PetscErrorCode TaoSetUp_SSFLS(Tao tao)
{
TAO_SSLS *ssls = (TAO_SSLS *)tao->data;
PetscErrorCode ierr;
PetscFunctionBegin;
ierr = VecDuplicate(tao->solution,&tao->gradient);CHKERRQ(ierr);
ierr = VecDuplicate(tao->solution,&tao->stepdirection);CHKERRQ(ierr);
ierr = VecDuplicate(tao->solution,&ssls->w);CHKERRQ(ierr);
ierr = VecDuplicate(tao->solution,&ssls->ff);CHKERRQ(ierr);
ierr = VecDuplicate(tao->solution,&ssls->dpsi);CHKERRQ(ierr);
ierr = VecDuplicate(tao->solution,&ssls->da);CHKERRQ(ierr);
ierr = VecDuplicate(tao->solution,&ssls->db);CHKERRQ(ierr);
ierr = VecDuplicate(tao->solution,&ssls->t1);CHKERRQ(ierr);
ierr = VecDuplicate(tao->solution,&ssls->t2);CHKERRQ(ierr);
if (!tao->XL) {
ierr = VecDuplicate(tao->solution,&tao->XL);CHKERRQ(ierr);
}
if (!tao->XU) {
ierr = VecDuplicate(tao->solution,&tao->XU);CHKERRQ(ierr);
}
ierr = TaoLineSearchSetVariableBounds(tao->linesearch,tao->XL,tao->XU);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
static PetscErrorCode TaoSolve_GPCG(Tao tao)
{
TAO_GPCG *gpcg = (TAO_GPCG *)tao->data;
PetscErrorCode ierr;
PetscInt its;
PetscReal actred,f,f_new,gnorm,gdx,stepsize,xtb;
PetscReal xtHx;
TaoConvergedReason reason = TAO_CONTINUE_ITERATING;
TaoLineSearchConvergedReason ls_status = TAOLINESEARCH_CONTINUE_ITERATING;
PetscFunctionBegin;
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);
/* Using f = .5*x'Hx + x'b + c and g=Hx + b, compute b,c */
ierr = TaoComputeHessian(tao,tao->solution,tao->hessian,tao->hessian_pre);CHKERRQ(ierr);
ierr = TaoComputeObjectiveAndGradient(tao,tao->solution,&f,tao->gradient);CHKERRQ(ierr);
ierr = VecCopy(tao->gradient, gpcg->B);CHKERRQ(ierr);
ierr = MatMult(tao->hessian,tao->solution,gpcg->Work);CHKERRQ(ierr);
ierr = VecDot(gpcg->Work, tao->solution, &xtHx);CHKERRQ(ierr);
ierr = VecAXPY(gpcg->B,-1.0,gpcg->Work);CHKERRQ(ierr);
ierr = VecDot(gpcg->B,tao->solution,&xtb);CHKERRQ(ierr);
gpcg->c=f-xtHx/2.0-xtb;
if (gpcg->Free_Local) {
ierr = ISDestroy(&gpcg->Free_Local);CHKERRQ(ierr);
}
ierr = VecWhichBetween(tao->XL,tao->solution,tao->XU,&gpcg->Free_Local);CHKERRQ(ierr);
/* Project the gradient and calculate the norm */
ierr = VecCopy(tao->gradient,gpcg->G_New);CHKERRQ(ierr);
ierr = VecBoundGradientProjection(tao->gradient,tao->solution,tao->XL,tao->XU,gpcg->PG);CHKERRQ(ierr);
ierr = VecNorm(gpcg->PG,NORM_2,&gpcg->gnorm);CHKERRQ(ierr);
tao->step=1.0;
gpcg->f = f;
/* Check Stopping Condition */
ierr=TaoMonitor(tao,tao->niter,f,gpcg->gnorm,0.0,tao->step,&reason);CHKERRQ(ierr);
while (reason == TAO_CONTINUE_ITERATING){
tao->ksp_its=0;
ierr = GPCGGradProjections(tao);CHKERRQ(ierr);
ierr = ISGetSize(gpcg->Free_Local,&gpcg->n_free);CHKERRQ(ierr);
f=gpcg->f; gnorm=gpcg->gnorm;
ierr = KSPReset(tao->ksp);CHKERRQ(ierr);
if (gpcg->n_free > 0){
/* Create a reduced linear system */
ierr = VecDestroy(&gpcg->R);CHKERRQ(ierr);
ierr = VecDestroy(&gpcg->DXFree);CHKERRQ(ierr);
ierr = TaoVecGetSubVec(tao->gradient,gpcg->Free_Local, tao->subset_type, 0.0, &gpcg->R);CHKERRQ(ierr);
ierr = VecScale(gpcg->R, -1.0);CHKERRQ(ierr);
ierr = TaoVecGetSubVec(tao->stepdirection,gpcg->Free_Local,tao->subset_type, 0.0, &gpcg->DXFree);CHKERRQ(ierr);
ierr = VecSet(gpcg->DXFree,0.0);CHKERRQ(ierr);
ierr = TaoMatGetSubMat(tao->hessian, gpcg->Free_Local, gpcg->Work, tao->subset_type, &gpcg->Hsub);CHKERRQ(ierr);
if (tao->hessian_pre == tao->hessian) {
ierr = MatDestroy(&gpcg->Hsub_pre);CHKERRQ(ierr);
ierr = PetscObjectReference((PetscObject)gpcg->Hsub);CHKERRQ(ierr);
gpcg->Hsub_pre = gpcg->Hsub;
} else {
ierr = TaoMatGetSubMat(tao->hessian, gpcg->Free_Local, gpcg->Work, tao->subset_type, &gpcg->Hsub_pre);CHKERRQ(ierr);
}
ierr = KSPReset(tao->ksp);CHKERRQ(ierr);
ierr = KSPSetOperators(tao->ksp,gpcg->Hsub,gpcg->Hsub_pre);CHKERRQ(ierr);
ierr = KSPSolve(tao->ksp,gpcg->R,gpcg->DXFree);CHKERRQ(ierr);
ierr = KSPGetIterationNumber(tao->ksp,&its);CHKERRQ(ierr);
tao->ksp_its+=its;
tao->ksp_tot_its+=its;
ierr = VecSet(tao->stepdirection,0.0);CHKERRQ(ierr);
ierr = VecISAXPY(tao->stepdirection,gpcg->Free_Local,1.0,gpcg->DXFree);CHKERRQ(ierr);
ierr = VecDot(tao->stepdirection,tao->gradient,&gdx);CHKERRQ(ierr);
ierr = TaoLineSearchSetInitialStepLength(tao->linesearch,1.0);CHKERRQ(ierr);
f_new=f;
ierr = TaoLineSearchApply(tao->linesearch,tao->solution,&f_new,tao->gradient,tao->stepdirection,&stepsize,&ls_status);CHKERRQ(ierr);
actred = f_new - f;
/* Evaluate the function and gradient at the new point */
ierr = VecBoundGradientProjection(tao->gradient,tao->solution,tao->XL,tao->XU, gpcg->PG);CHKERRQ(ierr);
ierr = VecNorm(gpcg->PG, NORM_2, &gnorm);CHKERRQ(ierr);
f=f_new;
ierr = ISDestroy(&gpcg->Free_Local);CHKERRQ(ierr);
ierr = VecWhichBetween(tao->XL,tao->solution,tao->XU,&gpcg->Free_Local);CHKERRQ(ierr);
} else {
actred = 0; gpcg->step=1.0;
/* if there were no free variables, no cg method */
}
tao->niter++;
ierr = TaoMonitor(tao,tao->niter,f,gnorm,0.0,gpcg->step,&reason);CHKERRQ(ierr);
gpcg->f=f;gpcg->gnorm=gnorm; gpcg->actred=actred;
if (reason!=TAO_CONTINUE_ITERATING) break;
} /* END MAIN LOOP */
PetscFunctionReturn(0);
}
static PetscErrorCode TaoSolve_TRON(Tao tao)
{
TAO_TRON *tron = (TAO_TRON *)tao->data;
PetscErrorCode ierr;
PetscInt its;
TaoConvergedReason reason = TAO_CONTINUE_ITERATING;
TaoLineSearchConvergedReason ls_reason = TAOLINESEARCH_CONTINUE_ITERATING;
PetscReal prered,actred,delta,f,f_new,rhok,gdx,xdiff,stepsize;
PetscFunctionBegin;
tron->pgstepsize=1.0;
tao->trust = tao->trust0;
/* Project the current point onto the feasible set */
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);
ierr = TaoComputeObjectiveAndGradient(tao,tao->solution,&tron->f,tao->gradient);CHKERRQ(ierr);
ierr = ISDestroy(&tron->Free_Local);CHKERRQ(ierr);
ierr = VecWhichBetween(tao->XL,tao->solution,tao->XU,&tron->Free_Local);CHKERRQ(ierr);
/* Project the gradient and calculate the norm */
ierr = VecBoundGradientProjection(tao->gradient,tao->solution, tao->XL, tao->XU, tao->gradient);CHKERRQ(ierr);
ierr = VecNorm(tao->gradient,NORM_2,&tron->gnorm);CHKERRQ(ierr);
if (PetscIsInfOrNanReal(tron->f) || PetscIsInfOrNanReal(tron->gnorm)) SETERRQ(PETSC_COMM_SELF,1, "User provided compute function generated Inf pr NaN");
if (tao->trust <= 0) {
tao->trust=PetscMax(tron->gnorm*tron->gnorm,1.0);
}
tron->stepsize=tao->trust;
ierr = TaoMonitor(tao, tao->niter, tron->f, tron->gnorm, 0.0, tron->stepsize, &reason);CHKERRQ(ierr);
while (reason==TAO_CONTINUE_ITERATING){
tao->ksp_its=0;
ierr = TronGradientProjections(tao,tron);CHKERRQ(ierr);
f=tron->f; delta=tao->trust;
tron->n_free_last = tron->n_free;
ierr = TaoComputeHessian(tao,tao->solution,tao->hessian,tao->hessian_pre);CHKERRQ(ierr);
ierr = ISGetSize(tron->Free_Local, &tron->n_free);CHKERRQ(ierr);
/* If no free variables */
if (tron->n_free == 0) {
actred=0;
ierr = PetscInfo(tao,"No free variables in tron iteration.\n");CHKERRQ(ierr);
ierr = VecNorm(tao->gradient,NORM_2,&tron->gnorm);CHKERRQ(ierr);
ierr = TaoMonitor(tao, tao->niter, tron->f, tron->gnorm, 0.0, delta, &reason);CHKERRQ(ierr);
if (!reason) {
reason = TAO_CONVERGED_STEPTOL;
ierr = TaoSetConvergedReason(tao,reason);CHKERRQ(ierr);
}
break;
}
/* use free_local to mask/submat gradient, hessian, stepdirection */
ierr = TaoVecGetSubVec(tao->gradient,tron->Free_Local,tao->subset_type,0.0,&tron->R);CHKERRQ(ierr);
ierr = TaoVecGetSubVec(tao->gradient,tron->Free_Local,tao->subset_type,0.0,&tron->DXFree);CHKERRQ(ierr);
ierr = VecSet(tron->DXFree,0.0);CHKERRQ(ierr);
ierr = VecScale(tron->R, -1.0);CHKERRQ(ierr);
ierr = TaoMatGetSubMat(tao->hessian, tron->Free_Local, tron->diag, tao->subset_type, &tron->H_sub);CHKERRQ(ierr);
if (tao->hessian == tao->hessian_pre) {
ierr = MatDestroy(&tron->Hpre_sub);CHKERRQ(ierr);
ierr = PetscObjectReference((PetscObject)(tron->H_sub));CHKERRQ(ierr);
tron->Hpre_sub = tron->H_sub;
} else {
ierr = TaoMatGetSubMat(tao->hessian_pre, tron->Free_Local, tron->diag, tao->subset_type,&tron->Hpre_sub);CHKERRQ(ierr);
}
ierr = KSPReset(tao->ksp);CHKERRQ(ierr);
ierr = KSPSetOperators(tao->ksp, tron->H_sub, tron->Hpre_sub);CHKERRQ(ierr);
while (1) {
/* Approximately solve the reduced linear system */
ierr = KSPSTCGSetRadius(tao->ksp,delta);CHKERRQ(ierr);
ierr = KSPSolve(tao->ksp, tron->R, tron->DXFree);CHKERRQ(ierr);
ierr = KSPGetIterationNumber(tao->ksp,&its);CHKERRQ(ierr);
tao->ksp_its+=its;
tao->ksp_tot_its+=its;
ierr = VecSet(tao->stepdirection,0.0);CHKERRQ(ierr);
/* Add dxfree matrix to compute step direction vector */
ierr = VecISAXPY(tao->stepdirection,tron->Free_Local,1.0,tron->DXFree);CHKERRQ(ierr);
if (0) {
PetscReal rhs,stepnorm;
ierr = VecNorm(tron->R,NORM_2,&rhs);CHKERRQ(ierr);
ierr = VecNorm(tron->DXFree,NORM_2,&stepnorm);CHKERRQ(ierr);
ierr = PetscPrintf(PETSC_COMM_WORLD,"|rhs|=%g\t|s|=%g\n",(double)rhs,(double)stepnorm);CHKERRQ(ierr);
}
ierr = VecDot(tao->gradient, tao->stepdirection, &gdx);CHKERRQ(ierr);
ierr = PetscInfo1(tao,"Expected decrease in function value: %14.12e\n",(double)gdx);CHKERRQ(ierr);
ierr = VecCopy(tao->solution, tron->X_New);CHKERRQ(ierr);
ierr = VecCopy(tao->gradient, tron->G_New);CHKERRQ(ierr);
stepsize=1.0;f_new=f;
ierr = TaoLineSearchSetInitialStepLength(tao->linesearch,1.0);CHKERRQ(ierr);
ierr = TaoLineSearchApply(tao->linesearch, tron->X_New, &f_new, tron->G_New, tao->stepdirection,&stepsize,&ls_reason);CHKERRQ(ierr);CHKERRQ(ierr);
ierr = TaoAddLineSearchCounts(tao);CHKERRQ(ierr);
ierr = MatMult(tao->hessian, tao->stepdirection, tron->Work);CHKERRQ(ierr);
ierr = VecAYPX(tron->Work, 0.5, tao->gradient);CHKERRQ(ierr);
ierr = VecDot(tao->stepdirection, tron->Work, &prered);CHKERRQ(ierr);
actred = f_new - f;
if (actred<0) {
rhok=PetscAbs(-actred/prered);
} else {
rhok=0.0;
}
/* Compare actual improvement to the quadratic model */
if (rhok > tron->eta1) { /* Accept the point */
/* d = x_new - x */
ierr = VecCopy(tron->X_New, tao->stepdirection);CHKERRQ(ierr);
ierr = VecAXPY(tao->stepdirection, -1.0, tao->solution);CHKERRQ(ierr);
ierr = VecNorm(tao->stepdirection, NORM_2, &xdiff);CHKERRQ(ierr);
xdiff *= stepsize;
/* Adjust trust region size */
if (rhok < tron->eta2 ){
delta = PetscMin(xdiff,delta)*tron->sigma1;
} else if (rhok > tron->eta4 ){
delta= PetscMin(xdiff,delta)*tron->sigma3;
} else if (rhok > tron->eta3 ){
delta=PetscMin(xdiff,delta)*tron->sigma2;
}
ierr = VecBoundGradientProjection(tron->G_New,tron->X_New, tao->XL, tao->XU, tao->gradient);CHKERRQ(ierr);
if (tron->Free_Local) {
ierr = ISDestroy(&tron->Free_Local);CHKERRQ(ierr);
}
ierr = VecWhichBetween(tao->XL, tron->X_New, tao->XU, &tron->Free_Local);CHKERRQ(ierr);
f=f_new;
ierr = VecNorm(tao->gradient,NORM_2,&tron->gnorm);CHKERRQ(ierr);
ierr = VecCopy(tron->X_New, tao->solution);CHKERRQ(ierr);
ierr = VecCopy(tron->G_New, tao->gradient);CHKERRQ(ierr);
break;
}
else if (delta <= 1e-30) {
break;
}
else {
delta /= 4.0;
}
} /* end linear solve loop */
tron->f=f; tron->actred=actred; tao->trust=delta;
tao->niter++;
ierr = TaoMonitor(tao, tao->niter, tron->f, tron->gnorm, 0.0, delta, &reason);CHKERRQ(ierr);
} /* END MAIN LOOP */
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);
}
