Actual source code: gmres.c
2: /*
3: This file implements GMRES (a Generalized Minimal Residual) method.
4: Reference: Saad and Schultz, 1986.
6: Some comments on left vs. right preconditioning, and restarts.
7: Left and right preconditioning.
8: If right preconditioning is chosen, then the problem being solved
9: by gmres is actually
10: My = AB^-1 y = f
11: so the initial residual is
12: r = f - Mx
13: Note that B^-1 y = x or y = B x, and if x is non-zero, the initial
14: residual is
15: r = f - A x
16: The final solution is then
17: x = B^-1 y
19: If left preconditioning is chosen, then the problem being solved is
20: My = B^-1 A x = B^-1 f,
21: and the initial residual is
22: r = B^-1(f - Ax)
24: Restarts: Restarts are basically solves with x0 not equal to zero.
25: Note that we can eliminate an extra application of B^-1 between
26: restarts as long as we don't require that the solution at the end
27: of an unsuccessful gmres iteration always be the solution x.
28: */
30: #include <../src/ksp/ksp/impls/gmres/gmresimpl.h>
31: #define GMRES_DELTA_DIRECTIONS 10
32: #define GMRES_DEFAULT_MAXK 30
33: static PetscErrorCode KSPGMRESUpdateHessenberg(KSP,PetscInt,PetscBool,PetscReal*);
34: static PetscErrorCode KSPGMRESBuildSoln(PetscScalar*,Vec,Vec,KSP,PetscInt);
36: PetscErrorCode KSPSetUp_GMRES(KSP ksp)
37: {
38: PetscInt hh,hes,rs,cc;
40: PetscInt max_k,k;
41: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
44: max_k = gmres->max_k; /* restart size */
45: hh = (max_k + 2) * (max_k + 1);
46: hes = (max_k + 1) * (max_k + 1);
47: rs = (max_k + 2);
48: cc = (max_k + 1);
50: PetscCalloc5(hh,&gmres->hh_origin,hes,&gmres->hes_origin,rs,&gmres->rs_origin,cc,&gmres->cc_origin,cc,&gmres->ss_origin);
51: PetscLogObjectMemory((PetscObject)ksp,(hh + hes + rs + 2*cc)*sizeof(PetscScalar));
53: if (ksp->calc_sings) {
54: /* Allocate workspace to hold Hessenberg matrix needed by lapack */
55: PetscMalloc1((max_k + 3)*(max_k + 9),&gmres->Rsvd);
56: PetscLogObjectMemory((PetscObject)ksp,(max_k + 3)*(max_k + 9)*sizeof(PetscScalar));
57: PetscMalloc1(6*(max_k+2),&gmres->Dsvd);
58: PetscLogObjectMemory((PetscObject)ksp,6*(max_k+2)*sizeof(PetscReal));
59: }
61: /* Allocate array to hold pointers to user vectors. Note that we need
62: 4 + max_k + 1 (since we need it+1 vectors, and it <= max_k) */
63: gmres->vecs_allocated = VEC_OFFSET + 2 + max_k + gmres->nextra_vecs;
65: PetscMalloc1(gmres->vecs_allocated,&gmres->vecs);
66: PetscMalloc1(VEC_OFFSET+2+max_k,&gmres->user_work);
67: PetscMalloc1(VEC_OFFSET+2+max_k,&gmres->mwork_alloc);
68: PetscLogObjectMemory((PetscObject)ksp,(VEC_OFFSET+2+max_k)*(sizeof(Vec*)+sizeof(PetscInt)) + gmres->vecs_allocated*sizeof(Vec));
70: if (gmres->q_preallocate) {
71: gmres->vv_allocated = VEC_OFFSET + 2 + max_k;
73: KSPCreateVecs(ksp,gmres->vv_allocated,&gmres->user_work[0],0,NULL);
74: PetscLogObjectParents(ksp,gmres->vv_allocated,gmres->user_work[0]);
76: gmres->mwork_alloc[0] = gmres->vv_allocated;
77: gmres->nwork_alloc = 1;
78: for (k=0; k<gmres->vv_allocated; k++) {
79: gmres->vecs[k] = gmres->user_work[0][k];
80: }
81: } else {
82: gmres->vv_allocated = 5;
84: KSPCreateVecs(ksp,5,&gmres->user_work[0],0,NULL);
85: PetscLogObjectParents(ksp,5,gmres->user_work[0]);
87: gmres->mwork_alloc[0] = 5;
88: gmres->nwork_alloc = 1;
89: for (k=0; k<gmres->vv_allocated; k++) {
90: gmres->vecs[k] = gmres->user_work[0][k];
91: }
92: }
93: return(0);
94: }
96: /*
97: Run gmres, possibly with restart. Return residual history if requested.
98: input parameters:
100: . gmres - structure containing parameters and work areas
102: output parameters:
103: . nres - residuals (from preconditioned system) at each step.
104: If restarting, consider passing nres+it. If null,
105: ignored
106: . itcount - number of iterations used. nres[0] to nres[itcount]
107: are defined. If null, ignored.
109: Notes:
110: On entry, the value in vector VEC_VV(0) should be the initial residual
111: (this allows shortcuts where the initial preconditioned residual is 0).
112: */
113: PetscErrorCode KSPGMRESCycle(PetscInt *itcount,KSP ksp)
114: {
115: KSP_GMRES *gmres = (KSP_GMRES*)(ksp->data);
116: PetscReal res,hapbnd,tt;
118: PetscInt it = 0, max_k = gmres->max_k;
119: PetscBool hapend = PETSC_FALSE;
122: if (itcount) *itcount = 0;
123: VecNormalize(VEC_VV(0),&res);
124: KSPCheckNorm(ksp,res);
126: /* the constant .1 is arbitrary, just some measure at how incorrect the residuals are */
127: if ((ksp->rnorm > 0.0) && (PetscAbsReal(res-ksp->rnorm) > gmres->breakdowntol*gmres->rnorm0)) {
128: 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);
129: else {
130: 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);
131: ksp->reason = KSP_DIVERGED_BREAKDOWN;
132: return(0);
133: }
134: }
135: *GRS(0) = gmres->rnorm0 = res;
137: /* check for the convergence */
138: PetscObjectSAWsTakeAccess((PetscObject)ksp);
139: ksp->rnorm = res;
140: PetscObjectSAWsGrantAccess((PetscObject)ksp);
141: gmres->it = (it - 1);
142: KSPLogResidualHistory(ksp,res);
143: KSPLogErrorHistory(ksp);
144: KSPMonitor(ksp,ksp->its,res);
145: if (!res) {
146: ksp->reason = KSP_CONVERGED_ATOL;
147: PetscInfo(ksp,"Converged due to zero residual norm on entry\n");
148: return(0);
149: }
151: (*ksp->converged)(ksp,ksp->its,res,&ksp->reason,ksp->cnvP);
152: while (!ksp->reason && it < max_k && ksp->its < ksp->max_it) {
153: if (it) {
154: KSPLogResidualHistory(ksp,res);
155: KSPLogErrorHistory(ksp);
156: KSPMonitor(ksp,ksp->its,res);
157: }
158: gmres->it = (it - 1);
159: if (gmres->vv_allocated <= it + VEC_OFFSET + 1) {
160: KSPGMRESGetNewVectors(ksp,it+1);
161: }
162: KSP_PCApplyBAorAB(ksp,VEC_VV(it),VEC_VV(1+it),VEC_TEMP_MATOP);
164: /* update hessenberg matrix and do Gram-Schmidt */
165: (*gmres->orthog)(ksp,it);
166: if (ksp->reason) break;
168: /* vv(i+1) . vv(i+1) */
169: VecNormalize(VEC_VV(it+1),&tt);
170: KSPCheckNorm(ksp,tt);
172: /* save the magnitude */
173: *HH(it+1,it) = tt;
174: *HES(it+1,it) = tt;
176: /* check for the happy breakdown */
177: hapbnd = PetscAbsScalar(tt / *GRS(it));
178: if (hapbnd > gmres->haptol) hapbnd = gmres->haptol;
179: if (tt < hapbnd) {
180: PetscInfo2(ksp,"Detected happy breakdown, current hapbnd = %14.12e tt = %14.12e\n",(double)hapbnd,(double)tt);
181: hapend = PETSC_TRUE;
182: }
183: KSPGMRESUpdateHessenberg(ksp,it,hapend,&res);
185: it++;
186: gmres->it = (it-1); /* For converged */
187: ksp->its++;
188: ksp->rnorm = res;
189: if (ksp->reason) break;
191: (*ksp->converged)(ksp,ksp->its,res,&ksp->reason,ksp->cnvP);
193: /* Catch error in happy breakdown and signal convergence and break from loop */
194: if (hapend) {
195: if (ksp->normtype == KSP_NORM_NONE) { /* convergence test was skipped in this case */
196: ksp->reason = KSP_CONVERGED_HAPPY_BREAKDOWN;
197: } else if (!ksp->reason) {
198: 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);
199: else {
200: ksp->reason = KSP_DIVERGED_BREAKDOWN;
201: break;
202: }
203: }
204: }
205: }
207: /* Monitor if we know that we will not return for a restart */
208: if (it && (ksp->reason || ksp->its >= ksp->max_it)) {
209: KSPLogResidualHistory(ksp,res);
210: KSPLogErrorHistory(ksp);
211: KSPMonitor(ksp,ksp->its,res);
212: }
214: if (itcount) *itcount = it;
216: /*
217: Down here we have to solve for the "best" coefficients of the Krylov
218: columns, add the solution values together, and possibly unwind the
219: preconditioning from the solution
220: */
221: /* Form the solution (or the solution so far) */
222: KSPGMRESBuildSoln(GRS(0),ksp->vec_sol,ksp->vec_sol,ksp,it-1);
223: return(0);
224: }
226: PetscErrorCode KSPSolve_GMRES(KSP ksp)
227: {
229: PetscInt its,itcount,i;
230: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
231: PetscBool guess_zero = ksp->guess_zero;
232: PetscInt N = gmres->max_k + 1;
235: if (ksp->calc_sings && !gmres->Rsvd) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ORDER,"Must call KSPSetComputeSingularValues() before KSPSetUp() is called");
237: PetscObjectSAWsTakeAccess((PetscObject)ksp);
238: ksp->its = 0;
239: PetscObjectSAWsGrantAccess((PetscObject)ksp);
241: itcount = 0;
242: gmres->fullcycle = 0;
243: ksp->reason = KSP_CONVERGED_ITERATING;
244: ksp->rnorm = -1.0; /* special marker for KSPGMRESCycle() */
245: while (!ksp->reason) {
246: KSPInitialResidual(ksp,ksp->vec_sol,VEC_TEMP,VEC_TEMP_MATOP,VEC_VV(0),ksp->vec_rhs);
247: KSPGMRESCycle(&its,ksp);
248: /* Store the Hessenberg matrix and the basis vectors of the Krylov subspace
249: if the cycle is complete for the computation of the Ritz pairs */
250: if (its == gmres->max_k) {
251: gmres->fullcycle++;
252: if (ksp->calc_ritz) {
253: if (!gmres->hes_ritz) {
254: PetscMalloc1(N*N,&gmres->hes_ritz);
255: PetscLogObjectMemory((PetscObject)ksp,N*N*sizeof(PetscScalar));
256: VecDuplicateVecs(VEC_VV(0),N,&gmres->vecb);
257: }
258: PetscArraycpy(gmres->hes_ritz,gmres->hes_origin,N*N);
259: for (i=0; i<gmres->max_k+1; i++) {
260: VecCopy(VEC_VV(i),gmres->vecb[i]);
261: }
262: }
263: }
264: itcount += its;
265: if (itcount >= ksp->max_it) {
266: if (!ksp->reason) ksp->reason = KSP_DIVERGED_ITS;
267: break;
268: }
269: ksp->guess_zero = PETSC_FALSE; /* every future call to KSPInitialResidual() will have nonzero guess */
270: }
271: ksp->guess_zero = guess_zero; /* restore if user provided nonzero initial guess */
272: return(0);
273: }
275: PetscErrorCode KSPReset_GMRES(KSP ksp)
276: {
277: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
279: PetscInt i;
282: /* Free the Hessenberg matrices */
283: PetscFree5(gmres->hh_origin,gmres->hes_origin,gmres->rs_origin,gmres->cc_origin,gmres->ss_origin);
284: PetscFree(gmres->hes_ritz);
286: /* free work vectors */
287: PetscFree(gmres->vecs);
288: for (i=0; i<gmres->nwork_alloc; i++) {
289: VecDestroyVecs(gmres->mwork_alloc[i],&gmres->user_work[i]);
290: }
291: gmres->nwork_alloc = 0;
292: if (gmres->vecb) {
293: VecDestroyVecs(gmres->max_k+1,&gmres->vecb);
294: }
296: PetscFree(gmres->user_work);
297: PetscFree(gmres->mwork_alloc);
298: PetscFree(gmres->nrs);
299: VecDestroy(&gmres->sol_temp);
300: PetscFree(gmres->Rsvd);
301: PetscFree(gmres->Dsvd);
302: PetscFree(gmres->orthogwork);
304: gmres->vv_allocated = 0;
305: gmres->vecs_allocated = 0;
306: gmres->sol_temp = NULL;
307: return(0);
308: }
310: PetscErrorCode KSPDestroy_GMRES(KSP ksp)
311: {
315: KSPReset_GMRES(ksp);
316: PetscFree(ksp->data);
317: /* clear composed functions */
318: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetPreAllocateVectors_C",NULL);
319: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetOrthogonalization_C",NULL);
320: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetOrthogonalization_C",NULL);
321: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetRestart_C",NULL);
322: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetRestart_C",NULL);
323: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetHapTol_C",NULL);
324: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetBreakdownTolerance_C",NULL);
325: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetCGSRefinementType_C",NULL);
326: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetCGSRefinementType_C",NULL);
327: return(0);
328: }
329: /*
330: KSPGMRESBuildSoln - create the solution from the starting vector and the
331: current iterates.
333: Input parameters:
334: nrs - work area of size it + 1.
335: vs - index of initial guess
336: vdest - index of result. Note that vs may == vdest (replace
337: guess with the solution).
339: This is an internal routine that knows about the GMRES internals.
340: */
341: static PetscErrorCode KSPGMRESBuildSoln(PetscScalar *nrs,Vec vs,Vec vdest,KSP ksp,PetscInt it)
342: {
343: PetscScalar tt;
345: PetscInt ii,k,j;
346: KSP_GMRES *gmres = (KSP_GMRES*)(ksp->data);
349: /* Solve for solution vector that minimizes the residual */
351: /* If it is < 0, no gmres steps have been performed */
352: if (it < 0) {
353: VecCopy(vs,vdest); /* VecCopy() is smart, exists immediately if vguess == vdest */
354: return(0);
355: }
356: if (*HH(it,it) != 0.0) {
357: nrs[it] = *GRS(it) / *HH(it,it);
358: } else {
359: if (ksp->errorifnotconverged) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_NOT_CONVERGED,"You reached the break down in GMRES; HH(it,it) = 0");
360: else ksp->reason = KSP_DIVERGED_BREAKDOWN;
362: 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)));
363: return(0);
364: }
365: for (ii=1; ii<=it; ii++) {
366: k = it - ii;
367: tt = *GRS(k);
368: for (j=k+1; j<=it; j++) tt = tt - *HH(k,j) * nrs[j];
369: if (*HH(k,k) == 0.0) {
370: 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);
371: else {
372: ksp->reason = KSP_DIVERGED_BREAKDOWN;
373: PetscInfo1(ksp,"Likely your matrix or preconditioner is singular. HH(k,k) is identically zero; k = %D\n",k);
374: return(0);
375: }
376: }
377: nrs[k] = tt / *HH(k,k);
378: }
380: /* Accumulate the correction to the solution of the preconditioned problem in TEMP */
381: VecSet(VEC_TEMP,0.0);
382: VecMAXPY(VEC_TEMP,it+1,nrs,&VEC_VV(0));
384: KSPUnwindPreconditioner(ksp,VEC_TEMP,VEC_TEMP_MATOP);
385: /* add solution to previous solution */
386: if (vdest != vs) {
387: VecCopy(vs,vdest);
388: }
389: VecAXPY(vdest,1.0,VEC_TEMP);
390: return(0);
391: }
392: /*
393: Do the scalar work for the orthogonalization. Return new residual norm.
394: */
395: static PetscErrorCode KSPGMRESUpdateHessenberg(KSP ksp,PetscInt it,PetscBool hapend,PetscReal *res)
396: {
397: PetscScalar *hh,*cc,*ss,tt;
398: PetscInt j;
399: KSP_GMRES *gmres = (KSP_GMRES*)(ksp->data);
402: hh = HH(0,it);
403: cc = CC(0);
404: ss = SS(0);
406: /* Apply all the previously computed plane rotations to the new column
407: of the Hessenberg matrix */
408: for (j=1; j<=it; j++) {
409: tt = *hh;
410: *hh = PetscConj(*cc) * tt + *ss * *(hh+1);
411: hh++;
412: *hh = *cc++ * *hh - (*ss++ * tt);
413: }
415: /*
416: compute the new plane rotation, and apply it to:
417: 1) the right-hand-side of the Hessenberg system
418: 2) the new column of the Hessenberg matrix
419: thus obtaining the updated value of the residual
420: */
421: if (!hapend) {
422: tt = PetscSqrtScalar(PetscConj(*hh) * *hh + PetscConj(*(hh+1)) * *(hh+1));
423: if (tt == 0.0) {
424: if (ksp->errorifnotconverged) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_NOT_CONVERGED,"tt == 0.0");
425: else {
426: ksp->reason = KSP_DIVERGED_NULL;
427: return(0);
428: }
429: }
430: *cc = *hh / tt;
431: *ss = *(hh+1) / tt;
432: *GRS(it+1) = -(*ss * *GRS(it));
433: *GRS(it) = PetscConj(*cc) * *GRS(it);
434: *hh = PetscConj(*cc) * *hh + *ss * *(hh+1);
435: *res = PetscAbsScalar(*GRS(it+1));
436: } else {
437: /* happy breakdown: HH(it+1, it) = 0, therefore we don't need to apply
438: another rotation matrix (so RH doesn't change). The new residual is
439: always the new sine term times the residual from last time (GRS(it)),
440: but now the new sine rotation would be zero...so the residual should
441: be zero...so we will multiply "zero" by the last residual. This might
442: not be exactly what we want to do here -could just return "zero". */
444: *res = 0.0;
445: }
446: return(0);
447: }
448: /*
449: This routine allocates more work vectors, starting from VEC_VV(it).
450: */
451: PetscErrorCode KSPGMRESGetNewVectors(KSP ksp,PetscInt it)
452: {
453: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
455: PetscInt nwork = gmres->nwork_alloc,k,nalloc;
458: nalloc = PetscMin(ksp->max_it,gmres->delta_allocate);
459: /* Adjust the number to allocate to make sure that we don't exceed the
460: number of available slots */
461: if (it + VEC_OFFSET + nalloc >= gmres->vecs_allocated) {
462: nalloc = gmres->vecs_allocated - it - VEC_OFFSET;
463: }
464: if (!nalloc) return(0);
466: gmres->vv_allocated += nalloc;
468: KSPCreateVecs(ksp,nalloc,&gmres->user_work[nwork],0,NULL);
469: PetscLogObjectParents(ksp,nalloc,gmres->user_work[nwork]);
471: gmres->mwork_alloc[nwork] = nalloc;
472: for (k=0; k<nalloc; k++) {
473: gmres->vecs[it+VEC_OFFSET+k] = gmres->user_work[nwork][k];
474: }
475: gmres->nwork_alloc++;
476: return(0);
477: }
479: PetscErrorCode KSPBuildSolution_GMRES(KSP ksp,Vec ptr,Vec *result)
480: {
481: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
485: if (!ptr) {
486: if (!gmres->sol_temp) {
487: VecDuplicate(ksp->vec_sol,&gmres->sol_temp);
488: PetscLogObjectParent((PetscObject)ksp,(PetscObject)gmres->sol_temp);
489: }
490: ptr = gmres->sol_temp;
491: }
492: if (!gmres->nrs) {
493: /* allocate the work area */
494: PetscMalloc1(gmres->max_k,&gmres->nrs);
495: PetscLogObjectMemory((PetscObject)ksp,gmres->max_k);
496: }
498: KSPGMRESBuildSoln(gmres->nrs,ksp->vec_sol,ptr,ksp,gmres->it);
499: if (result) *result = ptr;
500: return(0);
501: }
503: PetscErrorCode KSPView_GMRES(KSP ksp,PetscViewer viewer)
504: {
505: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
506: const char *cstr;
508: PetscBool iascii,isstring;
511: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
512: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERSTRING,&isstring);
513: if (gmres->orthog == KSPGMRESClassicalGramSchmidtOrthogonalization) {
514: switch (gmres->cgstype) {
515: case (KSP_GMRES_CGS_REFINE_NEVER):
516: cstr = "Classical (unmodified) Gram-Schmidt Orthogonalization with no iterative refinement";
517: break;
518: case (KSP_GMRES_CGS_REFINE_ALWAYS):
519: cstr = "Classical (unmodified) Gram-Schmidt Orthogonalization with one step of iterative refinement";
520: break;
521: case (KSP_GMRES_CGS_REFINE_IFNEEDED):
522: cstr = "Classical (unmodified) Gram-Schmidt Orthogonalization with one step of iterative refinement when needed";
523: break;
524: default:
525: SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ARG_OUTOFRANGE,"Unknown orthogonalization");
526: }
527: } else if (gmres->orthog == KSPGMRESModifiedGramSchmidtOrthogonalization) {
528: cstr = "Modified Gram-Schmidt Orthogonalization";
529: } else {
530: cstr = "unknown orthogonalization";
531: }
532: if (iascii) {
533: PetscViewerASCIIPrintf(viewer," restart=%D, using %s\n",gmres->max_k,cstr);
534: PetscViewerASCIIPrintf(viewer," happy breakdown tolerance %g\n",(double)gmres->haptol);
535: } else if (isstring) {
536: PetscViewerStringSPrintf(viewer,"%s restart %D",cstr,gmres->max_k);
537: }
538: return(0);
539: }
541: /*@C
542: KSPGMRESMonitorKrylov - Calls VecView() for each new direction in the GMRES accumulated Krylov space.
544: Collective on ksp
546: Input Parameters:
547: + ksp - the KSP context
548: . its - iteration number
549: . fgnorm - 2-norm of residual (or gradient)
550: - dummy - an collection of viewers created with KSPViewerCreate()
552: Options Database Keys:
553: . -ksp_gmres_kyrlov_monitor
555: Notes:
556: A new PETSCVIEWERDRAW is created for each Krylov vector so they can all be simultaneously viewed
557: Level: intermediate
559: .seealso: KSPMonitorSet(), KSPMonitorResidual(), VecView(), KSPViewersCreate(), KSPViewersDestroy()
560: @*/
561: PetscErrorCode KSPGMRESMonitorKrylov(KSP ksp,PetscInt its,PetscReal fgnorm,void *dummy)
562: {
563: PetscViewers viewers = (PetscViewers)dummy;
564: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
566: Vec x;
567: PetscViewer viewer;
568: PetscBool flg;
571: PetscViewersGetViewer(viewers,gmres->it+1,&viewer);
572: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&flg);
573: if (!flg) {
574: PetscViewerSetType(viewer,PETSCVIEWERDRAW);
575: PetscViewerDrawSetInfo(viewer,NULL,"Krylov GMRES Monitor",PETSC_DECIDE,PETSC_DECIDE,300,300);
576: }
577: x = VEC_VV(gmres->it+1);
578: VecView(x,viewer);
579: return(0);
580: }
582: PetscErrorCode KSPSetFromOptions_GMRES(PetscOptionItems *PetscOptionsObject,KSP ksp)
583: {
585: PetscInt restart;
586: PetscReal haptol,breakdowntol;
587: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
588: PetscBool flg;
591: PetscOptionsHead(PetscOptionsObject,"KSP GMRES Options");
592: PetscOptionsInt("-ksp_gmres_restart","Number of Krylov search directions","KSPGMRESSetRestart",gmres->max_k,&restart,&flg);
593: if (flg) { KSPGMRESSetRestart(ksp,restart); }
594: PetscOptionsReal("-ksp_gmres_haptol","Tolerance for exact convergence (happy ending)","KSPGMRESSetHapTol",gmres->haptol,&haptol,&flg);
595: if (flg) { KSPGMRESSetHapTol(ksp,haptol); }
596: PetscOptionsReal("-ksp_gmres_breakdown_tolerance","Divergence breakdown tolerance during GMRES restart","KSPGMRESSetBreakdownTolerance",gmres->breakdowntol,&breakdowntol,&flg);
597: if (flg) { KSPGMRESSetBreakdownTolerance(ksp,breakdowntol); }
598: flg = PETSC_FALSE;
599: PetscOptionsBool("-ksp_gmres_preallocate","Preallocate Krylov vectors","KSPGMRESSetPreAllocateVectors",flg,&flg,NULL);
600: if (flg) {KSPGMRESSetPreAllocateVectors(ksp);}
601: PetscOptionsBoolGroupBegin("-ksp_gmres_classicalgramschmidt","Classical (unmodified) Gram-Schmidt (fast)","KSPGMRESSetOrthogonalization",&flg);
602: if (flg) {KSPGMRESSetOrthogonalization(ksp,KSPGMRESClassicalGramSchmidtOrthogonalization);}
603: PetscOptionsBoolGroupEnd("-ksp_gmres_modifiedgramschmidt","Modified Gram-Schmidt (slow,more stable)","KSPGMRESSetOrthogonalization",&flg);
604: if (flg) {KSPGMRESSetOrthogonalization(ksp,KSPGMRESModifiedGramSchmidtOrthogonalization);}
605: PetscOptionsEnum("-ksp_gmres_cgs_refinement_type","Type of iterative refinement for classical (unmodified) Gram-Schmidt","KSPGMRESSetCGSRefinementType",
606: KSPGMRESCGSRefinementTypes,(PetscEnum)gmres->cgstype,(PetscEnum*)&gmres->cgstype,&flg);
607: flg = PETSC_FALSE;
608: PetscOptionsBool("-ksp_gmres_krylov_monitor","Plot the Krylov directions","KSPMonitorSet",flg,&flg,NULL);
609: if (flg) {
610: PetscViewers viewers;
611: PetscViewersCreate(PetscObjectComm((PetscObject)ksp),&viewers);
612: KSPMonitorSet(ksp,KSPGMRESMonitorKrylov,viewers,(PetscErrorCode (*)(void**))PetscViewersDestroy);
613: }
614: PetscOptionsTail();
615: return(0);
616: }
618: PetscErrorCode KSPGMRESSetHapTol_GMRES(KSP ksp,PetscReal tol)
619: {
620: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
623: if (tol < 0.0) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ARG_OUTOFRANGE,"Tolerance must be non-negative");
624: gmres->haptol = tol;
625: return(0);
626: }
628: PetscErrorCode KSPGMRESSetBreakdownTolerance_GMRES(KSP ksp,PetscReal tol)
629: {
630: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
633: if (tol == PETSC_DEFAULT) {
634: gmres->breakdowntol = 0.1;
635: return(0);
636: }
637: if (tol < 0.0) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ARG_OUTOFRANGE,"Breakdown tolerance must be non-negative");
638: gmres->breakdowntol = tol;
639: return(0);
640: }
642: PetscErrorCode KSPGMRESGetRestart_GMRES(KSP ksp,PetscInt *max_k)
643: {
644: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
647: *max_k = gmres->max_k;
648: return(0);
649: }
651: PetscErrorCode KSPGMRESSetRestart_GMRES(KSP ksp,PetscInt max_k)
652: {
653: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
657: if (max_k < 1) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ARG_OUTOFRANGE,"Restart must be positive");
658: if (!ksp->setupstage) {
659: gmres->max_k = max_k;
660: } else if (gmres->max_k != max_k) {
661: gmres->max_k = max_k;
662: ksp->setupstage = KSP_SETUP_NEW;
663: /* free the data structures, then create them again */
664: KSPReset_GMRES(ksp);
665: }
666: return(0);
667: }
669: PetscErrorCode KSPGMRESSetOrthogonalization_GMRES(KSP ksp,FCN fcn)
670: {
672: ((KSP_GMRES*)ksp->data)->orthog = fcn;
673: return(0);
674: }
676: PetscErrorCode KSPGMRESGetOrthogonalization_GMRES(KSP ksp,FCN *fcn)
677: {
679: *fcn = ((KSP_GMRES*)ksp->data)->orthog;
680: return(0);
681: }
683: PetscErrorCode KSPGMRESSetPreAllocateVectors_GMRES(KSP ksp)
684: {
685: KSP_GMRES *gmres;
688: gmres = (KSP_GMRES*)ksp->data;
689: gmres->q_preallocate = 1;
690: return(0);
691: }
693: PetscErrorCode KSPGMRESSetCGSRefinementType_GMRES(KSP ksp,KSPGMRESCGSRefinementType type)
694: {
695: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
698: gmres->cgstype = type;
699: return(0);
700: }
702: PetscErrorCode KSPGMRESGetCGSRefinementType_GMRES(KSP ksp,KSPGMRESCGSRefinementType *type)
703: {
704: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
707: *type = gmres->cgstype;
708: return(0);
709: }
711: /*@
712: KSPGMRESSetCGSRefinementType - Sets the type of iterative refinement to use
713: in the classical Gram Schmidt orthogonalization.
715: Logically Collective on ksp
717: Input Parameters:
718: + ksp - the Krylov space context
719: - type - the type of refinement
721: Options Database:
722: . -ksp_gmres_cgs_refinement_type <refine_never,refine_ifneeded,refine_always>
724: Level: intermediate
726: .seealso: KSPGMRESSetOrthogonalization(), KSPGMRESCGSRefinementType, KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESGetCGSRefinementType(),
727: KSPGMRESGetOrthogonalization()
728: @*/
729: PetscErrorCode KSPGMRESSetCGSRefinementType(KSP ksp,KSPGMRESCGSRefinementType type)
730: {
736: PetscTryMethod(ksp,"KSPGMRESSetCGSRefinementType_C",(KSP,KSPGMRESCGSRefinementType),(ksp,type));
737: return(0);
738: }
740: /*@
741: KSPGMRESGetCGSRefinementType - Gets the type of iterative refinement to use
742: in the classical Gram Schmidt orthogonalization.
744: Not Collective
746: Input Parameter:
747: . ksp - the Krylov space context
749: Output Parameter:
750: . type - the type of refinement
752: Options Database:
753: . -ksp_gmres_cgs_refinement_type <refine_never,refine_ifneeded,refine_always>
755: Level: intermediate
757: .seealso: KSPGMRESSetOrthogonalization(), KSPGMRESCGSRefinementType, KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESSetCGSRefinementType(),
758: KSPGMRESGetOrthogonalization()
759: @*/
760: PetscErrorCode KSPGMRESGetCGSRefinementType(KSP ksp,KSPGMRESCGSRefinementType *type)
761: {
766: PetscUseMethod(ksp,"KSPGMRESGetCGSRefinementType_C",(KSP,KSPGMRESCGSRefinementType*),(ksp,type));
767: return(0);
768: }
770: /*@
771: KSPGMRESSetRestart - Sets number of iterations at which GMRES, FGMRES and LGMRES restarts.
773: Logically Collective on ksp
775: Input Parameters:
776: + ksp - the Krylov space context
777: - restart - integer restart value
779: Options Database:
780: . -ksp_gmres_restart <positive integer>
782: Note: The default value is 30.
784: Level: intermediate
786: .seealso: KSPSetTolerances(), KSPGMRESSetOrthogonalization(), KSPGMRESSetPreAllocateVectors(), KSPGMRESGetRestart()
787: @*/
788: PetscErrorCode KSPGMRESSetRestart(KSP ksp, PetscInt restart)
789: {
795: PetscTryMethod(ksp,"KSPGMRESSetRestart_C",(KSP,PetscInt),(ksp,restart));
796: return(0);
797: }
799: /*@
800: KSPGMRESGetRestart - Gets number of iterations at which GMRES, FGMRES and LGMRES restarts.
802: Not Collective
804: Input Parameter:
805: . ksp - the Krylov space context
807: Output Parameter:
808: . restart - integer restart value
810: Note: The default value is 30.
812: Level: intermediate
814: .seealso: KSPSetTolerances(), KSPGMRESSetOrthogonalization(), KSPGMRESSetPreAllocateVectors(), KSPGMRESSetRestart()
815: @*/
816: PetscErrorCode KSPGMRESGetRestart(KSP ksp, PetscInt *restart)
817: {
821: PetscUseMethod(ksp,"KSPGMRESGetRestart_C",(KSP,PetscInt*),(ksp,restart));
822: return(0);
823: }
825: /*@
826: KSPGMRESSetHapTol - Sets tolerance for determining happy breakdown in GMRES, FGMRES and LGMRES.
828: Logically Collective on ksp
830: Input Parameters:
831: + ksp - the Krylov space context
832: - tol - the tolerance
834: Options Database:
835: . -ksp_gmres_haptol <positive real value>
837: Note: Happy breakdown is the rare case in GMRES where an 'exact' solution is obtained after
838: a certain number of iterations. If you attempt more iterations after this point unstable
839: things can happen hence very occasionally you may need to set this value to detect this condition
841: Level: intermediate
843: .seealso: KSPSetTolerances()
844: @*/
845: PetscErrorCode KSPGMRESSetHapTol(KSP ksp,PetscReal tol)
846: {
851: PetscTryMethod((ksp),"KSPGMRESSetHapTol_C",(KSP,PetscReal),((ksp),(tol)));
852: return(0);
853: }
855: /*@
856: KSPGMRESSetBreakdownTolerance - Sets tolerance for determining divergence breakdown in GMRES.
858: Logically Collective on ksp
860: Input Parameters:
861: + ksp - the Krylov space context
862: - tol - the tolerance
864: Options Database:
865: . -ksp_gmres_breakdown_tolerance <positive real value>
867: Note: divergence breakdown occurs when GMRES residual increases significantly
868: during restart
870: Level: intermediate
872: .seealso: KSPSetTolerances(), KSPGMRESSetHapTol()
873: @*/
874: PetscErrorCode KSPGMRESSetBreakdownTolerance(KSP ksp,PetscReal tol)
875: {
880: PetscTryMethod((ksp),"KSPGMRESSetBreakdownTolerance_C",(KSP,PetscReal),(ksp,tol));
881: return(0);
882: }
884: /*MC
885: KSPGMRES - Implements the Generalized Minimal Residual method.
886: (Saad and Schultz, 1986) with restart
888: Options Database Keys:
889: + -ksp_gmres_restart <restart> - the number of Krylov directions to orthogonalize against
890: . -ksp_gmres_haptol <tol> - sets the tolerance for "happy ending" (exact convergence)
891: . -ksp_gmres_preallocate - preallocate all the Krylov search directions initially (otherwise groups of
892: vectors are allocated as needed)
893: . -ksp_gmres_classicalgramschmidt - use classical (unmodified) Gram-Schmidt to orthogonalize against the Krylov space (fast) (the default)
894: . -ksp_gmres_modifiedgramschmidt - use modified Gram-Schmidt in the orthogonalization (more stable, but slower)
895: . -ksp_gmres_cgs_refinement_type <refine_never,refine_ifneeded,refine_always> - determine if iterative refinement is used to increase the
896: stability of the classical Gram-Schmidt orthogonalization.
897: - -ksp_gmres_krylov_monitor - plot the Krylov space generated
899: Level: beginner
901: Notes:
902: Left and right preconditioning are supported, but not symmetric preconditioning.
904: References:
905: . 1. - YOUCEF SAAD AND MARTIN H. SCHULTZ, GMRES: A GENERALIZED MINIMAL RESIDUAL ALGORITHM FOR SOLVING NONSYMMETRIC LINEAR SYSTEMS.
906: SIAM J. ScI. STAT. COMPUT. Vo|. 7, No. 3, July 1986.
908: .seealso: KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPFGMRES, KSPLGMRES,
909: KSPGMRESSetRestart(), KSPGMRESSetHapTol(), KSPGMRESSetPreAllocateVectors(), KSPGMRESSetOrthogonalization(), KSPGMRESGetOrthogonalization(),
910: KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESModifiedGramSchmidtOrthogonalization(),
911: KSPGMRESCGSRefinementType, KSPGMRESSetCGSRefinementType(), KSPGMRESGetCGSRefinementType(), KSPGMRESMonitorKrylov(), KSPSetPCSide()
913: M*/
915: PETSC_EXTERN PetscErrorCode KSPCreate_GMRES(KSP ksp)
916: {
917: KSP_GMRES *gmres;
921: PetscNewLog(ksp,&gmres);
922: ksp->data = (void*)gmres;
924: KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,4);
925: KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_RIGHT,3);
926: KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_SYMMETRIC,2);
927: KSPSetSupportedNorm(ksp,KSP_NORM_NONE,PC_RIGHT,1);
928: KSPSetSupportedNorm(ksp,KSP_NORM_NONE,PC_LEFT,1);
930: ksp->ops->buildsolution = KSPBuildSolution_GMRES;
931: ksp->ops->setup = KSPSetUp_GMRES;
932: ksp->ops->solve = KSPSolve_GMRES;
933: ksp->ops->reset = KSPReset_GMRES;
934: ksp->ops->destroy = KSPDestroy_GMRES;
935: ksp->ops->view = KSPView_GMRES;
936: ksp->ops->setfromoptions = KSPSetFromOptions_GMRES;
937: ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_GMRES;
938: ksp->ops->computeeigenvalues = KSPComputeEigenvalues_GMRES;
939: #if !defined(PETSC_USE_COMPLEX)
940: ksp->ops->computeritz = KSPComputeRitz_GMRES;
941: #endif
942: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetPreAllocateVectors_C",KSPGMRESSetPreAllocateVectors_GMRES);
943: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetOrthogonalization_C",KSPGMRESSetOrthogonalization_GMRES);
944: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetOrthogonalization_C",KSPGMRESGetOrthogonalization_GMRES);
945: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetRestart_C",KSPGMRESSetRestart_GMRES);
946: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetRestart_C",KSPGMRESGetRestart_GMRES);
947: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetHapTol_C",KSPGMRESSetHapTol_GMRES);
948: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetBreakdownTolerance_C",KSPGMRESSetBreakdownTolerance_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->breakdowntol = 0.1;
954: gmres->q_preallocate = 0;
955: gmres->delta_allocate = GMRES_DELTA_DIRECTIONS;
956: gmres->orthog = KSPGMRESClassicalGramSchmidtOrthogonalization;
957: gmres->nrs = NULL;
958: gmres->sol_temp = NULL;
959: gmres->max_k = GMRES_DEFAULT_MAXK;
960: gmres->Rsvd = NULL;
961: gmres->cgstype = KSP_GMRES_CGS_REFINE_NEVER;
962: gmres->orthogwork = NULL;
963: return(0);
964: }