Actual source code: pipefgmres.c
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: */
92: static PetscErrorCode KSPPIPEFGMRESCycle(PetscInt *itcount,KSP ksp)
93: {
94: KSP_PIPEFGMRES *pipefgmres = (KSP_PIPEFGMRES*)(ksp->data);
95: PetscReal res_norm;
96: PetscReal hapbnd,tt;
97: PetscScalar *hh,*hes,*lhh,shift = pipefgmres->shift;
98: PetscBool hapend = PETSC_FALSE; /* indicates happy breakdown ending */
100: PetscInt loc_it; /* local count of # of dir. in Krylov space */
101: PetscInt max_k = pipefgmres->max_k; /* max # of directions Krylov space */
102: PetscInt i,j,k;
103: Mat Amat,Pmat;
104: Vec Q,W; /* Pipelining vectors */
105: Vec *redux = pipefgmres->redux; /* workspace for single reduction */
108: if (itcount) *itcount = 0;
110: /* Assign simpler names to these vectors, allocated as pipelining workspace */
111: Q = VEC_Q;
112: W = VEC_W;
114: /* Allocate memory for orthogonalization work (freed in the GMRES Destroy routine)*/
115: /* Note that we add an extra value here to allow for a single reduction */
116: if (!pipefgmres->orthogwork) { PetscMalloc1(pipefgmres->max_k + 2 ,&pipefgmres->orthogwork);
117: }
118: lhh = pipefgmres->orthogwork;
120: /* Number of pseudo iterations since last restart is the number
121: of prestart directions */
122: loc_it = 0;
124: /* note: (pipefgmres->it) is always set one less than (loc_it) It is used in
125: KSPBUILDSolution_PIPEFGMRES, where it is passed to KSPPIPEFGMRESBuildSoln.
126: Note that when KSPPIPEFGMRESBuildSoln is called from this function,
127: (loc_it -1) is passed, so the two are equivalent */
128: pipefgmres->it = (loc_it - 1);
130: /* initial residual is in VEC_VV(0) - compute its norm*/
131: VecNorm(VEC_VV(0),NORM_2,&res_norm);
133: /* first entry in right-hand-side of hessenberg system is just
134: the initial residual norm */
135: *RS(0) = res_norm;
137: PetscObjectSAWsTakeAccess((PetscObject)ksp);
138: if (ksp->normtype != KSP_NORM_NONE) ksp->rnorm = res_norm;
139: else ksp->rnorm = 0;
140: PetscObjectSAWsGrantAccess((PetscObject)ksp);
141: KSPLogResidualHistory(ksp,ksp->rnorm);
142: KSPMonitor(ksp,ksp->its,ksp->rnorm);
144: /* check for the convergence - maybe the current guess is good enough */
145: (*ksp->converged)(ksp,ksp->its,ksp->rnorm,&ksp->reason,ksp->cnvP);
146: if (ksp->reason) {
147: if (itcount) *itcount = 0;
148: return(0);
149: }
151: /* scale VEC_VV (the initial residual) */
152: VecScale(VEC_VV(0),1.0/res_norm);
154: /* Fill the pipeline */
155: KSP_PCApply(ksp,VEC_VV(loc_it),PREVEC(loc_it));
156: PCGetOperators(ksp->pc,&Amat,&Pmat);
157: KSP_MatMult(ksp,Amat,PREVEC(loc_it),ZVEC(loc_it));
158: VecAXPY(ZVEC(loc_it),-shift,VEC_VV(loc_it)); /* Note shift */
160: /* MAIN ITERATION LOOP BEGINNING*/
161: /* keep iterating until we have converged OR generated the max number
162: of directions OR reached the max number of iterations for the method */
163: while (!ksp->reason && loc_it < max_k && ksp->its < ksp->max_it) {
164: if (loc_it) {
165: KSPLogResidualHistory(ksp,res_norm);
166: KSPMonitor(ksp,ksp->its,res_norm);
167: }
168: pipefgmres->it = (loc_it - 1);
170: /* see if more space is needed for work vectors */
171: if (pipefgmres->vv_allocated <= loc_it + VEC_OFFSET + 1) {
172: KSPPIPEFGMRESGetNewVectors(ksp,loc_it+1);
173: /* (loc_it+1) is passed in as number of the first vector that should
174: be allocated */
175: }
177: /* Note that these inner products are with "Z" now, so
178: in particular, lhh[loc_it] is the 'barred' or 'shifted' value,
179: not the value from the equivalent FGMRES run (even in exact arithmetic)
180: That is, the H we need for the Arnoldi relation is different from the
181: coefficients we use in the orthogonalization process,because of the shift */
183: /* Do some local twiddling to allow for a single reduction */
184: for (i=0;i<loc_it+1;i++){
185: redux[i] = VEC_VV(i);
186: }
187: redux[loc_it+1] = ZVEC(loc_it);
189: /* note the extra dot product which ends up in lh[loc_it+1], which computes ||z||^2 */
190: VecMDotBegin(ZVEC(loc_it),loc_it+2,redux,lhh);
192: /* Start the split reduction (This actually calls the MPI_Iallreduce, otherwise, the reduction is simply delayed until the "end" call)*/
193: PetscCommSplitReductionBegin(PetscObjectComm((PetscObject)ZVEC(loc_it)));
195: /* The work to be overlapped with the inner products follows.
196: This is application of the preconditioner and the operator
197: to compute intermediate quantites which will be combined (locally)
198: with the results of the inner products.
199: */
200: KSP_PCApply(ksp,ZVEC(loc_it),Q);
201: PCGetOperators(ksp->pc,&Amat,&Pmat);
202: KSP_MatMult(ksp,Amat,Q,W);
204: /* Compute inner products of the new direction with previous directions,
205: and the norm of the to-be-orthogonalized direction "Z".
206: This information is enough to build the required entries
207: of H. The inner product with VEC_VV(it_loc) is
208: *different* than in the standard FGMRES and need to be dealt with specially.
209: That is, for standard FGMRES the orthogonalization coefficients are the same
210: as the coefficients used in the Arnoldi relation to reconstruct, but here this
211: is not true (albeit only for the one entry of H which we "unshift" below. */
213: /* Finish the dot product, retrieving the extra entry */
214: VecMDotEnd(ZVEC(loc_it),loc_it+2,redux,lhh);
215: tt = PetscRealPart(lhh[loc_it+1]);
217: /* Hessenberg entries, and entries for (naive) classical Graham-Schmidt
218: Note that the Hessenberg entries require a shift, as these are for the
219: relation AU = VH, which is wrt unshifted basis vectors */
220: hh = HH(0,loc_it); hes=HES(0,loc_it);
221: for (j=0; j<loc_it; j++) {
222: hh[j] = lhh[j];
223: hes[j] = lhh[j];
224: }
225: hh[loc_it] = lhh[loc_it] + shift;
226: hes[loc_it] = lhh[loc_it] + shift;
228: /* we delay applying the shift here */
229: for (j=0; j<=loc_it; j++) {
230: lhh[j] = -lhh[j]; /* flip sign */
231: }
233: /* Compute the norm of the un-normalized new direction using the rearranged formula
234: Note that these are shifted ("barred") quantities */
235: for (k=0;k<=loc_it;k++) tt -= ((PetscReal)(PetscAbsScalar(lhh[k]) * PetscAbsScalar(lhh[k])));
236: /* On AVX512 this is accumulating roundoff errors for eg: tt=-2.22045e-16 */
237: if ((tt < 0.0) && tt > -PETSC_SMALL) tt = 0.0 ;
238: if (tt < 0.0) {
239: /* If we detect square root breakdown in the norm, we must restart the algorithm.
240: Here this means we simply break the current loop and reconstruct the solution
241: using the basis we have computed thus far. Note that by breaking immediately,
242: we do not update the iteration count, so computation done in this iteration
243: should be disregarded.
244: */
245: PetscInfo2(ksp,"Restart due to square root breakdown at it = %D, tt=%g\n",ksp->its,(double)tt);
246: break;
247: } else {
248: tt = PetscSqrtReal(tt);
249: }
251: /* new entry in hessenburg is the 2-norm of our new direction */
252: hh[loc_it+1] = tt;
253: hes[loc_it+1] = tt;
255: /* The recurred computation for the new direction
256: The division by tt is delayed to the happy breakdown check later
257: Note placement BEFORE the unshift
258: */
259: VecCopy(ZVEC(loc_it),VEC_VV(loc_it+1));
260: VecMAXPY(VEC_VV(loc_it+1),loc_it+1,lhh,&VEC_VV(0));
261: /* (VEC_VV(loc_it+1) is not normalized yet) */
263: /* The recurred computation for the preconditioned vector (u) */
264: VecCopy(Q,PREVEC(loc_it+1));
265: VecMAXPY(PREVEC(loc_it+1),loc_it+1,lhh,&PREVEC(0));
266: VecScale(PREVEC(loc_it+1),1.0/tt);
268: /* Unshift an entry in the GS coefficients ("removing the bar") */
269: lhh[loc_it] -= shift;
271: /* The recurred computation for z (Au)
272: Note placement AFTER the "unshift" */
273: VecCopy(W,ZVEC(loc_it+1));
274: VecMAXPY(ZVEC(loc_it+1),loc_it+1,lhh,&ZVEC(0));
275: VecScale(ZVEC(loc_it+1),1.0/tt);
277: /* Happy Breakdown Check */
278: hapbnd = PetscAbsScalar((tt) / *RS(loc_it));
279: /* RS(loc_it) contains the res_norm from the last iteration */
280: hapbnd = PetscMin(pipefgmres->haptol,hapbnd);
281: if (tt > hapbnd) {
282: /* scale new direction by its norm */
283: VecScale(VEC_VV(loc_it+1),1.0/tt);
284: } else {
285: /* This happens when the solution is exactly reached. */
286: /* So there is no new direction... */
287: VecSet(VEC_TEMP,0.0); /* set VEC_TEMP to 0 */
288: hapend = PETSC_TRUE;
289: }
290: /* note that for pipefgmres we could get HES(loc_it+1, loc_it) = 0 and the
291: current solution would not be exact if HES was singular. Note that
292: HH non-singular implies that HES is not singular, and HES is guaranteed
293: to be nonsingular when PREVECS are linearly independent and A is
294: nonsingular (in GMRES, the nonsingularity of A implies the nonsingularity
295: of HES). So we should really add a check to verify that HES is nonsingular.*/
297: /* Note that to be thorough, in debug mode, one could call a LAPACK routine
298: here to check that the hessenberg matrix is indeed non-singular (since
299: FGMRES does not guarantee this) */
301: /* Now apply rotations to new col of hessenberg (and right side of system),
302: calculate new rotation, and get new residual norm at the same time*/
303: KSPPIPEFGMRESUpdateHessenberg(ksp,loc_it,&hapend,&res_norm);
304: if (ksp->reason) break;
306: loc_it++;
307: pipefgmres->it = (loc_it-1); /* Add this here in case it has converged */
309: PetscObjectSAWsTakeAccess((PetscObject)ksp);
310: ksp->its++;
311: if (ksp->normtype != KSP_NORM_NONE) ksp->rnorm = res_norm;
312: else ksp->rnorm = 0;
313: PetscObjectSAWsGrantAccess((PetscObject)ksp);
315: (*ksp->converged)(ksp,ksp->its,ksp->rnorm,&ksp->reason,ksp->cnvP);
317: /* Catch error in happy breakdown and signal convergence and break from loop */
318: if (hapend) {
319: if (!ksp->reason) {
320: 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);
321: else {
322: ksp->reason = KSP_DIVERGED_BREAKDOWN;
323: break;
324: }
325: }
326: }
327: }
328: /* END OF ITERATION LOOP */
329: KSPLogResidualHistory(ksp,ksp->rnorm);
331: /*
332: Monitor if we know that we will not return for a restart */
333: if (loc_it && (ksp->reason || ksp->its >= ksp->max_it)) {
334: KSPMonitor(ksp,ksp->its,ksp->rnorm);
335: }
337: if (itcount) *itcount = loc_it;
339: /*
340: Down here we have to solve for the "best" coefficients of the Krylov
341: columns, add the solution values together, and possibly unwind the
342: preconditioning from the solution
343: */
345: /* Form the solution (or the solution so far) */
346: /* Note: must pass in (loc_it-1) for iteration count so that KSPPIPEGMRESIIBuildSoln
347: properly navigates */
349: KSPPIPEFGMRESBuildSoln(RS(0),ksp->vec_sol,ksp->vec_sol,ksp,loc_it-1);
351: return(0);
352: }
354: /*
355: KSPSolve_PIPEFGMRES - This routine applies the PIPEFGMRES method.
358: Input Parameter:
359: . ksp - the Krylov space object that was set to use pipefgmres
361: Output Parameter:
362: . outits - number of iterations used
364: */
365: static PetscErrorCode KSPSolve_PIPEFGMRES(KSP ksp)
366: {
368: PetscInt its,itcount;
369: KSP_PIPEFGMRES *pipefgmres = (KSP_PIPEFGMRES*)ksp->data;
370: PetscBool guess_zero = ksp->guess_zero;
373: /* We have not checked these routines for use with complex numbers. The inner products
374: are likely not defined correctly for that case */
375: if (PetscDefined(USE_COMPLEX) && !PetscDefined(SKIP_COMPLEX)) SETERRQ(PETSC_COMM_WORLD,PETSC_ERR_SUP,"PIPEFGMRES has not been implemented for use with complex scalars");
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, KSPFGMRES
693: 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);
716: KSPSetSupportedNorm(ksp,KSP_NORM_NONE,PC_RIGHT,1);
718: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetPreAllocateVectors_C",KSPGMRESSetPreAllocateVectors_GMRES);
719: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESSetRestart_C",KSPGMRESSetRestart_GMRES);
720: PetscObjectComposeFunction((PetscObject)ksp,"KSPGMRESGetRestart_C",KSPGMRESGetRestart_GMRES);
722: pipefgmres->nextra_vecs = 1;
723: pipefgmres->haptol = 1.0e-30;
724: pipefgmres->q_preallocate = 0;
725: pipefgmres->delta_allocate = PIPEFGMRES_DELTA_DIRECTIONS;
726: pipefgmres->orthog = NULL;
727: pipefgmres->nrs = NULL;
728: pipefgmres->sol_temp = NULL;
729: pipefgmres->max_k = PIPEFGMRES_DEFAULT_MAXK;
730: pipefgmres->Rsvd = NULL;
731: pipefgmres->orthogwork = NULL;
732: pipefgmres->cgstype = KSP_GMRES_CGS_REFINE_NEVER;
733: pipefgmres->shift = 1.0;
734: return(0);
735: }
737: static PetscErrorCode KSPPIPEFGMRESGetNewVectors(KSP ksp,PetscInt it)
738: {
739: KSP_PIPEFGMRES *pipefgmres = (KSP_PIPEFGMRES*)ksp->data;
740: PetscInt nwork = pipefgmres->nwork_alloc; /* number of work vector chunks allocated */
741: PetscInt nalloc; /* number to allocate */
743: PetscInt k;
746: nalloc = pipefgmres->delta_allocate; /* number of vectors to allocate
747: in a single chunk */
749: /* Adjust the number to allocate to make sure that we don't exceed the
750: number of available slots (pipefgmres->vecs_allocated)*/
751: if (it + VEC_OFFSET + nalloc >= pipefgmres->vecs_allocated) {
752: nalloc = pipefgmres->vecs_allocated - it - VEC_OFFSET;
753: }
754: if (!nalloc) return(0);
756: pipefgmres->vv_allocated += nalloc; /* vv_allocated is the number of vectors allocated */
758: /* work vectors */
759: KSPCreateVecs(ksp,nalloc,&pipefgmres->user_work[nwork],0,NULL);
760: PetscLogObjectParents(ksp,nalloc,pipefgmres->user_work[nwork]);
761: for (k=0; k < nalloc; k++) {
762: pipefgmres->vecs[it+VEC_OFFSET+k] = pipefgmres->user_work[nwork][k];
763: }
764: /* specify size of chunk allocated */
765: pipefgmres->mwork_alloc[nwork] = nalloc;
767: /* preconditioned vectors (note we don't use VEC_OFFSET) */
768: KSPCreateVecs(ksp,nalloc,&pipefgmres->prevecs_user_work[nwork],0,NULL);
769: PetscLogObjectParents(ksp,nalloc,pipefgmres->prevecs_user_work[nwork]);
770: for (k=0; k < nalloc; k++) {
771: pipefgmres->prevecs[it+k] = pipefgmres->prevecs_user_work[nwork][k];
772: }
774: KSPCreateVecs(ksp,nalloc,&pipefgmres->zvecs_user_work[nwork],0,NULL);
775: PetscLogObjectParents(ksp,nalloc,pipefgmres->zvecs_user_work[nwork]);
776: for (k=0; k < nalloc; k++) {
777: pipefgmres->zvecs[it+k] = pipefgmres->zvecs_user_work[nwork][k];
778: }
780: /* increment the number of work vector chunks */
781: pipefgmres->nwork_alloc++;
782: return(0);
783: }
785: /*@
786: KSPPIPEFGMRESSetShift - Set the shift parameter for the flexible, pipelined GMRES solver.
788: 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).
790: Logically Collective on ksp
792: Input Parameters:
793: + ksp - the Krylov space context
794: - shift - the shift
796: Level: intermediate
798: Options Database:
799: . -ksp_pipefgmres_shift <shift>
801: .seealso: KSPComputeEigenvalues()
802: @*/
803: PetscErrorCode KSPPIPEFGMRESSetShift(KSP ksp,PetscScalar shift)
804: {
805: KSP_PIPEFGMRES *pipefgmres = (KSP_PIPEFGMRES*)ksp->data;
810: pipefgmres->shift = shift;
811: return(0);
812: }