Actual source code: gmres.c
petsc-3.7.5 2017-01-01
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: KSPCreateVecs(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: KSPCreateVecs(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: if (itcount) *itcount = 0;
128: VecNormalize(VEC_VV(0),&res_norm);
129: KSPCheckNorm(ksp,res_norm);
130: res = res_norm;
131: *GRS(0) = res_norm;
133: /* check for the convergence */
134: PetscObjectSAWsTakeAccess((PetscObject)ksp);
135: ksp->rnorm = res;
136: PetscObjectSAWsGrantAccess((PetscObject)ksp);
137: gmres->it = (it - 1);
138: KSPLogResidualHistory(ksp,res);
139: KSPMonitor(ksp,ksp->its,res);
140: if (!res) {
141: ksp->reason = KSP_CONVERGED_ATOL;
142: PetscInfo(ksp,"Converged due to zero residual norm on entry\n");
143: return(0);
144: }
146: (*ksp->converged)(ksp,ksp->its,res,&ksp->reason,ksp->cnvP);
147: while (!ksp->reason && it < max_k && ksp->its < ksp->max_it) {
148: if (it) {
149: KSPLogResidualHistory(ksp,res);
150: KSPMonitor(ksp,ksp->its,res);
151: }
152: gmres->it = (it - 1);
153: if (gmres->vv_allocated <= it + VEC_OFFSET + 1) {
154: KSPGMRESGetNewVectors(ksp,it+1);
155: }
156: KSP_PCApplyBAorAB(ksp,VEC_VV(it),VEC_VV(1+it),VEC_TEMP_MATOP);
158: /* update hessenberg matrix and do Gram-Schmidt */
159: (*gmres->orthog)(ksp,it);
160: if (ksp->reason) break;
162: /* vv(i+1) . vv(i+1) */
163: VecNormalize(VEC_VV(it+1),&tt);
165: /* save the magnitude */
166: *HH(it+1,it) = tt;
167: *HES(it+1,it) = tt;
169: /* check for the happy breakdown */
170: hapbnd = PetscAbsScalar(tt / *GRS(it));
171: if (hapbnd > gmres->haptol) hapbnd = gmres->haptol;
172: if (tt < hapbnd) {
173: PetscInfo2(ksp,"Detected happy breakdown, current hapbnd = %14.12e tt = %14.12e\n",(double)hapbnd,(double)tt);
174: hapend = PETSC_TRUE;
175: }
176: KSPGMRESUpdateHessenberg(ksp,it,hapend,&res);
178: it++;
179: gmres->it = (it-1); /* For converged */
180: ksp->its++;
181: ksp->rnorm = res;
182: if (ksp->reason) break;
184: (*ksp->converged)(ksp,ksp->its,res,&ksp->reason,ksp->cnvP);
186: /* Catch error in happy breakdown and signal convergence and break from loop */
187: if (hapend) {
188: if (!ksp->reason) {
189: 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);
190: else {
191: ksp->reason = KSP_DIVERGED_BREAKDOWN;
192: break;
193: }
194: }
195: }
196: }
198: /* Monitor if we know that we will not return for a restart */
199: if (it && (ksp->reason || ksp->its >= ksp->max_it)) {
200: KSPLogResidualHistory(ksp,res);
201: KSPMonitor(ksp,ksp->its,res);
202: }
204: if (itcount) *itcount = it;
207: /*
208: Down here we have to solve for the "best" coefficients of the Krylov
209: columns, add the solution values together, and possibly unwind the
210: preconditioning from the solution
211: */
212: /* Form the solution (or the solution so far) */
213: KSPGMRESBuildSoln(GRS(0),ksp->vec_sol,ksp->vec_sol,ksp,it-1);
214: return(0);
215: }
219: PetscErrorCode KSPSolve_GMRES(KSP ksp)
220: {
222: PetscInt its,itcount,i;
223: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
224: PetscBool guess_zero = ksp->guess_zero;
225: PetscInt N = gmres->max_k + 1;
226: PetscBLASInt bN;
229: if (ksp->calc_sings && !gmres->Rsvd) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ORDER,"Must call KSPSetComputeSingularValues() before KSPSetUp() is called");
231: PetscObjectSAWsTakeAccess((PetscObject)ksp);
232: ksp->its = 0;
233: PetscObjectSAWsGrantAccess((PetscObject)ksp);
235: itcount = 0;
236: gmres->fullcycle = 0;
237: ksp->reason = KSP_CONVERGED_ITERATING;
238: while (!ksp->reason) {
239: KSPInitialResidual(ksp,ksp->vec_sol,VEC_TEMP,VEC_TEMP_MATOP,VEC_VV(0),ksp->vec_rhs);
240: KSPGMRESCycle(&its,ksp);
241: /* Store the Hessenberg matrix and the basis vectors of the Krylov subspace
242: if the cycle is complete for the computation of the Ritz pairs */
243: if (its == gmres->max_k) {
244: gmres->fullcycle++;
245: if (ksp->calc_ritz) {
246: if (!gmres->hes_ritz) {
247: PetscMalloc1(N*N,&gmres->hes_ritz);
248: PetscLogObjectMemory((PetscObject)ksp,N*N*sizeof(PetscScalar));
249: VecDuplicateVecs(VEC_VV(0),N,&gmres->vecb);
250: }
251: PetscBLASIntCast(N,&bN);
252: PetscMemcpy(gmres->hes_ritz,gmres->hes_origin,bN*bN*sizeof(PetscReal));
253: for (i=0; i<gmres->max_k+1; i++) {
254: VecCopy(VEC_VV(i),gmres->vecb[i]);
255: }
256: }
257: }
258: itcount += its;
259: if (itcount >= ksp->max_it) {
260: if (!ksp->reason) ksp->reason = KSP_DIVERGED_ITS;
261: break;
262: }
263: ksp->guess_zero = PETSC_FALSE; /* every future call to KSPInitialResidual() will have nonzero guess */
264: }
265: ksp->guess_zero = guess_zero; /* restore if user provided nonzero initial guess */
266: return(0);
267: }
271: PetscErrorCode KSPReset_GMRES(KSP ksp)
272: {
273: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
275: PetscInt i;
278: /* Free the Hessenberg matrices */
279: PetscFree6(gmres->hh_origin,gmres->hes_origin,gmres->rs_origin,gmres->cc_origin,gmres->ss_origin,gmres->hes_ritz);
281: /* free work vectors */
282: PetscFree(gmres->vecs);
283: for (i=0; i<gmres->nwork_alloc; i++) {
284: VecDestroyVecs(gmres->mwork_alloc[i],&gmres->user_work[i]);
285: }
286: gmres->nwork_alloc = 0;
287: if (gmres->vecb) {
288: VecDestroyVecs(gmres->max_k+1,&gmres->vecb);
289: }
291: PetscFree(gmres->user_work);
292: PetscFree(gmres->mwork_alloc);
293: PetscFree(gmres->nrs);
294: VecDestroy(&gmres->sol_temp);
295: PetscFree(gmres->Rsvd);
296: PetscFree(gmres->Dsvd);
297: PetscFree(gmres->orthogwork);
299: gmres->sol_temp = 0;
300: gmres->vv_allocated = 0;
301: gmres->vecs_allocated = 0;
302: gmres->sol_temp = 0;
303: return(0);
304: }
308: PetscErrorCode KSPDestroy_GMRES(KSP ksp)
309: {
313: KSPReset_GMRES(ksp);
314: PetscFree(ksp->data);
315: /* clear composed functions */
316: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetPreAllocateVectors_C",NULL);
317: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetOrthogonalization_C",NULL);
318: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetOrthogonalization_C",NULL);
319: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetRestart_C",NULL);
320: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetRestart_C",NULL);
321: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetHapTol_C",NULL);
322: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetCGSRefinementType_C",NULL);
323: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetCGSRefinementType_C",NULL);
324: return(0);
325: }
326: /*
327: KSPGMRESBuildSoln - create the solution from the starting vector and the
328: current iterates.
330: Input parameters:
331: nrs - work area of size it + 1.
332: vs - index of initial guess
333: vdest - index of result. Note that vs may == vdest (replace
334: guess with the solution).
336: This is an internal routine that knows about the GMRES internals.
337: */
340: static PetscErrorCode KSPGMRESBuildSoln(PetscScalar *nrs,Vec vs,Vec vdest,KSP ksp,PetscInt it)
341: {
342: PetscScalar tt;
344: PetscInt ii,k,j;
345: KSP_GMRES *gmres = (KSP_GMRES*)(ksp->data);
348: /* Solve for solution vector that minimizes the residual */
350: /* If it is < 0, no gmres steps have been performed */
351: if (it < 0) {
352: VecCopy(vs,vdest); /* VecCopy() is smart, exists immediately if vguess == vdest */
353: return(0);
354: }
355: if (*HH(it,it) != 0.0) {
356: nrs[it] = *GRS(it) / *HH(it,it);
357: } else {
358: ksp->reason = KSP_DIVERGED_BREAKDOWN;
360: 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)));
361: return(0);
362: }
363: for (ii=1; ii<=it; ii++) {
364: k = it - ii;
365: tt = *GRS(k);
366: for (j=k+1; j<=it; j++) tt = tt - *HH(k,j) * nrs[j];
367: if (*HH(k,k) == 0.0) {
368: ksp->reason = KSP_DIVERGED_BREAKDOWN;
370: PetscInfo1(ksp,"Likely your matrix or preconditioner is singular. HH(k,k) is identically zero; k = %D\n",k);
371: return(0);
372: }
373: nrs[k] = tt / *HH(k,k);
374: }
376: /* Accumulate the correction to the solution of the preconditioned problem in TEMP */
377: VecSet(VEC_TEMP,0.0);
378: VecMAXPY(VEC_TEMP,it+1,nrs,&VEC_VV(0));
380: KSPUnwindPreconditioner(ksp,VEC_TEMP,VEC_TEMP_MATOP);
381: /* add solution to previous solution */
382: if (vdest != vs) {
383: VecCopy(vs,vdest);
384: }
385: VecAXPY(vdest,1.0,VEC_TEMP);
386: return(0);
387: }
388: /*
389: Do the scalar work for the orthogonalization. Return new residual norm.
390: */
393: static PetscErrorCode KSPGMRESUpdateHessenberg(KSP ksp,PetscInt it,PetscBool hapend,PetscReal *res)
394: {
395: PetscScalar *hh,*cc,*ss,tt;
396: PetscInt j;
397: KSP_GMRES *gmres = (KSP_GMRES*)(ksp->data);
400: hh = HH(0,it);
401: cc = CC(0);
402: ss = SS(0);
404: /* Apply all the previously computed plane rotations to the new column
405: of the Hessenberg matrix */
406: for (j=1; j<=it; j++) {
407: tt = *hh;
408: *hh = PetscConj(*cc) * tt + *ss * *(hh+1);
409: hh++;
410: *hh = *cc++ * *hh - (*ss++ * tt);
411: }
413: /*
414: compute the new plane rotation, and apply it to:
415: 1) the right-hand-side of the Hessenberg system
416: 2) the new column of the Hessenberg matrix
417: thus obtaining the updated value of the residual
418: */
419: if (!hapend) {
420: tt = PetscSqrtScalar(PetscConj(*hh) * *hh + PetscConj(*(hh+1)) * *(hh+1));
421: if (tt == 0.0) {
422: ksp->reason = KSP_DIVERGED_NULL;
423: return(0);
424: }
425: *cc = *hh / tt;
426: *ss = *(hh+1) / tt;
427: *GRS(it+1) = -(*ss * *GRS(it));
428: *GRS(it) = PetscConj(*cc) * *GRS(it);
429: *hh = PetscConj(*cc) * *hh + *ss * *(hh+1);
430: *res = PetscAbsScalar(*GRS(it+1));
431: } else {
432: /* happy breakdown: HH(it+1, it) = 0, therfore we don't need to apply
433: another rotation matrix (so RH doesn't change). The new residual is
434: always the new sine term times the residual from last time (GRS(it)),
435: but now the new sine rotation would be zero...so the residual should
436: be zero...so we will multiply "zero" by the last residual. This might
437: not be exactly what we want to do here -could just return "zero". */
439: *res = 0.0;
440: }
441: return(0);
442: }
443: /*
444: This routine allocates more work vectors, starting from VEC_VV(it).
445: */
448: PetscErrorCode KSPGMRESGetNewVectors(KSP ksp,PetscInt it)
449: {
450: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
452: PetscInt nwork = gmres->nwork_alloc,k,nalloc;
455: nalloc = PetscMin(ksp->max_it,gmres->delta_allocate);
456: /* Adjust the number to allocate to make sure that we don't exceed the
457: number of available slots */
458: if (it + VEC_OFFSET + nalloc >= gmres->vecs_allocated) {
459: nalloc = gmres->vecs_allocated - it - VEC_OFFSET;
460: }
461: if (!nalloc) return(0);
463: gmres->vv_allocated += nalloc;
465: KSPCreateVecs(ksp,nalloc,&gmres->user_work[nwork],0,NULL);
466: PetscLogObjectParents(ksp,nalloc,gmres->user_work[nwork]);
468: gmres->mwork_alloc[nwork] = nalloc;
469: for (k=0; k<nalloc; k++) {
470: gmres->vecs[it+VEC_OFFSET+k] = gmres->user_work[nwork][k];
471: }
472: gmres->nwork_alloc++;
473: return(0);
474: }
478: PetscErrorCode KSPBuildSolution_GMRES(KSP ksp,Vec ptr,Vec *result)
479: {
480: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
484: if (!ptr) {
485: if (!gmres->sol_temp) {
486: VecDuplicate(ksp->vec_sol,&gmres->sol_temp);
487: PetscLogObjectParent((PetscObject)ksp,(PetscObject)gmres->sol_temp);
488: }
489: ptr = gmres->sol_temp;
490: }
491: if (!gmres->nrs) {
492: /* allocate the work area */
493: PetscMalloc1(gmres->max_k,&gmres->nrs);
494: PetscLogObjectMemory((PetscObject)ksp,gmres->max_k*sizeof(PetscScalar));
495: }
497: KSPGMRESBuildSoln(gmres->nrs,ksp->vec_sol,ptr,ksp,gmres->it);
498: if (result) *result = ptr;
499: return(0);
500: }
504: PetscErrorCode KSPView_GMRES(KSP ksp,PetscViewer viewer)
505: {
506: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
507: const char *cstr;
509: PetscBool iascii,isstring;
512: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
513: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERSTRING,&isstring);
514: if (gmres->orthog == KSPGMRESClassicalGramSchmidtOrthogonalization) {
515: switch (gmres->cgstype) {
516: case (KSP_GMRES_CGS_REFINE_NEVER):
517: cstr = "Classical (unmodified) Gram-Schmidt Orthogonalization with no iterative refinement";
518: break;
519: case (KSP_GMRES_CGS_REFINE_ALWAYS):
520: cstr = "Classical (unmodified) Gram-Schmidt Orthogonalization with one step of iterative refinement";
521: break;
522: case (KSP_GMRES_CGS_REFINE_IFNEEDED):
523: cstr = "Classical (unmodified) Gram-Schmidt Orthogonalization with one step of iterative refinement when needed";
524: break;
525: default:
526: SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ARG_OUTOFRANGE,"Unknown orthogonalization");
527: }
528: } else if (gmres->orthog == KSPGMRESModifiedGramSchmidtOrthogonalization) {
529: cstr = "Modified Gram-Schmidt Orthogonalization";
530: } else {
531: cstr = "unknown orthogonalization";
532: }
533: if (iascii) {
534: PetscViewerASCIIPrintf(viewer," GMRES: restart=%D, using %s\n",gmres->max_k,cstr);
535: PetscViewerASCIIPrintf(viewer," GMRES: happy breakdown tolerance %g\n",(double)gmres->haptol);
536: } else if (isstring) {
537: PetscViewerStringSPrintf(viewer,"%s restart %D",cstr,gmres->max_k);
538: }
539: return(0);
540: }
544: /*@C
545: KSPGMRESMonitorKrylov - Calls VecView() for each new direction in the GMRES accumulated Krylov space.
547: Collective on KSP
549: Input Parameters:
550: + ksp - the KSP context
551: . its - iteration number
552: . fgnorm - 2-norm of residual (or gradient)
553: - dummy - an collection of viewers created with KSPViewerCreate()
555: Options Database Keys:
556: . -ksp_gmres_kyrlov_monitor
558: Notes: A new PETSCVIEWERDRAW is created for each Krylov vector so they can all be simultaneously viewed
559: Level: intermediate
561: .keywords: KSP, nonlinear, vector, monitor, view, Krylov space
563: .seealso: KSPMonitorSet(), KSPMonitorDefault(), VecView(), KSPViewersCreate(), KSPViewersDestroy()
564: @*/
565: PetscErrorCode KSPGMRESMonitorKrylov(KSP ksp,PetscInt its,PetscReal fgnorm,void *dummy)
566: {
567: PetscViewers viewers = (PetscViewers)dummy;
568: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
570: Vec x;
571: PetscViewer viewer;
572: PetscBool flg;
575: PetscViewersGetViewer(viewers,gmres->it+1,&viewer);
576: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&flg);
577: if (!flg) {
578: PetscViewerSetType(viewer,PETSCVIEWERDRAW);
579: PetscViewerDrawSetInfo(viewer,NULL,"Krylov GMRES Monitor",PETSC_DECIDE,PETSC_DECIDE,300,300);
580: }
581: x = VEC_VV(gmres->it+1);
582: VecView(x,viewer);
583: return(0);
584: }
588: PetscErrorCode KSPSetFromOptions_GMRES(PetscOptionItems *PetscOptionsObject,KSP ksp)
589: {
591: PetscInt restart;
592: PetscReal haptol;
593: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
594: PetscBool flg;
597: PetscOptionsHead(PetscOptionsObject,"KSP GMRES Options");
598: PetscOptionsInt("-ksp_gmres_restart","Number of Krylov search directions","KSPGMRESSetRestart",gmres->max_k,&restart,&flg);
599: if (flg) { KSPGMRESSetRestart(ksp,restart); }
600: PetscOptionsReal("-ksp_gmres_haptol","Tolerance for exact convergence (happy ending)","KSPGMRESSetHapTol",gmres->haptol,&haptol,&flg);
601: if (flg) { KSPGMRESSetHapTol(ksp,haptol); }
602: flg = PETSC_FALSE;
603: PetscOptionsBool("-ksp_gmres_preallocate","Preallocate Krylov vectors","KSPGMRESSetPreAllocateVectors",flg,&flg,NULL);
604: if (flg) {KSPGMRESSetPreAllocateVectors(ksp);}
605: PetscOptionsBoolGroupBegin("-ksp_gmres_classicalgramschmidt","Classical (unmodified) Gram-Schmidt (fast)","KSPGMRESSetOrthogonalization",&flg);
606: if (flg) {KSPGMRESSetOrthogonalization(ksp,KSPGMRESClassicalGramSchmidtOrthogonalization);}
607: PetscOptionsBoolGroupEnd("-ksp_gmres_modifiedgramschmidt","Modified Gram-Schmidt (slow,more stable)","KSPGMRESSetOrthogonalization",&flg);
608: if (flg) {KSPGMRESSetOrthogonalization(ksp,KSPGMRESModifiedGramSchmidtOrthogonalization);}
609: PetscOptionsEnum("-ksp_gmres_cgs_refinement_type","Type of iterative refinement for classical (unmodified) Gram-Schmidt","KSPGMRESSetCGSRefinementType",
610: KSPGMRESCGSRefinementTypes,(PetscEnum)gmres->cgstype,(PetscEnum*)&gmres->cgstype,&flg);
611: flg = PETSC_FALSE;
612: PetscOptionsBool("-ksp_gmres_krylov_monitor","Plot the Krylov directions","KSPMonitorSet",flg,&flg,NULL);
613: if (flg) {
614: PetscViewers viewers;
615: PetscViewersCreate(PetscObjectComm((PetscObject)ksp),&viewers);
616: KSPMonitorSet(ksp,KSPGMRESMonitorKrylov,viewers,(PetscErrorCode (*)(void**))PetscViewersDestroy);
617: }
618: PetscOptionsTail();
619: return(0);
620: }
622: extern PetscErrorCode KSPComputeExtremeSingularValues_GMRES(KSP,PetscReal*,PetscReal*);
623: extern PetscErrorCode KSPComputeEigenvalues_GMRES(KSP,PetscInt,PetscReal*,PetscReal*,PetscInt*);
627: PetscErrorCode KSPGMRESSetHapTol_GMRES(KSP ksp,PetscReal tol)
628: {
629: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
632: if (tol < 0.0) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ARG_OUTOFRANGE,"Tolerance must be non-negative");
633: gmres->haptol = tol;
634: return(0);
635: }
639: PetscErrorCode KSPGMRESGetRestart_GMRES(KSP ksp,PetscInt *max_k)
640: {
641: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
644: *max_k = gmres->max_k;
645: return(0);
646: }
650: PetscErrorCode KSPGMRESSetRestart_GMRES(KSP ksp,PetscInt max_k)
651: {
652: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
656: if (max_k < 1) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ARG_OUTOFRANGE,"Restart must be positive");
657: if (!ksp->setupstage) {
658: gmres->max_k = max_k;
659: } else if (gmres->max_k != max_k) {
660: gmres->max_k = max_k;
661: ksp->setupstage = KSP_SETUP_NEW;
662: /* free the data structures, then create them again */
663: KSPReset_GMRES(ksp);
664: }
665: return(0);
666: }
670: PetscErrorCode KSPGMRESSetOrthogonalization_GMRES(KSP ksp,FCN fcn)
671: {
673: ((KSP_GMRES*)ksp->data)->orthog = fcn;
674: return(0);
675: }
679: PetscErrorCode KSPGMRESGetOrthogonalization_GMRES(KSP ksp,FCN *fcn)
680: {
682: *fcn = ((KSP_GMRES*)ksp->data)->orthog;
683: return(0);
684: }
688: PetscErrorCode KSPGMRESSetPreAllocateVectors_GMRES(KSP ksp)
689: {
690: KSP_GMRES *gmres;
693: gmres = (KSP_GMRES*)ksp->data;
694: gmres->q_preallocate = 1;
695: return(0);
696: }
700: PetscErrorCode KSPGMRESSetCGSRefinementType_GMRES(KSP ksp,KSPGMRESCGSRefinementType type)
701: {
702: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
705: gmres->cgstype = type;
706: return(0);
707: }
711: PetscErrorCode KSPGMRESGetCGSRefinementType_GMRES(KSP ksp,KSPGMRESCGSRefinementType *type)
712: {
713: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
716: *type = gmres->cgstype;
717: return(0);
718: }
722: /*@
723: KSPGMRESSetCGSRefinementType - Sets the type of iterative refinement to use
724: in the classical Gram Schmidt orthogonalization.
726: Logically Collective on KSP
728: Input Parameters:
729: + ksp - the Krylov space context
730: - type - the type of refinement
732: Options Database:
733: . -ksp_gmres_cgs_refinement_type <refine_never,refine_ifneeded,refine_always>
735: Level: intermediate
737: .keywords: KSP, GMRES, iterative refinement
739: .seealso: KSPGMRESSetOrthogonalization(), KSPGMRESCGSRefinementType, KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESGetCGSRefinementType(),
740: KSPGMRESGetOrthogonalization()
741: @*/
742: PetscErrorCode KSPGMRESSetCGSRefinementType(KSP ksp,KSPGMRESCGSRefinementType type)
743: {
749: PetscTryMethod(ksp,"KSPGMRESSetCGSRefinementType_C",(KSP,KSPGMRESCGSRefinementType),(ksp,type));
750: return(0);
751: }
755: /*@
756: KSPGMRESGetCGSRefinementType - Gets the type of iterative refinement to use
757: in the classical Gram Schmidt orthogonalization.
759: Not Collective
761: Input Parameter:
762: . ksp - the Krylov space context
764: Output Parameter:
765: . type - the type of refinement
767: Options Database:
768: . -ksp_gmres_cgs_refinement_type <never,ifneeded,always>
770: Level: intermediate
772: .keywords: KSP, GMRES, iterative refinement
774: .seealso: KSPGMRESSetOrthogonalization(), KSPGMRESCGSRefinementType, KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESSetCGSRefinementType(),
775: KSPGMRESGetOrthogonalization()
776: @*/
777: PetscErrorCode KSPGMRESGetCGSRefinementType(KSP ksp,KSPGMRESCGSRefinementType *type)
778: {
783: PetscUseMethod(ksp,"KSPGMRESGetCGSRefinementType_C",(KSP,KSPGMRESCGSRefinementType*),(ksp,type));
784: return(0);
785: }
790: /*@
791: KSPGMRESSetRestart - Sets number of iterations at which GMRES, FGMRES and LGMRES restarts.
793: Logically Collective on KSP
795: Input Parameters:
796: + ksp - the Krylov space context
797: - restart - integer restart value
799: Options Database:
800: . -ksp_gmres_restart <positive integer>
802: Note: The default value is 30.
804: Level: intermediate
806: .keywords: KSP, GMRES, restart, iterations
808: .seealso: KSPSetTolerances(), KSPGMRESSetOrthogonalization(), KSPGMRESSetPreAllocateVectors(), KSPGMRESGetRestart()
809: @*/
810: PetscErrorCode KSPGMRESSetRestart(KSP ksp, PetscInt restart)
811: {
817: PetscTryMethod(ksp,"KSPGMRESSetRestart_C",(KSP,PetscInt),(ksp,restart));
818: return(0);
819: }
823: /*@
824: KSPGMRESGetRestart - Gets number of iterations at which GMRES, FGMRES and LGMRES restarts.
826: Not Collective
828: Input Parameter:
829: . ksp - the Krylov space context
831: Output Parameter:
832: . restart - integer restart value
834: Note: The default value is 30.
836: Level: intermediate
838: .keywords: KSP, GMRES, restart, iterations
840: .seealso: KSPSetTolerances(), KSPGMRESSetOrthogonalization(), KSPGMRESSetPreAllocateVectors(), KSPGMRESSetRestart()
841: @*/
842: PetscErrorCode KSPGMRESGetRestart(KSP ksp, PetscInt *restart)
843: {
847: PetscUseMethod(ksp,"KSPGMRESGetRestart_C",(KSP,PetscInt*),(ksp,restart));
848: return(0);
849: }
853: /*@
854: KSPGMRESSetHapTol - Sets tolerance for determining happy breakdown in GMRES, FGMRES and LGMRES.
856: Logically Collective on KSP
858: Input Parameters:
859: + ksp - the Krylov space context
860: - tol - the tolerance
862: Options Database:
863: . -ksp_gmres_haptol <positive real value>
865: Note: Happy breakdown is the rare case in GMRES where an 'exact' solution is obtained after
866: a certain number of iterations. If you attempt more iterations after this point unstable
867: things can happen hence very occasionally you may need to set this value to detect this condition
869: Level: intermediate
871: .keywords: KSP, GMRES, tolerance
873: .seealso: KSPSetTolerances()
874: @*/
875: PetscErrorCode KSPGMRESSetHapTol(KSP ksp,PetscReal tol)
876: {
881: PetscTryMethod((ksp),"KSPGMRESSetHapTol_C",(KSP,PetscReal),((ksp),(tol)));
882: return(0);
883: }
885: /*MC
886: KSPGMRES - Implements the Generalized Minimal Residual method.
887: (Saad and Schultz, 1986) with restart
890: Options Database Keys:
891: + -ksp_gmres_restart <restart> - the number of Krylov directions to orthogonalize against
892: . -ksp_gmres_haptol <tol> - sets the tolerance for "happy ending" (exact convergence)
893: . -ksp_gmres_preallocate - preallocate all the Krylov search directions initially (otherwise groups of
894: vectors are allocated as needed)
895: . -ksp_gmres_classicalgramschmidt - use classical (unmodified) Gram-Schmidt to orthogonalize against the Krylov space (fast) (the default)
896: . -ksp_gmres_modifiedgramschmidt - use modified Gram-Schmidt in the orthogonalization (more stable, but slower)
897: . -ksp_gmres_cgs_refinement_type <never,ifneeded,always> - determine if iterative refinement is used to increase the
898: stability of the classical Gram-Schmidt orthogonalization.
899: - -ksp_gmres_krylov_monitor - plot the Krylov space generated
901: Level: beginner
903: Notes: Left and right preconditioning are supported, but not symmetric preconditioning.
905: References:
906: . 1. - YOUCEF SAAD AND MARTIN H. SCHULTZ, GMRES: A GENERALIZED MINIMAL RESIDUAL ALGORITHM FOR SOLVING NONSYMMETRIC LINEAR SYSTEMS.
907: SIAM J. ScI. STAT. COMPUT. Vo|. 7, No. 3, July 1986.
909: .seealso: KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPFGMRES, KSPLGMRES,
910: KSPGMRESSetRestart(), KSPGMRESSetHapTol(), KSPGMRESSetPreAllocateVectors(), KSPGMRESSetOrthogonalization(), KSPGMRESGetOrthogonalization(),
911: KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESModifiedGramSchmidtOrthogonalization(),
912: KSPGMRESCGSRefinementType, KSPGMRESSetCGSRefinementType(), KSPGMRESGetCGSRefinementType(), KSPGMRESMonitorKrylov(), KSPSetPCSide()
914: M*/
918: PETSC_EXTERN PetscErrorCode KSPCreate_GMRES(KSP ksp)
919: {
920: KSP_GMRES *gmres;
924: PetscNewLog(ksp,&gmres);
925: ksp->data = (void*)gmres;
927: KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,4);
928: KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_RIGHT,3);
929: KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_SYMMETRIC,2);
931: ksp->ops->buildsolution = KSPBuildSolution_GMRES;
932: ksp->ops->setup = KSPSetUp_GMRES;
933: ksp->ops->solve = KSPSolve_GMRES;
934: ksp->ops->reset = KSPReset_GMRES;
935: ksp->ops->destroy = KSPDestroy_GMRES;
936: ksp->ops->view = KSPView_GMRES;
937: ksp->ops->setfromoptions = KSPSetFromOptions_GMRES;
938: ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_GMRES;
939: ksp->ops->computeeigenvalues = KSPComputeEigenvalues_GMRES;
940: #if !defined(PETSC_USE_COMPLEX) && !defined(PETSC_HAVE_ESSL)
941: ksp->ops->computeritz = KSPComputeRitz_GMRES;
942: #endif
943: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetPreAllocateVectors_C",KSPGMRESSetPreAllocateVectors_GMRES);
944: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetOrthogonalization_C",KSPGMRESSetOrthogonalization_GMRES);
945: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetOrthogonalization_C",KSPGMRESGetOrthogonalization_GMRES);
946: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetRestart_C",KSPGMRESSetRestart_GMRES);
947: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetRestart_C",KSPGMRESGetRestart_GMRES);
948: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetHapTol_C",KSPGMRESSetHapTol_GMRES);
949: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetCGSRefinementType_C",KSPGMRESSetCGSRefinementType_GMRES);
950: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetCGSRefinementType_C",KSPGMRESGetCGSRefinementType_GMRES);
952: gmres->haptol = 1.0e-30;
953: gmres->q_preallocate = 0;
954: gmres->delta_allocate = GMRES_DELTA_DIRECTIONS;
955: gmres->orthog = KSPGMRESClassicalGramSchmidtOrthogonalization;
956: gmres->nrs = 0;
957: gmres->sol_temp = 0;
958: gmres->max_k = GMRES_DEFAULT_MAXK;
959: gmres->Rsvd = 0;
960: gmres->cgstype = KSP_GMRES_CGS_REFINE_NEVER;
961: gmres->orthogwork = 0;
962: return(0);
963: }