static PetscErrorCode KSPSolve_AGMRES(KSP ksp)
{
PetscErrorCode ierr;
PetscInt its;
KSP_AGMRES *agmres = (KSP_AGMRES*)ksp->data;
PetscBool guess_zero = ksp->guess_zero;
PetscReal res_old, res;
PetscInt test;
PetscFunctionBegin;
ierr = PetscObjectSAWsTakeAccess((PetscObject)ksp);CHKERRQ(ierr);
ksp->its = 0;
ierr = PetscObjectSAWsGrantAccess((PetscObject)ksp);CHKERRQ(ierr);
ksp->reason = KSP_CONVERGED_ITERATING;
if (!agmres->HasShifts) { /* Compute Shifts for the Newton basis */
ierr = KSPComputeShifts_DGMRES(ksp);CHKERRQ(ierr);
}
/* NOTE: At this step, the initial guess is not equal to zero since one cycle of the classical GMRES is performed to compute the shifts */
ierr = (*ksp->converged)(ksp,0,ksp->rnorm,&ksp->reason,ksp->cnvP);CHKERRQ(ierr);
while (!ksp->reason) {
ierr = KSPInitialResidual(ksp,ksp->vec_sol,VEC_TMP,VEC_TMP_MATOP,VEC_V(0),ksp->vec_rhs);CHKERRQ(ierr);
if ((ksp->pc_side == PC_LEFT) && agmres->r && agmres->DeflPrecond) {
ierr = KSPDGMRESApplyDeflation_DGMRES(ksp, VEC_V(0), VEC_TMP);CHKERRQ(ierr);
ierr = VecCopy(VEC_TMP, VEC_V(0));CHKERRQ(ierr);
agmres->matvecs += 1;
}
ierr = VecNormalize(VEC_V(0),&(ksp->rnorm));CHKERRQ(ierr);
KSPCheckNorm(ksp,ksp->rnorm);
res_old = ksp->rnorm; /* Record the residual norm to test if deflation is needed */
ksp->ops->buildsolution = KSPBuildSolution_AGMRES;
ierr = KSPAGMRESCycle(&its,ksp);CHKERRQ(ierr);
if (ksp->its >= ksp->max_it) {
if (!ksp->reason) ksp->reason = KSP_DIVERGED_ITS;
break;
}
/* compute the eigenvectors to augment the subspace : use an adaptive strategy */
res = ksp->rnorm;
if (!ksp->reason && agmres->neig > 0) {
test = agmres->max_k * PetscLogReal(ksp->rtol/res) / PetscLogReal(res/res_old); /* estimate the remaining number of steps */
if ((test > agmres->smv*(ksp->max_it-ksp->its)) || agmres->force) {
if (!agmres->force && ((test > agmres->bgv*(ksp->max_it-ksp->its)) && ((agmres->r + 1) < agmres->max_neig))) {
agmres->neig += 1; /* Augment the number of eigenvalues to deflate if the convergence is too slow */
}
ierr = KSPDGMRESComputeDeflationData_DGMRES(ksp,&agmres->neig);CHKERRQ(ierr);
}
}
ksp->guess_zero = PETSC_FALSE; /* every future call to KSPInitialResidual() will have nonzero guess */
}
ksp->guess_zero = guess_zero; /* restore if user has provided nonzero initial guess */
PetscFunctionReturn(0);
}
static PetscErrorCode KSPAGMRESBuildSoln(KSP ksp,PetscInt it)
{
KSP_AGMRES *agmres = (KSP_AGMRES*)ksp->data;
PetscErrorCode ierr;
PetscInt max_k = agmres->max_k; /* Size of the non-augmented Krylov basis */
PetscInt i, j;
PetscInt r = agmres->r; /* current number of augmented eigenvectors */
PetscBLASInt KspSize;
PetscBLASInt lC;
PetscBLASInt N;
PetscBLASInt ldH = N + 1;
PetscBLASInt lwork;
PetscBLASInt info, nrhs = 1;
PetscFunctionBegin;
ierr = PetscBLASIntCast(KSPSIZE,&KspSize);CHKERRQ(ierr);
ierr = PetscBLASIntCast(4 * (KspSize+1),&lwork);CHKERRQ(ierr);
ierr = PetscBLASIntCast(KspSize+1,&lC);CHKERRQ(ierr);
ierr = PetscBLASIntCast(MAXKSPSIZE + 1,&N);CHKERRQ(ierr);
ierr = PetscBLASIntCast(N + 1,&ldH);CHKERRQ(ierr);
/* Save a copy of the Hessenberg matrix */
for (j = 0; j < N-1; j++) {
for (i = 0; i < N; i++) {
*HS(i,j) = *H(i,j);
}
}
/* QR factorize the Hessenberg matrix */
#if defined(PETSC_MISSING_LAPACK_GEQRF)
SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"GEQRF - Lapack routine is unavailable.");
#else
PetscStackCallBLAS("LAPACKgeqrf",LAPACKgeqrf_(&lC, &KspSize, agmres->hh_origin, &ldH, agmres->tau, agmres->work, &lwork, &info));
if (info) SETERRQ1(PetscObjectComm((PetscObject)ksp), PETSC_ERR_LIB,"Error in LAPACK routine XGEQRF INFO=%d", info);
#endif
/* Update the right hand side of the least square problem */
ierr = PetscMemzero(agmres->nrs, N*sizeof(PetscScalar));CHKERRQ(ierr);
agmres->nrs[0] = ksp->rnorm;
#if defined(PETSC_MISSING_LAPACK_ORMQR)
SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"GEQRF - Lapack routine is unavailable.");
#else
PetscStackCallBLAS("LAPACKormqr",LAPACKormqr_("L", "T", &lC, &nrhs, &KspSize, agmres->hh_origin, &ldH, agmres->tau, agmres->nrs, &N, agmres->work, &lwork, &info));
if (info) SETERRQ1(PetscObjectComm((PetscObject)ksp), PETSC_ERR_LIB,"Error in LAPACK routine XORMQR INFO=%d",info);
#endif
ksp->rnorm = PetscAbsScalar(agmres->nrs[KspSize]);
/* solve the least-square problem */
#if defined(PETSC_MISSING_LAPACK_TRTRS)
SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"TRTRS - Lapack routine is unavailable.");
#else
PetscStackCallBLAS("LAPACKtrtrs",LAPACKtrtrs_("U", "N", "N", &KspSize, &nrhs, agmres->hh_origin, &ldH, agmres->nrs, &N, &info));
if (info) SETERRQ1(PetscObjectComm((PetscObject)ksp), PETSC_ERR_LIB,"Error in LAPACK routine XTRTRS INFO=%d",info);
#endif
/* Accumulate the correction to the solution of the preconditioned problem in VEC_TMP */
ierr = VecZeroEntries(VEC_TMP);CHKERRQ(ierr);
ierr = VecMAXPY(VEC_TMP, max_k, agmres->nrs, &VEC_V(0));CHKERRQ(ierr);
if (!agmres->DeflPrecond) { ierr = VecMAXPY(VEC_TMP, r, &agmres->nrs[max_k], agmres->U);CHKERRQ(ierr); }
if ((ksp->pc_side == PC_RIGHT) && agmres->r && agmres->DeflPrecond) {
ierr = KSPDGMRESApplyDeflation_DGMRES(ksp, VEC_TMP, VEC_TMP_MATOP);CHKERRQ(ierr);
ierr = VecCopy(VEC_TMP_MATOP, VEC_TMP);CHKERRQ(ierr);
}
ierr = KSPUnwindPreconditioner(ksp, VEC_TMP, VEC_TMP_MATOP);CHKERRQ(ierr);
/* add the solution to the previous one */
ierr = VecAXPY(ksp->vec_sol, 1.0, VEC_TMP);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
static PetscErrorCode KSPAGMRESBuildBasis(KSP ksp)
{
PetscErrorCode ierr;
KSP_AGMRES *agmres = (KSP_AGMRES*)ksp->data;
PetscReal *Rshift = agmres->Rshift;
PetscReal *Ishift = agmres->Ishift;
PetscReal *Scale = agmres->Scale;
PetscInt max_k = agmres->max_k;
PetscInt KspSize = KSPSIZE; /* if max_k == KspSizen then the basis should not be augmented */
PetscInt j = 1;
PetscFunctionBegin;
ierr = PetscLogEventBegin(KSP_AGMRESBuildBasis, ksp, 0,0,0);CHKERRQ(ierr);
Scale[0] = 1.0;
while (j <= max_k) {
if (Ishift[j-1] == 0) {
if ((ksp->pc_side == PC_LEFT) && agmres->r && agmres->DeflPrecond) {
/* Apply the precond-matrix operators */
ierr = KSP_PCApplyBAorAB(ksp, VEC_V(j-1), VEC_TMP, VEC_TMP_MATOP);CHKERRQ(ierr);
/* Then apply deflation as a preconditioner */
ierr = KSPDGMRESApplyDeflation_DGMRES(ksp, VEC_TMP, VEC_V(j));CHKERRQ(ierr);
} else if ((ksp->pc_side == PC_RIGHT) && agmres->r && agmres->DeflPrecond) {
ierr = KSPDGMRESApplyDeflation_DGMRES(ksp, VEC_V(j-1), VEC_TMP);CHKERRQ(ierr);
ierr = KSP_PCApplyBAorAB(ksp, VEC_TMP, VEC_V(j), VEC_TMP_MATOP);CHKERRQ(ierr);
} else {
ierr = KSP_PCApplyBAorAB(ksp, VEC_V(j-1), VEC_V(j), VEC_TMP_MATOP);CHKERRQ(ierr);
}
ierr = VecAXPY(VEC_V(j), -Rshift[j-1], VEC_V(j-1));CHKERRQ(ierr);
#if defined(KSP_AGMRES_NONORM)
Scale[j] = 1.0;
#else
ierr = VecScale(VEC_V(j), Scale[j-1]);CHKERRQ(ierr); /* This step can be postponed until all vectors are built */
ierr = VecNorm(VEC_V(j), NORM_2, &(Scale[j]));CHKERRQ(ierr);
Scale[j] = 1.0/Scale[j];
#endif
agmres->matvecs += 1;
j++;
} else {
if ((ksp->pc_side == PC_LEFT) && agmres->r && agmres->DeflPrecond) {
/* Apply the precond-matrix operators */
ierr = KSP_PCApplyBAorAB(ksp, VEC_V(j-1), VEC_TMP, VEC_TMP_MATOP);CHKERRQ(ierr);
/* Then apply deflation as a preconditioner */
ierr = KSPDGMRESApplyDeflation_DGMRES(ksp, VEC_TMP, VEC_V(j));CHKERRQ(ierr);
} else if ((ksp->pc_side == PC_RIGHT) && agmres->r && agmres->DeflPrecond) {
ierr = KSPDGMRESApplyDeflation_DGMRES(ksp, VEC_V(j-1), VEC_TMP);CHKERRQ(ierr);
ierr = KSP_PCApplyBAorAB(ksp, VEC_TMP, VEC_V(j), VEC_TMP_MATOP);CHKERRQ(ierr);
} else {
ierr = KSP_PCApplyBAorAB(ksp, VEC_V(j-1), VEC_V(j), VEC_TMP_MATOP);CHKERRQ(ierr);
}
ierr = VecAXPY(VEC_V(j), -Rshift[j-1], VEC_V(j-1));CHKERRQ(ierr);
#if defined(KSP_AGMRES_NONORM)
Scale[j] = 1.0;
#else
ierr = VecScale(VEC_V(j), Scale[j-1]);CHKERRQ(ierr);
ierr = VecNorm(VEC_V(j), NORM_2, &(Scale[j]));CHKERRQ(ierr);
Scale[j] = 1.0/Scale[j];
#endif
agmres->matvecs += 1;
j++;
if ((ksp->pc_side == PC_LEFT) && agmres->r && agmres->DeflPrecond) {
/* Apply the precond-matrix operators */
ierr = KSP_PCApplyBAorAB(ksp, VEC_V(j-1), VEC_TMP, VEC_TMP_MATOP);CHKERRQ(ierr);
/* Then apply deflation as a preconditioner */
ierr = KSPDGMRESApplyDeflation_DGMRES(ksp, VEC_TMP, VEC_V(j));CHKERRQ(ierr);
} else if ((ksp->pc_side == PC_RIGHT) && agmres->r && agmres->DeflPrecond) {
ierr = KSPDGMRESApplyDeflation_DGMRES(ksp, VEC_V(j-1), VEC_TMP);CHKERRQ(ierr);
ierr = KSP_PCApplyBAorAB(ksp, VEC_TMP, VEC_V(j), VEC_TMP_MATOP);CHKERRQ(ierr);
} else {
ierr = KSP_PCApplyBAorAB(ksp, VEC_V(j-1), VEC_V(j), VEC_TMP_MATOP);CHKERRQ(ierr);
}
ierr = VecAXPY(VEC_V(j), -Rshift[j-2], VEC_V(j-1));CHKERRQ(ierr);
ierr = VecAXPY(VEC_V(j), Scale[j-2]*Ishift[j-2]*Ishift[j-2], VEC_V(j-2));CHKERRQ(ierr);
#if defined(KSP_AGMRES_NONORM)
Scale[j] = 1.0;
#else
ierr = VecNorm(VEC_V(j), NORM_2, &(Scale[j]));CHKERRQ(ierr);
Scale[j] = 1.0/Scale[j];
#endif
agmres->matvecs += 1;
j++;
}
}
/* Augment the subspace with the eigenvectors*/
while (j <= KspSize) {
ierr = KSP_PCApplyBAorAB(ksp, agmres->U[j - max_k - 1], VEC_V(j), VEC_TMP_MATOP);CHKERRQ(ierr);
#if defined(KSP_AGMRES_NONORM)
Scale[j] = 1.0;
#else
ierr = VecScale(VEC_V(j), Scale[j-1]);CHKERRQ(ierr);
ierr = VecNorm(VEC_V(j), NORM_2, &(Scale[j]));CHKERRQ(ierr);
Scale[j] = 1.0/Scale[j];
#endif
agmres->matvecs += 1;
j++;
}
ierr = PetscLogEventEnd(KSP_AGMRESBuildBasis, ksp, 0,0,0);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
