PETSC_EXTERN void PETSC_STDCALL vecmedian_(Vec Vec1,Vec Vec2,Vec Vec3,Vec VMedian, int *__ierr ){
*__ierr = VecMedian(
(Vec)PetscToPointer((Vec1) ),
(Vec)PetscToPointer((Vec2) ),
(Vec)PetscToPointer((Vec3) ),
(Vec)PetscToPointer((VMedian) ));
}
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);
}
/* Push initial point away from bounds */
PetscErrorCode IPMPushInitialPoint(Tao tao)
{
TAO_IPM *ipmP = (TAO_IPM *)tao->data;
PetscErrorCode ierr;
PetscFunctionBegin;
ierr = TaoComputeVariableBounds(tao);CHKERRQ(ierr);
if (tao->XL && tao->XU) {
ierr = VecMedian(tao->XL, tao->solution, tao->XU, tao->solution);CHKERRQ(ierr);
}
if (ipmP->nb > 0) {
ierr = VecSet(ipmP->s,ipmP->pushs);CHKERRQ(ierr);
ierr = VecSet(ipmP->lamdai,ipmP->pushnu);CHKERRQ(ierr);
if (ipmP->mi > 0) {
ierr = VecSet(tao->DI,ipmP->pushnu);CHKERRQ(ierr);
}
}
if (ipmP->me > 0) {
ierr = VecSet(tao->DE,1.0);CHKERRQ(ierr);
ierr = VecSet(ipmP->lamdae,1.0);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
static PetscErrorCode TaoLineSearchApply_MT(TaoLineSearch ls, Vec x, PetscReal *f, Vec g, Vec s)
{
PetscErrorCode ierr;
TaoLineSearch_MT *mt;
PetscReal xtrapf = 4.0;
PetscReal finit, width, width1, dginit, fm, fxm, fym, dgm, dgxm, dgym;
PetscReal dgx, dgy, dg, dg2, fx, fy, stx, sty, dgtest;
PetscReal ftest1=0.0, ftest2=0.0;
PetscInt i, stage1,n1,n2,nn1,nn2;
PetscReal bstepmin1, bstepmin2, bstepmax;
PetscBool g_computed=PETSC_FALSE; /* to prevent extra gradient computation */
PetscFunctionBegin;
PetscValidHeaderSpecific(ls,TAOLINESEARCH_CLASSID,1);
PetscValidHeaderSpecific(x,VEC_CLASSID,2);
PetscValidScalarPointer(f,3);
PetscValidHeaderSpecific(g,VEC_CLASSID,4);
PetscValidHeaderSpecific(s,VEC_CLASSID,5);
/* comm,type,size checks are done in interface TaoLineSearchApply */
mt = (TaoLineSearch_MT*)(ls->data);
ls->reason = TAOLINESEARCH_CONTINUE_ITERATING;
/* Check work vector */
if (!mt->work) {
ierr = VecDuplicate(x,&mt->work);CHKERRQ(ierr);
mt->x = x;
ierr = PetscObjectReference((PetscObject)mt->x);CHKERRQ(ierr);
} else if (x != mt->x) {
ierr = VecDestroy(&mt->work);CHKERRQ(ierr);
ierr = VecDuplicate(x,&mt->work);CHKERRQ(ierr);
ierr = PetscObjectDereference((PetscObject)mt->x);CHKERRQ(ierr);
mt->x = x;
ierr = PetscObjectReference((PetscObject)mt->x);CHKERRQ(ierr);
}
if (ls->bounded) {
/* Compute step length needed to make all variables equal a bound */
/* Compute the smallest steplength that will make one nonbinding variable
equal the bound */
ierr = VecGetLocalSize(ls->upper,&n1);CHKERRQ(ierr);
ierr = VecGetLocalSize(mt->x, &n2);CHKERRQ(ierr);
ierr = VecGetSize(ls->upper,&nn1);CHKERRQ(ierr);
ierr = VecGetSize(mt->x,&nn2);CHKERRQ(ierr);
if (n1 != n2 || nn1 != nn2) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Variable vector not compatible with bounds vector");
ierr = VecScale(s,-1.0);CHKERRQ(ierr);
ierr = VecBoundGradientProjection(s,x,ls->lower,ls->upper,s);CHKERRQ(ierr);
ierr = VecScale(s,-1.0);CHKERRQ(ierr);
ierr = VecStepBoundInfo(x,s,ls->lower,ls->upper,&bstepmin1,&bstepmin2,&bstepmax);CHKERRQ(ierr);
ls->stepmax = PetscMin(bstepmax,1.0e15);
}
ierr = VecDot(g,s,&dginit);CHKERRQ(ierr);
if (PetscIsInfOrNanReal(dginit)) {
ierr = PetscInfo1(ls,"Initial Line Search step * g is Inf or Nan (%g)\n",(double)dginit);CHKERRQ(ierr);
ls->reason=TAOLINESEARCH_FAILED_INFORNAN;
PetscFunctionReturn(0);
}
if (dginit >= 0.0) {
ierr = PetscInfo1(ls,"Initial Line Search step * g is not descent direction (%g)\n",(double)dginit);CHKERRQ(ierr);
ls->reason = TAOLINESEARCH_FAILED_ASCENT;
PetscFunctionReturn(0);
}
/* Initialization */
mt->bracket = 0;
stage1 = 1;
finit = *f;
dgtest = ls->ftol * dginit;
width = ls->stepmax - ls->stepmin;
width1 = width * 2.0;
ierr = VecCopy(x,mt->work);CHKERRQ(ierr);
/* Variable dictionary:
stx, fx, dgx - the step, function, and derivative at the best step
sty, fy, dgy - the step, function, and derivative at the other endpoint
of the interval of uncertainty
step, f, dg - the step, function, and derivative at the current step */
stx = 0.0;
fx = finit;
dgx = dginit;
sty = 0.0;
fy = finit;
dgy = dginit;
ls->step=ls->initstep;
for (i=0; i< ls->max_funcs; i++) {
/* Set min and max steps to correspond to the interval of uncertainty */
if (mt->bracket) {
ls->stepmin = PetscMin(stx,sty);
ls->stepmax = PetscMax(stx,sty);
} else {
ls->stepmin = stx;
ls->stepmax = ls->step + xtrapf * (ls->step - stx);
}
/* Force the step to be within the bounds */
ls->step = PetscMax(ls->step,ls->stepmin);
ls->step = PetscMin(ls->step,ls->stepmax);
/* If an unusual termination is to occur, then let step be the lowest
point obtained thus far */
if ((stx!=0) && (((mt->bracket) && (ls->step <= ls->stepmin || ls->step >= ls->stepmax)) || ((mt->bracket) && (ls->stepmax - ls->stepmin <= ls->rtol * ls->stepmax)) ||
((ls->nfeval+ls->nfgeval) >= ls->max_funcs - 1) || (mt->infoc == 0))) {
ls->step = stx;
}
ierr = VecCopy(x,mt->work);CHKERRQ(ierr);
ierr = VecAXPY(mt->work,ls->step,s);CHKERRQ(ierr); /* W = X + step*S */
if (ls->bounded) {
ierr = VecMedian(ls->lower, mt->work, ls->upper, mt->work);CHKERRQ(ierr);
}
if (ls->usegts) {
ierr = TaoLineSearchComputeObjectiveAndGTS(ls,mt->work,f,&dg);CHKERRQ(ierr);
g_computed=PETSC_FALSE;
} else {
ierr = TaoLineSearchComputeObjectiveAndGradient(ls,mt->work,f,g);CHKERRQ(ierr);
g_computed=PETSC_TRUE;
if (ls->bounded) {
ierr = VecDot(g,x,&dg);CHKERRQ(ierr);
ierr = VecDot(g,mt->work,&dg2);CHKERRQ(ierr);
dg = (dg2 - dg)/ls->step;
} else {
ierr = VecDot(g,s,&dg);CHKERRQ(ierr);
}
}
if (0 == i) {
ls->f_fullstep=*f;
}
if (PetscIsInfOrNanReal(*f) || PetscIsInfOrNanReal(dg)) {
/* User provided compute function generated Not-a-Number, assume
domain violation and set function value and directional
derivative to infinity. */
*f = PETSC_INFINITY;
dg = PETSC_INFINITY;
}
ftest1 = finit + ls->step * dgtest;
if (ls->bounded) {
ftest2 = finit + ls->step * dgtest * ls->ftol;
}
/* Convergence testing */
if (((*f - ftest1 <= 1.0e-10 * PetscAbsReal(finit)) && (PetscAbsReal(dg) + ls->gtol*dginit <= 0.0))) {
ierr = PetscInfo(ls, "Line search success: Sufficient decrease and directional deriv conditions hold\n");CHKERRQ(ierr);
ls->reason = TAOLINESEARCH_SUCCESS;
break;
}
/* Check Armijo if beyond the first breakpoint */
if (ls->bounded && (*f <= ftest2) && (ls->step >= bstepmin2)) {
ierr = PetscInfo(ls,"Line search success: Sufficient decrease.\n");CHKERRQ(ierr);
ls->reason = TAOLINESEARCH_SUCCESS;
break;
}
/* Checks for bad cases */
if (((mt->bracket) && (ls->step <= ls->stepmin||ls->step >= ls->stepmax)) || (!mt->infoc)) {
ierr = PetscInfo(ls,"Rounding errors may prevent further progress. May not be a step satisfying\n");CHKERRQ(ierr);
ierr = PetscInfo(ls,"sufficient decrease and curvature conditions. Tolerances may be too small.\n");CHKERRQ(ierr);
ls->reason = TAOLINESEARCH_HALTED_OTHER;
break;
}
if ((ls->step == ls->stepmax) && (*f <= ftest1) && (dg <= dgtest)) {
ierr = PetscInfo1(ls,"Step is at the upper bound, stepmax (%g)\n",(double)ls->stepmax);CHKERRQ(ierr);
ls->reason = TAOLINESEARCH_HALTED_UPPERBOUND;
break;
}
if ((ls->step == ls->stepmin) && (*f >= ftest1) && (dg >= dgtest)) {
ierr = PetscInfo1(ls,"Step is at the lower bound, stepmin (%g)\n",(double)ls->stepmin);CHKERRQ(ierr);
ls->reason = TAOLINESEARCH_HALTED_LOWERBOUND;
break;
}
if ((mt->bracket) && (ls->stepmax - ls->stepmin <= ls->rtol*ls->stepmax)){
ierr = PetscInfo1(ls,"Relative width of interval of uncertainty is at most rtol (%g)\n",(double)ls->rtol);CHKERRQ(ierr);
ls->reason = TAOLINESEARCH_HALTED_RTOL;
break;
}
/* In the first stage, we seek a step for which the modified function
has a nonpositive value and nonnegative derivative */
if ((stage1) && (*f <= ftest1) && (dg >= dginit * PetscMin(ls->ftol, ls->gtol))) {
stage1 = 0;
}
/* A modified function is used to predict the step only if we
have not obtained a step for which the modified function has a
nonpositive function value and nonnegative derivative, and if a
lower function value has been obtained but the decrease is not
sufficient */
if ((stage1) && (*f <= fx) && (*f > ftest1)) {
fm = *f - ls->step * dgtest; /* Define modified function */
fxm = fx - stx * dgtest; /* and derivatives */
fym = fy - sty * dgtest;
dgm = dg - dgtest;
dgxm = dgx - dgtest;
dgym = dgy - dgtest;
/* if (dgxm * (ls->step - stx) >= 0.0) */
/* Update the interval of uncertainty and compute the new step */
ierr = Tao_mcstep(ls,&stx,&fxm,&dgxm,&sty,&fym,&dgym,&ls->step,&fm,&dgm);CHKERRQ(ierr);
fx = fxm + stx * dgtest; /* Reset the function and */
fy = fym + sty * dgtest; /* gradient values */
dgx = dgxm + dgtest;
dgy = dgym + dgtest;
} else {
/* Update the interval of uncertainty and compute the new step */
ierr = Tao_mcstep(ls,&stx,&fx,&dgx,&sty,&fy,&dgy,&ls->step,f,&dg);CHKERRQ(ierr);
}
/* Force a sufficient decrease in the interval of uncertainty */
if (mt->bracket) {
if (PetscAbsReal(sty - stx) >= 0.66 * width1) ls->step = stx + 0.5*(sty - stx);
width1 = width;
width = PetscAbsReal(sty - stx);
}
}
if ((ls->nfeval+ls->nfgeval) > ls->max_funcs) {
ierr = PetscInfo2(ls,"Number of line search function evals (%D) > maximum (%D)\n",(ls->nfeval+ls->nfgeval),ls->max_funcs);CHKERRQ(ierr);
ls->reason = TAOLINESEARCH_HALTED_MAXFCN;
}
/* Finish computations */
ierr = PetscInfo2(ls,"%D function evals in line search, step = %g\n",(ls->nfeval+ls->nfgeval),(double)ls->step);CHKERRQ(ierr);
/* Set new solution vector and compute gradient if needed */
ierr = VecCopy(mt->work,x);CHKERRQ(ierr);
if (!g_computed) {
ierr = TaoLineSearchComputeGradient(ls,mt->work,g);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
static PetscErrorCode TaoLineSearchApply_GPCG(TaoLineSearch ls, Vec x, PetscReal *f, Vec g, Vec s)
{
TaoLineSearch_GPCG *neP = (TaoLineSearch_GPCG *)ls->data;
PetscErrorCode ierr;
PetscInt i;
PetscBool g_computed=PETSC_FALSE; /* to prevent extra gradient computation */
PetscReal d1,finit,actred,prered,rho, gdx;
PetscFunctionBegin;
/* ls->stepmin - lower bound for step */
/* ls->stepmax - upper bound for step */
/* ls->rtol - relative tolerance for an acceptable step */
/* ls->ftol - tolerance for sufficient decrease condition */
/* ls->gtol - tolerance for curvature condition */
/* ls->nfeval - number of function evaluations */
/* ls->nfeval - number of function/gradient evaluations */
/* ls->max_funcs - maximum number of function evaluations */
ls->reason = TAOLINESEARCH_CONTINUE_ITERATING;
ls->step = ls->initstep;
if (!neP->W2) {
ierr = VecDuplicate(x,&neP->W2);CHKERRQ(ierr);
ierr = VecDuplicate(x,&neP->W1);CHKERRQ(ierr);
ierr = VecDuplicate(x,&neP->Gold);CHKERRQ(ierr);
neP->x = x;
ierr = PetscObjectReference((PetscObject)neP->x);CHKERRQ(ierr);
} else if (x != neP->x) {
ierr = VecDestroy(&neP->x);CHKERRQ(ierr);
ierr = VecDestroy(&neP->W1);CHKERRQ(ierr);
ierr = VecDestroy(&neP->W2);CHKERRQ(ierr);
ierr = VecDestroy(&neP->Gold);CHKERRQ(ierr);
ierr = VecDuplicate(x,&neP->W1);CHKERRQ(ierr);
ierr = VecDuplicate(x,&neP->W2);CHKERRQ(ierr);
ierr = VecDuplicate(x,&neP->Gold);CHKERRQ(ierr);
ierr = PetscObjectDereference((PetscObject)neP->x);CHKERRQ(ierr);
neP->x = x;
ierr = PetscObjectReference((PetscObject)neP->x);CHKERRQ(ierr);
}
ierr = VecDot(g,s,&gdx);CHKERRQ(ierr);
if (gdx > 0) {
ierr = PetscInfo1(ls,"Line search error: search direction is not descent direction. dot(g,s) = %g\n",(double)gdx);CHKERRQ(ierr);
ls->reason = TAOLINESEARCH_FAILED_ASCENT;
PetscFunctionReturn(0);
}
ierr = VecCopy(x,neP->W2);CHKERRQ(ierr);
ierr = VecCopy(g,neP->Gold);CHKERRQ(ierr);
if (ls->bounded) {
/* Compute the smallest steplength that will make one nonbinding variable equal the bound */
ierr = VecStepBoundInfo(x,s,ls->lower,ls->upper,&rho,&actred,&d1);CHKERRQ(ierr);
ls->step = PetscMin(ls->step,d1);
}
rho=0; actred=0;
if (ls->step < 0) {
ierr = PetscInfo1(ls,"Line search error: initial step parameter %g< 0\n",(double)ls->step);CHKERRQ(ierr);
ls->reason = TAOLINESEARCH_HALTED_OTHER;
PetscFunctionReturn(0);
}
/* Initialization */
finit = *f;
for (i=0; i< ls->max_funcs; i++) {
/* Force the step to be within the bounds */
ls->step = PetscMax(ls->step,ls->stepmin);
ls->step = PetscMin(ls->step,ls->stepmax);
ierr = VecCopy(x,neP->W2);CHKERRQ(ierr);
ierr = VecAXPY(neP->W2,ls->step,s);CHKERRQ(ierr);
if (ls->bounded) {
/* Make sure new vector is numerically within bounds */
ierr = VecMedian(neP->W2,ls->lower,ls->upper,neP->W2);CHKERRQ(ierr);
}
/* Gradient is not needed here. Unless there is a separate
gradient routine, compute it here anyway to prevent recomputing at
the end of the line search */
if (ls->hasobjective) {
ierr = TaoLineSearchComputeObjective(ls,neP->W2,f);CHKERRQ(ierr);
g_computed=PETSC_FALSE;
} else if (ls->usegts){
ierr = TaoLineSearchComputeObjectiveAndGTS(ls,neP->W2,f,&gdx);CHKERRQ(ierr);
g_computed=PETSC_FALSE;
} else {
ierr = TaoLineSearchComputeObjectiveAndGradient(ls,neP->W2,f,g);CHKERRQ(ierr);
g_computed=PETSC_TRUE;
}
if (0 == i) {
ls->f_fullstep = *f;
}
actred = *f - finit;
ierr = VecCopy(neP->W2,neP->W1);CHKERRQ(ierr);
ierr = VecAXPY(neP->W1,-1.0,x);CHKERRQ(ierr); /* W1 = W2 - X */
ierr = VecDot(neP->W1,neP->Gold,&prered);CHKERRQ(ierr);
if (fabs(prered)<1.0e-100) prered=1.0e-12;
rho = actred/prered;
/*
If sufficient progress has been obtained, accept the
point. Otherwise, backtrack.
*/
if (actred > 0) {
ierr = PetscInfo(ls,"Step resulted in ascent, rejecting.\n");CHKERRQ(ierr);
ls->step = (ls->step)/2;
} else if (rho > ls->ftol){
break;
} else{
ls->step = (ls->step)/2;
}
/* Convergence testing */
if (ls->step <= ls->stepmin || ls->step >= ls->stepmax) {
ls->reason = TAOLINESEARCH_HALTED_OTHER;
ierr = PetscInfo(ls,"Rounding errors may prevent further progress. May not be a step satisfying\n");CHKERRQ(ierr);
ierr = PetscInfo(ls,"sufficient decrease and curvature conditions. Tolerances may be too small.\n");CHKERRQ(ierr);
break;
}
if (ls->step == ls->stepmax) {
ierr = PetscInfo1(ls,"Step is at the upper bound, stepmax (%g)\n",(double)ls->stepmax);CHKERRQ(ierr);
ls->reason = TAOLINESEARCH_HALTED_UPPERBOUND;
break;
}
if (ls->step == ls->stepmin) {
ierr = PetscInfo1(ls,"Step is at the lower bound, stepmin (%g)\n",(double)ls->stepmin);CHKERRQ(ierr);
ls->reason = TAOLINESEARCH_HALTED_LOWERBOUND;
break;
}
if ((ls->nfeval+ls->nfgeval) >= ls->max_funcs) {
ierr = PetscInfo2(ls,"Number of line search function evals (%D) > maximum (%D)\n",ls->nfeval+ls->nfgeval,ls->max_funcs);CHKERRQ(ierr);
ls->reason = TAOLINESEARCH_HALTED_MAXFCN;
break;
}
if ((neP->bracket) && (ls->stepmax - ls->stepmin <= ls->rtol*ls->stepmax)){
ierr = PetscInfo1(ls,"Relative width of interval of uncertainty is at most rtol (%g)\n",(double)ls->rtol);CHKERRQ(ierr);
ls->reason = TAOLINESEARCH_HALTED_RTOL;
break;
}
}
ierr = PetscInfo2(ls,"%D function evals in line search, step = %g\n",ls->nfeval+ls->nfgeval,(double)ls->step);CHKERRQ(ierr);
/* set new solution vector and compute gradient if necessary */
ierr = VecCopy(neP->W2, x);CHKERRQ(ierr);
if (ls->reason == TAOLINESEARCH_CONTINUE_ITERATING) {
ls->reason = TAOLINESEARCH_SUCCESS;
}
if (!g_computed) {
ierr = TaoLineSearchComputeGradient(ls,x,g);CHKERRQ(ierr);
}
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_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 QPIPSetInitialPoint(TAO_BQPIP *qp, Tao tao)
{
PetscErrorCode ierr;
PetscReal two=2.0,p01=1;
PetscReal gap1,gap2,fff,mu;
PetscFunctionBegin;
/* Compute function, Gradient R=Hx+b, and Hessian */
ierr = TaoComputeVariableBounds(tao);CHKERRQ(ierr);
ierr = VecMedian(qp->XL, tao->solution, qp->XU, tao->solution);CHKERRQ(ierr);
ierr = MatMult(tao->hessian, tao->solution, tao->gradient);CHKERRQ(ierr);
ierr = VecCopy(qp->C0, qp->Work);CHKERRQ(ierr);
ierr = VecAXPY(qp->Work, 0.5, tao->gradient);CHKERRQ(ierr);
ierr = VecAXPY(tao->gradient, 1.0, qp->C0);CHKERRQ(ierr);
ierr = VecDot(tao->solution, qp->Work, &fff);CHKERRQ(ierr);
qp->pobj = fff + qp->c;
/* Initialize Primal Vectors */
/* T = XU - X; G = X - XL */
ierr = VecCopy(qp->XU, qp->T);CHKERRQ(ierr);
ierr = VecAXPY(qp->T, -1.0, tao->solution);CHKERRQ(ierr);
ierr = VecCopy(tao->solution, qp->G);CHKERRQ(ierr);
ierr = VecAXPY(qp->G, -1.0, qp->XL);CHKERRQ(ierr);
ierr = VecSet(qp->GZwork, p01);CHKERRQ(ierr);
ierr = VecSet(qp->TSwork, p01);CHKERRQ(ierr);
ierr = VecPointwiseMax(qp->G, qp->G, qp->GZwork);CHKERRQ(ierr);
ierr = VecPointwiseMax(qp->T, qp->T, qp->TSwork);CHKERRQ(ierr);
/* Initialize Dual Variable Vectors */
ierr = VecCopy(qp->G, qp->Z);CHKERRQ(ierr);
ierr = VecReciprocal(qp->Z);CHKERRQ(ierr);
ierr = VecCopy(qp->T, qp->S);CHKERRQ(ierr);
ierr = VecReciprocal(qp->S);CHKERRQ(ierr);
ierr = MatMult(tao->hessian, qp->Work, qp->RHS);CHKERRQ(ierr);
ierr = VecAbs(qp->RHS);CHKERRQ(ierr);
ierr = VecSet(qp->Work, p01);CHKERRQ(ierr);
ierr = VecPointwiseMax(qp->RHS, qp->RHS, qp->Work);CHKERRQ(ierr);
ierr = VecPointwiseDivide(qp->RHS, tao->gradient, qp->RHS);CHKERRQ(ierr);
ierr = VecNorm(qp->RHS, NORM_1, &gap1);CHKERRQ(ierr);
mu = PetscMin(10.0,(gap1+10.0)/qp->m);
ierr = VecScale(qp->S, mu);CHKERRQ(ierr);
ierr = VecScale(qp->Z, mu);CHKERRQ(ierr);
ierr = VecSet(qp->TSwork, p01);CHKERRQ(ierr);
ierr = VecSet(qp->GZwork, p01);CHKERRQ(ierr);
ierr = VecPointwiseMax(qp->S, qp->S, qp->TSwork);CHKERRQ(ierr);
ierr = VecPointwiseMax(qp->Z, qp->Z, qp->GZwork);CHKERRQ(ierr);
qp->mu=0;qp->dinfeas=1.0;qp->pinfeas=1.0;
while ( (qp->dinfeas+qp->pinfeas)/(qp->m+qp->n) >= qp->mu ){
ierr = VecScale(qp->G, two);CHKERRQ(ierr);
ierr = VecScale(qp->Z, two);CHKERRQ(ierr);
ierr = VecScale(qp->S, two);CHKERRQ(ierr);
ierr = VecScale(qp->T, two);CHKERRQ(ierr);
ierr = QPIPComputeResidual(qp,tao);CHKERRQ(ierr);
ierr = VecCopy(tao->solution, qp->R3);CHKERRQ(ierr);
ierr = VecAXPY(qp->R3, -1.0, qp->G);CHKERRQ(ierr);
ierr = VecAXPY(qp->R3, -1.0, qp->XL);CHKERRQ(ierr);
ierr = VecCopy(tao->solution, qp->R5);CHKERRQ(ierr);
ierr = VecAXPY(qp->R5, 1.0, qp->T);CHKERRQ(ierr);
ierr = VecAXPY(qp->R5, -1.0, qp->XU);CHKERRQ(ierr);
ierr = VecNorm(qp->R3, NORM_INFINITY, &gap1);CHKERRQ(ierr);
ierr = VecNorm(qp->R5, NORM_INFINITY, &gap2);CHKERRQ(ierr);
qp->pinfeas=PetscMax(gap1,gap2);
/* Compute the duality gap */
ierr = VecDot(qp->G, qp->Z, &gap1);CHKERRQ(ierr);
ierr = VecDot(qp->T, qp->S, &gap2);CHKERRQ(ierr);
qp->gap = (gap1+gap2);
qp->dobj = qp->pobj - qp->gap;
if (qp->m>0) qp->mu=qp->gap/(qp->m); else qp->mu=0.0;
qp->rgap=qp->gap/( PetscAbsReal(qp->dobj) + PetscAbsReal(qp->pobj) + 1.0 );
}
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);
}
/* @ TaoApply_Armijo - This routine performs a linesearch. It
backtracks until the (nonmonotone) Armijo conditions are satisfied.
Input Parameters:
+ tao - Tao context
. X - current iterate (on output X contains new iterate, X + step*S)
. S - search direction
. f - merit function evaluated at X
. G - gradient of merit function evaluated at X
. W - work vector
- step - initial estimate of step length
Output parameters:
+ f - merit function evaluated at new iterate, X + step*S
. G - gradient of merit function evaluated at new iterate, X + step*S
. X - new iterate
- step - final step length
@ */
static PetscErrorCode TaoLineSearchApply_Armijo(TaoLineSearch ls, Vec x, PetscReal *f, Vec g, Vec s)
{
TaoLineSearch_ARMIJO *armP = (TaoLineSearch_ARMIJO *)ls->data;
PetscErrorCode ierr;
PetscInt i;
PetscReal fact, ref, gdx;
PetscInt idx;
PetscBool g_computed=PETSC_FALSE; /* to prevent extra gradient computation */
PetscFunctionBegin;
ls->reason = TAOLINESEARCH_CONTINUE_ITERATING;
if (!armP->work) {
ierr = VecDuplicate(x,&armP->work);CHKERRQ(ierr);
armP->x = x;
ierr = PetscObjectReference((PetscObject)armP->x);CHKERRQ(ierr);
} else if (x != armP->x) {
/* If x has changed, then recreate work */
ierr = VecDestroy(&armP->work);CHKERRQ(ierr);
ierr = VecDuplicate(x,&armP->work);CHKERRQ(ierr);
ierr = PetscObjectDereference((PetscObject)armP->x);CHKERRQ(ierr);
armP->x = x;
ierr = PetscObjectReference((PetscObject)armP->x);CHKERRQ(ierr);
}
/* Check linesearch parameters */
if (armP->alpha < 1) {
ierr = PetscInfo1(ls,"Armijo line search error: alpha (%g) < 1\n", (double)armP->alpha);CHKERRQ(ierr);
ls->reason=TAOLINESEARCH_FAILED_BADPARAMETER;
} else if ((armP->beta <= 0) || (armP->beta >= 1)) {
ierr = PetscInfo1(ls,"Armijo line search error: beta (%g) invalid\n", (double)armP->beta);CHKERRQ(ierr);
ls->reason=TAOLINESEARCH_FAILED_BADPARAMETER;
} else if ((armP->beta_inf <= 0) || (armP->beta_inf >= 1)) {
ierr = PetscInfo1(ls,"Armijo line search error: beta_inf (%g) invalid\n", (double)armP->beta_inf);CHKERRQ(ierr);
ls->reason=TAOLINESEARCH_FAILED_BADPARAMETER;
} else if ((armP->sigma <= 0) || (armP->sigma >= 0.5)) {
ierr = PetscInfo1(ls,"Armijo line search error: sigma (%g) invalid\n", (double)armP->sigma);CHKERRQ(ierr);
ls->reason=TAOLINESEARCH_FAILED_BADPARAMETER;
} else if (armP->memorySize < 1) {
ierr = PetscInfo1(ls,"Armijo line search error: memory_size (%D) < 1\n", armP->memorySize);CHKERRQ(ierr);
ls->reason=TAOLINESEARCH_FAILED_BADPARAMETER;
} else if ((armP->referencePolicy != REFERENCE_MAX) && (armP->referencePolicy != REFERENCE_AVE) && (armP->referencePolicy != REFERENCE_MEAN)) {
ierr = PetscInfo(ls,"Armijo line search error: reference_policy invalid\n");CHKERRQ(ierr);
ls->reason=TAOLINESEARCH_FAILED_BADPARAMETER;
} else if ((armP->replacementPolicy != REPLACE_FIFO) && (armP->replacementPolicy != REPLACE_MRU)) {
ierr = PetscInfo(ls,"Armijo line search error: replacement_policy invalid\n");CHKERRQ(ierr);
ls->reason=TAOLINESEARCH_FAILED_BADPARAMETER;
} else if (PetscIsInfOrNanReal(*f)) {
ierr = PetscInfo(ls,"Armijo line search error: initial function inf or nan\n");CHKERRQ(ierr);
ls->reason=TAOLINESEARCH_FAILED_BADPARAMETER;
}
if (ls->reason != TAOLINESEARCH_CONTINUE_ITERATING) {
PetscFunctionReturn(0);
}
/* Check to see of the memory has been allocated. If not, allocate
the historical array and populate it with the initial function
values. */
if (!armP->memory) {
ierr = PetscMalloc1(armP->memorySize, &armP->memory );CHKERRQ(ierr);
}
if (!armP->memorySetup) {
for (i = 0; i < armP->memorySize; i++) {
armP->memory[i] = armP->alpha*(*f);
}
armP->current = 0;
armP->lastReference = armP->memory[0];
armP->memorySetup=PETSC_TRUE;
}
/* Calculate reference value (MAX) */
ref = armP->memory[0];
idx = 0;
for (i = 1; i < armP->memorySize; i++) {
if (armP->memory[i] > ref) {
ref = armP->memory[i];
idx = i;
}
}
if (armP->referencePolicy == REFERENCE_AVE) {
ref = 0;
for (i = 0; i < armP->memorySize; i++) {
ref += armP->memory[i];
}
ref = ref / armP->memorySize;
ref = PetscMax(ref, armP->memory[armP->current]);
} else if (armP->referencePolicy == REFERENCE_MEAN) {
ref = PetscMin(ref, 0.5*(armP->lastReference + armP->memory[armP->current]));
}
ierr = VecDot(g,s,&gdx);CHKERRQ(ierr);
if (PetscIsInfOrNanReal(gdx)) {
ierr = PetscInfo1(ls,"Initial Line Search step * g is Inf or Nan (%g)\n",(double)gdx);CHKERRQ(ierr);
ls->reason=TAOLINESEARCH_FAILED_INFORNAN;
PetscFunctionReturn(0);
}
if (gdx >= 0.0) {
ierr = PetscInfo1(ls,"Initial Line Search step is not descent direction (g's=%g)\n",(double)gdx);CHKERRQ(ierr);
ls->reason = TAOLINESEARCH_FAILED_ASCENT;
PetscFunctionReturn(0);
}
if (armP->nondescending) {
fact = armP->sigma;
} else {
fact = armP->sigma * gdx;
}
ls->step = ls->initstep;
while (ls->step >= ls->stepmin && (ls->nfeval+ls->nfgeval) < ls->max_funcs) {
/* Calculate iterate */
ierr = VecCopy(x,armP->work);CHKERRQ(ierr);
ierr = VecAXPY(armP->work,ls->step,s);CHKERRQ(ierr);
if (ls->bounded) {
ierr = VecMedian(ls->lower,armP->work,ls->upper,armP->work);CHKERRQ(ierr);
}
/* Calculate function at new iterate */
if (ls->hasobjective) {
ierr = TaoLineSearchComputeObjective(ls,armP->work,f);CHKERRQ(ierr);
g_computed=PETSC_FALSE;
} else if (ls->usegts) {
ierr = TaoLineSearchComputeObjectiveAndGTS(ls,armP->work,f,&gdx);CHKERRQ(ierr);
g_computed=PETSC_FALSE;
} else {
ierr = TaoLineSearchComputeObjectiveAndGradient(ls,armP->work,f,g);CHKERRQ(ierr);
g_computed=PETSC_TRUE;
}
if (ls->step == ls->initstep) {
ls->f_fullstep = *f;
}
if (PetscIsInfOrNanReal(*f)) {
ls->step *= armP->beta_inf;
} else {
/* Check descent condition */
if (armP->nondescending && *f <= ref - ls->step*fact*ref)
break;
if (!armP->nondescending && *f <= ref + ls->step*fact) {
break;
}
ls->step *= armP->beta;
}
}
/* Check termination */
if (PetscIsInfOrNanReal(*f)) {
ierr = PetscInfo(ls, "Function is inf or nan.\n");CHKERRQ(ierr);
ls->reason = TAOLINESEARCH_FAILED_INFORNAN;
} else if (ls->step < ls->stepmin) {
ierr = PetscInfo(ls, "Step length is below tolerance.\n");CHKERRQ(ierr);
ls->reason = TAOLINESEARCH_HALTED_RTOL;
} else if ((ls->nfeval+ls->nfgeval) >= ls->max_funcs) {
ierr = PetscInfo2(ls, "Number of line search function evals (%D) > maximum allowed (%D)\n",ls->nfeval+ls->nfgeval, ls->max_funcs);CHKERRQ(ierr);
ls->reason = TAOLINESEARCH_HALTED_MAXFCN;
}
if (ls->reason) {
PetscFunctionReturn(0);
}
/* Successful termination, update memory */
ls->reason = TAOLINESEARCH_SUCCESS;
armP->lastReference = ref;
if (armP->replacementPolicy == REPLACE_FIFO) {
armP->memory[armP->current++] = *f;
if (armP->current >= armP->memorySize) {
armP->current = 0;
}
} else {
armP->current = idx;
armP->memory[idx] = *f;
}
/* Update iterate and compute gradient */
ierr = VecCopy(armP->work,x);CHKERRQ(ierr);
if (!g_computed) {
ierr = TaoLineSearchComputeGradient(ls, x, g);CHKERRQ(ierr);
}
ierr = PetscInfo2(ls, "%D function evals in line search, step = %g\n",ls->nfeval, (double)ls->step);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);
}