Actual source code: gmres.c
petsc-3.5.4 2015-05-23
2: /*
3: This file implements GMRES (a Generalized Minimal Residual) method.
4: Reference: Saad and Schultz, 1986.
7: Some comments on left vs. right preconditioning, and restarts.
8: Left and right preconditioning.
9: If right preconditioning is chosen, then the problem being solved
10: by gmres is actually
11: My = AB^-1 y = f
12: so the initial residual is
13: r = f - Mx
14: Note that B^-1 y = x or y = B x, and if x is non-zero, the initial
15: residual is
16: r = f - A x
17: The final solution is then
18: x = B^-1 y
20: If left preconditioning is chosen, then the problem being solved is
21: My = B^-1 A x = B^-1 f,
22: and the initial residual is
23: r = B^-1(f - Ax)
25: Restarts: Restarts are basically solves with x0 not equal to zero.
26: Note that we can eliminate an extra application of B^-1 between
27: restarts as long as we don't require that the solution at the end
28: of an unsuccessful gmres iteration always be the solution x.
29: */
31: #include <../src/ksp/ksp/impls/gmres/gmresimpl.h> /*I "petscksp.h" I*/
32: #define GMRES_DELTA_DIRECTIONS 10
33: #define GMRES_DEFAULT_MAXK 30
34: static PetscErrorCode KSPGMRESUpdateHessenberg(KSP,PetscInt,PetscBool,PetscReal*);
35: static PetscErrorCode KSPGMRESBuildSoln(PetscScalar*,Vec,Vec,KSP,PetscInt);
39: PetscErrorCode KSPSetUp_GMRES(KSP ksp)
40: {
41: PetscInt hh,hes,rs,cc;
43: PetscInt max_k,k;
44: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
47: max_k = gmres->max_k; /* restart size */
48: hh = (max_k + 2) * (max_k + 1);
49: hes = (max_k + 1) * (max_k + 1);
50: rs = (max_k + 2);
51: cc = (max_k + 1);
53: PetscCalloc5(hh,&gmres->hh_origin,hes,&gmres->hes_origin,rs,&gmres->rs_origin,cc,&gmres->cc_origin,cc,&gmres->ss_origin);
54: PetscLogObjectMemory((PetscObject)ksp,(hh + hes + rs + 2*cc)*sizeof(PetscScalar));
56: if (ksp->calc_sings) {
57: /* Allocate workspace to hold Hessenberg matrix needed by lapack */
58: PetscMalloc1((max_k + 3)*(max_k + 9),&gmres->Rsvd);
59: PetscLogObjectMemory((PetscObject)ksp,(max_k + 3)*(max_k + 9)*sizeof(PetscScalar));
60: PetscMalloc1(6*(max_k+2),&gmres->Dsvd);
61: PetscLogObjectMemory((PetscObject)ksp,6*(max_k+2)*sizeof(PetscReal));
62: }
64: /* Allocate array to hold pointers to user vectors. Note that we need
65: 4 + max_k + 1 (since we need it+1 vectors, and it <= max_k) */
66: gmres->vecs_allocated = VEC_OFFSET + 2 + max_k + gmres->nextra_vecs;
68: PetscMalloc1((gmres->vecs_allocated),&gmres->vecs);
69: PetscMalloc1((VEC_OFFSET+2+max_k),&gmres->user_work);
70: PetscMalloc1((VEC_OFFSET+2+max_k),&gmres->mwork_alloc);
71: PetscLogObjectMemory((PetscObject)ksp,(VEC_OFFSET+2+max_k)*(sizeof(Vec*)+sizeof(PetscInt)) + gmres->vecs_allocated*sizeof(Vec));
73: if (gmres->q_preallocate) {
74: gmres->vv_allocated = VEC_OFFSET + 2 + max_k;
76: KSPGetVecs(ksp,gmres->vv_allocated,&gmres->user_work[0],0,NULL);
77: PetscLogObjectParents(ksp,gmres->vv_allocated,gmres->user_work[0]);
79: gmres->mwork_alloc[0] = gmres->vv_allocated;
80: gmres->nwork_alloc = 1;
81: for (k=0; k<gmres->vv_allocated; k++) {
82: gmres->vecs[k] = gmres->user_work[0][k];
83: }
84: } else {
85: gmres->vv_allocated = 5;
87: KSPGetVecs(ksp,5,&gmres->user_work[0],0,NULL);
88: PetscLogObjectParents(ksp,5,gmres->user_work[0]);
90: gmres->mwork_alloc[0] = 5;
91: gmres->nwork_alloc = 1;
92: for (k=0; k<gmres->vv_allocated; k++) {
93: gmres->vecs[k] = gmres->user_work[0][k];
94: }
95: }
96: return(0);
97: }
99: /*
100: Run gmres, possibly with restart. Return residual history if requested.
101: input parameters:
103: . gmres - structure containing parameters and work areas
105: output parameters:
106: . nres - residuals (from preconditioned system) at each step.
107: If restarting, consider passing nres+it. If null,
108: ignored
109: . itcount - number of iterations used. nres[0] to nres[itcount]
110: are defined. If null, ignored.
112: Notes:
113: On entry, the value in vector VEC_VV(0) should be the initial residual
114: (this allows shortcuts where the initial preconditioned residual is 0).
115: */
118: PetscErrorCode KSPGMRESCycle(PetscInt *itcount,KSP ksp)
119: {
120: KSP_GMRES *gmres = (KSP_GMRES*)(ksp->data);
121: PetscReal res_norm,res,hapbnd,tt;
123: PetscInt it = 0, max_k = gmres->max_k;
124: PetscBool hapend = PETSC_FALSE;
127: VecNormalize(VEC_VV(0),&res_norm);
128: res = res_norm;
129: *GRS(0) = res_norm;
131: /* check for the convergence */
132: PetscObjectSAWsTakeAccess((PetscObject)ksp);
133: ksp->rnorm = res;
134: PetscObjectSAWsGrantAccess((PetscObject)ksp);
135: gmres->it = (it - 1);
136: KSPLogResidualHistory(ksp,res);
137: KSPMonitor(ksp,ksp->its,res);
138: if (!res) {
139: if (itcount) *itcount = 0;
140: ksp->reason = KSP_CONVERGED_ATOL;
141: PetscInfo(ksp,"Converged due to zero residual norm on entry\n");
142: return(0);
143: }
145: (*ksp->converged)(ksp,ksp->its,res,&ksp->reason,ksp->cnvP);
146: while (!ksp->reason && it < max_k && ksp->its < ksp->max_it) {
147: if (it) {
148: KSPLogResidualHistory(ksp,res);
149: KSPMonitor(ksp,ksp->its,res);
150: }
151: gmres->it = (it - 1);
152: if (gmres->vv_allocated <= it + VEC_OFFSET + 1) {
153: KSPGMRESGetNewVectors(ksp,it+1);
154: }
155: KSP_PCApplyBAorAB(ksp,VEC_VV(it),VEC_VV(1+it),VEC_TEMP_MATOP);
157: /* update hessenberg matrix and do Gram-Schmidt */
158: (*gmres->orthog)(ksp,it);
160: /* vv(i+1) . vv(i+1) */
161: VecNormalize(VEC_VV(it+1),&tt);
163: /* save the magnitude */
164: *HH(it+1,it) = tt;
165: *HES(it+1,it) = tt;
167: /* check for the happy breakdown */
168: hapbnd = PetscAbsScalar(tt / *GRS(it));
169: if (hapbnd > gmres->haptol) hapbnd = gmres->haptol;
170: if (tt < hapbnd) {
171: PetscInfo2(ksp,"Detected happy breakdown, current hapbnd = %14.12e tt = %14.12e\n",(double)hapbnd,(double)tt);
172: hapend = PETSC_TRUE;
173: }
174: KSPGMRESUpdateHessenberg(ksp,it,hapend,&res);
176: it++;
177: gmres->it = (it-1); /* For converged */
178: ksp->its++;
179: ksp->rnorm = res;
180: if (ksp->reason) break;
182: (*ksp->converged)(ksp,ksp->its,res,&ksp->reason,ksp->cnvP);
184: /* Catch error in happy breakdown and signal convergence and break from loop */
185: if (hapend) {
186: if (!ksp->reason) {
187: 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);
188: else {
189: ksp->reason = KSP_DIVERGED_BREAKDOWN;
190: break;
191: }
192: }
193: }
194: }
196: /* Monitor if we know that we will not return for a restart */
197: if (it && (ksp->reason || ksp->its >= ksp->max_it)) {
198: KSPLogResidualHistory(ksp,res);
199: KSPMonitor(ksp,ksp->its,res);
200: }
202: if (itcount) *itcount = it;
205: /*
206: Down here we have to solve for the "best" coefficients of the Krylov
207: columns, add the solution values together, and possibly unwind the
208: preconditioning from the solution
209: */
210: /* Form the solution (or the solution so far) */
211: KSPGMRESBuildSoln(GRS(0),ksp->vec_sol,ksp->vec_sol,ksp,it-1);
212: return(0);
213: }
217: PetscErrorCode KSPSolve_GMRES(KSP ksp)
218: {
220: PetscInt its,itcount;
221: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
222: PetscBool guess_zero = ksp->guess_zero;
225: if (ksp->calc_sings && !gmres->Rsvd) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ORDER,"Must call KSPSetComputeSingularValues() before KSPSetUp() is called");
227: PetscObjectSAWsTakeAccess((PetscObject)ksp);
228: ksp->its = 0;
229: PetscObjectSAWsGrantAccess((PetscObject)ksp);
231: itcount = 0;
232: ksp->reason = KSP_CONVERGED_ITERATING;
233: while (!ksp->reason) {
234: KSPInitialResidual(ksp,ksp->vec_sol,VEC_TEMP,VEC_TEMP_MATOP,VEC_VV(0),ksp->vec_rhs);
235: KSPGMRESCycle(&its,ksp);
236: itcount += its;
237: if (itcount >= ksp->max_it) {
238: if (!ksp->reason) ksp->reason = KSP_DIVERGED_ITS;
239: break;
240: }
241: ksp->guess_zero = PETSC_FALSE; /* every future call to KSPInitialResidual() will have nonzero guess */
242: }
243: ksp->guess_zero = guess_zero; /* restore if user provided nonzero initial guess */
244: return(0);
245: }
249: PetscErrorCode KSPReset_GMRES(KSP ksp)
250: {
251: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
253: PetscInt i;
256: /* Free the Hessenberg matrices */
257: PetscFree5(gmres->hh_origin,gmres->hes_origin,gmres->rs_origin,gmres->cc_origin,gmres->ss_origin);
259: /* free work vectors */
260: PetscFree(gmres->vecs);
261: for (i=0; i<gmres->nwork_alloc; i++) {
262: VecDestroyVecs(gmres->mwork_alloc[i],&gmres->user_work[i]);
263: }
264: gmres->nwork_alloc = 0;
266: PetscFree(gmres->user_work);
267: PetscFree(gmres->mwork_alloc);
268: PetscFree(gmres->nrs);
269: VecDestroy(&gmres->sol_temp);
270: PetscFree(gmres->Rsvd);
271: PetscFree(gmres->Dsvd);
272: PetscFree(gmres->orthogwork);
274: gmres->sol_temp = 0;
275: gmres->vv_allocated = 0;
276: gmres->vecs_allocated = 0;
277: gmres->sol_temp = 0;
278: return(0);
279: }
283: PetscErrorCode KSPDestroy_GMRES(KSP ksp)
284: {
288: KSPReset_GMRES(ksp);
289: PetscFree(ksp->data);
290: /* clear composed functions */
291: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetPreAllocateVectors_C",NULL);
292: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetOrthogonalization_C",NULL);
293: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetOrthogonalization_C",NULL);
294: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetRestart_C",NULL);
295: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetRestart_C",NULL);
296: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetHapTol_C",NULL);
297: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetCGSRefinementType_C",NULL);
298: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetCGSRefinementType_C",NULL);
299: return(0);
300: }
301: /*
302: KSPGMRESBuildSoln - create the solution from the starting vector and the
303: current iterates.
305: Input parameters:
306: nrs - work area of size it + 1.
307: vs - index of initial guess
308: vdest - index of result. Note that vs may == vdest (replace
309: guess with the solution).
311: This is an internal routine that knows about the GMRES internals.
312: */
315: static PetscErrorCode KSPGMRESBuildSoln(PetscScalar *nrs,Vec vs,Vec vdest,KSP ksp,PetscInt it)
316: {
317: PetscScalar tt;
319: PetscInt ii,k,j;
320: KSP_GMRES *gmres = (KSP_GMRES*)(ksp->data);
323: /* Solve for solution vector that minimizes the residual */
325: /* If it is < 0, no gmres steps have been performed */
326: if (it < 0) {
327: VecCopy(vs,vdest); /* VecCopy() is smart, exists immediately if vguess == vdest */
328: return(0);
329: }
330: if (*HH(it,it) != 0.0) {
331: nrs[it] = *GRS(it) / *HH(it,it);
332: } else {
333: ksp->reason = KSP_DIVERGED_BREAKDOWN;
335: PetscInfo2(ksp,"Likely your matrix or preconditioner is singular. HH(it,it) is identically zero; it = %D GRS(it) = %g",it,(double)PetscAbsScalar(*GRS(it)));
336: return(0);
337: }
338: for (ii=1; ii<=it; ii++) {
339: k = it - ii;
340: tt = *GRS(k);
341: for (j=k+1; j<=it; j++) tt = tt - *HH(k,j) * nrs[j];
342: if (*HH(k,k) == 0.0) {
343: ksp->reason = KSP_DIVERGED_BREAKDOWN;
345: PetscInfo1(ksp,"Likely your matrix or preconditioner is singular. HH(k,k) is identically zero; k = %D",k);
346: return(0);
347: }
348: nrs[k] = tt / *HH(k,k);
349: }
351: /* Accumulate the correction to the solution of the preconditioned problem in TEMP */
352: VecSet(VEC_TEMP,0.0);
353: VecMAXPY(VEC_TEMP,it+1,nrs,&VEC_VV(0));
355: KSPUnwindPreconditioner(ksp,VEC_TEMP,VEC_TEMP_MATOP);
356: /* add solution to previous solution */
357: if (vdest != vs) {
358: VecCopy(vs,vdest);
359: }
360: VecAXPY(vdest,1.0,VEC_TEMP);
361: return(0);
362: }
363: /*
364: Do the scalar work for the orthogonalization. Return new residual norm.
365: */
368: static PetscErrorCode KSPGMRESUpdateHessenberg(KSP ksp,PetscInt it,PetscBool hapend,PetscReal *res)
369: {
370: PetscScalar *hh,*cc,*ss,tt;
371: PetscInt j;
372: KSP_GMRES *gmres = (KSP_GMRES*)(ksp->data);
375: hh = HH(0,it);
376: cc = CC(0);
377: ss = SS(0);
379: /* Apply all the previously computed plane rotations to the new column
380: of the Hessenberg matrix */
381: for (j=1; j<=it; j++) {
382: tt = *hh;
383: *hh = PetscConj(*cc) * tt + *ss * *(hh+1);
384: hh++;
385: *hh = *cc++ * *hh - (*ss++ * tt);
386: }
388: /*
389: compute the new plane rotation, and apply it to:
390: 1) the right-hand-side of the Hessenberg system
391: 2) the new column of the Hessenberg matrix
392: thus obtaining the updated value of the residual
393: */
394: if (!hapend) {
395: tt = PetscSqrtScalar(PetscConj(*hh) * *hh + PetscConj(*(hh+1)) * *(hh+1));
396: if (tt == 0.0) {
397: ksp->reason = KSP_DIVERGED_NULL;
398: return(0);
399: }
400: *cc = *hh / tt;
401: *ss = *(hh+1) / tt;
402: *GRS(it+1) = -(*ss * *GRS(it));
403: *GRS(it) = PetscConj(*cc) * *GRS(it);
404: *hh = PetscConj(*cc) * *hh + *ss * *(hh+1);
405: *res = PetscAbsScalar(*GRS(it+1));
406: } else {
407: /* happy breakdown: HH(it+1, it) = 0, therfore we don't need to apply
408: another rotation matrix (so RH doesn't change). The new residual is
409: always the new sine term times the residual from last time (GRS(it)),
410: but now the new sine rotation would be zero...so the residual should
411: be zero...so we will multiply "zero" by the last residual. This might
412: not be exactly what we want to do here -could just return "zero". */
414: *res = 0.0;
415: }
416: return(0);
417: }
418: /*
419: This routine allocates more work vectors, starting from VEC_VV(it).
420: */
423: PetscErrorCode KSPGMRESGetNewVectors(KSP ksp,PetscInt it)
424: {
425: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
427: PetscInt nwork = gmres->nwork_alloc,k,nalloc;
430: nalloc = PetscMin(ksp->max_it,gmres->delta_allocate);
431: /* Adjust the number to allocate to make sure that we don't exceed the
432: number of available slots */
433: if (it + VEC_OFFSET + nalloc >= gmres->vecs_allocated) {
434: nalloc = gmres->vecs_allocated - it - VEC_OFFSET;
435: }
436: if (!nalloc) return(0);
438: gmres->vv_allocated += nalloc;
440: KSPGetVecs(ksp,nalloc,&gmres->user_work[nwork],0,NULL);
441: PetscLogObjectParents(ksp,nalloc,gmres->user_work[nwork]);
443: gmres->mwork_alloc[nwork] = nalloc;
444: for (k=0; k<nalloc; k++) {
445: gmres->vecs[it+VEC_OFFSET+k] = gmres->user_work[nwork][k];
446: }
447: gmres->nwork_alloc++;
448: return(0);
449: }
453: PetscErrorCode KSPBuildSolution_GMRES(KSP ksp,Vec ptr,Vec *result)
454: {
455: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
459: if (!ptr) {
460: if (!gmres->sol_temp) {
461: VecDuplicate(ksp->vec_sol,&gmres->sol_temp);
462: PetscLogObjectParent((PetscObject)ksp,(PetscObject)gmres->sol_temp);
463: }
464: ptr = gmres->sol_temp;
465: }
466: if (!gmres->nrs) {
467: /* allocate the work area */
468: PetscMalloc1(gmres->max_k,&gmres->nrs);
469: PetscLogObjectMemory((PetscObject)ksp,gmres->max_k*sizeof(PetscScalar));
470: }
472: KSPGMRESBuildSoln(gmres->nrs,ksp->vec_sol,ptr,ksp,gmres->it);
473: if (result) *result = ptr;
474: return(0);
475: }
479: PetscErrorCode KSPView_GMRES(KSP ksp,PetscViewer viewer)
480: {
481: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
482: const char *cstr;
484: PetscBool iascii,isstring;
487: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
488: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERSTRING,&isstring);
489: if (gmres->orthog == KSPGMRESClassicalGramSchmidtOrthogonalization) {
490: switch (gmres->cgstype) {
491: case (KSP_GMRES_CGS_REFINE_NEVER):
492: cstr = "Classical (unmodified) Gram-Schmidt Orthogonalization with no iterative refinement";
493: break;
494: case (KSP_GMRES_CGS_REFINE_ALWAYS):
495: cstr = "Classical (unmodified) Gram-Schmidt Orthogonalization with one step of iterative refinement";
496: break;
497: case (KSP_GMRES_CGS_REFINE_IFNEEDED):
498: cstr = "Classical (unmodified) Gram-Schmidt Orthogonalization with one step of iterative refinement when needed";
499: break;
500: default:
501: SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ARG_OUTOFRANGE,"Unknown orthogonalization");
502: }
503: } else if (gmres->orthog == KSPGMRESModifiedGramSchmidtOrthogonalization) {
504: cstr = "Modified Gram-Schmidt Orthogonalization";
505: } else {
506: cstr = "unknown orthogonalization";
507: }
508: if (iascii) {
509: PetscViewerASCIIPrintf(viewer," GMRES: restart=%D, using %s\n",gmres->max_k,cstr);
510: PetscViewerASCIIPrintf(viewer," GMRES: happy breakdown tolerance %g\n",(double)gmres->haptol);
511: } else if (isstring) {
512: PetscViewerStringSPrintf(viewer,"%s restart %D",cstr,gmres->max_k);
513: }
514: return(0);
515: }
519: /*@C
520: KSPGMRESMonitorKrylov - Calls VecView() for each direction in the
521: GMRES accumulated Krylov space.
523: Collective on KSP
525: Input Parameters:
526: + ksp - the KSP context
527: . its - iteration number
528: . fgnorm - 2-norm of residual (or gradient)
529: - a viewers object created with PetscViewersCreate()
531: Level: intermediate
533: .keywords: KSP, nonlinear, vector, monitor, view, Krylov space
535: .seealso: KSPMonitorSet(), KSPMonitorDefault(), VecView(), PetscViewersCreate(), PetscViewersDestroy()
536: @*/
537: PetscErrorCode KSPGMRESMonitorKrylov(KSP ksp,PetscInt its,PetscReal fgnorm,void *dummy)
538: {
539: PetscViewers viewers = (PetscViewers)dummy;
540: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
542: Vec x;
543: PetscViewer viewer;
544: PetscBool flg;
547: PetscViewersGetViewer(viewers,gmres->it+1,&viewer);
548: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&flg);
549: if (!flg) {
550: PetscViewerSetType(viewer,PETSCVIEWERDRAW);
551: PetscViewerDrawSetInfo(viewer,NULL,"Krylov GMRES Monitor",PETSC_DECIDE,PETSC_DECIDE,300,300);
552: }
554: x = VEC_VV(gmres->it+1);
555: VecView(x,viewer);
556: return(0);
557: }
561: PetscErrorCode KSPSetFromOptions_GMRES(KSP ksp)
562: {
564: PetscInt restart;
565: PetscReal haptol;
566: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
567: PetscBool flg;
570: PetscOptionsHead("KSP GMRES Options");
571: PetscOptionsInt("-ksp_gmres_restart","Number of Krylov search directions","KSPGMRESSetRestart",gmres->max_k,&restart,&flg);
572: if (flg) { KSPGMRESSetRestart(ksp,restart); }
573: PetscOptionsReal("-ksp_gmres_haptol","Tolerance for exact convergence (happy ending)","KSPGMRESSetHapTol",gmres->haptol,&haptol,&flg);
574: if (flg) { KSPGMRESSetHapTol(ksp,haptol); }
575: flg = PETSC_FALSE;
576: PetscOptionsBool("-ksp_gmres_preallocate","Preallocate Krylov vectors","KSPGMRESSetPreAllocateVectors",flg,&flg,NULL);
577: if (flg) {KSPGMRESSetPreAllocateVectors(ksp);}
578: PetscOptionsBoolGroupBegin("-ksp_gmres_classicalgramschmidt","Classical (unmodified) Gram-Schmidt (fast)","KSPGMRESSetOrthogonalization",&flg);
579: if (flg) {KSPGMRESSetOrthogonalization(ksp,KSPGMRESClassicalGramSchmidtOrthogonalization);}
580: PetscOptionsBoolGroupEnd("-ksp_gmres_modifiedgramschmidt","Modified Gram-Schmidt (slow,more stable)","KSPGMRESSetOrthogonalization",&flg);
581: if (flg) {KSPGMRESSetOrthogonalization(ksp,KSPGMRESModifiedGramSchmidtOrthogonalization);}
582: PetscOptionsEnum("-ksp_gmres_cgs_refinement_type","Type of iterative refinement for classical (unmodified) Gram-Schmidt","KSPGMRESSetCGSRefinementType",
583: KSPGMRESCGSRefinementTypes,(PetscEnum)gmres->cgstype,(PetscEnum*)&gmres->cgstype,&flg);
584: flg = PETSC_FALSE;
585: PetscOptionsBool("-ksp_gmres_krylov_monitor","Plot the Krylov directions","KSPMonitorSet",flg,&flg,NULL);
586: if (flg) {
587: PetscViewers viewers;
588: PetscViewersCreate(PetscObjectComm((PetscObject)ksp),&viewers);
589: KSPMonitorSet(ksp,KSPGMRESMonitorKrylov,viewers,(PetscErrorCode (*)(void**))PetscViewersDestroy);
590: }
591: PetscOptionsTail();
592: return(0);
593: }
595: extern PetscErrorCode KSPComputeExtremeSingularValues_GMRES(KSP,PetscReal*,PetscReal*);
596: extern PetscErrorCode KSPComputeEigenvalues_GMRES(KSP,PetscInt,PetscReal*,PetscReal*,PetscInt*);
600: PetscErrorCode KSPGMRESSetHapTol_GMRES(KSP ksp,PetscReal tol)
601: {
602: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
605: if (tol < 0.0) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ARG_OUTOFRANGE,"Tolerance must be non-negative");
606: gmres->haptol = tol;
607: return(0);
608: }
612: PetscErrorCode KSPGMRESGetRestart_GMRES(KSP ksp,PetscInt *max_k)
613: {
614: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
617: *max_k = gmres->max_k;
618: return(0);
619: }
623: PetscErrorCode KSPGMRESSetRestart_GMRES(KSP ksp,PetscInt max_k)
624: {
625: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
629: if (max_k < 1) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ARG_OUTOFRANGE,"Restart must be positive");
630: if (!ksp->setupstage) {
631: gmres->max_k = max_k;
632: } else if (gmres->max_k != max_k) {
633: gmres->max_k = max_k;
634: ksp->setupstage = KSP_SETUP_NEW;
635: /* free the data structures, then create them again */
636: KSPReset_GMRES(ksp);
637: }
638: return(0);
639: }
643: PetscErrorCode KSPGMRESSetOrthogonalization_GMRES(KSP ksp,FCN fcn)
644: {
646: ((KSP_GMRES*)ksp->data)->orthog = fcn;
647: return(0);
648: }
652: PetscErrorCode KSPGMRESGetOrthogonalization_GMRES(KSP ksp,FCN *fcn)
653: {
655: *fcn = ((KSP_GMRES*)ksp->data)->orthog;
656: return(0);
657: }
661: PetscErrorCode KSPGMRESSetPreAllocateVectors_GMRES(KSP ksp)
662: {
663: KSP_GMRES *gmres;
666: gmres = (KSP_GMRES*)ksp->data;
667: gmres->q_preallocate = 1;
668: return(0);
669: }
673: PetscErrorCode KSPGMRESSetCGSRefinementType_GMRES(KSP ksp,KSPGMRESCGSRefinementType type)
674: {
675: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
678: gmres->cgstype = type;
679: return(0);
680: }
684: PetscErrorCode KSPGMRESGetCGSRefinementType_GMRES(KSP ksp,KSPGMRESCGSRefinementType *type)
685: {
686: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
689: *type = gmres->cgstype;
690: return(0);
691: }
695: /*@
696: KSPGMRESSetCGSRefinementType - Sets the type of iterative refinement to use
697: in the classical Gram Schmidt orthogonalization.
699: Logically Collective on KSP
701: Input Parameters:
702: + ksp - the Krylov space context
703: - type - the type of refinement
705: Options Database:
706: . -ksp_gmres_cgs_refinement_type <never,ifneeded,always>
708: Level: intermediate
710: .keywords: KSP, GMRES, iterative refinement
712: .seealso: KSPGMRESSetOrthogonalization(), KSPGMRESCGSRefinementType, KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESGetCGSRefinementType(),
713: KSPGMRESGetOrthogonalization()
714: @*/
715: PetscErrorCode KSPGMRESSetCGSRefinementType(KSP ksp,KSPGMRESCGSRefinementType type)
716: {
722: PetscTryMethod(ksp,"KSPGMRESSetCGSRefinementType_C",(KSP,KSPGMRESCGSRefinementType),(ksp,type));
723: return(0);
724: }
728: /*@
729: KSPGMRESGetCGSRefinementType - Gets the type of iterative refinement to use
730: in the classical Gram Schmidt orthogonalization.
732: Not Collective
734: Input Parameter:
735: . ksp - the Krylov space context
737: Output Parameter:
738: . type - the type of refinement
740: Options Database:
741: . -ksp_gmres_cgs_refinement_type <never,ifneeded,always>
743: Level: intermediate
745: .keywords: KSP, GMRES, iterative refinement
747: .seealso: KSPGMRESSetOrthogonalization(), KSPGMRESCGSRefinementType, KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESSetCGSRefinementType(),
748: KSPGMRESGetOrthogonalization()
749: @*/
750: PetscErrorCode KSPGMRESGetCGSRefinementType(KSP ksp,KSPGMRESCGSRefinementType *type)
751: {
756: PetscUseMethod(ksp,"KSPGMRESGetCGSRefinementType_C",(KSP,KSPGMRESCGSRefinementType*),(ksp,type));
757: return(0);
758: }
763: /*@
764: KSPGMRESSetRestart - Sets number of iterations at which GMRES, FGMRES and LGMRES restarts.
766: Logically Collective on KSP
768: Input Parameters:
769: + ksp - the Krylov space context
770: - restart - integer restart value
772: Options Database:
773: . -ksp_gmres_restart <positive integer>
775: Note: The default value is 30.
777: Level: intermediate
779: .keywords: KSP, GMRES, restart, iterations
781: .seealso: KSPSetTolerances(), KSPGMRESSetOrthogonalization(), KSPGMRESSetPreAllocateVectors(), KSPGMRESGetRestart()
782: @*/
783: PetscErrorCode KSPGMRESSetRestart(KSP ksp, PetscInt restart)
784: {
790: PetscTryMethod(ksp,"KSPGMRESSetRestart_C",(KSP,PetscInt),(ksp,restart));
791: return(0);
792: }
796: /*@
797: KSPGMRESGetRestart - Gets number of iterations at which GMRES, FGMRES and LGMRES restarts.
799: Not Collective
801: Input Parameter:
802: . ksp - the Krylov space context
804: Output Parameter:
805: . restart - integer restart value
807: Note: The default value is 30.
809: Level: intermediate
811: .keywords: KSP, GMRES, restart, iterations
813: .seealso: KSPSetTolerances(), KSPGMRESSetOrthogonalization(), KSPGMRESSetPreAllocateVectors(), KSPGMRESSetRestart()
814: @*/
815: PetscErrorCode KSPGMRESGetRestart(KSP ksp, PetscInt *restart)
816: {
820: PetscTryMethod(ksp,"KSPGMRESGetRestart_C",(KSP,PetscInt*),(ksp,restart));
821: return(0);
822: }
826: /*@
827: KSPGMRESSetHapTol - Sets tolerance for determining happy breakdown in GMRES, FGMRES and LGMRES.
829: Logically Collective on KSP
831: Input Parameters:
832: + ksp - the Krylov space context
833: - tol - the tolerance
835: Options Database:
836: . -ksp_gmres_haptol <positive real value>
838: Note: Happy breakdown is the rare case in GMRES where an 'exact' solution is obtained after
839: a certain number of iterations. If you attempt more iterations after this point unstable
840: things can happen hence very occasionally you may need to set this value to detect this condition
842: Level: intermediate
844: .keywords: KSP, GMRES, tolerance
846: .seealso: KSPSetTolerances()
847: @*/
848: PetscErrorCode KSPGMRESSetHapTol(KSP ksp,PetscReal tol)
849: {
854: PetscTryMethod((ksp),"KSPGMRESSetHapTol_C",(KSP,PetscReal),((ksp),(tol)));
855: return(0);
856: }
858: /*MC
859: KSPGMRES - Implements the Generalized Minimal Residual method.
860: (Saad and Schultz, 1986) with restart
863: Options Database Keys:
864: + -ksp_gmres_restart <restart> - the number of Krylov directions to orthogonalize against
865: . -ksp_gmres_haptol <tol> - sets the tolerance for "happy ending" (exact convergence)
866: . -ksp_gmres_preallocate - preallocate all the Krylov search directions initially (otherwise groups of
867: vectors are allocated as needed)
868: . -ksp_gmres_classicalgramschmidt - use classical (unmodified) Gram-Schmidt to orthogonalize against the Krylov space (fast) (the default)
869: . -ksp_gmres_modifiedgramschmidt - use modified Gram-Schmidt in the orthogonalization (more stable, but slower)
870: . -ksp_gmres_cgs_refinement_type <never,ifneeded,always> - determine if iterative refinement is used to increase the
871: stability of the classical Gram-Schmidt orthogonalization.
872: - -ksp_gmres_krylov_monitor - plot the Krylov space generated
874: Level: beginner
876: Notes: Left and right preconditioning are supported, but not symmetric preconditioning.
878: References:
879: GMRES: A GENERALIZED MINIMAL RESIDUAL ALGORITHM FOR SOLVING NONSYMMETRIC LINEAR SYSTEMS. YOUCEF SAAD AND MARTIN H. SCHULTZ,
880: SIAM J. ScI. STAT. COMPUT. Vo|. 7, No. 3, July 1986, pp. 856--869.
882: .seealso: KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPFGMRES, KSPLGMRES,
883: KSPGMRESSetRestart(), KSPGMRESSetHapTol(), KSPGMRESSetPreAllocateVectors(), KSPGMRESSetOrthogonalization(), KSPGMRESGetOrthogonalization(),
884: KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESModifiedGramSchmidtOrthogonalization(),
885: KSPGMRESCGSRefinementType, KSPGMRESSetCGSRefinementType(), KSPGMRESGetCGSRefinementType(), KSPGMRESMonitorKrylov(), KSPSetPCSide()
887: M*/
891: PETSC_EXTERN PetscErrorCode KSPCreate_GMRES(KSP ksp)
892: {
893: KSP_GMRES *gmres;
897: PetscNewLog(ksp,&gmres);
898: ksp->data = (void*)gmres;
900: KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,3);
901: KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_RIGHT,2);
903: ksp->ops->buildsolution = KSPBuildSolution_GMRES;
904: ksp->ops->setup = KSPSetUp_GMRES;
905: ksp->ops->solve = KSPSolve_GMRES;
906: ksp->ops->reset = KSPReset_GMRES;
907: ksp->ops->destroy = KSPDestroy_GMRES;
908: ksp->ops->view = KSPView_GMRES;
909: ksp->ops->setfromoptions = KSPSetFromOptions_GMRES;
910: ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_GMRES;
911: ksp->ops->computeeigenvalues = KSPComputeEigenvalues_GMRES;
913: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetPreAllocateVectors_C",KSPGMRESSetPreAllocateVectors_GMRES);
914: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetOrthogonalization_C",KSPGMRESSetOrthogonalization_GMRES);
915: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetOrthogonalization_C",KSPGMRESGetOrthogonalization_GMRES);
916: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetRestart_C",KSPGMRESSetRestart_GMRES);
917: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetRestart_C",KSPGMRESGetRestart_GMRES);
918: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetHapTol_C",KSPGMRESSetHapTol_GMRES);
919: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetCGSRefinementType_C",KSPGMRESSetCGSRefinementType_GMRES);
920: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetCGSRefinementType_C",KSPGMRESGetCGSRefinementType_GMRES);
922: gmres->haptol = 1.0e-30;
923: gmres->q_preallocate = 0;
924: gmres->delta_allocate = GMRES_DELTA_DIRECTIONS;
925: gmres->orthog = KSPGMRESClassicalGramSchmidtOrthogonalization;
926: gmres->nrs = 0;
927: gmres->sol_temp = 0;
928: gmres->max_k = GMRES_DEFAULT_MAXK;
929: gmres->Rsvd = 0;
930: gmres->cgstype = KSP_GMRES_CGS_REFINE_NEVER;
931: gmres->orthogwork = 0;
932: return(0);
933: }