Actual source code: aijfact.c
petsc-3.13.1 2020-05-02
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: PetscArrayzero(done,n);
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 && !A->symmetric && (ftype == MAT_FACTOR_CHOLESKY||ftype == MAT_FACTOR_ICC)) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Hermitian CHOLESKY or ICC 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: if (n==1) f = 1; /* prevent failure in corner case of 1x1 matrix with fill < 0.5 */
165: PetscFreeSpaceGet(PetscRealIntMultTruncate(f,ai[n]+1),&free_space);
166: current_space = free_space;
168: for (i=0; i<n; i++) {
169: /* copy previous fill into linked list */
170: nzi = 0;
171: nnz = ai[r[i]+1] - ai[r[i]];
172: ajtmp = aj + ai[r[i]];
173: PetscLLAddPerm(nnz,ajtmp,ic,n,nlnk,lnk,lnkbt);
174: nzi += nlnk;
176: /* add pivot rows into linked list */
177: row = lnk[n];
178: while (row < i) {
179: nzbd = bdiag[row] - bi[row] + 1; /* num of entries in the row with column index <= row */
180: ajtmp = bi_ptr[row] + nzbd; /* points to the entry next to the diagonal */
181: PetscLLAddSortedLU(ajtmp,row,nlnk,lnk,lnkbt,i,nzbd,im);
182: nzi += nlnk;
183: row = lnk[row];
184: }
185: bi[i+1] = bi[i] + nzi;
186: im[i] = nzi;
188: /* mark bdiag */
189: nzbd = 0;
190: nnz = nzi;
191: k = lnk[n];
192: while (nnz-- && k < i) {
193: nzbd++;
194: k = lnk[k];
195: }
196: bdiag[i] = bi[i] + nzbd;
198: /* if free space is not available, make more free space */
199: if (current_space->local_remaining<nzi) {
200: nnz = PetscIntMultTruncate(n - i,nzi); /* estimated and max additional space needed */
201: PetscFreeSpaceGet(nnz,¤t_space);
202: reallocs++;
203: }
205: /* copy data into free space, then initialize lnk */
206: PetscLLClean(n,n,nzi,lnk,current_space->array,lnkbt);
208: bi_ptr[i] = current_space->array;
209: current_space->array += nzi;
210: current_space->local_used += nzi;
211: current_space->local_remaining -= nzi;
212: }
213: #if defined(PETSC_USE_INFO)
214: if (ai[n] != 0) {
215: PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]);
216: PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)f,(double)af);
217: PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);
218: PetscInfo1(A,"PCFactorSetFill(pc,%g);\n",(double)af);
219: PetscInfo(A,"for best performance.\n");
220: } else {
221: PetscInfo(A,"Empty matrix\n");
222: }
223: #endif
225: ISRestoreIndices(isrow,&r);
226: ISRestoreIndices(isicol,&ic);
228: /* destroy list of free space and other temporary array(s) */
229: PetscMalloc1(bi[n]+1,&bj);
230: PetscFreeSpaceContiguous(&free_space,bj);
231: PetscLLDestroy(lnk,lnkbt);
232: PetscFree2(bi_ptr,im);
234: /* put together the new matrix */
235: MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,NULL);
236: PetscLogObjectParent((PetscObject)B,(PetscObject)isicol);
237: b = (Mat_SeqAIJ*)(B)->data;
239: b->free_a = PETSC_TRUE;
240: b->free_ij = PETSC_TRUE;
241: b->singlemalloc = PETSC_FALSE;
243: PetscMalloc1(bi[n]+1,&b->a);
244: b->j = bj;
245: b->i = bi;
246: b->diag = bdiag;
247: b->ilen = 0;
248: b->imax = 0;
249: b->row = isrow;
250: b->col = iscol;
251: PetscObjectReference((PetscObject)isrow);
252: PetscObjectReference((PetscObject)iscol);
253: b->icol = isicol;
254: PetscMalloc1(n+1,&b->solve_work);
256: /* In b structure: Free imax, ilen, old a, old j. Allocate solve_work, new a, new j */
257: PetscLogObjectMemory((PetscObject)B,(bi[n]-n)*(sizeof(PetscInt)+sizeof(PetscScalar)));
258: b->maxnz = b->nz = bi[n];
260: (B)->factortype = MAT_FACTOR_LU;
261: (B)->info.factor_mallocs = reallocs;
262: (B)->info.fill_ratio_given = f;
264: if (ai[n]) {
265: (B)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]);
266: } else {
267: (B)->info.fill_ratio_needed = 0.0;
268: }
269: (B)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_inplace;
270: if (a->inode.size) {
271: (B)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode_inplace;
272: }
273: return(0);
274: }
276: PetscErrorCode MatLUFactorSymbolic_SeqAIJ(Mat B,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
277: {
278: Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b;
279: IS isicol;
280: PetscErrorCode ierr;
281: const PetscInt *r,*ic,*ai=a->i,*aj=a->j,*ajtmp;
282: PetscInt i,n=A->rmap->n;
283: PetscInt *bi,*bj;
284: PetscInt *bdiag,row,nnz,nzi,reallocs=0,nzbd,*im;
285: PetscReal f;
286: PetscInt nlnk,*lnk,k,**bi_ptr;
287: PetscFreeSpaceList free_space=NULL,current_space=NULL;
288: PetscBT lnkbt;
289: PetscBool missing;
292: if (A->rmap->N != A->cmap->N) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"matrix must be square");
293: MatMissingDiagonal(A,&missing,&i);
294: if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i);
296: ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);
297: ISGetIndices(isrow,&r);
298: ISGetIndices(isicol,&ic);
300: /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */
301: PetscMalloc1(n+1,&bi);
302: PetscMalloc1(n+1,&bdiag);
303: bi[0] = bdiag[0] = 0;
305: /* linked list for storing column indices of the active row */
306: nlnk = n + 1;
307: PetscLLCreate(n,n,nlnk,lnk,lnkbt);
309: PetscMalloc2(n+1,&bi_ptr,n+1,&im);
311: /* initial FreeSpace size is f*(ai[n]+1) */
312: f = info->fill;
313: if (n==1) f = 1; /* prevent failure in corner case of 1x1 matrix with fill < 0.5 */
314: PetscFreeSpaceGet(PetscRealIntMultTruncate(f,ai[n]+1),&free_space);
315: current_space = free_space;
317: for (i=0; i<n; i++) {
318: /* copy previous fill into linked list */
319: nzi = 0;
320: nnz = ai[r[i]+1] - ai[r[i]];
321: ajtmp = aj + ai[r[i]];
322: PetscLLAddPerm(nnz,ajtmp,ic,n,nlnk,lnk,lnkbt);
323: nzi += nlnk;
325: /* add pivot rows into linked list */
326: row = lnk[n];
327: while (row < i) {
328: nzbd = bdiag[row] + 1; /* num of entries in the row with column index <= row */
329: ajtmp = bi_ptr[row] + nzbd; /* points to the entry next to the diagonal */
330: PetscLLAddSortedLU(ajtmp,row,nlnk,lnk,lnkbt,i,nzbd,im);
331: nzi += nlnk;
332: row = lnk[row];
333: }
334: bi[i+1] = bi[i] + nzi;
335: im[i] = nzi;
337: /* mark bdiag */
338: nzbd = 0;
339: nnz = nzi;
340: k = lnk[n];
341: while (nnz-- && k < i) {
342: nzbd++;
343: k = lnk[k];
344: }
345: bdiag[i] = nzbd; /* note: bdiag[i] = nnzL as input for PetscFreeSpaceContiguous_LU() */
347: /* if free space is not available, make more free space */
348: if (current_space->local_remaining<nzi) {
349: /* estimated additional space needed */
350: nnz = PetscIntMultTruncate(2,PetscIntMultTruncate(n-1,nzi));
351: PetscFreeSpaceGet(nnz,¤t_space);
352: reallocs++;
353: }
355: /* copy data into free space, then initialize lnk */
356: PetscLLClean(n,n,nzi,lnk,current_space->array,lnkbt);
358: bi_ptr[i] = current_space->array;
359: current_space->array += nzi;
360: current_space->local_used += nzi;
361: current_space->local_remaining -= nzi;
362: }
364: ISRestoreIndices(isrow,&r);
365: ISRestoreIndices(isicol,&ic);
367: /* copy free_space into bj and free free_space; set bi, bj, bdiag in new datastructure; */
368: PetscMalloc1(bi[n]+1,&bj);
369: PetscFreeSpaceContiguous_LU(&free_space,bj,n,bi,bdiag);
370: PetscLLDestroy(lnk,lnkbt);
371: PetscFree2(bi_ptr,im);
373: /* put together the new matrix */
374: MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,NULL);
375: PetscLogObjectParent((PetscObject)B,(PetscObject)isicol);
376: b = (Mat_SeqAIJ*)(B)->data;
378: b->free_a = PETSC_TRUE;
379: b->free_ij = PETSC_TRUE;
380: b->singlemalloc = PETSC_FALSE;
382: PetscMalloc1(bdiag[0]+1,&b->a);
384: b->j = bj;
385: b->i = bi;
386: b->diag = bdiag;
387: b->ilen = 0;
388: b->imax = 0;
389: b->row = isrow;
390: b->col = iscol;
391: PetscObjectReference((PetscObject)isrow);
392: PetscObjectReference((PetscObject)iscol);
393: b->icol = isicol;
394: PetscMalloc1(n+1,&b->solve_work);
396: /* In b structure: Free imax, ilen, old a, old j. Allocate solve_work, new a, new j */
397: PetscLogObjectMemory((PetscObject)B,(bdiag[0]+1)*(sizeof(PetscInt)+sizeof(PetscScalar)));
398: b->maxnz = b->nz = bdiag[0]+1;
400: B->factortype = MAT_FACTOR_LU;
401: B->info.factor_mallocs = reallocs;
402: B->info.fill_ratio_given = f;
404: if (ai[n]) {
405: B->info.fill_ratio_needed = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]);
406: } else {
407: B->info.fill_ratio_needed = 0.0;
408: }
409: #if defined(PETSC_USE_INFO)
410: if (ai[n] != 0) {
411: PetscReal af = B->info.fill_ratio_needed;
412: PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)f,(double)af);
413: PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);
414: PetscInfo1(A,"PCFactorSetFill(pc,%g);\n",(double)af);
415: PetscInfo(A,"for best performance.\n");
416: } else {
417: PetscInfo(A,"Empty matrix\n");
418: }
419: #endif
420: B->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ;
421: if (a->inode.size) {
422: B->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode;
423: }
424: MatSeqAIJCheckInode_FactorLU(B);
425: return(0);
426: }
428: /*
429: Trouble in factorization, should we dump the original matrix?
430: */
431: PetscErrorCode MatFactorDumpMatrix(Mat A)
432: {
434: PetscBool flg = PETSC_FALSE;
437: PetscOptionsGetBool(((PetscObject)A)->options,NULL,"-mat_factor_dump_on_error",&flg,NULL);
438: if (flg) {
439: PetscViewer viewer;
440: char filename[PETSC_MAX_PATH_LEN];
442: PetscSNPrintf(filename,PETSC_MAX_PATH_LEN,"matrix_factor_error.%d",PetscGlobalRank);
443: PetscViewerBinaryOpen(PetscObjectComm((PetscObject)A),filename,FILE_MODE_WRITE,&viewer);
444: MatView(A,viewer);
445: PetscViewerDestroy(&viewer);
446: }
447: return(0);
448: }
450: PetscErrorCode MatLUFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info)
451: {
452: Mat C =B;
453: Mat_SeqAIJ *a =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)C->data;
454: IS isrow = b->row,isicol = b->icol;
455: PetscErrorCode ierr;
456: const PetscInt *r,*ic,*ics;
457: const PetscInt n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bdiag=b->diag;
458: PetscInt i,j,k,nz,nzL,row,*pj;
459: const PetscInt *ajtmp,*bjtmp;
460: MatScalar *rtmp,*pc,multiplier,*pv;
461: const MatScalar *aa=a->a,*v;
462: PetscBool row_identity,col_identity;
463: FactorShiftCtx sctx;
464: const PetscInt *ddiag;
465: PetscReal rs;
466: MatScalar d;
469: /* MatPivotSetUp(): initialize shift context sctx */
470: PetscMemzero(&sctx,sizeof(FactorShiftCtx));
472: if (info->shifttype == (PetscReal) MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */
473: ddiag = a->diag;
474: sctx.shift_top = info->zeropivot;
475: for (i=0; i<n; i++) {
476: /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
477: d = (aa)[ddiag[i]];
478: rs = -PetscAbsScalar(d) - PetscRealPart(d);
479: v = aa+ai[i];
480: nz = ai[i+1] - ai[i];
481: for (j=0; j<nz; j++) rs += PetscAbsScalar(v[j]);
482: if (rs>sctx.shift_top) sctx.shift_top = rs;
483: }
484: sctx.shift_top *= 1.1;
485: sctx.nshift_max = 5;
486: sctx.shift_lo = 0.;
487: sctx.shift_hi = 1.;
488: }
490: ISGetIndices(isrow,&r);
491: ISGetIndices(isicol,&ic);
492: PetscMalloc1(n+1,&rtmp);
493: ics = ic;
495: do {
496: sctx.newshift = PETSC_FALSE;
497: for (i=0; i<n; i++) {
498: /* zero rtmp */
499: /* L part */
500: nz = bi[i+1] - bi[i];
501: bjtmp = bj + bi[i];
502: for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
504: /* U part */
505: nz = bdiag[i]-bdiag[i+1];
506: bjtmp = bj + bdiag[i+1]+1;
507: for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
509: /* load in initial (unfactored row) */
510: nz = ai[r[i]+1] - ai[r[i]];
511: ajtmp = aj + ai[r[i]];
512: v = aa + ai[r[i]];
513: for (j=0; j<nz; j++) {
514: rtmp[ics[ajtmp[j]]] = v[j];
515: }
516: /* ZeropivotApply() */
517: rtmp[i] += sctx.shift_amount; /* shift the diagonal of the matrix */
519: /* elimination */
520: bjtmp = bj + bi[i];
521: row = *bjtmp++;
522: nzL = bi[i+1] - bi[i];
523: for (k=0; k < nzL; k++) {
524: pc = rtmp + row;
525: if (*pc != 0.0) {
526: pv = b->a + bdiag[row];
527: multiplier = *pc * (*pv);
528: *pc = multiplier;
530: pj = b->j + bdiag[row+1]+1; /* beginning of U(row,:) */
531: pv = b->a + bdiag[row+1]+1;
532: nz = bdiag[row]-bdiag[row+1]-1; /* num of entries in U(row,:) excluding diag */
534: for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
535: PetscLogFlops(1+2*nz);
536: }
537: row = *bjtmp++;
538: }
540: /* finished row so stick it into b->a */
541: rs = 0.0;
542: /* L part */
543: pv = b->a + bi[i];
544: pj = b->j + bi[i];
545: nz = bi[i+1] - bi[i];
546: for (j=0; j<nz; j++) {
547: pv[j] = rtmp[pj[j]]; rs += PetscAbsScalar(pv[j]);
548: }
550: /* U part */
551: pv = b->a + bdiag[i+1]+1;
552: pj = b->j + bdiag[i+1]+1;
553: nz = bdiag[i] - bdiag[i+1]-1;
554: for (j=0; j<nz; j++) {
555: pv[j] = rtmp[pj[j]]; rs += PetscAbsScalar(pv[j]);
556: }
558: sctx.rs = rs;
559: sctx.pv = rtmp[i];
560: MatPivotCheck(B,A,info,&sctx,i);
561: if (sctx.newshift) break; /* break for-loop */
562: rtmp[i] = sctx.pv; /* sctx.pv might be updated in the case of MAT_SHIFT_INBLOCKS */
564: /* Mark diagonal and invert diagonal for simplier triangular solves */
565: pv = b->a + bdiag[i];
566: *pv = 1.0/rtmp[i];
568: } /* endof for (i=0; i<n; i++) { */
570: /* MatPivotRefine() */
571: if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE && !sctx.newshift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) {
572: /*
573: * if no shift in this attempt & shifting & started shifting & can refine,
574: * then try lower shift
575: */
576: sctx.shift_hi = sctx.shift_fraction;
577: sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.;
578: sctx.shift_amount = sctx.shift_fraction * sctx.shift_top;
579: sctx.newshift = PETSC_TRUE;
580: sctx.nshift++;
581: }
582: } while (sctx.newshift);
584: PetscFree(rtmp);
585: ISRestoreIndices(isicol,&ic);
586: ISRestoreIndices(isrow,&r);
588: ISIdentity(isrow,&row_identity);
589: ISIdentity(isicol,&col_identity);
590: if (b->inode.size) {
591: C->ops->solve = MatSolve_SeqAIJ_Inode;
592: } else if (row_identity && col_identity) {
593: C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering;
594: } else {
595: C->ops->solve = MatSolve_SeqAIJ;
596: }
597: C->ops->solveadd = MatSolveAdd_SeqAIJ;
598: C->ops->solvetranspose = MatSolveTranspose_SeqAIJ;
599: C->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ;
600: C->ops->matsolve = MatMatSolve_SeqAIJ;
601: C->assembled = PETSC_TRUE;
602: C->preallocated = PETSC_TRUE;
604: PetscLogFlops(C->cmap->n);
606: /* MatShiftView(A,info,&sctx) */
607: if (sctx.nshift) {
608: if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) {
609: 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);
610: } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) {
611: PetscInfo2(A,"number of shift_nz tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);
612: } else if (info->shifttype == (PetscReal)MAT_SHIFT_INBLOCKS) {
613: PetscInfo2(A,"number of shift_inblocks applied %D, each shift_amount %g\n",sctx.nshift,(double)info->shiftamount);
614: }
615: }
616: return(0);
617: }
619: PetscErrorCode MatLUFactorNumeric_SeqAIJ_inplace(Mat B,Mat A,const MatFactorInfo *info)
620: {
621: Mat C =B;
622: Mat_SeqAIJ *a =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)C->data;
623: IS isrow = b->row,isicol = b->icol;
624: PetscErrorCode ierr;
625: const PetscInt *r,*ic,*ics;
626: PetscInt nz,row,i,j,n=A->rmap->n,diag;
627: const PetscInt *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
628: const PetscInt *ajtmp,*bjtmp,*diag_offset = b->diag,*pj;
629: MatScalar *pv,*rtmp,*pc,multiplier,d;
630: const MatScalar *v,*aa=a->a;
631: PetscReal rs=0.0;
632: FactorShiftCtx sctx;
633: const PetscInt *ddiag;
634: PetscBool row_identity, col_identity;
637: /* MatPivotSetUp(): initialize shift context sctx */
638: PetscMemzero(&sctx,sizeof(FactorShiftCtx));
640: if (info->shifttype == (PetscReal) MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */
641: ddiag = a->diag;
642: sctx.shift_top = info->zeropivot;
643: for (i=0; i<n; i++) {
644: /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
645: d = (aa)[ddiag[i]];
646: rs = -PetscAbsScalar(d) - PetscRealPart(d);
647: v = aa+ai[i];
648: nz = ai[i+1] - ai[i];
649: for (j=0; j<nz; j++) rs += PetscAbsScalar(v[j]);
650: if (rs>sctx.shift_top) sctx.shift_top = rs;
651: }
652: sctx.shift_top *= 1.1;
653: sctx.nshift_max = 5;
654: sctx.shift_lo = 0.;
655: sctx.shift_hi = 1.;
656: }
658: ISGetIndices(isrow,&r);
659: ISGetIndices(isicol,&ic);
660: PetscMalloc1(n+1,&rtmp);
661: ics = ic;
663: do {
664: sctx.newshift = PETSC_FALSE;
665: for (i=0; i<n; i++) {
666: nz = bi[i+1] - bi[i];
667: bjtmp = bj + bi[i];
668: for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
670: /* load in initial (unfactored row) */
671: nz = ai[r[i]+1] - ai[r[i]];
672: ajtmp = aj + ai[r[i]];
673: v = aa + ai[r[i]];
674: for (j=0; j<nz; j++) {
675: rtmp[ics[ajtmp[j]]] = v[j];
676: }
677: rtmp[ics[r[i]]] += sctx.shift_amount; /* shift the diagonal of the matrix */
679: row = *bjtmp++;
680: while (row < i) {
681: pc = rtmp + row;
682: if (*pc != 0.0) {
683: pv = b->a + diag_offset[row];
684: pj = b->j + diag_offset[row] + 1;
685: multiplier = *pc / *pv++;
686: *pc = multiplier;
687: nz = bi[row+1] - diag_offset[row] - 1;
688: for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
689: PetscLogFlops(1+2*nz);
690: }
691: row = *bjtmp++;
692: }
693: /* finished row so stick it into b->a */
694: pv = b->a + bi[i];
695: pj = b->j + bi[i];
696: nz = bi[i+1] - bi[i];
697: diag = diag_offset[i] - bi[i];
698: rs = 0.0;
699: for (j=0; j<nz; j++) {
700: pv[j] = rtmp[pj[j]];
701: rs += PetscAbsScalar(pv[j]);
702: }
703: rs -= PetscAbsScalar(pv[diag]);
705: sctx.rs = rs;
706: sctx.pv = pv[diag];
707: MatPivotCheck(B,A,info,&sctx,i);
708: if (sctx.newshift) break;
709: pv[diag] = sctx.pv;
710: }
712: if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE && !sctx.newshift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) {
713: /*
714: * if no shift in this attempt & shifting & started shifting & can refine,
715: * then try lower shift
716: */
717: sctx.shift_hi = sctx.shift_fraction;
718: sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.;
719: sctx.shift_amount = sctx.shift_fraction * sctx.shift_top;
720: sctx.newshift = PETSC_TRUE;
721: sctx.nshift++;
722: }
723: } while (sctx.newshift);
725: /* invert diagonal entries for simplier triangular solves */
726: for (i=0; i<n; i++) {
727: b->a[diag_offset[i]] = 1.0/b->a[diag_offset[i]];
728: }
729: PetscFree(rtmp);
730: ISRestoreIndices(isicol,&ic);
731: ISRestoreIndices(isrow,&r);
733: ISIdentity(isrow,&row_identity);
734: ISIdentity(isicol,&col_identity);
735: if (row_identity && col_identity) {
736: C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering_inplace;
737: } else {
738: C->ops->solve = MatSolve_SeqAIJ_inplace;
739: }
740: C->ops->solveadd = MatSolveAdd_SeqAIJ_inplace;
741: C->ops->solvetranspose = MatSolveTranspose_SeqAIJ_inplace;
742: C->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ_inplace;
743: C->ops->matsolve = MatMatSolve_SeqAIJ_inplace;
745: C->assembled = PETSC_TRUE;
746: C->preallocated = PETSC_TRUE;
748: PetscLogFlops(C->cmap->n);
749: if (sctx.nshift) {
750: if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) {
751: 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);
752: } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) {
753: PetscInfo2(A,"number of shift_nz tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);
754: }
755: }
756: (C)->ops->solve = MatSolve_SeqAIJ_inplace;
757: (C)->ops->solvetranspose = MatSolveTranspose_SeqAIJ_inplace;
759: MatSeqAIJCheckInode(C);
760: return(0);
761: }
763: /*
764: This routine implements inplace ILU(0) with row or/and column permutations.
765: Input:
766: A - original matrix
767: Output;
768: A - a->i (rowptr) is same as original rowptr, but factored i-the row is stored in rowperm[i]
769: a->j (col index) is permuted by the inverse of colperm, then sorted
770: a->a reordered accordingly with a->j
771: a->diag (ptr to diagonal elements) is updated.
772: */
773: PetscErrorCode MatLUFactorNumeric_SeqAIJ_InplaceWithPerm(Mat B,Mat A,const MatFactorInfo *info)
774: {
775: Mat_SeqAIJ *a =(Mat_SeqAIJ*)A->data;
776: IS isrow = a->row,isicol = a->icol;
777: PetscErrorCode ierr;
778: const PetscInt *r,*ic,*ics;
779: PetscInt i,j,n=A->rmap->n,*ai=a->i,*aj=a->j;
780: PetscInt *ajtmp,nz,row;
781: PetscInt *diag = a->diag,nbdiag,*pj;
782: PetscScalar *rtmp,*pc,multiplier,d;
783: MatScalar *pv,*v;
784: PetscReal rs;
785: FactorShiftCtx sctx;
786: const MatScalar *aa=a->a,*vtmp;
789: if (A != B) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"input and output matrix must have same address");
791: /* MatPivotSetUp(): initialize shift context sctx */
792: PetscMemzero(&sctx,sizeof(FactorShiftCtx));
794: if (info->shifttype == (PetscReal) MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */
795: const PetscInt *ddiag = a->diag;
796: sctx.shift_top = info->zeropivot;
797: for (i=0; i<n; i++) {
798: /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
799: d = (aa)[ddiag[i]];
800: rs = -PetscAbsScalar(d) - PetscRealPart(d);
801: vtmp = aa+ai[i];
802: nz = ai[i+1] - ai[i];
803: for (j=0; j<nz; j++) rs += PetscAbsScalar(vtmp[j]);
804: if (rs>sctx.shift_top) sctx.shift_top = rs;
805: }
806: sctx.shift_top *= 1.1;
807: sctx.nshift_max = 5;
808: sctx.shift_lo = 0.;
809: sctx.shift_hi = 1.;
810: }
812: ISGetIndices(isrow,&r);
813: ISGetIndices(isicol,&ic);
814: PetscMalloc1(n+1,&rtmp);
815: PetscArrayzero(rtmp,n+1);
816: ics = ic;
818: #if defined(MV)
819: sctx.shift_top = 0.;
820: sctx.nshift_max = 0;
821: sctx.shift_lo = 0.;
822: sctx.shift_hi = 0.;
823: sctx.shift_fraction = 0.;
825: if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */
826: sctx.shift_top = 0.;
827: for (i=0; i<n; i++) {
828: /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
829: d = (a->a)[diag[i]];
830: rs = -PetscAbsScalar(d) - PetscRealPart(d);
831: v = a->a+ai[i];
832: nz = ai[i+1] - ai[i];
833: for (j=0; j<nz; j++) rs += PetscAbsScalar(v[j]);
834: if (rs>sctx.shift_top) sctx.shift_top = rs;
835: }
836: if (sctx.shift_top < info->zeropivot) sctx.shift_top = info->zeropivot;
837: sctx.shift_top *= 1.1;
838: sctx.nshift_max = 5;
839: sctx.shift_lo = 0.;
840: sctx.shift_hi = 1.;
841: }
843: sctx.shift_amount = 0.;
844: sctx.nshift = 0;
845: #endif
847: do {
848: sctx.newshift = PETSC_FALSE;
849: for (i=0; i<n; i++) {
850: /* load in initial unfactored row */
851: nz = ai[r[i]+1] - ai[r[i]];
852: ajtmp = aj + ai[r[i]];
853: v = a->a + ai[r[i]];
854: /* sort permuted ajtmp and values v accordingly */
855: for (j=0; j<nz; j++) ajtmp[j] = ics[ajtmp[j]];
856: PetscSortIntWithScalarArray(nz,ajtmp,v);
858: diag[r[i]] = ai[r[i]];
859: for (j=0; j<nz; j++) {
860: rtmp[ajtmp[j]] = v[j];
861: if (ajtmp[j] < i) diag[r[i]]++; /* update a->diag */
862: }
863: rtmp[r[i]] += sctx.shift_amount; /* shift the diagonal of the matrix */
865: row = *ajtmp++;
866: while (row < i) {
867: pc = rtmp + row;
868: if (*pc != 0.0) {
869: pv = a->a + diag[r[row]];
870: pj = aj + diag[r[row]] + 1;
872: multiplier = *pc / *pv++;
873: *pc = multiplier;
874: nz = ai[r[row]+1] - diag[r[row]] - 1;
875: for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
876: PetscLogFlops(1+2*nz);
877: }
878: row = *ajtmp++;
879: }
880: /* finished row so overwrite it onto a->a */
881: pv = a->a + ai[r[i]];
882: pj = aj + ai[r[i]];
883: nz = ai[r[i]+1] - ai[r[i]];
884: nbdiag = diag[r[i]] - ai[r[i]]; /* num of entries before the diagonal */
886: rs = 0.0;
887: for (j=0; j<nz; j++) {
888: pv[j] = rtmp[pj[j]];
889: if (j != nbdiag) rs += PetscAbsScalar(pv[j]);
890: }
892: sctx.rs = rs;
893: sctx.pv = pv[nbdiag];
894: MatPivotCheck(B,A,info,&sctx,i);
895: if (sctx.newshift) break;
896: pv[nbdiag] = sctx.pv;
897: }
899: if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE && !sctx.newshift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) {
900: /*
901: * if no shift in this attempt & shifting & started shifting & can refine,
902: * then try lower shift
903: */
904: sctx.shift_hi = sctx.shift_fraction;
905: sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.;
906: sctx.shift_amount = sctx.shift_fraction * sctx.shift_top;
907: sctx.newshift = PETSC_TRUE;
908: sctx.nshift++;
909: }
910: } while (sctx.newshift);
912: /* invert diagonal entries for simplier triangular solves */
913: for (i=0; i<n; i++) {
914: a->a[diag[r[i]]] = 1.0/a->a[diag[r[i]]];
915: }
917: PetscFree(rtmp);
918: ISRestoreIndices(isicol,&ic);
919: ISRestoreIndices(isrow,&r);
921: A->ops->solve = MatSolve_SeqAIJ_InplaceWithPerm;
922: A->ops->solveadd = MatSolveAdd_SeqAIJ_inplace;
923: A->ops->solvetranspose = MatSolveTranspose_SeqAIJ_inplace;
924: A->ops->solvetransposeadd = MatSolveTransposeAdd_SeqAIJ_inplace;
926: A->assembled = PETSC_TRUE;
927: A->preallocated = PETSC_TRUE;
929: PetscLogFlops(A->cmap->n);
930: if (sctx.nshift) {
931: if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) {
932: 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);
933: } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) {
934: PetscInfo2(A,"number of shift_nz tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);
935: }
936: }
937: return(0);
938: }
940: /* ----------------------------------------------------------- */
941: PetscErrorCode MatLUFactor_SeqAIJ(Mat A,IS row,IS col,const MatFactorInfo *info)
942: {
944: Mat C;
947: MatGetFactor(A,MATSOLVERPETSC,MAT_FACTOR_LU,&C);
948: MatLUFactorSymbolic(C,A,row,col,info);
949: MatLUFactorNumeric(C,A,info);
951: A->ops->solve = C->ops->solve;
952: A->ops->solvetranspose = C->ops->solvetranspose;
954: MatHeaderMerge(A,&C);
955: PetscLogObjectParent((PetscObject)A,(PetscObject)((Mat_SeqAIJ*)(A->data))->icol);
956: return(0);
957: }
958: /* ----------------------------------------------------------- */
961: PetscErrorCode MatSolve_SeqAIJ_inplace(Mat A,Vec bb,Vec xx)
962: {
963: Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
964: IS iscol = a->col,isrow = a->row;
965: PetscErrorCode ierr;
966: PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j;
967: PetscInt nz;
968: const PetscInt *rout,*cout,*r,*c;
969: PetscScalar *x,*tmp,*tmps,sum;
970: const PetscScalar *b;
971: const MatScalar *aa = a->a,*v;
974: if (!n) return(0);
976: VecGetArrayRead(bb,&b);
977: VecGetArrayWrite(xx,&x);
978: tmp = a->solve_work;
980: ISGetIndices(isrow,&rout); r = rout;
981: ISGetIndices(iscol,&cout); c = cout + (n-1);
983: /* forward solve the lower triangular */
984: tmp[0] = b[*r++];
985: tmps = tmp;
986: for (i=1; i<n; i++) {
987: v = aa + ai[i];
988: vi = aj + ai[i];
989: nz = a->diag[i] - ai[i];
990: sum = b[*r++];
991: PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
992: tmp[i] = sum;
993: }
995: /* backward solve the upper triangular */
996: for (i=n-1; i>=0; i--) {
997: v = aa + a->diag[i] + 1;
998: vi = aj + a->diag[i] + 1;
999: nz = ai[i+1] - a->diag[i] - 1;
1000: sum = tmp[i];
1001: PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
1002: x[*c--] = tmp[i] = sum*aa[a->diag[i]];
1003: }
1005: ISRestoreIndices(isrow,&rout);
1006: ISRestoreIndices(iscol,&cout);
1007: VecRestoreArrayRead(bb,&b);
1008: VecRestoreArrayWrite(xx,&x);
1009: PetscLogFlops(2.0*a->nz - A->cmap->n);
1010: return(0);
1011: }
1013: PetscErrorCode MatMatSolve_SeqAIJ_inplace(Mat A,Mat B,Mat X)
1014: {
1015: Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
1016: IS iscol = a->col,isrow = a->row;
1017: PetscErrorCode ierr;
1018: PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j;
1019: PetscInt nz,neq;
1020: const PetscInt *rout,*cout,*r,*c;
1021: PetscScalar *x,*tmp,*tmps,sum;
1022: const PetscScalar *aa = a->a,*v;
1023: const PetscScalar *b;
1024: PetscBool bisdense,xisdense;
1027: if (!n) return(0);
1029: PetscObjectTypeCompare((PetscObject)B,MATSEQDENSE,&bisdense);
1030: if (!bisdense) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"B matrix must be a SeqDense matrix");
1031: if (X != B) {
1032: PetscObjectTypeCompare((PetscObject)X,MATSEQDENSE,&xisdense);
1033: if (!xisdense) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"X matrix must be a SeqDense matrix");
1034: }
1036: MatDenseGetArrayRead(B,&b);
1037: MatDenseGetArray(X,&x);
1039: tmp = a->solve_work;
1040: ISGetIndices(isrow,&rout); r = rout;
1041: ISGetIndices(iscol,&cout); c = cout;
1043: for (neq=0; neq<B->cmap->n; neq++) {
1044: /* forward solve the lower triangular */
1045: tmp[0] = b[r[0]];
1046: tmps = tmp;
1047: for (i=1; i<n; i++) {
1048: v = aa + ai[i];
1049: vi = aj + ai[i];
1050: nz = a->diag[i] - ai[i];
1051: sum = b[r[i]];
1052: PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
1053: tmp[i] = sum;
1054: }
1055: /* backward solve the upper triangular */
1056: for (i=n-1; i>=0; i--) {
1057: v = aa + a->diag[i] + 1;
1058: vi = aj + a->diag[i] + 1;
1059: nz = ai[i+1] - a->diag[i] - 1;
1060: sum = tmp[i];
1061: PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
1062: x[c[i]] = tmp[i] = sum*aa[a->diag[i]];
1063: }
1065: b += n;
1066: x += n;
1067: }
1068: ISRestoreIndices(isrow,&rout);
1069: ISRestoreIndices(iscol,&cout);
1070: MatDenseRestoreArrayRead(B,&b);
1071: MatDenseRestoreArray(X,&x);
1072: PetscLogFlops(B->cmap->n*(2.0*a->nz - n));
1073: return(0);
1074: }
1076: PetscErrorCode MatMatSolve_SeqAIJ(Mat A,Mat B,Mat X)
1077: {
1078: Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
1079: IS iscol = a->col,isrow = a->row;
1080: PetscErrorCode ierr;
1081: PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j,*adiag = a->diag;
1082: PetscInt nz,neq;
1083: const PetscInt *rout,*cout,*r,*c;
1084: PetscScalar *x,*tmp,sum;
1085: const PetscScalar *b;
1086: const PetscScalar *aa = a->a,*v;
1087: PetscBool bisdense,xisdense;
1090: if (!n) return(0);
1092: PetscObjectTypeCompare((PetscObject)B,MATSEQDENSE,&bisdense);
1093: if (!bisdense) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"B matrix must be a SeqDense matrix");
1094: if (X != B) {
1095: PetscObjectTypeCompare((PetscObject)X,MATSEQDENSE,&xisdense);
1096: if (!xisdense) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"X matrix must be a SeqDense matrix");
1097: }
1099: MatDenseGetArrayRead(B,&b);
1100: MatDenseGetArray(X,&x);
1102: tmp = a->solve_work;
1103: ISGetIndices(isrow,&rout); r = rout;
1104: ISGetIndices(iscol,&cout); c = cout;
1106: for (neq=0; neq<B->cmap->n; neq++) {
1107: /* forward solve the lower triangular */
1108: tmp[0] = b[r[0]];
1109: v = aa;
1110: vi = aj;
1111: for (i=1; i<n; i++) {
1112: nz = ai[i+1] - ai[i];
1113: sum = b[r[i]];
1114: PetscSparseDenseMinusDot(sum,tmp,v,vi,nz);
1115: tmp[i] = sum;
1116: v += nz; vi += nz;
1117: }
1119: /* backward solve the upper triangular */
1120: for (i=n-1; i>=0; i--) {
1121: v = aa + adiag[i+1]+1;
1122: vi = aj + adiag[i+1]+1;
1123: nz = adiag[i]-adiag[i+1]-1;
1124: sum = tmp[i];
1125: PetscSparseDenseMinusDot(sum,tmp,v,vi,nz);
1126: x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */
1127: }
1129: b += n;
1130: x += n;
1131: }
1132: ISRestoreIndices(isrow,&rout);
1133: ISRestoreIndices(iscol,&cout);
1134: MatDenseRestoreArrayRead(B,&b);
1135: MatDenseRestoreArray(X,&x);
1136: PetscLogFlops(B->cmap->n*(2.0*a->nz - n));
1137: return(0);
1138: }
1140: PetscErrorCode MatSolve_SeqAIJ_InplaceWithPerm(Mat A,Vec bb,Vec xx)
1141: {
1142: Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
1143: IS iscol = a->col,isrow = a->row;
1144: PetscErrorCode ierr;
1145: const PetscInt *r,*c,*rout,*cout;
1146: PetscInt i, n = A->rmap->n,*vi,*ai = a->i,*aj = a->j;
1147: PetscInt nz,row;
1148: PetscScalar *x,*tmp,*tmps,sum;
1149: const PetscScalar *b;
1150: const MatScalar *aa = a->a,*v;
1153: if (!n) return(0);
1155: VecGetArrayRead(bb,&b);
1156: VecGetArrayWrite(xx,&x);
1157: tmp = a->solve_work;
1159: ISGetIndices(isrow,&rout); r = rout;
1160: ISGetIndices(iscol,&cout); c = cout + (n-1);
1162: /* forward solve the lower triangular */
1163: tmp[0] = b[*r++];
1164: tmps = tmp;
1165: for (row=1; row<n; row++) {
1166: i = rout[row]; /* permuted row */
1167: v = aa + ai[i];
1168: vi = aj + ai[i];
1169: nz = a->diag[i] - ai[i];
1170: sum = b[*r++];
1171: PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
1172: tmp[row] = sum;
1173: }
1175: /* backward solve the upper triangular */
1176: for (row=n-1; row>=0; row--) {
1177: i = rout[row]; /* permuted row */
1178: v = aa + a->diag[i] + 1;
1179: vi = aj + a->diag[i] + 1;
1180: nz = ai[i+1] - a->diag[i] - 1;
1181: sum = tmp[row];
1182: PetscSparseDenseMinusDot(sum,tmps,v,vi,nz);
1183: x[*c--] = tmp[row] = sum*aa[a->diag[i]];
1184: }
1186: ISRestoreIndices(isrow,&rout);
1187: ISRestoreIndices(iscol,&cout);
1188: VecRestoreArrayRead(bb,&b);
1189: VecRestoreArrayWrite(xx,&x);
1190: PetscLogFlops(2.0*a->nz - A->cmap->n);
1191: return(0);
1192: }
1194: /* ----------------------------------------------------------- */
1195: #include <../src/mat/impls/aij/seq/ftn-kernels/fsolve.h>
1196: PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering_inplace(Mat A,Vec bb,Vec xx)
1197: {
1198: Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
1199: PetscErrorCode ierr;
1200: PetscInt n = A->rmap->n;
1201: const PetscInt *ai = a->i,*aj = a->j,*adiag = a->diag;
1202: PetscScalar *x;
1203: const PetscScalar *b;
1204: const MatScalar *aa = a->a;
1205: #if !defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ)
1206: PetscInt adiag_i,i,nz,ai_i;
1207: const PetscInt *vi;
1208: const MatScalar *v;
1209: PetscScalar sum;
1210: #endif
1213: if (!n) return(0);
1215: VecGetArrayRead(bb,&b);
1216: VecGetArrayWrite(xx,&x);
1218: #if defined(PETSC_USE_FORTRAN_KERNEL_SOLVEAIJ)
1219: fortransolveaij_(&n,x,ai,aj,adiag,aa,b);
1220: #else
1221: /* forward solve the lower triangular */
1222: x[0] = b[0];
1223: for (i=1; i<n; i++) {
1224: ai_i = ai[i];
1225: v = aa + ai_i;
1226: vi = aj + ai_i;
1227: nz = adiag[i] - ai_i;
1228: sum = b[i];
1229: PetscSparseDenseMinusDot(sum,x,v,vi,nz);
1230: x[i] = sum;
1231: }
1233: /* backward solve the upper triangular */
1234: for (i=n-1; i>=0; i--) {
1235: adiag_i = adiag[i];
1236: v = aa + adiag_i + 1;
1237: vi = aj + adiag_i + 1;
1238: nz = ai[i+1] - adiag_i - 1;
1239: sum = x[i];
1240: PetscSparseDenseMinusDot(sum,x,v,vi,nz);
1241: x[i] = sum*aa[adiag_i];
1242: }
1243: #endif
1244: PetscLogFlops(2.0*a->nz - A->cmap->n);
1245: VecRestoreArrayRead(bb,&b);
1246: VecRestoreArrayWrite(xx,&x);
1247: return(0);
1248: }
1250: PetscErrorCode MatSolveAdd_SeqAIJ_inplace(Mat A,Vec bb,Vec yy,Vec xx)
1251: {
1252: Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
1253: IS iscol = a->col,isrow = a->row;
1254: PetscErrorCode ierr;
1255: PetscInt i, n = A->rmap->n,j;
1256: PetscInt nz;
1257: const PetscInt *rout,*cout,*r,*c,*vi,*ai = a->i,*aj = a->j;
1258: PetscScalar *x,*tmp,sum;
1259: const PetscScalar *b;
1260: const MatScalar *aa = a->a,*v;
1263: if (yy != xx) {VecCopy(yy,xx);}
1265: VecGetArrayRead(bb,&b);
1266: VecGetArray(xx,&x);
1267: tmp = a->solve_work;
1269: ISGetIndices(isrow,&rout); r = rout;
1270: ISGetIndices(iscol,&cout); c = cout + (n-1);
1272: /* forward solve the lower triangular */
1273: tmp[0] = b[*r++];
1274: for (i=1; i<n; i++) {
1275: v = aa + ai[i];
1276: vi = aj + ai[i];
1277: nz = a->diag[i] - ai[i];
1278: sum = b[*r++];
1279: for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]];
1280: tmp[i] = sum;
1281: }
1283: /* backward solve the upper triangular */
1284: for (i=n-1; i>=0; i--) {
1285: v = aa + a->diag[i] + 1;
1286: vi = aj + a->diag[i] + 1;
1287: nz = ai[i+1] - a->diag[i] - 1;
1288: sum = tmp[i];
1289: for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]];
1290: tmp[i] = sum*aa[a->diag[i]];
1291: x[*c--] += tmp[i];
1292: }
1294: ISRestoreIndices(isrow,&rout);
1295: ISRestoreIndices(iscol,&cout);
1296: VecRestoreArrayRead(bb,&b);
1297: VecRestoreArray(xx,&x);
1298: PetscLogFlops(2.0*a->nz);
1299: return(0);
1300: }
1302: PetscErrorCode MatSolveAdd_SeqAIJ(Mat A,Vec bb,Vec yy,Vec xx)
1303: {
1304: Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
1305: IS iscol = a->col,isrow = a->row;
1306: PetscErrorCode ierr;
1307: PetscInt i, n = A->rmap->n,j;
1308: PetscInt nz;
1309: const PetscInt *rout,*cout,*r,*c,*vi,*ai = a->i,*aj = a->j,*adiag = a->diag;
1310: PetscScalar *x,*tmp,sum;
1311: const PetscScalar *b;
1312: const MatScalar *aa = a->a,*v;
1315: if (yy != xx) {VecCopy(yy,xx);}
1317: VecGetArrayRead(bb,&b);
1318: VecGetArray(xx,&x);
1319: tmp = a->solve_work;
1321: ISGetIndices(isrow,&rout); r = rout;
1322: ISGetIndices(iscol,&cout); c = cout;
1324: /* forward solve the lower triangular */
1325: tmp[0] = b[r[0]];
1326: v = aa;
1327: vi = aj;
1328: for (i=1; i<n; i++) {
1329: nz = ai[i+1] - ai[i];
1330: sum = b[r[i]];
1331: for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]];
1332: tmp[i] = sum;
1333: v += nz;
1334: vi += nz;
1335: }
1337: /* backward solve the upper triangular */
1338: v = aa + adiag[n-1];
1339: vi = aj + adiag[n-1];
1340: for (i=n-1; i>=0; i--) {
1341: nz = adiag[i] - adiag[i+1] - 1;
1342: sum = tmp[i];
1343: for (j=0; j<nz; j++) sum -= v[j]*tmp[vi[j]];
1344: tmp[i] = sum*v[nz];
1345: x[c[i]] += tmp[i];
1346: v += nz+1; vi += nz+1;
1347: }
1349: ISRestoreIndices(isrow,&rout);
1350: ISRestoreIndices(iscol,&cout);
1351: VecRestoreArrayRead(bb,&b);
1352: VecRestoreArray(xx,&x);
1353: PetscLogFlops(2.0*a->nz);
1354: return(0);
1355: }
1357: PetscErrorCode MatSolveTranspose_SeqAIJ_inplace(Mat A,Vec bb,Vec xx)
1358: {
1359: Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
1360: IS iscol = a->col,isrow = a->row;
1361: PetscErrorCode ierr;
1362: const PetscInt *rout,*cout,*r,*c,*diag = a->diag,*ai = a->i,*aj = a->j,*vi;
1363: PetscInt i,n = A->rmap->n,j;
1364: PetscInt nz;
1365: PetscScalar *x,*tmp,s1;
1366: const MatScalar *aa = a->a,*v;
1367: const PetscScalar *b;
1370: VecGetArrayRead(bb,&b);
1371: VecGetArrayWrite(xx,&x);
1372: tmp = a->solve_work;
1374: ISGetIndices(isrow,&rout); r = rout;
1375: ISGetIndices(iscol,&cout); c = cout;
1377: /* copy the b into temp work space according to permutation */
1378: for (i=0; i<n; i++) tmp[i] = b[c[i]];
1380: /* forward solve the U^T */
1381: for (i=0; i<n; i++) {
1382: v = aa + diag[i];
1383: vi = aj + diag[i] + 1;
1384: nz = ai[i+1] - diag[i] - 1;
1385: s1 = tmp[i];
1386: s1 *= (*v++); /* multiply by inverse of diagonal entry */
1387: for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
1388: tmp[i] = s1;
1389: }
1391: /* backward solve the L^T */
1392: for (i=n-1; i>=0; i--) {
1393: v = aa + diag[i] - 1;
1394: vi = aj + diag[i] - 1;
1395: nz = diag[i] - ai[i];
1396: s1 = tmp[i];
1397: for (j=0; j>-nz; j--) tmp[vi[j]] -= s1*v[j];
1398: }
1400: /* copy tmp into x according to permutation */
1401: for (i=0; i<n; i++) x[r[i]] = tmp[i];
1403: ISRestoreIndices(isrow,&rout);
1404: ISRestoreIndices(iscol,&cout);
1405: VecRestoreArrayRead(bb,&b);
1406: VecRestoreArrayWrite(xx,&x);
1408: PetscLogFlops(2.0*a->nz-A->cmap->n);
1409: return(0);
1410: }
1412: PetscErrorCode MatSolveTranspose_SeqAIJ(Mat A,Vec bb,Vec xx)
1413: {
1414: Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
1415: IS iscol = a->col,isrow = a->row;
1416: PetscErrorCode ierr;
1417: const PetscInt *rout,*cout,*r,*c,*adiag = a->diag,*ai = a->i,*aj = a->j,*vi;
1418: PetscInt i,n = A->rmap->n,j;
1419: PetscInt nz;
1420: PetscScalar *x,*tmp,s1;
1421: const MatScalar *aa = a->a,*v;
1422: const PetscScalar *b;
1425: VecGetArrayRead(bb,&b);
1426: VecGetArrayWrite(xx,&x);
1427: tmp = a->solve_work;
1429: ISGetIndices(isrow,&rout); r = rout;
1430: ISGetIndices(iscol,&cout); c = cout;
1432: /* copy the b into temp work space according to permutation */
1433: for (i=0; i<n; i++) tmp[i] = b[c[i]];
1435: /* forward solve the U^T */
1436: for (i=0; i<n; i++) {
1437: v = aa + adiag[i+1] + 1;
1438: vi = aj + adiag[i+1] + 1;
1439: nz = adiag[i] - adiag[i+1] - 1;
1440: s1 = tmp[i];
1441: s1 *= v[nz]; /* multiply by inverse of diagonal entry */
1442: for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
1443: tmp[i] = s1;
1444: }
1446: /* backward solve the L^T */
1447: for (i=n-1; i>=0; i--) {
1448: v = aa + ai[i];
1449: vi = aj + ai[i];
1450: nz = ai[i+1] - ai[i];
1451: s1 = tmp[i];
1452: for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
1453: }
1455: /* copy tmp into x according to permutation */
1456: for (i=0; i<n; i++) x[r[i]] = tmp[i];
1458: ISRestoreIndices(isrow,&rout);
1459: ISRestoreIndices(iscol,&cout);
1460: VecRestoreArrayRead(bb,&b);
1461: VecRestoreArrayWrite(xx,&x);
1463: PetscLogFlops(2.0*a->nz-A->cmap->n);
1464: return(0);
1465: }
1467: PetscErrorCode MatSolveTransposeAdd_SeqAIJ_inplace(Mat A,Vec bb,Vec zz,Vec xx)
1468: {
1469: Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
1470: IS iscol = a->col,isrow = a->row;
1471: PetscErrorCode ierr;
1472: const PetscInt *rout,*cout,*r,*c,*diag = a->diag,*ai = a->i,*aj = a->j,*vi;
1473: PetscInt i,n = A->rmap->n,j;
1474: PetscInt nz;
1475: PetscScalar *x,*tmp,s1;
1476: const MatScalar *aa = a->a,*v;
1477: const PetscScalar *b;
1480: if (zz != xx) {VecCopy(zz,xx);}
1481: VecGetArrayRead(bb,&b);
1482: VecGetArray(xx,&x);
1483: tmp = a->solve_work;
1485: ISGetIndices(isrow,&rout); r = rout;
1486: ISGetIndices(iscol,&cout); c = cout;
1488: /* copy the b into temp work space according to permutation */
1489: for (i=0; i<n; i++) tmp[i] = b[c[i]];
1491: /* forward solve the U^T */
1492: for (i=0; i<n; i++) {
1493: v = aa + diag[i];
1494: vi = aj + diag[i] + 1;
1495: nz = ai[i+1] - diag[i] - 1;
1496: s1 = tmp[i];
1497: s1 *= (*v++); /* multiply by inverse of diagonal entry */
1498: for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
1499: tmp[i] = s1;
1500: }
1502: /* backward solve the L^T */
1503: for (i=n-1; i>=0; i--) {
1504: v = aa + diag[i] - 1;
1505: vi = aj + diag[i] - 1;
1506: nz = diag[i] - ai[i];
1507: s1 = tmp[i];
1508: for (j=0; j>-nz; j--) tmp[vi[j]] -= s1*v[j];
1509: }
1511: /* copy tmp into x according to permutation */
1512: for (i=0; i<n; i++) x[r[i]] += tmp[i];
1514: ISRestoreIndices(isrow,&rout);
1515: ISRestoreIndices(iscol,&cout);
1516: VecRestoreArrayRead(bb,&b);
1517: VecRestoreArray(xx,&x);
1519: PetscLogFlops(2.0*a->nz-A->cmap->n);
1520: return(0);
1521: }
1523: PetscErrorCode MatSolveTransposeAdd_SeqAIJ(Mat A,Vec bb,Vec zz,Vec xx)
1524: {
1525: Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
1526: IS iscol = a->col,isrow = a->row;
1527: PetscErrorCode ierr;
1528: const PetscInt *rout,*cout,*r,*c,*adiag = a->diag,*ai = a->i,*aj = a->j,*vi;
1529: PetscInt i,n = A->rmap->n,j;
1530: PetscInt nz;
1531: PetscScalar *x,*tmp,s1;
1532: const MatScalar *aa = a->a,*v;
1533: const PetscScalar *b;
1536: if (zz != xx) {VecCopy(zz,xx);}
1537: VecGetArrayRead(bb,&b);
1538: VecGetArray(xx,&x);
1539: tmp = a->solve_work;
1541: ISGetIndices(isrow,&rout); r = rout;
1542: ISGetIndices(iscol,&cout); c = cout;
1544: /* copy the b into temp work space according to permutation */
1545: for (i=0; i<n; i++) tmp[i] = b[c[i]];
1547: /* forward solve the U^T */
1548: for (i=0; i<n; i++) {
1549: v = aa + adiag[i+1] + 1;
1550: vi = aj + adiag[i+1] + 1;
1551: nz = adiag[i] - adiag[i+1] - 1;
1552: s1 = tmp[i];
1553: s1 *= v[nz]; /* multiply by inverse of diagonal entry */
1554: for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
1555: tmp[i] = s1;
1556: }
1559: /* backward solve the L^T */
1560: for (i=n-1; i>=0; i--) {
1561: v = aa + ai[i];
1562: vi = aj + ai[i];
1563: nz = ai[i+1] - ai[i];
1564: s1 = tmp[i];
1565: for (j=0; j<nz; j++) tmp[vi[j]] -= s1*v[j];
1566: }
1568: /* copy tmp into x according to permutation */
1569: for (i=0; i<n; i++) x[r[i]] += tmp[i];
1571: ISRestoreIndices(isrow,&rout);
1572: ISRestoreIndices(iscol,&cout);
1573: VecRestoreArrayRead(bb,&b);
1574: VecRestoreArray(xx,&x);
1576: PetscLogFlops(2.0*a->nz-A->cmap->n);
1577: return(0);
1578: }
1580: /* ----------------------------------------------------------------*/
1582: /*
1583: ilu() under revised new data structure.
1584: Factored arrays bj and ba are stored as
1585: L(0,:), L(1,:), ...,L(n-1,:), U(n-1,:),...,U(i,:),U(i-1,:),...,U(0,:)
1587: bi=fact->i is an array of size n+1, in which
1588: bi+
1589: bi[i]: points to 1st entry of L(i,:),i=0,...,n-1
1590: bi[n]: points to L(n-1,n-1)+1
1592: bdiag=fact->diag is an array of size n+1,in which
1593: bdiag[i]: points to diagonal of U(i,:), i=0,...,n-1
1594: bdiag[n]: points to entry of U(n-1,0)-1
1596: U(i,:) contains bdiag[i] as its last entry, i.e.,
1597: U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i])
1598: */
1599: PetscErrorCode MatILUFactorSymbolic_SeqAIJ_ilu0(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
1600: {
1601: Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b;
1603: const PetscInt n=A->rmap->n,*ai=a->i,*aj,*adiag=a->diag;
1604: PetscInt i,j,k=0,nz,*bi,*bj,*bdiag;
1605: IS isicol;
1608: ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);
1609: MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_FALSE);
1610: b = (Mat_SeqAIJ*)(fact)->data;
1612: /* allocate matrix arrays for new data structure */
1613: PetscMalloc3(ai[n]+1,&b->a,ai[n]+1,&b->j,n+1,&b->i);
1614: PetscLogObjectMemory((PetscObject)fact,ai[n]*(sizeof(PetscScalar)+sizeof(PetscInt))+(n+1)*sizeof(PetscInt));
1616: b->singlemalloc = PETSC_TRUE;
1617: if (!b->diag) {
1618: PetscMalloc1(n+1,&b->diag);
1619: PetscLogObjectMemory((PetscObject)fact,(n+1)*sizeof(PetscInt));
1620: }
1621: bdiag = b->diag;
1623: if (n > 0) {
1624: PetscArrayzero(b->a,ai[n]);
1625: }
1627: /* set bi and bj with new data structure */
1628: bi = b->i;
1629: bj = b->j;
1631: /* L part */
1632: bi[0] = 0;
1633: for (i=0; i<n; i++) {
1634: nz = adiag[i] - ai[i];
1635: bi[i+1] = bi[i] + nz;
1636: aj = a->j + ai[i];
1637: for (j=0; j<nz; j++) {
1638: /* *bj = aj[j]; bj++; */
1639: bj[k++] = aj[j];
1640: }
1641: }
1643: /* U part */
1644: bdiag[n] = bi[n]-1;
1645: for (i=n-1; i>=0; i--) {
1646: nz = ai[i+1] - adiag[i] - 1;
1647: aj = a->j + adiag[i] + 1;
1648: for (j=0; j<nz; j++) {
1649: /* *bj = aj[j]; bj++; */
1650: bj[k++] = aj[j];
1651: }
1652: /* diag[i] */
1653: /* *bj = i; bj++; */
1654: bj[k++] = i;
1655: bdiag[i] = bdiag[i+1] + nz + 1;
1656: }
1658: fact->factortype = MAT_FACTOR_ILU;
1659: fact->info.factor_mallocs = 0;
1660: fact->info.fill_ratio_given = info->fill;
1661: fact->info.fill_ratio_needed = 1.0;
1662: fact->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ;
1663: MatSeqAIJCheckInode_FactorLU(fact);
1665: b = (Mat_SeqAIJ*)(fact)->data;
1666: b->row = isrow;
1667: b->col = iscol;
1668: b->icol = isicol;
1669: PetscMalloc1(fact->rmap->n+1,&b->solve_work);
1670: PetscObjectReference((PetscObject)isrow);
1671: PetscObjectReference((PetscObject)iscol);
1672: return(0);
1673: }
1675: PetscErrorCode MatILUFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
1676: {
1677: Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b;
1678: IS isicol;
1679: PetscErrorCode ierr;
1680: const PetscInt *r,*ic;
1681: PetscInt n=A->rmap->n,*ai=a->i,*aj=a->j;
1682: PetscInt *bi,*cols,nnz,*cols_lvl;
1683: PetscInt *bdiag,prow,fm,nzbd,reallocs=0,dcount=0;
1684: PetscInt i,levels,diagonal_fill;
1685: PetscBool col_identity,row_identity,missing;
1686: PetscReal f;
1687: PetscInt nlnk,*lnk,*lnk_lvl=NULL;
1688: PetscBT lnkbt;
1689: PetscInt nzi,*bj,**bj_ptr,**bjlvl_ptr;
1690: PetscFreeSpaceList free_space =NULL,current_space=NULL;
1691: PetscFreeSpaceList free_space_lvl=NULL,current_space_lvl=NULL;
1694: 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);
1695: MatMissingDiagonal(A,&missing,&i);
1696: if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i);
1698: levels = (PetscInt)info->levels;
1699: ISIdentity(isrow,&row_identity);
1700: ISIdentity(iscol,&col_identity);
1701: if (!levels && row_identity && col_identity) {
1702: /* special case: ilu(0) with natural ordering */
1703: MatILUFactorSymbolic_SeqAIJ_ilu0(fact,A,isrow,iscol,info);
1704: if (a->inode.size) {
1705: fact->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode;
1706: }
1707: return(0);
1708: }
1710: ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);
1711: ISGetIndices(isrow,&r);
1712: ISGetIndices(isicol,&ic);
1714: /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */
1715: PetscMalloc1(n+1,&bi);
1716: PetscMalloc1(n+1,&bdiag);
1717: bi[0] = bdiag[0] = 0;
1718: PetscMalloc2(n,&bj_ptr,n,&bjlvl_ptr);
1720: /* create a linked list for storing column indices of the active row */
1721: nlnk = n + 1;
1722: PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);
1724: /* initial FreeSpace size is f*(ai[n]+1) */
1725: f = info->fill;
1726: diagonal_fill = (PetscInt)info->diagonal_fill;
1727: PetscFreeSpaceGet(PetscRealIntMultTruncate(f,ai[n]+1),&free_space);
1728: current_space = free_space;
1729: PetscFreeSpaceGet(PetscRealIntMultTruncate(f,ai[n]+1),&free_space_lvl);
1730: current_space_lvl = free_space_lvl;
1731: for (i=0; i<n; i++) {
1732: nzi = 0;
1733: /* copy current row into linked list */
1734: nnz = ai[r[i]+1] - ai[r[i]];
1735: 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);
1736: cols = aj + ai[r[i]];
1737: lnk[i] = -1; /* marker to indicate if diagonal exists */
1738: PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);
1739: nzi += nlnk;
1741: /* make sure diagonal entry is included */
1742: if (diagonal_fill && lnk[i] == -1) {
1743: fm = n;
1744: while (lnk[fm] < i) fm = lnk[fm];
1745: lnk[i] = lnk[fm]; /* insert diagonal into linked list */
1746: lnk[fm] = i;
1747: lnk_lvl[i] = 0;
1748: nzi++; dcount++;
1749: }
1751: /* add pivot rows into the active row */
1752: nzbd = 0;
1753: prow = lnk[n];
1754: while (prow < i) {
1755: nnz = bdiag[prow];
1756: cols = bj_ptr[prow] + nnz + 1;
1757: cols_lvl = bjlvl_ptr[prow] + nnz + 1;
1758: nnz = bi[prow+1] - bi[prow] - nnz - 1;
1759: PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);
1760: nzi += nlnk;
1761: prow = lnk[prow];
1762: nzbd++;
1763: }
1764: bdiag[i] = nzbd;
1765: bi[i+1] = bi[i] + nzi;
1766: /* if free space is not available, make more free space */
1767: if (current_space->local_remaining<nzi) {
1768: nnz = PetscIntMultTruncate(2,PetscIntMultTruncate(nzi,n - i)); /* estimated and max additional space needed */
1769: PetscFreeSpaceGet(nnz,¤t_space);
1770: PetscFreeSpaceGet(nnz,¤t_space_lvl);
1771: reallocs++;
1772: }
1774: /* copy data into free_space and free_space_lvl, then initialize lnk */
1775: PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);
1776: bj_ptr[i] = current_space->array;
1777: bjlvl_ptr[i] = current_space_lvl->array;
1779: /* make sure the active row i has diagonal entry */
1780: 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);
1782: current_space->array += nzi;
1783: current_space->local_used += nzi;
1784: current_space->local_remaining -= nzi;
1785: current_space_lvl->array += nzi;
1786: current_space_lvl->local_used += nzi;
1787: current_space_lvl->local_remaining -= nzi;
1788: }
1790: ISRestoreIndices(isrow,&r);
1791: ISRestoreIndices(isicol,&ic);
1792: /* copy free_space into bj and free free_space; set bi, bj, bdiag in new datastructure; */
1793: PetscMalloc1(bi[n]+1,&bj);
1794: PetscFreeSpaceContiguous_LU(&free_space,bj,n,bi,bdiag);
1796: PetscIncompleteLLDestroy(lnk,lnkbt);
1797: PetscFreeSpaceDestroy(free_space_lvl);
1798: PetscFree2(bj_ptr,bjlvl_ptr);
1800: #if defined(PETSC_USE_INFO)
1801: {
1802: PetscReal af = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]);
1803: PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)f,(double)af);
1804: PetscInfo1(A,"Run with -[sub_]pc_factor_fill %g or use \n",(double)af);
1805: PetscInfo1(A,"PCFactorSetFill([sub]pc,%g);\n",(double)af);
1806: PetscInfo(A,"for best performance.\n");
1807: if (diagonal_fill) {
1808: PetscInfo1(A,"Detected and replaced %D missing diagonals\n",dcount);
1809: }
1810: }
1811: #endif
1812: /* put together the new matrix */
1813: MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,NULL);
1814: PetscLogObjectParent((PetscObject)fact,(PetscObject)isicol);
1815: b = (Mat_SeqAIJ*)(fact)->data;
1817: b->free_a = PETSC_TRUE;
1818: b->free_ij = PETSC_TRUE;
1819: b->singlemalloc = PETSC_FALSE;
1821: PetscMalloc1(bdiag[0]+1,&b->a);
1823: b->j = bj;
1824: b->i = bi;
1825: b->diag = bdiag;
1826: b->ilen = 0;
1827: b->imax = 0;
1828: b->row = isrow;
1829: b->col = iscol;
1830: PetscObjectReference((PetscObject)isrow);
1831: PetscObjectReference((PetscObject)iscol);
1832: b->icol = isicol;
1834: PetscMalloc1(n+1,&b->solve_work);
1835: /* In b structure: Free imax, ilen, old a, old j.
1836: Allocate bdiag, solve_work, new a, new j */
1837: PetscLogObjectMemory((PetscObject)fact,(bdiag[0]+1)*(sizeof(PetscInt)+sizeof(PetscScalar)));
1838: b->maxnz = b->nz = bdiag[0]+1;
1840: (fact)->info.factor_mallocs = reallocs;
1841: (fact)->info.fill_ratio_given = f;
1842: (fact)->info.fill_ratio_needed = ((PetscReal)(bdiag[0]+1))/((PetscReal)ai[n]);
1843: (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ;
1844: if (a->inode.size) {
1845: (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode;
1846: }
1847: MatSeqAIJCheckInode_FactorLU(fact);
1848: return(0);
1849: }
1851: PetscErrorCode MatILUFactorSymbolic_SeqAIJ_inplace(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
1852: {
1853: Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data,*b;
1854: IS isicol;
1855: PetscErrorCode ierr;
1856: const PetscInt *r,*ic;
1857: PetscInt n=A->rmap->n,*ai=a->i,*aj=a->j;
1858: PetscInt *bi,*cols,nnz,*cols_lvl;
1859: PetscInt *bdiag,prow,fm,nzbd,reallocs=0,dcount=0;
1860: PetscInt i,levels,diagonal_fill;
1861: PetscBool col_identity,row_identity;
1862: PetscReal f;
1863: PetscInt nlnk,*lnk,*lnk_lvl=NULL;
1864: PetscBT lnkbt;
1865: PetscInt nzi,*bj,**bj_ptr,**bjlvl_ptr;
1866: PetscFreeSpaceList free_space =NULL,current_space=NULL;
1867: PetscFreeSpaceList free_space_lvl=NULL,current_space_lvl=NULL;
1868: PetscBool missing;
1871: 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);
1872: MatMissingDiagonal(A,&missing,&i);
1873: if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i);
1875: f = info->fill;
1876: levels = (PetscInt)info->levels;
1877: diagonal_fill = (PetscInt)info->diagonal_fill;
1879: ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);
1881: ISIdentity(isrow,&row_identity);
1882: ISIdentity(iscol,&col_identity);
1883: if (!levels && row_identity && col_identity) { /* special case: ilu(0) with natural ordering */
1884: MatDuplicateNoCreate_SeqAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_TRUE);
1886: (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_inplace;
1887: if (a->inode.size) {
1888: (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode_inplace;
1889: }
1890: fact->factortype = MAT_FACTOR_ILU;
1891: (fact)->info.factor_mallocs = 0;
1892: (fact)->info.fill_ratio_given = info->fill;
1893: (fact)->info.fill_ratio_needed = 1.0;
1895: b = (Mat_SeqAIJ*)(fact)->data;
1896: b->row = isrow;
1897: b->col = iscol;
1898: b->icol = isicol;
1899: PetscMalloc1((fact)->rmap->n+1,&b->solve_work);
1900: PetscObjectReference((PetscObject)isrow);
1901: PetscObjectReference((PetscObject)iscol);
1902: return(0);
1903: }
1905: ISGetIndices(isrow,&r);
1906: ISGetIndices(isicol,&ic);
1908: /* get new row and diagonal pointers, must be allocated separately because they will be given to the Mat_SeqAIJ and freed separately */
1909: PetscMalloc1(n+1,&bi);
1910: PetscMalloc1(n+1,&bdiag);
1911: bi[0] = bdiag[0] = 0;
1913: PetscMalloc2(n,&bj_ptr,n,&bjlvl_ptr);
1915: /* create a linked list for storing column indices of the active row */
1916: nlnk = n + 1;
1917: PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);
1919: /* initial FreeSpace size is f*(ai[n]+1) */
1920: PetscFreeSpaceGet(PetscRealIntMultTruncate(f,ai[n]+1),&free_space);
1921: current_space = free_space;
1922: PetscFreeSpaceGet(PetscRealIntMultTruncate(f,ai[n]+1),&free_space_lvl);
1923: current_space_lvl = free_space_lvl;
1925: for (i=0; i<n; i++) {
1926: nzi = 0;
1927: /* copy current row into linked list */
1928: nnz = ai[r[i]+1] - ai[r[i]];
1929: 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);
1930: cols = aj + ai[r[i]];
1931: lnk[i] = -1; /* marker to indicate if diagonal exists */
1932: PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);
1933: nzi += nlnk;
1935: /* make sure diagonal entry is included */
1936: if (diagonal_fill && lnk[i] == -1) {
1937: fm = n;
1938: while (lnk[fm] < i) fm = lnk[fm];
1939: lnk[i] = lnk[fm]; /* insert diagonal into linked list */
1940: lnk[fm] = i;
1941: lnk_lvl[i] = 0;
1942: nzi++; dcount++;
1943: }
1945: /* add pivot rows into the active row */
1946: nzbd = 0;
1947: prow = lnk[n];
1948: while (prow < i) {
1949: nnz = bdiag[prow];
1950: cols = bj_ptr[prow] + nnz + 1;
1951: cols_lvl = bjlvl_ptr[prow] + nnz + 1;
1952: nnz = bi[prow+1] - bi[prow] - nnz - 1;
1953: PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);
1954: nzi += nlnk;
1955: prow = lnk[prow];
1956: nzbd++;
1957: }
1958: bdiag[i] = nzbd;
1959: bi[i+1] = bi[i] + nzi;
1961: /* if free space is not available, make more free space */
1962: if (current_space->local_remaining<nzi) {
1963: nnz = PetscIntMultTruncate(nzi,n - i); /* estimated and max additional space needed */
1964: PetscFreeSpaceGet(nnz,¤t_space);
1965: PetscFreeSpaceGet(nnz,¤t_space_lvl);
1966: reallocs++;
1967: }
1969: /* copy data into free_space and free_space_lvl, then initialize lnk */
1970: PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);
1971: bj_ptr[i] = current_space->array;
1972: bjlvl_ptr[i] = current_space_lvl->array;
1974: /* make sure the active row i has diagonal entry */
1975: 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);
1977: current_space->array += nzi;
1978: current_space->local_used += nzi;
1979: current_space->local_remaining -= nzi;
1980: current_space_lvl->array += nzi;
1981: current_space_lvl->local_used += nzi;
1982: current_space_lvl->local_remaining -= nzi;
1983: }
1985: ISRestoreIndices(isrow,&r);
1986: ISRestoreIndices(isicol,&ic);
1988: /* destroy list of free space and other temporary arrays */
1989: PetscMalloc1(bi[n]+1,&bj);
1990: PetscFreeSpaceContiguous(&free_space,bj); /* copy free_space -> bj */
1991: PetscIncompleteLLDestroy(lnk,lnkbt);
1992: PetscFreeSpaceDestroy(free_space_lvl);
1993: PetscFree2(bj_ptr,bjlvl_ptr);
1995: #if defined(PETSC_USE_INFO)
1996: {
1997: PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]);
1998: PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)f,(double)af);
1999: PetscInfo1(A,"Run with -[sub_]pc_factor_fill %g or use \n",(double)af);
2000: PetscInfo1(A,"PCFactorSetFill([sub]pc,%g);\n",(double)af);
2001: PetscInfo(A,"for best performance.\n");
2002: if (diagonal_fill) {
2003: PetscInfo1(A,"Detected and replaced %D missing diagonals\n",dcount);
2004: }
2005: }
2006: #endif
2008: /* put together the new matrix */
2009: MatSeqAIJSetPreallocation_SeqAIJ(fact,MAT_SKIP_ALLOCATION,NULL);
2010: PetscLogObjectParent((PetscObject)fact,(PetscObject)isicol);
2011: b = (Mat_SeqAIJ*)(fact)->data;
2013: b->free_a = PETSC_TRUE;
2014: b->free_ij = PETSC_TRUE;
2015: b->singlemalloc = PETSC_FALSE;
2017: PetscMalloc1(bi[n],&b->a);
2018: b->j = bj;
2019: b->i = bi;
2020: for (i=0; i<n; i++) bdiag[i] += bi[i];
2021: b->diag = bdiag;
2022: b->ilen = 0;
2023: b->imax = 0;
2024: b->row = isrow;
2025: b->col = iscol;
2026: PetscObjectReference((PetscObject)isrow);
2027: PetscObjectReference((PetscObject)iscol);
2028: b->icol = isicol;
2029: PetscMalloc1(n+1,&b->solve_work);
2030: /* In b structure: Free imax, ilen, old a, old j.
2031: Allocate bdiag, solve_work, new a, new j */
2032: PetscLogObjectMemory((PetscObject)fact,(bi[n]-n) * (sizeof(PetscInt)+sizeof(PetscScalar)));
2033: b->maxnz = b->nz = bi[n];
2035: (fact)->info.factor_mallocs = reallocs;
2036: (fact)->info.fill_ratio_given = f;
2037: (fact)->info.fill_ratio_needed = ((PetscReal)bi[n])/((PetscReal)ai[n]);
2038: (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_inplace;
2039: if (a->inode.size) {
2040: (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqAIJ_Inode_inplace;
2041: }
2042: return(0);
2043: }
2045: PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ(Mat B,Mat A,const MatFactorInfo *info)
2046: {
2047: Mat C = B;
2048: Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data;
2049: Mat_SeqSBAIJ *b=(Mat_SeqSBAIJ*)C->data;
2050: IS ip=b->row,iip = b->icol;
2052: const PetscInt *rip,*riip;
2053: PetscInt i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bdiag=b->diag,*bjtmp;
2054: PetscInt *ai=a->i,*aj=a->j;
2055: PetscInt k,jmin,jmax,*c2r,*il,col,nexti,ili,nz;
2056: MatScalar *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi;
2057: PetscBool perm_identity;
2058: FactorShiftCtx sctx;
2059: PetscReal rs;
2060: MatScalar d,*v;
2063: /* MatPivotSetUp(): initialize shift context sctx */
2064: PetscMemzero(&sctx,sizeof(FactorShiftCtx));
2066: if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */
2067: sctx.shift_top = info->zeropivot;
2068: for (i=0; i<mbs; i++) {
2069: /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
2070: d = (aa)[a->diag[i]];
2071: rs = -PetscAbsScalar(d) - PetscRealPart(d);
2072: v = aa+ai[i];
2073: nz = ai[i+1] - ai[i];
2074: for (j=0; j<nz; j++) rs += PetscAbsScalar(v[j]);
2075: if (rs>sctx.shift_top) sctx.shift_top = rs;
2076: }
2077: sctx.shift_top *= 1.1;
2078: sctx.nshift_max = 5;
2079: sctx.shift_lo = 0.;
2080: sctx.shift_hi = 1.;
2081: }
2083: ISGetIndices(ip,&rip);
2084: ISGetIndices(iip,&riip);
2086: /* allocate working arrays
2087: c2r: linked list, keep track of pivot rows for a given column. c2r[col]: head of the list for a given col
2088: 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
2089: */
2090: PetscMalloc3(mbs,&rtmp,mbs,&il,mbs,&c2r);
2092: do {
2093: sctx.newshift = PETSC_FALSE;
2095: for (i=0; i<mbs; i++) c2r[i] = mbs;
2096: if (mbs) il[0] = 0;
2098: for (k = 0; k<mbs; k++) {
2099: /* zero rtmp */
2100: nz = bi[k+1] - bi[k];
2101: bjtmp = bj + bi[k];
2102: for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
2104: /* load in initial unfactored row */
2105: bval = ba + bi[k];
2106: jmin = ai[rip[k]]; jmax = ai[rip[k]+1];
2107: for (j = jmin; j < jmax; j++) {
2108: col = riip[aj[j]];
2109: if (col >= k) { /* only take upper triangular entry */
2110: rtmp[col] = aa[j];
2111: *bval++ = 0.0; /* for in-place factorization */
2112: }
2113: }
2114: /* shift the diagonal of the matrix: ZeropivotApply() */
2115: rtmp[k] += sctx.shift_amount; /* shift the diagonal of the matrix */
2117: /* modify k-th row by adding in those rows i with U(i,k)!=0 */
2118: dk = rtmp[k];
2119: i = c2r[k]; /* first row to be added to k_th row */
2121: while (i < k) {
2122: nexti = c2r[i]; /* next row to be added to k_th row */
2124: /* compute multiplier, update diag(k) and U(i,k) */
2125: ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */
2126: uikdi = -ba[ili]*ba[bdiag[i]]; /* diagonal(k) */
2127: dk += uikdi*ba[ili]; /* update diag[k] */
2128: ba[ili] = uikdi; /* -U(i,k) */
2130: /* add multiple of row i to k-th row */
2131: jmin = ili + 1; jmax = bi[i+1];
2132: if (jmin < jmax) {
2133: for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j];
2134: /* update il and c2r for row i */
2135: il[i] = jmin;
2136: j = bj[jmin]; c2r[i] = c2r[j]; c2r[j] = i;
2137: }
2138: i = nexti;
2139: }
2141: /* copy data into U(k,:) */
2142: rs = 0.0;
2143: jmin = bi[k]; jmax = bi[k+1]-1;
2144: if (jmin < jmax) {
2145: for (j=jmin; j<jmax; j++) {
2146: col = bj[j]; ba[j] = rtmp[col]; rs += PetscAbsScalar(ba[j]);
2147: }
2148: /* add the k-th row into il and c2r */
2149: il[k] = jmin;
2150: i = bj[jmin]; c2r[k] = c2r[i]; c2r[i] = k;
2151: }
2153: /* MatPivotCheck() */
2154: sctx.rs = rs;
2155: sctx.pv = dk;
2156: MatPivotCheck(B,A,info,&sctx,i);
2157: if (sctx.newshift) break;
2158: dk = sctx.pv;
2160: ba[bdiag[k]] = 1.0/dk; /* U(k,k) */
2161: }
2162: } while (sctx.newshift);
2164: PetscFree3(rtmp,il,c2r);
2165: ISRestoreIndices(ip,&rip);
2166: ISRestoreIndices(iip,&riip);
2168: ISIdentity(ip,&perm_identity);
2169: if (perm_identity) {
2170: B->ops->solve = MatSolve_SeqSBAIJ_1_NaturalOrdering;
2171: B->ops->solvetranspose = MatSolve_SeqSBAIJ_1_NaturalOrdering;
2172: B->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering;
2173: B->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering;
2174: } else {
2175: B->ops->solve = MatSolve_SeqSBAIJ_1;
2176: B->ops->solvetranspose = MatSolve_SeqSBAIJ_1;
2177: B->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1;
2178: B->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1;
2179: }
2181: C->assembled = PETSC_TRUE;
2182: C->preallocated = PETSC_TRUE;
2184: PetscLogFlops(C->rmap->n);
2186: /* MatPivotView() */
2187: if (sctx.nshift) {
2188: if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) {
2189: 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);
2190: } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) {
2191: PetscInfo2(A,"number of shift_nz tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);
2192: } else if (info->shifttype == (PetscReal)MAT_SHIFT_INBLOCKS) {
2193: PetscInfo2(A,"number of shift_inblocks applied %D, each shift_amount %g\n",sctx.nshift,(double)info->shiftamount);
2194: }
2195: }
2196: return(0);
2197: }
2199: PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ_inplace(Mat B,Mat A,const MatFactorInfo *info)
2200: {
2201: Mat C = B;
2202: Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data;
2203: Mat_SeqSBAIJ *b=(Mat_SeqSBAIJ*)C->data;
2204: IS ip=b->row,iip = b->icol;
2206: const PetscInt *rip,*riip;
2207: PetscInt i,j,mbs=A->rmap->n,*bi=b->i,*bj=b->j,*bcol,*bjtmp;
2208: PetscInt *ai=a->i,*aj=a->j;
2209: PetscInt k,jmin,jmax,*jl,*il,col,nexti,ili,nz;
2210: MatScalar *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi;
2211: PetscBool perm_identity;
2212: FactorShiftCtx sctx;
2213: PetscReal rs;
2214: MatScalar d,*v;
2217: /* MatPivotSetUp(): initialize shift context sctx */
2218: PetscMemzero(&sctx,sizeof(FactorShiftCtx));
2220: if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */
2221: sctx.shift_top = info->zeropivot;
2222: for (i=0; i<mbs; i++) {
2223: /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
2224: d = (aa)[a->diag[i]];
2225: rs = -PetscAbsScalar(d) - PetscRealPart(d);
2226: v = aa+ai[i];
2227: nz = ai[i+1] - ai[i];
2228: for (j=0; j<nz; j++) rs += PetscAbsScalar(v[j]);
2229: if (rs>sctx.shift_top) sctx.shift_top = rs;
2230: }
2231: sctx.shift_top *= 1.1;
2232: sctx.nshift_max = 5;
2233: sctx.shift_lo = 0.;
2234: sctx.shift_hi = 1.;
2235: }
2237: ISGetIndices(ip,&rip);
2238: ISGetIndices(iip,&riip);
2240: /* initialization */
2241: PetscMalloc3(mbs,&rtmp,mbs,&il,mbs,&jl);
2243: do {
2244: sctx.newshift = PETSC_FALSE;
2246: for (i=0; i<mbs; i++) jl[i] = mbs;
2247: il[0] = 0;
2249: for (k = 0; k<mbs; k++) {
2250: /* zero rtmp */
2251: nz = bi[k+1] - bi[k];
2252: bjtmp = bj + bi[k];
2253: for (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
2255: bval = ba + bi[k];
2256: /* initialize k-th row by the perm[k]-th row of A */
2257: jmin = ai[rip[k]]; jmax = ai[rip[k]+1];
2258: for (j = jmin; j < jmax; j++) {
2259: col = riip[aj[j]];
2260: if (col >= k) { /* only take upper triangular entry */
2261: rtmp[col] = aa[j];
2262: *bval++ = 0.0; /* for in-place factorization */
2263: }
2264: }
2265: /* shift the diagonal of the matrix */
2266: if (sctx.nshift) rtmp[k] += sctx.shift_amount;
2268: /* modify k-th row by adding in those rows i with U(i,k)!=0 */
2269: dk = rtmp[k];
2270: i = jl[k]; /* first row to be added to k_th row */
2272: while (i < k) {
2273: nexti = jl[i]; /* next row to be added to k_th row */
2275: /* compute multiplier, update diag(k) and U(i,k) */
2276: ili = il[i]; /* index of first nonzero element in U(i,k:bms-1) */
2277: uikdi = -ba[ili]*ba[bi[i]]; /* diagonal(k) */
2278: dk += uikdi*ba[ili];
2279: ba[ili] = uikdi; /* -U(i,k) */
2281: /* add multiple of row i to k-th row */
2282: jmin = ili + 1; jmax = bi[i+1];
2283: if (jmin < jmax) {
2284: for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j];
2285: /* update il and jl for row i */
2286: il[i] = jmin;
2287: j = bj[jmin]; jl[i] = jl[j]; jl[j] = i;
2288: }
2289: i = nexti;
2290: }
2292: /* shift the diagonals when zero pivot is detected */
2293: /* compute rs=sum of abs(off-diagonal) */
2294: rs = 0.0;
2295: jmin = bi[k]+1;
2296: nz = bi[k+1] - jmin;
2297: bcol = bj + jmin;
2298: for (j=0; j<nz; j++) {
2299: rs += PetscAbsScalar(rtmp[bcol[j]]);
2300: }
2302: sctx.rs = rs;
2303: sctx.pv = dk;
2304: MatPivotCheck(B,A,info,&sctx,k);
2305: if (sctx.newshift) break;
2306: dk = sctx.pv;
2308: /* copy data into U(k,:) */
2309: ba[bi[k]] = 1.0/dk; /* U(k,k) */
2310: jmin = bi[k]+1; jmax = bi[k+1];
2311: if (jmin < jmax) {
2312: for (j=jmin; j<jmax; j++) {
2313: col = bj[j]; ba[j] = rtmp[col];
2314: }
2315: /* add the k-th row into il and jl */
2316: il[k] = jmin;
2317: i = bj[jmin]; jl[k] = jl[i]; jl[i] = k;
2318: }
2319: }
2320: } while (sctx.newshift);
2322: PetscFree3(rtmp,il,jl);
2323: ISRestoreIndices(ip,&rip);
2324: ISRestoreIndices(iip,&riip);
2326: ISIdentity(ip,&perm_identity);
2327: if (perm_identity) {
2328: B->ops->solve = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace;
2329: B->ops->solvetranspose = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace;
2330: B->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1_NaturalOrdering_inplace;
2331: B->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1_NaturalOrdering_inplace;
2332: } else {
2333: B->ops->solve = MatSolve_SeqSBAIJ_1_inplace;
2334: B->ops->solvetranspose = MatSolve_SeqSBAIJ_1_inplace;
2335: B->ops->forwardsolve = MatForwardSolve_SeqSBAIJ_1_inplace;
2336: B->ops->backwardsolve = MatBackwardSolve_SeqSBAIJ_1_inplace;
2337: }
2339: C->assembled = PETSC_TRUE;
2340: C->preallocated = PETSC_TRUE;
2342: PetscLogFlops(C->rmap->n);
2343: if (sctx.nshift) {
2344: if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) {
2345: PetscInfo2(A,"number of shiftnz tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);
2346: } else if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) {
2347: PetscInfo2(A,"number of shiftpd tries %D, shift_amount %g\n",sctx.nshift,(double)sctx.shift_amount);
2348: }
2349: }
2350: return(0);
2351: }
2353: /*
2354: icc() under revised new data structure.
2355: Factored arrays bj and ba are stored as
2356: U(0,:),...,U(i,:),U(n-1,:)
2358: ui=fact->i is an array of size n+1, in which
2359: ui+
2360: ui[i]: points to 1st entry of U(i,:),i=0,...,n-1
2361: ui[n]: points to U(n-1,n-1)+1
2363: udiag=fact->diag is an array of size n,in which
2364: udiag[i]: points to diagonal of U(i,:), i=0,...,n-1
2366: U(i,:) contains udiag[i] as its last entry, i.e.,
2367: U(i,:) = (u[i,i+1],...,u[i,n-1],diag[i])
2368: */
2370: PetscErrorCode MatICCFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
2371: {
2372: Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
2373: Mat_SeqSBAIJ *b;
2374: PetscErrorCode ierr;
2375: PetscBool perm_identity,missing;
2376: PetscInt reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag;
2377: const PetscInt *rip,*riip;
2378: PetscInt jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow;
2379: PetscInt nlnk,*lnk,*lnk_lvl=NULL,d;
2380: PetscInt ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr;
2381: PetscReal fill =info->fill,levels=info->levels;
2382: PetscFreeSpaceList free_space =NULL,current_space=NULL;
2383: PetscFreeSpaceList free_space_lvl=NULL,current_space_lvl=NULL;
2384: PetscBT lnkbt;
2385: IS iperm;
2388: 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);
2389: MatMissingDiagonal(A,&missing,&d);
2390: if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d);
2391: ISIdentity(perm,&perm_identity);
2392: ISInvertPermutation(perm,PETSC_DECIDE,&iperm);
2394: PetscMalloc1(am+1,&ui);
2395: PetscMalloc1(am+1,&udiag);
2396: ui[0] = 0;
2398: /* ICC(0) without matrix ordering: simply rearrange column indices */
2399: if (!levels && perm_identity) {
2400: for (i=0; i<am; i++) {
2401: ncols = ai[i+1] - a->diag[i];
2402: ui[i+1] = ui[i] + ncols;
2403: udiag[i] = ui[i+1] - 1; /* points to the last entry of U(i,:) */
2404: }
2405: PetscMalloc1(ui[am]+1,&uj);
2406: cols = uj;
2407: for (i=0; i<am; i++) {
2408: aj = a->j + a->diag[i] + 1; /* 1st entry of U(i,:) without diagonal */
2409: ncols = ai[i+1] - a->diag[i] -1;
2410: for (j=0; j<ncols; j++) *cols++ = aj[j];
2411: *cols++ = i; /* diagoanl is located as the last entry of U(i,:) */
2412: }
2413: } else { /* case: levels>0 || (levels=0 && !perm_identity) */
2414: ISGetIndices(iperm,&riip);
2415: ISGetIndices(perm,&rip);
2417: /* initialization */
2418: PetscMalloc1(am+1,&ajtmp);
2420: /* jl: linked list for storing indices of the pivot rows
2421: il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
2422: PetscMalloc4(am,&uj_ptr,am,&uj_lvl_ptr,am,&jl,am,&il);
2423: for (i=0; i<am; i++) {
2424: jl[i] = am; il[i] = 0;
2425: }
2427: /* create and initialize a linked list for storing column indices of the active row k */
2428: nlnk = am + 1;
2429: PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);
2431: /* initial FreeSpace size is fill*(ai[am]+am)/2 */
2432: PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,(ai[am]+am)/2),&free_space);
2433: current_space = free_space;
2434: PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,(ai[am]+am)/2),&free_space_lvl);
2435: current_space_lvl = free_space_lvl;
2437: for (k=0; k<am; k++) { /* for each active row k */
2438: /* initialize lnk by the column indices of row rip[k] of A */
2439: nzk = 0;
2440: ncols = ai[rip[k]+1] - ai[rip[k]];
2441: 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);
2442: ncols_upper = 0;
2443: for (j=0; j<ncols; j++) {
2444: i = *(aj + ai[rip[k]] + j); /* unpermuted column index */
2445: if (riip[i] >= k) { /* only take upper triangular entry */
2446: ajtmp[ncols_upper] = i;
2447: ncols_upper++;
2448: }
2449: }
2450: PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);
2451: nzk += nlnk;
2453: /* update lnk by computing fill-in for each pivot row to be merged in */
2454: prow = jl[k]; /* 1st pivot row */
2456: while (prow < k) {
2457: nextprow = jl[prow];
2459: /* merge prow into k-th row */
2460: jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */
2461: jmax = ui[prow+1];
2462: ncols = jmax-jmin;
2463: i = jmin - ui[prow];
2464: cols = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */
2465: uj = uj_lvl_ptr[prow] + i; /* levels of cols */
2466: j = *(uj - 1);
2467: PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);
2468: nzk += nlnk;
2470: /* update il and jl for prow */
2471: if (jmin < jmax) {
2472: il[prow] = jmin;
2473: j = *cols; jl[prow] = jl[j]; jl[j] = prow;
2474: }
2475: prow = nextprow;
2476: }
2478: /* if free space is not available, make more free space */
2479: if (current_space->local_remaining<nzk) {
2480: i = am - k + 1; /* num of unfactored rows */
2481: i = PetscIntMultTruncate(i,PetscMin(nzk, i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */
2482: PetscFreeSpaceGet(i,¤t_space);
2483: PetscFreeSpaceGet(i,¤t_space_lvl);
2484: reallocs++;
2485: }
2487: /* copy data into free_space and free_space_lvl, then initialize lnk */
2488: if (nzk == 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k);
2489: PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);
2491: /* add the k-th row into il and jl */
2492: if (nzk > 1) {
2493: i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
2494: jl[k] = jl[i]; jl[i] = k;
2495: il[k] = ui[k] + 1;
2496: }
2497: uj_ptr[k] = current_space->array;
2498: uj_lvl_ptr[k] = current_space_lvl->array;
2500: current_space->array += nzk;
2501: current_space->local_used += nzk;
2502: current_space->local_remaining -= nzk;
2504: current_space_lvl->array += nzk;
2505: current_space_lvl->local_used += nzk;
2506: current_space_lvl->local_remaining -= nzk;
2508: ui[k+1] = ui[k] + nzk;
2509: }
2511: ISRestoreIndices(perm,&rip);
2512: ISRestoreIndices(iperm,&riip);
2513: PetscFree4(uj_ptr,uj_lvl_ptr,jl,il);
2514: PetscFree(ajtmp);
2516: /* copy free_space into uj and free free_space; set ui, uj, udiag in new datastructure; */
2517: PetscMalloc1(ui[am]+1,&uj);
2518: PetscFreeSpaceContiguous_Cholesky(&free_space,uj,am,ui,udiag); /* store matrix factor */
2519: PetscIncompleteLLDestroy(lnk,lnkbt);
2520: PetscFreeSpaceDestroy(free_space_lvl);
2522: } /* end of case: levels>0 || (levels=0 && !perm_identity) */
2524: /* put together the new matrix in MATSEQSBAIJ format */
2525: b = (Mat_SeqSBAIJ*)(fact)->data;
2526: b->singlemalloc = PETSC_FALSE;
2528: PetscMalloc1(ui[am]+1,&b->a);
2530: b->j = uj;
2531: b->i = ui;
2532: b->diag = udiag;
2533: b->free_diag = PETSC_TRUE;
2534: b->ilen = 0;
2535: b->imax = 0;
2536: b->row = perm;
2537: b->col = perm;
2538: PetscObjectReference((PetscObject)perm);
2539: PetscObjectReference((PetscObject)perm);
2540: b->icol = iperm;
2541: b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
2543: PetscMalloc1(am+1,&b->solve_work);
2544: PetscLogObjectMemory((PetscObject)fact,ui[am]*(sizeof(PetscInt)+sizeof(MatScalar)));
2546: b->maxnz = b->nz = ui[am];
2547: b->free_a = PETSC_TRUE;
2548: b->free_ij = PETSC_TRUE;
2550: fact->info.factor_mallocs = reallocs;
2551: fact->info.fill_ratio_given = fill;
2552: if (ai[am] != 0) {
2553: /* nonzeros in lower triangular part of A (including diagonals) = (ai[am]+am)/2 */
2554: fact->info.fill_ratio_needed = ((PetscReal)2*ui[am])/(ai[am]+am);
2555: } else {
2556: fact->info.fill_ratio_needed = 0.0;
2557: }
2558: #if defined(PETSC_USE_INFO)
2559: if (ai[am] != 0) {
2560: PetscReal af = fact->info.fill_ratio_needed;
2561: PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)fill,(double)af);
2562: PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);
2563: PetscInfo1(A,"PCFactorSetFill(pc,%g) for best performance.\n",(double)af);
2564: } else {
2565: PetscInfo(A,"Empty matrix\n");
2566: }
2567: #endif
2568: fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ;
2569: return(0);
2570: }
2572: PetscErrorCode MatICCFactorSymbolic_SeqAIJ_inplace(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
2573: {
2574: Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
2575: Mat_SeqSBAIJ *b;
2576: PetscErrorCode ierr;
2577: PetscBool perm_identity,missing;
2578: PetscInt reallocs=0,i,*ai=a->i,*aj=a->j,am=A->rmap->n,*ui,*udiag;
2579: const PetscInt *rip,*riip;
2580: PetscInt jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow;
2581: PetscInt nlnk,*lnk,*lnk_lvl=NULL,d;
2582: PetscInt ncols,ncols_upper,*cols,*ajtmp,*uj,**uj_ptr,**uj_lvl_ptr;
2583: PetscReal fill =info->fill,levels=info->levels;
2584: PetscFreeSpaceList free_space =NULL,current_space=NULL;
2585: PetscFreeSpaceList free_space_lvl=NULL,current_space_lvl=NULL;
2586: PetscBT lnkbt;
2587: IS iperm;
2590: 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);
2591: MatMissingDiagonal(A,&missing,&d);
2592: if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d);
2593: ISIdentity(perm,&perm_identity);
2594: ISInvertPermutation(perm,PETSC_DECIDE,&iperm);
2596: PetscMalloc1(am+1,&ui);
2597: PetscMalloc1(am+1,&udiag);
2598: ui[0] = 0;
2600: /* ICC(0) without matrix ordering: simply copies fill pattern */
2601: if (!levels && perm_identity) {
2603: for (i=0; i<am; i++) {
2604: ui[i+1] = ui[i] + ai[i+1] - a->diag[i];
2605: udiag[i] = ui[i];
2606: }
2607: PetscMalloc1(ui[am]+1,&uj);
2608: cols = uj;
2609: for (i=0; i<am; i++) {
2610: aj = a->j + a->diag[i];
2611: ncols = ui[i+1] - ui[i];
2612: for (j=0; j<ncols; j++) *cols++ = *aj++;
2613: }
2614: } else { /* case: levels>0 || (levels=0 && !perm_identity) */
2615: ISGetIndices(iperm,&riip);
2616: ISGetIndices(perm,&rip);
2618: /* initialization */
2619: PetscMalloc1(am+1,&ajtmp);
2621: /* jl: linked list for storing indices of the pivot rows
2622: il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
2623: PetscMalloc4(am,&uj_ptr,am,&uj_lvl_ptr,am,&jl,am,&il);
2624: for (i=0; i<am; i++) {
2625: jl[i] = am; il[i] = 0;
2626: }
2628: /* create and initialize a linked list for storing column indices of the active row k */
2629: nlnk = am + 1;
2630: PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);
2632: /* initial FreeSpace size is fill*(ai[am]+1) */
2633: PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,ai[am]+1),&free_space);
2634: current_space = free_space;
2635: PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,ai[am]+1),&free_space_lvl);
2636: current_space_lvl = free_space_lvl;
2638: for (k=0; k<am; k++) { /* for each active row k */
2639: /* initialize lnk by the column indices of row rip[k] of A */
2640: nzk = 0;
2641: ncols = ai[rip[k]+1] - ai[rip[k]];
2642: 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);
2643: ncols_upper = 0;
2644: for (j=0; j<ncols; j++) {
2645: i = *(aj + ai[rip[k]] + j); /* unpermuted column index */
2646: if (riip[i] >= k) { /* only take upper triangular entry */
2647: ajtmp[ncols_upper] = i;
2648: ncols_upper++;
2649: }
2650: }
2651: PetscIncompleteLLInit(ncols_upper,ajtmp,am,riip,nlnk,lnk,lnk_lvl,lnkbt);
2652: nzk += nlnk;
2654: /* update lnk by computing fill-in for each pivot row to be merged in */
2655: prow = jl[k]; /* 1st pivot row */
2657: while (prow < k) {
2658: nextprow = jl[prow];
2660: /* merge prow into k-th row */
2661: jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */
2662: jmax = ui[prow+1];
2663: ncols = jmax-jmin;
2664: i = jmin - ui[prow];
2665: cols = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */
2666: uj = uj_lvl_ptr[prow] + i; /* levels of cols */
2667: j = *(uj - 1);
2668: PetscICCLLAddSorted(ncols,cols,levels,uj,am,nlnk,lnk,lnk_lvl,lnkbt,j);
2669: nzk += nlnk;
2671: /* update il and jl for prow */
2672: if (jmin < jmax) {
2673: il[prow] = jmin;
2674: j = *cols; jl[prow] = jl[j]; jl[j] = prow;
2675: }
2676: prow = nextprow;
2677: }
2679: /* if free space is not available, make more free space */
2680: if (current_space->local_remaining<nzk) {
2681: i = am - k + 1; /* num of unfactored rows */
2682: i = PetscIntMultTruncate(i,PetscMin(nzk, i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */
2683: PetscFreeSpaceGet(i,¤t_space);
2684: PetscFreeSpaceGet(i,¤t_space_lvl);
2685: reallocs++;
2686: }
2688: /* copy data into free_space and free_space_lvl, then initialize lnk */
2689: if (!nzk) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Empty row %D in ICC matrix factor",k);
2690: PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);
2692: /* add the k-th row into il and jl */
2693: if (nzk > 1) {
2694: i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
2695: jl[k] = jl[i]; jl[i] = k;
2696: il[k] = ui[k] + 1;
2697: }
2698: uj_ptr[k] = current_space->array;
2699: uj_lvl_ptr[k] = current_space_lvl->array;
2701: current_space->array += nzk;
2702: current_space->local_used += nzk;
2703: current_space->local_remaining -= nzk;
2705: current_space_lvl->array += nzk;
2706: current_space_lvl->local_used += nzk;
2707: current_space_lvl->local_remaining -= nzk;
2709: ui[k+1] = ui[k] + nzk;
2710: }
2712: #if defined(PETSC_USE_INFO)
2713: if (ai[am] != 0) {
2714: PetscReal af = (PetscReal)ui[am]/((PetscReal)ai[am]);
2715: PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)fill,(double)af);
2716: PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);
2717: PetscInfo1(A,"PCFactorSetFill(pc,%g) for best performance.\n",(double)af);
2718: } else {
2719: PetscInfo(A,"Empty matrix\n");
2720: }
2721: #endif
2723: ISRestoreIndices(perm,&rip);
2724: ISRestoreIndices(iperm,&riip);
2725: PetscFree4(uj_ptr,uj_lvl_ptr,jl,il);
2726: PetscFree(ajtmp);
2728: /* destroy list of free space and other temporary array(s) */
2729: PetscMalloc1(ui[am]+1,&uj);
2730: PetscFreeSpaceContiguous(&free_space,uj);
2731: PetscIncompleteLLDestroy(lnk,lnkbt);
2732: PetscFreeSpaceDestroy(free_space_lvl);
2734: } /* end of case: levels>0 || (levels=0 && !perm_identity) */
2736: /* put together the new matrix in MATSEQSBAIJ format */
2738: b = (Mat_SeqSBAIJ*)fact->data;
2739: b->singlemalloc = PETSC_FALSE;
2741: PetscMalloc1(ui[am]+1,&b->a);
2743: b->j = uj;
2744: b->i = ui;
2745: b->diag = udiag;
2746: b->free_diag = PETSC_TRUE;
2747: b->ilen = 0;
2748: b->imax = 0;
2749: b->row = perm;
2750: b->col = perm;
2752: PetscObjectReference((PetscObject)perm);
2753: PetscObjectReference((PetscObject)perm);
2755: b->icol = iperm;
2756: b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
2757: PetscMalloc1(am+1,&b->solve_work);
2758: PetscLogObjectMemory((PetscObject)fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));
2759: b->maxnz = b->nz = ui[am];
2760: b->free_a = PETSC_TRUE;
2761: b->free_ij = PETSC_TRUE;
2763: fact->info.factor_mallocs = reallocs;
2764: fact->info.fill_ratio_given = fill;
2765: if (ai[am] != 0) {
2766: fact->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]);
2767: } else {
2768: fact->info.fill_ratio_needed = 0.0;
2769: }
2770: fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ_inplace;
2771: return(0);
2772: }
2774: PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
2775: {
2776: Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
2777: Mat_SeqSBAIJ *b;
2778: PetscErrorCode ierr;
2779: PetscBool perm_identity,missing;
2780: PetscReal fill = info->fill;
2781: const PetscInt *rip,*riip;
2782: PetscInt i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow;
2783: PetscInt *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow;
2784: PetscInt nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr,*udiag;
2785: PetscFreeSpaceList free_space=NULL,current_space=NULL;
2786: PetscBT lnkbt;
2787: IS iperm;
2790: 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);
2791: MatMissingDiagonal(A,&missing,&i);
2792: if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i);
2794: /* check whether perm is the identity mapping */
2795: ISIdentity(perm,&perm_identity);
2796: ISInvertPermutation(perm,PETSC_DECIDE,&iperm);
2797: ISGetIndices(iperm,&riip);
2798: ISGetIndices(perm,&rip);
2800: /* initialization */
2801: PetscMalloc1(am+1,&ui);
2802: PetscMalloc1(am+1,&udiag);
2803: ui[0] = 0;
2805: /* jl: linked list for storing indices of the pivot rows
2806: il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
2807: PetscMalloc4(am,&ui_ptr,am,&jl,am,&il,am,&cols);
2808: for (i=0; i<am; i++) {
2809: jl[i] = am; il[i] = 0;
2810: }
2812: /* create and initialize a linked list for storing column indices of the active row k */
2813: nlnk = am + 1;
2814: PetscLLCreate(am,am,nlnk,lnk,lnkbt);
2816: /* initial FreeSpace size is fill*(ai[am]+am)/2 */
2817: PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,(ai[am]+am)/2),&free_space);
2818: current_space = free_space;
2820: for (k=0; k<am; k++) { /* for each active row k */
2821: /* initialize lnk by the column indices of row rip[k] of A */
2822: nzk = 0;
2823: ncols = ai[rip[k]+1] - ai[rip[k]];
2824: 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);
2825: ncols_upper = 0;
2826: for (j=0; j<ncols; j++) {
2827: i = riip[*(aj + ai[rip[k]] + j)];
2828: if (i >= k) { /* only take upper triangular entry */
2829: cols[ncols_upper] = i;
2830: ncols_upper++;
2831: }
2832: }
2833: PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);
2834: nzk += nlnk;
2836: /* update lnk by computing fill-in for each pivot row to be merged in */
2837: prow = jl[k]; /* 1st pivot row */
2839: while (prow < k) {
2840: nextprow = jl[prow];
2841: /* merge prow into k-th row */
2842: jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */
2843: jmax = ui[prow+1];
2844: ncols = jmax-jmin;
2845: uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */
2846: PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);
2847: nzk += nlnk;
2849: /* update il and jl for prow */
2850: if (jmin < jmax) {
2851: il[prow] = jmin;
2852: j = *uj_ptr;
2853: jl[prow] = jl[j];
2854: jl[j] = prow;
2855: }
2856: prow = nextprow;
2857: }
2859: /* if free space is not available, make more free space */
2860: if (current_space->local_remaining<nzk) {
2861: i = am - k + 1; /* num of unfactored rows */
2862: i = PetscIntMultTruncate(i,PetscMin(nzk,i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */
2863: PetscFreeSpaceGet(i,¤t_space);
2864: reallocs++;
2865: }
2867: /* copy data into free space, then initialize lnk */
2868: PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);
2870: /* add the k-th row into il and jl */
2871: if (nzk > 1) {
2872: i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
2873: jl[k] = jl[i]; jl[i] = k;
2874: il[k] = ui[k] + 1;
2875: }
2876: ui_ptr[k] = current_space->array;
2878: current_space->array += nzk;
2879: current_space->local_used += nzk;
2880: current_space->local_remaining -= nzk;
2882: ui[k+1] = ui[k] + nzk;
2883: }
2885: ISRestoreIndices(perm,&rip);
2886: ISRestoreIndices(iperm,&riip);
2887: PetscFree4(ui_ptr,jl,il,cols);
2889: /* copy free_space into uj and free free_space; set ui, uj, udiag in new datastructure; */
2890: PetscMalloc1(ui[am]+1,&uj);
2891: PetscFreeSpaceContiguous_Cholesky(&free_space,uj,am,ui,udiag); /* store matrix factor */
2892: PetscLLDestroy(lnk,lnkbt);
2894: /* put together the new matrix in MATSEQSBAIJ format */
2896: b = (Mat_SeqSBAIJ*)fact->data;
2897: b->singlemalloc = PETSC_FALSE;
2898: b->free_a = PETSC_TRUE;
2899: b->free_ij = PETSC_TRUE;
2901: PetscMalloc1(ui[am]+1,&b->a);
2903: b->j = uj;
2904: b->i = ui;
2905: b->diag = udiag;
2906: b->free_diag = PETSC_TRUE;
2907: b->ilen = 0;
2908: b->imax = 0;
2909: b->row = perm;
2910: b->col = perm;
2912: PetscObjectReference((PetscObject)perm);
2913: PetscObjectReference((PetscObject)perm);
2915: b->icol = iperm;
2916: b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
2918: PetscMalloc1(am+1,&b->solve_work);
2919: PetscLogObjectMemory((PetscObject)fact,ui[am]*(sizeof(PetscInt)+sizeof(MatScalar)));
2921: b->maxnz = b->nz = ui[am];
2923: fact->info.factor_mallocs = reallocs;
2924: fact->info.fill_ratio_given = fill;
2925: if (ai[am] != 0) {
2926: /* nonzeros in lower triangular part of A (including diagonals) = (ai[am]+am)/2 */
2927: fact->info.fill_ratio_needed = ((PetscReal)2*ui[am])/(ai[am]+am);
2928: } else {
2929: fact->info.fill_ratio_needed = 0.0;
2930: }
2931: #if defined(PETSC_USE_INFO)
2932: if (ai[am] != 0) {
2933: PetscReal af = fact->info.fill_ratio_needed;
2934: PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)fill,(double)af);
2935: PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);
2936: PetscInfo1(A,"PCFactorSetFill(pc,%g) for best performance.\n",(double)af);
2937: } else {
2938: PetscInfo(A,"Empty matrix\n");
2939: }
2940: #endif
2941: fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ;
2942: return(0);
2943: }
2945: PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ_inplace(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
2946: {
2947: Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
2948: Mat_SeqSBAIJ *b;
2949: PetscErrorCode ierr;
2950: PetscBool perm_identity,missing;
2951: PetscReal fill = info->fill;
2952: const PetscInt *rip,*riip;
2953: PetscInt i,am=A->rmap->n,*ai=a->i,*aj=a->j,reallocs=0,prow;
2954: PetscInt *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow;
2955: PetscInt nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr;
2956: PetscFreeSpaceList free_space=NULL,current_space=NULL;
2957: PetscBT lnkbt;
2958: IS iperm;
2961: 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);
2962: MatMissingDiagonal(A,&missing,&i);
2963: if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i);
2965: /* check whether perm is the identity mapping */
2966: ISIdentity(perm,&perm_identity);
2967: ISInvertPermutation(perm,PETSC_DECIDE,&iperm);
2968: ISGetIndices(iperm,&riip);
2969: ISGetIndices(perm,&rip);
2971: /* initialization */
2972: PetscMalloc1(am+1,&ui);
2973: ui[0] = 0;
2975: /* jl: linked list for storing indices of the pivot rows
2976: il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
2977: PetscMalloc4(am,&ui_ptr,am,&jl,am,&il,am,&cols);
2978: for (i=0; i<am; i++) {
2979: jl[i] = am; il[i] = 0;
2980: }
2982: /* create and initialize a linked list for storing column indices of the active row k */
2983: nlnk = am + 1;
2984: PetscLLCreate(am,am,nlnk,lnk,lnkbt);
2986: /* initial FreeSpace size is fill*(ai[am]+1) */
2987: PetscFreeSpaceGet(PetscRealIntMultTruncate(fill,ai[am]+1),&free_space);
2988: current_space = free_space;
2990: for (k=0; k<am; k++) { /* for each active row k */
2991: /* initialize lnk by the column indices of row rip[k] of A */
2992: nzk = 0;
2993: ncols = ai[rip[k]+1] - ai[rip[k]];
2994: 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);
2995: ncols_upper = 0;
2996: for (j=0; j<ncols; j++) {
2997: i = riip[*(aj + ai[rip[k]] + j)];
2998: if (i >= k) { /* only take upper triangular entry */
2999: cols[ncols_upper] = i;
3000: ncols_upper++;
3001: }
3002: }
3003: PetscLLAdd(ncols_upper,cols,am,nlnk,lnk,lnkbt);
3004: nzk += nlnk;
3006: /* update lnk by computing fill-in for each pivot row to be merged in */
3007: prow = jl[k]; /* 1st pivot row */
3009: while (prow < k) {
3010: nextprow = jl[prow];
3011: /* merge prow into k-th row */
3012: jmin = il[prow] + 1; /* index of the 2nd nzero entry in U(prow,k:am-1) */
3013: jmax = ui[prow+1];
3014: ncols = jmax-jmin;
3015: uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:am-1) */
3016: PetscLLAddSorted(ncols,uj_ptr,am,nlnk,lnk,lnkbt);
3017: nzk += nlnk;
3019: /* update il and jl for prow */
3020: if (jmin < jmax) {
3021: il[prow] = jmin;
3022: j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow;
3023: }
3024: prow = nextprow;
3025: }
3027: /* if free space is not available, make more free space */
3028: if (current_space->local_remaining<nzk) {
3029: i = am - k + 1; /* num of unfactored rows */
3030: i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */
3031: PetscFreeSpaceGet(i,¤t_space);
3032: reallocs++;
3033: }
3035: /* copy data into free space, then initialize lnk */
3036: PetscLLClean(am,am,nzk,lnk,current_space->array,lnkbt);
3038: /* add the k-th row into il and jl */
3039: if (nzk-1 > 0) {
3040: i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
3041: jl[k] = jl[i]; jl[i] = k;
3042: il[k] = ui[k] + 1;
3043: }
3044: ui_ptr[k] = current_space->array;
3046: current_space->array += nzk;
3047: current_space->local_used += nzk;
3048: current_space->local_remaining -= nzk;
3050: ui[k+1] = ui[k] + nzk;
3051: }
3053: #if defined(PETSC_USE_INFO)
3054: if (ai[am] != 0) {
3055: PetscReal af = (PetscReal)(ui[am])/((PetscReal)ai[am]);
3056: PetscInfo3(A,"Reallocs %D Fill ratio:given %g needed %g\n",reallocs,(double)fill,(double)af);
3057: PetscInfo1(A,"Run with -pc_factor_fill %g or use \n",(double)af);
3058: PetscInfo1(A,"PCFactorSetFill(pc,%g) for best performance.\n",(double)af);
3059: } else {
3060: PetscInfo(A,"Empty matrix\n");
3061: }
3062: #endif
3064: ISRestoreIndices(perm,&rip);
3065: ISRestoreIndices(iperm,&riip);
3066: PetscFree4(ui_ptr,jl,il,cols);
3068: /* destroy list of free space and other temporary array(s) */
3069: PetscMalloc1(ui[am]+1,&uj);
3070: PetscFreeSpaceContiguous(&free_space,uj);
3071: PetscLLDestroy(lnk,lnkbt);
3073: /* put together the new matrix in MATSEQSBAIJ format */
3075: b = (Mat_SeqSBAIJ*)fact->data;
3076: b->singlemalloc = PETSC_FALSE;
3077: b->free_a = PETSC_TRUE;
3078: b->free_ij = PETSC_TRUE;
3080: PetscMalloc1(ui[am]+1,&b->a);
3082: b->j = uj;
3083: b->i = ui;
3084: b->diag = 0;
3085: b->ilen = 0;
3086: b->imax = 0;
3087: b->row = perm;
3088: b->col = perm;
3090: PetscObjectReference((PetscObject)perm);
3091: PetscObjectReference((PetscObject)perm);
3093: b->icol = iperm;
3094: b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
3096: PetscMalloc1(am+1,&b->solve_work);
3097: PetscLogObjectMemory((PetscObject)fact,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));
3098: b->maxnz = b->nz = ui[am];
3100: fact->info.factor_mallocs = reallocs;
3101: fact->info.fill_ratio_given = fill;
3102: if (ai[am] != 0) {
3103: fact->info.fill_ratio_needed = ((PetscReal)ui[am])/((PetscReal)ai[am]);
3104: } else {
3105: fact->info.fill_ratio_needed = 0.0;
3106: }
3107: fact->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqAIJ_inplace;
3108: return(0);
3109: }
3111: PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering(Mat A,Vec bb,Vec xx)
3112: {
3113: Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
3114: PetscErrorCode ierr;
3115: PetscInt n = A->rmap->n;
3116: const PetscInt *ai = a->i,*aj = a->j,*adiag = a->diag,*vi;
3117: PetscScalar *x,sum;
3118: const PetscScalar *b;
3119: const MatScalar *aa = a->a,*v;
3120: PetscInt i,nz;
3123: if (!n) return(0);
3125: VecGetArrayRead(bb,&b);
3126: VecGetArrayWrite(xx,&x);
3128: /* forward solve the lower triangular */
3129: x[0] = b[0];
3130: v = aa;
3131: vi = aj;
3132: for (i=1; i<n; i++) {
3133: nz = ai[i+1] - ai[i];
3134: sum = b[i];
3135: PetscSparseDenseMinusDot(sum,x,v,vi,nz);
3136: v += nz;
3137: vi += nz;
3138: x[i] = sum;
3139: }
3141: /* backward solve the upper triangular */
3142: for (i=n-1; i>=0; i--) {
3143: v = aa + adiag[i+1] + 1;
3144: vi = aj + adiag[i+1] + 1;
3145: nz = adiag[i] - adiag[i+1]-1;
3146: sum = x[i];
3147: PetscSparseDenseMinusDot(sum,x,v,vi,nz);
3148: x[i] = sum*v[nz]; /* x[i]=aa[adiag[i]]*sum; v++; */
3149: }
3151: PetscLogFlops(2.0*a->nz - A->cmap->n);
3152: VecRestoreArrayRead(bb,&b);
3153: VecRestoreArrayWrite(xx,&x);
3154: return(0);
3155: }
3157: PetscErrorCode MatSolve_SeqAIJ(Mat A,Vec bb,Vec xx)
3158: {
3159: Mat_SeqAIJ *a = (Mat_SeqAIJ*)A->data;
3160: IS iscol = a->col,isrow = a->row;
3161: PetscErrorCode ierr;
3162: PetscInt i,n=A->rmap->n,*vi,*ai=a->i,*aj=a->j,*adiag = a->diag,nz;
3163: const PetscInt *rout,*cout,*r,*c;
3164: PetscScalar *x,*tmp,sum;
3165: const PetscScalar *b;
3166: const MatScalar *aa = a->a,*v;
3169: if (!n) return(0);
3171: VecGetArrayRead(bb,&b);
3172: VecGetArrayWrite(xx,&x);
3173: tmp = a->solve_work;
3175: ISGetIndices(isrow,&rout); r = rout;
3176: ISGetIndices(iscol,&cout); c = cout;
3178: /* forward solve the lower triangular */
3179: tmp[0] = b[r[0]];
3180: v = aa;
3181: vi = aj;
3182: for (i=1; i<n; i++) {
3183: nz = ai[i+1] - ai[i];
3184: sum = b[r[i]];
3185: PetscSparseDenseMinusDot(sum,tmp,v,vi,nz);
3186: tmp[i] = sum;
3187: v += nz; vi += nz;
3188: }
3190: /* backward solve the upper triangular */
3191: for (i=n-1; i>=0; i--) {
3192: v = aa + adiag[i+1]+1;
3193: vi = aj + adiag[i+1]+1;
3194: nz = adiag[i]-adiag[i+1]-1;
3195: sum = tmp[i];
3196: PetscSparseDenseMinusDot(sum,tmp,v,vi,nz);
3197: x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */
3198: }
3200: ISRestoreIndices(isrow,&rout);
3201: ISRestoreIndices(iscol,&cout);
3202: VecRestoreArrayRead(bb,&b);
3203: VecRestoreArrayWrite(xx,&x);
3204: PetscLogFlops(2*a->nz - A->cmap->n);
3205: return(0);
3206: }
3208: /*
3209: 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
3210: */
3211: PetscErrorCode MatILUDTFactor_SeqAIJ(Mat A,IS isrow,IS iscol,const MatFactorInfo *info,Mat *fact)
3212: {
3213: Mat B = *fact;
3214: Mat_SeqAIJ *a=(Mat_SeqAIJ*)A->data,*b;
3215: IS isicol;
3217: const PetscInt *r,*ic;
3218: PetscInt i,n=A->rmap->n,*ai=a->i,*aj=a->j,*ajtmp,*adiag;
3219: PetscInt *bi,*bj,*bdiag,*bdiag_rev;
3220: PetscInt row,nzi,nzi_bl,nzi_bu,*im,nzi_al,nzi_au;
3221: PetscInt nlnk,*lnk;
3222: PetscBT lnkbt;
3223: PetscBool row_identity,icol_identity;
3224: MatScalar *aatmp,*pv,*batmp,*ba,*rtmp,*pc,multiplier,*vtmp,diag_tmp;
3225: const PetscInt *ics;
3226: PetscInt j,nz,*pj,*bjtmp,k,ncut,*jtmp;
3227: PetscReal dt =info->dt,shift=info->shiftamount;
3228: PetscInt dtcount=(PetscInt)info->dtcount,nnz_max;
3229: PetscBool missing;
3232: if (dt == PETSC_DEFAULT) dt = 0.005;
3233: if (dtcount == PETSC_DEFAULT) dtcount = (PetscInt)(1.5*a->rmax);
3235: /* ------- symbolic factorization, can be reused ---------*/
3236: MatMissingDiagonal(A,&missing,&i);
3237: if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i);
3238: adiag=a->diag;
3240: ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);
3242: /* bdiag is location of diagonal in factor */
3243: PetscMalloc1(n+1,&bdiag); /* becomes b->diag */
3244: PetscMalloc1(n+1,&bdiag_rev); /* temporary */
3246: /* allocate row pointers bi */
3247: PetscMalloc1(2*n+2,&bi);
3249: /* allocate bj and ba; max num of nonzero entries is (ai[n]+2*n*dtcount+2) */
3250: if (dtcount > n-1) dtcount = n-1; /* diagonal is excluded */
3251: nnz_max = ai[n]+2*n*dtcount+2;
3253: PetscMalloc1(nnz_max+1,&bj);
3254: PetscMalloc1(nnz_max+1,&ba);
3256: /* put together the new matrix */
3257: MatSeqAIJSetPreallocation_SeqAIJ(B,MAT_SKIP_ALLOCATION,NULL);
3258: PetscLogObjectParent((PetscObject)B,(PetscObject)isicol);
3259: b = (Mat_SeqAIJ*)B->data;
3261: b->free_a = PETSC_TRUE;
3262: b->free_ij = PETSC_TRUE;
3263: b->singlemalloc = PETSC_FALSE;
3265: b->a = ba;
3266: b->j = bj;
3267: b->i = bi;
3268: b->diag = bdiag;
3269: b->ilen = 0;
3270: b->imax = 0;
3271: b->row = isrow;
3272: b->col = iscol;
3273: PetscObjectReference((PetscObject)isrow);
3274: PetscObjectReference((PetscObject)iscol);
3275: b->icol = isicol;
3277: PetscMalloc1(n+1,&b->solve_work);
3278: PetscLogObjectMemory((PetscObject)B,nnz_max*(sizeof(PetscInt)+sizeof(MatScalar)));
3279: b->maxnz = nnz_max;
3281: B->factortype = MAT_FACTOR_ILUDT;
3282: B->info.factor_mallocs = 0;
3283: B->info.fill_ratio_given = ((PetscReal)nnz_max)/((PetscReal)ai[n]);
3284: /* ------- end of symbolic factorization ---------*/
3286: ISGetIndices(isrow,&r);
3287: ISGetIndices(isicol,&ic);
3288: ics = ic;
3290: /* linked list for storing column indices of the active row */
3291: nlnk = n + 1;
3292: PetscLLCreate(n,n,nlnk,lnk,lnkbt);
3294: /* im: used by PetscLLAddSortedLU(); jtmp: working array for column indices of active row */
3295: PetscMalloc2(n,&im,n,&jtmp);
3296: /* rtmp, vtmp: working arrays for sparse and contiguous row entries of active row */
3297: PetscMalloc2(n,&rtmp,n,&vtmp);
3298: PetscArrayzero(rtmp,n);
3300: bi[0] = 0;
3301: bdiag[0] = nnz_max-1; /* location of diag[0] in factor B */
3302: bdiag_rev[n] = bdiag[0];
3303: bi[2*n+1] = bdiag[0]+1; /* endof bj and ba array */
3304: for (i=0; i<n; i++) {
3305: /* copy initial fill into linked list */
3306: nzi = ai[r[i]+1] - ai[r[i]];
3307: 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);
3308: nzi_al = adiag[r[i]] - ai[r[i]];
3309: nzi_au = ai[r[i]+1] - adiag[r[i]] -1;
3310: ajtmp = aj + ai[r[i]];
3311: PetscLLAddPerm(nzi,ajtmp,ic,n,nlnk,lnk,lnkbt);
3313: /* load in initial (unfactored row) */
3314: aatmp = a->a + ai[r[i]];
3315: for (j=0; j<nzi; j++) {
3316: rtmp[ics[*ajtmp++]] = *aatmp++;
3317: }
3319: /* add pivot rows into linked list */
3320: row = lnk[n];
3321: while (row < i) {
3322: nzi_bl = bi[row+1] - bi[row] + 1;
3323: bjtmp = bj + bdiag[row+1]+1; /* points to 1st column next to the diagonal in U */
3324: PetscLLAddSortedLU(bjtmp,row,nlnk,lnk,lnkbt,i,nzi_bl,im);
3325: nzi += nlnk;
3326: row = lnk[row];
3327: }
3329: /* copy data from lnk into jtmp, then initialize lnk */
3330: PetscLLClean(n,n,nzi,lnk,jtmp,lnkbt);
3332: /* numerical factorization */
3333: bjtmp = jtmp;
3334: row = *bjtmp++; /* 1st pivot row */
3335: while (row < i) {
3336: pc = rtmp + row;
3337: pv = ba + bdiag[row]; /* 1./(diag of the pivot row) */
3338: multiplier = (*pc) * (*pv);
3339: *pc = multiplier;
3340: if (PetscAbsScalar(*pc) > dt) { /* apply tolerance dropping rule */
3341: pj = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */
3342: pv = ba + bdiag[row+1] + 1;
3343: nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */
3344: for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++);
3345: PetscLogFlops(1+2*nz);
3346: }
3347: row = *bjtmp++;
3348: }
3350: /* copy sparse rtmp into contiguous vtmp; separate L and U part */
3351: diag_tmp = rtmp[i]; /* save diagonal value - may not needed?? */
3352: nzi_bl = 0; j = 0;
3353: while (jtmp[j] < i) { /* Note: jtmp is sorted */
3354: vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0;
3355: nzi_bl++; j++;
3356: }
3357: nzi_bu = nzi - nzi_bl -1;
3358: while (j < nzi) {
3359: vtmp[j] = rtmp[jtmp[j]]; rtmp[jtmp[j]]=0.0;
3360: j++;
3361: }
3363: bjtmp = bj + bi[i];
3364: batmp = ba + bi[i];
3365: /* apply level dropping rule to L part */
3366: ncut = nzi_al + dtcount;
3367: if (ncut < nzi_bl) {
3368: PetscSortSplit(ncut,nzi_bl,vtmp,jtmp);
3369: PetscSortIntWithScalarArray(ncut,jtmp,vtmp);
3370: } else {
3371: ncut = nzi_bl;
3372: }
3373: for (j=0; j<ncut; j++) {
3374: bjtmp[j] = jtmp[j];
3375: batmp[j] = vtmp[j];
3376: }
3377: bi[i+1] = bi[i] + ncut;
3378: nzi = ncut + 1;
3380: /* apply level dropping rule to U part */
3381: ncut = nzi_au + dtcount;
3382: if (ncut < nzi_bu) {
3383: PetscSortSplit(ncut,nzi_bu,vtmp+nzi_bl+1,jtmp+nzi_bl+1);
3384: PetscSortIntWithScalarArray(ncut,jtmp+nzi_bl+1,vtmp+nzi_bl+1);
3385: } else {
3386: ncut = nzi_bu;
3387: }
3388: nzi += ncut;
3390: /* mark bdiagonal */
3391: bdiag[i+1] = bdiag[i] - (ncut + 1);
3392: bdiag_rev[n-i-1] = bdiag[i+1];
3393: bi[2*n - i] = bi[2*n - i +1] - (ncut + 1);
3394: bjtmp = bj + bdiag[i];
3395: batmp = ba + bdiag[i];
3396: *bjtmp = i;
3397: *batmp = diag_tmp; /* rtmp[i]; */
3398: if (*batmp == 0.0) {
3399: *batmp = dt+shift;
3400: }
3401: *batmp = 1.0/(*batmp); /* invert diagonal entries for simplier triangular solves */
3403: bjtmp = bj + bdiag[i+1]+1;
3404: batmp = ba + bdiag[i+1]+1;
3405: for (k=0; k<ncut; k++) {
3406: bjtmp[k] = jtmp[nzi_bl+1+k];
3407: batmp[k] = vtmp[nzi_bl+1+k];
3408: }
3410: im[i] = nzi; /* used by PetscLLAddSortedLU() */
3411: } /* for (i=0; i<n; i++) */
3412: 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]);
3414: ISRestoreIndices(isrow,&r);
3415: ISRestoreIndices(isicol,&ic);
3417: PetscLLDestroy(lnk,lnkbt);
3418: PetscFree2(im,jtmp);
3419: PetscFree2(rtmp,vtmp);
3420: PetscFree(bdiag_rev);
3422: PetscLogFlops(B->cmap->n);
3423: b->maxnz = b->nz = bi[n] + bdiag[0] - bdiag[n];
3425: ISIdentity(isrow,&row_identity);
3426: ISIdentity(isicol,&icol_identity);
3427: if (row_identity && icol_identity) {
3428: B->ops->solve = MatSolve_SeqAIJ_NaturalOrdering;
3429: } else {
3430: B->ops->solve = MatSolve_SeqAIJ;
3431: }
3433: B->ops->solveadd = 0;
3434: B->ops->solvetranspose = 0;
3435: B->ops->solvetransposeadd = 0;
3436: B->ops->matsolve = 0;
3437: B->assembled = PETSC_TRUE;
3438: B->preallocated = PETSC_TRUE;
3439: return(0);
3440: }
3442: /* a wraper of MatILUDTFactor_SeqAIJ() */
3443: /*
3444: 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
3445: */
3447: PetscErrorCode MatILUDTFactorSymbolic_SeqAIJ(Mat fact,Mat A,IS row,IS col,const MatFactorInfo *info)
3448: {
3452: MatILUDTFactor_SeqAIJ(A,row,col,info,&fact);
3453: return(0);
3454: }
3456: /*
3457: same as MatLUFactorNumeric_SeqAIJ(), except using contiguous array matrix factors
3458: - intend to replace existing MatLUFactorNumeric_SeqAIJ()
3459: */
3460: /*
3461: 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
3462: */
3464: PetscErrorCode MatILUDTFactorNumeric_SeqAIJ(Mat fact,Mat A,const MatFactorInfo *info)
3465: {
3466: Mat C =fact;
3467: Mat_SeqAIJ *a =(Mat_SeqAIJ*)A->data,*b=(Mat_SeqAIJ*)C->data;
3468: IS isrow = b->row,isicol = b->icol;
3470: const PetscInt *r,*ic,*ics;
3471: PetscInt i,j,k,n=A->rmap->n,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
3472: PetscInt *ajtmp,*bjtmp,nz,nzl,nzu,row,*bdiag = b->diag,*pj;
3473: MatScalar *rtmp,*pc,multiplier,*v,*pv,*aa=a->a;
3474: PetscReal dt=info->dt,shift=info->shiftamount;
3475: PetscBool row_identity, col_identity;
3478: ISGetIndices(isrow,&r);
3479: ISGetIndices(isicol,&ic);
3480: PetscMalloc1(n+1,&rtmp);
3481: ics = ic;
3483: for (i=0; i<n; i++) {
3484: /* initialize rtmp array */
3485: nzl = bi[i+1] - bi[i]; /* num of nozeros in L(i,:) */
3486: bjtmp = bj + bi[i];
3487: for (j=0; j<nzl; j++) rtmp[*bjtmp++] = 0.0;
3488: rtmp[i] = 0.0;
3489: nzu = bdiag[i] - bdiag[i+1]; /* num of nozeros in U(i,:) */
3490: bjtmp = bj + bdiag[i+1] + 1;
3491: for (j=0; j<nzu; j++) rtmp[*bjtmp++] = 0.0;
3493: /* load in initial unfactored row of A */
3494: nz = ai[r[i]+1] - ai[r[i]];
3495: ajtmp = aj + ai[r[i]];
3496: v = aa + ai[r[i]];
3497: for (j=0; j<nz; j++) {
3498: rtmp[ics[*ajtmp++]] = v[j];
3499: }
3501: /* numerical factorization */
3502: bjtmp = bj + bi[i]; /* point to 1st entry of L(i,:) */
3503: nzl = bi[i+1] - bi[i]; /* num of entries in L(i,:) */
3504: k = 0;
3505: while (k < nzl) {
3506: row = *bjtmp++;
3507: pc = rtmp + row;
3508: pv = b->a + bdiag[row]; /* 1./(diag of the pivot row) */
3509: multiplier = (*pc) * (*pv);
3510: *pc = multiplier;
3511: if (PetscAbsScalar(multiplier) > dt) {
3512: pj = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */
3513: pv = b->a + bdiag[row+1] + 1;
3514: nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */
3515: for (j=0; j<nz; j++) rtmp[*pj++] -= multiplier * (*pv++);
3516: PetscLogFlops(1+2*nz);
3517: }
3518: k++;
3519: }
3521: /* finished row so stick it into b->a */
3522: /* L-part */
3523: pv = b->a + bi[i];
3524: pj = bj + bi[i];
3525: nzl = bi[i+1] - bi[i];
3526: for (j=0; j<nzl; j++) {
3527: pv[j] = rtmp[pj[j]];
3528: }
3530: /* diagonal: invert diagonal entries for simplier triangular solves */
3531: if (rtmp[i] == 0.0) rtmp[i] = dt+shift;
3532: b->a[bdiag[i]] = 1.0/rtmp[i];
3534: /* U-part */
3535: pv = b->a + bdiag[i+1] + 1;
3536: pj = bj + bdiag[i+1] + 1;
3537: nzu = bdiag[i] - bdiag[i+1] - 1;
3538: for (j=0; j<nzu; j++) {
3539: pv[j] = rtmp[pj[j]];
3540: }
3541: }
3543: PetscFree(rtmp);
3544: ISRestoreIndices(isicol,&ic);
3545: ISRestoreIndices(isrow,&r);
3547: ISIdentity(isrow,&row_identity);
3548: ISIdentity(isicol,&col_identity);
3549: if (row_identity && col_identity) {
3550: C->ops->solve = MatSolve_SeqAIJ_NaturalOrdering;
3551: } else {
3552: C->ops->solve = MatSolve_SeqAIJ;
3553: }
3554: C->ops->solveadd = 0;
3555: C->ops->solvetranspose = 0;
3556: C->ops->solvetransposeadd = 0;
3557: C->ops->matsolve = 0;
3558: C->assembled = PETSC_TRUE;
3559: C->preallocated = PETSC_TRUE;
3561: PetscLogFlops(C->cmap->n);
3562: return(0);
3563: }