Actual source code: asa.c
2: /* --------------------------------------------------------------------
4: Contributed by Arvid Bessen, Columbia University, June 2007
5:
6: This file implements a ASA preconditioner in PETSc as part of PC.
8: The adaptive smoothed aggregation algorithm is described in the paper
9: "Adaptive Smoothed Aggregation (ASA)", M. Brezina, R. Falgout, S. MacLachlan,
10: T. Manteuffel, S. McCormick, and J. Ruge, SIAM Journal on Scientific Computing,
11: SISC Volume 25 Issue 6, Pages 1896-1920.
13: For an example usage of this preconditioner, see, e.g.
14: $PETSC_DIR/src/ksp/ksp/examples/tutorials/ex38.c ex39.c
15: and other files in that directory.
17: This code is still somewhat experimental. A number of improvements would be
18: - keep vectors allocated on each level, instead of destroying them
19: (see mainly PCApplyVcycleOnLevel_ASA)
20: - in PCCreateTransferOp_ASA we get all of the submatrices at once, this could
21: be optimized by differentiating between local and global matrices
22: - the code does not handle it gracefully if there is just one level
23: - if relaxation is sufficient, exit of PCInitializationStage_ASA is not
24: completely clean
25: - default values could be more reasonable, especially for parallel solves,
26: where we need a parallel LU or similar
27: - the richardson scaling parameter is somewhat special, should be treated in a
28: good default way
29: - a number of parameters for smoother (sor_omega, etc.) that we store explicitly
30: could be kept in the respective smoothers themselves
31: - some parameters have to be set via command line options, there are no direct
32: function calls available
33: - numerous other stuff
35: Example runs in parallel would be with parameters like
36: mpiexec ./program -pc_asa_coarse_pc_factor_mat_solver_package mumps -pc_asa_direct_solver 200
37: -pc_asa_max_cand_vecs 4 -pc_asa_mu_initial 50 -pc_asa_richardson_scale 1.0
38: -pc_asa_rq_improve 0.9 -asa_smoother_pc_type asm -asa_smoother_sub_pc_type sor
40: -------------------------------------------------------------------- */
42: /*
43: This defines the data structures for the smoothed aggregation procedure
44: */
45: #include <../src/ksp/pc/impls/asa/asa.h>
46: #include <petscblaslapack.h>
48: /* -------------------------------------------------------------------------- */
50: /* Event logging */
52: PetscLogEvent PC_InitializationStage_ASA, PC_GeneralSetupStage_ASA;
53: PetscLogEvent PC_CreateTransferOp_ASA, PC_CreateVcycle_ASA;
54: PetscBool asa_events_registered = PETSC_FALSE;
59: /*@C
60: PCASASetDM - Sets the coarse grid information for the grids
62: Collective on PC
64: Input Parameter:
65: + pc - the context
66: - dm - the DM object
68: Level: advanced
70: @*/
71: PetscErrorCode PCASASetDM(PC pc,DM dm)
72: {
77: PetscTryMethod(pc,"PCASASetDM_C",(PC,DM),(pc,dm));
78: return(0);
79: }
84: PetscErrorCode PCASASetDM_ASA(PC pc, DM dm)
85: {
87: PC_ASA *asa = (PC_ASA *) pc->data;
90: PetscObjectReference((PetscObject)dm);
91: asa->dm = dm;
92: return(0);
93: }
98: /*@C
99: PCASASetTolerances - Sets the convergence thresholds for ASA algorithm
101: Collective on PC
103: Input Parameter:
104: + pc - the context
105: . rtol - the relative convergence tolerance
106: (relative decrease in the residual norm)
107: . abstol - the absolute convergence tolerance
108: (absolute size of the residual norm)
109: . dtol - the divergence tolerance
110: (amount residual can increase before KSPDefaultConverged()
111: concludes that the method is diverging)
112: - maxits - maximum number of iterations to use
114: Notes:
115: Use PETSC_DEFAULT to retain the default value of any of the tolerances.
117: Level: advanced
118: @*/
119: PetscErrorCode PCASASetTolerances(PC pc, PetscReal rtol, PetscReal abstol,PetscReal dtol, PetscInt maxits)
120: {
125: PetscTryMethod(pc,"PCASASetTolerances_C",(PC,PetscReal,PetscReal,PetscReal,PetscInt),(pc,rtol,abstol,dtol,maxits));
126: return(0);
127: }
132: PetscErrorCode PCASASetTolerances_ASA(PC pc, PetscReal rtol, PetscReal abstol,PetscReal dtol, PetscInt maxits)
133: {
134: PC_ASA *asa = (PC_ASA *) pc->data;
138: if (rtol != PETSC_DEFAULT) asa->rtol = rtol;
139: if (abstol != PETSC_DEFAULT) asa->abstol = abstol;
140: if (dtol != PETSC_DEFAULT) asa->divtol = dtol;
141: if (maxits != PETSC_DEFAULT) asa->max_it = maxits;
142: return(0);
143: }
148: /*
149: PCCreateLevel_ASA - Creates one level for the ASA algorithm
151: Input Parameters:
152: + level - current level
153: . comm - MPI communicator object
154: . next - pointer to next level
155: . prev - pointer to previous level
156: . ksptype - the KSP type for the smoothers on this level
157: - pctype - the PC type for the smoothers on this level
159: Output Parameters:
160: . new_asa_lev - the newly created level
162: .keywords: ASA, create, levels, multigrid
163: */
164: PetscErrorCode PCCreateLevel_ASA(PC_ASA_level **new_asa_lev, int level,MPI_Comm comm, PC_ASA_level *prev,
165: PC_ASA_level *next,KSPType ksptype, PCType pctype)
166: {
168: PC_ASA_level *asa_lev;
169:
171: PetscMalloc(sizeof(PC_ASA_level), &asa_lev);
173: asa_lev->level = level;
174: asa_lev->size = 0;
176: asa_lev->A = 0;
177: asa_lev->B = 0;
178: asa_lev->x = 0;
179: asa_lev->b = 0;
180: asa_lev->r = 0;
181:
182: asa_lev->dm = 0;
183: asa_lev->aggnum = 0;
184: asa_lev->agg = 0;
185: asa_lev->loc_agg_dofs = 0;
186: asa_lev->agg_corr = 0;
187: asa_lev->bridge_corr = 0;
188:
189: asa_lev->P = 0;
190: asa_lev->Pt = 0;
191: asa_lev->smP = 0;
192: asa_lev->smPt = 0;
194: asa_lev->comm = comm;
196: asa_lev->smoothd = 0;
197: asa_lev->smoothu = 0;
199: asa_lev->prev = prev;
200: asa_lev->next = next;
201:
202: *new_asa_lev = asa_lev;
203: return(0);
204: }
208: PetscErrorCode PrintResNorm(Mat A, Vec x, Vec b, Vec r)
209: {
211: PetscBool destroyr = PETSC_FALSE;
212: PetscReal resnorm;
213: MPI_Comm Acomm;
216: if (!r) {
217: MatGetVecs(A, PETSC_NULL, &r);
218: destroyr = PETSC_TRUE;
219: }
220: MatMult(A, x, r);
221: VecAYPX(r, -1.0, b);
222: VecNorm(r, NORM_2, &resnorm);
223: PetscObjectGetComm((PetscObject) A, &Acomm);
224: PetscPrintf(Acomm, "Residual norm is %f.\n", resnorm);
226: if (destroyr) {
227: VecDestroy(&r);
228: }
229:
230: return(0);
231: }
235: PetscErrorCode PrintEnergyNormOfDiff(Mat A, Vec x, Vec y)
236: {
238: Vec vecdiff, Avecdiff;
239: PetscScalar dotprod;
240: PetscReal dotabs;
241: MPI_Comm Acomm;
244: VecDuplicate(x, &vecdiff);
245: VecWAXPY(vecdiff, -1.0, x, y);
246: MatGetVecs(A, PETSC_NULL, &Avecdiff);
247: MatMult(A, vecdiff, Avecdiff);
248: VecDot(vecdiff, Avecdiff, &dotprod);
249: dotabs = PetscAbsScalar(dotprod);
250: PetscObjectGetComm((PetscObject) A, &Acomm);
251: PetscPrintf(Acomm, "Energy norm %f.\n", dotabs);
252: VecDestroy(&vecdiff);
253: VecDestroy(&Avecdiff);
254: return(0);
255: }
257: /* -------------------------------------------------------------------------- */
258: /*
259: PCDestroyLevel_ASA - Destroys one level of the ASA preconditioner
261: Input Parameter:
262: . asa_lev - pointer to level that should be destroyed
264: */
267: PetscErrorCode PCDestroyLevel_ASA(PC_ASA_level *asa_lev)
268: {
272: MatDestroy(&(asa_lev->A));
273: MatDestroy(&(asa_lev->B));
274: VecDestroy(&(asa_lev->x));
275: VecDestroy(&(asa_lev->b));
276: VecDestroy(&(asa_lev->r));
278: if (asa_lev->dm) {DMDestroy(&asa_lev->dm);}
280: MatDestroy(&(asa_lev->agg));
281: PetscFree(asa_lev->loc_agg_dofs);
282: MatDestroy(&(asa_lev->agg_corr));
283: MatDestroy(&(asa_lev->bridge_corr));
285: MatDestroy(&(asa_lev->P));
286: MatDestroy(&(asa_lev->Pt));
287: MatDestroy(&(asa_lev->smP));
288: MatDestroy(&(asa_lev->smPt));
290: if (asa_lev->smoothd != asa_lev->smoothu) {
291: if (asa_lev->smoothd) {KSPDestroy(&asa_lev->smoothd);}
292: }
293: if (asa_lev->smoothu) {KSPDestroy(&asa_lev->smoothu);}
295: PetscFree(asa_lev);
296: return(0);
297: }
299: /* -------------------------------------------------------------------------- */
300: /*
301: PCComputeSpectralRadius_ASA - Computes the spectral radius of asa_lev->A
302: and stores it it asa_lev->spec_rad
304: Input Parameters:
305: . asa_lev - the level we are treating
307: Compute spectral radius with sqrt(||A||_1 ||A||_inf) >= ||A||_2 >= rho(A)
309: */
312: PetscErrorCode PCComputeSpectralRadius_ASA(PC_ASA_level *asa_lev)
313: {
315: PetscReal norm_1, norm_inf;
318: MatNorm(asa_lev->A, NORM_1, &norm_1);
319: MatNorm(asa_lev->A, NORM_INFINITY, &norm_inf);
320: asa_lev->spec_rad = PetscSqrtReal(norm_1*norm_inf);
321: return(0);
322: }
326: PetscErrorCode PCSetRichardsonScale_ASA(KSP ksp, PetscReal spec_rad, PetscReal richardson_scale) {
328: PC pc;
329: PetscBool flg;
330: PetscReal spec_rad_inv;
333: KSPSetInitialGuessNonzero(ksp, PETSC_TRUE);
334: if (richardson_scale != PETSC_DECIDE) {
335: KSPRichardsonSetScale(ksp, richardson_scale);
336: } else {
337: KSPGetPC(ksp, &pc);
338: PetscTypeCompare((PetscObject)(pc), PCNONE, &flg);
339: if (flg) {
340: /* WORK: this is just an educated guess. Any number between 0 and 2/rho(A)
341: should do. asa_lev->spec_rad has to be an upper bound on rho(A). */
342: spec_rad_inv = 1.0/spec_rad;
343: KSPRichardsonSetScale(ksp, spec_rad_inv);
344: } else {
345: SETERRQ(((PetscObject)ksp)->comm,PETSC_ERR_SUP, "Unknown PC type for smoother. Please specify scaling factor with -pc_asa_richardson_scale\n");
346: }
347: }
348: return(0);
349: }
353: PetscErrorCode PCSetSORomega_ASA(PC pc, PetscReal sor_omega)
354: {
358: PCSORSetSymmetric(pc, SOR_SYMMETRIC_SWEEP);
359: if (sor_omega != PETSC_DECIDE) {
360: PCSORSetOmega(pc, sor_omega);
361: }
362: return(0);
363: }
366: /* -------------------------------------------------------------------------- */
367: /*
368: PCSetupSmoothersOnLevel_ASA - Creates the smoothers of the level.
369: We assume that asa_lev->A and asa_lev->spec_rad are correctly computed
371: Input Parameters:
372: + asa - the data structure for the ASA preconditioner
373: . asa_lev - the level we are treating
374: - maxits - maximum number of iterations to use
375: */
378: PetscErrorCode PCSetupSmoothersOnLevel_ASA(PC_ASA *asa, PC_ASA_level *asa_lev, PetscInt maxits)
379: {
380: PetscErrorCode ierr;
381: PetscBool flg;
382: PC pc;
385: /* destroy old smoothers */
386: if (asa_lev->smoothu && asa_lev->smoothu != asa_lev->smoothd) {
387: KSPDestroy(&asa_lev->smoothu);
388: }
389: asa_lev->smoothu = 0;
390: if (asa_lev->smoothd) {
391: KSPDestroy(&asa_lev->smoothd);
392: }
393: asa_lev->smoothd = 0;
394: /* create smoothers */
395: KSPCreate(asa_lev->comm,&asa_lev->smoothd);
396: KSPSetType(asa_lev->smoothd, asa->ksptype_smooth);
397: KSPGetPC(asa_lev->smoothd,&pc);
398: PCSetType(pc,asa->pctype_smooth);
400: /* set up problems for smoothers */
401: KSPSetOperators(asa_lev->smoothd, asa_lev->A, asa_lev->A, DIFFERENT_NONZERO_PATTERN);
402: KSPSetTolerances(asa_lev->smoothd, asa->smoother_rtol, asa->smoother_abstol, asa->smoother_dtol, maxits);
403: PetscTypeCompare((PetscObject)(asa_lev->smoothd), KSPRICHARDSON, &flg);
404: if (flg) {
405: /* special parameters for certain smoothers */
406: KSPSetInitialGuessNonzero(asa_lev->smoothd, PETSC_TRUE);
407: KSPGetPC(asa_lev->smoothd, &pc);
408: PetscTypeCompare((PetscObject)pc, PCSOR, &flg);
409: if (flg) {
410: PCSetSORomega_ASA(pc, asa->sor_omega);
411: } else {
412: /* just set asa->richardson_scale to get some very basic smoother */
413: PCSetRichardsonScale_ASA(asa_lev->smoothd, asa_lev->spec_rad, asa->richardson_scale);
414: }
415: /* this would be the place to add support for other preconditioners */
416: }
417: KSPSetOptionsPrefix(asa_lev->smoothd, "asa_smoother_");
418: KSPSetFromOptions(asa_lev->smoothd);
419: /* set smoothu equal to smoothd, this could change later */
420: asa_lev->smoothu = asa_lev->smoothd;
421: return(0);
422: }
424: /* -------------------------------------------------------------------------- */
425: /*
426: PCSetupDirectSolversOnLevel_ASA - Creates the direct solvers on the coarsest level.
427: We assume that asa_lev->A and asa_lev->spec_rad are correctly computed
429: Input Parameters:
430: + asa - the data structure for the ASA preconditioner
431: . asa_lev - the level we are treating
432: - maxits - maximum number of iterations to use
433: */
436: PetscErrorCode PCSetupDirectSolversOnLevel_ASA(PC_ASA *asa, PC_ASA_level *asa_lev, PetscInt maxits)
437: {
438: PetscErrorCode ierr;
439: PetscBool flg;
440: PetscMPIInt comm_size;
441: PC pc;
444: if (asa_lev->smoothu && asa_lev->smoothu != asa_lev->smoothd) {
445: KSPDestroy(&asa_lev->smoothu);
446: }
447: asa_lev->smoothu = 0;
448: if (asa_lev->smoothd) {
449: KSPDestroy(&asa_lev->smoothd);
450: asa_lev->smoothd = 0;
451: }
452: PetscStrcmp(asa->ksptype_direct, KSPPREONLY, &flg);
453: if (flg) {
454: PetscStrcmp(asa->pctype_direct, PCLU, &flg);
455: if (flg) {
456: MPI_Comm_size(asa_lev->comm, &comm_size);
457: if (comm_size > 1) {
458: /* the LU PC will call MatSolve, we may have to set the correct type for the matrix
459: to have support for this in parallel */
460: MatConvert(asa_lev->A, asa->coarse_mat_type, MAT_REUSE_MATRIX, &(asa_lev->A));
461: }
462: }
463: }
464: /* create new solvers */
465: KSPCreate(asa_lev->comm,&asa_lev->smoothd);
466: KSPSetType(asa_lev->smoothd, asa->ksptype_direct);
467: KSPGetPC(asa_lev->smoothd,&pc);
468: PCSetType(pc,asa->pctype_direct);
469: /* set up problems for direct solvers */
470: KSPSetOperators(asa_lev->smoothd, asa_lev->A, asa_lev->A, DIFFERENT_NONZERO_PATTERN);
471: KSPSetTolerances(asa_lev->smoothd, asa->direct_rtol, asa->direct_abstol, asa->direct_dtol, maxits);
472: /* user can set any option by using -pc_asa_direct_xxx */
473: KSPSetOptionsPrefix(asa_lev->smoothd, "asa_coarse_");
474: KSPSetFromOptions(asa_lev->smoothd);
475: /* set smoothu equal to 0, not used */
476: asa_lev->smoothu = 0;
477: return(0);
478: }
480: /* -------------------------------------------------------------------------- */
481: /*
482: PCCreateAggregates_ASA - Creates the aggregates
484: Input Parameters:
485: . asa_lev - the level for which we should create the projection matrix
487: */
490: PetscErrorCode PCCreateAggregates_ASA(PC_ASA_level *asa_lev)
491: {
492: PetscInt m,n, m_loc,n_loc;
493: PetscInt m_loc_s, m_loc_e;
494: const PetscScalar one = 1.0;
495: PetscErrorCode ierr;
498: /* Create nodal aggregates A_i^l */
499: /* we use the DM grid information for that */
500: if (asa_lev->dm) {
501: /* coarsen DM and get the restriction matrix */
502: DMCoarsen(asa_lev->dm, PETSC_NULL, &(asa_lev->next->dm));
503: DMGetAggregates(asa_lev->next->dm, asa_lev->dm, &(asa_lev->agg));
504: MatGetSize(asa_lev->agg, &m, &n);
505: MatGetLocalSize(asa_lev->agg, &m_loc, &n_loc);
506: if (n!=asa_lev->size) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"DM interpolation matrix has incorrect size!\n");
507: asa_lev->next->size = m;
508: asa_lev->aggnum = m;
509: /* create the correlators, right now just identity matrices */
510: MatCreateMPIAIJ(asa_lev->comm, n_loc, n_loc, n, n, 1, PETSC_NULL, 1, PETSC_NULL,&(asa_lev->agg_corr));
511: MatGetOwnershipRange(asa_lev->agg_corr, &m_loc_s, &m_loc_e);
512: for (m=m_loc_s; m<m_loc_e; m++) {
513: MatSetValues(asa_lev->agg_corr, 1, &m, 1, &m, &one, INSERT_VALUES);
514: }
515: MatAssemblyBegin(asa_lev->agg_corr, MAT_FINAL_ASSEMBLY);
516: MatAssemblyEnd(asa_lev->agg_corr, MAT_FINAL_ASSEMBLY);
517: /* MatShift(asa_lev->agg_corr, 1.0); */
518: } else {
519: /* somehow define the aggregates without knowing the geometry */
520: /* future WORK */
521: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP, "Currently pure algebraic coarsening is not supported!");
522: }
523: return(0);
524: }
526: /* -------------------------------------------------------------------------- */
527: /*
528: PCCreateTransferOp_ASA - Creates the transfer operator P_{l+1}^l for current level
530: Input Parameters:
531: + asa_lev - the level for which should create the transfer operator
532: - construct_bridge - true, if we should construct a bridge operator, false for normal prolongator
534: If we add a second, third, ... candidate vector (i.e. more than one column in B), we
535: have to relate the additional dimensions to the original aggregates. This is done through
536: the "aggregate correlators" agg_corr and bridge_corr.
537: The aggregate that is used in the construction is then given by
538: asa_lev->agg * asa_lev->agg_corr
539: for the regular prolongator construction and
540: asa_lev->agg * asa_lev->bridge_corr
541: for the bridging prolongator constructions.
542: */
545: PetscErrorCode PCCreateTransferOp_ASA(PC_ASA_level *asa_lev, PetscBool construct_bridge)
546: {
549: const PetscReal Ca = 1e-3;
550: PetscReal cutoff;
551: PetscInt nodes_on_lev;
553: Mat logical_agg;
554: PetscInt mat_agg_loc_start, mat_agg_loc_end, mat_agg_loc_size;
555: PetscInt a;
556: const PetscInt *agg = 0;
557: PetscInt **agg_arr = 0;
559: IS *idxm_is_B_arr = 0;
560: PetscInt *idxn_B = 0;
561: IS idxn_is_B, *idxn_is_B_arr = 0;
563: Mat *b_submat_arr = 0;
565: PetscScalar *b_submat = 0, *b_submat_tp = 0;
566: PetscInt *idxm = 0, *idxn = 0;
567: PetscInt cand_vecs_num;
568: PetscInt *cand_vec_length = 0;
569: PetscInt max_cand_vec_length = 0;
570: PetscScalar **b_orth_arr = 0;
572: PetscInt i,j;
574: PetscScalar *tau = 0, *work = 0;
575: PetscBLASInt info,b1,b2;
577: PetscInt max_cand_vecs_to_add;
578: PetscInt *new_loc_agg_dofs = 0;
580: PetscInt total_loc_cols = 0;
581: PetscReal norm;
583: PetscInt a_loc_m, a_loc_n;
584: PetscInt mat_loc_col_start, mat_loc_col_end, mat_loc_col_size;
585: PetscInt loc_agg_dofs_sum;
586: PetscInt row, col;
587: PetscScalar val;
588: PetscMPIInt comm_size, comm_rank;
589: PetscInt *loc_cols = 0;
592: PetscLogEventBegin(PC_CreateTransferOp_ASA,0,0,0,0);
594: MatGetSize(asa_lev->B, &nodes_on_lev, PETSC_NULL);
596: /* If we add another candidate vector, we want to be able to judge, how much the new candidate
597: improves our current projection operators and whether it is worth adding it.
598: This is the precomputation necessary for implementing Notes (4.1) to (4.7).
599: We require that all candidate vectors x stored in B are normalized such that
600: <A x, x> = 1 and we thus do not have to compute this.
601: For each aggregate A we can now test condition (4.5) and (4.6) by computing
602: || quantity to check ||_{A}^2 <= cutoff * card(A)/N_l */
603: cutoff = Ca/(asa_lev->spec_rad);
605: /* compute logical aggregates by using the correlators */
606: if (construct_bridge) {
607: /* construct bridging operator */
608: MatMatMult(asa_lev->agg, asa_lev->bridge_corr, MAT_INITIAL_MATRIX, 1.0, &logical_agg);
609: } else {
610: /* construct "regular" prolongator */
611: MatMatMult(asa_lev->agg, asa_lev->agg_corr, MAT_INITIAL_MATRIX, 1.0, &logical_agg);
612: }
614: /* destroy correlator matrices for next level, these will be rebuilt in this routine */
615: if (asa_lev->next) {
616: MatDestroy(&(asa_lev->next->agg_corr));
617: MatDestroy(&(asa_lev->next->bridge_corr));
618: }
620: /* find out the correct local row indices */
621: MatGetOwnershipRange(logical_agg, &mat_agg_loc_start, &mat_agg_loc_end);
622: mat_agg_loc_size = mat_agg_loc_end-mat_agg_loc_start;
623:
624: cand_vecs_num = asa_lev->cand_vecs;
626: /* construct column indices idxn_B for reading from B */
627: PetscMalloc(sizeof(PetscInt)*(cand_vecs_num), &idxn_B);
628: for (i=0; i<cand_vecs_num; i++) {
629: idxn_B[i] = i;
630: }
631: ISCreateGeneral(asa_lev->comm, asa_lev->cand_vecs, idxn_B,PETSC_COPY_VALUES, &idxn_is_B);
632: PetscFree(idxn_B);
633: PetscMalloc(sizeof(IS)*mat_agg_loc_size, &idxn_is_B_arr);
634: for (a=0; a<mat_agg_loc_size; a++) {
635: idxn_is_B_arr[a] = idxn_is_B;
636: }
637: /* allocate storage for row indices idxm_B */
638: PetscMalloc(sizeof(IS)*mat_agg_loc_size, &idxm_is_B_arr);
640: /* Storage for the orthogonalized submatrices of B and their sizes */
641: PetscMalloc(sizeof(PetscInt)*mat_agg_loc_size, &cand_vec_length);
642: PetscMalloc(sizeof(PetscScalar*)*mat_agg_loc_size, &b_orth_arr);
643: /* Storage for the information about each aggregate */
644: PetscMalloc(sizeof(PetscInt*)*mat_agg_loc_size, &agg_arr);
645: /* Storage for the number of candidate vectors that are orthonormal and used in each submatrix */
646: PetscMalloc(sizeof(PetscInt)*mat_agg_loc_size, &new_loc_agg_dofs);
648: /* loop over local aggregates */
649: for (a=0; a<mat_agg_loc_size; a++) {
650: /* get info about current aggregate, this gives the rows we have to get from B */
651: MatGetRow(logical_agg, a+mat_agg_loc_start, &cand_vec_length[a], &agg, 0);
652: /* copy aggregate information */
653: PetscMalloc(sizeof(PetscInt)*cand_vec_length[a], &(agg_arr[a]));
654: PetscMemcpy(agg_arr[a], agg, sizeof(PetscInt)*cand_vec_length[a]);
655: /* restore row */
656: MatRestoreRow(logical_agg, a+mat_agg_loc_start, &cand_vec_length[a], &agg, 0);
657:
658: /* create index sets */
659: ISCreateGeneral(PETSC_COMM_SELF, cand_vec_length[a], agg_arr[a],PETSC_COPY_VALUES, &(idxm_is_B_arr[a]));
660: /* maximum candidate vector length */
661: if (cand_vec_length[a] > max_cand_vec_length) { max_cand_vec_length = cand_vec_length[a]; }
662: }
663: /* destroy logical_agg, no longer needed */
664: MatDestroy(&logical_agg);
666: /* get the entries for aggregate from B */
667: MatGetSubMatrices(asa_lev->B, mat_agg_loc_size, idxm_is_B_arr, idxn_is_B_arr, MAT_INITIAL_MATRIX, &b_submat_arr);
668:
669: /* clean up all the index sets */
670: for (a=0; a<mat_agg_loc_size; a++) { ISDestroy(&idxm_is_B_arr[a]); }
671: PetscFree(idxm_is_B_arr);
672: ISDestroy(&idxn_is_B);
673: PetscFree(idxn_is_B_arr);
674:
675: /* storage for the values from each submatrix */
676: PetscMalloc(sizeof(PetscScalar)*max_cand_vec_length*cand_vecs_num, &b_submat);
677: PetscMalloc(sizeof(PetscScalar)*max_cand_vec_length*cand_vecs_num, &b_submat_tp);
678: PetscMalloc(sizeof(PetscInt)*max_cand_vec_length, &idxm);
679: for (i=0; i<max_cand_vec_length; i++) { idxm[i] = i; }
680: PetscMalloc(sizeof(PetscInt)*cand_vecs_num, &idxn);
681: for (i=0; i<cand_vecs_num; i++) { idxn[i] = i; }
682: /* work storage for QR algorithm */
683: PetscMalloc(sizeof(PetscScalar)*max_cand_vec_length, &tau);
684: PetscMalloc(sizeof(PetscScalar)*cand_vecs_num, &work);
686: /* orthogonalize all submatrices and store them in b_orth_arr */
687: for (a=0; a<mat_agg_loc_size; a++) {
688: /* Get the entries for aggregate from B. This is row ordered (although internally
689: it is column ordered and we will waste some energy transposing it).
690: WORK: use something like MatGetArray(b_submat_arr[a], &b_submat) but be really
691: careful about all the different matrix types */
692: MatGetValues(b_submat_arr[a], cand_vec_length[a], idxm, cand_vecs_num, idxn, b_submat);
694: if (construct_bridge) {
695: /* if we are constructing a bridging restriction/interpolation operator, we have
696: to use the same number of dofs as in our previous construction */
697: max_cand_vecs_to_add = asa_lev->loc_agg_dofs[a];
698: } else {
699: /* for a normal restriction/interpolation operator, we should make sure that we
700: do not create linear dependence by accident */
701: max_cand_vecs_to_add = PetscMin(cand_vec_length[a], cand_vecs_num);
702: }
704: /* We use LAPACK to compute the QR decomposition of b_submat. For LAPACK we have to
705: transpose the matrix. We might throw out some column vectors during this process.
706: We are keeping count of the number of column vectors that we use (and therefore the
707: number of dofs on the lower level) in new_loc_agg_dofs[a]. */
708: new_loc_agg_dofs[a] = 0;
709: for (j=0; j<max_cand_vecs_to_add; j++) {
710: /* check for condition (4.5) */
711: norm = 0.0;
712: for (i=0; i<cand_vec_length[a]; i++) {
713: norm += PetscRealPart(b_submat[i*cand_vecs_num+j])*PetscRealPart(b_submat[i*cand_vecs_num+j])
714: + PetscImaginaryPart(b_submat[i*cand_vecs_num+j])*PetscImaginaryPart(b_submat[i*cand_vecs_num+j]);
715: }
716: /* only add candidate vector if bigger than cutoff or first candidate */
717: if ((!j) || (norm > cutoff*((PetscReal) cand_vec_length[a])/((PetscReal) nodes_on_lev))) {
718: /* passed criterion (4.5), we have not implemented criterion (4.6) yet */
719: for (i=0; i<cand_vec_length[a]; i++) {
720: b_submat_tp[new_loc_agg_dofs[a]*cand_vec_length[a]+i] = b_submat[i*cand_vecs_num+j];
721: }
722: new_loc_agg_dofs[a]++;
723: }
724: /* #ifdef PCASA_VERBOSE */
725: else {
726: PetscPrintf(asa_lev->comm, "Cutoff criteria invoked\n");
727: }
728: /* #endif */
729: }
731: CHKMEMQ;
732: /* orthogonalize b_submat_tp using the QR algorithm from LAPACK */
733: b1 = PetscBLASIntCast(*(cand_vec_length+a));
734: b2 = PetscBLASIntCast(*(new_loc_agg_dofs+a));
735: LAPACKgeqrf_(&b1, &b2, b_submat_tp, &b1, tau, work, &b2, &info);
736: if (info) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB, "LAPACKgeqrf_ LAPACK routine failed");
737: #if !defined(PETSC_MISSING_LAPACK_ORGQR)
738: LAPACKungqr_(&b1, &b2, &b2, b_submat_tp, &b1, tau, work, &b2, &info);
739: #else
740: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"ORGQR - Lapack routine is unavailable\nIf linking with ESSL you MUST also link with full LAPACK, for example\nuse ./configure with --with-blas-lib=libessl.a --with-lapack-lib=/usr/local/lib/liblapack.a'");
741: #endif
742: if (info) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB, "LAPACKungqr_ LAPACK routine failed");
744: /* Transpose b_submat_tp and store it in b_orth_arr[a]. If we are constructing a
745: bridging restriction/interpolation operator, we could end up with less dofs than
746: we previously had. We fill those up with zeros. */
747: if (!construct_bridge) {
748: PetscMalloc(sizeof(PetscScalar)*cand_vec_length[a]*new_loc_agg_dofs[a], b_orth_arr+a);
749: for (j=0; j<new_loc_agg_dofs[a]; j++) {
750: for (i=0; i<cand_vec_length[a]; i++) {
751: b_orth_arr[a][i*new_loc_agg_dofs[a]+j] = b_submat_tp[j*cand_vec_length[a]+i];
752: }
753: }
754: } else {
755: /* bridge, might have to fill up */
756: PetscMalloc(sizeof(PetscScalar)*cand_vec_length[a]*max_cand_vecs_to_add, b_orth_arr+a);
757: for (j=0; j<new_loc_agg_dofs[a]; j++) {
758: for (i=0; i<cand_vec_length[a]; i++) {
759: b_orth_arr[a][i*max_cand_vecs_to_add+j] = b_submat_tp[j*cand_vec_length[a]+i];
760: }
761: }
762: for (j=new_loc_agg_dofs[a]; j<max_cand_vecs_to_add; j++) {
763: for (i=0; i<cand_vec_length[a]; i++) {
764: b_orth_arr[a][i*max_cand_vecs_to_add+j] = 0.0;
765: }
766: }
767: new_loc_agg_dofs[a] = max_cand_vecs_to_add;
768: }
769: /* the number of columns in asa_lev->P that are local to this process */
770: total_loc_cols += new_loc_agg_dofs[a];
771: } /* end of loop over local aggregates */
773: /* destroy the submatrices, also frees all allocated space */
774: MatDestroyMatrices(mat_agg_loc_size, &b_submat_arr);
775: /* destroy all other workspace */
776: PetscFree(b_submat);
777: PetscFree(b_submat_tp);
778: PetscFree(idxm);
779: PetscFree(idxn);
780: PetscFree(tau);
781: PetscFree(work);
783: /* destroy old matrix P, Pt */
784: MatDestroy(&(asa_lev->P));
785: MatDestroy(&(asa_lev->Pt));
787: MatGetLocalSize(asa_lev->A, &a_loc_m, &a_loc_n);
789: /* determine local range */
790: MPI_Comm_size(asa_lev->comm, &comm_size);
791: MPI_Comm_rank(asa_lev->comm, &comm_rank);
792: PetscMalloc(comm_size*sizeof(PetscInt), &loc_cols);
793: MPI_Allgather(&total_loc_cols, 1, MPIU_INT, loc_cols, 1, MPIU_INT, asa_lev->comm);
794: mat_loc_col_start = 0;
795: for (i=0;i<comm_rank;i++) {
796: mat_loc_col_start += loc_cols[i];
797: }
798: mat_loc_col_end = mat_loc_col_start + loc_cols[i];
799: mat_loc_col_size = mat_loc_col_end-mat_loc_col_start;
800: if (mat_loc_col_size != total_loc_cols) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_COR, "Local size does not match matrix size");
801: PetscFree(loc_cols);
803: /* we now have enough information to create asa_lev->P */
804: MatCreateMPIAIJ(asa_lev->comm, a_loc_n, total_loc_cols, asa_lev->size, PETSC_DETERMINE,
805: cand_vecs_num, PETSC_NULL, cand_vecs_num, PETSC_NULL, &(asa_lev->P));
806: /* create asa_lev->Pt */
807: MatCreateMPIAIJ(asa_lev->comm, total_loc_cols, a_loc_n, PETSC_DETERMINE, asa_lev->size,
808: max_cand_vec_length, PETSC_NULL, max_cand_vec_length, PETSC_NULL, &(asa_lev->Pt));
809: if (asa_lev->next) {
810: /* create correlator for aggregates of next level */
811: MatCreateMPIAIJ(asa_lev->comm, mat_agg_loc_size, total_loc_cols, PETSC_DETERMINE, PETSC_DETERMINE,
812: cand_vecs_num, PETSC_NULL, cand_vecs_num, PETSC_NULL, &(asa_lev->next->agg_corr));
813: /* create asa_lev->next->bridge_corr matrix */
814: MatCreateMPIAIJ(asa_lev->comm, mat_agg_loc_size, total_loc_cols, PETSC_DETERMINE, PETSC_DETERMINE,
815: cand_vecs_num, PETSC_NULL, cand_vecs_num, PETSC_NULL, &(asa_lev->next->bridge_corr));
816: }
818: /* this is my own hack, but it should give the columns that we should write to */
819: MatGetOwnershipRangeColumn(asa_lev->P, &mat_loc_col_start, &mat_loc_col_end);
820: mat_loc_col_size = mat_loc_col_end-mat_loc_col_start;
821: if (mat_loc_col_size != total_loc_cols) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ, "The number of local columns in asa_lev->P assigned to this processor does not match the local vector size");
823: loc_agg_dofs_sum = 0;
824: /* construct P, Pt, agg_corr, bridge_corr */
825: for (a=0; a<mat_agg_loc_size; a++) {
826: /* store b_orth_arr[a] in P */
827: for (i=0; i<cand_vec_length[a]; i++) {
828: row = agg_arr[a][i];
829: for (j=0; j<new_loc_agg_dofs[a]; j++) {
830: col = mat_loc_col_start + loc_agg_dofs_sum + j;
831: val = b_orth_arr[a][i*new_loc_agg_dofs[a] + j];
832: MatSetValues(asa_lev->P, 1, &row, 1, &col, &val, INSERT_VALUES);
833: val = PetscConj(val);
834: MatSetValues(asa_lev->Pt, 1, &col, 1, &row, &val, INSERT_VALUES);
835: }
836: }
838: /* compute aggregate correlation matrices */
839: if (asa_lev->next) {
840: row = a+mat_agg_loc_start;
841: for (i=0; i<new_loc_agg_dofs[a]; i++) {
842: col = mat_loc_col_start + loc_agg_dofs_sum + i;
843: val = 1.0;
844: MatSetValues(asa_lev->next->agg_corr, 1, &row, 1, &col, &val, INSERT_VALUES);
845: /* for the bridge operator we leave out the newest candidates, i.e.
846: we set bridge_corr to 1.0 for all columns up to asa_lev->loc_agg_dofs[a] and to
847: 0.0 between asa_lev->loc_agg_dofs[a] and new_loc_agg_dofs[a] */
848: if (!(asa_lev->loc_agg_dofs && (i >= asa_lev->loc_agg_dofs[a]))) {
849: MatSetValues(asa_lev->next->bridge_corr, 1, &row, 1, &col, &val, INSERT_VALUES);
850: }
851: }
852: }
854: /* move to next entry point col */
855: loc_agg_dofs_sum += new_loc_agg_dofs[a];
856: } /* end of loop over local aggregates */
858: MatAssemblyBegin(asa_lev->P,MAT_FINAL_ASSEMBLY);
859: MatAssemblyEnd(asa_lev->P,MAT_FINAL_ASSEMBLY);
860: MatAssemblyBegin(asa_lev->Pt,MAT_FINAL_ASSEMBLY);
861: MatAssemblyEnd(asa_lev->Pt,MAT_FINAL_ASSEMBLY);
862: if (asa_lev->next) {
863: MatAssemblyBegin(asa_lev->next->agg_corr,MAT_FINAL_ASSEMBLY);
864: MatAssemblyEnd(asa_lev->next->agg_corr,MAT_FINAL_ASSEMBLY);
865: MatAssemblyBegin(asa_lev->next->bridge_corr,MAT_FINAL_ASSEMBLY);
866: MatAssemblyEnd(asa_lev->next->bridge_corr,MAT_FINAL_ASSEMBLY);
867: }
869: /* if we are not constructing a bridging operator, switch asa_lev->loc_agg_dofs
870: and new_loc_agg_dofs */
871: if (construct_bridge) {
872: PetscFree(new_loc_agg_dofs);
873: } else {
874: if (asa_lev->loc_agg_dofs) {
875: PetscFree(asa_lev->loc_agg_dofs);
876: }
877: asa_lev->loc_agg_dofs = new_loc_agg_dofs;
878: }
880: /* clean up */
881: for (a=0; a<mat_agg_loc_size; a++) {
882: PetscFree(b_orth_arr[a]);
883: PetscFree(agg_arr[a]);
884: }
885: PetscFree(cand_vec_length);
886: PetscFree(b_orth_arr);
887: PetscFree(agg_arr);
889: PetscLogEventEnd(PC_CreateTransferOp_ASA, 0,0,0,0);
890: return(0);
891: }
893: /* -------------------------------------------------------------------------- */
894: /*
895: PCSmoothProlongator_ASA - Computes the smoothed prolongators I and It on the level
897: Input Parameters:
898: . asa_lev - the level for which the smoothed prolongator is constructed
899: */
902: PetscErrorCode PCSmoothProlongator_ASA(PC_ASA_level *asa_lev)
903: {
907: MatDestroy(&(asa_lev->smP));
908: MatDestroy(&(asa_lev->smPt));
909: /* compute prolongator I_{l+1}^l = S_l P_{l+1}^l */
910: /* step 1: compute I_{l+1}^l = A_l P_{l+1}^l */
911: MatMatMult(asa_lev->A, asa_lev->P, MAT_INITIAL_MATRIX, 1, &(asa_lev->smP));
912: MatMatMult(asa_lev->Pt, asa_lev->A, MAT_INITIAL_MATRIX, 1, &(asa_lev->smPt));
913: /* step 2: shift and scale to get I_{l+1}^l = P_{l+1}^l - 4/(3/rho) A_l P_{l+1}^l */
914: MatAYPX(asa_lev->smP, -4./(3.*(asa_lev->spec_rad)), asa_lev->P, SUBSET_NONZERO_PATTERN);
915: MatAYPX(asa_lev->smPt, -4./(3.*(asa_lev->spec_rad)), asa_lev->Pt, SUBSET_NONZERO_PATTERN);
917: return(0);
918: }
921: /* -------------------------------------------------------------------------- */
922: /*
923: PCCreateVcycle_ASA - Creates the V-cycle, when aggregates are already defined
925: Input Parameters:
926: . asa - the preconditioner context
927: */
930: PetscErrorCode PCCreateVcycle_ASA(PC_ASA *asa)
931: {
933: PC_ASA_level *asa_lev, *asa_next_lev;
934: Mat AI;
937: PetscLogEventBegin(PC_CreateVcycle_ASA, 0,0,0,0);
939: if (!asa) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_NULL, "asa pointer is NULL");
940: if (!(asa->levellist)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_NULL, "no levels found");
941: asa_lev = asa->levellist;
942: PCComputeSpectralRadius_ASA(asa_lev);
943: PCSetupSmoothersOnLevel_ASA(asa, asa_lev, asa->nu);
945: while(asa_lev->next) {
946: asa_next_lev = asa_lev->next;
947: /* (a) aggregates are already constructed */
949: /* (b) construct B_{l+1} and P_{l+1}^l using (2.11) */
950: /* construct P_{l+1}^l */
951: PCCreateTransferOp_ASA(asa_lev, PETSC_FALSE);
953: /* construct B_{l+1} */
954: MatDestroy(&(asa_next_lev->B));
955: MatMatMult(asa_lev->Pt, asa_lev->B, MAT_INITIAL_MATRIX, 1, &(asa_next_lev->B));
956: asa_next_lev->cand_vecs = asa_lev->cand_vecs;
958: /* (c) construct smoothed prolongator */
959: PCSmoothProlongator_ASA(asa_lev);
960:
961: /* (d) construct coarse matrix */
962: /* Define coarse matrix A_{l+1} = (I_{l+1}^l)^T A_l I_{l+1}^l */
963: MatDestroy(&(asa_next_lev->A));
964: MatMatMult(asa_lev->A, asa_lev->smP, MAT_INITIAL_MATRIX, 1.0, &AI);
965: MatMatMult(asa_lev->smPt, AI, MAT_INITIAL_MATRIX, 1.0, &(asa_next_lev->A));
966: MatDestroy(&AI);
967: /* MatPtAP(asa_lev->A, asa_lev->smP, MAT_INITIAL_MATRIX, 1, &(asa_next_lev->A)); */
968: MatGetSize(asa_next_lev->A, PETSC_NULL, &(asa_next_lev->size));
969: PCComputeSpectralRadius_ASA(asa_next_lev);
970: PCSetupSmoothersOnLevel_ASA(asa, asa_next_lev, asa->nu);
971: /* create corresponding vectors x_{l+1}, b_{l+1}, r_{l+1} */
972: VecDestroy(&(asa_next_lev->x));
973: VecDestroy(&(asa_next_lev->b));
974: VecDestroy(&(asa_next_lev->r));
975: MatGetVecs(asa_next_lev->A, &(asa_next_lev->x), &(asa_next_lev->b));
976: MatGetVecs(asa_next_lev->A, PETSC_NULL, &(asa_next_lev->r));
978: /* go to next level */
979: asa_lev = asa_lev->next;
980: } /* end of while loop over the levels */
981: /* asa_lev now points to the coarsest level, set up direct solver there */
982: PCComputeSpectralRadius_ASA(asa_lev);
983: PCSetupDirectSolversOnLevel_ASA(asa, asa_lev, asa->nu);
985: PetscLogEventEnd(PC_CreateVcycle_ASA, 0,0,0,0);
986: return(0);
987: }
989: /* -------------------------------------------------------------------------- */
990: /*
991: PCAddCandidateToB_ASA - Inserts a candidate vector in B
993: Input Parameters:
994: + B - the matrix to insert into
995: . col_idx - the column we should insert to
996: . x - the vector to insert
997: - A - system matrix
999: Function will insert normalized x into B, such that <A x, x> = 1
1000: (x itself is not changed). If B is projected down then this property
1001: is kept. If <A_l x_l, x_l> = 1 and the next level is defined by
1002: x_{l+1} = Pt x_l and A_{l+1} = Pt A_l P then
1003: <A_{l+1} x_{l+1}, x_l> = <Pt A_l P Pt x_l, Pt x_l>
1004: = <A_l P Pt x_l, P Pt x_l> = <A_l x_l, x_l> = 1
1005: because of the definition of P in (2.11).
1006: */
1009: PetscErrorCode PCAddCandidateToB_ASA(Mat B, PetscInt col_idx, Vec x, Mat A)
1010: {
1012: Vec Ax;
1013: PetscScalar dotprod;
1014: PetscReal norm;
1015: PetscInt i, loc_start, loc_end;
1016: PetscScalar val, *vecarray;
1019: MatGetVecs(A, PETSC_NULL, &Ax);
1020: MatMult(A, x, Ax);
1021: VecDot(Ax, x, &dotprod);
1022: norm = PetscSqrtReal(PetscAbsScalar(dotprod));
1023: VecGetOwnershipRange(x, &loc_start, &loc_end);
1024: VecGetArray(x, &vecarray);
1025: for (i=loc_start; i<loc_end; i++) {
1026: val = vecarray[i-loc_start]/norm;
1027: MatSetValues(B, 1, &i, 1, &col_idx, &val, INSERT_VALUES);
1028: }
1029: MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);
1030: MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);
1031: VecRestoreArray(x, &vecarray);
1032: VecDestroy(&Ax);
1033: return(0);
1034: }
1036: /* -------------------------------------------------------------------------- */
1037: /*
1038: - x - a starting guess for a hard to approximate vector, if PETSC_NULL, will be generated
1039: */
1042: PetscErrorCode PCInitializationStage_ASA(PC_ASA *asa, Vec x)
1043: {
1045: PetscInt l;
1046: PC_ASA_level *asa_lev, *asa_next_lev;
1047: PetscRandom rctx; /* random number generator context */
1049: Vec ax;
1050: PetscScalar tmp;
1051: PetscReal prevnorm, norm;
1053: PetscBool skip_steps_f_i = PETSC_FALSE;
1054: PetscBool sufficiently_coarsened = PETSC_FALSE;
1056: PetscInt vec_size, vec_loc_size;
1057: PetscInt loc_vec_low, loc_vec_high;
1058: PetscInt i,j;
1060: /* Vec xhat = 0; */
1062: Mat AI;
1064: Vec cand_vec, cand_vec_new;
1065: PetscBool isrichardson;
1066: PC coarse_pc;
1069: PetscLogEventBegin(PC_InitializationStage_ASA,0,0,0,0);
1070: l=1;
1071: /* create first level */
1072: PCCreateLevel_ASA(&(asa->levellist), l, asa->comm, 0, 0, asa->ksptype_smooth, asa->pctype_smooth);
1073: asa_lev = asa->levellist;
1075: /* Set matrix */
1076: asa_lev->A = asa->A;
1077: MatGetSize(asa_lev->A, &i, &j);
1078: asa_lev->size = i;
1079: PCComputeSpectralRadius_ASA(asa_lev);
1080: PCSetupSmoothersOnLevel_ASA(asa, asa_lev, asa->mu_initial);
1082: /* Set DM */
1083: asa_lev->dm = asa->dm;
1084: PetscObjectReference((PetscObject)asa->dm);
1086: PetscPrintf(asa_lev->comm, "Initialization stage\n");
1088: if (x) {
1089: /* use starting guess */
1090: VecDestroy(&(asa_lev->x));
1091: VecDuplicate(x, &(asa_lev->x));
1092: VecCopy(x, asa_lev->x);
1093: } else {
1094: /* select random starting vector */
1095: VecDestroy(&(asa_lev->x));
1096: MatGetVecs(asa_lev->A, &(asa_lev->x), 0);
1097: PetscRandomCreate(asa_lev->comm,&rctx);
1098: PetscRandomSetFromOptions(rctx);
1099: VecSetRandom(asa_lev->x, rctx);
1100: PetscRandomDestroy(&rctx);
1101: }
1103: /* create right hand side */
1104: VecDestroy(&(asa_lev->b));
1105: MatGetVecs(asa_lev->A, &(asa_lev->b), 0);
1106: VecSet(asa_lev->b, 0.0);
1108: /* relax and check whether that's enough already */
1109: /* compute old norm */
1110: MatGetVecs(asa_lev->A, 0, &ax);
1111: MatMult(asa_lev->A, asa_lev->x, ax);
1112: VecDot(asa_lev->x, ax, &tmp);
1113: prevnorm = PetscAbsScalar(tmp);
1114: PetscPrintf(asa_lev->comm, "Residual norm of starting guess: %f\n", prevnorm);
1116: /* apply mu_initial relaxations */
1117: KSPSolve(asa_lev->smoothd, asa_lev->b, asa_lev->x);
1118: /* compute new norm */
1119: MatMult(asa_lev->A, asa_lev->x, ax);
1120: VecDot(asa_lev->x, ax, &tmp);
1121: norm = PetscAbsScalar(tmp);
1122: VecDestroy(&(ax));
1123: PetscPrintf(asa_lev->comm, "Residual norm of relaxation after %g %D relaxations: %g %g\n", asa->epsilon,asa->mu_initial, norm,prevnorm);
1125: /* Check if it already converges by itself */
1126: if (norm/prevnorm <= pow(asa->epsilon, asa->mu_initial)) {
1127: /* converges by relaxation alone */
1128: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP, "Relaxation should be sufficient to treat this problem. "
1129: "Use relaxation or decrease epsilon with -pc_asa_epsilon");
1130: } else {
1131: /* set the number of relaxations to asa->mu from asa->mu_initial */
1132: PCSetupSmoothersOnLevel_ASA(asa, asa_lev, asa->mu);
1134: /* Let's do some multigrid ! */
1135: sufficiently_coarsened = PETSC_FALSE;
1137: /* do the whole initialization stage loop */
1138: while (!sufficiently_coarsened) {
1139: PetscPrintf(asa_lev->comm, "Initialization stage: creating level %D\n", asa_lev->level+1);
1141: /* (a) Set candidate matrix B_l = x_l */
1142: /* get the correct vector sizes and data */
1143: VecGetSize(asa_lev->x, &vec_size);
1144: VecGetOwnershipRange(asa_lev->x, &loc_vec_low, &loc_vec_high);
1145: vec_loc_size = loc_vec_high - loc_vec_low;
1147: /* create matrix for candidates */
1148: MatCreateMPIDense(asa_lev->comm, vec_loc_size, PETSC_DECIDE, vec_size, asa->max_cand_vecs, PETSC_NULL, &(asa_lev->B));
1149: /* set the first column */
1150: PCAddCandidateToB_ASA(asa_lev->B, 0, asa_lev->x, asa_lev->A);
1151: asa_lev->cand_vecs = 1;
1153: /* create next level */
1154: PCCreateLevel_ASA(&(asa_lev->next), asa_lev->level+1, asa_lev->comm, asa_lev, PETSC_NULL, asa->ksptype_smooth, asa->pctype_smooth);
1155: asa_next_lev = asa_lev->next;
1157: /* (b) Create nodal aggregates A_i^l */
1158: PCCreateAggregates_ASA(asa_lev);
1159:
1160: /* (c) Define tentatative prolongator P_{l+1}^l and candidate matrix B_{l+1}
1161: using P_{l+1}^l B_{l+1} = B_l and (P_{l+1}^l)^T P_{l+1}^l = I */
1162: PCCreateTransferOp_ASA(asa_lev, PETSC_FALSE);
1164: /* future WORK: set correct fill ratios for all the operations below */
1165: MatMatMult(asa_lev->Pt, asa_lev->B, MAT_INITIAL_MATRIX, 1, &(asa_next_lev->B));
1166: asa_next_lev->cand_vecs = asa_lev->cand_vecs;
1168: /* (d) Define prolongator I_{l+1}^l = S_l P_{l+1}^l */
1169: PCSmoothProlongator_ASA(asa_lev);
1171: /* (e) Define coarse matrix A_{l+1} = (I_{l+1}^l)^T A_l I_{l+1}^l */
1172: MatMatMult(asa_lev->A, asa_lev->smP, MAT_INITIAL_MATRIX, 1.0, &AI);
1173: MatMatMult(asa_lev->smPt, AI, MAT_INITIAL_MATRIX, 1.0, &(asa_next_lev->A));
1174: MatDestroy(&AI);
1175: /* MatPtAP(asa_lev->A, asa_lev->smP, MAT_INITIAL_MATRIX, 1, &(asa_next_lev->A)); */
1176: MatGetSize(asa_next_lev->A, PETSC_NULL, &(asa_next_lev->size));
1177: PCComputeSpectralRadius_ASA(asa_next_lev);
1178: PCSetupSmoothersOnLevel_ASA(asa, asa_next_lev, asa->mu);
1180: /* coarse enough for direct solver? */
1181: MatGetSize(asa_next_lev->A, &i, &j);
1182: if (PetscMax(i,j) <= asa->direct_solver) {
1183: PetscPrintf(asa_lev->comm, "Level %D can be treated directly.\n"
1184: "Algorithm will use %D levels.\n", asa_next_lev->level,
1185: asa_next_lev->level);
1186: break; /* go to step 5 */
1187: }
1189: if (!skip_steps_f_i) {
1190: /* (f) Set x_{l+1} = B_{l+1}, we just compute it again */
1191: VecDestroy(&(asa_next_lev->x));
1192: MatGetVecs(asa_lev->P, &(asa_next_lev->x), 0);
1193: MatMult(asa_lev->Pt, asa_lev->x, asa_next_lev->x);
1195: /* /\* (g) Make copy \hat{x}_{l+1} = x_{l+1} *\/ */
1196: /* VecDuplicate(asa_next_lev->x, &xhat); */
1197: /* VecCopy(asa_next_lev->x, xhat); */
1198:
1199: /* Create b_{l+1} */
1200: VecDestroy(&(asa_next_lev->b));
1201: MatGetVecs(asa_next_lev->A, &(asa_next_lev->b), 0);
1202: VecSet(asa_next_lev->b, 0.0);
1204: /* (h) Relax mu times on A_{l+1} x = 0 */
1205: /* compute old norm */
1206: MatGetVecs(asa_next_lev->A, 0, &ax);
1207: MatMult(asa_next_lev->A, asa_next_lev->x, ax);
1208: VecDot(asa_next_lev->x, ax, &tmp);
1209: prevnorm = PetscAbsScalar(tmp);
1210: PetscPrintf(asa_next_lev->comm, "Residual norm of starting guess on level %D: %f\n", asa_next_lev->level, prevnorm);
1211: /* apply mu relaxations: WORK, make sure that mu is set correctly */
1212: KSPSolve(asa_next_lev->smoothd, asa_next_lev->b, asa_next_lev->x);
1213: /* compute new norm */
1214: MatMult(asa_next_lev->A, asa_next_lev->x, ax);
1215: VecDot(asa_next_lev->x, ax, &tmp);
1216: norm = PetscAbsScalar(tmp);
1217: VecDestroy(&(ax));
1218: PetscPrintf(asa_next_lev->comm, "Residual norm after Richardson iteration on level %D: %f\n", asa_next_lev->level, norm);
1219: /* (i) Check if it already converges by itself */
1220: if (norm/prevnorm <= pow(asa->epsilon, asa->mu)) {
1221: /* relaxation reduces error sufficiently */
1222: skip_steps_f_i = PETSC_TRUE;
1223: }
1224: }
1225: /* (j) go to next coarser level */
1226: l++;
1227: asa_lev = asa_next_lev;
1228: }
1229: /* Step 5. */
1230: asa->levels = asa_next_lev->level; /* WORK: correct? */
1232: /* Set up direct solvers on coarsest level */
1233: if (asa_next_lev->smoothd != asa_next_lev->smoothu) {
1234: if (asa_next_lev->smoothu) { KSPDestroy(&asa_next_lev->smoothu); }
1235: }
1236: KSPSetType(asa_next_lev->smoothd, asa->ksptype_direct);
1237: PetscTypeCompare((PetscObject)(asa_next_lev->smoothd), KSPRICHARDSON, &isrichardson);
1238: if (isrichardson) {
1239: KSPSetInitialGuessNonzero(asa_next_lev->smoothd, PETSC_TRUE);
1240: } else {
1241: KSPSetInitialGuessNonzero(asa_next_lev->smoothd, PETSC_FALSE);
1242: }
1243: KSPGetPC(asa_next_lev->smoothd, &coarse_pc);
1244: PCSetType(coarse_pc, asa->pctype_direct);
1245: asa_next_lev->smoothu = asa_next_lev->smoothd;
1246: PCSetupDirectSolversOnLevel_ASA(asa, asa_next_lev, asa->nu);
1248: /* update finest-level candidate matrix B_1 = I_2^1 I_3^2 ... I_{L-1}^{L-2} x_{L-1} */
1249: if (!asa_lev->prev) {
1250: /* just one relaxation level */
1251: VecDuplicate(asa_lev->x, &cand_vec);
1252: VecCopy(asa_lev->x, cand_vec);
1253: } else {
1254: /* interpolate up the chain */
1255: cand_vec = asa_lev->x;
1256: asa_lev->x = 0;
1257: while(asa_lev->prev) {
1258: /* interpolate to higher level */
1259: MatGetVecs(asa_lev->prev->smP, 0, &cand_vec_new);
1260: MatMult(asa_lev->prev->smP, cand_vec, cand_vec_new);
1261: VecDestroy(&(cand_vec));
1262: cand_vec = cand_vec_new;
1263:
1264: /* destroy all working vectors on the way */
1265: VecDestroy(&(asa_lev->x));
1266: VecDestroy(&(asa_lev->b));
1268: /* move to next higher level */
1269: asa_lev = asa_lev->prev;
1270: }
1271: }
1272: /* set the first column of B1 */
1273: PCAddCandidateToB_ASA(asa_lev->B, 0, cand_vec, asa_lev->A);
1274: VecDestroy(&(cand_vec));
1276: /* Step 6. Create V-cycle */
1277: PCCreateVcycle_ASA(asa);
1278: }
1279: PetscLogEventEnd(PC_InitializationStage_ASA,0,0,0,0);
1280: return(0);
1281: }
1283: /* -------------------------------------------------------------------------- */
1284: /*
1285: PCApplyVcycleOnLevel_ASA - Applies current V-cycle
1287: Input Parameters:
1288: + asa_lev - the current level we should recurse on
1289: - gamma - the number of recursive cycles we should run
1291: */
1294: PetscErrorCode PCApplyVcycleOnLevel_ASA(PC_ASA_level *asa_lev, PetscInt gamma)
1295: {
1297: PC_ASA_level *asa_next_lev;
1298: PetscInt g;
1301: if (!asa_lev) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_NULL, "Level is empty in PCApplyVcycleOnLevel_ASA");
1302: asa_next_lev = asa_lev->next;
1304: if (asa_next_lev) {
1305: /* 1. Presmoothing */
1306: KSPSolve(asa_lev->smoothd, asa_lev->b, asa_lev->x);
1307: /* 2. Coarse grid corrections */
1308: /* MatGetVecs(asa_lev->A, 0, &tmp); */
1309: /* MatGetVecs(asa_lev->smP, &(asa_next_lev->b), 0); */
1310: /* MatGetVecs(asa_next_lev->A, &(asa_next_lev->x), 0); */
1311: for (g=0; g<gamma; g++) {
1312: /* (a) get coarsened b_{l+1} = (I_{l+1}^l)^T (b_l - A_l x_l) */
1313: MatMult(asa_lev->A, asa_lev->x, asa_lev->r);
1314: VecAYPX(asa_lev->r, -1.0, asa_lev->b);
1315: MatMult(asa_lev->smPt, asa_lev->r, asa_next_lev->b);
1317: /* (b) Set x_{l+1} = 0 and recurse */
1318: VecSet(asa_next_lev->x, 0.0);
1319: PCApplyVcycleOnLevel_ASA(asa_next_lev, gamma);
1321: /* (c) correct solution x_l = x_l + I_{l+1}^l x_{l+1} */
1322: MatMultAdd(asa_lev->smP, asa_next_lev->x, asa_lev->x, asa_lev->x);
1323: }
1324: /* VecDestroy(&(asa_lev->r)); */
1325: /* /\* discard x_{l+1}, b_{l+1} *\/ */
1326: /* VecDestroy(&(asa_next_lev->x)); */
1327: /* VecDestroy(&(asa_next_lev->b)); */
1328:
1329: /* 3. Postsmoothing */
1330: KSPSolve(asa_lev->smoothu, asa_lev->b, asa_lev->x);
1331: } else {
1332: /* Base case: solve directly */
1333: KSPSolve(asa_lev->smoothd, asa_lev->b, asa_lev->x);
1334: }
1335: return(0);
1336: }
1339: /* -------------------------------------------------------------------------- */
1340: /*
1341: PCGeneralSetupStage_ASA - Applies the ASA preconditioner to a vector. Algorithm
1342: 4 from the ASA paper
1344: Input Parameters:
1345: + asa - the data structure for the ASA algorithm
1346: - cand - a possible candidate vector, if PETSC_NULL, will be constructed randomly
1348: Output Parameters:
1349: . cand_added - PETSC_TRUE, if new candidate vector added, PETSC_FALSE otherwise
1350: */
1353: PetscErrorCode PCGeneralSetupStage_ASA(PC_ASA *asa, Vec cand, PetscBool *cand_added)
1354: {
1356: PC_ASA_level *asa_lev, *asa_next_lev;
1358: PetscRandom rctx; /* random number generator context */
1359: PetscReal r;
1360: PetscScalar rs;
1361: PetscBool nd_fast;
1363: Vec ax;
1364: PetscScalar tmp;
1365: PetscReal norm, prevnorm = 0.0;
1366: PetscInt c;
1368: PetscInt loc_vec_low, loc_vec_high;
1369: PetscInt i;
1371: PetscBool skip_steps_d_j = PETSC_FALSE;
1373: PetscInt *idxm, *idxn;
1374: PetscScalar *v;
1376: Mat AI;
1378: Vec cand_vec, cand_vec_new;
1381: *cand_added = PETSC_FALSE;
1382:
1383: asa_lev = asa->levellist;
1384: if (asa_lev == 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_NULL, "No levels found in PCGeneralSetupStage_ASA");
1385: asa_next_lev = asa_lev->next;
1386: if (asa_next_lev == 0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_NULL, "Just one level, not implemented yet");
1387:
1388: PetscPrintf(asa_lev->comm, "General setup stage\n");
1390: PetscLogEventBegin(PC_GeneralSetupStage_ASA,0,0,0,0);
1392: /* 1. If max. dof per node on level 2 equals K, stop */
1393: if (asa_next_lev->cand_vecs >= asa->max_dof_lev_2) {
1394: PetscPrintf(PETSC_COMM_WORLD,
1395: "Maximum dof on level 2 reached: %D\n"
1396: "Consider increasing this limit by setting it with -pc_asa_max_dof_lev_2\n",
1397: asa->max_dof_lev_2);
1398: return(0);
1399: }
1401: /* 2. Create copy of B_1 (skipped, we just replace the last column in step 8.) */
1402:
1403: if (!cand) {
1404: /* 3. Select a random x_1 */
1405: VecDestroy(&(asa_lev->x));
1406: MatGetVecs(asa_lev->A, &(asa_lev->x), 0);
1407: PetscRandomCreate(asa_lev->comm,&rctx);
1408: PetscRandomSetFromOptions(rctx);
1409: VecGetOwnershipRange(asa_lev->x, &loc_vec_low, &loc_vec_high);
1410: for (i=loc_vec_low; i<loc_vec_high; i++) {
1411: PetscRandomGetValueReal(rctx, &r);
1412: rs = r;
1413: VecSetValues(asa_lev->x, 1, &i, &rs, INSERT_VALUES);
1414: }
1415: VecAssemblyBegin(asa_lev->x);
1416: VecAssemblyEnd(asa_lev->x);
1417: PetscRandomDestroy(&rctx);
1418: } else {
1419: VecDestroy(&(asa_lev->x));
1420: VecDuplicate(cand, &(asa_lev->x));
1421: VecCopy(cand, asa_lev->x);
1422: }
1424: /* create right hand side */
1425: VecDestroy(&(asa_lev->b));
1426: MatGetVecs(asa_lev->A, &(asa_lev->b), 0);
1427: VecSet(asa_lev->b, 0.0);
1428:
1429: /* Apply mu iterations of current V-cycle */
1430: nd_fast = PETSC_FALSE;
1431: MatGetVecs(asa_lev->A, 0, &ax);
1432: for (c=0; c<asa->mu; c++) {
1433: PCApplyVcycleOnLevel_ASA(asa_lev, asa->gamma);
1434:
1435: MatMult(asa_lev->A, asa_lev->x, ax);
1436: VecDot(asa_lev->x, ax, &tmp);
1437: norm = PetscAbsScalar(tmp);
1438: if (c>0) {
1439: if (norm/prevnorm < asa->epsilon) {
1440: nd_fast = PETSC_TRUE;
1441: break;
1442: }
1443: }
1444: prevnorm = norm;
1445: }
1446: VecDestroy(&(ax));
1448: /* 4. If energy norm decreases sufficiently fast, then stop */
1449: if (nd_fast) {
1450: PetscPrintf(asa_lev->comm, "nd_fast is true\n");
1451: return(0);
1452: }
1454: /* 5. Update B_1, by adding new column x_1 */
1455: if (asa_lev->cand_vecs >= asa->max_cand_vecs) {
1456: SETERRQ(PETSC_COMM_SELF,PETSC_ERR_MEM, "Number of candidate vectors will exceed allocated storage space");
1457: } else {
1458: PetscPrintf(asa_lev->comm, "Adding candidate vector %D\n", asa_lev->cand_vecs+1);
1459: }
1460: PCAddCandidateToB_ASA(asa_lev->B, asa_lev->cand_vecs, asa_lev->x, asa_lev->A);
1461: *cand_added = PETSC_TRUE;
1462: asa_lev->cand_vecs++;
1464: /* 6. loop over levels */
1465: while(asa_next_lev && asa_next_lev->next) {
1466: PetscPrintf(asa_lev->comm, "General setup stage: processing level %D\n", asa_next_lev->level);
1467: /* (a) define B_{l+1} and P_{l+1}^L */
1468: /* construct P_{l+1}^l */
1469: PCCreateTransferOp_ASA(asa_lev, PETSC_FALSE);
1471: /* construct B_{l+1} */
1472: MatDestroy(&(asa_next_lev->B));
1473: MatMatMult(asa_lev->Pt, asa_lev->B, MAT_INITIAL_MATRIX, 1.0, &(asa_next_lev->B));
1474: /* do not increase asa_next_lev->cand_vecs until step (j) */
1475:
1476: /* (b) construct prolongator I_{l+1}^l = S_l P_{l+1}^l */
1477: PCSmoothProlongator_ASA(asa_lev);
1478:
1479: /* (c) construct coarse matrix A_{l+1} = (I_{l+1}^l)^T A_l I_{l+1}^l */
1480: MatDestroy(&(asa_next_lev->A));
1481: MatMatMult(asa_lev->A, asa_lev->smP, MAT_INITIAL_MATRIX, 1.0, &AI);
1482: MatMatMult(asa_lev->smPt, AI, MAT_INITIAL_MATRIX, 1.0, &(asa_next_lev->A));
1483: MatDestroy(&AI);
1484: /* MatPtAP(asa_lev->A, asa_lev->smP, MAT_INITIAL_MATRIX, 1, &(asa_next_lev->A)); */
1485: MatGetSize(asa_next_lev->A, PETSC_NULL, &(asa_next_lev->size));
1486: PCComputeSpectralRadius_ASA(asa_next_lev);
1487: PCSetupSmoothersOnLevel_ASA(asa, asa_next_lev, asa->mu);
1489: if (! skip_steps_d_j) {
1490: /* (d) get vector x_{l+1} from last column in B_{l+1} */
1491: VecDestroy(&(asa_next_lev->x));
1492: MatGetVecs(asa_next_lev->B, 0, &(asa_next_lev->x));
1494: VecGetOwnershipRange(asa_next_lev->x, &loc_vec_low, &loc_vec_high);
1495: PetscMalloc(sizeof(PetscInt)*(loc_vec_high-loc_vec_low), &idxm);
1496: for (i=loc_vec_low; i<loc_vec_high; i++)
1497: idxm[i-loc_vec_low] = i;
1498: PetscMalloc(sizeof(PetscInt)*1, &idxn);
1499: idxn[0] = asa_next_lev->cand_vecs;
1501: PetscMalloc(sizeof(PetscScalar)*(loc_vec_high-loc_vec_low), &v);
1502: MatGetValues(asa_next_lev->B, loc_vec_high-loc_vec_low, idxm, 1, idxn, v);
1504: VecSetValues(asa_next_lev->x, loc_vec_high-loc_vec_low, idxm, v, INSERT_VALUES);
1505: VecAssemblyBegin(asa_next_lev->x);
1506: VecAssemblyEnd(asa_next_lev->x);
1508: PetscFree(v);
1509: PetscFree(idxm);
1510: PetscFree(idxn);
1511:
1512: /* (e) create bridge transfer operator P_{l+2}^{l+1}, by using the previously
1513: computed candidates */
1514: PCCreateTransferOp_ASA(asa_next_lev, PETSC_TRUE);
1516: /* (f) construct bridging prolongator I_{l+2}^{l+1} = S_{l+1} P_{l+2}^{l+1} */
1517: PCSmoothProlongator_ASA(asa_next_lev);
1519: /* (g) compute <A_{l+1} x_{l+1}, x_{l+1}> and save it */
1520: MatGetVecs(asa_next_lev->A, 0, &ax);
1521: MatMult(asa_next_lev->A, asa_next_lev->x, ax);
1522: VecDot(asa_next_lev->x, ax, &tmp);
1523: prevnorm = PetscAbsScalar(tmp);
1524: VecDestroy(&(ax));
1526: /* (h) apply mu iterations of current V-cycle */
1527: /* set asa_next_lev->b */
1528: VecDestroy(&(asa_next_lev->b));
1529: VecDestroy(&(asa_next_lev->r));
1530: MatGetVecs(asa_next_lev->A, &(asa_next_lev->b), &(asa_next_lev->r));
1531: VecSet(asa_next_lev->b, 0.0);
1532: /* apply V-cycle */
1533: for (c=0; c<asa->mu; c++) {
1534: PCApplyVcycleOnLevel_ASA(asa_next_lev, asa->gamma);
1535: }
1537: /* (i) check convergence */
1538: /* compute <A_{l+1} x_{l+1}, x_{l+1}> and save it */
1539: MatGetVecs(asa_next_lev->A, 0, &ax);
1540: MatMult(asa_next_lev->A, asa_next_lev->x, ax);
1541: VecDot(asa_next_lev->x, ax, &tmp);
1542: norm = PetscAbsScalar(tmp);
1543: VecDestroy(&(ax));
1545: if (norm/prevnorm <= pow(asa->epsilon, asa->mu)) skip_steps_d_j = PETSC_TRUE;
1546:
1547: /* (j) update candidate B_{l+1} */
1548: PCAddCandidateToB_ASA(asa_next_lev->B, asa_next_lev->cand_vecs, asa_next_lev->x, asa_next_lev->A);
1549: asa_next_lev->cand_vecs++;
1550: }
1551: /* go to next level */
1552: asa_lev = asa_lev->next;
1553: asa_next_lev = asa_next_lev->next;
1554: }
1556: /* 7. update the fine-level candidate */
1557: if (! asa_lev->prev) {
1558: /* just one coarsening level */
1559: VecDuplicate(asa_lev->x, &cand_vec);
1560: VecCopy(asa_lev->x, cand_vec);
1561: } else {
1562: cand_vec = asa_lev->x;
1563: asa_lev->x = 0;
1564: while(asa_lev->prev) {
1565: /* interpolate to higher level */
1566: MatGetVecs(asa_lev->prev->smP, 0, &cand_vec_new);
1567: MatMult(asa_lev->prev->smP, cand_vec, cand_vec_new);
1568: VecDestroy(&(cand_vec));
1569: cand_vec = cand_vec_new;
1571: /* destroy all working vectors on the way */
1572: VecDestroy(&(asa_lev->x));
1573: VecDestroy(&(asa_lev->b));
1575: /* move to next higher level */
1576: asa_lev = asa_lev->prev;
1577: }
1578: }
1579: /* 8. update B_1 by setting the last column of B_1 */
1580: PCAddCandidateToB_ASA(asa_lev->B, asa_lev->cand_vecs-1, cand_vec, asa_lev->A);
1581: VecDestroy(&(cand_vec));
1583: /* 9. create V-cycle */
1584: PCCreateVcycle_ASA(asa);
1585:
1586: PetscLogEventEnd(PC_GeneralSetupStage_ASA,0,0,0,0);
1587: return(0);
1588: }
1590: /* -------------------------------------------------------------------------- */
1591: /*
1592: PCConstructMultigrid_ASA - creates the multigrid preconditionier, this is a fairly
1593: involved process, which runs extensive testing to compute good candidate vectors
1595: Input Parameters:
1596: . pc - the preconditioner context
1598: */
1601: PetscErrorCode PCConstructMultigrid_ASA(PC pc)
1602: {
1604: PC_ASA *asa = (PC_ASA*)pc->data;
1605: PC_ASA_level *asa_lev;
1606: PetscInt i, ls, le;
1607: PetscScalar *d;
1608: PetscBool zeroflag = PETSC_FALSE;
1609: PetscReal rnorm, rnorm_start;
1610: PetscReal rq, rq_prev;
1611: PetscScalar rq_nom, rq_denom;
1612: PetscBool cand_added;
1613: PetscRandom rctx;
1617: /* check if we should scale with diagonal */
1618: if (asa->scale_diag) {
1619: /* Get diagonal scaling factors */
1620: MatGetVecs(pc->pmat,&(asa->invsqrtdiag),0);
1621: MatGetDiagonal(pc->pmat,asa->invsqrtdiag);
1622: /* compute (inverse) sqrt of diagonal */
1623: VecGetOwnershipRange(asa->invsqrtdiag, &ls, &le);
1624: VecGetArray(asa->invsqrtdiag, &d);
1625: for (i=0; i<le-ls; i++) {
1626: if (d[i] == 0.0) {
1627: d[i] = 1.0;
1628: zeroflag = PETSC_TRUE;
1629: } else {
1630: d[i] = 1./PetscSqrtReal(PetscAbsScalar(d[i]));
1631: }
1632: }
1633: VecRestoreArray(asa->invsqrtdiag,&d);
1634: VecAssemblyBegin(asa->invsqrtdiag);
1635: VecAssemblyEnd(asa->invsqrtdiag);
1636: if (zeroflag) {
1637: PetscInfo(pc,"Zero detected in diagonal of matrix, using 1 at those locations\n");
1638: }
1639:
1640: /* scale the matrix and store it: D^{-1/2} A D^{-1/2} */
1641: MatDuplicate(pc->pmat, MAT_COPY_VALUES, &(asa->A)); /* probably inefficient */
1642: MatDiagonalScale(asa->A, asa->invsqrtdiag, asa->invsqrtdiag);
1643: } else {
1644: /* don't scale */
1645: asa->A = pc->pmat;
1646: }
1647: /* Initialization stage */
1648: PCInitializationStage_ASA(asa, PETSC_NULL);
1649:
1650: /* get first level */
1651: asa_lev = asa->levellist;
1653: PetscRandomCreate(asa->comm,&rctx);
1654: PetscRandomSetFromOptions(rctx);
1655: VecSetRandom(asa_lev->x,rctx);
1657: /* compute starting residual */
1658: VecDestroy(&(asa_lev->r));
1659: MatGetVecs(asa_lev->A, PETSC_NULL, &(asa_lev->r));
1660: MatMult(asa_lev->A, asa_lev->x, asa_lev->r);
1661: /* starting residual norm */
1662: VecNorm(asa_lev->r, NORM_2, &rnorm_start);
1663: /* compute Rayleigh quotients */
1664: VecDot(asa_lev->x, asa_lev->r, &rq_nom);
1665: VecDot(asa_lev->x, asa_lev->x, &rq_denom);
1666: rq_prev = PetscAbsScalar(rq_nom / rq_denom);
1668: /* check if we have to add more candidates */
1669: for (i=0; i<asa->max_it; i++) {
1670: if (asa_lev->cand_vecs >= asa->max_cand_vecs) {
1671: /* reached limit for candidate vectors */
1672: break;
1673: }
1674: /* apply V-cycle */
1675: PCApplyVcycleOnLevel_ASA(asa_lev, asa->gamma);
1676: /* check convergence */
1677: MatMult(asa_lev->A, asa_lev->x, asa_lev->r);
1678: VecNorm(asa_lev->r, NORM_2, &rnorm);
1679: PetscPrintf(asa->comm, "After %D iterations residual norm is %f\n", i+1, rnorm);
1680: if (rnorm < rnorm_start*(asa->rtol) || rnorm < asa->abstol) {
1681: /* convergence */
1682: break;
1683: }
1684: /* compute new Rayleigh quotient */
1685: VecDot(asa_lev->x, asa_lev->r, &rq_nom);
1686: VecDot(asa_lev->x, asa_lev->x, &rq_denom);
1687: rq = PetscAbsScalar(rq_nom / rq_denom);
1688: PetscPrintf(asa->comm, "After %D iterations Rayleigh quotient of residual is %f\n", i+1, rq);
1689: /* test Rayleigh quotient decrease and add more candidate vectors if necessary */
1690: if (i && (rq > asa->rq_improve*rq_prev)) {
1691: /* improve interpolation by adding another candidate vector */
1692: PCGeneralSetupStage_ASA(asa, asa_lev->r, &cand_added);
1693: if (!cand_added) {
1694: /* either too many candidates for storage or cycle is already effective */
1695: PetscPrintf(asa->comm, "either too many candidates for storage or cycle is already effective\n");
1696: break;
1697: }
1698: VecSetRandom(asa_lev->x, rctx);
1699: rq_prev = rq*10000.; /* give the new V-cycle some grace period */
1700: } else {
1701: rq_prev = rq;
1702: }
1703: }
1705: VecDestroy(&(asa_lev->x));
1706: VecDestroy(&(asa_lev->b));
1707: PetscRandomDestroy(&rctx);
1708: asa->multigrid_constructed = PETSC_TRUE;
1709: return(0);
1710: }
1712: /* -------------------------------------------------------------------------- */
1713: /*
1714: PCApply_ASA - Applies the ASA preconditioner to a vector.
1716: Input Parameters:
1717: . pc - the preconditioner context
1718: . x - input vector
1720: Output Parameter:
1721: . y - output vector
1723: Application Interface Routine: PCApply()
1724: */
1727: PetscErrorCode PCApply_ASA(PC pc,Vec x,Vec y)
1728: {
1729: PC_ASA *asa = (PC_ASA*)pc->data;
1730: PC_ASA_level *asa_lev;
1735: if (!asa->multigrid_constructed) {
1736: PCConstructMultigrid_ASA(pc);
1737: }
1739: /* get first level */
1740: asa_lev = asa->levellist;
1742: /* set the right hand side */
1743: VecDuplicate(x, &(asa->b));
1744: VecCopy(x, asa->b);
1745: /* set starting vector */
1746: VecDestroy(&(asa->x));
1747: MatGetVecs(asa->A, &(asa->x), PETSC_NULL);
1748: VecSet(asa->x, 0.0);
1749:
1750: /* set vectors */
1751: asa_lev->x = asa->x;
1752: asa_lev->b = asa->b;
1754: PCApplyVcycleOnLevel_ASA(asa_lev, asa->gamma);
1755:
1756: /* Return solution */
1757: VecCopy(asa->x, y);
1759: /* delete working vectors */
1760: VecDestroy(&(asa->x));
1761: VecDestroy(&(asa->b));
1762: asa_lev->x = PETSC_NULL;
1763: asa_lev->b = PETSC_NULL;
1765: return(0);
1766: }
1768: /* -------------------------------------------------------------------------- */
1769: /*
1770: PCApplyRichardson_ASA - Applies the ASA iteration to solve a linear system
1772: Input Parameters:
1773: . pc - the preconditioner context
1774: . b - the right hand side
1776: Output Parameter:
1777: . x - output vector
1779: DOES NOT WORK!!!!!
1781: */
1784: PetscErrorCode PCApplyRichardson_ASA(PC pc,Vec b,Vec x,Vec w,PetscReal rtol,PetscReal abstol, PetscReal dtol,PetscInt its,PetscBool guesszero,PetscInt *outits,PCRichardsonConvergedReason *reason)
1785: {
1786: PC_ASA *asa = (PC_ASA*)pc->data;
1787: PC_ASA_level *asa_lev;
1788: PetscInt i;
1789: PetscReal rnorm, rnorm_start;
1794: if (! asa->multigrid_constructed) {
1795: PCConstructMultigrid_ASA(pc);
1796: }
1798: /* get first level */
1799: asa_lev = asa->levellist;
1801: /* set the right hand side */
1802: VecDuplicate(b, &(asa->b));
1803: if (asa->scale_diag) {
1804: VecPointwiseMult(asa->b, asa->invsqrtdiag, b);
1805: } else {
1806: VecCopy(b, asa->b);
1807: }
1808: /* set starting vector */
1809: VecDuplicate(x, &(asa->x));
1810: VecCopy(x, asa->x);
1811:
1812: /* compute starting residual */
1813: VecDestroy(&(asa->r));
1814: MatGetVecs(asa->A, &(asa->r), PETSC_NULL);
1815: MatMult(asa->A, asa->x, asa->r);
1816: VecAYPX(asa->r, -1.0, asa->b);
1817: /* starting residual norm */
1818: VecNorm(asa->r, NORM_2, &rnorm_start);
1820: /* set vectors */
1821: asa_lev->x = asa->x;
1822: asa_lev->b = asa->b;
1824: *reason = PCRICHARDSON_CONVERGED_ITS;
1825: /* **************** Full algorithm loop *********************************** */
1826: for (i=0; i<its; i++) {
1827: /* apply V-cycle */
1828: PCApplyVcycleOnLevel_ASA(asa_lev, asa->gamma);
1829: /* check convergence */
1830: MatMult(asa->A, asa->x, asa->r);
1831: VecAYPX(asa->r, -1.0, asa->b);
1832: VecNorm(asa->r, NORM_2, &rnorm);
1833: PetscPrintf(asa->comm, "After %D iterations residual norm is %f\n", i+1, rnorm);
1834: if (rnorm < rnorm_start*(rtol)) {
1835: *reason = PCRICHARDSON_CONVERGED_RTOL;
1836: break;
1837: } else if (rnorm < asa->abstol) {
1838: *reason = PCRICHARDSON_CONVERGED_ATOL;
1839: break;
1840: } else if (rnorm > rnorm_start*(dtol)) {
1841: *reason = PCRICHARDSON_DIVERGED_DTOL;
1842: break;
1843: }
1844: }
1845: *outits = i;
1846:
1847: /* Return solution */
1848: if (asa->scale_diag) {
1849: VecPointwiseMult(x, asa->x, asa->invsqrtdiag);
1850: } else {
1851: VecCopy(x, asa->x);
1852: }
1854: /* delete working vectors */
1855: VecDestroy(&(asa->x));
1856: VecDestroy(&(asa->b));
1857: VecDestroy(&(asa->r));
1858: asa_lev->x = PETSC_NULL;
1859: asa_lev->b = PETSC_NULL;
1860: return(0);
1861: }
1863: /* -------------------------------------------------------------------------- */
1864: /*
1865: PCDestroy_ASA - Destroys the private context for the ASA preconditioner
1866: that was created with PCCreate_ASA().
1868: Input Parameter:
1869: . pc - the preconditioner context
1871: Application Interface Routine: PCDestroy()
1872: */
1875: static PetscErrorCode PCDestroy_ASA(PC pc)
1876: {
1877: PC_ASA *asa;
1878: PC_ASA_level *asa_lev;
1879: PC_ASA_level *asa_next_level;
1884: asa = (PC_ASA*)pc->data;
1885: asa_lev = asa->levellist;
1887: /* Delete top level data */
1888: PetscFree(asa->ksptype_smooth);
1889: PetscFree(asa->pctype_smooth);
1890: PetscFree(asa->ksptype_direct);
1891: PetscFree(asa->pctype_direct);
1892: PetscFree(asa->coarse_mat_type);
1894: /* this is destroyed by the levels below */
1895: /* MatDestroy(&(asa->A)); */
1896: VecDestroy(&(asa->invsqrtdiag));
1897: VecDestroy(&(asa->b));
1898: VecDestroy(&(asa->x));
1899: VecDestroy(&(asa->r));
1901: if (asa->dm) {DMDestroy(&asa->dm);}
1903: /* Destroy each of the levels */
1904: while(asa_lev) {
1905: asa_next_level = asa_lev->next;
1906: PCDestroyLevel_ASA(asa_lev);
1907: asa_lev = asa_next_level;
1908: }
1910: PetscFree(asa);
1911: return(0);
1912: }
1916: static PetscErrorCode PCSetFromOptions_ASA(PC pc)
1917: {
1918: PC_ASA *asa = (PC_ASA*)pc->data;
1919: PetscBool flg;
1921: char type[20];
1926: PetscOptionsHead("ASA options");
1927: /* convergence parameters */
1928: PetscOptionsInt("-pc_asa_nu","Number of cycles to run smoother","No manual page yet",asa->nu,&(asa->nu),&flg);
1929: PetscOptionsInt("-pc_asa_gamma","Number of cycles to run coarse grid correction","No manual page yet",asa->gamma,&(asa->gamma),&flg);
1930: PetscOptionsReal("-pc_asa_epsilon","Tolerance for the relaxation method","No manual page yet",asa->epsilon,&(asa->epsilon),&flg);
1931: PetscOptionsInt("-pc_asa_mu","Number of cycles to relax in setup stages","No manual page yet",asa->mu,&(asa->mu),&flg);
1932: 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);
1933: 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);
1934: PetscOptionsBool("-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);
1935: /* type of smoother used */
1936: 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);
1937: if (flg) {
1938: PetscFree(asa->ksptype_smooth);
1939: PetscStrallocpy(type,&(asa->ksptype_smooth));
1940: }
1941: 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);
1942: if (flg) {
1943: PetscFree(asa->pctype_smooth);
1944: PetscStrallocpy(type,&(asa->pctype_smooth));
1945: }
1946: 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);
1947: if (flg) {
1948: PetscFree(asa->ksptype_direct);
1949: PetscStrallocpy(type,&(asa->ksptype_direct));
1950: }
1951: 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);
1952: if (flg) {
1953: PetscFree(asa->pctype_direct);
1954: PetscStrallocpy(type,&(asa->pctype_direct));
1955: }
1956: /* options specific for certain smoothers */
1957: 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);
1958: 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);
1959: /* options for direct solver */
1960: 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);
1961: if (flg) {
1962: PetscFree(asa->coarse_mat_type);
1963: PetscStrallocpy(type,&(asa->coarse_mat_type));
1964: }
1965: /* storage allocation parameters */
1966: PetscOptionsInt("-pc_asa_max_cand_vecs","Maximum number of candidate vectors","No manual page yet",asa->max_cand_vecs,&(asa->max_cand_vecs),&flg);
1967: 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);
1968: /* construction parameters */
1969: PetscOptionsReal("-pc_asa_rq_improve","Threshold in RQ improvement for adding another candidate","No manual page yet",asa->rq_improve,&(asa->rq_improve),&flg);
1970: PetscOptionsTail();
1971: return(0);
1972: }
1976: static PetscErrorCode PCView_ASA(PC pc,PetscViewer viewer)
1977: {
1978: PC_ASA *asa = (PC_ASA*)pc->data;
1980: PetscBool iascii;
1981: PC_ASA_level *asa_lev = asa->levellist;
1984: PetscTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
1985: if (iascii) {
1986: PetscViewerASCIIPrintf(viewer," ASA:\n");
1987: asa_lev = asa->levellist;
1988: while (asa_lev) {
1989: if (!asa_lev->next) {
1990: PetscViewerASCIIPrintf(viewer,"Coarse grid solver -- level %D -------------------------------\n",0);
1991: } else {
1992: PetscViewerASCIIPrintf(viewer,"Down solver (pre-smoother) on level ? -------------------------------\n");
1993: }
1994: PetscViewerASCIIPushTab(viewer);
1995: KSPView(asa_lev->smoothd,viewer);
1996: PetscViewerASCIIPopTab(viewer);
1997: if (asa_lev->next && asa_lev->smoothd == asa_lev->smoothu) {
1998: PetscViewerASCIIPrintf(viewer,"Up solver (post-smoother) same as down solver (pre-smoother)\n");
1999: } else if (asa_lev->next){
2000: PetscViewerASCIIPrintf(viewer,"Up solver (post-smoother) on level ? -------------------------------\n");
2001: PetscViewerASCIIPushTab(viewer);
2002: KSPView(asa_lev->smoothu,viewer);
2003: PetscViewerASCIIPopTab(viewer);
2004: }
2005: asa_lev = asa_lev->next;
2006: }
2007: } else {
2008: SETERRQ1(((PetscObject)pc)->comm,PETSC_ERR_SUP,"Viewer type %s not supported for PCASA",((PetscObject)viewer)->type_name);
2009: }
2010: return(0);
2011: }
2013: /* -------------------------------------------------------------------------- */
2014: /*
2015: PCCreate_ASA - Creates a ASA preconditioner context, PC_ASA,
2016: and sets this as the private data within the generic preconditioning
2017: context, PC, that was created within PCCreate().
2019: Input Parameter:
2020: . pc - the preconditioner context
2022: Application Interface Routine: PCCreate()
2023: */
2027: PetscErrorCode PCCreate_ASA(PC pc)
2028: {
2030: PC_ASA *asa;
2035: /*
2036: Set the pointers for the functions that are provided above.
2037: Now when the user-level routines (such as PCApply(), PCDestroy(), etc.)
2038: are called, they will automatically call these functions. Note we
2039: choose not to provide a couple of these functions since they are
2040: not needed.
2041: */
2042: pc->ops->apply = PCApply_ASA;
2043: /* pc->ops->applytranspose = PCApply_ASA;*/
2044: pc->ops->applyrichardson = PCApplyRichardson_ASA;
2045: pc->ops->setup = 0;
2046: pc->ops->destroy = PCDestroy_ASA;
2047: pc->ops->setfromoptions = PCSetFromOptions_ASA;
2048: pc->ops->view = PCView_ASA;
2050: /* Set the data to pointer to 0 */
2051: pc->data = (void*)0;
2053: PetscObjectComposeFunctionDynamic((PetscObject)pc,"PCASASetDM_C","PCASASetDM_ASA",PCASASetDM_ASA);
2054: PetscObjectComposeFunctionDynamic((PetscObject)pc,"PCASASetTolerances_C","PCASASetTolerances_ASA",PCASASetTolerances_ASA);
2056: /* register events */
2057: if (! asa_events_registered) {
2058: PetscLogEventRegister("PCInitializationStage_ASA", PC_CLASSID,&PC_InitializationStage_ASA);
2059: PetscLogEventRegister("PCGeneralSetupStage_ASA", PC_CLASSID,&PC_GeneralSetupStage_ASA);
2060: PetscLogEventRegister("PCCreateTransferOp_ASA", PC_CLASSID,&PC_CreateTransferOp_ASA);
2061: PetscLogEventRegister("PCCreateVcycle_ASA", PC_CLASSID,&PC_CreateVcycle_ASA);
2062: asa_events_registered = PETSC_TRUE;
2063: }
2065: /* Create new PC_ASA object */
2066: PetscNewLog(pc,PC_ASA,&asa);
2067: pc->data = (void*)asa;
2069: /* WORK: find some better initial values */
2070: asa->nu = 3;
2071: asa->gamma = 1;
2072: asa->epsilon = 1e-4;
2073: asa->mu = 3;
2074: asa->mu_initial = 20;
2075: asa->direct_solver = 100;
2076: asa->scale_diag = PETSC_TRUE;
2077: PetscStrallocpy(KSPRICHARDSON, (char **) &(asa->ksptype_smooth));
2078: PetscStrallocpy(PCSOR, (char **) &(asa->pctype_smooth));
2079: asa->smoother_rtol = 1e-10;
2080: asa->smoother_abstol = 1e-20;
2081: asa->smoother_dtol = PETSC_DEFAULT;
2082: PetscStrallocpy(KSPPREONLY, (char **) &(asa->ksptype_direct));
2083: PetscStrallocpy(PCREDUNDANT, (char **) &(asa->pctype_direct));
2084: asa->direct_rtol = 1e-10;
2085: asa->direct_abstol = 1e-20;
2086: asa->direct_dtol = PETSC_DEFAULT;
2087: asa->richardson_scale = PETSC_DECIDE;
2088: asa->sor_omega = PETSC_DECIDE;
2089: PetscStrallocpy(MATSAME, (char **) &(asa->coarse_mat_type));
2091: asa->max_cand_vecs = 4;
2092: asa->max_dof_lev_2 = 640; /* I don't think this parameter really matters, 640 should be enough for everyone! */
2094: asa->multigrid_constructed = PETSC_FALSE;
2096: asa->rtol = 1e-10;
2097: asa->abstol = 1e-15;
2098: asa->divtol = 1e5;
2099: asa->max_it = 10000;
2100: asa->rq_improve = 0.9;
2101:
2102: asa->A = 0;
2103: asa->invsqrtdiag = 0;
2104: asa->b = 0;
2105: asa->x = 0;
2106: asa->r = 0;
2108: asa->dm = 0;
2109:
2110: asa->levels = 0;
2111: asa->levellist = 0;
2113: asa->comm = ((PetscObject)pc)->comm;
2114: return(0);
2115: }