xref: /petsc/src/mat/impls/sbaij/seq/sbaijfact.c (revision 4c16a6a63b3f0cb96e981be782baf6b5e67536a1)
1 /* Using Modified Sparse Row (MSR) storage.
2 See page 85, "Iterative Methods ..." by Saad. */
3 
4 /*$Id: sbaijfact.c,v 1.40 2000/11/01 16:46:00 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   /* initialization */
211   printf("called MatCholeskyFactorNumeric_SeqSBAIJ_N \n");
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 #ifdef OLD
362   Mat                C = *B;
363   Mat_SeqBAIJ        *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
364   IS                 isrow = b->row,isicol = b->icol;
365   int                *r,*ic,ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
366   int                *ajtmpold,*ajtmp,nz,row,bslog,*ai=a->i,*aj=a->j,k,flg;
367   int                *diag_offset=b->diag,diag,bs=a->bs,bs2 = a->bs2,*v_pivots,*pj;
368   MatScalar          *ba = b->a,*aa = a->a,*pv,*v,*rtmp,*multiplier,*v_work,*pc,*w;
369 
370   PetscFunctionBegin;
371   printf("called MatCholeskyFactorNumeric_SeqSBAIJ_N \n");
372   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
373   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
374   rtmp = (MatScalar*)PetscMalloc(bs2*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
375   ierr = PetscMemzero(rtmp,bs2*(n+1)*sizeof(MatScalar));CHKERRQ(ierr);
376   /* generate work space needed by dense LU factorization */
377   v_work     = (MatScalar*)PetscMalloc(bs*sizeof(int) + (bs+bs2)*sizeof(MatScalar));CHKPTRQ(v_work);
378   multiplier = v_work + bs;
379   v_pivots   = (int*)(multiplier + bs2);
380 
381   /* flops in while loop */
382   bslog = 2*bs*bs2;
383 
384   for (i=0; i<n; i++) {
385     nz    = bi[i+1] - bi[i];
386     ajtmp = bj + bi[i];
387     for  (j=0; j<nz; j++) {
388       ierr = PetscMemzero(rtmp+bs2*ajtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
389     }
390     /* load in initial (unfactored row) */
391     nz       = ai[r[i]+1] - ai[r[i]];
392     ajtmpold = aj + ai[r[i]];
393     v        = aa + bs2*ai[r[i]];
394     for (j=0; j<nz; j++) {
395       ierr = PetscMemcpy(rtmp+bs2*ic[ajtmpold[j]],v+bs2*j,bs2*sizeof(MatScalar));CHKERRQ(ierr);
396     }
397     row = *ajtmp++;
398     while (row < i) {
399       pc = rtmp + bs2*row;
400 /*      if (*pc) { */
401       for (flg=0,k=0; k<bs2; k++) { if (pc[k]!=0.0) { flg =1; break; }}
402       if (flg) {
403         pv = ba + bs2*diag_offset[row];
404         pj = bj + diag_offset[row] + 1;
405         Kernel_A_gets_A_times_B(bs,pc,pv,multiplier);
406         nz = bi[row+1] - diag_offset[row] - 1;
407         pv += bs2;
408         for (j=0; j<nz; j++) {
409           Kernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j);
410         }
411         PLogFlops(bslog*(nz+1)-bs);
412       }
413         row = *ajtmp++;
414     }
415     /* finished row so stick it into b->a */
416     pv = ba + bs2*bi[i];
417     pj = bj + bi[i];
418     nz = bi[i+1] - bi[i];
419     for (j=0; j<nz; j++) {
420       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
421     }
422     diag = diag_offset[i] - bi[i];
423     /* invert diagonal block */
424     w = pv + bs2*diag;
425     Kernel_A_gets_inverse_A(bs,w,v_pivots,v_work);
426   }
427 
428   ierr = PetscFree(rtmp);CHKERRQ(ierr);
429   ierr = PetscFree(v_work);CHKERRQ(ierr);
430   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
431   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
432   C->factor = FACTOR_LU;
433   C->assembled = PETSC_TRUE;
434 #endif
435 
436 /* Version for when blocks are 7 by 7 */
437 #undef __FUNC__
438 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_7"
439 int MatCholeskyFactorNumeric_SeqSBAIJ_7(Mat A,Mat *B)
440 {
441   Mat                C = *B;
442   Mat_SeqSBAIJ       *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data;
443   IS                 perm = b->row;
444   int                *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
445   int                *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
446   MatScalar          *ba = b->a,*aa,*ap,*dk,*uik;
447   MatScalar          *u,*d,*w,*wp;
448 
449   PetscFunctionBegin;
450   /* initialization */
451   printf("called MatCholeskyFactorNumeric_SeqSBAIJ_7 \n");
452   w  = (MatScalar*)PetscMalloc(49*mbs*sizeof(MatScalar));CHKPTRQ(w);
453   ierr = PetscMemzero(w,49*mbs*sizeof(MatScalar));CHKERRQ(ierr);
454   il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il);
455   jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl);
456   for (i=0; i<mbs; i++) {
457     jl[i] = mbs; il[0] = 0;
458   }
459   dk    = (MatScalar*)PetscMalloc(49*sizeof(MatScalar));CHKPTRQ(dk);
460   uik   = (MatScalar*)PetscMalloc(49*sizeof(MatScalar));CHKPTRQ(uik);
461   ierr  = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr);
462 
463   /* check permutation */
464   if (!a->permute){
465     ai = a->i; aj = a->j; aa = a->a;
466   } else {
467     ai = a->inew; aj = a->jnew;
468     aa = (MatScalar*)PetscMalloc(49*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa);
469     ierr = PetscMemcpy(aa,a->a,49*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr);
470     a2anew  = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew);
471     ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr);
472 
473     for (i=0; i<mbs; i++){
474       jmin = ai[i]; jmax = ai[i+1];
475       for (j=jmin; j<jmax; j++){
476         while (a2anew[j] != j){
477           k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k;
478           for (k1=0; k1<49; k1++){
479             dk[k1]       = aa[k*49+k1];
480             aa[k*49+k1] = aa[j*49+k1];
481             aa[j*49+k1] = dk[k1];
482           }
483         }
484         /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */
485         if (i > aj[j]){
486           /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */
487           ap = aa + j*49;                     /* ptr to the beginning of j-th block of aa */
488           for (k=0; k<49; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */
489           for (k=0; k<7; k++){               /* j-th block of aa <- dk^T */
490             for (k1=0; k1<7; k1++) *ap++ = dk[k + 7*k1];
491           }
492         }
493       }
494     }
495     ierr = PetscFree(a2anew);CHKERRA(ierr);
496   }
497 
498   /* for each row k */
499   for (k = 0; k<mbs; k++){
500 
501     /*initialize k-th row with elements nonzero in row perm(k) of A */
502     jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1];
503     if (jmin < jmax) {
504       ap = aa + jmin*49;
505       for (j = jmin; j < jmax; j++){
506         vj = perm_ptr[aj[j]];         /* block col. index */
507         wp = w + vj*49;
508         for (i=0; i<49; i++) *wp++ = *ap++;
509       }
510     }
511 
512     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
513     ierr = PetscMemcpy(dk,w+k*49,49*sizeof(MatScalar));CHKERRQ(ierr);
514     i = jl[k]; /* first row to be added to k_th row  */
515 
516     while (i < mbs){
517       nexti = jl[i]; /* next row to be added to k_th row */
518 
519       /* compute multiplier */
520       ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
521 
522       /* uik = -inv(Di)*U_bar(i,k) */
523       d = ba + i*49;
524       u    = ba + ili*49;
525 
526       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]);
527       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]);
528       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]);
529       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]);
530       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]);
531       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]);
532       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]);
533 
534       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]);
535       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]);
536       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]);
537       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]);
538       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]);
539       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]);
540       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]);
541 
542       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]);
543       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]);
544       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]);
545       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]);
546       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]);
547       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]);
548       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]);
549 
550       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]);
551       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]);
552       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]);
553       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]);
554       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]);
555       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]);
556       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]);
557 
558       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]);
559       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]);
560       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]);
561       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]);
562       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]);
563       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]);
564       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]);
565 
566       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]);
567       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]);
568       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]);
569       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]);
570       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]);
571       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]);
572       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]);
573 
574       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]);
575       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]);
576       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]);
577       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]);
578       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]);
579       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]);
580       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]);
581 
582       /* update D(k) += -U(i,k)^T * U_bar(i,k) */
583       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];
584       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];
585       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];
586       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];
587       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];
588       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];
589       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];
590 
591       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];
592       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];
593       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];
594       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];
595       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];
596       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];
597       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];
598 
599       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];
600       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];
601       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];
602       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];
603       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];
604       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];
605       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];
606 
607       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];
608       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];
609       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];
610       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];
611       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];
612       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];
613       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];
614 
615       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];
616       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];
617       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];
618       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];
619       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];
620       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];
621       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];
622 
623       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];
624       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];
625       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];
626       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];
627       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];
628       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];
629       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];
630 
631       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];
632       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];
633       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];
634       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];
635       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];
636       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];
637       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];
638 
639       /* update -U(i,k) */
640       ierr = PetscMemcpy(ba+ili*49,uik,49*sizeof(MatScalar));CHKERRQ(ierr);
641 
642       /* add multiple of row i to k-th row ... */
643       jmin = ili + 1; jmax = bi[i+1];
644       if (jmin < jmax){
645         for (j=jmin; j<jmax; j++) {
646           /* w += -U(i,k)^T * U_bar(i,j) */
647           wp = w + bj[j]*49;
648           u = ba + j*49;
649 
650           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];
651           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];
652           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];
653           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];
654           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];
655           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];
656           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];
657 
658           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];
659           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];
660           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];
661           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];
662           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];
663           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];
664           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];
665 
666           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];
667           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];
668           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];
669           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];
670           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];
671           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];
672           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];
673 
674           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];
675           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];
676           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];
677           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];
678           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];
679           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];
680           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];
681 
682           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];
683           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];
684           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];
685           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];
686           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];
687           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];
688           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];
689 
690           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];
691           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];
692           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];
693           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];
694           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];
695           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];
696           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];
697 
698           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];
699           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];
700           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];
701           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];
702           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];
703           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];
704           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];
705         }
706 
707         /* ... add i to row list for next nonzero entry */
708         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
709         j     = bj[jmin];
710         jl[i] = jl[j]; jl[j] = i; /* update jl */
711       }
712       i = nexti;
713     }
714 
715     /* save nonzero entries in k-th row of U ... */
716 
717     /* invert diagonal block */
718     d = ba+k*49;
719     ierr = PetscMemcpy(d,dk,49*sizeof(MatScalar));CHKERRQ(ierr);
720     ierr = Kernel_A_gets_inverse_A_7(d);CHKERRQ(ierr);
721 
722     jmin = bi[k]; jmax = bi[k+1];
723     if (jmin < jmax) {
724       for (j=jmin; j<jmax; j++){
725          vj = bj[j];           /* block col. index of U */
726          u   = ba + j*49;
727          wp = w + vj*49;
728          for (k1=0; k1<49; k1++){
729            *u++        = *wp;
730            *wp++ = 0.0;
731          }
732       }
733 
734       /* ... add k to row list for first nonzero entry in k-th row */
735       il[k] = jmin;
736       i     = bj[jmin];
737       jl[k] = jl[i]; jl[i] = k;
738     }
739   }
740 
741   ierr = PetscFree(w);CHKERRQ(ierr);
742   ierr = PetscFree(il);CHKERRQ(ierr);
743   ierr = PetscFree(jl);CHKERRQ(ierr);
744   ierr = PetscFree(dk);CHKERRQ(ierr);
745   ierr = PetscFree(uik);CHKERRQ(ierr);
746   if (a->permute){
747     ierr = PetscFree(aa);CHKERRQ(ierr);
748   }
749 
750   ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr);
751   C->factor    = FACTOR_CHOLESKY;
752   C->assembled = PETSC_TRUE;
753   C->preallocated = PETSC_TRUE;
754   PLogFlops(1.3333*343*b->mbs); /* from inverting diagonal blocks */
755   PetscFunctionReturn(0);
756 }
757 
758 /*
759       Version for when blocks are 7 by 7 Using natural ordering
760 */
761 #undef __FUNC__
762 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_7_NaturalOrdering"
763 int MatCholeskyFactorNumeric_SeqSBAIJ_7_NaturalOrdering(Mat A,Mat *B)
764 {
765   Mat          C = *B;
766   Mat_SeqBAIJ  *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
767   int          ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
768   int          *ajtmpold,*ajtmp,nz,row;
769   int          *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
770   MatScalar    *pv,*v,*rtmp,*pc,*w,*x;
771   MatScalar    x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15;
772   MatScalar    x16,x17,x18,x19,x20,x21,x22,x23,x24,x25;
773   MatScalar    p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15;
774   MatScalar    p16,p17,p18,p19,p20,p21,p22,p23,p24,p25;
775   MatScalar    m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12,m13,m14,m15;
776   MatScalar    m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
777   MatScalar    p26,p27,p28,p29,p30,p31,p32,p33,p34,p35,p36;
778   MatScalar    p37,p38,p39,p40,p41,p42,p43,p44,p45,p46,p47,p48,p49;
779   MatScalar    x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36;
780   MatScalar    x37,x38,x39,x40,x41,x42,x43,x44,x45,x46,x47,x48,x49;
781   MatScalar    m26,m27,m28,m29,m30,m31,m32,m33,m34,m35,m36;
782   MatScalar    m37,m38,m39,m40,m41,m42,m43,m44,m45,m46,m47,m48,m49;
783   MatScalar    *ba = b->a,*aa = a->a;
784 
785   PetscFunctionBegin;
786   rtmp  = (MatScalar*)PetscMalloc(49*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
787   for (i=0; i<n; i++) {
788     nz    = bi[i+1] - bi[i];
789     ajtmp = bj + bi[i];
790     for  (j=0; j<nz; j++) {
791       x = rtmp+49*ajtmp[j];
792       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
793       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
794       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = x[25] = 0.0 ;
795       x[26] = x[27] = x[28] = x[29] = x[30] = x[31] = x[32] = x[33] = 0.0 ;
796       x[34] = x[35] = x[36] = x[37] = x[38] = x[39] = x[40] = x[41] = 0.0 ;
797       x[42] = x[43] = x[44] = x[45] = x[46] = x[47] = x[48] = 0.0 ;
798     }
799     /* load in initial (unfactored row) */
800     nz       = ai[i+1] - ai[i];
801     ajtmpold = aj + ai[i];
802     v        = aa + 49*ai[i];
803     for (j=0; j<nz; j++) {
804       x    = rtmp+49*ajtmpold[j];
805       x[0] =  v[0];  x[1] =  v[1];  x[2] =  v[2];  x[3] =  v[3];
806       x[4] =  v[4];  x[5] =  v[5];  x[6] =  v[6];  x[7] =  v[7];
807       x[8] =  v[8];  x[9] =  v[9];  x[10] = v[10]; x[11] = v[11];
808       x[12] = v[12]; x[13] = v[13]; x[14] = v[14]; x[15] = v[15];
809       x[16] = v[16]; x[17] = v[17]; x[18] = v[18]; x[19] = v[19];
810       x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23];
811       x[24] = v[24]; x[25] = v[25]; x[26] = v[26]; x[27] = v[27];
812       x[28] = v[28]; x[29] = v[29]; x[30] = v[30]; x[31] = v[31];
813       x[32] = v[32]; x[33] = v[33]; x[34] = v[34]; x[35] = v[35];
814       x[36] = v[36]; x[37] = v[37]; x[38] = v[38]; x[39] = v[39];
815       x[40] = v[40]; x[41] = v[41]; x[42] = v[42]; x[43] = v[43];
816       x[44] = v[44]; x[45] = v[45]; x[46] = v[46]; x[47] = v[47];
817       x[48] = v[48];
818       v    += 49;
819     }
820     row = *ajtmp++;
821     while (row < i) {
822       pc  = rtmp + 49*row;
823       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
824       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];
825       p9  = pc[8];  p10 = pc[9];  p11 = pc[10]; p12 = pc[11];
826       p13 = pc[12]; p14 = pc[13]; p15 = pc[14]; p16 = pc[15];
827       p17 = pc[16]; p18 = pc[17]; p19 = pc[18]; p20 = pc[19];
828       p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
829       p25 = pc[24]; p26 = pc[25]; p27 = pc[26]; p28 = pc[27];
830       p29 = pc[28]; p30 = pc[29]; p31 = pc[30]; p32 = pc[31];
831       p33 = pc[32]; p34 = pc[33]; p35 = pc[34]; p36 = pc[35];
832       p37 = pc[36]; p38 = pc[37]; p39 = pc[38]; p40 = pc[39];
833       p41 = pc[40]; p42 = pc[41]; p43 = pc[42]; p44 = pc[43];
834       p45 = pc[44]; p46 = pc[45]; p47 = pc[46]; p48 = pc[47];
835       p49 = pc[48];
836       if (p1  != 0.0 || p2  != 0.0 || p3  != 0.0 || p4  != 0.0 ||
837           p5  != 0.0 || p6  != 0.0 || p7  != 0.0 || p8  != 0.0 ||
838           p9  != 0.0 || p10 != 0.0 || p11 != 0.0 || p12 != 0.0 ||
839           p13 != 0.0 || p14 != 0.0 || p15 != 0.0 || p16 != 0.0 ||
840           p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 ||
841           p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 ||
842           p25 != 0.0 || p26 != 0.0 || p27 != 0.0 || p28 != 0.0 ||
843           p29 != 0.0 || p30 != 0.0 || p31 != 0.0 || p32 != 0.0 ||
844           p33 != 0.0 || p34 != 0.0 || p35 != 0.0 || p36 != 0.0 ||
845           p37 != 0.0 || p38 != 0.0 || p39 != 0.0 || p40 != 0.0 ||
846           p41 != 0.0 || p42 != 0.0 || p43 != 0.0 || p44 != 0.0 ||
847           p45 != 0.0 || p46 != 0.0 || p47 != 0.0 || p48 != 0.0 ||
848           p49 != 0.0) {
849         pv = ba + 49*diag_offset[row];
850         pj = bj + diag_offset[row] + 1;
851 	x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
852 	x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
853 	x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
854 	x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
855 	x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
856 	x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
857 	x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
858 	x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
859 	x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
860 	x37 = pv[36]; x38 = pv[37]; x39 = pv[38]; x40 = pv[39];
861 	x41 = pv[40]; x42 = pv[41]; x43 = pv[42]; x44 = pv[43];
862 	x45 = pv[44]; x46 = pv[45]; x47 = pv[46]; x48 = pv[47];
863         x49 = pv[48];
864         pc[0]  = m1  = p1*x1  + p8*x2   + p15*x3  + p22*x4  + p29*x5  + p36*x6 + p43*x7;
865         pc[1]  = m2  = p2*x1  + p9*x2   + p16*x3  + p23*x4  + p30*x5  + p37*x6 + p44*x7;
866         pc[2]  = m3  = p3*x1  + p10*x2  + p17*x3  + p24*x4  + p31*x5  + p38*x6 + p45*x7;
867         pc[3]  = m4  = p4*x1  + p11*x2  + p18*x3  + p25*x4  + p32*x5  + p39*x6 + p46*x7;
868         pc[4]  = m5  = p5*x1  + p12*x2  + p19*x3  + p26*x4  + p33*x5  + p40*x6 + p47*x7;
869         pc[5]  = m6  = p6*x1  + p13*x2  + p20*x3  + p27*x4  + p34*x5  + p41*x6 + p48*x7;
870         pc[6]  = m7  = p7*x1  + p14*x2  + p21*x3  + p28*x4  + p35*x5  + p42*x6 + p49*x7;
871 
872         pc[7]  = m8  = p1*x8  + p8*x9   + p15*x10 + p22*x11 + p29*x12 + p36*x13 + p43*x14;
873         pc[8]  = m9  = p2*x8  + p9*x9   + p16*x10 + p23*x11 + p30*x12 + p37*x13 + p44*x14;
874         pc[9]  = m10 = p3*x8  + p10*x9  + p17*x10 + p24*x11 + p31*x12 + p38*x13 + p45*x14;
875         pc[10] = m11 = p4*x8  + p11*x9  + p18*x10 + p25*x11 + p32*x12 + p39*x13 + p46*x14;
876         pc[11] = m12 = p5*x8  + p12*x9  + p19*x10 + p26*x11 + p33*x12 + p40*x13 + p47*x14;
877         pc[12] = m13 = p6*x8  + p13*x9  + p20*x10 + p27*x11 + p34*x12 + p41*x13 + p48*x14;
878         pc[13] = m14 = p7*x8  + p14*x9  + p21*x10 + p28*x11 + p35*x12 + p42*x13 + p49*x14;
879 
880         pc[14] = m15 = p1*x15 + p8*x16  + p15*x17 + p22*x18 + p29*x19 + p36*x20 + p43*x21;
881         pc[15] = m16 = p2*x15 + p9*x16  + p16*x17 + p23*x18 + p30*x19 + p37*x20 + p44*x21;
882         pc[16] = m17 = p3*x15 + p10*x16 + p17*x17 + p24*x18 + p31*x19 + p38*x20 + p45*x21;
883         pc[17] = m18 = p4*x15 + p11*x16 + p18*x17 + p25*x18 + p32*x19 + p39*x20 + p46*x21;
884         pc[18] = m19 = p5*x15 + p12*x16 + p19*x17 + p26*x18 + p33*x19 + p40*x20 + p47*x21;
885         pc[19] = m20 = p6*x15 + p13*x16 + p20*x17 + p27*x18 + p34*x19 + p41*x20 + p48*x21;
886         pc[20] = m21 = p7*x15 + p14*x16 + p21*x17 + p28*x18 + p35*x19 + p42*x20 + p49*x21;
887 
888         pc[21] = m22 = p1*x22 + p8*x23  + p15*x24 + p22*x25 + p29*x26 + p36*x27 + p43*x28;
889         pc[22] = m23 = p2*x22 + p9*x23  + p16*x24 + p23*x25 + p30*x26 + p37*x27 + p44*x28;
890         pc[23] = m24 = p3*x22 + p10*x23 + p17*x24 + p24*x25 + p31*x26 + p38*x27 + p45*x28;
891         pc[24] = m25 = p4*x22 + p11*x23 + p18*x24 + p25*x25 + p32*x26 + p39*x27 + p46*x28;
892         pc[25] = m26 = p5*x22 + p12*x23 + p19*x24 + p26*x25 + p33*x26 + p40*x27 + p47*x28;
893         pc[26] = m27 = p6*x22 + p13*x23 + p20*x24 + p27*x25 + p34*x26 + p41*x27 + p48*x28;
894         pc[27] = m28 = p7*x22 + p14*x23 + p21*x24 + p28*x25 + p35*x26 + p42*x27 + p49*x28;
895 
896         pc[28] = m29 = p1*x29 + p8*x30  + p15*x31 + p22*x32 + p29*x33 + p36*x34 + p43*x35;
897         pc[29] = m30 = p2*x29 + p9*x30  + p16*x31 + p23*x32 + p30*x33 + p37*x34 + p44*x35;
898         pc[30] = m31 = p3*x29 + p10*x30 + p17*x31 + p24*x32 + p31*x33 + p38*x34 + p45*x35;
899         pc[31] = m32 = p4*x29 + p11*x30 + p18*x31 + p25*x32 + p32*x33 + p39*x34 + p46*x35;
900         pc[32] = m33 = p5*x29 + p12*x30 + p19*x31 + p26*x32 + p33*x33 + p40*x34 + p47*x35;
901         pc[33] = m34 = p6*x29 + p13*x30 + p20*x31 + p27*x32 + p34*x33 + p41*x34 + p48*x35;
902         pc[34] = m35 = p7*x29 + p14*x30 + p21*x31 + p28*x32 + p35*x33 + p42*x34 + p49*x35;
903 
904         pc[35] = m36 = p1*x36 + p8*x37  + p15*x38 + p22*x39 + p29*x40 + p36*x41 + p43*x42;
905         pc[36] = m37 = p2*x36 + p9*x37  + p16*x38 + p23*x39 + p30*x40 + p37*x41 + p44*x42;
906         pc[37] = m38 = p3*x36 + p10*x37 + p17*x38 + p24*x39 + p31*x40 + p38*x41 + p45*x42;
907         pc[38] = m39 = p4*x36 + p11*x37 + p18*x38 + p25*x39 + p32*x40 + p39*x41 + p46*x42;
908         pc[39] = m40 = p5*x36 + p12*x37 + p19*x38 + p26*x39 + p33*x40 + p40*x41 + p47*x42;
909         pc[40] = m41 = p6*x36 + p13*x37 + p20*x38 + p27*x39 + p34*x40 + p41*x41 + p48*x42;
910         pc[41] = m42 = p7*x36 + p14*x37 + p21*x38 + p28*x39 + p35*x40 + p42*x41 + p49*x42;
911 
912         pc[42] = m43 = p1*x43 + p8*x44  + p15*x45 + p22*x46 + p29*x47 + p36*x48 + p43*x49;
913         pc[43] = m44 = p2*x43 + p9*x44  + p16*x45 + p23*x46 + p30*x47 + p37*x48 + p44*x49;
914         pc[44] = m45 = p3*x43 + p10*x44 + p17*x45 + p24*x46 + p31*x47 + p38*x48 + p45*x49;
915         pc[45] = m46 = p4*x43 + p11*x44 + p18*x45 + p25*x46 + p32*x47 + p39*x48 + p46*x49;
916         pc[46] = m47 = p5*x43 + p12*x44 + p19*x45 + p26*x46 + p33*x47 + p40*x48 + p47*x49;
917         pc[47] = m48 = p6*x43 + p13*x44 + p20*x45 + p27*x46 + p34*x47 + p41*x48 + p48*x49;
918         pc[48] = m49 = p7*x43 + p14*x44 + p21*x45 + p28*x46 + p35*x47 + p42*x48 + p49*x49;
919 
920         nz = bi[row+1] - diag_offset[row] - 1;
921         pv += 49;
922         for (j=0; j<nz; j++) {
923 	  x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
924 	  x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
925 	  x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
926 	  x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
927 	  x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
928 	  x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
929 	  x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
930 	  x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
931 	  x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
932 	  x37 = pv[36]; x38 = pv[37]; x39 = pv[38]; x40 = pv[39];
933 	  x41 = pv[40]; x42 = pv[41]; x43 = pv[42]; x44 = pv[43];
934 	  x45 = pv[44]; x46 = pv[45]; x47 = pv[46]; x48 = pv[47];
935 	  x49 = pv[48];
936 	  x    = rtmp + 49*pj[j];
937 	  x[0]  -= m1*x1  + m8*x2   + m15*x3  + m22*x4  + m29*x5  + m36*x6 + m43*x7;
938 	  x[1]  -= m2*x1  + m9*x2   + m16*x3  + m23*x4  + m30*x5  + m37*x6 + m44*x7;
939 	  x[2]  -= m3*x1  + m10*x2  + m17*x3  + m24*x4  + m31*x5  + m38*x6 + m45*x7;
940 	  x[3]  -= m4*x1  + m11*x2  + m18*x3  + m25*x4  + m32*x5  + m39*x6 + m46*x7;
941 	  x[4]  -= m5*x1  + m12*x2  + m19*x3  + m26*x4  + m33*x5  + m40*x6 + m47*x7;
942 	  x[5]  -= m6*x1  + m13*x2  + m20*x3  + m27*x4  + m34*x5  + m41*x6 + m48*x7;
943 	  x[6]  -= m7*x1  + m14*x2  + m21*x3  + m28*x4  + m35*x5  + m42*x6 + m49*x7;
944 
945 	  x[7]  -= m1*x8  + m8*x9   + m15*x10 + m22*x11 + m29*x12 + m36*x13 + m43*x14;
946 	  x[8]  -= m2*x8  + m9*x9   + m16*x10 + m23*x11 + m30*x12 + m37*x13 + m44*x14;
947 	  x[9]  -= m3*x8  + m10*x9  + m17*x10 + m24*x11 + m31*x12 + m38*x13 + m45*x14;
948 	  x[10] -= m4*x8  + m11*x9  + m18*x10 + m25*x11 + m32*x12 + m39*x13 + m46*x14;
949 	  x[11] -= m5*x8  + m12*x9  + m19*x10 + m26*x11 + m33*x12 + m40*x13 + m47*x14;
950 	  x[12] -= m6*x8  + m13*x9  + m20*x10 + m27*x11 + m34*x12 + m41*x13 + m48*x14;
951 	  x[13] -= m7*x8  + m14*x9  + m21*x10 + m28*x11 + m35*x12 + m42*x13 + m49*x14;
952 
953 	  x[14] -= m1*x15 + m8*x16  + m15*x17 + m22*x18 + m29*x19 + m36*x20 + m43*x21;
954 	  x[15] -= m2*x15 + m9*x16  + m16*x17 + m23*x18 + m30*x19 + m37*x20 + m44*x21;
955 	  x[16] -= m3*x15 + m10*x16 + m17*x17 + m24*x18 + m31*x19 + m38*x20 + m45*x21;
956 	  x[17] -= m4*x15 + m11*x16 + m18*x17 + m25*x18 + m32*x19 + m39*x20 + m46*x21;
957 	  x[18] -= m5*x15 + m12*x16 + m19*x17 + m26*x18 + m33*x19 + m40*x20 + m47*x21;
958 	  x[19] -= m6*x15 + m13*x16 + m20*x17 + m27*x18 + m34*x19 + m41*x20 + m48*x21;
959 	  x[20] -= m7*x15 + m14*x16 + m21*x17 + m28*x18 + m35*x19 + m42*x20 + m49*x21;
960 
961 	  x[21] -= m1*x22 + m8*x23  + m15*x24 + m22*x25 + m29*x26 + m36*x27 + m43*x28;
962 	  x[22] -= m2*x22 + m9*x23  + m16*x24 + m23*x25 + m30*x26 + m37*x27 + m44*x28;
963 	  x[23] -= m3*x22 + m10*x23 + m17*x24 + m24*x25 + m31*x26 + m38*x27 + m45*x28;
964 	  x[24] -= m4*x22 + m11*x23 + m18*x24 + m25*x25 + m32*x26 + m39*x27 + m46*x28;
965 	  x[25] -= m5*x22 + m12*x23 + m19*x24 + m26*x25 + m33*x26 + m40*x27 + m47*x28;
966 	  x[26] -= m6*x22 + m13*x23 + m20*x24 + m27*x25 + m34*x26 + m41*x27 + m48*x28;
967 	  x[27] -= m7*x22 + m14*x23 + m21*x24 + m28*x25 + m35*x26 + m42*x27 + m49*x28;
968 
969 	  x[28] -= m1*x29 + m8*x30  + m15*x31 + m22*x32 + m29*x33 + m36*x34 + m43*x35;
970 	  x[29] -= m2*x29 + m9*x30  + m16*x31 + m23*x32 + m30*x33 + m37*x34 + m44*x35;
971 	  x[30] -= m3*x29 + m10*x30 + m17*x31 + m24*x32 + m31*x33 + m38*x34 + m45*x35;
972 	  x[31] -= m4*x29 + m11*x30 + m18*x31 + m25*x32 + m32*x33 + m39*x34 + m46*x35;
973 	  x[32] -= m5*x29 + m12*x30 + m19*x31 + m26*x32 + m33*x33 + m40*x34 + m47*x35;
974 	  x[33] -= m6*x29 + m13*x30 + m20*x31 + m27*x32 + m34*x33 + m41*x34 + m48*x35;
975 	  x[34] -= m7*x29 + m14*x30 + m21*x31 + m28*x32 + m35*x33 + m42*x34 + m49*x35;
976 
977 	  x[35] -= m1*x36 + m8*x37  + m15*x38 + m22*x39 + m29*x40 + m36*x41 + m43*x42;
978 	  x[36] -= m2*x36 + m9*x37  + m16*x38 + m23*x39 + m30*x40 + m37*x41 + m44*x42;
979 	  x[37] -= m3*x36 + m10*x37 + m17*x38 + m24*x39 + m31*x40 + m38*x41 + m45*x42;
980 	  x[38] -= m4*x36 + m11*x37 + m18*x38 + m25*x39 + m32*x40 + m39*x41 + m46*x42;
981 	  x[39] -= m5*x36 + m12*x37 + m19*x38 + m26*x39 + m33*x40 + m40*x41 + m47*x42;
982 	  x[40] -= m6*x36 + m13*x37 + m20*x38 + m27*x39 + m34*x40 + m41*x41 + m48*x42;
983 	  x[41] -= m7*x36 + m14*x37 + m21*x38 + m28*x39 + m35*x40 + m42*x41 + m49*x42;
984 
985 	  x[42] -= m1*x43 + m8*x44  + m15*x45 + m22*x46 + m29*x47 + m36*x48 + m43*x49;
986 	  x[43] -= m2*x43 + m9*x44  + m16*x45 + m23*x46 + m30*x47 + m37*x48 + m44*x49;
987 	  x[44] -= m3*x43 + m10*x44 + m17*x45 + m24*x46 + m31*x47 + m38*x48 + m45*x49;
988 	  x[45] -= m4*x43 + m11*x44 + m18*x45 + m25*x46 + m32*x47 + m39*x48 + m46*x49;
989 	  x[46] -= m5*x43 + m12*x44 + m19*x45 + m26*x46 + m33*x47 + m40*x48 + m47*x49;
990 	  x[47] -= m6*x43 + m13*x44 + m20*x45 + m27*x46 + m34*x47 + m41*x48 + m48*x49;
991 	  x[48] -= m7*x43 + m14*x44 + m21*x45 + m28*x46 + m35*x47 + m42*x48 + m49*x49;
992           pv   += 49;
993         }
994         PLogFlops(686*nz+637);
995       }
996       row = *ajtmp++;
997     }
998     /* finished row so stick it into b->a */
999     pv = ba + 49*bi[i];
1000     pj = bj + bi[i];
1001     nz = bi[i+1] - bi[i];
1002     for (j=0; j<nz; j++) {
1003       x      = rtmp+49*pj[j];
1004       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
1005       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7];
1006       pv[8]  = x[8];  pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11];
1007       pv[12] = x[12]; pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
1008       pv[16] = x[16]; pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19];
1009       pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23];
1010       pv[24] = x[24]; pv[25] = x[25]; pv[26] = x[26]; pv[27] = x[27];
1011       pv[28] = x[28]; pv[29] = x[29]; pv[30] = x[30]; pv[31] = x[31];
1012       pv[32] = x[32]; pv[33] = x[33]; pv[34] = x[34]; pv[35] = x[35];
1013       pv[36] = x[36]; pv[37] = x[37]; pv[38] = x[38]; pv[39] = x[39];
1014       pv[40] = x[40]; pv[41] = x[41]; pv[42] = x[42]; pv[43] = x[43];
1015       pv[44] = x[44]; pv[45] = x[45]; pv[46] = x[46]; pv[47] = x[47];
1016       pv[48] = x[48];
1017       pv   += 49;
1018     }
1019     /* invert diagonal block */
1020     w = ba + 49*diag_offset[i];
1021     ierr = Kernel_A_gets_inverse_A_7(w);CHKERRQ(ierr);
1022   }
1023 
1024   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1025   C->factor    = FACTOR_LU;
1026   C->assembled = PETSC_TRUE;
1027   PLogFlops(1.3333*343*b->mbs); /* from inverting diagonal blocks */
1028   PetscFunctionReturn(0);
1029 }
1030 
1031 /* Version for when blocks are 6 by 6 */
1032 #undef __FUNC__
1033 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_6"
1034 int MatCholeskyFactorNumeric_SeqSBAIJ_6(Mat A,Mat *B)
1035 {
1036   Mat                C = *B;
1037   Mat_SeqSBAIJ       *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data;
1038   IS                 perm = b->row;
1039   int                *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
1040   int                *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
1041   MatScalar          *ba = b->a,*aa,*ap,*dk,*uik;
1042   MatScalar          *u,*d,*w,*wp;
1043 
1044   PetscFunctionBegin;
1045   /* initialization */
1046   w  = (MatScalar*)PetscMalloc(36*mbs*sizeof(MatScalar));CHKPTRQ(w);
1047   ierr = PetscMemzero(w,36*mbs*sizeof(MatScalar));CHKERRQ(ierr);
1048   il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il);
1049   jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl);
1050   for (i=0; i<mbs; i++) {
1051     jl[i] = mbs; il[0] = 0;
1052   }
1053   dk    = (MatScalar*)PetscMalloc(36*sizeof(MatScalar));CHKPTRQ(dk);
1054   uik   = (MatScalar*)PetscMalloc(36*sizeof(MatScalar));CHKPTRQ(uik);
1055   ierr  = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr);
1056 
1057   /* check permutation */
1058   if (!a->permute){
1059     ai = a->i; aj = a->j; aa = a->a;
1060   } else {
1061     ai = a->inew; aj = a->jnew;
1062     aa = (MatScalar*)PetscMalloc(36*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa);
1063     ierr = PetscMemcpy(aa,a->a,36*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr);
1064     a2anew  = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew);
1065     ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr);
1066 
1067     for (i=0; i<mbs; i++){
1068       jmin = ai[i]; jmax = ai[i+1];
1069       for (j=jmin; j<jmax; j++){
1070         while (a2anew[j] != j){
1071           k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k;
1072           for (k1=0; k1<36; k1++){
1073             dk[k1]       = aa[k*36+k1];
1074             aa[k*36+k1] = aa[j*36+k1];
1075             aa[j*36+k1] = dk[k1];
1076           }
1077         }
1078         /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */
1079         if (i > aj[j]){
1080           /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */
1081           ap = aa + j*36;                     /* ptr to the beginning of j-th block of aa */
1082           for (k=0; k<36; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */
1083           for (k=0; k<6; k++){               /* j-th block of aa <- dk^T */
1084             for (k1=0; k1<6; k1++) *ap++ = dk[k + 6*k1];
1085           }
1086         }
1087       }
1088     }
1089     ierr = PetscFree(a2anew);CHKERRA(ierr);
1090   }
1091 
1092   /* for each row k */
1093   for (k = 0; k<mbs; k++){
1094 
1095     /*initialize k-th row with elements nonzero in row perm(k) of A */
1096     jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1];
1097     if (jmin < jmax) {
1098       ap = aa + jmin*36;
1099       for (j = jmin; j < jmax; j++){
1100         vj = perm_ptr[aj[j]];         /* block col. index */
1101         wp = w + vj*36;
1102         for (i=0; i<36; i++) *wp++ = *ap++;
1103       }
1104     }
1105 
1106     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
1107     ierr = PetscMemcpy(dk,w+k*36,36*sizeof(MatScalar));CHKERRQ(ierr);
1108     i = jl[k]; /* first row to be added to k_th row  */
1109 
1110     while (i < mbs){
1111       nexti = jl[i]; /* next row to be added to k_th row */
1112 
1113       /* compute multiplier */
1114       ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
1115 
1116       /* uik = -inv(Di)*U_bar(i,k) */
1117       d = ba + i*36;
1118       u    = ba + ili*36;
1119 
1120       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]);
1121       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]);
1122       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]);
1123       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]);
1124       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]);
1125       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]);
1126 
1127       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]);
1128       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]);
1129       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]);
1130       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]);
1131       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]);
1132       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]);
1133 
1134       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]);
1135       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]);
1136       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]);
1137       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]);
1138       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]);
1139       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]);
1140 
1141       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]);
1142       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]);
1143       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]);
1144       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]);
1145       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]);
1146       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]);
1147 
1148       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]);
1149       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]);
1150       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]);
1151       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]);
1152       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]);
1153       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]);
1154 
1155       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]);
1156       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]);
1157       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]);
1158       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]);
1159       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]);
1160       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]);
1161 
1162       /* update D(k) += -U(i,k)^T * U_bar(i,k) */
1163       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];
1164       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];
1165       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];
1166       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];
1167       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];
1168       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];
1169 
1170       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];
1171       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];
1172       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];
1173       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];
1174       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];
1175       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];
1176 
1177       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];
1178       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];
1179       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];
1180       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];
1181       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];
1182       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];
1183 
1184       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];
1185       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];
1186       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];
1187       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];
1188       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];
1189       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];
1190 
1191       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];
1192       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];
1193       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];
1194       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];
1195       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];
1196       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];
1197 
1198       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];
1199       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];
1200       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];
1201       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];
1202       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];
1203       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];
1204 
1205       /* update -U(i,k) */
1206       ierr = PetscMemcpy(ba+ili*36,uik,36*sizeof(MatScalar));CHKERRQ(ierr);
1207 
1208       /* add multiple of row i to k-th row ... */
1209       jmin = ili + 1; jmax = bi[i+1];
1210       if (jmin < jmax){
1211         for (j=jmin; j<jmax; j++) {
1212           /* w += -U(i,k)^T * U_bar(i,j) */
1213           wp = w + bj[j]*36;
1214           u = ba + j*36;
1215           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];
1216           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];
1217           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];
1218           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];
1219           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];
1220           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];
1221 
1222           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];
1223           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];
1224           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];
1225           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];
1226           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];
1227           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];
1228 
1229           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];
1230           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];
1231           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];
1232           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];
1233           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];
1234           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];
1235 
1236           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];
1237           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];
1238           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];
1239           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];
1240           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];
1241           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];
1242 
1243           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];
1244           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];
1245           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];
1246           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];
1247           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];
1248           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];
1249 
1250           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];
1251           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];
1252           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];
1253           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];
1254           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];
1255           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];
1256         }
1257 
1258         /* ... add i to row list for next nonzero entry */
1259         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
1260         j     = bj[jmin];
1261         jl[i] = jl[j]; jl[j] = i; /* update jl */
1262       }
1263       i = nexti;
1264     }
1265 
1266     /* save nonzero entries in k-th row of U ... */
1267 
1268     /* invert diagonal block */
1269     d = ba+k*36;
1270     ierr = PetscMemcpy(d,dk,36*sizeof(MatScalar));CHKERRQ(ierr);
1271     ierr = Kernel_A_gets_inverse_A_6(d);CHKERRQ(ierr);
1272 
1273     jmin = bi[k]; jmax = bi[k+1];
1274     if (jmin < jmax) {
1275       for (j=jmin; j<jmax; j++){
1276          vj = bj[j];           /* block col. index of U */
1277          u   = ba + j*36;
1278          wp = w + vj*36;
1279          for (k1=0; k1<36; k1++){
1280            *u++        = *wp;
1281            *wp++ = 0.0;
1282          }
1283       }
1284 
1285       /* ... add k to row list for first nonzero entry in k-th row */
1286       il[k] = jmin;
1287       i     = bj[jmin];
1288       jl[k] = jl[i]; jl[i] = k;
1289     }
1290   }
1291 
1292   ierr = PetscFree(w);CHKERRQ(ierr);
1293   ierr = PetscFree(il);CHKERRQ(ierr);
1294   ierr = PetscFree(jl);CHKERRQ(ierr);
1295   ierr = PetscFree(dk);CHKERRQ(ierr);
1296   ierr = PetscFree(uik);CHKERRQ(ierr);
1297   if (a->permute){
1298     ierr = PetscFree(aa);CHKERRQ(ierr);
1299   }
1300 
1301   ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr);
1302   C->factor    = FACTOR_CHOLESKY;
1303   C->assembled = PETSC_TRUE;
1304   C->preallocated = PETSC_TRUE;
1305   PLogFlops(1.3333*216*b->mbs); /* from inverting diagonal blocks */
1306   PetscFunctionReturn(0);
1307 }
1308 
1309 /*
1310       Version for when blocks are 6 by 6 Using natural ordering
1311 */
1312 #undef __FUNC__
1313 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_6_NaturalOrdering"
1314 int MatCholeskyFactorNumeric_SeqSBAIJ_6_NaturalOrdering(Mat A,Mat *B)
1315 {
1316   Mat         C = *B;
1317   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
1318   int         ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
1319   int         *ajtmpold,*ajtmp,nz,row;
1320   int         *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
1321   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
1322   MatScalar   x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15;
1323   MatScalar   x16,x17,x18,x19,x20,x21,x22,x23,x24,x25;
1324   MatScalar   p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15;
1325   MatScalar   p16,p17,p18,p19,p20,p21,p22,p23,p24,p25;
1326   MatScalar   m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12,m13,m14,m15;
1327   MatScalar   m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
1328   MatScalar   p26,p27,p28,p29,p30,p31,p32,p33,p34,p35,p36;
1329   MatScalar   x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36;
1330   MatScalar   m26,m27,m28,m29,m30,m31,m32,m33,m34,m35,m36;
1331   MatScalar   *ba = b->a,*aa = a->a;
1332 
1333   PetscFunctionBegin;
1334   rtmp  = (MatScalar*)PetscMalloc(36*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
1335   for (i=0; i<n; i++) {
1336     nz    = bi[i+1] - bi[i];
1337     ajtmp = bj + bi[i];
1338     for  (j=0; j<nz; j++) {
1339       x = rtmp+36*ajtmp[j];
1340       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
1341       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
1342       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = x[25] = 0.0 ;
1343       x[26] = x[27] = x[28] = x[29] = x[30] = x[31] = x[32] = x[33] = 0.0 ;
1344       x[34] = x[35] = 0.0 ;
1345     }
1346     /* load in initial (unfactored row) */
1347     nz       = ai[i+1] - ai[i];
1348     ajtmpold = aj + ai[i];
1349     v        = aa + 36*ai[i];
1350     for (j=0; j<nz; j++) {
1351       x    = rtmp+36*ajtmpold[j];
1352       x[0] =  v[0];  x[1] =  v[1];  x[2] =  v[2];  x[3] =  v[3];
1353       x[4] =  v[4];  x[5] =  v[5];  x[6] =  v[6];  x[7] =  v[7];
1354       x[8] =  v[8];  x[9] =  v[9];  x[10] = v[10]; x[11] = v[11];
1355       x[12] = v[12]; x[13] = v[13]; x[14] = v[14]; x[15] = v[15];
1356       x[16] = v[16]; x[17] = v[17]; x[18] = v[18]; x[19] = v[19];
1357       x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23];
1358       x[24] = v[24]; x[25] = v[25]; x[26] = v[26]; x[27] = v[27];
1359       x[28] = v[28]; x[29] = v[29]; x[30] = v[30]; x[31] = v[31];
1360       x[32] = v[32]; x[33] = v[33]; x[34] = v[34]; x[35] = v[35];
1361       v    += 36;
1362     }
1363     row = *ajtmp++;
1364     while (row < i) {
1365       pc  = rtmp + 36*row;
1366       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
1367       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];
1368       p9  = pc[8];  p10 = pc[9];  p11 = pc[10]; p12 = pc[11];
1369       p13 = pc[12]; p14 = pc[13]; p15 = pc[14]; p16 = pc[15];
1370       p17 = pc[16]; p18 = pc[17]; p19 = pc[18]; p20 = pc[19];
1371       p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
1372       p25 = pc[24]; p26 = pc[25]; p27 = pc[26]; p28 = pc[27];
1373       p29 = pc[28]; p30 = pc[29]; p31 = pc[30]; p32 = pc[31];
1374       p33 = pc[32]; p34 = pc[33]; p35 = pc[34]; p36 = pc[35];
1375       if (p1  != 0.0 || p2  != 0.0 || p3  != 0.0 || p4  != 0.0 ||
1376           p5  != 0.0 || p6  != 0.0 || p7  != 0.0 || p8  != 0.0 ||
1377           p9  != 0.0 || p10 != 0.0 || p11 != 0.0 || p12 != 0.0 ||
1378           p13 != 0.0 || p14 != 0.0 || p15 != 0.0 || p16 != 0.0 ||
1379           p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 ||
1380           p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 ||
1381           p25 != 0.0 || p26 != 0.0 || p27 != 0.0 || p28 != 0.0 ||
1382           p29 != 0.0 || p30 != 0.0 || p31 != 0.0 || p32 != 0.0 ||
1383           p33 != 0.0 || p34 != 0.0 || p35 != 0.0 || p36 != 0.0) {
1384         pv = ba + 36*diag_offset[row];
1385         pj = bj + diag_offset[row] + 1;
1386 	x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
1387 	x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
1388 	x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
1389 	x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
1390 	x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
1391 	x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
1392 	x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
1393 	x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
1394 	x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
1395         pc[0]  = m1  = p1*x1  + p7*x2   + p13*x3  + p19*x4  + p25*x5  + p31*x6;
1396         pc[1]  = m2  = p2*x1  + p8*x2   + p14*x3  + p20*x4  + p26*x5  + p32*x6;
1397         pc[2]  = m3  = p3*x1  + p9*x2   + p15*x3  + p21*x4  + p27*x5  + p33*x6;
1398         pc[3]  = m4  = p4*x1  + p10*x2  + p16*x3  + p22*x4  + p28*x5  + p34*x6;
1399         pc[4]  = m5  = p5*x1  + p11*x2  + p17*x3  + p23*x4  + p29*x5  + p35*x6;
1400         pc[5]  = m6  = p6*x1  + p12*x2  + p18*x3  + p24*x4  + p30*x5  + p36*x6;
1401 
1402         pc[6]  = m7  = p1*x7  + p7*x8   + p13*x9  + p19*x10 + p25*x11 + p31*x12;
1403         pc[7]  = m8  = p2*x7  + p8*x8   + p14*x9  + p20*x10 + p26*x11 + p32*x12;
1404         pc[8]  = m9  = p3*x7  + p9*x8   + p15*x9  + p21*x10 + p27*x11 + p33*x12;
1405         pc[9]  = m10 = p4*x7  + p10*x8  + p16*x9  + p22*x10 + p28*x11 + p34*x12;
1406         pc[10] = m11 = p5*x7  + p11*x8  + p17*x9  + p23*x10 + p29*x11 + p35*x12;
1407         pc[11] = m12 = p6*x7  + p12*x8  + p18*x9  + p24*x10 + p30*x11 + p36*x12;
1408 
1409         pc[12] = m13 = p1*x13 + p7*x14  + p13*x15 + p19*x16 + p25*x17 + p31*x18;
1410         pc[13] = m14 = p2*x13 + p8*x14  + p14*x15 + p20*x16 + p26*x17 + p32*x18;
1411         pc[14] = m15 = p3*x13 + p9*x14  + p15*x15 + p21*x16 + p27*x17 + p33*x18;
1412         pc[15] = m16 = p4*x13 + p10*x14 + p16*x15 + p22*x16 + p28*x17 + p34*x18;
1413         pc[16] = m17 = p5*x13 + p11*x14 + p17*x15 + p23*x16 + p29*x17 + p35*x18;
1414         pc[17] = m18 = p6*x13 + p12*x14 + p18*x15 + p24*x16 + p30*x17 + p36*x18;
1415 
1416         pc[18] = m19 = p1*x19 + p7*x20  + p13*x21 + p19*x22 + p25*x23 + p31*x24;
1417         pc[19] = m20 = p2*x19 + p8*x20  + p14*x21 + p20*x22 + p26*x23 + p32*x24;
1418         pc[20] = m21 = p3*x19 + p9*x20  + p15*x21 + p21*x22 + p27*x23 + p33*x24;
1419         pc[21] = m22 = p4*x19 + p10*x20 + p16*x21 + p22*x22 + p28*x23 + p34*x24;
1420         pc[22] = m23 = p5*x19 + p11*x20 + p17*x21 + p23*x22 + p29*x23 + p35*x24;
1421         pc[23] = m24 = p6*x19 + p12*x20 + p18*x21 + p24*x22 + p30*x23 + p36*x24;
1422 
1423         pc[24] = m25 = p1*x25 + p7*x26  + p13*x27 + p19*x28 + p25*x29 + p31*x30;
1424         pc[25] = m26 = p2*x25 + p8*x26  + p14*x27 + p20*x28 + p26*x29 + p32*x30;
1425         pc[26] = m27 = p3*x25 + p9*x26  + p15*x27 + p21*x28 + p27*x29 + p33*x30;
1426         pc[27] = m28 = p4*x25 + p10*x26 + p16*x27 + p22*x28 + p28*x29 + p34*x30;
1427         pc[28] = m29 = p5*x25 + p11*x26 + p17*x27 + p23*x28 + p29*x29 + p35*x30;
1428         pc[29] = m30 = p6*x25 + p12*x26 + p18*x27 + p24*x28 + p30*x29 + p36*x30;
1429 
1430         pc[30] = m31 = p1*x31 + p7*x32  + p13*x33 + p19*x34 + p25*x35 + p31*x36;
1431         pc[31] = m32 = p2*x31 + p8*x32  + p14*x33 + p20*x34 + p26*x35 + p32*x36;
1432         pc[32] = m33 = p3*x31 + p9*x32  + p15*x33 + p21*x34 + p27*x35 + p33*x36;
1433         pc[33] = m34 = p4*x31 + p10*x32 + p16*x33 + p22*x34 + p28*x35 + p34*x36;
1434         pc[34] = m35 = p5*x31 + p11*x32 + p17*x33 + p23*x34 + p29*x35 + p35*x36;
1435         pc[35] = m36 = p6*x31 + p12*x32 + p18*x33 + p24*x34 + p30*x35 + p36*x36;
1436 
1437         nz = bi[row+1] - diag_offset[row] - 1;
1438         pv += 36;
1439         for (j=0; j<nz; j++) {
1440 	  x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
1441 	  x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
1442 	  x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
1443 	  x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
1444 	  x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
1445 	  x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
1446 	  x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
1447 	  x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
1448 	  x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
1449 	  x    = rtmp + 36*pj[j];
1450           x[0]  -= m1*x1  + m7*x2   + m13*x3  + m19*x4  + m25*x5  + m31*x6;
1451           x[1]  -= m2*x1  + m8*x2   + m14*x3  + m20*x4  + m26*x5  + m32*x6;
1452           x[2]  -= m3*x1  + m9*x2   + m15*x3  + m21*x4  + m27*x5  + m33*x6;
1453           x[3]  -= m4*x1  + m10*x2  + m16*x3  + m22*x4  + m28*x5  + m34*x6;
1454           x[4]  -= m5*x1  + m11*x2  + m17*x3  + m23*x4  + m29*x5  + m35*x6;
1455           x[5]  -= m6*x1  + m12*x2  + m18*x3  + m24*x4  + m30*x5  + m36*x6;
1456 
1457 	  x[6]  -= m1*x7  + m7*x8   + m13*x9  + m19*x10 + m25*x11 + m31*x12;
1458 	  x[7]  -= m2*x7  + m8*x8   + m14*x9  + m20*x10 + m26*x11 + m32*x12;
1459 	  x[8]  -= m3*x7  + m9*x8   + m15*x9  + m21*x10 + m27*x11 + m33*x12;
1460 	  x[9]  -= m4*x7  + m10*x8  + m16*x9  + m22*x10 + m28*x11 + m34*x12;
1461 	  x[10] -= m5*x7  + m11*x8  + m17*x9  + m23*x10 + m29*x11 + m35*x12;
1462 	  x[11] -= m6*x7  + m12*x8  + m18*x9  + m24*x10 + m30*x11 + m36*x12;
1463 
1464 	  x[12] -= m1*x13 + m7*x14  + m13*x15 + m19*x16 + m25*x17 + m31*x18;
1465 	  x[13] -= m2*x13 + m8*x14  + m14*x15 + m20*x16 + m26*x17 + m32*x18;
1466 	  x[14] -= m3*x13 + m9*x14  + m15*x15 + m21*x16 + m27*x17 + m33*x18;
1467 	  x[15] -= m4*x13 + m10*x14 + m16*x15 + m22*x16 + m28*x17 + m34*x18;
1468 	  x[16] -= m5*x13 + m11*x14 + m17*x15 + m23*x16 + m29*x17 + m35*x18;
1469 	  x[17] -= m6*x13 + m12*x14 + m18*x15 + m24*x16 + m30*x17 + m36*x18;
1470 
1471 	  x[18] -= m1*x19 + m7*x20  + m13*x21 + m19*x22 + m25*x23 + m31*x24;
1472 	  x[19] -= m2*x19 + m8*x20  + m14*x21 + m20*x22 + m26*x23 + m32*x24;
1473 	  x[20] -= m3*x19 + m9*x20  + m15*x21 + m21*x22 + m27*x23 + m33*x24;
1474 	  x[21] -= m4*x19 + m10*x20 + m16*x21 + m22*x22 + m28*x23 + m34*x24;
1475 	  x[22] -= m5*x19 + m11*x20 + m17*x21 + m23*x22 + m29*x23 + m35*x24;
1476 	  x[23] -= m6*x19 + m12*x20 + m18*x21 + m24*x22 + m30*x23 + m36*x24;
1477 
1478 	  x[24] -= m1*x25 + m7*x26  + m13*x27 + m19*x28 + m25*x29 + m31*x30;
1479 	  x[25] -= m2*x25 + m8*x26  + m14*x27 + m20*x28 + m26*x29 + m32*x30;
1480 	  x[26] -= m3*x25 + m9*x26  + m15*x27 + m21*x28 + m27*x29 + m33*x30;
1481 	  x[27] -= m4*x25 + m10*x26 + m16*x27 + m22*x28 + m28*x29 + m34*x30;
1482 	  x[28] -= m5*x25 + m11*x26 + m17*x27 + m23*x28 + m29*x29 + m35*x30;
1483 	  x[29] -= m6*x25 + m12*x26 + m18*x27 + m24*x28 + m30*x29 + m36*x30;
1484 
1485 	  x[30] -= m1*x31 + m7*x32  + m13*x33 + m19*x34 + m25*x35 + m31*x36;
1486 	  x[31] -= m2*x31 + m8*x32  + m14*x33 + m20*x34 + m26*x35 + m32*x36;
1487 	  x[32] -= m3*x31 + m9*x32  + m15*x33 + m21*x34 + m27*x35 + m33*x36;
1488 	  x[33] -= m4*x31 + m10*x32 + m16*x33 + m22*x34 + m28*x35 + m34*x36;
1489 	  x[34] -= m5*x31 + m11*x32 + m17*x33 + m23*x34 + m29*x35 + m35*x36;
1490 	  x[35] -= m6*x31 + m12*x32 + m18*x33 + m24*x34 + m30*x35 + m36*x36;
1491 
1492           pv   += 36;
1493         }
1494         PLogFlops(432*nz+396);
1495       }
1496       row = *ajtmp++;
1497     }
1498     /* finished row so stick it into b->a */
1499     pv = ba + 36*bi[i];
1500     pj = bj + bi[i];
1501     nz = bi[i+1] - bi[i];
1502     for (j=0; j<nz; j++) {
1503       x      = rtmp+36*pj[j];
1504       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
1505       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7];
1506       pv[8]  = x[8];  pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11];
1507       pv[12] = x[12]; pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
1508       pv[16] = x[16]; pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19];
1509       pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23];
1510       pv[24] = x[24]; pv[25] = x[25]; pv[26] = x[26]; pv[27] = x[27];
1511       pv[28] = x[28]; pv[29] = x[29]; pv[30] = x[30]; pv[31] = x[31];
1512       pv[32] = x[32]; pv[33] = x[33]; pv[34] = x[34]; pv[35] = x[35];
1513       pv   += 36;
1514     }
1515     /* invert diagonal block */
1516     w = ba + 36*diag_offset[i];
1517     ierr = Kernel_A_gets_inverse_A_6(w);CHKERRQ(ierr);
1518   }
1519 
1520   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1521   C->factor    = FACTOR_LU;
1522   C->assembled = PETSC_TRUE;
1523   PLogFlops(1.3333*216*b->mbs); /* from inverting diagonal blocks */
1524   PetscFunctionReturn(0);
1525 }
1526 
1527 /* Version for when blocks are 5 by 5  */
1528 #undef __FUNC__
1529 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_5"
1530 int MatCholeskyFactorNumeric_SeqSBAIJ_5(Mat A,Mat *B)
1531 {
1532   Mat                C = *B;
1533   Mat_SeqSBAIJ       *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data;
1534   IS                 perm = b->row;
1535   int                *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
1536   int                *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
1537   MatScalar          *ba = b->a,*aa,*ap,*dk,*uik;
1538   MatScalar          *u,*d,*rtmp,*rtmp_ptr;
1539 
1540   PetscFunctionBegin;
1541   /* initialization */
1542   rtmp  = (MatScalar*)PetscMalloc(25*mbs*sizeof(MatScalar));CHKPTRQ(rtmp);
1543   ierr = PetscMemzero(rtmp,25*mbs*sizeof(MatScalar));CHKERRQ(ierr);
1544   il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il);
1545   jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl);
1546   for (i=0; i<mbs; i++) {
1547     jl[i] = mbs; il[0] = 0;
1548   }
1549   dk    = (MatScalar*)PetscMalloc(25*sizeof(MatScalar));CHKPTRQ(dk);
1550   uik   = (MatScalar*)PetscMalloc(25*sizeof(MatScalar));CHKPTRQ(uik);
1551   ierr  = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr);
1552 
1553   /* check permutation */
1554   if (!a->permute){
1555     ai = a->i; aj = a->j; aa = a->a;
1556   } else {
1557     ai = a->inew; aj = a->jnew;
1558     aa = (MatScalar*)PetscMalloc(25*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa);
1559     ierr = PetscMemcpy(aa,a->a,25*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr);
1560     a2anew  = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew);
1561     ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr);
1562 
1563     for (i=0; i<mbs; i++){
1564       jmin = ai[i]; jmax = ai[i+1];
1565       for (j=jmin; j<jmax; j++){
1566         while (a2anew[j] != j){
1567           k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k;
1568           for (k1=0; k1<25; k1++){
1569             dk[k1]       = aa[k*25+k1];
1570             aa[k*25+k1] = aa[j*25+k1];
1571             aa[j*25+k1] = dk[k1];
1572           }
1573         }
1574         /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */
1575         if (i > aj[j]){
1576           /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */
1577           ap = aa + j*25;                     /* ptr to the beginning of j-th block of aa */
1578           for (k=0; k<25; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */
1579           for (k=0; k<5; k++){               /* j-th block of aa <- dk^T */
1580             for (k1=0; k1<5; k1++) *ap++ = dk[k + 5*k1];
1581           }
1582         }
1583       }
1584     }
1585     ierr = PetscFree(a2anew);CHKERRA(ierr);
1586   }
1587 
1588   /* for each row k */
1589   for (k = 0; k<mbs; k++){
1590 
1591     /*initialize k-th row with elements nonzero in row perm(k) of A */
1592     jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1];
1593     if (jmin < jmax) {
1594       ap = aa + jmin*25;
1595       for (j = jmin; j < jmax; j++){
1596         vj = perm_ptr[aj[j]];         /* block col. index */
1597         rtmp_ptr = rtmp + vj*25;
1598         for (i=0; i<25; i++) *rtmp_ptr++ = *ap++;
1599       }
1600     }
1601 
1602     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
1603     ierr = PetscMemcpy(dk,rtmp+k*25,25*sizeof(MatScalar));CHKERRQ(ierr);
1604     i = jl[k]; /* first row to be added to k_th row  */
1605 
1606     while (i < mbs){
1607       nexti = jl[i]; /* next row to be added to k_th row */
1608 
1609       /* compute multiplier */
1610       ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
1611 
1612       /* uik = -inv(Di)*U_bar(i,k) */
1613       d = ba + i*25;
1614       u    = ba + ili*25;
1615 
1616       uik[0] = -(d[0]*u[0] + d[5]*u[1] + d[10]*u[2] + d[15]*u[3] + d[20]*u[4]);
1617       uik[1] = -(d[1]*u[0] + d[6]*u[1] + d[11]*u[2] + d[16]*u[3] + d[21]*u[4]);
1618       uik[2] = -(d[2]*u[0] + d[7]*u[1] + d[12]*u[2] + d[17]*u[3] + d[22]*u[4]);
1619       uik[3] = -(d[3]*u[0] + d[8]*u[1] + d[13]*u[2] + d[18]*u[3] + d[23]*u[4]);
1620       uik[4] = -(d[4]*u[0] + d[9]*u[1] + d[14]*u[2] + d[19]*u[3] + d[24]*u[4]);
1621 
1622       uik[5] = -(d[0]*u[5] + d[5]*u[6] + d[10]*u[7] + d[15]*u[8] + d[20]*u[9]);
1623       uik[6] = -(d[1]*u[5] + d[6]*u[6] + d[11]*u[7] + d[16]*u[8] + d[21]*u[9]);
1624       uik[7] = -(d[2]*u[5] + d[7]*u[6] + d[12]*u[7] + d[17]*u[8] + d[22]*u[9]);
1625       uik[8] = -(d[3]*u[5] + d[8]*u[6] + d[13]*u[7] + d[18]*u[8] + d[23]*u[9]);
1626       uik[9] = -(d[4]*u[5] + d[9]*u[6] + d[14]*u[7] + d[19]*u[8] + d[24]*u[9]);
1627 
1628       uik[10]= -(d[0]*u[10] + d[5]*u[11] + d[10]*u[12] + d[15]*u[13] + d[20]*u[14]);
1629       uik[11]= -(d[1]*u[10] + d[6]*u[11] + d[11]*u[12] + d[16]*u[13] + d[21]*u[14]);
1630       uik[12]= -(d[2]*u[10] + d[7]*u[11] + d[12]*u[12] + d[17]*u[13] + d[22]*u[14]);
1631       uik[13]= -(d[3]*u[10] + d[8]*u[11] + d[13]*u[12] + d[18]*u[13] + d[23]*u[14]);
1632       uik[14]= -(d[4]*u[10] + d[9]*u[11] + d[14]*u[12] + d[19]*u[13] + d[24]*u[14]);
1633 
1634       uik[15]= -(d[0]*u[15] + d[5]*u[16] + d[10]*u[17] + d[15]*u[18] + d[20]*u[19]);
1635       uik[16]= -(d[1]*u[15] + d[6]*u[16] + d[11]*u[17] + d[16]*u[18] + d[21]*u[19]);
1636       uik[17]= -(d[2]*u[15] + d[7]*u[16] + d[12]*u[17] + d[17]*u[18] + d[22]*u[19]);
1637       uik[18]= -(d[3]*u[15] + d[8]*u[16] + d[13]*u[17] + d[18]*u[18] + d[23]*u[19]);
1638       uik[19]= -(d[4]*u[15] + d[9]*u[16] + d[14]*u[17] + d[19]*u[18] + d[24]*u[19]);
1639 
1640       uik[20]= -(d[0]*u[20] + d[5]*u[21] + d[10]*u[22] + d[15]*u[23] + d[20]*u[24]);
1641       uik[21]= -(d[1]*u[20] + d[6]*u[21] + d[11]*u[22] + d[16]*u[23] + d[21]*u[24]);
1642       uik[22]= -(d[2]*u[20] + d[7]*u[21] + d[12]*u[22] + d[17]*u[23] + d[22]*u[24]);
1643       uik[23]= -(d[3]*u[20] + d[8]*u[21] + d[13]*u[22] + d[18]*u[23] + d[23]*u[24]);
1644       uik[24]= -(d[4]*u[20] + d[9]*u[21] + d[14]*u[22] + d[19]*u[23] + d[24]*u[24]);
1645 
1646 
1647       /* update D(k) += -U(i,k)^T * U_bar(i,k) */
1648       dk[0] +=  uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3] + uik[4]*u[4];
1649       dk[1] +=  uik[5]*u[0] + uik[6]*u[1] + uik[7]*u[2] + uik[8]*u[3] + uik[9]*u[4];
1650       dk[2] += uik[10]*u[0]+ uik[11]*u[1]+ uik[12]*u[2]+ uik[13]*u[3]+ uik[14]*u[4];
1651       dk[3] += uik[15]*u[0]+ uik[16]*u[1]+ uik[17]*u[2]+ uik[18]*u[3]+ uik[19]*u[4];
1652       dk[4] += uik[20]*u[0]+ uik[21]*u[1]+ uik[22]*u[2]+ uik[23]*u[3]+ uik[24]*u[4];
1653 
1654       dk[5] +=  uik[0]*u[5] + uik[1]*u[6] + uik[2]*u[7] + uik[3]*u[8] + uik[4]*u[9];
1655       dk[6] +=  uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8] + uik[9]*u[9];
1656       dk[7] += uik[10]*u[5]+ uik[11]*u[6]+ uik[12]*u[7]+ uik[13]*u[8]+ uik[14]*u[9];
1657       dk[8] += uik[15]*u[5]+ uik[16]*u[6]+ uik[17]*u[7]+ uik[18]*u[8]+ uik[19]*u[9];
1658       dk[9] += uik[20]*u[5]+ uik[21]*u[6]+ uik[22]*u[7]+ uik[23]*u[8]+ uik[24]*u[9];
1659 
1660       dk[10] +=  uik[0]*u[10] + uik[1]*u[11] + uik[2]*u[12] + uik[3]*u[13] + uik[4]*u[14];
1661       dk[11] +=  uik[5]*u[10] + uik[6]*u[11] + uik[7]*u[12] + uik[8]*u[13] + uik[9]*u[14];
1662       dk[12] += uik[10]*u[10]+ uik[11]*u[11]+ uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14];
1663       dk[13] += uik[15]*u[10]+ uik[16]*u[11]+ uik[17]*u[12]+ uik[18]*u[13]+ uik[19]*u[14];
1664       dk[14] += uik[20]*u[10]+ uik[21]*u[11]+ uik[22]*u[12]+ uik[23]*u[13]+ uik[24]*u[14];
1665 
1666       dk[15] +=  uik[0]*u[15] + uik[1]*u[16] + uik[2]*u[17] + uik[3]*u[18] + uik[4]*u[19];
1667       dk[16] +=  uik[5]*u[15] + uik[6]*u[16] + uik[7]*u[17] + uik[8]*u[18] + uik[9]*u[19];
1668       dk[17] += uik[10]*u[15]+ uik[11]*u[16]+ uik[12]*u[17]+ uik[13]*u[18]+ uik[14]*u[19];
1669       dk[18] += uik[15]*u[15]+ uik[16]*u[16]+ uik[17]*u[17]+ uik[18]*u[18]+ uik[19]*u[19];
1670       dk[19] += uik[20]*u[15]+ uik[21]*u[16]+ uik[22]*u[17]+ uik[23]*u[18]+ uik[24]*u[19];
1671 
1672       dk[20] +=  uik[0]*u[20] + uik[1]*u[21] + uik[2]*u[22] + uik[3]*u[23] + uik[4]*u[24];
1673       dk[21] +=  uik[5]*u[20] + uik[6]*u[21] + uik[7]*u[22] + uik[8]*u[23] + uik[9]*u[24];
1674       dk[22] += uik[10]*u[20]+ uik[11]*u[21]+ uik[12]*u[22]+ uik[13]*u[23]+ uik[14]*u[24];
1675       dk[23] += uik[15]*u[20]+ uik[16]*u[21]+ uik[17]*u[22]+ uik[18]*u[23]+ uik[19]*u[24];
1676       dk[24] += uik[20]*u[20]+ uik[21]*u[21]+ uik[22]*u[22]+ uik[23]*u[23]+ uik[24]*u[24];
1677 
1678       /* update -U(i,k) */
1679       ierr = PetscMemcpy(ba+ili*25,uik,25*sizeof(MatScalar));CHKERRQ(ierr);
1680 
1681       /* add multiple of row i to k-th row ... */
1682       jmin = ili + 1; jmax = bi[i+1];
1683       if (jmin < jmax){
1684         for (j=jmin; j<jmax; j++) {
1685           /* rtmp += -U(i,k)^T * U_bar(i,j) */
1686           rtmp_ptr = rtmp + bj[j]*25;
1687           u = ba + j*25;
1688           rtmp_ptr[0] +=  uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3] + uik[4]*u[4];
1689           rtmp_ptr[1] +=  uik[5]*u[0] + uik[6]*u[1] + uik[7]*u[2] + uik[8]*u[3] + uik[9]*u[4];
1690           rtmp_ptr[2] += uik[10]*u[0]+ uik[11]*u[1]+ uik[12]*u[2]+ uik[13]*u[3]+ uik[14]*u[4];
1691           rtmp_ptr[3] += uik[15]*u[0]+ uik[16]*u[1]+ uik[17]*u[2]+ uik[18]*u[3]+ uik[19]*u[4];
1692           rtmp_ptr[4] += uik[20]*u[0]+ uik[21]*u[1]+ uik[22]*u[2]+ uik[23]*u[3]+ uik[24]*u[4];
1693 
1694           rtmp_ptr[5] +=  uik[0]*u[5] + uik[1]*u[6] + uik[2]*u[7] + uik[3]*u[8] + uik[4]*u[9];
1695           rtmp_ptr[6] +=  uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8] + uik[9]*u[9];
1696           rtmp_ptr[7] += uik[10]*u[5]+ uik[11]*u[6]+ uik[12]*u[7]+ uik[13]*u[8]+ uik[14]*u[9];
1697           rtmp_ptr[8] += uik[15]*u[5]+ uik[16]*u[6]+ uik[17]*u[7]+ uik[18]*u[8]+ uik[19]*u[9];
1698           rtmp_ptr[9] += uik[20]*u[5]+ uik[21]*u[6]+ uik[22]*u[7]+ uik[23]*u[8]+ uik[24]*u[9];
1699 
1700           rtmp_ptr[10] +=  uik[0]*u[10] + uik[1]*u[11] + uik[2]*u[12] + uik[3]*u[13] + uik[4]*u[14];
1701           rtmp_ptr[11] +=  uik[5]*u[10] + uik[6]*u[11] + uik[7]*u[12] + uik[8]*u[13] + uik[9]*u[14];
1702           rtmp_ptr[12] += uik[10]*u[10]+ uik[11]*u[11]+ uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14];
1703           rtmp_ptr[13] += uik[15]*u[10]+ uik[16]*u[11]+ uik[17]*u[12]+ uik[18]*u[13]+ uik[19]*u[14];
1704           rtmp_ptr[14] += uik[20]*u[10]+ uik[21]*u[11]+ uik[22]*u[12]+ uik[23]*u[13]+ uik[24]*u[14];
1705 
1706           rtmp_ptr[15] +=  uik[0]*u[15] + uik[1]*u[16] + uik[2]*u[17] + uik[3]*u[18] + uik[4]*u[19];
1707           rtmp_ptr[16] +=  uik[5]*u[15] + uik[6]*u[16] + uik[7]*u[17] + uik[8]*u[18] + uik[9]*u[19];
1708           rtmp_ptr[17] += uik[10]*u[15]+ uik[11]*u[16]+ uik[12]*u[17]+ uik[13]*u[18]+ uik[14]*u[19];
1709           rtmp_ptr[18] += uik[15]*u[15]+ uik[16]*u[16]+ uik[17]*u[17]+ uik[18]*u[18]+ uik[19]*u[19];
1710           rtmp_ptr[19] += uik[20]*u[15]+ uik[21]*u[16]+ uik[22]*u[17]+ uik[23]*u[18]+ uik[24]*u[19];
1711 
1712           rtmp_ptr[20] +=  uik[0]*u[20] + uik[1]*u[21] + uik[2]*u[22] + uik[3]*u[23] + uik[4]*u[24];
1713           rtmp_ptr[21] +=  uik[5]*u[20] + uik[6]*u[21] + uik[7]*u[22] + uik[8]*u[23] + uik[9]*u[24];
1714           rtmp_ptr[22] += uik[10]*u[20]+ uik[11]*u[21]+ uik[12]*u[22]+ uik[13]*u[23]+ uik[14]*u[24];
1715           rtmp_ptr[23] += uik[15]*u[20]+ uik[16]*u[21]+ uik[17]*u[22]+ uik[18]*u[23]+ uik[19]*u[24];
1716           rtmp_ptr[24] += uik[20]*u[20]+ uik[21]*u[21]+ uik[22]*u[22]+ uik[23]*u[23]+ uik[24]*u[24];
1717         }
1718 
1719         /* ... add i to row list for next nonzero entry */
1720         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
1721         j     = bj[jmin];
1722         jl[i] = jl[j]; jl[j] = i; /* update jl */
1723       }
1724       i = nexti;
1725     }
1726 
1727     /* save nonzero entries in k-th row of U ... */
1728 
1729     /* invert diagonal block */
1730     d = ba+k*25;
1731     ierr = PetscMemcpy(d,dk,25*sizeof(MatScalar));CHKERRQ(ierr);
1732     ierr = Kernel_A_gets_inverse_A_5(d);CHKERRQ(ierr);
1733 
1734     jmin = bi[k]; jmax = bi[k+1];
1735     if (jmin < jmax) {
1736       for (j=jmin; j<jmax; j++){
1737          vj = bj[j];           /* block col. index of U */
1738          u   = ba + j*25;
1739          rtmp_ptr = rtmp + vj*25;
1740          for (k1=0; k1<25; k1++){
1741            *u++        = *rtmp_ptr;
1742            *rtmp_ptr++ = 0.0;
1743          }
1744       }
1745 
1746       /* ... add k to row list for first nonzero entry in k-th row */
1747       il[k] = jmin;
1748       i     = bj[jmin];
1749       jl[k] = jl[i]; jl[i] = k;
1750     }
1751   }
1752 
1753   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1754   ierr = PetscFree(il);CHKERRQ(ierr);
1755   ierr = PetscFree(jl);CHKERRQ(ierr);
1756   ierr = PetscFree(dk);CHKERRQ(ierr);
1757   ierr = PetscFree(uik);CHKERRQ(ierr);
1758   if (a->permute){
1759     ierr = PetscFree(aa);CHKERRQ(ierr);
1760   }
1761 
1762   ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr);
1763   C->factor    = FACTOR_CHOLESKY;
1764   C->assembled = PETSC_TRUE;
1765   C->preallocated = PETSC_TRUE;
1766   PLogFlops(1.3333*125*b->mbs); /* from inverting diagonal blocks */
1767   PetscFunctionReturn(0);
1768 }
1769 
1770 /*
1771       Version for when blocks are 5 by 5 Using natural ordering
1772 */
1773 #undef __FUNC__
1774 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_5_NaturalOrdering"
1775 int MatCholeskyFactorNumeric_SeqSBAIJ_5_NaturalOrdering(Mat A,Mat *B)
1776 {
1777   Mat         C = *B;
1778   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
1779   int         ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
1780   int         *ajtmpold,*ajtmp,nz,row;
1781   int         *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
1782   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
1783   MatScalar   x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15;
1784   MatScalar   x16,x17,x18,x19,x20,x21,x22,x23,x24,x25;
1785   MatScalar   p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15;
1786   MatScalar   p16,p17,p18,p19,p20,p21,p22,p23,p24,p25;
1787   MatScalar   m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12,m13,m14,m15;
1788   MatScalar   m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
1789   MatScalar   *ba = b->a,*aa = a->a;
1790 
1791   PetscFunctionBegin;
1792   rtmp  = (MatScalar*)PetscMalloc(25*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
1793   for (i=0; i<n; i++) {
1794     nz    = bi[i+1] - bi[i];
1795     ajtmp = bj + bi[i];
1796     for  (j=0; j<nz; j++) {
1797       x = rtmp+25*ajtmp[j];
1798       x[0]  = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = x[9] = 0.0;
1799       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
1800       x[16] = x[17] = x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0;
1801     }
1802     /* load in initial (unfactored row) */
1803     nz       = ai[i+1] - ai[i];
1804     ajtmpold = aj + ai[i];
1805     v        = aa + 25*ai[i];
1806     for (j=0; j<nz; j++) {
1807       x    = rtmp+25*ajtmpold[j];
1808       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
1809       x[4]  = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
1810       x[9]  = v[9];  x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
1811       x[14] = v[14]; x[15] = v[15]; x[16] = v[16]; x[17] = v[17]; x[18] = v[18];
1812       x[19] = v[19]; x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23];
1813       x[24] = v[24];
1814       v    += 25;
1815     }
1816     row = *ajtmp++;
1817     while (row < i) {
1818       pc  = rtmp + 25*row;
1819       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
1820       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
1821       p10 = pc[9];  p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
1822       p15 = pc[14]; p16 = pc[15]; p17 = pc[16]; p18 = pc[17];
1823       p19 = pc[18]; p20 = pc[19]; p21 = pc[20]; p22 = pc[21]; p23 = pc[22];
1824       p24 = pc[23]; p25 = pc[24];
1825       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
1826           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
1827           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
1828           || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0
1829           || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 || p25 != 0.0) {
1830         pv = ba + 25*diag_offset[row];
1831         pj = bj + diag_offset[row] + 1;
1832         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
1833         x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
1834         x10 = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
1835         x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17]; x19 = pv[18];
1836         x20 = pv[19]; x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
1837         x25 = pv[24];
1838         pc[0] = m1 = p1*x1 + p6*x2  + p11*x3 + p16*x4 + p21*x5;
1839         pc[1] = m2 = p2*x1 + p7*x2  + p12*x3 + p17*x4 + p22*x5;
1840         pc[2] = m3 = p3*x1 + p8*x2  + p13*x3 + p18*x4 + p23*x5;
1841         pc[3] = m4 = p4*x1 + p9*x2  + p14*x3 + p19*x4 + p24*x5;
1842         pc[4] = m5 = p5*x1 + p10*x2 + p15*x3 + p20*x4 + p25*x5;
1843 
1844         pc[5]  = m6  = p1*x6 + p6*x7  + p11*x8 + p16*x9 + p21*x10;
1845         pc[6]  = m7  = p2*x6 + p7*x7  + p12*x8 + p17*x9 + p22*x10;
1846         pc[7]  = m8  = p3*x6 + p8*x7  + p13*x8 + p18*x9 + p23*x10;
1847         pc[8]  = m9  = p4*x6 + p9*x7  + p14*x8 + p19*x9 + p24*x10;
1848         pc[9]  = m10 = p5*x6 + p10*x7 + p15*x8 + p20*x9 + p25*x10;
1849 
1850         pc[10] = m11 = p1*x11 + p6*x12  + p11*x13 + p16*x14 + p21*x15;
1851         pc[11] = m12 = p2*x11 + p7*x12  + p12*x13 + p17*x14 + p22*x15;
1852         pc[12] = m13 = p3*x11 + p8*x12  + p13*x13 + p18*x14 + p23*x15;
1853         pc[13] = m14 = p4*x11 + p9*x12  + p14*x13 + p19*x14 + p24*x15;
1854         pc[14] = m15 = p5*x11 + p10*x12 + p15*x13 + p20*x14 + p25*x15;
1855 
1856         pc[15] = m16 = p1*x16 + p6*x17  + p11*x18 + p16*x19 + p21*x20;
1857         pc[16] = m17 = p2*x16 + p7*x17  + p12*x18 + p17*x19 + p22*x20;
1858         pc[17] = m18 = p3*x16 + p8*x17  + p13*x18 + p18*x19 + p23*x20;
1859         pc[18] = m19 = p4*x16 + p9*x17  + p14*x18 + p19*x19 + p24*x20;
1860         pc[19] = m20 = p5*x16 + p10*x17 + p15*x18 + p20*x19 + p25*x20;
1861 
1862         pc[20] = m21 = p1*x21 + p6*x22  + p11*x23 + p16*x24 + p21*x25;
1863         pc[21] = m22 = p2*x21 + p7*x22  + p12*x23 + p17*x24 + p22*x25;
1864         pc[22] = m23 = p3*x21 + p8*x22  + p13*x23 + p18*x24 + p23*x25;
1865         pc[23] = m24 = p4*x21 + p9*x22  + p14*x23 + p19*x24 + p24*x25;
1866         pc[24] = m25 = p5*x21 + p10*x22 + p15*x23 + p20*x24 + p25*x25;
1867 
1868         nz = bi[row+1] - diag_offset[row] - 1;
1869         pv += 25;
1870         for (j=0; j<nz; j++) {
1871           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
1872           x5   = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
1873           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
1874           x14  = pv[13]; x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17];
1875           x19 = pv[18];  x20 = pv[19]; x21 = pv[20]; x22 = pv[21]; x23 = pv[22];
1876           x24 = pv[23];  x25 = pv[24];
1877           x    = rtmp + 25*pj[j];
1878           x[0] -= m1*x1 + m6*x2   + m11*x3  + m16*x4 + m21*x5;
1879           x[1] -= m2*x1 + m7*x2   + m12*x3  + m17*x4 + m22*x5;
1880           x[2] -= m3*x1 + m8*x2   + m13*x3  + m18*x4 + m23*x5;
1881           x[3] -= m4*x1 + m9*x2   + m14*x3  + m19*x4 + m24*x5;
1882           x[4] -= m5*x1 + m10*x2  + m15*x3  + m20*x4 + m25*x5;
1883 
1884           x[5] -= m1*x6 + m6*x7   + m11*x8  + m16*x9 + m21*x10;
1885           x[6] -= m2*x6 + m7*x7   + m12*x8  + m17*x9 + m22*x10;
1886           x[7] -= m3*x6 + m8*x7   + m13*x8  + m18*x9 + m23*x10;
1887           x[8] -= m4*x6 + m9*x7   + m14*x8  + m19*x9 + m24*x10;
1888           x[9] -= m5*x6 + m10*x7  + m15*x8  + m20*x9 + m25*x10;
1889 
1890           x[10] -= m1*x11 + m6*x12  + m11*x13 + m16*x14 + m21*x15;
1891           x[11] -= m2*x11 + m7*x12  + m12*x13 + m17*x14 + m22*x15;
1892           x[12] -= m3*x11 + m8*x12  + m13*x13 + m18*x14 + m23*x15;
1893           x[13] -= m4*x11 + m9*x12  + m14*x13 + m19*x14 + m24*x15;
1894           x[14] -= m5*x11 + m10*x12 + m15*x13 + m20*x14 + m25*x15;
1895 
1896           x[15] -= m1*x16 + m6*x17  + m11*x18 + m16*x19 + m21*x20;
1897           x[16] -= m2*x16 + m7*x17  + m12*x18 + m17*x19 + m22*x20;
1898           x[17] -= m3*x16 + m8*x17  + m13*x18 + m18*x19 + m23*x20;
1899           x[18] -= m4*x16 + m9*x17  + m14*x18 + m19*x19 + m24*x20;
1900           x[19] -= m5*x16 + m10*x17 + m15*x18 + m20*x19 + m25*x20;
1901 
1902           x[20] -= m1*x21 + m6*x22  + m11*x23 + m16*x24 + m21*x25;
1903           x[21] -= m2*x21 + m7*x22  + m12*x23 + m17*x24 + m22*x25;
1904           x[22] -= m3*x21 + m8*x22  + m13*x23 + m18*x24 + m23*x25;
1905           x[23] -= m4*x21 + m9*x22  + m14*x23 + m19*x24 + m24*x25;
1906           x[24] -= m5*x21 + m10*x22 + m15*x23 + m20*x24 + m25*x25;
1907           pv   += 25;
1908         }
1909         PLogFlops(250*nz+225);
1910       }
1911       row = *ajtmp++;
1912     }
1913     /* finished row so stick it into b->a */
1914     pv = ba + 25*bi[i];
1915     pj = bj + bi[i];
1916     nz = bi[i+1] - bi[i];
1917     for (j=0; j<nz; j++) {
1918       x      = rtmp+25*pj[j];
1919       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
1920       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
1921       pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
1922       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; pv[16] = x[16]; pv[17] = x[17];
1923       pv[18] = x[18]; pv[19] = x[19]; pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22];
1924       pv[23] = x[23]; pv[24] = x[24];
1925       pv   += 25;
1926     }
1927     /* invert diagonal block */
1928     w = ba + 25*diag_offset[i];
1929     ierr = Kernel_A_gets_inverse_A_5(w);CHKERRQ(ierr);
1930   }
1931 
1932   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1933   C->factor    = FACTOR_LU;
1934   C->assembled = PETSC_TRUE;
1935   PLogFlops(1.3333*125*b->mbs); /* from inverting diagonal blocks */
1936   PetscFunctionReturn(0);
1937 }
1938 
1939 /*
1940       Version for when blocks are 4 by 4 Using natural ordering
1941 */
1942 #undef __FUNC__
1943 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_4_NaturalOrdering"
1944 int MatCholeskyFactorNumeric_SeqSBAIJ_4_NaturalOrdering(Mat A,Mat *B)
1945 {
1946   Mat         C = *B;
1947   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
1948   int         ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
1949   int         *ajtmpold,*ajtmp,nz,row;
1950   int         *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
1951   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
1952   MatScalar   p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
1953   MatScalar   p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
1954   MatScalar   p10,p11,p12,p13,p14,p15,p16,m10,m11,m12;
1955   MatScalar   m13,m14,m15,m16;
1956   MatScalar   *ba = b->a,*aa = a->a;
1957 
1958   PetscFunctionBegin;
1959   rtmp  = (MatScalar*)PetscMalloc(16*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
1960 
1961   for (i=0; i<n; i++) {
1962     nz    = bi[i+1] - bi[i];
1963     ajtmp = bj + bi[i];
1964     for  (j=0; j<nz; j++) {
1965       x = rtmp+16*ajtmp[j];
1966       x[0]  = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = x[9] = 0.0;
1967       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
1968     }
1969     /* load in initial (unfactored row) */
1970     nz       = ai[i+1] - ai[i];
1971     ajtmpold = aj + ai[i];
1972     v        = aa + 16*ai[i];
1973     for (j=0; j<nz; j++) {
1974       x    = rtmp+16*ajtmpold[j];
1975       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
1976       x[4]  = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
1977       x[9]  = v[9];  x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
1978       x[14] = v[14]; x[15] = v[15];
1979       v    += 16;
1980     }
1981     row = *ajtmp++;
1982     while (row < i) {
1983       pc  = rtmp + 16*row;
1984       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
1985       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
1986       p10 = pc[9];  p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
1987       p15 = pc[14]; p16 = pc[15];
1988       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
1989           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
1990           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
1991           || p16 != 0.0) {
1992         pv = ba + 16*diag_offset[row];
1993         pj = bj + diag_offset[row] + 1;
1994         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
1995         x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
1996         x10 = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
1997         x15 = pv[14]; x16 = pv[15];
1998         pc[0] = m1 = p1*x1 + p5*x2  + p9*x3  + p13*x4;
1999         pc[1] = m2 = p2*x1 + p6*x2  + p10*x3 + p14*x4;
2000         pc[2] = m3 = p3*x1 + p7*x2  + p11*x3 + p15*x4;
2001         pc[3] = m4 = p4*x1 + p8*x2  + p12*x3 + p16*x4;
2002 
2003         pc[4] = m5 = p1*x5 + p5*x6  + p9*x7  + p13*x8;
2004         pc[5] = m6 = p2*x5 + p6*x6  + p10*x7 + p14*x8;
2005         pc[6] = m7 = p3*x5 + p7*x6  + p11*x7 + p15*x8;
2006         pc[7] = m8 = p4*x5 + p8*x6  + p12*x7 + p16*x8;
2007 
2008         pc[8]  = m9  = p1*x9 + p5*x10  + p9*x11  + p13*x12;
2009         pc[9]  = m10 = p2*x9 + p6*x10  + p10*x11 + p14*x12;
2010         pc[10] = m11 = p3*x9 + p7*x10  + p11*x11 + p15*x12;
2011         pc[11] = m12 = p4*x9 + p8*x10  + p12*x11 + p16*x12;
2012 
2013         pc[12] = m13 = p1*x13 + p5*x14  + p9*x15  + p13*x16;
2014         pc[13] = m14 = p2*x13 + p6*x14  + p10*x15 + p14*x16;
2015         pc[14] = m15 = p3*x13 + p7*x14  + p11*x15 + p15*x16;
2016         pc[15] = m16 = p4*x13 + p8*x14  + p12*x15 + p16*x16;
2017 
2018         nz = bi[row+1] - diag_offset[row] - 1;
2019         pv += 16;
2020         for (j=0; j<nz; j++) {
2021           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
2022           x5   = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
2023           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
2024           x14  = pv[13]; x15 = pv[14]; x16 = pv[15];
2025           x    = rtmp + 16*pj[j];
2026           x[0] -= m1*x1 + m5*x2  + m9*x3  + m13*x4;
2027           x[1] -= m2*x1 + m6*x2  + m10*x3 + m14*x4;
2028           x[2] -= m3*x1 + m7*x2  + m11*x3 + m15*x4;
2029           x[3] -= m4*x1 + m8*x2  + m12*x3 + m16*x4;
2030 
2031           x[4] -= m1*x5 + m5*x6  + m9*x7  + m13*x8;
2032           x[5] -= m2*x5 + m6*x6  + m10*x7 + m14*x8;
2033           x[6] -= m3*x5 + m7*x6  + m11*x7 + m15*x8;
2034           x[7] -= m4*x5 + m8*x6  + m12*x7 + m16*x8;
2035 
2036           x[8]  -= m1*x9 + m5*x10 + m9*x11  + m13*x12;
2037           x[9]  -= m2*x9 + m6*x10 + m10*x11 + m14*x12;
2038           x[10] -= m3*x9 + m7*x10 + m11*x11 + m15*x12;
2039           x[11] -= m4*x9 + m8*x10 + m12*x11 + m16*x12;
2040 
2041           x[12] -= m1*x13 + m5*x14  + m9*x15  + m13*x16;
2042           x[13] -= m2*x13 + m6*x14  + m10*x15 + m14*x16;
2043           x[14] -= m3*x13 + m7*x14  + m11*x15 + m15*x16;
2044           x[15] -= m4*x13 + m8*x14  + m12*x15 + m16*x16;
2045 
2046           pv   += 16;
2047         }
2048         PLogFlops(128*nz+112);
2049       }
2050       row = *ajtmp++;
2051     }
2052     /* finished row so stick it into b->a */
2053     pv = ba + 16*bi[i];
2054     pj = bj + bi[i];
2055     nz = bi[i+1] - bi[i];
2056     for (j=0; j<nz; j++) {
2057       x      = rtmp+16*pj[j];
2058       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
2059       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
2060       pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
2061       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
2062       pv   += 16;
2063     }
2064     /* invert diagonal block */
2065     w = ba + 16*diag_offset[i];
2066     ierr = Kernel_A_gets_inverse_A_4(w);CHKERRQ(ierr);
2067   }
2068 
2069   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2070   C->factor    = FACTOR_LU;
2071   C->assembled = PETSC_TRUE;
2072   C->preallocated = PETSC_TRUE;
2073   PLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */
2074   PetscFunctionReturn(0);
2075 }
2076 
2077 /* Version for when blocks are 4 by 4  */
2078 #undef __FUNC__
2079 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_4"
2080 int MatCholeskyFactorNumeric_SeqSBAIJ_4(Mat A,Mat *B)
2081 {
2082   Mat                C = *B;
2083   Mat_SeqSBAIJ       *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data;
2084   IS                 perm = b->row;
2085   int                *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
2086   int                *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
2087   MatScalar          *ba = b->a,*aa,*ap,*dk,*uik;
2088   MatScalar          *u,*diag,*rtmp,*rtmp_ptr;
2089 
2090   PetscFunctionBegin;
2091   /* initialization */
2092   rtmp  = (MatScalar*)PetscMalloc(16*mbs*sizeof(MatScalar));CHKPTRQ(rtmp);
2093   ierr = PetscMemzero(rtmp,16*mbs*sizeof(MatScalar));CHKERRQ(ierr);
2094   il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il);
2095   jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl);
2096   for (i=0; i<mbs; i++) {
2097     jl[i] = mbs; il[0] = 0;
2098   }
2099   dk    = (MatScalar*)PetscMalloc(16*sizeof(MatScalar));CHKPTRQ(dk);
2100   uik   = (MatScalar*)PetscMalloc(16*sizeof(MatScalar));CHKPTRQ(uik);
2101   ierr  = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr);
2102 
2103   /* check permutation */
2104   if (!a->permute){
2105     ai = a->i; aj = a->j; aa = a->a;
2106   } else {
2107     ai = a->inew; aj = a->jnew;
2108     aa = (MatScalar*)PetscMalloc(16*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa);
2109     ierr = PetscMemcpy(aa,a->a,16*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr);
2110     a2anew  = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew);
2111     ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr);
2112 
2113     for (i=0; i<mbs; i++){
2114       jmin = ai[i]; jmax = ai[i+1];
2115       for (j=jmin; j<jmax; j++){
2116         while (a2anew[j] != j){
2117           k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k;
2118           for (k1=0; k1<16; k1++){
2119             dk[k1]       = aa[k*16+k1];
2120             aa[k*16+k1] = aa[j*16+k1];
2121             aa[j*16+k1] = dk[k1];
2122           }
2123         }
2124         /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */
2125         if (i > aj[j]){
2126           /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */
2127           ap = aa + j*16;                     /* ptr to the beginning of j-th block of aa */
2128           for (k=0; k<16; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */
2129           for (k=0; k<4; k++){               /* j-th block of aa <- dk^T */
2130             for (k1=0; k1<4; k1++) *ap++ = dk[k + 4*k1];
2131           }
2132         }
2133       }
2134     }
2135     ierr = PetscFree(a2anew);CHKERRA(ierr);
2136   }
2137 
2138   /* for each row k */
2139   for (k = 0; k<mbs; k++){
2140 
2141     /*initialize k-th row with elements nonzero in row perm(k) of A */
2142     jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1];
2143     if (jmin < jmax) {
2144       ap = aa + jmin*16;
2145       for (j = jmin; j < jmax; j++){
2146         vj = perm_ptr[aj[j]];         /* block col. index */
2147         rtmp_ptr = rtmp + vj*16;
2148         for (i=0; i<16; i++) *rtmp_ptr++ = *ap++;
2149       }
2150     }
2151 
2152     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
2153     ierr = PetscMemcpy(dk,rtmp+k*16,16*sizeof(MatScalar));CHKERRQ(ierr);
2154     i = jl[k]; /* first row to be added to k_th row  */
2155 
2156     while (i < mbs){
2157       nexti = jl[i]; /* next row to be added to k_th row */
2158 
2159       /* compute multiplier */
2160       ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
2161 
2162       /* uik = -inv(Di)*U_bar(i,k) */
2163       diag = ba + i*16;
2164       u    = ba + ili*16;
2165 
2166       uik[0] = -(diag[0]*u[0] + diag[4]*u[1] + diag[8]*u[2] + diag[12]*u[3]);
2167       uik[1] = -(diag[1]*u[0] + diag[5]*u[1] + diag[9]*u[2] + diag[13]*u[3]);
2168       uik[2] = -(diag[2]*u[0] + diag[6]*u[1] + diag[10]*u[2]+ diag[14]*u[3]);
2169       uik[3] = -(diag[3]*u[0] + diag[7]*u[1] + diag[11]*u[2]+ diag[15]*u[3]);
2170 
2171       uik[4] = -(diag[0]*u[4] + diag[4]*u[5] + diag[8]*u[6] + diag[12]*u[7]);
2172       uik[5] = -(diag[1]*u[4] + diag[5]*u[5] + diag[9]*u[6] + diag[13]*u[7]);
2173       uik[6] = -(diag[2]*u[4] + diag[6]*u[5] + diag[10]*u[6]+ diag[14]*u[7]);
2174       uik[7] = -(diag[3]*u[4] + diag[7]*u[5] + diag[11]*u[6]+ diag[15]*u[7]);
2175 
2176       uik[8] = -(diag[0]*u[8] + diag[4]*u[9] + diag[8]*u[10] + diag[12]*u[11]);
2177       uik[9] = -(diag[1]*u[8] + diag[5]*u[9] + diag[9]*u[10] + diag[13]*u[11]);
2178       uik[10]= -(diag[2]*u[8] + diag[6]*u[9] + diag[10]*u[10]+ diag[14]*u[11]);
2179       uik[11]= -(diag[3]*u[8] + diag[7]*u[9] + diag[11]*u[10]+ diag[15]*u[11]);
2180 
2181       uik[12]= -(diag[0]*u[12] + diag[4]*u[13] + diag[8]*u[14] + diag[12]*u[15]);
2182       uik[13]= -(diag[1]*u[12] + diag[5]*u[13] + diag[9]*u[14] + diag[13]*u[15]);
2183       uik[14]= -(diag[2]*u[12] + diag[6]*u[13] + diag[10]*u[14]+ diag[14]*u[15]);
2184       uik[15]= -(diag[3]*u[12] + diag[7]*u[13] + diag[11]*u[14]+ diag[15]*u[15]);
2185 
2186       /* update D(k) += -U(i,k)^T * U_bar(i,k) */
2187       dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3];
2188       dk[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3];
2189       dk[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3];
2190       dk[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3];
2191 
2192       dk[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7];
2193       dk[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7];
2194       dk[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7];
2195       dk[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7];
2196 
2197       dk[8] += uik[0]*u[8] + uik[1]*u[9] + uik[2]*u[10] + uik[3]*u[11];
2198       dk[9] += uik[4]*u[8] + uik[5]*u[9] + uik[6]*u[10] + uik[7]*u[11];
2199       dk[10]+= uik[8]*u[8] + uik[9]*u[9] + uik[10]*u[10]+ uik[11]*u[11];
2200       dk[11]+= uik[12]*u[8]+ uik[13]*u[9]+ uik[14]*u[10]+ uik[15]*u[11];
2201 
2202       dk[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15];
2203       dk[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15];
2204       dk[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15];
2205       dk[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15];
2206 
2207       /* update -U(i,k) */
2208       ierr = PetscMemcpy(ba+ili*16,uik,16*sizeof(MatScalar));CHKERRQ(ierr);
2209 
2210       /* add multiple of row i to k-th row ... */
2211       jmin = ili + 1; jmax = bi[i+1];
2212       if (jmin < jmax){
2213         for (j=jmin; j<jmax; j++) {
2214           /* rtmp += -U(i,k)^T * U_bar(i,j) */
2215           rtmp_ptr = rtmp + bj[j]*16;
2216           u = ba + j*16;
2217           rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3];
2218           rtmp_ptr[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3];
2219           rtmp_ptr[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3];
2220           rtmp_ptr[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3];
2221 
2222           rtmp_ptr[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7];
2223           rtmp_ptr[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7];
2224           rtmp_ptr[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7];
2225           rtmp_ptr[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7];
2226 
2227           rtmp_ptr[8] += uik[0]*u[8] + uik[1]*u[9] + uik[2]*u[10] + uik[3]*u[11];
2228           rtmp_ptr[9] += uik[4]*u[8] + uik[5]*u[9] + uik[6]*u[10] + uik[7]*u[11];
2229           rtmp_ptr[10]+= uik[8]*u[8] + uik[9]*u[9] + uik[10]*u[10]+ uik[11]*u[11];
2230           rtmp_ptr[11]+= uik[12]*u[8]+ uik[13]*u[9]+ uik[14]*u[10]+ uik[15]*u[11];
2231 
2232           rtmp_ptr[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15];
2233           rtmp_ptr[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15];
2234           rtmp_ptr[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15];
2235           rtmp_ptr[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15];
2236         }
2237 
2238         /* ... add i to row list for next nonzero entry */
2239         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
2240         j     = bj[jmin];
2241         jl[i] = jl[j]; jl[j] = i; /* update jl */
2242       }
2243       i = nexti;
2244     }
2245 
2246     /* save nonzero entries in k-th row of U ... */
2247 
2248     /* invert diagonal block */
2249     diag = ba+k*16;
2250     ierr = PetscMemcpy(diag,dk,16*sizeof(MatScalar));CHKERRQ(ierr);
2251     ierr = Kernel_A_gets_inverse_A_4(diag);CHKERRQ(ierr);
2252 
2253     jmin = bi[k]; jmax = bi[k+1];
2254     if (jmin < jmax) {
2255       for (j=jmin; j<jmax; j++){
2256          vj = bj[j];           /* block col. index of U */
2257          u   = ba + j*16;
2258          rtmp_ptr = rtmp + vj*16;
2259          for (k1=0; k1<16; k1++){
2260            *u++        = *rtmp_ptr;
2261            *rtmp_ptr++ = 0.0;
2262          }
2263       }
2264 
2265       /* ... add k to row list for first nonzero entry in k-th row */
2266       il[k] = jmin;
2267       i     = bj[jmin];
2268       jl[k] = jl[i]; jl[i] = k;
2269     }
2270   }
2271 
2272   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2273   ierr = PetscFree(il);CHKERRQ(ierr);
2274   ierr = PetscFree(jl);CHKERRQ(ierr);
2275   ierr = PetscFree(dk);CHKERRQ(ierr);
2276   ierr = PetscFree(uik);CHKERRQ(ierr);
2277   if (a->permute){
2278     ierr = PetscFree(aa);CHKERRQ(ierr);
2279   }
2280 
2281   ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr);
2282   C->factor    = FACTOR_CHOLESKY;
2283   C->assembled = PETSC_TRUE;
2284   C->preallocated = PETSC_TRUE;
2285   PLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */
2286   PetscFunctionReturn(0);
2287 }
2288 
2289 /* Version for when blocks are 3 by 3  */
2290 #undef __FUNC__
2291 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_3"
2292 int MatCholeskyFactorNumeric_SeqSBAIJ_3(Mat A,Mat *B)
2293 {
2294   Mat                C = *B;
2295   Mat_SeqSBAIJ       *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data;
2296   IS                 perm = b->row;
2297   int                *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
2298   int                *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
2299   MatScalar          *ba = b->a,*aa,*ap,*dk,*uik;
2300   MatScalar          *u,*diag,*rtmp,*rtmp_ptr;
2301 
2302   PetscFunctionBegin;
2303   /* initialization */
2304   rtmp  = (MatScalar*)PetscMalloc(9*mbs*sizeof(MatScalar));CHKPTRQ(rtmp);
2305   ierr = PetscMemzero(rtmp,9*mbs*sizeof(MatScalar));CHKERRQ(ierr);
2306   il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il);
2307   jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl);
2308   for (i=0; i<mbs; i++) {
2309     jl[i] = mbs; il[0] = 0;
2310   }
2311   dk  = (MatScalar*)PetscMalloc(9*sizeof(MatScalar));CHKPTRQ(dk);
2312   uik = (MatScalar*)PetscMalloc(9*sizeof(MatScalar));CHKPTRQ(uik);
2313   ierr  = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr);
2314 
2315   /* check permutation */
2316   if (!a->permute){
2317     ai = a->i; aj = a->j; aa = a->a;
2318   } else {
2319     ai = a->inew; aj = a->jnew;
2320     aa = (MatScalar*)PetscMalloc(9*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa);
2321     ierr = PetscMemcpy(aa,a->a,9*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr);
2322     a2anew  = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew);
2323     ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr);
2324 
2325     for (i=0; i<mbs; i++){
2326       jmin = ai[i]; jmax = ai[i+1];
2327       for (j=jmin; j<jmax; j++){
2328         while (a2anew[j] != j){
2329           k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k;
2330           for (k1=0; k1<9; k1++){
2331             dk[k1]       = aa[k*9+k1];
2332             aa[k*9+k1] = aa[j*9+k1];
2333             aa[j*9+k1] = dk[k1];
2334           }
2335         }
2336         /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */
2337         if (i > aj[j]){
2338           /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */
2339           ap = aa + j*9;                     /* ptr to the beginning of j-th block of aa */
2340           for (k=0; k<9; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */
2341           for (k=0; k<3; k++){               /* j-th block of aa <- dk^T */
2342             for (k1=0; k1<3; k1++) *ap++ = dk[k + 3*k1];
2343           }
2344         }
2345       }
2346     }
2347     ierr = PetscFree(a2anew);CHKERRA(ierr);
2348   }
2349 
2350   /* for each row k */
2351   for (k = 0; k<mbs; k++){
2352 
2353     /*initialize k-th row with elements nonzero in row perm(k) of A */
2354     jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1];
2355     if (jmin < jmax) {
2356       ap = aa + jmin*9;
2357       for (j = jmin; j < jmax; j++){
2358         vj = perm_ptr[aj[j]];         /* block col. index */
2359         rtmp_ptr = rtmp + vj*9;
2360         for (i=0; i<9; i++) *rtmp_ptr++ = *ap++;
2361       }
2362     }
2363 
2364     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
2365     ierr = PetscMemcpy(dk,rtmp+k*9,9*sizeof(MatScalar));CHKERRQ(ierr);
2366     i = jl[k]; /* first row to be added to k_th row  */
2367 
2368     while (i < mbs){
2369       nexti = jl[i]; /* next row to be added to k_th row */
2370 
2371       /* compute multiplier */
2372       ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
2373 
2374       /* uik = -inv(Di)*U_bar(i,k) */
2375       diag = ba + i*9;
2376       u    = ba + ili*9;
2377 
2378       uik[0] = -(diag[0]*u[0] + diag[3]*u[1] + diag[6]*u[2]);
2379       uik[1] = -(diag[1]*u[0] + diag[4]*u[1] + diag[7]*u[2]);
2380       uik[2] = -(diag[2]*u[0] + diag[5]*u[1] + diag[8]*u[2]);
2381 
2382       uik[3] = -(diag[0]*u[3] + diag[3]*u[4] + diag[6]*u[5]);
2383       uik[4] = -(diag[1]*u[3] + diag[4]*u[4] + diag[7]*u[5]);
2384       uik[5] = -(diag[2]*u[3] + diag[5]*u[4] + diag[8]*u[5]);
2385 
2386       uik[6] = -(diag[0]*u[6] + diag[3]*u[7] + diag[6]*u[8]);
2387       uik[7] = -(diag[1]*u[6] + diag[4]*u[7] + diag[7]*u[8]);
2388       uik[8] = -(diag[2]*u[6] + diag[5]*u[7] + diag[8]*u[8]);
2389 
2390       /* update D(k) += -U(i,k)^T * U_bar(i,k) */
2391       dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2];
2392       dk[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2];
2393       dk[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2];
2394 
2395       dk[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5];
2396       dk[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5];
2397       dk[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5];
2398 
2399       dk[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8];
2400       dk[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8];
2401       dk[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8];
2402 
2403       /* update -U(i,k) */
2404       ierr = PetscMemcpy(ba+ili*9,uik,9*sizeof(MatScalar));CHKERRQ(ierr);
2405 
2406       /* add multiple of row i to k-th row ... */
2407       jmin = ili + 1; jmax = bi[i+1];
2408       if (jmin < jmax){
2409         for (j=jmin; j<jmax; j++) {
2410           /* rtmp += -U(i,k)^T * U_bar(i,j) */
2411           rtmp_ptr = rtmp + bj[j]*9;
2412           u = ba + j*9;
2413           rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2];
2414           rtmp_ptr[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2];
2415           rtmp_ptr[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2];
2416 
2417           rtmp_ptr[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5];
2418           rtmp_ptr[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5];
2419           rtmp_ptr[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5];
2420 
2421           rtmp_ptr[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8];
2422           rtmp_ptr[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8];
2423           rtmp_ptr[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8];
2424         }
2425 
2426         /* ... add i to row list for next nonzero entry */
2427         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
2428         j     = bj[jmin];
2429         jl[i] = jl[j]; jl[j] = i; /* update jl */
2430       }
2431       i = nexti;
2432     }
2433 
2434     /* save nonzero entries in k-th row of U ... */
2435 
2436     /* invert diagonal block */
2437     diag = ba+k*9;
2438     ierr = PetscMemcpy(diag,dk,9*sizeof(MatScalar));CHKERRQ(ierr);
2439     ierr = Kernel_A_gets_inverse_A_3(diag);CHKERRQ(ierr);
2440 
2441     jmin = bi[k]; jmax = bi[k+1];
2442     if (jmin < jmax) {
2443       for (j=jmin; j<jmax; j++){
2444          vj = bj[j];           /* block col. index of U */
2445          u   = ba + j*9;
2446          rtmp_ptr = rtmp + vj*9;
2447          for (k1=0; k1<9; k1++){
2448            *u++        = *rtmp_ptr;
2449            *rtmp_ptr++ = 0.0;
2450          }
2451       }
2452 
2453       /* ... add k to row list for first nonzero entry in k-th row */
2454       il[k] = jmin;
2455       i     = bj[jmin];
2456       jl[k] = jl[i]; jl[i] = k;
2457     }
2458   }
2459 
2460   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2461   ierr = PetscFree(il);CHKERRQ(ierr);
2462   ierr = PetscFree(jl);CHKERRQ(ierr);
2463   ierr = PetscFree(dk);CHKERRQ(ierr);
2464   ierr = PetscFree(uik);CHKERRQ(ierr);
2465   if (a->permute){
2466     ierr = PetscFree(aa);CHKERRQ(ierr);
2467   }
2468 
2469   ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr);
2470   C->factor    = FACTOR_CHOLESKY;
2471   C->assembled = PETSC_TRUE;
2472   C->preallocated = PETSC_TRUE;
2473   PLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */
2474   PetscFunctionReturn(0);
2475 }
2476 
2477 /*
2478       Version for when blocks are 3 by 3 Using natural ordering
2479 */
2480 #undef __FUNC__
2481 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_3_NaturalOrdering"
2482 int MatCholeskyFactorNumeric_SeqSBAIJ_3_NaturalOrdering(Mat A,Mat *B)
2483 {
2484   Mat                C = *B;
2485   Mat_SeqBAIJ        *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
2486   int                ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
2487   int                *ajtmpold,*ajtmp,nz,row;
2488   int                *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
2489   MatScalar          *pv,*v,*rtmp,*pc,*w,*x;
2490   MatScalar          p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
2491   MatScalar          p5,p6,p7,p8,p9,x5,x6,x7,x8,x9;
2492   MatScalar          *ba = b->a,*aa = a->a;
2493 
2494   PetscFunctionBegin;
2495   rtmp  = (MatScalar*)PetscMalloc(9*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
2496 
2497   for (i=0; i<n; i++) {
2498     nz    = bi[i+1] - bi[i];
2499     ajtmp = bj + bi[i];
2500     for  (j=0; j<nz; j++) {
2501       x = rtmp+9*ajtmp[j];
2502       x[0]  = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = 0.0;
2503     }
2504     /* load in initial (unfactored row) */
2505     nz       = ai[i+1] - ai[i];
2506     ajtmpold = aj + ai[i];
2507     v        = aa + 9*ai[i];
2508     for (j=0; j<nz; j++) {
2509       x    = rtmp+9*ajtmpold[j];
2510       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
2511       x[4]  = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
2512       v    += 9;
2513     }
2514     row = *ajtmp++;
2515     while (row < i) {
2516       pc  = rtmp + 9*row;
2517       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
2518       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
2519       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
2520           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0) {
2521         pv = ba + 9*diag_offset[row];
2522         pj = bj + diag_offset[row] + 1;
2523         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
2524         x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
2525         pc[0] = m1 = p1*x1 + p4*x2 + p7*x3;
2526         pc[1] = m2 = p2*x1 + p5*x2 + p8*x3;
2527         pc[2] = m3 = p3*x1 + p6*x2 + p9*x3;
2528 
2529         pc[3] = m4 = p1*x4 + p4*x5 + p7*x6;
2530         pc[4] = m5 = p2*x4 + p5*x5 + p8*x6;
2531         pc[5] = m6 = p3*x4 + p6*x5 + p9*x6;
2532 
2533         pc[6] = m7 = p1*x7 + p4*x8 + p7*x9;
2534         pc[7] = m8 = p2*x7 + p5*x8 + p8*x9;
2535         pc[8] = m9 = p3*x7 + p6*x8 + p9*x9;
2536 
2537         nz = bi[row+1] - diag_offset[row] - 1;
2538         pv += 9;
2539         for (j=0; j<nz; j++) {
2540           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
2541           x5   = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
2542           x    = rtmp + 9*pj[j];
2543           x[0] -= m1*x1 + m4*x2 + m7*x3;
2544           x[1] -= m2*x1 + m5*x2 + m8*x3;
2545           x[2] -= m3*x1 + m6*x2 + m9*x3;
2546 
2547           x[3] -= m1*x4 + m4*x5 + m7*x6;
2548           x[4] -= m2*x4 + m5*x5 + m8*x6;
2549           x[5] -= m3*x4 + m6*x5 + m9*x6;
2550 
2551           x[6] -= m1*x7 + m4*x8 + m7*x9;
2552           x[7] -= m2*x7 + m5*x8 + m8*x9;
2553           x[8] -= m3*x7 + m6*x8 + m9*x9;
2554           pv   += 9;
2555         }
2556         PLogFlops(54*nz+36);
2557       }
2558       row = *ajtmp++;
2559     }
2560     /* finished row so stick it into b->a */
2561     pv = ba + 9*bi[i];
2562     pj = bj + bi[i];
2563     nz = bi[i+1] - bi[i];
2564     for (j=0; j<nz; j++) {
2565       x      = rtmp+9*pj[j];
2566       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
2567       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
2568       pv   += 9;
2569     }
2570     /* invert diagonal block */
2571     w = ba + 9*diag_offset[i];
2572     ierr = Kernel_A_gets_inverse_A_3(w);CHKERRQ(ierr);
2573   }
2574 
2575   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2576   C->factor    = FACTOR_CHOLESKY;
2577   C->assembled = PETSC_TRUE;
2578   C->preallocated = PETSC_TRUE;
2579   PLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */
2580   PetscFunctionReturn(0);
2581 }
2582 
2583 /*
2584     Numeric U^T*D*U factorization for SBAIJ format. Modified from SNF of YSMP.
2585     Version for blocks 2 by 2.
2586 */
2587 #undef __FUNC__
2588 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_2"
2589 int MatCholeskyFactorNumeric_SeqSBAIJ_2(Mat A,Mat *B)
2590 {
2591   Mat                C = *B;
2592   Mat_SeqSBAIJ       *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data;
2593   IS                 perm = b->row;
2594   int                *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
2595   int                *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
2596   MatScalar          *ba = b->a,*aa,*ap,*dk,*uik;
2597   MatScalar          *u,*diag,*rtmp,*rtmp_ptr;
2598 
2599   PetscFunctionBegin;
2600 
2601   /* initialization */
2602   /* il and jl record the first nonzero element in each row of the accessing
2603      window U(0:k, k:mbs-1).
2604      jl:    list of rows to be added to uneliminated rows
2605             i>= k: jl(i) is the first row to be added to row i
2606             i<  k: jl(i) is the row following row i in some list of rows
2607             jl(i) = mbs indicates the end of a list
2608      il(i): points to the first nonzero element in columns k,...,mbs-1 of
2609             row i of U */
2610   rtmp  = (MatScalar*)PetscMalloc(4*mbs*sizeof(MatScalar));CHKPTRQ(rtmp);
2611   ierr = PetscMemzero(rtmp,4*mbs*sizeof(MatScalar));CHKERRQ(ierr);
2612   il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il);
2613   jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl);
2614   for (i=0; i<mbs; i++) {
2615     jl[i] = mbs; il[0] = 0;
2616   }
2617   dk  = (MatScalar*)PetscMalloc(4*sizeof(MatScalar));CHKPTRQ(dk);
2618   uik = (MatScalar*)PetscMalloc(4*sizeof(MatScalar));CHKPTRQ(uik);
2619   ierr  = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr);
2620 
2621   /* check permutation */
2622   if (!a->permute){
2623     ai = a->i; aj = a->j; aa = a->a;
2624   } else {
2625     ai = a->inew; aj = a->jnew;
2626     aa = (MatScalar*)PetscMalloc(4*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa);
2627     ierr = PetscMemcpy(aa,a->a,4*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr);
2628     a2anew  = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew);
2629     ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr);
2630 
2631     for (i=0; i<mbs; i++){
2632       jmin = ai[i]; jmax = ai[i+1];
2633       for (j=jmin; j<jmax; j++){
2634         while (a2anew[j] != j){
2635           k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k;
2636           for (k1=0; k1<4; k1++){
2637             dk[k1]       = aa[k*4+k1];
2638             aa[k*4+k1] = aa[j*4+k1];
2639             aa[j*4+k1] = dk[k1];
2640           }
2641         }
2642         /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */
2643         if (i > aj[j]){
2644           /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */
2645           ap = aa + j*4;     /* ptr to the beginning of the block */
2646           dk[1] = ap[1];     /* swap ap[1] and ap[2] */
2647           ap[1] = ap[2];
2648           ap[2] = dk[1];
2649         }
2650       }
2651     }
2652     ierr = PetscFree(a2anew);CHKERRA(ierr);
2653   }
2654 
2655   /* for each row k */
2656   for (k = 0; k<mbs; k++){
2657 
2658     /*initialize k-th row with elements nonzero in row perm(k) of A */
2659     jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1];
2660     if (jmin < jmax) {
2661       ap = aa + jmin*4;
2662       for (j = jmin; j < jmax; j++){
2663         vj = perm_ptr[aj[j]];         /* block col. index */
2664         rtmp_ptr = rtmp + vj*4;
2665         for (i=0; i<4; i++) *rtmp_ptr++ = *ap++;
2666       }
2667     }
2668 
2669     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
2670     ierr = PetscMemcpy(dk,rtmp+k*4,4*sizeof(MatScalar));CHKERRQ(ierr);
2671     i = jl[k]; /* first row to be added to k_th row  */
2672 
2673     while (i < mbs){
2674       nexti = jl[i]; /* next row to be added to k_th row */
2675 
2676       /* compute multiplier */
2677       ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
2678 
2679       /* uik = -inv(Di)*U_bar(i,k): - ba[ili]*ba[i] */
2680       diag = ba + i*4;
2681       u    = ba + ili*4;
2682       uik[0] = -(diag[0]*u[0] + diag[2]*u[1]);
2683       uik[1] = -(diag[1]*u[0] + diag[3]*u[1]);
2684       uik[2] = -(diag[0]*u[2] + diag[2]*u[3]);
2685       uik[3] = -(diag[1]*u[2] + diag[3]*u[3]);
2686 
2687       /* update D(k) += -U(i,k)^T * U_bar(i,k): dk += uik*ba[ili] */
2688       dk[0] += uik[0]*u[0] + uik[1]*u[1];
2689       dk[1] += uik[2]*u[0] + uik[3]*u[1];
2690       dk[2] += uik[0]*u[2] + uik[1]*u[3];
2691       dk[3] += uik[2]*u[2] + uik[3]*u[3];
2692 
2693       /* update -U(i,k): ba[ili] = uik */
2694       ierr = PetscMemcpy(ba+ili*4,uik,4*sizeof(MatScalar));CHKERRQ(ierr);
2695 
2696       /* add multiple of row i to k-th row ... */
2697       jmin = ili + 1; jmax = bi[i+1];
2698       if (jmin < jmax){
2699         for (j=jmin; j<jmax; j++) {
2700           /* rtmp += -U(i,k)^T * U_bar(i,j): rtmp[bj[j]] += uik*ba[j]; */
2701           rtmp_ptr = rtmp + bj[j]*4;
2702           u = ba + j*4;
2703           rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1];
2704           rtmp_ptr[1] += uik[2]*u[0] + uik[3]*u[1];
2705           rtmp_ptr[2] += uik[0]*u[2] + uik[1]*u[3];
2706           rtmp_ptr[3] += uik[2]*u[2] + uik[3]*u[3];
2707         }
2708 
2709         /* ... add i to row list for next nonzero entry */
2710         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
2711         j     = bj[jmin];
2712         jl[i] = jl[j]; jl[j] = i; /* update jl */
2713       }
2714       i = nexti;
2715     }
2716 
2717     /* save nonzero entries in k-th row of U ... */
2718 
2719     /* invert diagonal block */
2720     diag = ba+k*4;
2721     ierr = PetscMemcpy(diag,dk,4*sizeof(MatScalar));CHKERRQ(ierr);
2722     ierr = Kernel_A_gets_inverse_A_2(diag);CHKERRQ(ierr);
2723 
2724     jmin = bi[k]; jmax = bi[k+1];
2725     if (jmin < jmax) {
2726       for (j=jmin; j<jmax; j++){
2727          vj = bj[j];           /* block col. index of U */
2728          u   = ba + j*4;
2729          rtmp_ptr = rtmp + vj*4;
2730          for (k1=0; k1<4; k1++){
2731            *u++        = *rtmp_ptr;
2732            *rtmp_ptr++ = 0.0;
2733          }
2734       }
2735 
2736       /* ... add k to row list for first nonzero entry in k-th row */
2737       il[k] = jmin;
2738       i     = bj[jmin];
2739       jl[k] = jl[i]; jl[i] = k;
2740     }
2741   }
2742 
2743   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2744   ierr = PetscFree(il);CHKERRQ(ierr);
2745   ierr = PetscFree(jl);CHKERRQ(ierr);
2746   ierr = PetscFree(dk);CHKERRQ(ierr);
2747   ierr = PetscFree(uik);CHKERRQ(ierr);
2748   if (a->permute) {
2749     ierr = PetscFree(aa);CHKERRQ(ierr);
2750   }
2751   ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr);
2752   C->factor    = FACTOR_CHOLESKY;
2753   C->assembled = PETSC_TRUE;
2754   C->preallocated = PETSC_TRUE;
2755   PLogFlops(1.3333*8*b->mbs); /* from inverting diagonal blocks */
2756   PetscFunctionReturn(0);
2757 }
2758 
2759 /*
2760       Version for when blocks are 2 by 2 Using natural ordering
2761 */
2762 #undef __FUNC__
2763 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_2_NaturalOrdering"
2764 int MatCholeskyFactorNumeric_SeqSBAIJ_2_NaturalOrdering(Mat A,Mat *B)
2765 {
2766   Mat                C = *B;
2767   Mat_SeqBAIJ        *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
2768   int                ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
2769   int                *ajtmpold,*ajtmp,nz,row;
2770   int                *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
2771   MatScalar          *pv,*v,*rtmp,*pc,*w,*x;
2772   MatScalar          p1,p2,p3,p4,m1,m2,m3,m4,x1,x2,x3,x4;
2773   MatScalar          *ba = b->a,*aa = a->a;
2774 
2775   PetscFunctionBegin;
2776   rtmp  = (MatScalar*)PetscMalloc(4*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
2777 
2778   for (i=0; i<n; i++) {
2779     nz    = bi[i+1] - bi[i];
2780     ajtmp = bj + bi[i];
2781     for  (j=0; j<nz; j++) {
2782       x = rtmp+4*ajtmp[j];
2783       x[0]  = x[1]  = x[2]  = x[3]  = 0.0;
2784     }
2785     /* load in initial (unfactored row) */
2786     nz       = ai[i+1] - ai[i];
2787     ajtmpold = aj + ai[i];
2788     v        = aa + 4*ai[i];
2789     for (j=0; j<nz; j++) {
2790       x    = rtmp+4*ajtmpold[j];
2791       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
2792       v    += 4;
2793     }
2794     row = *ajtmp++;
2795     while (row < i) {
2796       pc  = rtmp + 4*row;
2797       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
2798       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0) {
2799         pv = ba + 4*diag_offset[row];
2800         pj = bj + diag_offset[row] + 1;
2801         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
2802         pc[0] = m1 = p1*x1 + p3*x2;
2803         pc[1] = m2 = p2*x1 + p4*x2;
2804         pc[2] = m3 = p1*x3 + p3*x4;
2805         pc[3] = m4 = p2*x3 + p4*x4;
2806         nz = bi[row+1] - diag_offset[row] - 1;
2807         pv += 4;
2808         for (j=0; j<nz; j++) {
2809           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
2810           x    = rtmp + 4*pj[j];
2811           x[0] -= m1*x1 + m3*x2;
2812           x[1] -= m2*x1 + m4*x2;
2813           x[2] -= m1*x3 + m3*x4;
2814           x[3] -= m2*x3 + m4*x4;
2815           pv   += 4;
2816         }
2817         PLogFlops(16*nz+12);
2818       }
2819       row = *ajtmp++;
2820     }
2821     /* finished row so stick it into b->a */
2822     pv = ba + 4*bi[i];
2823     pj = bj + bi[i];
2824     nz = bi[i+1] - bi[i];
2825     for (j=0; j<nz; j++) {
2826       x      = rtmp+4*pj[j];
2827       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
2828       pv   += 4;
2829     }
2830     /* invert diagonal block */
2831     w = ba + 4*diag_offset[i];
2832     ierr = Kernel_A_gets_inverse_A_2(w);CHKERRQ(ierr);
2833   }
2834 
2835   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2836   C->factor    = FACTOR_LU;
2837   C->assembled = PETSC_TRUE;
2838   C->preallocated = PETSC_TRUE;
2839   PLogFlops(1.3333*8*b->mbs); /* from inverting diagonal blocks */
2840   PetscFunctionReturn(0);
2841 }
2842 
2843 /*
2844     Numeric U^T*D*U factorization for SBAIJ format. Modified from SNF of YSMP.
2845     Version for blocks are 1 by 1.
2846 */
2847 #undef __FUNC__
2848 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_1"
2849 int MatCholeskyFactorNumeric_SeqSBAIJ_1(Mat A,Mat *B)
2850 {
2851   Mat                C = *B;
2852   Mat_SeqSBAIJ       *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data;
2853   IS                 ip = b->row;
2854   int                *rip,ierr,i,j,mbs = a->mbs,*bi = b->i,*bj = b->j;
2855   int                *ai,*aj,*r;
2856   MatScalar          *rtmp;
2857   MatScalar          *ba = b->a,*aa,ak;
2858   MatScalar          dk,uikdi;
2859   int                k,jmin,jmax,*jl,*il,vj,nexti,ili;
2860 
2861   PetscFunctionBegin;
2862   ierr  = ISGetIndices(ip,&rip);CHKERRQ(ierr);
2863   if (!a->permute){
2864     ai = a->i; aj = a->j; aa = a->a;
2865   } else {
2866     ai = a->inew; aj = a->jnew;
2867     aa = (MatScalar*)PetscMalloc(ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa);
2868     ierr = PetscMemcpy(aa,a->a,ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr);
2869     r   = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(r);
2870     ierr= PetscMemcpy(r,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr);
2871 
2872     jmin = ai[0]; jmax = ai[mbs];
2873     for (j=jmin; j<jmax; j++){
2874       while (r[j] != j){
2875         k = r[j]; r[j] = r[k]; r[k] = k;
2876         ak = aa[k]; aa[k] = aa[j]; aa[j] = ak;
2877       }
2878     }
2879     ierr = PetscFree(r);CHKERRA(ierr);
2880   }
2881 
2882   /* initialization */
2883   /* il and jl record the first nonzero element in each row of the accessing
2884      window U(0:k, k:mbs-1).
2885      jl:    list of rows to be added to uneliminated rows
2886             i>= k: jl(i) is the first row to be added to row i
2887             i<  k: jl(i) is the row following row i in some list of rows
2888             jl(i) = mbs indicates the end of a list
2889      il(i): points to the first nonzero element in columns k,...,mbs-1 of
2890             row i of U */
2891   rtmp  = (MatScalar*)PetscMalloc(mbs*sizeof(MatScalar));CHKPTRQ(rtmp);
2892   il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il);
2893   jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl);
2894   for (i=0; i<mbs; i++) {
2895     rtmp[i] = 0.0; jl[i] = mbs; il[0] = 0;
2896   }
2897 
2898   /* for each row k */
2899   for (k = 0; k<mbs; k++){
2900 
2901     /*initialize k-th row with elements nonzero in row perm(k) of A */
2902     jmin = ai[rip[k]]; jmax = ai[rip[k]+1];
2903     if (jmin < jmax) {
2904       for (j = jmin; j < jmax; j++){
2905         vj = rip[aj[j]];
2906         /* if (k <= vj)*/ rtmp[vj] = aa[j];
2907       }
2908     }
2909 
2910     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
2911     dk = rtmp[k];
2912     i = jl[k]; /* first row to be added to k_th row  */
2913     /* printf(" k=%d, pivot row = %d\n",k,i); */
2914 
2915     while (i < mbs){
2916       nexti = jl[i]; /* next row to be added to k_th row */
2917 
2918       /* compute multiplier, update D(k) and U(i,k) */
2919       ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
2920       uikdi = - ba[ili]*ba[i];
2921       dk += uikdi*ba[ili];
2922       ba[ili] = uikdi; /* -U(i,k) */
2923 
2924       /* add multiple of row i to k-th row ... */
2925       jmin = ili + 1; jmax = bi[i+1];
2926       if (jmin < jmax){
2927         for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j];
2928         /* ... add i to row list for next nonzero entry */
2929         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
2930         j     = bj[jmin];
2931         jl[i] = jl[j]; jl[j] = i; /* update jl */
2932       }
2933       i = nexti; /* printf("                  pivot row i=%d\n",i);  */
2934     }
2935 
2936     /* check for zero pivot and save diagoanl element */
2937     if (dk == 0.0){
2938       SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot");
2939     }else if (PetscRealPart(dk) < 0){
2940       ierr = PetscPrintf(PETSC_COMM_SELF,"Negative pivot: d[%d] = %g\n",k,dk);
2941     }
2942 
2943     /* save nonzero entries in k-th row of U ... */
2944     ba[k] = 1.0/dk;
2945     jmin = bi[k]; jmax = bi[k+1];
2946     if (jmin < jmax) {
2947       for (j=jmin; j<jmax; j++){
2948          vj = bj[j]; ba[j] = rtmp[vj]; rtmp[vj] = 0.0;
2949       }
2950       /* ... add k to row list for first nonzero entry in k-th row */
2951       il[k] = jmin;
2952       i     = bj[jmin];
2953       jl[k] = jl[i]; jl[i] = k;
2954     }
2955   }
2956 
2957   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2958   ierr = PetscFree(il);CHKERRQ(ierr);
2959   ierr = PetscFree(jl);CHKERRQ(ierr);
2960   if (a->permute){
2961     ierr = PetscFree(aa);CHKERRQ(ierr);
2962   }
2963 
2964   ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr);
2965   C->factor    = FACTOR_CHOLESKY;
2966   C->assembled = PETSC_TRUE;
2967   C->preallocated = PETSC_TRUE;
2968   PLogFlops(b->mbs);
2969   PetscFunctionReturn(0);
2970 }
2971 
2972 #undef __FUNC__
2973 #define __FUNC__ "MatCholeskyFactor_SeqSBAIJ"
2974 int MatCholeskyFactor_SeqSBAIJ(Mat A,IS perm,PetscReal f)
2975 {
2976   int ierr;
2977   Mat C;
2978 
2979   PetscFunctionBegin;
2980   ierr = MatCholeskyFactorSymbolic(A,perm,f,&C);CHKERRQ(ierr);
2981   ierr = MatCholeskyFactorNumeric(A,&C);CHKERRQ(ierr);
2982   ierr = MatHeaderCopy(A,C);CHKERRQ(ierr);
2983   PetscFunctionReturn(0);
2984 }
2985 
2986 
2987