xref: /petsc/src/mat/impls/sbaij/seq/sbaijfact.c (revision ef03ded036f36641663ecc6dce7b752c397a5081)
1 /* Using Modified Sparse Row (MSR) storage.
2 See page 85, "Iterative Methods ..." by Saad. */
3 
4 /*$Id: sbaijfact.c,v 1.13 2000/09/07 16:13:53 hzhang Exp hzhang $*/
5 /*
6     Factorization code for SBAIJ format.
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   IS          iperm;
20   int         *rip,*riip,ierr,i,mbs = a->mbs,*ai = a->i,*aj = a->j;
21   int         *jutmp,bs = a->bs,bs2=a->bs2;
22   int         m,nzi,realloc = 0;
23   int         *jl,*q,jumin,jmin,jmax,juptr,nzk,qm,*iu,*ju,k,j,vj,umax,maxadd;
24   PetscTruth  *ident;
25 
26   PetscFunctionBegin;
27   PetscValidHeaderSpecific(perm,IS_COOKIE);
28   if (A->M != A->N) SETERRQ(PETSC_ERR_ARG_WRONG,0,"matrix must be square");
29 
30   ierr = ISIdentity(perm,ident);CHKERRQ(ierr);
31   if (!*ident) { /* for a non-trivial perm, the matrix A in SBAIJ format needs to be
32                    re-indexed so that A(perm(i),iperm(k)) is stored in the upper
33                    triangle. */
34     SETERRQ(PETSC_ERR_ARG_CORRUPT,0,"Call MatReIndexingSeqSBAIJ() to re-indexing (ai,aj,a)");
35   }
36 
37   ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr);
38   ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
39   ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr);
40 
41   /* initialization */
42   /* Don't know how many column pointers are needed so estimate.
43      Use Modified Sparse Row storage for u and ju, see Sasd pp.85 */
44   iu   = (int*)PetscMalloc((mbs+1)*sizeof(int));CHKPTRQ(iu);
45   umax = (int)(f*ai[mbs] + 1); umax += mbs + 1;
46   ju   = (int*)PetscMalloc(umax*sizeof(int));CHKPTRQ(ju);
47   iu[0] = mbs+1;
48   juptr = mbs;
49   jl =  (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl);
50   q  =  (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(q);
51   for (i=0; i<mbs; i++){
52     jl[i] = mbs; q[i] = 0;
53   }
54 
55   /* for each row k */
56   for (k=0; k<mbs; k++){
57     nzk = 0; /* num. of nz blocks in k-th block row with diagonal block excluded */
58     q[k] = mbs;
59     /* initialize nonzero structure of k-th row to row rip[k] of A */
60     jmin = ai[rip[k]];
61     jmax = ai[rip[k]+1];
62     for (j=jmin; j<jmax; j++){
63       vj = riip[aj[j]]; /* col. value */
64       if(vj > k){
65         qm = k;
66         do {
67           m  = qm; qm = q[m];
68         } while(qm < vj);
69         if (qm == vj) {
70           printf(" error: duplicate entry in A\n"); break;
71         }
72         nzk++;
73         q[m] = vj;
74         q[vj] = qm;
75       } /* if(vj > k) */
76     } /* for (j=jmin; j<jmax; j++) */
77 
78     /* modify nonzero structure of k-th row by computing fill-in
79        for each row i to be merged in */
80     i = k;
81     i = jl[i]; /* next pivot row (== mbs for symbolic factorization) */
82     /* printf(" next pivot row i=%d\n",i); */
83     while (i < mbs){
84       /* merge row i into k-th row */
85       nzi = iu[i+1] - (iu[i]+1);
86       jmin = iu[i] + 1; jmax = iu[i] + nzi;
87       qm = k;
88       for (j=jmin; j<jmax+1; j++){
89         vj = ju[j];
90         do {
91           m = qm; qm = q[m];
92         } while (qm < vj);
93         if (qm != vj){
94          nzk++; q[m] = vj; q[vj] = qm; qm = vj;
95         }
96       }
97       i = jl[i]; /* next pivot row */
98     }
99 
100     /* add k to row list for first nonzero element in k-th row */
101     if (nzk > 0){
102       i = q[k]; /* col value of first nonzero element in U(k, k+1:mbs-1) */
103       jl[k] = jl[i]; jl[i] = k;
104     }
105     iu[k+1] = iu[k] + nzk;   /* printf(" iu[%d]=%d, umax=%d\n", k+1, iu[k+1],umax);*/
106 
107     /* allocate more space to ju if needed */
108     if (iu[k+1] > umax) { printf("allocate more space, iu[%d]=%d > umax=%d\n",k+1, iu[k+1],umax);
109       /* estimate how much additional space we will need */
110       /* use the strategy suggested by David Hysom <hysom@perch-t.icase.edu> */
111       /* just double the memory each time */
112       maxadd = umax;
113       if (maxadd < nzk) maxadd = (mbs-k)*(nzk+1)/2;
114       umax += maxadd;
115 
116       /* allocate a longer ju */
117       jutmp = (int*)PetscMalloc(umax*sizeof(int));CHKPTRQ(jutmp);
118       ierr  = PetscMemcpy(jutmp,ju,iu[k]*sizeof(int));CHKERRQ(ierr);
119       ierr  = PetscFree(ju);CHKERRQ(ierr);
120       ju    = jutmp;
121       realloc++; /* count how many times we realloc */
122     }
123 
124     /* save nonzero structure of k-th row in ju */
125     i=k;
126     jumin = juptr + 1; juptr += nzk;
127     for (j=jumin; j<juptr+1; j++){
128       i=q[i];
129       ju[j]=i;
130     }
131   }
132 
133   if (ai[mbs] != 0) {
134     PetscReal af = ((PetscReal)iu[mbs])/((PetscReal)ai[mbs]);
135     PLogInfo(A,"MatCholeskyFactorSymbolic_SeqSBAIJ:Reallocs %d Fill ratio:given %g needed %g\n",realloc,f,af);
136     PLogInfo(A,"MatCholeskyFactorSymbolic_SeqSBAIJ:Run with -pc_lu_fill %g or use \n",af);
137     PLogInfo(A,"MatCholeskyFactorSymbolic_SeqSBAIJ:PCLUSetFill(pc,%g);\n",af);
138     PLogInfo(A,"MatCholeskyFactorSymbolic_SeqSBAIJ:for best performance.\n");
139   } else {
140      PLogInfo(A,"MatCholeskyFactorSymbolic_SeqSBAIJ:Empty matrix.\n");
141   }
142 
143   ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
144   ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr);
145 
146   ierr = PetscFree(q);CHKERRQ(ierr);
147   ierr = PetscFree(jl);CHKERRQ(ierr);
148 
149   /* put together the new matrix */
150   ierr = MatCreateSeqSBAIJ(A->comm,bs,bs*mbs,bs*mbs,0,PETSC_NULL,B);CHKERRQ(ierr);
151   PLogObjectParent(*B,iperm);
152   b = (Mat_SeqSBAIJ*)(*B)->data;
153   ierr = PetscFree(b->imax);CHKERRQ(ierr);
154   b->singlemalloc = PETSC_FALSE;
155   /* the next line frees the default space generated by the Create() */
156   ierr = PetscFree(b->a);CHKERRQ(ierr);
157   ierr = PetscFree(b->ilen);CHKERRQ(ierr);
158   b->a          = (MatScalar*)PetscMalloc((iu[mbs]+1)*sizeof(MatScalar)*bs2);CHKPTRQ(b->a);
159   b->j          = ju;
160   b->i          = iu;
161   b->diag       = 0;
162   b->ilen       = 0;
163   b->imax       = 0;
164   b->row        = perm;
165   ierr          = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
166   b->icol       = iperm;
167   b->solve_work = (Scalar*)PetscMalloc((bs*mbs+bs)*sizeof(Scalar));CHKPTRQ(b->solve_work);
168   /* In b structure:  Free imax, ilen, old a, old j.
169      Allocate idnew, solve_work, new a, new j */
170   PLogObjectMemory(*B,(iu[mbs]-mbs)*(sizeof(int)+sizeof(MatScalar)));
171   b->s_maxnz = b->s_nz = iu[mbs];
172 
173   (*B)->factor                 = FACTOR_LU;
174   (*B)->info.factor_mallocs    = realloc;
175   (*B)->info.fill_ratio_given  = f;
176   if (ai[mbs] != 0) {
177     (*B)->info.fill_ratio_needed = ((PetscReal)iu[mbs])/((PetscReal)ai[mbs]);
178   } else {
179     (*B)->info.fill_ratio_needed = 0.0;
180   }
181 
182 
183   PetscFunctionReturn(0);
184 }
185 
186 #undef __FUNC__
187 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_N"
188 int MatCholeskyFactorNumeric_SeqSBAIJ_N(Mat A,Mat *B)
189 {
190   Mat                C = *B;
191   Mat_SeqBAIJ        *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
192   IS                 isrow = b->row,isicol = b->icol;
193   int                *r,*ic,ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
194   int                *ajtmpold,*ajtmp,nz,row,bslog,*ai=a->i,*aj=a->j,k,flg;
195   int                *diag_offset=b->diag,diag,bs=a->bs,bs2 = a->bs2,*v_pivots,*pj;
196   MatScalar          *ba = b->a,*aa = a->a,*pv,*v,*rtmp,*multiplier,*v_work,*pc,*w;
197 
198   PetscFunctionBegin;
199   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
200   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
201   rtmp = (MatScalar*)PetscMalloc(bs2*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
202   ierr = PetscMemzero(rtmp,bs2*(n+1)*sizeof(MatScalar));CHKERRQ(ierr);
203   /* generate work space needed by dense LU factorization */
204   v_work     = (MatScalar*)PetscMalloc(bs*sizeof(int) + (bs+bs2)*sizeof(MatScalar));CHKPTRQ(v_work);
205   multiplier = v_work + bs;
206   v_pivots   = (int*)(multiplier + bs2);
207 
208   /* flops in while loop */
209   bslog = 2*bs*bs2;
210 
211   for (i=0; i<n; i++) {
212     nz    = bi[i+1] - bi[i];
213     ajtmp = bj + bi[i];
214     for  (j=0; j<nz; j++) {
215       ierr = PetscMemzero(rtmp+bs2*ajtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
216     }
217     /* load in initial (unfactored row) */
218     nz       = ai[r[i]+1] - ai[r[i]];
219     ajtmpold = aj + ai[r[i]];
220     v        = aa + bs2*ai[r[i]];
221     for (j=0; j<nz; j++) {
222       ierr = PetscMemcpy(rtmp+bs2*ic[ajtmpold[j]],v+bs2*j,bs2*sizeof(MatScalar));CHKERRQ(ierr);
223     }
224     row = *ajtmp++;
225     while (row < i) {
226       pc = rtmp + bs2*row;
227 /*      if (*pc) { */
228       for (flg=0,k=0; k<bs2; k++) { if (pc[k]!=0.0) { flg =1; break; }}
229       if (flg) {
230         pv = ba + bs2*diag_offset[row];
231         pj = bj + diag_offset[row] + 1;
232         Kernel_A_gets_A_times_B(bs,pc,pv,multiplier);
233         nz = bi[row+1] - diag_offset[row] - 1;
234         pv += bs2;
235         for (j=0; j<nz; j++) {
236           Kernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j);
237         }
238         PLogFlops(bslog*(nz+1)-bs);
239       }
240         row = *ajtmp++;
241     }
242     /* finished row so stick it into b->a */
243     pv = ba + bs2*bi[i];
244     pj = bj + bi[i];
245     nz = bi[i+1] - bi[i];
246     for (j=0; j<nz; j++) {
247       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
248     }
249     diag = diag_offset[i] - bi[i];
250     /* invert diagonal block */
251     w = pv + bs2*diag;
252     Kernel_A_gets_inverse_A(bs,w,v_pivots,v_work);
253   }
254 
255   ierr = PetscFree(rtmp);CHKERRQ(ierr);
256   ierr = PetscFree(v_work);CHKERRQ(ierr);
257   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
258   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
259   C->factor = FACTOR_LU;
260   C->assembled = PETSC_TRUE;
261   PLogFlops(1.3333*bs*bs2*b->mbs); /* from inverting diagonal blocks */
262   PetscFunctionReturn(0);
263 }
264 
265 /*
266       Version for when blocks are 7 by 7
267 */
268 #undef __FUNC__
269 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_7"
270 int MatCholeskyFactorNumeric_SeqSBAIJ_7(Mat A,Mat *B)
271 {
272   Mat         C = *B;
273   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
274   IS          isrow = b->row,isicol = b->icol;
275   int         *r,*ic,ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
276   int         *ajtmpold,*ajtmp,nz,row;
277   int         *diag_offset = b->diag,idx,*ai=a->i,*aj=a->j,*pj;
278   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
279   MatScalar   p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
280   MatScalar   p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
281   MatScalar   x17,x18,x19,x20,x21,x22,x23,x24,x25,p10,p11,p12,p13,p14;
282   MatScalar   p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,m10,m11,m12;
283   MatScalar   m13,m14,m15,m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
284   MatScalar   p26,p27,p28,p29,p30,p31,p32,p33,p34,p35,p36;
285   MatScalar   p37,p38,p39,p40,p41,p42,p43,p44,p45,p46,p47,p48,p49;
286   MatScalar   x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36;
287   MatScalar   x37,x38,x39,x40,x41,x42,x43,x44,x45,x46,x47,x48,x49;
288   MatScalar   m26,m27,m28,m29,m30,m31,m32,m33,m34,m35,m36;
289   MatScalar   m37,m38,m39,m40,m41,m42,m43,m44,m45,m46,m47,m48,m49;
290   MatScalar   *ba = b->a,*aa = a->a;
291 
292   PetscFunctionBegin;
293   ierr  = ISGetIndices(isrow,&r);CHKERRQ(ierr);
294   ierr  = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
295   rtmp  = (MatScalar*)PetscMalloc(49*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
296 
297   for (i=0; i<n; i++) {
298     nz    = bi[i+1] - bi[i];
299     ajtmp = bj + bi[i];
300     for  (j=0; j<nz; j++) {
301       x = rtmp+49*ajtmp[j];
302       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
303       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
304       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = x[25] = 0.0 ;
305       x[26] = x[27] = x[28] = x[29] = x[30] = x[31] = x[32] = x[33] = 0.0 ;
306       x[34] = x[35] = x[36] = x[37] = x[38] = x[39] = x[40] = x[41] = 0.0 ;
307       x[42] = x[43] = x[44] = x[45] = x[46] = x[47] = x[48] = 0.0 ;
308     }
309     /* load in initial (unfactored row) */
310     idx      = r[i];
311     nz       = ai[idx+1] - ai[idx];
312     ajtmpold = aj + ai[idx];
313     v        = aa + 49*ai[idx];
314     for (j=0; j<nz; j++) {
315       x    = rtmp+49*ic[ajtmpold[j]];
316       x[0] =  v[0];  x[1] =  v[1];  x[2] =  v[2];  x[3] =  v[3];
317       x[4] =  v[4];  x[5] =  v[5];  x[6] =  v[6];  x[7] =  v[7];
318       x[8] =  v[8];  x[9] =  v[9];  x[10] = v[10]; x[11] = v[11];
319       x[12] = v[12]; x[13] = v[13]; x[14] = v[14]; x[15] = v[15];
320       x[16] = v[16]; x[17] = v[17]; x[18] = v[18]; x[19] = v[19];
321       x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23];
322       x[24] = v[24]; x[25] = v[25]; x[26] = v[26]; x[27] = v[27];
323       x[28] = v[28]; x[29] = v[29]; x[30] = v[30]; x[31] = v[31];
324       x[32] = v[32]; x[33] = v[33]; x[34] = v[34]; x[35] = v[35];
325       x[36] = v[36]; x[37] = v[37]; x[38] = v[38]; x[39] = v[39];
326       x[40] = v[40]; x[41] = v[41]; x[42] = v[42]; x[43] = v[43];
327       x[44] = v[44]; x[45] = v[45]; x[46] = v[46]; x[47] = v[47];
328       x[48] = v[48];
329       v    += 49;
330     }
331     row = *ajtmp++;
332     while (row < i) {
333       pc  =  rtmp + 49*row;
334       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
335       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];
336       p9  = pc[8];  p10 = pc[9];  p11 = pc[10]; p12 = pc[11];
337       p13 = pc[12]; p14 = pc[13]; p15 = pc[14]; p16 = pc[15];
338       p17 = pc[16]; p18 = pc[17]; p19 = pc[18]; p20 = pc[19];
339       p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
340       p25 = pc[24]; p26 = pc[25]; p27 = pc[26]; p28 = pc[27];
341       p29 = pc[28]; p30 = pc[29]; p31 = pc[30]; p32 = pc[31];
342       p33 = pc[32]; p34 = pc[33]; p35 = pc[34]; p36 = pc[35];
343       p37 = pc[36]; p38 = pc[37]; p39 = pc[38]; p40 = pc[39];
344       p41 = pc[40]; p42 = pc[41]; p43 = pc[42]; p44 = pc[43];
345       p45 = pc[44]; p46 = pc[45]; p47 = pc[46]; p48 = pc[47];
346       p49 = pc[48];
347       if (p1  != 0.0 || p2  != 0.0 || p3  != 0.0 || p4  != 0.0 ||
348           p5  != 0.0 || p6  != 0.0 || p7  != 0.0 || p8  != 0.0 ||
349           p9  != 0.0 || p10 != 0.0 || p11 != 0.0 || p12 != 0.0 ||
350           p13 != 0.0 || p14 != 0.0 || p15 != 0.0 || p16 != 0.0 ||
351           p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 ||
352           p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 ||
353           p25 != 0.0 || p26 != 0.0 || p27 != 0.0 || p28 != 0.0 ||
354           p29 != 0.0 || p30 != 0.0 || p31 != 0.0 || p32 != 0.0 ||
355           p33 != 0.0 || p34 != 0.0 || p35 != 0.0 || p36 != 0.0 ||
356           p37 != 0.0 || p38 != 0.0 || p39 != 0.0 || p40 != 0.0 ||
357           p41 != 0.0 || p42 != 0.0 || p43 != 0.0 || p44 != 0.0 ||
358           p45 != 0.0 || p46 != 0.0 || p47 != 0.0 || p48 != 0.0 ||
359           p49 != 0.0) {
360         pv = ba + 49*diag_offset[row];
361         pj = bj + diag_offset[row] + 1;
362 	x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
363 	x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
364 	x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
365 	x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
366 	x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
367 	x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
368 	x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
369 	x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
370 	x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
371 	x37 = pv[36]; x38 = pv[37]; x39 = pv[38]; x40 = pv[39];
372 	x41 = pv[40]; x42 = pv[41]; x43 = pv[42]; x44 = pv[43];
373 	x45 = pv[44]; x46 = pv[45]; x47 = pv[46]; x48 = pv[47];
374 	x49 = pv[48];
375         pc[0]  = m1  = p1*x1  + p8*x2   + p15*x3  + p22*x4  + p29*x5  + p36*x6 + p43*x7;
376         pc[1]  = m2  = p2*x1  + p9*x2   + p16*x3  + p23*x4  + p30*x5  + p37*x6 + p44*x7;
377         pc[2]  = m3  = p3*x1  + p10*x2  + p17*x3  + p24*x4  + p31*x5  + p38*x6 + p45*x7;
378         pc[3]  = m4  = p4*x1  + p11*x2  + p18*x3  + p25*x4  + p32*x5  + p39*x6 + p46*x7;
379         pc[4]  = m5  = p5*x1  + p12*x2  + p19*x3  + p26*x4  + p33*x5  + p40*x6 + p47*x7;
380         pc[5]  = m6  = p6*x1  + p13*x2  + p20*x3  + p27*x4  + p34*x5  + p41*x6 + p48*x7;
381         pc[6]  = m7  = p7*x1  + p14*x2  + p21*x3  + p28*x4  + p35*x5  + p42*x6 + p49*x7;
382 
383         pc[7]  = m8  = p1*x8  + p8*x9   + p15*x10 + p22*x11 + p29*x12 + p36*x13 + p43*x14;
384         pc[8]  = m9  = p2*x8  + p9*x9   + p16*x10 + p23*x11 + p30*x12 + p37*x13 + p44*x14;
385         pc[9]  = m10 = p3*x8  + p10*x9  + p17*x10 + p24*x11 + p31*x12 + p38*x13 + p45*x14;
386         pc[10] = m11 = p4*x8  + p11*x9  + p18*x10 + p25*x11 + p32*x12 + p39*x13 + p46*x14;
387         pc[11] = m12 = p5*x8  + p12*x9  + p19*x10 + p26*x11 + p33*x12 + p40*x13 + p47*x14;
388         pc[12] = m13 = p6*x8  + p13*x9  + p20*x10 + p27*x11 + p34*x12 + p41*x13 + p48*x14;
389         pc[13] = m14 = p7*x8  + p14*x9  + p21*x10 + p28*x11 + p35*x12 + p42*x13 + p49*x14;
390 
391         pc[14] = m15 = p1*x15 + p8*x16  + p15*x17 + p22*x18 + p29*x19 + p36*x20 + p43*x21;
392         pc[15] = m16 = p2*x15 + p9*x16  + p16*x17 + p23*x18 + p30*x19 + p37*x20 + p44*x21;
393         pc[16] = m17 = p3*x15 + p10*x16 + p17*x17 + p24*x18 + p31*x19 + p38*x20 + p45*x21;
394         pc[17] = m18 = p4*x15 + p11*x16 + p18*x17 + p25*x18 + p32*x19 + p39*x20 + p46*x21;
395         pc[18] = m19 = p5*x15 + p12*x16 + p19*x17 + p26*x18 + p33*x19 + p40*x20 + p47*x21;
396         pc[19] = m20 = p6*x15 + p13*x16 + p20*x17 + p27*x18 + p34*x19 + p41*x20 + p48*x21;
397         pc[20] = m21 = p7*x15 + p14*x16 + p21*x17 + p28*x18 + p35*x19 + p42*x20 + p49*x21;
398 
399         pc[21] = m22 = p1*x22 + p8*x23  + p15*x24 + p22*x25 + p29*x26 + p36*x27 + p43*x28;
400         pc[22] = m23 = p2*x22 + p9*x23  + p16*x24 + p23*x25 + p30*x26 + p37*x27 + p44*x28;
401         pc[23] = m24 = p3*x22 + p10*x23 + p17*x24 + p24*x25 + p31*x26 + p38*x27 + p45*x28;
402         pc[24] = m25 = p4*x22 + p11*x23 + p18*x24 + p25*x25 + p32*x26 + p39*x27 + p46*x28;
403         pc[25] = m26 = p5*x22 + p12*x23 + p19*x24 + p26*x25 + p33*x26 + p40*x27 + p47*x28;
404         pc[26] = m27 = p6*x22 + p13*x23 + p20*x24 + p27*x25 + p34*x26 + p41*x27 + p48*x28;
405         pc[27] = m28 = p7*x22 + p14*x23 + p21*x24 + p28*x25 + p35*x26 + p42*x27 + p49*x28;
406 
407         pc[28] = m29 = p1*x29 + p8*x30  + p15*x31 + p22*x32 + p29*x33 + p36*x34 + p43*x35;
408         pc[29] = m30 = p2*x29 + p9*x30  + p16*x31 + p23*x32 + p30*x33 + p37*x34 + p44*x35;
409         pc[30] = m31 = p3*x29 + p10*x30 + p17*x31 + p24*x32 + p31*x33 + p38*x34 + p45*x35;
410         pc[31] = m32 = p4*x29 + p11*x30 + p18*x31 + p25*x32 + p32*x33 + p39*x34 + p46*x35;
411         pc[32] = m33 = p5*x29 + p12*x30 + p19*x31 + p26*x32 + p33*x33 + p40*x34 + p47*x35;
412         pc[33] = m34 = p6*x29 + p13*x30 + p20*x31 + p27*x32 + p34*x33 + p41*x34 + p48*x35;
413         pc[34] = m35 = p7*x29 + p14*x30 + p21*x31 + p28*x32 + p35*x33 + p42*x34 + p49*x35;
414 
415         pc[35] = m36 = p1*x36 + p8*x37  + p15*x38 + p22*x39 + p29*x40 + p36*x41 + p43*x42;
416         pc[36] = m37 = p2*x36 + p9*x37  + p16*x38 + p23*x39 + p30*x40 + p37*x41 + p44*x42;
417         pc[37] = m38 = p3*x36 + p10*x37 + p17*x38 + p24*x39 + p31*x40 + p38*x41 + p45*x42;
418         pc[38] = m39 = p4*x36 + p11*x37 + p18*x38 + p25*x39 + p32*x40 + p39*x41 + p46*x42;
419         pc[39] = m40 = p5*x36 + p12*x37 + p19*x38 + p26*x39 + p33*x40 + p40*x41 + p47*x42;
420         pc[40] = m41 = p6*x36 + p13*x37 + p20*x38 + p27*x39 + p34*x40 + p41*x41 + p48*x42;
421         pc[41] = m42 = p7*x36 + p14*x37 + p21*x38 + p28*x39 + p35*x40 + p42*x41 + p49*x42;
422 
423         pc[42] = m43 = p1*x43 + p8*x44  + p15*x45 + p22*x46 + p29*x47 + p36*x48 + p43*x49;
424         pc[43] = m44 = p2*x43 + p9*x44  + p16*x45 + p23*x46 + p30*x47 + p37*x48 + p44*x49;
425         pc[44] = m45 = p3*x43 + p10*x44 + p17*x45 + p24*x46 + p31*x47 + p38*x48 + p45*x49;
426         pc[45] = m46 = p4*x43 + p11*x44 + p18*x45 + p25*x46 + p32*x47 + p39*x48 + p46*x49;
427         pc[46] = m47 = p5*x43 + p12*x44 + p19*x45 + p26*x46 + p33*x47 + p40*x48 + p47*x49;
428         pc[47] = m48 = p6*x43 + p13*x44 + p20*x45 + p27*x46 + p34*x47 + p41*x48 + p48*x49;
429         pc[48] = m49 = p7*x43 + p14*x44 + p21*x45 + p28*x46 + p35*x47 + p42*x48 + p49*x49;
430 
431         nz = bi[row+1] - diag_offset[row] - 1;
432         pv += 49;
433         for (j=0; j<nz; j++) {
434 	  x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
435 	  x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
436 	  x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
437 	  x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
438 	  x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
439 	  x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
440 	  x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
441 	  x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
442 	  x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
443 	  x37 = pv[36]; x38 = pv[37]; x39 = pv[38]; x40 = pv[39];
444 	  x41 = pv[40]; x42 = pv[41]; x43 = pv[42]; x44 = pv[43];
445 	  x45 = pv[44]; x46 = pv[45]; x47 = pv[46]; x48 = pv[47];
446 	  x49 = pv[48];
447 	  x    = rtmp + 49*pj[j];
448 	  x[0]  -= m1*x1  + m8*x2   + m15*x3  + m22*x4  + m29*x5  + m36*x6 + m43*x7;
449 	  x[1]  -= m2*x1  + m9*x2   + m16*x3  + m23*x4  + m30*x5  + m37*x6 + m44*x7;
450 	  x[2]  -= m3*x1  + m10*x2  + m17*x3  + m24*x4  + m31*x5  + m38*x6 + m45*x7;
451 	  x[3]  -= m4*x1  + m11*x2  + m18*x3  + m25*x4  + m32*x5  + m39*x6 + m46*x7;
452 	  x[4]  -= m5*x1  + m12*x2  + m19*x3  + m26*x4  + m33*x5  + m40*x6 + m47*x7;
453 	  x[5]  -= m6*x1  + m13*x2  + m20*x3  + m27*x4  + m34*x5  + m41*x6 + m48*x7;
454 	  x[6]  -= m7*x1  + m14*x2  + m21*x3  + m28*x4  + m35*x5  + m42*x6 + m49*x7;
455 
456 	  x[7]  -= m1*x8  + m8*x9   + m15*x10 + m22*x11 + m29*x12 + m36*x13 + m43*x14;
457 	  x[8]  -= m2*x8  + m9*x9   + m16*x10 + m23*x11 + m30*x12 + m37*x13 + m44*x14;
458 	  x[9]  -= m3*x8  + m10*x9  + m17*x10 + m24*x11 + m31*x12 + m38*x13 + m45*x14;
459 	  x[10] -= m4*x8  + m11*x9  + m18*x10 + m25*x11 + m32*x12 + m39*x13 + m46*x14;
460 	  x[11] -= m5*x8  + m12*x9  + m19*x10 + m26*x11 + m33*x12 + m40*x13 + m47*x14;
461 	  x[12] -= m6*x8  + m13*x9  + m20*x10 + m27*x11 + m34*x12 + m41*x13 + m48*x14;
462 	  x[13] -= m7*x8  + m14*x9  + m21*x10 + m28*x11 + m35*x12 + m42*x13 + m49*x14;
463 
464 	  x[14] -= m1*x15 + m8*x16  + m15*x17 + m22*x18 + m29*x19 + m36*x20 + m43*x21;
465 	  x[15] -= m2*x15 + m9*x16  + m16*x17 + m23*x18 + m30*x19 + m37*x20 + m44*x21;
466 	  x[16] -= m3*x15 + m10*x16 + m17*x17 + m24*x18 + m31*x19 + m38*x20 + m45*x21;
467 	  x[17] -= m4*x15 + m11*x16 + m18*x17 + m25*x18 + m32*x19 + m39*x20 + m46*x21;
468 	  x[18] -= m5*x15 + m12*x16 + m19*x17 + m26*x18 + m33*x19 + m40*x20 + m47*x21;
469 	  x[19] -= m6*x15 + m13*x16 + m20*x17 + m27*x18 + m34*x19 + m41*x20 + m48*x21;
470 	  x[20] -= m7*x15 + m14*x16 + m21*x17 + m28*x18 + m35*x19 + m42*x20 + m49*x21;
471 
472 	  x[21] -= m1*x22 + m8*x23  + m15*x24 + m22*x25 + m29*x26 + m36*x27 + m43*x28;
473 	  x[22] -= m2*x22 + m9*x23  + m16*x24 + m23*x25 + m30*x26 + m37*x27 + m44*x28;
474 	  x[23] -= m3*x22 + m10*x23 + m17*x24 + m24*x25 + m31*x26 + m38*x27 + m45*x28;
475 	  x[24] -= m4*x22 + m11*x23 + m18*x24 + m25*x25 + m32*x26 + m39*x27 + m46*x28;
476 	  x[25] -= m5*x22 + m12*x23 + m19*x24 + m26*x25 + m33*x26 + m40*x27 + m47*x28;
477 	  x[26] -= m6*x22 + m13*x23 + m20*x24 + m27*x25 + m34*x26 + m41*x27 + m48*x28;
478 	  x[27] -= m7*x22 + m14*x23 + m21*x24 + m28*x25 + m35*x26 + m42*x27 + m49*x28;
479 
480 	  x[28] -= m1*x29 + m8*x30  + m15*x31 + m22*x32 + m29*x33 + m36*x34 + m43*x35;
481 	  x[29] -= m2*x29 + m9*x30  + m16*x31 + m23*x32 + m30*x33 + m37*x34 + m44*x35;
482 	  x[30] -= m3*x29 + m10*x30 + m17*x31 + m24*x32 + m31*x33 + m38*x34 + m45*x35;
483 	  x[31] -= m4*x29 + m11*x30 + m18*x31 + m25*x32 + m32*x33 + m39*x34 + m46*x35;
484 	  x[32] -= m5*x29 + m12*x30 + m19*x31 + m26*x32 + m33*x33 + m40*x34 + m47*x35;
485 	  x[33] -= m6*x29 + m13*x30 + m20*x31 + m27*x32 + m34*x33 + m41*x34 + m48*x35;
486 	  x[34] -= m7*x29 + m14*x30 + m21*x31 + m28*x32 + m35*x33 + m42*x34 + m49*x35;
487 
488 	  x[35] -= m1*x36 + m8*x37  + m15*x38 + m22*x39 + m29*x40 + m36*x41 + m43*x42;
489 	  x[36] -= m2*x36 + m9*x37  + m16*x38 + m23*x39 + m30*x40 + m37*x41 + m44*x42;
490 	  x[37] -= m3*x36 + m10*x37 + m17*x38 + m24*x39 + m31*x40 + m38*x41 + m45*x42;
491 	  x[38] -= m4*x36 + m11*x37 + m18*x38 + m25*x39 + m32*x40 + m39*x41 + m46*x42;
492 	  x[39] -= m5*x36 + m12*x37 + m19*x38 + m26*x39 + m33*x40 + m40*x41 + m47*x42;
493 	  x[40] -= m6*x36 + m13*x37 + m20*x38 + m27*x39 + m34*x40 + m41*x41 + m48*x42;
494 	  x[41] -= m7*x36 + m14*x37 + m21*x38 + m28*x39 + m35*x40 + m42*x41 + m49*x42;
495 
496 	  x[42] -= m1*x43 + m8*x44  + m15*x45 + m22*x46 + m29*x47 + m36*x48 + m43*x49;
497 	  x[43] -= m2*x43 + m9*x44  + m16*x45 + m23*x46 + m30*x47 + m37*x48 + m44*x49;
498 	  x[44] -= m3*x43 + m10*x44 + m17*x45 + m24*x46 + m31*x47 + m38*x48 + m45*x49;
499 	  x[45] -= m4*x43 + m11*x44 + m18*x45 + m25*x46 + m32*x47 + m39*x48 + m46*x49;
500 	  x[46] -= m5*x43 + m12*x44 + m19*x45 + m26*x46 + m33*x47 + m40*x48 + m47*x49;
501 	  x[47] -= m6*x43 + m13*x44 + m20*x45 + m27*x46 + m34*x47 + m41*x48 + m48*x49;
502 	  x[48] -= m7*x43 + m14*x44 + m21*x45 + m28*x46 + m35*x47 + m42*x48 + m49*x49;
503           pv   += 49;
504         }
505         PLogFlops(686*nz+637);
506       }
507       row = *ajtmp++;
508     }
509     /* finished row so stick it into b->a */
510     pv = ba + 49*bi[i];
511     pj = bj + bi[i];
512     nz = bi[i+1] - bi[i];
513     for (j=0; j<nz; j++) {
514       x      = rtmp+49*pj[j];
515       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
516       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7];
517       pv[8]  = x[8];  pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11];
518       pv[12] = x[12]; pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
519       pv[16] = x[16]; pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19];
520       pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23];
521       pv[24] = x[24]; pv[25] = x[25]; pv[26] = x[26]; pv[27] = x[27];
522       pv[28] = x[28]; pv[29] = x[29]; pv[30] = x[30]; pv[31] = x[31];
523       pv[32] = x[32]; pv[33] = x[33]; pv[34] = x[34]; pv[35] = x[35];
524       pv[36] = x[36]; pv[37] = x[37]; pv[38] = x[38]; pv[39] = x[39];
525       pv[40] = x[40]; pv[41] = x[41]; pv[42] = x[42]; pv[43] = x[43];
526       pv[44] = x[44]; pv[45] = x[45]; pv[46] = x[46]; pv[47] = x[47];
527       pv[48] = x[48];
528       pv   += 49;
529     }
530     /* invert diagonal block */
531     w = ba + 49*diag_offset[i];
532     ierr = Kernel_A_gets_inverse_A_7(w);CHKERRQ(ierr);
533   }
534 
535   ierr = PetscFree(rtmp);CHKERRQ(ierr);
536   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
537   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
538   C->factor = FACTOR_LU;
539   C->assembled = PETSC_TRUE;
540   PLogFlops(1.3333*343*b->mbs); /* from inverting diagonal blocks */
541   PetscFunctionReturn(0);
542 }
543 
544 /*
545       Version for when blocks are 7 by 7 Using natural ordering
546 */
547 #undef __FUNC__
548 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_7_NaturalOrdering"
549 int MatCholeskyFactorNumeric_SeqSBAIJ_7_NaturalOrdering(Mat A,Mat *B)
550 {
551   Mat          C = *B;
552   Mat_SeqBAIJ  *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
553   int          ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
554   int          *ajtmpold,*ajtmp,nz,row;
555   int          *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
556   MatScalar    *pv,*v,*rtmp,*pc,*w,*x;
557   MatScalar    x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15;
558   MatScalar    x16,x17,x18,x19,x20,x21,x22,x23,x24,x25;
559   MatScalar    p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15;
560   MatScalar    p16,p17,p18,p19,p20,p21,p22,p23,p24,p25;
561   MatScalar    m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12,m13,m14,m15;
562   MatScalar    m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
563   MatScalar    p26,p27,p28,p29,p30,p31,p32,p33,p34,p35,p36;
564   MatScalar    p37,p38,p39,p40,p41,p42,p43,p44,p45,p46,p47,p48,p49;
565   MatScalar    x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36;
566   MatScalar    x37,x38,x39,x40,x41,x42,x43,x44,x45,x46,x47,x48,x49;
567   MatScalar    m26,m27,m28,m29,m30,m31,m32,m33,m34,m35,m36;
568   MatScalar    m37,m38,m39,m40,m41,m42,m43,m44,m45,m46,m47,m48,m49;
569   MatScalar    *ba = b->a,*aa = a->a;
570 
571   PetscFunctionBegin;
572   rtmp  = (MatScalar*)PetscMalloc(49*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
573   for (i=0; i<n; i++) {
574     nz    = bi[i+1] - bi[i];
575     ajtmp = bj + bi[i];
576     for  (j=0; j<nz; j++) {
577       x = rtmp+49*ajtmp[j];
578       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
579       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
580       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = x[25] = 0.0 ;
581       x[26] = x[27] = x[28] = x[29] = x[30] = x[31] = x[32] = x[33] = 0.0 ;
582       x[34] = x[35] = x[36] = x[37] = x[38] = x[39] = x[40] = x[41] = 0.0 ;
583       x[42] = x[43] = x[44] = x[45] = x[46] = x[47] = x[48] = 0.0 ;
584     }
585     /* load in initial (unfactored row) */
586     nz       = ai[i+1] - ai[i];
587     ajtmpold = aj + ai[i];
588     v        = aa + 49*ai[i];
589     for (j=0; j<nz; j++) {
590       x    = rtmp+49*ajtmpold[j];
591       x[0] =  v[0];  x[1] =  v[1];  x[2] =  v[2];  x[3] =  v[3];
592       x[4] =  v[4];  x[5] =  v[5];  x[6] =  v[6];  x[7] =  v[7];
593       x[8] =  v[8];  x[9] =  v[9];  x[10] = v[10]; x[11] = v[11];
594       x[12] = v[12]; x[13] = v[13]; x[14] = v[14]; x[15] = v[15];
595       x[16] = v[16]; x[17] = v[17]; x[18] = v[18]; x[19] = v[19];
596       x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23];
597       x[24] = v[24]; x[25] = v[25]; x[26] = v[26]; x[27] = v[27];
598       x[28] = v[28]; x[29] = v[29]; x[30] = v[30]; x[31] = v[31];
599       x[32] = v[32]; x[33] = v[33]; x[34] = v[34]; x[35] = v[35];
600       x[36] = v[36]; x[37] = v[37]; x[38] = v[38]; x[39] = v[39];
601       x[40] = v[40]; x[41] = v[41]; x[42] = v[42]; x[43] = v[43];
602       x[44] = v[44]; x[45] = v[45]; x[46] = v[46]; x[47] = v[47];
603       x[48] = v[48];
604       v    += 49;
605     }
606     row = *ajtmp++;
607     while (row < i) {
608       pc  = rtmp + 49*row;
609       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
610       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];
611       p9  = pc[8];  p10 = pc[9];  p11 = pc[10]; p12 = pc[11];
612       p13 = pc[12]; p14 = pc[13]; p15 = pc[14]; p16 = pc[15];
613       p17 = pc[16]; p18 = pc[17]; p19 = pc[18]; p20 = pc[19];
614       p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
615       p25 = pc[24]; p26 = pc[25]; p27 = pc[26]; p28 = pc[27];
616       p29 = pc[28]; p30 = pc[29]; p31 = pc[30]; p32 = pc[31];
617       p33 = pc[32]; p34 = pc[33]; p35 = pc[34]; p36 = pc[35];
618       p37 = pc[36]; p38 = pc[37]; p39 = pc[38]; p40 = pc[39];
619       p41 = pc[40]; p42 = pc[41]; p43 = pc[42]; p44 = pc[43];
620       p45 = pc[44]; p46 = pc[45]; p47 = pc[46]; p48 = pc[47];
621       p49 = pc[48];
622       if (p1  != 0.0 || p2  != 0.0 || p3  != 0.0 || p4  != 0.0 ||
623           p5  != 0.0 || p6  != 0.0 || p7  != 0.0 || p8  != 0.0 ||
624           p9  != 0.0 || p10 != 0.0 || p11 != 0.0 || p12 != 0.0 ||
625           p13 != 0.0 || p14 != 0.0 || p15 != 0.0 || p16 != 0.0 ||
626           p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 ||
627           p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 ||
628           p25 != 0.0 || p26 != 0.0 || p27 != 0.0 || p28 != 0.0 ||
629           p29 != 0.0 || p30 != 0.0 || p31 != 0.0 || p32 != 0.0 ||
630           p33 != 0.0 || p34 != 0.0 || p35 != 0.0 || p36 != 0.0 ||
631           p37 != 0.0 || p38 != 0.0 || p39 != 0.0 || p40 != 0.0 ||
632           p41 != 0.0 || p42 != 0.0 || p43 != 0.0 || p44 != 0.0 ||
633           p45 != 0.0 || p46 != 0.0 || p47 != 0.0 || p48 != 0.0 ||
634           p49 != 0.0) {
635         pv = ba + 49*diag_offset[row];
636         pj = bj + diag_offset[row] + 1;
637 	x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
638 	x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
639 	x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
640 	x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
641 	x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
642 	x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
643 	x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
644 	x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
645 	x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
646 	x37 = pv[36]; x38 = pv[37]; x39 = pv[38]; x40 = pv[39];
647 	x41 = pv[40]; x42 = pv[41]; x43 = pv[42]; x44 = pv[43];
648 	x45 = pv[44]; x46 = pv[45]; x47 = pv[46]; x48 = pv[47];
649         x49 = pv[48];
650         pc[0]  = m1  = p1*x1  + p8*x2   + p15*x3  + p22*x4  + p29*x5  + p36*x6 + p43*x7;
651         pc[1]  = m2  = p2*x1  + p9*x2   + p16*x3  + p23*x4  + p30*x5  + p37*x6 + p44*x7;
652         pc[2]  = m3  = p3*x1  + p10*x2  + p17*x3  + p24*x4  + p31*x5  + p38*x6 + p45*x7;
653         pc[3]  = m4  = p4*x1  + p11*x2  + p18*x3  + p25*x4  + p32*x5  + p39*x6 + p46*x7;
654         pc[4]  = m5  = p5*x1  + p12*x2  + p19*x3  + p26*x4  + p33*x5  + p40*x6 + p47*x7;
655         pc[5]  = m6  = p6*x1  + p13*x2  + p20*x3  + p27*x4  + p34*x5  + p41*x6 + p48*x7;
656         pc[6]  = m7  = p7*x1  + p14*x2  + p21*x3  + p28*x4  + p35*x5  + p42*x6 + p49*x7;
657 
658         pc[7]  = m8  = p1*x8  + p8*x9   + p15*x10 + p22*x11 + p29*x12 + p36*x13 + p43*x14;
659         pc[8]  = m9  = p2*x8  + p9*x9   + p16*x10 + p23*x11 + p30*x12 + p37*x13 + p44*x14;
660         pc[9]  = m10 = p3*x8  + p10*x9  + p17*x10 + p24*x11 + p31*x12 + p38*x13 + p45*x14;
661         pc[10] = m11 = p4*x8  + p11*x9  + p18*x10 + p25*x11 + p32*x12 + p39*x13 + p46*x14;
662         pc[11] = m12 = p5*x8  + p12*x9  + p19*x10 + p26*x11 + p33*x12 + p40*x13 + p47*x14;
663         pc[12] = m13 = p6*x8  + p13*x9  + p20*x10 + p27*x11 + p34*x12 + p41*x13 + p48*x14;
664         pc[13] = m14 = p7*x8  + p14*x9  + p21*x10 + p28*x11 + p35*x12 + p42*x13 + p49*x14;
665 
666         pc[14] = m15 = p1*x15 + p8*x16  + p15*x17 + p22*x18 + p29*x19 + p36*x20 + p43*x21;
667         pc[15] = m16 = p2*x15 + p9*x16  + p16*x17 + p23*x18 + p30*x19 + p37*x20 + p44*x21;
668         pc[16] = m17 = p3*x15 + p10*x16 + p17*x17 + p24*x18 + p31*x19 + p38*x20 + p45*x21;
669         pc[17] = m18 = p4*x15 + p11*x16 + p18*x17 + p25*x18 + p32*x19 + p39*x20 + p46*x21;
670         pc[18] = m19 = p5*x15 + p12*x16 + p19*x17 + p26*x18 + p33*x19 + p40*x20 + p47*x21;
671         pc[19] = m20 = p6*x15 + p13*x16 + p20*x17 + p27*x18 + p34*x19 + p41*x20 + p48*x21;
672         pc[20] = m21 = p7*x15 + p14*x16 + p21*x17 + p28*x18 + p35*x19 + p42*x20 + p49*x21;
673 
674         pc[21] = m22 = p1*x22 + p8*x23  + p15*x24 + p22*x25 + p29*x26 + p36*x27 + p43*x28;
675         pc[22] = m23 = p2*x22 + p9*x23  + p16*x24 + p23*x25 + p30*x26 + p37*x27 + p44*x28;
676         pc[23] = m24 = p3*x22 + p10*x23 + p17*x24 + p24*x25 + p31*x26 + p38*x27 + p45*x28;
677         pc[24] = m25 = p4*x22 + p11*x23 + p18*x24 + p25*x25 + p32*x26 + p39*x27 + p46*x28;
678         pc[25] = m26 = p5*x22 + p12*x23 + p19*x24 + p26*x25 + p33*x26 + p40*x27 + p47*x28;
679         pc[26] = m27 = p6*x22 + p13*x23 + p20*x24 + p27*x25 + p34*x26 + p41*x27 + p48*x28;
680         pc[27] = m28 = p7*x22 + p14*x23 + p21*x24 + p28*x25 + p35*x26 + p42*x27 + p49*x28;
681 
682         pc[28] = m29 = p1*x29 + p8*x30  + p15*x31 + p22*x32 + p29*x33 + p36*x34 + p43*x35;
683         pc[29] = m30 = p2*x29 + p9*x30  + p16*x31 + p23*x32 + p30*x33 + p37*x34 + p44*x35;
684         pc[30] = m31 = p3*x29 + p10*x30 + p17*x31 + p24*x32 + p31*x33 + p38*x34 + p45*x35;
685         pc[31] = m32 = p4*x29 + p11*x30 + p18*x31 + p25*x32 + p32*x33 + p39*x34 + p46*x35;
686         pc[32] = m33 = p5*x29 + p12*x30 + p19*x31 + p26*x32 + p33*x33 + p40*x34 + p47*x35;
687         pc[33] = m34 = p6*x29 + p13*x30 + p20*x31 + p27*x32 + p34*x33 + p41*x34 + p48*x35;
688         pc[34] = m35 = p7*x29 + p14*x30 + p21*x31 + p28*x32 + p35*x33 + p42*x34 + p49*x35;
689 
690         pc[35] = m36 = p1*x36 + p8*x37  + p15*x38 + p22*x39 + p29*x40 + p36*x41 + p43*x42;
691         pc[36] = m37 = p2*x36 + p9*x37  + p16*x38 + p23*x39 + p30*x40 + p37*x41 + p44*x42;
692         pc[37] = m38 = p3*x36 + p10*x37 + p17*x38 + p24*x39 + p31*x40 + p38*x41 + p45*x42;
693         pc[38] = m39 = p4*x36 + p11*x37 + p18*x38 + p25*x39 + p32*x40 + p39*x41 + p46*x42;
694         pc[39] = m40 = p5*x36 + p12*x37 + p19*x38 + p26*x39 + p33*x40 + p40*x41 + p47*x42;
695         pc[40] = m41 = p6*x36 + p13*x37 + p20*x38 + p27*x39 + p34*x40 + p41*x41 + p48*x42;
696         pc[41] = m42 = p7*x36 + p14*x37 + p21*x38 + p28*x39 + p35*x40 + p42*x41 + p49*x42;
697 
698         pc[42] = m43 = p1*x43 + p8*x44  + p15*x45 + p22*x46 + p29*x47 + p36*x48 + p43*x49;
699         pc[43] = m44 = p2*x43 + p9*x44  + p16*x45 + p23*x46 + p30*x47 + p37*x48 + p44*x49;
700         pc[44] = m45 = p3*x43 + p10*x44 + p17*x45 + p24*x46 + p31*x47 + p38*x48 + p45*x49;
701         pc[45] = m46 = p4*x43 + p11*x44 + p18*x45 + p25*x46 + p32*x47 + p39*x48 + p46*x49;
702         pc[46] = m47 = p5*x43 + p12*x44 + p19*x45 + p26*x46 + p33*x47 + p40*x48 + p47*x49;
703         pc[47] = m48 = p6*x43 + p13*x44 + p20*x45 + p27*x46 + p34*x47 + p41*x48 + p48*x49;
704         pc[48] = m49 = p7*x43 + p14*x44 + p21*x45 + p28*x46 + p35*x47 + p42*x48 + p49*x49;
705 
706         nz = bi[row+1] - diag_offset[row] - 1;
707         pv += 49;
708         for (j=0; j<nz; j++) {
709 	  x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
710 	  x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
711 	  x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
712 	  x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
713 	  x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
714 	  x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
715 	  x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
716 	  x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
717 	  x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
718 	  x37 = pv[36]; x38 = pv[37]; x39 = pv[38]; x40 = pv[39];
719 	  x41 = pv[40]; x42 = pv[41]; x43 = pv[42]; x44 = pv[43];
720 	  x45 = pv[44]; x46 = pv[45]; x47 = pv[46]; x48 = pv[47];
721 	  x49 = pv[48];
722 	  x    = rtmp + 49*pj[j];
723 	  x[0]  -= m1*x1  + m8*x2   + m15*x3  + m22*x4  + m29*x5  + m36*x6 + m43*x7;
724 	  x[1]  -= m2*x1  + m9*x2   + m16*x3  + m23*x4  + m30*x5  + m37*x6 + m44*x7;
725 	  x[2]  -= m3*x1  + m10*x2  + m17*x3  + m24*x4  + m31*x5  + m38*x6 + m45*x7;
726 	  x[3]  -= m4*x1  + m11*x2  + m18*x3  + m25*x4  + m32*x5  + m39*x6 + m46*x7;
727 	  x[4]  -= m5*x1  + m12*x2  + m19*x3  + m26*x4  + m33*x5  + m40*x6 + m47*x7;
728 	  x[5]  -= m6*x1  + m13*x2  + m20*x3  + m27*x4  + m34*x5  + m41*x6 + m48*x7;
729 	  x[6]  -= m7*x1  + m14*x2  + m21*x3  + m28*x4  + m35*x5  + m42*x6 + m49*x7;
730 
731 	  x[7]  -= m1*x8  + m8*x9   + m15*x10 + m22*x11 + m29*x12 + m36*x13 + m43*x14;
732 	  x[8]  -= m2*x8  + m9*x9   + m16*x10 + m23*x11 + m30*x12 + m37*x13 + m44*x14;
733 	  x[9]  -= m3*x8  + m10*x9  + m17*x10 + m24*x11 + m31*x12 + m38*x13 + m45*x14;
734 	  x[10] -= m4*x8  + m11*x9  + m18*x10 + m25*x11 + m32*x12 + m39*x13 + m46*x14;
735 	  x[11] -= m5*x8  + m12*x9  + m19*x10 + m26*x11 + m33*x12 + m40*x13 + m47*x14;
736 	  x[12] -= m6*x8  + m13*x9  + m20*x10 + m27*x11 + m34*x12 + m41*x13 + m48*x14;
737 	  x[13] -= m7*x8  + m14*x9  + m21*x10 + m28*x11 + m35*x12 + m42*x13 + m49*x14;
738 
739 	  x[14] -= m1*x15 + m8*x16  + m15*x17 + m22*x18 + m29*x19 + m36*x20 + m43*x21;
740 	  x[15] -= m2*x15 + m9*x16  + m16*x17 + m23*x18 + m30*x19 + m37*x20 + m44*x21;
741 	  x[16] -= m3*x15 + m10*x16 + m17*x17 + m24*x18 + m31*x19 + m38*x20 + m45*x21;
742 	  x[17] -= m4*x15 + m11*x16 + m18*x17 + m25*x18 + m32*x19 + m39*x20 + m46*x21;
743 	  x[18] -= m5*x15 + m12*x16 + m19*x17 + m26*x18 + m33*x19 + m40*x20 + m47*x21;
744 	  x[19] -= m6*x15 + m13*x16 + m20*x17 + m27*x18 + m34*x19 + m41*x20 + m48*x21;
745 	  x[20] -= m7*x15 + m14*x16 + m21*x17 + m28*x18 + m35*x19 + m42*x20 + m49*x21;
746 
747 	  x[21] -= m1*x22 + m8*x23  + m15*x24 + m22*x25 + m29*x26 + m36*x27 + m43*x28;
748 	  x[22] -= m2*x22 + m9*x23  + m16*x24 + m23*x25 + m30*x26 + m37*x27 + m44*x28;
749 	  x[23] -= m3*x22 + m10*x23 + m17*x24 + m24*x25 + m31*x26 + m38*x27 + m45*x28;
750 	  x[24] -= m4*x22 + m11*x23 + m18*x24 + m25*x25 + m32*x26 + m39*x27 + m46*x28;
751 	  x[25] -= m5*x22 + m12*x23 + m19*x24 + m26*x25 + m33*x26 + m40*x27 + m47*x28;
752 	  x[26] -= m6*x22 + m13*x23 + m20*x24 + m27*x25 + m34*x26 + m41*x27 + m48*x28;
753 	  x[27] -= m7*x22 + m14*x23 + m21*x24 + m28*x25 + m35*x26 + m42*x27 + m49*x28;
754 
755 	  x[28] -= m1*x29 + m8*x30  + m15*x31 + m22*x32 + m29*x33 + m36*x34 + m43*x35;
756 	  x[29] -= m2*x29 + m9*x30  + m16*x31 + m23*x32 + m30*x33 + m37*x34 + m44*x35;
757 	  x[30] -= m3*x29 + m10*x30 + m17*x31 + m24*x32 + m31*x33 + m38*x34 + m45*x35;
758 	  x[31] -= m4*x29 + m11*x30 + m18*x31 + m25*x32 + m32*x33 + m39*x34 + m46*x35;
759 	  x[32] -= m5*x29 + m12*x30 + m19*x31 + m26*x32 + m33*x33 + m40*x34 + m47*x35;
760 	  x[33] -= m6*x29 + m13*x30 + m20*x31 + m27*x32 + m34*x33 + m41*x34 + m48*x35;
761 	  x[34] -= m7*x29 + m14*x30 + m21*x31 + m28*x32 + m35*x33 + m42*x34 + m49*x35;
762 
763 	  x[35] -= m1*x36 + m8*x37  + m15*x38 + m22*x39 + m29*x40 + m36*x41 + m43*x42;
764 	  x[36] -= m2*x36 + m9*x37  + m16*x38 + m23*x39 + m30*x40 + m37*x41 + m44*x42;
765 	  x[37] -= m3*x36 + m10*x37 + m17*x38 + m24*x39 + m31*x40 + m38*x41 + m45*x42;
766 	  x[38] -= m4*x36 + m11*x37 + m18*x38 + m25*x39 + m32*x40 + m39*x41 + m46*x42;
767 	  x[39] -= m5*x36 + m12*x37 + m19*x38 + m26*x39 + m33*x40 + m40*x41 + m47*x42;
768 	  x[40] -= m6*x36 + m13*x37 + m20*x38 + m27*x39 + m34*x40 + m41*x41 + m48*x42;
769 	  x[41] -= m7*x36 + m14*x37 + m21*x38 + m28*x39 + m35*x40 + m42*x41 + m49*x42;
770 
771 	  x[42] -= m1*x43 + m8*x44  + m15*x45 + m22*x46 + m29*x47 + m36*x48 + m43*x49;
772 	  x[43] -= m2*x43 + m9*x44  + m16*x45 + m23*x46 + m30*x47 + m37*x48 + m44*x49;
773 	  x[44] -= m3*x43 + m10*x44 + m17*x45 + m24*x46 + m31*x47 + m38*x48 + m45*x49;
774 	  x[45] -= m4*x43 + m11*x44 + m18*x45 + m25*x46 + m32*x47 + m39*x48 + m46*x49;
775 	  x[46] -= m5*x43 + m12*x44 + m19*x45 + m26*x46 + m33*x47 + m40*x48 + m47*x49;
776 	  x[47] -= m6*x43 + m13*x44 + m20*x45 + m27*x46 + m34*x47 + m41*x48 + m48*x49;
777 	  x[48] -= m7*x43 + m14*x44 + m21*x45 + m28*x46 + m35*x47 + m42*x48 + m49*x49;
778           pv   += 49;
779         }
780         PLogFlops(686*nz+637);
781       }
782       row = *ajtmp++;
783     }
784     /* finished row so stick it into b->a */
785     pv = ba + 49*bi[i];
786     pj = bj + bi[i];
787     nz = bi[i+1] - bi[i];
788     for (j=0; j<nz; j++) {
789       x      = rtmp+49*pj[j];
790       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
791       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7];
792       pv[8]  = x[8];  pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11];
793       pv[12] = x[12]; pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
794       pv[16] = x[16]; pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19];
795       pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23];
796       pv[24] = x[24]; pv[25] = x[25]; pv[26] = x[26]; pv[27] = x[27];
797       pv[28] = x[28]; pv[29] = x[29]; pv[30] = x[30]; pv[31] = x[31];
798       pv[32] = x[32]; pv[33] = x[33]; pv[34] = x[34]; pv[35] = x[35];
799       pv[36] = x[36]; pv[37] = x[37]; pv[38] = x[38]; pv[39] = x[39];
800       pv[40] = x[40]; pv[41] = x[41]; pv[42] = x[42]; pv[43] = x[43];
801       pv[44] = x[44]; pv[45] = x[45]; pv[46] = x[46]; pv[47] = x[47];
802       pv[48] = x[48];
803       pv   += 49;
804     }
805     /* invert diagonal block */
806     w = ba + 49*diag_offset[i];
807     ierr = Kernel_A_gets_inverse_A_7(w);CHKERRQ(ierr);
808   }
809 
810   ierr = PetscFree(rtmp);CHKERRQ(ierr);
811   C->factor    = FACTOR_LU;
812   C->assembled = PETSC_TRUE;
813   PLogFlops(1.3333*343*b->mbs); /* from inverting diagonal blocks */
814   PetscFunctionReturn(0);
815 }
816 
817 /* ------------------------------------------------------------*/
818 /*
819       Version for when blocks are 6 by 6
820 */
821 #undef __FUNC__
822 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_6"
823 int MatCholeskyFactorNumeric_SeqSBAIJ_6(Mat A,Mat *B)
824 {
825   Mat          C = *B;
826   Mat_SeqBAIJ  *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
827   IS           isrow = b->row,isicol = b->icol;
828   int          *r,*ic,ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
829   int          *ajtmpold,*ajtmp,nz,row;
830   int          *diag_offset = b->diag,idx,*ai=a->i,*aj=a->j,*pj;
831   MatScalar    *pv,*v,*rtmp,*pc,*w,*x;
832   MatScalar    p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
833   MatScalar    p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
834   MatScalar    x17,x18,x19,x20,x21,x22,x23,x24,x25,p10,p11,p12,p13,p14;
835   MatScalar    p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,m10,m11,m12;
836   MatScalar    m13,m14,m15,m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
837   MatScalar    p26,p27,p28,p29,p30,p31,p32,p33,p34,p35,p36;
838   MatScalar    x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36;
839   MatScalar    m26,m27,m28,m29,m30,m31,m32,m33,m34,m35,m36;
840   MatScalar    *ba = b->a,*aa = a->a;
841 
842   PetscFunctionBegin;
843   ierr  = ISGetIndices(isrow,&r);CHKERRQ(ierr);
844   ierr  = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
845   rtmp  = (MatScalar*)PetscMalloc(36*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
846 
847   for (i=0; i<n; i++) {
848     nz    = bi[i+1] - bi[i];
849     ajtmp = bj + bi[i];
850     for  (j=0; j<nz; j++) {
851       x = rtmp+36*ajtmp[j];
852       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
853       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
854       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = x[25] = 0.0 ;
855       x[26] = x[27] = x[28] = x[29] = x[30] = x[31] = x[32] = x[33] = 0.0 ;
856       x[34] = x[35] = 0.0 ;
857     }
858     /* load in initial (unfactored row) */
859     idx      = r[i];
860     nz       = ai[idx+1] - ai[idx];
861     ajtmpold = aj + ai[idx];
862     v        = aa + 36*ai[idx];
863     for (j=0; j<nz; j++) {
864       x    = rtmp+36*ic[ajtmpold[j]];
865       x[0] =  v[0];  x[1] =  v[1];  x[2] =  v[2];  x[3] =  v[3];
866       x[4] =  v[4];  x[5] =  v[5];  x[6] =  v[6];  x[7] =  v[7];
867       x[8] =  v[8];  x[9] =  v[9];  x[10] = v[10]; x[11] = v[11];
868       x[12] = v[12]; x[13] = v[13]; x[14] = v[14]; x[15] = v[15];
869       x[16] = v[16]; x[17] = v[17]; x[18] = v[18]; x[19] = v[19];
870       x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23];
871       x[24] = v[24]; x[25] = v[25]; x[26] = v[26]; x[27] = v[27];
872       x[28] = v[28]; x[29] = v[29]; x[30] = v[30]; x[31] = v[31];
873       x[32] = v[32]; x[33] = v[33]; x[34] = v[34]; x[35] = v[35];
874       v    += 36;
875     }
876     row = *ajtmp++;
877     while (row < i) {
878       pc  =  rtmp + 36*row;
879       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
880       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];
881       p9  = pc[8];  p10 = pc[9];  p11 = pc[10]; p12 = pc[11];
882       p13 = pc[12]; p14 = pc[13]; p15 = pc[14]; p16 = pc[15];
883       p17 = pc[16]; p18 = pc[17]; p19 = pc[18]; p20 = pc[19];
884       p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
885       p25 = pc[24]; p26 = pc[25]; p27 = pc[26]; p28 = pc[27];
886       p29 = pc[28]; p30 = pc[29]; p31 = pc[30]; p32 = pc[31];
887       p33 = pc[32]; p34 = pc[33]; p35 = pc[34]; p36 = pc[35];
888       if (p1  != 0.0 || p2  != 0.0 || p3  != 0.0 || p4  != 0.0 ||
889           p5  != 0.0 || p6  != 0.0 || p7  != 0.0 || p8  != 0.0 ||
890           p9  != 0.0 || p10 != 0.0 || p11 != 0.0 || p12 != 0.0 ||
891           p13 != 0.0 || p14 != 0.0 || p15 != 0.0 || p16 != 0.0 ||
892           p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 ||
893           p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 ||
894           p25 != 0.0 || p26 != 0.0 || p27 != 0.0 || p28 != 0.0 ||
895           p29 != 0.0 || p30 != 0.0 || p31 != 0.0 || p32 != 0.0 ||
896           p33 != 0.0 || p34 != 0.0 || p35 != 0.0 || p36 != 0.0) {
897         pv = ba + 36*diag_offset[row];
898         pj = bj + diag_offset[row] + 1;
899 	x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
900 	x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
901 	x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
902 	x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
903 	x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
904 	x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
905 	x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
906 	x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
907 	x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
908         pc[0]  = m1  = p1*x1  + p7*x2   + p13*x3  + p19*x4  + p25*x5  + p31*x6;
909         pc[1]  = m2  = p2*x1  + p8*x2   + p14*x3  + p20*x4  + p26*x5  + p32*x6;
910         pc[2]  = m3  = p3*x1  + p9*x2   + p15*x3  + p21*x4  + p27*x5  + p33*x6;
911         pc[3]  = m4  = p4*x1  + p10*x2  + p16*x3  + p22*x4  + p28*x5  + p34*x6;
912         pc[4]  = m5  = p5*x1  + p11*x2  + p17*x3  + p23*x4  + p29*x5  + p35*x6;
913         pc[5]  = m6  = p6*x1  + p12*x2  + p18*x3  + p24*x4  + p30*x5  + p36*x6;
914 
915         pc[6]  = m7  = p1*x7  + p7*x8   + p13*x9  + p19*x10 + p25*x11 + p31*x12;
916         pc[7]  = m8  = p2*x7  + p8*x8   + p14*x9  + p20*x10 + p26*x11 + p32*x12;
917         pc[8]  = m9  = p3*x7  + p9*x8   + p15*x9  + p21*x10 + p27*x11 + p33*x12;
918         pc[9]  = m10 = p4*x7  + p10*x8  + p16*x9  + p22*x10 + p28*x11 + p34*x12;
919         pc[10] = m11 = p5*x7  + p11*x8  + p17*x9  + p23*x10 + p29*x11 + p35*x12;
920         pc[11] = m12 = p6*x7  + p12*x8  + p18*x9  + p24*x10 + p30*x11 + p36*x12;
921 
922         pc[12] = m13 = p1*x13 + p7*x14  + p13*x15 + p19*x16 + p25*x17 + p31*x18;
923         pc[13] = m14 = p2*x13 + p8*x14  + p14*x15 + p20*x16 + p26*x17 + p32*x18;
924         pc[14] = m15 = p3*x13 + p9*x14  + p15*x15 + p21*x16 + p27*x17 + p33*x18;
925         pc[15] = m16 = p4*x13 + p10*x14 + p16*x15 + p22*x16 + p28*x17 + p34*x18;
926         pc[16] = m17 = p5*x13 + p11*x14 + p17*x15 + p23*x16 + p29*x17 + p35*x18;
927         pc[17] = m18 = p6*x13 + p12*x14 + p18*x15 + p24*x16 + p30*x17 + p36*x18;
928 
929         pc[18] = m19 = p1*x19 + p7*x20  + p13*x21 + p19*x22 + p25*x23 + p31*x24;
930         pc[19] = m20 = p2*x19 + p8*x20  + p14*x21 + p20*x22 + p26*x23 + p32*x24;
931         pc[20] = m21 = p3*x19 + p9*x20  + p15*x21 + p21*x22 + p27*x23 + p33*x24;
932         pc[21] = m22 = p4*x19 + p10*x20 + p16*x21 + p22*x22 + p28*x23 + p34*x24;
933         pc[22] = m23 = p5*x19 + p11*x20 + p17*x21 + p23*x22 + p29*x23 + p35*x24;
934         pc[23] = m24 = p6*x19 + p12*x20 + p18*x21 + p24*x22 + p30*x23 + p36*x24;
935 
936         pc[24] = m25 = p1*x25 + p7*x26  + p13*x27 + p19*x28 + p25*x29 + p31*x30;
937         pc[25] = m26 = p2*x25 + p8*x26  + p14*x27 + p20*x28 + p26*x29 + p32*x30;
938         pc[26] = m27 = p3*x25 + p9*x26  + p15*x27 + p21*x28 + p27*x29 + p33*x30;
939         pc[27] = m28 = p4*x25 + p10*x26 + p16*x27 + p22*x28 + p28*x29 + p34*x30;
940         pc[28] = m29 = p5*x25 + p11*x26 + p17*x27 + p23*x28 + p29*x29 + p35*x30;
941         pc[29] = m30 = p6*x25 + p12*x26 + p18*x27 + p24*x28 + p30*x29 + p36*x30;
942 
943         pc[30] = m31 = p1*x31 + p7*x32  + p13*x33 + p19*x34 + p25*x35 + p31*x36;
944         pc[31] = m32 = p2*x31 + p8*x32  + p14*x33 + p20*x34 + p26*x35 + p32*x36;
945         pc[32] = m33 = p3*x31 + p9*x32  + p15*x33 + p21*x34 + p27*x35 + p33*x36;
946         pc[33] = m34 = p4*x31 + p10*x32 + p16*x33 + p22*x34 + p28*x35 + p34*x36;
947         pc[34] = m35 = p5*x31 + p11*x32 + p17*x33 + p23*x34 + p29*x35 + p35*x36;
948         pc[35] = m36 = p6*x31 + p12*x32 + p18*x33 + p24*x34 + p30*x35 + p36*x36;
949 
950         nz = bi[row+1] - diag_offset[row] - 1;
951         pv += 36;
952         for (j=0; j<nz; j++) {
953 	  x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
954 	  x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
955 	  x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
956 	  x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
957 	  x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
958 	  x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
959 	  x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
960 	  x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
961 	  x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
962 	  x    = rtmp + 36*pj[j];
963           x[0]  -= m1*x1  + m7*x2   + m13*x3  + m19*x4  + m25*x5  + m31*x6;
964           x[1]  -= m2*x1  + m8*x2   + m14*x3  + m20*x4  + m26*x5  + m32*x6;
965           x[2]  -= m3*x1  + m9*x2   + m15*x3  + m21*x4  + m27*x5  + m33*x6;
966           x[3]  -= m4*x1  + m10*x2  + m16*x3  + m22*x4  + m28*x5  + m34*x6;
967           x[4]  -= m5*x1  + m11*x2  + m17*x3  + m23*x4  + m29*x5  + m35*x6;
968           x[5]  -= m6*x1  + m12*x2  + m18*x3  + m24*x4  + m30*x5  + m36*x6;
969 
970 	  x[6]  -= m1*x7  + m7*x8   + m13*x9  + m19*x10 + m25*x11 + m31*x12;
971 	  x[7]  -= m2*x7  + m8*x8   + m14*x9  + m20*x10 + m26*x11 + m32*x12;
972 	  x[8]  -= m3*x7  + m9*x8   + m15*x9  + m21*x10 + m27*x11 + m33*x12;
973 	  x[9]  -= m4*x7  + m10*x8  + m16*x9  + m22*x10 + m28*x11 + m34*x12;
974 	  x[10] -= m5*x7  + m11*x8  + m17*x9  + m23*x10 + m29*x11 + m35*x12;
975 	  x[11] -= m6*x7  + m12*x8  + m18*x9  + m24*x10 + m30*x11 + m36*x12;
976 
977 	  x[12] -= m1*x13 + m7*x14  + m13*x15 + m19*x16 + m25*x17 + m31*x18;
978 	  x[13] -= m2*x13 + m8*x14  + m14*x15 + m20*x16 + m26*x17 + m32*x18;
979 	  x[14] -= m3*x13 + m9*x14  + m15*x15 + m21*x16 + m27*x17 + m33*x18;
980 	  x[15] -= m4*x13 + m10*x14 + m16*x15 + m22*x16 + m28*x17 + m34*x18;
981 	  x[16] -= m5*x13 + m11*x14 + m17*x15 + m23*x16 + m29*x17 + m35*x18;
982 	  x[17] -= m6*x13 + m12*x14 + m18*x15 + m24*x16 + m30*x17 + m36*x18;
983 
984 	  x[18] -= m1*x19 + m7*x20  + m13*x21 + m19*x22 + m25*x23 + m31*x24;
985 	  x[19] -= m2*x19 + m8*x20  + m14*x21 + m20*x22 + m26*x23 + m32*x24;
986 	  x[20] -= m3*x19 + m9*x20  + m15*x21 + m21*x22 + m27*x23 + m33*x24;
987 	  x[21] -= m4*x19 + m10*x20 + m16*x21 + m22*x22 + m28*x23 + m34*x24;
988 	  x[22] -= m5*x19 + m11*x20 + m17*x21 + m23*x22 + m29*x23 + m35*x24;
989 	  x[23] -= m6*x19 + m12*x20 + m18*x21 + m24*x22 + m30*x23 + m36*x24;
990 
991 	  x[24] -= m1*x25 + m7*x26  + m13*x27 + m19*x28 + m25*x29 + m31*x30;
992 	  x[25] -= m2*x25 + m8*x26  + m14*x27 + m20*x28 + m26*x29 + m32*x30;
993 	  x[26] -= m3*x25 + m9*x26  + m15*x27 + m21*x28 + m27*x29 + m33*x30;
994 	  x[27] -= m4*x25 + m10*x26 + m16*x27 + m22*x28 + m28*x29 + m34*x30;
995 	  x[28] -= m5*x25 + m11*x26 + m17*x27 + m23*x28 + m29*x29 + m35*x30;
996 	  x[29] -= m6*x25 + m12*x26 + m18*x27 + m24*x28 + m30*x29 + m36*x30;
997 
998 	  x[30] -= m1*x31 + m7*x32  + m13*x33 + m19*x34 + m25*x35 + m31*x36;
999 	  x[31] -= m2*x31 + m8*x32  + m14*x33 + m20*x34 + m26*x35 + m32*x36;
1000 	  x[32] -= m3*x31 + m9*x32  + m15*x33 + m21*x34 + m27*x35 + m33*x36;
1001 	  x[33] -= m4*x31 + m10*x32 + m16*x33 + m22*x34 + m28*x35 + m34*x36;
1002 	  x[34] -= m5*x31 + m11*x32 + m17*x33 + m23*x34 + m29*x35 + m35*x36;
1003 	  x[35] -= m6*x31 + m12*x32 + m18*x33 + m24*x34 + m30*x35 + m36*x36;
1004 
1005           pv   += 36;
1006         }
1007         PLogFlops(432*nz+396);
1008       }
1009       row = *ajtmp++;
1010     }
1011     /* finished row so stick it into b->a */
1012     pv = ba + 36*bi[i];
1013     pj = bj + bi[i];
1014     nz = bi[i+1] - bi[i];
1015     for (j=0; j<nz; j++) {
1016       x      = rtmp+36*pj[j];
1017       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
1018       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7];
1019       pv[8]  = x[8];  pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11];
1020       pv[12] = x[12]; pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
1021       pv[16] = x[16]; pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19];
1022       pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23];
1023       pv[24] = x[24]; pv[25] = x[25]; pv[26] = x[26]; pv[27] = x[27];
1024       pv[28] = x[28]; pv[29] = x[29]; pv[30] = x[30]; pv[31] = x[31];
1025       pv[32] = x[32]; pv[33] = x[33]; pv[34] = x[34]; pv[35] = x[35];
1026       pv   += 36;
1027     }
1028     /* invert diagonal block */
1029     w = ba + 36*diag_offset[i];
1030     ierr = Kernel_A_gets_inverse_A_6(w);CHKERRQ(ierr);
1031   }
1032 
1033   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1034   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
1035   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
1036   C->factor = FACTOR_LU;
1037   C->assembled = PETSC_TRUE;
1038   PLogFlops(1.3333*216*b->mbs); /* from inverting diagonal blocks */
1039   PetscFunctionReturn(0);
1040 }
1041 /*
1042       Version for when blocks are 6 by 6 Using natural ordering
1043 */
1044 #undef __FUNC__
1045 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_6_NaturalOrdering"
1046 int MatCholeskyFactorNumeric_SeqSBAIJ_6_NaturalOrdering(Mat A,Mat *B)
1047 {
1048   Mat         C = *B;
1049   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
1050   int         ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
1051   int         *ajtmpold,*ajtmp,nz,row;
1052   int         *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
1053   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
1054   MatScalar   x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15;
1055   MatScalar   x16,x17,x18,x19,x20,x21,x22,x23,x24,x25;
1056   MatScalar   p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15;
1057   MatScalar   p16,p17,p18,p19,p20,p21,p22,p23,p24,p25;
1058   MatScalar   m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12,m13,m14,m15;
1059   MatScalar   m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
1060   MatScalar   p26,p27,p28,p29,p30,p31,p32,p33,p34,p35,p36;
1061   MatScalar   x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36;
1062   MatScalar   m26,m27,m28,m29,m30,m31,m32,m33,m34,m35,m36;
1063   MatScalar   *ba = b->a,*aa = a->a;
1064 
1065   PetscFunctionBegin;
1066   rtmp  = (MatScalar*)PetscMalloc(36*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
1067   for (i=0; i<n; i++) {
1068     nz    = bi[i+1] - bi[i];
1069     ajtmp = bj + bi[i];
1070     for  (j=0; j<nz; j++) {
1071       x = rtmp+36*ajtmp[j];
1072       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
1073       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
1074       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = x[25] = 0.0 ;
1075       x[26] = x[27] = x[28] = x[29] = x[30] = x[31] = x[32] = x[33] = 0.0 ;
1076       x[34] = x[35] = 0.0 ;
1077     }
1078     /* load in initial (unfactored row) */
1079     nz       = ai[i+1] - ai[i];
1080     ajtmpold = aj + ai[i];
1081     v        = aa + 36*ai[i];
1082     for (j=0; j<nz; j++) {
1083       x    = rtmp+36*ajtmpold[j];
1084       x[0] =  v[0];  x[1] =  v[1];  x[2] =  v[2];  x[3] =  v[3];
1085       x[4] =  v[4];  x[5] =  v[5];  x[6] =  v[6];  x[7] =  v[7];
1086       x[8] =  v[8];  x[9] =  v[9];  x[10] = v[10]; x[11] = v[11];
1087       x[12] = v[12]; x[13] = v[13]; x[14] = v[14]; x[15] = v[15];
1088       x[16] = v[16]; x[17] = v[17]; x[18] = v[18]; x[19] = v[19];
1089       x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23];
1090       x[24] = v[24]; x[25] = v[25]; x[26] = v[26]; x[27] = v[27];
1091       x[28] = v[28]; x[29] = v[29]; x[30] = v[30]; x[31] = v[31];
1092       x[32] = v[32]; x[33] = v[33]; x[34] = v[34]; x[35] = v[35];
1093       v    += 36;
1094     }
1095     row = *ajtmp++;
1096     while (row < i) {
1097       pc  = rtmp + 36*row;
1098       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
1099       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];
1100       p9  = pc[8];  p10 = pc[9];  p11 = pc[10]; p12 = pc[11];
1101       p13 = pc[12]; p14 = pc[13]; p15 = pc[14]; p16 = pc[15];
1102       p17 = pc[16]; p18 = pc[17]; p19 = pc[18]; p20 = pc[19];
1103       p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
1104       p25 = pc[24]; p26 = pc[25]; p27 = pc[26]; p28 = pc[27];
1105       p29 = pc[28]; p30 = pc[29]; p31 = pc[30]; p32 = pc[31];
1106       p33 = pc[32]; p34 = pc[33]; p35 = pc[34]; p36 = pc[35];
1107       if (p1  != 0.0 || p2  != 0.0 || p3  != 0.0 || p4  != 0.0 ||
1108           p5  != 0.0 || p6  != 0.0 || p7  != 0.0 || p8  != 0.0 ||
1109           p9  != 0.0 || p10 != 0.0 || p11 != 0.0 || p12 != 0.0 ||
1110           p13 != 0.0 || p14 != 0.0 || p15 != 0.0 || p16 != 0.0 ||
1111           p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 ||
1112           p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 ||
1113           p25 != 0.0 || p26 != 0.0 || p27 != 0.0 || p28 != 0.0 ||
1114           p29 != 0.0 || p30 != 0.0 || p31 != 0.0 || p32 != 0.0 ||
1115           p33 != 0.0 || p34 != 0.0 || p35 != 0.0 || p36 != 0.0) {
1116         pv = ba + 36*diag_offset[row];
1117         pj = bj + diag_offset[row] + 1;
1118 	x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
1119 	x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
1120 	x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
1121 	x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
1122 	x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
1123 	x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
1124 	x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
1125 	x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
1126 	x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
1127         pc[0]  = m1  = p1*x1  + p7*x2   + p13*x3  + p19*x4  + p25*x5  + p31*x6;
1128         pc[1]  = m2  = p2*x1  + p8*x2   + p14*x3  + p20*x4  + p26*x5  + p32*x6;
1129         pc[2]  = m3  = p3*x1  + p9*x2   + p15*x3  + p21*x4  + p27*x5  + p33*x6;
1130         pc[3]  = m4  = p4*x1  + p10*x2  + p16*x3  + p22*x4  + p28*x5  + p34*x6;
1131         pc[4]  = m5  = p5*x1  + p11*x2  + p17*x3  + p23*x4  + p29*x5  + p35*x6;
1132         pc[5]  = m6  = p6*x1  + p12*x2  + p18*x3  + p24*x4  + p30*x5  + p36*x6;
1133 
1134         pc[6]  = m7  = p1*x7  + p7*x8   + p13*x9  + p19*x10 + p25*x11 + p31*x12;
1135         pc[7]  = m8  = p2*x7  + p8*x8   + p14*x9  + p20*x10 + p26*x11 + p32*x12;
1136         pc[8]  = m9  = p3*x7  + p9*x8   + p15*x9  + p21*x10 + p27*x11 + p33*x12;
1137         pc[9]  = m10 = p4*x7  + p10*x8  + p16*x9  + p22*x10 + p28*x11 + p34*x12;
1138         pc[10] = m11 = p5*x7  + p11*x8  + p17*x9  + p23*x10 + p29*x11 + p35*x12;
1139         pc[11] = m12 = p6*x7  + p12*x8  + p18*x9  + p24*x10 + p30*x11 + p36*x12;
1140 
1141         pc[12] = m13 = p1*x13 + p7*x14  + p13*x15 + p19*x16 + p25*x17 + p31*x18;
1142         pc[13] = m14 = p2*x13 + p8*x14  + p14*x15 + p20*x16 + p26*x17 + p32*x18;
1143         pc[14] = m15 = p3*x13 + p9*x14  + p15*x15 + p21*x16 + p27*x17 + p33*x18;
1144         pc[15] = m16 = p4*x13 + p10*x14 + p16*x15 + p22*x16 + p28*x17 + p34*x18;
1145         pc[16] = m17 = p5*x13 + p11*x14 + p17*x15 + p23*x16 + p29*x17 + p35*x18;
1146         pc[17] = m18 = p6*x13 + p12*x14 + p18*x15 + p24*x16 + p30*x17 + p36*x18;
1147 
1148         pc[18] = m19 = p1*x19 + p7*x20  + p13*x21 + p19*x22 + p25*x23 + p31*x24;
1149         pc[19] = m20 = p2*x19 + p8*x20  + p14*x21 + p20*x22 + p26*x23 + p32*x24;
1150         pc[20] = m21 = p3*x19 + p9*x20  + p15*x21 + p21*x22 + p27*x23 + p33*x24;
1151         pc[21] = m22 = p4*x19 + p10*x20 + p16*x21 + p22*x22 + p28*x23 + p34*x24;
1152         pc[22] = m23 = p5*x19 + p11*x20 + p17*x21 + p23*x22 + p29*x23 + p35*x24;
1153         pc[23] = m24 = p6*x19 + p12*x20 + p18*x21 + p24*x22 + p30*x23 + p36*x24;
1154 
1155         pc[24] = m25 = p1*x25 + p7*x26  + p13*x27 + p19*x28 + p25*x29 + p31*x30;
1156         pc[25] = m26 = p2*x25 + p8*x26  + p14*x27 + p20*x28 + p26*x29 + p32*x30;
1157         pc[26] = m27 = p3*x25 + p9*x26  + p15*x27 + p21*x28 + p27*x29 + p33*x30;
1158         pc[27] = m28 = p4*x25 + p10*x26 + p16*x27 + p22*x28 + p28*x29 + p34*x30;
1159         pc[28] = m29 = p5*x25 + p11*x26 + p17*x27 + p23*x28 + p29*x29 + p35*x30;
1160         pc[29] = m30 = p6*x25 + p12*x26 + p18*x27 + p24*x28 + p30*x29 + p36*x30;
1161 
1162         pc[30] = m31 = p1*x31 + p7*x32  + p13*x33 + p19*x34 + p25*x35 + p31*x36;
1163         pc[31] = m32 = p2*x31 + p8*x32  + p14*x33 + p20*x34 + p26*x35 + p32*x36;
1164         pc[32] = m33 = p3*x31 + p9*x32  + p15*x33 + p21*x34 + p27*x35 + p33*x36;
1165         pc[33] = m34 = p4*x31 + p10*x32 + p16*x33 + p22*x34 + p28*x35 + p34*x36;
1166         pc[34] = m35 = p5*x31 + p11*x32 + p17*x33 + p23*x34 + p29*x35 + p35*x36;
1167         pc[35] = m36 = p6*x31 + p12*x32 + p18*x33 + p24*x34 + p30*x35 + p36*x36;
1168 
1169         nz = bi[row+1] - diag_offset[row] - 1;
1170         pv += 36;
1171         for (j=0; j<nz; j++) {
1172 	  x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
1173 	  x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
1174 	  x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
1175 	  x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
1176 	  x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
1177 	  x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
1178 	  x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
1179 	  x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
1180 	  x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
1181 	  x    = rtmp + 36*pj[j];
1182           x[0]  -= m1*x1  + m7*x2   + m13*x3  + m19*x4  + m25*x5  + m31*x6;
1183           x[1]  -= m2*x1  + m8*x2   + m14*x3  + m20*x4  + m26*x5  + m32*x6;
1184           x[2]  -= m3*x1  + m9*x2   + m15*x3  + m21*x4  + m27*x5  + m33*x6;
1185           x[3]  -= m4*x1  + m10*x2  + m16*x3  + m22*x4  + m28*x5  + m34*x6;
1186           x[4]  -= m5*x1  + m11*x2  + m17*x3  + m23*x4  + m29*x5  + m35*x6;
1187           x[5]  -= m6*x1  + m12*x2  + m18*x3  + m24*x4  + m30*x5  + m36*x6;
1188 
1189 	  x[6]  -= m1*x7  + m7*x8   + m13*x9  + m19*x10 + m25*x11 + m31*x12;
1190 	  x[7]  -= m2*x7  + m8*x8   + m14*x9  + m20*x10 + m26*x11 + m32*x12;
1191 	  x[8]  -= m3*x7  + m9*x8   + m15*x9  + m21*x10 + m27*x11 + m33*x12;
1192 	  x[9]  -= m4*x7  + m10*x8  + m16*x9  + m22*x10 + m28*x11 + m34*x12;
1193 	  x[10] -= m5*x7  + m11*x8  + m17*x9  + m23*x10 + m29*x11 + m35*x12;
1194 	  x[11] -= m6*x7  + m12*x8  + m18*x9  + m24*x10 + m30*x11 + m36*x12;
1195 
1196 	  x[12] -= m1*x13 + m7*x14  + m13*x15 + m19*x16 + m25*x17 + m31*x18;
1197 	  x[13] -= m2*x13 + m8*x14  + m14*x15 + m20*x16 + m26*x17 + m32*x18;
1198 	  x[14] -= m3*x13 + m9*x14  + m15*x15 + m21*x16 + m27*x17 + m33*x18;
1199 	  x[15] -= m4*x13 + m10*x14 + m16*x15 + m22*x16 + m28*x17 + m34*x18;
1200 	  x[16] -= m5*x13 + m11*x14 + m17*x15 + m23*x16 + m29*x17 + m35*x18;
1201 	  x[17] -= m6*x13 + m12*x14 + m18*x15 + m24*x16 + m30*x17 + m36*x18;
1202 
1203 	  x[18] -= m1*x19 + m7*x20  + m13*x21 + m19*x22 + m25*x23 + m31*x24;
1204 	  x[19] -= m2*x19 + m8*x20  + m14*x21 + m20*x22 + m26*x23 + m32*x24;
1205 	  x[20] -= m3*x19 + m9*x20  + m15*x21 + m21*x22 + m27*x23 + m33*x24;
1206 	  x[21] -= m4*x19 + m10*x20 + m16*x21 + m22*x22 + m28*x23 + m34*x24;
1207 	  x[22] -= m5*x19 + m11*x20 + m17*x21 + m23*x22 + m29*x23 + m35*x24;
1208 	  x[23] -= m6*x19 + m12*x20 + m18*x21 + m24*x22 + m30*x23 + m36*x24;
1209 
1210 	  x[24] -= m1*x25 + m7*x26  + m13*x27 + m19*x28 + m25*x29 + m31*x30;
1211 	  x[25] -= m2*x25 + m8*x26  + m14*x27 + m20*x28 + m26*x29 + m32*x30;
1212 	  x[26] -= m3*x25 + m9*x26  + m15*x27 + m21*x28 + m27*x29 + m33*x30;
1213 	  x[27] -= m4*x25 + m10*x26 + m16*x27 + m22*x28 + m28*x29 + m34*x30;
1214 	  x[28] -= m5*x25 + m11*x26 + m17*x27 + m23*x28 + m29*x29 + m35*x30;
1215 	  x[29] -= m6*x25 + m12*x26 + m18*x27 + m24*x28 + m30*x29 + m36*x30;
1216 
1217 	  x[30] -= m1*x31 + m7*x32  + m13*x33 + m19*x34 + m25*x35 + m31*x36;
1218 	  x[31] -= m2*x31 + m8*x32  + m14*x33 + m20*x34 + m26*x35 + m32*x36;
1219 	  x[32] -= m3*x31 + m9*x32  + m15*x33 + m21*x34 + m27*x35 + m33*x36;
1220 	  x[33] -= m4*x31 + m10*x32 + m16*x33 + m22*x34 + m28*x35 + m34*x36;
1221 	  x[34] -= m5*x31 + m11*x32 + m17*x33 + m23*x34 + m29*x35 + m35*x36;
1222 	  x[35] -= m6*x31 + m12*x32 + m18*x33 + m24*x34 + m30*x35 + m36*x36;
1223 
1224           pv   += 36;
1225         }
1226         PLogFlops(432*nz+396);
1227       }
1228       row = *ajtmp++;
1229     }
1230     /* finished row so stick it into b->a */
1231     pv = ba + 36*bi[i];
1232     pj = bj + bi[i];
1233     nz = bi[i+1] - bi[i];
1234     for (j=0; j<nz; j++) {
1235       x      = rtmp+36*pj[j];
1236       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
1237       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7];
1238       pv[8]  = x[8];  pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11];
1239       pv[12] = x[12]; pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
1240       pv[16] = x[16]; pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19];
1241       pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23];
1242       pv[24] = x[24]; pv[25] = x[25]; pv[26] = x[26]; pv[27] = x[27];
1243       pv[28] = x[28]; pv[29] = x[29]; pv[30] = x[30]; pv[31] = x[31];
1244       pv[32] = x[32]; pv[33] = x[33]; pv[34] = x[34]; pv[35] = x[35];
1245       pv   += 36;
1246     }
1247     /* invert diagonal block */
1248     w = ba + 36*diag_offset[i];
1249     ierr = Kernel_A_gets_inverse_A_6(w);CHKERRQ(ierr);
1250   }
1251 
1252   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1253   C->factor    = FACTOR_LU;
1254   C->assembled = PETSC_TRUE;
1255   PLogFlops(1.3333*216*b->mbs); /* from inverting diagonal blocks */
1256   PetscFunctionReturn(0);
1257 }
1258 
1259 /*
1260       Version for when blocks are 5 by 5
1261 */
1262 #undef __FUNC__
1263 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_5"
1264 int MatCholeskyFactorNumeric_SeqSBAIJ_5(Mat A,Mat *B)
1265 {
1266   Mat         C = *B;
1267   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
1268   IS          isrow = b->row,isicol = b->icol;
1269   int         *r,*ic,ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
1270   int         *ajtmpold,*ajtmp,nz,row;
1271   int         *diag_offset = b->diag,idx,*ai=a->i,*aj=a->j,*pj;
1272   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
1273   MatScalar   p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
1274   MatScalar   p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
1275   MatScalar   x17,x18,x19,x20,x21,x22,x23,x24,x25,p10,p11,p12,p13,p14;
1276   MatScalar   p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,m10,m11,m12;
1277   MatScalar   m13,m14,m15,m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
1278   MatScalar   *ba = b->a,*aa = a->a;
1279 
1280   PetscFunctionBegin;
1281   ierr  = ISGetIndices(isrow,&r);CHKERRQ(ierr);
1282   ierr  = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
1283   rtmp  = (MatScalar*)PetscMalloc(25*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
1284 
1285   for (i=0; i<n; i++) {
1286     nz    = bi[i+1] - bi[i];
1287     ajtmp = bj + bi[i];
1288     for  (j=0; j<nz; j++) {
1289       x = rtmp+25*ajtmp[j];
1290       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
1291       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
1292       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0;
1293     }
1294     /* load in initial (unfactored row) */
1295     idx      = r[i];
1296     nz       = ai[idx+1] - ai[idx];
1297     ajtmpold = aj + ai[idx];
1298     v        = aa + 25*ai[idx];
1299     for (j=0; j<nz; j++) {
1300       x    = rtmp+25*ic[ajtmpold[j]];
1301       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
1302       x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
1303       x[9] = v[9]; x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
1304       x[14] = v[14]; x[15] = v[15]; x[16] = v[16]; x[17] = v[17];
1305       x[18] = v[18]; x[19] = v[19]; x[20] = v[20]; x[21] = v[21];
1306       x[22] = v[22]; x[23] = v[23]; x[24] = v[24];
1307       v    += 25;
1308     }
1309     row = *ajtmp++;
1310     while (row < i) {
1311       pc = rtmp + 25*row;
1312       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
1313       p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
1314       p10 = pc[9]; p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
1315       p15 = pc[14]; p16 = pc[15]; p17 = pc[16]; p18 = pc[17]; p19 = pc[18];
1316       p20 = pc[19]; p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
1317       p25 = pc[24];
1318       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
1319           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
1320           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
1321           || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 ||
1322           p20 != 0.0 || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 ||
1323           p24 != 0.0 || p25 != 0.0) {
1324         pv = ba + 25*diag_offset[row];
1325         pj = bj + diag_offset[row] + 1;
1326         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
1327         x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
1328         x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
1329         x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17];
1330         x19 = pv[18]; x20 = pv[19]; x21 = pv[20]; x22 = pv[21];
1331         x23 = pv[22]; x24 = pv[23]; x25 = pv[24];
1332         pc[0] = m1 = p1*x1 + p6*x2  + p11*x3 + p16*x4 + p21*x5;
1333         pc[1] = m2 = p2*x1 + p7*x2  + p12*x3 + p17*x4 + p22*x5;
1334         pc[2] = m3 = p3*x1 + p8*x2  + p13*x3 + p18*x4 + p23*x5;
1335         pc[3] = m4 = p4*x1 + p9*x2  + p14*x3 + p19*x4 + p24*x5;
1336         pc[4] = m5 = p5*x1 + p10*x2 + p15*x3 + p20*x4 + p25*x5;
1337 
1338         pc[5] = m6 = p1*x6 + p6*x7  + p11*x8 + p16*x9 + p21*x10;
1339         pc[6] = m7 = p2*x6 + p7*x7  + p12*x8 + p17*x9 + p22*x10;
1340         pc[7] = m8 = p3*x6 + p8*x7  + p13*x8 + p18*x9 + p23*x10;
1341         pc[8] = m9 = p4*x6 + p9*x7  + p14*x8 + p19*x9 + p24*x10;
1342         pc[9] = m10 = p5*x6 + p10*x7 + p15*x8 + p20*x9 + p25*x10;
1343 
1344         pc[10] = m11 = p1*x11 + p6*x12  + p11*x13 + p16*x14 + p21*x15;
1345         pc[11] = m12 = p2*x11 + p7*x12  + p12*x13 + p17*x14 + p22*x15;
1346         pc[12] = m13 = p3*x11 + p8*x12  + p13*x13 + p18*x14 + p23*x15;
1347         pc[13] = m14 = p4*x11 + p9*x12  + p14*x13 + p19*x14 + p24*x15;
1348         pc[14] = m15 = p5*x11 + p10*x12 + p15*x13 + p20*x14 + p25*x15;
1349 
1350         pc[15] = m16 = p1*x16 + p6*x17  + p11*x18 + p16*x19 + p21*x20;
1351         pc[16] = m17 = p2*x16 + p7*x17  + p12*x18 + p17*x19 + p22*x20;
1352         pc[17] = m18 = p3*x16 + p8*x17  + p13*x18 + p18*x19 + p23*x20;
1353         pc[18] = m19 = p4*x16 + p9*x17  + p14*x18 + p19*x19 + p24*x20;
1354         pc[19] = m20 = p5*x16 + p10*x17 + p15*x18 + p20*x19 + p25*x20;
1355 
1356         pc[20] = m21 = p1*x21 + p6*x22  + p11*x23 + p16*x24 + p21*x25;
1357         pc[21] = m22 = p2*x21 + p7*x22  + p12*x23 + p17*x24 + p22*x25;
1358         pc[22] = m23 = p3*x21 + p8*x22  + p13*x23 + p18*x24 + p23*x25;
1359         pc[23] = m24 = p4*x21 + p9*x22  + p14*x23 + p19*x24 + p24*x25;
1360         pc[24] = m25 = p5*x21 + p10*x22 + p15*x23 + p20*x24 + p25*x25;
1361 
1362         nz = bi[row+1] - diag_offset[row] - 1;
1363         pv += 25;
1364         for (j=0; j<nz; j++) {
1365           x1   = pv[0];  x2 = pv[1];   x3  = pv[2];  x4  = pv[3];
1366           x5   = pv[4];  x6 = pv[5];   x7  = pv[6];  x8  = pv[7]; x9 = pv[8];
1367           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
1368           x14  = pv[13]; x15 = pv[14]; x16 = pv[15]; x17 = pv[16];
1369           x18  = pv[17]; x19 = pv[18]; x20 = pv[19]; x21 = pv[20];
1370           x22  = pv[21]; x23 = pv[22]; x24 = pv[23]; x25 = pv[24];
1371           x    = rtmp + 25*pj[j];
1372           x[0] -= m1*x1 + m6*x2  + m11*x3 + m16*x4 + m21*x5;
1373           x[1] -= m2*x1 + m7*x2  + m12*x3 + m17*x4 + m22*x5;
1374           x[2] -= m3*x1 + m8*x2  + m13*x3 + m18*x4 + m23*x5;
1375           x[3] -= m4*x1 + m9*x2  + m14*x3 + m19*x4 + m24*x5;
1376           x[4] -= m5*x1 + m10*x2 + m15*x3 + m20*x4 + m25*x5;
1377 
1378           x[5] -= m1*x6 + m6*x7  + m11*x8 + m16*x9 + m21*x10;
1379           x[6] -= m2*x6 + m7*x7  + m12*x8 + m17*x9 + m22*x10;
1380           x[7] -= m3*x6 + m8*x7  + m13*x8 + m18*x9 + m23*x10;
1381           x[8] -= m4*x6 + m9*x7  + m14*x8 + m19*x9 + m24*x10;
1382           x[9] -= m5*x6 + m10*x7 + m15*x8 + m20*x9 + m25*x10;
1383 
1384           x[10] -= m1*x11 + m6*x12  + m11*x13 + m16*x14 + m21*x15;
1385           x[11] -= m2*x11 + m7*x12  + m12*x13 + m17*x14 + m22*x15;
1386           x[12] -= m3*x11 + m8*x12  + m13*x13 + m18*x14 + m23*x15;
1387           x[13] -= m4*x11 + m9*x12  + m14*x13 + m19*x14 + m24*x15;
1388           x[14] -= m5*x11 + m10*x12 + m15*x13 + m20*x14 + m25*x15;
1389 
1390           x[15] -= m1*x16 + m6*x17  + m11*x18 + m16*x19 + m21*x20;
1391           x[16] -= m2*x16 + m7*x17  + m12*x18 + m17*x19 + m22*x20;
1392           x[17] -= m3*x16 + m8*x17  + m13*x18 + m18*x19 + m23*x20;
1393           x[18] -= m4*x16 + m9*x17  + m14*x18 + m19*x19 + m24*x20;
1394           x[19] -= m5*x16 + m10*x17 + m15*x18 + m20*x19 + m25*x20;
1395 
1396           x[20] -= m1*x21 + m6*x22  + m11*x23 + m16*x24 + m21*x25;
1397           x[21] -= m2*x21 + m7*x22  + m12*x23 + m17*x24 + m22*x25;
1398           x[22] -= m3*x21 + m8*x22  + m13*x23 + m18*x24 + m23*x25;
1399           x[23] -= m4*x21 + m9*x22  + m14*x23 + m19*x24 + m24*x25;
1400           x[24] -= m5*x21 + m10*x22 + m15*x23 + m20*x24 + m25*x25;
1401 
1402           pv   += 25;
1403         }
1404         PLogFlops(250*nz+225);
1405       }
1406       row = *ajtmp++;
1407     }
1408     /* finished row so stick it into b->a */
1409     pv = ba + 25*bi[i];
1410     pj = bj + bi[i];
1411     nz = bi[i+1] - bi[i];
1412     for (j=0; j<nz; j++) {
1413       x     = rtmp+25*pj[j];
1414       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
1415       pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
1416       pv[9] = x[9]; pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
1417       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; pv[16] = x[16];
1418       pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19]; pv[20] = x[20];
1419       pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23]; pv[24] = x[24];
1420       pv   += 25;
1421     }
1422     /* invert diagonal block */
1423     w = ba + 25*diag_offset[i];
1424     ierr = Kernel_A_gets_inverse_A_5(w);CHKERRQ(ierr);
1425   }
1426 
1427   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1428   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
1429   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
1430   C->factor = FACTOR_LU;
1431   C->assembled = PETSC_TRUE;
1432   PLogFlops(1.3333*125*b->mbs); /* from inverting diagonal blocks */
1433   PetscFunctionReturn(0);
1434 }
1435 /*
1436       Version for when blocks are 5 by 5 Using natural ordering
1437 */
1438 #undef __FUNC__
1439 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_5_NaturalOrdering"
1440 int MatCholeskyFactorNumeric_SeqSBAIJ_5_NaturalOrdering(Mat A,Mat *B)
1441 {
1442   Mat         C = *B;
1443   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
1444   int         ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
1445   int         *ajtmpold,*ajtmp,nz,row;
1446   int         *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
1447   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
1448   MatScalar   x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15;
1449   MatScalar   x16,x17,x18,x19,x20,x21,x22,x23,x24,x25;
1450   MatScalar   p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15;
1451   MatScalar   p16,p17,p18,p19,p20,p21,p22,p23,p24,p25;
1452   MatScalar   m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12,m13,m14,m15;
1453   MatScalar   m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
1454   MatScalar   *ba = b->a,*aa = a->a;
1455 
1456   PetscFunctionBegin;
1457   rtmp  = (MatScalar*)PetscMalloc(25*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
1458   for (i=0; i<n; i++) {
1459     nz    = bi[i+1] - bi[i];
1460     ajtmp = bj + bi[i];
1461     for  (j=0; j<nz; j++) {
1462       x = rtmp+25*ajtmp[j];
1463       x[0]  = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = x[9] = 0.0;
1464       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
1465       x[16] = x[17] = x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0;
1466     }
1467     /* load in initial (unfactored row) */
1468     nz       = ai[i+1] - ai[i];
1469     ajtmpold = aj + ai[i];
1470     v        = aa + 25*ai[i];
1471     for (j=0; j<nz; j++) {
1472       x    = rtmp+25*ajtmpold[j];
1473       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
1474       x[4]  = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
1475       x[9]  = v[9];  x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
1476       x[14] = v[14]; x[15] = v[15]; x[16] = v[16]; x[17] = v[17]; x[18] = v[18];
1477       x[19] = v[19]; x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23];
1478       x[24] = v[24];
1479       v    += 25;
1480     }
1481     row = *ajtmp++;
1482     while (row < i) {
1483       pc  = rtmp + 25*row;
1484       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
1485       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
1486       p10 = pc[9];  p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
1487       p15 = pc[14]; p16 = pc[15]; p17 = pc[16]; p18 = pc[17];
1488       p19 = pc[18]; p20 = pc[19]; p21 = pc[20]; p22 = pc[21]; p23 = pc[22];
1489       p24 = pc[23]; p25 = pc[24];
1490       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
1491           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
1492           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
1493           || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0
1494           || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 || p25 != 0.0) {
1495         pv = ba + 25*diag_offset[row];
1496         pj = bj + diag_offset[row] + 1;
1497         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
1498         x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
1499         x10 = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
1500         x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17]; x19 = pv[18];
1501         x20 = pv[19]; x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
1502         x25 = pv[24];
1503         pc[0] = m1 = p1*x1 + p6*x2  + p11*x3 + p16*x4 + p21*x5;
1504         pc[1] = m2 = p2*x1 + p7*x2  + p12*x3 + p17*x4 + p22*x5;
1505         pc[2] = m3 = p3*x1 + p8*x2  + p13*x3 + p18*x4 + p23*x5;
1506         pc[3] = m4 = p4*x1 + p9*x2  + p14*x3 + p19*x4 + p24*x5;
1507         pc[4] = m5 = p5*x1 + p10*x2 + p15*x3 + p20*x4 + p25*x5;
1508 
1509         pc[5]  = m6  = p1*x6 + p6*x7  + p11*x8 + p16*x9 + p21*x10;
1510         pc[6]  = m7  = p2*x6 + p7*x7  + p12*x8 + p17*x9 + p22*x10;
1511         pc[7]  = m8  = p3*x6 + p8*x7  + p13*x8 + p18*x9 + p23*x10;
1512         pc[8]  = m9  = p4*x6 + p9*x7  + p14*x8 + p19*x9 + p24*x10;
1513         pc[9]  = m10 = p5*x6 + p10*x7 + p15*x8 + p20*x9 + p25*x10;
1514 
1515         pc[10] = m11 = p1*x11 + p6*x12  + p11*x13 + p16*x14 + p21*x15;
1516         pc[11] = m12 = p2*x11 + p7*x12  + p12*x13 + p17*x14 + p22*x15;
1517         pc[12] = m13 = p3*x11 + p8*x12  + p13*x13 + p18*x14 + p23*x15;
1518         pc[13] = m14 = p4*x11 + p9*x12  + p14*x13 + p19*x14 + p24*x15;
1519         pc[14] = m15 = p5*x11 + p10*x12 + p15*x13 + p20*x14 + p25*x15;
1520 
1521         pc[15] = m16 = p1*x16 + p6*x17  + p11*x18 + p16*x19 + p21*x20;
1522         pc[16] = m17 = p2*x16 + p7*x17  + p12*x18 + p17*x19 + p22*x20;
1523         pc[17] = m18 = p3*x16 + p8*x17  + p13*x18 + p18*x19 + p23*x20;
1524         pc[18] = m19 = p4*x16 + p9*x17  + p14*x18 + p19*x19 + p24*x20;
1525         pc[19] = m20 = p5*x16 + p10*x17 + p15*x18 + p20*x19 + p25*x20;
1526 
1527         pc[20] = m21 = p1*x21 + p6*x22  + p11*x23 + p16*x24 + p21*x25;
1528         pc[21] = m22 = p2*x21 + p7*x22  + p12*x23 + p17*x24 + p22*x25;
1529         pc[22] = m23 = p3*x21 + p8*x22  + p13*x23 + p18*x24 + p23*x25;
1530         pc[23] = m24 = p4*x21 + p9*x22  + p14*x23 + p19*x24 + p24*x25;
1531         pc[24] = m25 = p5*x21 + p10*x22 + p15*x23 + p20*x24 + p25*x25;
1532 
1533         nz = bi[row+1] - diag_offset[row] - 1;
1534         pv += 25;
1535         for (j=0; j<nz; j++) {
1536           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
1537           x5   = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
1538           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
1539           x14  = pv[13]; x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17];
1540           x19 = pv[18];  x20 = pv[19]; x21 = pv[20]; x22 = pv[21]; x23 = pv[22];
1541           x24 = pv[23];  x25 = pv[24];
1542           x    = rtmp + 25*pj[j];
1543           x[0] -= m1*x1 + m6*x2   + m11*x3  + m16*x4 + m21*x5;
1544           x[1] -= m2*x1 + m7*x2   + m12*x3  + m17*x4 + m22*x5;
1545           x[2] -= m3*x1 + m8*x2   + m13*x3  + m18*x4 + m23*x5;
1546           x[3] -= m4*x1 + m9*x2   + m14*x3  + m19*x4 + m24*x5;
1547           x[4] -= m5*x1 + m10*x2  + m15*x3  + m20*x4 + m25*x5;
1548 
1549           x[5] -= m1*x6 + m6*x7   + m11*x8  + m16*x9 + m21*x10;
1550           x[6] -= m2*x6 + m7*x7   + m12*x8  + m17*x9 + m22*x10;
1551           x[7] -= m3*x6 + m8*x7   + m13*x8  + m18*x9 + m23*x10;
1552           x[8] -= m4*x6 + m9*x7   + m14*x8  + m19*x9 + m24*x10;
1553           x[9] -= m5*x6 + m10*x7  + m15*x8  + m20*x9 + m25*x10;
1554 
1555           x[10] -= m1*x11 + m6*x12  + m11*x13 + m16*x14 + m21*x15;
1556           x[11] -= m2*x11 + m7*x12  + m12*x13 + m17*x14 + m22*x15;
1557           x[12] -= m3*x11 + m8*x12  + m13*x13 + m18*x14 + m23*x15;
1558           x[13] -= m4*x11 + m9*x12  + m14*x13 + m19*x14 + m24*x15;
1559           x[14] -= m5*x11 + m10*x12 + m15*x13 + m20*x14 + m25*x15;
1560 
1561           x[15] -= m1*x16 + m6*x17  + m11*x18 + m16*x19 + m21*x20;
1562           x[16] -= m2*x16 + m7*x17  + m12*x18 + m17*x19 + m22*x20;
1563           x[17] -= m3*x16 + m8*x17  + m13*x18 + m18*x19 + m23*x20;
1564           x[18] -= m4*x16 + m9*x17  + m14*x18 + m19*x19 + m24*x20;
1565           x[19] -= m5*x16 + m10*x17 + m15*x18 + m20*x19 + m25*x20;
1566 
1567           x[20] -= m1*x21 + m6*x22  + m11*x23 + m16*x24 + m21*x25;
1568           x[21] -= m2*x21 + m7*x22  + m12*x23 + m17*x24 + m22*x25;
1569           x[22] -= m3*x21 + m8*x22  + m13*x23 + m18*x24 + m23*x25;
1570           x[23] -= m4*x21 + m9*x22  + m14*x23 + m19*x24 + m24*x25;
1571           x[24] -= m5*x21 + m10*x22 + m15*x23 + m20*x24 + m25*x25;
1572           pv   += 25;
1573         }
1574         PLogFlops(250*nz+225);
1575       }
1576       row = *ajtmp++;
1577     }
1578     /* finished row so stick it into b->a */
1579     pv = ba + 25*bi[i];
1580     pj = bj + bi[i];
1581     nz = bi[i+1] - bi[i];
1582     for (j=0; j<nz; j++) {
1583       x      = rtmp+25*pj[j];
1584       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
1585       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
1586       pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
1587       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; pv[16] = x[16]; pv[17] = x[17];
1588       pv[18] = x[18]; pv[19] = x[19]; pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22];
1589       pv[23] = x[23]; pv[24] = x[24];
1590       pv   += 25;
1591     }
1592     /* invert diagonal block */
1593     w = ba + 25*diag_offset[i];
1594     ierr = Kernel_A_gets_inverse_A_5(w);CHKERRQ(ierr);
1595   }
1596 
1597   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1598   C->factor    = FACTOR_LU;
1599   C->assembled = PETSC_TRUE;
1600   PLogFlops(1.3333*125*b->mbs); /* from inverting diagonal blocks */
1601   PetscFunctionReturn(0);
1602 }
1603 
1604 /*
1605       Version for when blocks are 4 by 4
1606 */
1607 #undef __FUNC__
1608 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_4"
1609 int MatCholeskyFactorNumeric_SeqSBAIJ_4(Mat A,Mat *B)
1610 {
1611   Mat         C = *B;
1612   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
1613   IS          isrow = b->row,isicol = b->icol;
1614   int         *r,*ic,ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
1615   int         *ajtmpold,*ajtmp,nz,row;
1616   int         *diag_offset = b->diag,idx,*ai=a->i,*aj=a->j,*pj;
1617   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
1618   MatScalar   p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
1619   MatScalar   p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
1620   MatScalar   p10,p11,p12,p13,p14,p15,p16,m10,m11,m12;
1621   MatScalar   m13,m14,m15,m16;
1622   MatScalar   *ba = b->a,*aa = a->a;
1623 
1624   PetscFunctionBegin;
1625   ierr  = ISGetIndices(isrow,&r);CHKERRQ(ierr);
1626   ierr  = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
1627   rtmp  = (MatScalar*)PetscMalloc(16*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
1628 
1629   for (i=0; i<n; i++) {
1630     nz    = bi[i+1] - bi[i];
1631     ajtmp = bj + bi[i];
1632     for  (j=0; j<nz; j++) {
1633       x = rtmp+16*ajtmp[j];
1634       x[0]  = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = x[9] = 0.0;
1635       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
1636     }
1637     /* load in initial (unfactored row) */
1638     idx      = r[i];
1639     nz       = ai[idx+1] - ai[idx];
1640     ajtmpold = aj + ai[idx];
1641     v        = aa + 16*ai[idx];
1642     for (j=0; j<nz; j++) {
1643       x    = rtmp+16*ic[ajtmpold[j]];
1644       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
1645       x[4]  = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
1646       x[9]  = v[9];  x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
1647       x[14] = v[14]; x[15] = v[15];
1648       v    += 16;
1649     }
1650     row = *ajtmp++;
1651     while (row < i) {
1652       pc  = rtmp + 16*row;
1653       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
1654       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
1655       p10 = pc[9];  p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
1656       p15 = pc[14]; p16 = pc[15];
1657       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
1658           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
1659           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
1660           || p16 != 0.0) {
1661         pv = ba + 16*diag_offset[row];
1662         pj = bj + diag_offset[row] + 1;
1663         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
1664         x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
1665         x10 = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
1666         x15 = pv[14]; x16 = pv[15];
1667         pc[0] = m1 = p1*x1 + p5*x2  + p9*x3  + p13*x4;
1668         pc[1] = m2 = p2*x1 + p6*x2  + p10*x3 + p14*x4;
1669         pc[2] = m3 = p3*x1 + p7*x2  + p11*x3 + p15*x4;
1670         pc[3] = m4 = p4*x1 + p8*x2  + p12*x3 + p16*x4;
1671 
1672         pc[4] = m5 = p1*x5 + p5*x6  + p9*x7  + p13*x8;
1673         pc[5] = m6 = p2*x5 + p6*x6  + p10*x7 + p14*x8;
1674         pc[6] = m7 = p3*x5 + p7*x6  + p11*x7 + p15*x8;
1675         pc[7] = m8 = p4*x5 + p8*x6  + p12*x7 + p16*x8;
1676 
1677         pc[8]  = m9  = p1*x9 + p5*x10  + p9*x11  + p13*x12;
1678         pc[9]  = m10 = p2*x9 + p6*x10  + p10*x11 + p14*x12;
1679         pc[10] = m11 = p3*x9 + p7*x10  + p11*x11 + p15*x12;
1680         pc[11] = m12 = p4*x9 + p8*x10  + p12*x11 + p16*x12;
1681 
1682         pc[12] = m13 = p1*x13 + p5*x14  + p9*x15  + p13*x16;
1683         pc[13] = m14 = p2*x13 + p6*x14  + p10*x15 + p14*x16;
1684         pc[14] = m15 = p3*x13 + p7*x14  + p11*x15 + p15*x16;
1685         pc[15] = m16 = p4*x13 + p8*x14  + p12*x15 + p16*x16;
1686 
1687         nz = bi[row+1] - diag_offset[row] - 1;
1688         pv += 16;
1689         for (j=0; j<nz; j++) {
1690           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
1691           x5   = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
1692           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
1693           x14  = pv[13]; x15 = pv[14]; x16 = pv[15];
1694           x    = rtmp + 16*pj[j];
1695           x[0] -= m1*x1 + m5*x2  + m9*x3  + m13*x4;
1696           x[1] -= m2*x1 + m6*x2  + m10*x3 + m14*x4;
1697           x[2] -= m3*x1 + m7*x2  + m11*x3 + m15*x4;
1698           x[3] -= m4*x1 + m8*x2  + m12*x3 + m16*x4;
1699 
1700           x[4] -= m1*x5 + m5*x6  + m9*x7  + m13*x8;
1701           x[5] -= m2*x5 + m6*x6  + m10*x7 + m14*x8;
1702           x[6] -= m3*x5 + m7*x6  + m11*x7 + m15*x8;
1703           x[7] -= m4*x5 + m8*x6  + m12*x7 + m16*x8;
1704 
1705           x[8]  -= m1*x9 + m5*x10 + m9*x11  + m13*x12;
1706           x[9]  -= m2*x9 + m6*x10 + m10*x11 + m14*x12;
1707           x[10] -= m3*x9 + m7*x10 + m11*x11 + m15*x12;
1708           x[11] -= m4*x9 + m8*x10 + m12*x11 + m16*x12;
1709 
1710           x[12] -= m1*x13 + m5*x14  + m9*x15  + m13*x16;
1711           x[13] -= m2*x13 + m6*x14  + m10*x15 + m14*x16;
1712           x[14] -= m3*x13 + m7*x14  + m11*x15 + m15*x16;
1713           x[15] -= m4*x13 + m8*x14  + m12*x15 + m16*x16;
1714 
1715           pv   += 16;
1716         }
1717         PLogFlops(128*nz+112);
1718       }
1719       row = *ajtmp++;
1720     }
1721     /* finished row so stick it into b->a */
1722     pv = ba + 16*bi[i];
1723     pj = bj + bi[i];
1724     nz = bi[i+1] - bi[i];
1725     for (j=0; j<nz; j++) {
1726       x      = rtmp+16*pj[j];
1727       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
1728       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
1729       pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
1730       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
1731       pv   += 16;
1732     }
1733     /* invert diagonal block */
1734     w = ba + 16*diag_offset[i];
1735     ierr = Kernel_A_gets_inverse_A_4(w);CHKERRQ(ierr);
1736   }
1737 
1738   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1739   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
1740   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
1741   C->factor = FACTOR_LU;
1742   C->assembled = PETSC_TRUE;
1743   PLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */
1744   PetscFunctionReturn(0);
1745 }
1746 /*
1747       Version for when blocks are 4 by 4 Using natural ordering
1748 */
1749 #undef __FUNC__
1750 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_4_NaturalOrdering"
1751 int MatCholeskyFactorNumeric_SeqSBAIJ_4_NaturalOrdering(Mat A,Mat *B)
1752 {
1753   Mat         C = *B;
1754   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
1755   int         ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
1756   int         *ajtmpold,*ajtmp,nz,row;
1757   int         *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
1758   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
1759   MatScalar   p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
1760   MatScalar   p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
1761   MatScalar   p10,p11,p12,p13,p14,p15,p16,m10,m11,m12;
1762   MatScalar   m13,m14,m15,m16;
1763   MatScalar   *ba = b->a,*aa = a->a;
1764 
1765   PetscFunctionBegin;
1766   rtmp  = (MatScalar*)PetscMalloc(16*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
1767 
1768   for (i=0; i<n; i++) {
1769     nz    = bi[i+1] - bi[i];
1770     ajtmp = bj + bi[i];
1771     for  (j=0; j<nz; j++) {
1772       x = rtmp+16*ajtmp[j];
1773       x[0]  = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = x[9] = 0.0;
1774       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
1775     }
1776     /* load in initial (unfactored row) */
1777     nz       = ai[i+1] - ai[i];
1778     ajtmpold = aj + ai[i];
1779     v        = aa + 16*ai[i];
1780     for (j=0; j<nz; j++) {
1781       x    = rtmp+16*ajtmpold[j];
1782       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
1783       x[4]  = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
1784       x[9]  = v[9];  x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
1785       x[14] = v[14]; x[15] = v[15];
1786       v    += 16;
1787     }
1788     row = *ajtmp++;
1789     while (row < i) {
1790       pc  = rtmp + 16*row;
1791       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
1792       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
1793       p10 = pc[9];  p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
1794       p15 = pc[14]; p16 = pc[15];
1795       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
1796           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
1797           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
1798           || p16 != 0.0) {
1799         pv = ba + 16*diag_offset[row];
1800         pj = bj + diag_offset[row] + 1;
1801         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
1802         x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
1803         x10 = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
1804         x15 = pv[14]; x16 = pv[15];
1805         pc[0] = m1 = p1*x1 + p5*x2  + p9*x3  + p13*x4;
1806         pc[1] = m2 = p2*x1 + p6*x2  + p10*x3 + p14*x4;
1807         pc[2] = m3 = p3*x1 + p7*x2  + p11*x3 + p15*x4;
1808         pc[3] = m4 = p4*x1 + p8*x2  + p12*x3 + p16*x4;
1809 
1810         pc[4] = m5 = p1*x5 + p5*x6  + p9*x7  + p13*x8;
1811         pc[5] = m6 = p2*x5 + p6*x6  + p10*x7 + p14*x8;
1812         pc[6] = m7 = p3*x5 + p7*x6  + p11*x7 + p15*x8;
1813         pc[7] = m8 = p4*x5 + p8*x6  + p12*x7 + p16*x8;
1814 
1815         pc[8]  = m9  = p1*x9 + p5*x10  + p9*x11  + p13*x12;
1816         pc[9]  = m10 = p2*x9 + p6*x10  + p10*x11 + p14*x12;
1817         pc[10] = m11 = p3*x9 + p7*x10  + p11*x11 + p15*x12;
1818         pc[11] = m12 = p4*x9 + p8*x10  + p12*x11 + p16*x12;
1819 
1820         pc[12] = m13 = p1*x13 + p5*x14  + p9*x15  + p13*x16;
1821         pc[13] = m14 = p2*x13 + p6*x14  + p10*x15 + p14*x16;
1822         pc[14] = m15 = p3*x13 + p7*x14  + p11*x15 + p15*x16;
1823         pc[15] = m16 = p4*x13 + p8*x14  + p12*x15 + p16*x16;
1824 
1825         nz = bi[row+1] - diag_offset[row] - 1;
1826         pv += 16;
1827         for (j=0; j<nz; j++) {
1828           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
1829           x5   = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
1830           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
1831           x14  = pv[13]; x15 = pv[14]; x16 = pv[15];
1832           x    = rtmp + 16*pj[j];
1833           x[0] -= m1*x1 + m5*x2  + m9*x3  + m13*x4;
1834           x[1] -= m2*x1 + m6*x2  + m10*x3 + m14*x4;
1835           x[2] -= m3*x1 + m7*x2  + m11*x3 + m15*x4;
1836           x[3] -= m4*x1 + m8*x2  + m12*x3 + m16*x4;
1837 
1838           x[4] -= m1*x5 + m5*x6  + m9*x7  + m13*x8;
1839           x[5] -= m2*x5 + m6*x6  + m10*x7 + m14*x8;
1840           x[6] -= m3*x5 + m7*x6  + m11*x7 + m15*x8;
1841           x[7] -= m4*x5 + m8*x6  + m12*x7 + m16*x8;
1842 
1843           x[8]  -= m1*x9 + m5*x10 + m9*x11  + m13*x12;
1844           x[9]  -= m2*x9 + m6*x10 + m10*x11 + m14*x12;
1845           x[10] -= m3*x9 + m7*x10 + m11*x11 + m15*x12;
1846           x[11] -= m4*x9 + m8*x10 + m12*x11 + m16*x12;
1847 
1848           x[12] -= m1*x13 + m5*x14  + m9*x15  + m13*x16;
1849           x[13] -= m2*x13 + m6*x14  + m10*x15 + m14*x16;
1850           x[14] -= m3*x13 + m7*x14  + m11*x15 + m15*x16;
1851           x[15] -= m4*x13 + m8*x14  + m12*x15 + m16*x16;
1852 
1853           pv   += 16;
1854         }
1855         PLogFlops(128*nz+112);
1856       }
1857       row = *ajtmp++;
1858     }
1859     /* finished row so stick it into b->a */
1860     pv = ba + 16*bi[i];
1861     pj = bj + bi[i];
1862     nz = bi[i+1] - bi[i];
1863     for (j=0; j<nz; j++) {
1864       x      = rtmp+16*pj[j];
1865       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
1866       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
1867       pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
1868       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
1869       pv   += 16;
1870     }
1871     /* invert diagonal block */
1872     w = ba + 16*diag_offset[i];
1873     ierr = Kernel_A_gets_inverse_A_4(w);CHKERRQ(ierr);
1874   }
1875 
1876   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1877   C->factor    = FACTOR_LU;
1878   C->assembled = PETSC_TRUE;
1879   PLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */
1880   PetscFunctionReturn(0);
1881 }
1882 
1883 /*
1884       Version for when blocks are 3 by 3
1885 */
1886 #undef __FUNC__
1887 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_3"
1888 int MatCholeskyFactorNumeric_SeqSBAIJ_3(Mat A,Mat *B)
1889 {
1890   Mat         C = *B;
1891   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
1892   IS          isrow = b->row,isicol = b->icol;
1893   int         *r,*ic,ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
1894   int         *ajtmpold,*ajtmp,nz,row,*ai=a->i,*aj=a->j;
1895   int         *diag_offset = b->diag,idx,*pj;
1896   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
1897   MatScalar   p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
1898   MatScalar   p5,p6,p7,p8,p9,x5,x6,x7,x8,x9;
1899   MatScalar   *ba = b->a,*aa = a->a;
1900 
1901   PetscFunctionBegin;
1902   ierr  = ISGetIndices(isrow,&r);CHKERRQ(ierr);
1903   ierr  = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
1904   rtmp  = (MatScalar*)PetscMalloc(9*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
1905 
1906   for (i=0; i<n; i++) {
1907     nz    = bi[i+1] - bi[i];
1908     ajtmp = bj + bi[i];
1909     for  (j=0; j<nz; j++) {
1910       x = rtmp + 9*ajtmp[j];
1911       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = 0.0;
1912     }
1913     /* load in initial (unfactored row) */
1914     idx      = r[i];
1915     nz       = ai[idx+1] - ai[idx];
1916     ajtmpold = aj + ai[idx];
1917     v        = aa + 9*ai[idx];
1918     for (j=0; j<nz; j++) {
1919       x    = rtmp + 9*ic[ajtmpold[j]];
1920       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
1921       x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
1922       v    += 9;
1923     }
1924     row = *ajtmp++;
1925     while (row < i) {
1926       pc = rtmp + 9*row;
1927       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
1928       p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
1929       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
1930           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0) {
1931         pv = ba + 9*diag_offset[row];
1932         pj = bj + diag_offset[row] + 1;
1933         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
1934         x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
1935         pc[0] = m1 = p1*x1 + p4*x2 + p7*x3;
1936         pc[1] = m2 = p2*x1 + p5*x2 + p8*x3;
1937         pc[2] = m3 = p3*x1 + p6*x2 + p9*x3;
1938 
1939         pc[3] = m4 = p1*x4 + p4*x5 + p7*x6;
1940         pc[4] = m5 = p2*x4 + p5*x5 + p8*x6;
1941         pc[5] = m6 = p3*x4 + p6*x5 + p9*x6;
1942 
1943         pc[6] = m7 = p1*x7 + p4*x8 + p7*x9;
1944         pc[7] = m8 = p2*x7 + p5*x8 + p8*x9;
1945         pc[8] = m9 = p3*x7 + p6*x8 + p9*x9;
1946         nz = bi[row+1] - diag_offset[row] - 1;
1947         pv += 9;
1948         for (j=0; j<nz; j++) {
1949           x1   = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
1950           x5   = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
1951           x    = rtmp + 9*pj[j];
1952           x[0] -= m1*x1 + m4*x2 + m7*x3;
1953           x[1] -= m2*x1 + m5*x2 + m8*x3;
1954           x[2] -= m3*x1 + m6*x2 + m9*x3;
1955 
1956           x[3] -= m1*x4 + m4*x5 + m7*x6;
1957           x[4] -= m2*x4 + m5*x5 + m8*x6;
1958           x[5] -= m3*x4 + m6*x5 + m9*x6;
1959 
1960           x[6] -= m1*x7 + m4*x8 + m7*x9;
1961           x[7] -= m2*x7 + m5*x8 + m8*x9;
1962           x[8] -= m3*x7 + m6*x8 + m9*x9;
1963           pv   += 9;
1964         }
1965         PLogFlops(54*nz+36);
1966       }
1967       row = *ajtmp++;
1968     }
1969     /* finished row so stick it into b->a */
1970     pv = ba + 9*bi[i];
1971     pj = bj + bi[i];
1972     nz = bi[i+1] - bi[i];
1973     for (j=0; j<nz; j++) {
1974       x     = rtmp + 9*pj[j];
1975       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
1976       pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
1977       pv   += 9;
1978     }
1979     /* invert diagonal block */
1980     w = ba + 9*diag_offset[i];
1981     ierr = Kernel_A_gets_inverse_A_3(w);CHKERRQ(ierr);
1982   }
1983 
1984   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1985   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
1986   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
1987   C->factor = FACTOR_LU;
1988   C->assembled = PETSC_TRUE;
1989   PLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */
1990   PetscFunctionReturn(0);
1991 }
1992 /*
1993       Version for when blocks are 3 by 3 Using natural ordering
1994 */
1995 #undef __FUNC__
1996 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_3_NaturalOrdering"
1997 int MatCholeskyFactorNumeric_SeqSBAIJ_3_NaturalOrdering(Mat A,Mat *B)
1998 {
1999   Mat                C = *B;
2000   Mat_SeqBAIJ        *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
2001   int                ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
2002   int                *ajtmpold,*ajtmp,nz,row;
2003   int                *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
2004   MatScalar          *pv,*v,*rtmp,*pc,*w,*x;
2005   MatScalar          p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
2006   MatScalar          p5,p6,p7,p8,p9,x5,x6,x7,x8,x9;
2007   MatScalar          *ba = b->a,*aa = a->a;
2008 
2009   PetscFunctionBegin;
2010   rtmp  = (MatScalar*)PetscMalloc(9*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
2011 
2012   for (i=0; i<n; i++) {
2013     nz    = bi[i+1] - bi[i];
2014     ajtmp = bj + bi[i];
2015     for  (j=0; j<nz; j++) {
2016       x = rtmp+9*ajtmp[j];
2017       x[0]  = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = 0.0;
2018     }
2019     /* load in initial (unfactored row) */
2020     nz       = ai[i+1] - ai[i];
2021     ajtmpold = aj + ai[i];
2022     v        = aa + 9*ai[i];
2023     for (j=0; j<nz; j++) {
2024       x    = rtmp+9*ajtmpold[j];
2025       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
2026       x[4]  = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
2027       v    += 9;
2028     }
2029     row = *ajtmp++;
2030     while (row < i) {
2031       pc  = rtmp + 9*row;
2032       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
2033       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
2034       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
2035           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0) {
2036         pv = ba + 9*diag_offset[row];
2037         pj = bj + diag_offset[row] + 1;
2038         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
2039         x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
2040         pc[0] = m1 = p1*x1 + p4*x2 + p7*x3;
2041         pc[1] = m2 = p2*x1 + p5*x2 + p8*x3;
2042         pc[2] = m3 = p3*x1 + p6*x2 + p9*x3;
2043 
2044         pc[3] = m4 = p1*x4 + p4*x5 + p7*x6;
2045         pc[4] = m5 = p2*x4 + p5*x5 + p8*x6;
2046         pc[5] = m6 = p3*x4 + p6*x5 + p9*x6;
2047 
2048         pc[6] = m7 = p1*x7 + p4*x8 + p7*x9;
2049         pc[7] = m8 = p2*x7 + p5*x8 + p8*x9;
2050         pc[8] = m9 = p3*x7 + p6*x8 + p9*x9;
2051 
2052         nz = bi[row+1] - diag_offset[row] - 1;
2053         pv += 9;
2054         for (j=0; j<nz; j++) {
2055           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
2056           x5   = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
2057           x    = rtmp + 9*pj[j];
2058           x[0] -= m1*x1 + m4*x2 + m7*x3;
2059           x[1] -= m2*x1 + m5*x2 + m8*x3;
2060           x[2] -= m3*x1 + m6*x2 + m9*x3;
2061 
2062           x[3] -= m1*x4 + m4*x5 + m7*x6;
2063           x[4] -= m2*x4 + m5*x5 + m8*x6;
2064           x[5] -= m3*x4 + m6*x5 + m9*x6;
2065 
2066           x[6] -= m1*x7 + m4*x8 + m7*x9;
2067           x[7] -= m2*x7 + m5*x8 + m8*x9;
2068           x[8] -= m3*x7 + m6*x8 + m9*x9;
2069           pv   += 9;
2070         }
2071         PLogFlops(54*nz+36);
2072       }
2073       row = *ajtmp++;
2074     }
2075     /* finished row so stick it into b->a */
2076     pv = ba + 9*bi[i];
2077     pj = bj + bi[i];
2078     nz = bi[i+1] - bi[i];
2079     for (j=0; j<nz; j++) {
2080       x      = rtmp+9*pj[j];
2081       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
2082       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
2083       pv   += 9;
2084     }
2085     /* invert diagonal block */
2086     w = ba + 9*diag_offset[i];
2087     ierr = Kernel_A_gets_inverse_A_3(w);CHKERRQ(ierr);
2088   }
2089 
2090   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2091   C->factor    = FACTOR_LU;
2092   C->assembled = PETSC_TRUE;
2093   PLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */
2094   PetscFunctionReturn(0);
2095 }
2096 
2097 /*
2098       Version for when blocks are 2 by 2
2099 */
2100 #undef __FUNC__
2101 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_2"
2102 int MatCholeskyFactorNumeric_SeqSBAIJ_2(Mat A,Mat *B)
2103 {
2104   Mat                C = *B;
2105   Mat_SeqBAIJ        *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
2106   IS                 isrow = b->row,isicol = b->icol;
2107   int                *r,*ic,ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
2108   int                *ajtmpold,*ajtmp,nz,row;
2109   int                *diag_offset=b->diag,idx,*ai=a->i,*aj=a->j,*pj;
2110   MatScalar          *pv,*v,*rtmp,m1,m2,m3,m4,*pc,*w,*x,x1,x2,x3,x4;
2111   MatScalar          p1,p2,p3,p4;
2112   MatScalar          *ba = b->a,*aa = a->a;
2113 
2114   PetscFunctionBegin;
2115   ierr  = ISGetIndices(isrow,&r);CHKERRQ(ierr);
2116   ierr  = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
2117   rtmp  = (MatScalar*)PetscMalloc(4*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
2118 
2119   for (i=0; i<n; i++) {
2120     nz    = bi[i+1] - bi[i];
2121     ajtmp = bj + bi[i];
2122     for  (j=0; j<nz; j++) {
2123       x = rtmp+4*ajtmp[j]; x[0] = x[1] = x[2] = x[3] = 0.0;
2124     }
2125     /* load in initial (unfactored row) */
2126     idx      = r[i];
2127     nz       = ai[idx+1] - ai[idx];
2128     ajtmpold = aj + ai[idx];
2129     v        = aa + 4*ai[idx];
2130     for (j=0; j<nz; j++) {
2131       x    = rtmp+4*ic[ajtmpold[j]];
2132       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
2133       v    += 4;
2134     }
2135     row = *ajtmp++;
2136     while (row < i) {
2137       pc = rtmp + 4*row;
2138       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
2139       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0) {
2140         pv = ba + 4*diag_offset[row];
2141         pj = bj + diag_offset[row] + 1;
2142         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
2143         pc[0] = m1 = p1*x1 + p3*x2;
2144         pc[1] = m2 = p2*x1 + p4*x2;
2145         pc[2] = m3 = p1*x3 + p3*x4;
2146         pc[3] = m4 = p2*x3 + p4*x4;
2147         nz = bi[row+1] - diag_offset[row] - 1;
2148         pv += 4;
2149         for (j=0; j<nz; j++) {
2150           x1   = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
2151           x    = rtmp + 4*pj[j];
2152           x[0] -= m1*x1 + m3*x2;
2153           x[1] -= m2*x1 + m4*x2;
2154           x[2] -= m1*x3 + m3*x4;
2155           x[3] -= m2*x3 + m4*x4;
2156           pv   += 4;
2157         }
2158         PLogFlops(16*nz+12);
2159       }
2160       row = *ajtmp++;
2161     }
2162     /* finished row so stick it into b->a */
2163     pv = ba + 4*bi[i];
2164     pj = bj + bi[i];
2165     nz = bi[i+1] - bi[i];
2166     for (j=0; j<nz; j++) {
2167       x     = rtmp+4*pj[j];
2168       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
2169       pv   += 4;
2170     }
2171     /* invert diagonal block */
2172     w = ba + 4*diag_offset[i];
2173     ierr = Kernel_A_gets_inverse_A_2(w);CHKERRQ(ierr);
2174     /*Kernel_A_gets_inverse_A(bs,w,v_pivots,v_work);*/
2175   }
2176 
2177   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2178   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
2179   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
2180   C->factor = FACTOR_LU;
2181   C->assembled = PETSC_TRUE;
2182   PLogFlops(1.3333*8*b->mbs); /* from inverting diagonal blocks */
2183   PetscFunctionReturn(0);
2184 }
2185 /*
2186       Version for when blocks are 2 by 2 Using natural ordering
2187 */
2188 #undef __FUNC__
2189 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_2_NaturalOrdering"
2190 int MatCholeskyFactorNumeric_SeqSBAIJ_2_NaturalOrdering(Mat A,Mat *B)
2191 {
2192   Mat                C = *B;
2193   Mat_SeqBAIJ        *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
2194   int                ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
2195   int                *ajtmpold,*ajtmp,nz,row;
2196   int                *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
2197   MatScalar          *pv,*v,*rtmp,*pc,*w,*x;
2198   MatScalar          p1,p2,p3,p4,m1,m2,m3,m4,x1,x2,x3,x4;
2199   MatScalar          *ba = b->a,*aa = a->a;
2200 
2201   PetscFunctionBegin;
2202   rtmp  = (MatScalar*)PetscMalloc(4*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
2203 
2204   for (i=0; i<n; i++) {
2205     nz    = bi[i+1] - bi[i];
2206     ajtmp = bj + bi[i];
2207     for  (j=0; j<nz; j++) {
2208       x = rtmp+4*ajtmp[j];
2209       x[0]  = x[1]  = x[2]  = x[3]  = 0.0;
2210     }
2211     /* load in initial (unfactored row) */
2212     nz       = ai[i+1] - ai[i];
2213     ajtmpold = aj + ai[i];
2214     v        = aa + 4*ai[i];
2215     for (j=0; j<nz; j++) {
2216       x    = rtmp+4*ajtmpold[j];
2217       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
2218       v    += 4;
2219     }
2220     row = *ajtmp++;
2221     while (row < i) {
2222       pc  = rtmp + 4*row;
2223       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
2224       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0) {
2225         pv = ba + 4*diag_offset[row];
2226         pj = bj + diag_offset[row] + 1;
2227         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
2228         pc[0] = m1 = p1*x1 + p3*x2;
2229         pc[1] = m2 = p2*x1 + p4*x2;
2230         pc[2] = m3 = p1*x3 + p3*x4;
2231         pc[3] = m4 = p2*x3 + p4*x4;
2232         nz = bi[row+1] - diag_offset[row] - 1;
2233         pv += 4;
2234         for (j=0; j<nz; j++) {
2235           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
2236           x    = rtmp + 4*pj[j];
2237           x[0] -= m1*x1 + m3*x2;
2238           x[1] -= m2*x1 + m4*x2;
2239           x[2] -= m1*x3 + m3*x4;
2240           x[3] -= m2*x3 + m4*x4;
2241           pv   += 4;
2242         }
2243         PLogFlops(16*nz+12);
2244       }
2245       row = *ajtmp++;
2246     }
2247     /* finished row so stick it into b->a */
2248     pv = ba + 4*bi[i];
2249     pj = bj + bi[i];
2250     nz = bi[i+1] - bi[i];
2251     for (j=0; j<nz; j++) {
2252       x      = rtmp+4*pj[j];
2253       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
2254       pv   += 4;
2255     }
2256     /* invert diagonal block */
2257     w = ba + 4*diag_offset[i];
2258     ierr = Kernel_A_gets_inverse_A_2(w);CHKERRQ(ierr);
2259     /*Kernel_A_gets_inverse_A(bs,w,v_pivots,v_work);*/
2260   }
2261 
2262   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2263   C->factor    = FACTOR_LU;
2264   C->assembled = PETSC_TRUE;
2265   PLogFlops(1.3333*8*b->mbs); /* from inverting diagonal blocks */
2266   PetscFunctionReturn(0);
2267 }
2268 
2269 /*
2270      Version for when blocks are 1 by 1.
2271 */
2272 #undef __FUNC__
2273 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_1"
2274 int MatCholeskyFactorNumeric_SeqSBAIJ_1(Mat A,Mat *B)
2275 {
2276   Mat                C = *B;
2277   Mat_SeqSBAIJ       *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data;
2278   IS                 ip = b->row;
2279   int                *rip,*riip,ierr,i,j,mbs = a->mbs,*bi = b->i,*bj = b->j;
2280   int                *ai = a->i,*aj = a->j;
2281   MatScalar          *rtmp;
2282   MatScalar          *ba = b->a,*aa = a->a;
2283   MatScalar          dk,uikdi;
2284   int                k,jmin,jmax,*jl,*il,vj,nexti,juj,ili;
2285 
2286   PetscFunctionBegin;
2287   ierr  = ISGetIndices(ip,&rip);CHKERRQ(ierr);
2288   riip = rip;
2289 
2290   /* INITIALIZATION */
2291   /* il and jl record the first nonzero element in each row of the accessing
2292      window U(0:k, k:mbs-1).
2293      jl:    list of rows to be added to uneliminated rows
2294             i>= k: jl(i) is the first row to be added to row i
2295             i<  k: jl(i) is the row following row i in some list of rows
2296             jl(i) = mbs indicates the end of a list
2297      il(i): points to the first nonzero element in columns k,...,mbs-1 of
2298             row i of U */
2299   rtmp  = (MatScalar*)PetscMalloc(mbs*sizeof(MatScalar));CHKPTRQ(rtmp);
2300   il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il);
2301   jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl);
2302   for (i=0; i<mbs; i++) {
2303     rtmp[i] = 0.0; jl[i] = mbs; il[0] = 0;
2304   }
2305 
2306   /* FOR EACH ROW K */
2307   for (k = 0; k<mbs; k++){
2308 
2309     /* INITIALIZE K-TH ROW WITH ELEMENTS NONZERO IN ROW P(K) OF A */
2310     jmin = ai[rip[k]]; jmax = ai[rip[k]+1];
2311     if (jmin < jmax) {
2312       for (j = jmin; j < jmax; j++){
2313         vj = riip[aj[j]];
2314         if (k <= vj) rtmp[vj] = aa[j];
2315       }
2316     }
2317 
2318     /* MODIFY K-TH ROW BY ADDING IN THOSE ROWS I WITH U(I,K) NE 0
2319        FOR EACH ROW I TO BE ADDED IN */
2320     dk = rtmp[k];
2321     i = jl[k]; /* first row to be added to k_th row  */
2322     /* printf(" k=%d, pivot row = %d\n",k,i); */
2323 
2324     while (i < mbs){
2325       nexti = jl[i]; /* next row to be added to k_th row */
2326       /* printf("      pivot row = %d\n", nexti); */
2327 
2328       /* COMPUTE MULTIPLIER AND UPDATE DIAGONAL ELEMENT */
2329       ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
2330       uikdi = - ba[ili]*ba[i];
2331       dk += uikdi*ba[ili];
2332       ba[ili] = uikdi; /* update U(i,k) */
2333 
2334       /* ADD MULTIPLE OF ROW I TO K-TH ROW ... */
2335       jmin = ili + 1; jmax = bi[i+1];
2336       if (jmin < jmax){
2337         for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j];
2338         /* ... AND ADD I TO ROW LIST FOR NEXT NONZERO ENTRY */
2339          il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
2340          j     = bj[jmin];
2341          jl[i] = jl[j]; jl[j] = i; /* update jl */
2342       }
2343       i = nexti;
2344       /* printf("                  pivot row i=%d\n",i);  */
2345     }
2346 
2347     /* CHECK FOR ZERO PIVOT AND SAVE DIAGONAL ELEMENT */
2348     if (dk == 0.0){
2349       SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,0,"Zero pivot");
2350     }
2351 
2352     /* SAVE NONZERO ENTRIES IN K-TH ROW OF U ... */
2353     ba[k] = 1.0/dk;
2354     jmin = bi[k]; jmax = bi[k+1];
2355     if (jmin < jmax) {
2356       for (j=jmin; j<jmax; j++){
2357          juj = bj[j]; ba[j] = rtmp[juj]; rtmp[juj] = 0.0;
2358       }
2359 
2360       /* ... AND ADD K TO ROW LIST FOR FIRST NONZERO ENTRY IN K-TH ROW */
2361       il[k] = jmin;
2362       i     = bj[jmin];
2363       jl[k] = jl[i]; jl[i] = k;
2364     }
2365   }
2366 
2367   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2368   ierr = PetscFree(il);CHKERRQ(ierr);
2369   ierr = PetscFree(jl);CHKERRQ(ierr);
2370 
2371   ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr);
2372   C->factor    = FACTOR_LU;
2373   C->assembled = PETSC_TRUE;
2374   PLogFlops(b->mbs);
2375   PetscFunctionReturn(0);
2376 }
2377 
2378 #undef __FUNC__
2379 #define __FUNC__ "MatCholeskyFactor_SeqSBAIJ"
2380 int MatCholeskyFactor_SeqSBAIJ(Mat A,IS perm,PetscReal f)
2381 {
2382   Mat_SeqSBAIJ    *mat = (Mat_SeqSBAIJ*)A->data;
2383   int            ierr,refct;
2384   Mat            C;
2385   PetscOps *Abops;
2386   MatOps   Aops;
2387 
2388   PetscFunctionBegin;
2389   ierr = MatCholeskyFactorSymbolic(A,perm,f,&C);CHKERRQ(ierr);
2390   ierr = MatCholeskyFactorNumeric(A,&C);CHKERRQ(ierr);
2391 
2392   /* free all the data structures from mat */
2393   ierr = PetscFree(mat->a);CHKERRQ(ierr);
2394   if (!mat->singlemalloc) {
2395     ierr = PetscFree(mat->i);CHKERRQ(ierr);
2396     ierr = PetscFree(mat->j);CHKERRQ(ierr);
2397   }
2398   if (mat->diag) {ierr = PetscFree(mat->diag);CHKERRQ(ierr);}
2399   if (mat->ilen) {ierr = PetscFree(mat->ilen);CHKERRQ(ierr);}
2400   if (mat->imax) {ierr = PetscFree(mat->imax);CHKERRQ(ierr);}
2401   if (mat->solve_work) {ierr = PetscFree(mat->solve_work);CHKERRQ(ierr);}
2402   if (mat->mult_work) {ierr = PetscFree(mat->mult_work);CHKERRQ(ierr);}
2403   if (mat->icol) {ierr = ISDestroy(mat->icol);CHKERRQ(ierr);}
2404   ierr = PetscFree(mat);CHKERRQ(ierr);
2405 
2406   ierr = MapDestroy(A->rmap);CHKERRQ(ierr);
2407   ierr = MapDestroy(A->cmap);CHKERRQ(ierr);
2408 
2409   /*
2410        This is horrible,horrible code. We need to keep the
2411     A pointers for the bops and ops but copy everything
2412     else from C.
2413   */
2414   Abops = A->bops;
2415   Aops  = A->ops;
2416   refct = A->refct;
2417   ierr  = PetscMemcpy(A,C,sizeof(struct _p_Mat));CHKERRQ(ierr);
2418   mat   = (Mat_SeqSBAIJ*)A->data;
2419   PLogObjectParent(A,mat->icol);
2420 
2421   A->bops  = Abops;
2422   A->ops   = Aops;
2423   A->qlist = 0;
2424   A->refct = refct;
2425   /* copy over the type_name and name */
2426   ierr     = PetscStrallocpy(C->type_name,&A->type_name);CHKERRQ(ierr);
2427   ierr     = PetscStrallocpy(C->name,&A->name);CHKERRQ(ierr);
2428 
2429   PetscHeaderDestroy(C);
2430   PetscFunctionReturn(0);
2431 }
2432 
2433 
2434