Date: 2016-07-24T17:03:49+00:00

Actual source code: ispai.c
petsc-3.7.3 2016-07-24
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      2: /*
      3:    3/99 Modified by Stephen Barnard to support SPAI version 3.0
      4: */

      6: /*
      7:       Provides an interface to the SPAI Sparse Approximate Inverse Preconditioner
      8:    Code written by Stephen Barnard.

     10:       Note: there is some BAD memory bleeding below!

     12:       This code needs work

     14:    1) get rid of all memory bleeding
     15:    2) fix PETSc/interface so that it gets if the matrix is symmetric from the matrix
     16:       rather than having the sp flag for PC_SPAI
     17:    3) fix to set the block size based on the matrix block size

     19: */
     20: #define PETSC_SKIP_COMPLEX /* since spai uses I which conflicts with some complex implementations */

     22: #include <petsc/private/pcimpl.h>        /*I "petscpc.h" I*/
     23: #include <../src/ksp/pc/impls/spai/petscspai.h>

     25: /*
     26:     These are the SPAI include files
     27: */
     28: EXTERN_C_BEGIN
     29: #define SPAI_USE_MPI /* required for setting SPAI_Comm correctly in basics.h */
     30: #include <spai.h>
     31: #include <matrix.h>
     32: EXTERN_C_END

     34: extern PetscErrorCode ConvertMatToMatrix(MPI_Comm,Mat,Mat,matrix**);
     35: extern PetscErrorCode ConvertMatrixToMat(MPI_Comm,matrix*,Mat*);
     36: extern PetscErrorCode ConvertVectorToVec(MPI_Comm,vector *v,Vec *Pv);
     37: extern PetscErrorCode MM_to_PETSC(char*,char*,char*);

     39: typedef struct {

     41:   matrix *B;                /* matrix in SPAI format */
     42:   matrix *BT;               /* transpose of matrix in SPAI format */
     43:   matrix *M;                /* the approximate inverse in SPAI format */

     45:   Mat PM;                   /* the approximate inverse PETSc format */

     47:   double epsilon;           /* tolerance */
     48:   int    nbsteps;           /* max number of "improvement" steps per line */
     49:   int    max;               /* max dimensions of is_I, q, etc. */
     50:   int    maxnew;            /* max number of new entries per step */
     51:   int    block_size;        /* constant block size */
     52:   int    cache_size;        /* one of (1,2,3,4,5,6) indicting size of cache */
     53:   int    verbose;           /* SPAI prints timing and statistics */

     55:   int      sp;              /* symmetric nonzero pattern */
     56:   MPI_Comm comm_spai;     /* communicator to be used with spai */
     57: } PC_SPAI;

     59: /**********************************************************************/

     63: static PetscErrorCode PCSetUp_SPAI(PC pc)
     64: {
     65:   PC_SPAI        *ispai = (PC_SPAI*)pc->data;
     67:   Mat            AT;

     70:   init_SPAI();

     72:   if (ispai->sp) {
     73:     ConvertMatToMatrix(ispai->comm_spai,pc->pmat,pc->pmat,&ispai->B);
     74:   } else {
     75:     /* Use the transpose to get the column nonzero structure. */
     76:     MatTranspose(pc->pmat,MAT_INITIAL_MATRIX,&AT);
     77:     ConvertMatToMatrix(ispai->comm_spai,pc->pmat,AT,&ispai->B);
     78:     MatDestroy(&AT);
     79:   }

     81:   /* Destroy the transpose */
     82:   /* Don't know how to do it. PETSc developers? */

     84:   /* construct SPAI preconditioner */
     85:   /* FILE *messages */     /* file for warning messages */
     86:   /* double epsilon */     /* tolerance */
     87:   /* int nbsteps */        /* max number of "improvement" steps per line */
     88:   /* int max */            /* max dimensions of is_I, q, etc. */
     89:   /* int maxnew */         /* max number of new entries per step */
     90:   /* int block_size */     /* block_size == 1 specifies scalar elments
     91:                               block_size == n specifies nxn constant-block elements
     92:                               block_size == 0 specifies variable-block elements */
     93:   /* int cache_size */     /* one of (1,2,3,4,5,6) indicting size of cache. cache_size == 0 indicates no caching */
     94:   /* int    verbose    */  /* verbose == 0 specifies that SPAI is silent
     95:                               verbose == 1 prints timing and matrix statistics */

     97:   bspai(ispai->B,&ispai->M,
     98:                stdout,
     99:                ispai->epsilon,
    100:                ispai->nbsteps,
    101:                ispai->max,
    102:                ispai->maxnew,
    103:                ispai->block_size,
    104:                ispai->cache_size,
    105:                ispai->verbose);

    107:   ConvertMatrixToMat(PetscObjectComm((PetscObject)pc),ispai->M,&ispai->PM);

    109:   /* free the SPAI matrices */
    110:   sp_free_matrix(ispai->B);
    111:   sp_free_matrix(ispai->M);
    112:   return(0);
    113: }

    115: /**********************************************************************/

    119: static PetscErrorCode PCApply_SPAI(PC pc,Vec xx,Vec y)
    120: {
    121:   PC_SPAI        *ispai = (PC_SPAI*)pc->data;

    125:   /* Now using PETSc's multiply */
    126:   MatMult(ispai->PM,xx,y);
    127:   return(0);
    128: }

    130: /**********************************************************************/

    134: static PetscErrorCode PCDestroy_SPAI(PC pc)
    135: {
    137:   PC_SPAI        *ispai = (PC_SPAI*)pc->data;

    140:   MatDestroy(&ispai->PM);
    141:   MPI_Comm_free(&(ispai->comm_spai));
    142:   PetscFree(pc->data);
    143:   return(0);
    144: }

    146: /**********************************************************************/

    150: static PetscErrorCode PCView_SPAI(PC pc,PetscViewer viewer)
    151: {
    152:   PC_SPAI        *ispai = (PC_SPAI*)pc->data;
    154:   PetscBool      iascii;

    157:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
    158:   if (iascii) {
    159:     PetscViewerASCIIPrintf(viewer,"    SPAI preconditioner\n");
    160:     PetscViewerASCIIPrintf(viewer,"    epsilon %g\n",   (double)ispai->epsilon);
    161:     PetscViewerASCIIPrintf(viewer,"    nbsteps %d\n",   ispai->nbsteps);
    162:     PetscViewerASCIIPrintf(viewer,"    max %d\n",       ispai->max);
    163:     PetscViewerASCIIPrintf(viewer,"    maxnew %d\n",    ispai->maxnew);
    164:     PetscViewerASCIIPrintf(viewer,"    block_size %d\n",ispai->block_size);
    165:     PetscViewerASCIIPrintf(viewer,"    cache_size %d\n",ispai->cache_size);
    166:     PetscViewerASCIIPrintf(viewer,"    verbose %d\n",   ispai->verbose);
    167:     PetscViewerASCIIPrintf(viewer,"    sp %d\n",        ispai->sp);
    168:   }
    169:   return(0);
    170: }

    174: static PetscErrorCode  PCSPAISetEpsilon_SPAI(PC pc,double epsilon1)
    175: {
    176:   PC_SPAI *ispai = (PC_SPAI*)pc->data;

    179:   ispai->epsilon = epsilon1;
    180:   return(0);
    181: }

    183: /**********************************************************************/

    187: static PetscErrorCode  PCSPAISetNBSteps_SPAI(PC pc,int nbsteps1)
    188: {
    189:   PC_SPAI *ispai = (PC_SPAI*)pc->data;

    192:   ispai->nbsteps = nbsteps1;
    193:   return(0);
    194: }

    196: /**********************************************************************/

    198: /* added 1/7/99 g.h. */
    201: static PetscErrorCode  PCSPAISetMax_SPAI(PC pc,int max1)
    202: {
    203:   PC_SPAI *ispai = (PC_SPAI*)pc->data;

    206:   ispai->max = max1;
    207:   return(0);
    208: }

    210: /**********************************************************************/

    214: static PetscErrorCode  PCSPAISetMaxNew_SPAI(PC pc,int maxnew1)
    215: {
    216:   PC_SPAI *ispai = (PC_SPAI*)pc->data;

    219:   ispai->maxnew = maxnew1;
    220:   return(0);
    221: }

    223: /**********************************************************************/

    227: static PetscErrorCode  PCSPAISetBlockSize_SPAI(PC pc,int block_size1)
    228: {
    229:   PC_SPAI *ispai = (PC_SPAI*)pc->data;

    232:   ispai->block_size = block_size1;
    233:   return(0);
    234: }

    236: /**********************************************************************/

    240: static PetscErrorCode  PCSPAISetCacheSize_SPAI(PC pc,int cache_size)
    241: {
    242:   PC_SPAI *ispai = (PC_SPAI*)pc->data;

    245:   ispai->cache_size = cache_size;
    246:   return(0);
    247: }

    249: /**********************************************************************/

    253: static PetscErrorCode  PCSPAISetVerbose_SPAI(PC pc,int verbose)
    254: {
    255:   PC_SPAI *ispai = (PC_SPAI*)pc->data;

    258:   ispai->verbose = verbose;
    259:   return(0);
    260: }

    262: /**********************************************************************/

    266: static PetscErrorCode  PCSPAISetSp_SPAI(PC pc,int sp)
    267: {
    268:   PC_SPAI *ispai = (PC_SPAI*)pc->data;

    271:   ispai->sp = sp;
    272:   return(0);
    273: }

    275: /* -------------------------------------------------------------------*/

    279: /*@
    280:   PCSPAISetEpsilon -- Set the tolerance for the SPAI preconditioner

    282:   Input Parameters:
    283: + pc - the preconditioner
    284: - eps - epsilon (default .4)

    286:   Notes:  Espilon must be between 0 and 1. It controls the
    287:                  quality of the approximation of M to the inverse of
    288:                  A. Higher values of epsilon lead to more work, more
    289:                  fill, and usually better preconditioners. In many
    290:                  cases the best choice of epsilon is the one that
    291:                  divides the total solution time equally between the
    292:                  preconditioner and the solver.

    294:   Level: intermediate

    296: .seealso: PCSPAI, PCSetType()
    297:   @*/
    298: PetscErrorCode  PCSPAISetEpsilon(PC pc,double epsilon1)
    299: {

    303:   PetscTryMethod(pc,"PCSPAISetEpsilon_C",(PC,double),(pc,epsilon1));
    304:   return(0);
    305: }

    307: /**********************************************************************/

    311: /*@
    312:   PCSPAISetNBSteps - set maximum number of improvement steps per row in
    313:         the SPAI preconditioner

    315:   Input Parameters:
    316: + pc - the preconditioner
    317: - n - number of steps (default 5)

    319:   Notes:  SPAI constructs to approximation to every column of
    320:                  the exact inverse of A in a series of improvement
    321:                  steps. The quality of the approximation is determined
    322:                  by epsilon. If an approximation achieving an accuracy
    323:                  of epsilon is not obtained after ns steps, SPAI simply
    324:                  uses the best approximation constructed so far.

    326:   Level: intermediate

    328: .seealso: PCSPAI, PCSetType(), PCSPAISetMaxNew()
    329: @*/
    330: PetscErrorCode  PCSPAISetNBSteps(PC pc,int nbsteps1)
    331: {

    335:   PetscTryMethod(pc,"PCSPAISetNBSteps_C",(PC,int),(pc,nbsteps1));
    336:   return(0);
    337: }

    339: /**********************************************************************/

    341: /* added 1/7/99 g.h. */
    344: /*@
    345:   PCSPAISetMax - set the size of various working buffers in
    346:         the SPAI preconditioner

    348:   Input Parameters:
    349: + pc - the preconditioner
    350: - n - size (default is 5000)

    352:   Level: intermediate

    354: .seealso: PCSPAI, PCSetType()
    355: @*/
    356: PetscErrorCode  PCSPAISetMax(PC pc,int max1)
    357: {

    361:   PetscTryMethod(pc,"PCSPAISetMax_C",(PC,int),(pc,max1));
    362:   return(0);
    363: }

    365: /**********************************************************************/

    369: /*@
    370:   PCSPAISetMaxNew - set maximum number of new nonzero candidates per step
    371:    in SPAI preconditioner

    373:   Input Parameters:
    374: + pc - the preconditioner
    375: - n - maximum number (default 5)

    377:   Level: intermediate

    379: .seealso: PCSPAI, PCSetType(), PCSPAISetNBSteps()
    380: @*/
    381: PetscErrorCode  PCSPAISetMaxNew(PC pc,int maxnew1)
    382: {

    386:   PetscTryMethod(pc,"PCSPAISetMaxNew_C",(PC,int),(pc,maxnew1));
    387:   return(0);
    388: }

    390: /**********************************************************************/

    394: /*@
    395:   PCSPAISetBlockSize - set the block size for the SPAI preconditioner

    397:   Input Parameters:
    398: + pc - the preconditioner
    399: - n - block size (default 1)

    401:   Notes: A block
    402:                  size of 1 treats A as a matrix of scalar elements. A
    403:                  block size of s > 1 treats A as a matrix of sxs
    404:                  blocks. A block size of 0 treats A as a matrix with
    405:                  variable sized blocks, which are determined by
    406:                  searching for dense square diagonal blocks in A.
    407:                  This can be very effective for finite-element
    408:                  matrices.

    410:                  SPAI will convert A to block form, use a block
    411:                  version of the preconditioner algorithm, and then
    412:                  convert the result back to scalar form.

    414:                  In many cases the a block-size parameter other than 1
    415:                  can lead to very significant improvement in
    416:                  performance.

    419:   Level: intermediate

    421: .seealso: PCSPAI, PCSetType()
    422: @*/
    423: PetscErrorCode  PCSPAISetBlockSize(PC pc,int block_size1)
    424: {

    428:   PetscTryMethod(pc,"PCSPAISetBlockSize_C",(PC,int),(pc,block_size1));
    429:   return(0);
    430: }

    432: /**********************************************************************/

    436: /*@
    437:   PCSPAISetCacheSize - specify cache size in the SPAI preconditioner

    439:   Input Parameters:
    440: + pc - the preconditioner
    441: - n -  cache size {0,1,2,3,4,5} (default 5)

    443:   Notes:    SPAI uses a hash table to cache messages and avoid
    444:                  redundant communication. If suggest always using
    445:                  5. This parameter is irrelevant in the serial
    446:                  version.

    448:   Level: intermediate

    450: .seealso: PCSPAI, PCSetType()
    451: @*/
    452: PetscErrorCode  PCSPAISetCacheSize(PC pc,int cache_size)
    453: {

    457:   PetscTryMethod(pc,"PCSPAISetCacheSize_C",(PC,int),(pc,cache_size));
    458:   return(0);
    459: }

    461: /**********************************************************************/

    465: /*@
    466:   PCSPAISetVerbose - verbosity level for the SPAI preconditioner

    468:   Input Parameters:
    469: + pc - the preconditioner
    470: - n - level (default 1)

    472:   Notes: print parameters, timings and matrix statistics

    474:   Level: intermediate

    476: .seealso: PCSPAI, PCSetType()
    477: @*/
    478: PetscErrorCode  PCSPAISetVerbose(PC pc,int verbose)
    479: {

    483:   PetscTryMethod(pc,"PCSPAISetVerbose_C",(PC,int),(pc,verbose));
    484:   return(0);
    485: }

    487: /**********************************************************************/

    491: /*@
    492:   PCSPAISetSp - specify a symmetric matrix sparsity pattern in the SPAI preconditioner

    494:   Input Parameters:
    495: + pc - the preconditioner
    496: - n - 0 or 1

    498:   Notes: If A has a symmetric nonzero pattern use -sp 1 to
    499:                  improve performance by eliminating some communication
    500:                  in the parallel version. Even if A does not have a
    501:                  symmetric nonzero pattern -sp 1 may well lead to good
    502:                  results, but the code will not follow the published
    503:                  SPAI algorithm exactly.

    506:   Level: intermediate

    508: .seealso: PCSPAI, PCSetType()
    509: @*/
    510: PetscErrorCode  PCSPAISetSp(PC pc,int sp)
    511: {

    515:   PetscTryMethod(pc,"PCSPAISetSp_C",(PC,int),(pc,sp));
    516:   return(0);
    517: }

    519: /**********************************************************************/

    521: /**********************************************************************/

    525: static PetscErrorCode PCSetFromOptions_SPAI(PetscOptionItems *PetscOptionsObject,PC pc)
    526: {
    527:   PC_SPAI        *ispai = (PC_SPAI*)pc->data;
    529:   int            nbsteps1,max1,maxnew1,block_size1,cache_size,verbose,sp;
    530:   double         epsilon1;
    531:   PetscBool      flg;

    534:   PetscOptionsHead(PetscOptionsObject,"SPAI options");
    535:   PetscOptionsReal("-pc_spai_epsilon","","PCSPAISetEpsilon",ispai->epsilon,&epsilon1,&flg);
    536:   if (flg) {
    537:     PCSPAISetEpsilon(pc,epsilon1);
    538:   }
    539:   PetscOptionsInt("-pc_spai_nbsteps","","PCSPAISetNBSteps",ispai->nbsteps,&nbsteps1,&flg);
    540:   if (flg) {
    541:     PCSPAISetNBSteps(pc,nbsteps1);
    542:   }
    543:   /* added 1/7/99 g.h. */
    544:   PetscOptionsInt("-pc_spai_max","","PCSPAISetMax",ispai->max,&max1,&flg);
    545:   if (flg) {
    546:     PCSPAISetMax(pc,max1);
    547:   }
    548:   PetscOptionsInt("-pc_spai_maxnew","","PCSPAISetMaxNew",ispai->maxnew,&maxnew1,&flg);
    549:   if (flg) {
    550:     PCSPAISetMaxNew(pc,maxnew1);
    551:   }
    552:   PetscOptionsInt("-pc_spai_block_size","","PCSPAISetBlockSize",ispai->block_size,&block_size1,&flg);
    553:   if (flg) {
    554:     PCSPAISetBlockSize(pc,block_size1);
    555:   }
    556:   PetscOptionsInt("-pc_spai_cache_size","","PCSPAISetCacheSize",ispai->cache_size,&cache_size,&flg);
    557:   if (flg) {
    558:     PCSPAISetCacheSize(pc,cache_size);
    559:   }
    560:   PetscOptionsInt("-pc_spai_verbose","","PCSPAISetVerbose",ispai->verbose,&verbose,&flg);
    561:   if (flg) {
    562:     PCSPAISetVerbose(pc,verbose);
    563:   }
    564:   PetscOptionsInt("-pc_spai_sp","","PCSPAISetSp",ispai->sp,&sp,&flg);
    565:   if (flg) {
    566:     PCSPAISetSp(pc,sp);
    567:   }
    568:   PetscOptionsTail();
    569:   return(0);
    570: }

    572: /**********************************************************************/

    574: /*MC
    575:    PCSPAI - Use the Sparse Approximate Inverse method of Grote and Barnard
    576:      as a preconditioner (SIAM J. Sci. Comput.; vol 18, nr 3)

    578:    Options Database Keys:
    579: +  -pc_spai_epsilon <eps> - set tolerance
    580: .  -pc_spai_nbstep <n> - set nbsteps
    581: .  -pc_spai_max <m> - set max
    582: .  -pc_spai_max_new <m> - set maxnew
    583: .  -pc_spai_block_size <n> - set block size
    584: .  -pc_spai_cache_size <n> - set cache size
    585: .  -pc_spai_sp <m> - set sp
    586: -  -pc_spai_set_verbose <true,false> - verbose output

    588:    Notes: This only works with AIJ matrices.

    590:    Level: beginner

    592:    Concepts: approximate inverse

    594: .seealso:  PCCreate(), PCSetType(), PCType (for list of available types), PC,
    595:     PCSPAISetEpsilon(), PCSPAISetMax(), PCSPAISetMaxNew(), PCSPAISetBlockSize(),
    596:     PCSPAISetVerbose(), PCSPAISetSp()
    597: M*/

    601: PETSC_EXTERN PetscErrorCode PCCreate_SPAI(PC pc)
    602: {
    603:   PC_SPAI        *ispai;

    607:   PetscNewLog(pc,&ispai);
    608:   pc->data = ispai;

    610:   pc->ops->destroy         = PCDestroy_SPAI;
    611:   pc->ops->apply           = PCApply_SPAI;
    612:   pc->ops->applyrichardson = 0;
    613:   pc->ops->setup           = PCSetUp_SPAI;
    614:   pc->ops->view            = PCView_SPAI;
    615:   pc->ops->setfromoptions  = PCSetFromOptions_SPAI;

    617:   ispai->epsilon    = .4;
    618:   ispai->nbsteps    = 5;
    619:   ispai->max        = 5000;
    620:   ispai->maxnew     = 5;
    621:   ispai->block_size = 1;
    622:   ispai->cache_size = 5;
    623:   ispai->verbose    = 0;

    625:   ispai->sp = 1;
    626:   MPI_Comm_dup(PetscObjectComm((PetscObject)pc),&(ispai->comm_spai));

    628:   PetscObjectComposeFunction((PetscObject)pc,"PCSPAISetEpsilon_C",PCSPAISetEpsilon_SPAI);
    629:   PetscObjectComposeFunction((PetscObject)pc,"PCSPAISetNBSteps_C",PCSPAISetNBSteps_SPAI);
    630:   PetscObjectComposeFunction((PetscObject)pc,"PCSPAISetMax_C",PCSPAISetMax_SPAI);
    631:   PetscObjectComposeFunction((PetscObject)pc,"PCSPAISetMaxNew_C",PCSPAISetMaxNew_SPAI);
    632:   PetscObjectComposeFunction((PetscObject)pc,"PCSPAISetBlockSize_C",PCSPAISetBlockSize_SPAI);
    633:   PetscObjectComposeFunction((PetscObject)pc,"PCSPAISetCacheSize_C",PCSPAISetCacheSize_SPAI);
    634:   PetscObjectComposeFunction((PetscObject)pc,"PCSPAISetVerbose_C",PCSPAISetVerbose_SPAI);
    635:   PetscObjectComposeFunction((PetscObject)pc,"PCSPAISetSp_C",PCSPAISetSp_SPAI);
    636:   return(0);
    637: }

    639: /**********************************************************************/

    641: /*
    642:    Converts from a PETSc matrix to an SPAI matrix
    643: */
    646: PetscErrorCode ConvertMatToMatrix(MPI_Comm comm, Mat A,Mat AT,matrix **B)
    647: {
    648:   matrix                  *M;
    649:   int                     i,j,col;
    650:   int                     row_indx;
    651:   int                     len,pe,local_indx,start_indx;
    652:   int                     *mapping;
    653:   PetscErrorCode          ierr;
    654:   const int               *cols;
    655:   const double            *vals;
    656:   int                     n,mnl,nnl,nz,rstart,rend;
    657:   PetscMPIInt             size,rank;
    658:   struct compressed_lines *rows;

    661:   MPI_Comm_size(comm,&size);
    662:   MPI_Comm_rank(comm,&rank);
    663:   MatGetSize(A,&n,&n);
    664:   MatGetLocalSize(A,&mnl,&nnl);

    666:   /*
    667:     not sure why a barrier is required. commenting out
    668:   MPI_Barrier(comm);
    669:   */

    671:   M = new_matrix((SPAI_Comm)comm);

    673:   M->n              = n;
    674:   M->bs             = 1;
    675:   M->max_block_size = 1;

    677:   M->mnls          = (int*)malloc(sizeof(int)*size);
    678:   M->start_indices = (int*)malloc(sizeof(int)*size);
    679:   M->pe            = (int*)malloc(sizeof(int)*n);
    680:   M->block_sizes   = (int*)malloc(sizeof(int)*n);
    681:   for (i=0; i<n; i++) M->block_sizes[i] = 1;

    683:   MPI_Allgather(&mnl,1,MPI_INT,M->mnls,1,MPI_INT,comm);

    685:   M->start_indices[0] = 0;
    686:   for (i=1; i<size; i++) M->start_indices[i] = M->start_indices[i-1] + M->mnls[i-1];

    688:   M->mnl            = M->mnls[M->myid];
    689:   M->my_start_index = M->start_indices[M->myid];

    691:   for (i=0; i<size; i++) {
    692:     start_indx = M->start_indices[i];
    693:     for (j=0; j<M->mnls[i]; j++) M->pe[start_indx+j] = i;
    694:   }

    696:   if (AT) {
    697:     M->lines = new_compressed_lines(M->mnls[rank],1);
    698:   } else {
    699:     M->lines = new_compressed_lines(M->mnls[rank],0);
    700:   }

    702:   rows = M->lines;

    704:   /* Determine the mapping from global indices to pointers */
    705:   PetscMalloc1(M->n,&mapping);
    706:   pe         = 0;
    707:   local_indx = 0;
    708:   for (i=0; i<M->n; i++) {
    709:     if (local_indx >= M->mnls[pe]) {
    710:       pe++;
    711:       local_indx = 0;
    712:     }
    713:     mapping[i] = local_indx + M->start_indices[pe];
    714:     local_indx++;
    715:   }

    717:   /*********************************************************/
    718:   /************** Set up the row structure *****************/
    719:   /*********************************************************/

    721:   MatGetOwnershipRange(A,&rstart,&rend);
    722:   for (i=rstart; i<rend; i++) {
    723:     row_indx = i - rstart;
    724:     MatGetRow(A,i,&nz,&cols,&vals);
    725:     /* allocate buffers */
    726:     rows->ptrs[row_indx] = (int*)malloc(nz*sizeof(int));
    727:     rows->A[row_indx]    = (double*)malloc(nz*sizeof(double));
    728:     /* copy the matrix */
    729:     for (j=0; j<nz; j++) {
    730:       col = cols[j];
    731:       len = rows->len[row_indx]++;

    733:       rows->ptrs[row_indx][len] = mapping[col];
    734:       rows->A[row_indx][len]    = vals[j];
    735:     }
    736:     rows->slen[row_indx] = rows->len[row_indx];

    738:     MatRestoreRow(A,i,&nz,&cols,&vals);
    739:   }

    742:   /************************************************************/
    743:   /************** Set up the column structure *****************/
    744:   /*********************************************************/

    746:   if (AT) {

    748:     for (i=rstart; i<rend; i++) {
    749:       row_indx = i - rstart;
    750:       MatGetRow(AT,i,&nz,&cols,&vals);
    751:       /* allocate buffers */
    752:       rows->rptrs[row_indx] = (int*)malloc(nz*sizeof(int));
    753:       /* copy the matrix (i.e., the structure) */
    754:       for (j=0; j<nz; j++) {
    755:         col = cols[j];
    756:         len = rows->rlen[row_indx]++;

    758:         rows->rptrs[row_indx][len] = mapping[col];
    759:       }
    760:       MatRestoreRow(AT,i,&nz,&cols,&vals);
    761:     }
    762:   }

    764:   PetscFree(mapping);

    766:   order_pointers(M);
    767:   M->maxnz = calc_maxnz(M);
    768:   *B       = M;
    769:   return(0);
    770: }

    772: /**********************************************************************/

    774: /*
    775:    Converts from an SPAI matrix B  to a PETSc matrix PB.
    776:    This assumes that the SPAI matrix B is stored in
    777:    COMPRESSED-ROW format.
    778: */
    781: PetscErrorCode ConvertMatrixToMat(MPI_Comm comm,matrix *B,Mat *PB)
    782: {
    783:   PetscMPIInt    size,rank;
    785:   int            m,n,M,N;
    786:   int            d_nz,o_nz;
    787:   int            *d_nnz,*o_nnz;
    788:   int            i,k,global_row,global_col,first_diag_col,last_diag_col;
    789:   PetscScalar    val;

    792:   MPI_Comm_size(comm,&size);
    793:   MPI_Comm_rank(comm,&rank);

    795:   m    = n = B->mnls[rank];
    796:   d_nz = o_nz = 0;

    798:   /* Determine preallocation for MatCreateMPIAIJ */
    799:   PetscMalloc1(m,&d_nnz);
    800:   PetscMalloc1(m,&o_nnz);
    801:   for (i=0; i<m; i++) d_nnz[i] = o_nnz[i] = 0;
    802:   first_diag_col = B->start_indices[rank];
    803:   last_diag_col  = first_diag_col + B->mnls[rank];
    804:   for (i=0; i<B->mnls[rank]; i++) {
    805:     for (k=0; k<B->lines->len[i]; k++) {
    806:       global_col = B->lines->ptrs[i][k];
    807:       if ((global_col >= first_diag_col) && (global_col < last_diag_col)) d_nnz[i]++;
    808:       else o_nnz[i]++;
    809:     }
    810:   }

    812:   M = N = B->n;
    813:   /* Here we only know how to create AIJ format */
    814:   MatCreate(comm,PB);
    815:   MatSetSizes(*PB,m,n,M,N);
    816:   MatSetType(*PB,MATAIJ);
    817:   MatSeqAIJSetPreallocation(*PB,d_nz,d_nnz);
    818:   MatMPIAIJSetPreallocation(*PB,d_nz,d_nnz,o_nz,o_nnz);

    820:   for (i=0; i<B->mnls[rank]; i++) {
    821:     global_row = B->start_indices[rank]+i;
    822:     for (k=0; k<B->lines->len[i]; k++) {
    823:       global_col = B->lines->ptrs[i][k];

    825:       val  = B->lines->A[i][k];
    826:       MatSetValues(*PB,1,&global_row,1,&global_col,&val,ADD_VALUES);
    827:     }
    828:   }

    830:   PetscFree(d_nnz);
    831:   PetscFree(o_nnz);

    833:   MatAssemblyBegin(*PB,MAT_FINAL_ASSEMBLY);
    834:   MatAssemblyEnd(*PB,MAT_FINAL_ASSEMBLY);
    835:   return(0);
    836: }

    838: /**********************************************************************/

    840: /*
    841:    Converts from an SPAI vector v  to a PETSc vec Pv.
    842: */
    845: PetscErrorCode ConvertVectorToVec(MPI_Comm comm,vector *v,Vec *Pv)
    846: {
    848:   PetscMPIInt    size,rank;
    849:   int            m,M,i,*mnls,*start_indices,*global_indices;

    852:   MPI_Comm_size(comm,&size);
    853:   MPI_Comm_rank(comm,&rank);

    855:   m = v->mnl;
    856:   M = v->n;

    859:   VecCreateMPI(comm,m,M,Pv);

    861:   PetscMalloc1(size,&mnls);
    862:   MPI_Allgather(&v->mnl,1,MPI_INT,mnls,1,MPI_INT,comm);

    864:   PetscMalloc1(size,&start_indices);

    866:   start_indices[0] = 0;
    867:   for (i=1; i<size; i++) start_indices[i] = start_indices[i-1] +mnls[i-1];

    869:   PetscMalloc1(v->mnl,&global_indices);
    870:   for (i=0; i<v->mnl; i++) global_indices[i] = start_indices[rank] + i;

    872:   PetscFree(mnls);
    873:   PetscFree(start_indices);

    875:   VecSetValues(*Pv,v->mnl,global_indices,v->v,INSERT_VALUES);
    876:   VecAssemblyBegin(*Pv);
    877:   VecAssemblyEnd(*Pv);

    879:   PetscFree(global_indices);
    880:   return(0);
    881: }