PETSC_EXTERN void PETSC_STDCALL vecpow_(Vec v,PetscScalar *p, int *__ierr ){
*__ierr = VecPow(
(Vec)PetscToPointer((v) ),*p);
}
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);
}