PETSC_EXTERN void PETSC_STDCALL taolinesearchsetobjectiveandgradientroutine_(TaoLineSearch *ls, void (PETSC_STDCALL *func)(TaoLineSearch*, Vec *, PetscReal *, Vec *, void *, PetscErrorCode *), void *ctx, PetscErrorCode *ierr)
{
CHKFORTRANNULLOBJECT(ctx);
PetscObjectAllocateFortranPointers(*ls,NFUNCS);
if (!func) {
*ierr = TaoLineSearchSetObjectiveAndGradientRoutine(*ls,0,ctx);
} else {
((PetscObject)*ls)->fortran_func_pointers[OBJGRAD] = (PetscVoidFunction)func;
*ierr = TaoLineSearchSetObjectiveAndGradientRoutine(*ls, ourtaolinesearchobjectiveandgradientroutine,ctx);
}
}
PETSC_EXTERN PetscErrorCode TaoCreate_GPCG(Tao tao)
{
TAO_GPCG *gpcg;
PetscErrorCode ierr;
PetscFunctionBegin;
tao->ops->setup = TaoSetup_GPCG;
tao->ops->solve = TaoSolve_GPCG;
tao->ops->view = TaoView_GPCG;
tao->ops->setfromoptions = TaoSetFromOptions_GPCG;
tao->ops->destroy = TaoDestroy_GPCG;
tao->ops->computedual = TaoComputeDual_GPCG;
ierr = PetscNewLog(tao,&gpcg);CHKERRQ(ierr);
tao->data = (void*)gpcg;
/* Override default settings (unless already changed) */
if (!tao->max_it_changed) tao->max_it=500;
if (!tao->max_funcs_changed) tao->max_funcs = 100000;
#if defined(PETSC_USE_REAL_SINGLE)
if (!tao->fatol_changed) tao->fatol=1e-6;
if (!tao->frtol_changed) tao->frtol=1e-6;
if (!tao->gatol_changed) tao->grtol=1e-6;
if (!tao->grtol_changed) tao->grtol=1e-6;
#else
if (!tao->fatol_changed) tao->fatol=1e-12;
if (!tao->frtol_changed) tao->frtol=1e-12;
if (!tao->gatol_changed) tao->grtol=1e-12;
if (!tao->grtol_changed) tao->grtol=1e-12;
#endif
/* Initialize pointers and variables */
gpcg->n=0;
gpcg->maxgpits = 8;
gpcg->pg_ftol = 0.1;
gpcg->gp_iterates=0; /* Cumulative number */
gpcg->total_gp_its = 0;
/* Initialize pointers and variables */
gpcg->n_bind=0;
gpcg->n_free = 0;
gpcg->n_upper=0;
gpcg->n_lower=0;
gpcg->subset_type = TAO_SUBSET_MASK;
gpcg->Hsub=NULL;
gpcg->Hsub_pre=NULL;
ierr = KSPCreate(((PetscObject)tao)->comm, &tao->ksp);CHKERRQ(ierr);
ierr = KSPSetOptionsPrefix(tao->ksp, tao->hdr.prefix);CHKERRQ(ierr);
ierr = KSPSetType(tao->ksp,KSPNASH);CHKERRQ(ierr);
ierr = TaoLineSearchCreate(((PetscObject)tao)->comm, &tao->linesearch);CHKERRQ(ierr);
ierr = TaoLineSearchSetType(tao->linesearch, TAOLINESEARCHGPCG);CHKERRQ(ierr);
ierr = TaoLineSearchSetObjectiveAndGradientRoutine(tao->linesearch, GPCGObjectiveAndGradient, tao);CHKERRQ(ierr);
ierr = TaoLineSearchSetOptionsPrefix(tao->linesearch,tao->hdr.prefix);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
static PetscErrorCode TaoSolve_SSILS(Tao tao)
{
TAO_SSLS *ssls = (TAO_SSLS *)tao->data;
PetscReal psi, ndpsi, normd, innerd, t=0;
PetscReal delta, rho;
PetscInt iter=0,kspits;
TaoConvergedReason reason;
TaoLineSearchConvergedReason ls_reason;
PetscErrorCode ierr;
PetscFunctionBegin;
/* Assume that Setup has been called!
Set the structure for the Jacobian and create a linear solver. */
delta = ssls->delta;
rho = ssls->rho;
ierr = TaoComputeVariableBounds(tao);CHKERRQ(ierr);
ierr = VecMedian(tao->XL,tao->solution,tao->XU,tao->solution);CHKERRQ(ierr);
ierr = TaoLineSearchSetObjectiveAndGradientRoutine(tao->linesearch,Tao_SSLS_FunctionGradient,tao);CHKERRQ(ierr);
ierr = TaoLineSearchSetObjectiveRoutine(tao->linesearch,Tao_SSLS_Function,tao);CHKERRQ(ierr);
/* Calculate the function value and fischer function value at the
current iterate */
ierr = TaoLineSearchComputeObjectiveAndGradient(tao->linesearch,tao->solution,&psi,ssls->dpsi);CHKERRQ(ierr);
ierr = VecNorm(ssls->dpsi,NORM_2,&ndpsi);CHKERRQ(ierr);
while (1) {
ierr=PetscInfo3(tao, "iter: %D, merit: %g, ndpsi: %g\n",iter, (double)ssls->merit, (double)ndpsi);CHKERRQ(ierr);
/* Check the termination criteria */
ierr = TaoMonitor(tao,iter++,ssls->merit,ndpsi,0.0,t,&reason);CHKERRQ(ierr);
if (reason!=TAO_CONTINUE_ITERATING) break;
/* Calculate direction. (Really negative of newton direction. Therefore,
rest of the code uses -d.) */
ierr = KSPSetOperators(tao->ksp,tao->jacobian,tao->jacobian_pre);CHKERRQ(ierr);
ierr = KSPSolve(tao->ksp,ssls->ff,tao->stepdirection);CHKERRQ(ierr);
ierr = KSPGetIterationNumber(tao->ksp,&kspits);CHKERRQ(ierr);
tao->ksp_its+=kspits;
ierr = VecNorm(tao->stepdirection,NORM_2,&normd);CHKERRQ(ierr);
ierr = VecDot(tao->stepdirection,ssls->dpsi,&innerd);CHKERRQ(ierr);
/* Make sure that we have a descent direction */
if (innerd <= delta*pow(normd, rho)) {
ierr = PetscInfo(tao, "newton direction not descent\n");CHKERRQ(ierr);
ierr = VecCopy(ssls->dpsi,tao->stepdirection);CHKERRQ(ierr);
ierr = VecDot(tao->stepdirection,ssls->dpsi,&innerd);CHKERRQ(ierr);
}
ierr = VecScale(tao->stepdirection, -1.0);CHKERRQ(ierr);
innerd = -innerd;
ierr = TaoLineSearchSetInitialStepLength(tao->linesearch,1.0);
ierr = TaoLineSearchApply(tao->linesearch,tao->solution,&psi,ssls->dpsi,tao->stepdirection,&t,&ls_reason);CHKERRQ(ierr);
ierr = VecNorm(ssls->dpsi,NORM_2,&ndpsi);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
/*MC
TAOGPCG - gradient projected conjugate gradient algorithm is an active-set
conjugate-gradient based method for bound-constrained minimization
Options Database Keys:
+ -tao_gpcg_maxpgits - maximum number of gradient projections for GPCG iterate
- -tao_subset_type - "subvec","mask","matrix-free", strategies for handling active-sets
Level: beginner
M*/
EXTERN_C_BEGIN
#undef __FUNCT__
#define __FUNCT__ "TaoCreate_GPCG"
PetscErrorCode TaoCreate_GPCG(Tao tao)
{
TAO_GPCG *gpcg;
PetscErrorCode ierr;
PetscFunctionBegin;
tao->ops->setup = TaoSetup_GPCG;
tao->ops->solve = TaoSolve_GPCG;
tao->ops->view = TaoView_GPCG;
tao->ops->setfromoptions = TaoSetFromOptions_GPCG;
tao->ops->destroy = TaoDestroy_GPCG;
tao->ops->computedual = TaoComputeDual_GPCG;
ierr = PetscNewLog(tao,&gpcg);CHKERRQ(ierr);
tao->data = (void*)gpcg;
tao->max_it = 500;
tao->max_funcs = 100000;
#if defined(PETSC_USE_REAL_SINGLE)
tao->fatol = 1e-6;
tao->frtol = 1e-6;
#else
tao->fatol = 1e-12;
tao->frtol = 1e-12;
#endif
/* Initialize pointers and variables */
gpcg->n=0;
gpcg->maxgpits = 8;
gpcg->pg_ftol = 0.1;
gpcg->gp_iterates=0; /* Cumulative number */
gpcg->total_gp_its = 0;
/* Initialize pointers and variables */
gpcg->n_bind=0;
gpcg->n_free = 0;
gpcg->n_upper=0;
gpcg->n_lower=0;
gpcg->subset_type = TAO_SUBSET_MASK;
/* gpcg->ksp_type = GPCG_KSP_STCG; */
ierr = KSPCreate(((PetscObject)tao)->comm, &tao->ksp);CHKERRQ(ierr);
ierr = KSPSetType(tao->ksp,KSPNASH);CHKERRQ(ierr);
ierr = TaoLineSearchCreate(((PetscObject)tao)->comm, &tao->linesearch);CHKERRQ(ierr);
ierr = TaoLineSearchSetType(tao->linesearch, TAOLINESEARCHGPCG);CHKERRQ(ierr);
ierr = TaoLineSearchSetObjectiveAndGradientRoutine(tao->linesearch, GPCGObjectiveAndGradient, tao);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
static PetscErrorCode TaoSolve_ASILS(Tao tao)
{
TAO_SSLS *asls = (TAO_SSLS *)tao->data;
PetscReal psi,ndpsi, normd, innerd, t=0;
PetscInt iter=0, nf;
PetscErrorCode ierr;
TaoConvergedReason reason;
TaoLineSearchConvergedReason ls_reason;
PetscFunctionBegin;
/* Assume that Setup has been called!
Set the structure for the Jacobian and create a linear solver. */
ierr = TaoComputeVariableBounds(tao);CHKERRQ(ierr);
ierr = TaoLineSearchSetObjectiveAndGradientRoutine(tao->linesearch,Tao_ASLS_FunctionGradient,tao);CHKERRQ(ierr);
ierr = TaoLineSearchSetObjectiveRoutine(tao->linesearch,Tao_SSLS_Function,tao);CHKERRQ(ierr);
/* Calculate the function value and fischer function value at the
current iterate */
ierr = TaoLineSearchComputeObjectiveAndGradient(tao->linesearch,tao->solution,&psi,asls->dpsi);CHKERRQ(ierr);
ierr = VecNorm(asls->dpsi,NORM_2,&ndpsi);CHKERRQ(ierr);
while (1) {
/* Check the termination criteria */
ierr = PetscInfo3(tao,"iter %D, merit: %g, ||dpsi||: %g\n",iter, (double)asls->merit, (double)ndpsi);CHKERRQ(ierr);
ierr = TaoMonitor(tao, iter++, asls->merit, ndpsi, 0.0, t, &reason);CHKERRQ(ierr);
if (TAO_CONTINUE_ITERATING != reason) break;
/* We are going to solve a linear system of equations. We need to
set the tolerances for the solve so that we maintain an asymptotic
rate of convergence that is superlinear.
Note: these tolerances are for the reduced system. We really need
to make sure that the full system satisfies the full-space conditions.
This rule gives superlinear asymptotic convergence
asls->atol = min(0.5, asls->merit*sqrt(asls->merit));
asls->rtol = 0.0;
This rule gives quadratic asymptotic convergence
asls->atol = min(0.5, asls->merit*asls->merit);
asls->rtol = 0.0;
Calculate a free and fixed set of variables. The fixed set of
variables are those for the d_b is approximately equal to zero.
The definition of approximately changes as we approach the solution
to the problem.
No one rule is guaranteed to work in all cases. The following
definition is based on the norm of the Jacobian matrix. If the
norm is large, the tolerance becomes smaller. */
ierr = MatNorm(tao->jacobian,NORM_1,&asls->identifier);CHKERRQ(ierr);
asls->identifier = PetscMin(asls->merit, 1e-2) / (1 + asls->identifier);
ierr = VecSet(asls->t1,-asls->identifier);CHKERRQ(ierr);
ierr = VecSet(asls->t2, asls->identifier);CHKERRQ(ierr);
ierr = ISDestroy(&asls->fixed);CHKERRQ(ierr);
ierr = ISDestroy(&asls->free);CHKERRQ(ierr);
ierr = VecWhichBetweenOrEqual(asls->t1, asls->db, asls->t2, &asls->fixed);CHKERRQ(ierr);
ierr = ISComplementVec(asls->fixed,asls->t1, &asls->free);CHKERRQ(ierr);
ierr = ISGetSize(asls->fixed,&nf);CHKERRQ(ierr);
ierr = PetscInfo1(tao,"Number of fixed variables: %D\n", nf);CHKERRQ(ierr);
/* We now have our partition. Now calculate the direction in the
fixed variable space. */
ierr = TaoVecGetSubVec(asls->ff, asls->fixed, tao->subset_type, 0.0, &asls->r1);
ierr = TaoVecGetSubVec(asls->da, asls->fixed, tao->subset_type, 1.0, &asls->r2);
ierr = VecPointwiseDivide(asls->r1,asls->r1,asls->r2);CHKERRQ(ierr);
ierr = VecSet(tao->stepdirection,0.0);CHKERRQ(ierr);
ierr = VecISAXPY(tao->stepdirection, asls->fixed,1.0,asls->r1);CHKERRQ(ierr);
/* Our direction in the Fixed Variable Set is fixed. Calculate the
information needed for the step in the Free Variable Set. To
do this, we need to know the diagonal perturbation and the
right hand side. */
ierr = TaoVecGetSubVec(asls->da, asls->free, tao->subset_type, 0.0, &asls->r1);CHKERRQ(ierr);
ierr = TaoVecGetSubVec(asls->ff, asls->free, tao->subset_type, 0.0, &asls->r2);CHKERRQ(ierr);
ierr = TaoVecGetSubVec(asls->db, asls->free, tao->subset_type, 1.0, &asls->r3);CHKERRQ(ierr);
ierr = VecPointwiseDivide(asls->r1,asls->r1, asls->r3);CHKERRQ(ierr);
ierr = VecPointwiseDivide(asls->r2,asls->r2, asls->r3);CHKERRQ(ierr);
/* r1 is the diagonal perturbation
r2 is the right hand side
r3 is no longer needed
Now need to modify r2 for our direction choice in the fixed
variable set: calculate t1 = J*d, take the reduced vector
of t1 and modify r2. */
ierr = MatMult(tao->jacobian, tao->stepdirection, asls->t1);CHKERRQ(ierr);
ierr = TaoVecGetSubVec(asls->t1,asls->free,tao->subset_type,0.0,&asls->r3);CHKERRQ(ierr);
ierr = VecAXPY(asls->r2, -1.0, asls->r3);CHKERRQ(ierr);
/* Calculate the reduced problem matrix and the direction */
if (!asls->w && (tao->subset_type == TAO_SUBSET_MASK || tao->subset_type == TAO_SUBSET_MATRIXFREE)) {
ierr = VecDuplicate(tao->solution, &asls->w);CHKERRQ(ierr);
}
ierr = TaoMatGetSubMat(tao->jacobian, asls->free, asls->w, tao->subset_type,&asls->J_sub);CHKERRQ(ierr);
if (tao->jacobian != tao->jacobian_pre) {
ierr = TaoMatGetSubMat(tao->jacobian_pre, asls->free, asls->w, tao->subset_type, &asls->Jpre_sub);CHKERRQ(ierr);
} else {
ierr = MatDestroy(&asls->Jpre_sub);CHKERRQ(ierr);
asls->Jpre_sub = asls->J_sub;
ierr = PetscObjectReference((PetscObject)(asls->Jpre_sub));CHKERRQ(ierr);
}
ierr = MatDiagonalSet(asls->J_sub, asls->r1,ADD_VALUES);CHKERRQ(ierr);
ierr = TaoVecGetSubVec(tao->stepdirection, asls->free, tao->subset_type, 0.0, &asls->dxfree);CHKERRQ(ierr);
ierr = VecSet(asls->dxfree, 0.0);CHKERRQ(ierr);
/* Calculate the reduced direction. (Really negative of Newton
direction. Therefore, rest of the code uses -d.) */
ierr = KSPReset(tao->ksp);
ierr = KSPSetOperators(tao->ksp, asls->J_sub, asls->Jpre_sub);CHKERRQ(ierr);
ierr = KSPSolve(tao->ksp, asls->r2, asls->dxfree);CHKERRQ(ierr);
/* Add the direction in the free variables back into the real direction. */
ierr = VecISAXPY(tao->stepdirection, asls->free, 1.0,asls->dxfree);CHKERRQ(ierr);
/* Check the real direction for descent and if not, use the negative
gradient direction. */
ierr = VecNorm(tao->stepdirection, NORM_2, &normd);CHKERRQ(ierr);
ierr = VecDot(tao->stepdirection, asls->dpsi, &innerd);CHKERRQ(ierr);
if (innerd <= asls->delta*pow(normd, asls->rho)) {
ierr = PetscInfo1(tao,"Gradient direction: %5.4e.\n", (double)innerd);CHKERRQ(ierr);
ierr = PetscInfo1(tao, "Iteration %D: newton direction not descent\n", iter);CHKERRQ(ierr);
ierr = VecCopy(asls->dpsi, tao->stepdirection);CHKERRQ(ierr);
ierr = VecDot(asls->dpsi, tao->stepdirection, &innerd);CHKERRQ(ierr);
}
ierr = VecScale(tao->stepdirection, -1.0);CHKERRQ(ierr);
innerd = -innerd;
/* We now have a correct descent direction. Apply a linesearch to
find the new iterate. */
ierr = TaoLineSearchSetInitialStepLength(tao->linesearch, 1.0);CHKERRQ(ierr);
ierr = TaoLineSearchApply(tao->linesearch, tao->solution, &psi,asls->dpsi, tao->stepdirection, &t, &ls_reason);CHKERRQ(ierr);
ierr = VecNorm(asls->dpsi, NORM_2, &ndpsi);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}