1: /*
2: Contributed by Patrick Sanan and Sascha M. Schnepp
3: */
5: #include <../src/ksp/ksp/impls/gmres/pipefgmres/pipefgmresimpl.h> 7: static PetscBool cited = PETSC_FALSE;
8: static const char citation[] =
9: "@article{SSM2016,\n"
10: " author = {P. Sanan and S.M. Schnepp and D.A. May},\n"
11: " title = {Pipelined, Flexible Krylov Subspace Methods},\n"
12: " journal = {SIAM Journal on Scientific Computing},\n"
13: " volume = {38},\n"
14: " number = {5},\n"
15: " pages = {C441-C470},\n"
16: " year = {2016},\n"
17: " doi = {10.1137/15M1049130},\n"
18: " URL = {http://dx.doi.org/10.1137/15M1049130},\n"
19: " eprint = {http://dx.doi.org/10.1137/15M1049130}\n"
20: "}\n";
22: #define PIPEFGMRES_DELTA_DIRECTIONS 10 23: #define PIPEFGMRES_DEFAULT_MAXK 30 25: static PetscErrorCode KSPPIPEFGMRESGetNewVectors(KSP,PetscInt);
26: static PetscErrorCode KSPPIPEFGMRESUpdateHessenberg(KSP,PetscInt,PetscBool*,PetscReal*);
27: static PetscErrorCode KSPPIPEFGMRESBuildSoln(PetscScalar*,Vec,Vec,KSP,PetscInt);
28: extern PetscErrorCode KSPReset_PIPEFGMRES(KSP);
30: /*
32: KSPSetUp_PIPEFGMRES - Sets up the workspace needed by pipefgmres.
34: This is called once, usually automatically by KSPSolve() or KSPSetUp(),
35: but can be called directly by KSPSetUp().
37: */
38: static PetscErrorCode KSPSetUp_PIPEFGMRES(KSP ksp) 39: {
41: PetscInt k;
42: KSP_PIPEFGMRES *pipefgmres = (KSP_PIPEFGMRES*)ksp->data;
43: const PetscInt max_k = pipefgmres->max_k;
46: KSPSetUp_GMRES(ksp);
48: PetscMalloc1((VEC_OFFSET+max_k),&pipefgmres->prevecs);
49: PetscMalloc1((VEC_OFFSET+max_k),&pipefgmres->prevecs_user_work);
50: PetscLogObjectMemory((PetscObject)ksp,(VEC_OFFSET+max_k)*(2*sizeof(void*)));
52: KSPCreateVecs(ksp,pipefgmres->vv_allocated,&pipefgmres->prevecs_user_work[0],0,NULL);
53: PetscLogObjectParents(ksp,pipefgmres->vv_allocated,pipefgmres->prevecs_user_work[0]);
54: for (k=0; k < pipefgmres->vv_allocated; k++) {
55: pipefgmres->prevecs[k] = pipefgmres->prevecs_user_work[0][k];
56: }
58: PetscMalloc1((VEC_OFFSET+max_k),&pipefgmres->zvecs);
59: PetscMalloc1((VEC_OFFSET+max_k),&pipefgmres->zvecs_user_work);
60: PetscLogObjectMemory((PetscObject)ksp,(VEC_OFFSET+max_k)*(2*sizeof(void*)));
62: PetscMalloc1((VEC_OFFSET+max_k),&pipefgmres->redux);
63: PetscLogObjectMemory((PetscObject)ksp,(VEC_OFFSET+max_k)*(sizeof(void*)));
65: KSPCreateVecs(ksp,pipefgmres->vv_allocated,&pipefgmres->zvecs_user_work[0],0,NULL);
66: PetscLogObjectParents(ksp,pipefgmres->vv_allocated,pipefgmres->zvecs_user_work[0]);
67: for (k=0; k < pipefgmres->vv_allocated; k++) {
68: pipefgmres->zvecs[k] = pipefgmres->zvecs_user_work[0][k];
69: }
71: return(0);
72: }
74: /*
76: KSPPIPEFGMRESCycle - Run pipefgmres, possibly with restart. Return residual
77: history if requested.
79: input parameters:
80: . pipefgmres - structure containing parameters and work areas
82: output parameters:
83: . itcount - number of iterations used. If null, ignored.
84: . converged - 0 if not converged
86: Notes:
87: On entry, the value in vector VEC_VV(0) should be
88: the initial residual.
91: */
93: static PetscErrorCode KSPPIPEFGMRESCycle(PetscInt *itcount,KSP ksp) 94: {
95: KSP_PIPEFGMRES *pipefgmres = (KSP_PIPEFGMRES*)(ksp->data);
96: PetscReal res_norm;
97: PetscReal hapbnd,tt;
98: PetscScalar *hh,*hes,*lhh,shift = pipefgmres->shift;
99: PetscBool hapend = PETSC_FALSE; /* indicates happy breakdown ending */
101: PetscInt loc_it; /* local count of # of dir. in Krylov space */
102: PetscInt max_k = pipefgmres->max_k; /* max # of directions Krylov space */
103: PetscInt i,j,k;
104: Mat Amat,Pmat;
105: Vec Q,W; /* Pipelining vectors */
106: Vec *redux = pipefgmres->redux; /* workspace for single reduction */
109: if (itcount) *itcount = 0;
111: /* Assign simpler names to these vectors, allocated as pipelining workspace */
112: Q = VEC_Q;
113: W = VEC_W;
115: /* Allocate memory for orthogonalization work (freed in the GMRES Destroy routine)*/
116: /* Note that we add an extra value here to allow for a single reduction */
117: if (!pipefgmres->orthogwork) { PetscMalloc1(pipefgmres->max_k + 2 ,&pipefgmres->orthogwork);
118: }
119: lhh = pipefgmres->orthogwork;
121: /* Number of pseudo iterations since last restart is the number
122: of prestart directions */
123: loc_it = 0;
125: /* note: (pipefgmres->it) is always set one less than (loc_it) It is used in
126: KSPBUILDSolution_PIPEFGMRES, where it is passed to KSPPIPEFGMRESBuildSoln.
127: Note that when KSPPIPEFGMRESBuildSoln is called from this function,
128: (loc_it -1) is passed, so the two are equivalent */
129: pipefgmres->it = (loc_it - 1);
131: /* initial residual is in VEC_VV(0) - compute its norm*/
132: VecNorm(VEC_VV(0),NORM_2,&res_norm);
134: /* first entry in right-hand-side of hessenberg system is just
135: the initial residual norm */
136: *RS(0) = res_norm;
138: ksp->rnorm = res_norm;
139: KSPLogResidualHistory(ksp,res_norm);
140: KSPMonitor(ksp,ksp->its,res_norm);
142: /* check for the convergence - maybe the current guess is good enough */
143: (*ksp->converged)(ksp,ksp->its,res_norm,&ksp->reason,ksp->cnvP);
144: if (ksp->reason) {
145: if (itcount) *itcount = 0;
146: return(0);
147: }
149: /* scale VEC_VV (the initial residual) */
150: VecScale(VEC_VV(0),1.0/res_norm);
152: /* Fill the pipeline */
153: KSP_PCApply(ksp,VEC_VV(loc_it),PREVEC(loc_it));
154: PCGetOperators(ksp->pc,&Amat,&Pmat);
155: KSP_MatMult(ksp,Amat,PREVEC(loc_it),ZVEC(loc_it));
156: VecAXPY(ZVEC(loc_it),-shift,VEC_VV(loc_it)); /* Note shift */
158: /* MAIN ITERATION LOOP BEGINNING*/
159: /* keep iterating until we have converged OR generated the max number
160: of directions OR reached the max number of iterations for the method */
161: while (!ksp->reason && loc_it < max_k && ksp->its < ksp->max_it) {
162: if (loc_it) {
163: KSPLogResidualHistory(ksp,res_norm);
164: KSPMonitor(ksp,ksp->its,res_norm);
165: }
166: pipefgmres->it = (loc_it - 1);
168: /* see if more space is needed for work vectors */
169: if (pipefgmres->vv_allocated <= loc_it + VEC_OFFSET + 1) {
170: KSPPIPEFGMRESGetNewVectors(ksp,loc_it+1);
171: /* (loc_it+1) is passed in as number of the first vector that should
172: be allocated */
173: }
175: /* Note that these inner products are with "Z" now, so
176: in particular, lhh[loc_it] is the 'barred' or 'shifted' value,
177: not the value from the equivalent FGMRES run (even in exact arithmetic)
178: That is, the H we need for the Arnoldi relation is different from the
179: coefficients we use in the orthogonalization process,because of the shift */
181: /* Do some local twiddling to allow for a single reduction */
182: for(i=0;i<loc_it+1;i++){
183: redux[i] = VEC_VV(i);
184: }
185: redux[loc_it+1] = ZVEC(loc_it);
187: /* note the extra dot product which ends up in lh[loc_it+1], which computes ||z||^2 */
188: VecMDotBegin(ZVEC(loc_it),loc_it+2,redux,lhh);
190: /* Start the split reduction (This actually calls the MPI_Iallreduce, otherwise, the reduction is simply delayed until the "end" call)*/
191: PetscCommSplitReductionBegin(PetscObjectComm((PetscObject)ZVEC(loc_it)));
193: /* The work to be overlapped with the inner products follows.
194: This is application of the preconditioner and the operator
195: to compute intermediate quantites which will be combined (locally)
196: with the results of the inner products.
197: */
198: KSP_PCApply(ksp,ZVEC(loc_it),Q);
199: PCGetOperators(ksp->pc,&Amat,&Pmat);
200: KSP_MatMult(ksp,Amat,Q,W);
202: /* Compute inner products of the new direction with previous directions,
203: and the norm of the to-be-orthogonalized direction "Z".
204: This information is enough to build the required entries
205: of H. The inner product with VEC_VV(it_loc) is
206: *different* than in the standard FGMRES and need to be dealt with specially.
207: That is, for standard FGMRES the orthogonalization coefficients are the same
208: as the coefficients used in the Arnoldi relation to reconstruct, but here this
209: is not true (albeit only for the one entry of H which we "unshift" below. */
211: /* Finish the dot product, retrieving the extra entry */
212: VecMDotEnd(ZVEC(loc_it),loc_it+2,redux,lhh);
213: tt = PetscRealPart(lhh[loc_it+1]);
215: /* Hessenberg entries, and entries for (naive) classical Graham-Schmidt
216: Note that the Hessenberg entries require a shift, as these are for the
217: relation AU = VH, which is wrt unshifted basis vectors */
218: hh = HH(0,loc_it); hes=HES(0,loc_it);
219: for (j=0; j<loc_it; j++) {
220: hh[j] = lhh[j];
221: hes[j] = lhh[j];
222: }
223: hh[loc_it] = lhh[loc_it] + shift;
224: hes[loc_it] = lhh[loc_it] + shift;
226: /* we delay applying the shift here */
227: for (j=0; j<=loc_it; j++) {
228: lhh[j] = -lhh[j]; /* flip sign */
229: }
231: /* Compute the norm of the un-normalized new direction using the rearranged formula
232: Note that these are shifted ("barred") quantities */
233: for(k=0;k<=loc_it;k++) tt -= ((PetscReal)(PetscAbsScalar(lhh[k]) * PetscAbsScalar(lhh[k])));
234: /* On AVX512 this is accumulating roundoff errors for eg: tt=-2.22045e-16 */
235: if ((tt < 0.0) && tt > -PETSC_SMALL) tt = 0.0 ;
236: if (tt < 0.0) {
237: /* If we detect square root breakdown in the norm, we must restart the algorithm.
238: Here this means we simply break the current loop and reconstruct the solution
239: using the basis we have computed thus far. Note that by breaking immediately,
240: we do not update the iteration count, so computation done in this iteration
241: should be disregarded.
242: */
243: PetscInfo2(ksp,"Restart due to square root breakdown at it = %D, tt=%g\n",ksp->its,(double)tt);
244: break;
245: } else {
246: tt = PetscSqrtReal(tt);
247: }
249: /* new entry in hessenburg is the 2-norm of our new direction */
250: hh[loc_it+1] = tt;
251: hes[loc_it+1] = tt;
253: /* The recurred computation for the new direction
254: The division by tt is delayed to the happy breakdown check later
255: Note placement BEFORE the unshift
256: */
257: VecCopy(ZVEC(loc_it),VEC_VV(loc_it+1));
258: VecMAXPY(VEC_VV(loc_it+1),loc_it+1,lhh,&VEC_VV(0));
259: /* (VEC_VV(loc_it+1) is not normalized yet) */
261: /* The recurred computation for the preconditioned vector (u) */
262: VecCopy(Q,PREVEC(loc_it+1));
263: VecMAXPY(PREVEC(loc_it+1),loc_it+1,lhh,&PREVEC(0));
264: VecScale(PREVEC(loc_it+1),1.0/tt);
266: /* Unshift an entry in the GS coefficients ("removing the bar") */
267: lhh[loc_it] -= shift;
269: /* The recurred computation for z (Au)
270: Note placement AFTER the "unshift" */
271: VecCopy(W,ZVEC(loc_it+1));
272: VecMAXPY(ZVEC(loc_it+1),loc_it+1,lhh,&ZVEC(0));
273: VecScale(ZVEC(loc_it+1),1.0/tt);
275: /* Happy Breakdown Check */
276: hapbnd = PetscAbsScalar((tt) / *RS(loc_it));
277: /* RS(loc_it) contains the res_norm from the last iteration */
278: hapbnd = PetscMin(pipefgmres->haptol,hapbnd);
279: if (tt > hapbnd) {
280: /* scale new direction by its norm */
281: VecScale(VEC_VV(loc_it+1),1.0/tt);
282: } else {
283: /* This happens when the solution is exactly reached. */
284: /* So there is no new direction... */
285: VecSet(VEC_TEMP,0.0); /* set VEC_TEMP to 0 */
286: hapend = PETSC_TRUE;
287: }
288: /* note that for pipefgmres we could get HES(loc_it+1, loc_it) = 0 and the
289: current solution would not be exact if HES was singular. Note that
290: HH non-singular implies that HES is not singular, and HES is guaranteed
291: to be nonsingular when PREVECS are linearly independent and A is
292: nonsingular (in GMRES, the nonsingularity of A implies the nonsingularity
293: of HES). So we should really add a check to verify that HES is nonsingular.*/
295: /* Note that to be thorough, in debug mode, one could call a LAPACK routine
296: here to check that the hessenberg matrix is indeed non-singular (since
297: FGMRES does not guarantee this) */
299: /* Now apply rotations to new col of hessenberg (and right side of system),
300: calculate new rotation, and get new residual norm at the same time*/
301: KSPPIPEFGMRESUpdateHessenberg(ksp,loc_it,&hapend,&res_norm);
302: if (ksp->reason) break;
304: loc_it++;
305: pipefgmres->it = (loc_it-1); /* Add this here in case it has converged */
307: PetscObjectSAWsTakeAccess((PetscObject)ksp);
308: ksp->its++;
309: ksp->rnorm = res_norm;
310: PetscObjectSAWsGrantAccess((PetscObject)ksp);
312: (*ksp->converged)(ksp,ksp->its,res_norm,&ksp->reason,ksp->cnvP);
314: /* Catch error in happy breakdown and signal convergence and break from loop */
315: if (hapend) {
316: if (!ksp->reason) {
317: 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_norm);
318: else {
319: ksp->reason = KSP_DIVERGED_BREAKDOWN;
320: break;
321: }
322: }
323: }
324: }
325: /* END OF ITERATION LOOP */
326: KSPLogResidualHistory(ksp,res_norm);
328: /*
329: Monitor if we know that we will not return for a restart */
330: if (loc_it && (ksp->reason || ksp->its >= ksp->max_it)) {
331: KSPMonitor(ksp,ksp->its,res_norm);
332: }
334: if (itcount) *itcount = loc_it;
336: /*
337: Down here we have to solve for the "best" coefficients of the Krylov
338: columns, add the solution values together, and possibly unwind the
339: preconditioning from the solution
340: */
342: /* Form the solution (or the solution so far) */
343: /* Note: must pass in (loc_it-1) for iteration count so that KSPPIPEGMRESIIBuildSoln
344: properly navigates */
346: KSPPIPEFGMRESBuildSoln(RS(0),ksp->vec_sol,ksp->vec_sol,ksp,loc_it-1);
348: return(0);
349: }
351: /*
352: KSPSolve_PIPEFGMRES - This routine applies the PIPEFGMRES method.
355: Input Parameter:
356: . ksp - the Krylov space object that was set to use pipefgmres
358: Output Parameter:
359: . outits - number of iterations used
361: */
362: static PetscErrorCode KSPSolve_PIPEFGMRES(KSP ksp)363: {
365: PetscInt its,itcount;
366: KSP_PIPEFGMRES *pipefgmres = (KSP_PIPEFGMRES*)ksp->data;
367: PetscBool guess_zero = ksp->guess_zero;
371: /* We have not checked these routines for use with complex numbers. The inner products
372: are likely not defined correctly for that case */
373: #if (defined(PETSC_USE_COMPLEX) && !defined(PETSC_SKIP_COMPLEX))
374: SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"PIPEFGMRES has not been implemented for use with complex scalars");
375: #endif
377: PetscCitationsRegister(citation,&cited);
379: if (ksp->calc_sings && !pipefgmres->Rsvd) SETERRQ(PetscObjectComm((PetscObject)ksp),PETSC_ERR_ORDER,"Must call KSPSetComputeSingularValues() before KSPSetUp() is called");
380: PetscObjectSAWsTakeAccess((PetscObject)ksp);
381: ksp->its = 0;
382: PetscObjectSAWsGrantAccess((PetscObject)ksp);
384: itcount = 0;
385: ksp->reason = KSP_CONVERGED_ITERATING;
386: while (!ksp->reason) {
387: KSPInitialResidual(ksp,ksp->vec_sol,VEC_TEMP,VEC_TEMP_MATOP,VEC_VV(0),ksp->vec_rhs);
388: KSPPIPEFGMRESCycle(&its,ksp);
389: itcount += its;
390: if (itcount >= ksp->max_it) {
391: if (!ksp->reason) ksp->reason = KSP_DIVERGED_ITS;
392: break;
393: }
394: ksp->guess_zero = PETSC_FALSE; /* every future call to KSPInitialResidual() will have nonzero guess */
395: }
396: ksp->guess_zero = guess_zero; /* restore if user provided nonzero initial guess */
397: return(0);
398: }
400: static PetscErrorCode KSPDestroy_PIPEFGMRES(KSP ksp)401: {
405: KSPReset_PIPEFGMRES(ksp);
406: KSPDestroy_GMRES(ksp);
407: return(0);
408: }
410: /*
411: KSPPIPEFGMRESBuildSoln - create the solution from the starting vector and the
412: current iterates.
414: Input parameters:
415: nrs - work area of size it + 1.
416: vguess - index of initial guess
417: vdest - index of result. Note that vguess may == vdest (replace
418: guess with the solution).
419: it - HH upper triangular part is a block of size (it+1) x (it+1)
421: This is an internal routine that knows about the PIPEFGMRES internals.
422: */
423: static PetscErrorCode KSPPIPEFGMRESBuildSoln(PetscScalar *nrs,Vec vguess,Vec vdest,KSP ksp,PetscInt it)424: {
425: PetscScalar tt;
427: PetscInt k,j;
428: KSP_PIPEFGMRES *pipefgmres = (KSP_PIPEFGMRES*)(ksp->data);
431: /* Solve for solution vector that minimizes the residual */
433: if (it < 0) { /* no pipefgmres steps have been performed */
434: VecCopy(vguess,vdest); /* VecCopy() is smart, exits immediately if vguess == vdest */
435: return(0);
436: }
438: /* solve the upper triangular system - RS is the right side and HH is
439: the upper triangular matrix - put soln in nrs */
440: if (*HH(it,it) != 0.0) nrs[it] = *RS(it) / *HH(it,it);
441: else nrs[it] = 0.0;
443: for (k=it-1; k>=0; k--) {
444: tt = *RS(k);
445: for (j=k+1; j<=it; j++) tt -= *HH(k,j) * nrs[j];
446: nrs[k] = tt / *HH(k,k);
447: }
449: /* Accumulate the correction to the solution of the preconditioned problem in VEC_TEMP */
450: VecZeroEntries(VEC_TEMP);
451: VecMAXPY(VEC_TEMP,it+1,nrs,&PREVEC(0));
453: /* add solution to previous solution */
454: if (vdest == vguess) {
455: VecAXPY(vdest,1.0,VEC_TEMP);
456: } else {
457: VecWAXPY(vdest,1.0,VEC_TEMP,vguess);
458: }
459: return(0);
460: }
462: /*
464: KSPPIPEFGMRESUpdateHessenberg - Do the scalar work for the orthogonalization.
465: Return new residual.
467: input parameters:
469: . ksp - Krylov space object
470: . it - plane rotations are applied to the (it+1)th column of the
471: modified hessenberg (i.e. HH(:,it))
472: . hapend - PETSC_FALSE not happy breakdown ending.
474: output parameters:
475: . res - the new residual
477: */
478: /*
479: . it - column of the Hessenberg that is complete, PIPEFGMRES is actually computing two columns ahead of this
480: */
481: static PetscErrorCode KSPPIPEFGMRESUpdateHessenberg(KSP ksp,PetscInt it,PetscBool *hapend,PetscReal *res)482: {
483: PetscScalar *hh,*cc,*ss,*rs;
484: PetscInt j;
485: PetscReal hapbnd;
486: KSP_PIPEFGMRES *pipefgmres = (KSP_PIPEFGMRES*)(ksp->data);
490: hh = HH(0,it); /* pointer to beginning of column to update */
491: cc = CC(0); /* beginning of cosine rotations */
492: ss = SS(0); /* beginning of sine rotations */
493: rs = RS(0); /* right hand side of least squares system */
495: /* The Hessenberg matrix is now correct through column it, save that form for possible spectral analysis */
496: for (j=0; j<=it+1; j++) *HES(j,it) = hh[j];
498: /* check for the happy breakdown */
499: hapbnd = PetscMin(PetscAbsScalar(hh[it+1] / rs[it]),pipefgmres->haptol);
500: if (PetscAbsScalar(hh[it+1]) < hapbnd) {
501: 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)));
502: *hapend = PETSC_TRUE;
503: }
505: /* Apply all the previously computed plane rotations to the new column
506: of the Hessenberg matrix */
507: /* Note: this uses the rotation [conj(c) s ; -s c], c= cos(theta), s= sin(theta),
508: and some refs have [c s ; -conj(s) c] (don't be confused!) */
510: for (j=0; j<it; j++) {
511: PetscScalar hhj = hh[j];
512: hh[j] = PetscConj(cc[j])*hhj + ss[j]*hh[j+1];
513: hh[j+1] = -ss[j] *hhj + cc[j]*hh[j+1];
514: }
516: /*
517: compute the new plane rotation, and apply it to:
518: 1) the right-hand-side of the Hessenberg system (RS)
519: note: it affects RS(it) and RS(it+1)
520: 2) the new column of the Hessenberg matrix
521: note: it affects HH(it,it) which is currently pointed to
522: by hh and HH(it+1, it) (*(hh+1))
523: thus obtaining the updated value of the residual...
524: */
526: /* compute new plane rotation */
528: if (!*hapend) {
529: PetscReal delta = PetscSqrtReal(PetscSqr(PetscAbsScalar(hh[it])) + PetscSqr(PetscAbsScalar(hh[it+1])));
530: if (delta == 0.0) {
531: ksp->reason = KSP_DIVERGED_NULL;
532: return(0);
533: }
535: cc[it] = hh[it] / delta; /* new cosine value */
536: ss[it] = hh[it+1] / delta; /* new sine value */
538: hh[it] = PetscConj(cc[it])*hh[it] + ss[it]*hh[it+1];
539: rs[it+1] = -ss[it]*rs[it];
540: rs[it] = PetscConj(cc[it])*rs[it];
541: *res = PetscAbsScalar(rs[it+1]);
542: } else { /* happy breakdown: HH(it+1, it) = 0, therefore we don't need to apply
543: another rotation matrix (so RH doesn't change). The new residual is
544: always the new sine term times the residual from last time (RS(it)),
545: but now the new sine rotation would be zero...so the residual should
546: be zero...so we will multiply "zero" by the last residual. This might
547: not be exactly what we want to do here -could just return "zero". */
549: *res = 0.0;
550: }
551: return(0);
552: }
554: /*
555: KSPBuildSolution_PIPEFGMRES
557: Input Parameter:
558: . ksp - the Krylov space object
559: . ptr-
561: Output Parameter:
562: . result - the solution
564: Note: this calls KSPPIPEFGMRESBuildSoln - the same function that KSPPIPEFGMRESCycle
565: calls directly.
567: */
568: PetscErrorCode KSPBuildSolution_PIPEFGMRES(KSP ksp,Vec ptr,Vec *result)569: {
570: KSP_PIPEFGMRES *pipefgmres = (KSP_PIPEFGMRES*)ksp->data;
574: if (!ptr) {
575: if (!pipefgmres->sol_temp) {
576: VecDuplicate(ksp->vec_sol,&pipefgmres->sol_temp);
577: PetscLogObjectParent((PetscObject)ksp,(PetscObject)pipefgmres->sol_temp);
578: }
579: ptr = pipefgmres->sol_temp;
580: }
581: if (!pipefgmres->nrs) {
582: /* allocate the work area */
583: PetscMalloc1(pipefgmres->max_k,&pipefgmres->nrs);
584: PetscLogObjectMemory((PetscObject)ksp,pipefgmres->max_k*sizeof(PetscScalar));
585: }
587: KSPPIPEFGMRESBuildSoln(pipefgmres->nrs,ksp->vec_sol,ptr,ksp,pipefgmres->it);
588: if (result) *result = ptr;
589: return(0);
590: }
592: PetscErrorCode KSPSetFromOptions_PIPEFGMRES(PetscOptionItems *PetscOptionsObject,KSP ksp)593: {
595: KSP_PIPEFGMRES *pipefgmres = (KSP_PIPEFGMRES*)ksp->data;
596: PetscBool flg;
597: PetscScalar shift;
600: KSPSetFromOptions_GMRES(PetscOptionsObject,ksp);
601: PetscOptionsHead(PetscOptionsObject,"KSP pipelined FGMRES Options");
602: PetscOptionsScalar("-ksp_pipefgmres_shift","shift parameter","KSPPIPEFGMRESSetShift",pipefgmres->shift,&shift,&flg);
603: if (flg) { KSPPIPEFGMRESSetShift(ksp,shift); }
604: PetscOptionsTail();
605: return(0);
606: }
608: PetscErrorCode KSPView_PIPEFGMRES(KSP ksp,PetscViewer viewer)609: {
610: KSP_PIPEFGMRES *pipefgmres = (KSP_PIPEFGMRES*)ksp->data;
612: PetscBool iascii,isstring;
615: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
616: PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERSTRING,&isstring);
618: if (iascii) {
619: PetscViewerASCIIPrintf(viewer," restart=%D\n",pipefgmres->max_k);
620: PetscViewerASCIIPrintf(viewer," happy breakdown tolerance %g\n",(double)pipefgmres->haptol);
621: #if defined(PETSC_USE_COMPLEX)
622: PetscViewerASCIIPrintf(viewer," shift=%g+%gi\n",PetscRealPart(pipefgmres->shift),PetscImaginaryPart(pipefgmres->shift));
623: #else
624: PetscViewerASCIIPrintf(viewer," shift=%g\n",pipefgmres->shift);
625: #endif
626: } else if (isstring) {
627: PetscViewerStringSPrintf(viewer,"restart %D",pipefgmres->max_k);
628: #if defined(PETSC_USE_COMPLEX)
629: PetscViewerStringSPrintf(viewer," shift=%g+%gi\n",PetscRealPart(pipefgmres->shift),PetscImaginaryPart(pipefgmres->shift));
630: #else
631: PetscViewerStringSPrintf(viewer," shift=%g\n",pipefgmres->shift);
632: #endif
633: }
634: return(0);
635: }
637: PetscErrorCode KSPReset_PIPEFGMRES(KSP ksp)638: {
639: KSP_PIPEFGMRES *pipefgmres = (KSP_PIPEFGMRES*)ksp->data;
640: PetscErrorCode ierr;
641: PetscInt i;
644: PetscFree(pipefgmres->prevecs);
645: PetscFree(pipefgmres->zvecs);
646: for (i=0; i<pipefgmres->nwork_alloc; i++) {
647: VecDestroyVecs(pipefgmres->mwork_alloc[i],&pipefgmres->prevecs_user_work[i]);
648: VecDestroyVecs(pipefgmres->mwork_alloc[i],&pipefgmres->zvecs_user_work[i]);
649: }
650: PetscFree(pipefgmres->prevecs_user_work);
651: PetscFree(pipefgmres->zvecs_user_work);
652: PetscFree(pipefgmres->redux);
653: KSPReset_GMRES(ksp);
654: return(0);
655: }
657: /*MC
658: KSPPIPEFGMRES - Implements the Pipelined Generalized Minimal Residual method.
660: A flexible, 1-stage pipelined variant of GMRES.
662: Options Database Keys:
663: + -ksp_gmres_restart <restart> - the number of Krylov directions to orthogonalize against
664: . -ksp_gmres_haptol <tol> - sets the tolerance for "happy ending" (exact convergence)
665: . -ksp_gmres_preallocate - preallocate all the Krylov search directions initially (otherwise groups of
666: . -ksp_pipefgmres_shift - the shift to use (defaults to 1. See KSPPIPEFGMRESSetShift()
667: vectors are allocated as needed)
668: - -ksp_gmres_krylov_monitor - plot the Krylov space generated
671: Level: intermediate
673: Notes:
675: This variant is not "explicitly normalized" like KSPPGMRES, and requires a shift parameter.
677: A heuristic for choosing the shift parameter is the largest eigenvalue of the preconditioned operator.
679: Only right preconditioning is supported (but this preconditioner may be nonlinear/variable/inexact, as with KSPFGMRES).
680: MPI configuration may be necessary for reductions to make asynchronous progress, which is important for performance of pipelined methods.
681: See the FAQ on the PETSc website for details.
683: Developer Notes:
684: This class is subclassed off of KSPGMRES.
686: Reference:
687: P. Sanan, S.M. Schnepp, and D.A. May,
688: "Pipelined, Flexible Krylov Subspace Methods,"
689: SIAM Journal on Scientific Computing 2016 38:5, C441-C470,
690: DOI: 10.1137/15M1049130
692: .seealso: KSPCreate(), KSPSetType(), KSPType (for list of available types), KSP, KSPLGMRES, KSPPIPECG, KSPPIPECR, KSPPGMRES, KSPFGMRES693: KSPGMRESSetRestart(), KSPGMRESSetHapTol(), KSPGMRESSetPreAllocateVectors(), KSPGMRESMonitorKrylov(), KSPPIPEFGMRESSetShift()
694: M*/
696: PETSC_EXTERN PetscErrorCode KSPCreate_PIPEFGMRES(KSP ksp)697: {
698: KSP_PIPEFGMRES *pipefgmres;
702: PetscNewLog(ksp,&pipefgmres);
704: ksp->data = (void*)pipefgmres;
705: ksp->ops->buildsolution = KSPBuildSolution_PIPEFGMRES;
706: ksp->ops->setup = KSPSetUp_PIPEFGMRES;
707: ksp->ops->solve = KSPSolve_PIPEFGMRES;
708: ksp->ops->reset = KSPReset_PIPEFGMRES;
709: ksp->ops->destroy = KSPDestroy_PIPEFGMRES;
710: ksp->ops->view = KSPView_PIPEFGMRES;
711: ksp->ops->setfromoptions = KSPSetFromOptions_PIPEFGMRES;
712: ksp->ops->computeextremesingularvalues = KSPComputeExtremeSingularValues_GMRES;
713: ksp->ops->computeeigenvalues = KSPComputeEigenvalues_GMRES;
715: KSPSetSupportedNorm(ksp,KSP_NORM_UNPRECONDITIONED,PC_RIGHT,3);
717: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetPreAllocateVectors_C",KSPGMRESSetPreAllocateVectors_GMRES);
718: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetRestart_C",KSPGMRESSetRestart_GMRES);
719: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetRestart_C",KSPGMRESGetRestart_GMRES);
721: pipefgmres->nextra_vecs = 1;
722: pipefgmres->haptol = 1.0e-30;
723: pipefgmres->q_preallocate = 0;
724: pipefgmres->delta_allocate = PIPEFGMRES_DELTA_DIRECTIONS;
725: pipefgmres->orthog = 0;
726: pipefgmres->nrs = 0;
727: pipefgmres->sol_temp = 0;
728: pipefgmres->max_k = PIPEFGMRES_DEFAULT_MAXK;
729: pipefgmres->Rsvd = 0;
730: pipefgmres->orthogwork = 0;
731: pipefgmres->cgstype = KSP_GMRES_CGS_REFINE_NEVER;
732: pipefgmres->shift = 1.0;
733: return(0);
734: }
736: static PetscErrorCode KSPPIPEFGMRESGetNewVectors(KSP ksp,PetscInt it)737: {
738: KSP_PIPEFGMRES *pipefgmres = (KSP_PIPEFGMRES*)ksp->data;
739: PetscInt nwork = pipefgmres->nwork_alloc; /* number of work vector chunks allocated */
740: PetscInt nalloc; /* number to allocate */
742: PetscInt k;
745: nalloc = pipefgmres->delta_allocate; /* number of vectors to allocate
746: in a single chunk */
748: /* Adjust the number to allocate to make sure that we don't exceed the
749: number of available slots (pipefgmres->vecs_allocated)*/
750: if (it + VEC_OFFSET + nalloc >= pipefgmres->vecs_allocated) {
751: nalloc = pipefgmres->vecs_allocated - it - VEC_OFFSET;
752: }
753: if (!nalloc) return(0);
755: pipefgmres->vv_allocated += nalloc; /* vv_allocated is the number of vectors allocated */
757: /* work vectors */
758: KSPCreateVecs(ksp,nalloc,&pipefgmres->user_work[nwork],0,NULL);
759: PetscLogObjectParents(ksp,nalloc,pipefgmres->user_work[nwork]);
760: for (k=0; k < nalloc; k++) {
761: pipefgmres->vecs[it+VEC_OFFSET+k] = pipefgmres->user_work[nwork][k];
762: }
763: /* specify size of chunk allocated */
764: pipefgmres->mwork_alloc[nwork] = nalloc;
766: /* preconditioned vectors (note we don't use VEC_OFFSET) */
767: KSPCreateVecs(ksp,nalloc,&pipefgmres->prevecs_user_work[nwork],0,NULL);
768: PetscLogObjectParents(ksp,nalloc,pipefgmres->prevecs_user_work[nwork]);
769: for (k=0; k < nalloc; k++) {
770: pipefgmres->prevecs[it+k] = pipefgmres->prevecs_user_work[nwork][k];
771: }
773: KSPCreateVecs(ksp,nalloc,&pipefgmres->zvecs_user_work[nwork],0,NULL);
774: PetscLogObjectParents(ksp,nalloc,pipefgmres->zvecs_user_work[nwork]);
775: for (k=0; k < nalloc; k++) {
776: pipefgmres->zvecs[it+k] = pipefgmres->zvecs_user_work[nwork][k];
777: }
779: /* increment the number of work vector chunks */
780: pipefgmres->nwork_alloc++;
781: return(0);
782: }
783: /*@
784: KSPPIPEFGMRESSetShift - Set the shift parameter for the flexible, pipelined GMRES solver.
786: A heuristic is to set this to be comparable to the largest eigenvalue of the preconditioned operator. This can be acheived with PETSc itself by using a few iterations of a Krylov method. See KSPComputeEigenvalues (and note the caveats there).
788: Logically Collective on KSP790: Input Parameters:
791: + ksp - the Krylov space context
792: - shift - the shift
794: Level: intermediate
796: Options Database:
797: . -ksp_pipefgmres_shift <shift>
799: .seealso: KSPComputeEigenvalues()
800: @*/
801: PetscErrorCodeKSPPIPEFGMRESSetShift(KSP ksp,PetscScalar shift)802: {
803: KSP_PIPEFGMRES *pipefgmres = (KSP_PIPEFGMRES*)ksp->data;
808: pipefgmres->shift = shift;
809: return(0);
810: }