PetscErrorCode KSPBuildSolution_LGMRES(KSP ksp,Vec ptr,Vec *result)
{
KSP_LGMRES *lgmres = (KSP_LGMRES *)ksp->data;
PetscErrorCode ierr;
PetscFunctionBegin;
if (!ptr) {
if (!lgmres->sol_temp) {
ierr = VecDuplicate(ksp->vec_sol,&lgmres->sol_temp);
CHKERRQ(ierr);
ierr = PetscLogObjectParent(ksp,lgmres->sol_temp);
CHKERRQ(ierr);
}
ptr = lgmres->sol_temp;
}
if (!lgmres->nrs) {
/* allocate the work area */
ierr = PetscMalloc(lgmres->max_k*sizeof(PetscScalar),&lgmres->nrs);
CHKERRQ(ierr);
ierr = PetscLogObjectMemory(ksp,lgmres->max_k*sizeof(PetscScalar));
CHKERRQ(ierr);
}
ierr = KSPLGMRESBuildSoln(lgmres->nrs,ksp->vec_sol,ptr,ksp,lgmres->it);
CHKERRQ(ierr);
if (result) *result = ptr;
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);
}