Actual source code: asa.c
1: #define PETSCKSP_DLL
3: /* --------------------------------------------------------------------
5: Contributed by Arvid Bessen, Columbia University, June 2007
6:
7: This file implements a ASA preconditioner in PETSc as part of PC.
9: The adaptive smoothed aggregation algorithm is described in the paper
10: "Adaptive Smoothed Aggregation (ASA)", M. Brezina, R. Falgout, S. MacLachlan,
11: T. Manteuffel, S. McCormick, and J. Ruge, SIAM Journal on Scientific Computing,
12: SISC Volume 25 Issue 6, Pages 1896-1920.
14: For an example usage of this preconditioner, see, e.g.
15: $PETSC_DIR/src/ksp/ksp/examples/tutorials/ex38.c ex39.c
16: and other files in that directory.
18: This code is still somewhat experimental. A number of improvements would be
19: - keep vectors allocated on each level, instead of destroying them
20: (see mainly PCApplyVcycleOnLevel_ASA)
21: - in PCCreateTransferOp_ASA we get all of the submatrices at once, this could
22: be optimized by differentiating between local and global matrices
23: - the code does not handle it gracefully if there is just one level
24: - if relaxation is sufficient, exit of PCInitializationStage_ASA is not
25: completely clean
26: - default values could be more reasonable, especially for parallel solves,
27: where we need a parallel LU or similar
28: - the richardson scaling parameter is somewhat special, should be treated in a
29: good default way
30: - a number of parameters for smoother (sor_omega, etc.) that we store explicitly
31: could be kept in the respective smoothers themselves
32: - some parameters have to be set via command line options, there are no direct
33: function calls available
34: - numerous other stuff
36: Example runs in parallel would be with parameters like
37: mpiexec ./program -pc_asa_coarse_mat_type aijmumps -pc_asa_direct_solver 200
38: -pc_asa_max_cand_vecs 4 -pc_asa_mu_initial 50 -pc_asa_richardson_scale 1.0
39: -pc_asa_rq_improve 0.9 -asa_smoother_pc_type asm -asa_smoother_sub_pc_type sor
41: -------------------------------------------------------------------- */
43: /*
44: This defines the data structures for the smoothed aggregation procedure
45: */
46: #include src/ksp/pc/impls/asa/asa.h
48: /*
49: We need the QR algorithm from LAPACK
50: */
51: #include petscblaslapack.h
53: /* -------------------------------------------------------------------------- */
55: /* Event logging */
57: PetscEvent PC_InitializationStage_ASA, PC_GeneralSetupStage_ASA;
58: PetscEvent PC_CreateTransferOp_ASA, PC_CreateVcycle_ASA;
59: PetscTruth asa_events_registered = PETSC_FALSE;
64: /*@C
65: PCASASetDM - Sets the coarse grid information for the grids
67: Collective on PC
69: Input Parameter:
70: + pc - the context
71: - dm - the DA or ADDA or VecPack object
73: Level: advanced
75: @*/
76: PetscErrorCode PCASASetDM(PC pc,DM dm)
77: {
78: PetscErrorCode ierr,(*f)(PC,DM);
82: PetscObjectQueryFunction((PetscObject)pc,"PCASASetDM_C",(void (**)(void))&f);
83: if (f) {
84: (*f)(pc,dm);
85: }
86: return(0);
87: }
91: PetscErrorCode PCASASetDM_ASA(PC pc, DM dm)
92: {
94: PC_ASA *asa = (PC_ASA *) pc->data;
97: PetscObjectReference((PetscObject)dm);
98: asa->dm = dm;
99: return(0);
100: }
104: /*@C
105: PCASASetTolerances - Sets the convergence thresholds for ASA algorithm
107: Collective on PC
109: Input Parameter:
110: + pc - the context
111: . rtol - the relative convergence tolerance
112: (relative decrease in the residual norm)
113: . abstol - the absolute convergence tolerance
114: (absolute size of the residual norm)
115: . dtol - the divergence tolerance
116: (amount residual can increase before KSPDefaultConverged()
117: concludes that the method is diverging)
118: - maxits - maximum number of iterations to use
120: Notes:
121: Use PETSC_DEFAULT to retain the default value of any of the tolerances.
123: Level: advanced
124: @*/
125: PetscErrorCode PCASASetTolerances(PC pc, PetscReal rtol, PetscReal abstol,PetscReal dtol, PetscInt maxits)
126: {
127: PetscErrorCode ierr,(*f)(PC,PetscReal,PetscReal,PetscReal,PetscInt);
131: PetscObjectQueryFunction((PetscObject)pc,"PCASASetTolerances_C",(void (**)(void))&f);
132: if (f) {
133: (*f)(pc,rtol,abstol,dtol,maxits);
134: }
135: return(0);
136: }
140: PetscErrorCode PCASASetTolerances_ASA(PC pc, PetscReal rtol, PetscReal abstol,PetscReal dtol, PetscInt maxits)
141: {
142: PC_ASA *asa = (PC_ASA *) pc->data;
146: if (rtol != PETSC_DEFAULT) asa->rtol = rtol;
147: if (abstol != PETSC_DEFAULT) asa->abstol = abstol;
148: if (dtol != PETSC_DEFAULT) asa->divtol = dtol;
149: if (maxits != PETSC_DEFAULT) asa->max_it = maxits;
150: return(0);
151: }
155: /*
156: PCCreateLevel_ASA - Creates one level for the ASA algorithm
158: Input Parameters:
159: + level - current level
160: . comm - MPI communicator object
161: . next - pointer to next level
162: . prev - pointer to previous level
163: . ksptype - the KSP type for the smoothers on this level
164: - pctype - the PC type for the smoothers on this level
166: Output Parameters:
167: . new_asa_lev - the newly created level
169: .keywords: ASA, create, levels, multigrid
170: */
171: PetscErrorCode PCCreateLevel_ASA(PC_ASA_level **new_asa_lev, int level,MPI_Comm comm, PC_ASA_level *prev,
172: PC_ASA_level *next,KSPType ksptype, PCType pctype)
173: {
175: PC_ASA_level *asa_lev;
176:
178: PetscMalloc(sizeof(PC_ASA_level), &asa_lev);
180: asa_lev->level = level;
181: asa_lev->size = 0;
183: asa_lev->A = 0;
184: asa_lev->B = 0;
185: asa_lev->x = 0;
186: asa_lev->b = 0;
187: asa_lev->r = 0;
188:
189: asa_lev->dm = 0;
190: asa_lev->aggnum = 0;
191: asa_lev->agg = 0;
192: asa_lev->loc_agg_dofs = 0;
193: asa_lev->agg_corr = 0;
194: asa_lev->bridge_corr = 0;
195:
196: asa_lev->P = 0;
197: asa_lev->Pt = 0;
198: asa_lev->smP = 0;
199: asa_lev->smPt = 0;
201: asa_lev->comm = comm;
203: asa_lev->smoothd = 0;
204: asa_lev->smoothu = 0;
206: asa_lev->prev = prev;
207: asa_lev->next = next;
208:
209: *new_asa_lev = asa_lev;
210: return(0);
211: }
215: PetscErrorCode SafeMatDestroy(Mat *m)
216: {
217: PetscErrorCode 0;
220: if (m && *m) {MatDestroy(*m); *m=0;}
221: PetscFunctionReturn(ierr);
222: }
226: PetscErrorCode SafeVecDestroy(Vec *v)
227: {
228: PetscErrorCode 0;
231: if (v && *v) {VecDestroy(*v); *v=0;}
232: PetscFunctionReturn(ierr);
233: }
237: PetscErrorCode PrintResNorm(Mat A, Vec x, Vec b, Vec r)
238: {
240: PetscTruth destroyr = PETSC_FALSE;
241: PetscReal resnorm;
242: MPI_Comm Acomm;
245: if (!r) {
246: MatGetVecs(A, PETSC_NULL, &r);
247: destroyr = PETSC_TRUE;
248: }
249: MatMult(A, x, r);
250: VecAYPX(r, -1.0, b);
251: VecNorm(r, NORM_2, &resnorm);
252: PetscObjectGetComm((PetscObject) A, &Acomm);
253: PetscPrintf(Acomm, "Residual norm is %f.\n", resnorm);
255: if (destroyr) {
256: VecDestroy(r);
257: }
258:
259: return(0);
260: }
264: PetscErrorCode PrintEnergyNormOfDiff(Mat A, Vec x, Vec y)
265: {
267: Vec vecdiff, Avecdiff;
268: PetscScalar dotprod;
269: PetscReal dotabs;
270: MPI_Comm Acomm;
272: VecDuplicate(x, &vecdiff);
273: VecWAXPY(vecdiff, -1.0, x, y);
274: MatGetVecs(A, PETSC_NULL, &Avecdiff);
275: MatMult(A, vecdiff, Avecdiff);
276: VecDot(vecdiff, Avecdiff, &dotprod);
277: dotabs = PetscAbsScalar(dotprod);
278: PetscObjectGetComm((PetscObject) A, &Acomm);
279: PetscPrintf(Acomm, "Energy norm %f.\n", dotabs);
280: VecDestroy(vecdiff);
281: VecDestroy(Avecdiff);
282: return(0);
283: }
285: /* -------------------------------------------------------------------------- */
286: /*
287: PCDestroyLevel_ASA - Destroys one level of the ASA preconditioner
289: Input Parameter:
290: . asa_lev - pointer to level that should be destroyed
292: */
295: PetscErrorCode PCDestroyLevel_ASA(PC_ASA_level *asa_lev)
296: {
300: SafeMatDestroy(&(asa_lev->A));
301: SafeMatDestroy(&(asa_lev->B));
302: SafeVecDestroy(&(asa_lev->x));
303: SafeVecDestroy(&(asa_lev->b));
304: SafeVecDestroy(&(asa_lev->r));
306: if (asa_lev->dm) {DMDestroy(asa_lev->dm);}
308: SafeMatDestroy(&(asa_lev->agg));
309: PetscFree(asa_lev->loc_agg_dofs);
310: SafeMatDestroy(&(asa_lev->agg_corr));
311: SafeMatDestroy(&(asa_lev->bridge_corr));
313: SafeMatDestroy(&(asa_lev->P));
314: SafeMatDestroy(&(asa_lev->Pt));
315: SafeMatDestroy(&(asa_lev->smP));
316: SafeMatDestroy(&(asa_lev->smPt));
318: if (asa_lev->smoothd != asa_lev->smoothu) {
319: if (asa_lev->smoothd) {KSPDestroy(asa_lev->smoothd);}
320: }
321: if (asa_lev->smoothu) {KSPDestroy(asa_lev->smoothu);}
323: PetscFree(asa_lev);
324: return(0);
325: }
327: /* -------------------------------------------------------------------------- */
328: /*
329: PCComputeSpectralRadius_ASA - Computes the spectral radius of asa_lev->A
330: and stores it it asa_lev->spec_rad
332: Input Parameters:
333: . asa_lev - the level we are treating
335: Compute spectral radius with sqrt(||A||_1 ||A||_inf) >= ||A||_2 >= rho(A)
337: */
340: PetscErrorCode PCComputeSpectralRadius_ASA(PC_ASA_level *asa_lev)
341: {
343: PetscReal norm_1, norm_inf;
346: MatNorm(asa_lev->A, NORM_1, &norm_1);
347: MatNorm(asa_lev->A, NORM_INFINITY, &norm_inf);
348: asa_lev->spec_rad = sqrt(norm_1*norm_inf);
349: return(0);
350: }
354: PetscErrorCode PCSetRichardsonScale_ASA(KSP ksp, PetscReal spec_rad, PetscReal richardson_scale) {
356: PC pc;
357: PetscTruth flg;
358: PetscReal spec_rad_inv;
361: KSPSetInitialGuessNonzero(ksp, PETSC_TRUE);
362: if (richardson_scale != PETSC_DECIDE) {
363: KSPRichardsonSetScale(ksp, richardson_scale);
364: } else {
365: KSPGetPC(ksp, &pc);
366: PetscTypeCompare((PetscObject)(pc), PCNONE, &flg);
367: if (flg) {
368: /* WORK: this is just an educated guess. Any number between 0 and 2/rho(A)
369: should do. asa_lev->spec_rad has to be an upper bound on rho(A). */
370: spec_rad_inv = 1.0/spec_rad;
371: KSPRichardsonSetScale(ksp, spec_rad_inv);
372: } else {
373: SETERRQ(PETSC_ERR_SUP, "Unknown PC type for smoother. Please specify scaling factor with -pc_asa_richardson_scale\n");
374: }
375: }
376: return(0);
377: }
381: PetscErrorCode PCSetSORomega_ASA(PC pc, PetscReal sor_omega)
382: {
386: PCSORSetSymmetric(pc, SOR_SYMMETRIC_SWEEP);
387: if (sor_omega != PETSC_DECIDE) {
388: PCSORSetOmega(pc, sor_omega);
389: }
390: return(0);
391: }
394: /* -------------------------------------------------------------------------- */
395: /*
396: PCSetupSmoothersOnLevel_ASA - Creates the smoothers of the level.
397: We assume that asa_lev->A and asa_lev->spec_rad are correctly computed
399: Input Parameters:
400: + asa - the data structure for the ASA preconditioner
401: . asa_lev - the level we are treating
402: - maxits - maximum number of iterations to use
403: */
406: PetscErrorCode PCSetupSmoothersOnLevel_ASA(PC_ASA *asa, PC_ASA_level *asa_lev, PetscInt maxits)
407: {
408: PetscErrorCode ierr;
409: PetscTruth flg;
410: PC pc;
413: /* destroy old smoothers */
414: if (asa_lev->smoothu && asa_lev->smoothu != asa_lev->smoothd) {
415: KSPDestroy(asa_lev->smoothu);
416: }
417: asa_lev->smoothu = 0;
418: if (asa_lev->smoothd) {
419: KSPDestroy(asa_lev->smoothd);
420: }
421: asa_lev->smoothd = 0;
422: /* create smoothers */
423: KSPCreate(asa_lev->comm,&asa_lev->smoothd);
424: KSPSetType(asa_lev->smoothd, asa->ksptype_smooth);
425: KSPGetPC(asa_lev->smoothd,&pc);
426: PCSetType(pc,asa->pctype_smooth);
428: /* set up problems for smoothers */
429: KSPSetOperators(asa_lev->smoothd, asa_lev->A, asa_lev->A, DIFFERENT_NONZERO_PATTERN);
430: KSPSetTolerances(asa_lev->smoothd, asa->smoother_rtol, asa->smoother_abstol, asa->smoother_dtol, maxits);
431: PetscTypeCompare((PetscObject)(asa_lev->smoothd), KSPRICHARDSON, &flg);
432: if (flg) {
433: /* special parameters for certain smoothers */
434: KSPSetInitialGuessNonzero(asa_lev->smoothd, PETSC_TRUE);
435: KSPGetPC(asa_lev->smoothd, &pc);
436: PetscTypeCompare((PetscObject)pc, PCSOR, &flg);
437: if (flg) {
438: PCSetSORomega_ASA(pc, asa->sor_omega);
439: } else {
440: /* just set asa->richardson_scale to get some very basic smoother */
441: PCSetRichardsonScale_ASA(asa_lev->smoothd, asa_lev->spec_rad, asa->richardson_scale);
442: }
443: /* this would be the place to add support for other preconditioners */
444: }
445: KSPSetOptionsPrefix(asa_lev->smoothd, "asa_smoother_");
446: KSPSetFromOptions(asa_lev->smoothd);
447: /* set smoothu equal to smoothd, this could change later */
448: asa_lev->smoothu = asa_lev->smoothd;
449: return(0);
450: }
452: /* -------------------------------------------------------------------------- */
453: /*
454: PCSetupDirectSolversOnLevel_ASA - Creates the direct solvers on the coarsest level.
455: We assume that asa_lev->A and asa_lev->spec_rad are correctly computed
457: Input Parameters:
458: + asa - the data structure for the ASA preconditioner
459: . asa_lev - the level we are treating
460: - maxits - maximum number of iterations to use
461: */
464: PetscErrorCode PCSetupDirectSolversOnLevel_ASA(PC_ASA *asa, PC_ASA_level *asa_lev, PetscInt maxits)
465: {
466: PetscErrorCode ierr;
467: PetscTruth flg;
468: PetscInt comm_size;
469: PC pc;
472: if (asa_lev->smoothu && asa_lev->smoothu != asa_lev->smoothd) {
473: KSPDestroy(asa_lev->smoothu);
474: }
475: asa_lev->smoothu = 0;
476: if (asa_lev->smoothd) {
477: KSPDestroy(asa_lev->smoothd);
478: asa_lev->smoothd = 0;
479: }
480: PetscStrcmp(asa->ksptype_direct, KSPPREONLY, &flg);
481: if (flg) {
482: PetscStrcmp(asa->pctype_direct, PCLU, &flg);
483: if (flg) {
484: MPI_Comm_size(asa_lev->comm, &comm_size);
485: if (comm_size > 1) {
486: /* the LU PC will call MatSolve, we may have to set the correct type for the matrix
487: to have support for this in parallel */
488: MatConvert(asa_lev->A, asa->coarse_mat_type, MAT_REUSE_MATRIX, &(asa_lev->A));
489: }
490: }
491: }
492: /* create new solvers */
493: KSPCreate(asa_lev->comm,&asa_lev->smoothd);
494: KSPSetType(asa_lev->smoothd, asa->ksptype_direct);
495: KSPGetPC(asa_lev->smoothd,&pc);
496: PCSetType(pc,asa->pctype_direct);
497: /* set up problems for direct solvers */
498: KSPSetOperators(asa_lev->smoothd, asa_lev->A, asa_lev->A, DIFFERENT_NONZERO_PATTERN);
499: KSPSetTolerances(asa_lev->smoothd, asa->direct_rtol, asa->direct_abstol, asa->direct_dtol, maxits);
500: /* user can set any option by using -pc_asa_direct_xxx */
501: KSPSetOptionsPrefix(asa_lev->smoothd, "asa_coarse_");
502: KSPSetFromOptions(asa_lev->smoothd);
503: /* set smoothu equal to 0, not used */
504: asa_lev->smoothu = 0;
505: return(0);
506: }
508: /* -------------------------------------------------------------------------- */
509: /*
510: PCCreateAggregates_ASA - Creates the aggregates
512: Input Parameters:
513: . asa_lev - the level for which we should create the projection matrix
515: */
518: PetscErrorCode PCCreateAggregates_ASA(PC_ASA_level *asa_lev)
519: {
520: PetscInt m,n, m_loc,n_loc;
521: PetscInt m_loc_s, m_loc_e;
522: const PetscScalar one = 1.0;
523: PetscErrorCode ierr;
526: /* Create nodal aggregates A_i^l */
527: /* we use the DM grid information for that */
528: if (asa_lev->dm) {
529: /* coarsen DM and get the restriction matrix */
530: DMCoarsen(asa_lev->dm, PETSC_NULL, &(asa_lev->next->dm));
531: DMGetAggregates(asa_lev->next->dm, asa_lev->dm, &(asa_lev->agg));
532: MatGetSize(asa_lev->agg, &m, &n);
533: MatGetLocalSize(asa_lev->agg, &m_loc, &n_loc);
534: if (n!=asa_lev->size) SETERRQ(PETSC_ERR_ARG_SIZ,"DM interpolation matrix has incorrect size!\n");
535: asa_lev->next->size = m;
536: asa_lev->aggnum = m;
537: /* create the correlators, right now just identity matrices */
538: MatCreateMPIAIJ(asa_lev->comm, n_loc, n_loc, n, n, 1, PETSC_NULL, 1, PETSC_NULL,&(asa_lev->agg_corr));
539: MatGetOwnershipRange(asa_lev->agg_corr, &m_loc_s, &m_loc_e);
540: for (m=m_loc_s; m<m_loc_e; m++) {
541: MatSetValues(asa_lev->agg_corr, 1, &m, 1, &m, &one, INSERT_VALUES);
542: }
543: MatAssemblyBegin(asa_lev->agg_corr, MAT_FINAL_ASSEMBLY);
544: MatAssemblyEnd(asa_lev->agg_corr, MAT_FINAL_ASSEMBLY);
545: /* MatShift(asa_lev->agg_corr, 1.0); */
546: } else {
547: /* somehow define the aggregates without knowing the geometry */
548: /* future WORK */
549: SETERRQ(PETSC_ERR_SUP, "Currently pure algebraic coarsening is not supported!");
550: }
551: return(0);
552: }
554: /* -------------------------------------------------------------------------- */
555: /*
556: PCCreateTransferOp_ASA - Creates the transfer operator P_{l+1}^l for current level
558: Input Parameters:
559: + asa_lev - the level for which should create the transfer operator
560: - construct_bridge - true, if we should construct a bridge operator, false for normal prolongator
562: If we add a second, third, ... candidate vector (i.e. more than one column in B), we
563: have to relate the additional dimensions to the original aggregates. This is done through
564: the "aggregate correlators" agg_corr and bridge_corr.
565: The aggregate that is used in the construction is then given by
566: asa_lev->agg * asa_lev->agg_corr
567: for the regular prolongator construction and
568: asa_lev->agg * asa_lev->bridge_corr
569: for the bridging prolongator constructions.
570: */
573: PetscErrorCode PCCreateTransferOp_ASA(PC_ASA_level *asa_lev, PetscTruth construct_bridge)
574: {
577: const PetscReal Ca = 1e-3;
578: PetscReal cutoff;
579: PetscInt nodes_on_lev;
581: Mat logical_agg;
582: PetscInt mat_agg_loc_start, mat_agg_loc_end, mat_agg_loc_size;
583: PetscInt a;
584: const PetscInt *agg = 0;
585: PetscInt **agg_arr = 0;
587: IS *idxm_is_B_arr = 0;
588: PetscInt *idxn_B = 0;
589: IS idxn_is_B, *idxn_is_B_arr = 0;
591: Mat *b_submat_arr = 0;
593: PetscScalar *b_submat = 0, *b_submat_tp = 0;
594: PetscInt *idxm = 0, *idxn = 0;
595: PetscInt cand_vecs_num;
596: PetscInt *cand_vec_length = 0;
597: PetscInt max_cand_vec_length = 0;
598: PetscScalar **b_orth_arr = 0;
600: PetscInt i,j;
602: PetscScalar *tau = 0, *work = 0;
603: PetscBLASInt info;
605: PetscInt max_cand_vecs_to_add;
606: PetscInt *new_loc_agg_dofs = 0;
608: PetscInt total_loc_cols = 0;
609: PetscReal norm;
611: PetscInt a_loc_m, a_loc_n;
612: PetscInt mat_loc_col_start, mat_loc_col_end, mat_loc_col_size;
613: PetscInt loc_agg_dofs_sum;
614: PetscInt row, col;
615: PetscScalar val;
616: PetscInt comm_size, comm_rank;
617: PetscInt *loc_cols = 0;
622: MatGetSize(asa_lev->B, &nodes_on_lev, PETSC_NULL);
624: /* If we add another candidate vector, we want to be able to judge, how much the new candidate
625: improves our current projection operators and whether it is worth adding it.
626: This is the precomputation necessary for implementing Notes (4.1) to (4.7).
627: We require that all candidate vectors x stored in B are normalized such that
628: <A x, x> = 1 and we thus do not have to compute this.
629: For each aggregate A we can now test condition (4.5) and (4.6) by computing
630: || quantity to check ||_{A}^2 <= cutoff * card(A)/N_l */
631: cutoff = Ca/(asa_lev->spec_rad);
633: /* compute logical aggregates by using the correlators */
634: if (construct_bridge) {
635: /* construct bridging operator */
636: MatMatMult(asa_lev->agg, asa_lev->bridge_corr, MAT_INITIAL_MATRIX, 1.0, &logical_agg);
637: } else {
638: /* construct "regular" prolongator */
639: MatMatMult(asa_lev->agg, asa_lev->agg_corr, MAT_INITIAL_MATRIX, 1.0, &logical_agg);
640: }
642: /* destroy correlator matrices for next level, these will be rebuilt in this routine */
643: if (asa_lev->next) {
644: SafeMatDestroy(&(asa_lev->next->agg_corr));
645: SafeMatDestroy(&(asa_lev->next->bridge_corr));
646: }
648: /* find out the correct local row indices */
649: MatGetOwnershipRange(logical_agg, &mat_agg_loc_start, &mat_agg_loc_end);
650: mat_agg_loc_size = mat_agg_loc_end-mat_agg_loc_start;
651:
652: cand_vecs_num = asa_lev->cand_vecs;
654: /* construct column indices idxn_B for reading from B */
655: PetscMalloc(sizeof(PetscInt)*(cand_vecs_num), &idxn_B);
656: for (i=0; i<cand_vecs_num; i++) {
657: idxn_B[i] = i;
658: }
659: ISCreateGeneral(asa_lev->comm, asa_lev->cand_vecs, idxn_B, &idxn_is_B);
660: PetscFree(idxn_B);
661: PetscMalloc(sizeof(IS)*mat_agg_loc_size, &idxn_is_B_arr);
662: for (a=0; a<mat_agg_loc_size; a++) {
663: idxn_is_B_arr[a] = idxn_is_B;
664: }
665: /* allocate storage for row indices idxm_B */
666: PetscMalloc(sizeof(IS)*mat_agg_loc_size, &idxm_is_B_arr);
668: /* Storage for the orthogonalized submatrices of B and their sizes */
669: PetscMalloc(sizeof(PetscInt)*mat_agg_loc_size, &cand_vec_length);
670: PetscMalloc(sizeof(PetscScalar*)*mat_agg_loc_size, &b_orth_arr);
671: /* Storage for the information about each aggregate */
672: PetscMalloc(sizeof(PetscInt*)*mat_agg_loc_size, &agg_arr);
673: /* Storage for the number of candidate vectors that are orthonormal and used in each submatrix */
674: PetscMalloc(sizeof(PetscInt)*mat_agg_loc_size, &new_loc_agg_dofs);
676: /* loop over local aggregates */
677: for (a=0; a<mat_agg_loc_size; a++) {
678: /* get info about current aggregate, this gives the rows we have to get from B */
679: MatGetRow(logical_agg, a+mat_agg_loc_start, &cand_vec_length[a], &agg, 0);
680: /* copy aggregate information */
681: PetscMalloc(sizeof(PetscInt)*cand_vec_length[a], &(agg_arr[a]));
682: PetscMemcpy(agg_arr[a], agg, sizeof(PetscInt)*cand_vec_length[a]);
683: /* restore row */
684: MatRestoreRow(logical_agg, a+mat_agg_loc_start, &cand_vec_length[a], &agg, 0);
685:
686: /* create index sets */
687: ISCreateGeneral(PETSC_COMM_SELF, cand_vec_length[a], agg_arr[a], &(idxm_is_B_arr[a]));
688: /* maximum candidate vector length */
689: if (cand_vec_length[a] > max_cand_vec_length) { max_cand_vec_length = cand_vec_length[a]; }
690: }
691: /* destroy logical_agg, no longer needed */
692: SafeMatDestroy(&logical_agg);
694: /* get the entries for aggregate from B */
695: MatGetSubMatrices(asa_lev->B, mat_agg_loc_size, idxm_is_B_arr, idxn_is_B_arr, MAT_INITIAL_MATRIX, &b_submat_arr);
696:
697: /* clean up all the index sets */
698: for (a=0; a<mat_agg_loc_size; a++) { ISDestroy(idxm_is_B_arr[a]); }
699: PetscFree(idxm_is_B_arr);
700: ISDestroy(idxn_is_B);
701: PetscFree(idxn_is_B_arr);
702:
703: /* storage for the values from each submatrix */
704: PetscMalloc(sizeof(PetscScalar)*max_cand_vec_length*cand_vecs_num, &b_submat);
705: PetscMalloc(sizeof(PetscScalar)*max_cand_vec_length*cand_vecs_num, &b_submat_tp);
706: PetscMalloc(sizeof(PetscInt)*max_cand_vec_length, &idxm);
707: for (i=0; i<max_cand_vec_length; i++) { idxm[i] = i; }
708: PetscMalloc(sizeof(PetscInt)*cand_vecs_num, &idxn);
709: for (i=0; i<cand_vecs_num; i++) { idxn[i] = i; }
710: /* work storage for QR algorithm */
711: PetscMalloc(sizeof(PetscScalar)*max_cand_vec_length, &tau);
712: PetscMalloc(sizeof(PetscScalar)*cand_vecs_num, &work);
714: /* orthogonalize all submatrices and store them in b_orth_arr */
715: for (a=0; a<mat_agg_loc_size; a++) {
716: /* Get the entries for aggregate from B. This is row ordered (although internally
717: it is column ordered and we will waste some energy transposing it).
718: WORK: use something like MatGetArray(b_submat_arr[a], &b_submat) but be really
719: careful about all the different matrix types */
720: MatGetValues(b_submat_arr[a], cand_vec_length[a], idxm, cand_vecs_num, idxn, b_submat);
722: if (construct_bridge) {
723: /* if we are constructing a bridging restriction/interpolation operator, we have
724: to use the same number of dofs as in our previous construction */
725: max_cand_vecs_to_add = asa_lev->loc_agg_dofs[a];
726: } else {
727: /* for a normal restriction/interpolation operator, we should make sure that we
728: do not create linear dependence by accident */
729: max_cand_vecs_to_add = PetscMin(cand_vec_length[a], cand_vecs_num);
730: }
732: /* We use LAPACK to compute the QR decomposition of b_submat. For LAPACK we have to
733: transpose the matrix. We might throw out some column vectors during this process.
734: We are keeping count of the number of column vectors that we use (and therefore the
735: number of dofs on the lower level) in new_loc_agg_dofs[a]. */
736: new_loc_agg_dofs[a] = 0;
737: for (j=0; j<max_cand_vecs_to_add; j++) {
738: /* check for condition (4.5) */
739: norm = 0.0;
740: for (i=0; i<cand_vec_length[a]; i++) {
741: norm += PetscRealPart(b_submat[i*cand_vecs_num+j])*PetscRealPart(b_submat[i*cand_vecs_num+j])
742: + PetscImaginaryPart(b_submat[i*cand_vecs_num+j])*PetscImaginaryPart(b_submat[i*cand_vecs_num+j]);
743: }
744: /* only add candidate vector if bigger than cutoff or first candidate */
745: if ((!j) || (norm > cutoff*((PetscReal) cand_vec_length[a])/((PetscReal) nodes_on_lev))) {
746: /* passed criterion (4.5), we have not implemented criterion (4.6) yet */
747: for (i=0; i<cand_vec_length[a]; i++) {
748: b_submat_tp[new_loc_agg_dofs[a]*cand_vec_length[a]+i] = b_submat[i*cand_vecs_num+j];
749: }
750: new_loc_agg_dofs[a]++;
751: }
752: /* #ifdef PCASA_VERBOSE */
753: else {
754: PetscPrintf(asa_lev->comm, "Cutoff criteria invoked\n");
755: }
756: /* #endif */
757: }
759: CHKMEMQ;
760: /* orthogonalize b_submat_tp using the QR algorithm from LAPACK */
761: LAPACKgeqrf_(cand_vec_length+a, new_loc_agg_dofs+a, b_submat_tp, cand_vec_length+a, tau, work, new_loc_agg_dofs+a, &info);
762: if (info) SETERRQ(PETSC_ERR_LIB, "LAPACKgeqrf_ LAPACK routine failed");
763: #if !defined(PETSC_MISSING_LAPACK_ORGQR)
764: LAPACKungqr_(cand_vec_length+a, new_loc_agg_dofs+a, new_loc_agg_dofs+a, b_submat_tp, cand_vec_length+a, tau, work, new_loc_agg_dofs+a, &info);
765: #else
766: SETERRQ(PETSC_ERR_SUP,"ORGQR - Lapack routine is unavailable\nIf linking with ESSL you MUST also link with full LAPACK, for example\nuse config/configure.py with --with-blas-lib=libessl.a --with-lapack-lib=/usr/local/lib/liblapack.a'");
767: #endif
768: if (info) SETERRQ(PETSC_ERR_LIB, "LAPACKungqr_ LAPACK routine failed");
770: /* Transpose b_submat_tp and store it in b_orth_arr[a]. If we are constructing a
771: bridging restriction/interpolation operator, we could end up with less dofs than
772: we previously had. We fill those up with zeros. */
773: if (!construct_bridge) {
774: PetscMalloc(sizeof(PetscScalar)*cand_vec_length[a]*new_loc_agg_dofs[a], b_orth_arr+a);
775: for (j=0; j<new_loc_agg_dofs[a]; j++) {
776: for (i=0; i<cand_vec_length[a]; i++) {
777: b_orth_arr[a][i*new_loc_agg_dofs[a]+j] = b_submat_tp[j*cand_vec_length[a]+i];
778: }
779: }
780: } else {
781: /* bridge, might have to fill up */
782: PetscMalloc(sizeof(PetscScalar)*cand_vec_length[a]*max_cand_vecs_to_add, b_orth_arr+a);
783: for (j=0; j<new_loc_agg_dofs[a]; j++) {
784: for (i=0; i<cand_vec_length[a]; i++) {
785: b_orth_arr[a][i*max_cand_vecs_to_add+j] = b_submat_tp[j*cand_vec_length[a]+i];
786: }
787: }
788: for (j=new_loc_agg_dofs[a]; j<max_cand_vecs_to_add; j++) {
789: for (i=0; i<cand_vec_length[a]; i++) {
790: b_orth_arr[a][i*max_cand_vecs_to_add+j] = 0.0;
791: }
792: }
793: new_loc_agg_dofs[a] = max_cand_vecs_to_add;
794: }
795: /* the number of columns in asa_lev->P that are local to this process */
796: total_loc_cols += new_loc_agg_dofs[a];
797: } /* end of loop over local aggregates */
799: /* destroy the submatrices, also frees all allocated space */
800: MatDestroyMatrices(mat_agg_loc_size, &b_submat_arr);
801: /* destroy all other workspace */
802: PetscFree(b_submat);
803: PetscFree(b_submat_tp);
804: PetscFree(idxm);
805: PetscFree(idxn);
806: PetscFree(tau);
807: PetscFree(work);
809: /* destroy old matrix P, Pt */
810: SafeMatDestroy(&(asa_lev->P));
811: SafeMatDestroy(&(asa_lev->Pt));
813: MatGetLocalSize(asa_lev->A, &a_loc_m, &a_loc_n);
815: /* determine local range */
816: MPI_Comm_size(asa_lev->comm, &comm_size);
817: MPI_Comm_rank(asa_lev->comm, &comm_rank);
818: PetscMalloc(comm_size*sizeof(PetscInt), &loc_cols);
819: MPI_Allgather(&total_loc_cols, 1, MPI_INT, loc_cols, 1, MPI_INT, asa_lev->comm);
820: mat_loc_col_start = 0;
821: for (i=0;i<comm_rank;i++) {
822: mat_loc_col_start += loc_cols[i];
823: }
824: mat_loc_col_end = mat_loc_col_start + loc_cols[i];
825: mat_loc_col_size = mat_loc_col_end-mat_loc_col_start;
826: if (mat_loc_col_size != total_loc_cols) SETERRQ(PETSC_ERR_COR, "Local size does not match matrix size");
827: PetscFree(loc_cols);
829: /* we now have enough information to create asa_lev->P */
830: MatCreateMPIAIJ(asa_lev->comm, a_loc_n, total_loc_cols, asa_lev->size, PETSC_DETERMINE,
831: cand_vecs_num, PETSC_NULL, cand_vecs_num, PETSC_NULL, &(asa_lev->P));
832: /* create asa_lev->Pt */
833: MatCreateMPIAIJ(asa_lev->comm, total_loc_cols, a_loc_n, PETSC_DETERMINE, asa_lev->size,
834: max_cand_vec_length, PETSC_NULL, max_cand_vec_length, PETSC_NULL, &(asa_lev->Pt));
835: if (asa_lev->next) {
836: /* create correlator for aggregates of next level */
837: MatCreateMPIAIJ(asa_lev->comm, mat_agg_loc_size, total_loc_cols, PETSC_DETERMINE, PETSC_DETERMINE,
838: cand_vecs_num, PETSC_NULL, cand_vecs_num, PETSC_NULL, &(asa_lev->next->agg_corr));
839: /* create asa_lev->next->bridge_corr matrix */
840: MatCreateMPIAIJ(asa_lev->comm, mat_agg_loc_size, total_loc_cols, PETSC_DETERMINE, PETSC_DETERMINE,
841: cand_vecs_num, PETSC_NULL, cand_vecs_num, PETSC_NULL, &(asa_lev->next->bridge_corr));
842: }
844: /* this is my own hack, but it should give the columns that we should write to */
845: MatGetOwnershipRangeColumn(asa_lev->P, &mat_loc_col_start, &mat_loc_col_end);
846: mat_loc_col_size = mat_loc_col_end-mat_loc_col_start;
847: if (mat_loc_col_size != total_loc_cols) SETERRQ(PETSC_ERR_ARG_SIZ, "The number of local columns in asa_lev->P assigned to this processor does not match the local vector size");
849: loc_agg_dofs_sum = 0;
850: /* construct P, Pt, agg_corr, bridge_corr */
851: for (a=0; a<mat_agg_loc_size; a++) {
852: /* store b_orth_arr[a] in P */
853: for (i=0; i<cand_vec_length[a]; i++) {
854: row = agg_arr[a][i];
855: for (j=0; j<new_loc_agg_dofs[a]; j++) {
856: col = mat_loc_col_start + loc_agg_dofs_sum + j;
857: val = b_orth_arr[a][i*new_loc_agg_dofs[a] + j];
858: MatSetValues(asa_lev->P, 1, &row, 1, &col, &val, INSERT_VALUES);
859: val = PetscConj(val);
860: MatSetValues(asa_lev->Pt, 1, &col, 1, &row, &val, INSERT_VALUES);
861: }
862: }
864: /* compute aggregate correlation matrices */
865: if (asa_lev->next) {
866: row = a+mat_agg_loc_start;
867: for (i=0; i<new_loc_agg_dofs[a]; i++) {
868: col = mat_loc_col_start + loc_agg_dofs_sum + i;
869: val = 1.0;
870: MatSetValues(asa_lev->next->agg_corr, 1, &row, 1, &col, &val, INSERT_VALUES);
871: /* for the bridge operator we leave out the newest candidates, i.e.
872: we set bridge_corr to 1.0 for all columns up to asa_lev->loc_agg_dofs[a] and to
873: 0.0 between asa_lev->loc_agg_dofs[a] and new_loc_agg_dofs[a] */
874: if (!(asa_lev->loc_agg_dofs && (i >= asa_lev->loc_agg_dofs[a]))) {
875: MatSetValues(asa_lev->next->bridge_corr, 1, &row, 1, &col, &val, INSERT_VALUES);
876: }
877: }
878: }
880: /* move to next entry point col */
881: loc_agg_dofs_sum += new_loc_agg_dofs[a];
882: } /* end of loop over local aggregates */
884: MatAssemblyBegin(asa_lev->P,MAT_FINAL_ASSEMBLY);
885: MatAssemblyEnd(asa_lev->P,MAT_FINAL_ASSEMBLY);
886: MatAssemblyBegin(asa_lev->Pt,MAT_FINAL_ASSEMBLY);
887: MatAssemblyEnd(asa_lev->Pt,MAT_FINAL_ASSEMBLY);
888: if (asa_lev->next) {
889: MatAssemblyBegin(asa_lev->next->agg_corr,MAT_FINAL_ASSEMBLY);
890: MatAssemblyEnd(asa_lev->next->agg_corr,MAT_FINAL_ASSEMBLY);
891: MatAssemblyBegin(asa_lev->next->bridge_corr,MAT_FINAL_ASSEMBLY);
892: MatAssemblyEnd(asa_lev->next->bridge_corr,MAT_FINAL_ASSEMBLY);
893: }
895: /* if we are not constructing a bridging operator, switch asa_lev->loc_agg_dofs
896: and new_loc_agg_dofs */
897: if (construct_bridge) {
898: PetscFree(new_loc_agg_dofs);
899: } else {
900: if (asa_lev->loc_agg_dofs) {
901: PetscFree(asa_lev->loc_agg_dofs);
902: }
903: asa_lev->loc_agg_dofs = new_loc_agg_dofs;
904: }
906: /* clean up */
907: for (a=0; a<mat_agg_loc_size; a++) {
908: PetscFree(b_orth_arr[a]);
909: PetscFree(agg_arr[a]);
910: }
911: PetscFree(cand_vec_length);
912: PetscFree(b_orth_arr);
913: PetscFree(agg_arr);
916: return(0);
917: }
919: /* -------------------------------------------------------------------------- */
920: /*
921: PCSmoothProlongator_ASA - Computes the smoothed prolongators I and It on the level
923: Input Parameters:
924: . asa_lev - the level for which the smoothed prolongator is constructed
925: */
928: PetscErrorCode PCSmoothProlongator_ASA(PC_ASA_level *asa_lev)
929: {
933: SafeMatDestroy(&(asa_lev->smP));
934: SafeMatDestroy(&(asa_lev->smPt));
935: /* compute prolongator I_{l+1}^l = S_l P_{l+1}^l */
936: /* step 1: compute I_{l+1}^l = A_l P_{l+1}^l */
937: MatMatMult(asa_lev->A, asa_lev->P, MAT_INITIAL_MATRIX, 1, &(asa_lev->smP));
938: MatMatMult(asa_lev->Pt, asa_lev->A, MAT_INITIAL_MATRIX, 1, &(asa_lev->smPt));
939: /* step 2: shift and scale to get I_{l+1}^l = P_{l+1}^l - 4/(3/rho) A_l P_{l+1}^l */
940: MatAYPX(asa_lev->smP, -4./(3.*(asa_lev->spec_rad)), asa_lev->P, SUBSET_NONZERO_PATTERN);
941: MatAYPX(asa_lev->smPt, -4./(3.*(asa_lev->spec_rad)), asa_lev->Pt, SUBSET_NONZERO_PATTERN);
943: return(0);
944: }
947: /* -------------------------------------------------------------------------- */
948: /*
949: PCCreateVcycle_ASA - Creates the V-cycle, when aggregates are already defined
951: Input Parameters:
952: . asa - the preconditioner context
953: */
956: PetscErrorCode PCCreateVcycle_ASA(PC_ASA *asa)
957: {
959: PC_ASA_level *asa_lev, *asa_next_lev;
960: Mat AI;
965: if (!asa) SETERRQ(PETSC_ERR_ARG_NULL, "asa pointer is NULL");
966: if (!(asa->levellist)) SETERRQ(PETSC_ERR_ARG_NULL, "no levels found");
967: asa_lev = asa->levellist;
968: PCComputeSpectralRadius_ASA(asa_lev);
969: PCSetupSmoothersOnLevel_ASA(asa, asa_lev, asa->nu);
971: while(asa_lev->next) {
972: asa_next_lev = asa_lev->next;
973: /* (a) aggregates are already constructed */
975: /* (b) construct B_{l+1} and P_{l+1}^l using (2.11) */
976: /* construct P_{l+1}^l */
977: PCCreateTransferOp_ASA(asa_lev, PETSC_FALSE);
979: /* construct B_{l+1} */
980: SafeMatDestroy(&(asa_next_lev->B));
981: MatMatMult(asa_lev->Pt, asa_lev->B, MAT_INITIAL_MATRIX, 1, &(asa_next_lev->B));
982: asa_next_lev->cand_vecs = asa_lev->cand_vecs;
984: /* (c) construct smoothed prolongator */
985: PCSmoothProlongator_ASA(asa_lev);
986:
987: /* (d) construct coarse matrix */
988: /* Define coarse matrix A_{l+1} = (I_{l+1}^l)^T A_l I_{l+1}^l */
989: SafeMatDestroy(&(asa_next_lev->A));
990: MatMatMult(asa_lev->A, asa_lev->smP, MAT_INITIAL_MATRIX, 1.0, &AI);
991: MatMatMult(asa_lev->smPt, AI, MAT_INITIAL_MATRIX, 1.0, &(asa_next_lev->A));
992: SafeMatDestroy(&AI);
993: /* MatPtAP(asa_lev->A, asa_lev->smP, MAT_INITIAL_MATRIX, 1, &(asa_next_lev->A)); */
994: MatGetSize(asa_next_lev->A, PETSC_NULL, &(asa_next_lev->size));
995: PCComputeSpectralRadius_ASA(asa_next_lev);
996: PCSetupSmoothersOnLevel_ASA(asa, asa_next_lev, asa->nu);
997: /* create corresponding vectors x_{l+1}, b_{l+1}, r_{l+1} */
998: SafeVecDestroy(&(asa_next_lev->x));
999: SafeVecDestroy(&(asa_next_lev->b));
1000: SafeVecDestroy(&(asa_next_lev->r));
1001: MatGetVecs(asa_next_lev->A, &(asa_next_lev->x), &(asa_next_lev->b));
1002: MatGetVecs(asa_next_lev->A, PETSC_NULL, &(asa_next_lev->r));
1004: /* go to next level */
1005: asa_lev = asa_lev->next;
1006: } /* end of while loop over the levels */
1007: /* asa_lev now points to the coarsest level, set up direct solver there */
1008: PCComputeSpectralRadius_ASA(asa_lev);
1009: PCSetupDirectSolversOnLevel_ASA(asa, asa_lev, asa->nu);
1012: return(0);
1013: }
1015: /* -------------------------------------------------------------------------- */
1016: /*
1017: PCAddCandidateToB_ASA - Inserts a candidate vector in B
1019: Input Parameters:
1020: + B - the matrix to insert into
1021: . col_idx - the column we should insert to
1022: . x - the vector to insert
1023: - A - system matrix
1025: Function will insert normalized x into B, such that <A x, x> = 1
1026: (x itself is not changed). If B is projected down then this property
1027: is kept. If <A_l x_l, x_l> = 1 and the next level is defined by
1028: x_{l+1} = Pt x_l and A_{l+1} = Pt A_l P then
1029: <A_{l+1} x_{l+1}, x_l> = <Pt A_l P Pt x_l, Pt x_l>
1030: = <A_l P Pt x_l, P Pt x_l> = <A_l x_l, x_l> = 1
1031: because of the definition of P in (2.11).
1032: */
1035: PetscErrorCode PCAddCandidateToB_ASA(Mat B, PetscInt col_idx, Vec x, Mat A)
1036: {
1038: Vec Ax;
1039: PetscScalar dotprod;
1040: PetscReal norm;
1041: PetscInt i, loc_start, loc_end;
1042: PetscScalar val, *vecarray;
1045: MatGetVecs(A, PETSC_NULL, &Ax);
1046: MatMult(A, x, Ax);
1047: VecDot(Ax, x, &dotprod);
1048: norm = PetscAbsScalar(PetscSqrtScalar(PetscAbsScalar(dotprod))); /* there has to be a better way */
1049: VecGetOwnershipRange(x, &loc_start, &loc_end);
1050: VecGetArray(x, &vecarray);
1051: for (i=loc_start; i<loc_end; i++) {
1052: val = vecarray[i-loc_start]/norm;
1053: MatSetValues(B, 1, &i, 1, &col_idx, &val, INSERT_VALUES);
1054: }
1055: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
1056: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
1057: VecRestoreArray(x, &vecarray);
1058: VecDestroy(Ax);
1059: return(0);
1060: }
1062: /* -------------------------------------------------------------------------- */
1063: /*
1064: - x - a starting guess for a hard to approximate vector, if PETSC_NULL, will be generated
1065: */
1068: PetscErrorCode PCInitializationStage_ASA(PC_ASA *asa, Vec x)
1069: {
1071: PetscInt l;
1072: PC_ASA_level *asa_lev, *asa_next_lev;
1073: PetscRandom rctx; /* random number generator context */
1075: Vec ax;
1076: PetscScalar tmp;
1077: PetscReal prevnorm, norm;
1079: PetscTruth skip_steps_f_i = PETSC_FALSE;
1080: PetscTruth sufficiently_coarsened = PETSC_FALSE;
1082: PetscInt vec_size, vec_loc_size;
1083: PetscInt loc_vec_low, loc_vec_high;
1084: PetscInt i,j;
1086: /* Vec xhat = 0; */
1088: Mat AI;
1090: Vec cand_vec, cand_vec_new;
1091: PetscTruth isrichardson;
1092: PC coarse_pc;
1096: l=1;
1097: /* create first level */
1098: PCCreateLevel_ASA(&(asa->levellist), l, asa->comm, 0, 0, asa->ksptype_smooth, asa->pctype_smooth);
1099: asa_lev = asa->levellist;
1101: /* Set matrix */
1102: asa_lev->A = asa->A;
1103: MatGetSize(asa_lev->A, &i, &j);
1104: asa_lev->size = i;
1105: PCComputeSpectralRadius_ASA(asa_lev);
1106: PCSetupSmoothersOnLevel_ASA(asa, asa_lev, asa->mu_initial);
1108: /* Set DM */
1109: asa_lev->dm = asa->dm;
1110: PetscObjectReference((PetscObject)asa->dm);
1112: PetscPrintf(asa_lev->comm, "Initialization stage\n");
1114: if (x) {
1115: /* use starting guess */
1116: SafeVecDestroy(&(asa_lev->x));
1117: VecDuplicate(x, &(asa_lev->x));
1118: VecCopy(x, asa_lev->x);
1119: } else {
1120: /* select random starting vector */
1121: SafeVecDestroy(&(asa_lev->x));
1122: MatGetVecs(asa_lev->A, &(asa_lev->x), 0);
1123: PetscRandomCreate(asa_lev->comm,&rctx);
1124: PetscRandomSetFromOptions(rctx);
1125: VecSetRandom(asa_lev->x, rctx);
1126: PetscRandomDestroy(rctx);
1127: }
1129: /* create right hand side */
1130: SafeVecDestroy(&(asa_lev->b));
1131: MatGetVecs(asa_lev->A, &(asa_lev->b), 0);
1132: VecSet(asa_lev->b, 0.0);
1134: /* relax and check whether that's enough already */
1135: /* compute old norm */
1136: MatGetVecs(asa_lev->A, 0, &ax);
1137: MatMult(asa_lev->A, asa_lev->x, ax);
1138: VecDot(asa_lev->x, ax, &tmp);
1139: prevnorm = PetscAbsScalar(tmp);
1140: PetscPrintf(asa_lev->comm, "Residual norm of starting guess: %f\n", prevnorm);
1142: /* apply mu_initial relaxations */
1143: KSPSolve(asa_lev->smoothd, asa_lev->b, asa_lev->x);
1144: /* compute new norm */
1145: MatMult(asa_lev->A, asa_lev->x, ax);
1146: VecDot(asa_lev->x, ax, &tmp);
1147: norm = PetscAbsScalar(tmp);
1148: SafeVecDestroy(&(ax));
1149: PetscPrintf(asa_lev->comm, "Residual norm of relaxation after %g %d relaxations: %g %g\n", asa->epsilon,asa->mu_initial, norm,prevnorm);
1151: /* Check if it already converges by itself */
1152: if (norm/prevnorm <= PetscAbsScalar(PetscPowScalar(asa->epsilon, asa->mu_initial))) {
1153: /* converges by relaxation alone */
1154: SETERRQ(PETSC_ERR_SUP, "Relaxation should be sufficient to treat this problem. "
1155: "Use relaxation or decrease epsilon with -pc_asa_epsilon");
1156: } else {
1157: /* set the number of relaxations to asa->mu from asa->mu_initial */
1158: PCSetupSmoothersOnLevel_ASA(asa, asa_lev, asa->mu);
1160: /* Let's do some multigrid ! */
1161: sufficiently_coarsened = PETSC_FALSE;
1163: /* do the whole initialization stage loop */
1164: while (!sufficiently_coarsened) {
1165: PetscPrintf(asa_lev->comm, "Initialization stage: creating level %d\n", asa_lev->level+1);
1167: /* (a) Set candidate matrix B_l = x_l */
1168: /* get the correct vector sizes and data */
1169: VecGetSize(asa_lev->x, &vec_size);
1170: VecGetOwnershipRange(asa_lev->x, &loc_vec_low, &loc_vec_high);
1171: vec_loc_size = loc_vec_high - loc_vec_low;
1173: /* create matrix for candidates */
1174: MatCreateMPIDense(asa_lev->comm, vec_loc_size, PETSC_DECIDE, vec_size, asa->max_cand_vecs, PETSC_NULL, &(asa_lev->B));
1175: /* set the first column */
1176: PCAddCandidateToB_ASA(asa_lev->B, 0, asa_lev->x, asa_lev->A);
1177: asa_lev->cand_vecs = 1;
1179: /* create next level */
1180: PCCreateLevel_ASA(&(asa_lev->next), asa_lev->level+1, asa_lev->comm, asa_lev, PETSC_NULL, asa->ksptype_smooth, asa->pctype_smooth);
1181: asa_next_lev = asa_lev->next;
1183: /* (b) Create nodal aggregates A_i^l */
1184: PCCreateAggregates_ASA(asa_lev);
1185:
1186: /* (c) Define tentatative prolongator P_{l+1}^l and candidate matrix B_{l+1}
1187: using P_{l+1}^l B_{l+1} = B_l and (P_{l+1}^l)^T P_{l+1}^l = I */
1188: PCCreateTransferOp_ASA(asa_lev, PETSC_FALSE);
1190: /* future WORK: set correct fill ratios for all the operations below */
1191: MatMatMult(asa_lev->Pt, asa_lev->B, MAT_INITIAL_MATRIX, 1, &(asa_next_lev->B));
1192: asa_next_lev->cand_vecs = asa_lev->cand_vecs;
1194: /* (d) Define prolongator I_{l+1}^l = S_l P_{l+1}^l */
1195: PCSmoothProlongator_ASA(asa_lev);
1197: /* (e) Define coarse matrix A_{l+1} = (I_{l+1}^l)^T A_l I_{l+1}^l */
1198: MatMatMult(asa_lev->A, asa_lev->smP, MAT_INITIAL_MATRIX, 1.0, &AI);
1199: MatMatMult(asa_lev->smPt, AI, MAT_INITIAL_MATRIX, 1.0, &(asa_next_lev->A));
1200: SafeMatDestroy(&AI);
1201: /* MatPtAP(asa_lev->A, asa_lev->smP, MAT_INITIAL_MATRIX, 1, &(asa_next_lev->A)); */
1202: MatGetSize(asa_next_lev->A, PETSC_NULL, &(asa_next_lev->size));
1203: PCComputeSpectralRadius_ASA(asa_next_lev);
1204: PCSetupSmoothersOnLevel_ASA(asa, asa_next_lev, asa->mu);
1206: /* coarse enough for direct solver? */
1207: MatGetSize(asa_next_lev->A, &i, &j);
1208: if (PetscMax(i,j) <= asa->direct_solver) {
1209: PetscPrintf(asa_lev->comm, "Level %d can be treated directly.\n"
1210: "Algorithm will use %d levels.\n", asa_next_lev->level,
1211: asa_next_lev->level);
1212: break; /* go to step 5 */
1213: }
1215: if (skip_steps_f_i == PETSC_FALSE) {
1216: /* (f) Set x_{l+1} = B_{l+1}, we just compute it again */
1217: SafeVecDestroy(&(asa_next_lev->x));
1218: MatGetVecs(asa_lev->P, &(asa_next_lev->x), 0);
1219: MatMult(asa_lev->Pt, asa_lev->x, asa_next_lev->x);
1221: /* /\* (g) Make copy \hat{x}_{l+1} = x_{l+1} *\/ */
1222: /* VecDuplicate(asa_next_lev->x, &xhat); */
1223: /* VecCopy(asa_next_lev->x, xhat); */
1224:
1225: /* Create b_{l+1} */
1226: SafeVecDestroy(&(asa_next_lev->b));
1227: MatGetVecs(asa_next_lev->A, &(asa_next_lev->b), 0);
1228: VecSet(asa_next_lev->b, 0.0);
1230: /* (h) Relax mu times on A_{l+1} x = 0 */
1231: /* compute old norm */
1232: MatGetVecs(asa_next_lev->A, 0, &ax);
1233: MatMult(asa_next_lev->A, asa_next_lev->x, ax);
1234: VecDot(asa_next_lev->x, ax, &tmp);
1235: prevnorm = PetscAbsScalar(tmp);
1236: PetscPrintf(asa_next_lev->comm, "Residual norm of starting guess on level %d: %f\n", asa_next_lev->level, prevnorm);
1237: /* apply mu relaxations: WORK, make sure that mu is set correctly */
1238: KSPSolve(asa_next_lev->smoothd, asa_next_lev->b, asa_next_lev->x);
1239: /* compute new norm */
1240: MatMult(asa_next_lev->A, asa_next_lev->x, ax);
1241: VecDot(asa_next_lev->x, ax, &tmp);
1242: norm = PetscAbsScalar(tmp);
1243: SafeVecDestroy(&(ax));
1244: PetscPrintf(asa_next_lev->comm, "Residual norm after Richardson iteration on level %d: %f\n", asa_next_lev->level, norm);
1245: /* (i) Check if it already converges by itself */
1246: if (norm/prevnorm <= PetscAbsScalar(PetscPowScalar(asa->epsilon, asa->mu))) {
1247: /* relaxation reduces error sufficiently */
1248: skip_steps_f_i = PETSC_TRUE;
1249: }
1250: }
1251: /* (j) go to next coarser level */
1252: l++;
1253: asa_lev = asa_next_lev;
1254: }
1255: /* Step 5. */
1256: asa->levels = asa_next_lev->level; /* WORK: correct? */
1258: /* Set up direct solvers on coarsest level */
1259: if (asa_next_lev->smoothd != asa_next_lev->smoothu) {
1260: if (asa_next_lev->smoothu) { KSPDestroy(asa_next_lev->smoothu); }
1261: }
1262: KSPSetType(asa_next_lev->smoothd, asa->ksptype_direct);
1263: PetscTypeCompare((PetscObject)(asa_next_lev->smoothd), KSPRICHARDSON, &isrichardson);
1264: if (isrichardson) {
1265: KSPSetInitialGuessNonzero(asa_next_lev->smoothd, PETSC_TRUE);
1266: } else {
1267: KSPSetInitialGuessNonzero(asa_next_lev->smoothd, PETSC_FALSE);
1268: }
1269: KSPGetPC(asa_next_lev->smoothd, &coarse_pc);
1270: PCSetType(coarse_pc, asa->pctype_direct);
1271: asa_next_lev->smoothu = asa_next_lev->smoothd;
1272: PCSetupDirectSolversOnLevel_ASA(asa, asa_next_lev, asa->nu);
1274: /* update finest-level candidate matrix B_1 = I_2^1 I_3^2 ... I_{L-1}^{L-2} x_{L-1} */
1275: if (!asa_lev->prev) {
1276: /* just one relaxation level */
1277: VecDuplicate(asa_lev->x, &cand_vec);
1278: VecCopy(asa_lev->x, cand_vec);
1279: } else {
1280: /* interpolate up the chain */
1281: cand_vec = asa_lev->x;
1282: asa_lev->x = 0;
1283: while(asa_lev->prev) {
1284: /* interpolate to higher level */
1285: MatGetVecs(asa_lev->prev->smP, 0, &cand_vec_new);
1286: MatMult(asa_lev->prev->smP, cand_vec, cand_vec_new);
1287: SafeVecDestroy(&(cand_vec));
1288: cand_vec = cand_vec_new;
1289:
1290: /* destroy all working vectors on the way */
1291: SafeVecDestroy(&(asa_lev->x));
1292: SafeVecDestroy(&(asa_lev->b));
1294: /* move to next higher level */
1295: asa_lev = asa_lev->prev;
1296: }
1297: }
1298: /* set the first column of B1 */
1299: PCAddCandidateToB_ASA(asa_lev->B, 0, cand_vec, asa_lev->A);
1300: SafeVecDestroy(&(cand_vec));
1302: /* Step 6. Create V-cycle */
1303: PCCreateVcycle_ASA(asa);
1304: }
1306: return(0);
1307: }
1309: /* -------------------------------------------------------------------------- */
1310: /*
1311: PCApplyVcycleOnLevel_ASA - Applies current V-cycle
1313: Input Parameters:
1314: + asa_lev - the current level we should recurse on
1315: - gamma - the number of recursive cycles we should run
1317: */
1320: PetscErrorCode PCApplyVcycleOnLevel_ASA(PC_ASA_level *asa_lev, PetscInt gamma)
1321: {
1323: PC_ASA_level *asa_next_lev;
1324: PetscInt g;
1327: if (!asa_lev) SETERRQ(PETSC_ERR_ARG_NULL, "Level is empty in PCApplyVcycleOnLevel_ASA");
1328: asa_next_lev = asa_lev->next;
1330: if (asa_next_lev) {
1331: /* 1. Presmoothing */
1332: KSPSolve(asa_lev->smoothd, asa_lev->b, asa_lev->x);
1333: /* 2. Coarse grid corrections */
1334: /* MatGetVecs(asa_lev->A, 0, &tmp); */
1335: /* MatGetVecs(asa_lev->smP, &(asa_next_lev->b), 0); */
1336: /* MatGetVecs(asa_next_lev->A, &(asa_next_lev->x), 0); */
1337: for (g=0; g<gamma; g++) {
1338: /* (a) get coarsened b_{l+1} = (I_{l+1}^l)^T (b_l - A_l x_l) */
1339: MatMult(asa_lev->A, asa_lev->x, asa_lev->r);
1340: VecAYPX(asa_lev->r, -1.0, asa_lev->b);
1341: MatMult(asa_lev->smPt, asa_lev->r, asa_next_lev->b);
1343: /* (b) Set x_{l+1} = 0 and recurse */
1344: VecSet(asa_next_lev->x, 0.0);
1345: PCApplyVcycleOnLevel_ASA(asa_next_lev, gamma);
1347: /* (c) correct solution x_l = x_l + I_{l+1}^l x_{l+1} */
1348: MatMultAdd(asa_lev->smP, asa_next_lev->x, asa_lev->x, asa_lev->x);
1349: }
1350: /* SafeVecDestroy(&(asa_lev->r)); */
1351: /* /\* discard x_{l+1}, b_{l+1} *\/ */
1352: /* SafeVecDestroy(&(asa_next_lev->x)); */
1353: /* SafeVecDestroy(&(asa_next_lev->b)); */
1354:
1355: /* 3. Postsmoothing */
1356: KSPSolve(asa_lev->smoothu, asa_lev->b, asa_lev->x);
1357: } else {
1358: /* Base case: solve directly */
1359: KSPSolve(asa_lev->smoothd, asa_lev->b, asa_lev->x);
1360: }
1361: return(0);
1362: }
1365: /* -------------------------------------------------------------------------- */
1366: /*
1367: PCGeneralSetupStage_ASA - Applies the ASA preconditioner to a vector. Algorithm
1368: 4 from the ASA paper
1370: Input Parameters:
1371: + asa - the data structure for the ASA algorithm
1372: - cand - a possible candidate vector, if PETSC_NULL, will be constructed randomly
1374: Output Parameters:
1375: . cand_added - PETSC_TRUE, if new candidate vector added, PETSC_FALSE otherwise
1376: */
1379: PetscErrorCode PCGeneralSetupStage_ASA(PC_ASA *asa, Vec cand, PetscTruth *cand_added)
1380: {
1382: PC_ASA_level *asa_lev, *asa_next_lev;
1384: PetscRandom rctx; /* random number generator context */
1385: PetscReal r;
1386: PetscScalar rs;
1387: PetscTruth nd_fast;
1389: Vec ax;
1390: PetscScalar tmp;
1391: PetscReal norm, prevnorm = 0.0;
1392: PetscInt c;
1394: PetscInt loc_vec_low, loc_vec_high;
1395: PetscInt i;
1397: PetscTruth skip_steps_d_j = PETSC_FALSE;
1399: PetscInt *idxm, *idxn;
1400: PetscScalar *v;
1402: Mat AI;
1404: Vec cand_vec, cand_vec_new;
1407: *cand_added = PETSC_FALSE;
1408:
1409: asa_lev = asa->levellist;
1410: if (asa_lev == 0) SETERRQ(PETSC_ERR_ARG_NULL, "No levels found in PCGeneralSetupStage_ASA");
1411: asa_next_lev = asa_lev->next;
1412: if (asa_next_lev == 0) SETERRQ(PETSC_ERR_ARG_NULL, "Just one level, not implemented yet");
1413:
1414: PetscPrintf(asa_lev->comm, "General setup stage\n");
1418: /* 1. If max. dof per node on level 2 equals K, stop */
1419: if (asa_next_lev->cand_vecs >= asa->max_dof_lev_2) {
1420: PetscPrintf(PETSC_COMM_WORLD,
1421: "Maximum dof on level 2 reached: %d\n"
1422: "Consider increasing this limit by setting it with -pc_asa_max_dof_lev_2\n",
1423: asa->max_dof_lev_2);
1424: return(0);
1425: }
1427: /* 2. Create copy of B_1 (skipped, we just replace the last column in step 8.) */
1428:
1429: if (!cand) {
1430: /* 3. Select a random x_1 */
1431: SafeVecDestroy(&(asa_lev->x));
1432: MatGetVecs(asa_lev->A, &(asa_lev->x), 0);
1433: PetscRandomCreate(asa_lev->comm,&rctx);
1434: PetscRandomSetFromOptions(rctx);
1435: VecGetOwnershipRange(asa_lev->x, &loc_vec_low, &loc_vec_high);
1436: for (i=loc_vec_low; i<loc_vec_high; i++) {
1437: PetscRandomGetValueReal(rctx, &r);
1438: rs = r;
1439: VecSetValues(asa_lev->x, 1, &i, &rs, INSERT_VALUES);
1440: }
1441: VecAssemblyBegin(asa_lev->x);
1442: VecAssemblyEnd(asa_lev->x);
1443: PetscRandomDestroy(rctx);
1444: } else {
1445: SafeVecDestroy(&(asa_lev->x));
1446: VecDuplicate(cand, &(asa_lev->x));
1447: VecCopy(cand, asa_lev->x);
1448: }
1450: /* create right hand side */
1451: SafeVecDestroy(&(asa_lev->b));
1452: MatGetVecs(asa_lev->A, &(asa_lev->b), 0);
1453: VecSet(asa_lev->b, 0.0);
1454:
1455: /* Apply mu iterations of current V-cycle */
1456: nd_fast = PETSC_FALSE;
1457: MatGetVecs(asa_lev->A, 0, &ax);
1458: for (c=0; c<asa->mu; c++) {
1459: PCApplyVcycleOnLevel_ASA(asa_lev, asa->gamma);
1460:
1461: MatMult(asa_lev->A, asa_lev->x, ax);
1462: VecDot(asa_lev->x, ax, &tmp);
1463: norm = PetscAbsScalar(tmp);
1464: if (c>0) {
1465: if (norm/prevnorm < asa->epsilon) {
1466: nd_fast = PETSC_TRUE;
1467: break;
1468: }
1469: }
1470: prevnorm = norm;
1471: }
1472: SafeVecDestroy(&(ax));
1474: /* 4. If energy norm decreases sufficiently fast, then stop */
1475: if (nd_fast) {
1476: PetscPrintf(asa_lev->comm, "nd_fast is true\n");
1477: return(0);
1478: }
1480: /* 5. Update B_1, by adding new column x_1 */
1481: if (asa_lev->cand_vecs >= asa->max_cand_vecs) {
1482: SETERRQ(PETSC_ERR_MEM, "Number of candidate vectors will exceed allocated storage space");
1483: } else {
1484: PetscPrintf(asa_lev->comm, "Adding candidate vector %d\n", asa_lev->cand_vecs+1);
1485: }
1486: PCAddCandidateToB_ASA(asa_lev->B, asa_lev->cand_vecs, asa_lev->x, asa_lev->A);
1487: *cand_added = PETSC_TRUE;
1488: asa_lev->cand_vecs++;
1490: /* 6. loop over levels */
1491: while(asa_next_lev && asa_next_lev->next) {
1492: PetscPrintf(asa_lev->comm, "General setup stage: processing level %d\n", asa_next_lev->level);
1493: /* (a) define B_{l+1} and P_{l+1}^L */
1494: /* construct P_{l+1}^l */
1495: PCCreateTransferOp_ASA(asa_lev, PETSC_FALSE);
1497: /* construct B_{l+1} */
1498: SafeMatDestroy(&(asa_next_lev->B));
1499: MatMatMult(asa_lev->Pt, asa_lev->B, MAT_INITIAL_MATRIX, 1.0, &(asa_next_lev->B));
1500: /* do not increase asa_next_lev->cand_vecs until step (j) */
1501:
1502: /* (b) construct prolongator I_{l+1}^l = S_l P_{l+1}^l */
1503: PCSmoothProlongator_ASA(asa_lev);
1504:
1505: /* (c) construct coarse matrix A_{l+1} = (I_{l+1}^l)^T A_l I_{l+1}^l */
1506: SafeMatDestroy(&(asa_next_lev->A));
1507: MatMatMult(asa_lev->A, asa_lev->smP, MAT_INITIAL_MATRIX, 1.0, &AI);
1508: MatMatMult(asa_lev->smPt, AI, MAT_INITIAL_MATRIX, 1.0, &(asa_next_lev->A));
1509: SafeMatDestroy(&AI);
1510: /* MatPtAP(asa_lev->A, asa_lev->smP, MAT_INITIAL_MATRIX, 1, &(asa_next_lev->A)); */
1511: MatGetSize(asa_next_lev->A, PETSC_NULL, &(asa_next_lev->size));
1512: PCComputeSpectralRadius_ASA(asa_next_lev);
1513: PCSetupSmoothersOnLevel_ASA(asa, asa_next_lev, asa->mu);
1515: if (! skip_steps_d_j) {
1516: /* (d) get vector x_{l+1} from last column in B_{l+1} */
1517: SafeVecDestroy(&(asa_next_lev->x));
1518: MatGetVecs(asa_next_lev->B, 0, &(asa_next_lev->x));
1520: VecGetOwnershipRange(asa_next_lev->x, &loc_vec_low, &loc_vec_high);
1521: PetscMalloc(sizeof(PetscInt)*(loc_vec_high-loc_vec_low), &idxm);
1522: for (i=loc_vec_low; i<loc_vec_high; i++)
1523: idxm[i-loc_vec_low] = i;
1524: PetscMalloc(sizeof(PetscInt)*1, &idxn);
1525: idxn[0] = asa_next_lev->cand_vecs;
1527: PetscMalloc(sizeof(PetscScalar)*(loc_vec_high-loc_vec_low), &v);
1528: MatGetValues(asa_next_lev->B, loc_vec_high-loc_vec_low, idxm, 1, idxn, v);
1530: VecSetValues(asa_next_lev->x, loc_vec_high-loc_vec_low, idxm, v, INSERT_VALUES);
1531: VecAssemblyBegin(asa_next_lev->x);
1532: VecAssemblyEnd(asa_next_lev->x);
1534: PetscFree(v);
1535: PetscFree(idxm);
1536: PetscFree(idxn);
1537:
1538: /* (e) create bridge transfer operator P_{l+2}^{l+1}, by using the previously
1539: computed candidates */
1540: PCCreateTransferOp_ASA(asa_next_lev, PETSC_TRUE);
1542: /* (f) construct bridging prolongator I_{l+2}^{l+1} = S_{l+1} P_{l+2}^{l+1} */
1543: PCSmoothProlongator_ASA(asa_next_lev);
1545: /* (g) compute <A_{l+1} x_{l+1}, x_{l+1}> and save it */
1546: MatGetVecs(asa_next_lev->A, 0, &ax);
1547: MatMult(asa_next_lev->A, asa_next_lev->x, ax);
1548: VecDot(asa_next_lev->x, ax, &tmp);
1549: prevnorm = PetscAbsScalar(tmp);
1550: SafeVecDestroy(&(ax));
1552: /* (h) apply mu iterations of current V-cycle */
1553: /* set asa_next_lev->b */
1554: SafeVecDestroy(&(asa_next_lev->b));
1555: SafeVecDestroy(&(asa_next_lev->r));
1556: MatGetVecs(asa_next_lev->A, &(asa_next_lev->b), &(asa_next_lev->r));
1557: VecSet(asa_next_lev->b, 0.0);
1558: /* apply V-cycle */
1559: for (c=0; c<asa->mu; c++) {
1560: PCApplyVcycleOnLevel_ASA(asa_next_lev, asa->gamma);
1561: }
1563: /* (i) check convergence */
1564: /* compute <A_{l+1} x_{l+1}, x_{l+1}> and save it */
1565: MatGetVecs(asa_next_lev->A, 0, &ax);
1566: MatMult(asa_next_lev->A, asa_next_lev->x, ax);
1567: VecDot(asa_next_lev->x, ax, &tmp);
1568: norm = PetscAbsScalar(tmp);
1569: SafeVecDestroy(&(ax));
1571: if (norm/prevnorm <= PetscAbsScalar(PetscPowScalar(asa->epsilon, asa->mu))) skip_steps_d_j = PETSC_TRUE;
1572:
1573: /* (j) update candidate B_{l+1} */
1574: PCAddCandidateToB_ASA(asa_next_lev->B, asa_next_lev->cand_vecs, asa_next_lev->x, asa_next_lev->A);
1575: asa_next_lev->cand_vecs++;
1576: }
1577: /* go to next level */
1578: asa_lev = asa_lev->next;
1579: asa_next_lev = asa_next_lev->next;
1580: }
1582: /* 7. update the fine-level candidate */
1583: if (! asa_lev->prev) {
1584: /* just one coarsening level */
1585: VecDuplicate(asa_lev->x, &cand_vec);
1586: VecCopy(asa_lev->x, cand_vec);
1587: } else {
1588: cand_vec = asa_lev->x;
1589: asa_lev->x = 0;
1590: while(asa_lev->prev) {
1591: /* interpolate to higher level */
1592: MatGetVecs(asa_lev->prev->smP, 0, &cand_vec_new);
1593: MatMult(asa_lev->prev->smP, cand_vec, cand_vec_new);
1594: SafeVecDestroy(&(cand_vec));
1595: cand_vec = cand_vec_new;
1597: /* destroy all working vectors on the way */
1598: SafeVecDestroy(&(asa_lev->x));
1599: SafeVecDestroy(&(asa_lev->b));
1601: /* move to next higher level */
1602: asa_lev = asa_lev->prev;
1603: }
1604: }
1605: /* 8. update B_1 by setting the last column of B_1 */
1606: PCAddCandidateToB_ASA(asa_lev->B, asa_lev->cand_vecs-1, cand_vec, asa_lev->A);
1607: SafeVecDestroy(&(cand_vec));
1609: /* 9. create V-cycle */
1610: PCCreateVcycle_ASA(asa);
1611:
1613: return(0);
1614: }
1616: /* -------------------------------------------------------------------------- */
1617: /*
1618: PCConstructMultigrid_ASA - creates the multigrid preconditionier, this is a fairly
1619: involved process, which runs extensive testing to compute good candidate vectors
1621: Input Parameters:
1622: . pc - the preconditioner context
1624: */
1627: PetscErrorCode PCConstructMultigrid_ASA(PC pc)
1628: {
1630: PC_ASA *asa = (PC_ASA*)pc->data;
1631: PC_ASA_level *asa_lev;
1632: PetscInt i, ls, le;
1633: PetscScalar *d;
1634: PetscTruth zeroflag = PETSC_FALSE;
1635: PetscReal rnorm, rnorm_start;
1636: PetscReal rq, rq_prev;
1637: PetscScalar rq_nom, rq_denom;
1638: PetscTruth cand_added;
1639: PetscRandom rctx;
1643: /* check if we should scale with diagonal */
1644: if (asa->scale_diag) {
1645: /* Get diagonal scaling factors */
1646: MatGetVecs(pc->pmat,&(asa->invsqrtdiag),0);
1647: MatGetDiagonal(pc->pmat,asa->invsqrtdiag);
1648: /* compute (inverse) sqrt of diagonal */
1649: VecGetOwnershipRange(asa->invsqrtdiag, &ls, &le);
1650: VecGetArray(asa->invsqrtdiag, &d);
1651: for (i=0; i<le-ls; i++) {
1652: if (d[i] == 0.0) {
1653: d[i] = 1.0;
1654: zeroflag = PETSC_TRUE;
1655: } else {
1656: d[i] = 1./sqrt(PetscAbsScalar(d[i]));
1657: }
1658: }
1659: VecRestoreArray(asa->invsqrtdiag,&d);
1660: VecAssemblyBegin(asa->invsqrtdiag);
1661: VecAssemblyEnd(asa->invsqrtdiag);
1662: if (zeroflag) {
1663: PetscInfo(pc,"Zero detected in diagonal of matrix, using 1 at those locations\n");
1664: }
1665:
1666: /* scale the matrix and store it: D^{-1/2} A D^{-1/2} */
1667: MatDuplicate(pc->pmat, MAT_COPY_VALUES, &(asa->A)); /* probably inefficient */
1668: MatDiagonalScale(asa->A, asa->invsqrtdiag, asa->invsqrtdiag);
1669: } else {
1670: /* don't scale */
1671: asa->A = pc->pmat;
1672: }
1673: /* Initialization stage */
1674: PCInitializationStage_ASA(asa, PETSC_NULL);
1675:
1676: /* get first level */
1677: asa_lev = asa->levellist;
1679: PetscRandomCreate(asa->comm,&rctx);
1680: PetscRandomSetFromOptions(rctx);
1681: VecSetRandom(asa_lev->x,rctx);
1683: /* compute starting residual */
1684: SafeVecDestroy(&(asa_lev->r));
1685: MatGetVecs(asa_lev->A, PETSC_NULL, &(asa_lev->r));
1686: MatMult(asa_lev->A, asa_lev->x, asa_lev->r);
1687: /* starting residual norm */
1688: VecNorm(asa_lev->r, NORM_2, &rnorm_start);
1689: /* compute Rayleigh quotients */
1690: VecDot(asa_lev->x, asa_lev->r, &rq_nom);
1691: VecDot(asa_lev->x, asa_lev->x, &rq_denom);
1692: rq_prev = PetscAbsScalar(rq_nom / rq_denom);
1694: /* check if we have to add more candidates */
1695: for (i=0; i<asa->max_it; i++) {
1696: if (asa_lev->cand_vecs >= asa->max_cand_vecs) {
1697: /* reached limit for candidate vectors */
1698: break;
1699: }
1700: /* apply V-cycle */
1701: PCApplyVcycleOnLevel_ASA(asa_lev, asa->gamma);
1702: /* check convergence */
1703: MatMult(asa_lev->A, asa_lev->x, asa_lev->r);
1704: VecNorm(asa_lev->r, NORM_2, &rnorm);
1705: PetscPrintf(asa->comm, "After %d iterations residual norm is %f\n", i+1, rnorm);
1706: if (rnorm < rnorm_start*(asa->rtol) || rnorm < asa->abstol) {
1707: /* convergence */
1708: break;
1709: }
1710: /* compute new Rayleigh quotient */
1711: VecDot(asa_lev->x, asa_lev->r, &rq_nom);
1712: VecDot(asa_lev->x, asa_lev->x, &rq_denom);
1713: rq = PetscAbsScalar(rq_nom / rq_denom);
1714: PetscPrintf(asa->comm, "After %d iterations Rayleigh quotient of residual is %f\n", i+1, rq);
1715: /* test Rayleigh quotient decrease and add more candidate vectors if necessary */
1716: if (i && (rq > asa->rq_improve*rq_prev)) {
1717: /* improve interpolation by adding another candidate vector */
1718: PCGeneralSetupStage_ASA(asa, asa_lev->r, &cand_added);
1719: if (!cand_added) {
1720: /* either too many candidates for storage or cycle is already effective */
1721: PetscPrintf(asa->comm, "either too many candidates for storage or cycle is already effective\n");
1722: break;
1723: }
1724: VecSetRandom(asa_lev->x, rctx);
1725: rq_prev = rq*10000.; /* give the new V-cycle some grace period */
1726: } else {
1727: rq_prev = rq;
1728: }
1729: }
1731: SafeVecDestroy(&(asa_lev->x));
1732: SafeVecDestroy(&(asa_lev->b));
1733: PetscRandomDestroy(rctx);
1734: asa->multigrid_constructed = PETSC_TRUE;
1735: return(0);
1736: }
1738: /* -------------------------------------------------------------------------- */
1739: /*
1740: PCApply_ASA - Applies the ASA preconditioner to a vector.
1742: Input Parameters:
1743: . pc - the preconditioner context
1744: . x - input vector
1746: Output Parameter:
1747: . y - output vector
1749: Application Interface Routine: PCApply()
1750: */
1753: PetscErrorCode PCApply_ASA(PC pc,Vec x,Vec y)
1754: {
1755: PC_ASA *asa = (PC_ASA*)pc->data;
1756: PC_ASA_level *asa_lev;
1761: if (!asa->multigrid_constructed) {
1762: PCConstructMultigrid_ASA(pc);
1763: }
1765: /* get first level */
1766: asa_lev = asa->levellist;
1768: /* set the right hand side */
1769: VecDuplicate(x, &(asa->b));
1770: VecCopy(x, asa->b);
1771: /* set starting vector */
1772: SafeVecDestroy(&(asa->x));
1773: MatGetVecs(asa->A, &(asa->x), PETSC_NULL);
1774: VecSet(asa->x, 0.0);
1775:
1776: /* set vectors */
1777: asa_lev->x = asa->x;
1778: asa_lev->b = asa->b;
1780: PCApplyVcycleOnLevel_ASA(asa_lev, asa->gamma);
1781:
1782: /* Return solution */
1783: VecCopy(asa->x, y);
1785: /* delete working vectors */
1786: SafeVecDestroy(&(asa->x));
1787: SafeVecDestroy(&(asa->b));
1788: asa_lev->x = PETSC_NULL;
1789: asa_lev->b = PETSC_NULL;
1791: return(0);
1792: }
1794: /* -------------------------------------------------------------------------- */
1795: /*
1796: PCApplyRichardson_ASA - Applies the ASA iteration to solve a linear system
1798: Input Parameters:
1799: . pc - the preconditioner context
1800: . b - the right hand side
1802: Output Parameter:
1803: . x - output vector
1805: DOES NOT WORK!!!!!
1807: */
1810: PetscErrorCode PCApplyRichardson_ASA(PC pc,Vec b,Vec x,Vec w,PetscReal rtol,PetscReal abstol, PetscReal dtol,PetscInt its)
1811: {
1812: PC_ASA *asa = (PC_ASA*)pc->data;
1813: PC_ASA_level *asa_lev;
1814: PetscInt i;
1815: PetscReal rnorm, rnorm_start;
1820: if (! asa->multigrid_constructed) {
1821: PCConstructMultigrid_ASA(pc);
1822: }
1824: /* get first level */
1825: asa_lev = asa->levellist;
1827: /* set the right hand side */
1828: VecDuplicate(b, &(asa->b));
1829: if (asa->scale_diag) {
1830: VecPointwiseMult(asa->b, asa->invsqrtdiag, b);
1831: } else {
1832: VecCopy(b, asa->b);
1833: }
1834: /* set starting vector */
1835: VecDuplicate(x, &(asa->x));
1836: VecCopy(x, asa->x);
1837:
1838: /* compute starting residual */
1839: SafeVecDestroy(&(asa->r));
1840: MatGetVecs(asa->A, &(asa->r), PETSC_NULL);
1841: MatMult(asa->A, asa->x, asa->r);
1842: VecAYPX(asa->r, -1.0, asa->b);
1843: /* starting residual norm */
1844: VecNorm(asa->r, NORM_2, &rnorm_start);
1846: /* set vectors */
1847: asa_lev->x = asa->x;
1848: asa_lev->b = asa->b;
1850: /* **************** Full algorithm loop *********************************** */
1851: for (i=0; i<its; i++) {
1852: /* apply V-cycle */
1853: PCApplyVcycleOnLevel_ASA(asa_lev, asa->gamma);
1854: /* check convergence */
1855: MatMult(asa->A, asa->x, asa->r);
1856: VecAYPX(asa->r, -1.0, asa->b);
1857: VecNorm(asa->r, NORM_2, &rnorm);
1858: PetscPrintf(asa->comm, "After %d iterations residual norm is %f\n", i+1, rnorm);
1859: if (rnorm < rnorm_start*(rtol) || rnorm < asa->abstol) {
1860: /* convergence */
1861: break;
1862: }
1863: if (rnorm > rnorm_start*(dtol)) {
1864: /* divergence */
1865: break;
1866: }
1867: }
1868:
1869: /* Return solution */
1870: if (asa->scale_diag) {
1871: VecPointwiseMult(x, asa->x, asa->invsqrtdiag);
1872: } else {
1873: VecCopy(x, asa->x);
1874: }
1876: /* delete working vectors */
1877: SafeVecDestroy(&(asa->x));
1878: SafeVecDestroy(&(asa->b));
1879: SafeVecDestroy(&(asa->r));
1880: asa_lev->x = PETSC_NULL;
1881: asa_lev->b = PETSC_NULL;
1882: return(0);
1883: }
1885: /* -------------------------------------------------------------------------- */
1886: /*
1887: PCDestroy_ASA - Destroys the private context for the ASA preconditioner
1888: that was created with PCCreate_ASA().
1890: Input Parameter:
1891: . pc - the preconditioner context
1893: Application Interface Routine: PCDestroy()
1894: */
1897: static PetscErrorCode PCDestroy_ASA(PC pc)
1898: {
1899: PC_ASA *asa;
1900: PC_ASA_level *asa_lev;
1901: PC_ASA_level *asa_next_level;
1906: asa = (PC_ASA*)pc->data;
1907: asa_lev = asa->levellist;
1909: /* Delete top level data */
1910: PetscFree(asa->ksptype_smooth);
1911: PetscFree(asa->pctype_smooth);
1912: PetscFree(asa->ksptype_direct);
1913: PetscFree(asa->pctype_direct);
1914: PetscFree(asa->coarse_mat_type);
1916: /* this is destroyed by the levels below */
1917: /* SafeMatDestroy(&(asa->A)); */
1918: SafeVecDestroy(&(asa->invsqrtdiag));
1919: SafeVecDestroy(&(asa->b));
1920: SafeVecDestroy(&(asa->x));
1921: SafeVecDestroy(&(asa->r));
1923: if (asa->dm) {DMDestroy(asa->dm);}
1925: /* Destroy each of the levels */
1926: while(asa_lev) {
1927: asa_next_level = asa_lev->next;
1928: PCDestroyLevel_ASA(asa_lev);
1929: asa_lev = asa_next_level;
1930: }
1932: PetscFree(asa);
1933: return(0);
1934: }
1938: static PetscErrorCode PCSetFromOptions_ASA(PC pc)
1939: {
1940: PC_ASA *asa = (PC_ASA*)pc->data;
1941: PetscTruth flg;
1943: char type[20];
1948: PetscOptionsHead("ASA options");
1949: /* convergence parameters */
1950: PetscOptionsInt("-pc_asa_nu","Number of cycles to run smoother","No manual page yet",asa->nu,&(asa->nu),&flg);
1951: PetscOptionsInt("-pc_asa_gamma","Number of cycles to run coarse grid correction","No manual page yet",asa->gamma,&(asa->gamma),&flg);
1952: PetscOptionsReal("-pc_asa_epsilon","Tolerance for the relaxation method","No manual page yet",asa->epsilon,&(asa->epsilon),&flg);
1953: PetscOptionsInt("-pc_asa_mu","Number of cycles to relax in setup stages","No manual page yet",asa->mu,&(asa->mu),&flg);
1954: PetscOptionsInt("-pc_asa_mu_initial","Number of cycles to relax for generating first candidate vector","No manual page yet",asa->mu_initial,&(asa->mu_initial),&flg);
1955: PetscOptionsInt("-pc_asa_direct_solver","For which matrix size should we use the direct solver?","No manual page yet",asa->direct_solver,&(asa->direct_solver),&flg);
1956: PetscOptionsTruth("-pc_asa_scale_diag","Should we scale the matrix with the inverse of its diagonal?","No manual page yet",asa->scale_diag,&(asa->scale_diag),&flg);
1957: /* type of smoother used */
1958: PetscOptionsList("-pc_asa_smoother_ksp_type","The type of KSP to be used in the smoothers","No manual page yet",KSPList,asa->ksptype_smooth,type,20,&flg);
1959: if (flg) {
1960: PetscFree(asa->ksptype_smooth);
1961: PetscStrallocpy(type,&(asa->ksptype_smooth));
1962: }
1963: PetscOptionsList("-pc_asa_smoother_pc_type","The type of PC to be used in the smoothers","No manual page yet",PCList,asa->pctype_smooth,type,20,&flg);
1964: if (flg) {
1965: PetscFree(asa->pctype_smooth);
1966: PetscStrallocpy(type,&(asa->pctype_smooth));
1967: }
1968: PetscOptionsList("-pc_asa_direct_ksp_type","The type of KSP to be used in the direct solver","No manual page yet",KSPList,asa->ksptype_direct,type,20,&flg);
1969: if (flg) {
1970: PetscFree(asa->ksptype_direct);
1971: PetscStrallocpy(type,&(asa->ksptype_direct));
1972: }
1973: PetscOptionsList("-pc_asa_direct_pc_type","The type of PC to be used in the direct solver","No manual page yet",PCList,asa->pctype_direct,type,20,&flg);
1974: if (flg) {
1975: PetscFree(asa->pctype_direct);
1976: PetscStrallocpy(type,&(asa->pctype_direct));
1977: }
1978: /* options specific for certain smoothers */
1979: PetscOptionsReal("-pc_asa_richardson_scale","Scaling parameter for preconditioning in relaxation, if smoothing KSP is Richardson","No manual page yet",asa->richardson_scale,&(asa->richardson_scale),&flg);
1980: PetscOptionsReal("-pc_asa_sor_omega","Scaling parameter for preconditioning in relaxation, if smoothing KSP is Richardson","No manual page yet",asa->sor_omega,&(asa->sor_omega),&flg);
1981: /* options for direct solver */
1982: PetscOptionsString("-pc_asa_coarse_mat_type","The coarse level matrix type (e.g. SuperLU, MUMPS, ...)","No manual page yet",asa->coarse_mat_type, type,20,&flg);
1983: if (flg) {
1984: PetscFree(asa->coarse_mat_type);
1985: PetscStrallocpy(type,&(asa->coarse_mat_type));
1986: }
1987: /* storage allocation parameters */
1988: PetscOptionsInt("-pc_asa_max_cand_vecs","Maximum number of candidate vectors","No manual page yet",asa->max_cand_vecs,&(asa->max_cand_vecs),&flg);
1989: PetscOptionsInt("-pc_asa_max_dof_lev_2","The maximum number of degrees of freedom per node on level 2 (K in paper)","No manual page yet",asa->max_dof_lev_2,&(asa->max_dof_lev_2),&flg);
1990: /* construction parameters */
1991: PetscOptionsReal("-pc_asa_rq_improve","Threshold in RQ improvement for adding another candidate","No manual page yet",asa->rq_improve,&(asa->rq_improve),&flg);
1992: PetscOptionsTail();
1993: return(0);
1994: }
1998: static PetscErrorCode PCView_ASA(PC pc,PetscViewer viewer)
1999: {
2000: PC_ASA *asa = (PC_ASA*)pc->data;
2002: PetscTruth iascii;
2003: PC_ASA_level *asa_lev = asa->levellist;
2006: PetscTypeCompare((PetscObject)viewer,PETSC_VIEWER_ASCII,&iascii);
2007: if (iascii) {
2008: PetscViewerASCIIPrintf(viewer," ASA:\n");
2009: asa_lev = asa->levellist;
2010: while (asa_lev) {
2011: if (!asa_lev->next) {
2012: PetscViewerASCIIPrintf(viewer,"Coarse gride solver -- level %D -------------------------------\n",0);
2013: } else {
2014: PetscViewerASCIIPrintf(viewer,"Down solver (pre-smoother) on level ? -------------------------------\n");
2015: }
2016: PetscViewerASCIIPushTab(viewer);
2017: KSPView(asa_lev->smoothd,viewer);
2018: PetscViewerASCIIPopTab(viewer);
2019: if (asa_lev->next && asa_lev->smoothd == asa_lev->smoothu) {
2020: PetscViewerASCIIPrintf(viewer,"Up solver (post-smoother) same as down solver (pre-smoother)\n");
2021: } else if (asa_lev->next){
2022: PetscViewerASCIIPrintf(viewer,"Up solver (post-smoother) on level ? -------------------------------\n");
2023: PetscViewerASCIIPushTab(viewer);
2024: KSPView(asa_lev->smoothu,viewer);
2025: PetscViewerASCIIPopTab(viewer);
2026: }
2027: asa_lev = asa_lev->next;
2028: }
2029: } else {
2030: SETERRQ1(PETSC_ERR_SUP,"Viewer type %s not supported for PCASA",((PetscObject)viewer)->type_name);
2031: }
2032: return(0);
2033: }
2035: /* -------------------------------------------------------------------------- */
2036: /*
2037: PCCreate_ASA - Creates a ASA preconditioner context, PC_ASA,
2038: and sets this as the private data within the generic preconditioning
2039: context, PC, that was created within PCCreate().
2041: Input Parameter:
2042: . pc - the preconditioner context
2044: Application Interface Routine: PCCreate()
2045: */
2049: PetscErrorCode PCCreate_ASA(PC pc)
2050: {
2052: PC_ASA *asa;
2057: /*
2058: Set the pointers for the functions that are provided above.
2059: Now when the user-level routines (such as PCApply(), PCDestroy(), etc.)
2060: are called, they will automatically call these functions. Note we
2061: choose not to provide a couple of these functions since they are
2062: not needed.
2063: */
2064: pc->ops->apply = PCApply_ASA;
2065: /* pc->ops->applytranspose = PCApply_ASA;*/
2066: pc->ops->applyrichardson = PCApplyRichardson_ASA;
2067: pc->ops->setup = 0;
2068: pc->ops->destroy = PCDestroy_ASA;
2069: pc->ops->setfromoptions = PCSetFromOptions_ASA;
2070: pc->ops->view = PCView_ASA;
2072: /* Set the data to pointer to 0 */
2073: pc->data = (void*)0;
2075: PetscObjectComposeFunctionDynamic((PetscObject)pc,"PCASASetDM_C","PCASASetDM_ASA",PCASASetDM_ASA);
2076: PetscObjectComposeFunctionDynamic((PetscObject)pc,"PCASASetTolerances_C","PCASASetTolerances_ASA",PCASASetTolerances_ASA);
2078: /* register events */
2079: if (! asa_events_registered) {
2084: asa_events_registered = PETSC_TRUE;
2085: }
2087: /* Create new PC_ASA object */
2088: PetscNewLog(pc,PC_ASA,&asa);
2089: pc->data = (void*)asa;
2091: /* WORK: find some better initial values */
2092: asa->nu = 3;
2093: asa->gamma = 1;
2094: asa->epsilon = 1e-4;
2095: asa->mu = 3;
2096: asa->mu_initial = 20;
2097: asa->direct_solver = 100;
2098: asa->scale_diag = PETSC_TRUE;
2099: PetscStrallocpy(KSPRICHARDSON, (char **) &(asa->ksptype_smooth));
2100: PetscStrallocpy(PCSOR, (char **) &(asa->pctype_smooth));
2101: asa->smoother_rtol = 1e-10;
2102: asa->smoother_abstol = 1e-20;
2103: asa->smoother_dtol = PETSC_DEFAULT;
2104: PetscStrallocpy(KSPPREONLY, (char **) &(asa->ksptype_direct));
2105: PetscStrallocpy(PCREDUNDANT, (char **) &(asa->pctype_direct));
2106: asa->direct_rtol = 1e-10;
2107: asa->direct_abstol = 1e-20;
2108: asa->direct_dtol = PETSC_DEFAULT;
2109: asa->richardson_scale = PETSC_DECIDE;
2110: asa->sor_omega = PETSC_DECIDE;
2111: PetscStrallocpy(MATSAME, (char **) &(asa->coarse_mat_type));
2113: asa->max_cand_vecs = 4;
2114: asa->max_dof_lev_2 = 640; /* I don't think this parameter really matters, 640 should be enough for everyone! */
2116: asa->multigrid_constructed = PETSC_FALSE;
2118: asa->rtol = 1e-10;
2119: asa->abstol = 1e-15;
2120: asa->divtol = 1e5;
2121: asa->max_it = 10000;
2122: asa->rq_improve = 0.9;
2123:
2124: asa->A = 0;
2125: asa->invsqrtdiag = 0;
2126: asa->b = 0;
2127: asa->x = 0;
2128: asa->r = 0;
2130: asa->dm = 0;
2131:
2132: asa->levels = 0;
2133: asa->levellist = 0;
2135: asa->comm = ((PetscObject)pc)->comm;
2136: return(0);
2137: }