Actual source code: aijfact.c
petsc-3.11.4 2019-09-28
2: #include <../src/mat/impls/aij/seq/aij.h>
3: #include <../src/mat/impls/sbaij/seq/sbaij.h>
4: #include <petscbt.h>
5: #include <../src/mat/utils/freespace.h>
7: /*
8: Computes an ordering to get most of the large numerical values in the lower triangular part of the matrix
10: This code does not work and is not called anywhere. It would be registered with MatOrderingRegisterAll()
11: */
12: PetscErrorCode MatGetOrdering_Flow_SeqAIJ(Mat mat,MatOrderingType type,IS *irow,IS *icol)
13: {
14: Mat_SeqAIJ *a = (Mat_SeqAIJ*)mat->data;
15: PetscErrorCode ierr;
16: PetscInt i,j,jj,k, kk,n = mat->rmap->n, current = 0, newcurrent = 0,*order;
17: const PetscInt *ai = a->i, *aj = a->j;
18: const PetscScalar *aa = a->a;
19: PetscBool *done;
20: PetscReal best,past = 0,future;
23: /* pick initial row */
24: best = -1;
25: for (i=0; i<n; i++) {
26: future = 0.0;
27: for (j=ai[i]; j<ai[i+1]; j++) {
28: if (aj[j] != i) future += PetscAbsScalar(aa[j]);
29: else past = PetscAbsScalar(aa[j]);
30: }
31: if (!future) future = 1.e-10; /* if there is zero in the upper diagonal part want to rank this row high */
32: if (past/future > best) {
33: best = past/future;
34: current = i;
35: }
36: }
38: PetscMalloc1(n,&done);
39: PetscMemzero(done,n*sizeof(PetscBool));
40: PetscMalloc1(n,&order);
41: order[0] = current;
42: for (i=0; i<n-1; i++) {
43: done[current] = PETSC_TRUE;
44: best = -1;
45: /* loop over all neighbors of current pivot */
46: for (j=ai[current]; j<ai[current+1]; j++) {
47: jj = aj[j];
48: if (done[jj]) continue;
49: /* loop over columns of potential next row computing weights for below and above diagonal */
50: past = future = 0.0;
51: for (k=ai[jj]; k<ai[jj+1]; k++) {
52: kk = aj[k];
53: if (done[kk]) past += PetscAbsScalar(aa[k]);
54: else if (kk != jj) future += PetscAbsScalar(aa[k]);
55: }
56: if (!future) future = 1.e-10; /* if there is zero in the upper diagonal part want to rank this row high */
57: if (past/future > best) {
58: best = past/future;
59: newcurrent = jj;
60: }
61: }
62: if (best == -1) { /* no neighbors to select from so select best of all that remain */
63: best = -1;
64: for (k=0; k<n; k++) {
65: if (done[k]) continue;
66: future = 0.0;
67: past = 0.0;
68: for (j=ai[k]; j<ai[k+1]; j++) {
69: kk = aj[j];
70: if (done[kk]) past += PetscAbsScalar(aa[j]);
71: else if (kk != k) future += PetscAbsScalar(aa[j]);
72: }
73: if (!future) future = 1.e-10; /* if there is zero in the upper diagonal part want to rank this row high */
74: if (past/future > best) {
75: best = past/future;
76: newcurrent = k;
77: }
78: }
79: }
80: if (current == newcurrent) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"newcurrent cannot be current");
81: current = newcurrent;
82: order[i+1] = current;
83: }
84: ISCreateGeneral(PETSC_COMM_SELF,n,order,PETSC_COPY_VALUES,irow);
85: *icol = *irow;
86: PetscObjectReference((PetscObject)*irow);
87: PetscFree(done);
88: PetscFree(order);
89: return(0);
90: }
92: PETSC_INTERN PetscErrorCode MatGetFactor_seqaij_petsc(Mat A,MatFactorType ftype,Mat *B)
93: {
94: PetscInt n = A->rmap->n;
98: #if defined(PETSC_USE_COMPLEX)
99: if (A->hermitian && (ftype == MAT_FACTOR_CHOLESKY || ftype == MAT_FACTOR_ICC)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Hermitian Factor is not supported");
100: #endif
101: MatCreate(PetscObjectComm((PetscObject)A),B);
102: MatSetSizes(*B,n,n,n,n);
103: if (ftype == MAT_FACTOR_LU || ftype == MAT_FACTOR_ILU || ftype == MAT_FACTOR_ILUDT) {
104: MatSetType(*B,MATSEQAIJ);
106: (*B)->ops->ilufactorsymbolic = MatILUFactorSymbolic_SeqAIJ;
107: (*B)->ops->lufactorsymbolic = MatLUFactorSymbolic_SeqAIJ;
109: MatSetBlockSizesFromMats(*B,A,A);
110: } else if (ftype == MAT_FACTOR_CHOLESKY || ftype == MAT_FACTOR_ICC) {
111: MatSetType(*B,MATSEQSBAIJ);
112: MatSeqSBAIJSetPreallocation(*B,1,MAT_SKIP_ALLOCATION,NULL);
114: (*B)->ops->iccfactorsymbolic = MatICCFactorSymbolic_SeqAIJ;
115: (*B)->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_SeqAIJ;
116: } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Factor type not supported");
117: (*B)->factortype = ftype;
119: PetscFree((*B)->solvertype);
120: PetscStrallocpy(MATSOLVERPETSC,&(*B)->solvertype);
121: return(0);
122: }
124: PetscErrorCode MatLUFactorSymbolic_SeqAIJ_inplace(Mat B,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
125: {
126: Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b;
127: IS isicol;
128: PetscErrorCode ierr;
129: const PetscInt *r,*ic;
130: PetscInt i,n=A->rmap->n,*ai=a->i,*aj=a->j;
131: PetscInt *bi,*bj,*ajtmp;
132: PetscInt *bdiag,row,nnz,nzi,reallocs=0,nzbd,*im;
133: PetscReal f;
134: PetscInt nlnk,*lnk,k,**bi_ptr;
135: PetscFreeSpaceList free_space=NULL,current_space=NULL;
136: PetscBT lnkbt;
137: PetscBool missing;
140: if (A->rmap->N != A->cmap->N) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"matrix must be square");
141: MatMissingDiagonal(A,&missing,&i);
142: if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i);
144: ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);
145: ISGetIndices(isrow,&r);
146: ISGetIndices(isicol,&ic);
148: /* get new row pointers */
149: PetscMalloc1(n+1,&bi);
150: bi[0] = 0;
152: /* bdiag is location of diagonal in factor */
153: PetscMalloc1(n+1,&bdiag);
154: bdiag[0] = 0;
156: /* linked list for storing column indices of the active row */
157: nlnk = n + 1;
158: PetscLLCreate(n,n,nlnk,lnk,lnkbt);
160: PetscMalloc2(n+1,&bi_ptr,n+1,&im);
162: /* initial FreeSpace size is f*(ai[n]+1) */
163: f = info->fill;
164: PetscFreeSpaceGet(PetscRealIntMultTruncate(f,ai[n]+1),&free_space);
165: current_space = free_space;
167: for (i=0; i<n; i++) {
168: /* copy previous fill into linked list */
169: nzi = 0;
170: nnz = ai[r[i]+1] - ai[r[i]];
171: ajtmp = aj + ai[r[i]];
172: PetscLLAddPerm(nnz,ajtmp,ic,n,nlnk,lnk,lnkbt);
173: nzi += nlnk;
175: /* add pivot rows into linked list */
176: row = lnk[n];
177: while (row < i) {
178: nzbd = bdiag[row] - bi[row] + 1; /* num of entries in the row with column index <= row */
179: ajtmp = bi_ptr[row] + nzbd; /* points to the entry next to the diagonal */
180: PetscLLAddSortedLU(ajtmp,row,nlnk,lnk,lnkbt,i,nzbd,im);
181: nzi += nlnk;
182: row = lnk[row];
183: }
184: bi[i+1] = bi[i] + nzi;
185: im[i] = nzi;
187: /* mark bdiag */
188: nzbd = 0;
189: nnz = nzi;
190: k = lnk[n];
191: while (nnz-- && k < i) {
192: nzbd++;
193: k = lnk[k];
194: }
195: bdiag[i] = bi[i] + nzbd;
197: /* if free space is not available, make more free space */
198: if (current_space->local_remaining<nzi) {
199: nnz = PetscIntMultTruncate(n - i,nzi); /* estimated and max additional space needed */
200: PetscFreeSpaceGet(nnz,¤t_space);
201: reallocs++;
202: }
204: /* copy data into free space, then initialize lnk */
205: PetscLLClean(n,n,nzi,lnk,current_space->array,lnkbt);
207: bi_ptr[i] = current_space->array;
208: current_space->array += nzi;
209: current_space->local_used += nzi;
210: current_space->local_remaining -= nzi;
211: }
212: #if defined(PETSC_USE_INFO)
213: if (ai[n] != 0) {
214: PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]);
215: PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)f,(double)af);
216: PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);
217: PetscInfo1(A,"PCFactorSetFill(pc,%g);\n",(double)af);
218: PetscInfo(A,"for best performance.\n");
219: } else {
220: PetscInfo(A,"Empty matrix\n");
221: }
222: #endif
224: ISRestoreIndices(isrow,&r);
225: ISRestoreIndices(isicol,&ic);
227: /* destroy list of free space and other temporary array(s) */
228: PetscMalloc1(bi[n]+1,&bj);
229: PetscFreeSpaceContiguous(&free_space,bj);
230: PetscLLDestroy(lnk,lnkbt);
231: PetscFree2(bi_ptr,im);
233: /* put together the new matrix */
234: MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,NULL);
235: PetscLogObjectParent((PetscObject)B,(PetscObject)isicol);
236: b = (Mat_SeqAIJ*)(B)->data;
238: b->free_a = PETSC_TRUE;
239: b->free_ij = PETSC_TRUE;
240: b->singlemalloc = PETSC_FALSE;
242: PetscMalloc1(bi[n]+1,&b->a);
243: b->j = bj;
244: b->i = bi;
245: b->diag = bdiag;
246: b->ilen = 0;
247: b->imax = 0;
248: b->row = isrow;
249: b->col = iscol;
250: PetscObjectReference((PetscObject)isrow);
251: PetscObjectReference((PetscObject)iscol);
252: b->icol = isicol;
253: PetscMalloc1(n+1,&b->solve_work);
255: /* In b structure: Free imax, ilen, old a, old j. Allocate solve_work, new a, new j */
256: PetscLogObjectMemory((PetscObject)B,(bi[n]-n)*(sizeof(PetscInt)+sizeof(PetscScalar)));
257: b->maxnz = b->nz = bi[n];
259: (B)->factortype = MAT_FACTOR_LU;
260: (B)->info.factor_mallocs = reallocs;
261: (B)->info.fill_ratio_given = f;
263: if (ai[n]) {
264: (B)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]);
265: } else {
266: (B)->info.fill_ratio_needed = 0.0;
267: }
268: (B)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_inplace;
269: if (a->inode.size) {
270: (B)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode_inplace;
271: }
272: return(0);
273: }
275: PetscErrorCode MatLUFactorSymbolic_SeqAIJ(Mat B,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
276: {
277: Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b;
278: IS isicol;
279: PetscErrorCode ierr;
280: const PetscInt *r,*ic,*ai=a->i,*aj=a->j,*ajtmp;
281: PetscInt i,n=A->rmap->n;
282: PetscInt *bi,*bj;
283: PetscInt *bdiag,row,nnz,nzi,reallocs=0,nzbd,*im;
284: PetscReal f;
285: PetscInt nlnk,*lnk,k,**bi_ptr;
286: PetscFreeSpaceList free_space=NULL,current_space=NULL;
287: PetscBT lnkbt;
288: PetscBool missing;
291: if (A->rmap->N != A->cmap->N) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"matrix must be square");
292: MatMissingDiagonal(A,&missing,&i);
293: if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i);
294:
295: ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);
296: ISGetIndices(isrow,&r);
297: ISGetIndices(isicol,&ic);
299: /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */
300: PetscMalloc1(n+1,&bi);
301: PetscMalloc1(n+1,&bdiag);
302: bi[0] = bdiag[0] = 0;
304: /* linked list for storing column indices of the active row */
305: nlnk = n + 1;
306: PetscLLCreate(n,n,nlnk,lnk,lnkbt);
308: PetscMalloc2(n+1,&bi_ptr,n+1,&im);
310: /* initial FreeSpace size is f*(ai[n]+1) */
311: f = info->fill;
312: PetscFreeSpaceGet(PetscRealIntMultTruncate(f,ai[n]+1),&free_space);
313: current_space = free_space;
315: for (i=0; i<n; i++) {
316: /* copy previous fill into linked list */
317: nzi = 0;
318: nnz = ai[r[i]+1] - ai[r[i]];
319: ajtmp = aj + ai[r[i]];
320: PetscLLAddPerm(nnz,ajtmp,ic,n,nlnk,lnk,lnkbt);
321: nzi += nlnk;
323: /* add pivot rows into linked list */
324: row = lnk[n];
325: while (row < i) {
326: nzbd = bdiag[row] + 1; /* num of entries in the row with column index <= row */
327: ajtmp = bi_ptr[row] + nzbd; /* points to the entry next to the diagonal */
328: PetscLLAddSortedLU(ajtmp,row,nlnk,lnk,lnkbt,i,nzbd,im);
329: nzi += nlnk;
330: row = lnk[row];
331: }
332: bi[i+1] = bi[i] + nzi;
333: im[i] = nzi;
335: /* mark bdiag */
336: nzbd = 0;
337: nnz = nzi;
338: k = lnk[n];
339: while (nnz-- && k < i) {
340: nzbd++;
341: k = lnk[k];
342: }
343: bdiag[i] = nzbd; /* note: bdiag[i] = nnzL as input for PetscFreeSpaceContiguous_LU() */
345: /* if free space is not available, make more free space */
346: if (current_space->local_remaining<nzi) {
347: /* estimated additional space needed */
348: nnz = PetscIntMultTruncate(2,PetscIntMultTruncate(n-1,nzi));
349: PetscFreeSpaceGet(nnz,¤t_space);
350: reallocs++;
351: }
353: /* copy data into free space, then initialize lnk */
354: PetscLLClean(n,n,nzi,lnk,current_space->array,lnkbt);
356: bi_ptr[i] = current_space->array;
357: current_space->array += nzi;
358: current_space->local_used += nzi;
359: current_space->local_remaining -= nzi;
360: }
362: ISRestoreIndices(isrow,&r);
363: ISRestoreIndices(isicol,&ic);
365: /* copy free_space into bj and free free_space; set bi, bj, bdiag in new datastructure; */
366: PetscMalloc1(bi[n]+1,&bj);
367: PetscFreeSpaceContiguous_LU(&free_space,bj,n,bi,bdiag);
368: PetscLLDestroy(lnk,lnkbt);
369: PetscFree2(bi_ptr,im);
371: /* put together the new matrix */
372: MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,NULL);
373: PetscLogObjectParent((PetscObject)B,(PetscObject)isicol);
374: b = (Mat_SeqAIJ*)(B)->data;
376: b->free_a = PETSC_TRUE;
377: b->free_ij = PETSC_TRUE;
378: b->singlemalloc = PETSC_FALSE;
380: PetscMalloc1(bdiag[0]+1,&b->a);
382: b->j = bj;
383: b->i = bi;
384: b->diag = bdiag;
385: b->ilen = 0;
386: b->imax = 0;
387: b->row = isrow;
388: b->col = iscol;
389: PetscObjectReference((PetscObject)isrow);
390: PetscObjectReference((PetscObject)iscol);
391: b->icol = isicol;
392: PetscMalloc1(n+1,&b->solve_work);
394: /* In b structure: Free imax, ilen, old a, old j. Allocate solve_work, new a, new j */
395: PetscLogObjectMemory((PetscObject)B,(bdiag[0]+1)*(sizeof(PetscInt)+sizeof(PetscScalar)));
396: b->maxnz = b->nz = bdiag[0]+1;
398: B->factortype = MAT_FACTOR_LU;
399: B->info.factor_mallocs = reallocs;
400: B->info.fill_ratio_given = f;
402: if (ai[n]) {
403: B->info.fill_ratio_needed = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]);
404: } else {
405: B->info.fill_ratio_needed = 0.0;
406: }
407: #if defined(PETSC_USE_INFO)
408: if (ai[n] != 0) {
409: PetscReal af = B->info.fill_ratio_needed;
410: PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)f,(double)af);
411: PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);
412: PetscInfo1(A,"PCFactorSetFill(pc,%g);\n",(double)af);
413: PetscInfo(A,"for best performance.\n");
414: } else {
415: PetscInfo(A,"Empty matrix\n");
416: }
417: #endif
418: B->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ;
419: if (a->inode.size) {
420: B->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode;
421: }
422: MatSeqAIJCheckInode_FactorLU(B);
423: return(0);
424: }
426: /*
427: Trouble in factorization, should we dump the original matrix?
428: */
429: PetscErrorCode MatFactorDumpMatrix(Mat A)
430: {
432: PetscBool flg = PETSC_FALSE;
435: PetscOptionsGetBool(((PetscObject)A)->options,NULL,"-mat_factor_dump_on_error",&flg,NULL);
436: if (flg) {
437: PetscViewer viewer;
438: char filename[PETSC_MAX_PATH_LEN];
440: PetscSNPrintf(filename,PETSC_MAX_PATH_LEN,"matrix_factor_error.%d",PetscGlobalRank);
441: PetscViewerBinaryOpen(PetscObjectComm((PetscObject)A),filename,FILE_MODE_WRITE,&viewer);
442: MatView(A,viewer);
443: PetscViewerDestroy(&viewer);
444: }
445: return(0);
446: }
448: PetscErrorCode MatLUFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info)
449: {
450: Mat C =B;
451: Mat_SeqAIJ *a =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)C->data;
452: IS isrow = b->row,isicol = b->icol;
453: PetscErrorCode ierr;
454: const PetscInt *r,*ic,*ics;
455: const PetscInt n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bdiag=b->diag;
456: PetscInt i,j,k,nz,nzL,row,*pj;
457: const PetscInt *ajtmp,*bjtmp;
458: MatScalar *rtmp,*pc,multiplier,*pv;
459: const MatScalar *aa=a->a,*v;
460: PetscBool row_identity,col_identity;
461: FactorShiftCtx sctx;
462: const PetscInt *ddiag;
463: PetscReal rs;
464: MatScalar d;
467: /* MatPivotSetUp(): initialize shift context sctx */
468: PetscMemzero(&sctx,sizeof(FactorShiftCtx));
470: if (info->shifttype == (PetscReal) MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */
471: ddiag = a->diag;
472: sctx.shift_top = info->zeropivot;
473: for (i=0; i<n; i++) {
474: /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
475: d = (aa)[ddiag[i]];
476: rs = -PetscAbsScalar(d) - PetscRealPart(d);
477: v = aa+ai[i];
478: nz = ai[i+1] - ai[i];
479: for (j=0; j<nz; j++) rs += PetscAbsScalar(v[j]);
480: if (rs>sctx.shift_top) sctx.shift_top = rs;
481: }
482: sctx.shift_top *= 1.1;
483: sctx.nshift_max = 5;
484: sctx.shift_lo = 0.;
485: sctx.shift_hi = 1.;
486: }
488: ISGetIndices(isrow,&r);
489: ISGetIndices(isicol,&ic);
490: PetscMalloc1(n+1,&rtmp);
491: ics = ic;
493: do {
494: sctx.newshift = PETSC_FALSE;
495: for (i=0; i<n; i++) {
496: /* zero rtmp */
497: /* L part */
498: nz = bi[i+1] - bi[i];
499: bjtmp = bj + bi[i];
500: for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
502: /* U part */
503: nz = bdiag[i]-bdiag[i+1];
504: bjtmp = bj + bdiag[i+1]+1;
505: for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
507: /* load in initial (unfactored row) */
508: nz = ai[r[i]+1] - ai[r[i]];
509: ajtmp = aj + ai[r[i]];
510: v = aa + ai[r[i]];
511: for (j=0; j<nz; j++) {
512: rtmp[ics[ajtmp[j]]] = v[j];
513: }
514: /* ZeropivotApply() */
515: rtmp[i] += sctx.shift_amount; /* shift the diagonal of the matrix */
517: /* elimination */
518: bjtmp = bj + bi[i];
519: row = *bjtmp++;
520: nzL = bi[i+1] - bi[i];
521: for (k=0; k < nzL; k++) {
522: pc = rtmp + row;
523: if (*pc != 0.0) {
524: pv = b->a + bdiag[row];
525: multiplier = *pc * (*pv);
526: *pc = multiplier;
528: pj = b->j + bdiag[row+1]+1; /* beginning of U(row,:) */
529: pv = b->a + bdiag[row+1]+1;
530: nz = bdiag[row]-bdiag[row+1]-1; /* num of entries in U(row,:) excluding diag */
532: for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
533: PetscLogFlops(1+2*nz);
534: }
535: row = *bjtmp++;
536: }
538: /* finished row so stick it into b->a */
539: rs = 0.0;
540: /* L part */
541: pv = b->a + bi[i];
542: pj = b->j + bi[i];
543: nz = bi[i+1] - bi[i];
544: for (j=0; j<nz; j++) {
545: pv[j] = rtmp[pj[j]]; rs += PetscAbsScalar(pv[j]);
546: }
548: /* U part */
549: pv = b->a + bdiag[i+1]+1;
550: pj = b->j + bdiag[i+1]+1;
551: nz = bdiag[i] - bdiag[i+1]-1;
552: for (j=0; j<nz; j++) {
553: pv[j] = rtmp[pj[j]]; rs += PetscAbsScalar(pv[j]);
554: }
556: sctx.rs = rs;
557: sctx.pv = rtmp[i];
558: MatPivotCheck(B,A,info,&sctx,i);
559: if (sctx.newshift) break; /* break for-loop */
560: rtmp[i] = sctx.pv; /* sctx.pv might be updated in the case of MAT_SHIFT_INBLOCKS */
562: /* Mark diagonal and invert diagonal for simplier triangular solves */
563: pv = b->a + bdiag[i];
564: *pv = 1.0/rtmp[i];
566: } /* endof for (i=0; i<n; i++) { */
568: /* MatPivotRefine() */
569: if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE && !sctx.newshift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) {
570: /*
571: * if no shift in this attempt & shifting & started shifting & can refine,
572: * then try lower shift
573: */
574: sctx.shift_hi = sctx.shift_fraction;
575: sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.;
576: sctx.shift_amount = sctx.shift_fraction * sctx.shift_top;
577: sctx.newshift = PETSC_TRUE;
578: sctx.nshift++;
579: }
580: } while (sctx.newshift);
582: PetscFree(rtmp);
583: ISRestoreIndices(isicol,&ic);
584: ISRestoreIndices(isrow,&r);
586: ISIdentity(isrow,&row_identity);
587: ISIdentity(isicol,&col_identity);
588: if (b->inode.size) {
589: C->ops->solve = MatSolve_SeqAIJ_Inode;
590: } else if (row_identity && col_identity) {
591: C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering;
592: } else {
593: C->ops->solve = MatSolve_SeqAIJ;
594: }
595: C->ops->solveadd = MatSolveAdd_SeqAIJ;
596: C->ops->solvetranspose = MatSolveTranspose_SeqAIJ;
597: C->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ;
598: C->ops->matsolve = MatMatSolve_SeqAIJ;
599: C->assembled = PETSC_TRUE;
600: C->preallocated = PETSC_TRUE;
602: PetscLogFlops(C->cmap->n);
604: /* MatShiftView(A,info,&sctx) */
605: if (sctx.nshift) {
606: if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) {
607: PetscInfo4(A,"number of shift_pd tries %D, shift_amount %g, diagonal shifted up by %e fraction top_value %e\n",sctx.nshift,(double)sctx.shift_amount,(double)sctx.shift_fraction,(double)sctx.shift_top);
608: } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) {
609: PetscInfo2(A,"number of shift_nz tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);
610: } else if (info->shifttype == (PetscReal)MAT_SHIFT_INBLOCKS) {
611: PetscInfo2(A,"number of shift_inblocks applied %D, each shift_amount %g\n",sctx.nshift,(double)info->shiftamount);
612: }
613: }
614: return(0);
615: }
617: PetscErrorCode MatLUFactorNumeric_SeqAIJ_inplace(Mat B,Mat A,const MatFactorInfo *info)
618: {
619: Mat C =B;
620: Mat_SeqAIJ *a =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)C->data;
621: IS isrow = b->row,isicol = b->icol;
622: PetscErrorCode ierr;
623: const PetscInt *r,*ic,*ics;
624: PetscInt nz,row,i,j,n=A->rmap->n,diag;
625: const PetscInt *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
626: const PetscInt *ajtmp,*bjtmp,*diag_offset = b->diag,*pj;
627: MatScalar *pv,*rtmp,*pc,multiplier,d;
628: const MatScalar *v,*aa=a->a;
629: PetscReal rs=0.0;
630: FactorShiftCtx sctx;
631: const PetscInt *ddiag;
632: PetscBool row_identity, col_identity;
635: /* MatPivotSetUp(): initialize shift context sctx */
636: PetscMemzero(&sctx,sizeof(FactorShiftCtx));
638: if (info->shifttype == (PetscReal) MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */
639: ddiag = a->diag;
640: sctx.shift_top = info->zeropivot;
641: for (i=0; i<n; i++) {
642: /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
643: d = (aa)[ddiag[i]];
644: rs = -PetscAbsScalar(d) - PetscRealPart(d);
645: v = aa+ai[i];
646: nz = ai[i+1] - ai[i];
647: for (j=0; j<nz; j++) rs += PetscAbsScalar(v[j]);
648: if (rs>sctx.shift_top) sctx.shift_top = rs;
649: }
650: sctx.shift_top *= 1.1;
651: sctx.nshift_max = 5;
652: sctx.shift_lo = 0.;
653: sctx.shift_hi = 1.;
654: }
656: ISGetIndices(isrow,&r);
657: ISGetIndices(isicol,&ic);
658: PetscMalloc1(n+1,&rtmp);
659: ics = ic;
661: do {
662: sctx.newshift = PETSC_FALSE;
663: for (i=0; i<n; i++) {
664: nz = bi[i+1] - bi[i];
665: bjtmp = bj + bi[i];
666: for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
668: /* load in initial (unfactored row) */
669: nz = ai[r[i]+1] - ai[r[i]];
670: ajtmp = aj + ai[r[i]];
671: v = aa + ai[r[i]];
672: for (j=0; j<nz; j++) {
673: rtmp[ics[ajtmp[j]]] = v[j];
674: }
675: rtmp[ics[r[i]]] += sctx.shift_amount; /* shift the diagonal of the matrix */
677: row = *bjtmp++;
678: while (row < i) {
679: pc = rtmp + row;
680: if (*pc != 0.0) {
681: pv = b->a + diag_offset[row];
682: pj = b->j + diag_offset[row] + 1;
683: multiplier = *pc / *pv++;
684: *pc = multiplier;
685: nz = bi[row+1] - diag_offset[row] - 1;
686: for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
687: PetscLogFlops(1+2*nz);
688: }
689: row = *bjtmp++;
690: }
691: /* finished row so stick it into b->a */
692: pv = b->a + bi[i];
693: pj = b->j + bi[i];
694: nz = bi[i+1] - bi[i];
695: diag = diag_offset[i] - bi[i];
696: rs = 0.0;
697: for (j=0; j<nz; j++) {
698: pv[j] = rtmp[pj[j]];
699: rs += PetscAbsScalar(pv[j]);
700: }
701: rs -= PetscAbsScalar(pv[diag]);
703: sctx.rs = rs;
704: sctx.pv = pv[diag];
705: MatPivotCheck(B,A,info,&sctx,i);
706: if (sctx.newshift) break;
707: pv[diag] = sctx.pv;
708: }
710: if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE && !sctx.newshift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) {
711: /*
712: * if no shift in this attempt & shifting & started shifting & can refine,
713: * then try lower shift
714: */
715: sctx.shift_hi = sctx.shift_fraction;
716: sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.;
717: sctx.shift_amount = sctx.shift_fraction * sctx.shift_top;
718: sctx.newshift = PETSC_TRUE;
719: sctx.nshift++;
720: }
721: } while (sctx.newshift);
723: /* invert diagonal entries for simplier triangular solves */
724: for (i=0; i<n; i++) {
725: b->a[diag_offset[i]] = 1.0/b->a[diag_offset[i]];
726: }
727: PetscFree(rtmp);
728: ISRestoreIndices(isicol,&ic);
729: ISRestoreIndices(isrow,&r);
731: ISIdentity(isrow,&row_identity);
732: ISIdentity(isicol,&col_identity);
733: if (row_identity && col_identity) {
734: C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_inplace;
735: } else {
736: C->ops->solve = MatSolve_SeqAIJ_inplace;
737: }
738: C->ops->solveadd = MatSolveAdd_SeqAIJ_inplace;
739: C->ops->solvetranspose = MatSolveTranspose_SeqAIJ_inplace;
740: C->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ_inplace;
741: C->ops->matsolve = MatMatSolve_SeqAIJ_inplace;
743: C->assembled = PETSC_TRUE;
744: C->preallocated = PETSC_TRUE;
746: PetscLogFlops(C->cmap->n);
747: if (sctx.nshift) {
748: if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) {
749: PetscInfo4(A,"number of shift_pd tries %D, shift_amount %g, diagonal shifted up by %e fraction top_value %e\n",sctx.nshift,(double)sctx.shift_amount,(double)sctx.shift_fraction,(double)sctx.shift_top);
750: } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) {
751: PetscInfo2(A,"number of shift_nz tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);
752: }
753: }
754: (C)->ops->solve = MatSolve_SeqAIJ_inplace;
755: (C)->ops->solvetranspose = MatSolveTranspose_SeqAIJ_inplace;
757: MatSeqAIJCheckInode(C);
758: return(0);
759: }
761: /*
762: This routine implements inplace ILU(0) with row or/and column permutations.
763: Input:
764: A - original matrix
765: Output;
766: A - a->i (rowptr) is same as original rowptr, but factored i-the row is stored in rowperm[i]
767: a->j (col index) is permuted by the inverse of colperm, then sorted
768: a->a reordered accordingly with a->j
769: a->diag (ptr to diagonal elements) is updated.
770: */
771: PetscErrorCode MatLUFactorNumeric_SeqAIJ_InplaceWithPerm(Mat B,Mat A,const MatFactorInfo *info)
772: {
773: Mat_SeqAIJ *a =(Mat_SeqAIJ*)A->data;
774: IS isrow = a->row,isicol = a->icol;
775: PetscErrorCode ierr;
776: const PetscInt *r,*ic,*ics;
777: PetscInt i,j,n=A->rmap->n,*ai=a->i,*aj=a->j;
778: PetscInt *ajtmp,nz,row;
779: PetscInt *diag = a->diag,nbdiag,*pj;
780: PetscScalar *rtmp,*pc,multiplier,d;
781: MatScalar *pv,*v;
782: PetscReal rs;
783: FactorShiftCtx sctx;
784: const MatScalar *aa=a->a,*vtmp;
787: if (A != B) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"input and output matrix must have same address");
789: /* MatPivotSetUp(): initialize shift context sctx */
790: PetscMemzero(&sctx,sizeof(FactorShiftCtx));
792: if (info->shifttype == (PetscReal) MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */
793: const PetscInt *ddiag = a->diag;
794: sctx.shift_top = info->zeropivot;
795: for (i=0; i<n; i++) {
796: /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
797: d = (aa)[ddiag[i]];
798: rs = -PetscAbsScalar(d) - PetscRealPart(d);
799: vtmp = aa+ai[i];
800: nz = ai[i+1] - ai[i];
801: for (j=0; j<nz; j++) rs += PetscAbsScalar(vtmp[j]);
802: if (rs>sctx.shift_top) sctx.shift_top = rs;
803: }
804: sctx.shift_top *= 1.1;
805: sctx.nshift_max = 5;
806: sctx.shift_lo = 0.;
807: sctx.shift_hi = 1.;
808: }
810: ISGetIndices(isrow,&r);
811: ISGetIndices(isicol,&ic);
812: PetscMalloc1(n+1,&rtmp);
813: PetscMemzero(rtmp,(n+1)*sizeof(PetscScalar));
814: ics = ic;
816: #if defined(MV)
817: sctx.shift_top = 0.;
818: sctx.nshift_max = 0;
819: sctx.shift_lo = 0.;
820: sctx.shift_hi = 0.;
821: sctx.shift_fraction = 0.;
823: if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */
824: sctx.shift_top = 0.;
825: for (i=0; i<n; i++) {
826: /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
827: d = (a->a)[diag[i]];
828: rs = -PetscAbsScalar(d) - PetscRealPart(d);
829: v = a->a+ai[i];
830: nz = ai[i+1] - ai[i];
831: for (j=0; j<nz; j++) rs += PetscAbsScalar(v[j]);
832: if (rs>sctx.shift_top) sctx.shift_top = rs;
833: }
834: if (sctx.shift_top < info->zeropivot) sctx.shift_top = info->zeropivot;
835: sctx.shift_top *= 1.1;
836: sctx.nshift_max = 5;
837: sctx.shift_lo = 0.;
838: sctx.shift_hi = 1.;
839: }
841: sctx.shift_amount = 0.;
842: sctx.nshift = 0;
843: #endif
845: do {
846: sctx.newshift = PETSC_FALSE;
847: for (i=0; i<n; i++) {
848: /* load in initial unfactored row */
849: nz = ai[r[i]+1] - ai[r[i]];
850: ajtmp = aj + ai[r[i]];
851: v = a->a + ai[r[i]];
852: /* sort permuted ajtmp and values v accordingly */
853: for (j=0; j<nz; j++) ajtmp[j] = ics[ajtmp[j]];
854: PetscSortIntWithScalarArray(nz,ajtmp,v);
856: diag[r[i]] = ai[r[i]];
857: for (j=0; j<nz; j++) {
858: rtmp[ajtmp[j]] = v[j];
859: if (ajtmp[j] < i) diag[r[i]]++; /* update a->diag */
860: }
861: rtmp[r[i]] += sctx.shift_amount; /* shift the diagonal of the matrix */
863: row = *ajtmp++;
864: while (row < i) {
865: pc = rtmp + row;
866: if (*pc != 0.0) {
867: pv = a->a + diag[r[row]];
868: pj = aj + diag[r[row]] + 1;
870: multiplier = *pc / *pv++;
871: *pc = multiplier;
872: nz = ai[r[row]+1] - diag[r[row]] - 1;
873: for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
874: PetscLogFlops(1+2*nz);
875: }
876: row = *ajtmp++;
877: }
878: /* finished row so overwrite it onto a->a */
879: pv = a->a + ai[r[i]];
880: pj = aj + ai[r[i]];
881: nz = ai[r[i]+1] - ai[r[i]];
882: nbdiag = diag[r[i]] - ai[r[i]]; /* num of entries before the diagonal */
884: rs = 0.0;
885: for (j=0; j<nz; j++) {
886: pv[j] = rtmp[pj[j]];
887: if (j != nbdiag) rs += PetscAbsScalar(pv[j]);
888: }
890: sctx.rs = rs;
891: sctx.pv = pv[nbdiag];
892: MatPivotCheck(B,A,info,&sctx,i);
893: if (sctx.newshift) break;
894: pv[nbdiag] = sctx.pv;
895: }
897: if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE && !sctx.newshift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) {
898: /*
899: * if no shift in this attempt & shifting & started shifting & can refine,
900: * then try lower shift
901: */
902: sctx.shift_hi = sctx.shift_fraction;
903: sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.;
904: sctx.shift_amount = sctx.shift_fraction * sctx.shift_top;
905: sctx.newshift = PETSC_TRUE;
906: sctx.nshift++;
907: }
908: } while (sctx.newshift);
910: /* invert diagonal entries for simplier triangular solves */
911: for (i=0; i<n; i++) {
912: a->a[diag[r[i]]] = 1.0/a->a[diag[r[i]]];
913: }
915: PetscFree(rtmp);
916: ISRestoreIndices(isicol,&ic);
917: ISRestoreIndices(isrow,&r);
919: A->ops->solve = MatSolve_SeqAIJ_InplaceWithPerm;
920: A->ops->solveadd = MatSolveAdd_SeqAIJ_inplace;
921: A->ops->solvetranspose = MatSolveTranspose_SeqAIJ_inplace;
922: A->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ_inplace;
924: A->assembled = PETSC_TRUE;
925: A->preallocated = PETSC_TRUE;
927: PetscLogFlops(A->cmap->n);
928: if (sctx.nshift) {
929: if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) {
930: PetscInfo4(A,"number of shift_pd tries %D, shift_amount %g, diagonal shifted up by %e fraction top_value %e\n",sctx.nshift,(double)sctx.shift_amount,(double)sctx.shift_fraction,(double)sctx.shift_top);
931: } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) {
932: PetscInfo2(A,"number of shift_nz tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);
933: }
934: }
935: return(0);
936: }
938: /* ----------------------------------------------------------- */
939: PetscErrorCode MatLUFactor_SeqAIJ(Mat A,IS row,IS col,const MatFactorInfo *info)
940: {
942: Mat C;
945: MatGetFactor(A,MATSOLVERPETSC,MAT_FACTOR_LU,&C);
946: MatLUFactorSymbolic(C,A,row,col,info);
947: MatLUFactorNumeric(C,A,info);
949: A->ops->solve = C->ops->solve;
950: A->ops->solvetranspose = C->ops->solvetranspose;
952: MatHeaderMerge(A,&C);
953: PetscLogObjectParent((PetscObject)A,(PetscObject)((Mat_SeqAIJ*)(A->data))->icol);
954: return(0);
955: }
956: /* ----------------------------------------------------------- */
959: PetscErrorCode MatSolve_SeqAIJ_inplace(Mat A,Vec bb,Vec xx)
960: {
961: Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
962: IS iscol = a->col,isrow = a->row;
963: PetscErrorCode ierr;
964: PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j;
965: PetscInt nz;
966: const PetscInt *rout,*cout,*r,*c;
967: PetscScalar *x,*tmp,*tmps,sum;
968: const PetscScalar *b;
969: const MatScalar *aa = a->a,*v;
972: if (!n) return(0);
974: VecGetArrayRead(bb,&b);
975: VecGetArray(xx,&x);
976: tmp = a->solve_work;
978: ISGetIndices(isrow,&rout); r = rout;
979: ISGetIndices(iscol,&cout); c = cout + (n-1);
981: /* forward solve the lower triangular */
982: tmp[0] = b[*r++];
983: tmps = tmp;
984: for (i=1; i<n; i++) {
985: v = aa + ai[i];
986: vi = aj + ai[i];
987: nz = a->diag[i] - ai[i];
988: sum = b[*r++];
989: PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
990: tmp[i] = sum;
991: }
993: /* backward solve the upper triangular */
994: for (i=n-1; i>=0; i--) {
995: v = aa + a->diag[i] + 1;
996: vi = aj + a->diag[i] + 1;
997: nz = ai[i+1] - a->diag[i] - 1;
998: sum = tmp[i];
999: PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
1000: x[*c--] = tmp[i] = sum*aa[a->diag[i]];
1001: }
1003: ISRestoreIndices(isrow,&rout);
1004: ISRestoreIndices(iscol,&cout);
1005: VecRestoreArrayRead(bb,&b);
1006: VecRestoreArray(xx,&x);
1007: PetscLogFlops(2.0*a->nz - A->cmap->n);
1008: return(0);
1009: }
1011: PetscErrorCode MatMatSolve_SeqAIJ_inplace(Mat A,Mat B,Mat X)
1012: {
1013: Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
1014: IS iscol = a->col,isrow = a->row;
1015: PetscErrorCode ierr;
1016: PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j;
1017: PetscInt nz,neq;
1018: const PetscInt *rout,*cout,*r,*c;
1019: PetscScalar *x,*b,*tmp,*tmps,sum;
1020: const MatScalar *aa = a->a,*v;
1021: PetscBool bisdense,xisdense;
1024: if (!n) return(0);
1026: PetscObjectTypeCompare((PetscObject)B,MATSEQDENSE,&bisdense);
1027: if (!bisdense) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"B matrix must be a SeqDense matrix");
1028: PetscObjectTypeCompare((PetscObject)X,MATSEQDENSE,&xisdense);
1029: if (!xisdense) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"X matrix must be a SeqDense matrix");
1031: MatDenseGetArray(B,&b);
1032: MatDenseGetArray(X,&x);
1034: tmp = a->solve_work;
1035: ISGetIndices(isrow,&rout); r = rout;
1036: ISGetIndices(iscol,&cout); c = cout;
1038: for (neq=0; neq<B->cmap->n; neq++) {
1039: /* forward solve the lower triangular */
1040: tmp[0] = b[r[0]];
1041: tmps = tmp;
1042: for (i=1; i<n; i++) {
1043: v = aa + ai[i];
1044: vi = aj + ai[i];
1045: nz = a->diag[i] - ai[i];
1046: sum = b[r[i]];
1047: PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
1048: tmp[i] = sum;
1049: }
1050: /* backward solve the upper triangular */
1051: for (i=n-1; i>=0; i--) {
1052: v = aa + a->diag[i] + 1;
1053: vi = aj + a->diag[i] + 1;
1054: nz = ai[i+1] - a->diag[i] - 1;
1055: sum = tmp[i];
1056: PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
1057: x[c[i]] = tmp[i] = sum*aa[a->diag[i]];
1058: }
1060: b += n;
1061: x += n;
1062: }
1063: ISRestoreIndices(isrow,&rout);
1064: ISRestoreIndices(iscol,&cout);
1065: MatDenseRestoreArray(B,&b);
1066: MatDenseRestoreArray(X,&x);
1067: PetscLogFlops(B->cmap->n*(2.0*a->nz - n));
1068: return(0);
1069: }
1071: PetscErrorCode MatMatSolve_SeqAIJ(Mat A,Mat B,Mat X)
1072: {
1073: Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
1074: IS iscol = a->col,isrow = a->row;
1075: PetscErrorCode ierr;
1076: PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j,*adiag = a->diag;
1077: PetscInt nz,neq;
1078: const PetscInt *rout,*cout,*r,*c;
1079: PetscScalar *x,*b,*tmp,sum;
1080: const MatScalar *aa = a->a,*v;
1081: PetscBool bisdense,xisdense;
1084: if (!n) return(0);
1086: PetscObjectTypeCompare((PetscObject)B,MATSEQDENSE,&bisdense);
1087: if (!bisdense) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"B matrix must be a SeqDense matrix");
1088: PetscObjectTypeCompare((PetscObject)X,MATSEQDENSE,&xisdense);
1089: if (!xisdense) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"X matrix must be a SeqDense matrix");
1091: MatDenseGetArray(B,&b);
1092: MatDenseGetArray(X,&x);
1094: tmp = a->solve_work;
1095: ISGetIndices(isrow,&rout); r = rout;
1096: ISGetIndices(iscol,&cout); c = cout;
1098: for (neq=0; neq<B->cmap->n; neq++) {
1099: /* forward solve the lower triangular */
1100: tmp[0] = b[r[0]];
1101: v = aa;
1102: vi = aj;
1103: for (i=1; i<n; i++) {
1104: nz = ai[i+1] - ai[i];
1105: sum = b[r[i]];
1106: PetscSparseDenseMinusDot(sum,tmp,v,vi,nz);
1107: tmp[i] = sum;
1108: v += nz; vi += nz;
1109: }
1111: /* backward solve the upper triangular */
1112: for (i=n-1; i>=0; i--) {
1113: v = aa + adiag[i+1]+1;
1114: vi = aj + adiag[i+1]+1;
1115: nz = adiag[i]-adiag[i+1]-1;
1116: sum = tmp[i];
1117: PetscSparseDenseMinusDot(sum,tmp,v,vi,nz);
1118: x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */
1119: }
1121: b += n;
1122: x += n;
1123: }
1124: ISRestoreIndices(isrow,&rout);
1125: ISRestoreIndices(iscol,&cout);
1126: MatDenseRestoreArray(B,&b);
1127: MatDenseRestoreArray(X,&x);
1128: PetscLogFlops(B->cmap->n*(2.0*a->nz - n));
1129: return(0);
1130: }
1132: PetscErrorCode MatSolve_SeqAIJ_InplaceWithPerm(Mat A,Vec bb,Vec xx)
1133: {
1134: Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
1135: IS iscol = a->col,isrow = a->row;
1136: PetscErrorCode ierr;
1137: const PetscInt *r,*c,*rout,*cout;
1138: PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j;
1139: PetscInt nz,row;
1140: PetscScalar *x,*b,*tmp,*tmps,sum;
1141: const MatScalar *aa = a->a,*v;
1144: if (!n) return(0);
1146: VecGetArray(bb,&b);
1147: VecGetArray(xx,&x);
1148: tmp = a->solve_work;
1150: ISGetIndices(isrow,&rout); r = rout;
1151: ISGetIndices(iscol,&cout); c = cout + (n-1);
1153: /* forward solve the lower triangular */
1154: tmp[0] = b[*r++];
1155: tmps = tmp;
1156: for (row=1; row<n; row++) {
1157: i = rout[row]; /* permuted row */
1158: v = aa + ai[i];
1159: vi = aj + ai[i];
1160: nz = a->diag[i] - ai[i];
1161: sum = b[*r++];
1162: PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
1163: tmp[row] = sum;
1164: }
1166: /* backward solve the upper triangular */
1167: for (row=n-1; row>=0; row--) {
1168: i = rout[row]; /* permuted row */
1169: v = aa + a->diag[i] + 1;
1170: vi = aj + a->diag[i] + 1;
1171: nz = ai[i+1] - a->diag[i] - 1;
1172: sum = tmp[row];
1173: PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
1174: x[*c--] = tmp[row] = sum*aa[a->diag[i]];
1175: }
1177: ISRestoreIndices(isrow,&rout);
1178: ISRestoreIndices(iscol,&cout);
1179: VecRestoreArray(bb,&b);
1180: VecRestoreArray(xx,&x);
1181: PetscLogFlops(2.0*a->nz - A->cmap->n);
1182: return(0);
1183: }
1185: /* ----------------------------------------------------------- */
1186: #include <../src/mat/impls/aij/seq/ftn-kernels/fsolve.h>
1187: PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering_inplace(Mat A,Vec bb,Vec xx)
1188: {
1189: Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
1190: PetscErrorCode ierr;
1191: PetscInt n = A->rmap->n;
1192: const PetscInt *ai = a->i,*aj = a->j,*adiag = a->diag;
1193: PetscScalar *x;
1194: const PetscScalar *b;
1195: const MatScalar *aa = a->a;
1196: #if !defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ)
1197: PetscInt adiag_i,i,nz,ai_i;
1198: const PetscInt *vi;
1199: const MatScalar *v;
1200: PetscScalar sum;
1201: #endif
1204: if (!n) return(0);
1206: VecGetArrayRead(bb,&b);
1207: VecGetArray(xx,&x);
1209: #if defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ)
1210: fortransolveaij_(&n,x,ai,aj,adiag,aa,b);
1211: #else
1212: /* forward solve the lower triangular */
1213: x[0] = b[0];
1214: for (i=1; i<n; i++) {
1215: ai_i = ai[i];
1216: v = aa + ai_i;
1217: vi = aj + ai_i;
1218: nz = adiag[i] - ai_i;
1219: sum = b[i];
1220: PetscSparseDenseMinusDot(sum,x,v,vi,nz);
1221: x[i] = sum;
1222: }
1224: /* backward solve the upper triangular */
1225: for (i=n-1; i>=0; i--) {
1226: adiag_i = adiag[i];
1227: v = aa + adiag_i + 1;
1228: vi = aj + adiag_i + 1;
1229: nz = ai[i+1] - adiag_i - 1;
1230: sum = x[i];
1231: PetscSparseDenseMinusDot(sum,x,v,vi,nz);
1232: x[i] = sum*aa[adiag_i];
1233: }
1234: #endif
1235: PetscLogFlops(2.0*a->nz - A->cmap->n);
1236: VecRestoreArrayRead(bb,&b);
1237: VecRestoreArray(xx,&x);
1238: return(0);
1239: }
1241: PetscErrorCode MatSolveAdd_SeqAIJ_inplace(Mat A,Vec bb,Vec yy,Vec xx)
1242: {
1243: Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
1244: IS iscol = a->col,isrow = a->row;
1245: PetscErrorCode ierr;
1246: PetscInt i, n = A->rmap->n,j;
1247: PetscInt nz;
1248: const PetscInt *rout,*cout,*r,*c,*vi,*ai = a->i,*aj = a->j;
1249: PetscScalar *x,*tmp,sum;
1250: const PetscScalar *b;
1251: const MatScalar *aa = a->a,*v;
1254: if (yy != xx) {VecCopy(yy,xx);}
1256: VecGetArrayRead(bb,&b);
1257: VecGetArray(xx,&x);
1258: tmp = a->solve_work;
1260: ISGetIndices(isrow,&rout); r = rout;
1261: ISGetIndices(iscol,&cout); c = cout + (n-1);
1263: /* forward solve the lower triangular */
1264: tmp[0] = b[*r++];
1265: for (i=1; i<n; i++) {
1266: v = aa + ai[i];
1267: vi = aj + ai[i];
1268: nz = a->diag[i] - ai[i];
1269: sum = b[*r++];
1270: for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]];
1271: tmp[i] = sum;
1272: }
1274: /* backward solve the upper triangular */
1275: for (i=n-1; i>=0; i--) {
1276: v = aa + a->diag[i] + 1;
1277: vi = aj + a->diag[i] + 1;
1278: nz = ai[i+1] - a->diag[i] - 1;
1279: sum = tmp[i];
1280: for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]];
1281: tmp[i] = sum*aa[a->diag[i]];
1282: x[*c--] += tmp[i];
1283: }
1285: ISRestoreIndices(isrow,&rout);
1286: ISRestoreIndices(iscol,&cout);
1287: VecRestoreArrayRead(bb,&b);
1288: VecRestoreArray(xx,&x);
1289: PetscLogFlops(2.0*a->nz);
1290: return(0);
1291: }
1293: PetscErrorCode MatSolveAdd_SeqAIJ(Mat A,Vec bb,Vec yy,Vec xx)
1294: {
1295: Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
1296: IS iscol = a->col,isrow = a->row;
1297: PetscErrorCode ierr;
1298: PetscInt i, n = A->rmap->n,j;
1299: PetscInt nz;
1300: const PetscInt *rout,*cout,*r,*c,*vi,*ai = a->i,*aj = a->j,*adiag = a->diag;
1301: PetscScalar *x,*tmp,sum;
1302: const PetscScalar *b;
1303: const MatScalar *aa = a->a,*v;
1306: if (yy != xx) {VecCopy(yy,xx);}
1308: VecGetArrayRead(bb,&b);
1309: VecGetArray(xx,&x);
1310: tmp = a->solve_work;
1312: ISGetIndices(isrow,&rout); r = rout;
1313: ISGetIndices(iscol,&cout); c = cout;
1315: /* forward solve the lower triangular */
1316: tmp[0] = b[r[0]];
1317: v = aa;
1318: vi = aj;
1319: for (i=1; i<n; i++) {
1320: nz = ai[i+1] - ai[i];
1321: sum = b[r[i]];
1322: for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]];
1323: tmp[i] = sum;
1324: v += nz;
1325: vi += nz;
1326: }
1328: /* backward solve the upper triangular */
1329: v = aa + adiag[n-1];
1330: vi = aj + adiag[n-1];
1331: for (i=n-1; i>=0; i--) {
1332: nz = adiag[i] - adiag[i+1] - 1;
1333: sum = tmp[i];
1334: for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]];
1335: tmp[i] = sum*v[nz];
1336: x[c[i]] += tmp[i];
1337: v += nz+1; vi += nz+1;
1338: }
1340: ISRestoreIndices(isrow,&rout);
1341: ISRestoreIndices(iscol,&cout);
1342: VecRestoreArrayRead(bb,&b);
1343: VecRestoreArray(xx,&x);
1344: PetscLogFlops(2.0*a->nz);
1345: return(0);
1346: }
1348: PetscErrorCode MatSolveTranspose_SeqAIJ_inplace(Mat A,Vec bb,Vec xx)
1349: {
1350: Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
1351: IS iscol = a->col,isrow = a->row;
1352: PetscErrorCode ierr;
1353: const PetscInt *rout,*cout,*r,*c,*diag = a->diag,*ai = a->i,*aj = a->j,*vi;
1354: PetscInt i,n = A->rmap->n,j;
1355: PetscInt nz;
1356: PetscScalar *x,*tmp,s1;
1357: const MatScalar *aa = a->a,*v;
1358: const PetscScalar *b;
1361: VecGetArrayRead(bb,&b);
1362: VecGetArray(xx,&x);
1363: tmp = a->solve_work;
1365: ISGetIndices(isrow,&rout); r = rout;
1366: ISGetIndices(iscol,&cout); c = cout;
1368: /* copy the b into temp work space according to permutation */
1369: for (i=0; i<n; i++) tmp[i] = b[c[i]];
1371: /* forward solve the U^T */
1372: for (i=0; i<n; i++) {
1373: v = aa + diag[i];
1374: vi = aj + diag[i] + 1;
1375: nz = ai[i+1] - diag[i] - 1;
1376: s1 = tmp[i];
1377: s1 *= (*v++); /* multiply by inverse of diagonal entry */
1378: for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
1379: tmp[i] = s1;
1380: }
1382: /* backward solve the L^T */
1383: for (i=n-1; i>=0; i--) {
1384: v = aa + diag[i] - 1;
1385: vi = aj + diag[i] - 1;
1386: nz = diag[i] - ai[i];
1387: s1 = tmp[i];
1388: for (j=0; j>-nz; j--) tmp[vi[j]] -= s1*v[j];
1389: }
1391: /* copy tmp into x according to permutation */
1392: for (i=0; i<n; i++) x[r[i]] = tmp[i];
1394: ISRestoreIndices(isrow,&rout);
1395: ISRestoreIndices(iscol,&cout);
1396: VecRestoreArrayRead(bb,&b);
1397: VecRestoreArray(xx,&x);
1399: PetscLogFlops(2.0*a->nz-A->cmap->n);
1400: return(0);
1401: }
1403: PetscErrorCode MatSolveTranspose_SeqAIJ(Mat A,Vec bb,Vec xx)
1404: {
1405: Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
1406: IS iscol = a->col,isrow = a->row;
1407: PetscErrorCode ierr;
1408: const PetscInt *rout,*cout,*r,*c,*adiag = a->diag,*ai = a->i,*aj = a->j,*vi;
1409: PetscInt i,n = A->rmap->n,j;
1410: PetscInt nz;
1411: PetscScalar *x,*tmp,s1;
1412: const MatScalar *aa = a->a,*v;
1413: const PetscScalar *b;
1416: VecGetArrayRead(bb,&b);
1417: VecGetArray(xx,&x);
1418: tmp = a->solve_work;
1420: ISGetIndices(isrow,&rout); r = rout;
1421: ISGetIndices(iscol,&cout); c = cout;
1423: /* copy the b into temp work space according to permutation */
1424: for (i=0; i<n; i++) tmp[i] = b[c[i]];
1426: /* forward solve the U^T */
1427: for (i=0; i<n; i++) {
1428: v = aa + adiag[i+1] + 1;
1429: vi = aj + adiag[i+1] + 1;
1430: nz = adiag[i] - adiag[i+1] - 1;
1431: s1 = tmp[i];
1432: s1 *= v[nz]; /* multiply by inverse of diagonal entry */
1433: for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
1434: tmp[i] = s1;
1435: }
1437: /* backward solve the L^T */
1438: for (i=n-1; i>=0; i--) {
1439: v = aa + ai[i];
1440: vi = aj + ai[i];
1441: nz = ai[i+1] - ai[i];
1442: s1 = tmp[i];
1443: for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
1444: }
1446: /* copy tmp into x according to permutation */
1447: for (i=0; i<n; i++) x[r[i]] = tmp[i];
1449: ISRestoreIndices(isrow,&rout);
1450: ISRestoreIndices(iscol,&cout);
1451: VecRestoreArrayRead(bb,&b);
1452: VecRestoreArray(xx,&x);
1454: PetscLogFlops(2.0*a->nz-A->cmap->n);
1455: return(0);
1456: }
1458: PetscErrorCode MatSolveTransposeAdd_SeqAIJ_inplace(Mat A,Vec bb,Vec zz,Vec xx)
1459: {
1460: Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
1461: IS iscol = a->col,isrow = a->row;
1462: PetscErrorCode ierr;
1463: const PetscInt *rout,*cout,*r,*c,*diag = a->diag,*ai = a->i,*aj = a->j,*vi;
1464: PetscInt i,n = A->rmap->n,j;
1465: PetscInt nz;
1466: PetscScalar *x,*tmp,s1;
1467: const MatScalar *aa = a->a,*v;
1468: const PetscScalar *b;
1471: if (zz != xx) {VecCopy(zz,xx);}
1472: VecGetArrayRead(bb,&b);
1473: VecGetArray(xx,&x);
1474: tmp = a->solve_work;
1476: ISGetIndices(isrow,&rout); r = rout;
1477: ISGetIndices(iscol,&cout); c = cout;
1479: /* copy the b into temp work space according to permutation */
1480: for (i=0; i<n; i++) tmp[i] = b[c[i]];
1482: /* forward solve the U^T */
1483: for (i=0; i<n; i++) {
1484: v = aa + diag[i];
1485: vi = aj + diag[i] + 1;
1486: nz = ai[i+1] - diag[i] - 1;
1487: s1 = tmp[i];
1488: s1 *= (*v++); /* multiply by inverse of diagonal entry */
1489: for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
1490: tmp[i] = s1;
1491: }
1493: /* backward solve the L^T */
1494: for (i=n-1; i>=0; i--) {
1495: v = aa + diag[i] - 1;
1496: vi = aj + diag[i] - 1;
1497: nz = diag[i] - ai[i];
1498: s1 = tmp[i];
1499: for (j=0; j>-nz; j--) tmp[vi[j]] -= s1*v[j];
1500: }
1502: /* copy tmp into x according to permutation */
1503: for (i=0; i<n; i++) x[r[i]] += tmp[i];
1505: ISRestoreIndices(isrow,&rout);
1506: ISRestoreIndices(iscol,&cout);
1507: VecRestoreArrayRead(bb,&b);
1508: VecRestoreArray(xx,&x);
1510: PetscLogFlops(2.0*a->nz-A->cmap->n);
1511: return(0);
1512: }
1514: PetscErrorCode MatSolveTransposeAdd_SeqAIJ(Mat A,Vec bb,Vec zz,Vec xx)
1515: {
1516: Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
1517: IS iscol = a->col,isrow = a->row;
1518: PetscErrorCode ierr;
1519: const PetscInt *rout,*cout,*r,*c,*adiag = a->diag,*ai = a->i,*aj = a->j,*vi;
1520: PetscInt i,n = A->rmap->n,j;
1521: PetscInt nz;
1522: PetscScalar *x,*tmp,s1;
1523: const MatScalar *aa = a->a,*v;
1524: const PetscScalar *b;
1527: if (zz != xx) {VecCopy(zz,xx);}
1528: VecGetArrayRead(bb,&b);
1529: VecGetArray(xx,&x);
1530: tmp = a->solve_work;
1532: ISGetIndices(isrow,&rout); r = rout;
1533: ISGetIndices(iscol,&cout); c = cout;
1535: /* copy the b into temp work space according to permutation */
1536: for (i=0; i<n; i++) tmp[i] = b[c[i]];
1538: /* forward solve the U^T */
1539: for (i=0; i<n; i++) {
1540: v = aa + adiag[i+1] + 1;
1541: vi = aj + adiag[i+1] + 1;
1542: nz = adiag[i] - adiag[i+1] - 1;
1543: s1 = tmp[i];
1544: s1 *= v[nz]; /* multiply by inverse of diagonal entry */
1545: for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
1546: tmp[i] = s1;
1547: }
1550: /* backward solve the L^T */
1551: for (i=n-1; i>=0; i--) {
1552: v = aa + ai[i];
1553: vi = aj + ai[i];
1554: nz = ai[i+1] - ai[i];
1555: s1 = tmp[i];
1556: for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
1557: }
1559: /* copy tmp into x according to permutation */
1560: for (i=0; i<n; i++) x[r[i]] += tmp[i];
1562: ISRestoreIndices(isrow,&rout);
1563: ISRestoreIndices(iscol,&cout);
1564: VecRestoreArrayRead(bb,&b);
1565: VecRestoreArray(xx,&x);
1567: PetscLogFlops(2.0*a->nz-A->cmap->n);
1568: return(0);
1569: }
1571: /* ----------------------------------------------------------------*/
1573: /*
1574: ilu() under revised new data structure.
1575: Factored arrays bj and ba are stored as
1576: L(0,:), L(1,:), ...,L(n-1,:), U(n-1,:),...,U(i,:),U(i-1,:),...,U(0,:)
1578: bi=fact->i is an array of size n+1, in which
1579: bi+
1580: bi[i]: points to 1st entry of L(i,:),i=0,...,n-1
1581: bi[n]: points to L(n-1,n-1)+1
1583: bdiag=fact->diag is an array of size n+1,in which
1584: bdiag[i]: points to diagonal of U(i,:), i=0,...,n-1
1585: bdiag[n]: points to entry of U(n-1,0)-1
1587: U(i,:) contains bdiag[i] as its last entry, i.e.,
1588: U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i])
1589: */
1590: PetscErrorCode MatILUFactorSymbolic_SeqAIJ_ilu0(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
1591: {
1592: Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b;
1594: const PetscInt n=A->rmap->n,*ai=a->i,*aj,*adiag=a->diag;
1595: PetscInt i,j,k=0,nz,*bi,*bj,*bdiag;
1596: IS isicol;
1599: ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);
1600: MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_FALSE);
1601: b = (Mat_SeqAIJ*)(fact)->data;
1603: /* allocate matrix arrays for new data structure */
1604: PetscMalloc3(ai[n]+1,&b->a,ai[n]+1,&b->j,n+1,&b->i);
1605: PetscLogObjectMemory((PetscObject)fact,ai[n]*(sizeof(PetscScalar)+sizeof(PetscInt))+(n+1)*sizeof(PetscInt));
1607: b->singlemalloc = PETSC_TRUE;
1608: if (!b->diag) {
1609: PetscMalloc1(n+1,&b->diag);
1610: PetscLogObjectMemory((PetscObject)fact,(n+1)*sizeof(PetscInt));
1611: }
1612: bdiag = b->diag;
1614: if (n > 0) {
1615: PetscMemzero(b->a,(ai[n])*sizeof(MatScalar));
1616: }
1618: /* set bi and bj with new data structure */
1619: bi = b->i;
1620: bj = b->j;
1622: /* L part */
1623: bi[0] = 0;
1624: for (i=0; i<n; i++) {
1625: nz = adiag[i] - ai[i];
1626: bi[i+1] = bi[i] + nz;
1627: aj = a->j + ai[i];
1628: for (j=0; j<nz; j++) {
1629: /* *bj = aj[j]; bj++; */
1630: bj[k++] = aj[j];
1631: }
1632: }
1634: /* U part */
1635: bdiag[n] = bi[n]-1;
1636: for (i=n-1; i>=0; i--) {
1637: nz = ai[i+1] - adiag[i] - 1;
1638: aj = a->j + adiag[i] + 1;
1639: for (j=0; j<nz; j++) {
1640: /* *bj = aj[j]; bj++; */
1641: bj[k++] = aj[j];
1642: }
1643: /* diag[i] */
1644: /* *bj = i; bj++; */
1645: bj[k++] = i;
1646: bdiag[i] = bdiag[i+1] + nz + 1;
1647: }
1649: fact->factortype = MAT_FACTOR_ILU;
1650: fact->info.factor_mallocs = 0;
1651: fact->info.fill_ratio_given = info->fill;
1652: fact->info.fill_ratio_needed = 1.0;
1653: fact->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ;
1654: MatSeqAIJCheckInode_FactorLU(fact);
1656: b = (Mat_SeqAIJ*)(fact)->data;
1657: b->row = isrow;
1658: b->col = iscol;
1659: b->icol = isicol;
1660: PetscMalloc1(fact->rmap->n+1,&b->solve_work);
1661: PetscObjectReference((PetscObject)isrow);
1662: PetscObjectReference((PetscObject)iscol);
1663: return(0);
1664: }
1666: PetscErrorCode MatILUFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
1667: {
1668: Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b;
1669: IS isicol;
1670: PetscErrorCode ierr;
1671: const PetscInt *r,*ic;
1672: PetscInt n=A->rmap->n,*ai=a->i,*aj=a->j;
1673: PetscInt *bi,*cols,nnz,*cols_lvl;
1674: PetscInt *bdiag,prow,fm,nzbd,reallocs=0,dcount=0;
1675: PetscInt i,levels,diagonal_fill;
1676: PetscBool col_identity,row_identity,missing;
1677: PetscReal f;
1678: PetscInt nlnk,*lnk,*lnk_lvl=NULL;
1679: PetscBT lnkbt;
1680: PetscInt nzi,*bj,**bj_ptr,**bjlvl_ptr;
1681: PetscFreeSpaceList free_space =NULL,current_space=NULL;
1682: PetscFreeSpaceList free_space_lvl=NULL,current_space_lvl=NULL;
1685: if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n);
1686: MatMissingDiagonal(A,&missing,&i);
1687: if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i);
1688:
1689: levels = (PetscInt)info->levels;
1690: ISIdentity(isrow,&row_identity);
1691: ISIdentity(iscol,&col_identity);
1692: if (!levels && row_identity && col_identity) {
1693: /* special case: ilu(0) with natural ordering */
1694: MatILUFactorSymbolic_SeqAIJ_ilu0(fact,A,isrow,iscol,info);
1695: if (a->inode.size) {
1696: fact->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode;
1697: }
1698: return(0);
1699: }
1701: ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);
1702: ISGetIndices(isrow,&r);
1703: ISGetIndices(isicol,&ic);
1705: /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */
1706: PetscMalloc1(n+1,&bi);
1707: PetscMalloc1(n+1,&bdiag);
1708: bi[0] = bdiag[0] = 0;
1709: PetscMalloc2(n,&bj_ptr,n,&bjlvl_ptr);
1711: /* create a linked list for storing column indices of the active row */
1712: nlnk = n + 1;
1713: PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);
1715: /* initial FreeSpace size is f*(ai[n]+1) */
1716: f = info->fill;
1717: diagonal_fill = (PetscInt)info->diagonal_fill;
1718: PetscFreeSpaceGet(PetscRealIntMultTruncate(f,ai[n]+1),&free_space);
1719: current_space = free_space;
1720: PetscFreeSpaceGet(PetscRealIntMultTruncate(f,ai[n]+1),&free_space_lvl);
1721: current_space_lvl = free_space_lvl;
1722: for (i=0; i<n; i++) {
1723: nzi = 0;
1724: /* copy current row into linked list */
1725: nnz = ai[r[i]+1] - ai[r[i]];
1726: if (!nnz) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
1727: cols = aj + ai[r[i]];
1728: lnk[i] = -1; /* marker to indicate if diagonal exists */
1729: PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);
1730: nzi += nlnk;
1732: /* make sure diagonal entry is included */
1733: if (diagonal_fill && lnk[i] == -1) {
1734: fm = n;
1735: while (lnk[fm] < i) fm = lnk[fm];
1736: lnk[i] = lnk[fm]; /* insert diagonal into linked list */
1737: lnk[fm] = i;
1738: lnk_lvl[i] = 0;
1739: nzi++; dcount++;
1740: }
1742: /* add pivot rows into the active row */
1743: nzbd = 0;
1744: prow = lnk[n];
1745: while (prow < i) {
1746: nnz = bdiag[prow];
1747: cols = bj_ptr[prow] + nnz + 1;
1748: cols_lvl = bjlvl_ptr[prow] + nnz + 1;
1749: nnz = bi[prow+1] - bi[prow] - nnz - 1;
1750: PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);
1751: nzi += nlnk;
1752: prow = lnk[prow];
1753: nzbd++;
1754: }
1755: bdiag[i] = nzbd;
1756: bi[i+1] = bi[i] + nzi;
1757: /* if free space is not available, make more free space */
1758: if (current_space->local_remaining<nzi) {
1759: nnz = PetscIntMultTruncate(2,PetscIntMultTruncate(nzi,n - i)); /* estimated and max additional space needed */
1760: PetscFreeSpaceGet(nnz,¤t_space);
1761: PetscFreeSpaceGet(nnz,¤t_space_lvl);
1762: reallocs++;
1763: }
1765: /* copy data into free_space and free_space_lvl, then initialize lnk */
1766: PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);
1767: bj_ptr[i] = current_space->array;
1768: bjlvl_ptr[i] = current_space_lvl->array;
1770: /* make sure the active row i has diagonal entry */
1771: if (*(bj_ptr[i]+bdiag[i]) != i) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\ntry running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i);
1773: current_space->array += nzi;
1774: current_space->local_used += nzi;
1775: current_space->local_remaining -= nzi;
1776: current_space_lvl->array += nzi;
1777: current_space_lvl->local_used += nzi;
1778: current_space_lvl->local_remaining -= nzi;
1779: }
1781: ISRestoreIndices(isrow,&r);
1782: ISRestoreIndices(isicol,&ic);
1783: /* copy free_space into bj and free free_space; set bi, bj, bdiag in new datastructure; */
1784: PetscMalloc1(bi[n]+1,&bj);
1785: PetscFreeSpaceContiguous_LU(&free_space,bj,n,bi,bdiag);
1787: PetscIncompleteLLDestroy(lnk,lnkbt);
1788: PetscFreeSpaceDestroy(free_space_lvl);
1789: PetscFree2(bj_ptr,bjlvl_ptr);
1791: #if defined(PETSC_USE_INFO)
1792: {
1793: PetscReal af = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]);
1794: PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)f,(double)af);
1795: PetscInfo1(A,"Run with -[sub_]pc_factor_fill %g or use \n",(double)af);
1796: PetscInfo1(A,"PCFactorSetFill([sub]pc,%g);\n",(double)af);
1797: PetscInfo(A,"for best performance.\n");
1798: if (diagonal_fill) {
1799: PetscInfo1(A,"Detected and replaced %D missing diagonals\n",dcount);
1800: }
1801: }
1802: #endif
1803: /* put together the new matrix */
1804: MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,NULL);
1805: PetscLogObjectParent((PetscObject)fact,(PetscObject)isicol);
1806: b = (Mat_SeqAIJ*)(fact)->data;
1808: b->free_a = PETSC_TRUE;
1809: b->free_ij = PETSC_TRUE;
1810: b->singlemalloc = PETSC_FALSE;
1812: PetscMalloc1(bdiag[0]+1,&b->a);
1814: b->j = bj;
1815: b->i = bi;
1816: b->diag = bdiag;
1817: b->ilen = 0;
1818: b->imax = 0;
1819: b->row = isrow;
1820: b->col = iscol;
1821: PetscObjectReference((PetscObject)isrow);
1822: PetscObjectReference((PetscObject)iscol);
1823: b->icol = isicol;
1825: PetscMalloc1(n+1,&b->solve_work);
1826: /* In b structure: Free imax, ilen, old a, old j.
1827: Allocate bdiag, solve_work, new a, new j */
1828: PetscLogObjectMemory((PetscObject)fact,(bdiag[0]+1)*(sizeof(PetscInt)+sizeof(PetscScalar)));
1829: b->maxnz = b->nz = bdiag[0]+1;
1831: (fact)->info.factor_mallocs = reallocs;
1832: (fact)->info.fill_ratio_given = f;
1833: (fact)->info.fill_ratio_needed = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]);
1834: (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ;
1835: if (a->inode.size) {
1836: (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode;
1837: }
1838: MatSeqAIJCheckInode_FactorLU(fact);
1839: return(0);
1840: }
1842: PetscErrorCode MatILUFactorSymbolic_SeqAIJ_inplace(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
1843: {
1844: Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b;
1845: IS isicol;
1846: PetscErrorCode ierr;
1847: const PetscInt *r,*ic;
1848: PetscInt n=A->rmap->n,*ai=a->i,*aj=a->j;
1849: PetscInt *bi,*cols,nnz,*cols_lvl;
1850: PetscInt *bdiag,prow,fm,nzbd,reallocs=0,dcount=0;
1851: PetscInt i,levels,diagonal_fill;
1852: PetscBool col_identity,row_identity;
1853: PetscReal f;
1854: PetscInt nlnk,*lnk,*lnk_lvl=NULL;
1855: PetscBT lnkbt;
1856: PetscInt nzi,*bj,**bj_ptr,**bjlvl_ptr;
1857: PetscFreeSpaceList free_space =NULL,current_space=NULL;
1858: PetscFreeSpaceList free_space_lvl=NULL,current_space_lvl=NULL;
1859: PetscBool missing;
1862: if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n);
1863: MatMissingDiagonal(A,&missing,&i);
1864: if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i);
1866: f = info->fill;
1867: levels = (PetscInt)info->levels;
1868: diagonal_fill = (PetscInt)info->diagonal_fill;
1870: ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);
1872: ISIdentity(isrow,&row_identity);
1873: ISIdentity(iscol,&col_identity);
1874: if (!levels && row_identity && col_identity) { /* special case: ilu(0) with natural ordering */
1875: MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_TRUE);
1877: (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_inplace;
1878: if (a->inode.size) {
1879: (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode_inplace;
1880: }
1881: fact->factortype = MAT_FACTOR_ILU;
1882: (fact)->info.factor_mallocs = 0;
1883: (fact)->info.fill_ratio_given = info->fill;
1884: (fact)->info.fill_ratio_needed = 1.0;
1886: b = (Mat_SeqAIJ*)(fact)->data;
1887: b->row = isrow;
1888: b->col = iscol;
1889: b->icol = isicol;
1890: PetscMalloc1((fact)->rmap->n+1,&b->solve_work);
1891: PetscObjectReference((PetscObject)isrow);
1892: PetscObjectReference((PetscObject)iscol);
1893: return(0);
1894: }
1896: ISGetIndices(isrow,&r);
1897: ISGetIndices(isicol,&ic);
1899: /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */
1900: PetscMalloc1(n+1,&bi);
1901: PetscMalloc1(n+1,&bdiag);
1902: bi[0] = bdiag[0] = 0;
1904: PetscMalloc2(n,&bj_ptr,n,&bjlvl_ptr);
1906: /* create a linked list for storing column indices of the active row */
1907: nlnk = n + 1;
1908: PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);
1910: /* initial FreeSpace size is f*(ai[n]+1) */
1911: PetscFreeSpaceGet(PetscRealIntMultTruncate(f,ai[n]+1),&free_space);
1912: current_space = free_space;
1913: PetscFreeSpaceGet(PetscRealIntMultTruncate(f,ai[n]+1),&free_space_lvl);
1914: current_space_lvl = free_space_lvl;
1916: for (i=0; i<n; i++) {
1917: nzi = 0;
1918: /* copy current row into linked list */
1919: nnz = ai[r[i]+1] - ai[r[i]];
1920: if (!nnz) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
1921: cols = aj + ai[r[i]];
1922: lnk[i] = -1; /* marker to indicate if diagonal exists */
1923: PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);
1924: nzi += nlnk;
1926: /* make sure diagonal entry is included */
1927: if (diagonal_fill && lnk[i] == -1) {
1928: fm = n;
1929: while (lnk[fm] < i) fm = lnk[fm];
1930: lnk[i] = lnk[fm]; /* insert diagonal into linked list */
1931: lnk[fm] = i;
1932: lnk_lvl[i] = 0;
1933: nzi++; dcount++;
1934: }
1936: /* add pivot rows into the active row */
1937: nzbd = 0;
1938: prow = lnk[n];
1939: while (prow < i) {
1940: nnz = bdiag[prow];
1941: cols = bj_ptr[prow] + nnz + 1;
1942: cols_lvl = bjlvl_ptr[prow] + nnz + 1;
1943: nnz = bi[prow+1] - bi[prow] - nnz - 1;
1944: PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);
1945: nzi += nlnk;
1946: prow = lnk[prow];
1947: nzbd++;
1948: }
1949: bdiag[i] = nzbd;
1950: bi[i+1] = bi[i] + nzi;
1952: /* if free space is not available, make more free space */
1953: if (current_space->local_remaining<nzi) {
1954: nnz = PetscIntMultTruncate(nzi,n - i); /* estimated and max additional space needed */
1955: PetscFreeSpaceGet(nnz,¤t_space);
1956: PetscFreeSpaceGet(nnz,¤t_space_lvl);
1957: reallocs++;
1958: }
1960: /* copy data into free_space and free_space_lvl, then initialize lnk */
1961: PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);
1962: bj_ptr[i] = current_space->array;
1963: bjlvl_ptr[i] = current_space_lvl->array;
1965: /* make sure the active row i has diagonal entry */
1966: if (*(bj_ptr[i]+bdiag[i]) != i) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\ntry running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i);
1968: current_space->array += nzi;
1969: current_space->local_used += nzi;
1970: current_space->local_remaining -= nzi;
1971: current_space_lvl->array += nzi;
1972: current_space_lvl->local_used += nzi;
1973: current_space_lvl->local_remaining -= nzi;
1974: }
1976: ISRestoreIndices(isrow,&r);
1977: ISRestoreIndices(isicol,&ic);
1979: /* destroy list of free space and other temporary arrays */
1980: PetscMalloc1(bi[n]+1,&bj);
1981: PetscFreeSpaceContiguous(&free_space,bj); /* copy free_space -> bj */
1982: PetscIncompleteLLDestroy(lnk,lnkbt);
1983: PetscFreeSpaceDestroy(free_space_lvl);
1984: PetscFree2(bj_ptr,bjlvl_ptr);
1986: #if defined(PETSC_USE_INFO)
1987: {
1988: PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]);
1989: PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)f,(double)af);
1990: PetscInfo1(A,"Run with -[sub_]pc_factor_fill %g or use \n",(double)af);
1991: PetscInfo1(A,"PCFactorSetFill([sub]pc,%g);\n",(double)af);
1992: PetscInfo(A,"for best performance.\n");
1993: if (diagonal_fill) {
1994: PetscInfo1(A,"Detected and replaced %D missing diagonals\n",dcount);
1995: }
1996: }
1997: #endif
1999: /* put together the new matrix */
2000: MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,NULL);
2001: PetscLogObjectParent((PetscObject)fact,(PetscObject)isicol);
2002: b = (Mat_SeqAIJ*)(fact)->data;
2004: b->free_a = PETSC_TRUE;
2005: b->free_ij = PETSC_TRUE;
2006: b->singlemalloc = PETSC_FALSE;
2008: PetscMalloc1(bi[n],&b->a);
2009: b->j = bj;
2010: b->i = bi;
2011: for (i=0; i<n; i++) bdiag[i] += bi[i];
2012: b->diag = bdiag;
2013: b->ilen = 0;
2014: b->imax = 0;
2015: b->row = isrow;
2016: b->col = iscol;
2017: PetscObjectReference((PetscObject)isrow);
2018: PetscObjectReference((PetscObject)iscol);
2019: b->icol = isicol;
2020: PetscMalloc1(n+1,&b->solve_work);
2021: /* In b structure: Free imax, ilen, old a, old j.
2022: Allocate bdiag, solve_work, new a, new j */
2023: PetscLogObjectMemory((PetscObject)fact,(bi[n]-n) * (sizeof(PetscInt)+sizeof(PetscScalar)));
2024: b->maxnz = b->nz = bi[n];
2026: (fact)->info.factor_mallocs = reallocs;
2027: (fact)->info.fill_ratio_given = f;
2028: (fact)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]);
2029: (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_inplace;
2030: if (a->inode.size) {
2031: (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode_inplace;
2032: }
2033: return(0);
2034: }
2036: PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info)
2037: {
2038: Mat C = B;
2039: Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data;
2040: Mat_SeqSBAIJ *b=(Mat_SeqSBAIJ*)C->data;
2041: IS ip=b->row,iip = b->icol;
2043: const PetscInt *rip,*riip;
2044: PetscInt i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bdiag=b->diag,*bjtmp;
2045: PetscInt *ai=a->i,*aj=a->j;
2046: PetscInt k,jmin,jmax,*c2r,*il,col,nexti,ili,nz;
2047: MatScalar *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi;
2048: PetscBool perm_identity;
2049: FactorShiftCtx sctx;
2050: PetscReal rs;
2051: MatScalar d,*v;
2054: /* MatPivotSetUp(): initialize shift context sctx */
2055: PetscMemzero(&sctx,sizeof(FactorShiftCtx));
2057: if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */
2058: sctx.shift_top = info->zeropivot;
2059: for (i=0; i<mbs; i++) {
2060: /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
2061: d = (aa)[a->diag[i]];
2062: rs = -PetscAbsScalar(d) - PetscRealPart(d);
2063: v = aa+ai[i];
2064: nz = ai[i+1] - ai[i];
2065: for (j=0; j<nz; j++) rs += PetscAbsScalar(v[j]);
2066: if (rs>sctx.shift_top) sctx.shift_top = rs;
2067: }
2068: sctx.shift_top *= 1.1;
2069: sctx.nshift_max = 5;
2070: sctx.shift_lo = 0.;
2071: sctx.shift_hi = 1.;
2072: }
2074: ISGetIndices(ip,&rip);
2075: ISGetIndices(iip,&riip);
2077: /* allocate working arrays
2078: c2r: linked list, keep track of pivot rows for a given column. c2r[col]: head of the list for a given col
2079: il: for active k row, il[i] gives the index of the 1st nonzero entry in U[i,k:n-1] in bj and ba arrays
2080: */
2081: PetscMalloc3(mbs,&rtmp,mbs,&il,mbs,&c2r);
2083: do {
2084: sctx.newshift = PETSC_FALSE;
2086: for (i=0; i<mbs; i++) c2r[i] = mbs;
2087: if (mbs) il[0] = 0;
2089: for (k = 0; k<mbs; k++) {
2090: /* zero rtmp */
2091: nz = bi[k+1] - bi[k];
2092: bjtmp = bj + bi[k];
2093: for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
2095: /* load in initial unfactored row */
2096: bval = ba + bi[k];
2097: jmin = ai[rip[k]]; jmax = ai[rip[k]+1];
2098: for (j = jmin; j < jmax; j++) {
2099: col = riip[aj[j]];
2100: if (col >= k) { /* only take upper triangular entry */
2101: rtmp[col] = aa[j];
2102: *bval++ = 0.0; /* for in-place factorization */
2103: }
2104: }
2105: /* shift the diagonal of the matrix: ZeropivotApply() */
2106: rtmp[k] += sctx.shift_amount; /* shift the diagonal of the matrix */
2108: /* modify k-th row by adding in those rows i with U(i,k)!=0 */
2109: dk = rtmp[k];
2110: i = c2r[k]; /* first row to be added to k_th row */
2112: while (i < k) {
2113: nexti = c2r[i]; /* next row to be added to k_th row */
2115: /* compute multiplier, update diag(k) and U(i,k) */
2116: ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */
2117: uikdi = -ba[ili]*ba[bdiag[i]]; /* diagonal(k) */
2118: dk += uikdi*ba[ili]; /* update diag[k] */
2119: ba[ili] = uikdi; /* -U(i,k) */
2121: /* add multiple of row i to k-th row */
2122: jmin = ili + 1; jmax = bi[i+1];
2123: if (jmin < jmax) {
2124: for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j];
2125: /* update il and c2r for row i */
2126: il[i] = jmin;
2127: j = bj[jmin]; c2r[i] = c2r[j]; c2r[j] = i;
2128: }
2129: i = nexti;
2130: }
2132: /* copy data into U(k,:) */
2133: rs = 0.0;
2134: jmin = bi[k]; jmax = bi[k+1]-1;
2135: if (jmin < jmax) {
2136: for (j=jmin; j<jmax; j++) {
2137: col = bj[j]; ba[j] = rtmp[col]; rs += PetscAbsScalar(ba[j]);
2138: }
2139: /* add the k-th row into il and c2r */
2140: il[k] = jmin;
2141: i = bj[jmin]; c2r[k] = c2r[i]; c2r[i] = k;
2142: }
2144: /* MatPivotCheck() */
2145: sctx.rs = rs;
2146: sctx.pv = dk;
2147: MatPivotCheck(B,A,info,&sctx,i);
2148: if (sctx.newshift) break;
2149: dk = sctx.pv;
2151: ba[bdiag[k]] = 1.0/dk; /* U(k,k) */
2152: }
2153: } while (sctx.newshift);
2155: PetscFree3(rtmp,il,c2r);
2156: ISRestoreIndices(ip,&rip);
2157: ISRestoreIndices(iip,&riip);
2159: ISIdentity(ip,&perm_identity);
2160: if (perm_identity) {
2161: B->ops->solve = MatSolve_SeqSBAIJ_1_NaturalOrdering;
2162: B->ops->solvetranspose = MatSolve_SeqSBAIJ_1_NaturalOrdering;
2163: B->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering;
2164: B->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering;
2165: } else {
2166: B->ops->solve = MatSolve_SeqSBAIJ_1;
2167: B->ops->solvetranspose = MatSolve_SeqSBAIJ_1;
2168: B->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1;
2169: B->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1;
2170: }
2172: C->assembled = PETSC_TRUE;
2173: C->preallocated = PETSC_TRUE;
2175: PetscLogFlops(C->rmap->n);
2177: /* MatPivotView() */
2178: if (sctx.nshift) {
2179: if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) {
2180: PetscInfo4(A,"number of shift_pd tries %D, shift_amount %g, diagonal shifted up by %e fraction top_value %e\n",sctx.nshift,(double)sctx.shift_amount,(double)sctx.shift_fraction,(double)sctx.shift_top);
2181: } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) {
2182: PetscInfo2(A,"number of shift_nz tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);
2183: } else if (info->shifttype == (PetscReal)MAT_SHIFT_INBLOCKS) {
2184: PetscInfo2(A,"number of shift_inblocks applied %D, each shift_amount %g\n",sctx.nshift,(double)info->shiftamount);
2185: }
2186: }
2187: return(0);
2188: }
2190: PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ_inplace(Mat B,Mat A,const MatFactorInfo *info)
2191: {
2192: Mat C = B;
2193: Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data;
2194: Mat_SeqSBAIJ *b=(Mat_SeqSBAIJ*)C->data;
2195: IS ip=b->row,iip = b->icol;
2197: const PetscInt *rip,*riip;
2198: PetscInt i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bcol,*bjtmp;
2199: PetscInt *ai=a->i,*aj=a->j;
2200: PetscInt k,jmin,jmax,*jl,*il,col,nexti,ili,nz;
2201: MatScalar *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi;
2202: PetscBool perm_identity;
2203: FactorShiftCtx sctx;
2204: PetscReal rs;
2205: MatScalar d,*v;
2208: /* MatPivotSetUp(): initialize shift context sctx */
2209: PetscMemzero(&sctx,sizeof(FactorShiftCtx));
2211: if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */
2212: sctx.shift_top = info->zeropivot;
2213: for (i=0; i<mbs; i++) {
2214: /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
2215: d = (aa)[a->diag[i]];
2216: rs = -PetscAbsScalar(d) - PetscRealPart(d);
2217: v = aa+ai[i];
2218: nz = ai[i+1] - ai[i];
2219: for (j=0; j<nz; j++) rs += PetscAbsScalar(v[j]);
2220: if (rs>sctx.shift_top) sctx.shift_top = rs;
2221: }
2222: sctx.shift_top *= 1.1;
2223: sctx.nshift_max = 5;
2224: sctx.shift_lo = 0.;
2225: sctx.shift_hi = 1.;
2226: }
2228: ISGetIndices(ip,&rip);
2229: ISGetIndices(iip,&riip);
2231: /* initialization */
2232: PetscMalloc3(mbs,&rtmp,mbs,&il,mbs,&jl);
2234: do {
2235: sctx.newshift = PETSC_FALSE;
2237: for (i=0; i<mbs; i++) jl[i] = mbs;
2238: il[0] = 0;
2240: for (k = 0; k<mbs; k++) {
2241: /* zero rtmp */
2242: nz = bi[k+1] - bi[k];
2243: bjtmp = bj + bi[k];
2244: for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
2246: bval = ba + bi[k];
2247: /* initialize k-th row by the perm[k]-th row of A */
2248: jmin = ai[rip[k]]; jmax = ai[rip[k]+1];
2249: for (j = jmin; j < jmax; j++) {
2250: col = riip[aj[j]];
2251: if (col >= k) { /* only take upper triangular entry */
2252: rtmp[col] = aa[j];
2253: *bval++ = 0.0; /* for in-place factorization */
2254: }
2255: }
2256: /* shift the diagonal of the matrix */
2257: if (sctx.nshift) rtmp[k] += sctx.shift_amount;
2259: /* modify k-th row by adding in those rows i with U(i,k)!=0 */
2260: dk = rtmp[k];
2261: i = jl[k]; /* first row to be added to k_th row */
2263: while (i < k) {
2264: nexti = jl[i]; /* next row to be added to k_th row */
2266: /* compute multiplier, update diag(k) and U(i,k) */
2267: ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */
2268: uikdi = -ba[ili]*ba[bi[i]]; /* diagonal(k) */
2269: dk += uikdi*ba[ili];
2270: ba[ili] = uikdi; /* -U(i,k) */
2272: /* add multiple of row i to k-th row */
2273: jmin = ili + 1; jmax = bi[i+1];
2274: if (jmin < jmax) {
2275: for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j];
2276: /* update il and jl for row i */
2277: il[i] = jmin;
2278: j = bj[jmin]; jl[i] = jl[j]; jl[j] = i;
2279: }
2280: i = nexti;
2281: }
2283: /* shift the diagonals when zero pivot is detected */
2284: /* compute rs=sum of abs(off-diagonal) */
2285: rs = 0.0;
2286: jmin = bi[k]+1;
2287: nz = bi[k+1] - jmin;
2288: bcol = bj + jmin;
2289: for (j=0; j<nz; j++) {
2290: rs += PetscAbsScalar(rtmp[bcol[j]]);
2291: }
2293: sctx.rs = rs;
2294: sctx.pv = dk;
2295: MatPivotCheck(B,A,info,&sctx,k);
2296: if (sctx.newshift) break;
2297: dk = sctx.pv;
2299: /* copy data into U(k,:) */
2300: ba[bi[k]] = 1.0/dk; /* U(k,k) */
2301: jmin = bi[k]+1; jmax = bi[k+1];
2302: if (jmin < jmax) {
2303: for (j=jmin; j<jmax; j++) {
2304: col = bj[j]; ba[j] = rtmp[col];
2305: }
2306: /* add the k-th row into il and jl */
2307: il[k] = jmin;
2308: i = bj[jmin]; jl[k] = jl[i]; jl[i] = k;
2309: }
2310: }
2311: } while (sctx.newshift);
2313: PetscFree3(rtmp,il,jl);
2314: ISRestoreIndices(ip,&rip);
2315: ISRestoreIndices(iip,&riip);
2317: ISIdentity(ip,&perm_identity);
2318: if (perm_identity) {
2319: B->ops->solve = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace;
2320: B->ops->solvetranspose = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace;
2321: B->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering_inplace;
2322: B->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering_inplace;
2323: } else {
2324: B->ops->solve = MatSolve_SeqSBAIJ_1_inplace;
2325: B->ops->solvetranspose = MatSolve_SeqSBAIJ_1_inplace;
2326: B->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1_inplace;
2327: B->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1_inplace;
2328: }
2330: C->assembled = PETSC_TRUE;
2331: C->preallocated = PETSC_TRUE;
2333: PetscLogFlops(C->rmap->n);
2334: if (sctx.nshift) {
2335: if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) {
2336: PetscInfo2(A,"number of shiftnz tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);
2337: } else if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) {
2338: PetscInfo2(A,"number of shiftpd tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);
2339: }
2340: }
2341: return(0);
2342: }
2344: /*
2345: icc() under revised new data structure.
2346: Factored arrays bj and ba are stored as
2347: U(0,:),...,U(i,:),U(n-1,:)
2349: ui=fact->i is an array of size n+1, in which
2350: ui+
2351: ui[i]: points to 1st entry of U(i,:),i=0,...,n-1
2352: ui[n]: points to U(n-1,n-1)+1
2354: udiag=fact->diag is an array of size n,in which
2355: udiag[i]: points to diagonal of U(i,:), i=0,...,n-1
2357: U(i,:) contains udiag[i] as its last entry, i.e.,
2358: U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i])
2359: */
2361: PetscErrorCode MatICCFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
2362: {
2363: Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
2364: Mat_SeqSBAIJ *b;
2365: PetscErrorCode ierr;
2366: PetscBool perm_identity,missing;
2367: PetscInt reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag;
2368: const PetscInt *rip,*riip;
2369: PetscInt jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow;
2370: PetscInt nlnk,*lnk,*lnk_lvl=NULL,d;
2371: PetscInt ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr;
2372: PetscReal fill =info->fill,levels=info->levels;
2373: PetscFreeSpaceList free_space =NULL,current_space=NULL;
2374: PetscFreeSpaceList free_space_lvl=NULL,current_space_lvl=NULL;
2375: PetscBT lnkbt;
2376: IS iperm;
2379: if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n);
2380: MatMissingDiagonal(A,&missing,&d);
2381: if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d);
2382: ISIdentity(perm,&perm_identity);
2383: ISInvertPermutation(perm,PETSC_DECIDE,&iperm);
2385: PetscMalloc1(am+1,&ui);
2386: PetscMalloc1(am+1,&udiag);
2387: ui[0] = 0;
2389: /* ICC(0) without matrix ordering: simply rearrange column indices */
2390: if (!levels && perm_identity) {
2391: for (i=0; i<am; i++) {
2392: ncols = ai[i+1] - a->diag[i];
2393: ui[i+1] = ui[i] + ncols;
2394: udiag[i] = ui[i+1] - 1; /* points to the last entry of U(i,:) */
2395: }
2396: PetscMalloc1(ui[am]+1,&uj);
2397: cols = uj;
2398: for (i=0; i<am; i++) {
2399: aj = a->j + a->diag[i] + 1; /* 1st entry of U(i,:) without diagonal */
2400: ncols = ai[i+1] - a->diag[i] -1;
2401: for (j=0; j<ncols; j++) *cols++ = aj[j];
2402: *cols++ = i; /* diagoanl is located as the last entry of U(i,:) */
2403: }
2404: } else { /* case: levels>0 || (levels=0 && !perm_identity) */
2405: ISGetIndices(iperm,&riip);
2406: ISGetIndices(perm,&rip);
2408: /* initialization */
2409: PetscMalloc1(am+1,&ajtmp);
2411: /* jl: linked list for storing indices of the pivot rows
2412: il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
2413: PetscMalloc4(am,&uj_ptr,am,&uj_lvl_ptr,am,&jl,am,&il);
2414: for (i=0; i<am; i++) {
2415: jl[i] = am; il[i] = 0;
2416: }
2418: /* create and initialize a linked list for storing column indices of the active row k */
2419: nlnk = am + 1;
2420: PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);
2422: /* initial FreeSpace size is fill*(ai[am]+am)/2 */
2423: PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,(ai[am]+am)/2),&free_space);
2424: current_space = free_space;
2425: PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,(ai[am]+am)/2),&free_space_lvl);
2426: current_space_lvl = free_space_lvl;
2428: for (k=0; k<am; k++) { /* for each active row k */
2429: /* initialize lnk by the column indices of row rip[k] of A */
2430: nzk = 0;
2431: ncols = ai[rip[k]+1] - ai[rip[k]];
2432: if (!ncols) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k);
2433: ncols_upper = 0;
2434: for (j=0; j<ncols; j++) {
2435: i = *(aj + ai[rip[k]] + j); /* unpermuted column index */
2436: if (riip[i] >= k) { /* only take upper triangular entry */
2437: ajtmp[ncols_upper] = i;
2438: ncols_upper++;
2439: }
2440: }
2441: PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);
2442: nzk += nlnk;
2444: /* update lnk by computing fill-in for each pivot row to be merged in */
2445: prow = jl[k]; /* 1st pivot row */
2447: while (prow < k) {
2448: nextprow = jl[prow];
2450: /* merge prow into k-th row */
2451: jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */
2452: jmax = ui[prow+1];
2453: ncols = jmax-jmin;
2454: i = jmin - ui[prow];
2455: cols = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */
2456: uj = uj_lvl_ptr[prow] + i; /* levels of cols */
2457: j = *(uj - 1);
2458: PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);
2459: nzk += nlnk;
2461: /* update il and jl for prow */
2462: if (jmin < jmax) {
2463: il[prow] = jmin;
2464: j = *cols; jl[prow] = jl[j]; jl[j] = prow;
2465: }
2466: prow = nextprow;
2467: }
2469: /* if free space is not available, make more free space */
2470: if (current_space->local_remaining<nzk) {
2471: i = am - k + 1; /* num of unfactored rows */
2472: i = PetscIntMultTruncate(i,PetscMin(nzk, i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */
2473: PetscFreeSpaceGet(i,¤t_space);
2474: PetscFreeSpaceGet(i,¤t_space_lvl);
2475: reallocs++;
2476: }
2478: /* copy data into free_space and free_space_lvl, then initialize lnk */
2479: if (nzk == 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k);
2480: PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);
2482: /* add the k-th row into il and jl */
2483: if (nzk > 1) {
2484: i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
2485: jl[k] = jl[i]; jl[i] = k;
2486: il[k] = ui[k] + 1;
2487: }
2488: uj_ptr[k] = current_space->array;
2489: uj_lvl_ptr[k] = current_space_lvl->array;
2491: current_space->array += nzk;
2492: current_space->local_used += nzk;
2493: current_space->local_remaining -= nzk;
2495: current_space_lvl->array += nzk;
2496: current_space_lvl->local_used += nzk;
2497: current_space_lvl->local_remaining -= nzk;
2499: ui[k+1] = ui[k] + nzk;
2500: }
2502: ISRestoreIndices(perm,&rip);
2503: ISRestoreIndices(iperm,&riip);
2504: PetscFree4(uj_ptr,uj_lvl_ptr,jl,il);
2505: PetscFree(ajtmp);
2507: /* copy free_space into uj and free free_space; set ui, uj, udiag in new datastructure; */
2508: PetscMalloc1(ui[am]+1,&uj);
2509: PetscFreeSpaceContiguous_Cholesky(&free_space,uj,am,ui,udiag); /* store matrix factor */
2510: PetscIncompleteLLDestroy(lnk,lnkbt);
2511: PetscFreeSpaceDestroy(free_space_lvl);
2513: } /* end of case: levels>0 || (levels=0 && !perm_identity) */
2515: /* put together the new matrix in MATSEQSBAIJ format */
2516: b = (Mat_SeqSBAIJ*)(fact)->data;
2517: b->singlemalloc = PETSC_FALSE;
2519: PetscMalloc1(ui[am]+1,&b->a);
2521: b->j = uj;
2522: b->i = ui;
2523: b->diag = udiag;
2524: b->free_diag = PETSC_TRUE;
2525: b->ilen = 0;
2526: b->imax = 0;
2527: b->row = perm;
2528: b->col = perm;
2529: PetscObjectReference((PetscObject)perm);
2530: PetscObjectReference((PetscObject)perm);
2531: b->icol = iperm;
2532: b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
2534: PetscMalloc1(am+1,&b->solve_work);
2535: PetscLogObjectMemory((PetscObject)fact,ui[am]*(sizeof(PetscInt)+sizeof(MatScalar)));
2537: b->maxnz = b->nz = ui[am];
2538: b->free_a = PETSC_TRUE;
2539: b->free_ij = PETSC_TRUE;
2541: fact->info.factor_mallocs = reallocs;
2542: fact->info.fill_ratio_given = fill;
2543: if (ai[am] != 0) {
2544: /* nonzeros in lower triangular part of A (including diagonals) = (ai[am]+am)/2 */
2545: fact->info.fill_ratio_needed = ((PetscReal)2*ui[am])/(ai[am]+am);
2546: } else {
2547: fact->info.fill_ratio_needed = 0.0;
2548: }
2549: #if defined(PETSC_USE_INFO)
2550: if (ai[am] != 0) {
2551: PetscReal af = fact->info.fill_ratio_needed;
2552: PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)fill,(double)af);
2553: PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);
2554: PetscInfo1(A,"PCFactorSetFill(pc,%g) for best performance.\n",(double)af);
2555: } else {
2556: PetscInfo(A,"Empty matrix.\n");
2557: }
2558: #endif
2559: fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ;
2560: return(0);
2561: }
2563: PetscErrorCode MatICCFactorSymbolic_SeqAIJ_inplace(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
2564: {
2565: Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
2566: Mat_SeqSBAIJ *b;
2567: PetscErrorCode ierr;
2568: PetscBool perm_identity,missing;
2569: PetscInt reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag;
2570: const PetscInt *rip,*riip;
2571: PetscInt jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow;
2572: PetscInt nlnk,*lnk,*lnk_lvl=NULL,d;
2573: PetscInt ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr;
2574: PetscReal fill =info->fill,levels=info->levels;
2575: PetscFreeSpaceList free_space =NULL,current_space=NULL;
2576: PetscFreeSpaceList free_space_lvl=NULL,current_space_lvl=NULL;
2577: PetscBT lnkbt;
2578: IS iperm;
2581: if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n);
2582: MatMissingDiagonal(A,&missing,&d);
2583: if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d);
2584: ISIdentity(perm,&perm_identity);
2585: ISInvertPermutation(perm,PETSC_DECIDE,&iperm);
2587: PetscMalloc1(am+1,&ui);
2588: PetscMalloc1(am+1,&udiag);
2589: ui[0] = 0;
2591: /* ICC(0) without matrix ordering: simply copies fill pattern */
2592: if (!levels && perm_identity) {
2594: for (i=0; i<am; i++) {
2595: ui[i+1] = ui[i] + ai[i+1] - a->diag[i];
2596: udiag[i] = ui[i];
2597: }
2598: PetscMalloc1(ui[am]+1,&uj);
2599: cols = uj;
2600: for (i=0; i<am; i++) {
2601: aj = a->j + a->diag[i];
2602: ncols = ui[i+1] - ui[i];
2603: for (j=0; j<ncols; j++) *cols++ = *aj++;
2604: }
2605: } else { /* case: levels>0 || (levels=0 && !perm_identity) */
2606: ISGetIndices(iperm,&riip);
2607: ISGetIndices(perm,&rip);
2609: /* initialization */
2610: PetscMalloc1(am+1,&ajtmp);
2612: /* jl: linked list for storing indices of the pivot rows
2613: il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
2614: PetscMalloc4(am,&uj_ptr,am,&uj_lvl_ptr,am,&jl,am,&il);
2615: for (i=0; i<am; i++) {
2616: jl[i] = am; il[i] = 0;
2617: }
2619: /* create and initialize a linked list for storing column indices of the active row k */
2620: nlnk = am + 1;
2621: PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);
2623: /* initial FreeSpace size is fill*(ai[am]+1) */
2624: PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,ai[am]+1),&free_space);
2625: current_space = free_space;
2626: PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,ai[am]+1),&free_space_lvl);
2627: current_space_lvl = free_space_lvl;
2629: for (k=0; k<am; k++) { /* for each active row k */
2630: /* initialize lnk by the column indices of row rip[k] of A */
2631: nzk = 0;
2632: ncols = ai[rip[k]+1] - ai[rip[k]];
2633: if (!ncols) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k);
2634: ncols_upper = 0;
2635: for (j=0; j<ncols; j++) {
2636: i = *(aj + ai[rip[k]] + j); /* unpermuted column index */
2637: if (riip[i] >= k) { /* only take upper triangular entry */
2638: ajtmp[ncols_upper] = i;
2639: ncols_upper++;
2640: }
2641: }
2642: PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);
2643: nzk += nlnk;
2645: /* update lnk by computing fill-in for each pivot row to be merged in */
2646: prow = jl[k]; /* 1st pivot row */
2648: while (prow < k) {
2649: nextprow = jl[prow];
2651: /* merge prow into k-th row */
2652: jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */
2653: jmax = ui[prow+1];
2654: ncols = jmax-jmin;
2655: i = jmin - ui[prow];
2656: cols = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */
2657: uj = uj_lvl_ptr[prow] + i; /* levels of cols */
2658: j = *(uj - 1);
2659: PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);
2660: nzk += nlnk;
2662: /* update il and jl for prow */
2663: if (jmin < jmax) {
2664: il[prow] = jmin;
2665: j = *cols; jl[prow] = jl[j]; jl[j] = prow;
2666: }
2667: prow = nextprow;
2668: }
2670: /* if free space is not available, make more free space */
2671: if (current_space->local_remaining<nzk) {
2672: i = am - k + 1; /* num of unfactored rows */
2673: i = PetscIntMultTruncate(i,PetscMin(nzk, i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */
2674: PetscFreeSpaceGet(i,¤t_space);
2675: PetscFreeSpaceGet(i,¤t_space_lvl);
2676: reallocs++;
2677: }
2679: /* copy data into free_space and free_space_lvl, then initialize lnk */
2680: if (!nzk) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k);
2681: PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);
2683: /* add the k-th row into il and jl */
2684: if (nzk > 1) {
2685: i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
2686: jl[k] = jl[i]; jl[i] = k;
2687: il[k] = ui[k] + 1;
2688: }
2689: uj_ptr[k] = current_space->array;
2690: uj_lvl_ptr[k] = current_space_lvl->array;
2692: current_space->array += nzk;
2693: current_space->local_used += nzk;
2694: current_space->local_remaining -= nzk;
2696: current_space_lvl->array += nzk;
2697: current_space_lvl->local_used += nzk;
2698: current_space_lvl->local_remaining -= nzk;
2700: ui[k+1] = ui[k] + nzk;
2701: }
2703: #if defined(PETSC_USE_INFO)
2704: if (ai[am] != 0) {
2705: PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]);
2706: PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)fill,(double)af);
2707: PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);
2708: PetscInfo1(A,"PCFactorSetFill(pc,%g) for best performance.\n",(double)af);
2709: } else {
2710: PetscInfo(A,"Empty matrix.\n");
2711: }
2712: #endif
2714: ISRestoreIndices(perm,&rip);
2715: ISRestoreIndices(iperm,&riip);
2716: PetscFree4(uj_ptr,uj_lvl_ptr,jl,il);
2717: PetscFree(ajtmp);
2719: /* destroy list of free space and other temporary array(s) */
2720: PetscMalloc1(ui[am]+1,&uj);
2721: PetscFreeSpaceContiguous(&free_space,uj);
2722: PetscIncompleteLLDestroy(lnk,lnkbt);
2723: PetscFreeSpaceDestroy(free_space_lvl);
2725: } /* end of case: levels>0 || (levels=0 && !perm_identity) */
2727: /* put together the new matrix in MATSEQSBAIJ format */
2729: b = (Mat_SeqSBAIJ*)fact->data;
2730: b->singlemalloc = PETSC_FALSE;
2732: PetscMalloc1(ui[am]+1,&b->a);
2734: b->j = uj;
2735: b->i = ui;
2736: b->diag = udiag;
2737: b->free_diag = PETSC_TRUE;
2738: b->ilen = 0;
2739: b->imax = 0;
2740: b->row = perm;
2741: b->col = perm;
2743: PetscObjectReference((PetscObject)perm);
2744: PetscObjectReference((PetscObject)perm);
2746: b->icol = iperm;
2747: b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
2748: PetscMalloc1(am+1,&b->solve_work);
2749: PetscLogObjectMemory((PetscObject)fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));
2750: b->maxnz = b->nz = ui[am];
2751: b->free_a = PETSC_TRUE;
2752: b->free_ij = PETSC_TRUE;
2754: fact->info.factor_mallocs = reallocs;
2755: fact->info.fill_ratio_given = fill;
2756: if (ai[am] != 0) {
2757: fact->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]);
2758: } else {
2759: fact->info.fill_ratio_needed = 0.0;
2760: }
2761: fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ_inplace;
2762: return(0);
2763: }
2765: PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
2766: {
2767: Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
2768: Mat_SeqSBAIJ *b;
2769: PetscErrorCode ierr;
2770: PetscBool perm_identity,missing;
2771: PetscReal fill = info->fill;
2772: const PetscInt *rip,*riip;
2773: PetscInt i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow;
2774: PetscInt *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow;
2775: PetscInt nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr,*udiag;
2776: PetscFreeSpaceList free_space=NULL,current_space=NULL;
2777: PetscBT lnkbt;
2778: IS iperm;
2781: if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n);
2782: MatMissingDiagonal(A,&missing,&i);
2783: if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i);
2785: /* check whether perm is the identity mapping */
2786: ISIdentity(perm,&perm_identity);
2787: ISInvertPermutation(perm,PETSC_DECIDE,&iperm);
2788: ISGetIndices(iperm,&riip);
2789: ISGetIndices(perm,&rip);
2791: /* initialization */
2792: PetscMalloc1(am+1,&ui);
2793: PetscMalloc1(am+1,&udiag);
2794: ui[0] = 0;
2796: /* jl: linked list for storing indices of the pivot rows
2797: il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
2798: PetscMalloc4(am,&ui_ptr,am,&jl,am,&il,am,&cols);
2799: for (i=0; i<am; i++) {
2800: jl[i] = am; il[i] = 0;
2801: }
2803: /* create and initialize a linked list for storing column indices of the active row k */
2804: nlnk = am + 1;
2805: PetscLLCreate(am,am,nlnk,lnk,lnkbt);
2807: /* initial FreeSpace size is fill*(ai[am]+am)/2 */
2808: PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,(ai[am]+am)/2),&free_space);
2809: current_space = free_space;
2811: for (k=0; k<am; k++) { /* for each active row k */
2812: /* initialize lnk by the column indices of row rip[k] of A */
2813: nzk = 0;
2814: ncols = ai[rip[k]+1] - ai[rip[k]];
2815: if (!ncols) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k);
2816: ncols_upper = 0;
2817: for (j=0; j<ncols; j++) {
2818: i = riip[*(aj + ai[rip[k]] + j)];
2819: if (i >= k) { /* only take upper triangular entry */
2820: cols[ncols_upper] = i;
2821: ncols_upper++;
2822: }
2823: }
2824: PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);
2825: nzk += nlnk;
2827: /* update lnk by computing fill-in for each pivot row to be merged in */
2828: prow = jl[k]; /* 1st pivot row */
2830: while (prow < k) {
2831: nextprow = jl[prow];
2832: /* merge prow into k-th row */
2833: jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */
2834: jmax = ui[prow+1];
2835: ncols = jmax-jmin;
2836: uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */
2837: PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);
2838: nzk += nlnk;
2840: /* update il and jl for prow */
2841: if (jmin < jmax) {
2842: il[prow] = jmin;
2843: j = *uj_ptr;
2844: jl[prow] = jl[j];
2845: jl[j] = prow;
2846: }
2847: prow = nextprow;
2848: }
2850: /* if free space is not available, make more free space */
2851: if (current_space->local_remaining<nzk) {
2852: i = am - k + 1; /* num of unfactored rows */
2853: i = PetscIntMultTruncate(i,PetscMin(nzk,i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */
2854: PetscFreeSpaceGet(i,¤t_space);
2855: reallocs++;
2856: }
2858: /* copy data into free space, then initialize lnk */
2859: PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);
2861: /* add the k-th row into il and jl */
2862: if (nzk > 1) {
2863: i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
2864: jl[k] = jl[i]; jl[i] = k;
2865: il[k] = ui[k] + 1;
2866: }
2867: ui_ptr[k] = current_space->array;
2869: current_space->array += nzk;
2870: current_space->local_used += nzk;
2871: current_space->local_remaining -= nzk;
2873: ui[k+1] = ui[k] + nzk;
2874: }
2876: ISRestoreIndices(perm,&rip);
2877: ISRestoreIndices(iperm,&riip);
2878: PetscFree4(ui_ptr,jl,il,cols);
2880: /* copy free_space into uj and free free_space; set ui, uj, udiag in new datastructure; */
2881: PetscMalloc1(ui[am]+1,&uj);
2882: PetscFreeSpaceContiguous_Cholesky(&free_space,uj,am,ui,udiag); /* store matrix factor */
2883: PetscLLDestroy(lnk,lnkbt);
2885: /* put together the new matrix in MATSEQSBAIJ format */
2887: b = (Mat_SeqSBAIJ*)fact->data;
2888: b->singlemalloc = PETSC_FALSE;
2889: b->free_a = PETSC_TRUE;
2890: b->free_ij = PETSC_TRUE;
2892: PetscMalloc1(ui[am]+1,&b->a);
2894: b->j = uj;
2895: b->i = ui;
2896: b->diag = udiag;
2897: b->free_diag = PETSC_TRUE;
2898: b->ilen = 0;
2899: b->imax = 0;
2900: b->row = perm;
2901: b->col = perm;
2903: PetscObjectReference((PetscObject)perm);
2904: PetscObjectReference((PetscObject)perm);
2906: b->icol = iperm;
2907: b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
2909: PetscMalloc1(am+1,&b->solve_work);
2910: PetscLogObjectMemory((PetscObject)fact,ui[am]*(sizeof(PetscInt)+sizeof(MatScalar)));
2912: b->maxnz = b->nz = ui[am];
2914: fact->info.factor_mallocs = reallocs;
2915: fact->info.fill_ratio_given = fill;
2916: if (ai[am] != 0) {
2917: /* nonzeros in lower triangular part of A (including diagonals) = (ai[am]+am)/2 */
2918: fact->info.fill_ratio_needed = ((PetscReal)2*ui[am])/(ai[am]+am);
2919: } else {
2920: fact->info.fill_ratio_needed = 0.0;
2921: }
2922: #if defined(PETSC_USE_INFO)
2923: if (ai[am] != 0) {
2924: PetscReal af = fact->info.fill_ratio_needed;
2925: PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)fill,(double)af);
2926: PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);
2927: PetscInfo1(A,"PCFactorSetFill(pc,%g) for best performance.\n",(double)af);
2928: } else {
2929: PetscInfo(A,"Empty matrix.\n");
2930: }
2931: #endif
2932: fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ;
2933: return(0);
2934: }
2936: PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ_inplace(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
2937: {
2938: Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
2939: Mat_SeqSBAIJ *b;
2940: PetscErrorCode ierr;
2941: PetscBool perm_identity,missing;
2942: PetscReal fill = info->fill;
2943: const PetscInt *rip,*riip;
2944: PetscInt i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow;
2945: PetscInt *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow;
2946: PetscInt nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr;
2947: PetscFreeSpaceList free_space=NULL,current_space=NULL;
2948: PetscBT lnkbt;
2949: IS iperm;
2952: if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n);
2953: MatMissingDiagonal(A,&missing,&i);
2954: if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i);
2956: /* check whether perm is the identity mapping */
2957: ISIdentity(perm,&perm_identity);
2958: ISInvertPermutation(perm,PETSC_DECIDE,&iperm);
2959: ISGetIndices(iperm,&riip);
2960: ISGetIndices(perm,&rip);
2962: /* initialization */
2963: PetscMalloc1(am+1,&ui);
2964: ui[0] = 0;
2966: /* jl: linked list for storing indices of the pivot rows
2967: il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
2968: PetscMalloc4(am,&ui_ptr,am,&jl,am,&il,am,&cols);
2969: for (i=0; i<am; i++) {
2970: jl[i] = am; il[i] = 0;
2971: }
2973: /* create and initialize a linked list for storing column indices of the active row k */
2974: nlnk = am + 1;
2975: PetscLLCreate(am,am,nlnk,lnk,lnkbt);
2977: /* initial FreeSpace size is fill*(ai[am]+1) */
2978: PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,ai[am]+1),&free_space);
2979: current_space = free_space;
2981: for (k=0; k<am; k++) { /* for each active row k */
2982: /* initialize lnk by the column indices of row rip[k] of A */
2983: nzk = 0;
2984: ncols = ai[rip[k]+1] - ai[rip[k]];
2985: if (!ncols) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_MAT_CH_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",rip[k],k);
2986: ncols_upper = 0;
2987: for (j=0; j<ncols; j++) {
2988: i = riip[*(aj + ai[rip[k]] + j)];
2989: if (i >= k) { /* only take upper triangular entry */
2990: cols[ncols_upper] = i;
2991: ncols_upper++;
2992: }
2993: }
2994: PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);
2995: nzk += nlnk;
2997: /* update lnk by computing fill-in for each pivot row to be merged in */
2998: prow = jl[k]; /* 1st pivot row */
3000: while (prow < k) {
3001: nextprow = jl[prow];
3002: /* merge prow into k-th row */
3003: jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */
3004: jmax = ui[prow+1];
3005: ncols = jmax-jmin;
3006: uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */
3007: PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);
3008: nzk += nlnk;
3010: /* update il and jl for prow */
3011: if (jmin < jmax) {
3012: il[prow] = jmin;
3013: j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow;
3014: }
3015: prow = nextprow;
3016: }
3018: /* if free space is not available, make more free space */
3019: if (current_space->local_remaining<nzk) {
3020: i = am - k + 1; /* num of unfactored rows */
3021: i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */
3022: PetscFreeSpaceGet(i,¤t_space);
3023: reallocs++;
3024: }
3026: /* copy data into free space, then initialize lnk */
3027: PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);
3029: /* add the k-th row into il and jl */
3030: if (nzk-1 > 0) {
3031: i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
3032: jl[k] = jl[i]; jl[i] = k;
3033: il[k] = ui[k] + 1;
3034: }
3035: ui_ptr[k] = current_space->array;
3037: current_space->array += nzk;
3038: current_space->local_used += nzk;
3039: current_space->local_remaining -= nzk;
3041: ui[k+1] = ui[k] + nzk;
3042: }
3044: #if defined(PETSC_USE_INFO)
3045: if (ai[am] != 0) {
3046: PetscReal af = (PetscReal)(ui[am])/((PetscReal)ai[am]);
3047: PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)fill,(double)af);
3048: PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);
3049: PetscInfo1(A,"PCFactorSetFill(pc,%g) for best performance.\n",(double)af);
3050: } else {
3051: PetscInfo(A,"Empty matrix.\n");
3052: }
3053: #endif
3055: ISRestoreIndices(perm,&rip);
3056: ISRestoreIndices(iperm,&riip);
3057: PetscFree4(ui_ptr,jl,il,cols);
3059: /* destroy list of free space and other temporary array(s) */
3060: PetscMalloc1(ui[am]+1,&uj);
3061: PetscFreeSpaceContiguous(&free_space,uj);
3062: PetscLLDestroy(lnk,lnkbt);
3064: /* put together the new matrix in MATSEQSBAIJ format */
3066: b = (Mat_SeqSBAIJ*)fact->data;
3067: b->singlemalloc = PETSC_FALSE;
3068: b->free_a = PETSC_TRUE;
3069: b->free_ij = PETSC_TRUE;
3071: PetscMalloc1(ui[am]+1,&b->a);
3073: b->j = uj;
3074: b->i = ui;
3075: b->diag = 0;
3076: b->ilen = 0;
3077: b->imax = 0;
3078: b->row = perm;
3079: b->col = perm;
3081: PetscObjectReference((PetscObject)perm);
3082: PetscObjectReference((PetscObject)perm);
3084: b->icol = iperm;
3085: b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
3087: PetscMalloc1(am+1,&b->solve_work);
3088: PetscLogObjectMemory((PetscObject)fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));
3089: b->maxnz = b->nz = ui[am];
3091: fact->info.factor_mallocs = reallocs;
3092: fact->info.fill_ratio_given = fill;
3093: if (ai[am] != 0) {
3094: fact->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]);
3095: } else {
3096: fact->info.fill_ratio_needed = 0.0;
3097: }
3098: fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ_inplace;
3099: return(0);
3100: }
3102: PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering(Mat A,Vec bb,Vec xx)
3103: {
3104: Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
3105: PetscErrorCode ierr;
3106: PetscInt n = A->rmap->n;
3107: const PetscInt *ai = a->i,*aj = a->j,*adiag = a->diag,*vi;
3108: PetscScalar *x,sum;
3109: const PetscScalar *b;
3110: const MatScalar *aa = a->a,*v;
3111: PetscInt i,nz;
3114: if (!n) return(0);
3116: VecGetArrayRead(bb,&b);
3117: VecGetArray(xx,&x);
3119: /* forward solve the lower triangular */
3120: x[0] = b[0];
3121: v = aa;
3122: vi = aj;
3123: for (i=1; i<n; i++) {
3124: nz = ai[i+1] - ai[i];
3125: sum = b[i];
3126: PetscSparseDenseMinusDot(sum,x,v,vi,nz);
3127: v += nz;
3128: vi += nz;
3129: x[i] = sum;
3130: }
3132: /* backward solve the upper triangular */
3133: for (i=n-1; i>=0; i--) {
3134: v = aa + adiag[i+1] + 1;
3135: vi = aj + adiag[i+1] + 1;
3136: nz = adiag[i] - adiag[i+1]-1;
3137: sum = x[i];
3138: PetscSparseDenseMinusDot(sum,x,v,vi,nz);
3139: x[i] = sum*v[nz]; /* x[i]=aa[adiag[i]]*sum; v++; */
3140: }
3142: PetscLogFlops(2.0*a->nz - A->cmap->n);
3143: VecRestoreArrayRead(bb,&b);
3144: VecRestoreArray(xx,&x);
3145: return(0);
3146: }
3148: PetscErrorCode MatSolve_SeqAIJ(Mat A,Vec bb,Vec xx)
3149: {
3150: Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
3151: IS iscol = a->col,isrow = a->row;
3152: PetscErrorCode ierr;
3153: PetscInt i,n=A->rmap->n,*vi,*ai=a->i,*aj=a->j,*adiag = a->diag,nz;
3154: const PetscInt *rout,*cout,*r,*c;
3155: PetscScalar *x,*tmp,sum;
3156: const PetscScalar *b;
3157: const MatScalar *aa = a->a,*v;
3160: if (!n) return(0);
3162: VecGetArrayRead(bb,&b);
3163: VecGetArray(xx,&x);
3164: tmp = a->solve_work;
3166: ISGetIndices(isrow,&rout); r = rout;
3167: ISGetIndices(iscol,&cout); c = cout;
3169: /* forward solve the lower triangular */
3170: tmp[0] = b[r[0]];
3171: v = aa;
3172: vi = aj;
3173: for (i=1; i<n; i++) {
3174: nz = ai[i+1] - ai[i];
3175: sum = b[r[i]];
3176: PetscSparseDenseMinusDot(sum,tmp,v,vi,nz);
3177: tmp[i] = sum;
3178: v += nz; vi += nz;
3179: }
3181: /* backward solve the upper triangular */
3182: for (i=n-1; i>=0; i--) {
3183: v = aa + adiag[i+1]+1;
3184: vi = aj + adiag[i+1]+1;
3185: nz = adiag[i]-adiag[i+1]-1;
3186: sum = tmp[i];
3187: PetscSparseDenseMinusDot(sum,tmp,v,vi,nz);
3188: x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */
3189: }
3191: ISRestoreIndices(isrow,&rout);
3192: ISRestoreIndices(iscol,&cout);
3193: VecRestoreArrayRead(bb,&b);
3194: VecRestoreArray(xx,&x);
3195: PetscLogFlops(2*a->nz - A->cmap->n);
3196: return(0);
3197: }
3199: /*
3200: This will get a new name and become a varient of MatILUFactor_SeqAIJ() there is no longer separate functions in the matrix function table for dt factors
3201: */
3202: PetscErrorCode MatILUDTFactor_SeqAIJ(Mat A,IS isrow,IS iscol,const MatFactorInfo *info,Mat *fact)
3203: {
3204: Mat B = *fact;
3205: Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b;
3206: IS isicol;
3208: const PetscInt *r,*ic;
3209: PetscInt i,n=A->rmap->n,*ai=a->i,*aj=a->j,*ajtmp,*adiag;
3210: PetscInt *bi,*bj,*bdiag,*bdiag_rev;
3211: PetscInt row,nzi,nzi_bl,nzi_bu,*im,nzi_al,nzi_au;
3212: PetscInt nlnk,*lnk;
3213: PetscBT lnkbt;
3214: PetscBool row_identity,icol_identity;
3215: MatScalar *aatmp,*pv,*batmp,*ba,*rtmp,*pc,multiplier,*vtmp,diag_tmp;
3216: const PetscInt *ics;
3217: PetscInt j,nz,*pj,*bjtmp,k,ncut,*jtmp;
3218: PetscReal dt =info->dt,shift=info->shiftamount;
3219: PetscInt dtcount=(PetscInt)info->dtcount,nnz_max;
3220: PetscBool missing;
3223: if (dt == PETSC_DEFAULT) dt = 0.005;
3224: if (dtcount == PETSC_DEFAULT) dtcount = (PetscInt)(1.5*a->rmax);
3226: /* ------- symbolic factorization, can be reused ---------*/
3227: MatMissingDiagonal(A,&missing,&i);
3228: if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i);
3229: adiag=a->diag;
3231: ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);
3233: /* bdiag is location of diagonal in factor */
3234: PetscMalloc1(n+1,&bdiag); /* becomes b->diag */
3235: PetscMalloc1(n+1,&bdiag_rev); /* temporary */
3237: /* allocate row pointers bi */
3238: PetscMalloc1(2*n+2,&bi);
3240: /* allocate bj and ba; max num of nonzero entries is (ai[n]+2*n*dtcount+2) */
3241: if (dtcount > n-1) dtcount = n-1; /* diagonal is excluded */
3242: nnz_max = ai[n]+2*n*dtcount+2;
3244: PetscMalloc1(nnz_max+1,&bj);
3245: PetscMalloc1(nnz_max+1,&ba);
3247: /* put together the new matrix */
3248: MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,NULL);
3249: PetscLogObjectParent((PetscObject)B,(PetscObject)isicol);
3250: b = (Mat_SeqAIJ*)B->data;
3252: b->free_a = PETSC_TRUE;
3253: b->free_ij = PETSC_TRUE;
3254: b->singlemalloc = PETSC_FALSE;
3256: b->a = ba;
3257: b->j = bj;
3258: b->i = bi;
3259: b->diag = bdiag;
3260: b->ilen = 0;
3261: b->imax = 0;
3262: b->row = isrow;
3263: b->col = iscol;
3264: PetscObjectReference((PetscObject)isrow);
3265: PetscObjectReference((PetscObject)iscol);
3266: b->icol = isicol;
3268: PetscMalloc1(n+1,&b->solve_work);
3269: PetscLogObjectMemory((PetscObject)B,nnz_max*(sizeof(PetscInt)+sizeof(MatScalar)));
3270: b->maxnz = nnz_max;
3272: B->factortype = MAT_FACTOR_ILUDT;
3273: B->info.factor_mallocs = 0;
3274: B->info.fill_ratio_given = ((PetscReal)nnz_max)/((PetscReal)ai[n]);
3275: /* ------- end of symbolic factorization ---------*/
3277: ISGetIndices(isrow,&r);
3278: ISGetIndices(isicol,&ic);
3279: ics = ic;
3281: /* linked list for storing column indices of the active row */
3282: nlnk = n + 1;
3283: PetscLLCreate(n,n,nlnk,lnk,lnkbt);
3285: /* im: used by PetscLLAddSortedLU(); jtmp: working array for column indices of active row */
3286: PetscMalloc2(n,&im,n,&jtmp);
3287: /* rtmp, vtmp: working arrays for sparse and contiguous row entries of active row */
3288: PetscMalloc2(n,&rtmp,n,&vtmp);
3289: PetscMemzero(rtmp,n*sizeof(MatScalar));
3291: bi[0] = 0;
3292: bdiag[0] = nnz_max-1; /* location of diag[0] in factor B */
3293: bdiag_rev[n] = bdiag[0];
3294: bi[2*n+1] = bdiag[0]+1; /* endof bj and ba array */
3295: for (i=0; i<n; i++) {
3296: /* copy initial fill into linked list */
3297: nzi = ai[r[i]+1] - ai[r[i]];
3298: if (!nzi) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
3299: nzi_al = adiag[r[i]] - ai[r[i]];
3300: nzi_au = ai[r[i]+1] - adiag[r[i]] -1;
3301: ajtmp = aj + ai[r[i]];
3302: PetscLLAddPerm(nzi,ajtmp,ic,n,nlnk,lnk,lnkbt);
3304: /* load in initial (unfactored row) */
3305: aatmp = a->a + ai[r[i]];
3306: for (j=0; j<nzi; j++) {
3307: rtmp[ics[*ajtmp++]] = *aatmp++;
3308: }
3310: /* add pivot rows into linked list */
3311: row = lnk[n];
3312: while (row < i) {
3313: nzi_bl = bi[row+1] - bi[row] + 1;
3314: bjtmp = bj + bdiag[row+1]+1; /* points to 1st column next to the diagonal in U */
3315: PetscLLAddSortedLU(bjtmp,row,nlnk,lnk,lnkbt,i,nzi_bl,im);
3316: nzi += nlnk;
3317: row = lnk[row];
3318: }
3320: /* copy data from lnk into jtmp, then initialize lnk */
3321: PetscLLClean(n,n,nzi,lnk,jtmp,lnkbt);
3323: /* numerical factorization */
3324: bjtmp = jtmp;
3325: row = *bjtmp++; /* 1st pivot row */
3326: while (row < i) {
3327: pc = rtmp + row;
3328: pv = ba + bdiag[row]; /* 1./(diag of the pivot row) */
3329: multiplier = (*pc) * (*pv);
3330: *pc = multiplier;
3331: if (PetscAbsScalar(*pc) > dt) { /* apply tolerance dropping rule */
3332: pj = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */
3333: pv = ba + bdiag[row+1] + 1;
3334: /* if (multiplier < -1.0 or multiplier >1.0) printf("row/prow %d, %d, multiplier %g\n",i,row,multiplier); */
3335: nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */
3336: for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++);
3337: PetscLogFlops(1+2*nz);
3338: }
3339: row = *bjtmp++;
3340: }
3342: /* copy sparse rtmp into contiguous vtmp; separate L and U part */
3343: diag_tmp = rtmp[i]; /* save diagonal value - may not needed?? */
3344: nzi_bl = 0; j = 0;
3345: while (jtmp[j] < i) { /* Note: jtmp is sorted */
3346: vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0;
3347: nzi_bl++; j++;
3348: }
3349: nzi_bu = nzi - nzi_bl -1;
3350: while (j < nzi) {
3351: vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0;
3352: j++;
3353: }
3355: bjtmp = bj + bi[i];
3356: batmp = ba + bi[i];
3357: /* apply level dropping rule to L part */
3358: ncut = nzi_al + dtcount;
3359: if (ncut < nzi_bl) {
3360: PetscSortSplit(ncut,nzi_bl,vtmp,jtmp);
3361: PetscSortIntWithScalarArray(ncut,jtmp,vtmp);
3362: } else {
3363: ncut = nzi_bl;
3364: }
3365: for (j=0; j<ncut; j++) {
3366: bjtmp[j] = jtmp[j];
3367: batmp[j] = vtmp[j];
3368: /* printf(" (%d,%g),",bjtmp[j],batmp[j]); */
3369: }
3370: bi[i+1] = bi[i] + ncut;
3371: nzi = ncut + 1;
3373: /* apply level dropping rule to U part */
3374: ncut = nzi_au + dtcount;
3375: if (ncut < nzi_bu) {
3376: PetscSortSplit(ncut,nzi_bu,vtmp+nzi_bl+1,jtmp+nzi_bl+1);
3377: PetscSortIntWithScalarArray(ncut,jtmp+nzi_bl+1,vtmp+nzi_bl+1);
3378: } else {
3379: ncut = nzi_bu;
3380: }
3381: nzi += ncut;
3383: /* mark bdiagonal */
3384: bdiag[i+1] = bdiag[i] - (ncut + 1);
3385: bdiag_rev[n-i-1] = bdiag[i+1];
3386: bi[2*n - i] = bi[2*n - i +1] - (ncut + 1);
3387: bjtmp = bj + bdiag[i];
3388: batmp = ba + bdiag[i];
3389: *bjtmp = i;
3390: *batmp = diag_tmp; /* rtmp[i]; */
3391: if (*batmp == 0.0) {
3392: *batmp = dt+shift;
3393: /* printf(" row %d add shift %g\n",i,shift); */
3394: }
3395: *batmp = 1.0/(*batmp); /* invert diagonal entries for simplier triangular solves */
3396: /* printf(" (%d,%g),",*bjtmp,*batmp); */
3398: bjtmp = bj + bdiag[i+1]+1;
3399: batmp = ba + bdiag[i+1]+1;
3400: for (k=0; k<ncut; k++) {
3401: bjtmp[k] = jtmp[nzi_bl+1+k];
3402: batmp[k] = vtmp[nzi_bl+1+k];
3403: /* printf(" (%d,%g),",bjtmp[k],batmp[k]); */
3404: }
3405: /* printf("\n"); */
3407: im[i] = nzi; /* used by PetscLLAddSortedLU() */
3408: /*
3409: printf("row %d: bi %d, bdiag %d\n",i,bi[i],bdiag[i]);
3410: printf(" ----------------------------\n");
3411: */
3412: } /* for (i=0; i<n; i++) */
3413: /* printf("end of L %d, beginning of U %d\n",bi[n],bdiag[n]); */
3414: if (bi[n] >= bdiag[n]) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"end of L array %d cannot >= the beginning of U array %d",bi[n],bdiag[n]);
3416: ISRestoreIndices(isrow,&r);
3417: ISRestoreIndices(isicol,&ic);
3419: PetscLLDestroy(lnk,lnkbt);
3420: PetscFree2(im,jtmp);
3421: PetscFree2(rtmp,vtmp);
3422: PetscFree(bdiag_rev);
3424: PetscLogFlops(B->cmap->n);
3425: b->maxnz = b->nz = bi[n] + bdiag[0] - bdiag[n];
3427: ISIdentity(isrow,&row_identity);
3428: ISIdentity(isicol,&icol_identity);
3429: if (row_identity && icol_identity) {
3430: B->ops->solve = MatSolve_SeqAIJ_NaturalOrdering;
3431: } else {
3432: B->ops->solve = MatSolve_SeqAIJ;
3433: }
3435: B->ops->solveadd = 0;
3436: B->ops->solvetranspose = 0;
3437: B->ops->solvetransposeadd = 0;
3438: B->ops->matsolve = 0;
3439: B->assembled = PETSC_TRUE;
3440: B->preallocated = PETSC_TRUE;
3441: return(0);
3442: }
3444: /* a wraper of MatILUDTFactor_SeqAIJ() */
3445: /*
3446: This will get a new name and become a varient of MatILUFactor_SeqAIJ() there is no longer separate functions in the matrix function table for dt factors
3447: */
3449: PetscErrorCode MatILUDTFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS row,IS col,const MatFactorInfo *info)
3450: {
3454: MatILUDTFactor_SeqAIJ(A,row,col,info,&fact);
3455: return(0);
3456: }
3458: /*
3459: same as MatLUFactorNumeric_SeqAIJ(), except using contiguous array matrix factors
3460: - intend to replace existing MatLUFactorNumeric_SeqAIJ()
3461: */
3462: /*
3463: This will get a new name and become a varient of MatILUFactor_SeqAIJ() there is no longer separate functions in the matrix function table for dt factors
3464: */
3466: PetscErrorCode MatILUDTFactorNumeric_SeqAIJ(Mat fact,Mat A,const MatFactorInfo *info)
3467: {
3468: Mat C =fact;
3469: Mat_SeqAIJ *a =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)C->data;
3470: IS isrow = b->row,isicol = b->icol;
3472: const PetscInt *r,*ic,*ics;
3473: PetscInt i,j,k,n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
3474: PetscInt *ajtmp,*bjtmp,nz,nzl,nzu,row,*bdiag = b->diag,*pj;
3475: MatScalar *rtmp,*pc,multiplier,*v,*pv,*aa=a->a;
3476: PetscReal dt=info->dt,shift=info->shiftamount;
3477: PetscBool row_identity, col_identity;
3480: ISGetIndices(isrow,&r);
3481: ISGetIndices(isicol,&ic);
3482: PetscMalloc1(n+1,&rtmp);
3483: ics = ic;
3485: for (i=0; i<n; i++) {
3486: /* initialize rtmp array */
3487: nzl = bi[i+1] - bi[i]; /* num of nozeros in L(i,:) */
3488: bjtmp = bj + bi[i];
3489: for (j=0; j<nzl; j++) rtmp[*bjtmp++] = 0.0;
3490: rtmp[i] = 0.0;
3491: nzu = bdiag[i] - bdiag[i+1]; /* num of nozeros in U(i,:) */
3492: bjtmp = bj + bdiag[i+1] + 1;
3493: for (j=0; j<nzu; j++) rtmp[*bjtmp++] = 0.0;
3495: /* load in initial unfactored row of A */
3496: /* printf("row %d\n",i); */
3497: nz = ai[r[i]+1] - ai[r[i]];
3498: ajtmp = aj + ai[r[i]];
3499: v = aa + ai[r[i]];
3500: for (j=0; j<nz; j++) {
3501: rtmp[ics[*ajtmp++]] = v[j];
3502: /* printf(" (%d,%g),",ics[ajtmp[j]],rtmp[ics[ajtmp[j]]]); */
3503: }
3504: /* printf("\n"); */
3506: /* numerical factorization */
3507: bjtmp = bj + bi[i]; /* point to 1st entry of L(i,:) */
3508: nzl = bi[i+1] - bi[i]; /* num of entries in L(i,:) */
3509: k = 0;
3510: while (k < nzl) {
3511: row = *bjtmp++;
3512: /* printf(" prow %d\n",row); */
3513: pc = rtmp + row;
3514: pv = b->a + bdiag[row]; /* 1./(diag of the pivot row) */
3515: multiplier = (*pc) * (*pv);
3516: *pc = multiplier;
3517: if (PetscAbsScalar(multiplier) > dt) {
3518: pj = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */
3519: pv = b->a + bdiag[row+1] + 1;
3520: nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */
3521: for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++);
3522: PetscLogFlops(1+2*nz);
3523: }
3524: k++;
3525: }
3527: /* finished row so stick it into b->a */
3528: /* L-part */
3529: pv = b->a + bi[i];
3530: pj = bj + bi[i];
3531: nzl = bi[i+1] - bi[i];
3532: for (j=0; j<nzl; j++) {
3533: pv[j] = rtmp[pj[j]];
3534: /* printf(" (%d,%g),",pj[j],pv[j]); */
3535: }
3537: /* diagonal: invert diagonal entries for simplier triangular solves */
3538: if (rtmp[i] == 0.0) rtmp[i] = dt+shift;
3539: b->a[bdiag[i]] = 1.0/rtmp[i];
3540: /* printf(" (%d,%g),",i,b->a[bdiag[i]]); */
3542: /* U-part */
3543: pv = b->a + bdiag[i+1] + 1;
3544: pj = bj + bdiag[i+1] + 1;
3545: nzu = bdiag[i] - bdiag[i+1] - 1;
3546: for (j=0; j<nzu; j++) {
3547: pv[j] = rtmp[pj[j]];
3548: /* printf(" (%d,%g),",pj[j],pv[j]); */
3549: }
3550: /* printf("\n"); */
3551: }
3553: PetscFree(rtmp);
3554: ISRestoreIndices(isicol,&ic);
3555: ISRestoreIndices(isrow,&r);
3557: ISIdentity(isrow,&row_identity);
3558: ISIdentity(isicol,&col_identity);
3559: if (row_identity && col_identity) {
3560: C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering;
3561: } else {
3562: C->ops->solve = MatSolve_SeqAIJ;
3563: }
3564: C->ops->solveadd = 0;
3565: C->ops->solvetranspose = 0;
3566: C->ops->solvetransposeadd = 0;
3567: C->ops->matsolve = 0;
3568: C->assembled = PETSC_TRUE;
3569: C->preallocated = PETSC_TRUE;
3571: PetscLogFlops(C->cmap->n);
3572: return(0);
3573: }