ctx->P);CHKERRQ(ierr);
ierr = VecDot(ctx->W,ctx->S[0],&ss_sum);CHKERRQ(ierr);
ys_sum = ctx->ys_rhistory[0];
} else {
ierr = VecCopy(ctx->P,ctx->Q);CHKERRQ(ierr);
ierr = VecReciprocal(ctx->Q);CHKERRQ(ierr);
/* Compute summations for scalar scaling */
yy_sum = 0; /* No safeguard required */
ys_sum = 0; /* No safeguard required */
ss_sum = 0; /* No safeguard required */
for (i = 0; i < PetscMin(ctx->nupdates, ctx->rescale_history); ++i) {
ierr = VecPointwiseMult(ctx->V,ctx->Y[i],ctx->P);CHKERRQ(ierr);
ierr = VecDot(ctx->V,ctx->Y[i],&yDy);CHKERRQ(ierr);
yy_sum += yDy;
ierr = VecPointwiseMult(ctx->W,ctx->S[i],ctx->Q);CHKERRQ(ierr);
ierr = VecDot(ctx->W,ctx->S[i],&sDs);CHKERRQ(ierr);
ss_sum += sDs;
ys_sum += ctx->ys_rhistory[i];
}
}
} else if (0.0 == ctx->r_beta) {
if (1 == PetscMin(ctx->nupdates, ctx->rescale_history)) {
/* Compute summations for scalar scaling */
ierr = VecPointwiseDivide(ctx->W,ctx->S[0],ctx->P);CHKERRQ(ierr);
ierr = VecDot(ctx->W, ctx->Y[0], &ys_sum);CHKERRQ(ierr);
ierr = VecDot(ctx->W, ctx->W, &ss_sum);CHKERRQ(ierr);
yy_sum += ctx->yy_rhistory[0];
} else {
ierr = VecCopy(ctx->Q, ctx->P);CHKERRQ(ierr);
ierr = VecReciprocal(ctx->Q);CHKERRQ(ierr);
/* Compute summations for scalar scaling */
yy_sum = 0; /* No safeguard required */
ys_sum = 0; /* No safeguard required */
ss_sum = 0; /* No safeguard required */
for (i = 0; i < PetscMin(ctx->nupdates, ctx->rescale_history); ++i) {
ierr = VecPointwiseMult(ctx->W, ctx->S[i], ctx->Q);CHKERRQ(ierr);
ierr = VecDot(ctx->W, ctx->Y[i], &yDs);CHKERRQ(ierr);
ys_sum += yDs;
ierr = VecDot(ctx->W, ctx->W, &sDs);CHKERRQ(ierr);
ss_sum += sDs;
yy_sum += ctx->yy_rhistory[i];
}
}
} else if (1.0 == ctx->r_beta) {
/* Compute summations for scalar scaling */
yy_sum = 0; /* No safeguard required */
ys_sum = 0; /* No safeguard required */
ss_sum = 0; /* No safeguard required */
for (i = 0; i < PetscMin(ctx->nupdates, ctx->rescale_history); ++i) {
ierr = VecPointwiseMult(ctx->V, ctx->Y[i], ctx->P);CHKERRQ(ierr);
ierr = VecDot(ctx->V, ctx->S[i], &yDs);CHKERRQ(ierr);
ys_sum += yDs;
ierr = VecDot(ctx->V, ctx->V, &yDy);CHKERRQ(ierr);
yy_sum += yDy;
ss_sum += ctx->ss_rhistory[i];
}
} else {
ierr = VecCopy(ctx->Q, ctx->P);CHKERRQ(ierr);
ierr = VecPow(ctx->P, ctx->r_beta);CHKERRQ(ierr);
ierr = VecPointwiseDivide(ctx->Q, ctx->P, ctx->Q);CHKERRQ(ierr);
/* Compute summations for scalar scaling */
yy_sum = 0; /* No safeguard required */
ys_sum = 0; /* No safeguard required */
ss_sum = 0; /* No safeguard required */
for (i = 0; i < PetscMin(ctx->nupdates, ctx->rescale_history); ++i) {
ierr = VecPointwiseMult(ctx->V, ctx->P, ctx->Y[i]);CHKERRQ(ierr);
ierr = VecPointwiseMult(ctx->W, ctx->Q, ctx->S[i]);CHKERRQ(ierr);
ierr = VecDot(ctx->V, ctx->V, &yDy);CHKERRQ(ierr);
ierr = VecDot(ctx->V, ctx->W, &yDs);CHKERRQ(ierr);
ierr = VecDot(ctx->W, ctx->W, &sDs);CHKERRQ(ierr);
yy_sum += yDy;
ys_sum += yDs;
ss_sum += sDs;
}
}
if (0.0 == ctx->r_alpha) {
/* Safeguard ys_sum */
if (0.0 == ys_sum) {
ys_sum = TAO_ZERO_SAFEGUARD;
}
sigmanew = ss_sum / ys_sum;
} else if (1.0 == ctx->r_alpha) {
/* Safeguard yy_sum */
if (0.0 == yy_sum) {
ys_sum = TAO_ZERO_SAFEGUARD;
}
sigmanew = ys_sum / yy_sum;
} else {
denom = 2*ctx->r_alpha*yy_sum;
/* Safeguard denom */
if (0.0 == denom) {
denom = TAO_ZERO_SAFEGUARD;
}
sigmanew = ((2*ctx->r_alpha-1)*ys_sum + PetscSqrtScalar((2*ctx->r_alpha-1)*(2*ctx->r_alpha-1)*ys_sum*ys_sum - 4*ctx->r_alpha*(ctx->r_alpha-1)*yy_sum*ss_sum)) / denom;
}
/* If Q has small values, then Q^(r_beta - 1) */
/* can have very large values. Hence, ys_sum */
/* and ss_sum can be infinity. In this case, */
/* sigmanew can either be not-a-number or infinity. */
if (PetscIsInfOrNanReal(sigmanew)) {
/* sigmanew is not-a-number; skip rescaling */
} else if (!sigmanew) {
/* sigmanew is zero; this is a bad case; skip rescaling */
} else {
/* sigmanew is positive */
ierr = VecScale(ctx->U, sigmanew);CHKERRQ(ierr);
}
break;
}
/* Modify for previous information */
switch(ctx->limitType) {
case MatLMVM_Limit_Average:
if (1.0 == ctx->mu) {
ierr = VecCopy(ctx->D, ctx->U);CHKERRQ(ierr);
} else if (ctx->mu) {
ierr = VecAXPBY(ctx->D,ctx->mu, 1.0-ctx->mu,ctx->U);CHKERRQ(ierr);
}
break;
case MatLMVM_Limit_Relative:
if (ctx->mu) {
/* P = (1-mu) * D */
ierr = VecAXPBY(ctx->P, 1.0-ctx->mu, 0.0, ctx->D);CHKERRQ(ierr);
/* Q = (1+mu) * D */
ierr = VecAXPBY(ctx->Q, 1.0+ctx->mu, 0.0, ctx->D);CHKERRQ(ierr);
ierr = VecMedian(ctx->P, ctx->U, ctx->Q, ctx->D);CHKERRQ(ierr);
}
break;
case MatLMVM_Limit_Absolute:
if (ctx->nu) {
ierr = VecCopy(ctx->P, ctx->D);CHKERRQ(ierr);
ierr = VecShift(ctx->P, -ctx->nu);CHKERRQ(ierr);
ierr = VecCopy(ctx->D, ctx->Q);CHKERRQ(ierr);
ierr = VecShift(ctx->Q, ctx->nu);CHKERRQ(ierr);
ierr = VecMedian(ctx->P, ctx->U, ctx->Q, ctx->P);CHKERRQ(ierr);
}
break;
default:
ierr = VecCopy(ctx->U, ctx->D);CHKERRQ(ierr);
break;
}
break;
}
ierr = PetscObjectDereference((PetscObject)ctx->Xprev);CHKERRQ(ierr);
ierr = PetscObjectDereference((PetscObject)ctx->Gprev);CHKERRQ(ierr);
ctx->Xprev = ctx->S[ctx->lm];
ctx->Gprev = ctx->Y[ctx->lm];
ierr = PetscObjectReference((PetscObject)ctx->S[ctx->lm]);CHKERRQ(ierr);
ierr = PetscObjectReference((PetscObject)ctx->Y[ctx->lm]);CHKERRQ(ierr);
} else {
++ctx->nrejects;
}
}
++ctx->iter;
ierr = VecCopy(x, ctx->Xprev);CHKERRQ(ierr);
ierr = VecCopy(g, ctx->Gprev);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
static PetscErrorCode TaoSolve_BLMVM(Tao tao)
{
PetscErrorCode ierr;
TAO_BLMVM *blmP = (TAO_BLMVM *)tao->data;
TaoConvergedReason reason = TAO_CONTINUE_ITERATING;
TaoLineSearchConvergedReason ls_status = TAOLINESEARCH_CONTINUE_ITERATING;
PetscReal f, fold, gdx, gnorm;
PetscReal stepsize = 1.0,delta;
PetscFunctionBegin;
/* Project initial point onto bounds */
ierr = TaoComputeVariableBounds(tao);CHKERRQ(ierr);
ierr = VecMedian(tao->XL,tao->solution,tao->XU,tao->solution);CHKERRQ(ierr);
ierr = TaoLineSearchSetVariableBounds(tao->linesearch,tao->XL,tao->XU);CHKERRQ(ierr);
/* Check convergence criteria */
ierr = TaoComputeObjectiveAndGradient(tao, tao->solution,&f,blmP->unprojected_gradient);CHKERRQ(ierr);
ierr = VecBoundGradientProjection(blmP->unprojected_gradient,tao->solution, tao->XL,tao->XU,tao->gradient);CHKERRQ(ierr);
ierr = TaoGradientNorm(tao, tao->gradient,NORM_2,&gnorm);CHKERRQ(ierr);
if (PetscIsInfOrNanReal(f) || PetscIsInfOrNanReal(gnorm)) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf pr NaN");
ierr = TaoMonitor(tao, tao->niter, f, gnorm, 0.0, stepsize, &reason);CHKERRQ(ierr);
if (reason != TAO_CONTINUE_ITERATING) PetscFunctionReturn(0);
/* Set initial scaling for the function */
if (f != 0.0) {
delta = 2.0*PetscAbsScalar(f) / (gnorm*gnorm);
} else {
delta = 2.0 / (gnorm*gnorm);
}
ierr = MatLMVMSetDelta(blmP->M,delta);CHKERRQ(ierr);
/* Set counter for gradient/reset steps */
blmP->grad = 0;
blmP->reset = 0;
/* Have not converged; continue with Newton method */
while (reason == TAO_CONTINUE_ITERATING) {
/* Compute direction */
ierr = MatLMVMUpdate(blmP->M, tao->solution, tao->gradient);CHKERRQ(ierr);
ierr = MatLMVMSolve(blmP->M, blmP->unprojected_gradient, tao->stepdirection);CHKERRQ(ierr);
ierr = VecBoundGradientProjection(tao->stepdirection,tao->solution,tao->XL,tao->XU,tao->gradient);CHKERRQ(ierr);
/* Check for success (descent direction) */
ierr = VecDot(blmP->unprojected_gradient, tao->gradient, &gdx);CHKERRQ(ierr);
if (gdx <= 0) {
/* Step is not descent or solve was not successful
Use steepest descent direction (scaled) */
++blmP->grad;
if (f != 0.0) {
delta = 2.0*PetscAbsScalar(f) / (gnorm*gnorm);
} else {
delta = 2.0 / (gnorm*gnorm);
}
ierr = MatLMVMSetDelta(blmP->M,delta);CHKERRQ(ierr);
ierr = MatLMVMReset(blmP->M);CHKERRQ(ierr);
ierr = MatLMVMUpdate(blmP->M, tao->solution, blmP->unprojected_gradient);CHKERRQ(ierr);
ierr = MatLMVMSolve(blmP->M,blmP->unprojected_gradient, tao->stepdirection);CHKERRQ(ierr);
}
ierr = VecScale(tao->stepdirection,-1.0);CHKERRQ(ierr);
/* Perform the linesearch */
fold = f;
ierr = VecCopy(tao->solution, blmP->Xold);CHKERRQ(ierr);
ierr = VecCopy(blmP->unprojected_gradient, blmP->Gold);CHKERRQ(ierr);
ierr = TaoLineSearchSetInitialStepLength(tao->linesearch,1.0);CHKERRQ(ierr);
ierr = TaoLineSearchApply(tao->linesearch, tao->solution, &f, blmP->unprojected_gradient, tao->stepdirection, &stepsize, &ls_status);CHKERRQ(ierr);
ierr = TaoAddLineSearchCounts(tao);CHKERRQ(ierr);
if (ls_status != TAOLINESEARCH_SUCCESS && ls_status != TAOLINESEARCH_SUCCESS_USER) {
/* Linesearch failed
Reset factors and use scaled (projected) gradient step */
++blmP->reset;
f = fold;
ierr = VecCopy(blmP->Xold, tao->solution);CHKERRQ(ierr);
ierr = VecCopy(blmP->Gold, blmP->unprojected_gradient);CHKERRQ(ierr);
if (f != 0.0) {
delta = 2.0* PetscAbsScalar(f) / (gnorm*gnorm);
} else {
delta = 2.0/ (gnorm*gnorm);
}
ierr = MatLMVMSetDelta(blmP->M,delta);CHKERRQ(ierr);
ierr = MatLMVMReset(blmP->M);CHKERRQ(ierr);
ierr = MatLMVMUpdate(blmP->M, tao->solution, blmP->unprojected_gradient);CHKERRQ(ierr);
ierr = MatLMVMSolve(blmP->M, blmP->unprojected_gradient, tao->stepdirection);CHKERRQ(ierr);
ierr = VecScale(tao->stepdirection, -1.0);CHKERRQ(ierr);
/* This may be incorrect; linesearch has values fo stepmax and stepmin
that should be reset. */
ierr = TaoLineSearchSetInitialStepLength(tao->linesearch,1.0);CHKERRQ(ierr);
ierr = TaoLineSearchApply(tao->linesearch,tao->solution,&f, blmP->unprojected_gradient, tao->stepdirection, &stepsize, &ls_status);CHKERRQ(ierr);
ierr = TaoAddLineSearchCounts(tao);CHKERRQ(ierr);
if (ls_status != TAOLINESEARCH_SUCCESS && ls_status != TAOLINESEARCH_SUCCESS_USER) {
tao->reason = TAO_DIVERGED_LS_FAILURE;
break;
}
}
/* Check for converged */
ierr = VecBoundGradientProjection(blmP->unprojected_gradient, tao->solution, tao->XL, tao->XU, tao->gradient);CHKERRQ(ierr);
ierr = TaoGradientNorm(tao, tao->gradient, NORM_2, &gnorm);CHKERRQ(ierr);
if (PetscIsInfOrNanReal(f) || PetscIsInfOrNanReal(gnorm)) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Not-a-Number");
tao->niter++;
ierr = TaoMonitor(tao, tao->niter, f, gnorm, 0.0, stepsize, &reason);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}