static PetscErrorCode TronGradientProjections(Tao tao,TAO_TRON *tron) { PetscErrorCode ierr; PetscInt i; TaoLineSearchConvergedReason ls_reason; PetscReal actred=-1.0,actred_max=0.0; PetscReal f_new; /* The gradient and function value passed into and out of this routine should be current and correct. The free, active, and binding variables should be already identified */ PetscFunctionBegin; if (tron->Free_Local) { ierr = ISDestroy(&tron->Free_Local);CHKERRQ(ierr); } ierr = VecWhichBetween(tao->XL,tao->solution,tao->XU,&tron->Free_Local);CHKERRQ(ierr); for (i=0;i<tron->maxgpits;i++){ if ( -actred <= (tron->pg_ftol)*actred_max) break; tron->gp_iterates++; tron->total_gp_its++; f_new=tron->f; ierr = VecCopy(tao->gradient, tao->stepdirection);CHKERRQ(ierr); ierr = VecScale(tao->stepdirection, -1.0);CHKERRQ(ierr); ierr = TaoLineSearchSetInitialStepLength(tao->linesearch,tron->pgstepsize);CHKERRQ(ierr); ierr = TaoLineSearchApply(tao->linesearch, tao->solution, &f_new, tao->gradient, tao->stepdirection, &tron->pgstepsize, &ls_reason);CHKERRQ(ierr); ierr = TaoAddLineSearchCounts(tao);CHKERRQ(ierr); /* Update the iterate */ actred = f_new - tron->f; actred_max = PetscMax(actred_max,-(f_new - tron->f)); tron->f = f_new; if (tron->Free_Local) { ierr = ISDestroy(&tron->Free_Local);CHKERRQ(ierr); } ierr = VecWhichBetween(tao->XL,tao->solution,tao->XU,&tron->Free_Local);CHKERRQ(ierr); } PetscFunctionReturn(0); }
static PetscErrorCode GPCGGradProjections(Tao tao) { PetscErrorCode ierr; TAO_GPCG *gpcg = (TAO_GPCG *)tao->data; PetscInt i; PetscReal actred=-1.0,actred_max=0.0, gAg,gtg=gpcg->gnorm,alpha; PetscReal f_new,gdx,stepsize; Vec DX=tao->stepdirection,XL=tao->XL,XU=tao->XU,Work=gpcg->Work; Vec X=tao->solution,G=tao->gradient; TaoLineSearchConvergedReason lsflag=TAOLINESEARCH_CONTINUE_ITERATING; /* The free, active, and binding variables should be already identified */ PetscFunctionBegin; for (i=0;i<gpcg->maxgpits;i++){ if ( -actred <= (gpcg->pg_ftol)*actred_max) break; ierr = VecBoundGradientProjection(G,X,XL,XU,DX);CHKERRQ(ierr); ierr = VecScale(DX,-1.0);CHKERRQ(ierr); ierr = VecDot(DX,G,&gdx);CHKERRQ(ierr); ierr = MatMult(tao->hessian,DX,Work);CHKERRQ(ierr); ierr = VecDot(DX,Work,&gAg);CHKERRQ(ierr); gpcg->gp_iterates++; gpcg->total_gp_its++; gtg=-gdx; alpha = PetscAbsReal(gtg/gAg); ierr = TaoLineSearchSetInitialStepLength(tao->linesearch,alpha);CHKERRQ(ierr); f_new=gpcg->f; ierr = TaoLineSearchApply(tao->linesearch,X,&f_new,G,DX,&stepsize,&lsflag);CHKERRQ(ierr); /* Update the iterate */ actred = f_new - gpcg->f; actred_max = PetscMax(actred_max,-(f_new - gpcg->f)); gpcg->f = f_new; ierr = ISDestroy(&gpcg->Free_Local);CHKERRQ(ierr); ierr = VecWhichBetween(XL,X,XU,&gpcg->Free_Local);CHKERRQ(ierr); } gpcg->gnorm=gtg; PetscFunctionReturn(0); } /* End gradient projections */
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_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); }
PETSC_EXTERN void PETSC_STDCALL vecwhichbetween_(Vec VecLow,Vec V,Vec VecHigh,IS *S, int *__ierr ){ *__ierr = VecWhichBetween( (Vec)PetscToPointer((VecLow) ), (Vec)PetscToPointer((V) ), (Vec)PetscToPointer((VecHigh) ),S); }