[petsc-users] Calling LAPACK routines from PETSc
Jed Brown
jed at jedbrown.org
Mon May 20 01:24:31 CDT 2019
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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