xref: /petsc/src/mat/impls/baij/seq/baijfact.c (revision 2205254efee3a00a594e5e2a3a70f74dcb40bc03) !
1 
2 /*
3     Factorization code for BAIJ format.
4 */
5 #include <../src/mat/impls/baij/seq/baij.h>
6 #include <../src/mat/blockinvert.h>
7 
8 #undef __FUNCT__
9 #define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_2"
10 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_2(Mat B,Mat A,const MatFactorInfo *info)
11 {
12   Mat             C=B;
13   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ *)C->data;
14   IS              isrow = b->row,isicol = b->icol;
15   PetscErrorCode  ierr;
16   const PetscInt  *r,*ic;
17   PetscInt        i,j,k,nz,nzL,row,*pj;
18   const PetscInt  n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,bs2=a->bs2;
19   const PetscInt  *ajtmp,*bjtmp,*bdiag=b->diag;
20   MatScalar       *rtmp,*pc,*mwork,*pv;
21   MatScalar       *aa=a->a,*v;
22   PetscInt        flg;
23   PetscReal       shift = info->shiftamount;
24 
25   PetscFunctionBegin;
26   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
27   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
28 
29   /* generate work space needed by the factorization */
30   ierr = PetscMalloc2(bs2*n,MatScalar,&rtmp,bs2,MatScalar,&mwork);CHKERRQ(ierr);
31   ierr = PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));CHKERRQ(ierr);
32 
33   for (i=0; i<n; i++) {
34     /* zero rtmp */
35     /* L part */
36     nz    = bi[i+1] - bi[i];
37     bjtmp = bj + bi[i];
38     for  (j=0; j<nz; j++) {
39       ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
40     }
41 
42     /* U part */
43     nz = bdiag[i] - bdiag[i+1];
44     bjtmp = bj + bdiag[i+1]+1;
45     for  (j=0; j<nz; j++) {
46       ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
47     }
48 
49     /* load in initial (unfactored row) */
50     nz    = ai[r[i]+1] - ai[r[i]];
51     ajtmp = aj + ai[r[i]];
52     v     = aa + bs2*ai[r[i]];
53     for (j=0; j<nz; j++) {
54       ierr = PetscMemcpy(rtmp+bs2*ic[ajtmp[j]],v+bs2*j,bs2*sizeof(MatScalar));CHKERRQ(ierr);
55     }
56 
57     /* elimination */
58     bjtmp = bj + bi[i];
59     nzL   = bi[i+1] - bi[i];
60     for (k=0;k < nzL;k++) {
61       row = bjtmp[k];
62       pc = rtmp + bs2*row;
63       for (flg=0,j=0; j<bs2; j++) {
64         if (pc[j] != (PetscScalar)0.0) {
65           flg = 1;
66           break;
67         }
68       }
69       if (flg) {
70         pv = b->a + bs2*bdiag[row];
71         /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
72         ierr = PetscKernel_A_gets_A_times_B_2(pc,pv,mwork);CHKERRQ(ierr);
73 
74         pj = b->j + bdiag[row+1]+1; /* begining of U(row,:) */
75         pv = b->a + bs2*(bdiag[row+1]+1);
76         nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries inU(row,:), excluding diag */
77         for (j=0; j<nz; j++) {
78           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
79           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
80           v    = rtmp + 4*pj[j];
81           ierr = PetscKernel_A_gets_A_minus_B_times_C_2(v,pc,pv);CHKERRQ(ierr);
82           pv  += 4;
83         }
84         ierr = PetscLogFlops(16*nz+12);CHKERRQ(ierr); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
85       }
86     }
87 
88     /* finished row so stick it into b->a */
89     /* L part */
90     pv   = b->a + bs2*bi[i] ;
91     pj   = b->j + bi[i] ;
92     nz   = bi[i+1] - bi[i];
93     for (j=0; j<nz; j++) {
94       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
95     }
96 
97     /* Mark diagonal and invert diagonal for simplier triangular solves */
98     pv   = b->a + bs2*bdiag[i];
99     pj   = b->j + bdiag[i];
100     ierr = PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));CHKERRQ(ierr);
101     /* ierr = PetscKernel_A_gets_inverse_A(bs,pv,v_pivots,v_work);CHKERRQ(ierr); */
102     ierr = PetscKernel_A_gets_inverse_A_2(pv,shift);CHKERRQ(ierr);
103 
104     /* U part */
105     pv = b->a + bs2*(bdiag[i+1]+1);
106     pj = b->j + bdiag[i+1]+1;
107     nz = bdiag[i] - bdiag[i+1] - 1;
108     for (j=0; j<nz; j++) {
109       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
110     }
111   }
112 
113   ierr = PetscFree2(rtmp,mwork);CHKERRQ(ierr);
114   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
115   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
116   C->ops->solve          = MatSolve_SeqBAIJ_2;
117   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_2;
118 
119   C->assembled = PETSC_TRUE;
120   ierr = PetscLogFlops(1.333333333333*2*2*2*n);CHKERRQ(ierr); /* from inverting diagonal blocks */
121   PetscFunctionReturn(0);
122 }
123 
124 #undef __FUNCT__
125 #define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_2_NaturalOrdering"
126 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_2_NaturalOrdering(Mat B,Mat A,const MatFactorInfo *info)
127 {
128   Mat             C=B;
129   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ *)C->data;
130   PetscErrorCode  ierr;
131   PetscInt        i,j,k,nz,nzL,row,*pj;
132   const PetscInt  n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,bs2=a->bs2;
133   const PetscInt  *ajtmp,*bjtmp,*bdiag=b->diag;
134   MatScalar       *rtmp,*pc,*mwork,*pv;
135   MatScalar       *aa=a->a,*v;
136   PetscInt       flg;
137   PetscReal      shift = info->shiftamount;
138 
139   PetscFunctionBegin;
140   /* generate work space needed by the factorization */
141   ierr = PetscMalloc2(bs2*n,MatScalar,&rtmp,bs2,MatScalar,&mwork);CHKERRQ(ierr);
142   ierr = PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));CHKERRQ(ierr);
143 
144   for (i=0; i<n; i++) {
145     /* zero rtmp */
146     /* L part */
147     nz    = bi[i+1] - bi[i];
148     bjtmp = bj + bi[i];
149     for  (j=0; j<nz; j++) {
150       ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
151     }
152 
153     /* U part */
154     nz = bdiag[i] - bdiag[i+1];
155     bjtmp = bj + bdiag[i+1]+1;
156     for  (j=0; j<nz; j++) {
157       ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
158     }
159 
160     /* load in initial (unfactored row) */
161     nz    = ai[i+1] - ai[i];
162     ajtmp = aj + ai[i];
163     v     = aa + bs2*ai[i];
164     for (j=0; j<nz; j++) {
165       ierr = PetscMemcpy(rtmp+bs2*ajtmp[j],v+bs2*j,bs2*sizeof(MatScalar));CHKERRQ(ierr);
166     }
167 
168     /* elimination */
169     bjtmp = bj + bi[i];
170     nzL   = bi[i+1] - bi[i];
171     for (k=0;k < nzL;k++) {
172       row = bjtmp[k];
173       pc = rtmp + bs2*row;
174       for (flg=0,j=0; j<bs2; j++) {
175         if (pc[j]!=(PetscScalar)0.0) {
176           flg = 1;
177           break;
178         }
179       }
180       if (flg) {
181         pv = b->a + bs2*bdiag[row];
182         /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
183         ierr = PetscKernel_A_gets_A_times_B_2(pc,pv,mwork);CHKERRQ(ierr);
184 
185         pj = b->j + bdiag[row+1]+1; /* beginning of U(row,:) */
186         pv = b->a + bs2*(bdiag[row+1]+1);
187         nz = bdiag[row]-bdiag[row+1] - 1; /* num of entries in U(row,:) excluding diag */
188         for (j=0; j<nz; j++) {
189           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
190           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
191           v    = rtmp + 4*pj[j];
192           ierr = PetscKernel_A_gets_A_minus_B_times_C_2(v,pc,pv);CHKERRQ(ierr);
193           pv  += 4;
194         }
195         ierr = PetscLogFlops(16*nz+12);CHKERRQ(ierr); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
196       }
197     }
198 
199     /* finished row so stick it into b->a */
200     /* L part */
201     pv   = b->a + bs2*bi[i] ;
202     pj   = b->j + bi[i] ;
203     nz   = bi[i+1] - bi[i];
204     for (j=0; j<nz; j++) {
205       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
206     }
207 
208     /* Mark diagonal and invert diagonal for simplier triangular solves */
209     pv   = b->a + bs2*bdiag[i];
210     pj   = b->j + bdiag[i];
211     ierr = PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));CHKERRQ(ierr);
212     /* ierr = PetscKernel_A_gets_inverse_A(bs,pv,v_pivots,v_work);CHKERRQ(ierr); */
213     ierr = PetscKernel_A_gets_inverse_A_2(pv,shift);CHKERRQ(ierr);
214 
215     /* U part */
216     /*
217     pv = b->a + bs2*bi[2*n-i];
218     pj = b->j + bi[2*n-i];
219     nz = bi[2*n-i+1] - bi[2*n-i] - 1;
220     */
221     pv = b->a + bs2*(bdiag[i+1]+1);
222     pj = b->j + bdiag[i+1]+1;
223     nz = bdiag[i] - bdiag[i+1] - 1;
224     for (j=0; j<nz; j++) {
225       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
226     }
227   }
228   ierr = PetscFree2(rtmp,mwork);CHKERRQ(ierr);
229 
230   C->ops->solve          = MatSolve_SeqBAIJ_2_NaturalOrdering;
231   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_2_NaturalOrdering;
232   C->assembled = PETSC_TRUE;
233   ierr = PetscLogFlops(1.333333333333*2*2*2*n);CHKERRQ(ierr); /* from inverting diagonal blocks */
234   PetscFunctionReturn(0);
235 }
236 
237 #undef __FUNCT__
238 #define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_2_inplace"
239 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_2_inplace(Mat B,Mat A,const MatFactorInfo *info)
240 {
241   Mat            C = B;
242   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
243   IS             isrow = b->row,isicol = b->icol;
244   PetscErrorCode ierr;
245   const PetscInt *r,*ic;
246   PetscInt       i,j,n = a->mbs,*bi = b->i,*bj = b->j;
247   PetscInt       *ajtmpold,*ajtmp,nz,row;
248   PetscInt       *diag_offset=b->diag,idx,*ai=a->i,*aj=a->j,*pj;
249   MatScalar      *pv,*v,*rtmp,m1,m2,m3,m4,*pc,*w,*x,x1,x2,x3,x4;
250   MatScalar      p1,p2,p3,p4;
251   MatScalar      *ba = b->a,*aa = a->a;
252   PetscReal      shift = info->shiftamount;
253 
254   PetscFunctionBegin;
255   ierr  = ISGetIndices(isrow,&r);CHKERRQ(ierr);
256   ierr  = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
257   ierr  = PetscMalloc(4*(n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
258 
259   for (i=0; i<n; i++) {
260     nz    = bi[i+1] - bi[i];
261     ajtmp = bj + bi[i];
262     for  (j=0; j<nz; j++) {
263       x = rtmp+4*ajtmp[j]; x[0] = x[1] = x[2] = x[3] = 0.0;
264     }
265     /* load in initial (unfactored row) */
266     idx      = r[i];
267     nz       = ai[idx+1] - ai[idx];
268     ajtmpold = aj + ai[idx];
269     v        = aa + 4*ai[idx];
270     for (j=0; j<nz; j++) {
271       x    = rtmp+4*ic[ajtmpold[j]];
272       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
273       v    += 4;
274     }
275     row = *ajtmp++;
276     while (row < i) {
277       pc = rtmp + 4*row;
278       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
279       if (p1 != (PetscScalar)0.0 || p2 != (PetscScalar)0.0 || p3 != (PetscScalar)0.0 || p4 != (PetscScalar)0.0) {
280         pv = ba + 4*diag_offset[row];
281         pj = bj + diag_offset[row] + 1;
282         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
283         pc[0] = m1 = p1*x1 + p3*x2;
284         pc[1] = m2 = p2*x1 + p4*x2;
285         pc[2] = m3 = p1*x3 + p3*x4;
286         pc[3] = m4 = p2*x3 + p4*x4;
287         nz = bi[row+1] - diag_offset[row] - 1;
288         pv += 4;
289         for (j=0; j<nz; j++) {
290           x1   = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
291           x    = rtmp + 4*pj[j];
292           x[0] -= m1*x1 + m3*x2;
293           x[1] -= m2*x1 + m4*x2;
294           x[2] -= m1*x3 + m3*x4;
295           x[3] -= m2*x3 + m4*x4;
296           pv   += 4;
297         }
298         ierr = PetscLogFlops(16.0*nz+12.0);CHKERRQ(ierr);
299       }
300       row = *ajtmp++;
301     }
302     /* finished row so stick it into b->a */
303     pv = ba + 4*bi[i];
304     pj = bj + bi[i];
305     nz = bi[i+1] - bi[i];
306     for (j=0; j<nz; j++) {
307       x     = rtmp+4*pj[j];
308       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
309       pv   += 4;
310     }
311     /* invert diagonal block */
312     w = ba + 4*diag_offset[i];
313     ierr = PetscKernel_A_gets_inverse_A_2(w,shift);CHKERRQ(ierr);
314   }
315 
316   ierr = PetscFree(rtmp);CHKERRQ(ierr);
317   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
318   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
319   C->ops->solve          = MatSolve_SeqBAIJ_2_inplace;
320   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_2_inplace;
321   C->assembled = PETSC_TRUE;
322   ierr = PetscLogFlops(1.333333333333*8*b->mbs);CHKERRQ(ierr); /* from inverting diagonal blocks */
323   PetscFunctionReturn(0);
324 }
325 /*
326       Version for when blocks are 2 by 2 Using natural ordering
327 */
328 #undef __FUNCT__
329 #define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_2_NaturalOrdering_inplace"
330 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_2_NaturalOrdering_inplace(Mat C,Mat A,const MatFactorInfo *info)
331 {
332   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
333   PetscErrorCode ierr;
334   PetscInt       i,j,n = a->mbs,*bi = b->i,*bj = b->j;
335   PetscInt       *ajtmpold,*ajtmp,nz,row;
336   PetscInt       *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
337   MatScalar      *pv,*v,*rtmp,*pc,*w,*x;
338   MatScalar      p1,p2,p3,p4,m1,m2,m3,m4,x1,x2,x3,x4;
339   MatScalar      *ba = b->a,*aa = a->a;
340   PetscReal      shift = info->shiftamount;
341 
342   PetscFunctionBegin;
343   ierr = PetscMalloc(4*(n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
344   for (i=0; i<n; i++) {
345     nz    = bi[i+1] - bi[i];
346     ajtmp = bj + bi[i];
347     for  (j=0; j<nz; j++) {
348       x = rtmp+4*ajtmp[j];
349       x[0]  = x[1]  = x[2]  = x[3]  = 0.0;
350     }
351     /* load in initial (unfactored row) */
352     nz       = ai[i+1] - ai[i];
353     ajtmpold = aj + ai[i];
354     v        = aa + 4*ai[i];
355     for (j=0; j<nz; j++) {
356       x    = rtmp+4*ajtmpold[j];
357       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
358       v    += 4;
359     }
360     row = *ajtmp++;
361     while (row < i) {
362       pc  = rtmp + 4*row;
363       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
364       if (p1 != (PetscScalar)0.0 || p2 != (PetscScalar)0.0 || p3 != (PetscScalar)0.0 || p4 != (PetscScalar)0.0) {
365         pv = ba + 4*diag_offset[row];
366         pj = bj + diag_offset[row] + 1;
367         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
368         pc[0] = m1 = p1*x1 + p3*x2;
369         pc[1] = m2 = p2*x1 + p4*x2;
370         pc[2] = m3 = p1*x3 + p3*x4;
371         pc[3] = m4 = p2*x3 + p4*x4;
372         nz = bi[row+1] - diag_offset[row] - 1;
373         pv += 4;
374         for (j=0; j<nz; j++) {
375           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
376           x    = rtmp + 4*pj[j];
377           x[0] -= m1*x1 + m3*x2;
378           x[1] -= m2*x1 + m4*x2;
379           x[2] -= m1*x3 + m3*x4;
380           x[3] -= m2*x3 + m4*x4;
381           pv   += 4;
382         }
383         ierr = PetscLogFlops(16.0*nz+12.0);CHKERRQ(ierr);
384       }
385       row = *ajtmp++;
386     }
387     /* finished row so stick it into b->a */
388     pv = ba + 4*bi[i];
389     pj = bj + bi[i];
390     nz = bi[i+1] - bi[i];
391     for (j=0; j<nz; j++) {
392       x      = rtmp+4*pj[j];
393       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
394       /*
395       printf(" col %d:",pj[j]);
396       PetscInt j1;
397       for (j1=0; j1<4; j1++) printf(" %g,",*(pv+j1));
398       printf("\n");
399       */
400       pv   += 4;
401     }
402     /* invert diagonal block */
403     w = ba + 4*diag_offset[i];
404     /*
405     printf(" \n%d -th: diag: ",i);
406     for (j=0; j<4; j++) {
407       printf(" %g,",w[j]);
408     }
409     printf("\n----------------------------\n");
410     */
411     ierr = PetscKernel_A_gets_inverse_A_2(w,shift);CHKERRQ(ierr);
412   }
413 
414   ierr = PetscFree(rtmp);CHKERRQ(ierr);
415   C->ops->solve          = MatSolve_SeqBAIJ_2_NaturalOrdering_inplace;
416   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_2_NaturalOrdering_inplace;
417   C->assembled = PETSC_TRUE;
418   ierr = PetscLogFlops(1.333333333333*8*b->mbs);CHKERRQ(ierr); /* from inverting diagonal blocks */
419   PetscFunctionReturn(0);
420 }
421 
422 /* ----------------------------------------------------------- */
423 /*
424      Version for when blocks are 1 by 1.
425 */
426 #undef __FUNCT__
427 #define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_1"
428 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_1(Mat B,Mat A,const MatFactorInfo *info)
429 {
430   Mat              C=B;
431   Mat_SeqBAIJ      *a=(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ *)C->data;
432   IS               isrow = b->row,isicol = b->icol;
433   PetscErrorCode   ierr;
434   const PetscInt   *r,*ic,*ics;
435   const PetscInt   n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j,*bdiag=b->diag;
436   PetscInt         i,j,k,nz,nzL,row,*pj;
437   const PetscInt   *ajtmp,*bjtmp;
438   MatScalar        *rtmp,*pc,multiplier,*pv;
439   const  MatScalar *aa=a->a,*v;
440   PetscBool        row_identity,col_identity;
441   FactorShiftCtx   sctx;
442   const PetscInt   *ddiag;
443   PetscReal        rs;
444   MatScalar        d;
445 
446   PetscFunctionBegin;
447   /* MatPivotSetUp(): initialize shift context sctx */
448   ierr = PetscMemzero(&sctx,sizeof(FactorShiftCtx));CHKERRQ(ierr);
449 
450   if (info->shifttype == (PetscReal) MAT_SHIFT_POSITIVE_DEFINITE) { /* set sctx.shift_top=max{rs} */
451     ddiag          = a->diag;
452     sctx.shift_top = info->zeropivot;
453     for (i=0; i<n; i++) {
454       /* calculate sum(|aij|)-RealPart(aii), amt of shift needed for this row */
455       d  = (aa)[ddiag[i]];
456       rs = -PetscAbsScalar(d) - PetscRealPart(d);
457       v  = aa+ai[i];
458       nz = ai[i+1] - ai[i];
459       for (j=0; j<nz; j++)
460         rs += PetscAbsScalar(v[j]);
461       if (rs>sctx.shift_top) sctx.shift_top = rs;
462     }
463     sctx.shift_top   *= 1.1;
464     sctx.nshift_max   = 5;
465     sctx.shift_lo     = 0.;
466     sctx.shift_hi     = 1.;
467   }
468 
469   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
470   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
471   ierr = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
472   ics  = ic;
473 
474   do {
475     sctx.newshift = PETSC_FALSE;
476     for (i=0; i<n; i++) {
477       /* zero rtmp */
478       /* L part */
479       nz    = bi[i+1] - bi[i];
480       bjtmp = bj + bi[i];
481       for  (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
482 
483       /* U part */
484       nz = bdiag[i]-bdiag[i+1];
485       bjtmp = bj + bdiag[i+1]+1;
486       for  (j=0; j<nz; j++) rtmp[bjtmp[j]] = 0.0;
487 
488       /* load in initial (unfactored row) */
489       nz    = ai[r[i]+1] - ai[r[i]];
490       ajtmp = aj + ai[r[i]];
491       v     = aa + ai[r[i]];
492       for (j=0; j<nz; j++) {
493         rtmp[ics[ajtmp[j]]] = v[j];
494       }
495       /* ZeropivotApply() */
496       rtmp[i] += sctx.shift_amount;  /* shift the diagonal of the matrix */
497 
498       /* elimination */
499       bjtmp = bj + bi[i];
500       row   = *bjtmp++;
501       nzL   = bi[i+1] - bi[i];
502       for (k=0; k < nzL;k++) {
503         pc = rtmp + row;
504         if (*pc != (PetscScalar)0.0) {
505           pv         = b->a + bdiag[row];
506           multiplier = *pc * (*pv);
507           *pc        = multiplier;
508           pj = b->j + bdiag[row+1]+1; /* beginning of U(row,:) */
509           pv = b->a + bdiag[row+1]+1;
510           nz = bdiag[row]-bdiag[row+1]-1; /* num of entries in U(row,:) excluding diag */
511           for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
512           ierr = PetscLogFlops(2.0*nz);CHKERRQ(ierr);
513         }
514         row = *bjtmp++;
515       }
516 
517       /* finished row so stick it into b->a */
518       rs = 0.0;
519       /* L part */
520       pv   = b->a + bi[i] ;
521       pj   = b->j + bi[i] ;
522       nz   = bi[i+1] - bi[i];
523       for (j=0; j<nz; j++) {
524         pv[j] = rtmp[pj[j]]; rs += PetscAbsScalar(pv[j]);
525       }
526 
527       /* U part */
528       pv = b->a + bdiag[i+1]+1;
529       pj = b->j + bdiag[i+1]+1;
530       nz = bdiag[i] - bdiag[i+1]-1;
531       for (j=0; j<nz; j++) {
532         pv[j] = rtmp[pj[j]]; rs += PetscAbsScalar(pv[j]);
533       }
534 
535       sctx.rs  = rs;
536       sctx.pv  = rtmp[i];
537       ierr = MatPivotCheck(A,info,&sctx,i);CHKERRQ(ierr);
538       if (sctx.newshift) break; /* break for-loop */
539       rtmp[i] = sctx.pv; /* sctx.pv might be updated in the case of MAT_SHIFT_INBLOCKS */
540 
541       /* Mark diagonal and invert diagonal for simplier triangular solves */
542       pv  = b->a + bdiag[i];
543       *pv = (PetscScalar)1.0/rtmp[i];
544 
545     } /* endof for (i=0; i<n; i++) { */
546 
547     /* MatPivotRefine() */
548     if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE && !sctx.newshift && sctx.shift_fraction>0 && sctx.nshift<sctx.nshift_max) {
549       /*
550        * if no shift in this attempt & shifting & started shifting & can refine,
551        * then try lower shift
552        */
553       sctx.shift_hi       = sctx.shift_fraction;
554       sctx.shift_fraction = (sctx.shift_hi+sctx.shift_lo)/2.;
555       sctx.shift_amount   = sctx.shift_fraction * sctx.shift_top;
556       sctx.newshift       = PETSC_TRUE;
557       sctx.nshift++;
558     }
559   } while (sctx.newshift);
560 
561   ierr = PetscFree(rtmp);CHKERRQ(ierr);
562   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
563   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
564 
565   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
566   ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr);
567   if (row_identity && col_identity) {
568     C->ops->solve = MatSolve_SeqBAIJ_1_NaturalOrdering;
569     C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_1_NaturalOrdering;
570   } else {
571     C->ops->solve = MatSolve_SeqBAIJ_1;
572     C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_1;
573   }
574   C->assembled     = PETSC_TRUE;
575   ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr);
576 
577   /* MatShiftView(A,info,&sctx) */
578   if (sctx.nshift) {
579     if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) {
580       ierr = PetscInfo4(A,"number of shift_pd tries %D, shift_amount %G, diagonal shifted up by %e fraction top_value %e\n",sctx.nshift,sctx.shift_amount,sctx.shift_fraction,sctx.shift_top);CHKERRQ(ierr);
581     } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) {
582       ierr = PetscInfo2(A,"number of shift_nz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
583     } else if (info->shifttype == (PetscReal)MAT_SHIFT_INBLOCKS) {
584       ierr = PetscInfo2(A,"number of shift_inblocks applied %D, each shift_amount %G\n",sctx.nshift,info->shiftamount);CHKERRQ(ierr);
585     }
586   }
587   PetscFunctionReturn(0);
588 }
589 
590 #undef __FUNCT__
591 #define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_1_inplace"
592 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_1_inplace(Mat C,Mat A,const MatFactorInfo *info)
593 {
594   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
595   IS             isrow = b->row,isicol = b->icol;
596   PetscErrorCode ierr;
597   const PetscInt *r,*ic;
598   PetscInt       i,j,n = a->mbs,*bi = b->i,*bj = b->j;
599   PetscInt       *ajtmpold,*ajtmp,nz,row,*ai = a->i,*aj = a->j;
600   PetscInt       *diag_offset = b->diag,diag,*pj;
601   MatScalar      *pv,*v,*rtmp,multiplier,*pc;
602   MatScalar      *ba = b->a,*aa = a->a;
603   PetscBool      row_identity, col_identity;
604 
605   PetscFunctionBegin;
606   ierr  = ISGetIndices(isrow,&r);CHKERRQ(ierr);
607   ierr  = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
608   ierr  = PetscMalloc((n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
609 
610   for (i=0; i<n; i++) {
611     nz    = bi[i+1] - bi[i];
612     ajtmp = bj + bi[i];
613     for  (j=0; j<nz; j++) rtmp[ajtmp[j]] = 0.0;
614 
615     /* load in initial (unfactored row) */
616     nz       = ai[r[i]+1] - ai[r[i]];
617     ajtmpold = aj + ai[r[i]];
618     v        = aa + ai[r[i]];
619     for (j=0; j<nz; j++) rtmp[ic[ajtmpold[j]]] =  v[j];
620 
621     row = *ajtmp++;
622     while (row < i) {
623       pc = rtmp + row;
624       if (*pc != 0.0) {
625         pv         = ba + diag_offset[row];
626         pj         = bj + diag_offset[row] + 1;
627         multiplier = *pc * *pv++;
628         *pc        = multiplier;
629         nz         = bi[row+1] - diag_offset[row] - 1;
630         for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
631         ierr = PetscLogFlops(1.0+2.0*nz);CHKERRQ(ierr);
632       }
633       row = *ajtmp++;
634     }
635     /* finished row so stick it into b->a */
636     pv = ba + bi[i];
637     pj = bj + bi[i];
638     nz = bi[i+1] - bi[i];
639     for (j=0; j<nz; j++) {pv[j] = rtmp[pj[j]];}
640     diag = diag_offset[i] - bi[i];
641     /* check pivot entry for current row */
642     if (pv[diag] == 0.0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot: row in original ordering %D in permuted ordering %D",r[i],i);
643     pv[diag] = 1.0/pv[diag];
644   }
645 
646   ierr = PetscFree(rtmp);CHKERRQ(ierr);
647   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
648   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
649   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
650   ierr = ISIdentity(isicol,&col_identity);CHKERRQ(ierr);
651   if (row_identity && col_identity) {
652     C->ops->solve          = MatSolve_SeqBAIJ_1_NaturalOrdering_inplace;
653     C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_1_NaturalOrdering_inplace;
654   } else {
655     C->ops->solve          = MatSolve_SeqBAIJ_1_inplace;
656     C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_1_inplace;
657   }
658   C->assembled = PETSC_TRUE;
659   ierr = PetscLogFlops(C->cmap->n);CHKERRQ(ierr);
660   PetscFunctionReturn(0);
661 }
662 
663 EXTERN_C_BEGIN
664 #undef __FUNCT__
665 #define __FUNCT__ "MatGetFactor_seqbaij_petsc"
666 PetscErrorCode MatGetFactor_seqbaij_petsc(Mat A,MatFactorType ftype,Mat *B)
667 {
668   PetscInt           n = A->rmap->n;
669   PetscErrorCode     ierr;
670 
671   PetscFunctionBegin;
672 #if defined(PETSC_USE_COMPLEX)
673   if (A->hermitian && (ftype == MAT_FACTOR_CHOLESKY || ftype == MAT_FACTOR_ICC))SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Hermitian Factor is not supported");
674 #endif
675   ierr = MatCreate(((PetscObject)A)->comm,B);CHKERRQ(ierr);
676   ierr = MatSetSizes(*B,n,n,n,n);CHKERRQ(ierr);
677   if (ftype == MAT_FACTOR_LU || ftype == MAT_FACTOR_ILU || ftype == MAT_FACTOR_ILUDT) {
678     ierr = MatSetType(*B,MATSEQBAIJ);CHKERRQ(ierr);
679     (*B)->ops->lufactorsymbolic  = MatLUFactorSymbolic_SeqBAIJ;
680     (*B)->ops->ilufactorsymbolic = MatILUFactorSymbolic_SeqBAIJ;
681   } else if (ftype == MAT_FACTOR_CHOLESKY || ftype == MAT_FACTOR_ICC) {
682     ierr = MatSetType(*B,MATSEQSBAIJ);CHKERRQ(ierr);
683     ierr = MatSeqSBAIJSetPreallocation(*B,A->rmap->bs,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
684     (*B)->ops->iccfactorsymbolic      = MatICCFactorSymbolic_SeqBAIJ;
685     (*B)->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_SeqBAIJ;
686   } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Factor type not supported");
687   (*B)->factortype = ftype;
688   PetscFunctionReturn(0);
689 }
690 EXTERN_C_END
691 
692 EXTERN_C_BEGIN
693 #undef __FUNCT__
694 #define __FUNCT__ "MatGetFactorAvailable_seqbaij_petsc"
695 PetscErrorCode MatGetFactorAvailable_seqbaij_petsc(Mat A,MatFactorType ftype,PetscBool  *flg)
696 {
697   PetscFunctionBegin;
698   *flg = PETSC_TRUE;
699   PetscFunctionReturn(0);
700 }
701 EXTERN_C_END
702 
703 /* ----------------------------------------------------------- */
704 #undef __FUNCT__
705 #define __FUNCT__ "MatLUFactor_SeqBAIJ"
706 PetscErrorCode MatLUFactor_SeqBAIJ(Mat A,IS row,IS col,const MatFactorInfo *info)
707 {
708   PetscErrorCode ierr;
709   Mat            C;
710 
711   PetscFunctionBegin;
712   ierr = MatGetFactor(A,MATSOLVERPETSC,MAT_FACTOR_LU,&C);CHKERRQ(ierr);
713   ierr = MatLUFactorSymbolic(C,A,row,col,info);CHKERRQ(ierr);
714   ierr = MatLUFactorNumeric(C,A,info);CHKERRQ(ierr);
715   A->ops->solve            = C->ops->solve;
716   A->ops->solvetranspose   = C->ops->solvetranspose;
717   ierr = MatHeaderMerge(A,C);CHKERRQ(ierr);
718   ierr = PetscLogObjectParent(A,((Mat_SeqBAIJ*)(A->data))->icol);CHKERRQ(ierr);
719   PetscFunctionReturn(0);
720 }
721 
722 #include <../src/mat/impls/sbaij/seq/sbaij.h>
723 #undef __FUNCT__
724 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqBAIJ_N"
725 PetscErrorCode MatCholeskyFactorNumeric_SeqBAIJ_N(Mat C,Mat A,const MatFactorInfo *info)
726 {
727   PetscErrorCode ierr;
728   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ*)A->data;
729   Mat_SeqSBAIJ   *b=(Mat_SeqSBAIJ*)C->data;
730   IS             ip=b->row;
731   const PetscInt *rip;
732   PetscInt       i,j,mbs=a->mbs,bs=A->rmap->bs,*bi=b->i,*bj=b->j,*bcol;
733   PetscInt       *ai=a->i,*aj=a->j;
734   PetscInt       k,jmin,jmax,*jl,*il,col,nexti,ili,nz;
735   MatScalar      *rtmp,*ba=b->a,*bval,*aa=a->a,dk,uikdi;
736   PetscReal      rs;
737   FactorShiftCtx sctx;
738 
739   PetscFunctionBegin;
740   if (bs > 1) {/* convert A to a SBAIJ matrix and apply Cholesky factorization from it */
741     if (!a->sbaijMat) {
742       ierr = MatConvert(A,MATSEQSBAIJ,MAT_INITIAL_MATRIX,&a->sbaijMat);CHKERRQ(ierr);
743     }
744     ierr = (a->sbaijMat)->ops->choleskyfactornumeric(C,a->sbaijMat,info);CHKERRQ(ierr);
745     ierr = MatDestroy(&a->sbaijMat);CHKERRQ(ierr);
746     PetscFunctionReturn(0);
747   }
748 
749   /* MatPivotSetUp(): initialize shift context sctx */
750   ierr = PetscMemzero(&sctx,sizeof(FactorShiftCtx));CHKERRQ(ierr);
751 
752   ierr  = ISGetIndices(ip,&rip);CHKERRQ(ierr);
753   ierr = PetscMalloc3(mbs,MatScalar,&rtmp,mbs,PetscInt,&il,mbs,PetscInt,&jl);CHKERRQ(ierr);
754 
755   sctx.shift_amount = 0.;
756   sctx.nshift       = 0;
757   do {
758     sctx.newshift = PETSC_FALSE;
759     for (i=0; i<mbs; i++) {
760       rtmp[i] = 0.0; jl[i] = mbs; il[0] = 0;
761     }
762 
763     for (k = 0; k<mbs; k++) {
764       bval = ba + bi[k];
765       /* initialize k-th row by the perm[k]-th row of A */
766       jmin = ai[rip[k]]; jmax = ai[rip[k]+1];
767       for (j = jmin; j < jmax; j++) {
768         col = rip[aj[j]];
769         if (col >= k) { /* only take upper triangular entry */
770           rtmp[col] = aa[j];
771           *bval++  = 0.0; /* for in-place factorization */
772         }
773       }
774 
775       /* shift the diagonal of the matrix */
776       if (sctx.nshift) rtmp[k] += sctx.shift_amount;
777 
778       /* modify k-th row by adding in those rows i with U(i,k)!=0 */
779       dk = rtmp[k];
780       i = jl[k]; /* first row to be added to k_th row  */
781 
782       while (i < k) {
783         nexti = jl[i]; /* next row to be added to k_th row */
784 
785         /* compute multiplier, update diag(k) and U(i,k) */
786         ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
787         uikdi = - ba[ili]*ba[bi[i]];  /* diagonal(k) */
788         dk += uikdi*ba[ili];
789         ba[ili] = uikdi; /* -U(i,k) */
790 
791         /* add multiple of row i to k-th row */
792         jmin = ili + 1; jmax = bi[i+1];
793         if (jmin < jmax) {
794           for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j];
795           /* update il and jl for row i */
796           il[i] = jmin;
797           j = bj[jmin]; jl[i] = jl[j]; jl[j] = i;
798         }
799         i = nexti;
800       }
801 
802       /* shift the diagonals when zero pivot is detected */
803       /* compute rs=sum of abs(off-diagonal) */
804       rs   = 0.0;
805       jmin = bi[k]+1;
806       nz   = bi[k+1] - jmin;
807       if (nz) {
808         bcol = bj + jmin;
809         while (nz--) {
810           rs += PetscAbsScalar(rtmp[*bcol]);
811           bcol++;
812         }
813       }
814 
815       sctx.rs = rs;
816       sctx.pv = dk;
817       ierr = MatPivotCheck(A,info,&sctx,k);CHKERRQ(ierr);
818       if (sctx.newshift) break;
819       dk = sctx.pv;
820 
821       /* copy data into U(k,:) */
822       ba[bi[k]] = 1.0/dk; /* U(k,k) */
823       jmin = bi[k]+1; jmax = bi[k+1];
824       if (jmin < jmax) {
825         for (j=jmin; j<jmax; j++) {
826           col = bj[j]; ba[j] = rtmp[col]; rtmp[col] = 0.0;
827         }
828         /* add the k-th row into il and jl */
829         il[k] = jmin;
830         i = bj[jmin]; jl[k] = jl[i]; jl[i] = k;
831       }
832     }
833   } while (sctx.newshift);
834   ierr = PetscFree3(rtmp,il,jl);CHKERRQ(ierr);
835 
836   ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr);
837   C->assembled    = PETSC_TRUE;
838   C->preallocated = PETSC_TRUE;
839   ierr = PetscLogFlops(C->rmap->N);CHKERRQ(ierr);
840   if (sctx.nshift) {
841     if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) {
842       ierr = PetscInfo2(A,"number of shiftpd tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
843     } else if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) {
844       ierr = PetscInfo2(A,"number of shiftnz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
845     }
846   }
847   PetscFunctionReturn(0);
848 }
849 
850 #undef __FUNCT__
851 #define __FUNCT__ "MatCholeskyFactorNumeric_SeqBAIJ_N_NaturalOrdering"
852 PetscErrorCode MatCholeskyFactorNumeric_SeqBAIJ_N_NaturalOrdering(Mat C,Mat A,const MatFactorInfo *info)
853 {
854   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ*)A->data;
855   Mat_SeqSBAIJ   *b=(Mat_SeqSBAIJ*)C->data;
856   PetscErrorCode ierr;
857   PetscInt       i,j,am=a->mbs;
858   PetscInt       *ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
859   PetscInt       k,jmin,*jl,*il,nexti,ili,*acol,*bcol,nz;
860   MatScalar      *rtmp,*ba=b->a,*aa=a->a,dk,uikdi,*aval,*bval;
861   PetscReal      rs;
862   FactorShiftCtx sctx;
863 
864   PetscFunctionBegin;
865   /* MatPivotSetUp(): initialize shift context sctx */
866   ierr = PetscMemzero(&sctx,sizeof(FactorShiftCtx));CHKERRQ(ierr);
867 
868   ierr = PetscMalloc3(am,MatScalar,&rtmp,am,PetscInt,&il,am,PetscInt,&jl);CHKERRQ(ierr);
869 
870   do {
871     sctx.newshift = PETSC_FALSE;
872     for (i=0; i<am; i++) {
873       rtmp[i] = 0.0; jl[i] = am; il[0] = 0;
874     }
875 
876     for (k = 0; k<am; k++) {
877     /* initialize k-th row with elements nonzero in row perm(k) of A */
878       nz   = ai[k+1] - ai[k];
879       acol = aj + ai[k];
880       aval = aa + ai[k];
881       bval = ba + bi[k];
882       while (nz--) {
883         if (*acol < k) { /* skip lower triangular entries */
884           acol++; aval++;
885         } else {
886           rtmp[*acol++] = *aval++;
887           *bval++       = 0.0; /* for in-place factorization */
888         }
889       }
890 
891       /* shift the diagonal of the matrix */
892       if (sctx.nshift) rtmp[k] += sctx.shift_amount;
893 
894       /* modify k-th row by adding in those rows i with U(i,k)!=0 */
895       dk = rtmp[k];
896       i  = jl[k]; /* first row to be added to k_th row  */
897 
898       while (i < k) {
899         nexti = jl[i]; /* next row to be added to k_th row */
900         /* compute multiplier, update D(k) and U(i,k) */
901         ili   = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
902         uikdi = - ba[ili]*ba[bi[i]];
903         dk   += uikdi*ba[ili];
904         ba[ili] = uikdi; /* -U(i,k) */
905 
906         /* add multiple of row i to k-th row ... */
907         jmin = ili + 1;
908         nz   = bi[i+1] - jmin;
909         if (nz > 0) {
910           bcol = bj + jmin;
911           bval = ba + jmin;
912           while (nz --) rtmp[*bcol++] += uikdi*(*bval++);
913           /* update il and jl for i-th row */
914           il[i] = jmin;
915           j = bj[jmin]; jl[i] = jl[j]; jl[j] = i;
916         }
917         i = nexti;
918       }
919 
920       /* shift the diagonals when zero pivot is detected */
921       /* compute rs=sum of abs(off-diagonal) */
922       rs   = 0.0;
923       jmin = bi[k]+1;
924       nz   = bi[k+1] - jmin;
925       if (nz) {
926         bcol = bj + jmin;
927         while (nz--) {
928           rs += PetscAbsScalar(rtmp[*bcol]);
929           bcol++;
930         }
931       }
932 
933       sctx.rs = rs;
934       sctx.pv = dk;
935       ierr = MatPivotCheck(A,info,&sctx,k);CHKERRQ(ierr);
936       if (sctx.newshift) break;    /* sctx.shift_amount is updated */
937       dk = sctx.pv;
938 
939       /* copy data into U(k,:) */
940       ba[bi[k]] = 1.0/dk;
941       jmin      = bi[k]+1;
942       nz        = bi[k+1] - jmin;
943       if (nz) {
944         bcol = bj + jmin;
945         bval = ba + jmin;
946         while (nz--) {
947           *bval++       = rtmp[*bcol];
948           rtmp[*bcol++] = 0.0;
949         }
950         /* add k-th row into il and jl */
951         il[k] = jmin;
952         i = bj[jmin]; jl[k] = jl[i]; jl[i] = k;
953       }
954     }
955   } while (sctx.newshift);
956   ierr = PetscFree3(rtmp,il,jl);CHKERRQ(ierr);
957 
958   C->ops->solve                 = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace;
959   C->ops->solvetranspose        = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace;
960   C->assembled    = PETSC_TRUE;
961   C->preallocated = PETSC_TRUE;
962   ierr = PetscLogFlops(C->rmap->N);CHKERRQ(ierr);
963     if (sctx.nshift) {
964       if (info->shifttype == (PetscReal)MAT_SHIFT_NONZERO) {
965       ierr = PetscInfo2(A,"number of shiftnz tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
966       } else if (info->shifttype == (PetscReal)MAT_SHIFT_POSITIVE_DEFINITE) {
967       ierr = PetscInfo2(A,"number of shiftpd tries %D, shift_amount %G\n",sctx.nshift,sctx.shift_amount);CHKERRQ(ierr);
968     }
969   }
970   PetscFunctionReturn(0);
971 }
972 
973 #include <petscbt.h>
974 #include <../src/mat/utils/freespace.h>
975 #undef __FUNCT__
976 #define __FUNCT__ "MatICCFactorSymbolic_SeqBAIJ"
977 PetscErrorCode MatICCFactorSymbolic_SeqBAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
978 {
979   Mat_SeqBAIJ        *a = (Mat_SeqBAIJ*)A->data;
980   Mat_SeqSBAIJ       *b;
981   Mat                B;
982   PetscErrorCode     ierr;
983   PetscBool          perm_identity;
984   PetscInt           reallocs=0,i,*ai=a->i,*aj=a->j,am=a->mbs,bs=A->rmap->bs,*ui;
985   const PetscInt     *rip;
986   PetscInt           jmin,jmax,nzk,k,j,*jl,prow,*il,nextprow;
987   PetscInt           nlnk,*lnk,*lnk_lvl=PETSC_NULL,ncols,ncols_upper,*cols,*cols_lvl,*uj,**uj_ptr,**uj_lvl_ptr;
988   PetscReal          fill=info->fill,levels=info->levels;
989   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
990   PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL;
991   PetscBT            lnkbt;
992 
993   PetscFunctionBegin;
994   if (bs > 1) {
995     if (!a->sbaijMat) {
996       ierr = MatConvert(A,MATSEQSBAIJ,MAT_INITIAL_MATRIX,&a->sbaijMat);CHKERRQ(ierr);
997     }
998     (fact)->ops->iccfactorsymbolic = MatICCFactorSymbolic_SeqSBAIJ;  /* undue the change made in MatGetFactor_seqbaij_petsc */
999     ierr = MatICCFactorSymbolic(fact,a->sbaijMat,perm,info);CHKERRQ(ierr);
1000     PetscFunctionReturn(0);
1001   }
1002 
1003   ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr);
1004   ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
1005 
1006   /* special case that simply copies fill pattern */
1007   if (!levels && perm_identity) {
1008     ierr = MatMarkDiagonal_SeqBAIJ(A);CHKERRQ(ierr);
1009     ierr = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr);
1010     for (i=0; i<am; i++) {
1011       ui[i] = ai[i+1] - a->diag[i]; /* ui: rowlengths - changes when !perm_identity */
1012     }
1013     B = fact;
1014     ierr = MatSeqSBAIJSetPreallocation(B,1,0,ui);CHKERRQ(ierr);
1015 
1016 
1017     b  = (Mat_SeqSBAIJ*)B->data;
1018     uj = b->j;
1019     for (i=0; i<am; i++) {
1020       aj = a->j + a->diag[i];
1021       for (j=0; j<ui[i]; j++) {
1022         *uj++ = *aj++;
1023       }
1024       b->ilen[i] = ui[i];
1025     }
1026     ierr = PetscFree(ui);CHKERRQ(ierr);
1027     B->factortype = MAT_FACTOR_NONE;
1028     ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1029     ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
1030     B->factortype = MAT_FACTOR_ICC;
1031 
1032     B->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqBAIJ_N_NaturalOrdering;
1033     PetscFunctionReturn(0);
1034   }
1035 
1036   /* initialization */
1037   ierr  = PetscMalloc((am+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr);
1038   ui[0] = 0;
1039   ierr  = PetscMalloc((2*am+1)*sizeof(PetscInt),&cols_lvl);CHKERRQ(ierr);
1040 
1041   /* jl: linked list for storing indices of the pivot rows
1042      il: il[i] points to the 1st nonzero entry of U(i,k:am-1) */
1043   ierr = PetscMalloc4(am,PetscInt*,&uj_ptr,am,PetscInt*,&uj_lvl_ptr,am,PetscInt,&il,am,PetscInt,&jl);CHKERRQ(ierr);
1044   for (i=0; i<am; i++) {
1045     jl[i] = am; il[i] = 0;
1046   }
1047 
1048   /* create and initialize a linked list for storing column indices of the active row k */
1049   nlnk = am + 1;
1050   ierr = PetscIncompleteLLCreate(am,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1051 
1052   /* initial FreeSpace size is fill*(ai[am]+am)/2 */
1053   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+am)/2),&free_space);CHKERRQ(ierr);
1054   current_space = free_space;
1055   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[am]+am)/2),&free_space_lvl);CHKERRQ(ierr);
1056   current_space_lvl = free_space_lvl;
1057 
1058   for (k=0; k<am; k++) {  /* for each active row k */
1059     /* initialize lnk by the column indices of row rip[k] of A */
1060     nzk   = 0;
1061     ncols = ai[rip[k]+1] - ai[rip[k]];
1062     ncols_upper = 0;
1063     cols        = cols_lvl + am;
1064     for (j=0; j<ncols; j++) {
1065       i = rip[*(aj + ai[rip[k]] + j)];
1066       if (i >= k) { /* only take upper triangular entry */
1067         cols[ncols_upper] = i;
1068         cols_lvl[ncols_upper] = -1;  /* initialize level for nonzero entries */
1069         ncols_upper++;
1070       }
1071     }
1072     ierr = PetscIncompleteLLAdd(ncols_upper,cols,levels,cols_lvl,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1073     nzk += nlnk;
1074 
1075     /* update lnk by computing fill-in for each pivot row to be merged in */
1076     prow = jl[k]; /* 1st pivot row */
1077 
1078     while (prow < k) {
1079       nextprow = jl[prow];
1080 
1081       /* merge prow into k-th row */
1082       jmin = il[prow] + 1;  /* index of the 2nd nzero entry in U(prow,k:am-1) */
1083       jmax = ui[prow+1];
1084       ncols = jmax-jmin;
1085       i     = jmin - ui[prow];
1086       cols = uj_ptr[prow] + i; /* points to the 2nd nzero entry in U(prow,k:am-1) */
1087       for (j=0; j<ncols; j++) cols_lvl[j] = *(uj_lvl_ptr[prow] + i + j);
1088       ierr = PetscIncompleteLLAddSorted(ncols,cols,levels,cols_lvl,am,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
1089       nzk += nlnk;
1090 
1091       /* update il and jl for prow */
1092       if (jmin < jmax) {
1093         il[prow] = jmin;
1094         j = *cols; jl[prow] = jl[j]; jl[j] = prow;
1095       }
1096       prow = nextprow;
1097     }
1098 
1099     /* if free space is not available, make more free space */
1100     if (current_space->local_remaining<nzk) {
1101       i = am - k + 1; /* num of unfactored rows */
1102       i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */
1103       ierr = PetscFreeSpaceGet(i,&current_space);CHKERRQ(ierr);
1104       ierr = PetscFreeSpaceGet(i,&current_space_lvl);CHKERRQ(ierr);
1105       reallocs++;
1106     }
1107 
1108     /* copy data into free_space and free_space_lvl, then initialize lnk */
1109     ierr = PetscIncompleteLLClean(am,am,nzk,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr);
1110 
1111     /* add the k-th row into il and jl */
1112     if (nzk-1 > 0) {
1113       i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:am-1) */
1114       jl[k] = jl[i]; jl[i] = k;
1115       il[k] = ui[k] + 1;
1116     }
1117     uj_ptr[k]     = current_space->array;
1118     uj_lvl_ptr[k] = current_space_lvl->array;
1119 
1120     current_space->array           += nzk;
1121     current_space->local_used      += nzk;
1122     current_space->local_remaining -= nzk;
1123 
1124     current_space_lvl->array           += nzk;
1125     current_space_lvl->local_used      += nzk;
1126     current_space_lvl->local_remaining -= nzk;
1127 
1128     ui[k+1] = ui[k] + nzk;
1129   }
1130 
1131   ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
1132   ierr = PetscFree4(uj_ptr,uj_lvl_ptr,il,jl);CHKERRQ(ierr);
1133   ierr = PetscFree(cols_lvl);CHKERRQ(ierr);
1134 
1135   /* copy free_space into uj and free free_space; set uj in new datastructure; */
1136   ierr = PetscMalloc((ui[am]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
1137   ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr);
1138   ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
1139   ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr);
1140 
1141   /* put together the new matrix in MATSEQSBAIJ format */
1142   B = fact;
1143   ierr = MatSeqSBAIJSetPreallocation(B,1,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
1144 
1145   b = (Mat_SeqSBAIJ*)B->data;
1146   b->singlemalloc = PETSC_FALSE;
1147   b->free_a       = PETSC_TRUE;
1148   b->free_ij       = PETSC_TRUE;
1149   ierr = PetscMalloc((ui[am]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr);
1150   b->j    = uj;
1151   b->i    = ui;
1152   b->diag = 0;
1153   b->ilen = 0;
1154   b->imax = 0;
1155   b->row  = perm;
1156   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
1157   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
1158   b->icol = perm;
1159   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
1160   ierr    = PetscMalloc((am+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
1161   ierr    = PetscLogObjectMemory(B,(ui[am]-am)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
1162   b->maxnz = b->nz = ui[am];
1163 
1164   B->info.factor_mallocs    = reallocs;
1165   B->info.fill_ratio_given  = fill;
1166   if (ai[am] != 0.) {
1167     /* nonzeros in lower triangular part of A (includign diagonals)= (ai[am]+am)/2 */
1168     B->info.fill_ratio_needed = ((PetscReal)2*ui[am])/(ai[am]+am);
1169   } else {
1170     B->info.fill_ratio_needed = 0.0;
1171   }
1172 #if defined(PETSC_USE_INFO)
1173   if (ai[am] != 0) {
1174     PetscReal af = B->info.fill_ratio_needed;
1175     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr);
1176     ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
1177     ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr);
1178   } else {
1179     ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr);
1180   }
1181 #endif
1182   if (perm_identity) {
1183     B->ops->solve           = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace;
1184     B->ops->solvetranspose  = MatSolve_SeqSBAIJ_1_NaturalOrdering_inplace;
1185     B->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqBAIJ_N_NaturalOrdering;
1186   } else {
1187     (fact)->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqBAIJ_N;
1188   }
1189   PetscFunctionReturn(0);
1190 }
1191 
1192 #undef __FUNCT__
1193 #define __FUNCT__ "MatCholeskyFactorSymbolic_SeqBAIJ"
1194 PetscErrorCode MatCholeskyFactorSymbolic_SeqBAIJ(Mat fact,Mat A,IS perm,const MatFactorInfo *info)
1195 {
1196   Mat_SeqBAIJ        *a = (Mat_SeqBAIJ*)A->data;
1197   Mat_SeqSBAIJ       *b;
1198   Mat                B;
1199   PetscErrorCode     ierr;
1200   PetscBool          perm_identity;
1201   PetscReal          fill = info->fill;
1202   const PetscInt     *rip;
1203   PetscInt           i,mbs=a->mbs,bs=A->rmap->bs,*ai=a->i,*aj=a->j,reallocs=0,prow;
1204   PetscInt           *jl,jmin,jmax,nzk,*ui,k,j,*il,nextprow;
1205   PetscInt           nlnk,*lnk,ncols,ncols_upper,*cols,*uj,**ui_ptr,*uj_ptr;
1206   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
1207   PetscBT            lnkbt;
1208 
1209   PetscFunctionBegin;
1210   if (bs > 1) { /* convert to seqsbaij */
1211     if (!a->sbaijMat) {
1212       ierr = MatConvert(A,MATSEQSBAIJ,MAT_INITIAL_MATRIX,&a->sbaijMat);CHKERRQ(ierr);
1213     }
1214     (fact)->ops->choleskyfactorsymbolic = MatCholeskyFactorSymbolic_SeqSBAIJ; /* undue the change made in MatGetFactor_seqbaij_petsc */
1215     ierr = MatCholeskyFactorSymbolic(fact,a->sbaijMat,perm,info);CHKERRQ(ierr);
1216     PetscFunctionReturn(0);
1217   }
1218 
1219   /* check whether perm is the identity mapping */
1220   ierr = ISIdentity(perm,&perm_identity);CHKERRQ(ierr);
1221   if (!perm_identity) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Matrix reordering is not supported");
1222   ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
1223 
1224   /* initialization */
1225   ierr  = PetscMalloc((mbs+1)*sizeof(PetscInt),&ui);CHKERRQ(ierr);
1226   ui[0] = 0;
1227 
1228   /* jl: linked list for storing indices of the pivot rows
1229      il: il[i] points to the 1st nonzero entry of U(i,k:mbs-1) */
1230   ierr = PetscMalloc4(mbs,PetscInt*,&ui_ptr,mbs,PetscInt,&il,mbs,PetscInt,&jl,mbs,PetscInt,&cols);CHKERRQ(ierr);
1231   for (i=0; i<mbs; i++) {
1232     jl[i] = mbs; il[i] = 0;
1233   }
1234 
1235   /* create and initialize a linked list for storing column indices of the active row k */
1236   nlnk = mbs + 1;
1237   ierr = PetscLLCreate(mbs,mbs,nlnk,lnk,lnkbt);CHKERRQ(ierr);
1238 
1239   /* initial FreeSpace size is fill* (ai[mbs]+mbs)/2 */
1240   ierr = PetscFreeSpaceGet((PetscInt)(fill*(ai[mbs]+mbs)/2),&free_space);CHKERRQ(ierr);
1241   current_space = free_space;
1242 
1243   for (k=0; k<mbs; k++) {  /* for each active row k */
1244     /* initialize lnk by the column indices of row rip[k] of A */
1245     nzk   = 0;
1246     ncols = ai[rip[k]+1] - ai[rip[k]];
1247     ncols_upper = 0;
1248     for (j=0; j<ncols; j++) {
1249       i = rip[*(aj + ai[rip[k]] + j)];
1250       if (i >= k) { /* only take upper triangular entry */
1251         cols[ncols_upper] = i;
1252         ncols_upper++;
1253       }
1254     }
1255     ierr = PetscLLAdd(ncols_upper,cols,mbs,nlnk,lnk,lnkbt);CHKERRQ(ierr);
1256     nzk += nlnk;
1257 
1258     /* update lnk by computing fill-in for each pivot row to be merged in */
1259     prow = jl[k]; /* 1st pivot row */
1260 
1261     while (prow < k) {
1262       nextprow = jl[prow];
1263       /* merge prow into k-th row */
1264       jmin = il[prow] + 1;  /* index of the 2nd nzero entry in U(prow,k:mbs-1) */
1265       jmax = ui[prow+1];
1266       ncols = jmax-jmin;
1267       uj_ptr = ui_ptr[prow] + jmin - ui[prow]; /* points to the 2nd nzero entry in U(prow,k:mbs-1) */
1268       ierr = PetscLLAddSorted(ncols,uj_ptr,mbs,nlnk,lnk,lnkbt);CHKERRQ(ierr);
1269       nzk += nlnk;
1270 
1271       /* update il and jl for prow */
1272       if (jmin < jmax) {
1273         il[prow] = jmin;
1274         j = *uj_ptr; jl[prow] = jl[j]; jl[j] = prow;
1275       }
1276       prow = nextprow;
1277     }
1278 
1279     /* if free space is not available, make more free space */
1280     if (current_space->local_remaining<nzk) {
1281       i = mbs - k + 1; /* num of unfactored rows */
1282       i = PetscMin(i*nzk, i*(i-1)); /* i*nzk, i*(i-1): estimated and max additional space needed */
1283       ierr = PetscFreeSpaceGet(i,&current_space);CHKERRQ(ierr);
1284       reallocs++;
1285     }
1286 
1287     /* copy data into free space, then initialize lnk */
1288     ierr = PetscLLClean(mbs,mbs,nzk,lnk,current_space->array,lnkbt);CHKERRQ(ierr);
1289 
1290     /* add the k-th row into il and jl */
1291     if (nzk-1 > 0) {
1292       i = current_space->array[1]; /* col value of the first nonzero element in U(k, k+1:mbs-1) */
1293       jl[k] = jl[i]; jl[i] = k;
1294       il[k] = ui[k] + 1;
1295     }
1296     ui_ptr[k] = current_space->array;
1297     current_space->array           += nzk;
1298     current_space->local_used      += nzk;
1299     current_space->local_remaining -= nzk;
1300 
1301     ui[k+1] = ui[k] + nzk;
1302   }
1303 
1304   ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
1305   ierr = PetscFree4(ui_ptr,il,jl,cols);CHKERRQ(ierr);
1306 
1307   /* copy free_space into uj and free free_space; set uj in new datastructure; */
1308   ierr = PetscMalloc((ui[mbs]+1)*sizeof(PetscInt),&uj);CHKERRQ(ierr);
1309   ierr = PetscFreeSpaceContiguous(&free_space,uj);CHKERRQ(ierr);
1310   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
1311 
1312   /* put together the new matrix in MATSEQSBAIJ format */
1313   B    = fact;
1314   ierr = MatSeqSBAIJSetPreallocation(B,bs,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
1315 
1316   b = (Mat_SeqSBAIJ*)B->data;
1317   b->singlemalloc = PETSC_FALSE;
1318   b->free_a       = PETSC_TRUE;
1319   b->free_ij      = PETSC_TRUE;
1320   ierr = PetscMalloc((ui[mbs]+1)*sizeof(MatScalar),&b->a);CHKERRQ(ierr);
1321   b->j    = uj;
1322   b->i    = ui;
1323   b->diag = 0;
1324   b->ilen = 0;
1325   b->imax = 0;
1326   b->row  = perm;
1327   b->pivotinblocks = PETSC_FALSE; /* need to get from MatFactorInfo */
1328   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
1329   b->icol = perm;
1330   ierr    = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
1331   ierr    = PetscMalloc((mbs+1)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
1332   ierr    = PetscLogObjectMemory(B,(ui[mbs]-mbs)*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
1333   b->maxnz = b->nz = ui[mbs];
1334 
1335   B->info.factor_mallocs    = reallocs;
1336   B->info.fill_ratio_given  = fill;
1337   if (ai[mbs] != 0.) {
1338     /* nonzeros in lower triangular part of A = (ai[mbs]+mbs)/2 */
1339     B->info.fill_ratio_needed = ((PetscReal)2*ui[mbs])/(ai[mbs]+mbs);
1340   } else {
1341     B->info.fill_ratio_needed = 0.0;
1342   }
1343 #if defined(PETSC_USE_INFO)
1344   if (ai[mbs] != 0.) {
1345     PetscReal af = B->info.fill_ratio_needed;
1346     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,fill,af);CHKERRQ(ierr);
1347     ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
1348     ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G) for best performance.\n",af);CHKERRQ(ierr);
1349   } else {
1350     ierr = PetscInfo(A,"Empty matrix.\n");CHKERRQ(ierr);
1351   }
1352 #endif
1353   if (perm_identity) {
1354     B->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqBAIJ_N_NaturalOrdering;
1355   } else {
1356     B->ops->choleskyfactornumeric = MatCholeskyFactorNumeric_SeqBAIJ_N;
1357   }
1358   PetscFunctionReturn(0);
1359 }
1360 
1361 #undef __FUNCT__
1362 #define __FUNCT__ "MatSolve_SeqBAIJ_N_NaturalOrdering"
1363 PetscErrorCode MatSolve_SeqBAIJ_N_NaturalOrdering(Mat A,Vec bb,Vec xx)
1364 {
1365   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ *)A->data;
1366   PetscErrorCode ierr;
1367   const PetscInt *ai=a->i,*aj=a->j,*adiag=a->diag,*vi;
1368   PetscInt       i,k,n=a->mbs;
1369   PetscInt       nz,bs=A->rmap->bs,bs2=a->bs2;
1370   MatScalar      *aa=a->a,*v;
1371   PetscScalar    *x,*b,*s,*t,*ls;
1372 
1373   PetscFunctionBegin;
1374   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
1375   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1376   t  = a->solve_work;
1377 
1378   /* forward solve the lower triangular */
1379   ierr = PetscMemcpy(t,b,bs*sizeof(PetscScalar));CHKERRQ(ierr); /* copy 1st block of b to t */
1380 
1381   for (i=1; i<n; i++) {
1382     v   = aa + bs2*ai[i];
1383     vi  = aj + ai[i];
1384     nz = ai[i+1] - ai[i];
1385     s = t + bs*i;
1386     ierr = PetscMemcpy(s,b+bs*i,bs*sizeof(PetscScalar));CHKERRQ(ierr); /* copy i_th block of b to t */
1387     for (k=0;k<nz;k++) {
1388       PetscKernel_v_gets_v_minus_A_times_w(bs,s,v,t+bs*vi[k]);
1389       v += bs2;
1390     }
1391   }
1392 
1393   /* backward solve the upper triangular */
1394   ls = a->solve_work + A->cmap->n;
1395   for (i=n-1; i>=0; i--) {
1396     v  = aa + bs2*(adiag[i+1]+1);
1397     vi = aj + adiag[i+1]+1;
1398     nz = adiag[i] - adiag[i+1]-1;
1399     ierr = PetscMemcpy(ls,t+i*bs,bs*sizeof(PetscScalar));CHKERRQ(ierr);
1400     for (k=0;k<nz;k++) {
1401       PetscKernel_v_gets_v_minus_A_times_w(bs,ls,v,t+bs*vi[k]);
1402       v += bs2;
1403     }
1404     PetscKernel_w_gets_A_times_v(bs,ls,aa+bs2*adiag[i],t+i*bs); /* *inv(diagonal[i]) */
1405     ierr = PetscMemcpy(x+i*bs,t+i*bs,bs*sizeof(PetscScalar));CHKERRQ(ierr);
1406   }
1407 
1408   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
1409   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1410   ierr = PetscLogFlops(2.0*(a->bs2)*(a->nz) - A->rmap->bs*A->cmap->n);CHKERRQ(ierr);
1411   PetscFunctionReturn(0);
1412 }
1413 
1414 #undef __FUNCT__
1415 #define __FUNCT__ "MatSolve_SeqBAIJ_N"
1416 PetscErrorCode MatSolve_SeqBAIJ_N(Mat A,Vec bb,Vec xx)
1417 {
1418   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ *)A->data;
1419   IS             iscol=a->col,isrow=a->row;
1420   PetscErrorCode ierr;
1421   const PetscInt *r,*c,*rout,*cout,*ai=a->i,*aj=a->j,*adiag=a->diag,*vi;
1422   PetscInt       i,m,n=a->mbs;
1423   PetscInt       nz,bs=A->rmap->bs,bs2=a->bs2;
1424   MatScalar      *aa=a->a,*v;
1425   PetscScalar    *x,*b,*s,*t,*ls;
1426 
1427   PetscFunctionBegin;
1428   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
1429   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1430   t  = a->solve_work;
1431 
1432   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1433   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1434 
1435   /* forward solve the lower triangular */
1436   ierr = PetscMemcpy(t,b+bs*r[0],bs*sizeof(PetscScalar));CHKERRQ(ierr);
1437   for (i=1; i<n; i++) {
1438     v   = aa + bs2*ai[i];
1439     vi  = aj + ai[i];
1440     nz = ai[i+1] - ai[i];
1441     s = t + bs*i;
1442     ierr = PetscMemcpy(s,b+bs*r[i],bs*sizeof(PetscScalar));CHKERRQ(ierr);
1443     for (m=0;m<nz;m++) {
1444       PetscKernel_v_gets_v_minus_A_times_w(bs,s,v,t+bs*vi[m]);
1445       v += bs2;
1446     }
1447   }
1448 
1449   /* backward solve the upper triangular */
1450   ls = a->solve_work + A->cmap->n;
1451   for (i=n-1; i>=0; i--) {
1452     v  = aa + bs2*(adiag[i+1]+1);
1453     vi = aj + adiag[i+1]+1;
1454     nz = adiag[i] - adiag[i+1] - 1;
1455     ierr = PetscMemcpy(ls,t+i*bs,bs*sizeof(PetscScalar));CHKERRQ(ierr);
1456     for (m=0;m<nz;m++) {
1457       PetscKernel_v_gets_v_minus_A_times_w(bs,ls,v,t+bs*vi[m]);
1458       v += bs2;
1459     }
1460     PetscKernel_w_gets_A_times_v(bs,ls,v,t+i*bs); /* *inv(diagonal[i]) */
1461     ierr = PetscMemcpy(x + bs*c[i],t+i*bs,bs*sizeof(PetscScalar));CHKERRQ(ierr);
1462   }
1463   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1464   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1465   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
1466   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1467   ierr = PetscLogFlops(2.0*(a->bs2)*(a->nz) - A->rmap->bs*A->cmap->n);CHKERRQ(ierr);
1468   PetscFunctionReturn(0);
1469 }
1470 
1471 #undef __FUNCT__
1472 #define __FUNCT__ "MatBlockAbs_privat"
1473 /*
1474     For each block in an block array saves the largest absolute value in the block into another array
1475 */
1476 static PetscErrorCode MatBlockAbs_private(PetscInt nbs,PetscInt bs2,PetscScalar *blockarray,PetscReal *absarray)
1477 {
1478   PetscErrorCode     ierr;
1479   PetscInt           i,j;
1480 
1481   PetscFunctionBegin;
1482   ierr = PetscMemzero(absarray,(nbs+1)*sizeof(PetscReal));CHKERRQ(ierr);
1483   for (i=0; i<nbs; i++) {
1484     for (j=0; j<bs2; j++) {
1485       if (absarray[i] < PetscAbsScalar(blockarray[i*nbs+j])) absarray[i] = PetscAbsScalar(blockarray[i*nbs+j]);
1486     }
1487   }
1488   PetscFunctionReturn(0);
1489 }
1490 
1491 #undef __FUNCT__
1492 #define __FUNCT__ "MatILUDTFactor_SeqBAIJ"
1493 /*
1494      This needs to be renamed and called by the regular MatILUFactor_SeqBAIJ when drop tolerance is used
1495 */
1496 PetscErrorCode MatILUDTFactor_SeqBAIJ(Mat A,IS isrow,IS iscol,const MatFactorInfo *info,Mat *fact)
1497 {
1498   Mat                B = *fact;
1499   Mat_SeqBAIJ        *a=(Mat_SeqBAIJ*)A->data,*b;
1500   IS                 isicol;
1501   PetscErrorCode     ierr;
1502   const PetscInt     *r,*ic;
1503   PetscInt           i,mbs=a->mbs,bs=A->rmap->bs,bs2=a->bs2,*ai=a->i,*aj=a->j,*ajtmp,*adiag;
1504   PetscInt           *bi,*bj,*bdiag;
1505 
1506   PetscInt           row,nzi,nzi_bl,nzi_bu,*im,dtcount,nzi_al,nzi_au;
1507   PetscInt           nlnk,*lnk;
1508   PetscBT            lnkbt;
1509   PetscBool          row_identity,icol_identity;
1510   MatScalar          *aatmp,*pv,*batmp,*ba,*rtmp,*pc,*multiplier,*vtmp;
1511   PetscInt           j,nz,*pj,*bjtmp,k,ncut,*jtmp;
1512 
1513   PetscReal          dt=info->dt; /* shift=info->shiftamount; */
1514   PetscInt           nnz_max;
1515   PetscBool          missing;
1516   PetscReal          *vtmp_abs;
1517   MatScalar          *v_work;
1518   PetscInt           *v_pivots;
1519 
1520   PetscFunctionBegin;
1521   /* ------- symbolic factorization, can be reused ---------*/
1522   ierr = MatMissingDiagonal(A,&missing,&i);CHKERRQ(ierr);
1523   if (missing) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",i);
1524   adiag=a->diag;
1525 
1526   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
1527 
1528   /* bdiag is location of diagonal in factor */
1529   ierr = PetscMalloc((mbs+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);
1530 
1531   /* allocate row pointers bi */
1532   ierr = PetscMalloc((2*mbs+2)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
1533 
1534   /* allocate bj and ba; max num of nonzero entries is (ai[n]+2*n*dtcount+2) */
1535   dtcount = (PetscInt)info->dtcount;
1536   if (dtcount > mbs-1) dtcount = mbs-1;
1537   nnz_max  = ai[mbs]+2*mbs*dtcount +2;
1538   /* printf("MatILUDTFactor_SeqBAIJ, bs %d, ai[mbs] %d, nnz_max  %d, dtcount %d\n",bs,ai[mbs],nnz_max,dtcount); */
1539   ierr = PetscMalloc(nnz_max*sizeof(PetscInt),&bj);CHKERRQ(ierr);
1540   nnz_max = nnz_max*bs2;
1541   ierr = PetscMalloc(nnz_max*sizeof(MatScalar),&ba);CHKERRQ(ierr);
1542 
1543   /* put together the new matrix */
1544   ierr = MatSeqBAIJSetPreallocation_SeqBAIJ(B,bs,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
1545   ierr = PetscLogObjectParent(B,isicol);CHKERRQ(ierr);
1546   b    = (Mat_SeqBAIJ*)(B)->data;
1547   b->free_a       = PETSC_TRUE;
1548   b->free_ij      = PETSC_TRUE;
1549   b->singlemalloc = PETSC_FALSE;
1550   b->a          = ba;
1551   b->j          = bj;
1552   b->i          = bi;
1553   b->diag       = bdiag;
1554   b->ilen       = 0;
1555   b->imax       = 0;
1556   b->row        = isrow;
1557   b->col        = iscol;
1558   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
1559   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
1560   b->icol       = isicol;
1561   ierr = PetscMalloc((bs*(mbs+1))*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
1562 
1563   ierr = PetscLogObjectMemory(B,nnz_max*(sizeof(PetscInt)+sizeof(MatScalar)));CHKERRQ(ierr);
1564   b->maxnz = nnz_max/bs2;
1565 
1566   (B)->factortype            = MAT_FACTOR_ILUDT;
1567   (B)->info.factor_mallocs   = 0;
1568   (B)->info.fill_ratio_given = ((PetscReal)nnz_max)/((PetscReal)(ai[mbs]*bs2));
1569   CHKMEMQ;
1570   /* ------- end of symbolic factorization ---------*/
1571   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
1572   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
1573 
1574   /* linked list for storing column indices of the active row */
1575   nlnk = mbs + 1;
1576   ierr = PetscLLCreate(mbs,mbs,nlnk,lnk,lnkbt);CHKERRQ(ierr);
1577 
1578   /* im: used by PetscLLAddSortedLU(); jtmp: working array for column indices of active row */
1579   ierr = PetscMalloc2(mbs,PetscInt,&im,mbs,PetscInt,&jtmp);CHKERRQ(ierr);
1580   /* rtmp, vtmp: working arrays for sparse and contiguous row entries of active row */
1581   ierr = PetscMalloc2(mbs*bs2,MatScalar,&rtmp,mbs*bs2,MatScalar,&vtmp);CHKERRQ(ierr);
1582   ierr = PetscMalloc((mbs+1)*sizeof(PetscReal),&vtmp_abs);CHKERRQ(ierr);
1583   ierr = PetscMalloc3(bs,MatScalar,&v_work,bs2,MatScalar,&multiplier,bs,PetscInt,&v_pivots);CHKERRQ(ierr);
1584 
1585   bi[0]    = 0;
1586   bdiag[0] = (nnz_max/bs2)-1; /* location of diagonal in factor B */
1587   bi[2*mbs+1] = bdiag[0]+1; /* endof bj and ba array */
1588   for (i=0; i<mbs; i++) {
1589     /* copy initial fill into linked list */
1590     nzi = 0; /* nonzeros for active row i */
1591     nzi = ai[r[i]+1] - ai[r[i]];
1592     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);
1593     nzi_al = adiag[r[i]] - ai[r[i]];
1594     nzi_au = ai[r[i]+1] - adiag[r[i]] -1;
1595     /* printf("row %d, nzi_al/au %d %d\n",i,nzi_al,nzi_au); */
1596 
1597     /* load in initial unfactored row */
1598     ajtmp = aj + ai[r[i]];
1599     ierr = PetscLLAddPerm(nzi,ajtmp,ic,mbs,nlnk,lnk,lnkbt);CHKERRQ(ierr);
1600     ierr = PetscMemzero(rtmp,mbs*bs2*sizeof(PetscScalar));CHKERRQ(ierr);
1601     aatmp = a->a + bs2*ai[r[i]];
1602     for (j=0; j<nzi; j++) {
1603       ierr = PetscMemcpy(rtmp+bs2*ic[ajtmp[j]],aatmp+bs2*j,bs2*sizeof(MatScalar));CHKERRQ(ierr);
1604     }
1605 
1606     /* add pivot rows into linked list */
1607     row = lnk[mbs];
1608     while (row < i) {
1609       nzi_bl = bi[row+1] - bi[row] + 1;
1610       bjtmp = bj + bdiag[row+1]+1; /* points to 1st column next to the diagonal in U */
1611       ierr  = PetscLLAddSortedLU(bjtmp,row,nlnk,lnk,lnkbt,i,nzi_bl,im);CHKERRQ(ierr);
1612       nzi  += nlnk;
1613       row   = lnk[row];
1614     }
1615 
1616     /* copy data from lnk into jtmp, then initialize lnk */
1617     ierr = PetscLLClean(mbs,mbs,nzi,lnk,jtmp,lnkbt);CHKERRQ(ierr);
1618 
1619     /* numerical factorization */
1620     bjtmp = jtmp;
1621     row   = *bjtmp++; /* 1st pivot row */
1622 
1623     while  (row < i) {
1624       pc = rtmp + bs2*row;
1625       pv = ba + bs2*bdiag[row]; /* inv(diag) of the pivot row */
1626       PetscKernel_A_gets_A_times_B(bs,pc,pv,multiplier); /* pc= multiplier = pc*inv(diag[row]) */
1627       ierr = MatBlockAbs_private(1,bs2,pc,vtmp_abs);CHKERRQ(ierr);
1628       if (vtmp_abs[0] > dt) { /* apply tolerance dropping rule */
1629         pj         = bj + bdiag[row+1] + 1; /* point to 1st entry of U(row,:) */
1630         pv         = ba + bs2*(bdiag[row+1] + 1);
1631         nz         = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:), excluding diagonal */
1632         for (j=0; j<nz; j++) {
1633           PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j);
1634         }
1635         /* ierr = PetscLogFlops(bslog*(nz+1.0)-bs);CHKERRQ(ierr); */
1636       }
1637       row = *bjtmp++;
1638     }
1639 
1640     /* copy sparse rtmp into contiguous vtmp; separate L and U part */
1641     nzi_bl = 0; j = 0;
1642     while (jtmp[j] < i) { /* L-part. Note: jtmp is sorted */
1643       ierr = PetscMemcpy(vtmp+bs2*j,rtmp+bs2*jtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
1644       nzi_bl++; j++;
1645     }
1646     nzi_bu = nzi - nzi_bl -1;
1647     /* printf("nzi %d, nzi_bl %d, nzi_bu %d\n",nzi,nzi_bl,nzi_bu); */
1648 
1649     while (j < nzi) { /* U-part */
1650       ierr = PetscMemcpy(vtmp+bs2*j,rtmp+bs2*jtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
1651       /*
1652       printf(" col %d: ",jtmp[j]);
1653       for (j1=0; j1<bs2; j1++) printf(" %g",*(vtmp+bs2*j+j1));
1654       printf(" \n");
1655       */
1656       j++;
1657     }
1658 
1659     ierr = MatBlockAbs_private(nzi,bs2,vtmp,vtmp_abs);CHKERRQ(ierr);
1660     /*
1661     printf(" row %d, nzi %d, vtmp_abs\n",i,nzi);
1662     for (j1=0; j1<nzi; j1++) printf(" (%d %g),",jtmp[j1],vtmp_abs[j1]);
1663     printf(" \n");
1664     */
1665     bjtmp = bj + bi[i];
1666     batmp = ba + bs2*bi[i];
1667     /* apply level dropping rule to L part */
1668     ncut = nzi_al + dtcount;
1669     if (ncut < nzi_bl) {
1670       ierr = PetscSortSplitReal(ncut,nzi_bl,vtmp_abs,jtmp);CHKERRQ(ierr);
1671       ierr = PetscSortIntWithScalarArray(ncut,jtmp,vtmp);CHKERRQ(ierr);
1672     } else {
1673       ncut = nzi_bl;
1674     }
1675     for (j=0; j<ncut; j++) {
1676       bjtmp[j] = jtmp[j];
1677       ierr = PetscMemcpy(batmp+bs2*j,rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
1678       /*
1679       printf(" col %d: ",bjtmp[j]);
1680       for (j1=0; j1<bs2; j1++) printf(" %g,",*(batmp+bs2*j+j1));
1681       printf("\n");
1682       */
1683     }
1684     bi[i+1] = bi[i] + ncut;
1685     nzi = ncut + 1;
1686 
1687     /* apply level dropping rule to U part */
1688     ncut = nzi_au + dtcount;
1689     if (ncut < nzi_bu) {
1690       ierr = PetscSortSplitReal(ncut,nzi_bu,vtmp_abs+nzi_bl+1,jtmp+nzi_bl+1);CHKERRQ(ierr);
1691       ierr = PetscSortIntWithScalarArray(ncut,jtmp+nzi_bl+1,vtmp+nzi_bl+1);CHKERRQ(ierr);
1692     } else {
1693       ncut = nzi_bu;
1694     }
1695     nzi += ncut;
1696 
1697     /* mark bdiagonal */
1698     bdiag[i+1]    = bdiag[i] - (ncut + 1);
1699     bi[2*mbs - i] = bi[2*mbs - i +1] - (ncut + 1);
1700 
1701     bjtmp = bj + bdiag[i];
1702     batmp = ba + bs2*bdiag[i];
1703     ierr = PetscMemcpy(batmp,rtmp+bs2*i,bs2*sizeof(MatScalar));CHKERRQ(ierr);
1704     *bjtmp = i;
1705     /*
1706     printf(" diag %d: ",*bjtmp);
1707     for (j=0; j<bs2; j++) {
1708       printf(" %g,",batmp[j]);
1709     }
1710     printf("\n");
1711     */
1712     bjtmp = bj + bdiag[i+1]+1;
1713     batmp = ba + (bdiag[i+1]+1)*bs2;
1714 
1715     for (k=0; k<ncut; k++) {
1716       bjtmp[k] = jtmp[nzi_bl+1+k];
1717       ierr = PetscMemcpy(batmp+bs2*k,rtmp+bs2*bjtmp[k],bs2*sizeof(MatScalar));CHKERRQ(ierr);
1718       /*
1719       printf(" col %d:",bjtmp[k]);
1720       for (j1=0; j1<bs2; j1++) printf(" %g,",*(batmp+bs2*k+j1));
1721       printf("\n");
1722       */
1723     }
1724 
1725     im[i] = nzi; /* used by PetscLLAddSortedLU() */
1726 
1727     /* invert diagonal block for simplier triangular solves - add shift??? */
1728     batmp = ba + bs2*bdiag[i];
1729     ierr = PetscKernel_A_gets_inverse_A(bs,batmp,v_pivots,v_work);CHKERRQ(ierr);
1730   } /* for (i=0; i<mbs; i++) */
1731   ierr = PetscFree3(v_work,multiplier,v_pivots);CHKERRQ(ierr);
1732 
1733   /* printf("end of L %d, beginning of U %d\n",bi[mbs],bdiag[mbs]); */
1734   if (bi[mbs] >= bdiag[mbs]) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"end of L array %d cannot >= the beginning of U array %d",bi[mbs],bdiag[mbs]);
1735 
1736   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
1737   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
1738 
1739   ierr = PetscLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
1740 
1741   ierr = PetscFree2(im,jtmp);CHKERRQ(ierr);
1742   ierr = PetscFree2(rtmp,vtmp);CHKERRQ(ierr);
1743 
1744   ierr = PetscLogFlops(bs2*B->cmap->n);CHKERRQ(ierr);
1745   b->maxnz = b->nz = bi[mbs] + bdiag[0] - bdiag[mbs];
1746 
1747   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
1748   ierr = ISIdentity(isicol,&icol_identity);CHKERRQ(ierr);
1749   if (row_identity && icol_identity) {
1750     B->ops->solve = MatSolve_SeqBAIJ_N_NaturalOrdering;
1751   } else {
1752     B->ops->solve = MatSolve_SeqBAIJ_N;
1753   }
1754 
1755   B->ops->solveadd          = 0;
1756   B->ops->solvetranspose    = 0;
1757   B->ops->solvetransposeadd = 0;
1758   B->ops->matsolve          = 0;
1759   B->assembled              = PETSC_TRUE;
1760   B->preallocated           = PETSC_TRUE;
1761   PetscFunctionReturn(0);
1762 }
1763