Actual source code: gmres.c
petsc-3.14.6 2021-03-30
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: 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: KSPMonitor(ksp,ksp->its,res);
156: }
157: gmres->it = (it - 1);
158: if (gmres->vv_allocated <= it + VEC_OFFSET + 1) {
159: KSPGMRESGetNewVectors(ksp,it+1);
160: }
161: KSP_PCApplyBAorAB(ksp,VEC_VV(it),VEC_VV(1+it),VEC_TEMP_MATOP);
163: /* update hessenberg matrix and do Gram-Schmidt */
164: (*gmres->orthog)(ksp,it);
165: if (ksp->reason) break;
167: /* vv(i+1) . vv(i+1) */
168: VecNormalize(VEC_VV(it+1),&tt);
169: KSPCheckNorm(ksp,tt);
171: /* save the magnitude */
172: *HH(it+1,it) = tt;
173: *HES(it+1,it) = tt;
175: /* check for the happy breakdown */
176: hapbnd = PetscAbsScalar(tt / *GRS(it));
177: if (hapbnd > gmres->haptol) hapbnd = gmres->haptol;
178: if (tt < hapbnd) {
179: PetscInfo2(ksp,"Detected happy breakdown, current hapbnd = %14.12e tt = %14.12e\n",(double)hapbnd,(double)tt);
180: hapend = PETSC_TRUE;
181: }
182: KSPGMRESUpdateHessenberg(ksp,it,hapend,&res);
184: it++;
185: gmres->it = (it-1); /* For converged */
186: ksp->its++;
187: ksp->rnorm = res;
188: if (ksp->reason) break;
190: (*ksp->converged)(ksp,ksp->its,res,&ksp->reason,ksp->cnvP);
192: /* Catch error in happy breakdown and signal convergence and break from loop */
193: if (hapend) {
194: if (ksp->normtype == KSP_NORM_NONE) { /* convergence test was skipped in this case */
195: ksp->reason = KSP_CONVERGED_HAPPY_BREAKDOWN;
196: } else if (!ksp->reason) {
197: 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);
198: else {
199: ksp->reason = KSP_DIVERGED_BREAKDOWN;
200: break;
201: }
202: }
203: }
204: }
206: /* Monitor if we know that we will not return for a restart */
207: if (it && (ksp->reason || ksp->its >= ksp->max_it)) {
208: KSPLogResidualHistory(ksp,res);
209: KSPMonitor(ksp,ksp->its,res);
210: }
212: if (itcount) *itcount = it;
215: /*
216: Down here we have to solve for the "best" coefficients of the Krylov
217: columns, add the solution values together, and possibly unwind the
218: preconditioning from the solution
219: */
220: /* Form the solution (or the solution so far) */
221: KSPGMRESBuildSoln(GRS(0),ksp->vec_sol,ksp->vec_sol,ksp,it-1);
222: return(0);
223: }
225: PetscErrorCode KSPSolve_GMRES(KSP ksp)
226: {
228: PetscInt its,itcount,i;
229: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
230: PetscBool guess_zero = ksp->guess_zero;
231: PetscInt N = gmres->max_k + 1;
234: if (ksp->calc_sings && !gmres->Rsvd) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ORDER,"Must call KSPSetComputeSingularValues() before KSPSetUp() is called");
236: PetscObjectSAWsTakeAccess((PetscObject)ksp);
237: ksp->its = 0;
238: PetscObjectSAWsGrantAccess((PetscObject)ksp);
240: itcount = 0;
241: gmres->fullcycle = 0;
242: ksp->reason = KSP_CONVERGED_ITERATING;
243: ksp->rnorm = -1.0; /* special marker for KSPGMRESCycle() */
244: while (!ksp->reason) {
245: KSPInitialResidual(ksp,ksp->vec_sol,VEC_TEMP,VEC_TEMP_MATOP,VEC_VV(0),ksp->vec_rhs);
246: KSPGMRESCycle(&its,ksp);
247: /* Store the Hessenberg matrix and the basis vectors of the Krylov subspace
248: if the cycle is complete for the computation of the Ritz pairs */
249: if (its == gmres->max_k) {
250: gmres->fullcycle++;
251: if (ksp->calc_ritz) {
252: if (!gmres->hes_ritz) {
253: PetscMalloc1(N*N,&gmres->hes_ritz);
254: PetscLogObjectMemory((PetscObject)ksp,N*N*sizeof(PetscScalar));
255: VecDuplicateVecs(VEC_VV(0),N,&gmres->vecb);
256: }
257: PetscArraycpy(gmres->hes_ritz,gmres->hes_origin,N*N);
258: for (i=0; i<gmres->max_k+1; i++) {
259: VecCopy(VEC_VV(i),gmres->vecb[i]);
260: }
261: }
262: }
263: itcount += its;
264: if (itcount >= ksp->max_it) {
265: if (!ksp->reason) ksp->reason = KSP_DIVERGED_ITS;
266: break;
267: }
268: ksp->guess_zero = PETSC_FALSE; /* every future call to KSPInitialResidual() will have nonzero guess */
269: }
270: ksp->guess_zero = guess_zero; /* restore if user provided nonzero initial guess */
271: return(0);
272: }
274: PetscErrorCode KSPReset_GMRES(KSP ksp)
275: {
276: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
278: PetscInt i;
281: /* Free the Hessenberg matrices */
282: PetscFree5(gmres->hh_origin,gmres->hes_origin,gmres->rs_origin,gmres->cc_origin,gmres->ss_origin);
283: PetscFree(gmres->hes_ritz);
285: /* free work vectors */
286: PetscFree(gmres->vecs);
287: for (i=0; i<gmres->nwork_alloc; i++) {
288: VecDestroyVecs(gmres->mwork_alloc[i],&gmres->user_work[i]);
289: }
290: gmres->nwork_alloc = 0;
291: if (gmres->vecb) {
292: VecDestroyVecs(gmres->max_k+1,&gmres->vecb);
293: }
295: PetscFree(gmres->user_work);
296: PetscFree(gmres->mwork_alloc);
297: PetscFree(gmres->nrs);
298: VecDestroy(&gmres->sol_temp);
299: PetscFree(gmres->Rsvd);
300: PetscFree(gmres->Dsvd);
301: PetscFree(gmres->orthogwork);
303: gmres->vv_allocated = 0;
304: gmres->vecs_allocated = 0;
305: gmres->sol_temp = NULL;
306: return(0);
307: }
309: PetscErrorCode KSPDestroy_GMRES(KSP ksp)
310: {
314: KSPReset_GMRES(ksp);
315: PetscFree(ksp->data);
316: /* clear composed functions */
317: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetPreAllocateVectors_C",NULL);
318: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetOrthogonalization_C",NULL);
319: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetOrthogonalization_C",NULL);
320: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetRestart_C",NULL);
321: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetRestart_C",NULL);
322: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetHapTol_C",NULL);
323: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetBreakdownTolerance_C",NULL);
324: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetCGSRefinementType_C",NULL);
325: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetCGSRefinementType_C",NULL);
326: return(0);
327: }
328: /*
329: KSPGMRESBuildSoln - create the solution from the starting vector and the
330: current iterates.
332: Input parameters:
333: nrs - work area of size it + 1.
334: vs - index of initial guess
335: vdest - index of result. Note that vs may == vdest (replace
336: guess with the solution).
338: This is an internal routine that knows about the GMRES internals.
339: */
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: if (ksp->errorifnotconverged) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_NOT_CONVERGED,"You reached the break down in GMRES; HH(it,it) = 0");
359: else ksp->reason = KSP_DIVERGED_BREAKDOWN;
361: 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)));
362: return(0);
363: }
364: for (ii=1; ii<=it; ii++) {
365: k = it - ii;
366: tt = *GRS(k);
367: for (j=k+1; j<=it; j++) tt = tt - *HH(k,j) * nrs[j];
368: if (*HH(k,k) == 0.0) {
369: 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);
370: else {
371: ksp->reason = KSP_DIVERGED_BREAKDOWN;
372: PetscInfo1(ksp,"Likely your matrix or preconditioner is singular. HH(k,k) is identically zero; k = %D\n",k);
373: return(0);
374: }
375: }
376: nrs[k] = tt / *HH(k,k);
377: }
379: /* Accumulate the correction to the solution of the preconditioned problem in TEMP */
380: VecSet(VEC_TEMP,0.0);
381: VecMAXPY(VEC_TEMP,it+1,nrs,&VEC_VV(0));
383: KSPUnwindPreconditioner(ksp,VEC_TEMP,VEC_TEMP_MATOP);
384: /* add solution to previous solution */
385: if (vdest != vs) {
386: VecCopy(vs,vdest);
387: }
388: VecAXPY(vdest,1.0,VEC_TEMP);
389: return(0);
390: }
391: /*
392: Do the scalar work for the orthogonalization. Return new residual norm.
393: */
394: static PetscErrorCode KSPGMRESUpdateHessenberg(KSP ksp,PetscInt it,PetscBool hapend,PetscReal *res)
395: {
396: PetscScalar *hh,*cc,*ss,tt;
397: PetscInt j;
398: KSP_GMRES *gmres = (KSP_GMRES*)(ksp->data);
401: hh = HH(0,it);
402: cc = CC(0);
403: ss = SS(0);
405: /* Apply all the previously computed plane rotations to the new column
406: of the Hessenberg matrix */
407: for (j=1; j<=it; j++) {
408: tt = *hh;
409: *hh = PetscConj(*cc) * tt + *ss * *(hh+1);
410: hh++;
411: *hh = *cc++ * *hh - (*ss++ * tt);
412: }
414: /*
415: compute the new plane rotation, and apply it to:
416: 1) the right-hand-side of the Hessenberg system
417: 2) the new column of the Hessenberg matrix
418: thus obtaining the updated value of the residual
419: */
420: if (!hapend) {
421: tt = PetscSqrtScalar(PetscConj(*hh) * *hh + PetscConj(*(hh+1)) * *(hh+1));
422: if (tt == 0.0) {
423: if (ksp->errorifnotconverged) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_NOT_CONVERGED,"tt == 0.0");
424: else {
425: ksp->reason = KSP_DIVERGED_NULL;
426: return(0);
427: }
428: }
429: *cc = *hh / tt;
430: *ss = *(hh+1) / tt;
431: *GRS(it+1) = -(*ss * *GRS(it));
432: *GRS(it) = PetscConj(*cc) * *GRS(it);
433: *hh = PetscConj(*cc) * *hh + *ss * *(hh+1);
434: *res = PetscAbsScalar(*GRS(it+1));
435: } else {
436: /* happy breakdown: HH(it+1, it) = 0, therfore we don't need to apply
437: another rotation matrix (so RH doesn't change). The new residual is
438: always the new sine term times the residual from last time (GRS(it)),
439: but now the new sine rotation would be zero...so the residual should
440: be zero...so we will multiply "zero" by the last residual. This might
441: not be exactly what we want to do here -could just return "zero". */
443: *res = 0.0;
444: }
445: return(0);
446: }
447: /*
448: This routine allocates more work vectors, starting from VEC_VV(it).
449: */
450: PetscErrorCode KSPGMRESGetNewVectors(KSP ksp,PetscInt it)
451: {
452: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
454: PetscInt nwork = gmres->nwork_alloc,k,nalloc;
457: nalloc = PetscMin(ksp->max_it,gmres->delta_allocate);
458: /* Adjust the number to allocate to make sure that we don't exceed the
459: number of available slots */
460: if (it + VEC_OFFSET + nalloc >= gmres->vecs_allocated) {
461: nalloc = gmres->vecs_allocated - it - VEC_OFFSET;
462: }
463: if (!nalloc) return(0);
465: gmres->vv_allocated += nalloc;
467: KSPCreateVecs(ksp,nalloc,&gmres->user_work[nwork],0,NULL);
468: PetscLogObjectParents(ksp,nalloc,gmres->user_work[nwork]);
470: gmres->mwork_alloc[nwork] = nalloc;
471: for (k=0; k<nalloc; k++) {
472: gmres->vecs[it+VEC_OFFSET+k] = gmres->user_work[nwork][k];
473: }
474: gmres->nwork_alloc++;
475: return(0);
476: }
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);
495: }
497: KSPGMRESBuildSoln(gmres->nrs,ksp->vec_sol,ptr,ksp,gmres->it);
498: if (result) *result = ptr;
499: return(0);
500: }
502: PetscErrorCode KSPView_GMRES(KSP ksp,PetscViewer viewer)
503: {
504: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
505: const char *cstr;
507: PetscBool iascii,isstring;
510: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
511: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERSTRING,&isstring);
512: if (gmres->orthog == KSPGMRESClassicalGramSchmidtOrthogonalization) {
513: switch (gmres->cgstype) {
514: case (KSP_GMRES_CGS_REFINE_NEVER):
515: cstr = "Classical (unmodified) Gram-Schmidt Orthogonalization with no iterative refinement";
516: break;
517: case (KSP_GMRES_CGS_REFINE_ALWAYS):
518: cstr = "Classical (unmodified) Gram-Schmidt Orthogonalization with one step of iterative refinement";
519: break;
520: case (KSP_GMRES_CGS_REFINE_IFNEEDED):
521: cstr = "Classical (unmodified) Gram-Schmidt Orthogonalization with one step of iterative refinement when needed";
522: break;
523: default:
524: SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ARG_OUTOFRANGE,"Unknown orthogonalization");
525: }
526: } else if (gmres->orthog == KSPGMRESModifiedGramSchmidtOrthogonalization) {
527: cstr = "Modified Gram-Schmidt Orthogonalization";
528: } else {
529: cstr = "unknown orthogonalization";
530: }
531: if (iascii) {
532: PetscViewerASCIIPrintf(viewer," restart=%D, using %s\n",gmres->max_k,cstr);
533: PetscViewerASCIIPrintf(viewer," happy breakdown tolerance %g\n",(double)gmres->haptol);
534: } else if (isstring) {
535: PetscViewerStringSPrintf(viewer,"%s restart %D",cstr,gmres->max_k);
536: }
537: return(0);
538: }
540: /*@C
541: KSPGMRESMonitorKrylov - Calls VecView() for each new direction in the GMRES accumulated Krylov space.
543: Collective on ksp
545: Input Parameters:
546: + ksp - the KSP context
547: . its - iteration number
548: . fgnorm - 2-norm of residual (or gradient)
549: - dummy - an collection of viewers created with KSPViewerCreate()
551: Options Database Keys:
552: . -ksp_gmres_kyrlov_monitor
554: Notes:
555: A new PETSCVIEWERDRAW is created for each Krylov vector so they can all be simultaneously viewed
556: Level: intermediate
558: .seealso: KSPMonitorSet(), KSPMonitorDefault(), VecView(), KSPViewersCreate(), KSPViewersDestroy()
559: @*/
560: PetscErrorCode KSPGMRESMonitorKrylov(KSP ksp,PetscInt its,PetscReal fgnorm,void *dummy)
561: {
562: PetscViewers viewers = (PetscViewers)dummy;
563: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
565: Vec x;
566: PetscViewer viewer;
567: PetscBool flg;
570: PetscViewersGetViewer(viewers,gmres->it+1,&viewer);
571: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&flg);
572: if (!flg) {
573: PetscViewerSetType(viewer,PETSCVIEWERDRAW);
574: PetscViewerDrawSetInfo(viewer,NULL,"Krylov GMRES Monitor",PETSC_DECIDE,PETSC_DECIDE,300,300);
575: }
576: x = VEC_VV(gmres->it+1);
577: VecView(x,viewer);
578: return(0);
579: }
581: PetscErrorCode KSPSetFromOptions_GMRES(PetscOptionItems *PetscOptionsObject,KSP ksp)
582: {
584: PetscInt restart;
585: PetscReal haptol,breakdowntol;
586: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
587: PetscBool flg;
590: PetscOptionsHead(PetscOptionsObject,"KSP GMRES Options");
591: PetscOptionsInt("-ksp_gmres_restart","Number of Krylov search directions","KSPGMRESSetRestart",gmres->max_k,&restart,&flg);
592: if (flg) { KSPGMRESSetRestart(ksp,restart); }
593: PetscOptionsReal("-ksp_gmres_haptol","Tolerance for exact convergence (happy ending)","KSPGMRESSetHapTol",gmres->haptol,&haptol,&flg);
594: if (flg) { KSPGMRESSetHapTol(ksp,haptol); }
595: PetscOptionsReal("-ksp_gmres_breakdown_tolerance","Divergence breakdown tolerance during GMRES restart","KSPGMRESSetBreakdownTolerance",gmres->breakdowntol,&breakdowntol,&flg);
596: if (flg) { KSPGMRESSetBreakdownTolerance(ksp,breakdowntol); }
597: flg = PETSC_FALSE;
598: PetscOptionsBool("-ksp_gmres_preallocate","Preallocate Krylov vectors","KSPGMRESSetPreAllocateVectors",flg,&flg,NULL);
599: if (flg) {KSPGMRESSetPreAllocateVectors(ksp);}
600: PetscOptionsBoolGroupBegin("-ksp_gmres_classicalgramschmidt","Classical (unmodified) Gram-Schmidt (fast)","KSPGMRESSetOrthogonalization",&flg);
601: if (flg) {KSPGMRESSetOrthogonalization(ksp,KSPGMRESClassicalGramSchmidtOrthogonalization);}
602: PetscOptionsBoolGroupEnd("-ksp_gmres_modifiedgramschmidt","Modified Gram-Schmidt (slow,more stable)","KSPGMRESSetOrthogonalization",&flg);
603: if (flg) {KSPGMRESSetOrthogonalization(ksp,KSPGMRESModifiedGramSchmidtOrthogonalization);}
604: PetscOptionsEnum("-ksp_gmres_cgs_refinement_type","Type of iterative refinement for classical (unmodified) Gram-Schmidt","KSPGMRESSetCGSRefinementType",
605: KSPGMRESCGSRefinementTypes,(PetscEnum)gmres->cgstype,(PetscEnum*)&gmres->cgstype,&flg);
606: flg = PETSC_FALSE;
607: PetscOptionsBool("-ksp_gmres_krylov_monitor","Plot the Krylov directions","KSPMonitorSet",flg,&flg,NULL);
608: if (flg) {
609: PetscViewers viewers;
610: PetscViewersCreate(PetscObjectComm((PetscObject)ksp),&viewers);
611: KSPMonitorSet(ksp,KSPGMRESMonitorKrylov,viewers,(PetscErrorCode (*)(void**))PetscViewersDestroy);
612: }
613: PetscOptionsTail();
614: return(0);
615: }
617: PetscErrorCode KSPGMRESSetHapTol_GMRES(KSP ksp,PetscReal tol)
618: {
619: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
622: if (tol < 0.0) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ARG_OUTOFRANGE,"Tolerance must be non-negative");
623: gmres->haptol = tol;
624: return(0);
625: }
627: PetscErrorCode KSPGMRESSetBreakdownTolerance_GMRES(KSP ksp,PetscReal tol)
628: {
629: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
632: if (tol == PETSC_DEFAULT) {
633: gmres->breakdowntol = 0.1;
634: return(0);
635: }
636: if (tol < 0.0) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ARG_OUTOFRANGE,"Breakdown tolerance must be non-negative");
637: gmres->breakdowntol = tol;
638: return(0);
639: }
641: PetscErrorCode KSPGMRESGetRestart_GMRES(KSP ksp,PetscInt *max_k)
642: {
643: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
646: *max_k = gmres->max_k;
647: return(0);
648: }
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: }
668: PetscErrorCode KSPGMRESSetOrthogonalization_GMRES(KSP ksp,FCN fcn)
669: {
671: ((KSP_GMRES*)ksp->data)->orthog = fcn;
672: return(0);
673: }
675: PetscErrorCode KSPGMRESGetOrthogonalization_GMRES(KSP ksp,FCN *fcn)
676: {
678: *fcn = ((KSP_GMRES*)ksp->data)->orthog;
679: return(0);
680: }
682: PetscErrorCode KSPGMRESSetPreAllocateVectors_GMRES(KSP ksp)
683: {
684: KSP_GMRES *gmres;
687: gmres = (KSP_GMRES*)ksp->data;
688: gmres->q_preallocate = 1;
689: return(0);
690: }
692: PetscErrorCode KSPGMRESSetCGSRefinementType_GMRES(KSP ksp,KSPGMRESCGSRefinementType type)
693: {
694: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
697: gmres->cgstype = type;
698: return(0);
699: }
701: PetscErrorCode KSPGMRESGetCGSRefinementType_GMRES(KSP ksp,KSPGMRESCGSRefinementType *type)
702: {
703: KSP_GMRES *gmres = (KSP_GMRES*)ksp->data;
706: *type = gmres->cgstype;
707: return(0);
708: }
710: /*@
711: KSPGMRESSetCGSRefinementType - Sets the type of iterative refinement to use
712: in the classical Gram Schmidt orthogonalization.
714: Logically Collective on ksp
716: Input Parameters:
717: + ksp - the Krylov space context
718: - type - the type of refinement
720: Options Database:
721: . -ksp_gmres_cgs_refinement_type <refine_never,refine_ifneeded,refine_always>
723: Level: intermediate
725: .seealso: KSPGMRESSetOrthogonalization(), KSPGMRESCGSRefinementType, KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESGetCGSRefinementType(),
726: KSPGMRESGetOrthogonalization()
727: @*/
728: PetscErrorCode KSPGMRESSetCGSRefinementType(KSP ksp,KSPGMRESCGSRefinementType type)
729: {
735: PetscTryMethod(ksp,"KSPGMRESSetCGSRefinementType_C",(KSP,KSPGMRESCGSRefinementType),(ksp,type));
736: return(0);
737: }
739: /*@
740: KSPGMRESGetCGSRefinementType - Gets the type of iterative refinement to use
741: in the classical Gram Schmidt orthogonalization.
743: Not Collective
745: Input Parameter:
746: . ksp - the Krylov space context
748: Output Parameter:
749: . type - the type of refinement
751: Options Database:
752: . -ksp_gmres_cgs_refinement_type <refine_never,refine_ifneeded,refine_always>
754: Level: intermediate
756: .seealso: KSPGMRESSetOrthogonalization(), KSPGMRESCGSRefinementType, KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESSetCGSRefinementType(),
757: KSPGMRESGetOrthogonalization()
758: @*/
759: PetscErrorCode KSPGMRESGetCGSRefinementType(KSP ksp,KSPGMRESCGSRefinementType *type)
760: {
765: PetscUseMethod(ksp,"KSPGMRESGetCGSRefinementType_C",(KSP,KSPGMRESCGSRefinementType*),(ksp,type));
766: return(0);
767: }
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
889: Options Database Keys:
890: + -ksp_gmres_restart <restart> - the number of Krylov directions to orthogonalize against
891: . -ksp_gmres_haptol <tol> - sets the tolerance for "happy ending" (exact convergence)
892: . -ksp_gmres_preallocate - preallocate all the Krylov search directions initially (otherwise groups of
893: vectors are allocated as needed)
894: . -ksp_gmres_classicalgramschmidt - use classical (unmodified) Gram-Schmidt to orthogonalize against the Krylov space (fast) (the default)
895: . -ksp_gmres_modifiedgramschmidt - use modified Gram-Schmidt in the orthogonalization (more stable, but slower)
896: . -ksp_gmres_cgs_refinement_type <refine_never,refine_ifneeded,refine_always> - determine if iterative refinement is used to increase the
897: stability of the classical Gram-Schmidt orthogonalization.
898: - -ksp_gmres_krylov_monitor - plot the Krylov space generated
900: Level: beginner
902: Notes:
903: 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*/
916: PETSC_EXTERN PetscErrorCode KSPCreate_GMRES(KSP ksp)
917: {
918: KSP_GMRES *gmres;
922: PetscNewLog(ksp,&gmres);
923: ksp->data = (void*)gmres;
925: KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,4);
926: KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_RIGHT,3);
927: KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_SYMMETRIC,2);
928: KSPSetSupportedNorm(ksp,KSP_NORM_NONE,PC_RIGHT,1);
929: KSPSetSupportedNorm(ksp,KSP_NORM_NONE,PC_LEFT,1);
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,"KSPGMRESSetBreakdownTolerance_C",KSPGMRESSetBreakdownTolerance_GMRES);
950: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetCGSRefinementType_C",KSPGMRESSetCGSRefinementType_GMRES);
951: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetCGSRefinementType_C",KSPGMRESGetCGSRefinementType_GMRES);
953: gmres->haptol = 1.0e-30;
954: gmres->breakdowntol = 0.1;
955: gmres->q_preallocate = 0;
956: gmres->delta_allocate = GMRES_DELTA_DIRECTIONS;
957: gmres->orthog = KSPGMRESClassicalGramSchmidtOrthogonalization;
958: gmres->nrs = NULL;
959: gmres->sol_temp = NULL;
960: gmres->max_k = GMRES_DEFAULT_MAXK;
961: gmres->Rsvd = NULL;
962: gmres->cgstype = KSP_GMRES_CGS_REFINE_NEVER;
963: gmres->orthogwork = NULL;
964: return(0);
965: }