PetscErrorCode KSPSolve_FGMRES(KSP ksp)
{
PetscErrorCode ierr;
PetscInt cycle_its = 0; /* iterations done in a call to KSPFGMRESCycle */
KSP_FGMRES *fgmres = (KSP_FGMRES*)ksp->data;
PetscBool diagonalscale;
PetscFunctionBegin;
ierr = PCGetDiagonalScale(ksp->pc,&diagonalscale);CHKERRQ(ierr);
if (diagonalscale) SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_SUP,"Krylov method %s does not support diagonal scaling",((PetscObject)ksp)->type_name);
ierr = PetscObjectSAWsTakeAccess((PetscObject)ksp);CHKERRQ(ierr);
ksp->its = 0;
ierr = PetscObjectSAWsGrantAccess((PetscObject)ksp);CHKERRQ(ierr);
/* Compute the initial (NOT preconditioned) residual */
if (!ksp->guess_zero) {
ierr = KSPFGMRESResidual(ksp);CHKERRQ(ierr);
} else { /* guess is 0 so residual is F (which is in ksp->vec_rhs) */
ierr = VecCopy(ksp->vec_rhs,VEC_VV(0));CHKERRQ(ierr);
}
/* now the residual is in VEC_VV(0) - which is what
KSPFGMRESCycle expects... */
ierr = KSPFGMRESCycle(&cycle_its,ksp);CHKERRQ(ierr);
while (!ksp->reason) {
ierr = KSPFGMRESResidual(ksp);CHKERRQ(ierr);
if (ksp->its >= ksp->max_it) break;
ierr = KSPFGMRESCycle(&cycle_its,ksp);CHKERRQ(ierr);
}
/* mark lack of convergence */
if (ksp->its >= ksp->max_it && !ksp->reason) ksp->reason = KSP_DIVERGED_ITS;
PetscFunctionReturn(0);
}
static PetscErrorCode KSPSolve_PGMRES(KSP ksp)
{
PetscErrorCode ierr;
PetscInt its,itcount;
KSP_PGMRES *pgmres = (KSP_PGMRES*)ksp->data;
PetscBool guess_zero = ksp->guess_zero;
PetscFunctionBegin;
if (ksp->calc_sings && !pgmres->Rsvd) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ORDER,"Must call KSPSetComputeSingularValues() before KSPSetUp() is called");
ierr = PetscObjectAMSTakeAccess((PetscObject)ksp);CHKERRQ(ierr);
ksp->its = 0;
ierr = PetscObjectAMSGrantAccess((PetscObject)ksp);CHKERRQ(ierr);
itcount = 0;
ksp->reason = KSP_CONVERGED_ITERATING;
while (!ksp->reason) {
ierr = KSPInitialResidual(ksp,ksp->vec_sol,VEC_TEMP,VEC_TEMP_MATOP,VEC_VV(0),ksp->vec_rhs);CHKERRQ(ierr);
ierr = KSPPGMRESCycle(&its,ksp);CHKERRQ(ierr);
itcount += its;
if (itcount >= ksp->max_it) {
if (!ksp->reason) ksp->reason = KSP_DIVERGED_ITS;
break;
}
ksp->guess_zero = PETSC_FALSE; /* every future call to KSPInitialResidual() will have nonzero guess */
}
ksp->guess_zero = guess_zero; /* restore if user provided nonzero initial guess */
PetscFunctionReturn(0);
}
PetscErrorCode KSPGMRESModifiedGramSchmidtOrthogonalization(KSP ksp,PetscInt it)
{
KSP_GMRES *gmres = (KSP_GMRES*)(ksp->data);
PetscErrorCode ierr;
PetscInt j;
PetscScalar *hh,*hes;
PetscFunctionBegin;
ierr = PetscLogEventBegin(KSP_GMRESOrthogonalization,ksp,0,0,0);CHKERRQ(ierr);
/* update Hessenberg matrix and do Gram-Schmidt */
hh = HH(0,it);
hes = HES(0,it);
for (j=0; j<=it; j++) {
/* (vv(it+1), vv(j)) */
ierr = VecDot(VEC_VV(it+1),VEC_VV(j),hh);CHKERRQ(ierr);
KSPCheckDot(ksp,*hh);
*hes++ = *hh;
/* vv(it+1) <- vv(it+1) - hh[it+1][j] vv(j) */
ierr = VecAXPY(VEC_VV(it+1),-(*hh++),VEC_VV(j));CHKERRQ(ierr);
}
ierr = PetscLogEventEnd(KSP_GMRESOrthogonalization,ksp,0,0,0);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/*
KSPFGMRESResidual - This routine computes the initial residual (NOT PRECONDITIONED)
*/
static PetscErrorCode KSPFGMRESResidual(KSP ksp)
{
KSP_FGMRES *fgmres = (KSP_FGMRES*)(ksp->data);
Mat Amat,Pmat;
PetscErrorCode ierr;
PetscFunctionBegin;
ierr = PCGetOperators(ksp->pc,&Amat,&Pmat);CHKERRQ(ierr);
/* put A*x into VEC_TEMP */
ierr = KSP_MatMult(ksp,Amat,ksp->vec_sol,VEC_TEMP);CHKERRQ(ierr);
/* now put residual (-A*x + f) into vec_vv(0) */
ierr = VecWAXPY(VEC_VV(0),-1.0,VEC_TEMP,ksp->vec_rhs);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
static PetscErrorCode KSPGMRESBuildSoln(PetscScalar *nrs,Vec vs,Vec vdest,KSP ksp,PetscInt it)
{
PetscScalar tt;
PetscErrorCode ierr;
PetscInt ii,k,j;
KSP_GMRES *gmres = (KSP_GMRES*)(ksp->data);
PetscFunctionBegin;
/* Solve for solution vector that minimizes the residual */
/* If it is < 0, no gmres steps have been performed */
if (it < 0) {
ierr = VecCopy(vs,vdest);CHKERRQ(ierr); /* VecCopy() is smart, exists immediately if vguess == vdest */
PetscFunctionReturn(0);
}
if (*HH(it,it) != 0.0) {
nrs[it] = *GRS(it) / *HH(it,it);
} else {
ksp->reason = KSP_DIVERGED_BREAKDOWN;
ierr = PetscInfo2(ksp,"Likely your matrix or preconditioner is singular. HH(it,it) is identically zero; it = %D GRS(it) = %G",it,PetscAbsScalar(*GRS(it)));CHKERRQ(ierr);
PetscFunctionReturn(0);
}
for (ii=1; ii<=it; ii++) {
k = it - ii;
tt = *GRS(k);
for (j=k+1; j<=it; j++) tt = tt - *HH(k,j) * nrs[j];
if (*HH(k,k) == 0.0) {
ksp->reason = KSP_DIVERGED_BREAKDOWN;
ierr = PetscInfo1(ksp,"Likely your matrix or preconditioner is singular. HH(k,k) is identically zero; k = %D",k);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
nrs[k] = tt / *HH(k,k);
}
/* Accumulate the correction to the solution of the preconditioned problem in TEMP */
ierr = VecSet(VEC_TEMP,0.0);CHKERRQ(ierr);
ierr = VecMAXPY(VEC_TEMP,it+1,nrs,&VEC_VV(0));CHKERRQ(ierr);
ierr = KSPUnwindPreconditioner(ksp,VEC_TEMP,VEC_TEMP_MATOP);CHKERRQ(ierr);
/* add solution to previous solution */
if (vdest != vs) {
ierr = VecCopy(vs,vdest);CHKERRQ(ierr);
}
ierr = VecAXPY(vdest,1.0,VEC_TEMP);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode KSPSolve_LGMRES(KSP ksp)
{
PetscErrorCode ierr;
PetscInt cycle_its; /* iterations done in a call to KSPLGMRESCycle */
PetscInt itcount; /* running total of iterations, incl. those in restarts */
KSP_LGMRES *lgmres = (KSP_LGMRES *)ksp->data;
PetscBool guess_zero = ksp->guess_zero;
PetscInt ii; /*LGMRES_MOD variable */
PetscFunctionBegin;
if (ksp->calc_sings && !lgmres->Rsvd) SETERRQ(((PetscObject)ksp)->comm,PETSC_ERR_ORDER,"Must call KSPSetComputeSingularValues() before KSPSetUp() is called");
ierr = PetscObjectTakeAccess(ksp);
CHKERRQ(ierr);
ksp->its = 0;
lgmres->aug_ct = 0;
lgmres->matvecs = 0;
ierr = PetscObjectGrantAccess(ksp);
CHKERRQ(ierr);
/* initialize */
itcount = 0;
ksp->reason = KSP_CONVERGED_ITERATING;
/*LGMRES_MOD*/
for (ii=0; ii<lgmres->aug_dim; ii++) {
lgmres->aug_order[ii] = 0;
}
while (!ksp->reason) {
/* calc residual - puts in VEC_VV(0) */
ierr = KSPInitialResidual(ksp,ksp->vec_sol,VEC_TEMP,VEC_TEMP_MATOP,VEC_VV(0),ksp->vec_rhs);
CHKERRQ(ierr);
ierr = KSPLGMRESCycle(&cycle_its,ksp);
CHKERRQ(ierr);
itcount += cycle_its;
if (itcount >= ksp->max_it) {
if (!ksp->reason) ksp->reason = KSP_DIVERGED_ITS;
break;
}
ksp->guess_zero = PETSC_FALSE; /* every future call to KSPInitialResidual() will have nonzero guess */
}
ksp->guess_zero = guess_zero; /* restore if user provided nonzero initial guess */
PetscFunctionReturn(0);
}
/*@C
KSPGMRESMonitorKrylov - Calls VecView() for each direction in the
GMRES accumulated Krylov space.
Collective on KSP
Input Parameters:
+ ksp - the KSP context
. its - iteration number
. fgnorm - 2-norm of residual (or gradient)
- a viewers object created with PetscViewersCreate()
Level: intermediate
.keywords: KSP, nonlinear, vector, monitor, view, Krylov space
.seealso: KSPMonitorSet(), KSPMonitorDefault(), VecView(), PetscViewersCreate(), PetscViewersDestroy()
@*/
PetscErrorCode KSPGMRESMonitorKrylov(KSP ksp,PetscInt its,PetscReal fgnorm,void *dummy)
{
PetscViewers viewers = (PetscViewers)dummy;
KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
PetscErrorCode ierr;
Vec x;
PetscViewer viewer;
PetscBool flg;
PetscFunctionBegin;
ierr = PetscViewersGetViewer(viewers,gmres->it+1,&viewer);CHKERRQ(ierr);
ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&flg);CHKERRQ(ierr);
if (!flg) {
ierr = PetscViewerSetType(viewer,PETSCVIEWERDRAW);CHKERRQ(ierr);
ierr = PetscViewerDrawSetInfo(viewer,NULL,"Krylov GMRES Monitor",PETSC_DECIDE,PETSC_DECIDE,300,300);CHKERRQ(ierr);
}
x = VEC_VV(gmres->it+1);
ierr = VecView(x,viewer);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
static PetscErrorCode KSPPGMRESBuildSoln(PetscScalar *nrs,Vec vguess,Vec vdest,KSP ksp,PetscInt it)
{
PetscScalar tt;
PetscErrorCode ierr;
PetscInt k,j;
KSP_PGMRES *pgmres = (KSP_PGMRES*)(ksp->data);
PetscFunctionBegin;
/* Solve for solution vector that minimizes the residual */
if (it < 0) { /* no pgmres steps have been performed */
ierr = VecCopy(vguess,vdest);CHKERRQ(ierr); /* VecCopy() is smart, exits immediately if vguess == vdest */
PetscFunctionReturn(0);
}
/* solve the upper triangular system - RS is the right side and HH is
the upper triangular matrix - put soln in nrs */
if (*HH(it,it) != 0.0) nrs[it] = *RS(it) / *HH(it,it);
else nrs[it] = 0.0;
for (k=it-1; k>=0; k--) {
tt = *RS(k);
for (j=k+1; j<=it; j++) tt -= *HH(k,j) * nrs[j];
nrs[k] = tt / *HH(k,k);
}
/* Accumulate the correction to the solution of the preconditioned problem in TEMP */
ierr = VecZeroEntries(VEC_TEMP);CHKERRQ(ierr);
ierr = VecMAXPY(VEC_TEMP,it+1,nrs,&VEC_VV(0));CHKERRQ(ierr);
ierr = KSPUnwindPreconditioner(ksp,VEC_TEMP,VEC_TEMP_MATOP);CHKERRQ(ierr);
/* add solution to previous solution */
if (vdest == vguess) {
ierr = VecAXPY(vdest,1.0,VEC_TEMP);CHKERRQ(ierr);
} else {
ierr = VecWAXPY(vdest,1.0,VEC_TEMP,vguess);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
/*
KSPSolve_PIPEFGMRES - This routine applies the PIPEFGMRES method.
Input Parameter:
. ksp - the Krylov space object that was set to use pipefgmres
Output Parameter:
. outits - number of iterations used
*/
static PetscErrorCode KSPSolve_PIPEFGMRES(KSP ksp)
{
PetscErrorCode ierr;
PetscInt its,itcount;
KSP_PIPEFGMRES *pipefgmres = (KSP_PIPEFGMRES*)ksp->data;
PetscBool guess_zero = ksp->guess_zero;
PetscFunctionBegin;
/* We have not checked these routines for use with complex numbers. The inner products
are likely not defined correctly for that case */
#if (defined(PETSC_USE_COMPLEX) && !defined(PETSC_SKIP_COMPLEX))
SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"PIPEFGMRES has not been implemented for use with complex scalars");
#endif
ierr = PetscCitationsRegister(citation,&cited);CHKERRQ(ierr);
if (ksp->calc_sings && !pipefgmres->Rsvd) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ORDER,"Must call KSPSetComputeSingularValues() before KSPSetUp() is called");
ierr = PetscObjectSAWsTakeAccess((PetscObject)ksp);CHKERRQ(ierr);
ksp->its = 0;
ierr = PetscObjectSAWsGrantAccess((PetscObject)ksp);CHKERRQ(ierr);
itcount = 0;
ksp->reason = KSP_CONVERGED_ITERATING;
while (!ksp->reason) {
ierr = KSPInitialResidual(ksp,ksp->vec_sol,VEC_TEMP,VEC_TEMP_MATOP,VEC_VV(0),ksp->vec_rhs);CHKERRQ(ierr);
ierr = KSPPIPEFGMRESCycle(&its,ksp);CHKERRQ(ierr);
itcount += its;
if (itcount >= ksp->max_it) {
if (!ksp->reason) ksp->reason = KSP_DIVERGED_ITS;
break;
}
ksp->guess_zero = PETSC_FALSE; /* every future call to KSPInitialResidual() will have nonzero guess */
}
ksp->guess_zero = guess_zero; /* restore if user provided nonzero initial guess */
PetscFunctionReturn(0);
}
PetscErrorCode KSPFGMRESCycle(PetscInt *itcount,KSP ksp)
{
KSP_FGMRES *fgmres = (KSP_FGMRES*)(ksp->data);
PetscReal res_norm;
PetscReal hapbnd,tt;
PetscBool hapend = PETSC_FALSE; /* indicates happy breakdown ending */
PetscErrorCode ierr;
PetscInt loc_it; /* local count of # of dir. in Krylov space */
PetscInt max_k = fgmres->max_k; /* max # of directions Krylov space */
Mat Amat,Pmat;
MatStructure pflag;
PetscFunctionBegin;
/* Number of pseudo iterations since last restart is the number
of prestart directions */
loc_it = 0;
/* note: (fgmres->it) is always set one less than (loc_it) It is used in
KSPBUILDSolution_FGMRES, where it is passed to KSPFGMRESBuildSoln.
Note that when KSPFGMRESBuildSoln is called from this function,
(loc_it -1) is passed, so the two are equivalent */
fgmres->it = (loc_it - 1);
/* initial residual is in VEC_VV(0) - compute its norm*/
ierr = VecNorm(VEC_VV(0),NORM_2,&res_norm);CHKERRQ(ierr);
/* first entry in right-hand-side of hessenberg system is just
the initial residual norm */
*RS(0) = res_norm;
ksp->rnorm = res_norm;
ierr = KSPLogResidualHistory(ksp,res_norm);CHKERRQ(ierr);
ierr = KSPMonitor(ksp,ksp->its,res_norm);CHKERRQ(ierr);
/* check for the convergence - maybe the current guess is good enough */
ierr = (*ksp->converged)(ksp,ksp->its,res_norm,&ksp->reason,ksp->cnvP);CHKERRQ(ierr);
if (ksp->reason) {
if (itcount) *itcount = 0;
PetscFunctionReturn(0);
}
/* scale VEC_VV (the initial residual) */
ierr = VecScale(VEC_VV(0),1.0/res_norm);CHKERRQ(ierr);
/* MAIN ITERATION LOOP BEGINNING*/
/* keep iterating until we have converged OR generated the max number
of directions OR reached the max number of iterations for the method */
while (!ksp->reason && loc_it < max_k && ksp->its < ksp->max_it) {
if (loc_it) {
ierr = KSPLogResidualHistory(ksp,res_norm);CHKERRQ(ierr);
ierr = KSPMonitor(ksp,ksp->its,res_norm);CHKERRQ(ierr);
}
fgmres->it = (loc_it - 1);
/* see if more space is needed for work vectors */
if (fgmres->vv_allocated <= loc_it + VEC_OFFSET + 1) {
ierr = KSPFGMRESGetNewVectors(ksp,loc_it+1);CHKERRQ(ierr);
/* (loc_it+1) is passed in as number of the first vector that should
be allocated */
}
/* CHANGE THE PRECONDITIONER? */
/* ModifyPC is the callback function that can be used to
change the PC or its attributes before its applied */
(*fgmres->modifypc)(ksp,ksp->its,loc_it,res_norm,fgmres->modifyctx);
/* apply PRECONDITIONER to direction vector and store with
preconditioned vectors in prevec */
ierr = KSP_PCApply(ksp,VEC_VV(loc_it),PREVEC(loc_it));CHKERRQ(ierr);
ierr = PCGetOperators(ksp->pc,&Amat,&Pmat,&pflag);CHKERRQ(ierr);
/* Multiply preconditioned vector by operator - put in VEC_VV(loc_it+1) */
ierr = MatMult(Amat,PREVEC(loc_it),VEC_VV(1+loc_it));CHKERRQ(ierr);
/* update hessenberg matrix and do Gram-Schmidt - new direction is in
VEC_VV(1+loc_it)*/
ierr = (*fgmres->orthog)(ksp,loc_it);CHKERRQ(ierr);
/* new entry in hessenburg is the 2-norm of our new direction */
ierr = VecNorm(VEC_VV(loc_it+1),NORM_2,&tt);CHKERRQ(ierr);
*HH(loc_it+1,loc_it) = tt;
*HES(loc_it+1,loc_it) = tt;
/* Happy Breakdown Check */
hapbnd = PetscAbsScalar((tt) / *RS(loc_it));
/* RS(loc_it) contains the res_norm from the last iteration */
hapbnd = PetscMin(fgmres->haptol,hapbnd);
if (tt > hapbnd) {
/* scale new direction by its norm */
ierr = VecScale(VEC_VV(loc_it+1),1.0/tt);CHKERRQ(ierr);
} else {
/* This happens when the solution is exactly reached. */
/* So there is no new direction... */
ierr = VecSet(VEC_TEMP,0.0);CHKERRQ(ierr); /* set VEC_TEMP to 0 */
hapend = PETSC_TRUE;
}
/* note that for FGMRES we could get HES(loc_it+1, loc_it) = 0 and the
current solution would not be exact if HES was singular. Note that
HH non-singular implies that HES is no singular, and HES is guaranteed
to be nonsingular when PREVECS are linearly independent and A is
nonsingular (in GMRES, the nonsingularity of A implies the nonsingularity
of HES). So we should really add a check to verify that HES is nonsingular.*/
/* Now apply rotations to new col of hessenberg (and right side of system),
calculate new rotation, and get new residual norm at the same time*/
ierr = KSPFGMRESUpdateHessenberg(ksp,loc_it,hapend,&res_norm);CHKERRQ(ierr);
if (ksp->reason) break;
loc_it++;
fgmres->it = (loc_it-1); /* Add this here in case it has converged */
ierr = PetscObjectSAWsTakeAccess((PetscObject)ksp);CHKERRQ(ierr);
ksp->its++;
ksp->rnorm = res_norm;
ierr = PetscObjectSAWsGrantAccess((PetscObject)ksp);CHKERRQ(ierr);
ierr = (*ksp->converged)(ksp,ksp->its,res_norm,&ksp->reason,ksp->cnvP);CHKERRQ(ierr);
/* Catch error in happy breakdown and signal convergence and break from loop */
if (hapend) {
if (!ksp->reason) {
if (ksp->errorifnotconverged) SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_NOT_CONVERGED,"You reached the happy break down, but convergence was not indicated. Residual norm = %G",res_norm);
else {
ksp->reason = KSP_DIVERGED_BREAKDOWN;
break;
}
}
}
}
/* END OF ITERATION LOOP */
ierr = KSPLogResidualHistory(ksp,res_norm);CHKERRQ(ierr);
/*
Monitor if we know that we will not return for a restart */
if (loc_it && (ksp->reason || ksp->its >= ksp->max_it)) {
ierr = KSPMonitor(ksp,ksp->its,res_norm);CHKERRQ(ierr);
}
if (itcount) *itcount = loc_it;
/*
Down here we have to solve for the "best" coefficients of the Krylov
columns, add the solution values together, and possibly unwind the
preconditioning from the solution
*/
/* Form the solution (or the solution so far) */
/* Note: must pass in (loc_it-1) for iteration count so that KSPFGMRESBuildSoln
properly navigates */
ierr = KSPFGMRESBuildSoln(RS(0),ksp->vec_sol,ksp->vec_sol,ksp,loc_it-1);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
static PetscErrorCode KSPPGMRESCycle(PetscInt *itcount,KSP ksp)
{
KSP_PGMRES *pgmres = (KSP_PGMRES*)(ksp->data);
PetscReal res_norm,res,newnorm;
PetscErrorCode ierr;
PetscInt it = 0,j,k;
PetscBool hapend = PETSC_FALSE;
PetscFunctionBegin;
if (itcount) *itcount = 0;
ierr = VecNormalize(VEC_VV(0),&res_norm);CHKERRQ(ierr);
res = res_norm;
*RS(0) = res_norm;
/* check for the convergence */
ierr = PetscObjectAMSTakeAccess((PetscObject)ksp);CHKERRQ(ierr);
ksp->rnorm = res;
ierr = PetscObjectAMSGrantAccess((PetscObject)ksp);CHKERRQ(ierr);
pgmres->it = it-2;
ierr = KSPLogResidualHistory(ksp,res);CHKERRQ(ierr);
ierr = KSPMonitor(ksp,ksp->its,res);CHKERRQ(ierr);
if (!res) {
ksp->reason = KSP_CONVERGED_ATOL;
ierr = PetscInfo(ksp,"Converged due to zero residual norm on entry\n");CHKERRQ(ierr);
PetscFunctionReturn(0);
}
ierr = (*ksp->converged)(ksp,ksp->its,res,&ksp->reason,ksp->cnvP);CHKERRQ(ierr);
for (; !ksp->reason; it++) {
Vec Zcur,Znext;
if (pgmres->vv_allocated <= it + VEC_OFFSET + 1) {
ierr = KSPGMRESGetNewVectors(ksp,it+1);CHKERRQ(ierr);
}
/* VEC_VV(it-1) is orthogonal, it will be normalized once the VecNorm arrives. */
Zcur = VEC_VV(it); /* Zcur is not yet orthogonal, but the VecMDot to orthogonalize it has been started. */
Znext = VEC_VV(it+1); /* This iteration will compute Znext, update with a deferred correction once we know how
* Zcur relates to the previous vectors, and start the reduction to orthogonalize it. */
if (it < pgmres->max_k+1 && ksp->its+1 < PetscMax(2,ksp->max_it)) { /* We don't know whether what we have computed is enough, so apply the matrix. */
ierr = KSP_PCApplyBAorAB(ksp,Zcur,Znext,VEC_TEMP_MATOP);CHKERRQ(ierr);
}
if (it > 1) { /* Complete the pending reduction */
ierr = VecNormEnd(VEC_VV(it-1),NORM_2,&newnorm);CHKERRQ(ierr);
*HH(it-1,it-2) = newnorm;
}
if (it > 0) { /* Finish the reduction computing the latest column of H */
ierr = VecMDotEnd(Zcur,it,&(VEC_VV(0)),HH(0,it-1));CHKERRQ(ierr);
}
if (it > 1) {
/* normalize the base vector from two iterations ago, basis is complete up to here */
ierr = VecScale(VEC_VV(it-1),1./ *HH(it-1,it-2));CHKERRQ(ierr);
ierr = KSPPGMRESUpdateHessenberg(ksp,it-2,&hapend,&res);CHKERRQ(ierr);
pgmres->it = it-2;
ksp->its++;
ksp->rnorm = res;
ierr = (*ksp->converged)(ksp,ksp->its,res,&ksp->reason,ksp->cnvP);CHKERRQ(ierr);
if (it < pgmres->max_k+1 || ksp->reason || ksp->its == ksp->max_it) { /* Monitor if we are done or still iterating, but not before a restart. */
ierr = KSPLogResidualHistory(ksp,res);CHKERRQ(ierr);
ierr = KSPMonitor(ksp,ksp->its,res);CHKERRQ(ierr);
}
if (ksp->reason) break;
/* Catch error in happy breakdown and signal convergence and break from loop */
if (hapend) {
if (ksp->errorifnotconverged) SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_NOT_CONVERGED,"You reached the happy break down, but convergence was not indicated. Residual norm = %G",res);
else {
ksp->reason = KSP_DIVERGED_BREAKDOWN;
break;
}
}
if (!(it < pgmres->max_k+1 && ksp->its < ksp->max_it)) break;
/* The it-2 column of H was not scaled when we computed Zcur, apply correction */
ierr = VecScale(Zcur,1./ *HH(it-1,it-2));CHKERRQ(ierr);
/* And Znext computed in this iteration was computed using the under-scaled Zcur */
ierr = VecScale(Znext,1./ *HH(it-1,it-2));CHKERRQ(ierr);
/* In the previous iteration, we projected an unnormalized Zcur against the Krylov basis, so we need to fix the column of H resulting from that projection. */
for (k=0; k<it; k++) *HH(k,it-1) /= *HH(it-1,it-2);
/* When Zcur was projected against the Krylov basis, VV(it-1) was still not normalized, so fix that too. This
* column is complete except for HH(it,it-1) which we won't know until the next iteration. */
*HH(it-1,it-1) /= *HH(it-1,it-2);
}
if (it > 0) {
PetscScalar *work;
if (!pgmres->orthogwork) {ierr = PetscMalloc((pgmres->max_k + 2)*sizeof(PetscScalar),&pgmres->orthogwork);CHKERRQ(ierr);}
work = pgmres->orthogwork;
/* Apply correction computed by the VecMDot in the last iteration to Znext. The original form is
*
* Znext -= sum_{j=0}^{i-1} Z[j+1] * H[j,i-1]
*
* where
*
* Z[j] = sum_{k=0}^j V[k] * H[k,j-1]
*
* substituting
*
* Znext -= sum_{j=0}^{i-1} sum_{k=0}^{j+1} V[k] * H[k,j] * H[j,i-1]
*
* rearranging the iteration space from row-column to column-row
*
* Znext -= sum_{k=0}^i sum_{j=k-1}^{i-1} V[k] * H[k,j] * H[j,i-1]
*
* Note that column it-1 of HH is correct. For all previous columns, we must look at HES because HH has already
* been transformed to upper triangular form.
*/
for (k=0; k<it+1; k++) {
work[k] = 0;
for (j=PetscMax(0,k-1); j<it-1; j++) work[k] -= *HES(k,j) * *HH(j,it-1);
}
ierr = VecMAXPY(Znext,it+1,work,&VEC_VV(0));CHKERRQ(ierr);
ierr = VecAXPY(Znext,-*HH(it-1,it-1),Zcur);CHKERRQ(ierr);
/* Orthogonalize Zcur against existing basis vectors. */
for (k=0; k<it; k++) work[k] = -*HH(k,it-1);
ierr = VecMAXPY(Zcur,it,work,&VEC_VV(0));CHKERRQ(ierr);
/* Zcur is now orthogonal, and will be referred to as VEC_VV(it) again, though it is still not normalized. */
/* Begin computing the norm of the new vector, will be normalized after the MatMult in the next iteration. */
ierr = VecNormBegin(VEC_VV(it),NORM_2,&newnorm);CHKERRQ(ierr);
}
/* Compute column of H (to the diagonal, but not the subdiagonal) to be able to orthogonalize the newest vector. */
ierr = VecMDotBegin(Znext,it+1,&VEC_VV(0),HH(0,it));CHKERRQ(ierr);
/* Start an asynchronous split-mode reduction, the result of the MDot and Norm will be collected on the next iteration. */
ierr = PetscCommSplitReductionBegin(PetscObjectComm((PetscObject)Znext));CHKERRQ(ierr);
}
if (itcount) *itcount = it-1; /* Number of iterations actually completed. */
/*
Down here we have to solve for the "best" coefficients of the Krylov
columns, add the solution values together, and possibly unwind the
preconditioning from the solution
*/
/* Form the solution (or the solution so far) */
ierr = KSPPGMRESBuildSoln(RS(0),ksp->vec_sol,ksp->vec_sol,ksp,it-2);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode KSPGMRESCycle(PetscInt *itcount,KSP ksp)
{
KSP_GMRES *gmres = (KSP_GMRES*)(ksp->data);
PetscReal res_norm,res,hapbnd,tt;
PetscErrorCode ierr;
PetscInt it = 0, max_k = gmres->max_k;
PetscBool hapend = PETSC_FALSE;
PetscFunctionBegin;
ierr = VecNormalize(VEC_VV(0),&res_norm);CHKERRQ(ierr);
res = res_norm;
*GRS(0) = res_norm;
/* check for the convergence */
ierr = PetscObjectAMSTakeAccess((PetscObject)ksp);CHKERRQ(ierr);
ksp->rnorm = res;
ierr = PetscObjectAMSGrantAccess((PetscObject)ksp);CHKERRQ(ierr);
gmres->it = (it - 1);
ierr = KSPLogResidualHistory(ksp,res);CHKERRQ(ierr);
ierr = KSPMonitor(ksp,ksp->its,res);CHKERRQ(ierr);
if (!res) {
if (itcount) *itcount = 0;
ksp->reason = KSP_CONVERGED_ATOL;
ierr = PetscInfo(ksp,"Converged due to zero residual norm on entry\n");CHKERRQ(ierr);
PetscFunctionReturn(0);
}
ierr = (*ksp->converged)(ksp,ksp->its,res,&ksp->reason,ksp->cnvP);CHKERRQ(ierr);
while (!ksp->reason && it < max_k && ksp->its < ksp->max_it) {
if (it) {
ierr = KSPLogResidualHistory(ksp,res);CHKERRQ(ierr);
ierr = KSPMonitor(ksp,ksp->its,res);CHKERRQ(ierr);
}
gmres->it = (it - 1);
if (gmres->vv_allocated <= it + VEC_OFFSET + 1) {
ierr = KSPGMRESGetNewVectors(ksp,it+1);CHKERRQ(ierr);
}
ierr = KSP_PCApplyBAorAB(ksp,VEC_VV(it),VEC_VV(1+it),VEC_TEMP_MATOP);CHKERRQ(ierr);
/* update hessenberg matrix and do Gram-Schmidt */
ierr = (*gmres->orthog)(ksp,it);CHKERRQ(ierr);
/* vv(i+1) . vv(i+1) */
ierr = VecNormalize(VEC_VV(it+1),&tt);CHKERRQ(ierr);
/* save the magnitude */
*HH(it+1,it) = tt;
*HES(it+1,it) = tt;
/* check for the happy breakdown */
hapbnd = PetscAbsScalar(tt / *GRS(it));
if (hapbnd > gmres->haptol) hapbnd = gmres->haptol;
if (tt < hapbnd) {
ierr = PetscInfo2(ksp,"Detected happy breakdown, current hapbnd = %14.12e tt = %14.12e\n",(double)hapbnd,(double)tt);CHKERRQ(ierr);
hapend = PETSC_TRUE;
}
ierr = KSPGMRESUpdateHessenberg(ksp,it,hapend,&res);CHKERRQ(ierr);
it++;
gmres->it = (it-1); /* For converged */
ksp->its++;
ksp->rnorm = res;
if (ksp->reason) break;
ierr = (*ksp->converged)(ksp,ksp->its,res,&ksp->reason,ksp->cnvP);CHKERRQ(ierr);
/* Catch error in happy breakdown and signal convergence and break from loop */
if (hapend) {
if (!ksp->reason) {
if (ksp->errorifnotconverged) SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_NOT_CONVERGED,"You reached the happy break down, but convergence was not indicated. Residual norm = %G",res);
else {
ksp->reason = KSP_DIVERGED_BREAKDOWN;
break;
}
}
}
}
/* Monitor if we know that we will not return for a restart */
if (it && (ksp->reason || ksp->its >= ksp->max_it)) {
ierr = KSPLogResidualHistory(ksp,res);CHKERRQ(ierr);
ierr = KSPMonitor(ksp,ksp->its,res);CHKERRQ(ierr);
}
if (itcount) *itcount = it;
/*
Down here we have to solve for the "best" coefficients of the Krylov
columns, add the solution values together, and possibly unwind the
preconditioning from the solution
*/
/* Form the solution (or the solution so far) */
ierr = KSPGMRESBuildSoln(GRS(0),ksp->vec_sol,ksp->vec_sol,ksp,it-1);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
static PetscErrorCode KSPPIPEFGMRESCycle(PetscInt *itcount,KSP ksp)
{
KSP_PIPEFGMRES *pipefgmres = (KSP_PIPEFGMRES*)(ksp->data);
PetscReal res_norm;
PetscReal hapbnd,tt;
PetscScalar *hh,*hes,*lhh,shift = pipefgmres->shift;
PetscBool hapend = PETSC_FALSE; /* indicates happy breakdown ending */
PetscErrorCode ierr;
PetscInt loc_it; /* local count of # of dir. in Krylov space */
PetscInt max_k = pipefgmres->max_k; /* max # of directions Krylov space */
PetscInt i,j,k;
Mat Amat,Pmat;
Vec Q,W; /* Pipelining vectors */
Vec *redux = pipefgmres->redux; /* workspace for single reduction */
PetscFunctionBegin;
if (itcount) *itcount = 0;
/* Assign simpler names to these vectors, allocated as pipelining workspace */
Q = VEC_Q;
W = VEC_W;
/* Allocate memory for orthogonalization work (freed in the GMRES Destroy routine)*/
/* Note that we add an extra value here to allow for a single reduction */
if (!pipefgmres->orthogwork) { ierr = PetscMalloc1(pipefgmres->max_k + 2 ,&pipefgmres->orthogwork);CHKERRQ(ierr);
}
lhh = pipefgmres->orthogwork;
/* Number of pseudo iterations since last restart is the number
of prestart directions */
loc_it = 0;
/* note: (pipefgmres->it) is always set one less than (loc_it) It is used in
KSPBUILDSolution_PIPEFGMRES, where it is passed to KSPPIPEFGMRESBuildSoln.
Note that when KSPPIPEFGMRESBuildSoln is called from this function,
(loc_it -1) is passed, so the two are equivalent */
pipefgmres->it = (loc_it - 1);
/* initial residual is in VEC_VV(0) - compute its norm*/
ierr = VecNorm(VEC_VV(0),NORM_2,&res_norm);CHKERRQ(ierr);
/* first entry in right-hand-side of hessenberg system is just
the initial residual norm */
*RS(0) = res_norm;
ksp->rnorm = res_norm;
ierr = KSPLogResidualHistory(ksp,res_norm);CHKERRQ(ierr);
ierr = KSPMonitor(ksp,ksp->its,res_norm);CHKERRQ(ierr);
/* check for the convergence - maybe the current guess is good enough */
ierr = (*ksp->converged)(ksp,ksp->its,res_norm,&ksp->reason,ksp->cnvP);CHKERRQ(ierr);
if (ksp->reason) {
if (itcount) *itcount = 0;
PetscFunctionReturn(0);
}
/* scale VEC_VV (the initial residual) */
ierr = VecScale(VEC_VV(0),1.0/res_norm);CHKERRQ(ierr);
/* Fill the pipeline */
ierr = KSP_PCApply(ksp,VEC_VV(loc_it),PREVEC(loc_it));CHKERRQ(ierr);
ierr = PCGetOperators(ksp->pc,&Amat,&Pmat);CHKERRQ(ierr);
ierr = KSP_MatMult(ksp,Amat,PREVEC(loc_it),ZVEC(loc_it));CHKERRQ(ierr);
ierr = VecAXPY(ZVEC(loc_it),-shift,VEC_VV(loc_it));CHKERRQ(ierr); /* Note shift */
/* MAIN ITERATION LOOP BEGINNING*/
/* keep iterating until we have converged OR generated the max number
of directions OR reached the max number of iterations for the method */
while (!ksp->reason && loc_it < max_k && ksp->its < ksp->max_it) {
if (loc_it) {
ierr = KSPLogResidualHistory(ksp,res_norm);CHKERRQ(ierr);
ierr = KSPMonitor(ksp,ksp->its,res_norm);CHKERRQ(ierr);
}
pipefgmres->it = (loc_it - 1);
/* see if more space is needed for work vectors */
if (pipefgmres->vv_allocated <= loc_it + VEC_OFFSET + 1) {
ierr = KSPPIPEFGMRESGetNewVectors(ksp,loc_it+1);CHKERRQ(ierr);
/* (loc_it+1) is passed in as number of the first vector that should
be allocated */
}
/* Note that these inner products are with "Z" now, so
in particular, lhh[loc_it] is the 'barred' or 'shifted' value,
not the value from the equivalent FGMRES run (even in exact arithmetic)
That is, the H we need for the Arnoldi relation is different from the
coefficients we use in the orthogonalization process,because of the shift */
/* Do some local twiddling to allow for a single reduction */
for(i=0;i<loc_it+1;i++){
redux[i] = VEC_VV(i);
}
redux[loc_it+1] = ZVEC(loc_it);
/* note the extra dot product which ends up in lh[loc_it+1], which computes ||z||^2 */
ierr = VecMDotBegin(ZVEC(loc_it),loc_it+2,redux,lhh);CHKERRQ(ierr);
/* Start the split reduction (This actually calls the MPI_Iallreduce, otherwise, the reduction is simply delayed until the "end" call)*/
ierr = PetscCommSplitReductionBegin(PetscObjectComm((PetscObject)ZVEC(loc_it)));CHKERRQ(ierr);
/* The work to be overlapped with the inner products follows.
This is application of the preconditioner and the operator
to compute intermediate quantites which will be combined (locally)
with the results of the inner products.
*/
ierr = KSP_PCApply(ksp,ZVEC(loc_it),Q);CHKERRQ(ierr);
ierr = PCGetOperators(ksp->pc,&Amat,&Pmat);CHKERRQ(ierr);
ierr = KSP_MatMult(ksp,Amat,Q,W);CHKERRQ(ierr);
/* Compute inner products of the new direction with previous directions,
and the norm of the to-be-orthogonalized direction "Z".
This information is enough to build the required entries
of H. The inner product with VEC_VV(it_loc) is
*different* than in the standard FGMRES and need to be dealt with specially.
That is, for standard FGMRES the orthogonalization coefficients are the same
as the coefficients used in the Arnoldi relation to reconstruct, but here this
is not true (albeit only for the one entry of H which we "unshift" below. */
/* Finish the dot product, retrieving the extra entry */
ierr = VecMDotEnd(ZVEC(loc_it),loc_it+2,redux,lhh);CHKERRQ(ierr);
tt = PetscRealPart(lhh[loc_it+1]);
/* Hessenberg entries, and entries for (naive) classical Graham-Schmidt
Note that the Hessenberg entries require a shift, as these are for the
relation AU = VH, which is wrt unshifted basis vectors */
hh = HH(0,loc_it); hes=HES(0,loc_it);
for (j=0; j<loc_it; j++) {
hh[j] = lhh[j];
hes[j] = lhh[j];
}
hh[loc_it] = lhh[loc_it] + shift;
hes[loc_it] = lhh[loc_it] + shift;
/* we delay applying the shift here */
for (j=0; j<=loc_it; j++) {
lhh[j] = -lhh[j]; /* flip sign */
}
/* Compute the norm of the un-normalized new direction using the rearranged formula
Note that these are shifted ("barred") quantities */
for(k=0;k<=loc_it;k++) tt -= ((PetscReal)(PetscAbsScalar(lhh[k]) * PetscAbsScalar(lhh[k])));
/* On AVX512 this is accumulating roundoff errors for eg: tt=-2.22045e-16 */
if ((tt < 0.0) && tt > -PETSC_SMALL) tt = 0.0 ;
if (tt < 0.0) {
/* If we detect square root breakdown in the norm, we must restart the algorithm.
Here this means we simply break the current loop and reconstruct the solution
using the basis we have computed thus far. Note that by breaking immediately,
we do not update the iteration count, so computation done in this iteration
should be disregarded.
*/
ierr = PetscInfo2(ksp,"Restart due to square root breakdown at it = %D, tt=%g\n",ksp->its,(double)tt);CHKERRQ(ierr);
break;
} else {
tt = PetscSqrtReal(tt);
}
/* new entry in hessenburg is the 2-norm of our new direction */
hh[loc_it+1] = tt;
hes[loc_it+1] = tt;
/* The recurred computation for the new direction
The division by tt is delayed to the happy breakdown check later
Note placement BEFORE the unshift
*/
ierr = VecCopy(ZVEC(loc_it),VEC_VV(loc_it+1));CHKERRQ(ierr);
ierr = VecMAXPY(VEC_VV(loc_it+1),loc_it+1,lhh,&VEC_VV(0));CHKERRQ(ierr);
/* (VEC_VV(loc_it+1) is not normalized yet) */
/* The recurred computation for the preconditioned vector (u) */
ierr = VecCopy(Q,PREVEC(loc_it+1));CHKERRQ(ierr);
ierr = VecMAXPY(PREVEC(loc_it+1),loc_it+1,lhh,&PREVEC(0));CHKERRQ(ierr);
ierr = VecScale(PREVEC(loc_it+1),1.0/tt);CHKERRQ(ierr);
/* Unshift an entry in the GS coefficients ("removing the bar") */
lhh[loc_it] -= shift;
/* The recurred computation for z (Au)
Note placement AFTER the "unshift" */
ierr = VecCopy(W,ZVEC(loc_it+1));CHKERRQ(ierr);
ierr = VecMAXPY(ZVEC(loc_it+1),loc_it+1,lhh,&ZVEC(0));CHKERRQ(ierr);
ierr = VecScale(ZVEC(loc_it+1),1.0/tt);CHKERRQ(ierr);
/* Happy Breakdown Check */
hapbnd = PetscAbsScalar((tt) / *RS(loc_it));
/* RS(loc_it) contains the res_norm from the last iteration */
hapbnd = PetscMin(pipefgmres->haptol,hapbnd);
if (tt > hapbnd) {
/* scale new direction by its norm */
ierr = VecScale(VEC_VV(loc_it+1),1.0/tt);CHKERRQ(ierr);
} else {
/* This happens when the solution is exactly reached. */
/* So there is no new direction... */
ierr = VecSet(VEC_TEMP,0.0);CHKERRQ(ierr); /* set VEC_TEMP to 0 */
hapend = PETSC_TRUE;
}
/* note that for pipefgmres we could get HES(loc_it+1, loc_it) = 0 and the
current solution would not be exact if HES was singular. Note that
HH non-singular implies that HES is not singular, and HES is guaranteed
to be nonsingular when PREVECS are linearly independent and A is
nonsingular (in GMRES, the nonsingularity of A implies the nonsingularity
of HES). So we should really add a check to verify that HES is nonsingular.*/
/* Note that to be thorough, in debug mode, one could call a LAPACK routine
here to check that the hessenberg matrix is indeed non-singular (since
FGMRES does not guarantee this) */
/* Now apply rotations to new col of hessenberg (and right side of system),
calculate new rotation, and get new residual norm at the same time*/
ierr = KSPPIPEFGMRESUpdateHessenberg(ksp,loc_it,&hapend,&res_norm);CHKERRQ(ierr);
if (ksp->reason) break;
loc_it++;
pipefgmres->it = (loc_it-1); /* Add this here in case it has converged */
ierr = PetscObjectSAWsTakeAccess((PetscObject)ksp);CHKERRQ(ierr);
ksp->its++;
ksp->rnorm = res_norm;
ierr = PetscObjectSAWsGrantAccess((PetscObject)ksp);CHKERRQ(ierr);
ierr = (*ksp->converged)(ksp,ksp->its,res_norm,&ksp->reason,ksp->cnvP);CHKERRQ(ierr);
/* Catch error in happy breakdown and signal convergence and break from loop */
if (hapend) {
if (!ksp->reason) {
if (ksp->errorifnotconverged) SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_NOT_CONVERGED,"You reached the happy break down, but convergence was not indicated. Residual norm = %g",(double)res_norm);
else {
ksp->reason = KSP_DIVERGED_BREAKDOWN;
break;
}
}
}
}
/* END OF ITERATION LOOP */
ierr = KSPLogResidualHistory(ksp,res_norm);CHKERRQ(ierr);
/*
Monitor if we know that we will not return for a restart */
if (loc_it && (ksp->reason || ksp->its >= ksp->max_it)) {
ierr = KSPMonitor(ksp,ksp->its,res_norm);CHKERRQ(ierr);
}
if (itcount) *itcount = loc_it;
/*
Down here we have to solve for the "best" coefficients of the Krylov
columns, add the solution values together, and possibly unwind the
preconditioning from the solution
*/
/* Form the solution (or the solution so far) */
/* Note: must pass in (loc_it-1) for iteration count so that KSPPIPEGMRESIIBuildSoln
properly navigates */
ierr = KSPPIPEFGMRESBuildSoln(RS(0),ksp->vec_sol,ksp->vec_sol,ksp,loc_it-1);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
static PetscErrorCode KSPLGMRESBuildSoln(PetscScalar *nrs,Vec vguess,Vec vdest,KSP ksp,PetscInt it)
{
PetscScalar tt;
PetscErrorCode ierr;
PetscInt ii,k,j;
KSP_LGMRES *lgmres = (KSP_LGMRES*)(ksp->data);
/*LGMRES_MOD */
PetscInt it_arnoldi, it_aug;
PetscInt jj, spot = 0;
PetscFunctionBegin;
/* Solve for solution vector that minimizes the residual */
/* If it is < 0, no lgmres steps have been performed */
if (it < 0) {
ierr = VecCopy(vguess,vdest);CHKERRQ(ierr); /* VecCopy() is smart, exists immediately if vguess == vdest */
PetscFunctionReturn(0);
}
/* so (it+1) lgmres steps HAVE been performed */
/* LGMRES_MOD - determine if we need to use augvecs for the soln - do not assume that
this is called after the total its allowed for an approx space */
if (lgmres->approx_constant) {
it_arnoldi = lgmres->max_k - lgmres->aug_ct;
} else {
it_arnoldi = lgmres->max_k - lgmres->aug_dim;
}
if (it_arnoldi >= it +1) {
it_aug = 0;
it_arnoldi = it+1;
} else {
it_aug = (it + 1) - it_arnoldi;
}
/* now it_arnoldi indicates the number of matvecs that took place */
lgmres->matvecs += it_arnoldi;
/* solve the upper triangular system - GRS is the right side and HH is
the upper triangular matrix - put soln in nrs */
if (*HH(it,it) == 0.0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_CONV_FAILED,"HH(it,it) is identically zero; it = %D GRS(it) = %G",it,PetscAbsScalar(*GRS(it)));
if (*HH(it,it) != 0.0) {
nrs[it] = *GRS(it) / *HH(it,it);
} else {
nrs[it] = 0.0;
}
for (ii=1; ii<=it; ii++) {
k = it - ii;
tt = *GRS(k);
for (j=k+1; j<=it; j++) tt = tt - *HH(k,j) * nrs[j];
nrs[k] = tt / *HH(k,k);
}
/* Accumulate the correction to the soln of the preconditioned prob. in VEC_TEMP */
ierr = VecSet(VEC_TEMP,0.0);CHKERRQ(ierr); /* set VEC_TEMP components to 0 */
/*LGMRES_MOD - if augmenting has happened we need to form the solution
using the augvecs */
if (!it_aug) { /* all its are from arnoldi */
ierr = VecMAXPY(VEC_TEMP,it+1,nrs,&VEC_VV(0));CHKERRQ(ierr);
} else { /*use aug vecs */
/*first do regular krylov directions */
ierr = VecMAXPY(VEC_TEMP,it_arnoldi,nrs,&VEC_VV(0));CHKERRQ(ierr);
/*now add augmented portions - add contribution of aug vectors one at a time*/
for (ii=0; ii<it_aug; ii++) {
for (jj=0; jj<lgmres->aug_dim; jj++) {
if (lgmres->aug_order[jj] == (ii+1)) {
spot = jj;
break; /* must have this because there will be duplicates before aug_ct = aug_dim */
}
}
ierr = VecAXPY(VEC_TEMP,nrs[it_arnoldi+ii],AUGVEC(spot));CHKERRQ(ierr);
}
}
/* now VEC_TEMP is what we want to keep for augmenting purposes - grab before the
preconditioner is "unwound" from right-precondtioning*/
ierr = VecCopy(VEC_TEMP, AUG_TEMP);CHKERRQ(ierr);
ierr = KSPUnwindPreconditioner(ksp,VEC_TEMP,VEC_TEMP_MATOP);CHKERRQ(ierr);
/* add solution to previous solution */
/* put updated solution into vdest.*/
ierr = VecCopy(vguess,vdest);CHKERRQ(ierr);
ierr = VecAXPY(vdest,1.0,VEC_TEMP);CHKERRQ(ierr);
PetscFunctionReturn(0);
}
PetscErrorCode KSPLGMRESCycle(PetscInt *itcount,KSP ksp)
{
KSP_LGMRES *lgmres = (KSP_LGMRES*)(ksp->data);
PetscReal res_norm, res;
PetscReal hapbnd, tt;
PetscScalar tmp;
PetscBool hapend = PETSC_FALSE; /* indicates happy breakdown ending */
PetscErrorCode ierr;
PetscInt loc_it; /* local count of # of dir. in Krylov space */
PetscInt max_k = lgmres->max_k; /* max approx space size */
PetscInt max_it = ksp->max_it; /* max # of overall iterations for the method */
/* LGMRES_MOD - new variables*/
PetscInt aug_dim = lgmres->aug_dim;
PetscInt spot = 0;
PetscInt order = 0;
PetscInt it_arnoldi; /* number of arnoldi steps to take */
PetscInt it_total; /* total number of its to take (=approx space size)*/
PetscInt ii, jj;
PetscReal tmp_norm;
PetscScalar inv_tmp_norm;
PetscScalar *avec;
PetscFunctionBegin;
/* Number of pseudo iterations since last restart is the number
of prestart directions */
loc_it = 0;
/* LGMRES_MOD: determine number of arnoldi steps to take */
/* if approx_constant then we keep the space the same size even if
we don't have the full number of aug vectors yet*/
if (lgmres->approx_constant) it_arnoldi = max_k - lgmres->aug_ct;
else it_arnoldi = max_k - aug_dim;
it_total = it_arnoldi + lgmres->aug_ct;
/* initial residual is in VEC_VV(0) - compute its norm*/
ierr = VecNorm(VEC_VV(0),NORM_2,&res_norm);CHKERRQ(ierr);
res = res_norm;
/* first entry in right-hand-side of hessenberg system is just
the initial residual norm */
*GRS(0) = res_norm;
/* check for the convergence */
if (!res) {
if (itcount) *itcount = 0;
ksp->reason = KSP_CONVERGED_ATOL;
ierr = PetscInfo(ksp,"Converged due to zero residual norm on entry\n");CHKERRQ(ierr);
PetscFunctionReturn(0);
}
/* scale VEC_VV (the initial residual) */
tmp = 1.0/res_norm; ierr = VecScale(VEC_VV(0),tmp);CHKERRQ(ierr);
ksp->rnorm = res;
/* note: (lgmres->it) is always set one less than (loc_it) It is used in
KSPBUILDSolution_LGMRES, where it is passed to KSPLGMRESBuildSoln.
Note that when KSPLGMRESBuildSoln is called from this function,
(loc_it -1) is passed, so the two are equivalent */
lgmres->it = (loc_it - 1);
/* MAIN ITERATION LOOP BEGINNING*/
/* keep iterating until we have converged OR generated the max number
of directions OR reached the max number of iterations for the method */
ierr = (*ksp->converged)(ksp,ksp->its,res,&ksp->reason,ksp->cnvP);CHKERRQ(ierr);
while (!ksp->reason && loc_it < it_total && ksp->its < max_it) { /* LGMRES_MOD: changed to it_total */
ierr = KSPLogResidualHistory(ksp,res);CHKERRQ(ierr);
lgmres->it = (loc_it - 1);
ierr = KSPMonitor(ksp,ksp->its,res);CHKERRQ(ierr);
/* see if more space is needed for work vectors */
if (lgmres->vv_allocated <= loc_it + VEC_OFFSET + 1) {
ierr = KSPLGMRESGetNewVectors(ksp,loc_it+1);CHKERRQ(ierr);
/* (loc_it+1) is passed in as number of the first vector that should
be allocated */
}
/*LGMRES_MOD: decide whether this is an arnoldi step or an aug step */
if (loc_it < it_arnoldi) { /* Arnoldi */
ierr = KSP_PCApplyBAorAB(ksp,VEC_VV(loc_it),VEC_VV(1+loc_it),VEC_TEMP_MATOP);CHKERRQ(ierr);
} else { /*aug step */
order = loc_it - it_arnoldi + 1; /* which aug step */
for (ii=0; ii<aug_dim; ii++) {
if (lgmres->aug_order[ii] == order) {
spot = ii;
break; /* must have this because there will be duplicates before aug_ct = aug_dim */
}
}
ierr = VecCopy(A_AUGVEC(spot), VEC_VV(1+loc_it));CHKERRQ(ierr);
/*note: an alternate implementation choice would be to only save the AUGVECS and
not A_AUGVEC and then apply the PC here to the augvec */
}
/* update hessenberg matrix and do Gram-Schmidt - new direction is in
VEC_VV(1+loc_it)*/
ierr = (*lgmres->orthog)(ksp,loc_it);CHKERRQ(ierr);
/* new entry in hessenburg is the 2-norm of our new direction */
ierr = VecNorm(VEC_VV(loc_it+1),NORM_2,&tt);CHKERRQ(ierr);
*HH(loc_it+1,loc_it) = tt;
*HES(loc_it+1,loc_it) = tt;
/* check for the happy breakdown */
hapbnd = PetscAbsScalar(tt / *GRS(loc_it)); /* GRS(loc_it) contains the res_norm from the last iteration */
if (hapbnd > lgmres->haptol) hapbnd = lgmres->haptol;
if (tt > hapbnd) {
tmp = 1.0/tt;
ierr = VecScale(VEC_VV(loc_it+1),tmp);CHKERRQ(ierr); /* scale new direction by its norm */
} else {
ierr = PetscInfo2(ksp,"Detected happy breakdown, current hapbnd = %G tt = %G\n",hapbnd,tt);CHKERRQ(ierr);
hapend = PETSC_TRUE;
}
/* Now apply rotations to new col of hessenberg (and right side of system),
calculate new rotation, and get new residual norm at the same time*/
ierr = KSPLGMRESUpdateHessenberg(ksp,loc_it,hapend,&res);CHKERRQ(ierr);
if (ksp->reason) break;
loc_it++;
lgmres->it = (loc_it-1); /* Add this here in case it has converged */
ierr = PetscObjectSAWsTakeAccess((PetscObject)ksp);CHKERRQ(ierr);
ksp->its++;
ksp->rnorm = res;
ierr = PetscObjectSAWsGrantAccess((PetscObject)ksp);CHKERRQ(ierr);
ierr = (*ksp->converged)(ksp,ksp->its,res,&ksp->reason,ksp->cnvP);CHKERRQ(ierr);
/* Catch error in happy breakdown and signal convergence and break from loop */
if (hapend) {
if (!ksp->reason) {
if (ksp->errorifnotconverged) SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_NOT_CONVERGED,"You reached the happy break down, but convergence was not indicated. Residual norm = %G",res);
else {
ksp->reason = KSP_DIVERGED_BREAKDOWN;
break;
}
}
}
}
/* END OF ITERATION LOOP */
ierr = KSPLogResidualHistory(ksp,res);CHKERRQ(ierr);
/* Monitor if we know that we will not return for a restart */
if (ksp->reason || ksp->its >= max_it) {
ierr = KSPMonitor(ksp, ksp->its, res);CHKERRQ(ierr);
}
if (itcount) *itcount = loc_it;
/*
Down here we have to solve for the "best" coefficients of the Krylov
columns, add the solution values together, and possibly unwind the
preconditioning from the solution
*/
/* Form the solution (or the solution so far) */
/* Note: must pass in (loc_it-1) for iteration count so that KSPLGMRESBuildSoln
properly navigates */
ierr = KSPLGMRESBuildSoln(GRS(0),ksp->vec_sol,ksp->vec_sol,ksp,loc_it-1);CHKERRQ(ierr);
/* LGMRES_MOD collect aug vector and A*augvector for future restarts -
only if we will be restarting (i.e. this cycle performed it_total
iterations) */
if (!ksp->reason && ksp->its < max_it && aug_dim > 0) {
/*AUG_TEMP contains the new augmentation vector (assigned in KSPLGMRESBuildSoln) */
if (!lgmres->aug_ct) {
spot = 0;
lgmres->aug_ct++;
} else if (lgmres->aug_ct < aug_dim) {
spot = lgmres->aug_ct;
lgmres->aug_ct++;
} else { /* truncate */
for (ii=0; ii<aug_dim; ii++) {
if (lgmres->aug_order[ii] == aug_dim) spot = ii;
}
}
ierr = VecCopy(AUG_TEMP, AUGVEC(spot));CHKERRQ(ierr);
/*need to normalize */
ierr = VecNorm(AUGVEC(spot), NORM_2, &tmp_norm);CHKERRQ(ierr);
inv_tmp_norm = 1.0/tmp_norm;
ierr = VecScale(AUGVEC(spot),inv_tmp_norm);CHKERRQ(ierr);
/*set new aug vector to order 1 - move all others back one */
for (ii=0; ii < aug_dim; ii++) AUG_ORDER(ii)++;
AUG_ORDER(spot) = 1;
/*now add the A*aug vector to A_AUGVEC(spot) - this is independ. of preconditioning type*/
/* want V*H*y - y is in GRS, V is in VEC_VV and H is in HES */
/* first do H+*y */
avec = lgmres->hwork;
ierr = PetscMemzero(avec,(it_total+1)*sizeof(*avec));CHKERRQ(ierr);
for (ii=0; ii < it_total + 1; ii++) {
for (jj=0; jj <= ii+1 && jj < it_total+1; jj++) {
avec[jj] += *HES(jj ,ii) * *GRS(ii);
}
}
/*now multiply result by V+ */
ierr = VecSet(VEC_TEMP,0.0);CHKERRQ(ierr);
ierr = VecMAXPY(VEC_TEMP, it_total+1, avec, &VEC_VV(0));CHKERRQ(ierr); /*answer is in VEC_TEMP*/
/*copy answer to aug location and scale*/
ierr = VecCopy(VEC_TEMP, A_AUGVEC(spot));CHKERRQ(ierr);
ierr = VecScale(A_AUGVEC(spot),inv_tmp_norm);CHKERRQ(ierr);
}
PetscFunctionReturn(0);
}
