xref: /petsc/src/mat/impls/sbaij/seq/sbaijfact.c (revision 9706f0430baa50c57158d451c18ca1666868863b)
1 /* Using Modified Sparse Row (MSR) storage.
2 See page 85, "Iterative Methods ..." by Saad. */
3 
4 /*$Id: sbaijfact.c,v 1.42 2000/11/02 20:48:29 hzhang Exp hzhang $*/
5 /*
6     Symbolic U^T*D*U factorization for SBAIJ format. Modified from SSF of YSMP.
7 */
8 #include "sbaij.h"
9 #include "src/mat/impls/baij/seq/baij.h"
10 #include "src/vec/vecimpl.h"
11 #include "src/inline/ilu.h"
12 #include "include/petscis.h"
13 
14 #undef __FUNC__
15 #define __FUNC__ "MatCholeskyFactorSymbolic_SeqSBAIJ"
16 int MatCholeskyFactorSymbolic_SeqSBAIJ(Mat A,IS perm,PetscReal f,Mat *B)
17 {
18   Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b;
19   int         *rip,ierr,i,mbs = a->mbs,*ai,*aj;
20   int         *jutmp,bs = a->bs,bs2=a->bs2;
21   int         m,nzi,realloc = 0;
22   int         *jl,*q,jumin,jmin,jmax,juptr,nzk,qm,*iu,*ju,k,j,vj,umax,maxadd;
23   /* PetscTruth  ident; */
24 
25   PetscFunctionBegin;
26   PetscValidHeaderSpecific(perm,IS_COOKIE);
27   if (A->M != A->N) SETERRQ(PETSC_ERR_ARG_WRONG,"matrix must be square");
28 
29   /* check whether perm is the identity mapping */
30   /*
31   ierr = ISView(perm, VIEWER_STDOUT_SELF);CHKERRA(ierr);
32   ierr = ISIdentity(perm,&ident);CHKERRQ(ierr);
33   printf("ident = %d\n", ident);
34   */
35   ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
36   for (i=0; i<mbs; i++){
37     if (rip[i] != i){
38       a->permute = PETSC_TRUE;
39       /* printf("non-trivial perm\n"); */
40       break;
41     }
42   }
43 
44   if (!a->permute){ /* without permutation */
45     ai = a->i; aj = a->j;
46   } else {       /* non-trivial permutation */
47     ierr = MatReorderingSeqSBAIJ(A, perm);CHKERRA(ierr);
48     ai = a->inew; aj = a->jnew;
49   }
50 
51   /* initialization */
52   /* Don't know how many column pointers are needed so estimate.
53      Use Modified Sparse Row storage for u and ju, see Sasd pp.85 */
54   iu   = (int*)PetscMalloc((mbs+1)*sizeof(int));CHKPTRQ(iu);
55   umax = (int)(f*ai[mbs] + 1); umax += mbs + 1;
56   ju   = (int*)PetscMalloc(umax*sizeof(int));CHKPTRQ(ju);
57   iu[0] = mbs+1;
58   juptr = mbs;
59   jl =  (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl);
60   q  =  (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(q);
61   for (i=0; i<mbs; i++){
62     jl[i] = mbs; q[i] = 0;
63   }
64 
65   /* for each row k */
66   for (k=0; k<mbs; k++){
67     nzk = 0; /* num. of nz blocks in k-th block row with diagonal block excluded */
68     q[k] = mbs;
69     /* initialize nonzero structure of k-th row to row rip[k] of A */
70     jmin = ai[rip[k]];
71     jmax = ai[rip[k]+1];
72     for (j=jmin; j<jmax; j++){
73       vj = rip[aj[j]]; /* col. value */
74       if(vj > k){
75         qm = k;
76         do {
77           m  = qm; qm = q[m];
78         } while(qm < vj);
79         if (qm == vj) {
80           printf(" error: duplicate entry in A\n"); break;
81         }
82         nzk++;
83         q[m] = vj;
84         q[vj] = qm;
85       } /* if(vj > k) */
86     } /* for (j=jmin; j<jmax; j++) */
87 
88     /* modify nonzero structure of k-th row by computing fill-in
89        for each row i to be merged in */
90     i = k;
91     i = jl[i]; /* next pivot row (== mbs for symbolic factorization) */
92     /* printf(" next pivot row i=%d\n",i); */
93     while (i < mbs){
94       /* merge row i into k-th row */
95       nzi = iu[i+1] - (iu[i]+1);
96       jmin = iu[i] + 1; jmax = iu[i] + nzi;
97       qm = k;
98       for (j=jmin; j<jmax+1; j++){
99         vj = ju[j];
100         do {
101           m = qm; qm = q[m];
102         } while (qm < vj);
103         if (qm != vj){
104          nzk++; q[m] = vj; q[vj] = qm; qm = vj;
105         }
106       }
107       i = jl[i]; /* next pivot row */
108     }
109 
110     /* add k to row list for first nonzero element in k-th row */
111     if (nzk > 0){
112       i = q[k]; /* col value of first nonzero element in U(k, k+1:mbs-1) */
113       jl[k] = jl[i]; jl[i] = k;
114     }
115     iu[k+1] = iu[k] + nzk;   /* printf(" iu[%d]=%d, umax=%d\n", k+1, iu[k+1],umax);*/
116 
117     /* allocate more space to ju if needed */
118     if (iu[k+1] > umax) { printf("allocate more space, iu[%d]=%d > umax=%d\n",k+1, iu[k+1],umax);
119       /* estimate how much additional space we will need */
120       /* use the strategy suggested by David Hysom <hysom@perch-t.icase.edu> */
121       /* just double the memory each time */
122       maxadd = umax;
123       if (maxadd < nzk) maxadd = (mbs-k)*(nzk+1)/2;
124       umax += maxadd;
125 
126       /* allocate a longer ju */
127       jutmp = (int*)PetscMalloc(umax*sizeof(int));CHKPTRQ(jutmp);
128       ierr  = PetscMemcpy(jutmp,ju,iu[k]*sizeof(int));CHKERRQ(ierr);
129       ierr  = PetscFree(ju);CHKERRQ(ierr);
130       ju    = jutmp;
131       realloc++; /* count how many times we realloc */
132     }
133 
134     /* save nonzero structure of k-th row in ju */
135     i=k;
136     jumin = juptr + 1; juptr += nzk;
137     for (j=jumin; j<juptr+1; j++){
138       i=q[i];
139       ju[j]=i;
140     }
141   }
142 
143   if (ai[mbs] != 0) {
144     PetscReal af = ((PetscReal)iu[mbs])/((PetscReal)ai[mbs]);
145     PLogInfo(A,"MatCholeskyFactorSymbolic_SeqSBAIJ:Reallocs %d Fill ratio:given %g needed %g\n",realloc,f,af);
146     PLogInfo(A,"MatCholeskyFactorSymbolic_SeqSBAIJ:Run with -pc_lu_fill %g or use \n",af);
147     PLogInfo(A,"MatCholeskyFactorSymbolic_SeqSBAIJ:PCLUSetFill(pc,%g);\n",af);
148     PLogInfo(A,"MatCholeskyFactorSymbolic_SeqSBAIJ:for best performance.\n");
149   } else {
150      PLogInfo(A,"MatCholeskyFactorSymbolic_SeqSBAIJ:Empty matrix.\n");
151   }
152 
153   ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
154   ierr = PetscFree(q);CHKERRQ(ierr);
155   ierr = PetscFree(jl);CHKERRQ(ierr);
156 
157   /* put together the new matrix */
158   ierr = MatCreateSeqSBAIJ(A->comm,bs,bs*mbs,bs*mbs,0,PETSC_NULL,B);CHKERRQ(ierr);
159   /* PLogObjectParent(*B,iperm); */
160   b = (Mat_SeqSBAIJ*)(*B)->data;
161   ierr = PetscFree(b->imax);CHKERRQ(ierr);
162   b->singlemalloc = PETSC_FALSE;
163   /* the next line frees the default space generated by the Create() */
164   ierr = PetscFree(b->a);CHKERRQ(ierr);
165   ierr = PetscFree(b->ilen);CHKERRQ(ierr);
166   b->a          = (MatScalar*)PetscMalloc((iu[mbs]+1)*sizeof(MatScalar)*bs2);CHKPTRQ(b->a);
167   b->j          = ju;
168   b->i          = iu;
169   b->diag       = 0;
170   b->ilen       = 0;
171   b->imax       = 0;
172   b->row        = perm;
173   ierr          = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
174   b->icol       = perm;
175   ierr          = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
176   b->solve_work = (Scalar*)PetscMalloc((bs*mbs+bs)*sizeof(Scalar));CHKPTRQ(b->solve_work);
177   /* In b structure:  Free imax, ilen, old a, old j.
178      Allocate idnew, solve_work, new a, new j */
179   PLogObjectMemory(*B,(iu[mbs]-mbs)*(sizeof(int)+sizeof(MatScalar)));
180   b->s_maxnz = b->s_nz = iu[mbs];
181 
182   (*B)->factor                 = FACTOR_CHOLESKY;
183   (*B)->info.factor_mallocs    = realloc;
184   (*B)->info.fill_ratio_given  = f;
185   if (ai[mbs] != 0) {
186     (*B)->info.fill_ratio_needed = ((PetscReal)iu[mbs])/((PetscReal)ai[mbs]);
187   } else {
188     (*B)->info.fill_ratio_needed = 0.0;
189   }
190 
191   PetscFunctionReturn(0);
192 }
193 
194 #undef __FUNC__
195 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_N"
196 int MatCholeskyFactorNumeric_SeqSBAIJ_N(Mat A,Mat *B)
197 {
198   Mat                C = *B;
199   Mat_SeqSBAIJ       *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data;
200   IS                 perm = b->row;
201   int                *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
202   int                *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
203   int                bs=a->bs,bs2 = a->bs2;
204   MatScalar          *ba = b->a,*aa,*ap,*dk,*uik;
205   MatScalar          *u,*diag,*rtmp,*rtmp_ptr;
206   MatScalar          *W,*work;
207   int                *pivots;
208 
209   PetscFunctionBegin;
210 
211   /* initialization */
212   rtmp  = (MatScalar*)PetscMalloc(bs2*mbs*sizeof(MatScalar));CHKPTRQ(rtmp);
213   ierr  = PetscMemzero(rtmp,bs2*mbs*sizeof(MatScalar));CHKERRQ(ierr);
214   il    = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il);
215   jl    = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl);
216   for (i=0; i<mbs; i++) {
217     jl[i] = mbs; il[0] = 0;
218   }
219   dk    = (MatScalar*)PetscMalloc(bs2*sizeof(MatScalar));CHKPTRQ(dk);
220   uik   = (MatScalar*)PetscMalloc(bs2*sizeof(MatScalar));CHKPTRQ(uik);
221   W     = (MatScalar*)PetscMalloc(bs2*sizeof(MatScalar));CHKPTRQ(W);
222   work  = (MatScalar*)PetscMalloc(bs*sizeof(MatScalar));CHKPTRQ(work);
223   pivots= (int*)PetscMalloc(bs*sizeof(int));CHKPTRQ(pivots);
224 
225   ierr  = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr);
226 
227   /* check permutation */
228   if (!a->permute){
229     ai = a->i; aj = a->j; aa = a->a;
230   } else {
231     ai = a->inew; aj = a->jnew;
232     aa = (MatScalar*)PetscMalloc(bs2*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa);
233     ierr = PetscMemcpy(aa,a->a,bs2*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr);
234     a2anew  = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew);
235     ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr);
236 
237     for (i=0; i<mbs; i++){
238       jmin = ai[i]; jmax = ai[i+1];
239       for (j=jmin; j<jmax; j++){
240         while (a2anew[j] != j){
241           k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k;
242           for (k1=0; k1<bs2; k1++){
243             dk[k1]       = aa[k*bs2+k1];
244             aa[k*bs2+k1] = aa[j*bs2+k1];
245             aa[j*bs2+k1] = dk[k1];
246           }
247         }
248         /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */
249         if (i > aj[j]){
250           /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */
251           ap = aa + j*bs2;                     /* ptr to the beginning of j-th block of aa */
252           for (k=0; k<bs2; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */
253           for (k=0; k<bs; k++){               /* j-th block of aa <- dk^T */
254             for (k1=0; k1<bs; k1++) *ap++ = dk[k + bs*k1];
255           }
256         }
257       }
258     }
259     ierr = PetscFree(a2anew);CHKERRA(ierr);
260   }
261 
262   /* for each row k */
263   for (k = 0; k<mbs; k++){
264 
265     /*initialize k-th row with elements nonzero in row perm(k) of A */
266     jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1];
267     if (jmin < jmax) {
268       ap = aa + jmin*bs2;
269       for (j = jmin; j < jmax; j++){
270         vj = perm_ptr[aj[j]];         /* block col. index */
271         rtmp_ptr = rtmp + vj*bs2;
272         for (i=0; i<bs2; i++) *rtmp_ptr++ = *ap++;
273       }
274     }
275 
276     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
277     ierr = PetscMemcpy(dk,rtmp+k*bs2,bs2*sizeof(MatScalar));CHKERRQ(ierr);
278     i = jl[k]; /* first row to be added to k_th row  */
279 
280     while (i < mbs){
281       nexti = jl[i]; /* next row to be added to k_th row */
282 
283       /* compute multiplier */
284       ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
285 
286       /* uik = -inv(Di)*U_bar(i,k) */
287       diag = ba + i*bs2;
288       u    = ba + ili*bs2;
289       ierr = PetscMemzero(uik,bs2*sizeof(MatScalar));CHKERRQ(ierr);
290       Kernel_A_gets_A_minus_B_times_C(bs,uik,diag,u);
291 
292       /* update D(k) += -U(i,k)^T * U_bar(i,k) */
293       Kernel_A_gets_A_plus_Btranspose_times_C(bs,dk,uik,u);
294 
295       /* update -U(i,k) */
296       ierr = PetscMemcpy(ba+ili*bs2,uik,bs2*sizeof(MatScalar));CHKERRQ(ierr);
297 
298       /* add multiple of row i to k-th row ... */
299       jmin = ili + 1; jmax = bi[i+1];
300       if (jmin < jmax){
301         for (j=jmin; j<jmax; j++) {
302           /* rtmp += -U(i,k)^T * U_bar(i,j) */
303           rtmp_ptr = rtmp + bj[j]*bs2;
304           u = ba + j*bs2;
305           Kernel_A_gets_A_plus_Btranspose_times_C(bs,rtmp_ptr,uik,u);
306         }
307 
308         /* ... add i to row list for next nonzero entry */
309         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
310         j     = bj[jmin];
311         jl[i] = jl[j]; jl[j] = i; /* update jl */
312       }
313       i = nexti;
314     }
315 
316     /* save nonzero entries in k-th row of U ... */
317 
318     /* invert diagonal block */
319     diag = ba+k*bs2;
320     ierr = PetscMemcpy(diag,dk,bs2*sizeof(MatScalar));CHKERRQ(ierr);
321     Kernel_A_gets_inverse_A(bs,diag,pivots,work);
322 
323     jmin = bi[k]; jmax = bi[k+1];
324     if (jmin < jmax) {
325       for (j=jmin; j<jmax; j++){
326          vj = bj[j];           /* block col. index of U */
327          u   = ba + j*bs2;
328          rtmp_ptr = rtmp + vj*bs2;
329          for (k1=0; k1<bs2; k1++){
330            *u++        = *rtmp_ptr;
331            *rtmp_ptr++ = 0.0;
332          }
333       }
334 
335       /* ... add k to row list for first nonzero entry in k-th row */
336       il[k] = jmin;
337       i     = bj[jmin];
338       jl[k] = jl[i]; jl[i] = k;
339     }
340   }
341 
342   ierr = PetscFree(rtmp);CHKERRQ(ierr);
343   ierr = PetscFree(il);CHKERRQ(ierr);
344   ierr = PetscFree(jl);CHKERRQ(ierr);
345   ierr = PetscFree(dk);CHKERRQ(ierr);
346   ierr = PetscFree(uik);CHKERRQ(ierr);
347   ierr = PetscFree(W);CHKERRQ(ierr);
348   ierr = PetscFree(work);CHKERRQ(ierr);
349   ierr = PetscFree(pivots);CHKERRQ(ierr);
350   if (a->permute){
351     ierr = PetscFree(aa);CHKERRQ(ierr);
352   }
353 
354   ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr);
355   C->factor    = FACTOR_CHOLESKY;
356   C->assembled = PETSC_TRUE;
357   C->preallocated = PETSC_TRUE;
358   PLogFlops(1.3333*bs*bs2*b->mbs); /* from inverting diagonal blocks */
359   PetscFunctionReturn(0);
360 }
361 
362 /* Version for when blocks are 7 by 7 */
363 #undef __FUNC__
364 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_7"
365 int MatCholeskyFactorNumeric_SeqSBAIJ_7(Mat A,Mat *B)
366 {
367   Mat                C = *B;
368   Mat_SeqSBAIJ       *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data;
369   IS                 perm = b->row;
370   int                *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
371   int                *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
372   MatScalar          *ba = b->a,*aa,*ap,*dk,*uik;
373   MatScalar          *u,*d,*w,*wp;
374 
375   PetscFunctionBegin;
376   /* initialization */
377   printf("called MatCholeskyFactorNumeric_SeqSBAIJ_7 \n");
378   w  = (MatScalar*)PetscMalloc(49*mbs*sizeof(MatScalar));CHKPTRQ(w);
379   ierr = PetscMemzero(w,49*mbs*sizeof(MatScalar));CHKERRQ(ierr);
380   il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il);
381   jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl);
382   for (i=0; i<mbs; i++) {
383     jl[i] = mbs; il[0] = 0;
384   }
385   dk    = (MatScalar*)PetscMalloc(49*sizeof(MatScalar));CHKPTRQ(dk);
386   uik   = (MatScalar*)PetscMalloc(49*sizeof(MatScalar));CHKPTRQ(uik);
387   ierr  = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr);
388 
389   /* check permutation */
390   if (!a->permute){
391     ai = a->i; aj = a->j; aa = a->a;
392   } else {
393     ai = a->inew; aj = a->jnew;
394     aa = (MatScalar*)PetscMalloc(49*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa);
395     ierr = PetscMemcpy(aa,a->a,49*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr);
396     a2anew  = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew);
397     ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr);
398 
399     for (i=0; i<mbs; i++){
400       jmin = ai[i]; jmax = ai[i+1];
401       for (j=jmin; j<jmax; j++){
402         while (a2anew[j] != j){
403           k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k;
404           for (k1=0; k1<49; k1++){
405             dk[k1]       = aa[k*49+k1];
406             aa[k*49+k1] = aa[j*49+k1];
407             aa[j*49+k1] = dk[k1];
408           }
409         }
410         /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */
411         if (i > aj[j]){
412           /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */
413           ap = aa + j*49;                     /* ptr to the beginning of j-th block of aa */
414           for (k=0; k<49; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */
415           for (k=0; k<7; k++){               /* j-th block of aa <- dk^T */
416             for (k1=0; k1<7; k1++) *ap++ = dk[k + 7*k1];
417           }
418         }
419       }
420     }
421     ierr = PetscFree(a2anew);CHKERRA(ierr);
422   }
423 
424   /* for each row k */
425   for (k = 0; k<mbs; k++){
426 
427     /*initialize k-th row with elements nonzero in row perm(k) of A */
428     jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1];
429     if (jmin < jmax) {
430       ap = aa + jmin*49;
431       for (j = jmin; j < jmax; j++){
432         vj = perm_ptr[aj[j]];         /* block col. index */
433         wp = w + vj*49;
434         for (i=0; i<49; i++) *wp++ = *ap++;
435       }
436     }
437 
438     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
439     ierr = PetscMemcpy(dk,w+k*49,49*sizeof(MatScalar));CHKERRQ(ierr);
440     i = jl[k]; /* first row to be added to k_th row  */
441 
442     while (i < mbs){
443       nexti = jl[i]; /* next row to be added to k_th row */
444 
445       /* compute multiplier */
446       ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
447 
448       /* uik = -inv(Di)*U_bar(i,k) */
449       d = ba + i*49;
450       u    = ba + ili*49;
451 
452       uik[0] = -(d[0]*u[0] + d[7]*u[1]+ d[14]*u[2]+ d[21]*u[3]+ d[28]*u[4]+ d[35]*u[5]+ d[42]*u[6]);
453       uik[1] = -(d[1]*u[0] + d[8]*u[1]+ d[15]*u[2]+ d[22]*u[3]+ d[29]*u[4]+ d[36]*u[5]+ d[43]*u[6]);
454       uik[2] = -(d[2]*u[0] + d[9]*u[1]+ d[16]*u[2]+ d[23]*u[3]+ d[30]*u[4]+ d[37]*u[5]+ d[44]*u[6]);
455       uik[3] = -(d[3]*u[0]+ d[10]*u[1]+ d[17]*u[2]+ d[24]*u[3]+ d[31]*u[4]+ d[38]*u[5]+ d[45]*u[6]);
456       uik[4] = -(d[4]*u[0]+ d[11]*u[1]+ d[18]*u[2]+ d[25]*u[3]+ d[32]*u[4]+ d[39]*u[5]+ d[46]*u[6]);
457       uik[5] = -(d[5]*u[0]+ d[12]*u[1]+ d[19]*u[2]+ d[26]*u[3]+ d[33]*u[4]+ d[40]*u[5]+ d[47]*u[6]);
458       uik[6] = -(d[6]*u[0]+ d[13]*u[1]+ d[20]*u[2]+ d[27]*u[3]+ d[34]*u[4]+ d[41]*u[5]+ d[48]*u[6]);
459 
460       uik[7] = -(d[0]*u[7] + d[7]*u[8]+ d[14]*u[9]+ d[21]*u[10]+ d[28]*u[11]+ d[35]*u[12]+ d[42]*u[13]);
461       uik[8] = -(d[1]*u[7] + d[8]*u[8]+ d[15]*u[9]+ d[22]*u[10]+ d[29]*u[11]+ d[36]*u[12]+ d[43]*u[13]);
462       uik[9] = -(d[2]*u[7] + d[9]*u[8]+ d[16]*u[9]+ d[23]*u[10]+ d[30]*u[11]+ d[37]*u[12]+ d[44]*u[13]);
463       uik[10]= -(d[3]*u[7]+ d[10]*u[8]+ d[17]*u[9]+ d[24]*u[10]+ d[31]*u[11]+ d[38]*u[12]+ d[45]*u[13]);
464       uik[11]= -(d[4]*u[7]+ d[11]*u[8]+ d[18]*u[9]+ d[25]*u[10]+ d[32]*u[11]+ d[39]*u[12]+ d[46]*u[13]);
465       uik[12]= -(d[5]*u[7]+ d[12]*u[8]+ d[19]*u[9]+ d[26]*u[10]+ d[33]*u[11]+ d[40]*u[12]+ d[47]*u[13]);
466       uik[13]= -(d[6]*u[7]+ d[13]*u[8]+ d[20]*u[9]+ d[27]*u[10]+ d[34]*u[11]+ d[41]*u[12]+ d[48]*u[13]);
467 
468       uik[14]= -(d[0]*u[14] + d[7]*u[15]+ d[14]*u[16]+ d[21]*u[17]+ d[28]*u[18]+ d[35]*u[19]+ d[42]*u[20]);
469       uik[15]= -(d[1]*u[14] + d[8]*u[15]+ d[15]*u[16]+ d[22]*u[17]+ d[29]*u[18]+ d[36]*u[19]+ d[43]*u[20]);
470       uik[16]= -(d[2]*u[14] + d[9]*u[15]+ d[16]*u[16]+ d[23]*u[17]+ d[30]*u[18]+ d[37]*u[19]+ d[44]*u[20]);
471       uik[17]= -(d[3]*u[14]+ d[10]*u[15]+ d[17]*u[16]+ d[24]*u[17]+ d[31]*u[18]+ d[38]*u[19]+ d[45]*u[20]);
472       uik[18]= -(d[4]*u[14]+ d[11]*u[15]+ d[18]*u[16]+ d[25]*u[17]+ d[32]*u[18]+ d[39]*u[19]+ d[46]*u[20]);
473       uik[19]= -(d[5]*u[14]+ d[12]*u[15]+ d[19]*u[16]+ d[26]*u[17]+ d[33]*u[18]+ d[40]*u[19]+ d[47]*u[20]);
474       uik[20]= -(d[6]*u[14]+ d[13]*u[15]+ d[20]*u[16]+ d[27]*u[17]+ d[34]*u[18]+ d[41]*u[19]+ d[48]*u[20]);
475 
476       uik[21]= -(d[0]*u[21] + d[7]*u[22]+ d[14]*u[23]+ d[21]*u[24]+ d[28]*u[25]+ d[35]*u[26]+ d[42]*u[27]);
477       uik[22]= -(d[1]*u[21] + d[8]*u[22]+ d[15]*u[23]+ d[22]*u[24]+ d[29]*u[25]+ d[36]*u[26]+ d[43]*u[27]);
478       uik[23]= -(d[2]*u[21] + d[9]*u[22]+ d[16]*u[23]+ d[23]*u[24]+ d[30]*u[25]+ d[37]*u[26]+ d[44]*u[27]);
479       uik[24]= -(d[3]*u[21]+ d[10]*u[22]+ d[17]*u[23]+ d[24]*u[24]+ d[31]*u[25]+ d[38]*u[26]+ d[45]*u[27]);
480       uik[25]= -(d[4]*u[21]+ d[11]*u[22]+ d[18]*u[23]+ d[25]*u[24]+ d[32]*u[25]+ d[39]*u[26]+ d[46]*u[27]);
481       uik[26]= -(d[5]*u[21]+ d[12]*u[22]+ d[19]*u[23]+ d[26]*u[24]+ d[33]*u[25]+ d[40]*u[26]+ d[47]*u[27]);
482       uik[27]= -(d[6]*u[21]+ d[13]*u[22]+ d[20]*u[23]+ d[27]*u[24]+ d[34]*u[25]+ d[41]*u[26]+ d[48]*u[27]);
483 
484       uik[28]= -(d[0]*u[28] + d[7]*u[29]+ d[14]*u[30]+ d[21]*u[31]+ d[28]*u[32]+ d[35]*u[33]+ d[42]*u[34]);
485       uik[29]= -(d[1]*u[28] + d[8]*u[29]+ d[15]*u[30]+ d[22]*u[31]+ d[29]*u[32]+ d[36]*u[33]+ d[43]*u[34]);
486       uik[30]= -(d[2]*u[28] + d[9]*u[29]+ d[16]*u[30]+ d[23]*u[31]+ d[30]*u[32]+ d[37]*u[33]+ d[44]*u[34]);
487       uik[31]= -(d[3]*u[28]+ d[10]*u[29]+ d[17]*u[30]+ d[24]*u[31]+ d[31]*u[32]+ d[38]*u[33]+ d[45]*u[34]);
488       uik[32]= -(d[4]*u[28]+ d[11]*u[29]+ d[18]*u[30]+ d[25]*u[31]+ d[32]*u[32]+ d[39]*u[33]+ d[46]*u[34]);
489       uik[33]= -(d[5]*u[28]+ d[12]*u[29]+ d[19]*u[30]+ d[26]*u[31]+ d[33]*u[32]+ d[40]*u[33]+ d[47]*u[34]);
490       uik[34]= -(d[6]*u[28]+ d[13]*u[29]+ d[20]*u[30]+ d[27]*u[31]+ d[34]*u[32]+ d[41]*u[33]+ d[48]*u[34]);
491 
492       uik[35]= -(d[0]*u[35] + d[7]*u[36]+ d[14]*u[37]+ d[21]*u[38]+ d[28]*u[39]+ d[35]*u[40]+ d[42]*u[41]);
493       uik[36]= -(d[1]*u[35] + d[8]*u[36]+ d[15]*u[37]+ d[22]*u[38]+ d[29]*u[39]+ d[36]*u[40]+ d[43]*u[41]);
494       uik[37]= -(d[2]*u[35] + d[9]*u[36]+ d[16]*u[37]+ d[23]*u[38]+ d[30]*u[39]+ d[37]*u[40]+ d[44]*u[41]);
495       uik[38]= -(d[3]*u[35]+ d[10]*u[36]+ d[17]*u[37]+ d[24]*u[38]+ d[31]*u[39]+ d[38]*u[40]+ d[45]*u[41]);
496       uik[39]= -(d[4]*u[35]+ d[11]*u[36]+ d[18]*u[37]+ d[25]*u[38]+ d[32]*u[39]+ d[39]*u[40]+ d[46]*u[41]);
497       uik[40]= -(d[5]*u[35]+ d[12]*u[36]+ d[19]*u[37]+ d[26]*u[38]+ d[33]*u[39]+ d[40]*u[40]+ d[47]*u[41]);
498       uik[41]= -(d[6]*u[35]+ d[13]*u[36]+ d[20]*u[37]+ d[27]*u[38]+ d[34]*u[39]+ d[41]*u[40]+ d[48]*u[41]);
499 
500       uik[42]= -(d[0]*u[42] + d[7]*u[43]+ d[14]*u[44]+ d[21]*u[45]+ d[28]*u[46]+ d[35]*u[47]+ d[42]*u[48]);
501       uik[43]= -(d[1]*u[42] + d[8]*u[43]+ d[15]*u[44]+ d[22]*u[45]+ d[29]*u[46]+ d[36]*u[47]+ d[43]*u[48]);
502       uik[44]= -(d[2]*u[42] + d[9]*u[43]+ d[16]*u[44]+ d[23]*u[45]+ d[30]*u[46]+ d[37]*u[47]+ d[44]*u[48]);
503       uik[45]= -(d[3]*u[42]+ d[10]*u[43]+ d[17]*u[44]+ d[24]*u[45]+ d[31]*u[46]+ d[38]*u[47]+ d[45]*u[48]);
504       uik[46]= -(d[4]*u[42]+ d[11]*u[43]+ d[18]*u[44]+ d[25]*u[45]+ d[32]*u[46]+ d[39]*u[47]+ d[46]*u[48]);
505       uik[47]= -(d[5]*u[42]+ d[12]*u[43]+ d[19]*u[44]+ d[26]*u[45]+ d[33]*u[46]+ d[40]*u[47]+ d[47]*u[48]);
506       uik[48]= -(d[6]*u[42]+ d[13]*u[43]+ d[20]*u[44]+ d[27]*u[45]+ d[34]*u[46]+ d[41]*u[47]+ d[48]*u[48]);
507 
508       /* update D(k) += -U(i,k)^T * U_bar(i,k) */
509       dk[0]+=  uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6];
510       dk[1]+=  uik[7]*u[0] + uik[8]*u[1] + uik[9]*u[2]+ uik[10]*u[3]+ uik[11]*u[4]+ uik[12]*u[5]+ uik[13]*u[6];
511       dk[2]+= uik[14]*u[0]+ uik[15]*u[1]+ uik[16]*u[2]+ uik[17]*u[3]+ uik[18]*u[4]+ uik[19]*u[5]+ uik[20]*u[6];
512       dk[3]+= uik[21]*u[0]+ uik[22]*u[1]+ uik[23]*u[2]+ uik[24]*u[3]+ uik[25]*u[4]+ uik[26]*u[5]+ uik[27]*u[6];
513       dk[4]+= uik[28]*u[0]+ uik[29]*u[1]+ uik[30]*u[2]+ uik[31]*u[3]+ uik[32]*u[4]+ uik[33]*u[5]+ uik[34]*u[6];
514       dk[5]+= uik[35]*u[0]+ uik[36]*u[1]+ uik[37]*u[2]+ uik[38]*u[3]+ uik[39]*u[4]+ uik[40]*u[5]+ uik[41]*u[6];
515       dk[6]+= uik[42]*u[0]+ uik[43]*u[1]+ uik[44]*u[2]+ uik[45]*u[3]+ uik[46]*u[4]+ uik[47]*u[5]+ uik[48]*u[6];
516 
517       dk[7]+=  uik[0]*u[7] + uik[1]*u[8] + uik[2]*u[9] + uik[3]*u[10] + uik[4]*u[11] + uik[5]*u[12] + uik[6]*u[13];
518       dk[8]+=  uik[7]*u[7] + uik[8]*u[8] + uik[9]*u[9]+ uik[10]*u[10]+ uik[11]*u[11]+ uik[12]*u[12]+ uik[13]*u[13];
519       dk[9]+= uik[14]*u[7]+ uik[15]*u[8]+ uik[16]*u[9]+ uik[17]*u[10]+ uik[18]*u[11]+ uik[19]*u[12]+ uik[20]*u[13];
520       dk[10]+=uik[21]*u[7]+ uik[22]*u[8]+ uik[23]*u[9]+ uik[24]*u[10]+ uik[25]*u[11]+ uik[26]*u[12]+ uik[27]*u[13];
521       dk[11]+=uik[28]*u[7]+ uik[29]*u[8]+ uik[30]*u[9]+ uik[31]*u[10]+ uik[32]*u[11]+ uik[33]*u[12]+ uik[34]*u[13];
522       dk[12]+=uik[35]*u[7]+ uik[36]*u[8]+ uik[37]*u[9]+ uik[38]*u[10]+ uik[39]*u[11]+ uik[40]*u[12]+ uik[41]*u[13];
523       dk[13]+=uik[42]*u[7]+ uik[43]*u[8]+ uik[44]*u[9]+ uik[45]*u[10]+ uik[46]*u[11]+ uik[47]*u[12]+ uik[48]*u[13];
524 
525       dk[14]+=  uik[0]*u[14] + uik[1]*u[15] + uik[2]*u[16] + uik[3]*u[17] + uik[4]*u[18] + uik[5]*u[19] + uik[6]*u[20];
526       dk[15]+=  uik[7]*u[14] + uik[8]*u[15] + uik[9]*u[16]+ uik[10]*u[17]+ uik[11]*u[18]+ uik[12]*u[19]+ uik[13]*u[20];
527       dk[16]+= uik[14]*u[14]+ uik[15]*u[15]+ uik[16]*u[16]+ uik[17]*u[17]+ uik[18]*u[18]+ uik[19]*u[19]+ uik[20]*u[20];
528       dk[17]+= uik[21]*u[14]+ uik[22]*u[15]+ uik[23]*u[16]+ uik[24]*u[17]+ uik[25]*u[18]+ uik[26]*u[19]+ uik[27]*u[20];
529       dk[18]+= uik[28]*u[14]+ uik[29]*u[15]+ uik[30]*u[16]+ uik[31]*u[17]+ uik[32]*u[18]+ uik[33]*u[19]+ uik[34]*u[20];
530       dk[19]+= uik[35]*u[14]+ uik[36]*u[15]+ uik[37]*u[16]+ uik[38]*u[17]+ uik[39]*u[18]+ uik[40]*u[19]+ uik[41]*u[20];
531       dk[20]+= uik[42]*u[14]+ uik[43]*u[15]+ uik[44]*u[16]+ uik[45]*u[17]+ uik[46]*u[18]+ uik[47]*u[19]+ uik[48]*u[20];
532 
533       dk[21]+=  uik[0]*u[21] + uik[1]*u[22] + uik[2]*u[23] + uik[3]*u[24] + uik[4]*u[25] + uik[5]*u[26] + uik[6]*u[27];
534       dk[22]+=  uik[7]*u[21] + uik[8]*u[22] + uik[9]*u[23]+ uik[10]*u[24]+ uik[11]*u[25]+ uik[12]*u[26]+ uik[13]*u[27];
535       dk[23]+= uik[14]*u[21]+ uik[15]*u[22]+ uik[16]*u[23]+ uik[17]*u[24]+ uik[18]*u[25]+ uik[19]*u[26]+ uik[20]*u[27];
536       dk[24]+= uik[21]*u[21]+ uik[22]*u[22]+ uik[23]*u[23]+ uik[24]*u[24]+ uik[25]*u[25]+ uik[26]*u[26]+ uik[27]*u[27];
537       dk[25]+= uik[28]*u[21]+ uik[29]*u[22]+ uik[30]*u[23]+ uik[31]*u[24]+ uik[32]*u[25]+ uik[33]*u[26]+ uik[34]*u[27];
538       dk[26]+= uik[35]*u[21]+ uik[36]*u[22]+ uik[37]*u[23]+ uik[38]*u[24]+ uik[39]*u[25]+ uik[40]*u[26]+ uik[41]*u[27];
539       dk[27]+= uik[42]*u[21]+ uik[43]*u[22]+ uik[44]*u[23]+ uik[45]*u[24]+ uik[46]*u[25]+ uik[47]*u[26]+ uik[48]*u[27];
540 
541       dk[28]+=  uik[0]*u[28] + uik[1]*u[29] + uik[2]*u[30] + uik[3]*u[31] + uik[4]*u[32] + uik[5]*u[33] + uik[6]*u[34];
542       dk[29]+=  uik[7]*u[28] + uik[8]*u[29] + uik[9]*u[30]+ uik[10]*u[31]+ uik[11]*u[32]+ uik[12]*u[33]+ uik[13]*u[34];
543       dk[30]+= uik[14]*u[28]+ uik[15]*u[29]+ uik[16]*u[30]+ uik[17]*u[31]+ uik[18]*u[32]+ uik[19]*u[33]+ uik[20]*u[34];
544       dk[31]+= uik[21]*u[28]+ uik[22]*u[29]+ uik[23]*u[30]+ uik[24]*u[31]+ uik[25]*u[32]+ uik[26]*u[33]+ uik[27]*u[34];
545       dk[32]+= uik[28]*u[28]+ uik[29]*u[29]+ uik[30]*u[30]+ uik[31]*u[31]+ uik[32]*u[32]+ uik[33]*u[33]+ uik[34]*u[34];
546       dk[33]+= uik[35]*u[28]+ uik[36]*u[29]+ uik[37]*u[30]+ uik[38]*u[31]+ uik[39]*u[32]+ uik[40]*u[33]+ uik[41]*u[34];
547       dk[34]+= uik[42]*u[28]+ uik[43]*u[29]+ uik[44]*u[30]+ uik[45]*u[31]+ uik[46]*u[32]+ uik[47]*u[33]+ uik[48]*u[34];
548 
549       dk[35]+=  uik[0]*u[35] + uik[1]*u[36] + uik[2]*u[37] + uik[3]*u[38] + uik[4]*u[39] + uik[5]*u[40] + uik[6]*u[41];
550       dk[36]+=  uik[7]*u[35] + uik[8]*u[36] + uik[9]*u[37]+ uik[10]*u[38]+ uik[11]*u[39]+ uik[12]*u[40]+ uik[13]*u[41];
551       dk[37]+= uik[14]*u[35]+ uik[15]*u[36]+ uik[16]*u[37]+ uik[17]*u[38]+ uik[18]*u[39]+ uik[19]*u[40]+ uik[20]*u[41];
552       dk[38]+= uik[21]*u[35]+ uik[22]*u[36]+ uik[23]*u[37]+ uik[24]*u[38]+ uik[25]*u[39]+ uik[26]*u[40]+ uik[27]*u[41];
553       dk[39]+= uik[28]*u[35]+ uik[29]*u[36]+ uik[30]*u[37]+ uik[31]*u[38]+ uik[32]*u[39]+ uik[33]*u[40]+ uik[34]*u[41];
554       dk[40]+= uik[35]*u[35]+ uik[36]*u[36]+ uik[37]*u[37]+ uik[38]*u[38]+ uik[39]*u[39]+ uik[40]*u[40]+ uik[41]*u[41];
555       dk[41]+= uik[42]*u[35]+ uik[43]*u[36]+ uik[44]*u[37]+ uik[45]*u[38]+ uik[46]*u[39]+ uik[47]*u[40]+ uik[48]*u[41];
556 
557       dk[42]+=  uik[0]*u[42] + uik[1]*u[43] + uik[2]*u[44] + uik[3]*u[45] + uik[4]*u[46] + uik[5]*u[47] + uik[6]*u[48];
558       dk[43]+=  uik[7]*u[42] + uik[8]*u[43] + uik[9]*u[44]+ uik[10]*u[45]+ uik[11]*u[46]+ uik[12]*u[47]+ uik[13]*u[48];
559       dk[44]+= uik[14]*u[42]+ uik[15]*u[43]+ uik[16]*u[44]+ uik[17]*u[45]+ uik[18]*u[46]+ uik[19]*u[47]+ uik[20]*u[48];
560       dk[45]+= uik[21]*u[42]+ uik[22]*u[43]+ uik[23]*u[44]+ uik[24]*u[45]+ uik[25]*u[46]+ uik[26]*u[47]+ uik[27]*u[48];
561       dk[46]+= uik[28]*u[42]+ uik[29]*u[43]+ uik[30]*u[44]+ uik[31]*u[45]+ uik[32]*u[46]+ uik[33]*u[47]+ uik[34]*u[48];
562       dk[47]+= uik[35]*u[42]+ uik[36]*u[43]+ uik[37]*u[44]+ uik[38]*u[45]+ uik[39]*u[46]+ uik[40]*u[47]+ uik[41]*u[48];
563       dk[48]+= uik[42]*u[42]+ uik[43]*u[43]+ uik[44]*u[44]+ uik[45]*u[45]+ uik[46]*u[46]+ uik[47]*u[47]+ uik[48]*u[48];
564 
565       /* update -U(i,k) */
566       ierr = PetscMemcpy(ba+ili*49,uik,49*sizeof(MatScalar));CHKERRQ(ierr);
567 
568       /* add multiple of row i to k-th row ... */
569       jmin = ili + 1; jmax = bi[i+1];
570       if (jmin < jmax){
571         for (j=jmin; j<jmax; j++) {
572           /* w += -U(i,k)^T * U_bar(i,j) */
573           wp = w + bj[j]*49;
574           u = ba + j*49;
575 
576           wp[0]+=  uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6];
577           wp[1]+=  uik[7]*u[0] + uik[8]*u[1] + uik[9]*u[2]+ uik[10]*u[3]+ uik[11]*u[4]+ uik[12]*u[5]+ uik[13]*u[6];
578           wp[2]+= uik[14]*u[0]+ uik[15]*u[1]+ uik[16]*u[2]+ uik[17]*u[3]+ uik[18]*u[4]+ uik[19]*u[5]+ uik[20]*u[6];
579           wp[3]+= uik[21]*u[0]+ uik[22]*u[1]+ uik[23]*u[2]+ uik[24]*u[3]+ uik[25]*u[4]+ uik[26]*u[5]+ uik[27]*u[6];
580           wp[4]+= uik[28]*u[0]+ uik[29]*u[1]+ uik[30]*u[2]+ uik[31]*u[3]+ uik[32]*u[4]+ uik[33]*u[5]+ uik[34]*u[6];
581           wp[5]+= uik[35]*u[0]+ uik[36]*u[1]+ uik[37]*u[2]+ uik[38]*u[3]+ uik[39]*u[4]+ uik[40]*u[5]+ uik[41]*u[6];
582           wp[6]+= uik[42]*u[0]+ uik[43]*u[1]+ uik[44]*u[2]+ uik[45]*u[3]+ uik[46]*u[4]+ uik[47]*u[5]+ uik[48]*u[6];
583 
584           wp[7]+=  uik[0]*u[7] + uik[1]*u[8] + uik[2]*u[9] + uik[3]*u[10] + uik[4]*u[11] + uik[5]*u[12] + uik[6]*u[13];
585           wp[8]+=  uik[7]*u[7] + uik[8]*u[8] + uik[9]*u[9]+ uik[10]*u[10]+ uik[11]*u[11]+ uik[12]*u[12]+ uik[13]*u[13];
586           wp[9]+= uik[14]*u[7]+ uik[15]*u[8]+ uik[16]*u[9]+ uik[17]*u[10]+ uik[18]*u[11]+ uik[19]*u[12]+ uik[20]*u[13];
587           wp[10]+=uik[21]*u[7]+ uik[22]*u[8]+ uik[23]*u[9]+ uik[24]*u[10]+ uik[25]*u[11]+ uik[26]*u[12]+ uik[27]*u[13];
588           wp[11]+=uik[28]*u[7]+ uik[29]*u[8]+ uik[30]*u[9]+ uik[31]*u[10]+ uik[32]*u[11]+ uik[33]*u[12]+ uik[34]*u[13];
589           wp[12]+=uik[35]*u[7]+ uik[36]*u[8]+ uik[37]*u[9]+ uik[38]*u[10]+ uik[39]*u[11]+ uik[40]*u[12]+ uik[41]*u[13];
590           wp[13]+=uik[42]*u[7]+ uik[43]*u[8]+ uik[44]*u[9]+ uik[45]*u[10]+ uik[46]*u[11]+ uik[47]*u[12]+ uik[48]*u[13];
591 
592           wp[14]+=  uik[0]*u[14] + uik[1]*u[15] + uik[2]*u[16] + uik[3]*u[17] + uik[4]*u[18] + uik[5]*u[19] + uik[6]*u[20];
593           wp[15]+=  uik[7]*u[14] + uik[8]*u[15] + uik[9]*u[16]+ uik[10]*u[17]+ uik[11]*u[18]+ uik[12]*u[19]+ uik[13]*u[20];
594           wp[16]+= uik[14]*u[14]+ uik[15]*u[15]+ uik[16]*u[16]+ uik[17]*u[17]+ uik[18]*u[18]+ uik[19]*u[19]+ uik[20]*u[20];
595           wp[17]+= uik[21]*u[14]+ uik[22]*u[15]+ uik[23]*u[16]+ uik[24]*u[17]+ uik[25]*u[18]+ uik[26]*u[19]+ uik[27]*u[20];
596           wp[18]+= uik[28]*u[14]+ uik[29]*u[15]+ uik[30]*u[16]+ uik[31]*u[17]+ uik[32]*u[18]+ uik[33]*u[19]+ uik[34]*u[20];
597           wp[19]+= uik[35]*u[14]+ uik[36]*u[15]+ uik[37]*u[16]+ uik[38]*u[17]+ uik[39]*u[18]+ uik[40]*u[19]+ uik[41]*u[20];
598           wp[20]+= uik[42]*u[14]+ uik[43]*u[15]+ uik[44]*u[16]+ uik[45]*u[17]+ uik[46]*u[18]+ uik[47]*u[19]+ uik[48]*u[20];
599 
600           wp[21]+=  uik[0]*u[21] + uik[1]*u[22] + uik[2]*u[23] + uik[3]*u[24] + uik[4]*u[25] + uik[5]*u[26] + uik[6]*u[27];
601           wp[22]+=  uik[7]*u[21] + uik[8]*u[22] + uik[9]*u[23]+ uik[10]*u[24]+ uik[11]*u[25]+ uik[12]*u[26]+ uik[13]*u[27];
602           wp[23]+= uik[14]*u[21]+ uik[15]*u[22]+ uik[16]*u[23]+ uik[17]*u[24]+ uik[18]*u[25]+ uik[19]*u[26]+ uik[20]*u[27];
603           wp[24]+= uik[21]*u[21]+ uik[22]*u[22]+ uik[23]*u[23]+ uik[24]*u[24]+ uik[25]*u[25]+ uik[26]*u[26]+ uik[27]*u[27];
604           wp[25]+= uik[28]*u[21]+ uik[29]*u[22]+ uik[30]*u[23]+ uik[31]*u[24]+ uik[32]*u[25]+ uik[33]*u[26]+ uik[34]*u[27];
605           wp[26]+= uik[35]*u[21]+ uik[36]*u[22]+ uik[37]*u[23]+ uik[38]*u[24]+ uik[39]*u[25]+ uik[40]*u[26]+ uik[41]*u[27];
606           wp[27]+= uik[42]*u[21]+ uik[43]*u[22]+ uik[44]*u[23]+ uik[45]*u[24]+ uik[46]*u[25]+ uik[47]*u[26]+ uik[48]*u[27];
607 
608           wp[28]+=  uik[0]*u[28] + uik[1]*u[29] + uik[2]*u[30] + uik[3]*u[31] + uik[4]*u[32] + uik[5]*u[33] + uik[6]*u[34];
609           wp[29]+=  uik[7]*u[28] + uik[8]*u[29] + uik[9]*u[30]+ uik[10]*u[31]+ uik[11]*u[32]+ uik[12]*u[33]+ uik[13]*u[34];
610           wp[30]+= uik[14]*u[28]+ uik[15]*u[29]+ uik[16]*u[30]+ uik[17]*u[31]+ uik[18]*u[32]+ uik[19]*u[33]+ uik[20]*u[34];
611           wp[31]+= uik[21]*u[28]+ uik[22]*u[29]+ uik[23]*u[30]+ uik[24]*u[31]+ uik[25]*u[32]+ uik[26]*u[33]+ uik[27]*u[34];
612           wp[32]+= uik[28]*u[28]+ uik[29]*u[29]+ uik[30]*u[30]+ uik[31]*u[31]+ uik[32]*u[32]+ uik[33]*u[33]+ uik[34]*u[34];
613           wp[33]+= uik[35]*u[28]+ uik[36]*u[29]+ uik[37]*u[30]+ uik[38]*u[31]+ uik[39]*u[32]+ uik[40]*u[33]+ uik[41]*u[34];
614           wp[34]+= uik[42]*u[28]+ uik[43]*u[29]+ uik[44]*u[30]+ uik[45]*u[31]+ uik[46]*u[32]+ uik[47]*u[33]+ uik[48]*u[34];
615 
616           wp[35]+=  uik[0]*u[35] + uik[1]*u[36] + uik[2]*u[37] + uik[3]*u[38] + uik[4]*u[39] + uik[5]*u[40] + uik[6]*u[41];
617           wp[36]+=  uik[7]*u[35] + uik[8]*u[36] + uik[9]*u[37]+ uik[10]*u[38]+ uik[11]*u[39]+ uik[12]*u[40]+ uik[13]*u[41];
618           wp[37]+= uik[14]*u[35]+ uik[15]*u[36]+ uik[16]*u[37]+ uik[17]*u[38]+ uik[18]*u[39]+ uik[19]*u[40]+ uik[20]*u[41];
619           wp[38]+= uik[21]*u[35]+ uik[22]*u[36]+ uik[23]*u[37]+ uik[24]*u[38]+ uik[25]*u[39]+ uik[26]*u[40]+ uik[27]*u[41];
620           wp[39]+= uik[28]*u[35]+ uik[29]*u[36]+ uik[30]*u[37]+ uik[31]*u[38]+ uik[32]*u[39]+ uik[33]*u[40]+ uik[34]*u[41];
621           wp[40]+= uik[35]*u[35]+ uik[36]*u[36]+ uik[37]*u[37]+ uik[38]*u[38]+ uik[39]*u[39]+ uik[40]*u[40]+ uik[41]*u[41];
622           wp[41]+= uik[42]*u[35]+ uik[43]*u[36]+ uik[44]*u[37]+ uik[45]*u[38]+ uik[46]*u[39]+ uik[47]*u[40]+ uik[48]*u[41];
623 
624           wp[42]+=  uik[0]*u[42] + uik[1]*u[43] + uik[2]*u[44] + uik[3]*u[45] + uik[4]*u[46] + uik[5]*u[47] + uik[6]*u[48];
625           wp[43]+=  uik[7]*u[42] + uik[8]*u[43] + uik[9]*u[44]+ uik[10]*u[45]+ uik[11]*u[46]+ uik[12]*u[47]+ uik[13]*u[48];
626           wp[44]+= uik[14]*u[42]+ uik[15]*u[43]+ uik[16]*u[44]+ uik[17]*u[45]+ uik[18]*u[46]+ uik[19]*u[47]+ uik[20]*u[48];
627           wp[45]+= uik[21]*u[42]+ uik[22]*u[43]+ uik[23]*u[44]+ uik[24]*u[45]+ uik[25]*u[46]+ uik[26]*u[47]+ uik[27]*u[48];
628           wp[46]+= uik[28]*u[42]+ uik[29]*u[43]+ uik[30]*u[44]+ uik[31]*u[45]+ uik[32]*u[46]+ uik[33]*u[47]+ uik[34]*u[48];
629           wp[47]+= uik[35]*u[42]+ uik[36]*u[43]+ uik[37]*u[44]+ uik[38]*u[45]+ uik[39]*u[46]+ uik[40]*u[47]+ uik[41]*u[48];
630           wp[48]+= uik[42]*u[42]+ uik[43]*u[43]+ uik[44]*u[44]+ uik[45]*u[45]+ uik[46]*u[46]+ uik[47]*u[47]+ uik[48]*u[48];
631         }
632 
633         /* ... add i to row list for next nonzero entry */
634         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
635         j     = bj[jmin];
636         jl[i] = jl[j]; jl[j] = i; /* update jl */
637       }
638       i = nexti;
639     }
640 
641     /* save nonzero entries in k-th row of U ... */
642 
643     /* invert diagonal block */
644     d = ba+k*49;
645     ierr = PetscMemcpy(d,dk,49*sizeof(MatScalar));CHKERRQ(ierr);
646     ierr = Kernel_A_gets_inverse_A_7(d);CHKERRQ(ierr);
647 
648     jmin = bi[k]; jmax = bi[k+1];
649     if (jmin < jmax) {
650       for (j=jmin; j<jmax; j++){
651          vj = bj[j];           /* block col. index of U */
652          u   = ba + j*49;
653          wp = w + vj*49;
654          for (k1=0; k1<49; k1++){
655            *u++        = *wp;
656            *wp++ = 0.0;
657          }
658       }
659 
660       /* ... add k to row list for first nonzero entry in k-th row */
661       il[k] = jmin;
662       i     = bj[jmin];
663       jl[k] = jl[i]; jl[i] = k;
664     }
665   }
666 
667   ierr = PetscFree(w);CHKERRQ(ierr);
668   ierr = PetscFree(il);CHKERRQ(ierr);
669   ierr = PetscFree(jl);CHKERRQ(ierr);
670   ierr = PetscFree(dk);CHKERRQ(ierr);
671   ierr = PetscFree(uik);CHKERRQ(ierr);
672   if (a->permute){
673     ierr = PetscFree(aa);CHKERRQ(ierr);
674   }
675 
676   ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr);
677   C->factor    = FACTOR_CHOLESKY;
678   C->assembled = PETSC_TRUE;
679   C->preallocated = PETSC_TRUE;
680   PLogFlops(1.3333*343*b->mbs); /* from inverting diagonal blocks */
681   PetscFunctionReturn(0);
682 }
683 
684 /*
685       Version for when blocks are 7 by 7 Using natural ordering
686 */
687 #undef __FUNC__
688 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_7_NaturalOrdering"
689 int MatCholeskyFactorNumeric_SeqSBAIJ_7_NaturalOrdering(Mat A,Mat *B)
690 {
691   Mat          C = *B;
692   Mat_SeqBAIJ  *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
693   int          ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
694   int          *ajtmpold,*ajtmp,nz,row;
695   int          *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
696   MatScalar    *pv,*v,*rtmp,*pc,*w,*x;
697   MatScalar    x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15;
698   MatScalar    x16,x17,x18,x19,x20,x21,x22,x23,x24,x25;
699   MatScalar    p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15;
700   MatScalar    p16,p17,p18,p19,p20,p21,p22,p23,p24,p25;
701   MatScalar    m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12,m13,m14,m15;
702   MatScalar    m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
703   MatScalar    p26,p27,p28,p29,p30,p31,p32,p33,p34,p35,p36;
704   MatScalar    p37,p38,p39,p40,p41,p42,p43,p44,p45,p46,p47,p48,p49;
705   MatScalar    x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36;
706   MatScalar    x37,x38,x39,x40,x41,x42,x43,x44,x45,x46,x47,x48,x49;
707   MatScalar    m26,m27,m28,m29,m30,m31,m32,m33,m34,m35,m36;
708   MatScalar    m37,m38,m39,m40,m41,m42,m43,m44,m45,m46,m47,m48,m49;
709   MatScalar    *ba = b->a,*aa = a->a;
710 
711   PetscFunctionBegin;
712   rtmp  = (MatScalar*)PetscMalloc(49*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
713   for (i=0; i<n; i++) {
714     nz    = bi[i+1] - bi[i];
715     ajtmp = bj + bi[i];
716     for  (j=0; j<nz; j++) {
717       x = rtmp+49*ajtmp[j];
718       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
719       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
720       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = x[25] = 0.0 ;
721       x[26] = x[27] = x[28] = x[29] = x[30] = x[31] = x[32] = x[33] = 0.0 ;
722       x[34] = x[35] = x[36] = x[37] = x[38] = x[39] = x[40] = x[41] = 0.0 ;
723       x[42] = x[43] = x[44] = x[45] = x[46] = x[47] = x[48] = 0.0 ;
724     }
725     /* load in initial (unfactored row) */
726     nz       = ai[i+1] - ai[i];
727     ajtmpold = aj + ai[i];
728     v        = aa + 49*ai[i];
729     for (j=0; j<nz; j++) {
730       x    = rtmp+49*ajtmpold[j];
731       x[0] =  v[0];  x[1] =  v[1];  x[2] =  v[2];  x[3] =  v[3];
732       x[4] =  v[4];  x[5] =  v[5];  x[6] =  v[6];  x[7] =  v[7];
733       x[8] =  v[8];  x[9] =  v[9];  x[10] = v[10]; x[11] = v[11];
734       x[12] = v[12]; x[13] = v[13]; x[14] = v[14]; x[15] = v[15];
735       x[16] = v[16]; x[17] = v[17]; x[18] = v[18]; x[19] = v[19];
736       x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23];
737       x[24] = v[24]; x[25] = v[25]; x[26] = v[26]; x[27] = v[27];
738       x[28] = v[28]; x[29] = v[29]; x[30] = v[30]; x[31] = v[31];
739       x[32] = v[32]; x[33] = v[33]; x[34] = v[34]; x[35] = v[35];
740       x[36] = v[36]; x[37] = v[37]; x[38] = v[38]; x[39] = v[39];
741       x[40] = v[40]; x[41] = v[41]; x[42] = v[42]; x[43] = v[43];
742       x[44] = v[44]; x[45] = v[45]; x[46] = v[46]; x[47] = v[47];
743       x[48] = v[48];
744       v    += 49;
745     }
746     row = *ajtmp++;
747     while (row < i) {
748       pc  = rtmp + 49*row;
749       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
750       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];
751       p9  = pc[8];  p10 = pc[9];  p11 = pc[10]; p12 = pc[11];
752       p13 = pc[12]; p14 = pc[13]; p15 = pc[14]; p16 = pc[15];
753       p17 = pc[16]; p18 = pc[17]; p19 = pc[18]; p20 = pc[19];
754       p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
755       p25 = pc[24]; p26 = pc[25]; p27 = pc[26]; p28 = pc[27];
756       p29 = pc[28]; p30 = pc[29]; p31 = pc[30]; p32 = pc[31];
757       p33 = pc[32]; p34 = pc[33]; p35 = pc[34]; p36 = pc[35];
758       p37 = pc[36]; p38 = pc[37]; p39 = pc[38]; p40 = pc[39];
759       p41 = pc[40]; p42 = pc[41]; p43 = pc[42]; p44 = pc[43];
760       p45 = pc[44]; p46 = pc[45]; p47 = pc[46]; p48 = pc[47];
761       p49 = pc[48];
762       if (p1  != 0.0 || p2  != 0.0 || p3  != 0.0 || p4  != 0.0 ||
763           p5  != 0.0 || p6  != 0.0 || p7  != 0.0 || p8  != 0.0 ||
764           p9  != 0.0 || p10 != 0.0 || p11 != 0.0 || p12 != 0.0 ||
765           p13 != 0.0 || p14 != 0.0 || p15 != 0.0 || p16 != 0.0 ||
766           p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 ||
767           p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 ||
768           p25 != 0.0 || p26 != 0.0 || p27 != 0.0 || p28 != 0.0 ||
769           p29 != 0.0 || p30 != 0.0 || p31 != 0.0 || p32 != 0.0 ||
770           p33 != 0.0 || p34 != 0.0 || p35 != 0.0 || p36 != 0.0 ||
771           p37 != 0.0 || p38 != 0.0 || p39 != 0.0 || p40 != 0.0 ||
772           p41 != 0.0 || p42 != 0.0 || p43 != 0.0 || p44 != 0.0 ||
773           p45 != 0.0 || p46 != 0.0 || p47 != 0.0 || p48 != 0.0 ||
774           p49 != 0.0) {
775         pv = ba + 49*diag_offset[row];
776         pj = bj + diag_offset[row] + 1;
777 	x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
778 	x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
779 	x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
780 	x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
781 	x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
782 	x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
783 	x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
784 	x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
785 	x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
786 	x37 = pv[36]; x38 = pv[37]; x39 = pv[38]; x40 = pv[39];
787 	x41 = pv[40]; x42 = pv[41]; x43 = pv[42]; x44 = pv[43];
788 	x45 = pv[44]; x46 = pv[45]; x47 = pv[46]; x48 = pv[47];
789         x49 = pv[48];
790         pc[0]  = m1  = p1*x1  + p8*x2   + p15*x3  + p22*x4  + p29*x5  + p36*x6 + p43*x7;
791         pc[1]  = m2  = p2*x1  + p9*x2   + p16*x3  + p23*x4  + p30*x5  + p37*x6 + p44*x7;
792         pc[2]  = m3  = p3*x1  + p10*x2  + p17*x3  + p24*x4  + p31*x5  + p38*x6 + p45*x7;
793         pc[3]  = m4  = p4*x1  + p11*x2  + p18*x3  + p25*x4  + p32*x5  + p39*x6 + p46*x7;
794         pc[4]  = m5  = p5*x1  + p12*x2  + p19*x3  + p26*x4  + p33*x5  + p40*x6 + p47*x7;
795         pc[5]  = m6  = p6*x1  + p13*x2  + p20*x3  + p27*x4  + p34*x5  + p41*x6 + p48*x7;
796         pc[6]  = m7  = p7*x1  + p14*x2  + p21*x3  + p28*x4  + p35*x5  + p42*x6 + p49*x7;
797 
798         pc[7]  = m8  = p1*x8  + p8*x9   + p15*x10 + p22*x11 + p29*x12 + p36*x13 + p43*x14;
799         pc[8]  = m9  = p2*x8  + p9*x9   + p16*x10 + p23*x11 + p30*x12 + p37*x13 + p44*x14;
800         pc[9]  = m10 = p3*x8  + p10*x9  + p17*x10 + p24*x11 + p31*x12 + p38*x13 + p45*x14;
801         pc[10] = m11 = p4*x8  + p11*x9  + p18*x10 + p25*x11 + p32*x12 + p39*x13 + p46*x14;
802         pc[11] = m12 = p5*x8  + p12*x9  + p19*x10 + p26*x11 + p33*x12 + p40*x13 + p47*x14;
803         pc[12] = m13 = p6*x8  + p13*x9  + p20*x10 + p27*x11 + p34*x12 + p41*x13 + p48*x14;
804         pc[13] = m14 = p7*x8  + p14*x9  + p21*x10 + p28*x11 + p35*x12 + p42*x13 + p49*x14;
805 
806         pc[14] = m15 = p1*x15 + p8*x16  + p15*x17 + p22*x18 + p29*x19 + p36*x20 + p43*x21;
807         pc[15] = m16 = p2*x15 + p9*x16  + p16*x17 + p23*x18 + p30*x19 + p37*x20 + p44*x21;
808         pc[16] = m17 = p3*x15 + p10*x16 + p17*x17 + p24*x18 + p31*x19 + p38*x20 + p45*x21;
809         pc[17] = m18 = p4*x15 + p11*x16 + p18*x17 + p25*x18 + p32*x19 + p39*x20 + p46*x21;
810         pc[18] = m19 = p5*x15 + p12*x16 + p19*x17 + p26*x18 + p33*x19 + p40*x20 + p47*x21;
811         pc[19] = m20 = p6*x15 + p13*x16 + p20*x17 + p27*x18 + p34*x19 + p41*x20 + p48*x21;
812         pc[20] = m21 = p7*x15 + p14*x16 + p21*x17 + p28*x18 + p35*x19 + p42*x20 + p49*x21;
813 
814         pc[21] = m22 = p1*x22 + p8*x23  + p15*x24 + p22*x25 + p29*x26 + p36*x27 + p43*x28;
815         pc[22] = m23 = p2*x22 + p9*x23  + p16*x24 + p23*x25 + p30*x26 + p37*x27 + p44*x28;
816         pc[23] = m24 = p3*x22 + p10*x23 + p17*x24 + p24*x25 + p31*x26 + p38*x27 + p45*x28;
817         pc[24] = m25 = p4*x22 + p11*x23 + p18*x24 + p25*x25 + p32*x26 + p39*x27 + p46*x28;
818         pc[25] = m26 = p5*x22 + p12*x23 + p19*x24 + p26*x25 + p33*x26 + p40*x27 + p47*x28;
819         pc[26] = m27 = p6*x22 + p13*x23 + p20*x24 + p27*x25 + p34*x26 + p41*x27 + p48*x28;
820         pc[27] = m28 = p7*x22 + p14*x23 + p21*x24 + p28*x25 + p35*x26 + p42*x27 + p49*x28;
821 
822         pc[28] = m29 = p1*x29 + p8*x30  + p15*x31 + p22*x32 + p29*x33 + p36*x34 + p43*x35;
823         pc[29] = m30 = p2*x29 + p9*x30  + p16*x31 + p23*x32 + p30*x33 + p37*x34 + p44*x35;
824         pc[30] = m31 = p3*x29 + p10*x30 + p17*x31 + p24*x32 + p31*x33 + p38*x34 + p45*x35;
825         pc[31] = m32 = p4*x29 + p11*x30 + p18*x31 + p25*x32 + p32*x33 + p39*x34 + p46*x35;
826         pc[32] = m33 = p5*x29 + p12*x30 + p19*x31 + p26*x32 + p33*x33 + p40*x34 + p47*x35;
827         pc[33] = m34 = p6*x29 + p13*x30 + p20*x31 + p27*x32 + p34*x33 + p41*x34 + p48*x35;
828         pc[34] = m35 = p7*x29 + p14*x30 + p21*x31 + p28*x32 + p35*x33 + p42*x34 + p49*x35;
829 
830         pc[35] = m36 = p1*x36 + p8*x37  + p15*x38 + p22*x39 + p29*x40 + p36*x41 + p43*x42;
831         pc[36] = m37 = p2*x36 + p9*x37  + p16*x38 + p23*x39 + p30*x40 + p37*x41 + p44*x42;
832         pc[37] = m38 = p3*x36 + p10*x37 + p17*x38 + p24*x39 + p31*x40 + p38*x41 + p45*x42;
833         pc[38] = m39 = p4*x36 + p11*x37 + p18*x38 + p25*x39 + p32*x40 + p39*x41 + p46*x42;
834         pc[39] = m40 = p5*x36 + p12*x37 + p19*x38 + p26*x39 + p33*x40 + p40*x41 + p47*x42;
835         pc[40] = m41 = p6*x36 + p13*x37 + p20*x38 + p27*x39 + p34*x40 + p41*x41 + p48*x42;
836         pc[41] = m42 = p7*x36 + p14*x37 + p21*x38 + p28*x39 + p35*x40 + p42*x41 + p49*x42;
837 
838         pc[42] = m43 = p1*x43 + p8*x44  + p15*x45 + p22*x46 + p29*x47 + p36*x48 + p43*x49;
839         pc[43] = m44 = p2*x43 + p9*x44  + p16*x45 + p23*x46 + p30*x47 + p37*x48 + p44*x49;
840         pc[44] = m45 = p3*x43 + p10*x44 + p17*x45 + p24*x46 + p31*x47 + p38*x48 + p45*x49;
841         pc[45] = m46 = p4*x43 + p11*x44 + p18*x45 + p25*x46 + p32*x47 + p39*x48 + p46*x49;
842         pc[46] = m47 = p5*x43 + p12*x44 + p19*x45 + p26*x46 + p33*x47 + p40*x48 + p47*x49;
843         pc[47] = m48 = p6*x43 + p13*x44 + p20*x45 + p27*x46 + p34*x47 + p41*x48 + p48*x49;
844         pc[48] = m49 = p7*x43 + p14*x44 + p21*x45 + p28*x46 + p35*x47 + p42*x48 + p49*x49;
845 
846         nz = bi[row+1] - diag_offset[row] - 1;
847         pv += 49;
848         for (j=0; j<nz; j++) {
849 	  x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
850 	  x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
851 	  x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
852 	  x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
853 	  x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
854 	  x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
855 	  x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
856 	  x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
857 	  x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
858 	  x37 = pv[36]; x38 = pv[37]; x39 = pv[38]; x40 = pv[39];
859 	  x41 = pv[40]; x42 = pv[41]; x43 = pv[42]; x44 = pv[43];
860 	  x45 = pv[44]; x46 = pv[45]; x47 = pv[46]; x48 = pv[47];
861 	  x49 = pv[48];
862 	  x    = rtmp + 49*pj[j];
863 	  x[0]  -= m1*x1  + m8*x2   + m15*x3  + m22*x4  + m29*x5  + m36*x6 + m43*x7;
864 	  x[1]  -= m2*x1  + m9*x2   + m16*x3  + m23*x4  + m30*x5  + m37*x6 + m44*x7;
865 	  x[2]  -= m3*x1  + m10*x2  + m17*x3  + m24*x4  + m31*x5  + m38*x6 + m45*x7;
866 	  x[3]  -= m4*x1  + m11*x2  + m18*x3  + m25*x4  + m32*x5  + m39*x6 + m46*x7;
867 	  x[4]  -= m5*x1  + m12*x2  + m19*x3  + m26*x4  + m33*x5  + m40*x6 + m47*x7;
868 	  x[5]  -= m6*x1  + m13*x2  + m20*x3  + m27*x4  + m34*x5  + m41*x6 + m48*x7;
869 	  x[6]  -= m7*x1  + m14*x2  + m21*x3  + m28*x4  + m35*x5  + m42*x6 + m49*x7;
870 
871 	  x[7]  -= m1*x8  + m8*x9   + m15*x10 + m22*x11 + m29*x12 + m36*x13 + m43*x14;
872 	  x[8]  -= m2*x8  + m9*x9   + m16*x10 + m23*x11 + m30*x12 + m37*x13 + m44*x14;
873 	  x[9]  -= m3*x8  + m10*x9  + m17*x10 + m24*x11 + m31*x12 + m38*x13 + m45*x14;
874 	  x[10] -= m4*x8  + m11*x9  + m18*x10 + m25*x11 + m32*x12 + m39*x13 + m46*x14;
875 	  x[11] -= m5*x8  + m12*x9  + m19*x10 + m26*x11 + m33*x12 + m40*x13 + m47*x14;
876 	  x[12] -= m6*x8  + m13*x9  + m20*x10 + m27*x11 + m34*x12 + m41*x13 + m48*x14;
877 	  x[13] -= m7*x8  + m14*x9  + m21*x10 + m28*x11 + m35*x12 + m42*x13 + m49*x14;
878 
879 	  x[14] -= m1*x15 + m8*x16  + m15*x17 + m22*x18 + m29*x19 + m36*x20 + m43*x21;
880 	  x[15] -= m2*x15 + m9*x16  + m16*x17 + m23*x18 + m30*x19 + m37*x20 + m44*x21;
881 	  x[16] -= m3*x15 + m10*x16 + m17*x17 + m24*x18 + m31*x19 + m38*x20 + m45*x21;
882 	  x[17] -= m4*x15 + m11*x16 + m18*x17 + m25*x18 + m32*x19 + m39*x20 + m46*x21;
883 	  x[18] -= m5*x15 + m12*x16 + m19*x17 + m26*x18 + m33*x19 + m40*x20 + m47*x21;
884 	  x[19] -= m6*x15 + m13*x16 + m20*x17 + m27*x18 + m34*x19 + m41*x20 + m48*x21;
885 	  x[20] -= m7*x15 + m14*x16 + m21*x17 + m28*x18 + m35*x19 + m42*x20 + m49*x21;
886 
887 	  x[21] -= m1*x22 + m8*x23  + m15*x24 + m22*x25 + m29*x26 + m36*x27 + m43*x28;
888 	  x[22] -= m2*x22 + m9*x23  + m16*x24 + m23*x25 + m30*x26 + m37*x27 + m44*x28;
889 	  x[23] -= m3*x22 + m10*x23 + m17*x24 + m24*x25 + m31*x26 + m38*x27 + m45*x28;
890 	  x[24] -= m4*x22 + m11*x23 + m18*x24 + m25*x25 + m32*x26 + m39*x27 + m46*x28;
891 	  x[25] -= m5*x22 + m12*x23 + m19*x24 + m26*x25 + m33*x26 + m40*x27 + m47*x28;
892 	  x[26] -= m6*x22 + m13*x23 + m20*x24 + m27*x25 + m34*x26 + m41*x27 + m48*x28;
893 	  x[27] -= m7*x22 + m14*x23 + m21*x24 + m28*x25 + m35*x26 + m42*x27 + m49*x28;
894 
895 	  x[28] -= m1*x29 + m8*x30  + m15*x31 + m22*x32 + m29*x33 + m36*x34 + m43*x35;
896 	  x[29] -= m2*x29 + m9*x30  + m16*x31 + m23*x32 + m30*x33 + m37*x34 + m44*x35;
897 	  x[30] -= m3*x29 + m10*x30 + m17*x31 + m24*x32 + m31*x33 + m38*x34 + m45*x35;
898 	  x[31] -= m4*x29 + m11*x30 + m18*x31 + m25*x32 + m32*x33 + m39*x34 + m46*x35;
899 	  x[32] -= m5*x29 + m12*x30 + m19*x31 + m26*x32 + m33*x33 + m40*x34 + m47*x35;
900 	  x[33] -= m6*x29 + m13*x30 + m20*x31 + m27*x32 + m34*x33 + m41*x34 + m48*x35;
901 	  x[34] -= m7*x29 + m14*x30 + m21*x31 + m28*x32 + m35*x33 + m42*x34 + m49*x35;
902 
903 	  x[35] -= m1*x36 + m8*x37  + m15*x38 + m22*x39 + m29*x40 + m36*x41 + m43*x42;
904 	  x[36] -= m2*x36 + m9*x37  + m16*x38 + m23*x39 + m30*x40 + m37*x41 + m44*x42;
905 	  x[37] -= m3*x36 + m10*x37 + m17*x38 + m24*x39 + m31*x40 + m38*x41 + m45*x42;
906 	  x[38] -= m4*x36 + m11*x37 + m18*x38 + m25*x39 + m32*x40 + m39*x41 + m46*x42;
907 	  x[39] -= m5*x36 + m12*x37 + m19*x38 + m26*x39 + m33*x40 + m40*x41 + m47*x42;
908 	  x[40] -= m6*x36 + m13*x37 + m20*x38 + m27*x39 + m34*x40 + m41*x41 + m48*x42;
909 	  x[41] -= m7*x36 + m14*x37 + m21*x38 + m28*x39 + m35*x40 + m42*x41 + m49*x42;
910 
911 	  x[42] -= m1*x43 + m8*x44  + m15*x45 + m22*x46 + m29*x47 + m36*x48 + m43*x49;
912 	  x[43] -= m2*x43 + m9*x44  + m16*x45 + m23*x46 + m30*x47 + m37*x48 + m44*x49;
913 	  x[44] -= m3*x43 + m10*x44 + m17*x45 + m24*x46 + m31*x47 + m38*x48 + m45*x49;
914 	  x[45] -= m4*x43 + m11*x44 + m18*x45 + m25*x46 + m32*x47 + m39*x48 + m46*x49;
915 	  x[46] -= m5*x43 + m12*x44 + m19*x45 + m26*x46 + m33*x47 + m40*x48 + m47*x49;
916 	  x[47] -= m6*x43 + m13*x44 + m20*x45 + m27*x46 + m34*x47 + m41*x48 + m48*x49;
917 	  x[48] -= m7*x43 + m14*x44 + m21*x45 + m28*x46 + m35*x47 + m42*x48 + m49*x49;
918           pv   += 49;
919         }
920         PLogFlops(686*nz+637);
921       }
922       row = *ajtmp++;
923     }
924     /* finished row so stick it into b->a */
925     pv = ba + 49*bi[i];
926     pj = bj + bi[i];
927     nz = bi[i+1] - bi[i];
928     for (j=0; j<nz; j++) {
929       x      = rtmp+49*pj[j];
930       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
931       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7];
932       pv[8]  = x[8];  pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11];
933       pv[12] = x[12]; pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
934       pv[16] = x[16]; pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19];
935       pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23];
936       pv[24] = x[24]; pv[25] = x[25]; pv[26] = x[26]; pv[27] = x[27];
937       pv[28] = x[28]; pv[29] = x[29]; pv[30] = x[30]; pv[31] = x[31];
938       pv[32] = x[32]; pv[33] = x[33]; pv[34] = x[34]; pv[35] = x[35];
939       pv[36] = x[36]; pv[37] = x[37]; pv[38] = x[38]; pv[39] = x[39];
940       pv[40] = x[40]; pv[41] = x[41]; pv[42] = x[42]; pv[43] = x[43];
941       pv[44] = x[44]; pv[45] = x[45]; pv[46] = x[46]; pv[47] = x[47];
942       pv[48] = x[48];
943       pv   += 49;
944     }
945     /* invert diagonal block */
946     w = ba + 49*diag_offset[i];
947     ierr = Kernel_A_gets_inverse_A_7(w);CHKERRQ(ierr);
948   }
949 
950   ierr = PetscFree(rtmp);CHKERRQ(ierr);
951   C->factor    = FACTOR_LU;
952   C->assembled = PETSC_TRUE;
953   PLogFlops(1.3333*343*b->mbs); /* from inverting diagonal blocks */
954   PetscFunctionReturn(0);
955 }
956 
957 /* Version for when blocks are 6 by 6 */
958 #undef __FUNC__
959 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_6"
960 int MatCholeskyFactorNumeric_SeqSBAIJ_6(Mat A,Mat *B)
961 {
962   Mat                C = *B;
963   Mat_SeqSBAIJ       *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data;
964   IS                 perm = b->row;
965   int                *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
966   int                *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
967   MatScalar          *ba = b->a,*aa,*ap,*dk,*uik;
968   MatScalar          *u,*d,*w,*wp;
969 
970   PetscFunctionBegin;
971   /* initialization */
972   w  = (MatScalar*)PetscMalloc(36*mbs*sizeof(MatScalar));CHKPTRQ(w);
973   ierr = PetscMemzero(w,36*mbs*sizeof(MatScalar));CHKERRQ(ierr);
974   il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il);
975   jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl);
976   for (i=0; i<mbs; i++) {
977     jl[i] = mbs; il[0] = 0;
978   }
979   dk    = (MatScalar*)PetscMalloc(36*sizeof(MatScalar));CHKPTRQ(dk);
980   uik   = (MatScalar*)PetscMalloc(36*sizeof(MatScalar));CHKPTRQ(uik);
981   ierr  = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr);
982 
983   /* check permutation */
984   if (!a->permute){
985     ai = a->i; aj = a->j; aa = a->a;
986   } else {
987     ai = a->inew; aj = a->jnew;
988     aa = (MatScalar*)PetscMalloc(36*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa);
989     ierr = PetscMemcpy(aa,a->a,36*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr);
990     a2anew  = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew);
991     ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr);
992 
993     for (i=0; i<mbs; i++){
994       jmin = ai[i]; jmax = ai[i+1];
995       for (j=jmin; j<jmax; j++){
996         while (a2anew[j] != j){
997           k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k;
998           for (k1=0; k1<36; k1++){
999             dk[k1]       = aa[k*36+k1];
1000             aa[k*36+k1] = aa[j*36+k1];
1001             aa[j*36+k1] = dk[k1];
1002           }
1003         }
1004         /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */
1005         if (i > aj[j]){
1006           /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */
1007           ap = aa + j*36;                     /* ptr to the beginning of j-th block of aa */
1008           for (k=0; k<36; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */
1009           for (k=0; k<6; k++){               /* j-th block of aa <- dk^T */
1010             for (k1=0; k1<6; k1++) *ap++ = dk[k + 6*k1];
1011           }
1012         }
1013       }
1014     }
1015     ierr = PetscFree(a2anew);CHKERRA(ierr);
1016   }
1017 
1018   /* for each row k */
1019   for (k = 0; k<mbs; k++){
1020 
1021     /*initialize k-th row with elements nonzero in row perm(k) of A */
1022     jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1];
1023     if (jmin < jmax) {
1024       ap = aa + jmin*36;
1025       for (j = jmin; j < jmax; j++){
1026         vj = perm_ptr[aj[j]];         /* block col. index */
1027         wp = w + vj*36;
1028         for (i=0; i<36; i++) *wp++ = *ap++;
1029       }
1030     }
1031 
1032     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
1033     ierr = PetscMemcpy(dk,w+k*36,36*sizeof(MatScalar));CHKERRQ(ierr);
1034     i = jl[k]; /* first row to be added to k_th row  */
1035 
1036     while (i < mbs){
1037       nexti = jl[i]; /* next row to be added to k_th row */
1038 
1039       /* compute multiplier */
1040       ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
1041 
1042       /* uik = -inv(Di)*U_bar(i,k) */
1043       d = ba + i*36;
1044       u    = ba + ili*36;
1045 
1046       uik[0] = -(d[0]*u[0] + d[6]*u[1] + d[12]*u[2] + d[18]*u[3] + d[24]*u[4] + d[30]*u[5]);
1047       uik[1] = -(d[1]*u[0] + d[7]*u[1] + d[13]*u[2] + d[19]*u[3] + d[25]*u[4] + d[31]*u[5]);
1048       uik[2] = -(d[2]*u[0] + d[8]*u[1] + d[14]*u[2] + d[20]*u[3] + d[26]*u[4] + d[32]*u[5]);
1049       uik[3] = -(d[3]*u[0] + d[9]*u[1] + d[15]*u[2] + d[21]*u[3] + d[27]*u[4] + d[33]*u[5]);
1050       uik[4] = -(d[4]*u[0]+ d[10]*u[1] + d[16]*u[2] + d[22]*u[3] + d[28]*u[4] + d[34]*u[5]);
1051       uik[5] = -(d[5]*u[0]+ d[11]*u[1] + d[17]*u[2] + d[23]*u[3] + d[29]*u[4] + d[35]*u[5]);
1052 
1053       uik[6] = -(d[0]*u[6] + d[6]*u[7] + d[12]*u[8] + d[18]*u[9] + d[24]*u[10] + d[30]*u[11]);
1054       uik[7] = -(d[1]*u[6] + d[7]*u[7] + d[13]*u[8] + d[19]*u[9] + d[25]*u[10] + d[31]*u[11]);
1055       uik[8] = -(d[2]*u[6] + d[8]*u[7] + d[14]*u[8] + d[20]*u[9] + d[26]*u[10] + d[32]*u[11]);
1056       uik[9] = -(d[3]*u[6] + d[9]*u[7] + d[15]*u[8] + d[21]*u[9] + d[27]*u[10] + d[33]*u[11]);
1057       uik[10]= -(d[4]*u[6]+ d[10]*u[7] + d[16]*u[8] + d[22]*u[9] + d[28]*u[10] + d[34]*u[11]);
1058       uik[11]= -(d[5]*u[6]+ d[11]*u[7] + d[17]*u[8] + d[23]*u[9] + d[29]*u[10] + d[35]*u[11]);
1059 
1060       uik[12] = -(d[0]*u[12] + d[6]*u[13] + d[12]*u[14] + d[18]*u[15] + d[24]*u[16] + d[30]*u[17]);
1061       uik[13] = -(d[1]*u[12] + d[7]*u[13] + d[13]*u[14] + d[19]*u[15] + d[25]*u[16] + d[31]*u[17]);
1062       uik[14] = -(d[2]*u[12] + d[8]*u[13] + d[14]*u[14] + d[20]*u[15] + d[26]*u[16] + d[32]*u[17]);
1063       uik[15] = -(d[3]*u[12] + d[9]*u[13] + d[15]*u[14] + d[21]*u[15] + d[27]*u[16] + d[33]*u[17]);
1064       uik[16] = -(d[4]*u[12]+ d[10]*u[13] + d[16]*u[14] + d[22]*u[15] + d[28]*u[16] + d[34]*u[17]);
1065       uik[17] = -(d[5]*u[12]+ d[11]*u[13] + d[17]*u[14] + d[23]*u[15] + d[29]*u[16] + d[35]*u[17]);
1066 
1067       uik[18] = -(d[0]*u[18] + d[6]*u[19] + d[12]*u[20] + d[18]*u[21] + d[24]*u[22] + d[30]*u[23]);
1068       uik[19] = -(d[1]*u[18] + d[7]*u[19] + d[13]*u[20] + d[19]*u[21] + d[25]*u[22] + d[31]*u[23]);
1069       uik[20] = -(d[2]*u[18] + d[8]*u[19] + d[14]*u[20] + d[20]*u[21] + d[26]*u[22] + d[32]*u[23]);
1070       uik[21] = -(d[3]*u[18] + d[9]*u[19] + d[15]*u[20] + d[21]*u[21] + d[27]*u[22] + d[33]*u[23]);
1071       uik[22] = -(d[4]*u[18]+ d[10]*u[19] + d[16]*u[20] + d[22]*u[21] + d[28]*u[22] + d[34]*u[23]);
1072       uik[23] = -(d[5]*u[18]+ d[11]*u[19] + d[17]*u[20] + d[23]*u[21] + d[29]*u[22] + d[35]*u[23]);
1073 
1074       uik[24] = -(d[0]*u[24] + d[6]*u[25] + d[12]*u[26] + d[18]*u[27] + d[24]*u[28] + d[30]*u[29]);
1075       uik[25] = -(d[1]*u[24] + d[7]*u[25] + d[13]*u[26] + d[19]*u[27] + d[25]*u[28] + d[31]*u[29]);
1076       uik[26] = -(d[2]*u[24] + d[8]*u[25] + d[14]*u[26] + d[20]*u[27] + d[26]*u[28] + d[32]*u[29]);
1077       uik[27] = -(d[3]*u[24] + d[9]*u[25] + d[15]*u[26] + d[21]*u[27] + d[27]*u[28] + d[33]*u[29]);
1078       uik[28] = -(d[4]*u[24]+ d[10]*u[25] + d[16]*u[26] + d[22]*u[27] + d[28]*u[28] + d[34]*u[29]);
1079       uik[29] = -(d[5]*u[24]+ d[11]*u[25] + d[17]*u[26] + d[23]*u[27] + d[29]*u[28] + d[35]*u[29]);
1080 
1081       uik[30] = -(d[0]*u[30] + d[6]*u[31] + d[12]*u[32] + d[18]*u[33] + d[24]*u[34] + d[30]*u[35]);
1082       uik[31] = -(d[1]*u[30] + d[7]*u[31] + d[13]*u[32] + d[19]*u[33] + d[25]*u[34] + d[31]*u[35]);
1083       uik[32] = -(d[2]*u[30] + d[8]*u[31] + d[14]*u[32] + d[20]*u[33] + d[26]*u[34] + d[32]*u[35]);
1084       uik[33] = -(d[3]*u[30] + d[9]*u[31] + d[15]*u[32] + d[21]*u[33] + d[27]*u[34] + d[33]*u[35]);
1085       uik[34] = -(d[4]*u[30]+ d[10]*u[31] + d[16]*u[32] + d[22]*u[33] + d[28]*u[34] + d[34]*u[35]);
1086       uik[35] = -(d[5]*u[30]+ d[11]*u[31] + d[17]*u[32] + d[23]*u[33] + d[29]*u[34] + d[35]*u[35]);
1087 
1088       /* update D(k) += -U(i,k)^T * U_bar(i,k) */
1089       dk[0] +=  uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5];
1090       dk[1] +=  uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2] + uik[9]*u[3]+ uik[10]*u[4]+ uik[11]*u[5];
1091       dk[2] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3]+ uik[16]*u[4]+ uik[17]*u[5];
1092       dk[3] += uik[18]*u[0]+ uik[19]*u[1]+ uik[20]*u[2]+ uik[21]*u[3]+ uik[22]*u[4]+ uik[23]*u[5];
1093       dk[4] += uik[24]*u[0]+ uik[25]*u[1]+ uik[26]*u[2]+ uik[27]*u[3]+ uik[28]*u[4]+ uik[29]*u[5];
1094       dk[5] += uik[30]*u[0]+ uik[31]*u[1]+ uik[32]*u[2]+ uik[33]*u[3]+ uik[34]*u[4]+ uik[35]*u[5];
1095 
1096       dk[6] +=  uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8] + uik[3]*u[9] + uik[4]*u[10] + uik[5]*u[11];
1097       dk[7] +=  uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8] + uik[9]*u[9]+ uik[10]*u[10]+ uik[11]*u[11];
1098       dk[8] += uik[12]*u[6]+ uik[13]*u[7]+ uik[14]*u[8]+ uik[15]*u[9]+ uik[16]*u[10]+ uik[17]*u[11];
1099       dk[9] += uik[18]*u[6]+ uik[19]*u[7]+ uik[20]*u[8]+ uik[21]*u[9]+ uik[22]*u[10]+ uik[23]*u[11];
1100       dk[10]+= uik[24]*u[6]+ uik[25]*u[7]+ uik[26]*u[8]+ uik[27]*u[9]+ uik[28]*u[10]+ uik[29]*u[11];
1101       dk[11]+= uik[30]*u[6]+ uik[31]*u[7]+ uik[32]*u[8]+ uik[33]*u[9]+ uik[34]*u[10]+ uik[35]*u[11];
1102 
1103       dk[12]+=  uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15] + uik[4]*u[16] + uik[5]*u[17];
1104       dk[13]+=  uik[6]*u[12] + uik[7]*u[13] + uik[8]*u[14] + uik[9]*u[15]+ uik[10]*u[16]+ uik[11]*u[17];
1105       dk[14]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15]+ uik[16]*u[16]+ uik[17]*u[17];
1106       dk[15]+= uik[18]*u[12]+ uik[19]*u[13]+ uik[20]*u[14]+ uik[21]*u[15]+ uik[22]*u[16]+ uik[23]*u[17];
1107       dk[16]+= uik[24]*u[12]+ uik[25]*u[13]+ uik[26]*u[14]+ uik[27]*u[15]+ uik[28]*u[16]+ uik[29]*u[17];
1108       dk[17]+= uik[30]*u[12]+ uik[31]*u[13]+ uik[32]*u[14]+ uik[33]*u[15]+ uik[34]*u[16]+ uik[35]*u[17];
1109 
1110       dk[18]+=  uik[0]*u[18] + uik[1]*u[19] + uik[2]*u[20] + uik[3]*u[21] + uik[4]*u[22] + uik[5]*u[23];
1111       dk[19]+=  uik[6]*u[18] + uik[7]*u[19] + uik[8]*u[20] + uik[9]*u[21]+ uik[10]*u[22]+ uik[11]*u[23];
1112       dk[20]+= uik[12]*u[18]+ uik[13]*u[19]+ uik[14]*u[20]+ uik[15]*u[21]+ uik[16]*u[22]+ uik[17]*u[23];
1113       dk[21]+= uik[18]*u[18]+ uik[19]*u[19]+ uik[20]*u[20]+ uik[21]*u[21]+ uik[22]*u[22]+ uik[23]*u[23];
1114       dk[22]+= uik[24]*u[18]+ uik[25]*u[19]+ uik[26]*u[20]+ uik[27]*u[21]+ uik[28]*u[22]+ uik[29]*u[23];
1115       dk[23]+= uik[30]*u[18]+ uik[31]*u[19]+ uik[32]*u[20]+ uik[33]*u[21]+ uik[34]*u[22]+ uik[35]*u[23];
1116 
1117       dk[24]+=  uik[0]*u[24] + uik[1]*u[25] + uik[2]*u[26] + uik[3]*u[27] + uik[4]*u[28] + uik[5]*u[29];
1118       dk[25]+=  uik[6]*u[24] + uik[7]*u[25] + uik[8]*u[26] + uik[9]*u[27]+ uik[10]*u[28]+ uik[11]*u[29];
1119       dk[26]+= uik[12]*u[24]+ uik[13]*u[25]+ uik[14]*u[26]+ uik[15]*u[27]+ uik[16]*u[28]+ uik[17]*u[29];
1120       dk[27]+= uik[18]*u[24]+ uik[19]*u[25]+ uik[20]*u[26]+ uik[21]*u[27]+ uik[22]*u[28]+ uik[23]*u[29];
1121       dk[28]+= uik[24]*u[24]+ uik[25]*u[25]+ uik[26]*u[26]+ uik[27]*u[27]+ uik[28]*u[28]+ uik[29]*u[29];
1122       dk[29]+= uik[30]*u[24]+ uik[31]*u[25]+ uik[32]*u[26]+ uik[33]*u[27]+ uik[34]*u[28]+ uik[35]*u[29];
1123 
1124       dk[30]+=  uik[0]*u[30] + uik[1]*u[31] + uik[2]*u[32] + uik[3]*u[33] + uik[4]*u[34] + uik[5]*u[35];
1125       dk[31]+=  uik[6]*u[30] + uik[7]*u[31] + uik[8]*u[32] + uik[9]*u[33]+ uik[10]*u[34]+ uik[11]*u[35];
1126       dk[32]+= uik[12]*u[30]+ uik[13]*u[31]+ uik[14]*u[32]+ uik[15]*u[33]+ uik[16]*u[34]+ uik[17]*u[35];
1127       dk[33]+= uik[18]*u[30]+ uik[19]*u[31]+ uik[20]*u[32]+ uik[21]*u[33]+ uik[22]*u[34]+ uik[23]*u[35];
1128       dk[34]+= uik[24]*u[30]+ uik[25]*u[31]+ uik[26]*u[32]+ uik[27]*u[33]+ uik[28]*u[34]+ uik[29]*u[35];
1129       dk[35]+= uik[30]*u[30]+ uik[31]*u[31]+ uik[32]*u[32]+ uik[33]*u[33]+ uik[34]*u[34]+ uik[35]*u[35];
1130 
1131       /* update -U(i,k) */
1132       ierr = PetscMemcpy(ba+ili*36,uik,36*sizeof(MatScalar));CHKERRQ(ierr);
1133 
1134       /* add multiple of row i to k-th row ... */
1135       jmin = ili + 1; jmax = bi[i+1];
1136       if (jmin < jmax){
1137         for (j=jmin; j<jmax; j++) {
1138           /* w += -U(i,k)^T * U_bar(i,j) */
1139           wp = w + bj[j]*36;
1140           u = ba + j*36;
1141           wp[0] +=  uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5];
1142           wp[1] +=  uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2] + uik[9]*u[3]+ uik[10]*u[4]+ uik[11]*u[5];
1143           wp[2] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3]+ uik[16]*u[4]+ uik[17]*u[5];
1144           wp[3] += uik[18]*u[0]+ uik[19]*u[1]+ uik[20]*u[2]+ uik[21]*u[3]+ uik[22]*u[4]+ uik[23]*u[5];
1145           wp[4] += uik[24]*u[0]+ uik[25]*u[1]+ uik[26]*u[2]+ uik[27]*u[3]+ uik[28]*u[4]+ uik[29]*u[5];
1146           wp[5] += uik[30]*u[0]+ uik[31]*u[1]+ uik[32]*u[2]+ uik[33]*u[3]+ uik[34]*u[4]+ uik[35]*u[5];
1147 
1148           wp[6] +=  uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8] + uik[3]*u[9] + uik[4]*u[10] + uik[5]*u[11];
1149           wp[7] +=  uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8] + uik[9]*u[9]+ uik[10]*u[10]+ uik[11]*u[11];
1150           wp[8] += uik[12]*u[6]+ uik[13]*u[7]+ uik[14]*u[8]+ uik[15]*u[9]+ uik[16]*u[10]+ uik[17]*u[11];
1151           wp[9] += uik[18]*u[6]+ uik[19]*u[7]+ uik[20]*u[8]+ uik[21]*u[9]+ uik[22]*u[10]+ uik[23]*u[11];
1152           wp[10]+= uik[24]*u[6]+ uik[25]*u[7]+ uik[26]*u[8]+ uik[27]*u[9]+ uik[28]*u[10]+ uik[29]*u[11];
1153           wp[11]+= uik[30]*u[6]+ uik[31]*u[7]+ uik[32]*u[8]+ uik[33]*u[9]+ uik[34]*u[10]+ uik[35]*u[11];
1154 
1155           wp[12]+=  uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15] + uik[4]*u[16] + uik[5]*u[17];
1156           wp[13]+=  uik[6]*u[12] + uik[7]*u[13] + uik[8]*u[14] + uik[9]*u[15]+ uik[10]*u[16]+ uik[11]*u[17];
1157           wp[14]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15]+ uik[16]*u[16]+ uik[17]*u[17];
1158           wp[15]+= uik[18]*u[12]+ uik[19]*u[13]+ uik[20]*u[14]+ uik[21]*u[15]+ uik[22]*u[16]+ uik[23]*u[17];
1159           wp[16]+= uik[24]*u[12]+ uik[25]*u[13]+ uik[26]*u[14]+ uik[27]*u[15]+ uik[28]*u[16]+ uik[29]*u[17];
1160           wp[17]+= uik[30]*u[12]+ uik[31]*u[13]+ uik[32]*u[14]+ uik[33]*u[15]+ uik[34]*u[16]+ uik[35]*u[17];
1161 
1162           wp[18]+=  uik[0]*u[18] + uik[1]*u[19] + uik[2]*u[20] + uik[3]*u[21] + uik[4]*u[22] + uik[5]*u[23];
1163           wp[19]+=  uik[6]*u[18] + uik[7]*u[19] + uik[8]*u[20] + uik[9]*u[21]+ uik[10]*u[22]+ uik[11]*u[23];
1164           wp[20]+= uik[12]*u[18]+ uik[13]*u[19]+ uik[14]*u[20]+ uik[15]*u[21]+ uik[16]*u[22]+ uik[17]*u[23];
1165           wp[21]+= uik[18]*u[18]+ uik[19]*u[19]+ uik[20]*u[20]+ uik[21]*u[21]+ uik[22]*u[22]+ uik[23]*u[23];
1166           wp[22]+= uik[24]*u[18]+ uik[25]*u[19]+ uik[26]*u[20]+ uik[27]*u[21]+ uik[28]*u[22]+ uik[29]*u[23];
1167           wp[23]+= uik[30]*u[18]+ uik[31]*u[19]+ uik[32]*u[20]+ uik[33]*u[21]+ uik[34]*u[22]+ uik[35]*u[23];
1168 
1169           wp[24]+=  uik[0]*u[24] + uik[1]*u[25] + uik[2]*u[26] + uik[3]*u[27] + uik[4]*u[28] + uik[5]*u[29];
1170           wp[25]+=  uik[6]*u[24] + uik[7]*u[25] + uik[8]*u[26] + uik[9]*u[27]+ uik[10]*u[28]+ uik[11]*u[29];
1171           wp[26]+= uik[12]*u[24]+ uik[13]*u[25]+ uik[14]*u[26]+ uik[15]*u[27]+ uik[16]*u[28]+ uik[17]*u[29];
1172           wp[27]+= uik[18]*u[24]+ uik[19]*u[25]+ uik[20]*u[26]+ uik[21]*u[27]+ uik[22]*u[28]+ uik[23]*u[29];
1173           wp[28]+= uik[24]*u[24]+ uik[25]*u[25]+ uik[26]*u[26]+ uik[27]*u[27]+ uik[28]*u[28]+ uik[29]*u[29];
1174           wp[29]+= uik[30]*u[24]+ uik[31]*u[25]+ uik[32]*u[26]+ uik[33]*u[27]+ uik[34]*u[28]+ uik[35]*u[29];
1175 
1176           wp[30]+=  uik[0]*u[30] + uik[1]*u[31] + uik[2]*u[32] + uik[3]*u[33] + uik[4]*u[34] + uik[5]*u[35];
1177           wp[31]+=  uik[6]*u[30] + uik[7]*u[31] + uik[8]*u[32] + uik[9]*u[33]+ uik[10]*u[34]+ uik[11]*u[35];
1178           wp[32]+= uik[12]*u[30]+ uik[13]*u[31]+ uik[14]*u[32]+ uik[15]*u[33]+ uik[16]*u[34]+ uik[17]*u[35];
1179           wp[33]+= uik[18]*u[30]+ uik[19]*u[31]+ uik[20]*u[32]+ uik[21]*u[33]+ uik[22]*u[34]+ uik[23]*u[35];
1180           wp[34]+= uik[24]*u[30]+ uik[25]*u[31]+ uik[26]*u[32]+ uik[27]*u[33]+ uik[28]*u[34]+ uik[29]*u[35];
1181           wp[35]+= uik[30]*u[30]+ uik[31]*u[31]+ uik[32]*u[32]+ uik[33]*u[33]+ uik[34]*u[34]+ uik[35]*u[35];
1182         }
1183 
1184         /* ... add i to row list for next nonzero entry */
1185         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
1186         j     = bj[jmin];
1187         jl[i] = jl[j]; jl[j] = i; /* update jl */
1188       }
1189       i = nexti;
1190     }
1191 
1192     /* save nonzero entries in k-th row of U ... */
1193 
1194     /* invert diagonal block */
1195     d = ba+k*36;
1196     ierr = PetscMemcpy(d,dk,36*sizeof(MatScalar));CHKERRQ(ierr);
1197     ierr = Kernel_A_gets_inverse_A_6(d);CHKERRQ(ierr);
1198 
1199     jmin = bi[k]; jmax = bi[k+1];
1200     if (jmin < jmax) {
1201       for (j=jmin; j<jmax; j++){
1202          vj = bj[j];           /* block col. index of U */
1203          u   = ba + j*36;
1204          wp = w + vj*36;
1205          for (k1=0; k1<36; k1++){
1206            *u++        = *wp;
1207            *wp++ = 0.0;
1208          }
1209       }
1210 
1211       /* ... add k to row list for first nonzero entry in k-th row */
1212       il[k] = jmin;
1213       i     = bj[jmin];
1214       jl[k] = jl[i]; jl[i] = k;
1215     }
1216   }
1217 
1218   ierr = PetscFree(w);CHKERRQ(ierr);
1219   ierr = PetscFree(il);CHKERRQ(ierr);
1220   ierr = PetscFree(jl);CHKERRQ(ierr);
1221   ierr = PetscFree(dk);CHKERRQ(ierr);
1222   ierr = PetscFree(uik);CHKERRQ(ierr);
1223   if (a->permute){
1224     ierr = PetscFree(aa);CHKERRQ(ierr);
1225   }
1226 
1227   ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr);
1228   C->factor    = FACTOR_CHOLESKY;
1229   C->assembled = PETSC_TRUE;
1230   C->preallocated = PETSC_TRUE;
1231   PLogFlops(1.3333*216*b->mbs); /* from inverting diagonal blocks */
1232   PetscFunctionReturn(0);
1233 }
1234 
1235 /*
1236       Version for when blocks are 6 by 6 Using natural ordering
1237 */
1238 #undef __FUNC__
1239 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_6_NaturalOrdering"
1240 int MatCholeskyFactorNumeric_SeqSBAIJ_6_NaturalOrdering(Mat A,Mat *B)
1241 {
1242   Mat         C = *B;
1243   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
1244   int         ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
1245   int         *ajtmpold,*ajtmp,nz,row;
1246   int         *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
1247   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
1248   MatScalar   x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15;
1249   MatScalar   x16,x17,x18,x19,x20,x21,x22,x23,x24,x25;
1250   MatScalar   p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15;
1251   MatScalar   p16,p17,p18,p19,p20,p21,p22,p23,p24,p25;
1252   MatScalar   m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12,m13,m14,m15;
1253   MatScalar   m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
1254   MatScalar   p26,p27,p28,p29,p30,p31,p32,p33,p34,p35,p36;
1255   MatScalar   x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36;
1256   MatScalar   m26,m27,m28,m29,m30,m31,m32,m33,m34,m35,m36;
1257   MatScalar   *ba = b->a,*aa = a->a;
1258 
1259   PetscFunctionBegin;
1260   rtmp  = (MatScalar*)PetscMalloc(36*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
1261   for (i=0; i<n; i++) {
1262     nz    = bi[i+1] - bi[i];
1263     ajtmp = bj + bi[i];
1264     for  (j=0; j<nz; j++) {
1265       x = rtmp+36*ajtmp[j];
1266       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
1267       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
1268       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = x[25] = 0.0 ;
1269       x[26] = x[27] = x[28] = x[29] = x[30] = x[31] = x[32] = x[33] = 0.0 ;
1270       x[34] = x[35] = 0.0 ;
1271     }
1272     /* load in initial (unfactored row) */
1273     nz       = ai[i+1] - ai[i];
1274     ajtmpold = aj + ai[i];
1275     v        = aa + 36*ai[i];
1276     for (j=0; j<nz; j++) {
1277       x    = rtmp+36*ajtmpold[j];
1278       x[0] =  v[0];  x[1] =  v[1];  x[2] =  v[2];  x[3] =  v[3];
1279       x[4] =  v[4];  x[5] =  v[5];  x[6] =  v[6];  x[7] =  v[7];
1280       x[8] =  v[8];  x[9] =  v[9];  x[10] = v[10]; x[11] = v[11];
1281       x[12] = v[12]; x[13] = v[13]; x[14] = v[14]; x[15] = v[15];
1282       x[16] = v[16]; x[17] = v[17]; x[18] = v[18]; x[19] = v[19];
1283       x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23];
1284       x[24] = v[24]; x[25] = v[25]; x[26] = v[26]; x[27] = v[27];
1285       x[28] = v[28]; x[29] = v[29]; x[30] = v[30]; x[31] = v[31];
1286       x[32] = v[32]; x[33] = v[33]; x[34] = v[34]; x[35] = v[35];
1287       v    += 36;
1288     }
1289     row = *ajtmp++;
1290     while (row < i) {
1291       pc  = rtmp + 36*row;
1292       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
1293       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];
1294       p9  = pc[8];  p10 = pc[9];  p11 = pc[10]; p12 = pc[11];
1295       p13 = pc[12]; p14 = pc[13]; p15 = pc[14]; p16 = pc[15];
1296       p17 = pc[16]; p18 = pc[17]; p19 = pc[18]; p20 = pc[19];
1297       p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
1298       p25 = pc[24]; p26 = pc[25]; p27 = pc[26]; p28 = pc[27];
1299       p29 = pc[28]; p30 = pc[29]; p31 = pc[30]; p32 = pc[31];
1300       p33 = pc[32]; p34 = pc[33]; p35 = pc[34]; p36 = pc[35];
1301       if (p1  != 0.0 || p2  != 0.0 || p3  != 0.0 || p4  != 0.0 ||
1302           p5  != 0.0 || p6  != 0.0 || p7  != 0.0 || p8  != 0.0 ||
1303           p9  != 0.0 || p10 != 0.0 || p11 != 0.0 || p12 != 0.0 ||
1304           p13 != 0.0 || p14 != 0.0 || p15 != 0.0 || p16 != 0.0 ||
1305           p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 ||
1306           p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 ||
1307           p25 != 0.0 || p26 != 0.0 || p27 != 0.0 || p28 != 0.0 ||
1308           p29 != 0.0 || p30 != 0.0 || p31 != 0.0 || p32 != 0.0 ||
1309           p33 != 0.0 || p34 != 0.0 || p35 != 0.0 || p36 != 0.0) {
1310         pv = ba + 36*diag_offset[row];
1311         pj = bj + diag_offset[row] + 1;
1312 	x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
1313 	x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
1314 	x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
1315 	x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
1316 	x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
1317 	x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
1318 	x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
1319 	x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
1320 	x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
1321         pc[0]  = m1  = p1*x1  + p7*x2   + p13*x3  + p19*x4  + p25*x5  + p31*x6;
1322         pc[1]  = m2  = p2*x1  + p8*x2   + p14*x3  + p20*x4  + p26*x5  + p32*x6;
1323         pc[2]  = m3  = p3*x1  + p9*x2   + p15*x3  + p21*x4  + p27*x5  + p33*x6;
1324         pc[3]  = m4  = p4*x1  + p10*x2  + p16*x3  + p22*x4  + p28*x5  + p34*x6;
1325         pc[4]  = m5  = p5*x1  + p11*x2  + p17*x3  + p23*x4  + p29*x5  + p35*x6;
1326         pc[5]  = m6  = p6*x1  + p12*x2  + p18*x3  + p24*x4  + p30*x5  + p36*x6;
1327 
1328         pc[6]  = m7  = p1*x7  + p7*x8   + p13*x9  + p19*x10 + p25*x11 + p31*x12;
1329         pc[7]  = m8  = p2*x7  + p8*x8   + p14*x9  + p20*x10 + p26*x11 + p32*x12;
1330         pc[8]  = m9  = p3*x7  + p9*x8   + p15*x9  + p21*x10 + p27*x11 + p33*x12;
1331         pc[9]  = m10 = p4*x7  + p10*x8  + p16*x9  + p22*x10 + p28*x11 + p34*x12;
1332         pc[10] = m11 = p5*x7  + p11*x8  + p17*x9  + p23*x10 + p29*x11 + p35*x12;
1333         pc[11] = m12 = p6*x7  + p12*x8  + p18*x9  + p24*x10 + p30*x11 + p36*x12;
1334 
1335         pc[12] = m13 = p1*x13 + p7*x14  + p13*x15 + p19*x16 + p25*x17 + p31*x18;
1336         pc[13] = m14 = p2*x13 + p8*x14  + p14*x15 + p20*x16 + p26*x17 + p32*x18;
1337         pc[14] = m15 = p3*x13 + p9*x14  + p15*x15 + p21*x16 + p27*x17 + p33*x18;
1338         pc[15] = m16 = p4*x13 + p10*x14 + p16*x15 + p22*x16 + p28*x17 + p34*x18;
1339         pc[16] = m17 = p5*x13 + p11*x14 + p17*x15 + p23*x16 + p29*x17 + p35*x18;
1340         pc[17] = m18 = p6*x13 + p12*x14 + p18*x15 + p24*x16 + p30*x17 + p36*x18;
1341 
1342         pc[18] = m19 = p1*x19 + p7*x20  + p13*x21 + p19*x22 + p25*x23 + p31*x24;
1343         pc[19] = m20 = p2*x19 + p8*x20  + p14*x21 + p20*x22 + p26*x23 + p32*x24;
1344         pc[20] = m21 = p3*x19 + p9*x20  + p15*x21 + p21*x22 + p27*x23 + p33*x24;
1345         pc[21] = m22 = p4*x19 + p10*x20 + p16*x21 + p22*x22 + p28*x23 + p34*x24;
1346         pc[22] = m23 = p5*x19 + p11*x20 + p17*x21 + p23*x22 + p29*x23 + p35*x24;
1347         pc[23] = m24 = p6*x19 + p12*x20 + p18*x21 + p24*x22 + p30*x23 + p36*x24;
1348 
1349         pc[24] = m25 = p1*x25 + p7*x26  + p13*x27 + p19*x28 + p25*x29 + p31*x30;
1350         pc[25] = m26 = p2*x25 + p8*x26  + p14*x27 + p20*x28 + p26*x29 + p32*x30;
1351         pc[26] = m27 = p3*x25 + p9*x26  + p15*x27 + p21*x28 + p27*x29 + p33*x30;
1352         pc[27] = m28 = p4*x25 + p10*x26 + p16*x27 + p22*x28 + p28*x29 + p34*x30;
1353         pc[28] = m29 = p5*x25 + p11*x26 + p17*x27 + p23*x28 + p29*x29 + p35*x30;
1354         pc[29] = m30 = p6*x25 + p12*x26 + p18*x27 + p24*x28 + p30*x29 + p36*x30;
1355 
1356         pc[30] = m31 = p1*x31 + p7*x32  + p13*x33 + p19*x34 + p25*x35 + p31*x36;
1357         pc[31] = m32 = p2*x31 + p8*x32  + p14*x33 + p20*x34 + p26*x35 + p32*x36;
1358         pc[32] = m33 = p3*x31 + p9*x32  + p15*x33 + p21*x34 + p27*x35 + p33*x36;
1359         pc[33] = m34 = p4*x31 + p10*x32 + p16*x33 + p22*x34 + p28*x35 + p34*x36;
1360         pc[34] = m35 = p5*x31 + p11*x32 + p17*x33 + p23*x34 + p29*x35 + p35*x36;
1361         pc[35] = m36 = p6*x31 + p12*x32 + p18*x33 + p24*x34 + p30*x35 + p36*x36;
1362 
1363         nz = bi[row+1] - diag_offset[row] - 1;
1364         pv += 36;
1365         for (j=0; j<nz; j++) {
1366 	  x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
1367 	  x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
1368 	  x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
1369 	  x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
1370 	  x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
1371 	  x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
1372 	  x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
1373 	  x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
1374 	  x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
1375 	  x    = rtmp + 36*pj[j];
1376           x[0]  -= m1*x1  + m7*x2   + m13*x3  + m19*x4  + m25*x5  + m31*x6;
1377           x[1]  -= m2*x1  + m8*x2   + m14*x3  + m20*x4  + m26*x5  + m32*x6;
1378           x[2]  -= m3*x1  + m9*x2   + m15*x3  + m21*x4  + m27*x5  + m33*x6;
1379           x[3]  -= m4*x1  + m10*x2  + m16*x3  + m22*x4  + m28*x5  + m34*x6;
1380           x[4]  -= m5*x1  + m11*x2  + m17*x3  + m23*x4  + m29*x5  + m35*x6;
1381           x[5]  -= m6*x1  + m12*x2  + m18*x3  + m24*x4  + m30*x5  + m36*x6;
1382 
1383 	  x[6]  -= m1*x7  + m7*x8   + m13*x9  + m19*x10 + m25*x11 + m31*x12;
1384 	  x[7]  -= m2*x7  + m8*x8   + m14*x9  + m20*x10 + m26*x11 + m32*x12;
1385 	  x[8]  -= m3*x7  + m9*x8   + m15*x9  + m21*x10 + m27*x11 + m33*x12;
1386 	  x[9]  -= m4*x7  + m10*x8  + m16*x9  + m22*x10 + m28*x11 + m34*x12;
1387 	  x[10] -= m5*x7  + m11*x8  + m17*x9  + m23*x10 + m29*x11 + m35*x12;
1388 	  x[11] -= m6*x7  + m12*x8  + m18*x9  + m24*x10 + m30*x11 + m36*x12;
1389 
1390 	  x[12] -= m1*x13 + m7*x14  + m13*x15 + m19*x16 + m25*x17 + m31*x18;
1391 	  x[13] -= m2*x13 + m8*x14  + m14*x15 + m20*x16 + m26*x17 + m32*x18;
1392 	  x[14] -= m3*x13 + m9*x14  + m15*x15 + m21*x16 + m27*x17 + m33*x18;
1393 	  x[15] -= m4*x13 + m10*x14 + m16*x15 + m22*x16 + m28*x17 + m34*x18;
1394 	  x[16] -= m5*x13 + m11*x14 + m17*x15 + m23*x16 + m29*x17 + m35*x18;
1395 	  x[17] -= m6*x13 + m12*x14 + m18*x15 + m24*x16 + m30*x17 + m36*x18;
1396 
1397 	  x[18] -= m1*x19 + m7*x20  + m13*x21 + m19*x22 + m25*x23 + m31*x24;
1398 	  x[19] -= m2*x19 + m8*x20  + m14*x21 + m20*x22 + m26*x23 + m32*x24;
1399 	  x[20] -= m3*x19 + m9*x20  + m15*x21 + m21*x22 + m27*x23 + m33*x24;
1400 	  x[21] -= m4*x19 + m10*x20 + m16*x21 + m22*x22 + m28*x23 + m34*x24;
1401 	  x[22] -= m5*x19 + m11*x20 + m17*x21 + m23*x22 + m29*x23 + m35*x24;
1402 	  x[23] -= m6*x19 + m12*x20 + m18*x21 + m24*x22 + m30*x23 + m36*x24;
1403 
1404 	  x[24] -= m1*x25 + m7*x26  + m13*x27 + m19*x28 + m25*x29 + m31*x30;
1405 	  x[25] -= m2*x25 + m8*x26  + m14*x27 + m20*x28 + m26*x29 + m32*x30;
1406 	  x[26] -= m3*x25 + m9*x26  + m15*x27 + m21*x28 + m27*x29 + m33*x30;
1407 	  x[27] -= m4*x25 + m10*x26 + m16*x27 + m22*x28 + m28*x29 + m34*x30;
1408 	  x[28] -= m5*x25 + m11*x26 + m17*x27 + m23*x28 + m29*x29 + m35*x30;
1409 	  x[29] -= m6*x25 + m12*x26 + m18*x27 + m24*x28 + m30*x29 + m36*x30;
1410 
1411 	  x[30] -= m1*x31 + m7*x32  + m13*x33 + m19*x34 + m25*x35 + m31*x36;
1412 	  x[31] -= m2*x31 + m8*x32  + m14*x33 + m20*x34 + m26*x35 + m32*x36;
1413 	  x[32] -= m3*x31 + m9*x32  + m15*x33 + m21*x34 + m27*x35 + m33*x36;
1414 	  x[33] -= m4*x31 + m10*x32 + m16*x33 + m22*x34 + m28*x35 + m34*x36;
1415 	  x[34] -= m5*x31 + m11*x32 + m17*x33 + m23*x34 + m29*x35 + m35*x36;
1416 	  x[35] -= m6*x31 + m12*x32 + m18*x33 + m24*x34 + m30*x35 + m36*x36;
1417 
1418           pv   += 36;
1419         }
1420         PLogFlops(432*nz+396);
1421       }
1422       row = *ajtmp++;
1423     }
1424     /* finished row so stick it into b->a */
1425     pv = ba + 36*bi[i];
1426     pj = bj + bi[i];
1427     nz = bi[i+1] - bi[i];
1428     for (j=0; j<nz; j++) {
1429       x      = rtmp+36*pj[j];
1430       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
1431       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7];
1432       pv[8]  = x[8];  pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11];
1433       pv[12] = x[12]; pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
1434       pv[16] = x[16]; pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19];
1435       pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23];
1436       pv[24] = x[24]; pv[25] = x[25]; pv[26] = x[26]; pv[27] = x[27];
1437       pv[28] = x[28]; pv[29] = x[29]; pv[30] = x[30]; pv[31] = x[31];
1438       pv[32] = x[32]; pv[33] = x[33]; pv[34] = x[34]; pv[35] = x[35];
1439       pv   += 36;
1440     }
1441     /* invert diagonal block */
1442     w = ba + 36*diag_offset[i];
1443     ierr = Kernel_A_gets_inverse_A_6(w);CHKERRQ(ierr);
1444   }
1445 
1446   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1447   C->factor    = FACTOR_LU;
1448   C->assembled = PETSC_TRUE;
1449   PLogFlops(1.3333*216*b->mbs); /* from inverting diagonal blocks */
1450   PetscFunctionReturn(0);
1451 }
1452 
1453 /* Version for when blocks are 5 by 5  */
1454 #undef __FUNC__
1455 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_5"
1456 int MatCholeskyFactorNumeric_SeqSBAIJ_5(Mat A,Mat *B)
1457 {
1458   Mat                C = *B;
1459   Mat_SeqSBAIJ       *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data;
1460   IS                 perm = b->row;
1461   int                *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
1462   int                *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
1463   MatScalar          *ba = b->a,*aa,*ap,*dk,*uik;
1464   MatScalar          *u,*d,*rtmp,*rtmp_ptr;
1465 
1466   PetscFunctionBegin;
1467   /* initialization */
1468   rtmp  = (MatScalar*)PetscMalloc(25*mbs*sizeof(MatScalar));CHKPTRQ(rtmp);
1469   ierr = PetscMemzero(rtmp,25*mbs*sizeof(MatScalar));CHKERRQ(ierr);
1470   il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il);
1471   jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl);
1472   for (i=0; i<mbs; i++) {
1473     jl[i] = mbs; il[0] = 0;
1474   }
1475   dk    = (MatScalar*)PetscMalloc(25*sizeof(MatScalar));CHKPTRQ(dk);
1476   uik   = (MatScalar*)PetscMalloc(25*sizeof(MatScalar));CHKPTRQ(uik);
1477   ierr  = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr);
1478 
1479   /* check permutation */
1480   if (!a->permute){
1481     ai = a->i; aj = a->j; aa = a->a;
1482   } else {
1483     ai = a->inew; aj = a->jnew;
1484     aa = (MatScalar*)PetscMalloc(25*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa);
1485     ierr = PetscMemcpy(aa,a->a,25*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr);
1486     a2anew  = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew);
1487     ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr);
1488 
1489     for (i=0; i<mbs; i++){
1490       jmin = ai[i]; jmax = ai[i+1];
1491       for (j=jmin; j<jmax; j++){
1492         while (a2anew[j] != j){
1493           k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k;
1494           for (k1=0; k1<25; k1++){
1495             dk[k1]       = aa[k*25+k1];
1496             aa[k*25+k1] = aa[j*25+k1];
1497             aa[j*25+k1] = dk[k1];
1498           }
1499         }
1500         /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */
1501         if (i > aj[j]){
1502           /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */
1503           ap = aa + j*25;                     /* ptr to the beginning of j-th block of aa */
1504           for (k=0; k<25; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */
1505           for (k=0; k<5; k++){               /* j-th block of aa <- dk^T */
1506             for (k1=0; k1<5; k1++) *ap++ = dk[k + 5*k1];
1507           }
1508         }
1509       }
1510     }
1511     ierr = PetscFree(a2anew);CHKERRA(ierr);
1512   }
1513 
1514   /* for each row k */
1515   for (k = 0; k<mbs; k++){
1516 
1517     /*initialize k-th row with elements nonzero in row perm(k) of A */
1518     jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1];
1519     if (jmin < jmax) {
1520       ap = aa + jmin*25;
1521       for (j = jmin; j < jmax; j++){
1522         vj = perm_ptr[aj[j]];         /* block col. index */
1523         rtmp_ptr = rtmp + vj*25;
1524         for (i=0; i<25; i++) *rtmp_ptr++ = *ap++;
1525       }
1526     }
1527 
1528     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
1529     ierr = PetscMemcpy(dk,rtmp+k*25,25*sizeof(MatScalar));CHKERRQ(ierr);
1530     i = jl[k]; /* first row to be added to k_th row  */
1531 
1532     while (i < mbs){
1533       nexti = jl[i]; /* next row to be added to k_th row */
1534 
1535       /* compute multiplier */
1536       ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
1537 
1538       /* uik = -inv(Di)*U_bar(i,k) */
1539       d = ba + i*25;
1540       u    = ba + ili*25;
1541 
1542       uik[0] = -(d[0]*u[0] + d[5]*u[1] + d[10]*u[2] + d[15]*u[3] + d[20]*u[4]);
1543       uik[1] = -(d[1]*u[0] + d[6]*u[1] + d[11]*u[2] + d[16]*u[3] + d[21]*u[4]);
1544       uik[2] = -(d[2]*u[0] + d[7]*u[1] + d[12]*u[2] + d[17]*u[3] + d[22]*u[4]);
1545       uik[3] = -(d[3]*u[0] + d[8]*u[1] + d[13]*u[2] + d[18]*u[3] + d[23]*u[4]);
1546       uik[4] = -(d[4]*u[0] + d[9]*u[1] + d[14]*u[2] + d[19]*u[3] + d[24]*u[4]);
1547 
1548       uik[5] = -(d[0]*u[5] + d[5]*u[6] + d[10]*u[7] + d[15]*u[8] + d[20]*u[9]);
1549       uik[6] = -(d[1]*u[5] + d[6]*u[6] + d[11]*u[7] + d[16]*u[8] + d[21]*u[9]);
1550       uik[7] = -(d[2]*u[5] + d[7]*u[6] + d[12]*u[7] + d[17]*u[8] + d[22]*u[9]);
1551       uik[8] = -(d[3]*u[5] + d[8]*u[6] + d[13]*u[7] + d[18]*u[8] + d[23]*u[9]);
1552       uik[9] = -(d[4]*u[5] + d[9]*u[6] + d[14]*u[7] + d[19]*u[8] + d[24]*u[9]);
1553 
1554       uik[10]= -(d[0]*u[10] + d[5]*u[11] + d[10]*u[12] + d[15]*u[13] + d[20]*u[14]);
1555       uik[11]= -(d[1]*u[10] + d[6]*u[11] + d[11]*u[12] + d[16]*u[13] + d[21]*u[14]);
1556       uik[12]= -(d[2]*u[10] + d[7]*u[11] + d[12]*u[12] + d[17]*u[13] + d[22]*u[14]);
1557       uik[13]= -(d[3]*u[10] + d[8]*u[11] + d[13]*u[12] + d[18]*u[13] + d[23]*u[14]);
1558       uik[14]= -(d[4]*u[10] + d[9]*u[11] + d[14]*u[12] + d[19]*u[13] + d[24]*u[14]);
1559 
1560       uik[15]= -(d[0]*u[15] + d[5]*u[16] + d[10]*u[17] + d[15]*u[18] + d[20]*u[19]);
1561       uik[16]= -(d[1]*u[15] + d[6]*u[16] + d[11]*u[17] + d[16]*u[18] + d[21]*u[19]);
1562       uik[17]= -(d[2]*u[15] + d[7]*u[16] + d[12]*u[17] + d[17]*u[18] + d[22]*u[19]);
1563       uik[18]= -(d[3]*u[15] + d[8]*u[16] + d[13]*u[17] + d[18]*u[18] + d[23]*u[19]);
1564       uik[19]= -(d[4]*u[15] + d[9]*u[16] + d[14]*u[17] + d[19]*u[18] + d[24]*u[19]);
1565 
1566       uik[20]= -(d[0]*u[20] + d[5]*u[21] + d[10]*u[22] + d[15]*u[23] + d[20]*u[24]);
1567       uik[21]= -(d[1]*u[20] + d[6]*u[21] + d[11]*u[22] + d[16]*u[23] + d[21]*u[24]);
1568       uik[22]= -(d[2]*u[20] + d[7]*u[21] + d[12]*u[22] + d[17]*u[23] + d[22]*u[24]);
1569       uik[23]= -(d[3]*u[20] + d[8]*u[21] + d[13]*u[22] + d[18]*u[23] + d[23]*u[24]);
1570       uik[24]= -(d[4]*u[20] + d[9]*u[21] + d[14]*u[22] + d[19]*u[23] + d[24]*u[24]);
1571 
1572 
1573       /* update D(k) += -U(i,k)^T * U_bar(i,k) */
1574       dk[0] +=  uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3] + uik[4]*u[4];
1575       dk[1] +=  uik[5]*u[0] + uik[6]*u[1] + uik[7]*u[2] + uik[8]*u[3] + uik[9]*u[4];
1576       dk[2] += uik[10]*u[0]+ uik[11]*u[1]+ uik[12]*u[2]+ uik[13]*u[3]+ uik[14]*u[4];
1577       dk[3] += uik[15]*u[0]+ uik[16]*u[1]+ uik[17]*u[2]+ uik[18]*u[3]+ uik[19]*u[4];
1578       dk[4] += uik[20]*u[0]+ uik[21]*u[1]+ uik[22]*u[2]+ uik[23]*u[3]+ uik[24]*u[4];
1579 
1580       dk[5] +=  uik[0]*u[5] + uik[1]*u[6] + uik[2]*u[7] + uik[3]*u[8] + uik[4]*u[9];
1581       dk[6] +=  uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8] + uik[9]*u[9];
1582       dk[7] += uik[10]*u[5]+ uik[11]*u[6]+ uik[12]*u[7]+ uik[13]*u[8]+ uik[14]*u[9];
1583       dk[8] += uik[15]*u[5]+ uik[16]*u[6]+ uik[17]*u[7]+ uik[18]*u[8]+ uik[19]*u[9];
1584       dk[9] += uik[20]*u[5]+ uik[21]*u[6]+ uik[22]*u[7]+ uik[23]*u[8]+ uik[24]*u[9];
1585 
1586       dk[10] +=  uik[0]*u[10] + uik[1]*u[11] + uik[2]*u[12] + uik[3]*u[13] + uik[4]*u[14];
1587       dk[11] +=  uik[5]*u[10] + uik[6]*u[11] + uik[7]*u[12] + uik[8]*u[13] + uik[9]*u[14];
1588       dk[12] += uik[10]*u[10]+ uik[11]*u[11]+ uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14];
1589       dk[13] += uik[15]*u[10]+ uik[16]*u[11]+ uik[17]*u[12]+ uik[18]*u[13]+ uik[19]*u[14];
1590       dk[14] += uik[20]*u[10]+ uik[21]*u[11]+ uik[22]*u[12]+ uik[23]*u[13]+ uik[24]*u[14];
1591 
1592       dk[15] +=  uik[0]*u[15] + uik[1]*u[16] + uik[2]*u[17] + uik[3]*u[18] + uik[4]*u[19];
1593       dk[16] +=  uik[5]*u[15] + uik[6]*u[16] + uik[7]*u[17] + uik[8]*u[18] + uik[9]*u[19];
1594       dk[17] += uik[10]*u[15]+ uik[11]*u[16]+ uik[12]*u[17]+ uik[13]*u[18]+ uik[14]*u[19];
1595       dk[18] += uik[15]*u[15]+ uik[16]*u[16]+ uik[17]*u[17]+ uik[18]*u[18]+ uik[19]*u[19];
1596       dk[19] += uik[20]*u[15]+ uik[21]*u[16]+ uik[22]*u[17]+ uik[23]*u[18]+ uik[24]*u[19];
1597 
1598       dk[20] +=  uik[0]*u[20] + uik[1]*u[21] + uik[2]*u[22] + uik[3]*u[23] + uik[4]*u[24];
1599       dk[21] +=  uik[5]*u[20] + uik[6]*u[21] + uik[7]*u[22] + uik[8]*u[23] + uik[9]*u[24];
1600       dk[22] += uik[10]*u[20]+ uik[11]*u[21]+ uik[12]*u[22]+ uik[13]*u[23]+ uik[14]*u[24];
1601       dk[23] += uik[15]*u[20]+ uik[16]*u[21]+ uik[17]*u[22]+ uik[18]*u[23]+ uik[19]*u[24];
1602       dk[24] += uik[20]*u[20]+ uik[21]*u[21]+ uik[22]*u[22]+ uik[23]*u[23]+ uik[24]*u[24];
1603 
1604       /* update -U(i,k) */
1605       ierr = PetscMemcpy(ba+ili*25,uik,25*sizeof(MatScalar));CHKERRQ(ierr);
1606 
1607       /* add multiple of row i to k-th row ... */
1608       jmin = ili + 1; jmax = bi[i+1];
1609       if (jmin < jmax){
1610         for (j=jmin; j<jmax; j++) {
1611           /* rtmp += -U(i,k)^T * U_bar(i,j) */
1612           rtmp_ptr = rtmp + bj[j]*25;
1613           u = ba + j*25;
1614           rtmp_ptr[0] +=  uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3] + uik[4]*u[4];
1615           rtmp_ptr[1] +=  uik[5]*u[0] + uik[6]*u[1] + uik[7]*u[2] + uik[8]*u[3] + uik[9]*u[4];
1616           rtmp_ptr[2] += uik[10]*u[0]+ uik[11]*u[1]+ uik[12]*u[2]+ uik[13]*u[3]+ uik[14]*u[4];
1617           rtmp_ptr[3] += uik[15]*u[0]+ uik[16]*u[1]+ uik[17]*u[2]+ uik[18]*u[3]+ uik[19]*u[4];
1618           rtmp_ptr[4] += uik[20]*u[0]+ uik[21]*u[1]+ uik[22]*u[2]+ uik[23]*u[3]+ uik[24]*u[4];
1619 
1620           rtmp_ptr[5] +=  uik[0]*u[5] + uik[1]*u[6] + uik[2]*u[7] + uik[3]*u[8] + uik[4]*u[9];
1621           rtmp_ptr[6] +=  uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8] + uik[9]*u[9];
1622           rtmp_ptr[7] += uik[10]*u[5]+ uik[11]*u[6]+ uik[12]*u[7]+ uik[13]*u[8]+ uik[14]*u[9];
1623           rtmp_ptr[8] += uik[15]*u[5]+ uik[16]*u[6]+ uik[17]*u[7]+ uik[18]*u[8]+ uik[19]*u[9];
1624           rtmp_ptr[9] += uik[20]*u[5]+ uik[21]*u[6]+ uik[22]*u[7]+ uik[23]*u[8]+ uik[24]*u[9];
1625 
1626           rtmp_ptr[10] +=  uik[0]*u[10] + uik[1]*u[11] + uik[2]*u[12] + uik[3]*u[13] + uik[4]*u[14];
1627           rtmp_ptr[11] +=  uik[5]*u[10] + uik[6]*u[11] + uik[7]*u[12] + uik[8]*u[13] + uik[9]*u[14];
1628           rtmp_ptr[12] += uik[10]*u[10]+ uik[11]*u[11]+ uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14];
1629           rtmp_ptr[13] += uik[15]*u[10]+ uik[16]*u[11]+ uik[17]*u[12]+ uik[18]*u[13]+ uik[19]*u[14];
1630           rtmp_ptr[14] += uik[20]*u[10]+ uik[21]*u[11]+ uik[22]*u[12]+ uik[23]*u[13]+ uik[24]*u[14];
1631 
1632           rtmp_ptr[15] +=  uik[0]*u[15] + uik[1]*u[16] + uik[2]*u[17] + uik[3]*u[18] + uik[4]*u[19];
1633           rtmp_ptr[16] +=  uik[5]*u[15] + uik[6]*u[16] + uik[7]*u[17] + uik[8]*u[18] + uik[9]*u[19];
1634           rtmp_ptr[17] += uik[10]*u[15]+ uik[11]*u[16]+ uik[12]*u[17]+ uik[13]*u[18]+ uik[14]*u[19];
1635           rtmp_ptr[18] += uik[15]*u[15]+ uik[16]*u[16]+ uik[17]*u[17]+ uik[18]*u[18]+ uik[19]*u[19];
1636           rtmp_ptr[19] += uik[20]*u[15]+ uik[21]*u[16]+ uik[22]*u[17]+ uik[23]*u[18]+ uik[24]*u[19];
1637 
1638           rtmp_ptr[20] +=  uik[0]*u[20] + uik[1]*u[21] + uik[2]*u[22] + uik[3]*u[23] + uik[4]*u[24];
1639           rtmp_ptr[21] +=  uik[5]*u[20] + uik[6]*u[21] + uik[7]*u[22] + uik[8]*u[23] + uik[9]*u[24];
1640           rtmp_ptr[22] += uik[10]*u[20]+ uik[11]*u[21]+ uik[12]*u[22]+ uik[13]*u[23]+ uik[14]*u[24];
1641           rtmp_ptr[23] += uik[15]*u[20]+ uik[16]*u[21]+ uik[17]*u[22]+ uik[18]*u[23]+ uik[19]*u[24];
1642           rtmp_ptr[24] += uik[20]*u[20]+ uik[21]*u[21]+ uik[22]*u[22]+ uik[23]*u[23]+ uik[24]*u[24];
1643         }
1644 
1645         /* ... add i to row list for next nonzero entry */
1646         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
1647         j     = bj[jmin];
1648         jl[i] = jl[j]; jl[j] = i; /* update jl */
1649       }
1650       i = nexti;
1651     }
1652 
1653     /* save nonzero entries in k-th row of U ... */
1654 
1655     /* invert diagonal block */
1656     d = ba+k*25;
1657     ierr = PetscMemcpy(d,dk,25*sizeof(MatScalar));CHKERRQ(ierr);
1658     ierr = Kernel_A_gets_inverse_A_5(d);CHKERRQ(ierr);
1659 
1660     jmin = bi[k]; jmax = bi[k+1];
1661     if (jmin < jmax) {
1662       for (j=jmin; j<jmax; j++){
1663          vj = bj[j];           /* block col. index of U */
1664          u   = ba + j*25;
1665          rtmp_ptr = rtmp + vj*25;
1666          for (k1=0; k1<25; k1++){
1667            *u++        = *rtmp_ptr;
1668            *rtmp_ptr++ = 0.0;
1669          }
1670       }
1671 
1672       /* ... add k to row list for first nonzero entry in k-th row */
1673       il[k] = jmin;
1674       i     = bj[jmin];
1675       jl[k] = jl[i]; jl[i] = k;
1676     }
1677   }
1678 
1679   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1680   ierr = PetscFree(il);CHKERRQ(ierr);
1681   ierr = PetscFree(jl);CHKERRQ(ierr);
1682   ierr = PetscFree(dk);CHKERRQ(ierr);
1683   ierr = PetscFree(uik);CHKERRQ(ierr);
1684   if (a->permute){
1685     ierr = PetscFree(aa);CHKERRQ(ierr);
1686   }
1687 
1688   ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr);
1689   C->factor    = FACTOR_CHOLESKY;
1690   C->assembled = PETSC_TRUE;
1691   C->preallocated = PETSC_TRUE;
1692   PLogFlops(1.3333*125*b->mbs); /* from inverting diagonal blocks */
1693   PetscFunctionReturn(0);
1694 }
1695 
1696 /*
1697       Version for when blocks are 5 by 5 Using natural ordering
1698 */
1699 #undef __FUNC__
1700 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_5_NaturalOrdering"
1701 int MatCholeskyFactorNumeric_SeqSBAIJ_5_NaturalOrdering(Mat A,Mat *B)
1702 {
1703   Mat         C = *B;
1704   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
1705   int         ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
1706   int         *ajtmpold,*ajtmp,nz,row;
1707   int         *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
1708   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
1709   MatScalar   x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15;
1710   MatScalar   x16,x17,x18,x19,x20,x21,x22,x23,x24,x25;
1711   MatScalar   p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15;
1712   MatScalar   p16,p17,p18,p19,p20,p21,p22,p23,p24,p25;
1713   MatScalar   m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12,m13,m14,m15;
1714   MatScalar   m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
1715   MatScalar   *ba = b->a,*aa = a->a;
1716 
1717   PetscFunctionBegin;
1718   rtmp  = (MatScalar*)PetscMalloc(25*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
1719   for (i=0; i<n; i++) {
1720     nz    = bi[i+1] - bi[i];
1721     ajtmp = bj + bi[i];
1722     for  (j=0; j<nz; j++) {
1723       x = rtmp+25*ajtmp[j];
1724       x[0]  = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = x[9] = 0.0;
1725       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
1726       x[16] = x[17] = x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0;
1727     }
1728     /* load in initial (unfactored row) */
1729     nz       = ai[i+1] - ai[i];
1730     ajtmpold = aj + ai[i];
1731     v        = aa + 25*ai[i];
1732     for (j=0; j<nz; j++) {
1733       x    = rtmp+25*ajtmpold[j];
1734       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
1735       x[4]  = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
1736       x[9]  = v[9];  x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
1737       x[14] = v[14]; x[15] = v[15]; x[16] = v[16]; x[17] = v[17]; x[18] = v[18];
1738       x[19] = v[19]; x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23];
1739       x[24] = v[24];
1740       v    += 25;
1741     }
1742     row = *ajtmp++;
1743     while (row < i) {
1744       pc  = rtmp + 25*row;
1745       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
1746       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
1747       p10 = pc[9];  p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
1748       p15 = pc[14]; p16 = pc[15]; p17 = pc[16]; p18 = pc[17];
1749       p19 = pc[18]; p20 = pc[19]; p21 = pc[20]; p22 = pc[21]; p23 = pc[22];
1750       p24 = pc[23]; p25 = pc[24];
1751       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
1752           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
1753           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
1754           || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0
1755           || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 || p25 != 0.0) {
1756         pv = ba + 25*diag_offset[row];
1757         pj = bj + diag_offset[row] + 1;
1758         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
1759         x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
1760         x10 = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
1761         x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17]; x19 = pv[18];
1762         x20 = pv[19]; x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
1763         x25 = pv[24];
1764         pc[0] = m1 = p1*x1 + p6*x2  + p11*x3 + p16*x4 + p21*x5;
1765         pc[1] = m2 = p2*x1 + p7*x2  + p12*x3 + p17*x4 + p22*x5;
1766         pc[2] = m3 = p3*x1 + p8*x2  + p13*x3 + p18*x4 + p23*x5;
1767         pc[3] = m4 = p4*x1 + p9*x2  + p14*x3 + p19*x4 + p24*x5;
1768         pc[4] = m5 = p5*x1 + p10*x2 + p15*x3 + p20*x4 + p25*x5;
1769 
1770         pc[5]  = m6  = p1*x6 + p6*x7  + p11*x8 + p16*x9 + p21*x10;
1771         pc[6]  = m7  = p2*x6 + p7*x7  + p12*x8 + p17*x9 + p22*x10;
1772         pc[7]  = m8  = p3*x6 + p8*x7  + p13*x8 + p18*x9 + p23*x10;
1773         pc[8]  = m9  = p4*x6 + p9*x7  + p14*x8 + p19*x9 + p24*x10;
1774         pc[9]  = m10 = p5*x6 + p10*x7 + p15*x8 + p20*x9 + p25*x10;
1775 
1776         pc[10] = m11 = p1*x11 + p6*x12  + p11*x13 + p16*x14 + p21*x15;
1777         pc[11] = m12 = p2*x11 + p7*x12  + p12*x13 + p17*x14 + p22*x15;
1778         pc[12] = m13 = p3*x11 + p8*x12  + p13*x13 + p18*x14 + p23*x15;
1779         pc[13] = m14 = p4*x11 + p9*x12  + p14*x13 + p19*x14 + p24*x15;
1780         pc[14] = m15 = p5*x11 + p10*x12 + p15*x13 + p20*x14 + p25*x15;
1781 
1782         pc[15] = m16 = p1*x16 + p6*x17  + p11*x18 + p16*x19 + p21*x20;
1783         pc[16] = m17 = p2*x16 + p7*x17  + p12*x18 + p17*x19 + p22*x20;
1784         pc[17] = m18 = p3*x16 + p8*x17  + p13*x18 + p18*x19 + p23*x20;
1785         pc[18] = m19 = p4*x16 + p9*x17  + p14*x18 + p19*x19 + p24*x20;
1786         pc[19] = m20 = p5*x16 + p10*x17 + p15*x18 + p20*x19 + p25*x20;
1787 
1788         pc[20] = m21 = p1*x21 + p6*x22  + p11*x23 + p16*x24 + p21*x25;
1789         pc[21] = m22 = p2*x21 + p7*x22  + p12*x23 + p17*x24 + p22*x25;
1790         pc[22] = m23 = p3*x21 + p8*x22  + p13*x23 + p18*x24 + p23*x25;
1791         pc[23] = m24 = p4*x21 + p9*x22  + p14*x23 + p19*x24 + p24*x25;
1792         pc[24] = m25 = p5*x21 + p10*x22 + p15*x23 + p20*x24 + p25*x25;
1793 
1794         nz = bi[row+1] - diag_offset[row] - 1;
1795         pv += 25;
1796         for (j=0; j<nz; j++) {
1797           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
1798           x5   = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
1799           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
1800           x14  = pv[13]; x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17];
1801           x19 = pv[18];  x20 = pv[19]; x21 = pv[20]; x22 = pv[21]; x23 = pv[22];
1802           x24 = pv[23];  x25 = pv[24];
1803           x    = rtmp + 25*pj[j];
1804           x[0] -= m1*x1 + m6*x2   + m11*x3  + m16*x4 + m21*x5;
1805           x[1] -= m2*x1 + m7*x2   + m12*x3  + m17*x4 + m22*x5;
1806           x[2] -= m3*x1 + m8*x2   + m13*x3  + m18*x4 + m23*x5;
1807           x[3] -= m4*x1 + m9*x2   + m14*x3  + m19*x4 + m24*x5;
1808           x[4] -= m5*x1 + m10*x2  + m15*x3  + m20*x4 + m25*x5;
1809 
1810           x[5] -= m1*x6 + m6*x7   + m11*x8  + m16*x9 + m21*x10;
1811           x[6] -= m2*x6 + m7*x7   + m12*x8  + m17*x9 + m22*x10;
1812           x[7] -= m3*x6 + m8*x7   + m13*x8  + m18*x9 + m23*x10;
1813           x[8] -= m4*x6 + m9*x7   + m14*x8  + m19*x9 + m24*x10;
1814           x[9] -= m5*x6 + m10*x7  + m15*x8  + m20*x9 + m25*x10;
1815 
1816           x[10] -= m1*x11 + m6*x12  + m11*x13 + m16*x14 + m21*x15;
1817           x[11] -= m2*x11 + m7*x12  + m12*x13 + m17*x14 + m22*x15;
1818           x[12] -= m3*x11 + m8*x12  + m13*x13 + m18*x14 + m23*x15;
1819           x[13] -= m4*x11 + m9*x12  + m14*x13 + m19*x14 + m24*x15;
1820           x[14] -= m5*x11 + m10*x12 + m15*x13 + m20*x14 + m25*x15;
1821 
1822           x[15] -= m1*x16 + m6*x17  + m11*x18 + m16*x19 + m21*x20;
1823           x[16] -= m2*x16 + m7*x17  + m12*x18 + m17*x19 + m22*x20;
1824           x[17] -= m3*x16 + m8*x17  + m13*x18 + m18*x19 + m23*x20;
1825           x[18] -= m4*x16 + m9*x17  + m14*x18 + m19*x19 + m24*x20;
1826           x[19] -= m5*x16 + m10*x17 + m15*x18 + m20*x19 + m25*x20;
1827 
1828           x[20] -= m1*x21 + m6*x22  + m11*x23 + m16*x24 + m21*x25;
1829           x[21] -= m2*x21 + m7*x22  + m12*x23 + m17*x24 + m22*x25;
1830           x[22] -= m3*x21 + m8*x22  + m13*x23 + m18*x24 + m23*x25;
1831           x[23] -= m4*x21 + m9*x22  + m14*x23 + m19*x24 + m24*x25;
1832           x[24] -= m5*x21 + m10*x22 + m15*x23 + m20*x24 + m25*x25;
1833           pv   += 25;
1834         }
1835         PLogFlops(250*nz+225);
1836       }
1837       row = *ajtmp++;
1838     }
1839     /* finished row so stick it into b->a */
1840     pv = ba + 25*bi[i];
1841     pj = bj + bi[i];
1842     nz = bi[i+1] - bi[i];
1843     for (j=0; j<nz; j++) {
1844       x      = rtmp+25*pj[j];
1845       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
1846       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
1847       pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
1848       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; pv[16] = x[16]; pv[17] = x[17];
1849       pv[18] = x[18]; pv[19] = x[19]; pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22];
1850       pv[23] = x[23]; pv[24] = x[24];
1851       pv   += 25;
1852     }
1853     /* invert diagonal block */
1854     w = ba + 25*diag_offset[i];
1855     ierr = Kernel_A_gets_inverse_A_5(w);CHKERRQ(ierr);
1856   }
1857 
1858   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1859   C->factor    = FACTOR_LU;
1860   C->assembled = PETSC_TRUE;
1861   PLogFlops(1.3333*125*b->mbs); /* from inverting diagonal blocks */
1862   PetscFunctionReturn(0);
1863 }
1864 
1865 /*
1866       Version for when blocks are 4 by 4 Using natural ordering
1867 */
1868 #undef __FUNC__
1869 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_4_NaturalOrdering"
1870 int MatCholeskyFactorNumeric_SeqSBAIJ_4_NaturalOrdering(Mat A,Mat *B)
1871 {
1872   Mat         C = *B;
1873   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
1874   int         ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
1875   int         *ajtmpold,*ajtmp,nz,row;
1876   int         *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
1877   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
1878   MatScalar   p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
1879   MatScalar   p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
1880   MatScalar   p10,p11,p12,p13,p14,p15,p16,m10,m11,m12;
1881   MatScalar   m13,m14,m15,m16;
1882   MatScalar   *ba = b->a,*aa = a->a;
1883 
1884   PetscFunctionBegin;
1885   rtmp  = (MatScalar*)PetscMalloc(16*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
1886 
1887   for (i=0; i<n; i++) {
1888     nz    = bi[i+1] - bi[i];
1889     ajtmp = bj + bi[i];
1890     for  (j=0; j<nz; j++) {
1891       x = rtmp+16*ajtmp[j];
1892       x[0]  = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = x[9] = 0.0;
1893       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
1894     }
1895     /* load in initial (unfactored row) */
1896     nz       = ai[i+1] - ai[i];
1897     ajtmpold = aj + ai[i];
1898     v        = aa + 16*ai[i];
1899     for (j=0; j<nz; j++) {
1900       x    = rtmp+16*ajtmpold[j];
1901       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
1902       x[4]  = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
1903       x[9]  = v[9];  x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
1904       x[14] = v[14]; x[15] = v[15];
1905       v    += 16;
1906     }
1907     row = *ajtmp++;
1908     while (row < i) {
1909       pc  = rtmp + 16*row;
1910       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
1911       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
1912       p10 = pc[9];  p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
1913       p15 = pc[14]; p16 = pc[15];
1914       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
1915           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
1916           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
1917           || p16 != 0.0) {
1918         pv = ba + 16*diag_offset[row];
1919         pj = bj + diag_offset[row] + 1;
1920         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
1921         x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
1922         x10 = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
1923         x15 = pv[14]; x16 = pv[15];
1924         pc[0] = m1 = p1*x1 + p5*x2  + p9*x3  + p13*x4;
1925         pc[1] = m2 = p2*x1 + p6*x2  + p10*x3 + p14*x4;
1926         pc[2] = m3 = p3*x1 + p7*x2  + p11*x3 + p15*x4;
1927         pc[3] = m4 = p4*x1 + p8*x2  + p12*x3 + p16*x4;
1928 
1929         pc[4] = m5 = p1*x5 + p5*x6  + p9*x7  + p13*x8;
1930         pc[5] = m6 = p2*x5 + p6*x6  + p10*x7 + p14*x8;
1931         pc[6] = m7 = p3*x5 + p7*x6  + p11*x7 + p15*x8;
1932         pc[7] = m8 = p4*x5 + p8*x6  + p12*x7 + p16*x8;
1933 
1934         pc[8]  = m9  = p1*x9 + p5*x10  + p9*x11  + p13*x12;
1935         pc[9]  = m10 = p2*x9 + p6*x10  + p10*x11 + p14*x12;
1936         pc[10] = m11 = p3*x9 + p7*x10  + p11*x11 + p15*x12;
1937         pc[11] = m12 = p4*x9 + p8*x10  + p12*x11 + p16*x12;
1938 
1939         pc[12] = m13 = p1*x13 + p5*x14  + p9*x15  + p13*x16;
1940         pc[13] = m14 = p2*x13 + p6*x14  + p10*x15 + p14*x16;
1941         pc[14] = m15 = p3*x13 + p7*x14  + p11*x15 + p15*x16;
1942         pc[15] = m16 = p4*x13 + p8*x14  + p12*x15 + p16*x16;
1943 
1944         nz = bi[row+1] - diag_offset[row] - 1;
1945         pv += 16;
1946         for (j=0; j<nz; j++) {
1947           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
1948           x5   = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
1949           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
1950           x14  = pv[13]; x15 = pv[14]; x16 = pv[15];
1951           x    = rtmp + 16*pj[j];
1952           x[0] -= m1*x1 + m5*x2  + m9*x3  + m13*x4;
1953           x[1] -= m2*x1 + m6*x2  + m10*x3 + m14*x4;
1954           x[2] -= m3*x1 + m7*x2  + m11*x3 + m15*x4;
1955           x[3] -= m4*x1 + m8*x2  + m12*x3 + m16*x4;
1956 
1957           x[4] -= m1*x5 + m5*x6  + m9*x7  + m13*x8;
1958           x[5] -= m2*x5 + m6*x6  + m10*x7 + m14*x8;
1959           x[6] -= m3*x5 + m7*x6  + m11*x7 + m15*x8;
1960           x[7] -= m4*x5 + m8*x6  + m12*x7 + m16*x8;
1961 
1962           x[8]  -= m1*x9 + m5*x10 + m9*x11  + m13*x12;
1963           x[9]  -= m2*x9 + m6*x10 + m10*x11 + m14*x12;
1964           x[10] -= m3*x9 + m7*x10 + m11*x11 + m15*x12;
1965           x[11] -= m4*x9 + m8*x10 + m12*x11 + m16*x12;
1966 
1967           x[12] -= m1*x13 + m5*x14  + m9*x15  + m13*x16;
1968           x[13] -= m2*x13 + m6*x14  + m10*x15 + m14*x16;
1969           x[14] -= m3*x13 + m7*x14  + m11*x15 + m15*x16;
1970           x[15] -= m4*x13 + m8*x14  + m12*x15 + m16*x16;
1971 
1972           pv   += 16;
1973         }
1974         PLogFlops(128*nz+112);
1975       }
1976       row = *ajtmp++;
1977     }
1978     /* finished row so stick it into b->a */
1979     pv = ba + 16*bi[i];
1980     pj = bj + bi[i];
1981     nz = bi[i+1] - bi[i];
1982     for (j=0; j<nz; j++) {
1983       x      = rtmp+16*pj[j];
1984       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
1985       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
1986       pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
1987       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
1988       pv   += 16;
1989     }
1990     /* invert diagonal block */
1991     w = ba + 16*diag_offset[i];
1992     ierr = Kernel_A_gets_inverse_A_4(w);CHKERRQ(ierr);
1993   }
1994 
1995   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1996   C->factor    = FACTOR_LU;
1997   C->assembled = PETSC_TRUE;
1998   C->preallocated = PETSC_TRUE;
1999   PLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */
2000   PetscFunctionReturn(0);
2001 }
2002 
2003 /* Version for when blocks are 4 by 4  */
2004 #undef __FUNC__
2005 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_4"
2006 int MatCholeskyFactorNumeric_SeqSBAIJ_4(Mat A,Mat *B)
2007 {
2008   Mat                C = *B;
2009   Mat_SeqSBAIJ       *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data;
2010   IS                 perm = b->row;
2011   int                *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
2012   int                *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
2013   MatScalar          *ba = b->a,*aa,*ap,*dk,*uik;
2014   MatScalar          *u,*diag,*rtmp,*rtmp_ptr;
2015 
2016   PetscFunctionBegin;
2017   /* initialization */
2018   rtmp  = (MatScalar*)PetscMalloc(16*mbs*sizeof(MatScalar));CHKPTRQ(rtmp);
2019   ierr = PetscMemzero(rtmp,16*mbs*sizeof(MatScalar));CHKERRQ(ierr);
2020   il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il);
2021   jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl);
2022   for (i=0; i<mbs; i++) {
2023     jl[i] = mbs; il[0] = 0;
2024   }
2025   dk    = (MatScalar*)PetscMalloc(16*sizeof(MatScalar));CHKPTRQ(dk);
2026   uik   = (MatScalar*)PetscMalloc(16*sizeof(MatScalar));CHKPTRQ(uik);
2027   ierr  = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr);
2028 
2029   /* check permutation */
2030   if (!a->permute){
2031     ai = a->i; aj = a->j; aa = a->a;
2032   } else {
2033     ai = a->inew; aj = a->jnew;
2034     aa = (MatScalar*)PetscMalloc(16*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa);
2035     ierr = PetscMemcpy(aa,a->a,16*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr);
2036     a2anew  = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew);
2037     ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr);
2038 
2039     for (i=0; i<mbs; i++){
2040       jmin = ai[i]; jmax = ai[i+1];
2041       for (j=jmin; j<jmax; j++){
2042         while (a2anew[j] != j){
2043           k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k;
2044           for (k1=0; k1<16; k1++){
2045             dk[k1]       = aa[k*16+k1];
2046             aa[k*16+k1] = aa[j*16+k1];
2047             aa[j*16+k1] = dk[k1];
2048           }
2049         }
2050         /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */
2051         if (i > aj[j]){
2052           /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */
2053           ap = aa + j*16;                     /* ptr to the beginning of j-th block of aa */
2054           for (k=0; k<16; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */
2055           for (k=0; k<4; k++){               /* j-th block of aa <- dk^T */
2056             for (k1=0; k1<4; k1++) *ap++ = dk[k + 4*k1];
2057           }
2058         }
2059       }
2060     }
2061     ierr = PetscFree(a2anew);CHKERRA(ierr);
2062   }
2063 
2064   /* for each row k */
2065   for (k = 0; k<mbs; k++){
2066 
2067     /*initialize k-th row with elements nonzero in row perm(k) of A */
2068     jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1];
2069     if (jmin < jmax) {
2070       ap = aa + jmin*16;
2071       for (j = jmin; j < jmax; j++){
2072         vj = perm_ptr[aj[j]];         /* block col. index */
2073         rtmp_ptr = rtmp + vj*16;
2074         for (i=0; i<16; i++) *rtmp_ptr++ = *ap++;
2075       }
2076     }
2077 
2078     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
2079     ierr = PetscMemcpy(dk,rtmp+k*16,16*sizeof(MatScalar));CHKERRQ(ierr);
2080     i = jl[k]; /* first row to be added to k_th row  */
2081 
2082     while (i < mbs){
2083       nexti = jl[i]; /* next row to be added to k_th row */
2084 
2085       /* compute multiplier */
2086       ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
2087 
2088       /* uik = -inv(Di)*U_bar(i,k) */
2089       diag = ba + i*16;
2090       u    = ba + ili*16;
2091 
2092       uik[0] = -(diag[0]*u[0] + diag[4]*u[1] + diag[8]*u[2] + diag[12]*u[3]);
2093       uik[1] = -(diag[1]*u[0] + diag[5]*u[1] + diag[9]*u[2] + diag[13]*u[3]);
2094       uik[2] = -(diag[2]*u[0] + diag[6]*u[1] + diag[10]*u[2]+ diag[14]*u[3]);
2095       uik[3] = -(diag[3]*u[0] + diag[7]*u[1] + diag[11]*u[2]+ diag[15]*u[3]);
2096 
2097       uik[4] = -(diag[0]*u[4] + diag[4]*u[5] + diag[8]*u[6] + diag[12]*u[7]);
2098       uik[5] = -(diag[1]*u[4] + diag[5]*u[5] + diag[9]*u[6] + diag[13]*u[7]);
2099       uik[6] = -(diag[2]*u[4] + diag[6]*u[5] + diag[10]*u[6]+ diag[14]*u[7]);
2100       uik[7] = -(diag[3]*u[4] + diag[7]*u[5] + diag[11]*u[6]+ diag[15]*u[7]);
2101 
2102       uik[8] = -(diag[0]*u[8] + diag[4]*u[9] + diag[8]*u[10] + diag[12]*u[11]);
2103       uik[9] = -(diag[1]*u[8] + diag[5]*u[9] + diag[9]*u[10] + diag[13]*u[11]);
2104       uik[10]= -(diag[2]*u[8] + diag[6]*u[9] + diag[10]*u[10]+ diag[14]*u[11]);
2105       uik[11]= -(diag[3]*u[8] + diag[7]*u[9] + diag[11]*u[10]+ diag[15]*u[11]);
2106 
2107       uik[12]= -(diag[0]*u[12] + diag[4]*u[13] + diag[8]*u[14] + diag[12]*u[15]);
2108       uik[13]= -(diag[1]*u[12] + diag[5]*u[13] + diag[9]*u[14] + diag[13]*u[15]);
2109       uik[14]= -(diag[2]*u[12] + diag[6]*u[13] + diag[10]*u[14]+ diag[14]*u[15]);
2110       uik[15]= -(diag[3]*u[12] + diag[7]*u[13] + diag[11]*u[14]+ diag[15]*u[15]);
2111 
2112       /* update D(k) += -U(i,k)^T * U_bar(i,k) */
2113       dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3];
2114       dk[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3];
2115       dk[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3];
2116       dk[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3];
2117 
2118       dk[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7];
2119       dk[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7];
2120       dk[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7];
2121       dk[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7];
2122 
2123       dk[8] += uik[0]*u[8] + uik[1]*u[9] + uik[2]*u[10] + uik[3]*u[11];
2124       dk[9] += uik[4]*u[8] + uik[5]*u[9] + uik[6]*u[10] + uik[7]*u[11];
2125       dk[10]+= uik[8]*u[8] + uik[9]*u[9] + uik[10]*u[10]+ uik[11]*u[11];
2126       dk[11]+= uik[12]*u[8]+ uik[13]*u[9]+ uik[14]*u[10]+ uik[15]*u[11];
2127 
2128       dk[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15];
2129       dk[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15];
2130       dk[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15];
2131       dk[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15];
2132 
2133       /* update -U(i,k) */
2134       ierr = PetscMemcpy(ba+ili*16,uik,16*sizeof(MatScalar));CHKERRQ(ierr);
2135 
2136       /* add multiple of row i to k-th row ... */
2137       jmin = ili + 1; jmax = bi[i+1];
2138       if (jmin < jmax){
2139         for (j=jmin; j<jmax; j++) {
2140           /* rtmp += -U(i,k)^T * U_bar(i,j) */
2141           rtmp_ptr = rtmp + bj[j]*16;
2142           u = ba + j*16;
2143           rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3];
2144           rtmp_ptr[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3];
2145           rtmp_ptr[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3];
2146           rtmp_ptr[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3];
2147 
2148           rtmp_ptr[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7];
2149           rtmp_ptr[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7];
2150           rtmp_ptr[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7];
2151           rtmp_ptr[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7];
2152 
2153           rtmp_ptr[8] += uik[0]*u[8] + uik[1]*u[9] + uik[2]*u[10] + uik[3]*u[11];
2154           rtmp_ptr[9] += uik[4]*u[8] + uik[5]*u[9] + uik[6]*u[10] + uik[7]*u[11];
2155           rtmp_ptr[10]+= uik[8]*u[8] + uik[9]*u[9] + uik[10]*u[10]+ uik[11]*u[11];
2156           rtmp_ptr[11]+= uik[12]*u[8]+ uik[13]*u[9]+ uik[14]*u[10]+ uik[15]*u[11];
2157 
2158           rtmp_ptr[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15];
2159           rtmp_ptr[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15];
2160           rtmp_ptr[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15];
2161           rtmp_ptr[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15];
2162         }
2163 
2164         /* ... add i to row list for next nonzero entry */
2165         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
2166         j     = bj[jmin];
2167         jl[i] = jl[j]; jl[j] = i; /* update jl */
2168       }
2169       i = nexti;
2170     }
2171 
2172     /* save nonzero entries in k-th row of U ... */
2173 
2174     /* invert diagonal block */
2175     diag = ba+k*16;
2176     ierr = PetscMemcpy(diag,dk,16*sizeof(MatScalar));CHKERRQ(ierr);
2177     ierr = Kernel_A_gets_inverse_A_4(diag);CHKERRQ(ierr);
2178 
2179     jmin = bi[k]; jmax = bi[k+1];
2180     if (jmin < jmax) {
2181       for (j=jmin; j<jmax; j++){
2182          vj = bj[j];           /* block col. index of U */
2183          u   = ba + j*16;
2184          rtmp_ptr = rtmp + vj*16;
2185          for (k1=0; k1<16; k1++){
2186            *u++        = *rtmp_ptr;
2187            *rtmp_ptr++ = 0.0;
2188          }
2189       }
2190 
2191       /* ... add k to row list for first nonzero entry in k-th row */
2192       il[k] = jmin;
2193       i     = bj[jmin];
2194       jl[k] = jl[i]; jl[i] = k;
2195     }
2196   }
2197 
2198   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2199   ierr = PetscFree(il);CHKERRQ(ierr);
2200   ierr = PetscFree(jl);CHKERRQ(ierr);
2201   ierr = PetscFree(dk);CHKERRQ(ierr);
2202   ierr = PetscFree(uik);CHKERRQ(ierr);
2203   if (a->permute){
2204     ierr = PetscFree(aa);CHKERRQ(ierr);
2205   }
2206 
2207   ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr);
2208   C->factor    = FACTOR_CHOLESKY;
2209   C->assembled = PETSC_TRUE;
2210   C->preallocated = PETSC_TRUE;
2211   PLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */
2212   PetscFunctionReturn(0);
2213 }
2214 
2215 /* Version for when blocks are 3 by 3  */
2216 #undef __FUNC__
2217 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_3"
2218 int MatCholeskyFactorNumeric_SeqSBAIJ_3(Mat A,Mat *B)
2219 {
2220   Mat                C = *B;
2221   Mat_SeqSBAIJ       *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data;
2222   IS                 perm = b->row;
2223   int                *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
2224   int                *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
2225   MatScalar          *ba = b->a,*aa,*ap,*dk,*uik;
2226   MatScalar          *u,*diag,*rtmp,*rtmp_ptr;
2227 
2228   PetscFunctionBegin;
2229   /* initialization */
2230   rtmp  = (MatScalar*)PetscMalloc(9*mbs*sizeof(MatScalar));CHKPTRQ(rtmp);
2231   ierr = PetscMemzero(rtmp,9*mbs*sizeof(MatScalar));CHKERRQ(ierr);
2232   il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il);
2233   jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl);
2234   for (i=0; i<mbs; i++) {
2235     jl[i] = mbs; il[0] = 0;
2236   }
2237   dk  = (MatScalar*)PetscMalloc(9*sizeof(MatScalar));CHKPTRQ(dk);
2238   uik = (MatScalar*)PetscMalloc(9*sizeof(MatScalar));CHKPTRQ(uik);
2239   ierr  = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr);
2240 
2241   /* check permutation */
2242   if (!a->permute){
2243     ai = a->i; aj = a->j; aa = a->a;
2244   } else {
2245     ai = a->inew; aj = a->jnew;
2246     aa = (MatScalar*)PetscMalloc(9*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa);
2247     ierr = PetscMemcpy(aa,a->a,9*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr);
2248     a2anew  = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew);
2249     ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr);
2250 
2251     for (i=0; i<mbs; i++){
2252       jmin = ai[i]; jmax = ai[i+1];
2253       for (j=jmin; j<jmax; j++){
2254         while (a2anew[j] != j){
2255           k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k;
2256           for (k1=0; k1<9; k1++){
2257             dk[k1]       = aa[k*9+k1];
2258             aa[k*9+k1] = aa[j*9+k1];
2259             aa[j*9+k1] = dk[k1];
2260           }
2261         }
2262         /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */
2263         if (i > aj[j]){
2264           /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */
2265           ap = aa + j*9;                     /* ptr to the beginning of j-th block of aa */
2266           for (k=0; k<9; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */
2267           for (k=0; k<3; k++){               /* j-th block of aa <- dk^T */
2268             for (k1=0; k1<3; k1++) *ap++ = dk[k + 3*k1];
2269           }
2270         }
2271       }
2272     }
2273     ierr = PetscFree(a2anew);CHKERRA(ierr);
2274   }
2275 
2276   /* for each row k */
2277   for (k = 0; k<mbs; k++){
2278 
2279     /*initialize k-th row with elements nonzero in row perm(k) of A */
2280     jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1];
2281     if (jmin < jmax) {
2282       ap = aa + jmin*9;
2283       for (j = jmin; j < jmax; j++){
2284         vj = perm_ptr[aj[j]];         /* block col. index */
2285         rtmp_ptr = rtmp + vj*9;
2286         for (i=0; i<9; i++) *rtmp_ptr++ = *ap++;
2287       }
2288     }
2289 
2290     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
2291     ierr = PetscMemcpy(dk,rtmp+k*9,9*sizeof(MatScalar));CHKERRQ(ierr);
2292     i = jl[k]; /* first row to be added to k_th row  */
2293 
2294     while (i < mbs){
2295       nexti = jl[i]; /* next row to be added to k_th row */
2296 
2297       /* compute multiplier */
2298       ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
2299 
2300       /* uik = -inv(Di)*U_bar(i,k) */
2301       diag = ba + i*9;
2302       u    = ba + ili*9;
2303 
2304       uik[0] = -(diag[0]*u[0] + diag[3]*u[1] + diag[6]*u[2]);
2305       uik[1] = -(diag[1]*u[0] + diag[4]*u[1] + diag[7]*u[2]);
2306       uik[2] = -(diag[2]*u[0] + diag[5]*u[1] + diag[8]*u[2]);
2307 
2308       uik[3] = -(diag[0]*u[3] + diag[3]*u[4] + diag[6]*u[5]);
2309       uik[4] = -(diag[1]*u[3] + diag[4]*u[4] + diag[7]*u[5]);
2310       uik[5] = -(diag[2]*u[3] + diag[5]*u[4] + diag[8]*u[5]);
2311 
2312       uik[6] = -(diag[0]*u[6] + diag[3]*u[7] + diag[6]*u[8]);
2313       uik[7] = -(diag[1]*u[6] + diag[4]*u[7] + diag[7]*u[8]);
2314       uik[8] = -(diag[2]*u[6] + diag[5]*u[7] + diag[8]*u[8]);
2315 
2316       /* update D(k) += -U(i,k)^T * U_bar(i,k) */
2317       dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2];
2318       dk[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2];
2319       dk[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2];
2320 
2321       dk[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5];
2322       dk[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5];
2323       dk[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5];
2324 
2325       dk[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8];
2326       dk[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8];
2327       dk[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8];
2328 
2329       /* update -U(i,k) */
2330       ierr = PetscMemcpy(ba+ili*9,uik,9*sizeof(MatScalar));CHKERRQ(ierr);
2331 
2332       /* add multiple of row i to k-th row ... */
2333       jmin = ili + 1; jmax = bi[i+1];
2334       if (jmin < jmax){
2335         for (j=jmin; j<jmax; j++) {
2336           /* rtmp += -U(i,k)^T * U_bar(i,j) */
2337           rtmp_ptr = rtmp + bj[j]*9;
2338           u = ba + j*9;
2339           rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2];
2340           rtmp_ptr[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2];
2341           rtmp_ptr[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2];
2342 
2343           rtmp_ptr[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5];
2344           rtmp_ptr[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5];
2345           rtmp_ptr[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5];
2346 
2347           rtmp_ptr[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8];
2348           rtmp_ptr[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8];
2349           rtmp_ptr[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8];
2350         }
2351 
2352         /* ... add i to row list for next nonzero entry */
2353         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
2354         j     = bj[jmin];
2355         jl[i] = jl[j]; jl[j] = i; /* update jl */
2356       }
2357       i = nexti;
2358     }
2359 
2360     /* save nonzero entries in k-th row of U ... */
2361 
2362     /* invert diagonal block */
2363     diag = ba+k*9;
2364     ierr = PetscMemcpy(diag,dk,9*sizeof(MatScalar));CHKERRQ(ierr);
2365     ierr = Kernel_A_gets_inverse_A_3(diag);CHKERRQ(ierr);
2366 
2367     jmin = bi[k]; jmax = bi[k+1];
2368     if (jmin < jmax) {
2369       for (j=jmin; j<jmax; j++){
2370          vj = bj[j];           /* block col. index of U */
2371          u   = ba + j*9;
2372          rtmp_ptr = rtmp + vj*9;
2373          for (k1=0; k1<9; k1++){
2374            *u++        = *rtmp_ptr;
2375            *rtmp_ptr++ = 0.0;
2376          }
2377       }
2378 
2379       /* ... add k to row list for first nonzero entry in k-th row */
2380       il[k] = jmin;
2381       i     = bj[jmin];
2382       jl[k] = jl[i]; jl[i] = k;
2383     }
2384   }
2385 
2386   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2387   ierr = PetscFree(il);CHKERRQ(ierr);
2388   ierr = PetscFree(jl);CHKERRQ(ierr);
2389   ierr = PetscFree(dk);CHKERRQ(ierr);
2390   ierr = PetscFree(uik);CHKERRQ(ierr);
2391   if (a->permute){
2392     ierr = PetscFree(aa);CHKERRQ(ierr);
2393   }
2394 
2395   ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr);
2396   C->factor    = FACTOR_CHOLESKY;
2397   C->assembled = PETSC_TRUE;
2398   C->preallocated = PETSC_TRUE;
2399   PLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */
2400   PetscFunctionReturn(0);
2401 }
2402 
2403 /*
2404       Version for when blocks are 3 by 3 Using natural ordering
2405 */
2406 #undef __FUNC__
2407 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_3_NaturalOrdering"
2408 int MatCholeskyFactorNumeric_SeqSBAIJ_3_NaturalOrdering(Mat A,Mat *B)
2409 {
2410   Mat                C = *B;
2411   Mat_SeqBAIJ        *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
2412   int                ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
2413   int                *ajtmpold,*ajtmp,nz,row;
2414   int                *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
2415   MatScalar          *pv,*v,*rtmp,*pc,*w,*x;
2416   MatScalar          p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
2417   MatScalar          p5,p6,p7,p8,p9,x5,x6,x7,x8,x9;
2418   MatScalar          *ba = b->a,*aa = a->a;
2419 
2420   PetscFunctionBegin;
2421   rtmp  = (MatScalar*)PetscMalloc(9*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
2422 
2423   for (i=0; i<n; i++) {
2424     nz    = bi[i+1] - bi[i];
2425     ajtmp = bj + bi[i];
2426     for  (j=0; j<nz; j++) {
2427       x = rtmp+9*ajtmp[j];
2428       x[0]  = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = 0.0;
2429     }
2430     /* load in initial (unfactored row) */
2431     nz       = ai[i+1] - ai[i];
2432     ajtmpold = aj + ai[i];
2433     v        = aa + 9*ai[i];
2434     for (j=0; j<nz; j++) {
2435       x    = rtmp+9*ajtmpold[j];
2436       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
2437       x[4]  = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
2438       v    += 9;
2439     }
2440     row = *ajtmp++;
2441     while (row < i) {
2442       pc  = rtmp + 9*row;
2443       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
2444       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
2445       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
2446           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0) {
2447         pv = ba + 9*diag_offset[row];
2448         pj = bj + diag_offset[row] + 1;
2449         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
2450         x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
2451         pc[0] = m1 = p1*x1 + p4*x2 + p7*x3;
2452         pc[1] = m2 = p2*x1 + p5*x2 + p8*x3;
2453         pc[2] = m3 = p3*x1 + p6*x2 + p9*x3;
2454 
2455         pc[3] = m4 = p1*x4 + p4*x5 + p7*x6;
2456         pc[4] = m5 = p2*x4 + p5*x5 + p8*x6;
2457         pc[5] = m6 = p3*x4 + p6*x5 + p9*x6;
2458 
2459         pc[6] = m7 = p1*x7 + p4*x8 + p7*x9;
2460         pc[7] = m8 = p2*x7 + p5*x8 + p8*x9;
2461         pc[8] = m9 = p3*x7 + p6*x8 + p9*x9;
2462 
2463         nz = bi[row+1] - diag_offset[row] - 1;
2464         pv += 9;
2465         for (j=0; j<nz; j++) {
2466           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
2467           x5   = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
2468           x    = rtmp + 9*pj[j];
2469           x[0] -= m1*x1 + m4*x2 + m7*x3;
2470           x[1] -= m2*x1 + m5*x2 + m8*x3;
2471           x[2] -= m3*x1 + m6*x2 + m9*x3;
2472 
2473           x[3] -= m1*x4 + m4*x5 + m7*x6;
2474           x[4] -= m2*x4 + m5*x5 + m8*x6;
2475           x[5] -= m3*x4 + m6*x5 + m9*x6;
2476 
2477           x[6] -= m1*x7 + m4*x8 + m7*x9;
2478           x[7] -= m2*x7 + m5*x8 + m8*x9;
2479           x[8] -= m3*x7 + m6*x8 + m9*x9;
2480           pv   += 9;
2481         }
2482         PLogFlops(54*nz+36);
2483       }
2484       row = *ajtmp++;
2485     }
2486     /* finished row so stick it into b->a */
2487     pv = ba + 9*bi[i];
2488     pj = bj + bi[i];
2489     nz = bi[i+1] - bi[i];
2490     for (j=0; j<nz; j++) {
2491       x      = rtmp+9*pj[j];
2492       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
2493       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
2494       pv   += 9;
2495     }
2496     /* invert diagonal block */
2497     w = ba + 9*diag_offset[i];
2498     ierr = Kernel_A_gets_inverse_A_3(w);CHKERRQ(ierr);
2499   }
2500 
2501   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2502   C->factor    = FACTOR_CHOLESKY;
2503   C->assembled = PETSC_TRUE;
2504   C->preallocated = PETSC_TRUE;
2505   PLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */
2506   PetscFunctionReturn(0);
2507 }
2508 
2509 /*
2510     Numeric U^T*D*U factorization for SBAIJ format. Modified from SNF of YSMP.
2511     Version for blocks 2 by 2.
2512 */
2513 #undef __FUNC__
2514 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_2"
2515 int MatCholeskyFactorNumeric_SeqSBAIJ_2(Mat A,Mat *B)
2516 {
2517   Mat                C = *B;
2518   Mat_SeqSBAIJ       *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data;
2519   IS                 perm = b->row;
2520   int                *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
2521   int                *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
2522   MatScalar          *ba = b->a,*aa,*ap,*dk,*uik;
2523   MatScalar          *u,*diag,*rtmp,*rtmp_ptr;
2524 
2525   PetscFunctionBegin;
2526 
2527   /* initialization */
2528   /* il and jl record the first nonzero element in each row of the accessing
2529      window U(0:k, k:mbs-1).
2530      jl:    list of rows to be added to uneliminated rows
2531             i>= k: jl(i) is the first row to be added to row i
2532             i<  k: jl(i) is the row following row i in some list of rows
2533             jl(i) = mbs indicates the end of a list
2534      il(i): points to the first nonzero element in columns k,...,mbs-1 of
2535             row i of U */
2536   rtmp  = (MatScalar*)PetscMalloc(4*mbs*sizeof(MatScalar));CHKPTRQ(rtmp);
2537   ierr = PetscMemzero(rtmp,4*mbs*sizeof(MatScalar));CHKERRQ(ierr);
2538   il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il);
2539   jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl);
2540   for (i=0; i<mbs; i++) {
2541     jl[i] = mbs; il[0] = 0;
2542   }
2543   dk  = (MatScalar*)PetscMalloc(4*sizeof(MatScalar));CHKPTRQ(dk);
2544   uik = (MatScalar*)PetscMalloc(4*sizeof(MatScalar));CHKPTRQ(uik);
2545   ierr  = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr);
2546 
2547   /* check permutation */
2548   if (!a->permute){
2549     ai = a->i; aj = a->j; aa = a->a;
2550   } else {
2551     ai = a->inew; aj = a->jnew;
2552     aa = (MatScalar*)PetscMalloc(4*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa);
2553     ierr = PetscMemcpy(aa,a->a,4*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr);
2554     a2anew  = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew);
2555     ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr);
2556 
2557     for (i=0; i<mbs; i++){
2558       jmin = ai[i]; jmax = ai[i+1];
2559       for (j=jmin; j<jmax; j++){
2560         while (a2anew[j] != j){
2561           k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k;
2562           for (k1=0; k1<4; k1++){
2563             dk[k1]       = aa[k*4+k1];
2564             aa[k*4+k1] = aa[j*4+k1];
2565             aa[j*4+k1] = dk[k1];
2566           }
2567         }
2568         /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */
2569         if (i > aj[j]){
2570           /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */
2571           ap = aa + j*4;     /* ptr to the beginning of the block */
2572           dk[1] = ap[1];     /* swap ap[1] and ap[2] */
2573           ap[1] = ap[2];
2574           ap[2] = dk[1];
2575         }
2576       }
2577     }
2578     ierr = PetscFree(a2anew);CHKERRA(ierr);
2579   }
2580 
2581   /* for each row k */
2582   for (k = 0; k<mbs; k++){
2583 
2584     /*initialize k-th row with elements nonzero in row perm(k) of A */
2585     jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1];
2586     if (jmin < jmax) {
2587       ap = aa + jmin*4;
2588       for (j = jmin; j < jmax; j++){
2589         vj = perm_ptr[aj[j]];         /* block col. index */
2590         rtmp_ptr = rtmp + vj*4;
2591         for (i=0; i<4; i++) *rtmp_ptr++ = *ap++;
2592       }
2593     }
2594 
2595     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
2596     ierr = PetscMemcpy(dk,rtmp+k*4,4*sizeof(MatScalar));CHKERRQ(ierr);
2597     i = jl[k]; /* first row to be added to k_th row  */
2598 
2599     while (i < mbs){
2600       nexti = jl[i]; /* next row to be added to k_th row */
2601 
2602       /* compute multiplier */
2603       ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
2604 
2605       /* uik = -inv(Di)*U_bar(i,k): - ba[ili]*ba[i] */
2606       diag = ba + i*4;
2607       u    = ba + ili*4;
2608       uik[0] = -(diag[0]*u[0] + diag[2]*u[1]);
2609       uik[1] = -(diag[1]*u[0] + diag[3]*u[1]);
2610       uik[2] = -(diag[0]*u[2] + diag[2]*u[3]);
2611       uik[3] = -(diag[1]*u[2] + diag[3]*u[3]);
2612 
2613       /* update D(k) += -U(i,k)^T * U_bar(i,k): dk += uik*ba[ili] */
2614       dk[0] += uik[0]*u[0] + uik[1]*u[1];
2615       dk[1] += uik[2]*u[0] + uik[3]*u[1];
2616       dk[2] += uik[0]*u[2] + uik[1]*u[3];
2617       dk[3] += uik[2]*u[2] + uik[3]*u[3];
2618 
2619       /* update -U(i,k): ba[ili] = uik */
2620       ierr = PetscMemcpy(ba+ili*4,uik,4*sizeof(MatScalar));CHKERRQ(ierr);
2621 
2622       /* add multiple of row i to k-th row ... */
2623       jmin = ili + 1; jmax = bi[i+1];
2624       if (jmin < jmax){
2625         for (j=jmin; j<jmax; j++) {
2626           /* rtmp += -U(i,k)^T * U_bar(i,j): rtmp[bj[j]] += uik*ba[j]; */
2627           rtmp_ptr = rtmp + bj[j]*4;
2628           u = ba + j*4;
2629           rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1];
2630           rtmp_ptr[1] += uik[2]*u[0] + uik[3]*u[1];
2631           rtmp_ptr[2] += uik[0]*u[2] + uik[1]*u[3];
2632           rtmp_ptr[3] += uik[2]*u[2] + uik[3]*u[3];
2633         }
2634 
2635         /* ... add i to row list for next nonzero entry */
2636         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
2637         j     = bj[jmin];
2638         jl[i] = jl[j]; jl[j] = i; /* update jl */
2639       }
2640       i = nexti;
2641     }
2642 
2643     /* save nonzero entries in k-th row of U ... */
2644 
2645     /* invert diagonal block */
2646     diag = ba+k*4;
2647     ierr = PetscMemcpy(diag,dk,4*sizeof(MatScalar));CHKERRQ(ierr);
2648     ierr = Kernel_A_gets_inverse_A_2(diag);CHKERRQ(ierr);
2649 
2650     jmin = bi[k]; jmax = bi[k+1];
2651     if (jmin < jmax) {
2652       for (j=jmin; j<jmax; j++){
2653          vj = bj[j];           /* block col. index of U */
2654          u   = ba + j*4;
2655          rtmp_ptr = rtmp + vj*4;
2656          for (k1=0; k1<4; k1++){
2657            *u++        = *rtmp_ptr;
2658            *rtmp_ptr++ = 0.0;
2659          }
2660       }
2661 
2662       /* ... add k to row list for first nonzero entry in k-th row */
2663       il[k] = jmin;
2664       i     = bj[jmin];
2665       jl[k] = jl[i]; jl[i] = k;
2666     }
2667   }
2668 
2669   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2670   ierr = PetscFree(il);CHKERRQ(ierr);
2671   ierr = PetscFree(jl);CHKERRQ(ierr);
2672   ierr = PetscFree(dk);CHKERRQ(ierr);
2673   ierr = PetscFree(uik);CHKERRQ(ierr);
2674   if (a->permute) {
2675     ierr = PetscFree(aa);CHKERRQ(ierr);
2676   }
2677   ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr);
2678   C->factor    = FACTOR_CHOLESKY;
2679   C->assembled = PETSC_TRUE;
2680   C->preallocated = PETSC_TRUE;
2681   PLogFlops(1.3333*8*b->mbs); /* from inverting diagonal blocks */
2682   PetscFunctionReturn(0);
2683 }
2684 
2685 /*
2686       Version for when blocks are 2 by 2 Using natural ordering
2687 */
2688 #undef __FUNC__
2689 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_2_NaturalOrdering"
2690 int MatCholeskyFactorNumeric_SeqSBAIJ_2_NaturalOrdering(Mat A,Mat *B)
2691 {
2692   Mat                C = *B;
2693   Mat_SeqBAIJ        *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
2694   int                ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
2695   int                *ajtmpold,*ajtmp,nz,row;
2696   int                *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
2697   MatScalar          *pv,*v,*rtmp,*pc,*w,*x;
2698   MatScalar          p1,p2,p3,p4,m1,m2,m3,m4,x1,x2,x3,x4;
2699   MatScalar          *ba = b->a,*aa = a->a;
2700 
2701   PetscFunctionBegin;
2702   rtmp  = (MatScalar*)PetscMalloc(4*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
2703 
2704   for (i=0; i<n; i++) {
2705     nz    = bi[i+1] - bi[i];
2706     ajtmp = bj + bi[i];
2707     for  (j=0; j<nz; j++) {
2708       x = rtmp+4*ajtmp[j];
2709       x[0]  = x[1]  = x[2]  = x[3]  = 0.0;
2710     }
2711     /* load in initial (unfactored row) */
2712     nz       = ai[i+1] - ai[i];
2713     ajtmpold = aj + ai[i];
2714     v        = aa + 4*ai[i];
2715     for (j=0; j<nz; j++) {
2716       x    = rtmp+4*ajtmpold[j];
2717       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
2718       v    += 4;
2719     }
2720     row = *ajtmp++;
2721     while (row < i) {
2722       pc  = rtmp + 4*row;
2723       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
2724       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0) {
2725         pv = ba + 4*diag_offset[row];
2726         pj = bj + diag_offset[row] + 1;
2727         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
2728         pc[0] = m1 = p1*x1 + p3*x2;
2729         pc[1] = m2 = p2*x1 + p4*x2;
2730         pc[2] = m3 = p1*x3 + p3*x4;
2731         pc[3] = m4 = p2*x3 + p4*x4;
2732         nz = bi[row+1] - diag_offset[row] - 1;
2733         pv += 4;
2734         for (j=0; j<nz; j++) {
2735           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
2736           x    = rtmp + 4*pj[j];
2737           x[0] -= m1*x1 + m3*x2;
2738           x[1] -= m2*x1 + m4*x2;
2739           x[2] -= m1*x3 + m3*x4;
2740           x[3] -= m2*x3 + m4*x4;
2741           pv   += 4;
2742         }
2743         PLogFlops(16*nz+12);
2744       }
2745       row = *ajtmp++;
2746     }
2747     /* finished row so stick it into b->a */
2748     pv = ba + 4*bi[i];
2749     pj = bj + bi[i];
2750     nz = bi[i+1] - bi[i];
2751     for (j=0; j<nz; j++) {
2752       x      = rtmp+4*pj[j];
2753       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
2754       pv   += 4;
2755     }
2756     /* invert diagonal block */
2757     w = ba + 4*diag_offset[i];
2758     ierr = Kernel_A_gets_inverse_A_2(w);CHKERRQ(ierr);
2759   }
2760 
2761   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2762   C->factor    = FACTOR_LU;
2763   C->assembled = PETSC_TRUE;
2764   C->preallocated = PETSC_TRUE;
2765   PLogFlops(1.3333*8*b->mbs); /* from inverting diagonal blocks */
2766   PetscFunctionReturn(0);
2767 }
2768 
2769 /*
2770     Numeric U^T*D*U factorization for SBAIJ format. Modified from SNF of YSMP.
2771     Version for blocks are 1 by 1.
2772 */
2773 #undef __FUNC__
2774 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_1"
2775 int MatCholeskyFactorNumeric_SeqSBAIJ_1(Mat A,Mat *B)
2776 {
2777   Mat                C = *B;
2778   Mat_SeqSBAIJ       *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data;
2779   IS                 ip = b->row;
2780   int                *rip,ierr,i,j,mbs = a->mbs,*bi = b->i,*bj = b->j;
2781   int                *ai,*aj,*r;
2782   MatScalar          *rtmp;
2783   MatScalar          *ba = b->a,*aa,ak;
2784   MatScalar          dk,uikdi;
2785   int                k,jmin,jmax,*jl,*il,vj,nexti,ili;
2786 
2787   PetscFunctionBegin;
2788   ierr  = ISGetIndices(ip,&rip);CHKERRQ(ierr);
2789   if (!a->permute){
2790     ai = a->i; aj = a->j; aa = a->a;
2791   } else {
2792     ai = a->inew; aj = a->jnew;
2793     aa = (MatScalar*)PetscMalloc(ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa);
2794     ierr = PetscMemcpy(aa,a->a,ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr);
2795     r   = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(r);
2796     ierr= PetscMemcpy(r,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr);
2797 
2798     jmin = ai[0]; jmax = ai[mbs];
2799     for (j=jmin; j<jmax; j++){
2800       while (r[j] != j){
2801         k = r[j]; r[j] = r[k]; r[k] = k;
2802         ak = aa[k]; aa[k] = aa[j]; aa[j] = ak;
2803       }
2804     }
2805     ierr = PetscFree(r);CHKERRA(ierr);
2806   }
2807 
2808   /* initialization */
2809   /* il and jl record the first nonzero element in each row of the accessing
2810      window U(0:k, k:mbs-1).
2811      jl:    list of rows to be added to uneliminated rows
2812             i>= k: jl(i) is the first row to be added to row i
2813             i<  k: jl(i) is the row following row i in some list of rows
2814             jl(i) = mbs indicates the end of a list
2815      il(i): points to the first nonzero element in columns k,...,mbs-1 of
2816             row i of U */
2817   rtmp  = (MatScalar*)PetscMalloc(mbs*sizeof(MatScalar));CHKPTRQ(rtmp);
2818   il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il);
2819   jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl);
2820   for (i=0; i<mbs; i++) {
2821     rtmp[i] = 0.0; jl[i] = mbs; il[0] = 0;
2822   }
2823 
2824   /* for each row k */
2825   for (k = 0; k<mbs; k++){
2826 
2827     /*initialize k-th row with elements nonzero in row perm(k) of A */
2828     jmin = ai[rip[k]]; jmax = ai[rip[k]+1];
2829     if (jmin < jmax) {
2830       for (j = jmin; j < jmax; j++){
2831         vj = rip[aj[j]];
2832         /* if (k <= vj)*/ rtmp[vj] = aa[j];
2833       }
2834     }
2835 
2836     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
2837     dk = rtmp[k];
2838     i = jl[k]; /* first row to be added to k_th row  */
2839     /* printf(" k=%d, pivot row = %d\n",k,i); */
2840 
2841     while (i < mbs){
2842       nexti = jl[i]; /* next row to be added to k_th row */
2843 
2844       /* compute multiplier, update D(k) and U(i,k) */
2845       ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
2846       uikdi = - ba[ili]*ba[i];
2847       dk += uikdi*ba[ili];
2848       ba[ili] = uikdi; /* -U(i,k) */
2849 
2850       /* add multiple of row i to k-th row ... */
2851       jmin = ili + 1; jmax = bi[i+1];
2852       if (jmin < jmax){
2853         for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j];
2854         /* ... add i to row list for next nonzero entry */
2855         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
2856         j     = bj[jmin];
2857         jl[i] = jl[j]; jl[j] = i; /* update jl */
2858       }
2859       i = nexti; /* printf("                  pivot row i=%d\n",i);  */
2860     }
2861 
2862     /* check for zero pivot and save diagoanl element */
2863     if (dk == 0.0){
2864       SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot");
2865     }else if (PetscRealPart(dk) < 0){
2866       ierr = PetscPrintf(PETSC_COMM_SELF,"Negative pivot: d[%d] = %g\n",k,dk);
2867     }
2868 
2869     /* save nonzero entries in k-th row of U ... */
2870     ba[k] = 1.0/dk;
2871     jmin = bi[k]; jmax = bi[k+1];
2872     if (jmin < jmax) {
2873       for (j=jmin; j<jmax; j++){
2874          vj = bj[j]; ba[j] = rtmp[vj]; rtmp[vj] = 0.0;
2875       }
2876       /* ... add k to row list for first nonzero entry in k-th row */
2877       il[k] = jmin;
2878       i     = bj[jmin];
2879       jl[k] = jl[i]; jl[i] = k;
2880     }
2881   }
2882 
2883   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2884   ierr = PetscFree(il);CHKERRQ(ierr);
2885   ierr = PetscFree(jl);CHKERRQ(ierr);
2886   if (a->permute){
2887     ierr = PetscFree(aa);CHKERRQ(ierr);
2888   }
2889 
2890   ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr);
2891   C->factor    = FACTOR_CHOLESKY;
2892   C->assembled = PETSC_TRUE;
2893   C->preallocated = PETSC_TRUE;
2894   PLogFlops(b->mbs);
2895   PetscFunctionReturn(0);
2896 }
2897 
2898 #undef __FUNC__
2899 #define __FUNC__ "MatCholeskyFactor_SeqSBAIJ"
2900 int MatCholeskyFactor_SeqSBAIJ(Mat A,IS perm,PetscReal f)
2901 {
2902   int ierr;
2903   Mat C;
2904 
2905   PetscFunctionBegin;
2906   ierr = MatCholeskyFactorSymbolic(A,perm,f,&C);CHKERRQ(ierr);
2907   ierr = MatCholeskyFactorNumeric(A,&C);CHKERRQ(ierr);
2908   ierr = MatHeaderCopy(A,C);CHKERRQ(ierr);
2909   PetscFunctionReturn(0);
2910 }
2911 
2912 
2913