2: /*
3: This file implements PGMRES (a Pipelined Generalized Minimal Residual method)
4: */
6: #include <../src/ksp/ksp/impls/gmres/pgmres/pgmresimpl.h> /*I "petscksp.h" I*/
7: #define PGMRES_DELTA_DIRECTIONS 10 8: #define PGMRES_DEFAULT_MAXK 30 10: static PetscErrorCode KSPPGMRESUpdateHessenberg(KSP,PetscInt,PetscBool*,PetscReal*);
11: static PetscErrorCode KSPPGMRESBuildSoln(PetscScalar*,Vec,Vec,KSP,PetscInt);
13: /*
15: KSPSetUp_PGMRES - Sets up the workspace needed by pgmres.
17: This is called once, usually automatically by KSPSolve() or KSPSetUp(),
18: but can be called directly by KSPSetUp().
20: */
23: static PetscErrorCode KSPSetUp_PGMRES(KSP ksp) 24: {
28: KSPSetUp_GMRES(ksp);
29: return(0);
30: }
32: /*
34: KSPPGMRESCycle - Run pgmres, possibly with restart. Return residual
35: history if requested.
37: input parameters:
38: . pgmres - structure containing parameters and work areas
40: output parameters:
41: . itcount - number of iterations used. If null, ignored.
42: . converged - 0 if not converged
44: Notes:
45: On entry, the value in vector VEC_VV(0) should be
46: the initial residual.
49: */
52: static PetscErrorCode KSPPGMRESCycle(PetscInt *itcount,KSP ksp) 53: {
54: KSP_PGMRES *pgmres = (KSP_PGMRES*)(ksp->data);
55: PetscReal res_norm,res,newnorm;
57: PetscInt it = 0,j,k;
58: PetscBool hapend = PETSC_FALSE;
61: if (itcount) *itcount = 0;
62: VecNormalize(VEC_VV(0),&res_norm);
63: KSPCheckNorm(ksp,res_norm);
64: res = res_norm;
65: *RS(0) = res_norm;
67: /* check for the convergence */
68: PetscObjectSAWsTakeAccess((PetscObject)ksp);
69: ksp->rnorm = res;
70: PetscObjectSAWsGrantAccess((PetscObject)ksp);
71: pgmres->it = it-2;
72: KSPLogResidualHistory(ksp,res);
73: KSPMonitor(ksp,ksp->its,res);
74: if (!res) {
75: ksp->reason = KSP_CONVERGED_ATOL;
76: PetscInfo(ksp,"Converged due to zero residual norm on entry\n");
77: return(0);
78: }
80: (*ksp->converged)(ksp,ksp->its,res,&ksp->reason,ksp->cnvP);
81: for (; !ksp->reason; it++) {
82: Vec Zcur,Znext;
83: if (pgmres->vv_allocated <= it + VEC_OFFSET + 1) {
84: KSPGMRESGetNewVectors(ksp,it+1);
85: }
86: /* VEC_VV(it-1) is orthogonal, it will be normalized once the VecNorm arrives. */
87: Zcur = VEC_VV(it); /* Zcur is not yet orthogonal, but the VecMDot to orthogonalize it has been started. */
88: Znext = VEC_VV(it+1); /* This iteration will compute Znext, update with a deferred correction once we know how
89: * Zcur relates to the previous vectors, and start the reduction to orthogonalize it. */
91: if (it < pgmres->max_k+1 && ksp->its+1 < PetscMax(2,ksp->max_it)) { /* We don't know whether what we have computed is enough, so apply the matrix. */
92: KSP_PCApplyBAorAB(ksp,Zcur,Znext,VEC_TEMP_MATOP);
93: }
95: if (it > 1) { /* Complete the pending reduction */
96: VecNormEnd(VEC_VV(it-1),NORM_2,&newnorm);
97: *HH(it-1,it-2) = newnorm;
98: }
99: if (it > 0) { /* Finish the reduction computing the latest column of H */
100: VecMDotEnd(Zcur,it,&(VEC_VV(0)),HH(0,it-1));
101: }
103: if (it > 1) {
104: /* normalize the base vector from two iterations ago, basis is complete up to here */
105: VecScale(VEC_VV(it-1),1./ *HH(it-1,it-2));
107: KSPPGMRESUpdateHessenberg(ksp,it-2,&hapend,&res);
108: pgmres->it = it-2;
109: ksp->its++;
110: ksp->rnorm = res;
112: (*ksp->converged)(ksp,ksp->its,res,&ksp->reason,ksp->cnvP);
113: if (it < pgmres->max_k+1 || ksp->reason || ksp->its == ksp->max_it) { /* Monitor if we are done or still iterating, but not before a restart. */
114: KSPLogResidualHistory(ksp,res);
115: KSPMonitor(ksp,ksp->its,res);
116: }
117: if (ksp->reason) break;
118: /* Catch error in happy breakdown and signal convergence and break from loop */
119: if (hapend) {
120: 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);
121: else {
122: ksp->reason = KSP_DIVERGED_BREAKDOWN;
123: break;
124: }
125: }
127: if (!(it < pgmres->max_k+1 && ksp->its < ksp->max_it)) break;
129: /* The it-2 column of H was not scaled when we computed Zcur, apply correction */
130: VecScale(Zcur,1./ *HH(it-1,it-2));
131: /* And Znext computed in this iteration was computed using the under-scaled Zcur */
132: VecScale(Znext,1./ *HH(it-1,it-2));
134: /* In the previous iteration, we projected an unnormalized Zcur against the Krylov basis, so we need to fix the column of H resulting from that projection. */
135: for (k=0; k<it; k++) *HH(k,it-1) /= *HH(it-1,it-2);
136: /* When Zcur was projected against the Krylov basis, VV(it-1) was still not normalized, so fix that too. This
137: * column is complete except for HH(it,it-1) which we won't know until the next iteration. */
138: *HH(it-1,it-1) /= *HH(it-1,it-2);
139: }
141: if (it > 0) {
142: PetscScalar *work;
143: if (!pgmres->orthogwork) {PetscMalloc1(pgmres->max_k + 2,&pgmres->orthogwork);}
144: work = pgmres->orthogwork;
145: /* Apply correction computed by the VecMDot in the last iteration to Znext. The original form is
146: *
147: * Znext -= sum_{j=0}^{i-1} Z[j+1] * H[j,i-1]
148: *
149: * where
150: *
151: * Z[j] = sum_{k=0}^j V[k] * H[k,j-1]
152: *
153: * substituting
154: *
155: * Znext -= sum_{j=0}^{i-1} sum_{k=0}^{j+1} V[k] * H[k,j] * H[j,i-1]
156: *
157: * rearranging the iteration space from row-column to column-row
158: *
159: * Znext -= sum_{k=0}^i sum_{j=k-1}^{i-1} V[k] * H[k,j] * H[j,i-1]
160: *
161: * Note that column it-1 of HH is correct. For all previous columns, we must look at HES because HH has already
162: * been transformed to upper triangular form.
163: */
164: for (k=0; k<it+1; k++) {
165: work[k] = 0;
166: for (j=PetscMax(0,k-1); j<it-1; j++) work[k] -= *HES(k,j) * *HH(j,it-1);
167: }
168: VecMAXPY(Znext,it+1,work,&VEC_VV(0));
169: VecAXPY(Znext,-*HH(it-1,it-1),Zcur);
171: /* Orthogonalize Zcur against existing basis vectors. */
172: for (k=0; k<it; k++) work[k] = -*HH(k,it-1);
173: VecMAXPY(Zcur,it,work,&VEC_VV(0));
174: /* Zcur is now orthogonal, and will be referred to as VEC_VV(it) again, though it is still not normalized. */
175: /* Begin computing the norm of the new vector, will be normalized after the MatMult in the next iteration. */
176: VecNormBegin(VEC_VV(it),NORM_2,&newnorm);
177: }
179: /* Compute column of H (to the diagonal, but not the subdiagonal) to be able to orthogonalize the newest vector. */
180: VecMDotBegin(Znext,it+1,&VEC_VV(0),HH(0,it));
182: /* Start an asynchronous split-mode reduction, the result of the MDot and Norm will be collected on the next iteration. */
183: PetscCommSplitReductionBegin(PetscObjectComm((PetscObject)Znext));
184: }
186: if (itcount) *itcount = it-1; /* Number of iterations actually completed. */
188: /*
189: Down here we have to solve for the "best" coefficients of the Krylov
190: columns, add the solution values together, and possibly unwind the
191: preconditioning from the solution
192: */
193: /* Form the solution (or the solution so far) */
194: KSPPGMRESBuildSoln(RS(0),ksp->vec_sol,ksp->vec_sol,ksp,it-2);
195: return(0);
196: }
198: /*
199: KSPSolve_PGMRES - This routine applies the PGMRES method.
202: Input Parameter:
203: . ksp - the Krylov space object that was set to use pgmres
205: Output Parameter:
206: . outits - number of iterations used
208: */
211: static PetscErrorCode KSPSolve_PGMRES(KSP ksp)212: {
214: PetscInt its,itcount;
215: KSP_PGMRES *pgmres = (KSP_PGMRES*)ksp->data;
216: PetscBool guess_zero = ksp->guess_zero;
219: if (ksp->calc_sings && !pgmres->Rsvd) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ORDER,"Must call KSPSetComputeSingularValues() before KSPSetUp() is called");
220: PetscObjectSAWsTakeAccess((PetscObject)ksp);
221: ksp->its = 0;
222: PetscObjectSAWsGrantAccess((PetscObject)ksp);
224: itcount = 0;
225: ksp->reason = KSP_CONVERGED_ITERATING;
226: while (!ksp->reason) {
227: KSPInitialResidual(ksp,ksp->vec_sol,VEC_TEMP,VEC_TEMP_MATOP,VEC_VV(0),ksp->vec_rhs);
228: KSPPGMRESCycle(&its,ksp);
229: itcount += its;
230: if (itcount >= ksp->max_it) {
231: if (!ksp->reason) ksp->reason = KSP_DIVERGED_ITS;
232: break;
233: }
234: ksp->guess_zero = PETSC_FALSE; /* every future call to KSPInitialResidual() will have nonzero guess */
235: }
236: ksp->guess_zero = guess_zero; /* restore if user provided nonzero initial guess */
237: return(0);
238: }
242: static PetscErrorCode KSPDestroy_PGMRES(KSP ksp)243: {
247: KSPDestroy_GMRES(ksp);
248: return(0);
249: }
251: /*
252: KSPPGMRESBuildSoln - create the solution from the starting vector and the
253: current iterates.
255: Input parameters:
256: nrs - work area of size it + 1.
257: vguess - index of initial guess
258: vdest - index of result. Note that vguess may == vdest (replace
259: guess with the solution).
260: it - HH upper triangular part is a block of size (it+1) x (it+1)
262: This is an internal routine that knows about the PGMRES internals.
263: */
266: static PetscErrorCode KSPPGMRESBuildSoln(PetscScalar *nrs,Vec vguess,Vec vdest,KSP ksp,PetscInt it)267: {
268: PetscScalar tt;
270: PetscInt k,j;
271: KSP_PGMRES *pgmres = (KSP_PGMRES*)(ksp->data);
274: /* Solve for solution vector that minimizes the residual */
276: if (it < 0) { /* no pgmres steps have been performed */
277: VecCopy(vguess,vdest); /* VecCopy() is smart, exits immediately if vguess == vdest */
278: return(0);
279: }
281: /* solve the upper triangular system - RS is the right side and HH is
282: the upper triangular matrix - put soln in nrs */
283: if (*HH(it,it) != 0.0) nrs[it] = *RS(it) / *HH(it,it);
284: else nrs[it] = 0.0;
286: for (k=it-1; k>=0; k--) {
287: tt = *RS(k);
288: for (j=k+1; j<=it; j++) tt -= *HH(k,j) * nrs[j];
289: nrs[k] = tt / *HH(k,k);
290: }
292: /* Accumulate the correction to the solution of the preconditioned problem in TEMP */
293: VecZeroEntries(VEC_TEMP);
294: VecMAXPY(VEC_TEMP,it+1,nrs,&VEC_VV(0));
295: KSPUnwindPreconditioner(ksp,VEC_TEMP,VEC_TEMP_MATOP);
296: /* add solution to previous solution */
297: if (vdest == vguess) {
298: VecAXPY(vdest,1.0,VEC_TEMP);
299: } else {
300: VecWAXPY(vdest,1.0,VEC_TEMP,vguess);
301: }
302: return(0);
303: }
305: /*
307: KSPPGMRESUpdateHessenberg - Do the scalar work for the orthogonalization.
308: Return new residual.
310: input parameters:
312: . ksp - Krylov space object
313: . it - plane rotations are applied to the (it+1)th column of the
314: modified hessenberg (i.e. HH(:,it))
315: . hapend - PETSC_FALSE not happy breakdown ending.
317: output parameters:
318: . res - the new residual
320: */
323: /*
324: . it - column of the Hessenberg that is complete, PGMRES is actually computing two columns ahead of this
325: */
326: static PetscErrorCode KSPPGMRESUpdateHessenberg(KSP ksp,PetscInt it,PetscBool *hapend,PetscReal *res)327: {
328: PetscScalar *hh,*cc,*ss,*rs;
329: PetscInt j;
330: PetscReal hapbnd;
331: KSP_PGMRES *pgmres = (KSP_PGMRES*)(ksp->data);
335: hh = HH(0,it); /* pointer to beginning of column to update */
336: cc = CC(0); /* beginning of cosine rotations */
337: ss = SS(0); /* beginning of sine rotations */
338: rs = RS(0); /* right hand side of least squares system */
340: /* The Hessenberg matrix is now correct through column it, save that form for possible spectral analysis */
341: for (j=0; j<=it+1; j++) *HES(j,it) = hh[j];
343: /* check for the happy breakdown */
344: hapbnd = PetscMin(PetscAbsScalar(hh[it+1] / rs[it]),pgmres->haptol);
345: if (PetscAbsScalar(hh[it+1]) < hapbnd) {
346: PetscInfo4(ksp,"Detected happy breakdown, current hapbnd = %14.12e H(%D,%D) = %14.12e\n",(double)hapbnd,it+1,it,(double)PetscAbsScalar(*HH(it+1,it)));
347: *hapend = PETSC_TRUE;
348: }
350: /* Apply all the previously computed plane rotations to the new column
351: of the Hessenberg matrix */
352: /* Note: this uses the rotation [conj(c) s ; -s c], c= cos(theta), s= sin(theta),
353: and some refs have [c s ; -conj(s) c] (don't be confused!) */
355: for (j=0; j<it; j++) {
356: PetscScalar hhj = hh[j];
357: hh[j] = PetscConj(cc[j])*hhj + ss[j]*hh[j+1];
358: hh[j+1] = -ss[j] *hhj + cc[j]*hh[j+1];
359: }
361: /*
362: compute the new plane rotation, and apply it to:
363: 1) the right-hand-side of the Hessenberg system (RS)
364: note: it affects RS(it) and RS(it+1)
365: 2) the new column of the Hessenberg matrix
366: note: it affects HH(it,it) which is currently pointed to
367: by hh and HH(it+1, it) (*(hh+1))
368: thus obtaining the updated value of the residual...
369: */
371: /* compute new plane rotation */
373: if (!*hapend) {
374: PetscReal delta = PetscSqrtReal(PetscSqr(PetscAbsScalar(hh[it])) + PetscSqr(PetscAbsScalar(hh[it+1])));
375: if (delta == 0.0) {
376: ksp->reason = KSP_DIVERGED_NULL;
377: return(0);
378: }
380: cc[it] = hh[it] / delta; /* new cosine value */
381: ss[it] = hh[it+1] / delta; /* new sine value */
383: hh[it] = PetscConj(cc[it])*hh[it] + ss[it]*hh[it+1];
384: rs[it+1] = -ss[it]*rs[it];
385: rs[it] = PetscConj(cc[it])*rs[it];
386: *res = PetscAbsScalar(rs[it+1]);
387: } else { /* happy breakdown: HH(it+1, it) = 0, therefore we don't need to apply
388: another rotation matrix (so RH doesn't change). The new residual is
389: always the new sine term times the residual from last time (RS(it)),
390: but now the new sine rotation would be zero...so the residual should
391: be zero...so we will multiply "zero" by the last residual. This might
392: not be exactly what we want to do here -could just return "zero". */
394: *res = 0.0;
395: }
396: return(0);
397: }
399: /*
400: KSPBuildSolution_PGMRES
402: Input Parameter:
403: . ksp - the Krylov space object
404: . ptr-
406: Output Parameter:
407: . result - the solution
409: Note: this calls KSPPGMRESBuildSoln - the same function that KSPPGMRESCycle
410: calls directly.
412: */
415: PetscErrorCode KSPBuildSolution_PGMRES(KSP ksp,Vec ptr,Vec *result)416: {
417: KSP_PGMRES *pgmres = (KSP_PGMRES*)ksp->data;
421: if (!ptr) {
422: if (!pgmres->sol_temp) {
423: VecDuplicate(ksp->vec_sol,&pgmres->sol_temp);
424: PetscLogObjectParent((PetscObject)ksp,(PetscObject)pgmres->sol_temp);
425: }
426: ptr = pgmres->sol_temp;
427: }
428: if (!pgmres->nrs) {
429: /* allocate the work area */
430: PetscMalloc1(pgmres->max_k,&pgmres->nrs);
431: PetscLogObjectMemory((PetscObject)ksp,pgmres->max_k*sizeof(PetscScalar));
432: }
434: KSPPGMRESBuildSoln(pgmres->nrs,ksp->vec_sol,ptr,ksp,pgmres->it);
435: if (result) *result = ptr;
436: return(0);
437: }
441: PetscErrorCode KSPSetFromOptions_PGMRES(PetscOptionItems *PetscOptionsObject,KSP ksp)442: {
446: KSPSetFromOptions_GMRES(PetscOptionsObject,ksp);
447: PetscOptionsHead(PetscOptionsObject,"KSP pipelined GMRES Options");
448: PetscOptionsTail();
449: return(0);
450: }
454: PetscErrorCode KSPReset_PGMRES(KSP ksp)455: {
459: KSPReset_GMRES(ksp);
460: return(0);
461: }
463: /*MC
464: KSPPGMRES - Implements the Pipelined Generalized Minimal Residual method.
466: Options Database Keys:
467: + -ksp_gmres_restart <restart> - the number of Krylov directions to orthogonalize against
468: . -ksp_gmres_haptol <tol> - sets the tolerance for "happy ending" (exact convergence)
469: . -ksp_gmres_preallocate - preallocate all the Krylov search directions initially (otherwise groups of
470: vectors are allocated as needed)
471: . -ksp_gmres_classicalgramschmidt - use classical (unmodified) Gram-Schmidt to orthogonalize against the Krylov space (fast) (the default)
472: . -ksp_gmres_modifiedgramschmidt - use modified Gram-Schmidt in the orthogonalization (more stable, but slower)
473: . -ksp_gmres_cgs_refinement_type <never,ifneeded,always> - determine if iterative refinement is used to increase the
474: stability of the classical Gram-Schmidt orthogonalization.
475: - -ksp_gmres_krylov_monitor - plot the Krylov space generated
477: Level: beginner
479: Notes:
480: MPI configuration may be necessary for reductions to make asynchronous progress, which is important for performance of pipelined methods.
481: See the FAQ on the PETSc website for details.
483: Reference:
484: Ghysels, Ashby, Meerbergen, Vanroose, Hiding global communication latencies in the GMRES algorithm on massively parallel machines, 2012.
486: Developer Notes: This object is subclassed off of KSPGMRES488: .seealso: KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPGMRES, KSPLGMRES, KSPPIPECG, KSPPIPECR,
489: KSPGMRESSetRestart(), KSPGMRESSetHapTol(), KSPGMRESSetPreAllocateVectors(), KSPGMRESSetOrthogonalization(), KSPGMRESGetOrthogonalization(),
490: KSPGMRESClassicalGramSchmidtOrthogonalization(), KSPGMRESModifiedGramSchmidtOrthogonalization(),
491: KSPGMRESCGSRefinementType, KSPGMRESSetCGSRefinementType(), KSPGMRESGetCGSRefinementType(), KSPGMRESMonitorKrylov()
492: M*/
496: PETSC_EXTERN PetscErrorCode KSPCreate_PGMRES(KSP ksp)497: {
498: KSP_PGMRES *pgmres;
502: PetscNewLog(ksp,&pgmres);
504: ksp->data = (void*)pgmres;
505: ksp->ops->buildsolution = KSPBuildSolution_PGMRES;
506: ksp->ops->setup = KSPSetUp_PGMRES;
507: ksp->ops->solve = KSPSolve_PGMRES;
508: ksp->ops->reset = KSPReset_PGMRES;
509: ksp->ops->destroy = KSPDestroy_PGMRES;
510: ksp->ops->view = KSPView_GMRES;
511: ksp->ops->setfromoptions = KSPSetFromOptions_PGMRES;
512: ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_GMRES;
513: ksp->ops->computeeigenvalues = KSPComputeEigenvalues_GMRES;
515: KSPSetSupportedNorm(ksp,KSP_NORM_PRECONDITIONED,PC_LEFT,3);
516: KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_RIGHT,2);
518: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetPreAllocateVectors_C",KSPGMRESSetPreAllocateVectors_GMRES);
519: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetOrthogonalization_C",KSPGMRESSetOrthogonalization_GMRES);
520: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetOrthogonalization_C",KSPGMRESGetOrthogonalization_GMRES);
521: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetRestart_C",KSPGMRESSetRestart_GMRES);
522: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetRestart_C",KSPGMRESGetRestart_GMRES);
523: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetCGSRefinementType_C",KSPGMRESSetCGSRefinementType_GMRES);
524: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetCGSRefinementType_C",KSPGMRESGetCGSRefinementType_GMRES);
526: pgmres->nextra_vecs = 1;
527: pgmres->haptol = 1.0e-30;
528: pgmres->q_preallocate = 0;
529: pgmres->delta_allocate = PGMRES_DELTA_DIRECTIONS;
530: pgmres->orthog = KSPGMRESClassicalGramSchmidtOrthogonalization;
531: pgmres->nrs = 0;
532: pgmres->sol_temp = 0;
533: pgmres->max_k = PGMRES_DEFAULT_MAXK;
534: pgmres->Rsvd = 0;
535: pgmres->orthogwork = 0;
536: pgmres->cgstype = KSP_GMRES_CGS_REFINE_NEVER;
537: return(0);
538: }