Actual source code: spbas.c

petsc-3.5.2 2014-09-08
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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>
 11: - -pc_factor_drop_tolerance

 13:   Level: beginner

 15:    Contributed by: Bas van 't Hof

 17: .seealso: PCFactorSetMatSolverPackage(), MatSolverPackage, PCFactorSetLevels(), PCFactorSetDropTolerance()

 19: M*/

 21: /*
 22:   spbas_memory_requirement:
 23:     Calculate the number of bytes needed to store tha matrix
 24: */
 27: long int spbas_memory_requirement(spbas_matrix matrix)
 28: {
 29:   long int memreq = 6 * sizeof(PetscInt)  + /* nrows, ncols, nnz, n_alloc_icol, n_alloc_val, col_idx_type */
 30:                     sizeof(PetscBool)               + /* block_data */
 31:                     sizeof(PetscScalar**)           + /* values */
 32:                     sizeof(PetscScalar*)            + /* alloc_val */
 33:                     2 * sizeof(int**)               + /* icols, icols0 */
 34:                     2 * sizeof(PetscInt*)           + /* row_nnz, alloc_icol */
 35:                     matrix.nrows * sizeof(PetscInt) + /* row_nnz[*] */
 36:                     matrix.nrows * sizeof(PetscInt*); /* icols[*] */

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

 41:   /* icols[*][*] */
 42:   if (matrix.block_data) memreq += matrix.n_alloc_icol * sizeof(PetscInt);
 43:   else memreq += matrix.nnz * sizeof(PetscInt);

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

 54: /*
 55:   spbas_allocate_pattern:
 56:     allocate the pattern arrays row_nnz, icols and optionally values
 57: */
 60: PetscErrorCode spbas_allocate_pattern(spbas_matrix * result, PetscBool do_values)
 61: {
 63:   PetscInt       nrows        = result->nrows;
 64:   PetscInt       col_idx_type = result->col_idx_type;

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

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

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

 87: /*
 88: spbas_allocate_data:
 89:    in case of block_data:
 90:        Allocate the data arrays alloc_icol and optionally alloc_val,
 91:        set appropriate pointers from icols and values;
 92:    in case of !block_data:
 93:        Allocate the arrays icols[i] and optionally values[i]
 94: */
 97: PetscErrorCode spbas_allocate_data(spbas_matrix * result)
 98: {
 99:   PetscInt       i;
100:   PetscInt       nnz   = result->nnz;
101:   PetscInt       nrows = result->nrows;
102:   PetscInt       r_nnz;
104:   PetscBool      do_values  = (result->values != NULL) ? PETSC_TRUE : PETSC_FALSE;
105:   PetscBool      block_data = result->block_data;

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

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

114:     result->icols[0] = result->alloc_icol;
115:     for (i=1; i<nrows; i++)  {
116:       result->icols[i] = result->icols[i-1] + result->row_nnz[i-1];
117:     }

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

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

125:       result->values[0] = result->alloc_val;
126:       for (i=1; i<nrows; i++) {
127:         result->values[i] = result->values[i-1] + result->row_nnz[i-1];
128:       }
129:     }
130:   } else {
131:     for (i=0; i<nrows; i++)   {
132:       r_nnz = result->row_nnz[i];
133:       PetscMalloc1(r_nnz, &result->icols[i]);
134:     }
135:     if (do_values) {
136:       for (i=0; i<nrows; i++)  {
137:         r_nnz = result->row_nnz[i];
138:         PetscMalloc1(r_nnz, &result->values[i]);
139:       }
140:     }
141:   }
142:   return(0);
143: }

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

162:   if (nnz1<nnz2) return -1;
163:   if (nnz1>nnz2) return 1;

165:   if (col_idx_type == SPBAS_COLUMN_NUMBERS) {
166:     for (j=0; j<nnz1; j++) {
167:       if (icol1[j]< icol2[j]) return -1;
168:       if (icol1[j]> icol2[j]) return 1;
169:     }
170:   } else if (col_idx_type == SPBAS_DIAGONAL_OFFSETS) {
171:     for (j=0; j<nnz1; j++) {
172:       if (icol1[j]-i1< icol2[j]-i2) return -1;
173:       if (icol1[j]-i1> icol2[j]-i2) return 1;
174:     }
175:   } else if (col_idx_type == SPBAS_OFFSET_ARRAY) {
176:     for (j=1; j<nnz1; j++) {
177:       if (icol1[j]-icol1[0] < icol2[j]-icol2[0]) return -1;
178:       if (icol1[j]-icol1[0] > icol2[j]-icol2[0]) return 1;
179:     }
180:   }
181:   return 0;
182: }

184: /*
185:   spbas_mergesort_icols:
186:     return a sorting of the rows in which identical sparseness patterns are
187:     next to each other
188: */
191: PetscErrorCode spbas_mergesort_icols(PetscInt nrows, PetscInt * irow_in, PetscInt * icol_in,PetscInt col_idx_type, PetscInt *isort)
192: {
194:   PetscInt       istep;       /* Chunk-sizes of already sorted parts of arrays */
195:   PetscInt       i, i1, i2;   /* Loop counters for (partly) sorted arrays */
196:   PetscInt       istart, i1end, i2end; /* start of newly sorted array part, end of both  parts */
197:   PetscInt       *ialloc;     /* Allocated arrays */
198:   PetscInt       *iswap;      /* auxiliary pointers for swapping */
199:   PetscInt       *ihlp1;      /* Pointers to new version of arrays, */
200:   PetscInt       *ihlp2;      /* Pointers to previous version of arrays, */

203:   PetscMalloc1(nrows,&ialloc);

205:   ihlp1 = ialloc;
206:   ihlp2 = isort;

208:   /* Sorted array chunks are first 1 long, and increase until they are the complete array */
209:   for (istep=1; istep<nrows; istep*=2) {
210:     /*
211:       Combine sorted parts
212:           istart:istart+istep-1 and istart+istep-1:istart+2*istep-1
213:       of ihlp2 and vhlp2

215:       into one sorted part
216:           istart:istart+2*istep-1
217:       of ihlp1 and vhlp1
218:     */
219:     for (istart=0; istart<nrows; istart+=2*istep) {
220:       /* Set counters and bound array part endings */
221:       i1=istart;        i1end = i1+istep;  if (i1end>nrows) i1end=nrows;
222:       i2=istart+istep;  i2end = i2+istep;  if (i2end>nrows) i2end=nrows;

224:       /* Merge the two array parts */
225:       for (i=istart; i<i2end; i++)  {
226:         if (i1<i1end && i2<i2end && spbas_row_order_icol(ihlp2[i1], ihlp2[i2], irow_in, icol_in, col_idx_type) < 0) {
227:           ihlp1[i] = ihlp2[i1];
228:           i1++;
229:         } else if (i2<i2end) {
230:           ihlp1[i] = ihlp2[i2];
231:           i2++;
232:         } else {
233:           ihlp1[i] = ihlp2[i1];
234:           i1++;
235:         }
236:       }
237:     }

239:     /* Swap the two array sets */
240:     iswap = ihlp2; ihlp2 = ihlp1; ihlp1 = iswap;
241:   }

243:   /* Copy one more time in case the sorted arrays are the temporary ones */
244:   if (ihlp2 != isort) {
245:     for (i=0; i<nrows; i++) isort[i] = ihlp2[i];
246:   }
247:   PetscFree(ialloc);
248:   return(0);
249: }



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

277:   /* Allocate the structure of the new matrix */
278:   B->nrows        = nrows;
279:   B->ncols        = ncols;
280:   B->nnz          = nnz;
281:   B->col_idx_type = col_idx_type;
282:   B->block_data   = PETSC_TRUE;

284:   spbas_allocate_pattern(B, no_values);

286:   /* When using an offset array, set it */
287:   if (col_idx_type==SPBAS_OFFSET_ARRAY)  {
288:     for (i=0; i<nrows; i++) B->icol0[i] = icol_in[irow_in[i]];
289:   }

291:   /* Allocate the ordering for the rows */
292:   PetscMalloc1(nrows,&isort);
293:   PetscMalloc1(nrows,&ipoint);
294:   PetscMalloc1(nrows,&used);

296:   /*  Initialize the sorting */
297:   PetscMemzero((void*) used, nrows*sizeof(PetscBool));
298:   for (i = 0; i<nrows; i++)  {
299:     B->row_nnz[i] = irow_in[i+1]-irow_in[i];
300:     isort[i]      = i;
301:     ipoint[i]     = i;
302:   }

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

308:   /* Replace identical rows with the first one in the list */
309:   for (i=1; i<nrows; i++) {
310:     if (spbas_row_order_icol(isort[i-1], isort[i], irow_in, icol_in, col_idx_type) == 0) {
311:       ipoint[isort[i]] = ipoint[isort[i-1]];
312:     }
313:   }

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

318:   /* Calculate needed memory */
319:   B->n_alloc_icol = 0;
320:   for (i=0; i<nrows; i++)  {
321:     if (used[i]) B->n_alloc_icol += B->row_nnz[i];
322:   }
323:   PetscMalloc1(B->n_alloc_icol,&B->alloc_icol);

325:   /* Fill in the diagonal offsets for the rows which store their own data */
326:   ptr = 0;
327:   for (i=0; i<B->nrows; i++) {
328:     if (used[i]) {
329:       B->icols[i] = &B->alloc_icol[ptr];
330:       icols = &icol_in[irow_in[i]];
331:       row_nnz = B->row_nnz[i];
332:       if (col_idx_type == SPBAS_COLUMN_NUMBERS) {
333:         for (j=0; j<row_nnz; j++) {
334:           B->icols[i][j] = icols[j];
335:         }
336:       } else if (col_idx_type == SPBAS_DIAGONAL_OFFSETS) {
337:         for (j=0; j<row_nnz; j++) {
338:           B->icols[i][j] = icols[j]-i;
339:         }
340:       } else if (col_idx_type == SPBAS_OFFSET_ARRAY) {
341:         for (j=0; j<row_nnz; j++) {
342:           B->icols[i][j] = icols[j]-icols[0];
343:         }
344:       }
345:       ptr += B->row_nnz[i];
346:     }
347:   }

349:   /* Point to the right places for all data */
350:   for (i=0; i<nrows; i++) {
351:     B->icols[i] = B->icols[ipoint[i]];
352:   }
353:   PetscInfo(NULL,"Row patterns have been compressed\n");
354:   PetscInfo1(NULL,"         (%g nonzeros per row)\n", (double) ((PetscReal) nnz / (PetscReal) nrows));

356:   ierr=PetscFree(isort);
357:   ierr=PetscFree(used);
358:   ierr=PetscFree(ipoint);

360:   mem_compressed = spbas_memory_requirement(*B);
361:   *mem_reduction = 100.0 * (PetscReal)(mem_orig-mem_compressed)/ (PetscReal) mem_orig;
362:   return(0);
363: }

365: /*
366:    spbas_incomplete_cholesky
367:        Incomplete Cholesky decomposition
368: */
369: #include <../src/mat/impls/aij/seq/bas/spbas_cholesky.h>

371: /*
372:   spbas_delete : de-allocate the arrays owned by this matrix
373: */
376: PetscErrorCode spbas_delete(spbas_matrix matrix)
377: {
378:   PetscInt       i;

382:   if (matrix.block_data) {
383:     ierr=PetscFree(matrix.alloc_icol);
384:     if (matrix.values) {ierr=PetscFree(matrix.alloc_val);}
385:   } else {
386:     for (i=0; i<matrix.nrows; i++) { ierr=PetscFree(matrix.icols[i]);}
387:     PetscFree(matrix.icols);
388:     if (matrix.values) {
389:       for (i=0; i<matrix.nrows; i++) { ierr=PetscFree(matrix.values[i]);}
390:     }
391:   }

393:   ierr=PetscFree(matrix.row_nnz);
394:   ierr=PetscFree(matrix.icols);
395:   if (matrix.col_idx_type == SPBAS_OFFSET_ARRAY) {ierr=PetscFree(matrix.icol0);}
396:   ierr=PetscFree(matrix.values);
397:   return(0);
398: }

400: /*
401: spbas_matrix_to_crs:
402:    Convert an spbas_matrix to compessed row storage
403: */
406: PetscErrorCode spbas_matrix_to_crs(spbas_matrix matrix_A,MatScalar **val_out, PetscInt **irow_out, PetscInt **icol_out)
407: {
408:   PetscInt       nrows = matrix_A.nrows;
409:   PetscInt       nnz   = matrix_A.nnz;
410:   PetscInt       i,j,r_nnz,i0;
411:   PetscInt       *irow;
412:   PetscInt       *icol;
413:   PetscInt       *icol_A;
414:   MatScalar      *val;
415:   PetscScalar    *val_A;
416:   PetscInt       col_idx_type = matrix_A.col_idx_type;
417:   PetscBool      do_values    = matrix_A.values ? PETSC_TRUE : PETSC_FALSE;

421:   PetscMalloc(sizeof(PetscInt) * (nrows+1), &irow);
422:   PetscMalloc(sizeof(PetscInt) * nnz, &icol);
423:   *icol_out = icol;
424:   *irow_out = irow;
425:   if (do_values) {
426:     PetscMalloc(sizeof(MatScalar) * nnz, &val);
427:     *val_out = val; *icol_out = icol; *irow_out=irow;
428:   }

430:   irow[0]=0;
431:   for (i=0; i<nrows; i++) {
432:     r_nnz     = matrix_A.row_nnz[i];
433:     i0        = irow[i];
434:     irow[i+1] = i0 + r_nnz;
435:     icol_A    = matrix_A.icols[i];

437:     if (do_values) {
438:       val_A = matrix_A.values[i];
439:       for (j=0; j<r_nnz; j++) {
440:         icol[i0+j] = icol_A[j];
441:         val[i0+j]  = val_A[j];
442:       }
443:     } else {
444:       for (j=0; j<r_nnz; j++) icol[i0+j] = icol_A[j];
445:     }

447:     if (col_idx_type == SPBAS_DIAGONAL_OFFSETS) {
448:       for (j=0; j<r_nnz; j++) icol[i0+j] += i;
449:     } else if (col_idx_type == SPBAS_OFFSET_ARRAY) {
450:       i0 = matrix_A.icol0[i];
451:       for (j=0; j<r_nnz; j++) icol[i0+j] += i0;
452:     }
453:   }
454:   return(0);
455: }


458: /*
459:     spbas_transpose
460:        return the transpose of a matrix
461: */
464: PetscErrorCode spbas_transpose(spbas_matrix in_matrix, spbas_matrix * result)
465: {
466:   PetscInt       col_idx_type = in_matrix.col_idx_type;
467:   PetscInt       nnz          = in_matrix.nnz;
468:   PetscInt       ncols        = in_matrix.nrows;
469:   PetscInt       nrows        = in_matrix.ncols;
470:   PetscInt       i,j,k;
471:   PetscInt       r_nnz;
472:   PetscInt       *irow;
473:   PetscInt       icol0 = 0;
474:   PetscScalar    * val;

478:   /* Copy input values */
479:   result->nrows        = nrows;
480:   result->ncols        = ncols;
481:   result->nnz          = nnz;
482:   result->col_idx_type = SPBAS_COLUMN_NUMBERS;
483:   result->block_data   = PETSC_TRUE;

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

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

491:   for (i=0; i<ncols; i++) {
492:     r_nnz = in_matrix.row_nnz[i];
493:     irow  = in_matrix.icols[i];
494:     if (col_idx_type == SPBAS_COLUMN_NUMBERS)  {
495:       for (j=0; j<r_nnz; j++) result->row_nnz[irow[j]]++;
496:     } else if (col_idx_type == SPBAS_DIAGONAL_OFFSETS)  {
497:       for (j=0; j<r_nnz; j++) result->row_nnz[i+irow[j]]++;
498:     } else if (col_idx_type == SPBAS_OFFSET_ARRAY) {
499:       icol0=in_matrix.icol0[i];
500:       for (j=0; j<r_nnz; j++) result->row_nnz[icol0+irow[j]]++;
501:     }
502:   }

504:   /* Set the pointers to the data */
505:   spbas_allocate_data(result);

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

510:   /* Fill the data arrays */
511:   if (in_matrix.values) {
512:     for (i=0; i<ncols; i++) {
513:       r_nnz = in_matrix.row_nnz[i];
514:       irow  = in_matrix.icols[i];
515:       val   = in_matrix.values[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];
520:       for (j=0; j<r_nnz; j++)  {
521:         k = icol0 + irow[j];
522:         result->icols[k][result->row_nnz[k]]  = i;
523:         result->values[k][result->row_nnz[k]] = val[j];
524:         result->row_nnz[k]++;
525:       }
526:     }
527:   } else {
528:     for (i=0; i<ncols; i++) {
529:       r_nnz = in_matrix.row_nnz[i];
530:       irow  = in_matrix.icols[i];

532:       if      (col_idx_type == SPBAS_COLUMN_NUMBERS)   icol0=0;
533:       else if (col_idx_type == SPBAS_DIAGONAL_OFFSETS) icol0=i;
534:       else if (col_idx_type == SPBAS_OFFSET_ARRAY)     icol0=in_matrix.icol0[i];

536:       for (j=0; j<r_nnz; j++) {
537:         k = icol0 + irow[j];
538:         result->icols[k][result->row_nnz[k]] = i;
539:         result->row_nnz[k]++;
540:       }
541:     }
542:   }
543:   return(0);
544: }

546: /*
547:    spbas_mergesort

549:       mergesort for an array of intergers and an array of associated
550:       reals

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

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

557: */
560: PetscErrorCode spbas_mergesort(PetscInt nnz, PetscInt *icol, PetscScalar *val)
561: {
562:   PetscInt       istep;       /* Chunk-sizes of already sorted parts of arrays */
563:   PetscInt       i, i1, i2;   /* Loop counters for (partly) sorted arrays */
564:   PetscInt       istart, i1end, i2end; /* start of newly sorted array part, end of both parts */
565:   PetscInt       *ialloc;     /* Allocated arrays */
566:   PetscScalar    *valloc=NULL;
567:   PetscInt       *iswap;      /* auxiliary pointers for swapping */
568:   PetscScalar    *vswap;
569:   PetscInt       *ihlp1;      /* Pointers to new version of arrays, */
570:   PetscScalar    *vhlp1=NULL;  /* (arrays under construction) */
571:   PetscInt       *ihlp2;      /* Pointers to previous version of arrays, */
572:   PetscScalar    *vhlp2=NULL;

575:   PetscMalloc1(nnz,&ialloc);
576:   ihlp1 = ialloc;
577:   ihlp2 = icol;

579:   if (val) {
580:     PetscMalloc1(nnz,&valloc);
581:     vhlp1 = valloc;
582:     vhlp2 = val;
583:   }


586:   /* Sorted array chunks are first 1 long, and increase until they are the complete array */
587:   for (istep=1; istep<nnz; istep*=2) {
588:     /*
589:       Combine sorted parts
590:           istart:istart+istep-1 and istart+istep-1:istart+2*istep-1
591:       of ihlp2 and vhlp2

593:       into one sorted part
594:           istart:istart+2*istep-1
595:       of ihlp1 and vhlp1
596:     */
597:     for (istart=0; istart<nnz; istart+=2*istep) {
598:       /* Set counters and bound array part endings */
599:       i1=istart;        i1end = i1+istep;  if (i1end>nnz) i1end=nnz;
600:       i2=istart+istep;  i2end = i2+istep;  if (i2end>nnz) i2end=nnz;

602:       /* Merge the two array parts */
603:       if (val) {
604:         for (i=istart; i<i2end; i++) {
605:           if (i1<i1end && i2<i2end && ihlp2[i1] < ihlp2[i2]) {
606:             ihlp1[i] = ihlp2[i1];
607:             vhlp1[i] = vhlp2[i1];
608:             i1++;
609:           } else if (i2<i2end) {
610:             ihlp1[i] = ihlp2[i2];
611:             vhlp1[i] = vhlp2[i2];
612:             i2++;
613:           } else {
614:             ihlp1[i] = ihlp2[i1];
615:             vhlp1[i] = vhlp2[i1];
616:             i1++;
617:           }
618:         }
619:       } else {
620:         for (i=istart; i<i2end; i++) {
621:           if (i1<i1end && i2<i2end && ihlp2[i1] < ihlp2[i2]) {
622:             ihlp1[i] = ihlp2[i1];
623:             i1++;
624:           } else if (i2<i2end) {
625:             ihlp1[i] = ihlp2[i2];
626:             i2++;
627:           } else {
628:             ihlp1[i] = ihlp2[i1];
629:             i1++;
630:           }
631:         }
632:       }
633:     }

635:     /* Swap the two array sets */
636:     iswap = ihlp2; ihlp2 = ihlp1; ihlp1 = iswap;
637:     vswap = vhlp2; vhlp2 = vhlp1; vhlp1 = vswap;
638:   }

640:   /* Copy one more time in case the sorted arrays are the temporary ones */
641:   if (ihlp2 != icol) {
642:     for (i=0; i<nnz; i++) icol[i] = ihlp2[i];
643:     if (val) {
644:       for (i=0; i<nnz; i++) val[i] = vhlp2[i];
645:     }
646:   }

648:   PetscFree(ialloc);
649:   if (val) {PetscFree(valloc);}
650:   return(0);
651: }

653: /*
654:   spbas_apply_reordering_rows:
655:     apply the given reordering to the rows:  matrix_A = matrix_A(perm,:);
656: */
659: PetscErrorCode spbas_apply_reordering_rows(spbas_matrix *matrix_A, const PetscInt *permutation)
660: {
661:   PetscInt       i,j,ip;
662:   PetscInt       nrows=matrix_A->nrows;
663:   PetscInt       * row_nnz;
664:   PetscInt       **icols;
665:   PetscBool      do_values = matrix_A->values ? PETSC_TRUE : PETSC_FALSE;
666:   PetscScalar    **vals    = NULL;

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

672:   if (do_values) {
673:     PetscMalloc(sizeof(PetscScalar*)*nrows, &vals);
674:   }
675:   PetscMalloc(sizeof(PetscInt)*nrows, &row_nnz);
676:   PetscMalloc(sizeof(PetscInt*)*nrows, &icols);

678:   for (i=0; i<nrows; i++) {
679:     ip = permutation[i];
680:     if (do_values) vals[i] = matrix_A->values[ip];
681:     icols[i]   = matrix_A->icols[ip];
682:     row_nnz[i] = matrix_A->row_nnz[ip];
683:     for (j=0; j<row_nnz[i]; j++) icols[i][j] += ip-i;
684:   }

686:   if (do_values) { PetscFree(matrix_A->values);}
687:   PetscFree(matrix_A->icols);
688:   PetscFree(matrix_A->row_nnz);

690:   if (do_values) matrix_A->values = vals;
691:   matrix_A->icols   = icols;
692:   matrix_A->row_nnz = row_nnz;
693:   return(0);
694: }


697: /*
698:   spbas_apply_reordering_cols:
699:     apply the given reordering to the columns:  matrix_A(:,perm) = matrix_A;
700: */
703: PetscErrorCode spbas_apply_reordering_cols(spbas_matrix *matrix_A,const PetscInt *permutation)
704: {
705:   PetscInt       i,j;
706:   PetscInt       nrows=matrix_A->nrows;
707:   PetscInt       row_nnz;
708:   PetscInt       *icols;
709:   PetscBool      do_values = matrix_A->values ? PETSC_TRUE : PETSC_FALSE;
710:   PetscScalar    *vals     = NULL;

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

716:   for (i=0; i<nrows; i++) {
717:     icols   = matrix_A->icols[i];
718:     row_nnz = matrix_A->row_nnz[i];
719:     if (do_values) vals = matrix_A->values[i];

721:     for (j=0; j<row_nnz; j++) {
722:       icols[j] = permutation[i+icols[j]]-i;
723:     }
724:     spbas_mergesort(row_nnz, icols, vals);
725:   }
726:   return(0);
727: }

729: /*
730:   spbas_apply_reordering:
731:     apply the given reordering:  matrix_A(perm,perm) = matrix_A;
732: */
735: PetscErrorCode spbas_apply_reordering(spbas_matrix *matrix_A, const PetscInt *permutation, const PetscInt * inv_perm)
736: {

740:   spbas_apply_reordering_rows(matrix_A, inv_perm);
741:   spbas_apply_reordering_cols(matrix_A, permutation);
742:   return(0);
743: }

747: PetscErrorCode spbas_pattern_only(PetscInt nrows, PetscInt ncols, PetscInt *ai, PetscInt *aj, spbas_matrix * result)
748: {
749:   spbas_matrix   retval;
750:   PetscInt       i, j, i0, r_nnz;

754:   /* Copy input values */
755:   retval.nrows = nrows;
756:   retval.ncols = ncols;
757:   retval.nnz   = ai[nrows];

759:   retval.block_data   = PETSC_TRUE;
760:   retval.col_idx_type = SPBAS_DIAGONAL_OFFSETS;

762:   /* Allocate output matrix */
763:   spbas_allocate_pattern(&retval, PETSC_FALSE);
764:   for (i=0; i<nrows; i++) retval.row_nnz[i] = ai[i+1]-ai[i];
765:   spbas_allocate_data(&retval);
766:   /* Copy the structure */
767:   for (i = 0; i<retval.nrows; i++)  {
768:     i0    = ai[i];
769:     r_nnz = ai[i+1]-i0;

771:     for (j=0; j<r_nnz; j++) {
772:       retval.icols[i][j] = aj[i0+j]-i;
773:     }
774:   }
775:   *result = retval;
776:   return(0);
777: }


780: /*
781:    spbas_mark_row_power:
782:       Mark the columns in row 'row' which are nonzero in
783:           matrix^2log(marker).
784: */
787: PetscErrorCode spbas_mark_row_power(PetscInt *iwork,             /* marker-vector */
788:                                     PetscInt row,                /* row for which the columns are marked */
789:                                     spbas_matrix * in_matrix,    /* matrix for which the power is being  calculated */
790:                                     PetscInt marker,             /* marker-value: 2^power */
791:                                     PetscInt minmrk,             /* lower bound for marked points */
792:                                     PetscInt maxmrk)             /* upper bound for marked points */
793: {
795:   PetscInt       i,j, nnz;

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

800:   /* For higher powers, call this function recursively */
801:   if (marker>1) {
802:     for (i=0; i<nnz; i++) {
803:       j = row + in_matrix->icols[row][i];
804:       if (minmrk<=j && j<maxmrk && iwork[j] < marker) {
805:         spbas_mark_row_power(iwork, row + in_matrix->icols[row][i],in_matrix, marker/2,minmrk,maxmrk);
806:         iwork[j] |= marker;
807:       }
808:     }
809:   } else {
810:     /*  Mark the columns reached */
811:     for (i=0; i<nnz; i++)  {
812:       j = row + in_matrix->icols[row][i];
813:       if (minmrk<=j && j<maxmrk) iwork[j] |= 1;
814:     }
815:   }
816:   return(0);
817: }


820: /*
821:    spbas_power
822:       Calculate sparseness patterns for incomplete Cholesky decompositions
823:       of a given order: (almost) all nonzeros of the matrix^(order+1) which
824:       are inside the band width are found and stored in the output sparseness
825:       pattern.
826: */
829: PetscErrorCode spbas_power(spbas_matrix in_matrix,PetscInt power, spbas_matrix * result)
830: {
831:   spbas_matrix   retval;
832:   PetscInt       nrows = in_matrix.nrows;
833:   PetscInt       ncols = in_matrix.ncols;
834:   PetscInt       i, j, kend;
835:   PetscInt       nnz, inz;
836:   PetscInt       *iwork;
837:   PetscInt       marker;
838:   PetscInt       maxmrk=0;

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

847:   /* Copy input values*/
848:   retval.nrows        = ncols;
849:   retval.ncols        = nrows;
850:   retval.nnz          = 0;
851:   retval.col_idx_type = SPBAS_DIAGONAL_OFFSETS;
852:   retval.block_data   = PETSC_FALSE;

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

857:   /* Allocate marker array */
858:   PetscMalloc1(nrows, &iwork);

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

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

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

869:     nnz  = in_matrix.row_nnz[i];
870:     kend = i+in_matrix.icols[i][nnz-1];
871:     if (maxmrk<=kend) maxmrk=kend+1;
872:     spbas_mark_row_power(iwork, i, &in_matrix, marker, i, maxmrk);

874:     /* Count the columns*/
875:     nnz = 0;
876:     for (j=i; j<maxmrk; j++) nnz+= (iwork[j]!=0);

878:     /* Allocate the column indices */
879:     retval.row_nnz[i] = nnz;
880:     PetscMalloc1(nnz,&retval.icols[i]);

882:     /* Administrate the column indices */
883:     inz = 0;
884:     for (j=i; j<maxmrk; j++) {
885:       if (iwork[j]) {
886:         retval.icols[i][inz] = j-i;
887:         inz++;
888:         iwork[j]=0;
889:       }
890:     }
891:     retval.nnz += nnz;
892:   };
893:   PetscFree(iwork);
894:   *result = retval;
895:   return(0);
896: }



900: /*
901:    spbas_keep_upper:
902:       remove the lower part of the matrix: keep the upper part
903: */
906: PetscErrorCode spbas_keep_upper(spbas_matrix * inout_matrix)
907: {
908:   PetscInt i, j;
909:   PetscInt jstart;

912:   if (inout_matrix->block_data) SETERRQ(PETSC_COMM_SELF, PETSC_ERR_SUP_SYS, "Not yet for block data matrices\n");
913:   for (i=0; i<inout_matrix->nrows; i++)  {
914:     for (jstart=0; (jstart<inout_matrix->row_nnz[i]) && (inout_matrix->icols[i][jstart]<0); jstart++) {}
915:     if (jstart>0) {
916:       for (j=0; j<inout_matrix->row_nnz[i]-jstart; j++) {
917:         inout_matrix->icols[i][j] = inout_matrix->icols[i][j+jstart];
918:       }

920:       if (inout_matrix->values) {
921:         for (j=0; j<inout_matrix->row_nnz[i]-jstart; j++) {
922:           inout_matrix->values[i][j] = inout_matrix->values[i][j+jstart];
923:         }
924:       }

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

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

930:       if (inout_matrix->values) {
931:         inout_matrix->values[i] = (PetscScalar*) realloc((void*) inout_matrix->values[i], inout_matrix->row_nnz[i]*sizeof(PetscScalar));
932:       }
933:       inout_matrix->nnz -= jstart;
934:     }
935:   }
936:   return(0);
937: }