xref: /petsc/src/mat/impls/sbaij/seq/sbaijfact.c (revision 0aa0ce063ac8cc059b4cd43b1a791f8a185818cf)
1 /* Using Modified Sparse Row (MSR) storage.
2 See page 85, "Iterative Methods ..." by Saad. */
3 
4 /*$Id: sbaijfact.c,v 1.39 2000/10/31 19:39:49 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_SeqBAIJ        *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
200   IS                 isrow = b->row,isicol = b->icol;
201   int                *r,*ic,ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
202   int                *ajtmpold,*ajtmp,nz,row,bslog,*ai=a->i,*aj=a->j,k,flg;
203   int                *diag_offset=b->diag,diag,bs=a->bs,bs2 = a->bs2,*v_pivots,*pj;
204   MatScalar          *ba = b->a,*aa = a->a,*pv,*v,*rtmp,*multiplier,*v_work,*pc,*w;
205 
206   PetscFunctionBegin;
207   printf("called MatCholeskyFactorNumeric_SeqSBAIJ_N \n");
208   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
209   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
210   rtmp = (MatScalar*)PetscMalloc(bs2*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
211   ierr = PetscMemzero(rtmp,bs2*(n+1)*sizeof(MatScalar));CHKERRQ(ierr);
212   /* generate work space needed by dense LU factorization */
213   v_work     = (MatScalar*)PetscMalloc(bs*sizeof(int) + (bs+bs2)*sizeof(MatScalar));CHKPTRQ(v_work);
214   multiplier = v_work + bs;
215   v_pivots   = (int*)(multiplier + bs2);
216 
217   /* flops in while loop */
218   bslog = 2*bs*bs2;
219 
220   for (i=0; i<n; i++) {
221     nz    = bi[i+1] - bi[i];
222     ajtmp = bj + bi[i];
223     for  (j=0; j<nz; j++) {
224       ierr = PetscMemzero(rtmp+bs2*ajtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
225     }
226     /* load in initial (unfactored row) */
227     nz       = ai[r[i]+1] - ai[r[i]];
228     ajtmpold = aj + ai[r[i]];
229     v        = aa + bs2*ai[r[i]];
230     for (j=0; j<nz; j++) {
231       ierr = PetscMemcpy(rtmp+bs2*ic[ajtmpold[j]],v+bs2*j,bs2*sizeof(MatScalar));CHKERRQ(ierr);
232     }
233     row = *ajtmp++;
234     while (row < i) {
235       pc = rtmp + bs2*row;
236 /*      if (*pc) { */
237       for (flg=0,k=0; k<bs2; k++) { if (pc[k]!=0.0) { flg =1; break; }}
238       if (flg) {
239         pv = ba + bs2*diag_offset[row];
240         pj = bj + diag_offset[row] + 1;
241         Kernel_A_gets_A_times_B(bs,pc,pv,multiplier);
242         nz = bi[row+1] - diag_offset[row] - 1;
243         pv += bs2;
244         for (j=0; j<nz; j++) {
245           Kernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j);
246         }
247         PLogFlops(bslog*(nz+1)-bs);
248       }
249         row = *ajtmp++;
250     }
251     /* finished row so stick it into b->a */
252     pv = ba + bs2*bi[i];
253     pj = bj + bi[i];
254     nz = bi[i+1] - bi[i];
255     for (j=0; j<nz; j++) {
256       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
257     }
258     diag = diag_offset[i] - bi[i];
259     /* invert diagonal block */
260     w = pv + bs2*diag;
261     Kernel_A_gets_inverse_A(bs,w,v_pivots,v_work);
262   }
263 
264   ierr = PetscFree(rtmp);CHKERRQ(ierr);
265   ierr = PetscFree(v_work);CHKERRQ(ierr);
266   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
267   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
268   C->factor = FACTOR_LU;
269   C->assembled = PETSC_TRUE;
270   PLogFlops(1.3333*bs*bs2*b->mbs); /* from inverting diagonal blocks */
271   PetscFunctionReturn(0);
272 }
273 
274 /* Version for when blocks are 7 by 7 */
275 #undef __FUNC__
276 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_7"
277 int MatCholeskyFactorNumeric_SeqSBAIJ_7(Mat A,Mat *B)
278 {
279   Mat                C = *B;
280   Mat_SeqSBAIJ       *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data;
281   IS                 perm = b->row;
282   int                *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
283   int                *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
284   MatScalar          *ba = b->a,*aa,*ap,*dk,*uik;
285   MatScalar          *u,*d,*w,*wp;
286 
287   PetscFunctionBegin;
288   /* initialization */
289   w  = (MatScalar*)PetscMalloc(49*mbs*sizeof(MatScalar));CHKPTRQ(w);
290   ierr = PetscMemzero(w,49*mbs*sizeof(MatScalar));CHKERRQ(ierr);
291   il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il);
292   jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl);
293   for (i=0; i<mbs; i++) {
294     jl[i] = mbs; il[0] = 0;
295   }
296   dk    = (MatScalar*)PetscMalloc(49*sizeof(MatScalar));CHKPTRQ(dk);
297   uik   = (MatScalar*)PetscMalloc(49*sizeof(MatScalar));CHKPTRQ(uik);
298   ierr  = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr);
299 
300   /* check permutation */
301   if (!a->permute){
302     ai = a->i; aj = a->j; aa = a->a;
303   } else {
304     ai = a->inew; aj = a->jnew;
305     aa = (MatScalar*)PetscMalloc(49*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa);
306     ierr = PetscMemcpy(aa,a->a,49*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr);
307     a2anew  = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew);
308     ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr);
309 
310     for (i=0; i<mbs; i++){
311       jmin = ai[i]; jmax = ai[i+1];
312       for (j=jmin; j<jmax; j++){
313         while (a2anew[j] != j){
314           k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k;
315           for (k1=0; k1<49; k1++){
316             dk[k1]       = aa[k*49+k1];
317             aa[k*49+k1] = aa[j*49+k1];
318             aa[j*49+k1] = dk[k1];
319           }
320         }
321         /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */
322         if (i > aj[j]){
323           /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */
324           ap = aa + j*49;                     /* ptr to the beginning of j-th block of aa */
325           for (k=0; k<49; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */
326           for (k=0; k<7; k++){               /* j-th block of aa <- dk^T */
327             for (k1=0; k1<7; k1++) *ap++ = dk[k + 7*k1];
328           }
329         }
330       }
331     }
332     ierr = PetscFree(a2anew);CHKERRA(ierr);
333   }
334 
335   /* for each row k */
336   for (k = 0; k<mbs; k++){
337 
338     /*initialize k-th row with elements nonzero in row perm(k) of A */
339     jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1];
340     if (jmin < jmax) {
341       ap = aa + jmin*49;
342       for (j = jmin; j < jmax; j++){
343         vj = perm_ptr[aj[j]];         /* block col. index */
344         wp = w + vj*49;
345         for (i=0; i<49; i++) *wp++ = *ap++;
346       }
347     }
348 
349     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
350     ierr = PetscMemcpy(dk,w+k*49,49*sizeof(MatScalar));CHKERRQ(ierr);
351     i = jl[k]; /* first row to be added to k_th row  */
352 
353     while (i < mbs){
354       nexti = jl[i]; /* next row to be added to k_th row */
355 
356       /* compute multiplier */
357       ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
358 
359       /* uik = -inv(Di)*U_bar(i,k) */
360       d = ba + i*49;
361       u    = ba + ili*49;
362 
363       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]);
364       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]);
365       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]);
366       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]);
367       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]);
368       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]);
369       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]);
370 
371       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]);
372       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]);
373       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]);
374       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]);
375       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]);
376       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]);
377       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]);
378 
379       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]);
380       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]);
381       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]);
382       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]);
383       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]);
384       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]);
385       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]);
386 
387       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]);
388       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]);
389       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]);
390       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]);
391       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]);
392       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]);
393       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]);
394 
395       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]);
396       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]);
397       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]);
398       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]);
399       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]);
400       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]);
401       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]);
402 
403       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]);
404       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]);
405       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]);
406       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]);
407       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]);
408       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]);
409       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]);
410 
411       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]);
412       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]);
413       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]);
414       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]);
415       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]);
416       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]);
417       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]);
418 
419       /* update D(k) += -U(i,k)^T * U_bar(i,k) */
420       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];
421       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];
422       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];
423       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];
424       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];
425       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];
426       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];
427 
428       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];
429       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];
430       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];
431       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];
432       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];
433       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];
434       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];
435 
436       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];
437       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];
438       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];
439       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];
440       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];
441       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];
442       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];
443 
444       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];
445       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];
446       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];
447       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];
448       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];
449       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];
450       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];
451 
452       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];
453       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];
454       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];
455       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];
456       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];
457       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];
458       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];
459 
460       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];
461       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];
462       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];
463       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];
464       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];
465       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];
466       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];
467 
468       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];
469       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];
470       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];
471       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];
472       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];
473       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];
474       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];
475 
476       /* update -U(i,k) */
477       ierr = PetscMemcpy(ba+ili*49,uik,49*sizeof(MatScalar));CHKERRQ(ierr);
478 
479       /* add multiple of row i to k-th row ... */
480       jmin = ili + 1; jmax = bi[i+1];
481       if (jmin < jmax){
482         for (j=jmin; j<jmax; j++) {
483           /* w += -U(i,k)^T * U_bar(i,j) */
484           wp = w + bj[j]*49;
485           u = ba + j*49;
486 
487           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];
488           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];
489           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];
490           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];
491           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];
492           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];
493           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];
494 
495           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];
496           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];
497           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];
498           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];
499           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];
500           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];
501           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];
502 
503           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];
504           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];
505           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];
506           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];
507           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];
508           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];
509           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];
510 
511           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];
512           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];
513           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];
514           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];
515           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];
516           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];
517           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];
518 
519           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];
520           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];
521           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];
522           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];
523           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];
524           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];
525           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];
526 
527           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];
528           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];
529           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];
530           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];
531           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];
532           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];
533           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];
534 
535           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];
536           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];
537           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];
538           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];
539           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];
540           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];
541           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];
542         }
543 
544         /* ... add i to row list for next nonzero entry */
545         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
546         j     = bj[jmin];
547         jl[i] = jl[j]; jl[j] = i; /* update jl */
548       }
549       i = nexti;
550     }
551 
552     /* save nonzero entries in k-th row of U ... */
553 
554     /* invert diagonal block */
555     d = ba+k*49;
556     ierr = PetscMemcpy(d,dk,49*sizeof(MatScalar));CHKERRQ(ierr);
557     ierr = Kernel_A_gets_inverse_A_7(d);CHKERRQ(ierr);
558 
559     jmin = bi[k]; jmax = bi[k+1];
560     if (jmin < jmax) {
561       for (j=jmin; j<jmax; j++){
562          vj = bj[j];           /* block col. index of U */
563          u   = ba + j*49;
564          wp = w + vj*49;
565          for (k1=0; k1<49; k1++){
566            *u++        = *wp;
567            *wp++ = 0.0;
568          }
569       }
570 
571       /* ... add k to row list for first nonzero entry in k-th row */
572       il[k] = jmin;
573       i     = bj[jmin];
574       jl[k] = jl[i]; jl[i] = k;
575     }
576   }
577 
578   ierr = PetscFree(w);CHKERRQ(ierr);
579   ierr = PetscFree(il);CHKERRQ(ierr);
580   ierr = PetscFree(jl);CHKERRQ(ierr);
581   ierr = PetscFree(dk);CHKERRQ(ierr);
582   ierr = PetscFree(uik);CHKERRQ(ierr);
583   if (a->permute){
584     ierr = PetscFree(aa);CHKERRQ(ierr);
585   }
586 
587   ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr);
588   C->factor    = FACTOR_CHOLESKY;
589   C->assembled = PETSC_TRUE;
590   C->preallocated = PETSC_TRUE;
591   PLogFlops(1.3333*343*b->mbs); /* from inverting diagonal blocks */
592   PetscFunctionReturn(0);
593 }
594 
595 /*
596       Version for when blocks are 7 by 7 Using natural ordering
597 */
598 #undef __FUNC__
599 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_7_NaturalOrdering"
600 int MatCholeskyFactorNumeric_SeqSBAIJ_7_NaturalOrdering(Mat A,Mat *B)
601 {
602   Mat          C = *B;
603   Mat_SeqBAIJ  *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
604   int          ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
605   int          *ajtmpold,*ajtmp,nz,row;
606   int          *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
607   MatScalar    *pv,*v,*rtmp,*pc,*w,*x;
608   MatScalar    x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15;
609   MatScalar    x16,x17,x18,x19,x20,x21,x22,x23,x24,x25;
610   MatScalar    p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15;
611   MatScalar    p16,p17,p18,p19,p20,p21,p22,p23,p24,p25;
612   MatScalar    m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12,m13,m14,m15;
613   MatScalar    m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
614   MatScalar    p26,p27,p28,p29,p30,p31,p32,p33,p34,p35,p36;
615   MatScalar    p37,p38,p39,p40,p41,p42,p43,p44,p45,p46,p47,p48,p49;
616   MatScalar    x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36;
617   MatScalar    x37,x38,x39,x40,x41,x42,x43,x44,x45,x46,x47,x48,x49;
618   MatScalar    m26,m27,m28,m29,m30,m31,m32,m33,m34,m35,m36;
619   MatScalar    m37,m38,m39,m40,m41,m42,m43,m44,m45,m46,m47,m48,m49;
620   MatScalar    *ba = b->a,*aa = a->a;
621 
622   PetscFunctionBegin;
623   rtmp  = (MatScalar*)PetscMalloc(49*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
624   for (i=0; i<n; i++) {
625     nz    = bi[i+1] - bi[i];
626     ajtmp = bj + bi[i];
627     for  (j=0; j<nz; j++) {
628       x = rtmp+49*ajtmp[j];
629       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
630       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
631       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = x[25] = 0.0 ;
632       x[26] = x[27] = x[28] = x[29] = x[30] = x[31] = x[32] = x[33] = 0.0 ;
633       x[34] = x[35] = x[36] = x[37] = x[38] = x[39] = x[40] = x[41] = 0.0 ;
634       x[42] = x[43] = x[44] = x[45] = x[46] = x[47] = x[48] = 0.0 ;
635     }
636     /* load in initial (unfactored row) */
637     nz       = ai[i+1] - ai[i];
638     ajtmpold = aj + ai[i];
639     v        = aa + 49*ai[i];
640     for (j=0; j<nz; j++) {
641       x    = rtmp+49*ajtmpold[j];
642       x[0] =  v[0];  x[1] =  v[1];  x[2] =  v[2];  x[3] =  v[3];
643       x[4] =  v[4];  x[5] =  v[5];  x[6] =  v[6];  x[7] =  v[7];
644       x[8] =  v[8];  x[9] =  v[9];  x[10] = v[10]; x[11] = v[11];
645       x[12] = v[12]; x[13] = v[13]; x[14] = v[14]; x[15] = v[15];
646       x[16] = v[16]; x[17] = v[17]; x[18] = v[18]; x[19] = v[19];
647       x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23];
648       x[24] = v[24]; x[25] = v[25]; x[26] = v[26]; x[27] = v[27];
649       x[28] = v[28]; x[29] = v[29]; x[30] = v[30]; x[31] = v[31];
650       x[32] = v[32]; x[33] = v[33]; x[34] = v[34]; x[35] = v[35];
651       x[36] = v[36]; x[37] = v[37]; x[38] = v[38]; x[39] = v[39];
652       x[40] = v[40]; x[41] = v[41]; x[42] = v[42]; x[43] = v[43];
653       x[44] = v[44]; x[45] = v[45]; x[46] = v[46]; x[47] = v[47];
654       x[48] = v[48];
655       v    += 49;
656     }
657     row = *ajtmp++;
658     while (row < i) {
659       pc  = rtmp + 49*row;
660       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
661       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];
662       p9  = pc[8];  p10 = pc[9];  p11 = pc[10]; p12 = pc[11];
663       p13 = pc[12]; p14 = pc[13]; p15 = pc[14]; p16 = pc[15];
664       p17 = pc[16]; p18 = pc[17]; p19 = pc[18]; p20 = pc[19];
665       p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
666       p25 = pc[24]; p26 = pc[25]; p27 = pc[26]; p28 = pc[27];
667       p29 = pc[28]; p30 = pc[29]; p31 = pc[30]; p32 = pc[31];
668       p33 = pc[32]; p34 = pc[33]; p35 = pc[34]; p36 = pc[35];
669       p37 = pc[36]; p38 = pc[37]; p39 = pc[38]; p40 = pc[39];
670       p41 = pc[40]; p42 = pc[41]; p43 = pc[42]; p44 = pc[43];
671       p45 = pc[44]; p46 = pc[45]; p47 = pc[46]; p48 = pc[47];
672       p49 = pc[48];
673       if (p1  != 0.0 || p2  != 0.0 || p3  != 0.0 || p4  != 0.0 ||
674           p5  != 0.0 || p6  != 0.0 || p7  != 0.0 || p8  != 0.0 ||
675           p9  != 0.0 || p10 != 0.0 || p11 != 0.0 || p12 != 0.0 ||
676           p13 != 0.0 || p14 != 0.0 || p15 != 0.0 || p16 != 0.0 ||
677           p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 ||
678           p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 ||
679           p25 != 0.0 || p26 != 0.0 || p27 != 0.0 || p28 != 0.0 ||
680           p29 != 0.0 || p30 != 0.0 || p31 != 0.0 || p32 != 0.0 ||
681           p33 != 0.0 || p34 != 0.0 || p35 != 0.0 || p36 != 0.0 ||
682           p37 != 0.0 || p38 != 0.0 || p39 != 0.0 || p40 != 0.0 ||
683           p41 != 0.0 || p42 != 0.0 || p43 != 0.0 || p44 != 0.0 ||
684           p45 != 0.0 || p46 != 0.0 || p47 != 0.0 || p48 != 0.0 ||
685           p49 != 0.0) {
686         pv = ba + 49*diag_offset[row];
687         pj = bj + diag_offset[row] + 1;
688 	x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
689 	x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
690 	x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
691 	x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
692 	x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
693 	x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
694 	x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
695 	x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
696 	x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
697 	x37 = pv[36]; x38 = pv[37]; x39 = pv[38]; x40 = pv[39];
698 	x41 = pv[40]; x42 = pv[41]; x43 = pv[42]; x44 = pv[43];
699 	x45 = pv[44]; x46 = pv[45]; x47 = pv[46]; x48 = pv[47];
700         x49 = pv[48];
701         pc[0]  = m1  = p1*x1  + p8*x2   + p15*x3  + p22*x4  + p29*x5  + p36*x6 + p43*x7;
702         pc[1]  = m2  = p2*x1  + p9*x2   + p16*x3  + p23*x4  + p30*x5  + p37*x6 + p44*x7;
703         pc[2]  = m3  = p3*x1  + p10*x2  + p17*x3  + p24*x4  + p31*x5  + p38*x6 + p45*x7;
704         pc[3]  = m4  = p4*x1  + p11*x2  + p18*x3  + p25*x4  + p32*x5  + p39*x6 + p46*x7;
705         pc[4]  = m5  = p5*x1  + p12*x2  + p19*x3  + p26*x4  + p33*x5  + p40*x6 + p47*x7;
706         pc[5]  = m6  = p6*x1  + p13*x2  + p20*x3  + p27*x4  + p34*x5  + p41*x6 + p48*x7;
707         pc[6]  = m7  = p7*x1  + p14*x2  + p21*x3  + p28*x4  + p35*x5  + p42*x6 + p49*x7;
708 
709         pc[7]  = m8  = p1*x8  + p8*x9   + p15*x10 + p22*x11 + p29*x12 + p36*x13 + p43*x14;
710         pc[8]  = m9  = p2*x8  + p9*x9   + p16*x10 + p23*x11 + p30*x12 + p37*x13 + p44*x14;
711         pc[9]  = m10 = p3*x8  + p10*x9  + p17*x10 + p24*x11 + p31*x12 + p38*x13 + p45*x14;
712         pc[10] = m11 = p4*x8  + p11*x9  + p18*x10 + p25*x11 + p32*x12 + p39*x13 + p46*x14;
713         pc[11] = m12 = p5*x8  + p12*x9  + p19*x10 + p26*x11 + p33*x12 + p40*x13 + p47*x14;
714         pc[12] = m13 = p6*x8  + p13*x9  + p20*x10 + p27*x11 + p34*x12 + p41*x13 + p48*x14;
715         pc[13] = m14 = p7*x8  + p14*x9  + p21*x10 + p28*x11 + p35*x12 + p42*x13 + p49*x14;
716 
717         pc[14] = m15 = p1*x15 + p8*x16  + p15*x17 + p22*x18 + p29*x19 + p36*x20 + p43*x21;
718         pc[15] = m16 = p2*x15 + p9*x16  + p16*x17 + p23*x18 + p30*x19 + p37*x20 + p44*x21;
719         pc[16] = m17 = p3*x15 + p10*x16 + p17*x17 + p24*x18 + p31*x19 + p38*x20 + p45*x21;
720         pc[17] = m18 = p4*x15 + p11*x16 + p18*x17 + p25*x18 + p32*x19 + p39*x20 + p46*x21;
721         pc[18] = m19 = p5*x15 + p12*x16 + p19*x17 + p26*x18 + p33*x19 + p40*x20 + p47*x21;
722         pc[19] = m20 = p6*x15 + p13*x16 + p20*x17 + p27*x18 + p34*x19 + p41*x20 + p48*x21;
723         pc[20] = m21 = p7*x15 + p14*x16 + p21*x17 + p28*x18 + p35*x19 + p42*x20 + p49*x21;
724 
725         pc[21] = m22 = p1*x22 + p8*x23  + p15*x24 + p22*x25 + p29*x26 + p36*x27 + p43*x28;
726         pc[22] = m23 = p2*x22 + p9*x23  + p16*x24 + p23*x25 + p30*x26 + p37*x27 + p44*x28;
727         pc[23] = m24 = p3*x22 + p10*x23 + p17*x24 + p24*x25 + p31*x26 + p38*x27 + p45*x28;
728         pc[24] = m25 = p4*x22 + p11*x23 + p18*x24 + p25*x25 + p32*x26 + p39*x27 + p46*x28;
729         pc[25] = m26 = p5*x22 + p12*x23 + p19*x24 + p26*x25 + p33*x26 + p40*x27 + p47*x28;
730         pc[26] = m27 = p6*x22 + p13*x23 + p20*x24 + p27*x25 + p34*x26 + p41*x27 + p48*x28;
731         pc[27] = m28 = p7*x22 + p14*x23 + p21*x24 + p28*x25 + p35*x26 + p42*x27 + p49*x28;
732 
733         pc[28] = m29 = p1*x29 + p8*x30  + p15*x31 + p22*x32 + p29*x33 + p36*x34 + p43*x35;
734         pc[29] = m30 = p2*x29 + p9*x30  + p16*x31 + p23*x32 + p30*x33 + p37*x34 + p44*x35;
735         pc[30] = m31 = p3*x29 + p10*x30 + p17*x31 + p24*x32 + p31*x33 + p38*x34 + p45*x35;
736         pc[31] = m32 = p4*x29 + p11*x30 + p18*x31 + p25*x32 + p32*x33 + p39*x34 + p46*x35;
737         pc[32] = m33 = p5*x29 + p12*x30 + p19*x31 + p26*x32 + p33*x33 + p40*x34 + p47*x35;
738         pc[33] = m34 = p6*x29 + p13*x30 + p20*x31 + p27*x32 + p34*x33 + p41*x34 + p48*x35;
739         pc[34] = m35 = p7*x29 + p14*x30 + p21*x31 + p28*x32 + p35*x33 + p42*x34 + p49*x35;
740 
741         pc[35] = m36 = p1*x36 + p8*x37  + p15*x38 + p22*x39 + p29*x40 + p36*x41 + p43*x42;
742         pc[36] = m37 = p2*x36 + p9*x37  + p16*x38 + p23*x39 + p30*x40 + p37*x41 + p44*x42;
743         pc[37] = m38 = p3*x36 + p10*x37 + p17*x38 + p24*x39 + p31*x40 + p38*x41 + p45*x42;
744         pc[38] = m39 = p4*x36 + p11*x37 + p18*x38 + p25*x39 + p32*x40 + p39*x41 + p46*x42;
745         pc[39] = m40 = p5*x36 + p12*x37 + p19*x38 + p26*x39 + p33*x40 + p40*x41 + p47*x42;
746         pc[40] = m41 = p6*x36 + p13*x37 + p20*x38 + p27*x39 + p34*x40 + p41*x41 + p48*x42;
747         pc[41] = m42 = p7*x36 + p14*x37 + p21*x38 + p28*x39 + p35*x40 + p42*x41 + p49*x42;
748 
749         pc[42] = m43 = p1*x43 + p8*x44  + p15*x45 + p22*x46 + p29*x47 + p36*x48 + p43*x49;
750         pc[43] = m44 = p2*x43 + p9*x44  + p16*x45 + p23*x46 + p30*x47 + p37*x48 + p44*x49;
751         pc[44] = m45 = p3*x43 + p10*x44 + p17*x45 + p24*x46 + p31*x47 + p38*x48 + p45*x49;
752         pc[45] = m46 = p4*x43 + p11*x44 + p18*x45 + p25*x46 + p32*x47 + p39*x48 + p46*x49;
753         pc[46] = m47 = p5*x43 + p12*x44 + p19*x45 + p26*x46 + p33*x47 + p40*x48 + p47*x49;
754         pc[47] = m48 = p6*x43 + p13*x44 + p20*x45 + p27*x46 + p34*x47 + p41*x48 + p48*x49;
755         pc[48] = m49 = p7*x43 + p14*x44 + p21*x45 + p28*x46 + p35*x47 + p42*x48 + p49*x49;
756 
757         nz = bi[row+1] - diag_offset[row] - 1;
758         pv += 49;
759         for (j=0; j<nz; j++) {
760 	  x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
761 	  x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
762 	  x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
763 	  x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
764 	  x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
765 	  x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
766 	  x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
767 	  x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
768 	  x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
769 	  x37 = pv[36]; x38 = pv[37]; x39 = pv[38]; x40 = pv[39];
770 	  x41 = pv[40]; x42 = pv[41]; x43 = pv[42]; x44 = pv[43];
771 	  x45 = pv[44]; x46 = pv[45]; x47 = pv[46]; x48 = pv[47];
772 	  x49 = pv[48];
773 	  x    = rtmp + 49*pj[j];
774 	  x[0]  -= m1*x1  + m8*x2   + m15*x3  + m22*x4  + m29*x5  + m36*x6 + m43*x7;
775 	  x[1]  -= m2*x1  + m9*x2   + m16*x3  + m23*x4  + m30*x5  + m37*x6 + m44*x7;
776 	  x[2]  -= m3*x1  + m10*x2  + m17*x3  + m24*x4  + m31*x5  + m38*x6 + m45*x7;
777 	  x[3]  -= m4*x1  + m11*x2  + m18*x3  + m25*x4  + m32*x5  + m39*x6 + m46*x7;
778 	  x[4]  -= m5*x1  + m12*x2  + m19*x3  + m26*x4  + m33*x5  + m40*x6 + m47*x7;
779 	  x[5]  -= m6*x1  + m13*x2  + m20*x3  + m27*x4  + m34*x5  + m41*x6 + m48*x7;
780 	  x[6]  -= m7*x1  + m14*x2  + m21*x3  + m28*x4  + m35*x5  + m42*x6 + m49*x7;
781 
782 	  x[7]  -= m1*x8  + m8*x9   + m15*x10 + m22*x11 + m29*x12 + m36*x13 + m43*x14;
783 	  x[8]  -= m2*x8  + m9*x9   + m16*x10 + m23*x11 + m30*x12 + m37*x13 + m44*x14;
784 	  x[9]  -= m3*x8  + m10*x9  + m17*x10 + m24*x11 + m31*x12 + m38*x13 + m45*x14;
785 	  x[10] -= m4*x8  + m11*x9  + m18*x10 + m25*x11 + m32*x12 + m39*x13 + m46*x14;
786 	  x[11] -= m5*x8  + m12*x9  + m19*x10 + m26*x11 + m33*x12 + m40*x13 + m47*x14;
787 	  x[12] -= m6*x8  + m13*x9  + m20*x10 + m27*x11 + m34*x12 + m41*x13 + m48*x14;
788 	  x[13] -= m7*x8  + m14*x9  + m21*x10 + m28*x11 + m35*x12 + m42*x13 + m49*x14;
789 
790 	  x[14] -= m1*x15 + m8*x16  + m15*x17 + m22*x18 + m29*x19 + m36*x20 + m43*x21;
791 	  x[15] -= m2*x15 + m9*x16  + m16*x17 + m23*x18 + m30*x19 + m37*x20 + m44*x21;
792 	  x[16] -= m3*x15 + m10*x16 + m17*x17 + m24*x18 + m31*x19 + m38*x20 + m45*x21;
793 	  x[17] -= m4*x15 + m11*x16 + m18*x17 + m25*x18 + m32*x19 + m39*x20 + m46*x21;
794 	  x[18] -= m5*x15 + m12*x16 + m19*x17 + m26*x18 + m33*x19 + m40*x20 + m47*x21;
795 	  x[19] -= m6*x15 + m13*x16 + m20*x17 + m27*x18 + m34*x19 + m41*x20 + m48*x21;
796 	  x[20] -= m7*x15 + m14*x16 + m21*x17 + m28*x18 + m35*x19 + m42*x20 + m49*x21;
797 
798 	  x[21] -= m1*x22 + m8*x23  + m15*x24 + m22*x25 + m29*x26 + m36*x27 + m43*x28;
799 	  x[22] -= m2*x22 + m9*x23  + m16*x24 + m23*x25 + m30*x26 + m37*x27 + m44*x28;
800 	  x[23] -= m3*x22 + m10*x23 + m17*x24 + m24*x25 + m31*x26 + m38*x27 + m45*x28;
801 	  x[24] -= m4*x22 + m11*x23 + m18*x24 + m25*x25 + m32*x26 + m39*x27 + m46*x28;
802 	  x[25] -= m5*x22 + m12*x23 + m19*x24 + m26*x25 + m33*x26 + m40*x27 + m47*x28;
803 	  x[26] -= m6*x22 + m13*x23 + m20*x24 + m27*x25 + m34*x26 + m41*x27 + m48*x28;
804 	  x[27] -= m7*x22 + m14*x23 + m21*x24 + m28*x25 + m35*x26 + m42*x27 + m49*x28;
805 
806 	  x[28] -= m1*x29 + m8*x30  + m15*x31 + m22*x32 + m29*x33 + m36*x34 + m43*x35;
807 	  x[29] -= m2*x29 + m9*x30  + m16*x31 + m23*x32 + m30*x33 + m37*x34 + m44*x35;
808 	  x[30] -= m3*x29 + m10*x30 + m17*x31 + m24*x32 + m31*x33 + m38*x34 + m45*x35;
809 	  x[31] -= m4*x29 + m11*x30 + m18*x31 + m25*x32 + m32*x33 + m39*x34 + m46*x35;
810 	  x[32] -= m5*x29 + m12*x30 + m19*x31 + m26*x32 + m33*x33 + m40*x34 + m47*x35;
811 	  x[33] -= m6*x29 + m13*x30 + m20*x31 + m27*x32 + m34*x33 + m41*x34 + m48*x35;
812 	  x[34] -= m7*x29 + m14*x30 + m21*x31 + m28*x32 + m35*x33 + m42*x34 + m49*x35;
813 
814 	  x[35] -= m1*x36 + m8*x37  + m15*x38 + m22*x39 + m29*x40 + m36*x41 + m43*x42;
815 	  x[36] -= m2*x36 + m9*x37  + m16*x38 + m23*x39 + m30*x40 + m37*x41 + m44*x42;
816 	  x[37] -= m3*x36 + m10*x37 + m17*x38 + m24*x39 + m31*x40 + m38*x41 + m45*x42;
817 	  x[38] -= m4*x36 + m11*x37 + m18*x38 + m25*x39 + m32*x40 + m39*x41 + m46*x42;
818 	  x[39] -= m5*x36 + m12*x37 + m19*x38 + m26*x39 + m33*x40 + m40*x41 + m47*x42;
819 	  x[40] -= m6*x36 + m13*x37 + m20*x38 + m27*x39 + m34*x40 + m41*x41 + m48*x42;
820 	  x[41] -= m7*x36 + m14*x37 + m21*x38 + m28*x39 + m35*x40 + m42*x41 + m49*x42;
821 
822 	  x[42] -= m1*x43 + m8*x44  + m15*x45 + m22*x46 + m29*x47 + m36*x48 + m43*x49;
823 	  x[43] -= m2*x43 + m9*x44  + m16*x45 + m23*x46 + m30*x47 + m37*x48 + m44*x49;
824 	  x[44] -= m3*x43 + m10*x44 + m17*x45 + m24*x46 + m31*x47 + m38*x48 + m45*x49;
825 	  x[45] -= m4*x43 + m11*x44 + m18*x45 + m25*x46 + m32*x47 + m39*x48 + m46*x49;
826 	  x[46] -= m5*x43 + m12*x44 + m19*x45 + m26*x46 + m33*x47 + m40*x48 + m47*x49;
827 	  x[47] -= m6*x43 + m13*x44 + m20*x45 + m27*x46 + m34*x47 + m41*x48 + m48*x49;
828 	  x[48] -= m7*x43 + m14*x44 + m21*x45 + m28*x46 + m35*x47 + m42*x48 + m49*x49;
829           pv   += 49;
830         }
831         PLogFlops(686*nz+637);
832       }
833       row = *ajtmp++;
834     }
835     /* finished row so stick it into b->a */
836     pv = ba + 49*bi[i];
837     pj = bj + bi[i];
838     nz = bi[i+1] - bi[i];
839     for (j=0; j<nz; j++) {
840       x      = rtmp+49*pj[j];
841       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
842       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7];
843       pv[8]  = x[8];  pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11];
844       pv[12] = x[12]; pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
845       pv[16] = x[16]; pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19];
846       pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23];
847       pv[24] = x[24]; pv[25] = x[25]; pv[26] = x[26]; pv[27] = x[27];
848       pv[28] = x[28]; pv[29] = x[29]; pv[30] = x[30]; pv[31] = x[31];
849       pv[32] = x[32]; pv[33] = x[33]; pv[34] = x[34]; pv[35] = x[35];
850       pv[36] = x[36]; pv[37] = x[37]; pv[38] = x[38]; pv[39] = x[39];
851       pv[40] = x[40]; pv[41] = x[41]; pv[42] = x[42]; pv[43] = x[43];
852       pv[44] = x[44]; pv[45] = x[45]; pv[46] = x[46]; pv[47] = x[47];
853       pv[48] = x[48];
854       pv   += 49;
855     }
856     /* invert diagonal block */
857     w = ba + 49*diag_offset[i];
858     ierr = Kernel_A_gets_inverse_A_7(w);CHKERRQ(ierr);
859   }
860 
861   ierr = PetscFree(rtmp);CHKERRQ(ierr);
862   C->factor    = FACTOR_LU;
863   C->assembled = PETSC_TRUE;
864   PLogFlops(1.3333*343*b->mbs); /* from inverting diagonal blocks */
865   PetscFunctionReturn(0);
866 }
867 
868 /* Version for when blocks are 6 by 6 */
869 #undef __FUNC__
870 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_6"
871 int MatCholeskyFactorNumeric_SeqSBAIJ_6(Mat A,Mat *B)
872 {
873   Mat                C = *B;
874   Mat_SeqSBAIJ       *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data;
875   IS                 perm = b->row;
876   int                *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
877   int                *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
878   MatScalar          *ba = b->a,*aa,*ap,*dk,*uik;
879   MatScalar          *u,*d,*w,*wp;
880 
881   PetscFunctionBegin;
882   /* initialization */
883   w  = (MatScalar*)PetscMalloc(36*mbs*sizeof(MatScalar));CHKPTRQ(w);
884   ierr = PetscMemzero(w,36*mbs*sizeof(MatScalar));CHKERRQ(ierr);
885   il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il);
886   jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl);
887   for (i=0; i<mbs; i++) {
888     jl[i] = mbs; il[0] = 0;
889   }
890   dk    = (MatScalar*)PetscMalloc(36*sizeof(MatScalar));CHKPTRQ(dk);
891   uik   = (MatScalar*)PetscMalloc(36*sizeof(MatScalar));CHKPTRQ(uik);
892   ierr  = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr);
893 
894   /* check permutation */
895   if (!a->permute){
896     ai = a->i; aj = a->j; aa = a->a;
897   } else {
898     ai = a->inew; aj = a->jnew;
899     aa = (MatScalar*)PetscMalloc(36*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa);
900     ierr = PetscMemcpy(aa,a->a,36*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr);
901     a2anew  = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew);
902     ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr);
903 
904     for (i=0; i<mbs; i++){
905       jmin = ai[i]; jmax = ai[i+1];
906       for (j=jmin; j<jmax; j++){
907         while (a2anew[j] != j){
908           k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k;
909           for (k1=0; k1<36; k1++){
910             dk[k1]       = aa[k*36+k1];
911             aa[k*36+k1] = aa[j*36+k1];
912             aa[j*36+k1] = dk[k1];
913           }
914         }
915         /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */
916         if (i > aj[j]){
917           /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */
918           ap = aa + j*36;                     /* ptr to the beginning of j-th block of aa */
919           for (k=0; k<36; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */
920           for (k=0; k<6; k++){               /* j-th block of aa <- dk^T */
921             for (k1=0; k1<6; k1++) *ap++ = dk[k + 6*k1];
922           }
923         }
924       }
925     }
926     ierr = PetscFree(a2anew);CHKERRA(ierr);
927   }
928 
929   /* for each row k */
930   for (k = 0; k<mbs; k++){
931 
932     /*initialize k-th row with elements nonzero in row perm(k) of A */
933     jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1];
934     if (jmin < jmax) {
935       ap = aa + jmin*36;
936       for (j = jmin; j < jmax; j++){
937         vj = perm_ptr[aj[j]];         /* block col. index */
938         wp = w + vj*36;
939         for (i=0; i<36; i++) *wp++ = *ap++;
940       }
941     }
942 
943     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
944     ierr = PetscMemcpy(dk,w+k*36,36*sizeof(MatScalar));CHKERRQ(ierr);
945     i = jl[k]; /* first row to be added to k_th row  */
946 
947     while (i < mbs){
948       nexti = jl[i]; /* next row to be added to k_th row */
949 
950       /* compute multiplier */
951       ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
952 
953       /* uik = -inv(Di)*U_bar(i,k) */
954       d = ba + i*36;
955       u    = ba + ili*36;
956 
957       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]);
958       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]);
959       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]);
960       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]);
961       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]);
962       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]);
963 
964       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]);
965       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]);
966       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]);
967       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]);
968       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]);
969       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]);
970 
971       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]);
972       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]);
973       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]);
974       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]);
975       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]);
976       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]);
977 
978       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]);
979       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]);
980       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]);
981       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]);
982       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]);
983       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]);
984 
985       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]);
986       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]);
987       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]);
988       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]);
989       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]);
990       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]);
991 
992       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]);
993       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]);
994       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]);
995       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]);
996       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]);
997       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]);
998 
999       /* update D(k) += -U(i,k)^T * U_bar(i,k) */
1000       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];
1001       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];
1002       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];
1003       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];
1004       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];
1005       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];
1006 
1007       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];
1008       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];
1009       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];
1010       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];
1011       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];
1012       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];
1013 
1014       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];
1015       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];
1016       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];
1017       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];
1018       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];
1019       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];
1020 
1021       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];
1022       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];
1023       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];
1024       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];
1025       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];
1026       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];
1027 
1028       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];
1029       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];
1030       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];
1031       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];
1032       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];
1033       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];
1034 
1035       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];
1036       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];
1037       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];
1038       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];
1039       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];
1040       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];
1041 
1042       /* update -U(i,k) */
1043       ierr = PetscMemcpy(ba+ili*36,uik,36*sizeof(MatScalar));CHKERRQ(ierr);
1044 
1045       /* add multiple of row i to k-th row ... */
1046       jmin = ili + 1; jmax = bi[i+1];
1047       if (jmin < jmax){
1048         for (j=jmin; j<jmax; j++) {
1049           /* w += -U(i,k)^T * U_bar(i,j) */
1050           wp = w + bj[j]*36;
1051           u = ba + j*36;
1052           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];
1053           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];
1054           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];
1055           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];
1056           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];
1057           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];
1058 
1059           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];
1060           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];
1061           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];
1062           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];
1063           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];
1064           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];
1065 
1066           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];
1067           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];
1068           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];
1069           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];
1070           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];
1071           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];
1072 
1073           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];
1074           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];
1075           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];
1076           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];
1077           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];
1078           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];
1079 
1080           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];
1081           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];
1082           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];
1083           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];
1084           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];
1085           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];
1086 
1087           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];
1088           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];
1089           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];
1090           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];
1091           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];
1092           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];
1093         }
1094 
1095         /* ... add i to row list for next nonzero entry */
1096         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
1097         j     = bj[jmin];
1098         jl[i] = jl[j]; jl[j] = i; /* update jl */
1099       }
1100       i = nexti;
1101     }
1102 
1103     /* save nonzero entries in k-th row of U ... */
1104 
1105     /* invert diagonal block */
1106     d = ba+k*36;
1107     ierr = PetscMemcpy(d,dk,36*sizeof(MatScalar));CHKERRQ(ierr);
1108     ierr = Kernel_A_gets_inverse_A_6(d);CHKERRQ(ierr);
1109 
1110     jmin = bi[k]; jmax = bi[k+1];
1111     if (jmin < jmax) {
1112       for (j=jmin; j<jmax; j++){
1113          vj = bj[j];           /* block col. index of U */
1114          u   = ba + j*36;
1115          wp = w + vj*36;
1116          for (k1=0; k1<36; k1++){
1117            *u++        = *wp;
1118            *wp++ = 0.0;
1119          }
1120       }
1121 
1122       /* ... add k to row list for first nonzero entry in k-th row */
1123       il[k] = jmin;
1124       i     = bj[jmin];
1125       jl[k] = jl[i]; jl[i] = k;
1126     }
1127   }
1128 
1129   ierr = PetscFree(w);CHKERRQ(ierr);
1130   ierr = PetscFree(il);CHKERRQ(ierr);
1131   ierr = PetscFree(jl);CHKERRQ(ierr);
1132   ierr = PetscFree(dk);CHKERRQ(ierr);
1133   ierr = PetscFree(uik);CHKERRQ(ierr);
1134   if (a->permute){
1135     ierr = PetscFree(aa);CHKERRQ(ierr);
1136   }
1137 
1138   ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr);
1139   C->factor    = FACTOR_CHOLESKY;
1140   C->assembled = PETSC_TRUE;
1141   C->preallocated = PETSC_TRUE;
1142   PLogFlops(1.3333*216*b->mbs); /* from inverting diagonal blocks */
1143   PetscFunctionReturn(0);
1144 }
1145 
1146 /*
1147       Version for when blocks are 6 by 6 Using natural ordering
1148 */
1149 #undef __FUNC__
1150 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_6_NaturalOrdering"
1151 int MatCholeskyFactorNumeric_SeqSBAIJ_6_NaturalOrdering(Mat A,Mat *B)
1152 {
1153   Mat         C = *B;
1154   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
1155   int         ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
1156   int         *ajtmpold,*ajtmp,nz,row;
1157   int         *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
1158   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
1159   MatScalar   x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15;
1160   MatScalar   x16,x17,x18,x19,x20,x21,x22,x23,x24,x25;
1161   MatScalar   p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15;
1162   MatScalar   p16,p17,p18,p19,p20,p21,p22,p23,p24,p25;
1163   MatScalar   m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12,m13,m14,m15;
1164   MatScalar   m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
1165   MatScalar   p26,p27,p28,p29,p30,p31,p32,p33,p34,p35,p36;
1166   MatScalar   x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36;
1167   MatScalar   m26,m27,m28,m29,m30,m31,m32,m33,m34,m35,m36;
1168   MatScalar   *ba = b->a,*aa = a->a;
1169 
1170   PetscFunctionBegin;
1171   rtmp  = (MatScalar*)PetscMalloc(36*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
1172   for (i=0; i<n; i++) {
1173     nz    = bi[i+1] - bi[i];
1174     ajtmp = bj + bi[i];
1175     for  (j=0; j<nz; j++) {
1176       x = rtmp+36*ajtmp[j];
1177       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
1178       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
1179       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = x[25] = 0.0 ;
1180       x[26] = x[27] = x[28] = x[29] = x[30] = x[31] = x[32] = x[33] = 0.0 ;
1181       x[34] = x[35] = 0.0 ;
1182     }
1183     /* load in initial (unfactored row) */
1184     nz       = ai[i+1] - ai[i];
1185     ajtmpold = aj + ai[i];
1186     v        = aa + 36*ai[i];
1187     for (j=0; j<nz; j++) {
1188       x    = rtmp+36*ajtmpold[j];
1189       x[0] =  v[0];  x[1] =  v[1];  x[2] =  v[2];  x[3] =  v[3];
1190       x[4] =  v[4];  x[5] =  v[5];  x[6] =  v[6];  x[7] =  v[7];
1191       x[8] =  v[8];  x[9] =  v[9];  x[10] = v[10]; x[11] = v[11];
1192       x[12] = v[12]; x[13] = v[13]; x[14] = v[14]; x[15] = v[15];
1193       x[16] = v[16]; x[17] = v[17]; x[18] = v[18]; x[19] = v[19];
1194       x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23];
1195       x[24] = v[24]; x[25] = v[25]; x[26] = v[26]; x[27] = v[27];
1196       x[28] = v[28]; x[29] = v[29]; x[30] = v[30]; x[31] = v[31];
1197       x[32] = v[32]; x[33] = v[33]; x[34] = v[34]; x[35] = v[35];
1198       v    += 36;
1199     }
1200     row = *ajtmp++;
1201     while (row < i) {
1202       pc  = rtmp + 36*row;
1203       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
1204       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];
1205       p9  = pc[8];  p10 = pc[9];  p11 = pc[10]; p12 = pc[11];
1206       p13 = pc[12]; p14 = pc[13]; p15 = pc[14]; p16 = pc[15];
1207       p17 = pc[16]; p18 = pc[17]; p19 = pc[18]; p20 = pc[19];
1208       p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
1209       p25 = pc[24]; p26 = pc[25]; p27 = pc[26]; p28 = pc[27];
1210       p29 = pc[28]; p30 = pc[29]; p31 = pc[30]; p32 = pc[31];
1211       p33 = pc[32]; p34 = pc[33]; p35 = pc[34]; p36 = pc[35];
1212       if (p1  != 0.0 || p2  != 0.0 || p3  != 0.0 || p4  != 0.0 ||
1213           p5  != 0.0 || p6  != 0.0 || p7  != 0.0 || p8  != 0.0 ||
1214           p9  != 0.0 || p10 != 0.0 || p11 != 0.0 || p12 != 0.0 ||
1215           p13 != 0.0 || p14 != 0.0 || p15 != 0.0 || p16 != 0.0 ||
1216           p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 ||
1217           p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 ||
1218           p25 != 0.0 || p26 != 0.0 || p27 != 0.0 || p28 != 0.0 ||
1219           p29 != 0.0 || p30 != 0.0 || p31 != 0.0 || p32 != 0.0 ||
1220           p33 != 0.0 || p34 != 0.0 || p35 != 0.0 || p36 != 0.0) {
1221         pv = ba + 36*diag_offset[row];
1222         pj = bj + diag_offset[row] + 1;
1223 	x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
1224 	x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
1225 	x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
1226 	x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
1227 	x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
1228 	x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
1229 	x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
1230 	x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
1231 	x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
1232         pc[0]  = m1  = p1*x1  + p7*x2   + p13*x3  + p19*x4  + p25*x5  + p31*x6;
1233         pc[1]  = m2  = p2*x1  + p8*x2   + p14*x3  + p20*x4  + p26*x5  + p32*x6;
1234         pc[2]  = m3  = p3*x1  + p9*x2   + p15*x3  + p21*x4  + p27*x5  + p33*x6;
1235         pc[3]  = m4  = p4*x1  + p10*x2  + p16*x3  + p22*x4  + p28*x5  + p34*x6;
1236         pc[4]  = m5  = p5*x1  + p11*x2  + p17*x3  + p23*x4  + p29*x5  + p35*x6;
1237         pc[5]  = m6  = p6*x1  + p12*x2  + p18*x3  + p24*x4  + p30*x5  + p36*x6;
1238 
1239         pc[6]  = m7  = p1*x7  + p7*x8   + p13*x9  + p19*x10 + p25*x11 + p31*x12;
1240         pc[7]  = m8  = p2*x7  + p8*x8   + p14*x9  + p20*x10 + p26*x11 + p32*x12;
1241         pc[8]  = m9  = p3*x7  + p9*x8   + p15*x9  + p21*x10 + p27*x11 + p33*x12;
1242         pc[9]  = m10 = p4*x7  + p10*x8  + p16*x9  + p22*x10 + p28*x11 + p34*x12;
1243         pc[10] = m11 = p5*x7  + p11*x8  + p17*x9  + p23*x10 + p29*x11 + p35*x12;
1244         pc[11] = m12 = p6*x7  + p12*x8  + p18*x9  + p24*x10 + p30*x11 + p36*x12;
1245 
1246         pc[12] = m13 = p1*x13 + p7*x14  + p13*x15 + p19*x16 + p25*x17 + p31*x18;
1247         pc[13] = m14 = p2*x13 + p8*x14  + p14*x15 + p20*x16 + p26*x17 + p32*x18;
1248         pc[14] = m15 = p3*x13 + p9*x14  + p15*x15 + p21*x16 + p27*x17 + p33*x18;
1249         pc[15] = m16 = p4*x13 + p10*x14 + p16*x15 + p22*x16 + p28*x17 + p34*x18;
1250         pc[16] = m17 = p5*x13 + p11*x14 + p17*x15 + p23*x16 + p29*x17 + p35*x18;
1251         pc[17] = m18 = p6*x13 + p12*x14 + p18*x15 + p24*x16 + p30*x17 + p36*x18;
1252 
1253         pc[18] = m19 = p1*x19 + p7*x20  + p13*x21 + p19*x22 + p25*x23 + p31*x24;
1254         pc[19] = m20 = p2*x19 + p8*x20  + p14*x21 + p20*x22 + p26*x23 + p32*x24;
1255         pc[20] = m21 = p3*x19 + p9*x20  + p15*x21 + p21*x22 + p27*x23 + p33*x24;
1256         pc[21] = m22 = p4*x19 + p10*x20 + p16*x21 + p22*x22 + p28*x23 + p34*x24;
1257         pc[22] = m23 = p5*x19 + p11*x20 + p17*x21 + p23*x22 + p29*x23 + p35*x24;
1258         pc[23] = m24 = p6*x19 + p12*x20 + p18*x21 + p24*x22 + p30*x23 + p36*x24;
1259 
1260         pc[24] = m25 = p1*x25 + p7*x26  + p13*x27 + p19*x28 + p25*x29 + p31*x30;
1261         pc[25] = m26 = p2*x25 + p8*x26  + p14*x27 + p20*x28 + p26*x29 + p32*x30;
1262         pc[26] = m27 = p3*x25 + p9*x26  + p15*x27 + p21*x28 + p27*x29 + p33*x30;
1263         pc[27] = m28 = p4*x25 + p10*x26 + p16*x27 + p22*x28 + p28*x29 + p34*x30;
1264         pc[28] = m29 = p5*x25 + p11*x26 + p17*x27 + p23*x28 + p29*x29 + p35*x30;
1265         pc[29] = m30 = p6*x25 + p12*x26 + p18*x27 + p24*x28 + p30*x29 + p36*x30;
1266 
1267         pc[30] = m31 = p1*x31 + p7*x32  + p13*x33 + p19*x34 + p25*x35 + p31*x36;
1268         pc[31] = m32 = p2*x31 + p8*x32  + p14*x33 + p20*x34 + p26*x35 + p32*x36;
1269         pc[32] = m33 = p3*x31 + p9*x32  + p15*x33 + p21*x34 + p27*x35 + p33*x36;
1270         pc[33] = m34 = p4*x31 + p10*x32 + p16*x33 + p22*x34 + p28*x35 + p34*x36;
1271         pc[34] = m35 = p5*x31 + p11*x32 + p17*x33 + p23*x34 + p29*x35 + p35*x36;
1272         pc[35] = m36 = p6*x31 + p12*x32 + p18*x33 + p24*x34 + p30*x35 + p36*x36;
1273 
1274         nz = bi[row+1] - diag_offset[row] - 1;
1275         pv += 36;
1276         for (j=0; j<nz; j++) {
1277 	  x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
1278 	  x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
1279 	  x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
1280 	  x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
1281 	  x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
1282 	  x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
1283 	  x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
1284 	  x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
1285 	  x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
1286 	  x    = rtmp + 36*pj[j];
1287           x[0]  -= m1*x1  + m7*x2   + m13*x3  + m19*x4  + m25*x5  + m31*x6;
1288           x[1]  -= m2*x1  + m8*x2   + m14*x3  + m20*x4  + m26*x5  + m32*x6;
1289           x[2]  -= m3*x1  + m9*x2   + m15*x3  + m21*x4  + m27*x5  + m33*x6;
1290           x[3]  -= m4*x1  + m10*x2  + m16*x3  + m22*x4  + m28*x5  + m34*x6;
1291           x[4]  -= m5*x1  + m11*x2  + m17*x3  + m23*x4  + m29*x5  + m35*x6;
1292           x[5]  -= m6*x1  + m12*x2  + m18*x3  + m24*x4  + m30*x5  + m36*x6;
1293 
1294 	  x[6]  -= m1*x7  + m7*x8   + m13*x9  + m19*x10 + m25*x11 + m31*x12;
1295 	  x[7]  -= m2*x7  + m8*x8   + m14*x9  + m20*x10 + m26*x11 + m32*x12;
1296 	  x[8]  -= m3*x7  + m9*x8   + m15*x9  + m21*x10 + m27*x11 + m33*x12;
1297 	  x[9]  -= m4*x7  + m10*x8  + m16*x9  + m22*x10 + m28*x11 + m34*x12;
1298 	  x[10] -= m5*x7  + m11*x8  + m17*x9  + m23*x10 + m29*x11 + m35*x12;
1299 	  x[11] -= m6*x7  + m12*x8  + m18*x9  + m24*x10 + m30*x11 + m36*x12;
1300 
1301 	  x[12] -= m1*x13 + m7*x14  + m13*x15 + m19*x16 + m25*x17 + m31*x18;
1302 	  x[13] -= m2*x13 + m8*x14  + m14*x15 + m20*x16 + m26*x17 + m32*x18;
1303 	  x[14] -= m3*x13 + m9*x14  + m15*x15 + m21*x16 + m27*x17 + m33*x18;
1304 	  x[15] -= m4*x13 + m10*x14 + m16*x15 + m22*x16 + m28*x17 + m34*x18;
1305 	  x[16] -= m5*x13 + m11*x14 + m17*x15 + m23*x16 + m29*x17 + m35*x18;
1306 	  x[17] -= m6*x13 + m12*x14 + m18*x15 + m24*x16 + m30*x17 + m36*x18;
1307 
1308 	  x[18] -= m1*x19 + m7*x20  + m13*x21 + m19*x22 + m25*x23 + m31*x24;
1309 	  x[19] -= m2*x19 + m8*x20  + m14*x21 + m20*x22 + m26*x23 + m32*x24;
1310 	  x[20] -= m3*x19 + m9*x20  + m15*x21 + m21*x22 + m27*x23 + m33*x24;
1311 	  x[21] -= m4*x19 + m10*x20 + m16*x21 + m22*x22 + m28*x23 + m34*x24;
1312 	  x[22] -= m5*x19 + m11*x20 + m17*x21 + m23*x22 + m29*x23 + m35*x24;
1313 	  x[23] -= m6*x19 + m12*x20 + m18*x21 + m24*x22 + m30*x23 + m36*x24;
1314 
1315 	  x[24] -= m1*x25 + m7*x26  + m13*x27 + m19*x28 + m25*x29 + m31*x30;
1316 	  x[25] -= m2*x25 + m8*x26  + m14*x27 + m20*x28 + m26*x29 + m32*x30;
1317 	  x[26] -= m3*x25 + m9*x26  + m15*x27 + m21*x28 + m27*x29 + m33*x30;
1318 	  x[27] -= m4*x25 + m10*x26 + m16*x27 + m22*x28 + m28*x29 + m34*x30;
1319 	  x[28] -= m5*x25 + m11*x26 + m17*x27 + m23*x28 + m29*x29 + m35*x30;
1320 	  x[29] -= m6*x25 + m12*x26 + m18*x27 + m24*x28 + m30*x29 + m36*x30;
1321 
1322 	  x[30] -= m1*x31 + m7*x32  + m13*x33 + m19*x34 + m25*x35 + m31*x36;
1323 	  x[31] -= m2*x31 + m8*x32  + m14*x33 + m20*x34 + m26*x35 + m32*x36;
1324 	  x[32] -= m3*x31 + m9*x32  + m15*x33 + m21*x34 + m27*x35 + m33*x36;
1325 	  x[33] -= m4*x31 + m10*x32 + m16*x33 + m22*x34 + m28*x35 + m34*x36;
1326 	  x[34] -= m5*x31 + m11*x32 + m17*x33 + m23*x34 + m29*x35 + m35*x36;
1327 	  x[35] -= m6*x31 + m12*x32 + m18*x33 + m24*x34 + m30*x35 + m36*x36;
1328 
1329           pv   += 36;
1330         }
1331         PLogFlops(432*nz+396);
1332       }
1333       row = *ajtmp++;
1334     }
1335     /* finished row so stick it into b->a */
1336     pv = ba + 36*bi[i];
1337     pj = bj + bi[i];
1338     nz = bi[i+1] - bi[i];
1339     for (j=0; j<nz; j++) {
1340       x      = rtmp+36*pj[j];
1341       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
1342       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7];
1343       pv[8]  = x[8];  pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11];
1344       pv[12] = x[12]; pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
1345       pv[16] = x[16]; pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19];
1346       pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23];
1347       pv[24] = x[24]; pv[25] = x[25]; pv[26] = x[26]; pv[27] = x[27];
1348       pv[28] = x[28]; pv[29] = x[29]; pv[30] = x[30]; pv[31] = x[31];
1349       pv[32] = x[32]; pv[33] = x[33]; pv[34] = x[34]; pv[35] = x[35];
1350       pv   += 36;
1351     }
1352     /* invert diagonal block */
1353     w = ba + 36*diag_offset[i];
1354     ierr = Kernel_A_gets_inverse_A_6(w);CHKERRQ(ierr);
1355   }
1356 
1357   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1358   C->factor    = FACTOR_LU;
1359   C->assembled = PETSC_TRUE;
1360   PLogFlops(1.3333*216*b->mbs); /* from inverting diagonal blocks */
1361   PetscFunctionReturn(0);
1362 }
1363 
1364 /* Version for when blocks are 5 by 5  */
1365 #undef __FUNC__
1366 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_5"
1367 int MatCholeskyFactorNumeric_SeqSBAIJ_5(Mat A,Mat *B)
1368 {
1369   Mat                C = *B;
1370   Mat_SeqSBAIJ       *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data;
1371   IS                 perm = b->row;
1372   int                *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
1373   int                *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
1374   MatScalar          *ba = b->a,*aa,*ap,*dk,*uik;
1375   MatScalar          *u,*d,*rtmp,*rtmp_ptr;
1376 
1377   PetscFunctionBegin;
1378   /* initialization */
1379   rtmp  = (MatScalar*)PetscMalloc(25*mbs*sizeof(MatScalar));CHKPTRQ(rtmp);
1380   ierr = PetscMemzero(rtmp,25*mbs*sizeof(MatScalar));CHKERRQ(ierr);
1381   il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il);
1382   jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl);
1383   for (i=0; i<mbs; i++) {
1384     jl[i] = mbs; il[0] = 0;
1385   }
1386   dk    = (MatScalar*)PetscMalloc(25*sizeof(MatScalar));CHKPTRQ(dk);
1387   uik   = (MatScalar*)PetscMalloc(25*sizeof(MatScalar));CHKPTRQ(uik);
1388   ierr  = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr);
1389 
1390   /* check permutation */
1391   if (!a->permute){
1392     ai = a->i; aj = a->j; aa = a->a;
1393   } else {
1394     ai = a->inew; aj = a->jnew;
1395     aa = (MatScalar*)PetscMalloc(25*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa);
1396     ierr = PetscMemcpy(aa,a->a,25*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr);
1397     a2anew  = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew);
1398     ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr);
1399 
1400     for (i=0; i<mbs; i++){
1401       jmin = ai[i]; jmax = ai[i+1];
1402       for (j=jmin; j<jmax; j++){
1403         while (a2anew[j] != j){
1404           k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k;
1405           for (k1=0; k1<25; k1++){
1406             dk[k1]       = aa[k*25+k1];
1407             aa[k*25+k1] = aa[j*25+k1];
1408             aa[j*25+k1] = dk[k1];
1409           }
1410         }
1411         /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */
1412         if (i > aj[j]){
1413           /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */
1414           ap = aa + j*25;                     /* ptr to the beginning of j-th block of aa */
1415           for (k=0; k<25; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */
1416           for (k=0; k<5; k++){               /* j-th block of aa <- dk^T */
1417             for (k1=0; k1<5; k1++) *ap++ = dk[k + 5*k1];
1418           }
1419         }
1420       }
1421     }
1422     ierr = PetscFree(a2anew);CHKERRA(ierr);
1423   }
1424 
1425   /* for each row k */
1426   for (k = 0; k<mbs; k++){
1427 
1428     /*initialize k-th row with elements nonzero in row perm(k) of A */
1429     jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1];
1430     if (jmin < jmax) {
1431       ap = aa + jmin*25;
1432       for (j = jmin; j < jmax; j++){
1433         vj = perm_ptr[aj[j]];         /* block col. index */
1434         rtmp_ptr = rtmp + vj*25;
1435         for (i=0; i<25; i++) *rtmp_ptr++ = *ap++;
1436       }
1437     }
1438 
1439     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
1440     ierr = PetscMemcpy(dk,rtmp+k*25,25*sizeof(MatScalar));CHKERRQ(ierr);
1441     i = jl[k]; /* first row to be added to k_th row  */
1442 
1443     while (i < mbs){
1444       nexti = jl[i]; /* next row to be added to k_th row */
1445 
1446       /* compute multiplier */
1447       ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
1448 
1449       /* uik = -inv(Di)*U_bar(i,k) */
1450       d = ba + i*25;
1451       u    = ba + ili*25;
1452 
1453       uik[0] = -(d[0]*u[0] + d[5]*u[1] + d[10]*u[2] + d[15]*u[3] + d[20]*u[4]);
1454       uik[1] = -(d[1]*u[0] + d[6]*u[1] + d[11]*u[2] + d[16]*u[3] + d[21]*u[4]);
1455       uik[2] = -(d[2]*u[0] + d[7]*u[1] + d[12]*u[2] + d[17]*u[3] + d[22]*u[4]);
1456       uik[3] = -(d[3]*u[0] + d[8]*u[1] + d[13]*u[2] + d[18]*u[3] + d[23]*u[4]);
1457       uik[4] = -(d[4]*u[0] + d[9]*u[1] + d[14]*u[2] + d[19]*u[3] + d[24]*u[4]);
1458 
1459       uik[5] = -(d[0]*u[5] + d[5]*u[6] + d[10]*u[7] + d[15]*u[8] + d[20]*u[9]);
1460       uik[6] = -(d[1]*u[5] + d[6]*u[6] + d[11]*u[7] + d[16]*u[8] + d[21]*u[9]);
1461       uik[7] = -(d[2]*u[5] + d[7]*u[6] + d[12]*u[7] + d[17]*u[8] + d[22]*u[9]);
1462       uik[8] = -(d[3]*u[5] + d[8]*u[6] + d[13]*u[7] + d[18]*u[8] + d[23]*u[9]);
1463       uik[9] = -(d[4]*u[5] + d[9]*u[6] + d[14]*u[7] + d[19]*u[8] + d[24]*u[9]);
1464 
1465       uik[10]= -(d[0]*u[10] + d[5]*u[11] + d[10]*u[12] + d[15]*u[13] + d[20]*u[14]);
1466       uik[11]= -(d[1]*u[10] + d[6]*u[11] + d[11]*u[12] + d[16]*u[13] + d[21]*u[14]);
1467       uik[12]= -(d[2]*u[10] + d[7]*u[11] + d[12]*u[12] + d[17]*u[13] + d[22]*u[14]);
1468       uik[13]= -(d[3]*u[10] + d[8]*u[11] + d[13]*u[12] + d[18]*u[13] + d[23]*u[14]);
1469       uik[14]= -(d[4]*u[10] + d[9]*u[11] + d[14]*u[12] + d[19]*u[13] + d[24]*u[14]);
1470 
1471       uik[15]= -(d[0]*u[15] + d[5]*u[16] + d[10]*u[17] + d[15]*u[18] + d[20]*u[19]);
1472       uik[16]= -(d[1]*u[15] + d[6]*u[16] + d[11]*u[17] + d[16]*u[18] + d[21]*u[19]);
1473       uik[17]= -(d[2]*u[15] + d[7]*u[16] + d[12]*u[17] + d[17]*u[18] + d[22]*u[19]);
1474       uik[18]= -(d[3]*u[15] + d[8]*u[16] + d[13]*u[17] + d[18]*u[18] + d[23]*u[19]);
1475       uik[19]= -(d[4]*u[15] + d[9]*u[16] + d[14]*u[17] + d[19]*u[18] + d[24]*u[19]);
1476 
1477       uik[20]= -(d[0]*u[20] + d[5]*u[21] + d[10]*u[22] + d[15]*u[23] + d[20]*u[24]);
1478       uik[21]= -(d[1]*u[20] + d[6]*u[21] + d[11]*u[22] + d[16]*u[23] + d[21]*u[24]);
1479       uik[22]= -(d[2]*u[20] + d[7]*u[21] + d[12]*u[22] + d[17]*u[23] + d[22]*u[24]);
1480       uik[23]= -(d[3]*u[20] + d[8]*u[21] + d[13]*u[22] + d[18]*u[23] + d[23]*u[24]);
1481       uik[24]= -(d[4]*u[20] + d[9]*u[21] + d[14]*u[22] + d[19]*u[23] + d[24]*u[24]);
1482 
1483 
1484       /* update D(k) += -U(i,k)^T * U_bar(i,k) */
1485       dk[0] +=  uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3] + uik[4]*u[4];
1486       dk[1] +=  uik[5]*u[0] + uik[6]*u[1] + uik[7]*u[2] + uik[8]*u[3] + uik[9]*u[4];
1487       dk[2] += uik[10]*u[0]+ uik[11]*u[1]+ uik[12]*u[2]+ uik[13]*u[3]+ uik[14]*u[4];
1488       dk[3] += uik[15]*u[0]+ uik[16]*u[1]+ uik[17]*u[2]+ uik[18]*u[3]+ uik[19]*u[4];
1489       dk[4] += uik[20]*u[0]+ uik[21]*u[1]+ uik[22]*u[2]+ uik[23]*u[3]+ uik[24]*u[4];
1490 
1491       dk[5] +=  uik[0]*u[5] + uik[1]*u[6] + uik[2]*u[7] + uik[3]*u[8] + uik[4]*u[9];
1492       dk[6] +=  uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8] + uik[9]*u[9];
1493       dk[7] += uik[10]*u[5]+ uik[11]*u[6]+ uik[12]*u[7]+ uik[13]*u[8]+ uik[14]*u[9];
1494       dk[8] += uik[15]*u[5]+ uik[16]*u[6]+ uik[17]*u[7]+ uik[18]*u[8]+ uik[19]*u[9];
1495       dk[9] += uik[20]*u[5]+ uik[21]*u[6]+ uik[22]*u[7]+ uik[23]*u[8]+ uik[24]*u[9];
1496 
1497       dk[10] +=  uik[0]*u[10] + uik[1]*u[11] + uik[2]*u[12] + uik[3]*u[13] + uik[4]*u[14];
1498       dk[11] +=  uik[5]*u[10] + uik[6]*u[11] + uik[7]*u[12] + uik[8]*u[13] + uik[9]*u[14];
1499       dk[12] += uik[10]*u[10]+ uik[11]*u[11]+ uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14];
1500       dk[13] += uik[15]*u[10]+ uik[16]*u[11]+ uik[17]*u[12]+ uik[18]*u[13]+ uik[19]*u[14];
1501       dk[14] += uik[20]*u[10]+ uik[21]*u[11]+ uik[22]*u[12]+ uik[23]*u[13]+ uik[24]*u[14];
1502 
1503       dk[15] +=  uik[0]*u[15] + uik[1]*u[16] + uik[2]*u[17] + uik[3]*u[18] + uik[4]*u[19];
1504       dk[16] +=  uik[5]*u[15] + uik[6]*u[16] + uik[7]*u[17] + uik[8]*u[18] + uik[9]*u[19];
1505       dk[17] += uik[10]*u[15]+ uik[11]*u[16]+ uik[12]*u[17]+ uik[13]*u[18]+ uik[14]*u[19];
1506       dk[18] += uik[15]*u[15]+ uik[16]*u[16]+ uik[17]*u[17]+ uik[18]*u[18]+ uik[19]*u[19];
1507       dk[19] += uik[20]*u[15]+ uik[21]*u[16]+ uik[22]*u[17]+ uik[23]*u[18]+ uik[24]*u[19];
1508 
1509       dk[20] +=  uik[0]*u[20] + uik[1]*u[21] + uik[2]*u[22] + uik[3]*u[23] + uik[4]*u[24];
1510       dk[21] +=  uik[5]*u[20] + uik[6]*u[21] + uik[7]*u[22] + uik[8]*u[23] + uik[9]*u[24];
1511       dk[22] += uik[10]*u[20]+ uik[11]*u[21]+ uik[12]*u[22]+ uik[13]*u[23]+ uik[14]*u[24];
1512       dk[23] += uik[15]*u[20]+ uik[16]*u[21]+ uik[17]*u[22]+ uik[18]*u[23]+ uik[19]*u[24];
1513       dk[24] += uik[20]*u[20]+ uik[21]*u[21]+ uik[22]*u[22]+ uik[23]*u[23]+ uik[24]*u[24];
1514 
1515       /* update -U(i,k) */
1516       ierr = PetscMemcpy(ba+ili*25,uik,25*sizeof(MatScalar));CHKERRQ(ierr);
1517 
1518       /* add multiple of row i to k-th row ... */
1519       jmin = ili + 1; jmax = bi[i+1];
1520       if (jmin < jmax){
1521         for (j=jmin; j<jmax; j++) {
1522           /* rtmp += -U(i,k)^T * U_bar(i,j) */
1523           rtmp_ptr = rtmp + bj[j]*25;
1524           u = ba + j*25;
1525           rtmp_ptr[0] +=  uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3] + uik[4]*u[4];
1526           rtmp_ptr[1] +=  uik[5]*u[0] + uik[6]*u[1] + uik[7]*u[2] + uik[8]*u[3] + uik[9]*u[4];
1527           rtmp_ptr[2] += uik[10]*u[0]+ uik[11]*u[1]+ uik[12]*u[2]+ uik[13]*u[3]+ uik[14]*u[4];
1528           rtmp_ptr[3] += uik[15]*u[0]+ uik[16]*u[1]+ uik[17]*u[2]+ uik[18]*u[3]+ uik[19]*u[4];
1529           rtmp_ptr[4] += uik[20]*u[0]+ uik[21]*u[1]+ uik[22]*u[2]+ uik[23]*u[3]+ uik[24]*u[4];
1530 
1531           rtmp_ptr[5] +=  uik[0]*u[5] + uik[1]*u[6] + uik[2]*u[7] + uik[3]*u[8] + uik[4]*u[9];
1532           rtmp_ptr[6] +=  uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8] + uik[9]*u[9];
1533           rtmp_ptr[7] += uik[10]*u[5]+ uik[11]*u[6]+ uik[12]*u[7]+ uik[13]*u[8]+ uik[14]*u[9];
1534           rtmp_ptr[8] += uik[15]*u[5]+ uik[16]*u[6]+ uik[17]*u[7]+ uik[18]*u[8]+ uik[19]*u[9];
1535           rtmp_ptr[9] += uik[20]*u[5]+ uik[21]*u[6]+ uik[22]*u[7]+ uik[23]*u[8]+ uik[24]*u[9];
1536 
1537           rtmp_ptr[10] +=  uik[0]*u[10] + uik[1]*u[11] + uik[2]*u[12] + uik[3]*u[13] + uik[4]*u[14];
1538           rtmp_ptr[11] +=  uik[5]*u[10] + uik[6]*u[11] + uik[7]*u[12] + uik[8]*u[13] + uik[9]*u[14];
1539           rtmp_ptr[12] += uik[10]*u[10]+ uik[11]*u[11]+ uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14];
1540           rtmp_ptr[13] += uik[15]*u[10]+ uik[16]*u[11]+ uik[17]*u[12]+ uik[18]*u[13]+ uik[19]*u[14];
1541           rtmp_ptr[14] += uik[20]*u[10]+ uik[21]*u[11]+ uik[22]*u[12]+ uik[23]*u[13]+ uik[24]*u[14];
1542 
1543           rtmp_ptr[15] +=  uik[0]*u[15] + uik[1]*u[16] + uik[2]*u[17] + uik[3]*u[18] + uik[4]*u[19];
1544           rtmp_ptr[16] +=  uik[5]*u[15] + uik[6]*u[16] + uik[7]*u[17] + uik[8]*u[18] + uik[9]*u[19];
1545           rtmp_ptr[17] += uik[10]*u[15]+ uik[11]*u[16]+ uik[12]*u[17]+ uik[13]*u[18]+ uik[14]*u[19];
1546           rtmp_ptr[18] += uik[15]*u[15]+ uik[16]*u[16]+ uik[17]*u[17]+ uik[18]*u[18]+ uik[19]*u[19];
1547           rtmp_ptr[19] += uik[20]*u[15]+ uik[21]*u[16]+ uik[22]*u[17]+ uik[23]*u[18]+ uik[24]*u[19];
1548 
1549           rtmp_ptr[20] +=  uik[0]*u[20] + uik[1]*u[21] + uik[2]*u[22] + uik[3]*u[23] + uik[4]*u[24];
1550           rtmp_ptr[21] +=  uik[5]*u[20] + uik[6]*u[21] + uik[7]*u[22] + uik[8]*u[23] + uik[9]*u[24];
1551           rtmp_ptr[22] += uik[10]*u[20]+ uik[11]*u[21]+ uik[12]*u[22]+ uik[13]*u[23]+ uik[14]*u[24];
1552           rtmp_ptr[23] += uik[15]*u[20]+ uik[16]*u[21]+ uik[17]*u[22]+ uik[18]*u[23]+ uik[19]*u[24];
1553           rtmp_ptr[24] += uik[20]*u[20]+ uik[21]*u[21]+ uik[22]*u[22]+ uik[23]*u[23]+ uik[24]*u[24];
1554         }
1555 
1556         /* ... add i to row list for next nonzero entry */
1557         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
1558         j     = bj[jmin];
1559         jl[i] = jl[j]; jl[j] = i; /* update jl */
1560       }
1561       i = nexti;
1562     }
1563 
1564     /* save nonzero entries in k-th row of U ... */
1565 
1566     /* invert diagonal block */
1567     d = ba+k*25;
1568     ierr = PetscMemcpy(d,dk,25*sizeof(MatScalar));CHKERRQ(ierr);
1569     ierr = Kernel_A_gets_inverse_A_5(d);CHKERRQ(ierr);
1570 
1571     jmin = bi[k]; jmax = bi[k+1];
1572     if (jmin < jmax) {
1573       for (j=jmin; j<jmax; j++){
1574          vj = bj[j];           /* block col. index of U */
1575          u   = ba + j*25;
1576          rtmp_ptr = rtmp + vj*25;
1577          for (k1=0; k1<25; k1++){
1578            *u++        = *rtmp_ptr;
1579            *rtmp_ptr++ = 0.0;
1580          }
1581       }
1582 
1583       /* ... add k to row list for first nonzero entry in k-th row */
1584       il[k] = jmin;
1585       i     = bj[jmin];
1586       jl[k] = jl[i]; jl[i] = k;
1587     }
1588   }
1589 
1590   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1591   ierr = PetscFree(il);CHKERRQ(ierr);
1592   ierr = PetscFree(jl);CHKERRQ(ierr);
1593   ierr = PetscFree(dk);CHKERRQ(ierr);
1594   ierr = PetscFree(uik);CHKERRQ(ierr);
1595   if (a->permute){
1596     ierr = PetscFree(aa);CHKERRQ(ierr);
1597   }
1598 
1599   ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr);
1600   C->factor    = FACTOR_CHOLESKY;
1601   C->assembled = PETSC_TRUE;
1602   C->preallocated = PETSC_TRUE;
1603   PLogFlops(1.3333*125*b->mbs); /* from inverting diagonal blocks */
1604   PetscFunctionReturn(0);
1605 }
1606 
1607 /*
1608       Version for when blocks are 5 by 5 Using natural ordering
1609 */
1610 #undef __FUNC__
1611 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_5_NaturalOrdering"
1612 int MatCholeskyFactorNumeric_SeqSBAIJ_5_NaturalOrdering(Mat A,Mat *B)
1613 {
1614   Mat         C = *B;
1615   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
1616   int         ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
1617   int         *ajtmpold,*ajtmp,nz,row;
1618   int         *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
1619   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
1620   MatScalar   x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15;
1621   MatScalar   x16,x17,x18,x19,x20,x21,x22,x23,x24,x25;
1622   MatScalar   p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15;
1623   MatScalar   p16,p17,p18,p19,p20,p21,p22,p23,p24,p25;
1624   MatScalar   m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12,m13,m14,m15;
1625   MatScalar   m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
1626   MatScalar   *ba = b->a,*aa = a->a;
1627 
1628   PetscFunctionBegin;
1629   rtmp  = (MatScalar*)PetscMalloc(25*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
1630   for (i=0; i<n; i++) {
1631     nz    = bi[i+1] - bi[i];
1632     ajtmp = bj + bi[i];
1633     for  (j=0; j<nz; j++) {
1634       x = rtmp+25*ajtmp[j];
1635       x[0]  = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = x[9] = 0.0;
1636       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
1637       x[16] = x[17] = x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0;
1638     }
1639     /* load in initial (unfactored row) */
1640     nz       = ai[i+1] - ai[i];
1641     ajtmpold = aj + ai[i];
1642     v        = aa + 25*ai[i];
1643     for (j=0; j<nz; j++) {
1644       x    = rtmp+25*ajtmpold[j];
1645       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
1646       x[4]  = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
1647       x[9]  = v[9];  x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
1648       x[14] = v[14]; x[15] = v[15]; x[16] = v[16]; x[17] = v[17]; x[18] = v[18];
1649       x[19] = v[19]; x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23];
1650       x[24] = v[24];
1651       v    += 25;
1652     }
1653     row = *ajtmp++;
1654     while (row < i) {
1655       pc  = rtmp + 25*row;
1656       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
1657       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
1658       p10 = pc[9];  p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
1659       p15 = pc[14]; p16 = pc[15]; p17 = pc[16]; p18 = pc[17];
1660       p19 = pc[18]; p20 = pc[19]; p21 = pc[20]; p22 = pc[21]; p23 = pc[22];
1661       p24 = pc[23]; p25 = pc[24];
1662       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
1663           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
1664           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
1665           || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0
1666           || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 || p25 != 0.0) {
1667         pv = ba + 25*diag_offset[row];
1668         pj = bj + diag_offset[row] + 1;
1669         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
1670         x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
1671         x10 = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
1672         x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17]; x19 = pv[18];
1673         x20 = pv[19]; x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
1674         x25 = pv[24];
1675         pc[0] = m1 = p1*x1 + p6*x2  + p11*x3 + p16*x4 + p21*x5;
1676         pc[1] = m2 = p2*x1 + p7*x2  + p12*x3 + p17*x4 + p22*x5;
1677         pc[2] = m3 = p3*x1 + p8*x2  + p13*x3 + p18*x4 + p23*x5;
1678         pc[3] = m4 = p4*x1 + p9*x2  + p14*x3 + p19*x4 + p24*x5;
1679         pc[4] = m5 = p5*x1 + p10*x2 + p15*x3 + p20*x4 + p25*x5;
1680 
1681         pc[5]  = m6  = p1*x6 + p6*x7  + p11*x8 + p16*x9 + p21*x10;
1682         pc[6]  = m7  = p2*x6 + p7*x7  + p12*x8 + p17*x9 + p22*x10;
1683         pc[7]  = m8  = p3*x6 + p8*x7  + p13*x8 + p18*x9 + p23*x10;
1684         pc[8]  = m9  = p4*x6 + p9*x7  + p14*x8 + p19*x9 + p24*x10;
1685         pc[9]  = m10 = p5*x6 + p10*x7 + p15*x8 + p20*x9 + p25*x10;
1686 
1687         pc[10] = m11 = p1*x11 + p6*x12  + p11*x13 + p16*x14 + p21*x15;
1688         pc[11] = m12 = p2*x11 + p7*x12  + p12*x13 + p17*x14 + p22*x15;
1689         pc[12] = m13 = p3*x11 + p8*x12  + p13*x13 + p18*x14 + p23*x15;
1690         pc[13] = m14 = p4*x11 + p9*x12  + p14*x13 + p19*x14 + p24*x15;
1691         pc[14] = m15 = p5*x11 + p10*x12 + p15*x13 + p20*x14 + p25*x15;
1692 
1693         pc[15] = m16 = p1*x16 + p6*x17  + p11*x18 + p16*x19 + p21*x20;
1694         pc[16] = m17 = p2*x16 + p7*x17  + p12*x18 + p17*x19 + p22*x20;
1695         pc[17] = m18 = p3*x16 + p8*x17  + p13*x18 + p18*x19 + p23*x20;
1696         pc[18] = m19 = p4*x16 + p9*x17  + p14*x18 + p19*x19 + p24*x20;
1697         pc[19] = m20 = p5*x16 + p10*x17 + p15*x18 + p20*x19 + p25*x20;
1698 
1699         pc[20] = m21 = p1*x21 + p6*x22  + p11*x23 + p16*x24 + p21*x25;
1700         pc[21] = m22 = p2*x21 + p7*x22  + p12*x23 + p17*x24 + p22*x25;
1701         pc[22] = m23 = p3*x21 + p8*x22  + p13*x23 + p18*x24 + p23*x25;
1702         pc[23] = m24 = p4*x21 + p9*x22  + p14*x23 + p19*x24 + p24*x25;
1703         pc[24] = m25 = p5*x21 + p10*x22 + p15*x23 + p20*x24 + p25*x25;
1704 
1705         nz = bi[row+1] - diag_offset[row] - 1;
1706         pv += 25;
1707         for (j=0; j<nz; j++) {
1708           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
1709           x5   = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
1710           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
1711           x14  = pv[13]; x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17];
1712           x19 = pv[18];  x20 = pv[19]; x21 = pv[20]; x22 = pv[21]; x23 = pv[22];
1713           x24 = pv[23];  x25 = pv[24];
1714           x    = rtmp + 25*pj[j];
1715           x[0] -= m1*x1 + m6*x2   + m11*x3  + m16*x4 + m21*x5;
1716           x[1] -= m2*x1 + m7*x2   + m12*x3  + m17*x4 + m22*x5;
1717           x[2] -= m3*x1 + m8*x2   + m13*x3  + m18*x4 + m23*x5;
1718           x[3] -= m4*x1 + m9*x2   + m14*x3  + m19*x4 + m24*x5;
1719           x[4] -= m5*x1 + m10*x2  + m15*x3  + m20*x4 + m25*x5;
1720 
1721           x[5] -= m1*x6 + m6*x7   + m11*x8  + m16*x9 + m21*x10;
1722           x[6] -= m2*x6 + m7*x7   + m12*x8  + m17*x9 + m22*x10;
1723           x[7] -= m3*x6 + m8*x7   + m13*x8  + m18*x9 + m23*x10;
1724           x[8] -= m4*x6 + m9*x7   + m14*x8  + m19*x9 + m24*x10;
1725           x[9] -= m5*x6 + m10*x7  + m15*x8  + m20*x9 + m25*x10;
1726 
1727           x[10] -= m1*x11 + m6*x12  + m11*x13 + m16*x14 + m21*x15;
1728           x[11] -= m2*x11 + m7*x12  + m12*x13 + m17*x14 + m22*x15;
1729           x[12] -= m3*x11 + m8*x12  + m13*x13 + m18*x14 + m23*x15;
1730           x[13] -= m4*x11 + m9*x12  + m14*x13 + m19*x14 + m24*x15;
1731           x[14] -= m5*x11 + m10*x12 + m15*x13 + m20*x14 + m25*x15;
1732 
1733           x[15] -= m1*x16 + m6*x17  + m11*x18 + m16*x19 + m21*x20;
1734           x[16] -= m2*x16 + m7*x17  + m12*x18 + m17*x19 + m22*x20;
1735           x[17] -= m3*x16 + m8*x17  + m13*x18 + m18*x19 + m23*x20;
1736           x[18] -= m4*x16 + m9*x17  + m14*x18 + m19*x19 + m24*x20;
1737           x[19] -= m5*x16 + m10*x17 + m15*x18 + m20*x19 + m25*x20;
1738 
1739           x[20] -= m1*x21 + m6*x22  + m11*x23 + m16*x24 + m21*x25;
1740           x[21] -= m2*x21 + m7*x22  + m12*x23 + m17*x24 + m22*x25;
1741           x[22] -= m3*x21 + m8*x22  + m13*x23 + m18*x24 + m23*x25;
1742           x[23] -= m4*x21 + m9*x22  + m14*x23 + m19*x24 + m24*x25;
1743           x[24] -= m5*x21 + m10*x22 + m15*x23 + m20*x24 + m25*x25;
1744           pv   += 25;
1745         }
1746         PLogFlops(250*nz+225);
1747       }
1748       row = *ajtmp++;
1749     }
1750     /* finished row so stick it into b->a */
1751     pv = ba + 25*bi[i];
1752     pj = bj + bi[i];
1753     nz = bi[i+1] - bi[i];
1754     for (j=0; j<nz; j++) {
1755       x      = rtmp+25*pj[j];
1756       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
1757       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
1758       pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
1759       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; pv[16] = x[16]; pv[17] = x[17];
1760       pv[18] = x[18]; pv[19] = x[19]; pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22];
1761       pv[23] = x[23]; pv[24] = x[24];
1762       pv   += 25;
1763     }
1764     /* invert diagonal block */
1765     w = ba + 25*diag_offset[i];
1766     ierr = Kernel_A_gets_inverse_A_5(w);CHKERRQ(ierr);
1767   }
1768 
1769   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1770   C->factor    = FACTOR_LU;
1771   C->assembled = PETSC_TRUE;
1772   PLogFlops(1.3333*125*b->mbs); /* from inverting diagonal blocks */
1773   PetscFunctionReturn(0);
1774 }
1775 
1776 /*
1777       Version for when blocks are 4 by 4 Using natural ordering
1778 */
1779 #undef __FUNC__
1780 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_4_NaturalOrdering"
1781 int MatCholeskyFactorNumeric_SeqSBAIJ_4_NaturalOrdering(Mat A,Mat *B)
1782 {
1783   Mat         C = *B;
1784   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
1785   int         ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
1786   int         *ajtmpold,*ajtmp,nz,row;
1787   int         *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
1788   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
1789   MatScalar   p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
1790   MatScalar   p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
1791   MatScalar   p10,p11,p12,p13,p14,p15,p16,m10,m11,m12;
1792   MatScalar   m13,m14,m15,m16;
1793   MatScalar   *ba = b->a,*aa = a->a;
1794 
1795   PetscFunctionBegin;
1796   rtmp  = (MatScalar*)PetscMalloc(16*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
1797 
1798   for (i=0; i<n; i++) {
1799     nz    = bi[i+1] - bi[i];
1800     ajtmp = bj + bi[i];
1801     for  (j=0; j<nz; j++) {
1802       x = rtmp+16*ajtmp[j];
1803       x[0]  = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = x[9] = 0.0;
1804       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
1805     }
1806     /* load in initial (unfactored row) */
1807     nz       = ai[i+1] - ai[i];
1808     ajtmpold = aj + ai[i];
1809     v        = aa + 16*ai[i];
1810     for (j=0; j<nz; j++) {
1811       x    = rtmp+16*ajtmpold[j];
1812       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
1813       x[4]  = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
1814       x[9]  = v[9];  x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
1815       x[14] = v[14]; x[15] = v[15];
1816       v    += 16;
1817     }
1818     row = *ajtmp++;
1819     while (row < i) {
1820       pc  = rtmp + 16*row;
1821       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
1822       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
1823       p10 = pc[9];  p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
1824       p15 = pc[14]; p16 = pc[15];
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) {
1829         pv = ba + 16*diag_offset[row];
1830         pj = bj + diag_offset[row] + 1;
1831         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
1832         x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
1833         x10 = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
1834         x15 = pv[14]; x16 = pv[15];
1835         pc[0] = m1 = p1*x1 + p5*x2  + p9*x3  + p13*x4;
1836         pc[1] = m2 = p2*x1 + p6*x2  + p10*x3 + p14*x4;
1837         pc[2] = m3 = p3*x1 + p7*x2  + p11*x3 + p15*x4;
1838         pc[3] = m4 = p4*x1 + p8*x2  + p12*x3 + p16*x4;
1839 
1840         pc[4] = m5 = p1*x5 + p5*x6  + p9*x7  + p13*x8;
1841         pc[5] = m6 = p2*x5 + p6*x6  + p10*x7 + p14*x8;
1842         pc[6] = m7 = p3*x5 + p7*x6  + p11*x7 + p15*x8;
1843         pc[7] = m8 = p4*x5 + p8*x6  + p12*x7 + p16*x8;
1844 
1845         pc[8]  = m9  = p1*x9 + p5*x10  + p9*x11  + p13*x12;
1846         pc[9]  = m10 = p2*x9 + p6*x10  + p10*x11 + p14*x12;
1847         pc[10] = m11 = p3*x9 + p7*x10  + p11*x11 + p15*x12;
1848         pc[11] = m12 = p4*x9 + p8*x10  + p12*x11 + p16*x12;
1849 
1850         pc[12] = m13 = p1*x13 + p5*x14  + p9*x15  + p13*x16;
1851         pc[13] = m14 = p2*x13 + p6*x14  + p10*x15 + p14*x16;
1852         pc[14] = m15 = p3*x13 + p7*x14  + p11*x15 + p15*x16;
1853         pc[15] = m16 = p4*x13 + p8*x14  + p12*x15 + p16*x16;
1854 
1855         nz = bi[row+1] - diag_offset[row] - 1;
1856         pv += 16;
1857         for (j=0; j<nz; j++) {
1858           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
1859           x5   = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
1860           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
1861           x14  = pv[13]; x15 = pv[14]; x16 = pv[15];
1862           x    = rtmp + 16*pj[j];
1863           x[0] -= m1*x1 + m5*x2  + m9*x3  + m13*x4;
1864           x[1] -= m2*x1 + m6*x2  + m10*x3 + m14*x4;
1865           x[2] -= m3*x1 + m7*x2  + m11*x3 + m15*x4;
1866           x[3] -= m4*x1 + m8*x2  + m12*x3 + m16*x4;
1867 
1868           x[4] -= m1*x5 + m5*x6  + m9*x7  + m13*x8;
1869           x[5] -= m2*x5 + m6*x6  + m10*x7 + m14*x8;
1870           x[6] -= m3*x5 + m7*x6  + m11*x7 + m15*x8;
1871           x[7] -= m4*x5 + m8*x6  + m12*x7 + m16*x8;
1872 
1873           x[8]  -= m1*x9 + m5*x10 + m9*x11  + m13*x12;
1874           x[9]  -= m2*x9 + m6*x10 + m10*x11 + m14*x12;
1875           x[10] -= m3*x9 + m7*x10 + m11*x11 + m15*x12;
1876           x[11] -= m4*x9 + m8*x10 + m12*x11 + m16*x12;
1877 
1878           x[12] -= m1*x13 + m5*x14  + m9*x15  + m13*x16;
1879           x[13] -= m2*x13 + m6*x14  + m10*x15 + m14*x16;
1880           x[14] -= m3*x13 + m7*x14  + m11*x15 + m15*x16;
1881           x[15] -= m4*x13 + m8*x14  + m12*x15 + m16*x16;
1882 
1883           pv   += 16;
1884         }
1885         PLogFlops(128*nz+112);
1886       }
1887       row = *ajtmp++;
1888     }
1889     /* finished row so stick it into b->a */
1890     pv = ba + 16*bi[i];
1891     pj = bj + bi[i];
1892     nz = bi[i+1] - bi[i];
1893     for (j=0; j<nz; j++) {
1894       x      = rtmp+16*pj[j];
1895       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
1896       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
1897       pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
1898       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
1899       pv   += 16;
1900     }
1901     /* invert diagonal block */
1902     w = ba + 16*diag_offset[i];
1903     ierr = Kernel_A_gets_inverse_A_4(w);CHKERRQ(ierr);
1904   }
1905 
1906   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1907   C->factor    = FACTOR_LU;
1908   C->assembled = PETSC_TRUE;
1909   C->preallocated = PETSC_TRUE;
1910   PLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */
1911   PetscFunctionReturn(0);
1912 }
1913 
1914 /* Version for when blocks are 4 by 4  */
1915 #undef __FUNC__
1916 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_4"
1917 int MatCholeskyFactorNumeric_SeqSBAIJ_4(Mat A,Mat *B)
1918 {
1919   Mat                C = *B;
1920   Mat_SeqSBAIJ       *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data;
1921   IS                 perm = b->row;
1922   int                *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
1923   int                *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
1924   MatScalar          *ba = b->a,*aa,*ap,*dk,*uik;
1925   MatScalar          *u,*diag,*rtmp,*rtmp_ptr;
1926 
1927   PetscFunctionBegin;
1928   /* initialization */
1929   rtmp  = (MatScalar*)PetscMalloc(16*mbs*sizeof(MatScalar));CHKPTRQ(rtmp);
1930   ierr = PetscMemzero(rtmp,16*mbs*sizeof(MatScalar));CHKERRQ(ierr);
1931   il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il);
1932   jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl);
1933   for (i=0; i<mbs; i++) {
1934     jl[i] = mbs; il[0] = 0;
1935   }
1936   dk    = (MatScalar*)PetscMalloc(16*sizeof(MatScalar));CHKPTRQ(dk);
1937   uik   = (MatScalar*)PetscMalloc(16*sizeof(MatScalar));CHKPTRQ(uik);
1938   ierr  = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr);
1939 
1940   /* check permutation */
1941   if (!a->permute){
1942     ai = a->i; aj = a->j; aa = a->a;
1943   } else {
1944     ai = a->inew; aj = a->jnew;
1945     aa = (MatScalar*)PetscMalloc(16*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa);
1946     ierr = PetscMemcpy(aa,a->a,16*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr);
1947     a2anew  = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew);
1948     ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr);
1949 
1950     for (i=0; i<mbs; i++){
1951       jmin = ai[i]; jmax = ai[i+1];
1952       for (j=jmin; j<jmax; j++){
1953         while (a2anew[j] != j){
1954           k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k;
1955           for (k1=0; k1<16; k1++){
1956             dk[k1]       = aa[k*16+k1];
1957             aa[k*16+k1] = aa[j*16+k1];
1958             aa[j*16+k1] = dk[k1];
1959           }
1960         }
1961         /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */
1962         if (i > aj[j]){
1963           /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */
1964           ap = aa + j*16;                     /* ptr to the beginning of j-th block of aa */
1965           for (k=0; k<16; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */
1966           for (k=0; k<4; k++){               /* j-th block of aa <- dk^T */
1967             for (k1=0; k1<4; k1++) *ap++ = dk[k + 4*k1];
1968           }
1969         }
1970       }
1971     }
1972     ierr = PetscFree(a2anew);CHKERRA(ierr);
1973   }
1974 
1975   /* for each row k */
1976   for (k = 0; k<mbs; k++){
1977 
1978     /*initialize k-th row with elements nonzero in row perm(k) of A */
1979     jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1];
1980     if (jmin < jmax) {
1981       ap = aa + jmin*16;
1982       for (j = jmin; j < jmax; j++){
1983         vj = perm_ptr[aj[j]];         /* block col. index */
1984         rtmp_ptr = rtmp + vj*16;
1985         for (i=0; i<16; i++) *rtmp_ptr++ = *ap++;
1986       }
1987     }
1988 
1989     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
1990     ierr = PetscMemcpy(dk,rtmp+k*16,16*sizeof(MatScalar));CHKERRQ(ierr);
1991     i = jl[k]; /* first row to be added to k_th row  */
1992 
1993     while (i < mbs){
1994       nexti = jl[i]; /* next row to be added to k_th row */
1995 
1996       /* compute multiplier */
1997       ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
1998 
1999       /* uik = -inv(Di)*U_bar(i,k) */
2000       diag = ba + i*16;
2001       u    = ba + ili*16;
2002 
2003       uik[0] = -(diag[0]*u[0] + diag[4]*u[1] + diag[8]*u[2] + diag[12]*u[3]);
2004       uik[1] = -(diag[1]*u[0] + diag[5]*u[1] + diag[9]*u[2] + diag[13]*u[3]);
2005       uik[2] = -(diag[2]*u[0] + diag[6]*u[1] + diag[10]*u[2]+ diag[14]*u[3]);
2006       uik[3] = -(diag[3]*u[0] + diag[7]*u[1] + diag[11]*u[2]+ diag[15]*u[3]);
2007 
2008       uik[4] = -(diag[0]*u[4] + diag[4]*u[5] + diag[8]*u[6] + diag[12]*u[7]);
2009       uik[5] = -(diag[1]*u[4] + diag[5]*u[5] + diag[9]*u[6] + diag[13]*u[7]);
2010       uik[6] = -(diag[2]*u[4] + diag[6]*u[5] + diag[10]*u[6]+ diag[14]*u[7]);
2011       uik[7] = -(diag[3]*u[4] + diag[7]*u[5] + diag[11]*u[6]+ diag[15]*u[7]);
2012 
2013       uik[8] = -(diag[0]*u[8] + diag[4]*u[9] + diag[8]*u[10] + diag[12]*u[11]);
2014       uik[9] = -(diag[1]*u[8] + diag[5]*u[9] + diag[9]*u[10] + diag[13]*u[11]);
2015       uik[10]= -(diag[2]*u[8] + diag[6]*u[9] + diag[10]*u[10]+ diag[14]*u[11]);
2016       uik[11]= -(diag[3]*u[8] + diag[7]*u[9] + diag[11]*u[10]+ diag[15]*u[11]);
2017 
2018       uik[12]= -(diag[0]*u[12] + diag[4]*u[13] + diag[8]*u[14] + diag[12]*u[15]);
2019       uik[13]= -(diag[1]*u[12] + diag[5]*u[13] + diag[9]*u[14] + diag[13]*u[15]);
2020       uik[14]= -(diag[2]*u[12] + diag[6]*u[13] + diag[10]*u[14]+ diag[14]*u[15]);
2021       uik[15]= -(diag[3]*u[12] + diag[7]*u[13] + diag[11]*u[14]+ diag[15]*u[15]);
2022 
2023       /* update D(k) += -U(i,k)^T * U_bar(i,k) */
2024       dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3];
2025       dk[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3];
2026       dk[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3];
2027       dk[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3];
2028 
2029       dk[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7];
2030       dk[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7];
2031       dk[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7];
2032       dk[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7];
2033 
2034       dk[8] += uik[0]*u[8] + uik[1]*u[9] + uik[2]*u[10] + uik[3]*u[11];
2035       dk[9] += uik[4]*u[8] + uik[5]*u[9] + uik[6]*u[10] + uik[7]*u[11];
2036       dk[10]+= uik[8]*u[8] + uik[9]*u[9] + uik[10]*u[10]+ uik[11]*u[11];
2037       dk[11]+= uik[12]*u[8]+ uik[13]*u[9]+ uik[14]*u[10]+ uik[15]*u[11];
2038 
2039       dk[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15];
2040       dk[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15];
2041       dk[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15];
2042       dk[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15];
2043 
2044       /* update -U(i,k) */
2045       ierr = PetscMemcpy(ba+ili*16,uik,16*sizeof(MatScalar));CHKERRQ(ierr);
2046 
2047       /* add multiple of row i to k-th row ... */
2048       jmin = ili + 1; jmax = bi[i+1];
2049       if (jmin < jmax){
2050         for (j=jmin; j<jmax; j++) {
2051           /* rtmp += -U(i,k)^T * U_bar(i,j) */
2052           rtmp_ptr = rtmp + bj[j]*16;
2053           u = ba + j*16;
2054           rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3];
2055           rtmp_ptr[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3];
2056           rtmp_ptr[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3];
2057           rtmp_ptr[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3];
2058 
2059           rtmp_ptr[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7];
2060           rtmp_ptr[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7];
2061           rtmp_ptr[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7];
2062           rtmp_ptr[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7];
2063 
2064           rtmp_ptr[8] += uik[0]*u[8] + uik[1]*u[9] + uik[2]*u[10] + uik[3]*u[11];
2065           rtmp_ptr[9] += uik[4]*u[8] + uik[5]*u[9] + uik[6]*u[10] + uik[7]*u[11];
2066           rtmp_ptr[10]+= uik[8]*u[8] + uik[9]*u[9] + uik[10]*u[10]+ uik[11]*u[11];
2067           rtmp_ptr[11]+= uik[12]*u[8]+ uik[13]*u[9]+ uik[14]*u[10]+ uik[15]*u[11];
2068 
2069           rtmp_ptr[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15];
2070           rtmp_ptr[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15];
2071           rtmp_ptr[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15];
2072           rtmp_ptr[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15];
2073         }
2074 
2075         /* ... add i to row list for next nonzero entry */
2076         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
2077         j     = bj[jmin];
2078         jl[i] = jl[j]; jl[j] = i; /* update jl */
2079       }
2080       i = nexti;
2081     }
2082 
2083     /* save nonzero entries in k-th row of U ... */
2084 
2085     /* invert diagonal block */
2086     diag = ba+k*16;
2087     ierr = PetscMemcpy(diag,dk,16*sizeof(MatScalar));CHKERRQ(ierr);
2088     ierr = Kernel_A_gets_inverse_A_4(diag);CHKERRQ(ierr);
2089 
2090     jmin = bi[k]; jmax = bi[k+1];
2091     if (jmin < jmax) {
2092       for (j=jmin; j<jmax; j++){
2093          vj = bj[j];           /* block col. index of U */
2094          u   = ba + j*16;
2095          rtmp_ptr = rtmp + vj*16;
2096          for (k1=0; k1<16; k1++){
2097            *u++        = *rtmp_ptr;
2098            *rtmp_ptr++ = 0.0;
2099          }
2100       }
2101 
2102       /* ... add k to row list for first nonzero entry in k-th row */
2103       il[k] = jmin;
2104       i     = bj[jmin];
2105       jl[k] = jl[i]; jl[i] = k;
2106     }
2107   }
2108 
2109   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2110   ierr = PetscFree(il);CHKERRQ(ierr);
2111   ierr = PetscFree(jl);CHKERRQ(ierr);
2112   ierr = PetscFree(dk);CHKERRQ(ierr);
2113   ierr = PetscFree(uik);CHKERRQ(ierr);
2114   if (a->permute){
2115     ierr = PetscFree(aa);CHKERRQ(ierr);
2116   }
2117 
2118   ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr);
2119   C->factor    = FACTOR_CHOLESKY;
2120   C->assembled = PETSC_TRUE;
2121   C->preallocated = PETSC_TRUE;
2122   PLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */
2123   PetscFunctionReturn(0);
2124 }
2125 
2126 /* Version for when blocks are 3 by 3  */
2127 #undef __FUNC__
2128 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_3"
2129 int MatCholeskyFactorNumeric_SeqSBAIJ_3(Mat A,Mat *B)
2130 {
2131   Mat                C = *B;
2132   Mat_SeqSBAIJ       *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data;
2133   IS                 perm = b->row;
2134   int                *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
2135   int                *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
2136   MatScalar          *ba = b->a,*aa,*ap,*dk,*uik;
2137   MatScalar          *u,*diag,*rtmp,*rtmp_ptr;
2138 
2139   PetscFunctionBegin;
2140   /* initialization */
2141   rtmp  = (MatScalar*)PetscMalloc(9*mbs*sizeof(MatScalar));CHKPTRQ(rtmp);
2142   ierr = PetscMemzero(rtmp,9*mbs*sizeof(MatScalar));CHKERRQ(ierr);
2143   il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il);
2144   jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl);
2145   for (i=0; i<mbs; i++) {
2146     jl[i] = mbs; il[0] = 0;
2147   }
2148   dk  = (MatScalar*)PetscMalloc(9*sizeof(MatScalar));CHKPTRQ(dk);
2149   uik = (MatScalar*)PetscMalloc(9*sizeof(MatScalar));CHKPTRQ(uik);
2150   ierr  = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr);
2151 
2152   /* check permutation */
2153   if (!a->permute){
2154     ai = a->i; aj = a->j; aa = a->a;
2155   } else {
2156     ai = a->inew; aj = a->jnew;
2157     aa = (MatScalar*)PetscMalloc(9*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa);
2158     ierr = PetscMemcpy(aa,a->a,9*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr);
2159     a2anew  = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew);
2160     ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr);
2161 
2162     for (i=0; i<mbs; i++){
2163       jmin = ai[i]; jmax = ai[i+1];
2164       for (j=jmin; j<jmax; j++){
2165         while (a2anew[j] != j){
2166           k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k;
2167           for (k1=0; k1<9; k1++){
2168             dk[k1]       = aa[k*9+k1];
2169             aa[k*9+k1] = aa[j*9+k1];
2170             aa[j*9+k1] = dk[k1];
2171           }
2172         }
2173         /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */
2174         if (i > aj[j]){
2175           /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */
2176           ap = aa + j*9;                     /* ptr to the beginning of j-th block of aa */
2177           for (k=0; k<9; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */
2178           for (k=0; k<3; k++){               /* j-th block of aa <- dk^T */
2179             for (k1=0; k1<3; k1++) *ap++ = dk[k + 3*k1];
2180           }
2181         }
2182       }
2183     }
2184     ierr = PetscFree(a2anew);CHKERRA(ierr);
2185   }
2186 
2187   /* for each row k */
2188   for (k = 0; k<mbs; k++){
2189 
2190     /*initialize k-th row with elements nonzero in row perm(k) of A */
2191     jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1];
2192     if (jmin < jmax) {
2193       ap = aa + jmin*9;
2194       for (j = jmin; j < jmax; j++){
2195         vj = perm_ptr[aj[j]];         /* block col. index */
2196         rtmp_ptr = rtmp + vj*9;
2197         for (i=0; i<9; i++) *rtmp_ptr++ = *ap++;
2198       }
2199     }
2200 
2201     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
2202     ierr = PetscMemcpy(dk,rtmp+k*9,9*sizeof(MatScalar));CHKERRQ(ierr);
2203     i = jl[k]; /* first row to be added to k_th row  */
2204 
2205     while (i < mbs){
2206       nexti = jl[i]; /* next row to be added to k_th row */
2207 
2208       /* compute multiplier */
2209       ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
2210 
2211       /* uik = -inv(Di)*U_bar(i,k) */
2212       diag = ba + i*9;
2213       u    = ba + ili*9;
2214 
2215       uik[0] = -(diag[0]*u[0] + diag[3]*u[1] + diag[6]*u[2]);
2216       uik[1] = -(diag[1]*u[0] + diag[4]*u[1] + diag[7]*u[2]);
2217       uik[2] = -(diag[2]*u[0] + diag[5]*u[1] + diag[8]*u[2]);
2218 
2219       uik[3] = -(diag[0]*u[3] + diag[3]*u[4] + diag[6]*u[5]);
2220       uik[4] = -(diag[1]*u[3] + diag[4]*u[4] + diag[7]*u[5]);
2221       uik[5] = -(diag[2]*u[3] + diag[5]*u[4] + diag[8]*u[5]);
2222 
2223       uik[6] = -(diag[0]*u[6] + diag[3]*u[7] + diag[6]*u[8]);
2224       uik[7] = -(diag[1]*u[6] + diag[4]*u[7] + diag[7]*u[8]);
2225       uik[8] = -(diag[2]*u[6] + diag[5]*u[7] + diag[8]*u[8]);
2226 
2227       /* update D(k) += -U(i,k)^T * U_bar(i,k) */
2228       dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2];
2229       dk[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2];
2230       dk[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2];
2231 
2232       dk[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5];
2233       dk[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5];
2234       dk[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5];
2235 
2236       dk[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8];
2237       dk[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8];
2238       dk[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8];
2239 
2240       /* update -U(i,k) */
2241       ierr = PetscMemcpy(ba+ili*9,uik,9*sizeof(MatScalar));CHKERRQ(ierr);
2242 
2243       /* add multiple of row i to k-th row ... */
2244       jmin = ili + 1; jmax = bi[i+1];
2245       if (jmin < jmax){
2246         for (j=jmin; j<jmax; j++) {
2247           /* rtmp += -U(i,k)^T * U_bar(i,j) */
2248           rtmp_ptr = rtmp + bj[j]*9;
2249           u = ba + j*9;
2250           rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2];
2251           rtmp_ptr[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2];
2252           rtmp_ptr[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2];
2253 
2254           rtmp_ptr[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5];
2255           rtmp_ptr[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5];
2256           rtmp_ptr[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5];
2257 
2258           rtmp_ptr[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8];
2259           rtmp_ptr[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8];
2260           rtmp_ptr[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8];
2261         }
2262 
2263         /* ... add i to row list for next nonzero entry */
2264         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
2265         j     = bj[jmin];
2266         jl[i] = jl[j]; jl[j] = i; /* update jl */
2267       }
2268       i = nexti;
2269     }
2270 
2271     /* save nonzero entries in k-th row of U ... */
2272 
2273     /* invert diagonal block */
2274     diag = ba+k*9;
2275     ierr = PetscMemcpy(diag,dk,9*sizeof(MatScalar));CHKERRQ(ierr);
2276     ierr = Kernel_A_gets_inverse_A_3(diag);CHKERRQ(ierr);
2277 
2278     jmin = bi[k]; jmax = bi[k+1];
2279     if (jmin < jmax) {
2280       for (j=jmin; j<jmax; j++){
2281          vj = bj[j];           /* block col. index of U */
2282          u   = ba + j*9;
2283          rtmp_ptr = rtmp + vj*9;
2284          for (k1=0; k1<9; k1++){
2285            *u++        = *rtmp_ptr;
2286            *rtmp_ptr++ = 0.0;
2287          }
2288       }
2289 
2290       /* ... add k to row list for first nonzero entry in k-th row */
2291       il[k] = jmin;
2292       i     = bj[jmin];
2293       jl[k] = jl[i]; jl[i] = k;
2294     }
2295   }
2296 
2297   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2298   ierr = PetscFree(il);CHKERRQ(ierr);
2299   ierr = PetscFree(jl);CHKERRQ(ierr);
2300   ierr = PetscFree(dk);CHKERRQ(ierr);
2301   ierr = PetscFree(uik);CHKERRQ(ierr);
2302   if (a->permute){
2303     ierr = PetscFree(aa);CHKERRQ(ierr);
2304   }
2305 
2306   ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr);
2307   C->factor    = FACTOR_CHOLESKY;
2308   C->assembled = PETSC_TRUE;
2309   C->preallocated = PETSC_TRUE;
2310   PLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */
2311   PetscFunctionReturn(0);
2312 }
2313 
2314 /*
2315       Version for when blocks are 3 by 3 Using natural ordering
2316 */
2317 #undef __FUNC__
2318 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_3_NaturalOrdering"
2319 int MatCholeskyFactorNumeric_SeqSBAIJ_3_NaturalOrdering(Mat A,Mat *B)
2320 {
2321   Mat                C = *B;
2322   Mat_SeqBAIJ        *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
2323   int                ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
2324   int                *ajtmpold,*ajtmp,nz,row;
2325   int                *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
2326   MatScalar          *pv,*v,*rtmp,*pc,*w,*x;
2327   MatScalar          p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
2328   MatScalar          p5,p6,p7,p8,p9,x5,x6,x7,x8,x9;
2329   MatScalar          *ba = b->a,*aa = a->a;
2330 
2331   PetscFunctionBegin;
2332   rtmp  = (MatScalar*)PetscMalloc(9*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
2333 
2334   for (i=0; i<n; i++) {
2335     nz    = bi[i+1] - bi[i];
2336     ajtmp = bj + bi[i];
2337     for  (j=0; j<nz; j++) {
2338       x = rtmp+9*ajtmp[j];
2339       x[0]  = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = 0.0;
2340     }
2341     /* load in initial (unfactored row) */
2342     nz       = ai[i+1] - ai[i];
2343     ajtmpold = aj + ai[i];
2344     v        = aa + 9*ai[i];
2345     for (j=0; j<nz; j++) {
2346       x    = rtmp+9*ajtmpold[j];
2347       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
2348       x[4]  = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
2349       v    += 9;
2350     }
2351     row = *ajtmp++;
2352     while (row < i) {
2353       pc  = rtmp + 9*row;
2354       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
2355       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
2356       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
2357           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0) {
2358         pv = ba + 9*diag_offset[row];
2359         pj = bj + diag_offset[row] + 1;
2360         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
2361         x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
2362         pc[0] = m1 = p1*x1 + p4*x2 + p7*x3;
2363         pc[1] = m2 = p2*x1 + p5*x2 + p8*x3;
2364         pc[2] = m3 = p3*x1 + p6*x2 + p9*x3;
2365 
2366         pc[3] = m4 = p1*x4 + p4*x5 + p7*x6;
2367         pc[4] = m5 = p2*x4 + p5*x5 + p8*x6;
2368         pc[5] = m6 = p3*x4 + p6*x5 + p9*x6;
2369 
2370         pc[6] = m7 = p1*x7 + p4*x8 + p7*x9;
2371         pc[7] = m8 = p2*x7 + p5*x8 + p8*x9;
2372         pc[8] = m9 = p3*x7 + p6*x8 + p9*x9;
2373 
2374         nz = bi[row+1] - diag_offset[row] - 1;
2375         pv += 9;
2376         for (j=0; j<nz; j++) {
2377           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
2378           x5   = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
2379           x    = rtmp + 9*pj[j];
2380           x[0] -= m1*x1 + m4*x2 + m7*x3;
2381           x[1] -= m2*x1 + m5*x2 + m8*x3;
2382           x[2] -= m3*x1 + m6*x2 + m9*x3;
2383 
2384           x[3] -= m1*x4 + m4*x5 + m7*x6;
2385           x[4] -= m2*x4 + m5*x5 + m8*x6;
2386           x[5] -= m3*x4 + m6*x5 + m9*x6;
2387 
2388           x[6] -= m1*x7 + m4*x8 + m7*x9;
2389           x[7] -= m2*x7 + m5*x8 + m8*x9;
2390           x[8] -= m3*x7 + m6*x8 + m9*x9;
2391           pv   += 9;
2392         }
2393         PLogFlops(54*nz+36);
2394       }
2395       row = *ajtmp++;
2396     }
2397     /* finished row so stick it into b->a */
2398     pv = ba + 9*bi[i];
2399     pj = bj + bi[i];
2400     nz = bi[i+1] - bi[i];
2401     for (j=0; j<nz; j++) {
2402       x      = rtmp+9*pj[j];
2403       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
2404       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
2405       pv   += 9;
2406     }
2407     /* invert diagonal block */
2408     w = ba + 9*diag_offset[i];
2409     ierr = Kernel_A_gets_inverse_A_3(w);CHKERRQ(ierr);
2410   }
2411 
2412   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2413   C->factor    = FACTOR_CHOLESKY;
2414   C->assembled = PETSC_TRUE;
2415   C->preallocated = PETSC_TRUE;
2416   PLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */
2417   PetscFunctionReturn(0);
2418 }
2419 
2420 /*
2421     Numeric U^T*D*U factorization for SBAIJ format. Modified from SNF of YSMP.
2422     Version for blocks 2 by 2.
2423 */
2424 #undef __FUNC__
2425 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_2"
2426 int MatCholeskyFactorNumeric_SeqSBAIJ_2(Mat A,Mat *B)
2427 {
2428   Mat                C = *B;
2429   Mat_SeqSBAIJ       *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data;
2430   IS                 perm = b->row;
2431   int                *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
2432   int                *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
2433   MatScalar          *ba = b->a,*aa,*ap,*dk,*uik;
2434   MatScalar          *u,*diag,*rtmp,*rtmp_ptr;
2435 
2436   PetscFunctionBegin;
2437 
2438   /* initialization */
2439   /* il and jl record the first nonzero element in each row of the accessing
2440      window U(0:k, k:mbs-1).
2441      jl:    list of rows to be added to uneliminated rows
2442             i>= k: jl(i) is the first row to be added to row i
2443             i<  k: jl(i) is the row following row i in some list of rows
2444             jl(i) = mbs indicates the end of a list
2445      il(i): points to the first nonzero element in columns k,...,mbs-1 of
2446             row i of U */
2447   rtmp  = (MatScalar*)PetscMalloc(4*mbs*sizeof(MatScalar));CHKPTRQ(rtmp);
2448   ierr = PetscMemzero(rtmp,4*mbs*sizeof(MatScalar));CHKERRQ(ierr);
2449   il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il);
2450   jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl);
2451   for (i=0; i<mbs; i++) {
2452     jl[i] = mbs; il[0] = 0;
2453   }
2454   dk  = (MatScalar*)PetscMalloc(4*sizeof(MatScalar));CHKPTRQ(dk);
2455   uik = (MatScalar*)PetscMalloc(4*sizeof(MatScalar));CHKPTRQ(uik);
2456   ierr  = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr);
2457 
2458   /* check permutation */
2459   if (!a->permute){
2460     ai = a->i; aj = a->j; aa = a->a;
2461   } else {
2462     ai = a->inew; aj = a->jnew;
2463     aa = (MatScalar*)PetscMalloc(4*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa);
2464     ierr = PetscMemcpy(aa,a->a,4*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr);
2465     a2anew  = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew);
2466     ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr);
2467 
2468     for (i=0; i<mbs; i++){
2469       jmin = ai[i]; jmax = ai[i+1];
2470       for (j=jmin; j<jmax; j++){
2471         while (a2anew[j] != j){
2472           k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k;
2473           for (k1=0; k1<4; k1++){
2474             dk[k1]       = aa[k*4+k1];
2475             aa[k*4+k1] = aa[j*4+k1];
2476             aa[j*4+k1] = dk[k1];
2477           }
2478         }
2479         /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */
2480         if (i > aj[j]){
2481           /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */
2482           ap = aa + j*4;     /* ptr to the beginning of the block */
2483           dk[1] = ap[1];     /* swap ap[1] and ap[2] */
2484           ap[1] = ap[2];
2485           ap[2] = dk[1];
2486         }
2487       }
2488     }
2489     ierr = PetscFree(a2anew);CHKERRA(ierr);
2490   }
2491 
2492   /* for each row k */
2493   for (k = 0; k<mbs; k++){
2494 
2495     /*initialize k-th row with elements nonzero in row perm(k) of A */
2496     jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1];
2497     if (jmin < jmax) {
2498       ap = aa + jmin*4;
2499       for (j = jmin; j < jmax; j++){
2500         vj = perm_ptr[aj[j]];         /* block col. index */
2501         rtmp_ptr = rtmp + vj*4;
2502         for (i=0; i<4; i++) *rtmp_ptr++ = *ap++;
2503       }
2504     }
2505 
2506     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
2507     ierr = PetscMemcpy(dk,rtmp+k*4,4*sizeof(MatScalar));CHKERRQ(ierr);
2508     i = jl[k]; /* first row to be added to k_th row  */
2509 
2510     while (i < mbs){
2511       nexti = jl[i]; /* next row to be added to k_th row */
2512 
2513       /* compute multiplier */
2514       ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
2515 
2516       /* uik = -inv(Di)*U_bar(i,k): - ba[ili]*ba[i] */
2517       diag = ba + i*4;
2518       u    = ba + ili*4;
2519       uik[0] = -(diag[0]*u[0] + diag[2]*u[1]);
2520       uik[1] = -(diag[1]*u[0] + diag[3]*u[1]);
2521       uik[2] = -(diag[0]*u[2] + diag[2]*u[3]);
2522       uik[3] = -(diag[1]*u[2] + diag[3]*u[3]);
2523 
2524       /* update D(k) += -U(i,k)^T * U_bar(i,k): dk += uik*ba[ili] */
2525       dk[0] += uik[0]*u[0] + uik[1]*u[1];
2526       dk[1] += uik[2]*u[0] + uik[3]*u[1];
2527       dk[2] += uik[0]*u[2] + uik[1]*u[3];
2528       dk[3] += uik[2]*u[2] + uik[3]*u[3];
2529 
2530       /* update -U(i,k): ba[ili] = uik */
2531       ierr = PetscMemcpy(ba+ili*4,uik,4*sizeof(MatScalar));CHKERRQ(ierr);
2532 
2533       /* add multiple of row i to k-th row ... */
2534       jmin = ili + 1; jmax = bi[i+1];
2535       if (jmin < jmax){
2536         for (j=jmin; j<jmax; j++) {
2537           /* rtmp += -U(i,k)^T * U_bar(i,j): rtmp[bj[j]] += uik*ba[j]; */
2538           rtmp_ptr = rtmp + bj[j]*4;
2539           u = ba + j*4;
2540           rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1];
2541           rtmp_ptr[1] += uik[2]*u[0] + uik[3]*u[1];
2542           rtmp_ptr[2] += uik[0]*u[2] + uik[1]*u[3];
2543           rtmp_ptr[3] += uik[2]*u[2] + uik[3]*u[3];
2544         }
2545 
2546         /* ... add i to row list for next nonzero entry */
2547         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
2548         j     = bj[jmin];
2549         jl[i] = jl[j]; jl[j] = i; /* update jl */
2550       }
2551       i = nexti;
2552     }
2553 
2554     /* save nonzero entries in k-th row of U ... */
2555 
2556     /* invert diagonal block */
2557     diag = ba+k*4;
2558     ierr = PetscMemcpy(diag,dk,4*sizeof(MatScalar));CHKERRQ(ierr);
2559     ierr = Kernel_A_gets_inverse_A_2(diag);CHKERRQ(ierr);
2560 
2561     jmin = bi[k]; jmax = bi[k+1];
2562     if (jmin < jmax) {
2563       for (j=jmin; j<jmax; j++){
2564          vj = bj[j];           /* block col. index of U */
2565          u   = ba + j*4;
2566          rtmp_ptr = rtmp + vj*4;
2567          for (k1=0; k1<4; k1++){
2568            *u++        = *rtmp_ptr;
2569            *rtmp_ptr++ = 0.0;
2570          }
2571       }
2572 
2573       /* ... add k to row list for first nonzero entry in k-th row */
2574       il[k] = jmin;
2575       i     = bj[jmin];
2576       jl[k] = jl[i]; jl[i] = k;
2577     }
2578   }
2579 
2580   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2581   ierr = PetscFree(il);CHKERRQ(ierr);
2582   ierr = PetscFree(jl);CHKERRQ(ierr);
2583   ierr = PetscFree(dk);CHKERRQ(ierr);
2584   ierr = PetscFree(uik);CHKERRQ(ierr);
2585   if (a->permute) {
2586     ierr = PetscFree(aa);CHKERRQ(ierr);
2587   }
2588   ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr);
2589   C->factor    = FACTOR_CHOLESKY;
2590   C->assembled = PETSC_TRUE;
2591   C->preallocated = PETSC_TRUE;
2592   PLogFlops(1.3333*8*b->mbs); /* from inverting diagonal blocks */
2593   PetscFunctionReturn(0);
2594 }
2595 
2596 /*
2597       Version for when blocks are 2 by 2 Using natural ordering
2598 */
2599 #undef __FUNC__
2600 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_2_NaturalOrdering"
2601 int MatCholeskyFactorNumeric_SeqSBAIJ_2_NaturalOrdering(Mat A,Mat *B)
2602 {
2603   Mat                C = *B;
2604   Mat_SeqBAIJ        *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
2605   int                ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
2606   int                *ajtmpold,*ajtmp,nz,row;
2607   int                *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
2608   MatScalar          *pv,*v,*rtmp,*pc,*w,*x;
2609   MatScalar          p1,p2,p3,p4,m1,m2,m3,m4,x1,x2,x3,x4;
2610   MatScalar          *ba = b->a,*aa = a->a;
2611 
2612   PetscFunctionBegin;
2613   rtmp  = (MatScalar*)PetscMalloc(4*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
2614 
2615   for (i=0; i<n; i++) {
2616     nz    = bi[i+1] - bi[i];
2617     ajtmp = bj + bi[i];
2618     for  (j=0; j<nz; j++) {
2619       x = rtmp+4*ajtmp[j];
2620       x[0]  = x[1]  = x[2]  = x[3]  = 0.0;
2621     }
2622     /* load in initial (unfactored row) */
2623     nz       = ai[i+1] - ai[i];
2624     ajtmpold = aj + ai[i];
2625     v        = aa + 4*ai[i];
2626     for (j=0; j<nz; j++) {
2627       x    = rtmp+4*ajtmpold[j];
2628       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
2629       v    += 4;
2630     }
2631     row = *ajtmp++;
2632     while (row < i) {
2633       pc  = rtmp + 4*row;
2634       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
2635       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0) {
2636         pv = ba + 4*diag_offset[row];
2637         pj = bj + diag_offset[row] + 1;
2638         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
2639         pc[0] = m1 = p1*x1 + p3*x2;
2640         pc[1] = m2 = p2*x1 + p4*x2;
2641         pc[2] = m3 = p1*x3 + p3*x4;
2642         pc[3] = m4 = p2*x3 + p4*x4;
2643         nz = bi[row+1] - diag_offset[row] - 1;
2644         pv += 4;
2645         for (j=0; j<nz; j++) {
2646           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
2647           x    = rtmp + 4*pj[j];
2648           x[0] -= m1*x1 + m3*x2;
2649           x[1] -= m2*x1 + m4*x2;
2650           x[2] -= m1*x3 + m3*x4;
2651           x[3] -= m2*x3 + m4*x4;
2652           pv   += 4;
2653         }
2654         PLogFlops(16*nz+12);
2655       }
2656       row = *ajtmp++;
2657     }
2658     /* finished row so stick it into b->a */
2659     pv = ba + 4*bi[i];
2660     pj = bj + bi[i];
2661     nz = bi[i+1] - bi[i];
2662     for (j=0; j<nz; j++) {
2663       x      = rtmp+4*pj[j];
2664       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
2665       pv   += 4;
2666     }
2667     /* invert diagonal block */
2668     w = ba + 4*diag_offset[i];
2669     ierr = Kernel_A_gets_inverse_A_2(w);CHKERRQ(ierr);
2670   }
2671 
2672   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2673   C->factor    = FACTOR_LU;
2674   C->assembled = PETSC_TRUE;
2675   C->preallocated = PETSC_TRUE;
2676   PLogFlops(1.3333*8*b->mbs); /* from inverting diagonal blocks */
2677   PetscFunctionReturn(0);
2678 }
2679 
2680 /*
2681     Numeric U^T*D*U factorization for SBAIJ format. Modified from SNF of YSMP.
2682     Version for blocks are 1 by 1.
2683 */
2684 #undef __FUNC__
2685 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_1"
2686 int MatCholeskyFactorNumeric_SeqSBAIJ_1(Mat A,Mat *B)
2687 {
2688   Mat                C = *B;
2689   Mat_SeqSBAIJ       *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data;
2690   IS                 ip = b->row;
2691   int                *rip,ierr,i,j,mbs = a->mbs,*bi = b->i,*bj = b->j;
2692   int                *ai,*aj,*r;
2693   MatScalar          *rtmp;
2694   MatScalar          *ba = b->a,*aa,ak;
2695   MatScalar          dk,uikdi;
2696   int                k,jmin,jmax,*jl,*il,vj,nexti,ili;
2697 
2698   PetscFunctionBegin;
2699   ierr  = ISGetIndices(ip,&rip);CHKERRQ(ierr);
2700   if (!a->permute){
2701     ai = a->i; aj = a->j; aa = a->a;
2702   } else {
2703     ai = a->inew; aj = a->jnew;
2704     aa = (MatScalar*)PetscMalloc(ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa);
2705     ierr = PetscMemcpy(aa,a->a,ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr);
2706     r   = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(r);
2707     ierr= PetscMemcpy(r,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr);
2708 
2709     jmin = ai[0]; jmax = ai[mbs];
2710     for (j=jmin; j<jmax; j++){
2711       while (r[j] != j){
2712         k = r[j]; r[j] = r[k]; r[k] = k;
2713         ak = aa[k]; aa[k] = aa[j]; aa[j] = ak;
2714       }
2715     }
2716     ierr = PetscFree(r);CHKERRA(ierr);
2717   }
2718 
2719   /* initialization */
2720   /* il and jl record the first nonzero element in each row of the accessing
2721      window U(0:k, k:mbs-1).
2722      jl:    list of rows to be added to uneliminated rows
2723             i>= k: jl(i) is the first row to be added to row i
2724             i<  k: jl(i) is the row following row i in some list of rows
2725             jl(i) = mbs indicates the end of a list
2726      il(i): points to the first nonzero element in columns k,...,mbs-1 of
2727             row i of U */
2728   rtmp  = (MatScalar*)PetscMalloc(mbs*sizeof(MatScalar));CHKPTRQ(rtmp);
2729   il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il);
2730   jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl);
2731   for (i=0; i<mbs; i++) {
2732     rtmp[i] = 0.0; jl[i] = mbs; il[0] = 0;
2733   }
2734 
2735   /* for each row k */
2736   for (k = 0; k<mbs; k++){
2737 
2738     /*initialize k-th row with elements nonzero in row perm(k) of A */
2739     jmin = ai[rip[k]]; jmax = ai[rip[k]+1];
2740     if (jmin < jmax) {
2741       for (j = jmin; j < jmax; j++){
2742         vj = rip[aj[j]];
2743         /* if (k <= vj)*/ rtmp[vj] = aa[j];
2744       }
2745     }
2746 
2747     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
2748     dk = rtmp[k];
2749     i = jl[k]; /* first row to be added to k_th row  */
2750     /* printf(" k=%d, pivot row = %d\n",k,i); */
2751 
2752     while (i < mbs){
2753       nexti = jl[i]; /* next row to be added to k_th row */
2754 
2755       /* compute multiplier, update D(k) and U(i,k) */
2756       ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
2757       uikdi = - ba[ili]*ba[i];
2758       dk += uikdi*ba[ili];
2759       ba[ili] = uikdi; /* -U(i,k) */
2760 
2761       /* add multiple of row i to k-th row ... */
2762       jmin = ili + 1; jmax = bi[i+1];
2763       if (jmin < jmax){
2764         for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j];
2765         /* ... add i to row list for next nonzero entry */
2766         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
2767         j     = bj[jmin];
2768         jl[i] = jl[j]; jl[j] = i; /* update jl */
2769       }
2770       i = nexti; /* printf("                  pivot row i=%d\n",i);  */
2771     }
2772 
2773     /* check for zero pivot and save diagoanl element */
2774     if (dk == 0.0){
2775       SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot");
2776     }else if (PetscRealPart(dk) < 0){
2777       ierr = PetscPrintf(PETSC_COMM_SELF,"Negative pivot: d[%d] = %g\n",k,dk);
2778     }
2779 
2780     /* save nonzero entries in k-th row of U ... */
2781     ba[k] = 1.0/dk;
2782     jmin = bi[k]; jmax = bi[k+1];
2783     if (jmin < jmax) {
2784       for (j=jmin; j<jmax; j++){
2785          vj = bj[j]; ba[j] = rtmp[vj]; rtmp[vj] = 0.0;
2786       }
2787       /* ... add k to row list for first nonzero entry in k-th row */
2788       il[k] = jmin;
2789       i     = bj[jmin];
2790       jl[k] = jl[i]; jl[i] = k;
2791     }
2792   }
2793 
2794   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2795   ierr = PetscFree(il);CHKERRQ(ierr);
2796   ierr = PetscFree(jl);CHKERRQ(ierr);
2797   if (a->permute){
2798     ierr = PetscFree(aa);CHKERRQ(ierr);
2799   }
2800 
2801   ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr);
2802   C->factor    = FACTOR_CHOLESKY;
2803   C->assembled = PETSC_TRUE;
2804   C->preallocated = PETSC_TRUE;
2805   PLogFlops(b->mbs);
2806   PetscFunctionReturn(0);
2807 }
2808 
2809 #undef __FUNC__
2810 #define __FUNC__ "MatCholeskyFactor_SeqSBAIJ"
2811 int MatCholeskyFactor_SeqSBAIJ(Mat A,IS perm,PetscReal f)
2812 {
2813   int ierr;
2814   Mat C;
2815 
2816   PetscFunctionBegin;
2817   ierr = MatCholeskyFactorSymbolic(A,perm,f,&C);CHKERRQ(ierr);
2818   ierr = MatCholeskyFactorNumeric(A,&C);CHKERRQ(ierr);
2819   ierr = MatHeaderCopy(A,C);CHKERRQ(ierr);
2820   PetscFunctionReturn(0);
2821 }
2822 
2823 
2824