Actual source code: spbas.c

petsc-3.10.3 2018-12-18
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  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:   PetscMalloc1(nrows,&used);

289:   /*  Initialize the sorting */
290:   PetscMemzero((void*) used, nrows*sizeof(PetscBool));
291:   for (i = 0; i<nrows; i++)  {
292:     B->row_nnz[i] = irow_in[i+1]-irow_in[i];
293:     isort[i]      = i;
294:     ipoint[i]     = i;
295:   }

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

301:   /* Replace identical rows with the first one in the list */
302:   for (i=1; i<nrows; i++) {
303:     if (spbas_row_order_icol(isort[i-1], isort[i], irow_in, icol_in, col_idx_type) == 0) {
304:       ipoint[isort[i]] = ipoint[isort[i-1]];
305:     }
306:   }

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

311:   /* Calculate needed memory */
312:   B->n_alloc_icol = 0;
313:   for (i=0; i<nrows; i++)  {
314:     if (used[i]) B->n_alloc_icol += B->row_nnz[i];
315:   }
316:   PetscMalloc1(B->n_alloc_icol,&B->alloc_icol);

318:   /* Fill in the diagonal offsets for the rows which store their own data */
319:   ptr = 0;
320:   for (i=0; i<B->nrows; i++) {
321:     if (used[i]) {
322:       B->icols[i] = &B->alloc_icol[ptr];
323:       icols = &icol_in[irow_in[i]];
324:       row_nnz = B->row_nnz[i];
325:       if (col_idx_type == SPBAS_COLUMN_NUMBERS) {
326:         for (j=0; j<row_nnz; j++) {
327:           B->icols[i][j] = icols[j];
328:         }
329:       } else if (col_idx_type == SPBAS_DIAGONAL_OFFSETS) {
330:         for (j=0; j<row_nnz; j++) {
331:           B->icols[i][j] = icols[j]-i;
332:         }
333:       } else if (col_idx_type == SPBAS_OFFSET_ARRAY) {
334:         for (j=0; j<row_nnz; j++) {
335:           B->icols[i][j] = icols[j]-icols[0];
336:         }
337:       }
338:       ptr += B->row_nnz[i];
339:     }
340:   }

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

349:   ierr=PetscFree(isort);
350:   ierr=PetscFree(used);
351:   ierr=PetscFree(ipoint);

353:   mem_compressed = spbas_memory_requirement(*B);
354:   *mem_reduction = 100.0 * (PetscReal)(mem_orig-mem_compressed)/ (PetscReal) mem_orig;
355:   return(0);
356: }

358: /*
359:    spbas_incomplete_cholesky
360:        Incomplete Cholesky decomposition
361: */
362: #include <../src/mat/impls/aij/seq/bas/spbas_cholesky.h>

364: /*
365:   spbas_delete : de-allocate the arrays owned by this matrix
366: */
367: PetscErrorCode spbas_delete(spbas_matrix matrix)
368: {
369:   PetscInt       i;

373:   if (matrix.block_data) {
374:     ierr=PetscFree(matrix.alloc_icol);
375:     if (matrix.values) {ierr=PetscFree(matrix.alloc_val);}
376:   } else {
377:     for (i=0; i<matrix.nrows; i++) { ierr=PetscFree(matrix.icols[i]);}
378:     PetscFree(matrix.icols);
379:     if (matrix.values) {
380:       for (i=0; i<matrix.nrows; i++) { ierr=PetscFree(matrix.values[i]);}
381:     }
382:   }

384:   ierr=PetscFree(matrix.row_nnz);
385:   ierr=PetscFree(matrix.icols);
386:   if (matrix.col_idx_type == SPBAS_OFFSET_ARRAY) {ierr=PetscFree(matrix.icol0);}
387:   ierr=PetscFree(matrix.values);
388:   return(0);
389: }

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

410:   PetscMalloc1(nrows+1, &irow);
411:   PetscMalloc1(nnz, &icol);
412:   *icol_out = icol;
413:   *irow_out = irow;
414:   if (do_values) {
415:     PetscMalloc1(nnz, &val);
416:     *val_out = val; *icol_out = icol; *irow_out=irow;
417:   }

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

426:     if (do_values) {
427:       val_A = matrix_A.values[i];
428:       for (j=0; j<r_nnz; j++) {
429:         icol[i0+j] = icol_A[j];
430:         val[i0+j]  = val_A[j];
431:       }
432:     } else {
433:       for (j=0; j<r_nnz; j++) icol[i0+j] = icol_A[j];
434:     }

436:     if (col_idx_type == SPBAS_DIAGONAL_OFFSETS) {
437:       for (j=0; j<r_nnz; j++) icol[i0+j] += i;
438:     } else if (col_idx_type == SPBAS_OFFSET_ARRAY) {
439:       i0 = matrix_A.icol0[i];
440:       for (j=0; j<r_nnz; j++) icol[i0+j] += i0;
441:     }
442:   }
443:   return(0);
444: }


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

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

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

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

478:   for (i=0; i<ncols; i++) {
479:     r_nnz = in_matrix.row_nnz[i];
480:     irow  = in_matrix.icols[i];
481:     if (col_idx_type == SPBAS_COLUMN_NUMBERS)  {
482:       for (j=0; j<r_nnz; j++) result->row_nnz[irow[j]]++;
483:     } else if (col_idx_type == SPBAS_DIAGONAL_OFFSETS)  {
484:       for (j=0; j<r_nnz; j++) result->row_nnz[i+irow[j]]++;
485:     } else if (col_idx_type == SPBAS_OFFSET_ARRAY) {
486:       icol0=in_matrix.icol0[i];
487:       for (j=0; j<r_nnz; j++) result->row_nnz[icol0+irow[j]]++;
488:     }
489:   }

491:   /* Set the pointers to the data */
492:   spbas_allocate_data(result);

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

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

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

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

523:       for (j=0; j<r_nnz; j++) {
524:         k = icol0 + irow[j];
525:         result->icols[k][result->row_nnz[k]] = i;
526:         result->row_nnz[k]++;
527:       }
528:     }
529:   }
530:   return(0);
531: }

533: /*
534:    spbas_mergesort

536:       mergesort for an array of integers and an array of associated
537:       reals

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

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

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

560:   PetscMalloc1(nnz,&ialloc);
561:   ihlp1 = ialloc;
562:   ihlp2 = icol;

564:   if (val) {
565:     PetscMalloc1(nnz,&valloc);
566:     vhlp1 = valloc;
567:     vhlp2 = val;
568:   }


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

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

587:       /* Merge the two array parts */
588:       if (val) {
589:         for (i=istart; i<i2end; i++) {
590:           if (i1<i1end && i2<i2end && ihlp2[i1] < ihlp2[i2]) {
591:             ihlp1[i] = ihlp2[i1];
592:             vhlp1[i] = vhlp2[i1];
593:             i1++;
594:           } else if (i2<i2end) {
595:             ihlp1[i] = ihlp2[i2];
596:             vhlp1[i] = vhlp2[i2];
597:             i2++;
598:           } else {
599:             ihlp1[i] = ihlp2[i1];
600:             vhlp1[i] = vhlp2[i1];
601:             i1++;
602:           }
603:         }
604:       } else {
605:         for (i=istart; i<i2end; i++) {
606:           if (i1<i1end && i2<i2end && ihlp2[i1] < ihlp2[i2]) {
607:             ihlp1[i] = ihlp2[i1];
608:             i1++;
609:           } else if (i2<i2end) {
610:             ihlp1[i] = ihlp2[i2];
611:             i2++;
612:           } else {
613:             ihlp1[i] = ihlp2[i1];
614:             i1++;
615:           }
616:         }
617:       }
618:     }

620:     /* Swap the two array sets */
621:     iswap = ihlp2; ihlp2 = ihlp1; ihlp1 = iswap;
622:     vswap = vhlp2; vhlp2 = vhlp1; vhlp1 = vswap;
623:   }

625:   /* Copy one more time in case the sorted arrays are the temporary ones */
626:   if (ihlp2 != icol) {
627:     for (i=0; i<nnz; i++) icol[i] = ihlp2[i];
628:     if (val) {
629:       for (i=0; i<nnz; i++) val[i] = vhlp2[i];
630:     }
631:   }

633:   PetscFree(ialloc);
634:   if (val) {PetscFree(valloc);}
635:   return(0);
636: }

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

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

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

661:   for (i=0; i<nrows; i++) {
662:     ip = permutation[i];
663:     if (do_values) vals[i] = matrix_A->values[ip];
664:     icols[i]   = matrix_A->icols[ip];
665:     row_nnz[i] = matrix_A->row_nnz[ip];
666:     for (j=0; j<row_nnz[i]; j++) icols[i][j] += ip-i;
667:   }

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

673:   if (do_values) matrix_A->values = vals;
674:   matrix_A->icols   = icols;
675:   matrix_A->row_nnz = row_nnz;
676:   return(0);
677: }


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

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

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

702:     for (j=0; j<row_nnz; j++) {
703:       icols[j] = permutation[i+icols[j]]-i;
704:     }
705:     spbas_mergesort(row_nnz, icols, vals);
706:   }
707:   return(0);
708: }

710: /*
711:   spbas_apply_reordering:
712:     apply the given reordering:  matrix_A(perm,perm) = matrix_A;
713: */
714: PetscErrorCode spbas_apply_reordering(spbas_matrix *matrix_A, const PetscInt *permutation, const PetscInt * inv_perm)
715: {

719:   spbas_apply_reordering_rows(matrix_A, inv_perm);
720:   spbas_apply_reordering_cols(matrix_A, permutation);
721:   return(0);
722: }

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

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

736:   retval.block_data   = PETSC_TRUE;
737:   retval.col_idx_type = SPBAS_DIAGONAL_OFFSETS;

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

748:     for (j=0; j<r_nnz; j++) {
749:       retval.icols[i][j] = aj[i0+j]-i;
750:     }
751:   }
752:   *result = retval;
753:   return(0);
754: }


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

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

775:   /* For higher powers, call this function recursively */
776:   if (marker>1) {
777:     for (i=0; i<nnz; i++) {
778:       j = row + in_matrix->icols[row][i];
779:       if (minmrk<=j && j<maxmrk && iwork[j] < marker) {
780:         spbas_mark_row_power(iwork, row + in_matrix->icols[row][i],in_matrix, marker/2,minmrk,maxmrk);
781:         iwork[j] |= marker;
782:       }
783:     }
784:   } else {
785:     /*  Mark the columns reached */
786:     for (i=0; i<nnz; i++)  {
787:       j = row + in_matrix->icols[row][i];
788:       if (minmrk<=j && j<maxmrk) iwork[j] |= 1;
789:     }
790:   }
791:   return(0);
792: }


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

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

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

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

830:   /* Allocate marker array */
831:   PetscMalloc1(nrows, &iwork);

833:   /* Erase the pattern for this row */
834:   PetscMemzero((void*) iwork, retval.nrows*sizeof(PetscInt));

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

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

842:     nnz  = in_matrix.row_nnz[i];
843:     kend = i+in_matrix.icols[i][nnz-1];
844:     if (maxmrk<=kend) maxmrk=kend+1;
845:     spbas_mark_row_power(iwork, i, &in_matrix, marker, i, maxmrk);

847:     /* Count the columns*/
848:     nnz = 0;
849:     for (j=i; j<maxmrk; j++) nnz+= (iwork[j]!=0);

851:     /* Allocate the column indices */
852:     retval.row_nnz[i] = nnz;
853:     PetscMalloc1(nnz,&retval.icols[i]);

855:     /* Administrate the column indices */
856:     inz = 0;
857:     for (j=i; j<maxmrk; j++) {
858:       if (iwork[j]) {
859:         retval.icols[i][inz] = j-i;
860:         inz++;
861:         iwork[j]=0;
862:       }
863:     }
864:     retval.nnz += nnz;
865:   };
866:   PetscFree(iwork);
867:   *result = retval;
868:   return(0);
869: }



873: /*
874:    spbas_keep_upper:
875:       remove the lower part of the matrix: keep the upper part
876: */
877: PetscErrorCode spbas_keep_upper(spbas_matrix * inout_matrix)
878: {
879:   PetscInt i, j;
880:   PetscInt jstart;

883:   if (inout_matrix->block_data) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP_SYS, "Not yet for block data matrices\n");
884:   for (i=0; i<inout_matrix->nrows; i++)  {
885:     for (jstart=0; (jstart<inout_matrix->row_nnz[i]) && (inout_matrix->icols[i][jstart]<0); jstart++) {}
886:     if (jstart>0) {
887:       for (j=0; j<inout_matrix->row_nnz[i]-jstart; j++) {
888:         inout_matrix->icols[i][j] = inout_matrix->icols[i][j+jstart];
889:       }

891:       if (inout_matrix->values) {
892:         for (j=0; j<inout_matrix->row_nnz[i]-jstart; j++) {
893:           inout_matrix->values[i][j] = inout_matrix->values[i][j+jstart];
894:         }
895:       }

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

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

901:       if (inout_matrix->values) {
902:         inout_matrix->values[i] = (PetscScalar*) realloc((void*) inout_matrix->values[i], inout_matrix->row_nnz[i]*sizeof(PetscScalar));
903:       }
904:       inout_matrix->nnz -= jstart;
905:     }
906:   }
907:   return(0);
908: }