Actual source code: blockmat.c

      2: /*
      3:    This provides a matrix that consists of Mats
      4: */

      6: #include <petsc/private/matimpl.h>
      7: #include <../src/mat/impls/baij/seq/baij.h>

      9: typedef struct {
     10:   SEQAIJHEADER(Mat);
     11:   SEQBAIJHEADER;
     12:   Mat *diags;

     14:   Vec left,right,middle,workb;                 /* dummy vectors to perform local parts of product */
     15: } Mat_BlockMat;

     17: static PetscErrorCode MatSOR_BlockMat_Symmetric(Mat A,Vec bb,PetscReal omega,MatSORType flag,PetscReal fshift,PetscInt its,PetscInt lits,Vec xx)
     18: {
     19:   Mat_BlockMat      *a = (Mat_BlockMat*)A->data;
     20:   PetscScalar       *x;
     21:   const Mat         *v;
     22:   const PetscScalar *b;
     23:   PetscErrorCode    ierr;
     24:   PetscInt          n = A->cmap->n,i,mbs = n/A->rmap->bs,j,bs = A->rmap->bs;
     25:   const PetscInt    *idx;
     26:   IS                row,col;
     27:   MatFactorInfo     info;
     28:   Vec               left = a->left,right = a->right, middle = a->middle;
     29:   Mat               *diag;

     32:   its = its*lits;
     33:   if (its <= 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Relaxation requires global its %D and local its %D both positive",its,lits);
     34:   if (flag & SOR_EISENSTAT) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support yet for Eisenstat");
     35:   if (omega != 1.0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support yet for omega not equal to 1.0");
     36:   if (fshift) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support yet for fshift");
     37:   if ((flag & SOR_BACKWARD_SWEEP || flag & SOR_LOCAL_BACKWARD_SWEEP) && !(flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP)) {
     38:     SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Cannot do backward sweep without forward sweep");
     39:   }

     41:   if (!a->diags) {
     42:     PetscMalloc1(mbs,&a->diags);
     43:     MatFactorInfoInitialize(&info);
     44:     for (i=0; i<mbs; i++) {
     45:       MatGetOrdering(a->a[a->diag[i]], MATORDERINGND,&row,&col);
     46:       MatCholeskyFactorSymbolic(a->diags[i],a->a[a->diag[i]],row,&info);
     47:       MatCholeskyFactorNumeric(a->diags[i],a->a[a->diag[i]],&info);
     48:       ISDestroy(&row);
     49:       ISDestroy(&col);
     50:     }
     51:     VecDuplicate(bb,&a->workb);
     52:   }
     53:   diag = a->diags;

     55:   VecSet(xx,0.0);
     56:   VecGetArray(xx,&x);
     57:   /* copy right hand side because it must be modified during iteration */
     58:   VecCopy(bb,a->workb);
     59:   VecGetArrayRead(a->workb,&b);

     61:   /* need to add code for when initial guess is zero, see MatSOR_SeqAIJ */
     62:   while (its--) {
     63:     if (flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP) {

     65:       for (i=0; i<mbs; i++) {
     66:         n   = a->i[i+1] - a->i[i] - 1;
     67:         idx = a->j + a->i[i] + 1;
     68:         v   = a->a + a->i[i] + 1;

     70:         VecSet(left,0.0);
     71:         for (j=0; j<n; j++) {
     72:           VecPlaceArray(right,x + idx[j]*bs);
     73:           MatMultAdd(v[j],right,left,left);
     74:           VecResetArray(right);
     75:         }
     76:         VecPlaceArray(right,b + i*bs);
     77:         VecAYPX(left,-1.0,right);
     78:         VecResetArray(right);

     80:         VecPlaceArray(right,x + i*bs);
     81:         MatSolve(diag[i],left,right);

     83:         /* now adjust right hand side, see MatSOR_SeqSBAIJ */
     84:         for (j=0; j<n; j++) {
     85:           MatMultTranspose(v[j],right,left);
     86:           VecPlaceArray(middle,b + idx[j]*bs);
     87:           VecAXPY(middle,-1.0,left);
     88:           VecResetArray(middle);
     89:         }
     90:         VecResetArray(right);

     92:       }
     93:     }
     94:     if (flag & SOR_BACKWARD_SWEEP || flag & SOR_LOCAL_BACKWARD_SWEEP) {

     96:       for (i=mbs-1; i>=0; i--) {
     97:         n   = a->i[i+1] - a->i[i] - 1;
     98:         idx = a->j + a->i[i] + 1;
     99:         v   = a->a + a->i[i] + 1;

    101:         VecSet(left,0.0);
    102:         for (j=0; j<n; j++) {
    103:           VecPlaceArray(right,x + idx[j]*bs);
    104:           MatMultAdd(v[j],right,left,left);
    105:           VecResetArray(right);
    106:         }
    107:         VecPlaceArray(right,b + i*bs);
    108:         VecAYPX(left,-1.0,right);
    109:         VecResetArray(right);

    111:         VecPlaceArray(right,x + i*bs);
    112:         MatSolve(diag[i],left,right);
    113:         VecResetArray(right);

    115:       }
    116:     }
    117:   }
    118:   VecRestoreArray(xx,&x);
    119:   VecRestoreArrayRead(a->workb,&b);
    120:   return(0);
    121: }

    123: static PetscErrorCode MatSOR_BlockMat(Mat A,Vec bb,PetscReal omega,MatSORType flag,PetscReal fshift,PetscInt its,PetscInt lits,Vec xx)
    124: {
    125:   Mat_BlockMat      *a = (Mat_BlockMat*)A->data;
    126:   PetscScalar       *x;
    127:   const Mat         *v;
    128:   const PetscScalar *b;
    129:   PetscErrorCode    ierr;
    130:   PetscInt          n = A->cmap->n,i,mbs = n/A->rmap->bs,j,bs = A->rmap->bs;
    131:   const PetscInt    *idx;
    132:   IS                row,col;
    133:   MatFactorInfo     info;
    134:   Vec               left = a->left,right = a->right;
    135:   Mat               *diag;

    138:   its = its*lits;
    139:   if (its <= 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Relaxation requires global its %D and local its %D both positive",its,lits);
    140:   if (flag & SOR_EISENSTAT) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support yet for Eisenstat");
    141:   if (omega != 1.0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support yet for omega not equal to 1.0");
    142:   if (fshift) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support yet for fshift");

    144:   if (!a->diags) {
    145:     PetscMalloc1(mbs,&a->diags);
    146:     MatFactorInfoInitialize(&info);
    147:     for (i=0; i<mbs; i++) {
    148:       MatGetOrdering(a->a[a->diag[i]], MATORDERINGND,&row,&col);
    149:       MatLUFactorSymbolic(a->diags[i],a->a[a->diag[i]],row,col,&info);
    150:       MatLUFactorNumeric(a->diags[i],a->a[a->diag[i]],&info);
    151:       ISDestroy(&row);
    152:       ISDestroy(&col);
    153:     }
    154:   }
    155:   diag = a->diags;

    157:   VecSet(xx,0.0);
    158:   VecGetArray(xx,&x);
    159:   VecGetArrayRead(bb,&b);

    161:   /* need to add code for when initial guess is zero, see MatSOR_SeqAIJ */
    162:   while (its--) {
    163:     if (flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP) {

    165:       for (i=0; i<mbs; i++) {
    166:         n   = a->i[i+1] - a->i[i];
    167:         idx = a->j + a->i[i];
    168:         v   = a->a + a->i[i];

    170:         VecSet(left,0.0);
    171:         for (j=0; j<n; j++) {
    172:           if (idx[j] != i) {
    173:             VecPlaceArray(right,x + idx[j]*bs);
    174:             MatMultAdd(v[j],right,left,left);
    175:             VecResetArray(right);
    176:           }
    177:         }
    178:         VecPlaceArray(right,b + i*bs);
    179:         VecAYPX(left,-1.0,right);
    180:         VecResetArray(right);

    182:         VecPlaceArray(right,x + i*bs);
    183:         MatSolve(diag[i],left,right);
    184:         VecResetArray(right);
    185:       }
    186:     }
    187:     if (flag & SOR_BACKWARD_SWEEP || flag & SOR_LOCAL_BACKWARD_SWEEP) {

    189:       for (i=mbs-1; i>=0; i--) {
    190:         n   = a->i[i+1] - a->i[i];
    191:         idx = a->j + a->i[i];
    192:         v   = a->a + a->i[i];

    194:         VecSet(left,0.0);
    195:         for (j=0; j<n; j++) {
    196:           if (idx[j] != i) {
    197:             VecPlaceArray(right,x + idx[j]*bs);
    198:             MatMultAdd(v[j],right,left,left);
    199:             VecResetArray(right);
    200:           }
    201:         }
    202:         VecPlaceArray(right,b + i*bs);
    203:         VecAYPX(left,-1.0,right);
    204:         VecResetArray(right);

    206:         VecPlaceArray(right,x + i*bs);
    207:         MatSolve(diag[i],left,right);
    208:         VecResetArray(right);

    210:       }
    211:     }
    212:   }
    213:   VecRestoreArray(xx,&x);
    214:   VecRestoreArrayRead(bb,&b);
    215:   return(0);
    216: }

    218: static PetscErrorCode MatSetValues_BlockMat(Mat A,PetscInt m,const PetscInt im[],PetscInt n,const PetscInt in[],const PetscScalar v[],InsertMode is)
    219: {
    220:   Mat_BlockMat   *a = (Mat_BlockMat*)A->data;
    221:   PetscInt       *rp,k,low,high,t,ii,row,nrow,i,col,l,rmax,N,lastcol = -1;
    222:   PetscInt       *imax=a->imax,*ai=a->i,*ailen=a->ilen;
    223:   PetscInt       *aj  =a->j,nonew=a->nonew,bs=A->rmap->bs,brow,bcol;
    225:   PetscInt       ridx,cidx;
    226:   PetscBool      roworiented=a->roworiented;
    227:   MatScalar      value;
    228:   Mat            *ap,*aa = a->a;

    231:   for (k=0; k<m; k++) { /* loop over added rows */
    232:     row  = im[k];
    233:     brow = row/bs;
    234:     if (row < 0) continue;
    235:     if (PetscUnlikelyDebug(row >= A->rmap->N)) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Row too large: row %D max %D",row,A->rmap->N-1);
    236:     rp   = aj + ai[brow];
    237:     ap   = aa + ai[brow];
    238:     rmax = imax[brow];
    239:     nrow = ailen[brow];
    240:     low  = 0;
    241:     high = nrow;
    242:     for (l=0; l<n; l++) { /* loop over added columns */
    243:       if (in[l] < 0) continue;
    244:       if (PetscUnlikelyDebug(in[l] >= A->cmap->n)) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Column too large: col %D max %D",in[l],A->cmap->n-1);
    245:       col = in[l]; bcol = col/bs;
    246:       if (A->symmetric && brow > bcol) continue;
    247:       ridx = row % bs; cidx = col % bs;
    248:       if (roworiented) value = v[l + k*n];
    249:       else value = v[k + l*m];

    251:       if (col <= lastcol) low = 0;
    252:       else high = nrow;
    253:       lastcol = col;
    254:       while (high-low > 7) {
    255:         t = (low+high)/2;
    256:         if (rp[t] > bcol) high = t;
    257:         else              low  = t;
    258:       }
    259:       for (i=low; i<high; i++) {
    260:         if (rp[i] > bcol) break;
    261:         if (rp[i] == bcol) goto noinsert1;
    262:       }
    263:       if (nonew == 1) goto noinsert1;
    264:       if (nonew == -1) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero (%D, %D) in the matrix", row, col);
    265:       MatSeqXAIJReallocateAIJ(A,a->mbs,1,nrow,brow,bcol,rmax,aa,ai,aj,rp,ap,imax,nonew,Mat);
    266:       N = nrow++ - 1; high++;
    267:       /* shift up all the later entries in this row */
    268:       for (ii=N; ii>=i; ii--) {
    269:         rp[ii+1] = rp[ii];
    270:         ap[ii+1] = ap[ii];
    271:       }
    272:       if (N>=i) ap[i] = NULL;
    273:       rp[i] = bcol;
    274:       a->nz++;
    275:       A->nonzerostate++;
    276: noinsert1:;
    277:       if (!*(ap+i)) {
    278:         MatCreateSeqAIJ(PETSC_COMM_SELF,bs,bs,0,NULL,ap+i);
    279:       }
    280:       MatSetValues(ap[i],1,&ridx,1,&cidx,&value,is);
    281:       low  = i;
    282:     }
    283:     ailen[brow] = nrow;
    284:   }
    285:   return(0);
    286: }

    288: static PetscErrorCode MatLoad_BlockMat(Mat newmat, PetscViewer viewer)
    289: {
    290:   PetscErrorCode    ierr;
    291:   Mat               tmpA;
    292:   PetscInt          i,j,m,n,bs = 1,ncols,*lens,currentcol,mbs,**ii,*ilens,nextcol,*llens,cnt = 0;
    293:   const PetscInt    *cols;
    294:   const PetscScalar *values;
    295:   PetscBool         flg = PETSC_FALSE,notdone;
    296:   Mat_SeqAIJ        *a;
    297:   Mat_BlockMat      *amat;

    300:   /* force binary viewer to load .info file if it has not yet done so */
    301:   PetscViewerSetUp(viewer);
    302:   MatCreate(PETSC_COMM_SELF,&tmpA);
    303:   MatSetType(tmpA,MATSEQAIJ);
    304:   MatLoad_SeqAIJ(tmpA,viewer);

    306:   MatGetLocalSize(tmpA,&m,&n);
    307:   PetscOptionsBegin(PETSC_COMM_SELF,NULL,"Options for loading BlockMat matrix 1","Mat");
    308:   PetscOptionsInt("-matload_block_size","Set the blocksize used to store the matrix","MatLoad",bs,&bs,NULL);
    309:   PetscOptionsBool("-matload_symmetric","Store the matrix as symmetric","MatLoad",flg,&flg,NULL);
    310:   PetscOptionsEnd();

    312:   /* Determine number of nonzero blocks for each block row */
    313:   a    = (Mat_SeqAIJ*) tmpA->data;
    314:   mbs  = m/bs;
    315:   PetscMalloc3(mbs,&lens,bs,&ii,bs,&ilens);
    316:   PetscArrayzero(lens,mbs);

    318:   for (i=0; i<mbs; i++) {
    319:     for (j=0; j<bs; j++) {
    320:       ii[j]    = a->j + a->i[i*bs + j];
    321:       ilens[j] = a->i[i*bs + j + 1] - a->i[i*bs + j];
    322:     }

    324:     currentcol = -1;
    325:     while (PETSC_TRUE) {
    326:       notdone = PETSC_FALSE;
    327:       nextcol = 1000000000;
    328:       for (j=0; j<bs; j++) {
    329:         while ((ilens[j] > 0 && ii[j][0]/bs <= currentcol)) {
    330:           ii[j]++;
    331:           ilens[j]--;
    332:         }
    333:         if (ilens[j] > 0) {
    334:           notdone = PETSC_TRUE;
    335:           nextcol = PetscMin(nextcol,ii[j][0]/bs);
    336:         }
    337:       }
    338:       if (!notdone) break;
    339:       if (!flg || (nextcol >= i)) lens[i]++;
    340:       currentcol = nextcol;
    341:     }
    342:   }

    344:   if (newmat->rmap->n < 0 && newmat->rmap->N < 0 && newmat->cmap->n < 0 && newmat->cmap->N < 0) {
    345:     MatSetSizes(newmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);
    346:   }
    347:   MatBlockMatSetPreallocation(newmat,bs,0,lens);
    348:   if (flg) {
    349:     MatSetOption(newmat,MAT_SYMMETRIC,PETSC_TRUE);
    350:   }
    351:   amat = (Mat_BlockMat*)(newmat)->data;

    353:   /* preallocate the submatrices */
    354:   PetscMalloc1(bs,&llens);
    355:   for (i=0; i<mbs; i++) { /* loops for block rows */
    356:     for (j=0; j<bs; j++) {
    357:       ii[j]    = a->j + a->i[i*bs + j];
    358:       ilens[j] = a->i[i*bs + j + 1] - a->i[i*bs + j];
    359:     }

    361:     currentcol = 1000000000;
    362:     for (j=0; j<bs; j++) { /* loop over rows in block finding first nonzero block */
    363:       if (ilens[j] > 0) {
    364:         currentcol = PetscMin(currentcol,ii[j][0]/bs);
    365:       }
    366:     }

    368:     while (PETSC_TRUE) {  /* loops over blocks in block row */
    369:       notdone = PETSC_FALSE;
    370:       nextcol = 1000000000;
    371:       PetscArrayzero(llens,bs);
    372:       for (j=0; j<bs; j++) { /* loop over rows in block */
    373:         while ((ilens[j] > 0 && ii[j][0]/bs <= currentcol)) { /* loop over columns in row */
    374:           ii[j]++;
    375:           ilens[j]--;
    376:           llens[j]++;
    377:         }
    378:         if (ilens[j] > 0) {
    379:           notdone = PETSC_TRUE;
    380:           nextcol = PetscMin(nextcol,ii[j][0]/bs);
    381:         }
    382:       }
    383:       if (cnt >= amat->maxnz) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Number of blocks found greater than expected %D",cnt);
    384:       if (!flg || currentcol >= i) {
    385:         amat->j[cnt] = currentcol;
    386:         MatCreateSeqAIJ(PETSC_COMM_SELF,bs,bs,0,llens,amat->a+cnt++);
    387:       }

    389:       if (!notdone) break;
    390:       currentcol = nextcol;
    391:     }
    392:     amat->ilen[i] = lens[i];
    393:   }

    395:   PetscFree3(lens,ii,ilens);
    396:   PetscFree(llens);

    398:   /* copy over the matrix, one row at a time */
    399:   for (i=0; i<m; i++) {
    400:     MatGetRow(tmpA,i,&ncols,&cols,&values);
    401:     MatSetValues(newmat,1,&i,ncols,cols,values,INSERT_VALUES);
    402:     MatRestoreRow(tmpA,i,&ncols,&cols,&values);
    403:   }
    404:   MatAssemblyBegin(newmat,MAT_FINAL_ASSEMBLY);
    405:   MatAssemblyEnd(newmat,MAT_FINAL_ASSEMBLY);
    406:   return(0);
    407: }

    409: static PetscErrorCode MatView_BlockMat(Mat A,PetscViewer viewer)
    410: {
    411:   Mat_BlockMat      *a = (Mat_BlockMat*)A->data;
    412:   PetscErrorCode    ierr;
    413:   const char        *name;
    414:   PetscViewerFormat format;

    417:   PetscObjectGetName((PetscObject)A,&name);
    418:   PetscViewerGetFormat(viewer,&format);
    419:   if (format == PETSC_VIEWER_ASCII_FACTOR_INFO || format == PETSC_VIEWER_ASCII_INFO) {
    420:     PetscViewerASCIIPrintf(viewer,"Nonzero block matrices = %D \n",a->nz);
    421:     if (A->symmetric) {
    422:       PetscViewerASCIIPrintf(viewer,"Only upper triangular part of symmetric matrix is stored\n");
    423:     }
    424:   }
    425:   return(0);
    426: }

    428: static PetscErrorCode MatDestroy_BlockMat(Mat mat)
    429: {
    431:   Mat_BlockMat   *bmat = (Mat_BlockMat*)mat->data;
    432:   PetscInt       i;

    435:   VecDestroy(&bmat->right);
    436:   VecDestroy(&bmat->left);
    437:   VecDestroy(&bmat->middle);
    438:   VecDestroy(&bmat->workb);
    439:   if (bmat->diags) {
    440:     for (i=0; i<mat->rmap->n/mat->rmap->bs; i++) {
    441:       MatDestroy(&bmat->diags[i]);
    442:     }
    443:   }
    444:   if (bmat->a) {
    445:     for (i=0; i<bmat->nz; i++) {
    446:       MatDestroy(&bmat->a[i]);
    447:     }
    448:   }
    449:   MatSeqXAIJFreeAIJ(mat,(PetscScalar**)&bmat->a,&bmat->j,&bmat->i);
    450:   PetscFree(mat->data);
    451:   return(0);
    452: }

    454: static PetscErrorCode MatMult_BlockMat(Mat A,Vec x,Vec y)
    455: {
    456:   Mat_BlockMat   *bmat = (Mat_BlockMat*)A->data;
    458:   PetscScalar    *xx,*yy;
    459:   PetscInt       *aj,i,*ii,jrow,m = A->rmap->n/A->rmap->bs,bs = A->rmap->bs,n,j;
    460:   Mat            *aa;

    463:   /*
    464:      Standard CSR multiply except each entry is a Mat
    465:   */
    466:   VecGetArray(x,&xx);

    468:   VecSet(y,0.0);
    469:   VecGetArray(y,&yy);
    470:   aj   = bmat->j;
    471:   aa   = bmat->a;
    472:   ii   = bmat->i;
    473:   for (i=0; i<m; i++) {
    474:     jrow = ii[i];
    475:     VecPlaceArray(bmat->left,yy + bs*i);
    476:     n    = ii[i+1] - jrow;
    477:     for (j=0; j<n; j++) {
    478:       VecPlaceArray(bmat->right,xx + bs*aj[jrow]);
    479:       MatMultAdd(aa[jrow],bmat->right,bmat->left,bmat->left);
    480:       VecResetArray(bmat->right);
    481:       jrow++;
    482:     }
    483:     VecResetArray(bmat->left);
    484:   }
    485:   VecRestoreArray(x,&xx);
    486:   VecRestoreArray(y,&yy);
    487:   return(0);
    488: }

    490: PetscErrorCode MatMult_BlockMat_Symmetric(Mat A,Vec x,Vec y)
    491: {
    492:   Mat_BlockMat   *bmat = (Mat_BlockMat*)A->data;
    494:   PetscScalar    *xx,*yy;
    495:   PetscInt       *aj,i,*ii,jrow,m = A->rmap->n/A->rmap->bs,bs = A->rmap->bs,n,j;
    496:   Mat            *aa;

    499:   /*
    500:      Standard CSR multiply except each entry is a Mat
    501:   */
    502:   VecGetArray(x,&xx);

    504:   VecSet(y,0.0);
    505:   VecGetArray(y,&yy);
    506:   aj   = bmat->j;
    507:   aa   = bmat->a;
    508:   ii   = bmat->i;
    509:   for (i=0; i<m; i++) {
    510:     jrow = ii[i];
    511:     n    = ii[i+1] - jrow;
    512:     VecPlaceArray(bmat->left,yy + bs*i);
    513:     VecPlaceArray(bmat->middle,xx + bs*i);
    514:     /* if we ALWAYS required a diagonal entry then could remove this if test */
    515:     if (aj[jrow] == i) {
    516:       VecPlaceArray(bmat->right,xx + bs*aj[jrow]);
    517:       MatMultAdd(aa[jrow],bmat->right,bmat->left,bmat->left);
    518:       VecResetArray(bmat->right);
    519:       jrow++;
    520:       n--;
    521:     }
    522:     for (j=0; j<n; j++) {
    523:       VecPlaceArray(bmat->right,xx + bs*aj[jrow]);            /* upper triangular part */
    524:       MatMultAdd(aa[jrow],bmat->right,bmat->left,bmat->left);
    525:       VecResetArray(bmat->right);

    527:       VecPlaceArray(bmat->right,yy + bs*aj[jrow]);            /* lower triangular part */
    528:       MatMultTransposeAdd(aa[jrow],bmat->middle,bmat->right,bmat->right);
    529:       VecResetArray(bmat->right);
    530:       jrow++;
    531:     }
    532:     VecResetArray(bmat->left);
    533:     VecResetArray(bmat->middle);
    534:   }
    535:   VecRestoreArray(x,&xx);
    536:   VecRestoreArray(y,&yy);
    537:   return(0);
    538: }

    540: static PetscErrorCode MatMultAdd_BlockMat(Mat A,Vec x,Vec y,Vec z)
    541: {
    543:   return(0);
    544: }

    546: static PetscErrorCode MatMultTranspose_BlockMat(Mat A,Vec x,Vec y)
    547: {
    549:   return(0);
    550: }

    552: static PetscErrorCode MatMultTransposeAdd_BlockMat(Mat A,Vec x,Vec y,Vec z)
    553: {
    555:   return(0);
    556: }

    558: /*
    559:      Adds diagonal pointers to sparse matrix structure.
    560: */
    561: static PetscErrorCode MatMarkDiagonal_BlockMat(Mat A)
    562: {
    563:   Mat_BlockMat   *a = (Mat_BlockMat*)A->data;
    565:   PetscInt       i,j,mbs = A->rmap->n/A->rmap->bs;

    568:   if (!a->diag) {
    569:     PetscMalloc1(mbs,&a->diag);
    570:   }
    571:   for (i=0; i<mbs; i++) {
    572:     a->diag[i] = a->i[i+1];
    573:     for (j=a->i[i]; j<a->i[i+1]; j++) {
    574:       if (a->j[j] == i) {
    575:         a->diag[i] = j;
    576:         break;
    577:       }
    578:     }
    579:   }
    580:   return(0);
    581: }

    583: static PetscErrorCode MatCreateSubMatrix_BlockMat(Mat A,IS isrow,IS iscol,MatReuse scall,Mat *B)
    584: {
    585:   Mat_BlockMat   *a = (Mat_BlockMat*)A->data;
    586:   Mat_SeqAIJ     *c;
    588:   PetscInt       i,k,first,step,lensi,nrows,ncols;
    589:   PetscInt       *j_new,*i_new,*aj = a->j,*ailen = a->ilen;
    590:   PetscScalar    *a_new;
    591:   Mat            C,*aa = a->a;
    592:   PetscBool      stride,equal;

    595:   ISEqual(isrow,iscol,&equal);
    596:   if (!equal) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only for identical column and row indices");
    597:   PetscObjectTypeCompare((PetscObject)iscol,ISSTRIDE,&stride);
    598:   if (!stride) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only for stride indices");
    599:   ISStrideGetInfo(iscol,&first,&step);
    600:   if (step != A->rmap->bs) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Can only select one entry from each block");

    602:   ISGetLocalSize(isrow,&nrows);
    603:   ncols = nrows;

    605:   /* create submatrix */
    606:   if (scall == MAT_REUSE_MATRIX) {
    607:     PetscInt n_cols,n_rows;
    608:     C    = *B;
    609:     MatGetSize(C,&n_rows,&n_cols);
    610:     if (n_rows != nrows || n_cols != ncols) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Reused submatrix wrong size");
    611:     MatZeroEntries(C);
    612:   } else {
    613:     MatCreate(PetscObjectComm((PetscObject)A),&C);
    614:     MatSetSizes(C,nrows,ncols,PETSC_DETERMINE,PETSC_DETERMINE);
    615:     if (A->symmetric) {
    616:       MatSetType(C,MATSEQSBAIJ);
    617:     } else {
    618:       MatSetType(C,MATSEQAIJ);
    619:     }
    620:     MatSeqAIJSetPreallocation(C,0,ailen);
    621:     MatSeqSBAIJSetPreallocation(C,1,0,ailen);
    622:   }
    623:   c = (Mat_SeqAIJ*)C->data;

    625:   /* loop over rows inserting into submatrix */
    626:   a_new = c->a;
    627:   j_new = c->j;
    628:   i_new = c->i;

    630:   for (i=0; i<nrows; i++) {
    631:     lensi = ailen[i];
    632:     for (k=0; k<lensi; k++) {
    633:       *j_new++ = *aj++;
    634:       MatGetValue(*aa++,first,first,a_new++);
    635:     }
    636:     i_new[i+1] = i_new[i] + lensi;
    637:     c->ilen[i] = lensi;
    638:   }

    640:   MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);
    641:   MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);
    642:   *B   = C;
    643:   return(0);
    644: }

    646: static PetscErrorCode MatAssemblyEnd_BlockMat(Mat A,MatAssemblyType mode)
    647: {
    648:   Mat_BlockMat   *a = (Mat_BlockMat*)A->data;
    650:   PetscInt       fshift = 0,i,j,*ai = a->i,*aj = a->j,*imax = a->imax;
    651:   PetscInt       m      = a->mbs,*ip,N,*ailen = a->ilen,rmax = 0;
    652:   Mat            *aa    = a->a,*ap;

    655:   if (mode == MAT_FLUSH_ASSEMBLY) return(0);

    657:   if (m) rmax = ailen[0]; /* determine row with most nonzeros */
    658:   for (i=1; i<m; i++) {
    659:     /* move each row back by the amount of empty slots (fshift) before it*/
    660:     fshift += imax[i-1] - ailen[i-1];
    661:     rmax    = PetscMax(rmax,ailen[i]);
    662:     if (fshift) {
    663:       ip = aj + ai[i];
    664:       ap = aa + ai[i];
    665:       N  = ailen[i];
    666:       for (j=0; j<N; j++) {
    667:         ip[j-fshift] = ip[j];
    668:         ap[j-fshift] = ap[j];
    669:       }
    670:     }
    671:     ai[i] = ai[i-1] + ailen[i-1];
    672:   }
    673:   if (m) {
    674:     fshift += imax[m-1] - ailen[m-1];
    675:     ai[m]   = ai[m-1] + ailen[m-1];
    676:   }
    677:   /* reset ilen and imax for each row */
    678:   for (i=0; i<m; i++) {
    679:     ailen[i] = imax[i] = ai[i+1] - ai[i];
    680:   }
    681:   a->nz = ai[m];
    682:   for (i=0; i<a->nz; i++) {
    683:     if (PetscUnlikelyDebug(!aa[i])) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Null matrix at location %D column %D nz %D",i,aj[i],a->nz);
    684:     MatAssemblyBegin(aa[i],MAT_FINAL_ASSEMBLY);
    685:     MatAssemblyEnd(aa[i],MAT_FINAL_ASSEMBLY);
    686:   }
    687:   PetscInfo4(A,"Matrix size: %D X %D; storage space: %D unneeded,%D used\n",m,A->cmap->n/A->cmap->bs,fshift,a->nz);
    688:   PetscInfo1(A,"Number of mallocs during MatSetValues() is %D\n",a->reallocs);
    689:   PetscInfo1(A,"Maximum nonzeros in any row is %D\n",rmax);

    691:   A->info.mallocs    += a->reallocs;
    692:   a->reallocs         = 0;
    693:   A->info.nz_unneeded = (double)fshift;
    694:   a->rmax             = rmax;
    695:   MatMarkDiagonal_BlockMat(A);
    696:   return(0);
    697: }

    699: static PetscErrorCode MatSetOption_BlockMat(Mat A,MatOption opt,PetscBool flg)
    700: {
    703:   if (opt == MAT_SYMMETRIC && flg) {
    704:     A->ops->sor  = MatSOR_BlockMat_Symmetric;
    705:     A->ops->mult = MatMult_BlockMat_Symmetric;
    706:   } else {
    707:     PetscInfo1(A,"Unused matrix option %s\n",MatOptions[opt]);
    708:   }
    709:   return(0);
    710: }

    713: static struct _MatOps MatOps_Values = {MatSetValues_BlockMat,
    714:                                        NULL,
    715:                                        NULL,
    716:                                        MatMult_BlockMat,
    717:                                /*  4*/ MatMultAdd_BlockMat,
    718:                                        MatMultTranspose_BlockMat,
    719:                                        MatMultTransposeAdd_BlockMat,
    720:                                        NULL,
    721:                                        NULL,
    722:                                        NULL,
    723:                                /* 10*/ NULL,
    724:                                        NULL,
    725:                                        NULL,
    726:                                        MatSOR_BlockMat,
    727:                                        NULL,
    728:                                /* 15*/ NULL,
    729:                                        NULL,
    730:                                        NULL,
    731:                                        NULL,
    732:                                        NULL,
    733:                                /* 20*/ NULL,
    734:                                        MatAssemblyEnd_BlockMat,
    735:                                        MatSetOption_BlockMat,
    736:                                        NULL,
    737:                                /* 24*/ NULL,
    738:                                        NULL,
    739:                                        NULL,
    740:                                        NULL,
    741:                                        NULL,
    742:                                /* 29*/ NULL,
    743:                                        NULL,
    744:                                        NULL,
    745:                                        NULL,
    746:                                        NULL,
    747:                                /* 34*/ NULL,
    748:                                        NULL,
    749:                                        NULL,
    750:                                        NULL,
    751:                                        NULL,
    752:                                /* 39*/ NULL,
    753:                                        NULL,
    754:                                        NULL,
    755:                                        NULL,
    756:                                        NULL,
    757:                                /* 44*/ NULL,
    758:                                        NULL,
    759:                                        MatShift_Basic,
    760:                                        NULL,
    761:                                        NULL,
    762:                                /* 49*/ NULL,
    763:                                        NULL,
    764:                                        NULL,
    765:                                        NULL,
    766:                                        NULL,
    767:                                /* 54*/ NULL,
    768:                                        NULL,
    769:                                        NULL,
    770:                                        NULL,
    771:                                        NULL,
    772:                                /* 59*/ MatCreateSubMatrix_BlockMat,
    773:                                        MatDestroy_BlockMat,
    774:                                        MatView_BlockMat,
    775:                                        NULL,
    776:                                        NULL,
    777:                                /* 64*/ NULL,
    778:                                        NULL,
    779:                                        NULL,
    780:                                        NULL,
    781:                                        NULL,
    782:                                /* 69*/ NULL,
    783:                                        NULL,
    784:                                        NULL,
    785:                                        NULL,
    786:                                        NULL,
    787:                                /* 74*/ NULL,
    788:                                        NULL,
    789:                                        NULL,
    790:                                        NULL,
    791:                                        NULL,
    792:                                /* 79*/ NULL,
    793:                                        NULL,
    794:                                        NULL,
    795:                                        NULL,
    796:                                        MatLoad_BlockMat,
    797:                                /* 84*/ NULL,
    798:                                        NULL,
    799:                                        NULL,
    800:                                        NULL,
    801:                                        NULL,
    802:                                /* 89*/ NULL,
    803:                                        NULL,
    804:                                        NULL,
    805:                                        NULL,
    806:                                        NULL,
    807:                                /* 94*/ NULL,
    808:                                        NULL,
    809:                                        NULL,
    810:                                        NULL,
    811:                                        NULL,
    812:                                /* 99*/ NULL,
    813:                                        NULL,
    814:                                        NULL,
    815:                                        NULL,
    816:                                        NULL,
    817:                                /*104*/ NULL,
    818:                                        NULL,
    819:                                        NULL,
    820:                                        NULL,
    821:                                        NULL,
    822:                                /*109*/ NULL,
    823:                                        NULL,
    824:                                        NULL,
    825:                                        NULL,
    826:                                        NULL,
    827:                                /*114*/ NULL,
    828:                                        NULL,
    829:                                        NULL,
    830:                                        NULL,
    831:                                        NULL,
    832:                                /*119*/ NULL,
    833:                                        NULL,
    834:                                        NULL,
    835:                                        NULL,
    836:                                        NULL,
    837:                                /*124*/ NULL,
    838:                                        NULL,
    839:                                        NULL,
    840:                                        NULL,
    841:                                        NULL,
    842:                                /*129*/ NULL,
    843:                                        NULL,
    844:                                        NULL,
    845:                                        NULL,
    846:                                        NULL,
    847:                                /*134*/ NULL,
    848:                                        NULL,
    849:                                        NULL,
    850:                                        NULL,
    851:                                        NULL,
    852:                                /*139*/ NULL,
    853:                                        NULL,
    854:                                        NULL
    855: };

    857: /*@C
    858:    MatBlockMatSetPreallocation - For good matrix assembly performance
    859:    the user should preallocate the matrix storage by setting the parameter nz
    860:    (or the array nnz).  By setting these parameters accurately, performance
    861:    during matrix assembly can be increased by more than a factor of 50.

    863:    Collective

    865:    Input Parameters:
    866: +  B - The matrix
    867: .  bs - size of each block in matrix
    868: .  nz - number of nonzeros per block row (same for all rows)
    869: -  nnz - array containing the number of nonzeros in the various block rows
    870:          (possibly different for each row) or NULL

    872:    Notes:
    873:      If nnz is given then nz is ignored

    875:    Specify the preallocated storage with either nz or nnz (not both).
    876:    Set nz=PETSC_DEFAULT and nnz=NULL for PETSc to control dynamic memory
    877:    allocation.  For large problems you MUST preallocate memory or you
    878:    will get TERRIBLE performance, see the users' manual chapter on matrices.

    880:    Level: intermediate

    882: .seealso: MatCreate(), MatCreateBlockMat(), MatSetValues()

    884: @*/
    885: PetscErrorCode  MatBlockMatSetPreallocation(Mat B,PetscInt bs,PetscInt nz,const PetscInt nnz[])
    886: {

    890:   PetscTryMethod(B,"MatBlockMatSetPreallocation_C",(Mat,PetscInt,PetscInt,const PetscInt[]),(B,bs,nz,nnz));
    891:   return(0);
    892: }

    894: static PetscErrorCode  MatBlockMatSetPreallocation_BlockMat(Mat A,PetscInt bs,PetscInt nz,PetscInt *nnz)
    895: {
    896:   Mat_BlockMat   *bmat = (Mat_BlockMat*)A->data;
    898:   PetscInt       i;

    901:   PetscLayoutSetBlockSize(A->rmap,bs);
    902:   PetscLayoutSetBlockSize(A->cmap,bs);
    903:   PetscLayoutSetUp(A->rmap);
    904:   PetscLayoutSetUp(A->cmap);
    905:   PetscLayoutGetBlockSize(A->rmap,&bs);

    907:   if (nz == PETSC_DEFAULT || nz == PETSC_DECIDE) nz = 5;
    908:   if (nz < 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"nz cannot be less than 0: value %d",nz);
    909:   if (nnz) {
    910:     for (i=0; i<A->rmap->n/bs; i++) {
    911:       if (nnz[i] < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"nnz cannot be less than 0: local row %d value %d",i,nnz[i]);
    912:       if (nnz[i] > A->cmap->n/bs) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"nnz cannot be greater than row length: local row %d value %d rowlength %d",i,nnz[i],A->cmap->n/bs);
    913:     }
    914:   }
    915:   bmat->mbs = A->rmap->n/bs;

    917:   VecCreateSeqWithArray(PETSC_COMM_SELF,1,bs,NULL,&bmat->right);
    918:   VecCreateSeqWithArray(PETSC_COMM_SELF,1,bs,NULL,&bmat->middle);
    919:   VecCreateSeq(PETSC_COMM_SELF,bs,&bmat->left);

    921:   if (!bmat->imax) {
    922:     PetscMalloc2(A->rmap->n,&bmat->imax,A->rmap->n,&bmat->ilen);
    923:     PetscLogObjectMemory((PetscObject)A,2*A->rmap->n*sizeof(PetscInt));
    924:   }
    925:   if (nnz) {
    926:     nz = 0;
    927:     for (i=0; i<A->rmap->n/A->rmap->bs; i++) {
    928:       bmat->imax[i] = nnz[i];
    929:       nz           += nnz[i];
    930:     }
    931:   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Currently requires block row by row preallocation");

    933:   /* bmat->ilen will count nonzeros in each row so far. */
    934:   for (i=0; i<bmat->mbs; i++) bmat->ilen[i] = 0;

    936:   /* allocate the matrix space */
    937:   MatSeqXAIJFreeAIJ(A,(PetscScalar**)&bmat->a,&bmat->j,&bmat->i);
    938:   PetscMalloc3(nz,&bmat->a,nz,&bmat->j,A->rmap->n+1,&bmat->i);
    939:   PetscLogObjectMemory((PetscObject)A,(A->rmap->n+1)*sizeof(PetscInt)+nz*(sizeof(PetscScalar)+sizeof(PetscInt)));
    940:   bmat->i[0] = 0;
    941:   for (i=1; i<bmat->mbs+1; i++) {
    942:     bmat->i[i] = bmat->i[i-1] + bmat->imax[i-1];
    943:   }
    944:   bmat->singlemalloc = PETSC_TRUE;
    945:   bmat->free_a       = PETSC_TRUE;
    946:   bmat->free_ij      = PETSC_TRUE;

    948:   bmat->nz            = 0;
    949:   bmat->maxnz         = nz;
    950:   A->info.nz_unneeded = (double)bmat->maxnz;
    951:   MatSetOption(A,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE);
    952:   return(0);
    953: }

    955: /*MC
    956:    MATBLOCKMAT - A matrix that is defined by a set of Mat's that represents a sparse block matrix
    957:                  consisting of (usually) sparse blocks.

    959:   Level: advanced

    961: .seealso: MatCreateBlockMat()

    963: M*/

    965: PETSC_EXTERN PetscErrorCode MatCreate_BlockMat(Mat A)
    966: {
    967:   Mat_BlockMat   *b;

    971:   PetscNewLog(A,&b);
    972:   A->data = (void*)b;
    973:   PetscMemcpy(A->ops,&MatOps_Values,sizeof(struct _MatOps));

    975:   A->assembled    = PETSC_TRUE;
    976:   A->preallocated = PETSC_FALSE;
    977:   PetscObjectChangeTypeName((PetscObject)A,MATBLOCKMAT);

    979:   PetscObjectComposeFunction((PetscObject)A,"MatBlockMatSetPreallocation_C",MatBlockMatSetPreallocation_BlockMat);
    980:   return(0);
    981: }

    983: /*@C
    984:    MatCreateBlockMat - Creates a new matrix in which each block contains a uniform-size sequential Mat object

    986:   Collective

    988:    Input Parameters:
    989: +  comm - MPI communicator
    990: .  m - number of rows
    991: .  n  - number of columns
    992: .  bs - size of each submatrix
    993: .  nz  - expected maximum number of nonzero blocks in row (use PETSC_DEFAULT if not known)
    994: -  nnz - expected number of nonzers per block row if known (use NULL otherwise)

    997:    Output Parameter:
    998: .  A - the matrix

    1000:    Level: intermediate

    1002:    Notes:
    1003:     Matrices of this type are nominally-sparse matrices in which each "entry" is a Mat object.  Each Mat must
    1004:    have the same size and be sequential.  The local and global sizes must be compatible with this decomposition.

    1006:    For matrices containing parallel submatrices and variable block sizes, see MATNEST.

    1008: .seealso: MATBLOCKMAT, MatCreateNest()
    1009: @*/
    1010: PetscErrorCode  MatCreateBlockMat(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt bs,PetscInt nz,PetscInt *nnz, Mat *A)
    1011: {

    1015:   MatCreate(comm,A);
    1016:   MatSetSizes(*A,m,n,PETSC_DETERMINE,PETSC_DETERMINE);
    1017:   MatSetType(*A,MATBLOCKMAT);
    1018:   MatBlockMatSetPreallocation(*A,bs,nz,nnz);
    1019:   return(0);
    1020: }