Actual source code: gmres.c
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>
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);
37: PetscErrorCode KSPSetUp_GMRES(KSP ksp)
38: {
39: PetscInt hh,hes,rs,cc;
41: PetscInt max_k,k;
42: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
45: max_k = gmres->max_k; /* restart size */
46: hh = (max_k + 2) * (max_k + 1);
47: hes = (max_k + 1) * (max_k + 1);
48: rs = (max_k + 2);
49: cc = (max_k + 1);
51: PetscCalloc5(hh,&gmres->hh_origin,hes,&gmres->hes_origin,rs,&gmres->rs_origin,cc,&gmres->cc_origin,cc,&gmres->ss_origin);
52: PetscLogObjectMemory((PetscObject)ksp,(hh + hes + rs + 2*cc)*sizeof(PetscScalar));
54: if (ksp->calc_sings) {
55: /* Allocate workspace to hold Hessenberg matrix needed by lapack */
56: PetscMalloc1((max_k + 3)*(max_k + 9),&gmres->Rsvd);
57: PetscLogObjectMemory((PetscObject)ksp,(max_k + 3)*(max_k + 9)*sizeof(PetscScalar));
58: PetscMalloc1(6*(max_k+2),&gmres->Dsvd);
59: PetscLogObjectMemory((PetscObject)ksp,6*(max_k+2)*sizeof(PetscReal));
60: }
62: /* Allocate array to hold pointers to user vectors. Note that we need
63: 4 + max_k + 1 (since we need it+1 vectors, and it <= max_k) */
64: gmres->vecs_allocated = VEC_OFFSET + 2 + max_k + gmres->nextra_vecs;
66: PetscMalloc1(gmres->vecs_allocated,&gmres->vecs);
67: PetscMalloc1(VEC_OFFSET+2+max_k,&gmres->user_work);
68: PetscMalloc1(VEC_OFFSET+2+max_k,&gmres->mwork_alloc);
69: PetscLogObjectMemory((PetscObject)ksp,(VEC_OFFSET+2+max_k)*(sizeof(Vec*)+sizeof(PetscInt)) + gmres->vecs_allocated*sizeof(Vec));
71: if (gmres->q_preallocate) {
72: gmres->vv_allocated = VEC_OFFSET + 2 + max_k;
74: KSPCreateVecs(ksp,gmres->vv_allocated,&gmres->user_work[0],0,NULL);
75: PetscLogObjectParents(ksp,gmres->vv_allocated,gmres->user_work[0]);
77: gmres->mwork_alloc[0] = gmres->vv_allocated;
78: gmres->nwork_alloc = 1;
79: for (k=0; k<gmres->vv_allocated; k++) {
80: gmres->vecs[k] = gmres->user_work[0][k];
81: }
82: } else {
83: gmres->vv_allocated = 5;
85: KSPCreateVecs(ksp,5,&gmres->user_work[0],0,NULL);
86: PetscLogObjectParents(ksp,5,gmres->user_work[0]);
88: gmres->mwork_alloc[0] = 5;
89: gmres->nwork_alloc = 1;
90: for (k=0; k<gmres->vv_allocated; k++) {
91: gmres->vecs[k] = gmres->user_work[0][k];
92: }
93: }
94: return(0);
95: }
97: /*
98: Run gmres, possibly with restart. Return residual history if requested.
99: input parameters:
101: . gmres - structure containing parameters and work areas
103: output parameters:
104: . nres - residuals (from preconditioned system) at each step.
105: If restarting, consider passing nres+it. If null,
106: ignored
107: . itcount - number of iterations used. nres[0] to nres[itcount]
108: are defined. If null, ignored.
110: Notes:
111: On entry, the value in vector VEC_VV(0) should be the initial residual
112: (this allows shortcuts where the initial preconditioned residual is 0).
113: */
114: PetscErrorCode KSPGMRESCycle(PetscInt *itcount,KSP ksp)
115: {
116: KSP_GMRES *gmres = (KSP_GMRES*)(ksp->data);
117: PetscReal res,hapbnd,tt;
119: PetscInt it = 0, max_k = gmres->max_k;
120: PetscBool hapend = PETSC_FALSE;
123: if (itcount) *itcount = 0;
124: VecNormalize(VEC_VV(0),&res);
125: KSPCheckNorm(ksp,res);
127: /* the constant .1 is arbitrary, just some measure at how incorrect the residuals are */
128: if ((ksp->rnorm > 0.0) && (PetscAbsReal(res-ksp->rnorm) > gmres->breakdowntol*gmres->rnorm0)) {
129: if (ksp->errorifnotconverged) SETERRQ3(PetscObjectComm((PetscObject)ksp),PETSC_ERR_CONV_FAILED,"Residual norm computed by GMRES recursion formula %g is far from the computed residual norm %g at restart, residual norm at start of cycle %g",(double)ksp->rnorm,(double)res,(double)gmres->rnorm0);
130: else {
131: PetscInfo3(ksp,"Residual norm computed by GMRES recursion formula %g is far from the computed residual norm %g at restart, residual norm at start of cycle %g",(double)ksp->rnorm,(double)res,(double)gmres->rnorm0);
132: ksp->reason = KSP_DIVERGED_BREAKDOWN;
133: return(0);
134: }
135: }
136: *GRS(0) = gmres->rnorm0 = res;
138: /* check for the convergence */
139: PetscObjectSAWsTakeAccess((PetscObject)ksp);
140: ksp->rnorm = res;
141: PetscObjectSAWsGrantAccess((PetscObject)ksp);
142: gmres->it = (it - 1);
143: KSPLogResidualHistory(ksp,res);
144: KSPLogErrorHistory(ksp);
145: KSPMonitor(ksp,ksp->its,res);
146: if (!res) {
147: ksp->reason = KSP_CONVERGED_ATOL;
148: PetscInfo(ksp,"Converged due to zero residual norm on entry\n");
149: return(0);
150: }
152: (*ksp->converged)(ksp,ksp->its,res,&ksp->reason,ksp->cnvP);
153: while (!ksp->reason && it < max_k && ksp->its < ksp->max_it) {
154: if (it) {
155: KSPLogResidualHistory(ksp,res);
156: KSPLogErrorHistory(ksp);
157: KSPMonitor(ksp,ksp->its,res);
158: }
159: gmres->it = (it - 1);
160: if (gmres->vv_allocated <= it + VEC_OFFSET + 1) {
161: KSPGMRESGetNewVectors(ksp,it+1);
162: }
163: KSP_PCApplyBAorAB(ksp,VEC_VV(it),VEC_VV(1+it),VEC_TEMP_MATOP);
165: /* update hessenberg matrix and do Gram-Schmidt */
166: (*gmres->orthog)(ksp,it);
167: if (ksp->reason) break;
169: /* vv(i+1) . vv(i+1) */
170: VecNormalize(VEC_VV(it+1),&tt);
171: KSPCheckNorm(ksp,tt);
173: /* save the magnitude */
174: *HH(it+1,it) = tt;
175: *HES(it+1,it) = tt;
177: /* check for the happy breakdown */
178: hapbnd = PetscAbsScalar(tt / *GRS(it));
179: if (hapbnd > gmres->haptol) hapbnd = gmres->haptol;
180: if (tt < hapbnd) {
181: PetscInfo2(ksp,"Detected happy breakdown, current hapbnd = %14.12e tt = %14.12e\n",(double)hapbnd,(double)tt);
182: hapend = PETSC_TRUE;
183: }
184: KSPGMRESUpdateHessenberg(ksp,it,hapend,&res);
186: it++;
187: gmres->it = (it-1); /* For converged */
188: ksp->its++;
189: ksp->rnorm = res;
190: if (ksp->reason) break;
192: (*ksp->converged)(ksp,ksp->its,res,&ksp->reason,ksp->cnvP);
194: /* Catch error in happy breakdown and signal convergence and break from loop */
195: if (hapend) {
196: if (ksp->normtype == KSP_NORM_NONE) { /* convergence test was skipped in this case */
197: ksp->reason = KSP_CONVERGED_HAPPY_BREAKDOWN;
198: } else if (!ksp->reason) {
199: 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);
200: else {
201: ksp->reason = KSP_DIVERGED_BREAKDOWN;
202: break;
203: }
204: }
205: }
206: }
208: /* Monitor if we know that we will not return for a restart */
209: if (it && (ksp->reason || ksp->its >= ksp->max_it)) {
210: KSPLogResidualHistory(ksp,res);
211: KSPLogErrorHistory(ksp);
212: KSPMonitor(ksp,ksp->its,res);
213: }
215: if (itcount) *itcount = it;
218: /*
219: Down here we have to solve for the "best" coefficients of the Krylov
220: columns, add the solution values together, and possibly unwind the
221: preconditioning from the solution
222: */
223: /* Form the solution (or the solution so far) */
224: KSPGMRESBuildSoln(GRS(0),ksp->vec_sol,ksp->vec_sol,ksp,it-1);
225: return(0);
226: }
228: PetscErrorCode KSPSolve_GMRES(KSP ksp)
229: {
231: PetscInt its,itcount,i;
232: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
233: PetscBool guess_zero = ksp->guess_zero;
234: PetscInt N = gmres->max_k + 1;
237: if (ksp->calc_sings && !gmres->Rsvd) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ORDER,"Must call KSPSetComputeSingularValues() before KSPSetUp() is called");
239: PetscObjectSAWsTakeAccess((PetscObject)ksp);
240: ksp->its = 0;
241: PetscObjectSAWsGrantAccess((PetscObject)ksp);
243: itcount = 0;
244: gmres->fullcycle = 0;
245: ksp->reason = KSP_CONVERGED_ITERATING;
246: ksp->rnorm = -1.0; /* special marker for KSPGMRESCycle() */
247: while (!ksp->reason) {
248: KSPInitialResidual(ksp,ksp->vec_sol,VEC_TEMP,VEC_TEMP_MATOP,VEC_VV(0),ksp->vec_rhs);
249: KSPGMRESCycle(&its,ksp);
250: /* Store the Hessenberg matrix and the basis vectors of the Krylov subspace
251: if the cycle is complete for the computation of the Ritz pairs */
252: if (its == gmres->max_k) {
253: gmres->fullcycle++;
254: if (ksp->calc_ritz) {
255: if (!gmres->hes_ritz) {
256: PetscMalloc1(N*N,&gmres->hes_ritz);
257: PetscLogObjectMemory((PetscObject)ksp,N*N*sizeof(PetscScalar));
258: VecDuplicateVecs(VEC_VV(0),N,&gmres->vecb);
259: }
260: PetscArraycpy(gmres->hes_ritz,gmres->hes_origin,N*N);
261: for (i=0; i<gmres->max_k+1; i++) {
262: VecCopy(VEC_VV(i),gmres->vecb[i]);
263: }
264: }
265: }
266: itcount += its;
267: if (itcount >= ksp->max_it) {
268: if (!ksp->reason) ksp->reason = KSP_DIVERGED_ITS;
269: break;
270: }
271: ksp->guess_zero = PETSC_FALSE; /* every future call to KSPInitialResidual() will have nonzero guess */
272: }
273: ksp->guess_zero = guess_zero; /* restore if user provided nonzero initial guess */
274: return(0);
275: }
277: PetscErrorCode KSPReset_GMRES(KSP ksp)
278: {
279: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
281: PetscInt i;
284: /* Free the Hessenberg matrices */
285: PetscFree5(gmres->hh_origin,gmres->hes_origin,gmres->rs_origin,gmres->cc_origin,gmres->ss_origin);
286: PetscFree(gmres->hes_ritz);
288: /* free work vectors */
289: PetscFree(gmres->vecs);
290: for (i=0; i<gmres->nwork_alloc; i++) {
291: VecDestroyVecs(gmres->mwork_alloc[i],&gmres->user_work[i]);
292: }
293: gmres->nwork_alloc = 0;
294: if (gmres->vecb) {
295: VecDestroyVecs(gmres->max_k+1,&gmres->vecb);
296: }
298: PetscFree(gmres->user_work);
299: PetscFree(gmres->mwork_alloc);
300: PetscFree(gmres->nrs);
301: VecDestroy(&gmres->sol_temp);
302: PetscFree(gmres->Rsvd);
303: PetscFree(gmres->Dsvd);
304: PetscFree(gmres->orthogwork);
306: gmres->vv_allocated = 0;
307: gmres->vecs_allocated = 0;
308: gmres->sol_temp = NULL;
309: return(0);
310: }
312: PetscErrorCode KSPDestroy_GMRES(KSP ksp)
313: {
317: KSPReset_GMRES(ksp);
318: PetscFree(ksp->data);
319: /* clear composed functions */
320: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetPreAllocateVectors_C",NULL);
321: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetOrthogonalization_C",NULL);
322: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetOrthogonalization_C",NULL);
323: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetRestart_C",NULL);
324: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetRestart_C",NULL);
325: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetHapTol_C",NULL);
326: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetBreakdownTolerance_C",NULL);
327: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetCGSRefinementType_C",NULL);
328: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetCGSRefinementType_C",NULL);
329: return(0);
330: }
331: /*
332: KSPGMRESBuildSoln - create the solution from the starting vector and the
333: current iterates.
335: Input parameters:
336: nrs - work area of size it + 1.
337: vs - index of initial guess
338: vdest - index of result. Note that vs may == vdest (replace
339: guess with the solution).
341: This is an internal routine that knows about the GMRES internals.
342: */
343: static PetscErrorCode KSPGMRESBuildSoln(PetscScalar *nrs,Vec vs,Vec vdest,KSP ksp,PetscInt it)
344: {
345: PetscScalar tt;
347: PetscInt ii,k,j;
348: KSP_GMRES *gmres = (KSP_GMRES*)(ksp->data);
351: /* Solve for solution vector that minimizes the residual */
353: /* If it is < 0, no gmres steps have been performed */
354: if (it < 0) {
355: VecCopy(vs,vdest); /* VecCopy() is smart, exists immediately if vguess == vdest */
356: return(0);
357: }
358: if (*HH(it,it) != 0.0) {
359: nrs[it] = *GRS(it) / *HH(it,it);
360: } else {
361: if (ksp->errorifnotconverged) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_NOT_CONVERGED,"You reached the break down in GMRES; HH(it,it) = 0");
362: else ksp->reason = KSP_DIVERGED_BREAKDOWN;
364: 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)));
365: return(0);
366: }
367: for (ii=1; ii<=it; ii++) {
368: k = it - ii;
369: tt = *GRS(k);
370: for (j=k+1; j<=it; j++) tt = tt - *HH(k,j) * nrs[j];
371: if (*HH(k,k) == 0.0) {
372: if (ksp->errorifnotconverged) SETERRQ1(PetscObjectComm((PetscObject)ksp),PETSC_ERR_NOT_CONVERGED,"Likely your matrix or preconditioner is singular. HH(k,k) is identically zero; k = %D\n",k);
373: else {
374: ksp->reason = KSP_DIVERGED_BREAKDOWN;
375: PetscInfo1(ksp,"Likely your matrix or preconditioner is singular. HH(k,k) is identically zero; k = %D\n",k);
376: return(0);
377: }
378: }
379: nrs[k] = tt / *HH(k,k);
380: }
382: /* Accumulate the correction to the solution of the preconditioned problem in TEMP */
383: VecSet(VEC_TEMP,0.0);
384: VecMAXPY(VEC_TEMP,it+1,nrs,&VEC_VV(0));
386: KSPUnwindPreconditioner(ksp,VEC_TEMP,VEC_TEMP_MATOP);
387: /* add solution to previous solution */
388: if (vdest != vs) {
389: VecCopy(vs,vdest);
390: }
391: VecAXPY(vdest,1.0,VEC_TEMP);
392: return(0);
393: }
394: /*
395: Do the scalar work for the orthogonalization. Return new residual norm.
396: */
397: static PetscErrorCode KSPGMRESUpdateHessenberg(KSP ksp,PetscInt it,PetscBool hapend,PetscReal *res)
398: {
399: PetscScalar *hh,*cc,*ss,tt;
400: PetscInt j;
401: KSP_GMRES *gmres = (KSP_GMRES*)(ksp->data);
404: hh = HH(0,it);
405: cc = CC(0);
406: ss = SS(0);
408: /* Apply all the previously computed plane rotations to the new column
409: of the Hessenberg matrix */
410: for (j=1; j<=it; j++) {
411: tt = *hh;
412: *hh = PetscConj(*cc) * tt + *ss * *(hh+1);
413: hh++;
414: *hh = *cc++ * *hh - (*ss++ * tt);
415: }
417: /*
418: compute the new plane rotation, and apply it to:
419: 1) the right-hand-side of the Hessenberg system
420: 2) the new column of the Hessenberg matrix
421: thus obtaining the updated value of the residual
422: */
423: if (!hapend) {
424: tt = PetscSqrtScalar(PetscConj(*hh) * *hh + PetscConj(*(hh+1)) * *(hh+1));
425: if (tt == 0.0) {
426: if (ksp->errorifnotconverged) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_NOT_CONVERGED,"tt == 0.0");
427: else {
428: ksp->reason = KSP_DIVERGED_NULL;
429: return(0);
430: }
431: }
432: *cc = *hh / tt;
433: *ss = *(hh+1) / tt;
434: *GRS(it+1) = -(*ss * *GRS(it));
435: *GRS(it) = PetscConj(*cc) * *GRS(it);
436: *hh = PetscConj(*cc) * *hh + *ss * *(hh+1);
437: *res = PetscAbsScalar(*GRS(it+1));
438: } else {
439: /* happy breakdown: HH(it+1, it) = 0, therfore we don't need to apply
440: another rotation matrix (so RH doesn't change). The new residual is
441: always the new sine term times the residual from last time (GRS(it)),
442: but now the new sine rotation would be zero...so the residual should
443: be zero...so we will multiply "zero" by the last residual. This might
444: not be exactly what we want to do here -could just return "zero". */
446: *res = 0.0;
447: }
448: return(0);
449: }
450: /*
451: This routine allocates more work vectors, starting from VEC_VV(it).
452: */
453: PetscErrorCode KSPGMRESGetNewVectors(KSP ksp,PetscInt it)
454: {
455: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
457: PetscInt nwork = gmres->nwork_alloc,k,nalloc;
460: nalloc = PetscMin(ksp->max_it,gmres->delta_allocate);
461: /* Adjust the number to allocate to make sure that we don't exceed the
462: number of available slots */
463: if (it + VEC_OFFSET + nalloc >= gmres->vecs_allocated) {
464: nalloc = gmres->vecs_allocated - it - VEC_OFFSET;
465: }
466: if (!nalloc) return(0);
468: gmres->vv_allocated += nalloc;
470: KSPCreateVecs(ksp,nalloc,&gmres->user_work[nwork],0,NULL);
471: PetscLogObjectParents(ksp,nalloc,gmres->user_work[nwork]);
473: gmres->mwork_alloc[nwork] = nalloc;
474: for (k=0; k<nalloc; k++) {
475: gmres->vecs[it+VEC_OFFSET+k] = gmres->user_work[nwork][k];
476: }
477: gmres->nwork_alloc++;
478: return(0);
479: }
481: PetscErrorCode KSPBuildSolution_GMRES(KSP ksp,Vec ptr,Vec *result)
482: {
483: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
487: if (!ptr) {
488: if (!gmres->sol_temp) {
489: VecDuplicate(ksp->vec_sol,&gmres->sol_temp);
490: PetscLogObjectParent((PetscObject)ksp,(PetscObject)gmres->sol_temp);
491: }
492: ptr = gmres->sol_temp;
493: }
494: if (!gmres->nrs) {
495: /* allocate the work area */
496: PetscMalloc1(gmres->max_k,&gmres->nrs);
497: PetscLogObjectMemory((PetscObject)ksp,gmres->max_k);
498: }
500: KSPGMRESBuildSoln(gmres->nrs,ksp->vec_sol,ptr,ksp,gmres->it);
501: if (result) *result = ptr;
502: return(0);
503: }
505: PetscErrorCode KSPView_GMRES(KSP ksp,PetscViewer viewer)
506: {
507: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
508: const char *cstr;
510: PetscBool iascii,isstring;
513: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
514: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERSTRING,&isstring);
515: if (gmres->orthog == KSPGMRESClassicalGramSchmidtOrthogonalization) {
516: switch (gmres->cgstype) {
517: case (KSP_GMRES_CGS_REFINE_NEVER):
518: cstr = "Classical (unmodified) Gram-Schmidt Orthogonalization with no iterative refinement";
519: break;
520: case (KSP_GMRES_CGS_REFINE_ALWAYS):
521: cstr = "Classical (unmodified) Gram-Schmidt Orthogonalization with one step of iterative refinement";
522: break;
523: case (KSP_GMRES_CGS_REFINE_IFNEEDED):
524: cstr = "Classical (unmodified) Gram-Schmidt Orthogonalization with one step of iterative refinement when needed";
525: break;
526: default:
527: SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ARG_OUTOFRANGE,"Unknown orthogonalization");
528: }
529: } else if (gmres->orthog == KSPGMRESModifiedGramSchmidtOrthogonalization) {
530: cstr = "Modified Gram-Schmidt Orthogonalization";
531: } else {
532: cstr = "unknown orthogonalization";
533: }
534: if (iascii) {
535: PetscViewerASCIIPrintf(viewer," restart=%D, using %s\n",gmres->max_k,cstr);
536: PetscViewerASCIIPrintf(viewer," happy breakdown tolerance %g\n",(double)gmres->haptol);
537: } else if (isstring) {
538: PetscViewerStringSPrintf(viewer,"%s restart %D",cstr,gmres->max_k);
539: }
540: return(0);
541: }
543: /*@C
544: KSPGMRESMonitorKrylov - Calls VecView() for each new direction in the GMRES accumulated Krylov space.
546: Collective on ksp
548: Input Parameters:
549: + ksp - the KSP context
550: . its - iteration number
551: . fgnorm - 2-norm of residual (or gradient)
552: - dummy - an collection of viewers created with KSPViewerCreate()
554: Options Database Keys:
555: . -ksp_gmres_kyrlov_monitor
557: Notes:
558: A new PETSCVIEWERDRAW is created for each Krylov vector so they can all be simultaneously viewed
559: Level: intermediate
561: .seealso: KSPMonitorSet(), KSPMonitorResidual(), VecView(), KSPViewersCreate(), KSPViewersDestroy()
562: @*/
563: PetscErrorCode KSPGMRESMonitorKrylov(KSP ksp,PetscInt its,PetscReal fgnorm,void *dummy)
564: {
565: PetscViewers viewers = (PetscViewers)dummy;
566: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
568: Vec x;
569: PetscViewer viewer;
570: PetscBool flg;
573: PetscViewersGetViewer(viewers,gmres->it+1,&viewer);
574: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&flg);
575: if (!flg) {
576: PetscViewerSetType(viewer,PETSCVIEWERDRAW);
577: PetscViewerDrawSetInfo(viewer,NULL,"Krylov GMRES Monitor",PETSC_DECIDE,PETSC_DECIDE,300,300);
578: }
579: x = VEC_VV(gmres->it+1);
580: VecView(x,viewer);
581: return(0);
582: }
584: PetscErrorCode KSPSetFromOptions_GMRES(PetscOptionItems *PetscOptionsObject,KSP ksp)
585: {
587: PetscInt restart;
588: PetscReal haptol,breakdowntol;
589: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
590: PetscBool flg;
593: PetscOptionsHead(PetscOptionsObject,"KSP GMRES Options");
594: PetscOptionsInt("-ksp_gmres_restart","Number of Krylov search directions","KSPGMRESSetRestart",gmres->max_k,&restart,&flg);
595: if (flg) { KSPGMRESSetRestart(ksp,restart); }
596: PetscOptionsReal("-ksp_gmres_haptol","Tolerance for exact convergence (happy ending)","KSPGMRESSetHapTol",gmres->haptol,&haptol,&flg);
597: if (flg) { KSPGMRESSetHapTol(ksp,haptol); }
598: PetscOptionsReal("-ksp_gmres_breakdown_tolerance","Divergence breakdown tolerance during GMRES restart","KSPGMRESSetBreakdownTolerance",gmres->breakdowntol,&breakdowntol,&flg);
599: if (flg) { KSPGMRESSetBreakdownTolerance(ksp,breakdowntol); }
600: flg = PETSC_FALSE;
601: PetscOptionsBool("-ksp_gmres_preallocate","Preallocate Krylov vectors","KSPGMRESSetPreAllocateVectors",flg,&flg,NULL);
602: if (flg) {KSPGMRESSetPreAllocateVectors(ksp);}
603: PetscOptionsBoolGroupBegin("-ksp_gmres_classicalgramschmidt","Classical (unmodified) Gram-Schmidt (fast)","KSPGMRESSetOrthogonalization",&flg);
604: if (flg) {KSPGMRESSetOrthogonalization(ksp,KSPGMRESClassicalGramSchmidtOrthogonalization);}
605: PetscOptionsBoolGroupEnd("-ksp_gmres_modifiedgramschmidt","Modified Gram-Schmidt (slow,more stable)","KSPGMRESSetOrthogonalization",&flg);
606: if (flg) {KSPGMRESSetOrthogonalization(ksp,KSPGMRESModifiedGramSchmidtOrthogonalization);}
607: PetscOptionsEnum("-ksp_gmres_cgs_refinement_type","Type of iterative refinement for classical (unmodified) Gram-Schmidt","KSPGMRESSetCGSRefinementType",
608: KSPGMRESCGSRefinementTypes,(PetscEnum)gmres->cgstype,(PetscEnum*)&gmres->cgstype,&flg);
609: flg = PETSC_FALSE;
610: PetscOptionsBool("-ksp_gmres_krylov_monitor","Plot the Krylov directions","KSPMonitorSet",flg,&flg,NULL);
611: if (flg) {
612: PetscViewers viewers;
613: PetscViewersCreate(PetscObjectComm((PetscObject)ksp),&viewers);
614: KSPMonitorSet(ksp,KSPGMRESMonitorKrylov,viewers,(PetscErrorCode (*)(void**))PetscViewersDestroy);
615: }
616: PetscOptionsTail();
617: return(0);
618: }
620: PetscErrorCode KSPGMRESSetHapTol_GMRES(KSP ksp,PetscReal tol)
621: {
622: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
625: if (tol < 0.0) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ARG_OUTOFRANGE,"Tolerance must be non-negative");
626: gmres->haptol = tol;
627: return(0);
628: }
630: PetscErrorCode KSPGMRESSetBreakdownTolerance_GMRES(KSP ksp,PetscReal tol)
631: {
632: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
635: if (tol == PETSC_DEFAULT) {
636: gmres->breakdowntol = 0.1;
637: return(0);
638: }
639: if (tol < 0.0) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ARG_OUTOFRANGE,"Breakdown tolerance must be non-negative");
640: gmres->breakdowntol = tol;
641: return(0);
642: }
644: PetscErrorCode KSPGMRESGetRestart_GMRES(KSP ksp,PetscInt *max_k)
645: {
646: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
649: *max_k = gmres->max_k;
650: return(0);
651: }
653: PetscErrorCode KSPGMRESSetRestart_GMRES(KSP ksp,PetscInt max_k)
654: {
655: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
659: if (max_k < 1) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ARG_OUTOFRANGE,"Restart must be positive");
660: if (!ksp->setupstage) {
661: gmres->max_k = max_k;
662: } else if (gmres->max_k != max_k) {
663: gmres->max_k = max_k;
664: ksp->setupstage = KSP_SETUP_NEW;
665: /* free the data structures, then create them again */
666: KSPReset_GMRES(ksp);
667: }
668: return(0);
669: }
671: PetscErrorCode KSPGMRESSetOrthogonalization_GMRES(KSP ksp,FCN fcn)
672: {
674: ((KSP_GMRES*)ksp->data)->orthog = fcn;
675: return(0);
676: }
678: PetscErrorCode KSPGMRESGetOrthogonalization_GMRES(KSP ksp,FCN *fcn)
679: {
681: *fcn = ((KSP_GMRES*)ksp->data)->orthog;
682: return(0);
683: }
685: PetscErrorCode KSPGMRESSetPreAllocateVectors_GMRES(KSP ksp)
686: {
687: KSP_GMRES *gmres;
690: gmres = (KSP_GMRES*)ksp->data;
691: gmres->q_preallocate = 1;
692: return(0);
693: }
695: PetscErrorCode KSPGMRESSetCGSRefinementType_GMRES(KSP ksp,KSPGMRESCGSRefinementType type)
696: {
697: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
700: gmres->cgstype = type;
701: return(0);
702: }
704: PetscErrorCode KSPGMRESGetCGSRefinementType_GMRES(KSP ksp,KSPGMRESCGSRefinementType *type)
705: {
706: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
709: *type = gmres->cgstype;
710: return(0);
711: }
713: /*@
714: KSPGMRESSetCGSRefinementType - Sets the type of iterative refinement to use
715: in the classical Gram Schmidt orthogonalization.
717: Logically Collective on ksp
719: Input Parameters:
720: + ksp - the Krylov space context
721: - type - the type of refinement
723: Options Database:
724: . -ksp_gmres_cgs_refinement_type <refine_never,refine_ifneeded,refine_always>
726: Level: intermediate
728: .seealso: KSPGMRESSetOrthogonalization(), KSPGMRESCGSRefinementType, KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESGetCGSRefinementType(),
729: KSPGMRESGetOrthogonalization()
730: @*/
731: PetscErrorCode KSPGMRESSetCGSRefinementType(KSP ksp,KSPGMRESCGSRefinementType type)
732: {
738: PetscTryMethod(ksp,"KSPGMRESSetCGSRefinementType_C",(KSP,KSPGMRESCGSRefinementType),(ksp,type));
739: return(0);
740: }
742: /*@
743: KSPGMRESGetCGSRefinementType - Gets the type of iterative refinement to use
744: in the classical Gram Schmidt orthogonalization.
746: Not Collective
748: Input Parameter:
749: . ksp - the Krylov space context
751: Output Parameter:
752: . type - the type of refinement
754: Options Database:
755: . -ksp_gmres_cgs_refinement_type <refine_never,refine_ifneeded,refine_always>
757: Level: intermediate
759: .seealso: KSPGMRESSetOrthogonalization(), KSPGMRESCGSRefinementType, KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESSetCGSRefinementType(),
760: KSPGMRESGetOrthogonalization()
761: @*/
762: PetscErrorCode KSPGMRESGetCGSRefinementType(KSP ksp,KSPGMRESCGSRefinementType *type)
763: {
768: PetscUseMethod(ksp,"KSPGMRESGetCGSRefinementType_C",(KSP,KSPGMRESCGSRefinementType*),(ksp,type));
769: return(0);
770: }
773: /*@
774: KSPGMRESSetRestart - Sets number of iterations at which GMRES, FGMRES and LGMRES restarts.
776: Logically Collective on ksp
778: Input Parameters:
779: + ksp - the Krylov space context
780: - restart - integer restart value
782: Options Database:
783: . -ksp_gmres_restart <positive integer>
785: Note: The default value is 30.
787: Level: intermediate
789: .seealso: KSPSetTolerances(), KSPGMRESSetOrthogonalization(), KSPGMRESSetPreAllocateVectors(), KSPGMRESGetRestart()
790: @*/
791: PetscErrorCode KSPGMRESSetRestart(KSP ksp, PetscInt restart)
792: {
798: PetscTryMethod(ksp,"KSPGMRESSetRestart_C",(KSP,PetscInt),(ksp,restart));
799: return(0);
800: }
802: /*@
803: KSPGMRESGetRestart - Gets number of iterations at which GMRES, FGMRES and LGMRES restarts.
805: Not Collective
807: Input Parameter:
808: . ksp - the Krylov space context
810: Output Parameter:
811: . restart - integer restart value
813: Note: The default value is 30.
815: Level: intermediate
817: .seealso: KSPSetTolerances(), KSPGMRESSetOrthogonalization(), KSPGMRESSetPreAllocateVectors(), KSPGMRESSetRestart()
818: @*/
819: PetscErrorCode KSPGMRESGetRestart(KSP ksp, PetscInt *restart)
820: {
824: PetscUseMethod(ksp,"KSPGMRESGetRestart_C",(KSP,PetscInt*),(ksp,restart));
825: return(0);
826: }
828: /*@
829: KSPGMRESSetHapTol - Sets tolerance for determining happy breakdown in GMRES, FGMRES and LGMRES.
831: Logically Collective on ksp
833: Input Parameters:
834: + ksp - the Krylov space context
835: - tol - the tolerance
837: Options Database:
838: . -ksp_gmres_haptol <positive real value>
840: Note: Happy breakdown is the rare case in GMRES where an 'exact' solution is obtained after
841: a certain number of iterations. If you attempt more iterations after this point unstable
842: things can happen hence very occasionally you may need to set this value to detect this condition
844: Level: intermediate
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: /*@
859: KSPGMRESSetBreakdownTolerance - Sets tolerance for determining divergence breakdown in GMRES.
861: Logically Collective on ksp
863: Input Parameters:
864: + ksp - the Krylov space context
865: - tol - the tolerance
867: Options Database:
868: . -ksp_gmres_breakdown_tolerance <positive real value>
870: Note: divergence breakdown occurs when GMRES residual increases significantly
871: during restart
873: Level: intermediate
875: .seealso: KSPSetTolerances(), KSPGMRESSetHapTol()
876: @*/
877: PetscErrorCode KSPGMRESSetBreakdownTolerance(KSP ksp,PetscReal tol)
878: {
883: PetscTryMethod((ksp),"KSPGMRESSetBreakdownTolerance_C",(KSP,PetscReal),(ksp,tol));
884: return(0);
885: }
887: /*MC
888: KSPGMRES - Implements the Generalized Minimal Residual method.
889: (Saad and Schultz, 1986) with restart
892: Options Database Keys:
893: + -ksp_gmres_restart <restart> - the number of Krylov directions to orthogonalize against
894: . -ksp_gmres_haptol <tol> - sets the tolerance for "happy ending" (exact convergence)
895: . -ksp_gmres_preallocate - preallocate all the Krylov search directions initially (otherwise groups of
896: vectors are allocated as needed)
897: . -ksp_gmres_classicalgramschmidt - use classical (unmodified) Gram-Schmidt to orthogonalize against the Krylov space (fast) (the default)
898: . -ksp_gmres_modifiedgramschmidt - use modified Gram-Schmidt in the orthogonalization (more stable, but slower)
899: . -ksp_gmres_cgs_refinement_type <refine_never,refine_ifneeded,refine_always> - determine if iterative refinement is used to increase the
900: stability of the classical Gram-Schmidt orthogonalization.
901: - -ksp_gmres_krylov_monitor - plot the Krylov space generated
903: Level: beginner
905: Notes:
906: Left and right preconditioning are supported, but not symmetric preconditioning.
908: References:
909: . 1. - YOUCEF SAAD AND MARTIN H. SCHULTZ, GMRES: A GENERALIZED MINIMAL RESIDUAL ALGORITHM FOR SOLVING NONSYMMETRIC LINEAR SYSTEMS.
910: SIAM J. ScI. STAT. COMPUT. Vo|. 7, No. 3, July 1986.
912: .seealso: KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPFGMRES, KSPLGMRES,
913: KSPGMRESSetRestart(), KSPGMRESSetHapTol(), KSPGMRESSetPreAllocateVectors(), KSPGMRESSetOrthogonalization(), KSPGMRESGetOrthogonalization(),
914: KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESModifiedGramSchmidtOrthogonalization(),
915: KSPGMRESCGSRefinementType, KSPGMRESSetCGSRefinementType(), KSPGMRESGetCGSRefinementType(), KSPGMRESMonitorKrylov(), KSPSetPCSide()
917: M*/
919: PETSC_EXTERN PetscErrorCode KSPCreate_GMRES(KSP ksp)
920: {
921: KSP_GMRES *gmres;
925: PetscNewLog(ksp,&gmres);
926: ksp->data = (void*)gmres;
928: KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,4);
929: KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_RIGHT,3);
930: KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_SYMMETRIC,2);
931: KSPSetSupportedNorm(ksp,KSP_NORM_NONE,PC_RIGHT,1);
932: KSPSetSupportedNorm(ksp,KSP_NORM_NONE,PC_LEFT,1);
934: ksp->ops->buildsolution = KSPBuildSolution_GMRES;
935: ksp->ops->setup = KSPSetUp_GMRES;
936: ksp->ops->solve = KSPSolve_GMRES;
937: ksp->ops->reset = KSPReset_GMRES;
938: ksp->ops->destroy = KSPDestroy_GMRES;
939: ksp->ops->view = KSPView_GMRES;
940: ksp->ops->setfromoptions = KSPSetFromOptions_GMRES;
941: ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_GMRES;
942: ksp->ops->computeeigenvalues = KSPComputeEigenvalues_GMRES;
943: #if !defined(PETSC_USE_COMPLEX) && !defined(PETSC_HAVE_ESSL)
944: ksp->ops->computeritz = KSPComputeRitz_GMRES;
945: #endif
946: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetPreAllocateVectors_C",KSPGMRESSetPreAllocateVectors_GMRES);
947: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetOrthogonalization_C",KSPGMRESSetOrthogonalization_GMRES);
948: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetOrthogonalization_C",KSPGMRESGetOrthogonalization_GMRES);
949: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetRestart_C",KSPGMRESSetRestart_GMRES);
950: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetRestart_C",KSPGMRESGetRestart_GMRES);
951: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetHapTol_C",KSPGMRESSetHapTol_GMRES);
952: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetBreakdownTolerance_C",KSPGMRESSetBreakdownTolerance_GMRES);
953: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetCGSRefinementType_C",KSPGMRESSetCGSRefinementType_GMRES);
954: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetCGSRefinementType_C",KSPGMRESGetCGSRefinementType_GMRES);
956: gmres->haptol = 1.0e-30;
957: gmres->breakdowntol = 0.1;
958: gmres->q_preallocate = 0;
959: gmres->delta_allocate = GMRES_DELTA_DIRECTIONS;
960: gmres->orthog = KSPGMRESClassicalGramSchmidtOrthogonalization;
961: gmres->nrs = NULL;
962: gmres->sol_temp = NULL;
963: gmres->max_k = GMRES_DEFAULT_MAXK;
964: gmres->Rsvd = NULL;
965: gmres->cgstype = KSP_GMRES_CGS_REFINE_NEVER;
966: gmres->orthogwork = NULL;
967: return(0);
968: }