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. <bsm...@mcs.anl.gov> wrote: > > > > On May 20, 2019, at 2:28 AM, Dave Lee <davelee2...@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. <bsm...@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@mcs.anl.gov> wrote: > > > > > > Dave Lee via petsc-users <petsc-users@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); > > >> } > > > >