Actual source code: spbas.c

petsc-master 2019-09-16
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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:   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: }