Actual source code: spbas.c

      1: #include <../src/mat/impls/aij/seq/aij.h>
      2: #include <../src/mat/impls/aij/seq/bas/spbas.h>

      4: /*MC
      5:   MATSOLVERBAS -  Provides ICC(k) with drop tolerance

      7:   Works with MATAIJ  matrices

      9:   Options Database Keys:
     10: + -pc_factor_levels <l> - number of levels of fill
     11: - -pc_factor_drop_tolerance - is not currently hooked up to do anything

     13:   Level: intermediate

     15:    Contributed by: Bas van 't Hof

     17:    Notes:
     18:     Since this currently hooked up to use drop tolerance it should produce the same factors and hence convergence as the PETSc ICC, for higher
     19:      levels of fill it does not. This needs to be investigated. Unless you are interested in drop tolerance ICC and willing to work through the code
     20:      we recommend not using this functionality.

     22: .seealso: PCFactorSetMatSolverType(), MatSolverType, PCFactorSetLevels(), PCFactorSetDropTolerance()

     24: M*/

     26: /*
     27:   spbas_memory_requirement:
     28:     Calculate the number of bytes needed to store tha matrix
     29: */
     30: size_t spbas_memory_requirement(spbas_matrix matrix)
     31: {
     32:   size_t memreq = 6 * sizeof(PetscInt)  + /* nrows, ncols, nnz, n_alloc_icol, n_alloc_val, col_idx_type */
     33:                     sizeof(PetscBool)               + /* block_data */
     34:                     sizeof(PetscScalar**)           + /* values */
     35:                     sizeof(PetscScalar*)            + /* alloc_val */
     36:                     2 * sizeof(PetscInt**)          + /* icols, icols0 */
     37:                     2 * sizeof(PetscInt*)           + /* row_nnz, alloc_icol */
     38:                     matrix.nrows * sizeof(PetscInt) + /* row_nnz[*] */
     39:                     matrix.nrows * sizeof(PetscInt*); /* icols[*] */

     41:   /* icol0[*] */
     42:   if (matrix.col_idx_type == SPBAS_OFFSET_ARRAY) memreq += matrix.nrows * sizeof(PetscInt);

     44:   /* icols[*][*] */
     45:   if (matrix.block_data) memreq += matrix.n_alloc_icol * sizeof(PetscInt);
     46:   else memreq += matrix.nnz * sizeof(PetscInt);

     48:   if (matrix.values) {
     49:     memreq += matrix.nrows * sizeof(PetscScalar*); /* values[*] */
     50:     /* values[*][*] */
     51:     if (matrix.block_data) memreq += matrix.n_alloc_val  * sizeof(PetscScalar);
     52:     else memreq += matrix.nnz * sizeof(PetscScalar);
     53:   }
     54:   return memreq;
     55: }

     57: /*
     58:   spbas_allocate_pattern:
     59:     allocate the pattern arrays row_nnz, icols and optionally values
     60: */
     61: PetscErrorCode spbas_allocate_pattern(spbas_matrix * result, PetscBool do_values)
     62: {
     64:   PetscInt       nrows        = result->nrows;
     65:   PetscInt       col_idx_type = result->col_idx_type;

     68:   /* Allocate sparseness pattern */
     69:   PetscMalloc1(nrows,&result->row_nnz);
     70:   PetscMalloc1(nrows,&result->icols);

     72:   /* If offsets are given wrt an array, create array */
     73:   if (col_idx_type == SPBAS_OFFSET_ARRAY) {
     74:     PetscMalloc1(nrows,&result->icol0);
     75:   } else  {
     76:     result->icol0 = NULL;
     77:   }

     79:   /* If values are given, allocate values array */
     80:   if (do_values)  {
     81:     PetscMalloc1(nrows,&result->values);
     82:   } else {
     83:     result->values = NULL;
     84:   }
     85:   return(0);
     86: }

     88: /*
     89: spbas_allocate_data:
     90:    in case of block_data:
     91:        Allocate the data arrays alloc_icol and optionally alloc_val,
     92:        set appropriate pointers from icols and values;
     93:    in case of !block_data:
     94:        Allocate the arrays icols[i] and optionally values[i]
     95: */
     96: PetscErrorCode spbas_allocate_data(spbas_matrix * result)
     97: {
     98:   PetscInt       i;
     99:   PetscInt       nnz   = result->nnz;
    100:   PetscInt       nrows = result->nrows;
    101:   PetscInt       r_nnz;
    103:   PetscBool      do_values  = (result->values) ? PETSC_TRUE : PETSC_FALSE;
    104:   PetscBool      block_data = result->block_data;

    107:   if (block_data) {
    108:     /* Allocate the column number array and point to it */
    109:     result->n_alloc_icol = nnz;

    111:     PetscMalloc1(nnz, &result->alloc_icol);

    113:     result->icols[0] = result->alloc_icol;
    114:     for (i=1; i<nrows; i++)  {
    115:       result->icols[i] = result->icols[i-1] + result->row_nnz[i-1];
    116:     }

    118:     /* Allocate the value array and point to it */
    119:     if (do_values) {
    120:       result->n_alloc_val = nnz;

    122:       PetscMalloc1(nnz, &result->alloc_val);

    124:       result->values[0] = result->alloc_val;
    125:       for (i=1; i<nrows; i++) {
    126:         result->values[i] = result->values[i-1] + result->row_nnz[i-1];
    127:       }
    128:     }
    129:   } else {
    130:     for (i=0; i<nrows; i++)   {
    131:       r_nnz = result->row_nnz[i];
    132:       PetscMalloc1(r_nnz, &result->icols[i]);
    133:     }
    134:     if (do_values) {
    135:       for (i=0; i<nrows; i++)  {
    136:         r_nnz = result->row_nnz[i];
    137:         PetscMalloc1(r_nnz, &result->values[i]);
    138:       }
    139:     }
    140:   }
    141:   return(0);
    142: }

    144: /*
    145:   spbas_row_order_icol
    146:      determine if row i1 should come
    147:        + before row i2 in the sorted rows (return -1),
    148:        + after (return 1)
    149:        + is identical (return 0).
    150: */
    151: int spbas_row_order_icol(PetscInt i1, PetscInt i2, PetscInt *irow_in, PetscInt *icol_in,PetscInt col_idx_type)
    152: {
    153:   PetscInt j;
    154:   PetscInt nnz1    = irow_in[i1+1] - irow_in[i1];
    155:   PetscInt nnz2    = irow_in[i2+1] - irow_in[i2];
    156:   PetscInt * icol1 = &icol_in[irow_in[i1]];
    157:   PetscInt * icol2 = &icol_in[irow_in[i2]];

    159:   if (nnz1<nnz2) return -1;
    160:   if (nnz1>nnz2) return 1;

    162:   if (col_idx_type == SPBAS_COLUMN_NUMBERS) {
    163:     for (j=0; j<nnz1; j++) {
    164:       if (icol1[j]< icol2[j]) return -1;
    165:       if (icol1[j]> icol2[j]) return 1;
    166:     }
    167:   } else if (col_idx_type == SPBAS_DIAGONAL_OFFSETS) {
    168:     for (j=0; j<nnz1; j++) {
    169:       if (icol1[j]-i1< icol2[j]-i2) return -1;
    170:       if (icol1[j]-i1> icol2[j]-i2) return 1;
    171:     }
    172:   } else if (col_idx_type == SPBAS_OFFSET_ARRAY) {
    173:     for (j=1; j<nnz1; j++) {
    174:       if (icol1[j]-icol1[0] < icol2[j]-icol2[0]) return -1;
    175:       if (icol1[j]-icol1[0] > icol2[j]-icol2[0]) return 1;
    176:     }
    177:   }
    178:   return 0;
    179: }

    181: /*
    182:   spbas_mergesort_icols:
    183:     return a sorting of the rows in which identical sparseness patterns are
    184:     next to each other
    185: */
    186: PetscErrorCode spbas_mergesort_icols(PetscInt nrows, PetscInt * irow_in, PetscInt * icol_in,PetscInt col_idx_type, PetscInt *isort)
    187: {
    189:   PetscInt       istep;       /* Chunk-sizes of already sorted parts of arrays */
    190:   PetscInt       i, i1, i2;   /* Loop counters for (partly) sorted arrays */
    191:   PetscInt       istart, i1end, i2end; /* start of newly sorted array part, end of both  parts */
    192:   PetscInt       *ialloc;     /* Allocated arrays */
    193:   PetscInt       *iswap;      /* auxiliary pointers for swapping */
    194:   PetscInt       *ihlp1;      /* Pointers to new version of arrays, */
    195:   PetscInt       *ihlp2;      /* Pointers to previous version of arrays, */

    198:   PetscMalloc1(nrows,&ialloc);

    200:   ihlp1 = ialloc;
    201:   ihlp2 = isort;

    203:   /* Sorted array chunks are first 1 long, and increase until they are the complete array */
    204:   for (istep=1; istep<nrows; istep*=2) {
    205:     /*
    206:       Combine sorted parts
    207:           istart:istart+istep-1 and istart+istep-1:istart+2*istep-1
    208:       of ihlp2 and vhlp2

    210:       into one sorted part
    211:           istart:istart+2*istep-1
    212:       of ihlp1 and vhlp1
    213:     */
    214:     for (istart=0; istart<nrows; istart+=2*istep) {
    215:       /* Set counters and bound array part endings */
    216:       i1=istart;        i1end = i1+istep;  if (i1end>nrows) i1end=nrows;
    217:       i2=istart+istep;  i2end = i2+istep;  if (i2end>nrows) i2end=nrows;

    219:       /* Merge the two array parts */
    220:       for (i=istart; i<i2end; i++)  {
    221:         if (i1<i1end && i2<i2end && spbas_row_order_icol(ihlp2[i1], ihlp2[i2], irow_in, icol_in, col_idx_type) < 0) {
    222:           ihlp1[i] = ihlp2[i1];
    223:           i1++;
    224:         } else if (i2<i2end) {
    225:           ihlp1[i] = ihlp2[i2];
    226:           i2++;
    227:         } else {
    228:           ihlp1[i] = ihlp2[i1];
    229:           i1++;
    230:         }
    231:       }
    232:     }

    234:     /* Swap the two array sets */
    235:     iswap = ihlp2; ihlp2 = ihlp1; ihlp1 = iswap;
    236:   }

    238:   /* Copy one more time in case the sorted arrays are the temporary ones */
    239:   if (ihlp2 != isort) {
    240:     for (i=0; i<nrows; i++) isort[i] = ihlp2[i];
    241:   }
    242:   PetscFree(ialloc);
    243:   return(0);
    244: }

    248: /*
    249:   spbas_compress_pattern:
    250:      calculate a compressed sparseness pattern for a sparseness pattern
    251:      given in compressed row storage. The compressed sparseness pattern may
    252:      require (much) less memory.
    253: */
    254: PetscErrorCode spbas_compress_pattern(PetscInt *irow_in, PetscInt *icol_in, PetscInt nrows, PetscInt ncols, PetscInt col_idx_type, spbas_matrix *B,PetscReal *mem_reduction)
    255: {
    256:   PetscInt        nnz      = irow_in[nrows];
    257:   size_t          mem_orig = (nrows + nnz) * sizeof(PetscInt);
    258:   size_t          mem_compressed;
    259:   PetscErrorCode  ierr;
    260:   PetscInt        *isort;
    261:   PetscInt        *icols;
    262:   PetscInt        row_nnz;
    263:   PetscInt        *ipoint;
    264:   PetscBool       *used;
    265:   PetscInt        ptr;
    266:   PetscInt        i,j;
    267:   const PetscBool no_values = PETSC_FALSE;

    270:   /* Allocate the structure of the new matrix */
    271:   B->nrows        = nrows;
    272:   B->ncols        = ncols;
    273:   B->nnz          = nnz;
    274:   B->col_idx_type = col_idx_type;
    275:   B->block_data   = PETSC_TRUE;

    277:   spbas_allocate_pattern(B, no_values);

    279:   /* When using an offset array, set it */
    280:   if (col_idx_type==SPBAS_OFFSET_ARRAY)  {
    281:     for (i=0; i<nrows; i++) B->icol0[i] = icol_in[irow_in[i]];
    282:   }

    284:   /* Allocate the ordering for the rows */
    285:   PetscMalloc1(nrows,&isort);
    286:   PetscMalloc1(nrows,&ipoint);
    287:   PetscCalloc1(nrows,&used);

    289:   for (i = 0; i<nrows; i++)  {
    290:     B->row_nnz[i] = irow_in[i+1]-irow_in[i];
    291:     isort[i]      = i;
    292:     ipoint[i]     = i;
    293:   }

    295:   /* Sort the rows so that identical columns will be next to each other */
    296:   spbas_mergesort_icols(nrows, irow_in, icol_in, col_idx_type, isort);
    297:   PetscInfo(NULL,"Rows have been sorted for patterns\n");

    299:   /* Replace identical rows with the first one in the list */
    300:   for (i=1; i<nrows; i++) {
    301:     if (spbas_row_order_icol(isort[i-1], isort[i], irow_in, icol_in, col_idx_type) == 0) {
    302:       ipoint[isort[i]] = ipoint[isort[i-1]];
    303:     }
    304:   }

    306:   /* Collect the rows which are used*/
    307:   for (i=0; i<nrows; i++) used[ipoint[i]] = PETSC_TRUE;

    309:   /* Calculate needed memory */
    310:   B->n_alloc_icol = 0;
    311:   for (i=0; i<nrows; i++)  {
    312:     if (used[i]) B->n_alloc_icol += B->row_nnz[i];
    313:   }
    314:   PetscMalloc1(B->n_alloc_icol,&B->alloc_icol);

    316:   /* Fill in the diagonal offsets for the rows which store their own data */
    317:   ptr = 0;
    318:   for (i=0; i<B->nrows; i++) {
    319:     if (used[i]) {
    320:       B->icols[i] = &B->alloc_icol[ptr];
    321:       icols = &icol_in[irow_in[i]];
    322:       row_nnz = B->row_nnz[i];
    323:       if (col_idx_type == SPBAS_COLUMN_NUMBERS) {
    324:         for (j=0; j<row_nnz; j++) {
    325:           B->icols[i][j] = icols[j];
    326:         }
    327:       } else if (col_idx_type == SPBAS_DIAGONAL_OFFSETS) {
    328:         for (j=0; j<row_nnz; j++) {
    329:           B->icols[i][j] = icols[j]-i;
    330:         }
    331:       } else if (col_idx_type == SPBAS_OFFSET_ARRAY) {
    332:         for (j=0; j<row_nnz; j++) {
    333:           B->icols[i][j] = icols[j]-icols[0];
    334:         }
    335:       }
    336:       ptr += B->row_nnz[i];
    337:     }
    338:   }

    340:   /* Point to the right places for all data */
    341:   for (i=0; i<nrows; i++) {
    342:     B->icols[i] = B->icols[ipoint[i]];
    343:   }
    344:   PetscInfo(NULL,"Row patterns have been compressed\n");
    345:   PetscInfo1(NULL,"         (%g nonzeros per row)\n", (double) ((PetscReal) nnz / (PetscReal) nrows));

    347:   ierr=PetscFree(isort);
    348:   ierr=PetscFree(used);
    349:   ierr=PetscFree(ipoint);

    351:   mem_compressed = spbas_memory_requirement(*B);
    352:   *mem_reduction = 100.0 * (PetscReal)(mem_orig-mem_compressed)/ (PetscReal) mem_orig;
    353:   return(0);
    354: }

    356: /*
    357:    spbas_incomplete_cholesky
    358:        Incomplete Cholesky decomposition
    359: */
    360: #include <../src/mat/impls/aij/seq/bas/spbas_cholesky.h>

    362: /*
    363:   spbas_delete : de-allocate the arrays owned by this matrix
    364: */
    365: PetscErrorCode spbas_delete(spbas_matrix matrix)
    366: {
    367:   PetscInt       i;

    371:   if (matrix.block_data) {
    372:     ierr=PetscFree(matrix.alloc_icol);
    373:     if (matrix.values) {ierr=PetscFree(matrix.alloc_val);}
    374:   } else {
    375:     for (i=0; i<matrix.nrows; i++) { ierr=PetscFree(matrix.icols[i]);}
    376:     PetscFree(matrix.icols);
    377:     if (matrix.values) {
    378:       for (i=0; i<matrix.nrows; i++) { ierr=PetscFree(matrix.values[i]);}
    379:     }
    380:   }

    382:   ierr=PetscFree(matrix.row_nnz);
    383:   ierr=PetscFree(matrix.icols);
    384:   if (matrix.col_idx_type == SPBAS_OFFSET_ARRAY) {ierr=PetscFree(matrix.icol0);}
    385:   ierr=PetscFree(matrix.values);
    386:   return(0);
    387: }

    389: /*
    390: spbas_matrix_to_crs:
    391:    Convert an spbas_matrix to compessed row storage
    392: */
    393: PetscErrorCode spbas_matrix_to_crs(spbas_matrix matrix_A,MatScalar **val_out, PetscInt **irow_out, PetscInt **icol_out)
    394: {
    395:   PetscInt       nrows = matrix_A.nrows;
    396:   PetscInt       nnz   = matrix_A.nnz;
    397:   PetscInt       i,j,r_nnz,i0;
    398:   PetscInt       *irow;
    399:   PetscInt       *icol;
    400:   PetscInt       *icol_A;
    401:   MatScalar      *val;
    402:   PetscScalar    *val_A;
    403:   PetscInt       col_idx_type = matrix_A.col_idx_type;
    404:   PetscBool      do_values    = matrix_A.values ? PETSC_TRUE : PETSC_FALSE;

    408:   PetscMalloc1(nrows+1, &irow);
    409:   PetscMalloc1(nnz, &icol);
    410:   *icol_out = icol;
    411:   *irow_out = irow;
    412:   if (do_values) {
    413:     PetscMalloc1(nnz, &val);
    414:     *val_out = val; *icol_out = icol; *irow_out=irow;
    415:   }

    417:   irow[0]=0;
    418:   for (i=0; i<nrows; i++) {
    419:     r_nnz     = matrix_A.row_nnz[i];
    420:     i0        = irow[i];
    421:     irow[i+1] = i0 + r_nnz;
    422:     icol_A    = matrix_A.icols[i];

    424:     if (do_values) {
    425:       val_A = matrix_A.values[i];
    426:       for (j=0; j<r_nnz; j++) {
    427:         icol[i0+j] = icol_A[j];
    428:         val[i0+j]  = val_A[j];
    429:       }
    430:     } else {
    431:       for (j=0; j<r_nnz; j++) icol[i0+j] = icol_A[j];
    432:     }

    434:     if (col_idx_type == SPBAS_DIAGONAL_OFFSETS) {
    435:       for (j=0; j<r_nnz; j++) icol[i0+j] += i;
    436:     } else if (col_idx_type == SPBAS_OFFSET_ARRAY) {
    437:       i0 = matrix_A.icol0[i];
    438:       for (j=0; j<r_nnz; j++) icol[i0+j] += i0;
    439:     }
    440:   }
    441:   return(0);
    442: }

    445: /*
    446:     spbas_transpose
    447:        return the transpose of a matrix
    448: */
    449: PetscErrorCode spbas_transpose(spbas_matrix in_matrix, spbas_matrix * result)
    450: {
    451:   PetscInt       col_idx_type = in_matrix.col_idx_type;
    452:   PetscInt       nnz          = in_matrix.nnz;
    453:   PetscInt       ncols        = in_matrix.nrows;
    454:   PetscInt       nrows        = in_matrix.ncols;
    455:   PetscInt       i,j,k;
    456:   PetscInt       r_nnz;
    457:   PetscInt       *irow;
    458:   PetscInt       icol0 = 0;
    459:   PetscScalar    * val;

    463:   /* Copy input values */
    464:   result->nrows        = nrows;
    465:   result->ncols        = ncols;
    466:   result->nnz          = nnz;
    467:   result->col_idx_type = SPBAS_COLUMN_NUMBERS;
    468:   result->block_data   = PETSC_TRUE;

    470:   /* Allocate sparseness pattern */
    471:    spbas_allocate_pattern(result, in_matrix.values ? PETSC_TRUE : PETSC_FALSE);

    473:   /*  Count the number of nonzeros in each row */
    474:   for (i = 0; i<nrows; i++) result->row_nnz[i] = 0;

    476:   for (i=0; i<ncols; i++) {
    477:     r_nnz = in_matrix.row_nnz[i];
    478:     irow  = in_matrix.icols[i];
    479:     if (col_idx_type == SPBAS_COLUMN_NUMBERS)  {
    480:       for (j=0; j<r_nnz; j++) result->row_nnz[irow[j]]++;
    481:     } else if (col_idx_type == SPBAS_DIAGONAL_OFFSETS)  {
    482:       for (j=0; j<r_nnz; j++) result->row_nnz[i+irow[j]]++;
    483:     } else if (col_idx_type == SPBAS_OFFSET_ARRAY) {
    484:       icol0=in_matrix.icol0[i];
    485:       for (j=0; j<r_nnz; j++) result->row_nnz[icol0+irow[j]]++;
    486:     }
    487:   }

    489:   /* Set the pointers to the data */
    490:   spbas_allocate_data(result);

    492:   /* Reset the number of nonzeros in each row */
    493:   for (i = 0; i<nrows; i++) result->row_nnz[i] = 0;

    495:   /* Fill the data arrays */
    496:   if (in_matrix.values) {
    497:     for (i=0; i<ncols; i++) {
    498:       r_nnz = in_matrix.row_nnz[i];
    499:       irow  = in_matrix.icols[i];
    500:       val   = in_matrix.values[i];

    502:       if      (col_idx_type == SPBAS_COLUMN_NUMBERS)   icol0 = 0;
    503:       else if (col_idx_type == SPBAS_DIAGONAL_OFFSETS) icol0 = i;
    504:       else if (col_idx_type == SPBAS_OFFSET_ARRAY)     icol0 = in_matrix.icol0[i];
    505:       for (j=0; j<r_nnz; j++)  {
    506:         k = icol0 + irow[j];
    507:         result->icols[k][result->row_nnz[k]]  = i;
    508:         result->values[k][result->row_nnz[k]] = val[j];
    509:         result->row_nnz[k]++;
    510:       }
    511:     }
    512:   } else {
    513:     for (i=0; i<ncols; i++) {
    514:       r_nnz = in_matrix.row_nnz[i];
    515:       irow  = in_matrix.icols[i];

    517:       if      (col_idx_type == SPBAS_COLUMN_NUMBERS)   icol0=0;
    518:       else if (col_idx_type == SPBAS_DIAGONAL_OFFSETS) icol0=i;
    519:       else if (col_idx_type == SPBAS_OFFSET_ARRAY)     icol0=in_matrix.icol0[i];

    521:       for (j=0; j<r_nnz; j++) {
    522:         k = icol0 + irow[j];
    523:         result->icols[k][result->row_nnz[k]] = i;
    524:         result->row_nnz[k]++;
    525:       }
    526:     }
    527:   }
    528:   return(0);
    529: }

    531: /*
    532:    spbas_mergesort

    534:       mergesort for an array of integers and an array of associated
    535:       reals

    537:       on output, icol[0..nnz-1] is increasing;
    538:                   val[0..nnz-1] has undergone the same permutation as icol

    540:       NB: val may be NULL: in that case, only the integers are sorted

    542: */
    543: PetscErrorCode spbas_mergesort(PetscInt nnz, PetscInt *icol, PetscScalar *val)
    544: {
    545:   PetscInt       istep;       /* Chunk-sizes of already sorted parts of arrays */
    546:   PetscInt       i, i1, i2;   /* Loop counters for (partly) sorted arrays */
    547:   PetscInt       istart, i1end, i2end; /* start of newly sorted array part, end of both parts */
    548:   PetscInt       *ialloc;     /* Allocated arrays */
    549:   PetscScalar    *valloc=NULL;
    550:   PetscInt       *iswap;      /* auxiliary pointers for swapping */
    551:   PetscScalar    *vswap;
    552:   PetscInt       *ihlp1;      /* Pointers to new version of arrays, */
    553:   PetscScalar    *vhlp1=NULL;  /* (arrays under construction) */
    554:   PetscInt       *ihlp2;      /* Pointers to previous version of arrays, */
    555:   PetscScalar    *vhlp2=NULL;

    558:   PetscMalloc1(nnz,&ialloc);
    559:   ihlp1 = ialloc;
    560:   ihlp2 = icol;

    562:   if (val) {
    563:     PetscMalloc1(nnz,&valloc);
    564:     vhlp1 = valloc;
    565:     vhlp2 = val;
    566:   }

    569:   /* Sorted array chunks are first 1 long, and increase until they are the complete array */
    570:   for (istep=1; istep<nnz; istep*=2) {
    571:     /*
    572:       Combine sorted parts
    573:           istart:istart+istep-1 and istart+istep-1:istart+2*istep-1
    574:       of ihlp2 and vhlp2

    576:       into one sorted part
    577:           istart:istart+2*istep-1
    578:       of ihlp1 and vhlp1
    579:     */
    580:     for (istart=0; istart<nnz; istart+=2*istep) {
    581:       /* Set counters and bound array part endings */
    582:       i1=istart;        i1end = i1+istep;  if (i1end>nnz) i1end=nnz;
    583:       i2=istart+istep;  i2end = i2+istep;  if (i2end>nnz) i2end=nnz;

    585:       /* Merge the two array parts */
    586:       if (val) {
    587:         for (i=istart; i<i2end; i++) {
    588:           if (i1<i1end && i2<i2end && ihlp2[i1] < ihlp2[i2]) {
    589:             ihlp1[i] = ihlp2[i1];
    590:             vhlp1[i] = vhlp2[i1];
    591:             i1++;
    592:           } else if (i2<i2end) {
    593:             ihlp1[i] = ihlp2[i2];
    594:             vhlp1[i] = vhlp2[i2];
    595:             i2++;
    596:           } else {
    597:             ihlp1[i] = ihlp2[i1];
    598:             vhlp1[i] = vhlp2[i1];
    599:             i1++;
    600:           }
    601:         }
    602:       } else {
    603:         for (i=istart; i<i2end; i++) {
    604:           if (i1<i1end && i2<i2end && ihlp2[i1] < ihlp2[i2]) {
    605:             ihlp1[i] = ihlp2[i1];
    606:             i1++;
    607:           } else if (i2<i2end) {
    608:             ihlp1[i] = ihlp2[i2];
    609:             i2++;
    610:           } else {
    611:             ihlp1[i] = ihlp2[i1];
    612:             i1++;
    613:           }
    614:         }
    615:       }
    616:     }

    618:     /* Swap the two array sets */
    619:     iswap = ihlp2; ihlp2 = ihlp1; ihlp1 = iswap;
    620:     vswap = vhlp2; vhlp2 = vhlp1; vhlp1 = vswap;
    621:   }

    623:   /* Copy one more time in case the sorted arrays are the temporary ones */
    624:   if (ihlp2 != icol) {
    625:     for (i=0; i<nnz; i++) icol[i] = ihlp2[i];
    626:     if (val) {
    627:       for (i=0; i<nnz; i++) val[i] = vhlp2[i];
    628:     }
    629:   }

    631:   PetscFree(ialloc);
    632:   if (val) {PetscFree(valloc);}
    633:   return(0);
    634: }

    636: /*
    637:   spbas_apply_reordering_rows:
    638:     apply the given reordering to the rows:  matrix_A = matrix_A(perm,:);
    639: */
    640: PetscErrorCode spbas_apply_reordering_rows(spbas_matrix *matrix_A, const PetscInt *permutation)
    641: {
    642:   PetscInt       i,j,ip;
    643:   PetscInt       nrows=matrix_A->nrows;
    644:   PetscInt       * row_nnz;
    645:   PetscInt       **icols;
    646:   PetscBool      do_values = matrix_A->values ? PETSC_TRUE : PETSC_FALSE;
    647:   PetscScalar    **vals    = NULL;

    651:   if (matrix_A->col_idx_type != SPBAS_DIAGONAL_OFFSETS) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP_SYS,"must have diagonal offsets in pattern\n");

    653:   if (do_values) {
    654:     PetscMalloc1(nrows, &vals);
    655:   }
    656:   PetscMalloc1(nrows, &row_nnz);
    657:   PetscMalloc1(nrows, &icols);

    659:   for (i=0; i<nrows; i++) {
    660:     ip = permutation[i];
    661:     if (do_values) vals[i] = matrix_A->values[ip];
    662:     icols[i]   = matrix_A->icols[ip];
    663:     row_nnz[i] = matrix_A->row_nnz[ip];
    664:     for (j=0; j<row_nnz[i]; j++) icols[i][j] += ip-i;
    665:   }

    667:   if (do_values) { PetscFree(matrix_A->values);}
    668:   PetscFree(matrix_A->icols);
    669:   PetscFree(matrix_A->row_nnz);

    671:   if (do_values) matrix_A->values = vals;
    672:   matrix_A->icols   = icols;
    673:   matrix_A->row_nnz = row_nnz;
    674:   return(0);
    675: }

    678: /*
    679:   spbas_apply_reordering_cols:
    680:     apply the given reordering to the columns:  matrix_A(:,perm) = matrix_A;
    681: */
    682: PetscErrorCode spbas_apply_reordering_cols(spbas_matrix *matrix_A,const PetscInt *permutation)
    683: {
    684:   PetscInt       i,j;
    685:   PetscInt       nrows=matrix_A->nrows;
    686:   PetscInt       row_nnz;
    687:   PetscInt       *icols;
    688:   PetscBool      do_values = matrix_A->values ? PETSC_TRUE : PETSC_FALSE;
    689:   PetscScalar    *vals     = NULL;

    693:   if (matrix_A->col_idx_type != SPBAS_DIAGONAL_OFFSETS) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP_SYS, "must have diagonal offsets in pattern\n");

    695:   for (i=0; i<nrows; i++) {
    696:     icols   = matrix_A->icols[i];
    697:     row_nnz = matrix_A->row_nnz[i];
    698:     if (do_values) vals = matrix_A->values[i];

    700:     for (j=0; j<row_nnz; j++) {
    701:       icols[j] = permutation[i+icols[j]]-i;
    702:     }
    703:     spbas_mergesort(row_nnz, icols, vals);
    704:   }
    705:   return(0);
    706: }

    708: /*
    709:   spbas_apply_reordering:
    710:     apply the given reordering:  matrix_A(perm,perm) = matrix_A;
    711: */
    712: PetscErrorCode spbas_apply_reordering(spbas_matrix *matrix_A, const PetscInt *permutation, const PetscInt * inv_perm)
    713: {

    717:   spbas_apply_reordering_rows(matrix_A, inv_perm);
    718:   spbas_apply_reordering_cols(matrix_A, permutation);
    719:   return(0);
    720: }

    722: PetscErrorCode spbas_pattern_only(PetscInt nrows, PetscInt ncols, PetscInt *ai, PetscInt *aj, spbas_matrix * result)
    723: {
    724:   spbas_matrix   retval;
    725:   PetscInt       i, j, i0, r_nnz;

    729:   /* Copy input values */
    730:   retval.nrows = nrows;
    731:   retval.ncols = ncols;
    732:   retval.nnz   = ai[nrows];

    734:   retval.block_data   = PETSC_TRUE;
    735:   retval.col_idx_type = SPBAS_DIAGONAL_OFFSETS;

    737:   /* Allocate output matrix */
    738:   spbas_allocate_pattern(&retval, PETSC_FALSE);
    739:   for (i=0; i<nrows; i++) retval.row_nnz[i] = ai[i+1]-ai[i];
    740:   spbas_allocate_data(&retval);
    741:   /* Copy the structure */
    742:   for (i = 0; i<retval.nrows; i++)  {
    743:     i0    = ai[i];
    744:     r_nnz = ai[i+1]-i0;

    746:     for (j=0; j<r_nnz; j++) {
    747:       retval.icols[i][j] = aj[i0+j]-i;
    748:     }
    749:   }
    750:   *result = retval;
    751:   return(0);
    752: }

    755: /*
    756:    spbas_mark_row_power:
    757:       Mark the columns in row 'row' which are nonzero in
    758:           matrix^2log(marker).
    759: */
    760: PetscErrorCode spbas_mark_row_power(PetscInt *iwork,             /* marker-vector */
    761:                                     PetscInt row,                /* row for which the columns are marked */
    762:                                     spbas_matrix * in_matrix,    /* matrix for which the power is being  calculated */
    763:                                     PetscInt marker,             /* marker-value: 2^power */
    764:                                     PetscInt minmrk,             /* lower bound for marked points */
    765:                                     PetscInt maxmrk)             /* upper bound for marked points */
    766: {
    768:   PetscInt       i,j, nnz;

    771:   nnz = in_matrix->row_nnz[row];

    773:   /* For higher powers, call this function recursively */
    774:   if (marker>1) {
    775:     for (i=0; i<nnz; i++) {
    776:       j = row + in_matrix->icols[row][i];
    777:       if (minmrk<=j && j<maxmrk && iwork[j] < marker) {
    778:         spbas_mark_row_power(iwork, row + in_matrix->icols[row][i],in_matrix, marker/2,minmrk,maxmrk);
    779:         iwork[j] |= marker;
    780:       }
    781:     }
    782:   } else {
    783:     /*  Mark the columns reached */
    784:     for (i=0; i<nnz; i++)  {
    785:       j = row + in_matrix->icols[row][i];
    786:       if (minmrk<=j && j<maxmrk) iwork[j] |= 1;
    787:     }
    788:   }
    789:   return(0);
    790: }

    793: /*
    794:    spbas_power
    795:       Calculate sparseness patterns for incomplete Cholesky decompositions
    796:       of a given order: (almost) all nonzeros of the matrix^(order+1) which
    797:       are inside the band width are found and stored in the output sparseness
    798:       pattern.
    799: */
    800: PetscErrorCode spbas_power(spbas_matrix in_matrix,PetscInt power, spbas_matrix * result)
    801: {
    802:   spbas_matrix   retval;
    803:   PetscInt       nrows = in_matrix.nrows;
    804:   PetscInt       ncols = in_matrix.ncols;
    805:   PetscInt       i, j, kend;
    806:   PetscInt       nnz, inz;
    807:   PetscInt       *iwork;
    808:   PetscInt       marker;
    809:   PetscInt       maxmrk=0;

    813:   if (in_matrix.col_idx_type != SPBAS_DIAGONAL_OFFSETS) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP_SYS,"must have diagonal offsets in pattern\n");
    814:   if (ncols != nrows) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Dimension error\n");
    815:   if (in_matrix.values) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_ARG_INCOMP, "Input array must be sparseness pattern (no values)");
    816:   if (power<=0) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP_SYS, "Power must be 1 or up");

    818:   /* Copy input values*/
    819:   retval.nrows        = ncols;
    820:   retval.ncols        = nrows;
    821:   retval.nnz          = 0;
    822:   retval.col_idx_type = SPBAS_DIAGONAL_OFFSETS;
    823:   retval.block_data   = PETSC_FALSE;

    825:   /* Allocate sparseness pattern */
    826:    spbas_allocate_pattern(&retval, in_matrix.values ? PETSC_TRUE : PETSC_FALSE);

    828:   /* Allocate marker array: note sure the max needed so use the max of the two */
    829:   PetscCalloc1(PetscMax(ncols,nrows), &iwork);

    831:   /* Calculate marker values */
    832:   marker = 1; for (i=1; i<power; i++) marker*=2;

    834:   for (i=0; i<nrows; i++)  {
    835:     /* Calculate the pattern for each row */

    837:     nnz  = in_matrix.row_nnz[i];
    838:     kend = i+in_matrix.icols[i][nnz-1];
    839:     if (maxmrk<=kend) maxmrk=kend+1;
    840:     spbas_mark_row_power(iwork, i, &in_matrix, marker, i, maxmrk);

    842:     /* Count the columns*/
    843:     nnz = 0;
    844:     for (j=i; j<maxmrk; j++) nnz+= (iwork[j]!=0);

    846:     /* Allocate the column indices */
    847:     retval.row_nnz[i] = nnz;
    848:     PetscMalloc1(nnz,&retval.icols[i]);

    850:     /* Administrate the column indices */
    851:     inz = 0;
    852:     for (j=i; j<maxmrk; j++) {
    853:       if (iwork[j]) {
    854:         retval.icols[i][inz] = j-i;
    855:         inz++;
    856:         iwork[j] = 0;
    857:       }
    858:     }
    859:     retval.nnz += nnz;
    860:   };
    861:   PetscFree(iwork);
    862:   *result = retval;
    863:   return(0);
    864: }

    868: /*
    869:    spbas_keep_upper:
    870:       remove the lower part of the matrix: keep the upper part
    871: */
    872: PetscErrorCode spbas_keep_upper(spbas_matrix * inout_matrix)
    873: {
    874:   PetscInt i, j;
    875:   PetscInt jstart;

    878:   if (inout_matrix->block_data) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP_SYS, "Not yet for block data matrices\n");
    879:   for (i=0; i<inout_matrix->nrows; i++)  {
    880:     for (jstart=0; (jstart<inout_matrix->row_nnz[i]) && (inout_matrix->icols[i][jstart]<0); jstart++) {}
    881:     if (jstart>0) {
    882:       for (j=0; j<inout_matrix->row_nnz[i]-jstart; j++) {
    883:         inout_matrix->icols[i][j] = inout_matrix->icols[i][j+jstart];
    884:       }

    886:       if (inout_matrix->values) {
    887:         for (j=0; j<inout_matrix->row_nnz[i]-jstart; j++) {
    888:           inout_matrix->values[i][j] = inout_matrix->values[i][j+jstart];
    889:         }
    890:       }

    892:       inout_matrix->row_nnz[i] -= jstart;

    894:       inout_matrix->icols[i] = (PetscInt*) realloc((void*) inout_matrix->icols[i], inout_matrix->row_nnz[i]*sizeof(PetscInt));

    896:       if (inout_matrix->values) {
    897:         inout_matrix->values[i] = (PetscScalar*) realloc((void*) inout_matrix->values[i], inout_matrix->row_nnz[i]*sizeof(PetscScalar));
    898:       }
    899:       inout_matrix->nnz -= jstart;
    900:     }
    901:   }
    902:   return(0);
    903: }