[petsc-users] Calling LAPACK routines from PETSc
Dave Lee
davelee2804 at gmail.com
Mon May 20 03:31:28 CDT 2019
Thanks Barry,
I found some helpful examples on the intel lapack site - moral of the
story: using C ordering for input matrix, but transposed output matrices
leads to a consistent solution.
Cheers, Dave.
On Mon, May 20, 2019 at 6:07 PM Smith, Barry F. <bsmith at mcs.anl.gov> wrote:
>
>
> > On May 20, 2019, at 2:28 AM, Dave Lee <davelee2804 at gmail.com> wrote:
> >
> > Thanks Jed and Barry,
> >
> > So, just to confirm,
> >
> > -- From the KSP_GMRES structure, if I call *HH(a,b), that will return
> the row a, column b entry of the Hessenberg matrix (while the back end
> array *hh_origin array is ordering using the Fortran convention)
> >
> > -- Matrices are passed into and returned from
> PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_() using Fortran indexing, and
> need to be transposed to get back to C ordering
>
> In general, I guess depending on what you want to do with them you don'
> need to transpose them. Why would you want to? Just leave them as little
> column oriented blogs and with them what you need directly.
>
> Just do stuff and you'll find it works out.
>
> >
> > Are both of these statements correct?
> >
> > Cheers, Dave.
> >
> > On Mon, May 20, 2019 at 4:34 PM Smith, Barry F. <bsmith at mcs.anl.gov>
> wrote:
> >
> > The little work arrays in GMRES tend to be stored in Fortran
> ordering; there is no C style p[][] indexing into such arrays. Thus the
> arrays can safely be sent to LAPACK. The only trick is knowing the two
> dimensions and as Jed say the "leading dimension parameter. He gave you a
> place to look
> >
> > > On May 20, 2019, at 1:24 AM, Jed Brown via petsc-users <
> petsc-users at mcs.anl.gov> wrote:
> > >
> > > Dave Lee via petsc-users <petsc-users at mcs.anl.gov> writes:
> > >
> > >> Hi Petsc,
> > >>
> > >> I'm attempting to implement a "hookstep" for the SNES trust region
> solver.
> > >> Essentially what I'm trying to do is replace the solution of the least
> > >> squares problem at the end of each GMRES solve with a modified
> solution
> > >> with a norm that is constrained to be within the size of the trust
> region.
> > >>
> > >> In order to do this I need to perform an SVD on the Hessenberg matrix,
> > >> which copying the function KSPComputeExtremeSingularValues(), I'm
> trying to
> > >> do by accessing the LAPACK function dgesvd() via the
> PetscStackCallBLAS()
> > >> machinery. One thing I'm confused about however is the ordering of
> the 2D
> > >> arrays into and out of this function, given that that C and FORTRAN
> arrays
> > >> use reverse indexing, ie: C[j+1][i+1] = F[i,j].
> > >>
> > >> Given that the Hessenberg matrix has k+1 rows and k columns, should I
> be
> > >> still be initializing this as H[row][col] and passing this into
> > >> PetscStackCallBLAS("LAPACKgesvd",LAPACKgrsvd_(...))
> > >> or should I be transposing this before passing it in?
> > >
> > > LAPACK terminology is with respect to Fortran ordering. There is a
> > > "leading dimension" parameter so that you can operate on non-contiguous
> > > blocks. See KSPComputeExtremeSingularValues_GMRES for an example.
> > >
> > >> Also for the left and right singular vector matrices that are
> returned by
> > >> this function, should I be transposing these before I interpret them
> as C
> > >> arrays?
> > >>
> > >> I've attached my modified version of gmres.c in case this is helpful.
> If
> > >> you grep for DRL (my initials) then you'll see my changes to the code.
> > >>
> > >> Cheers, Dave.
> > >>
> > >> /*
> > >> This file implements GMRES (a Generalized Minimal Residual) method.
> > >> Reference: Saad and Schultz, 1986.
> > >>
> > >>
> > >> Some comments on left vs. right preconditioning, and restarts.
> > >> Left and right preconditioning.
> > >> If right preconditioning is chosen, then the problem being solved
> > >> by gmres is actually
> > >> My = AB^-1 y = f
> > >> so the initial residual is
> > >> r = f - Mx
> > >> Note that B^-1 y = x or y = B x, and if x is non-zero, the initial
> > >> residual is
> > >> r = f - A x
> > >> The final solution is then
> > >> x = B^-1 y
> > >>
> > >> If left preconditioning is chosen, then the problem being solved is
> > >> My = B^-1 A x = B^-1 f,
> > >> and the initial residual is
> > >> r = B^-1(f - Ax)
> > >>
> > >> Restarts: Restarts are basically solves with x0 not equal to zero.
> > >> Note that we can eliminate an extra application of B^-1 between
> > >> restarts as long as we don't require that the solution at the end
> > >> of an unsuccessful gmres iteration always be the solution x.
> > >> */
> > >>
> > >> #include <../src/ksp/ksp/impls/gmres/gmresimpl.h> /*I
> "petscksp.h" I*/
> > >> #include <petscblaslapack.h> // DRL
> > >> #define GMRES_DELTA_DIRECTIONS 10
> > >> #define GMRES_DEFAULT_MAXK 30
> > >> static PetscErrorCode
> KSPGMRESUpdateHessenberg(KSP,PetscInt,PetscBool,PetscReal*);
> > >> static PetscErrorCode
> KSPGMRESBuildSoln(PetscScalar*,Vec,Vec,KSP,PetscInt);
> > >>
> > >> PetscErrorCode KSPSetUp_GMRES(KSP ksp)
> > >> {
> > >> PetscInt hh,hes,rs,cc;
> > >> PetscErrorCode ierr;
> > >> PetscInt max_k,k;
> > >> KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
> > >>
> > >> PetscFunctionBegin;
> > >> max_k = gmres->max_k; /* restart size */
> > >> hh = (max_k + 2) * (max_k + 1);
> > >> hes = (max_k + 1) * (max_k + 1);
> > >> rs = (max_k + 2);
> > >> cc = (max_k + 1);
> > >>
> > >> ierr =
> PetscCalloc5(hh,&gmres->hh_origin,hes,&gmres->hes_origin,rs,&gmres->rs_origin,cc,&gmres->cc_origin,cc,&gmres->ss_origin);CHKERRQ(ierr);
> > >> ierr = PetscLogObjectMemory((PetscObject)ksp,(hh + hes + rs +
> 2*cc)*sizeof(PetscScalar));CHKERRQ(ierr);
> > >>
> > >> if (ksp->calc_sings) {
> > >> /* Allocate workspace to hold Hessenberg matrix needed by lapack */
> > >> ierr = PetscMalloc1((max_k + 3)*(max_k +
> 9),&gmres->Rsvd);CHKERRQ(ierr);
> > >> ierr = PetscLogObjectMemory((PetscObject)ksp,(max_k + 3)*(max_k +
> 9)*sizeof(PetscScalar));CHKERRQ(ierr);
> > >> ierr = PetscMalloc1(6*(max_k+2),&gmres->Dsvd);CHKERRQ(ierr);
> > >> ierr =
> PetscLogObjectMemory((PetscObject)ksp,6*(max_k+2)*sizeof(PetscReal));CHKERRQ(ierr);
> > >> }
> > >>
> > >> /* Allocate array to hold pointers to user vectors. Note that we
> need
> > >> 4 + max_k + 1 (since we need it+1 vectors, and it <= max_k) */
> > >> gmres->vecs_allocated = VEC_OFFSET + 2 + max_k + gmres->nextra_vecs;
> > >>
> > >> ierr =
> PetscMalloc1(gmres->vecs_allocated,&gmres->vecs);CHKERRQ(ierr);
> > >> ierr =
> PetscMalloc1(VEC_OFFSET+2+max_k,&gmres->user_work);CHKERRQ(ierr);
> > >> ierr =
> PetscMalloc1(VEC_OFFSET+2+max_k,&gmres->mwork_alloc);CHKERRQ(ierr);
> > >> ierr =
> PetscLogObjectMemory((PetscObject)ksp,(VEC_OFFSET+2+max_k)*(sizeof(Vec*)+sizeof(PetscInt))
> + gmres->vecs_allocated*sizeof(Vec));CHKERRQ(ierr);
> > >>
> > >> if (gmres->q_preallocate) {
> > >> gmres->vv_allocated = VEC_OFFSET + 2 + max_k;
> > >>
> > >> ierr =
> KSPCreateVecs(ksp,gmres->vv_allocated,&gmres->user_work[0],0,NULL);CHKERRQ(ierr);
> > >> ierr =
> PetscLogObjectParents(ksp,gmres->vv_allocated,gmres->user_work[0]);CHKERRQ(ierr);
> > >>
> > >> gmres->mwork_alloc[0] = gmres->vv_allocated;
> > >> gmres->nwork_alloc = 1;
> > >> for (k=0; k<gmres->vv_allocated; k++) {
> > >> gmres->vecs[k] = gmres->user_work[0][k];
> > >> }
> > >> } else {
> > >> gmres->vv_allocated = 5;
> > >>
> > >> ierr =
> KSPCreateVecs(ksp,5,&gmres->user_work[0],0,NULL);CHKERRQ(ierr);
> > >> ierr =
> PetscLogObjectParents(ksp,5,gmres->user_work[0]);CHKERRQ(ierr);
> > >>
> > >> gmres->mwork_alloc[0] = 5;
> > >> gmres->nwork_alloc = 1;
> > >> for (k=0; k<gmres->vv_allocated; k++) {
> > >> gmres->vecs[k] = gmres->user_work[0][k];
> > >> }
> > >> }
> > >> PetscFunctionReturn(0);
> > >> }
> > >>
> > >> /*
> > >> Run gmres, possibly with restart. Return residual history if
> requested.
> > >> input parameters:
> > >>
> > >> . gmres - structure containing parameters and work areas
> > >>
> > >> output parameters:
> > >> . nres - residuals (from preconditioned system) at each
> step.
> > >> If restarting, consider passing nres+it. If null,
> > >> ignored
> > >> . itcount - number of iterations used. nres[0] to
> nres[itcount]
> > >> are defined. If null, ignored.
> > >>
> > >> Notes:
> > >> On entry, the value in vector VEC_VV(0) should be the initial
> residual
> > >> (this allows shortcuts where the initial preconditioned residual
> is 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;
> > >> if (itcount) *itcount = 0;
> > >> ierr = VecNormalize(VEC_VV(0),&res_norm);CHKERRQ(ierr);
> > >> KSPCheckNorm(ksp,res_norm);
> > >> res = res_norm;
> > >> *GRS(0) = res_norm;
> > >>
> > >> /* check for the convergence */
> > >> ierr =
> PetscObjectSAWsTakeAccess((PetscObject)ksp);CHKERRQ(ierr);
> > >> ksp->rnorm = res;
> > >> ierr =
> PetscObjectSAWsGrantAccess((PetscObject)ksp);CHKERRQ(ierr);
> > >> gmres->it = (it - 1);
> > >> 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);
> > >> 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);
> > >> if (ksp->reason) break;
> > >>
> > >> /* 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",(double)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);
> > >> }
> > >>
> > >> PetscErrorCode KSPSolve_GMRES(KSP ksp)
> > >> {
> > >> PetscErrorCode ierr;
> > >> PetscInt its,itcount,i;
> > >> KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
> > >> PetscBool guess_zero = ksp->guess_zero;
> > >> PetscInt N = gmres->max_k + 1;
> > >> PetscBLASInt bN;
> > >>
> > >> PetscFunctionBegin;
> > >> if (ksp->calc_sings && !gmres->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;
> > >> gmres->fullcycle = 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 = KSPGMRESCycle(&its,ksp);CHKERRQ(ierr);
> > >> /* Store the Hessenberg matrix and the basis vectors of the Krylov
> subspace
> > >> if the cycle is complete for the computation of the Ritz pairs */
> > >> if (its == gmres->max_k) {
> > >> gmres->fullcycle++;
> > >> if (ksp->calc_ritz) {
> > >> if (!gmres->hes_ritz) {
> > >> ierr = PetscMalloc1(N*N,&gmres->hes_ritz);CHKERRQ(ierr);
> > >> ierr =
> PetscLogObjectMemory((PetscObject)ksp,N*N*sizeof(PetscScalar));CHKERRQ(ierr);
> > >> ierr =
> VecDuplicateVecs(VEC_VV(0),N,&gmres->vecb);CHKERRQ(ierr);
> > >> }
> > >> ierr = PetscBLASIntCast(N,&bN);CHKERRQ(ierr);
> > >> ierr =
> PetscMemcpy(gmres->hes_ritz,gmres->hes_origin,bN*bN*sizeof(PetscReal));CHKERRQ(ierr);
> > >> for (i=0; i<gmres->max_k+1; i++) {
> > >> ierr = VecCopy(VEC_VV(i),gmres->vecb[i]);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 KSPReset_GMRES(KSP ksp)
> > >> {
> > >> KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
> > >> PetscErrorCode ierr;
> > >> PetscInt i;
> > >>
> > >> PetscFunctionBegin;
> > >> /* Free the Hessenberg matrices */
> > >> ierr =
> PetscFree6(gmres->hh_origin,gmres->hes_origin,gmres->rs_origin,gmres->cc_origin,gmres->ss_origin,gmres->hes_ritz);CHKERRQ(ierr);
> > >>
> > >> /* free work vectors */
> > >> ierr = PetscFree(gmres->vecs);CHKERRQ(ierr);
> > >> for (i=0; i<gmres->nwork_alloc; i++) {
> > >> ierr =
> VecDestroyVecs(gmres->mwork_alloc[i],&gmres->user_work[i]);CHKERRQ(ierr);
> > >> }
> > >> gmres->nwork_alloc = 0;
> > >> if (gmres->vecb) {
> > >> ierr = VecDestroyVecs(gmres->max_k+1,&gmres->vecb);CHKERRQ(ierr);
> > >> }
> > >>
> > >> ierr = PetscFree(gmres->user_work);CHKERRQ(ierr);
> > >> ierr = PetscFree(gmres->mwork_alloc);CHKERRQ(ierr);
> > >> ierr = PetscFree(gmres->nrs);CHKERRQ(ierr);
> > >> ierr = VecDestroy(&gmres->sol_temp);CHKERRQ(ierr);
> > >> ierr = PetscFree(gmres->Rsvd);CHKERRQ(ierr);
> > >> ierr = PetscFree(gmres->Dsvd);CHKERRQ(ierr);
> > >> ierr = PetscFree(gmres->orthogwork);CHKERRQ(ierr);
> > >>
> > >> gmres->sol_temp = 0;
> > >> gmres->vv_allocated = 0;
> > >> gmres->vecs_allocated = 0;
> > >> gmres->sol_temp = 0;
> > >> PetscFunctionReturn(0);
> > >> }
> > >>
> > >> PetscErrorCode KSPDestroy_GMRES(KSP ksp)
> > >> {
> > >> PetscErrorCode ierr;
> > >>
> > >> PetscFunctionBegin;
> > >> ierr = KSPReset_GMRES(ksp);CHKERRQ(ierr);
> > >> ierr = PetscFree(ksp->data);CHKERRQ(ierr);
> > >> /* clear composed functions */
> > >> ierr =
> PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetPreAllocateVectors_C",NULL);CHKERRQ(ierr);
> > >> ierr =
> PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetOrthogonalization_C",NULL);CHKERRQ(ierr);
> > >> ierr =
> PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetOrthogonalization_C",NULL);CHKERRQ(ierr);
> > >> ierr =
> PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetRestart_C",NULL);CHKERRQ(ierr);
> > >> ierr =
> PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetRestart_C",NULL);CHKERRQ(ierr);
> > >> ierr =
> PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetHapTol_C",NULL);CHKERRQ(ierr);
> > >> ierr =
> PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetCGSRefinementType_C",NULL);CHKERRQ(ierr);
> > >> ierr =
> PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetCGSRefinementType_C",NULL);CHKERRQ(ierr);
> > >> PetscFunctionReturn(0);
> > >> }
> > >> /*
> > >> KSPGMRESBuildSoln - create the solution from the starting vector
> and the
> > >> current iterates.
> > >>
> > >> Input parameters:
> > >> nrs - work area of size it + 1.
> > >> vs - index of initial guess
> > >> vdest - index of result. Note that vs may == vdest (replace
> > >> guess with the solution).
> > >>
> > >> This is an internal routine that knows about the GMRES internals.
> > >> */
> > >> 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\n",it,(double)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\n",k);CHKERRQ(ierr);
> > >> PetscFunctionReturn(0);
> > >> }
> > >> nrs[k] = tt / *HH(k,k);
> > >> }
> > >>
> > >> /* Perform the hookstep correction - DRL */
> > >> if(gmres->delta > 0.0 && gmres->it > 0) { // Apply the hookstep to
> correct the GMRES solution (if required)
> > >> printf("\t\tapplying hookstep: initial delta: %lf", gmres->delta);
> > >> PetscInt N = gmres->max_k+2, ii, jj, j0;
> > >> PetscBLASInt nRows, nCols, lwork, lierr;
> > >> PetscScalar *R, *work;
> > >> PetscReal* S;
> > >> PetscScalar *U, *VT, *p, *q, *y;
> > >> PetscScalar bnorm, mu, qMag, qMag2, delta2;
> > >>
> > >> ierr = PetscMalloc1((gmres->max_k + 3)*(gmres->max_k +
> 9),&R);CHKERRQ(ierr);
> > >> work = R + N*N;
> > >> ierr = PetscMalloc1(6*(gmres->max_k+2),&S);CHKERRQ(ierr);
> > >>
> > >> ierr = PetscBLASIntCast(gmres->it+1,&nRows);CHKERRQ(ierr);
> > >> ierr = PetscBLASIntCast(gmres->it+0,&nCols);CHKERRQ(ierr);
> > >> ierr = PetscBLASIntCast(5*N,&lwork);CHKERRQ(ierr);
> > >> //ierr =
> PetscMemcpy(R,gmres->hes_origin,(gmres->max_k+2)*(gmres->max_k+1)*sizeof(PetscScalar));CHKERRQ(ierr);
> > >> ierr = PetscMalloc1(nRows*nCols,&R);CHKERRQ(ierr);
> > >> for (ii = 0; ii < nRows; ii++) {
> > >> for (jj = 0; jj < nCols; jj++) {
> > >> R[ii*nCols+jj] = *HH(ii,jj);
> > >> // Ensure Hessenberg structure
> > >> //if (ii > jj+1) R[ii*nCols+jj] = 0.0;
> > >> }
> > >> }
> > >>
> > >> ierr = PetscMalloc1(nRows*nRows,&U);CHKERRQ(ierr);
> > >> ierr = PetscMalloc1(nCols*nCols,&VT);CHKERRQ(ierr);
> > >> ierr = PetscMalloc1(nRows,&p);CHKERRQ(ierr);
> > >> ierr = PetscMalloc1(nCols,&q);CHKERRQ(ierr);
> > >> ierr = PetscMalloc1(nRows,&y);CHKERRQ(ierr);
> > >>
> > >>
> printf("\n\n");for(ii=0;ii<nRows;ii++){for(jj=0;jj<nCols;jj++){printf("\t%g",R[ii*nCols+jj]);}printf("\n");}printf("\n");
> > >>
> > >> // Perform an SVD on the Hessenberg matrix
> > >> ierr = PetscFPTrapPush(PETSC_FP_TRAP_OFF);CHKERRQ(ierr);
> > >>
> PetscStackCallBLAS("LAPACKgesvd",LAPACKgesvd_("A","A",&nRows,&nCols,R,&nRows,S,U,&nRows,VT,&nCols,work,&lwork,&lierr));
> > >> if (lierr) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_LIB,"Error in SVD
> Lapack routine %d",(int)lierr);
> > >> ierr = PetscFPTrapPop();CHKERRQ(ierr);
> > >>
> > >> // Compute p = ||b|| U^T e_1
> > >> ierr = VecNorm(ksp->vec_rhs,NORM_2,&bnorm);CHKERRQ(ierr);
> > >> for (ii=0; ii<nRows; ii++) {
> > >> p[ii] = bnorm*U[ii*nRows];
> > >> }
> > >>
> > >> // Solve the root finding problem for \mu such that ||q|| < \delta
> (where \delta is the radius of the trust region)
> > >> // This step is largely copied from Ashley Willis' openpipeflow:
> doi.org/10.1016/j.softx.2017.05.003
> > >> mu = S[nCols-1]*S[nCols-1]*1.0e-6;
> > >> if (mu < 1.0e-99) mu = 1.0e-99;
> > >> qMag = 1.0e+99;
> > >>
> > >> while (qMag > gmres->delta) {
> > >> mu *= 1.1;
> > >> qMag2 = 0.0;
> > >> for (ii=0; ii<nCols; ii++) {
> > >> q[ii] = p[ii]*S[ii]/(mu + S[ii]*S[ii]);
> > >> qMag2 += q[ii]*q[ii];
> > >> }
> > >> qMag = PetscSqrtScalar(qMag2);
> > >> }
> > >>
> > >> // Expand y in terms of the right singular vectors as y = V q
> > >> for (ii=0; ii<nCols; ii++) {
> > >> y[ii] = 0.0;
> > >> for (jj=0; jj<nCols; jj++) {
> > >> y[ii] += VT[jj*nCols+ii]*q[jj]; // transpose of the transpose
> > >> }
> > >> }
> > >>
> > >> // Recompute the size of the trust region, \delta
> > >> delta2 = 0.0;
> > >> for (ii=0; ii<nRows; ii++) {
> > >> j0 = (ii < 2) ? 0 : ii - 1;
> > >> p[ii] = 0.0;
> > >> for (jj=j0; jj<nCols; jj++) {
> > >> p[ii] -= R[ii*nCols+jj]*y[jj];
> > >> }
> > >> if (ii == 0) {
> > >> p[ii] += bnorm;
> > >> }
> > >> delta2 += p[ii]*p[ii];
> > >> }
> > >> gmres->delta = PetscSqrtScalar(delta2);
> > >> printf("\t\t...final delta: %lf.\n", gmres->delta);
> > >>
> > >> // Pass the orthnomalized Krylov vector weights back out
> > >> for (ii=0; ii<nCols; ii++) {
> > >> nrs[ii] = y[ii];
> > >> }
> > >>
> > >> ierr = PetscFree(R);CHKERRQ(ierr);
> > >> ierr = PetscFree(S);CHKERRQ(ierr);
> > >> ierr = PetscFree(U);CHKERRQ(ierr);
> > >> ierr = PetscFree(VT);CHKERRQ(ierr);
> > >> ierr = PetscFree(p);CHKERRQ(ierr);
> > >> ierr = PetscFree(q);CHKERRQ(ierr);
> > >> ierr = PetscFree(y);CHKERRQ(ierr);
> > >> }
> > >> /*** DRL ***/
> > >>
> > >> /* Accumulate the correction to the solution of the preconditioned
> problem in TEMP */
> > >> ierr = VecSet(VEC_TEMP,0.0);CHKERRQ(ierr);
> > >> if (gmres->delta > 0.0) {
> > >> ierr = VecMAXPY(VEC_TEMP,it,nrs,&VEC_VV(0));CHKERRQ(ierr); // DRL
> > >> } else {
> > >> 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);
> > >> }
> > >> /*
> > >> Do the scalar work for the orthogonalization. Return new residual
> norm.
> > >> */
> > >> static PetscErrorCode KSPGMRESUpdateHessenberg(KSP ksp,PetscInt
> it,PetscBool hapend,PetscReal *res)
> > >> {
> > >> PetscScalar *hh,*cc,*ss,tt;
> > >> PetscInt j;
> > >> KSP_GMRES *gmres = (KSP_GMRES*)(ksp->data);
> > >>
> > >> PetscFunctionBegin;
> > >> hh = HH(0,it);
> > >> cc = CC(0);
> > >> ss = SS(0);
> > >>
> > >> /* Apply all the previously computed plane rotations to the new
> column
> > >> of the Hessenberg matrix */
> > >> for (j=1; j<=it; j++) {
> > >> tt = *hh;
> > >> *hh = PetscConj(*cc) * tt + *ss * *(hh+1);
> > >> hh++;
> > >> *hh = *cc++ * *hh - (*ss++ * tt);
> > >> }
> > >>
> > >> /*
> > >> compute the new plane rotation, and apply it to:
> > >> 1) the right-hand-side of the Hessenberg system
> > >> 2) the new column of the Hessenberg matrix
> > >> thus obtaining the updated value of the residual
> > >> */
> > >> if (!hapend) {
> > >> tt = PetscSqrtScalar(PetscConj(*hh) * *hh + PetscConj(*(hh+1)) *
> *(hh+1));
> > >> if (tt == 0.0) {
> > >> ksp->reason = KSP_DIVERGED_NULL;
> > >> PetscFunctionReturn(0);
> > >> }
> > >> *cc = *hh / tt;
> > >> *ss = *(hh+1) / tt;
> > >> *GRS(it+1) = -(*ss * *GRS(it));
> > >> *GRS(it) = PetscConj(*cc) * *GRS(it);
> > >> *hh = PetscConj(*cc) * *hh + *ss * *(hh+1);
> > >> *res = PetscAbsScalar(*GRS(it+1));
> > >> } else {
> > >> /* happy breakdown: HH(it+1, it) = 0, therfore we don't need to
> apply
> > >> another rotation matrix (so RH doesn't change). The new
> residual is
> > >> always the new sine term times the residual from last time
> (GRS(it)),
> > >> but now the new sine rotation would be zero...so the
> residual should
> > >> be zero...so we will multiply "zero" by the last
> residual. This might
> > >> not be exactly what we want to do here -could just return
> "zero". */
> > >>
> > >> *res = 0.0;
> > >> }
> > >> PetscFunctionReturn(0);
> > >> }
> > >> /*
> > >> This routine allocates more work vectors, starting from VEC_VV(it).
> > >> */
> > >> PetscErrorCode KSPGMRESGetNewVectors(KSP ksp,PetscInt it)
> > >> {
> > >> KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
> > >> PetscErrorCode ierr;
> > >> PetscInt nwork = gmres->nwork_alloc,k,nalloc;
> > >>
> > >> PetscFunctionBegin;
> > >> nalloc = PetscMin(ksp->max_it,gmres->delta_allocate);
> > >> /* Adjust the number to allocate to make sure that we don't exceed
> the
> > >> number of available slots */
> > >> if (it + VEC_OFFSET + nalloc >= gmres->vecs_allocated) {
> > >> nalloc = gmres->vecs_allocated - it - VEC_OFFSET;
> > >> }
> > >> if (!nalloc) PetscFunctionReturn(0);
> > >>
> > >> gmres->vv_allocated += nalloc;
> > >>
> > >> ierr =
> KSPCreateVecs(ksp,nalloc,&gmres->user_work[nwork],0,NULL);CHKERRQ(ierr);
> > >> ierr =
> PetscLogObjectParents(ksp,nalloc,gmres->user_work[nwork]);CHKERRQ(ierr);
> > >>
> > >> gmres->mwork_alloc[nwork] = nalloc;
> > >> for (k=0; k<nalloc; k++) {
> > >> gmres->vecs[it+VEC_OFFSET+k] = gmres->user_work[nwork][k];
> > >> }
> > >> gmres->nwork_alloc++;
> > >> PetscFunctionReturn(0);
> > >> }
> > >>
> > >> PetscErrorCode KSPBuildSolution_GMRES(KSP ksp,Vec ptr,Vec *result)
> > >> {
> > >> KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
> > >> PetscErrorCode ierr;
> > >>
> > >> PetscFunctionBegin;
> > >> if (!ptr) {
> > >> if (!gmres->sol_temp) {
> > >> ierr = VecDuplicate(ksp->vec_sol,&gmres->sol_temp);CHKERRQ(ierr);
> > >> ierr =
> PetscLogObjectParent((PetscObject)ksp,(PetscObject)gmres->sol_temp);CHKERRQ(ierr);
> > >> }
> > >> ptr = gmres->sol_temp;
> > >> }
> > >> if (!gmres->nrs) {
> > >> /* allocate the work area */
> > >> ierr = PetscMalloc1(gmres->max_k,&gmres->nrs);CHKERRQ(ierr);
> > >> ierr =
> PetscLogObjectMemory((PetscObject)ksp,gmres->max_k*sizeof(PetscScalar));CHKERRQ(ierr);
> > >> }
> > >>
> > >> ierr =
> KSPGMRESBuildSoln(gmres->nrs,ksp->vec_sol,ptr,ksp,gmres->it);CHKERRQ(ierr);
> > >> if (result) *result = ptr;
> > >> PetscFunctionReturn(0);
> > >> }
> > >>
> > >> PetscErrorCode KSPView_GMRES(KSP ksp,PetscViewer viewer)
> > >> {
> > >> KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
> > >> const char *cstr;
> > >> PetscErrorCode ierr;
> > >> PetscBool iascii,isstring;
> > >>
> > >> PetscFunctionBegin;
> > >> ierr =
> PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
> > >> ierr =
> PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERSTRING,&isstring);CHKERRQ(ierr);
> > >> if (gmres->orthog == KSPGMRESClassicalGramSchmidtOrthogonalization) {
> > >> switch (gmres->cgstype) {
> > >> case (KSP_GMRES_CGS_REFINE_NEVER):
> > >> cstr = "Classical (unmodified) Gram-Schmidt Orthogonalization
> with no iterative refinement";
> > >> break;
> > >> case (KSP_GMRES_CGS_REFINE_ALWAYS):
> > >> cstr = "Classical (unmodified) Gram-Schmidt Orthogonalization
> with one step of iterative refinement";
> > >> break;
> > >> case (KSP_GMRES_CGS_REFINE_IFNEEDED):
> > >> cstr = "Classical (unmodified) Gram-Schmidt Orthogonalization
> with one step of iterative refinement when needed";
> > >> break;
> > >> default:
> > >>
> SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ARG_OUTOFRANGE,"Unknown
> orthogonalization");
> > >> }
> > >> } else if (gmres->orthog ==
> KSPGMRESModifiedGramSchmidtOrthogonalization) {
> > >> cstr = "Modified Gram-Schmidt Orthogonalization";
> > >> } else {
> > >> cstr = "unknown orthogonalization";
> > >> }
> > >> if (iascii) {
> > >> ierr = PetscViewerASCIIPrintf(viewer," restart=%D, using
> %s\n",gmres->max_k,cstr);CHKERRQ(ierr);
> > >> ierr = PetscViewerASCIIPrintf(viewer," happy breakdown tolerance
> %g\n",(double)gmres->haptol);CHKERRQ(ierr);
> > >> } else if (isstring) {
> > >> ierr = PetscViewerStringSPrintf(viewer,"%s restart
> %D",cstr,gmres->max_k);CHKERRQ(ierr);
> > >> }
> > >> PetscFunctionReturn(0);
> > >> }
> > >>
> > >> /*@C
> > >> KSPGMRESMonitorKrylov - Calls VecView() for each new 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)
> > >> - dummy - an collection of viewers created with KSPViewerCreate()
> > >>
> > >> Options Database Keys:
> > >> . -ksp_gmres_kyrlov_monitor
> > >>
> > >> Notes: A new PETSCVIEWERDRAW is created for each Krylov vector so
> they can all be simultaneously viewed
> > >> Level: intermediate
> > >>
> > >> .keywords: KSP, nonlinear, vector, monitor, view, Krylov space
> > >>
> > >> .seealso: KSPMonitorSet(), KSPMonitorDefault(), VecView(),
> KSPViewersCreate(), KSPViewersDestroy()
> > >> @*/
> > >> 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);
> > >> }
> > >>
> > >> PetscErrorCode KSPSetFromOptions_GMRES(PetscOptionItems
> *PetscOptionsObject,KSP ksp)
> > >> {
> > >> PetscErrorCode ierr;
> > >> PetscInt restart;
> > >> PetscReal haptol;
> > >> KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
> > >> PetscBool flg;
> > >>
> > >> PetscFunctionBegin;
> > >> ierr = PetscOptionsHead(PetscOptionsObject,"KSP GMRES
> Options");CHKERRQ(ierr);
> > >> ierr = PetscOptionsInt("-ksp_gmres_restart","Number of Krylov search
> directions","KSPGMRESSetRestart",gmres->max_k,&restart,&flg);CHKERRQ(ierr);
> > >> if (flg) { ierr = KSPGMRESSetRestart(ksp,restart);CHKERRQ(ierr); }
> > >> ierr = PetscOptionsReal("-ksp_gmres_haptol","Tolerance for exact
> convergence (happy
> ending)","KSPGMRESSetHapTol",gmres->haptol,&haptol,&flg);CHKERRQ(ierr);
> > >> if (flg) { ierr = KSPGMRESSetHapTol(ksp,haptol);CHKERRQ(ierr); }
> > >> flg = PETSC_FALSE;
> > >> ierr = PetscOptionsBool("-ksp_gmres_preallocate","Preallocate Krylov
> vectors","KSPGMRESSetPreAllocateVectors",flg,&flg,NULL);CHKERRQ(ierr);
> > >> if (flg) {ierr = KSPGMRESSetPreAllocateVectors(ksp);CHKERRQ(ierr);}
> > >> ierr =
> PetscOptionsBoolGroupBegin("-ksp_gmres_classicalgramschmidt","Classical
> (unmodified) Gram-Schmidt
> (fast)","KSPGMRESSetOrthogonalization",&flg);CHKERRQ(ierr);
> > >> if (flg) {ierr =
> KSPGMRESSetOrthogonalization(ksp,KSPGMRESClassicalGramSchmidtOrthogonalization);CHKERRQ(ierr);}
> > >> ierr =
> PetscOptionsBoolGroupEnd("-ksp_gmres_modifiedgramschmidt","Modified
> Gram-Schmidt (slow,more
> stable)","KSPGMRESSetOrthogonalization",&flg);CHKERRQ(ierr);
> > >> if (flg) {ierr =
> KSPGMRESSetOrthogonalization(ksp,KSPGMRESModifiedGramSchmidtOrthogonalization);CHKERRQ(ierr);}
> > >> ierr = PetscOptionsEnum("-ksp_gmres_cgs_refinement_type","Type of
> iterative refinement for classical (unmodified)
> Gram-Schmidt","KSPGMRESSetCGSRefinementType",
> > >>
> KSPGMRESCGSRefinementTypes,(PetscEnum)gmres->cgstype,(PetscEnum*)&gmres->cgstype,&flg);CHKERRQ(ierr);
> > >> flg = PETSC_FALSE;
> > >> ierr = PetscOptionsBool("-ksp_gmres_krylov_monitor","Plot the Krylov
> directions","KSPMonitorSet",flg,&flg,NULL);CHKERRQ(ierr);
> > >> if (flg) {
> > >> PetscViewers viewers;
> > >> ierr =
> PetscViewersCreate(PetscObjectComm((PetscObject)ksp),&viewers);CHKERRQ(ierr);
> > >> ierr =
> KSPMonitorSet(ksp,KSPGMRESMonitorKrylov,viewers,(PetscErrorCode
> (*)(void**))PetscViewersDestroy);CHKERRQ(ierr);
> > >> }
> > >> ierr = PetscOptionsTail();CHKERRQ(ierr);
> > >> PetscFunctionReturn(0);
> > >> }
> > >>
> > >> PetscErrorCode KSPGMRESSetHapTol_GMRES(KSP ksp,PetscReal tol)
> > >> {
> > >> KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
> > >>
> > >> PetscFunctionBegin;
> > >> if (tol < 0.0)
> SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ARG_OUTOFRANGE,"Tolerance
> must be non-negative");
> > >> gmres->haptol = tol;
> > >> PetscFunctionReturn(0);
> > >> }
> > >>
> > >> PetscErrorCode KSPGMRESGetRestart_GMRES(KSP ksp,PetscInt *max_k)
> > >> {
> > >> KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
> > >>
> > >> PetscFunctionBegin;
> > >> *max_k = gmres->max_k;
> > >> PetscFunctionReturn(0);
> > >> }
> > >>
> > >> PetscErrorCode KSPGMRESSetRestart_GMRES(KSP ksp,PetscInt max_k)
> > >> {
> > >> KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
> > >> PetscErrorCode ierr;
> > >>
> > >> PetscFunctionBegin;
> > >> if (max_k < 1)
> SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ARG_OUTOFRANGE,"Restart
> must be positive");
> > >> if (!ksp->setupstage) {
> > >> gmres->max_k = max_k;
> > >> } else if (gmres->max_k != max_k) {
> > >> gmres->max_k = max_k;
> > >> ksp->setupstage = KSP_SETUP_NEW;
> > >> /* free the data structures, then create them again */
> > >> ierr = KSPReset_GMRES(ksp);CHKERRQ(ierr);
> > >> }
> > >> PetscFunctionReturn(0);
> > >> }
> > >>
> > >> PetscErrorCode KSPGMRESSetOrthogonalization_GMRES(KSP ksp,FCN fcn)
> > >> {
> > >> PetscFunctionBegin;
> > >> ((KSP_GMRES*)ksp->data)->orthog = fcn;
> > >> PetscFunctionReturn(0);
> > >> }
> > >>
> > >> PetscErrorCode KSPGMRESGetOrthogonalization_GMRES(KSP ksp,FCN *fcn)
> > >> {
> > >> PetscFunctionBegin;
> > >> *fcn = ((KSP_GMRES*)ksp->data)->orthog;
> > >> PetscFunctionReturn(0);
> > >> }
> > >>
> > >> PetscErrorCode KSPGMRESSetPreAllocateVectors_GMRES(KSP ksp)
> > >> {
> > >> KSP_GMRES *gmres;
> > >>
> > >> PetscFunctionBegin;
> > >> gmres = (KSP_GMRES*)ksp->data;
> > >> gmres->q_preallocate = 1;
> > >> PetscFunctionReturn(0);
> > >> }
> > >>
> > >> PetscErrorCode KSPGMRESSetCGSRefinementType_GMRES(KSP
> ksp,KSPGMRESCGSRefinementType type)
> > >> {
> > >> KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
> > >>
> > >> PetscFunctionBegin;
> > >> gmres->cgstype = type;
> > >> PetscFunctionReturn(0);
> > >> }
> > >>
> > >> PetscErrorCode KSPGMRESGetCGSRefinementType_GMRES(KSP
> ksp,KSPGMRESCGSRefinementType *type)
> > >> {
> > >> KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
> > >>
> > >> PetscFunctionBegin;
> > >> *type = gmres->cgstype;
> > >> PetscFunctionReturn(0);
> > >> }
> > >>
> > >> /*@
> > >> KSPGMRESSetCGSRefinementType - Sets the type of iterative
> refinement to use
> > >> in the classical Gram Schmidt orthogonalization.
> > >>
> > >> Logically Collective on KSP
> > >>
> > >> Input Parameters:
> > >> + ksp - the Krylov space context
> > >> - type - the type of refinement
> > >>
> > >> Options Database:
> > >> . -ksp_gmres_cgs_refinement_type
> <refine_never,refine_ifneeded,refine_always>
> > >>
> > >> Level: intermediate
> > >>
> > >> .keywords: KSP, GMRES, iterative refinement
> > >>
> > >> .seealso: KSPGMRESSetOrthogonalization(), KSPGMRESCGSRefinementType,
> KSPGMRESClassicalGramSchmidtOrthogonalization(),
> KSPGMRESGetCGSRefinementType(),
> > >> KSPGMRESGetOrthogonalization()
> > >> @*/
> > >> PetscErrorCode KSPGMRESSetCGSRefinementType(KSP
> ksp,KSPGMRESCGSRefinementType type)
> > >> {
> > >> PetscErrorCode ierr;
> > >>
> > >> PetscFunctionBegin;
> > >> PetscValidHeaderSpecific(ksp,KSP_CLASSID,1);
> > >> PetscValidLogicalCollectiveEnum(ksp,type,2);
> > >> ierr =
> PetscTryMethod(ksp,"KSPGMRESSetCGSRefinementType_C",(KSP,KSPGMRESCGSRefinementType),(ksp,type));CHKERRQ(ierr);
> > >> PetscFunctionReturn(0);
> > >> }
> > >>
> > >> /*@
> > >> KSPGMRESGetCGSRefinementType - Gets the type of iterative
> refinement to use
> > >> in the classical Gram Schmidt orthogonalization.
> > >>
> > >> Not Collective
> > >>
> > >> Input Parameter:
> > >> . ksp - the Krylov space context
> > >>
> > >> Output Parameter:
> > >> . type - the type of refinement
> > >>
> > >> Options Database:
> > >> . -ksp_gmres_cgs_refinement_type <never,ifneeded,always>
> > >>
> > >> Level: intermediate
> > >>
> > >> .keywords: KSP, GMRES, iterative refinement
> > >>
> > >> .seealso: KSPGMRESSetOrthogonalization(), KSPGMRESCGSRefinementType,
> KSPGMRESClassicalGramSchmidtOrthogonalization(),
> KSPGMRESSetCGSRefinementType(),
> > >> KSPGMRESGetOrthogonalization()
> > >> @*/
> > >> PetscErrorCode KSPGMRESGetCGSRefinementType(KSP
> ksp,KSPGMRESCGSRefinementType *type)
> > >> {
> > >> PetscErrorCode ierr;
> > >>
> > >> PetscFunctionBegin;
> > >> PetscValidHeaderSpecific(ksp,KSP_CLASSID,1);
> > >> ierr =
> PetscUseMethod(ksp,"KSPGMRESGetCGSRefinementType_C",(KSP,KSPGMRESCGSRefinementType*),(ksp,type));CHKERRQ(ierr);
> > >> PetscFunctionReturn(0);
> > >> }
> > >>
> > >>
> > >> /*@
> > >> KSPGMRESSetRestart - Sets number of iterations at which GMRES,
> FGMRES and LGMRES restarts.
> > >>
> > >> Logically Collective on KSP
> > >>
> > >> Input Parameters:
> > >> + ksp - the Krylov space context
> > >> - restart - integer restart value
> > >>
> > >> Options Database:
> > >> . -ksp_gmres_restart <positive integer>
> > >>
> > >> Note: The default value is 30.
> > >>
> > >> Level: intermediate
> > >>
> > >> .keywords: KSP, GMRES, restart, iterations
> > >>
> > >> .seealso: KSPSetTolerances(), KSPGMRESSetOrthogonalization(),
> KSPGMRESSetPreAllocateVectors(), KSPGMRESGetRestart()
> > >> @*/
> > >> PetscErrorCode KSPGMRESSetRestart(KSP ksp, PetscInt restart)
> > >> {
> > >> PetscErrorCode ierr;
> > >>
> > >> PetscFunctionBegin;
> > >> PetscValidLogicalCollectiveInt(ksp,restart,2);
> > >>
> > >> ierr =
> PetscTryMethod(ksp,"KSPGMRESSetRestart_C",(KSP,PetscInt),(ksp,restart));CHKERRQ(ierr);
> > >> PetscFunctionReturn(0);
> > >> }
> > >>
> > >> /*@
> > >> KSPGMRESGetRestart - Gets number of iterations at which GMRES,
> FGMRES and LGMRES restarts.
> > >>
> > >> Not Collective
> > >>
> > >> Input Parameter:
> > >> . ksp - the Krylov space context
> > >>
> > >> Output Parameter:
> > >> . restart - integer restart value
> > >>
> > >> Note: The default value is 30.
> > >>
> > >> Level: intermediate
> > >>
> > >> .keywords: KSP, GMRES, restart, iterations
> > >>
> > >> .seealso: KSPSetTolerances(), KSPGMRESSetOrthogonalization(),
> KSPGMRESSetPreAllocateVectors(), KSPGMRESSetRestart()
> > >> @*/
> > >> PetscErrorCode KSPGMRESGetRestart(KSP ksp, PetscInt *restart)
> > >> {
> > >> PetscErrorCode ierr;
> > >>
> > >> PetscFunctionBegin;
> > >> ierr =
> PetscUseMethod(ksp,"KSPGMRESGetRestart_C",(KSP,PetscInt*),(ksp,restart));CHKERRQ(ierr);
> > >> PetscFunctionReturn(0);
> > >> }
> > >>
> > >> /*@
> > >> KSPGMRESSetHapTol - Sets tolerance for determining happy breakdown
> in GMRES, FGMRES and LGMRES.
> > >>
> > >> Logically Collective on KSP
> > >>
> > >> Input Parameters:
> > >> + ksp - the Krylov space context
> > >> - tol - the tolerance
> > >>
> > >> Options Database:
> > >> . -ksp_gmres_haptol <positive real value>
> > >>
> > >> Note: Happy breakdown is the rare case in GMRES where an 'exact'
> solution is obtained after
> > >> a certain number of iterations. If you attempt more
> iterations after this point unstable
> > >> things can happen hence very occasionally you may need to set
> this value to detect this condition
> > >>
> > >> Level: intermediate
> > >>
> > >> .keywords: KSP, GMRES, tolerance
> > >>
> > >> .seealso: KSPSetTolerances()
> > >> @*/
> > >> PetscErrorCode KSPGMRESSetHapTol(KSP ksp,PetscReal tol)
> > >> {
> > >> PetscErrorCode ierr;
> > >>
> > >> PetscFunctionBegin;
> > >> PetscValidLogicalCollectiveReal(ksp,tol,2);
> > >> ierr =
> PetscTryMethod((ksp),"KSPGMRESSetHapTol_C",(KSP,PetscReal),((ksp),(tol)));CHKERRQ(ierr);
> > >> PetscFunctionReturn(0);
> > >> }
> > >>
> > >> /*MC
> > >> KSPGMRES - Implements the Generalized Minimal Residual method.
> > >> (Saad and Schultz, 1986) with restart
> > >>
> > >>
> > >> Options Database Keys:
> > >> + -ksp_gmres_restart <restart> - the number of Krylov directions to
> orthogonalize against
> > >> . -ksp_gmres_haptol <tol> - sets the tolerance for "happy ending"
> (exact convergence)
> > >> . -ksp_gmres_preallocate - preallocate all the Krylov search
> directions initially (otherwise groups of
> > >> vectors are allocated as needed)
> > >> . -ksp_gmres_classicalgramschmidt - use classical (unmodified)
> Gram-Schmidt to orthogonalize against the Krylov space (fast) (the default)
> > >> . -ksp_gmres_modifiedgramschmidt - use modified Gram-Schmidt in the
> orthogonalization (more stable, but slower)
> > >> . -ksp_gmres_cgs_refinement_type <never,ifneeded,always> -
> determine if iterative refinement is used to increase the
> > >> stability of the classical
> Gram-Schmidt orthogonalization.
> > >> - -ksp_gmres_krylov_monitor - plot the Krylov space generated
> > >>
> > >> Level: beginner
> > >>
> > >> Notes: Left and right preconditioning are supported, but not
> symmetric preconditioning.
> > >>
> > >> References:
> > >> . 1. - YOUCEF SAAD AND MARTIN H. SCHULTZ, GMRES: A GENERALIZED
> MINIMAL RESIDUAL ALGORITHM FOR SOLVING NONSYMMETRIC LINEAR SYSTEMS.
> > >> SIAM J. ScI. STAT. COMPUT. Vo|. 7, No. 3, July 1986.
> > >>
> > >> .seealso: KSPCreate(), KSPSetType(), KSPType (for list of available
> types), KSP, KSPFGMRES, KSPLGMRES,
> > >> KSPGMRESSetRestart(), KSPGMRESSetHapTol(),
> KSPGMRESSetPreAllocateVectors(), KSPGMRESSetOrthogonalization(),
> KSPGMRESGetOrthogonalization(),
> > >> KSPGMRESClassicalGramSchmidtOrthogonalization(),
> KSPGMRESModifiedGramSchmidtOrthogonalization(),
> > >> KSPGMRESCGSRefinementType, KSPGMRESSetCGSRefinementType(),
> KSPGMRESGetCGSRefinementType(), KSPGMRESMonitorKrylov(), KSPSetPCSide()
> > >>
> > >> M*/
> > >>
> > >> PETSC_EXTERN PetscErrorCode KSPCreate_GMRES(KSP ksp)
> > >> {
> > >> KSP_GMRES *gmres;
> > >> PetscErrorCode ierr;
> > >>
> > >> PetscFunctionBegin;
> > >> ierr = PetscNewLog(ksp,&gmres);CHKERRQ(ierr);
> > >> ksp->data = (void*)gmres;
> > >>
> > >> ierr =
> KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,4);CHKERRQ(ierr);
> > >> ierr =
> KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_RIGHT,3);CHKERRQ(ierr);
> > >> ierr =
> KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_SYMMETRIC,2);CHKERRQ(ierr);
> > >> ierr =
> KSPSetSupportedNorm(ksp,KSP_NORM_NONE,PC_RIGHT,1);CHKERRQ(ierr);
> > >> ierr =
> KSPSetSupportedNorm(ksp,KSP_NORM_NONE,PC_LEFT,1);CHKERRQ(ierr);
> > >>
> > >> ksp->ops->buildsolution = KSPBuildSolution_GMRES;
> > >> ksp->ops->setup = KSPSetUp_GMRES;
> > >> ksp->ops->solve = KSPSolve_GMRES;
> > >> ksp->ops->reset = KSPReset_GMRES;
> > >> ksp->ops->destroy = KSPDestroy_GMRES;
> > >> ksp->ops->view = KSPView_GMRES;
> > >> ksp->ops->setfromoptions = KSPSetFromOptions_GMRES;
> > >> ksp->ops->computeextremesingularvalues =
> KSPComputeExtremeSingularValues_GMRES;
> > >> ksp->ops->computeeigenvalues = KSPComputeEigenvalues_GMRES;
> > >> #if !defined(PETSC_USE_COMPLEX) && !defined(PETSC_HAVE_ESSL)
> > >> ksp->ops->computeritz = KSPComputeRitz_GMRES;
> > >> #endif
> > >> ierr =
> PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetPreAllocateVectors_C",KSPGMRESSetPreAllocateVectors_GMRES);CHKERRQ(ierr);
> > >> ierr =
> PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetOrthogonalization_C",KSPGMRESSetOrthogonalization_GMRES);CHKERRQ(ierr);
> > >> ierr =
> PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetOrthogonalization_C",KSPGMRESGetOrthogonalization_GMRES);CHKERRQ(ierr);
> > >> ierr =
> PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetRestart_C",KSPGMRESSetRestart_GMRES);CHKERRQ(ierr);
> > >> ierr =
> PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetRestart_C",KSPGMRESGetRestart_GMRES);CHKERRQ(ierr);
> > >> ierr =
> PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetHapTol_C",KSPGMRESSetHapTol_GMRES);CHKERRQ(ierr);
> > >> ierr =
> PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetCGSRefinementType_C",KSPGMRESSetCGSRefinementType_GMRES);CHKERRQ(ierr);
> > >> ierr =
> PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetCGSRefinementType_C",KSPGMRESGetCGSRefinementType_GMRES);CHKERRQ(ierr);
> > >>
> > >> gmres->haptol = 1.0e-30;
> > >> gmres->q_preallocate = 0;
> > >> gmres->delta_allocate = GMRES_DELTA_DIRECTIONS;
> > >> gmres->orthog =
> KSPGMRESClassicalGramSchmidtOrthogonalization;
> > >> gmres->nrs = 0;
> > >> gmres->sol_temp = 0;
> > >> gmres->max_k = GMRES_DEFAULT_MAXK;
> > >> gmres->Rsvd = 0;
> > >> gmres->cgstype = KSP_GMRES_CGS_REFINE_NEVER;
> > >> gmres->orthogwork = 0;
> > >> gmres->delta = -1.0; // DRL
> > >> PetscFunctionReturn(0);
> > >> }
> >
>
>
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