xref: /petsc/src/mat/impls/sbaij/seq/sbaijfact.c (revision 9860f2b2bd85261ba9e18b0aa847f58df91754e2)
1 /* Using Modified Sparse Row (MSR) storage.
2 See page 85, "Iterative Methods ..." by Saad. */
3 
4 /*$Id: sbaijfact.c,v 1.15 2000/09/11 15:02:08 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,*aj;
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   PetscTruth flg_perm = PETSC_FALSE; /* non-trivial permutation */
26 
27   PetscFunctionBegin;
28   PetscValidHeaderSpecific(perm,IS_COOKIE);
29   if (A->M != A->N) SETERRQ(PETSC_ERR_ARG_WRONG,0,"matrix must be square");
30 
31 #ifdef ISIdentity
32   ierr = ISIdentity(perm,ident);CHKERRQ(ierr);
33   if (!*ident) { /* for a non-trivial perm, the matrix A in SBAIJ format needs to be
34                    re-indexed so that A(perm(i),iperm(k)) is stored in the upper
35                    triangle. */
36     SETERRQ(PETSC_ERR_ARG_CORRUPT,0,"Call MatReIndexingSeqSBAIJ() to re-indexing (ai,aj,a)");
37   }
38 #endif
39 
40   if (!flg_perm){ /* no permutation */
41     ai = a->i; aj = a->j;
42   } else {       /* non-trivial permutation */
43     /*
44     printf("2, called symbolic factor\n");
45     ierr = ISView(perm, VIEWER_STDOUT_SELF);CHKERRA(ierr);
46     */
47     ierr = MatReorderingSeqSBAIJ(A, perm);CHKERRA(ierr);
48     /* a = (Mat_SeqSBAIJ*)A->data; */
49 
50     ai = a->inew; aj = a->jnew;
51     printf("ainew= %d %d \n",a->inew[0],a->inew[mbs]);
52     printf("ajnew=%d %d\n",a->jnew[0],a->jnew[a->i[mbs]-1]);
53   }
54 
55   ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr);
56   ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
57   ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr);
58 
59   /* initialization */
60   /* Don't know how many column pointers are needed so estimate.
61      Use Modified Sparse Row storage for u and ju, see Sasd pp.85 */
62   iu   = (int*)PetscMalloc((mbs+1)*sizeof(int));CHKPTRQ(iu);
63   umax = (int)(f*ai[mbs] + 1); umax += mbs + 1;
64   ju   = (int*)PetscMalloc(umax*sizeof(int));CHKPTRQ(ju);
65   iu[0] = mbs+1;
66   juptr = mbs;
67   jl =  (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl);
68   q  =  (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(q);
69   for (i=0; i<mbs; i++){
70     jl[i] = mbs; q[i] = 0;
71   }
72 
73   /* for each row k */
74   for (k=0; k<mbs; k++){
75     nzk = 0; /* num. of nz blocks in k-th block row with diagonal block excluded */
76     q[k] = mbs;
77     /* initialize nonzero structure of k-th row to row rip[k] of A */
78     jmin = ai[rip[k]];
79     jmax = ai[rip[k]+1];
80     for (j=jmin; j<jmax; j++){
81       vj = riip[aj[j]]; /* col. value */
82       if(vj > k){
83         qm = k;
84         do {
85           m  = qm; qm = q[m];
86         } while(qm < vj);
87         if (qm == vj) {
88           printf(" error: duplicate entry in A\n"); break;
89         }
90         nzk++;
91         q[m] = vj;
92         q[vj] = qm;
93       } /* if(vj > k) */
94     } /* for (j=jmin; j<jmax; j++) */
95 
96     /* modify nonzero structure of k-th row by computing fill-in
97        for each row i to be merged in */
98     i = k;
99     i = jl[i]; /* next pivot row (== mbs for symbolic factorization) */
100     /* printf(" next pivot row i=%d\n",i); */
101     while (i < mbs){
102       /* merge row i into k-th row */
103       nzi = iu[i+1] - (iu[i]+1);
104       jmin = iu[i] + 1; jmax = iu[i] + nzi;
105       qm = k;
106       for (j=jmin; j<jmax+1; j++){
107         vj = ju[j];
108         do {
109           m = qm; qm = q[m];
110         } while (qm < vj);
111         if (qm != vj){
112          nzk++; q[m] = vj; q[vj] = qm; qm = vj;
113         }
114       }
115       i = jl[i]; /* next pivot row */
116     }
117 
118     /* add k to row list for first nonzero element in k-th row */
119     if (nzk > 0){
120       i = q[k]; /* col value of first nonzero element in U(k, k+1:mbs-1) */
121       jl[k] = jl[i]; jl[i] = k;
122     }
123     iu[k+1] = iu[k] + nzk;   /* printf(" iu[%d]=%d, umax=%d\n", k+1, iu[k+1],umax);*/
124 
125     /* allocate more space to ju if needed */
126     if (iu[k+1] > umax) { printf("allocate more space, iu[%d]=%d > umax=%d\n",k+1, iu[k+1],umax);
127       /* estimate how much additional space we will need */
128       /* use the strategy suggested by David Hysom <hysom@perch-t.icase.edu> */
129       /* just double the memory each time */
130       maxadd = umax;
131       if (maxadd < nzk) maxadd = (mbs-k)*(nzk+1)/2;
132       umax += maxadd;
133 
134       /* allocate a longer ju */
135       jutmp = (int*)PetscMalloc(umax*sizeof(int));CHKPTRQ(jutmp);
136       ierr  = PetscMemcpy(jutmp,ju,iu[k]*sizeof(int));CHKERRQ(ierr);
137       ierr  = PetscFree(ju);CHKERRQ(ierr);
138       ju    = jutmp;
139       realloc++; /* count how many times we realloc */
140     }
141 
142     /* save nonzero structure of k-th row in ju */
143     i=k;
144     jumin = juptr + 1; juptr += nzk;
145     for (j=jumin; j<juptr+1; j++){
146       i=q[i];
147       ju[j]=i;
148     }
149   }
150 
151   if (ai[mbs] != 0) {
152     PetscReal af = ((PetscReal)iu[mbs])/((PetscReal)ai[mbs]);
153     PLogInfo(A,"MatCholeskyFactorSymbolic_SeqSBAIJ:Reallocs %d Fill ratio:given %g needed %g\n",realloc,f,af);
154     PLogInfo(A,"MatCholeskyFactorSymbolic_SeqSBAIJ:Run with -pc_lu_fill %g or use \n",af);
155     PLogInfo(A,"MatCholeskyFactorSymbolic_SeqSBAIJ:PCLUSetFill(pc,%g);\n",af);
156     PLogInfo(A,"MatCholeskyFactorSymbolic_SeqSBAIJ:for best performance.\n");
157   } else {
158      PLogInfo(A,"MatCholeskyFactorSymbolic_SeqSBAIJ:Empty matrix.\n");
159   }
160 
161   ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
162   ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr);
163 
164   ierr = PetscFree(q);CHKERRQ(ierr);
165   ierr = PetscFree(jl);CHKERRQ(ierr);
166 
167   /* put together the new matrix */
168   ierr = MatCreateSeqSBAIJ(A->comm,bs,bs*mbs,bs*mbs,0,PETSC_NULL,B);CHKERRQ(ierr);
169   PLogObjectParent(*B,iperm);
170   b = (Mat_SeqSBAIJ*)(*B)->data;
171   ierr = PetscFree(b->imax);CHKERRQ(ierr);
172   b->singlemalloc = PETSC_FALSE;
173   /* the next line frees the default space generated by the Create() */
174   ierr = PetscFree(b->a);CHKERRQ(ierr);
175   ierr = PetscFree(b->ilen);CHKERRQ(ierr);
176   b->a          = (MatScalar*)PetscMalloc((iu[mbs]+1)*sizeof(MatScalar)*bs2);CHKPTRQ(b->a);
177   b->j          = ju;
178   b->i          = iu;
179   b->diag       = 0;
180   b->ilen       = 0;
181   b->imax       = 0;
182   b->row        = perm;
183   ierr          = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
184   b->icol       = iperm;
185   b->solve_work = (Scalar*)PetscMalloc((bs*mbs+bs)*sizeof(Scalar));CHKPTRQ(b->solve_work);
186   /* In b structure:  Free imax, ilen, old a, old j.
187      Allocate idnew, solve_work, new a, new j */
188   PLogObjectMemory(*B,(iu[mbs]-mbs)*(sizeof(int)+sizeof(MatScalar)));
189   b->s_maxnz = b->s_nz = iu[mbs];
190 
191   (*B)->factor                 = FACTOR_LU;
192   (*B)->info.factor_mallocs    = realloc;
193   (*B)->info.fill_ratio_given  = f;
194   if (ai[mbs] != 0) {
195     (*B)->info.fill_ratio_needed = ((PetscReal)iu[mbs])/((PetscReal)ai[mbs]);
196   } else {
197     (*B)->info.fill_ratio_needed = 0.0;
198   }
199 
200 
201   PetscFunctionReturn(0);
202 }
203 
204 #undef __FUNC__
205 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_N"
206 int MatCholeskyFactorNumeric_SeqSBAIJ_N(Mat A,Mat *B)
207 {
208   Mat                C = *B;
209   Mat_SeqBAIJ        *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
210   IS                 isrow = b->row,isicol = b->icol;
211   int                *r,*ic,ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
212   int                *ajtmpold,*ajtmp,nz,row,bslog,*ai=a->i,*aj=a->j,k,flg;
213   int                *diag_offset=b->diag,diag,bs=a->bs,bs2 = a->bs2,*v_pivots,*pj;
214   MatScalar          *ba = b->a,*aa = a->a,*pv,*v,*rtmp,*multiplier,*v_work,*pc,*w;
215 
216   PetscFunctionBegin;
217   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
218   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
219   rtmp = (MatScalar*)PetscMalloc(bs2*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
220   ierr = PetscMemzero(rtmp,bs2*(n+1)*sizeof(MatScalar));CHKERRQ(ierr);
221   /* generate work space needed by dense LU factorization */
222   v_work     = (MatScalar*)PetscMalloc(bs*sizeof(int) + (bs+bs2)*sizeof(MatScalar));CHKPTRQ(v_work);
223   multiplier = v_work + bs;
224   v_pivots   = (int*)(multiplier + bs2);
225 
226   /* flops in while loop */
227   bslog = 2*bs*bs2;
228 
229   for (i=0; i<n; i++) {
230     nz    = bi[i+1] - bi[i];
231     ajtmp = bj + bi[i];
232     for  (j=0; j<nz; j++) {
233       ierr = PetscMemzero(rtmp+bs2*ajtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
234     }
235     /* load in initial (unfactored row) */
236     nz       = ai[r[i]+1] - ai[r[i]];
237     ajtmpold = aj + ai[r[i]];
238     v        = aa + bs2*ai[r[i]];
239     for (j=0; j<nz; j++) {
240       ierr = PetscMemcpy(rtmp+bs2*ic[ajtmpold[j]],v+bs2*j,bs2*sizeof(MatScalar));CHKERRQ(ierr);
241     }
242     row = *ajtmp++;
243     while (row < i) {
244       pc = rtmp + bs2*row;
245 /*      if (*pc) { */
246       for (flg=0,k=0; k<bs2; k++) { if (pc[k]!=0.0) { flg =1; break; }}
247       if (flg) {
248         pv = ba + bs2*diag_offset[row];
249         pj = bj + diag_offset[row] + 1;
250         Kernel_A_gets_A_times_B(bs,pc,pv,multiplier);
251         nz = bi[row+1] - diag_offset[row] - 1;
252         pv += bs2;
253         for (j=0; j<nz; j++) {
254           Kernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j);
255         }
256         PLogFlops(bslog*(nz+1)-bs);
257       }
258         row = *ajtmp++;
259     }
260     /* finished row so stick it into b->a */
261     pv = ba + bs2*bi[i];
262     pj = bj + bi[i];
263     nz = bi[i+1] - bi[i];
264     for (j=0; j<nz; j++) {
265       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
266     }
267     diag = diag_offset[i] - bi[i];
268     /* invert diagonal block */
269     w = pv + bs2*diag;
270     Kernel_A_gets_inverse_A(bs,w,v_pivots,v_work);
271   }
272 
273   ierr = PetscFree(rtmp);CHKERRQ(ierr);
274   ierr = PetscFree(v_work);CHKERRQ(ierr);
275   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
276   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
277   C->factor = FACTOR_LU;
278   C->assembled = PETSC_TRUE;
279   PLogFlops(1.3333*bs*bs2*b->mbs); /* from inverting diagonal blocks */
280   PetscFunctionReturn(0);
281 }
282 
283 /*
284       Version for when blocks are 7 by 7
285 */
286 #undef __FUNC__
287 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_7"
288 int MatCholeskyFactorNumeric_SeqSBAIJ_7(Mat A,Mat *B)
289 {
290   Mat         C = *B;
291   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
292   IS          isrow = b->row,isicol = b->icol;
293   int         *r,*ic,ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
294   int         *ajtmpold,*ajtmp,nz,row;
295   int         *diag_offset = b->diag,idx,*ai=a->i,*aj=a->j,*pj;
296   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
297   MatScalar   p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
298   MatScalar   p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
299   MatScalar   x17,x18,x19,x20,x21,x22,x23,x24,x25,p10,p11,p12,p13,p14;
300   MatScalar   p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,m10,m11,m12;
301   MatScalar   m13,m14,m15,m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
302   MatScalar   p26,p27,p28,p29,p30,p31,p32,p33,p34,p35,p36;
303   MatScalar   p37,p38,p39,p40,p41,p42,p43,p44,p45,p46,p47,p48,p49;
304   MatScalar   x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36;
305   MatScalar   x37,x38,x39,x40,x41,x42,x43,x44,x45,x46,x47,x48,x49;
306   MatScalar   m26,m27,m28,m29,m30,m31,m32,m33,m34,m35,m36;
307   MatScalar   m37,m38,m39,m40,m41,m42,m43,m44,m45,m46,m47,m48,m49;
308   MatScalar   *ba = b->a,*aa = a->a;
309 
310   PetscFunctionBegin;
311   ierr  = ISGetIndices(isrow,&r);CHKERRQ(ierr);
312   ierr  = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
313   rtmp  = (MatScalar*)PetscMalloc(49*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
314 
315   for (i=0; i<n; i++) {
316     nz    = bi[i+1] - bi[i];
317     ajtmp = bj + bi[i];
318     for  (j=0; j<nz; j++) {
319       x = rtmp+49*ajtmp[j];
320       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
321       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
322       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = x[25] = 0.0 ;
323       x[26] = x[27] = x[28] = x[29] = x[30] = x[31] = x[32] = x[33] = 0.0 ;
324       x[34] = x[35] = x[36] = x[37] = x[38] = x[39] = x[40] = x[41] = 0.0 ;
325       x[42] = x[43] = x[44] = x[45] = x[46] = x[47] = x[48] = 0.0 ;
326     }
327     /* load in initial (unfactored row) */
328     idx      = r[i];
329     nz       = ai[idx+1] - ai[idx];
330     ajtmpold = aj + ai[idx];
331     v        = aa + 49*ai[idx];
332     for (j=0; j<nz; j++) {
333       x    = rtmp+49*ic[ajtmpold[j]];
334       x[0] =  v[0];  x[1] =  v[1];  x[2] =  v[2];  x[3] =  v[3];
335       x[4] =  v[4];  x[5] =  v[5];  x[6] =  v[6];  x[7] =  v[7];
336       x[8] =  v[8];  x[9] =  v[9];  x[10] = v[10]; x[11] = v[11];
337       x[12] = v[12]; x[13] = v[13]; x[14] = v[14]; x[15] = v[15];
338       x[16] = v[16]; x[17] = v[17]; x[18] = v[18]; x[19] = v[19];
339       x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23];
340       x[24] = v[24]; x[25] = v[25]; x[26] = v[26]; x[27] = v[27];
341       x[28] = v[28]; x[29] = v[29]; x[30] = v[30]; x[31] = v[31];
342       x[32] = v[32]; x[33] = v[33]; x[34] = v[34]; x[35] = v[35];
343       x[36] = v[36]; x[37] = v[37]; x[38] = v[38]; x[39] = v[39];
344       x[40] = v[40]; x[41] = v[41]; x[42] = v[42]; x[43] = v[43];
345       x[44] = v[44]; x[45] = v[45]; x[46] = v[46]; x[47] = v[47];
346       x[48] = v[48];
347       v    += 49;
348     }
349     row = *ajtmp++;
350     while (row < i) {
351       pc  =  rtmp + 49*row;
352       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
353       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];
354       p9  = pc[8];  p10 = pc[9];  p11 = pc[10]; p12 = pc[11];
355       p13 = pc[12]; p14 = pc[13]; p15 = pc[14]; p16 = pc[15];
356       p17 = pc[16]; p18 = pc[17]; p19 = pc[18]; p20 = pc[19];
357       p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
358       p25 = pc[24]; p26 = pc[25]; p27 = pc[26]; p28 = pc[27];
359       p29 = pc[28]; p30 = pc[29]; p31 = pc[30]; p32 = pc[31];
360       p33 = pc[32]; p34 = pc[33]; p35 = pc[34]; p36 = pc[35];
361       p37 = pc[36]; p38 = pc[37]; p39 = pc[38]; p40 = pc[39];
362       p41 = pc[40]; p42 = pc[41]; p43 = pc[42]; p44 = pc[43];
363       p45 = pc[44]; p46 = pc[45]; p47 = pc[46]; p48 = pc[47];
364       p49 = pc[48];
365       if (p1  != 0.0 || p2  != 0.0 || p3  != 0.0 || p4  != 0.0 ||
366           p5  != 0.0 || p6  != 0.0 || p7  != 0.0 || p8  != 0.0 ||
367           p9  != 0.0 || p10 != 0.0 || p11 != 0.0 || p12 != 0.0 ||
368           p13 != 0.0 || p14 != 0.0 || p15 != 0.0 || p16 != 0.0 ||
369           p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 ||
370           p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 ||
371           p25 != 0.0 || p26 != 0.0 || p27 != 0.0 || p28 != 0.0 ||
372           p29 != 0.0 || p30 != 0.0 || p31 != 0.0 || p32 != 0.0 ||
373           p33 != 0.0 || p34 != 0.0 || p35 != 0.0 || p36 != 0.0 ||
374           p37 != 0.0 || p38 != 0.0 || p39 != 0.0 || p40 != 0.0 ||
375           p41 != 0.0 || p42 != 0.0 || p43 != 0.0 || p44 != 0.0 ||
376           p45 != 0.0 || p46 != 0.0 || p47 != 0.0 || p48 != 0.0 ||
377           p49 != 0.0) {
378         pv = ba + 49*diag_offset[row];
379         pj = bj + diag_offset[row] + 1;
380 	x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
381 	x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
382 	x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
383 	x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
384 	x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
385 	x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
386 	x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
387 	x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
388 	x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
389 	x37 = pv[36]; x38 = pv[37]; x39 = pv[38]; x40 = pv[39];
390 	x41 = pv[40]; x42 = pv[41]; x43 = pv[42]; x44 = pv[43];
391 	x45 = pv[44]; x46 = pv[45]; x47 = pv[46]; x48 = pv[47];
392 	x49 = pv[48];
393         pc[0]  = m1  = p1*x1  + p8*x2   + p15*x3  + p22*x4  + p29*x5  + p36*x6 + p43*x7;
394         pc[1]  = m2  = p2*x1  + p9*x2   + p16*x3  + p23*x4  + p30*x5  + p37*x6 + p44*x7;
395         pc[2]  = m3  = p3*x1  + p10*x2  + p17*x3  + p24*x4  + p31*x5  + p38*x6 + p45*x7;
396         pc[3]  = m4  = p4*x1  + p11*x2  + p18*x3  + p25*x4  + p32*x5  + p39*x6 + p46*x7;
397         pc[4]  = m5  = p5*x1  + p12*x2  + p19*x3  + p26*x4  + p33*x5  + p40*x6 + p47*x7;
398         pc[5]  = m6  = p6*x1  + p13*x2  + p20*x3  + p27*x4  + p34*x5  + p41*x6 + p48*x7;
399         pc[6]  = m7  = p7*x1  + p14*x2  + p21*x3  + p28*x4  + p35*x5  + p42*x6 + p49*x7;
400 
401         pc[7]  = m8  = p1*x8  + p8*x9   + p15*x10 + p22*x11 + p29*x12 + p36*x13 + p43*x14;
402         pc[8]  = m9  = p2*x8  + p9*x9   + p16*x10 + p23*x11 + p30*x12 + p37*x13 + p44*x14;
403         pc[9]  = m10 = p3*x8  + p10*x9  + p17*x10 + p24*x11 + p31*x12 + p38*x13 + p45*x14;
404         pc[10] = m11 = p4*x8  + p11*x9  + p18*x10 + p25*x11 + p32*x12 + p39*x13 + p46*x14;
405         pc[11] = m12 = p5*x8  + p12*x9  + p19*x10 + p26*x11 + p33*x12 + p40*x13 + p47*x14;
406         pc[12] = m13 = p6*x8  + p13*x9  + p20*x10 + p27*x11 + p34*x12 + p41*x13 + p48*x14;
407         pc[13] = m14 = p7*x8  + p14*x9  + p21*x10 + p28*x11 + p35*x12 + p42*x13 + p49*x14;
408 
409         pc[14] = m15 = p1*x15 + p8*x16  + p15*x17 + p22*x18 + p29*x19 + p36*x20 + p43*x21;
410         pc[15] = m16 = p2*x15 + p9*x16  + p16*x17 + p23*x18 + p30*x19 + p37*x20 + p44*x21;
411         pc[16] = m17 = p3*x15 + p10*x16 + p17*x17 + p24*x18 + p31*x19 + p38*x20 + p45*x21;
412         pc[17] = m18 = p4*x15 + p11*x16 + p18*x17 + p25*x18 + p32*x19 + p39*x20 + p46*x21;
413         pc[18] = m19 = p5*x15 + p12*x16 + p19*x17 + p26*x18 + p33*x19 + p40*x20 + p47*x21;
414         pc[19] = m20 = p6*x15 + p13*x16 + p20*x17 + p27*x18 + p34*x19 + p41*x20 + p48*x21;
415         pc[20] = m21 = p7*x15 + p14*x16 + p21*x17 + p28*x18 + p35*x19 + p42*x20 + p49*x21;
416 
417         pc[21] = m22 = p1*x22 + p8*x23  + p15*x24 + p22*x25 + p29*x26 + p36*x27 + p43*x28;
418         pc[22] = m23 = p2*x22 + p9*x23  + p16*x24 + p23*x25 + p30*x26 + p37*x27 + p44*x28;
419         pc[23] = m24 = p3*x22 + p10*x23 + p17*x24 + p24*x25 + p31*x26 + p38*x27 + p45*x28;
420         pc[24] = m25 = p4*x22 + p11*x23 + p18*x24 + p25*x25 + p32*x26 + p39*x27 + p46*x28;
421         pc[25] = m26 = p5*x22 + p12*x23 + p19*x24 + p26*x25 + p33*x26 + p40*x27 + p47*x28;
422         pc[26] = m27 = p6*x22 + p13*x23 + p20*x24 + p27*x25 + p34*x26 + p41*x27 + p48*x28;
423         pc[27] = m28 = p7*x22 + p14*x23 + p21*x24 + p28*x25 + p35*x26 + p42*x27 + p49*x28;
424 
425         pc[28] = m29 = p1*x29 + p8*x30  + p15*x31 + p22*x32 + p29*x33 + p36*x34 + p43*x35;
426         pc[29] = m30 = p2*x29 + p9*x30  + p16*x31 + p23*x32 + p30*x33 + p37*x34 + p44*x35;
427         pc[30] = m31 = p3*x29 + p10*x30 + p17*x31 + p24*x32 + p31*x33 + p38*x34 + p45*x35;
428         pc[31] = m32 = p4*x29 + p11*x30 + p18*x31 + p25*x32 + p32*x33 + p39*x34 + p46*x35;
429         pc[32] = m33 = p5*x29 + p12*x30 + p19*x31 + p26*x32 + p33*x33 + p40*x34 + p47*x35;
430         pc[33] = m34 = p6*x29 + p13*x30 + p20*x31 + p27*x32 + p34*x33 + p41*x34 + p48*x35;
431         pc[34] = m35 = p7*x29 + p14*x30 + p21*x31 + p28*x32 + p35*x33 + p42*x34 + p49*x35;
432 
433         pc[35] = m36 = p1*x36 + p8*x37  + p15*x38 + p22*x39 + p29*x40 + p36*x41 + p43*x42;
434         pc[36] = m37 = p2*x36 + p9*x37  + p16*x38 + p23*x39 + p30*x40 + p37*x41 + p44*x42;
435         pc[37] = m38 = p3*x36 + p10*x37 + p17*x38 + p24*x39 + p31*x40 + p38*x41 + p45*x42;
436         pc[38] = m39 = p4*x36 + p11*x37 + p18*x38 + p25*x39 + p32*x40 + p39*x41 + p46*x42;
437         pc[39] = m40 = p5*x36 + p12*x37 + p19*x38 + p26*x39 + p33*x40 + p40*x41 + p47*x42;
438         pc[40] = m41 = p6*x36 + p13*x37 + p20*x38 + p27*x39 + p34*x40 + p41*x41 + p48*x42;
439         pc[41] = m42 = p7*x36 + p14*x37 + p21*x38 + p28*x39 + p35*x40 + p42*x41 + p49*x42;
440 
441         pc[42] = m43 = p1*x43 + p8*x44  + p15*x45 + p22*x46 + p29*x47 + p36*x48 + p43*x49;
442         pc[43] = m44 = p2*x43 + p9*x44  + p16*x45 + p23*x46 + p30*x47 + p37*x48 + p44*x49;
443         pc[44] = m45 = p3*x43 + p10*x44 + p17*x45 + p24*x46 + p31*x47 + p38*x48 + p45*x49;
444         pc[45] = m46 = p4*x43 + p11*x44 + p18*x45 + p25*x46 + p32*x47 + p39*x48 + p46*x49;
445         pc[46] = m47 = p5*x43 + p12*x44 + p19*x45 + p26*x46 + p33*x47 + p40*x48 + p47*x49;
446         pc[47] = m48 = p6*x43 + p13*x44 + p20*x45 + p27*x46 + p34*x47 + p41*x48 + p48*x49;
447         pc[48] = m49 = p7*x43 + p14*x44 + p21*x45 + p28*x46 + p35*x47 + p42*x48 + p49*x49;
448 
449         nz = bi[row+1] - diag_offset[row] - 1;
450         pv += 49;
451         for (j=0; j<nz; j++) {
452 	  x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
453 	  x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
454 	  x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
455 	  x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
456 	  x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
457 	  x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
458 	  x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
459 	  x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
460 	  x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
461 	  x37 = pv[36]; x38 = pv[37]; x39 = pv[38]; x40 = pv[39];
462 	  x41 = pv[40]; x42 = pv[41]; x43 = pv[42]; x44 = pv[43];
463 	  x45 = pv[44]; x46 = pv[45]; x47 = pv[46]; x48 = pv[47];
464 	  x49 = pv[48];
465 	  x    = rtmp + 49*pj[j];
466 	  x[0]  -= m1*x1  + m8*x2   + m15*x3  + m22*x4  + m29*x5  + m36*x6 + m43*x7;
467 	  x[1]  -= m2*x1  + m9*x2   + m16*x3  + m23*x4  + m30*x5  + m37*x6 + m44*x7;
468 	  x[2]  -= m3*x1  + m10*x2  + m17*x3  + m24*x4  + m31*x5  + m38*x6 + m45*x7;
469 	  x[3]  -= m4*x1  + m11*x2  + m18*x3  + m25*x4  + m32*x5  + m39*x6 + m46*x7;
470 	  x[4]  -= m5*x1  + m12*x2  + m19*x3  + m26*x4  + m33*x5  + m40*x6 + m47*x7;
471 	  x[5]  -= m6*x1  + m13*x2  + m20*x3  + m27*x4  + m34*x5  + m41*x6 + m48*x7;
472 	  x[6]  -= m7*x1  + m14*x2  + m21*x3  + m28*x4  + m35*x5  + m42*x6 + m49*x7;
473 
474 	  x[7]  -= m1*x8  + m8*x9   + m15*x10 + m22*x11 + m29*x12 + m36*x13 + m43*x14;
475 	  x[8]  -= m2*x8  + m9*x9   + m16*x10 + m23*x11 + m30*x12 + m37*x13 + m44*x14;
476 	  x[9]  -= m3*x8  + m10*x9  + m17*x10 + m24*x11 + m31*x12 + m38*x13 + m45*x14;
477 	  x[10] -= m4*x8  + m11*x9  + m18*x10 + m25*x11 + m32*x12 + m39*x13 + m46*x14;
478 	  x[11] -= m5*x8  + m12*x9  + m19*x10 + m26*x11 + m33*x12 + m40*x13 + m47*x14;
479 	  x[12] -= m6*x8  + m13*x9  + m20*x10 + m27*x11 + m34*x12 + m41*x13 + m48*x14;
480 	  x[13] -= m7*x8  + m14*x9  + m21*x10 + m28*x11 + m35*x12 + m42*x13 + m49*x14;
481 
482 	  x[14] -= m1*x15 + m8*x16  + m15*x17 + m22*x18 + m29*x19 + m36*x20 + m43*x21;
483 	  x[15] -= m2*x15 + m9*x16  + m16*x17 + m23*x18 + m30*x19 + m37*x20 + m44*x21;
484 	  x[16] -= m3*x15 + m10*x16 + m17*x17 + m24*x18 + m31*x19 + m38*x20 + m45*x21;
485 	  x[17] -= m4*x15 + m11*x16 + m18*x17 + m25*x18 + m32*x19 + m39*x20 + m46*x21;
486 	  x[18] -= m5*x15 + m12*x16 + m19*x17 + m26*x18 + m33*x19 + m40*x20 + m47*x21;
487 	  x[19] -= m6*x15 + m13*x16 + m20*x17 + m27*x18 + m34*x19 + m41*x20 + m48*x21;
488 	  x[20] -= m7*x15 + m14*x16 + m21*x17 + m28*x18 + m35*x19 + m42*x20 + m49*x21;
489 
490 	  x[21] -= m1*x22 + m8*x23  + m15*x24 + m22*x25 + m29*x26 + m36*x27 + m43*x28;
491 	  x[22] -= m2*x22 + m9*x23  + m16*x24 + m23*x25 + m30*x26 + m37*x27 + m44*x28;
492 	  x[23] -= m3*x22 + m10*x23 + m17*x24 + m24*x25 + m31*x26 + m38*x27 + m45*x28;
493 	  x[24] -= m4*x22 + m11*x23 + m18*x24 + m25*x25 + m32*x26 + m39*x27 + m46*x28;
494 	  x[25] -= m5*x22 + m12*x23 + m19*x24 + m26*x25 + m33*x26 + m40*x27 + m47*x28;
495 	  x[26] -= m6*x22 + m13*x23 + m20*x24 + m27*x25 + m34*x26 + m41*x27 + m48*x28;
496 	  x[27] -= m7*x22 + m14*x23 + m21*x24 + m28*x25 + m35*x26 + m42*x27 + m49*x28;
497 
498 	  x[28] -= m1*x29 + m8*x30  + m15*x31 + m22*x32 + m29*x33 + m36*x34 + m43*x35;
499 	  x[29] -= m2*x29 + m9*x30  + m16*x31 + m23*x32 + m30*x33 + m37*x34 + m44*x35;
500 	  x[30] -= m3*x29 + m10*x30 + m17*x31 + m24*x32 + m31*x33 + m38*x34 + m45*x35;
501 	  x[31] -= m4*x29 + m11*x30 + m18*x31 + m25*x32 + m32*x33 + m39*x34 + m46*x35;
502 	  x[32] -= m5*x29 + m12*x30 + m19*x31 + m26*x32 + m33*x33 + m40*x34 + m47*x35;
503 	  x[33] -= m6*x29 + m13*x30 + m20*x31 + m27*x32 + m34*x33 + m41*x34 + m48*x35;
504 	  x[34] -= m7*x29 + m14*x30 + m21*x31 + m28*x32 + m35*x33 + m42*x34 + m49*x35;
505 
506 	  x[35] -= m1*x36 + m8*x37  + m15*x38 + m22*x39 + m29*x40 + m36*x41 + m43*x42;
507 	  x[36] -= m2*x36 + m9*x37  + m16*x38 + m23*x39 + m30*x40 + m37*x41 + m44*x42;
508 	  x[37] -= m3*x36 + m10*x37 + m17*x38 + m24*x39 + m31*x40 + m38*x41 + m45*x42;
509 	  x[38] -= m4*x36 + m11*x37 + m18*x38 + m25*x39 + m32*x40 + m39*x41 + m46*x42;
510 	  x[39] -= m5*x36 + m12*x37 + m19*x38 + m26*x39 + m33*x40 + m40*x41 + m47*x42;
511 	  x[40] -= m6*x36 + m13*x37 + m20*x38 + m27*x39 + m34*x40 + m41*x41 + m48*x42;
512 	  x[41] -= m7*x36 + m14*x37 + m21*x38 + m28*x39 + m35*x40 + m42*x41 + m49*x42;
513 
514 	  x[42] -= m1*x43 + m8*x44  + m15*x45 + m22*x46 + m29*x47 + m36*x48 + m43*x49;
515 	  x[43] -= m2*x43 + m9*x44  + m16*x45 + m23*x46 + m30*x47 + m37*x48 + m44*x49;
516 	  x[44] -= m3*x43 + m10*x44 + m17*x45 + m24*x46 + m31*x47 + m38*x48 + m45*x49;
517 	  x[45] -= m4*x43 + m11*x44 + m18*x45 + m25*x46 + m32*x47 + m39*x48 + m46*x49;
518 	  x[46] -= m5*x43 + m12*x44 + m19*x45 + m26*x46 + m33*x47 + m40*x48 + m47*x49;
519 	  x[47] -= m6*x43 + m13*x44 + m20*x45 + m27*x46 + m34*x47 + m41*x48 + m48*x49;
520 	  x[48] -= m7*x43 + m14*x44 + m21*x45 + m28*x46 + m35*x47 + m42*x48 + m49*x49;
521           pv   += 49;
522         }
523         PLogFlops(686*nz+637);
524       }
525       row = *ajtmp++;
526     }
527     /* finished row so stick it into b->a */
528     pv = ba + 49*bi[i];
529     pj = bj + bi[i];
530     nz = bi[i+1] - bi[i];
531     for (j=0; j<nz; j++) {
532       x      = rtmp+49*pj[j];
533       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
534       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7];
535       pv[8]  = x[8];  pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11];
536       pv[12] = x[12]; pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
537       pv[16] = x[16]; pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19];
538       pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23];
539       pv[24] = x[24]; pv[25] = x[25]; pv[26] = x[26]; pv[27] = x[27];
540       pv[28] = x[28]; pv[29] = x[29]; pv[30] = x[30]; pv[31] = x[31];
541       pv[32] = x[32]; pv[33] = x[33]; pv[34] = x[34]; pv[35] = x[35];
542       pv[36] = x[36]; pv[37] = x[37]; pv[38] = x[38]; pv[39] = x[39];
543       pv[40] = x[40]; pv[41] = x[41]; pv[42] = x[42]; pv[43] = x[43];
544       pv[44] = x[44]; pv[45] = x[45]; pv[46] = x[46]; pv[47] = x[47];
545       pv[48] = x[48];
546       pv   += 49;
547     }
548     /* invert diagonal block */
549     w = ba + 49*diag_offset[i];
550     ierr = Kernel_A_gets_inverse_A_7(w);CHKERRQ(ierr);
551   }
552 
553   ierr = PetscFree(rtmp);CHKERRQ(ierr);
554   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
555   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
556   C->factor = FACTOR_LU;
557   C->assembled = PETSC_TRUE;
558   PLogFlops(1.3333*343*b->mbs); /* from inverting diagonal blocks */
559   PetscFunctionReturn(0);
560 }
561 
562 /*
563       Version for when blocks are 7 by 7 Using natural ordering
564 */
565 #undef __FUNC__
566 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_7_NaturalOrdering"
567 int MatCholeskyFactorNumeric_SeqSBAIJ_7_NaturalOrdering(Mat A,Mat *B)
568 {
569   Mat          C = *B;
570   Mat_SeqBAIJ  *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
571   int          ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
572   int          *ajtmpold,*ajtmp,nz,row;
573   int          *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
574   MatScalar    *pv,*v,*rtmp,*pc,*w,*x;
575   MatScalar    x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15;
576   MatScalar    x16,x17,x18,x19,x20,x21,x22,x23,x24,x25;
577   MatScalar    p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15;
578   MatScalar    p16,p17,p18,p19,p20,p21,p22,p23,p24,p25;
579   MatScalar    m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12,m13,m14,m15;
580   MatScalar    m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
581   MatScalar    p26,p27,p28,p29,p30,p31,p32,p33,p34,p35,p36;
582   MatScalar    p37,p38,p39,p40,p41,p42,p43,p44,p45,p46,p47,p48,p49;
583   MatScalar    x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36;
584   MatScalar    x37,x38,x39,x40,x41,x42,x43,x44,x45,x46,x47,x48,x49;
585   MatScalar    m26,m27,m28,m29,m30,m31,m32,m33,m34,m35,m36;
586   MatScalar    m37,m38,m39,m40,m41,m42,m43,m44,m45,m46,m47,m48,m49;
587   MatScalar    *ba = b->a,*aa = a->a;
588 
589   PetscFunctionBegin;
590   rtmp  = (MatScalar*)PetscMalloc(49*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
591   for (i=0; i<n; i++) {
592     nz    = bi[i+1] - bi[i];
593     ajtmp = bj + bi[i];
594     for  (j=0; j<nz; j++) {
595       x = rtmp+49*ajtmp[j];
596       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
597       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
598       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = x[25] = 0.0 ;
599       x[26] = x[27] = x[28] = x[29] = x[30] = x[31] = x[32] = x[33] = 0.0 ;
600       x[34] = x[35] = x[36] = x[37] = x[38] = x[39] = x[40] = x[41] = 0.0 ;
601       x[42] = x[43] = x[44] = x[45] = x[46] = x[47] = x[48] = 0.0 ;
602     }
603     /* load in initial (unfactored row) */
604     nz       = ai[i+1] - ai[i];
605     ajtmpold = aj + ai[i];
606     v        = aa + 49*ai[i];
607     for (j=0; j<nz; j++) {
608       x    = rtmp+49*ajtmpold[j];
609       x[0] =  v[0];  x[1] =  v[1];  x[2] =  v[2];  x[3] =  v[3];
610       x[4] =  v[4];  x[5] =  v[5];  x[6] =  v[6];  x[7] =  v[7];
611       x[8] =  v[8];  x[9] =  v[9];  x[10] = v[10]; x[11] = v[11];
612       x[12] = v[12]; x[13] = v[13]; x[14] = v[14]; x[15] = v[15];
613       x[16] = v[16]; x[17] = v[17]; x[18] = v[18]; x[19] = v[19];
614       x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23];
615       x[24] = v[24]; x[25] = v[25]; x[26] = v[26]; x[27] = v[27];
616       x[28] = v[28]; x[29] = v[29]; x[30] = v[30]; x[31] = v[31];
617       x[32] = v[32]; x[33] = v[33]; x[34] = v[34]; x[35] = v[35];
618       x[36] = v[36]; x[37] = v[37]; x[38] = v[38]; x[39] = v[39];
619       x[40] = v[40]; x[41] = v[41]; x[42] = v[42]; x[43] = v[43];
620       x[44] = v[44]; x[45] = v[45]; x[46] = v[46]; x[47] = v[47];
621       x[48] = v[48];
622       v    += 49;
623     }
624     row = *ajtmp++;
625     while (row < i) {
626       pc  = rtmp + 49*row;
627       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
628       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];
629       p9  = pc[8];  p10 = pc[9];  p11 = pc[10]; p12 = pc[11];
630       p13 = pc[12]; p14 = pc[13]; p15 = pc[14]; p16 = pc[15];
631       p17 = pc[16]; p18 = pc[17]; p19 = pc[18]; p20 = pc[19];
632       p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
633       p25 = pc[24]; p26 = pc[25]; p27 = pc[26]; p28 = pc[27];
634       p29 = pc[28]; p30 = pc[29]; p31 = pc[30]; p32 = pc[31];
635       p33 = pc[32]; p34 = pc[33]; p35 = pc[34]; p36 = pc[35];
636       p37 = pc[36]; p38 = pc[37]; p39 = pc[38]; p40 = pc[39];
637       p41 = pc[40]; p42 = pc[41]; p43 = pc[42]; p44 = pc[43];
638       p45 = pc[44]; p46 = pc[45]; p47 = pc[46]; p48 = pc[47];
639       p49 = pc[48];
640       if (p1  != 0.0 || p2  != 0.0 || p3  != 0.0 || p4  != 0.0 ||
641           p5  != 0.0 || p6  != 0.0 || p7  != 0.0 || p8  != 0.0 ||
642           p9  != 0.0 || p10 != 0.0 || p11 != 0.0 || p12 != 0.0 ||
643           p13 != 0.0 || p14 != 0.0 || p15 != 0.0 || p16 != 0.0 ||
644           p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 ||
645           p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 ||
646           p25 != 0.0 || p26 != 0.0 || p27 != 0.0 || p28 != 0.0 ||
647           p29 != 0.0 || p30 != 0.0 || p31 != 0.0 || p32 != 0.0 ||
648           p33 != 0.0 || p34 != 0.0 || p35 != 0.0 || p36 != 0.0 ||
649           p37 != 0.0 || p38 != 0.0 || p39 != 0.0 || p40 != 0.0 ||
650           p41 != 0.0 || p42 != 0.0 || p43 != 0.0 || p44 != 0.0 ||
651           p45 != 0.0 || p46 != 0.0 || p47 != 0.0 || p48 != 0.0 ||
652           p49 != 0.0) {
653         pv = ba + 49*diag_offset[row];
654         pj = bj + diag_offset[row] + 1;
655 	x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
656 	x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
657 	x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
658 	x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
659 	x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
660 	x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
661 	x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
662 	x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
663 	x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
664 	x37 = pv[36]; x38 = pv[37]; x39 = pv[38]; x40 = pv[39];
665 	x41 = pv[40]; x42 = pv[41]; x43 = pv[42]; x44 = pv[43];
666 	x45 = pv[44]; x46 = pv[45]; x47 = pv[46]; x48 = pv[47];
667         x49 = pv[48];
668         pc[0]  = m1  = p1*x1  + p8*x2   + p15*x3  + p22*x4  + p29*x5  + p36*x6 + p43*x7;
669         pc[1]  = m2  = p2*x1  + p9*x2   + p16*x3  + p23*x4  + p30*x5  + p37*x6 + p44*x7;
670         pc[2]  = m3  = p3*x1  + p10*x2  + p17*x3  + p24*x4  + p31*x5  + p38*x6 + p45*x7;
671         pc[3]  = m4  = p4*x1  + p11*x2  + p18*x3  + p25*x4  + p32*x5  + p39*x6 + p46*x7;
672         pc[4]  = m5  = p5*x1  + p12*x2  + p19*x3  + p26*x4  + p33*x5  + p40*x6 + p47*x7;
673         pc[5]  = m6  = p6*x1  + p13*x2  + p20*x3  + p27*x4  + p34*x5  + p41*x6 + p48*x7;
674         pc[6]  = m7  = p7*x1  + p14*x2  + p21*x3  + p28*x4  + p35*x5  + p42*x6 + p49*x7;
675 
676         pc[7]  = m8  = p1*x8  + p8*x9   + p15*x10 + p22*x11 + p29*x12 + p36*x13 + p43*x14;
677         pc[8]  = m9  = p2*x8  + p9*x9   + p16*x10 + p23*x11 + p30*x12 + p37*x13 + p44*x14;
678         pc[9]  = m10 = p3*x8  + p10*x9  + p17*x10 + p24*x11 + p31*x12 + p38*x13 + p45*x14;
679         pc[10] = m11 = p4*x8  + p11*x9  + p18*x10 + p25*x11 + p32*x12 + p39*x13 + p46*x14;
680         pc[11] = m12 = p5*x8  + p12*x9  + p19*x10 + p26*x11 + p33*x12 + p40*x13 + p47*x14;
681         pc[12] = m13 = p6*x8  + p13*x9  + p20*x10 + p27*x11 + p34*x12 + p41*x13 + p48*x14;
682         pc[13] = m14 = p7*x8  + p14*x9  + p21*x10 + p28*x11 + p35*x12 + p42*x13 + p49*x14;
683 
684         pc[14] = m15 = p1*x15 + p8*x16  + p15*x17 + p22*x18 + p29*x19 + p36*x20 + p43*x21;
685         pc[15] = m16 = p2*x15 + p9*x16  + p16*x17 + p23*x18 + p30*x19 + p37*x20 + p44*x21;
686         pc[16] = m17 = p3*x15 + p10*x16 + p17*x17 + p24*x18 + p31*x19 + p38*x20 + p45*x21;
687         pc[17] = m18 = p4*x15 + p11*x16 + p18*x17 + p25*x18 + p32*x19 + p39*x20 + p46*x21;
688         pc[18] = m19 = p5*x15 + p12*x16 + p19*x17 + p26*x18 + p33*x19 + p40*x20 + p47*x21;
689         pc[19] = m20 = p6*x15 + p13*x16 + p20*x17 + p27*x18 + p34*x19 + p41*x20 + p48*x21;
690         pc[20] = m21 = p7*x15 + p14*x16 + p21*x17 + p28*x18 + p35*x19 + p42*x20 + p49*x21;
691 
692         pc[21] = m22 = p1*x22 + p8*x23  + p15*x24 + p22*x25 + p29*x26 + p36*x27 + p43*x28;
693         pc[22] = m23 = p2*x22 + p9*x23  + p16*x24 + p23*x25 + p30*x26 + p37*x27 + p44*x28;
694         pc[23] = m24 = p3*x22 + p10*x23 + p17*x24 + p24*x25 + p31*x26 + p38*x27 + p45*x28;
695         pc[24] = m25 = p4*x22 + p11*x23 + p18*x24 + p25*x25 + p32*x26 + p39*x27 + p46*x28;
696         pc[25] = m26 = p5*x22 + p12*x23 + p19*x24 + p26*x25 + p33*x26 + p40*x27 + p47*x28;
697         pc[26] = m27 = p6*x22 + p13*x23 + p20*x24 + p27*x25 + p34*x26 + p41*x27 + p48*x28;
698         pc[27] = m28 = p7*x22 + p14*x23 + p21*x24 + p28*x25 + p35*x26 + p42*x27 + p49*x28;
699 
700         pc[28] = m29 = p1*x29 + p8*x30  + p15*x31 + p22*x32 + p29*x33 + p36*x34 + p43*x35;
701         pc[29] = m30 = p2*x29 + p9*x30  + p16*x31 + p23*x32 + p30*x33 + p37*x34 + p44*x35;
702         pc[30] = m31 = p3*x29 + p10*x30 + p17*x31 + p24*x32 + p31*x33 + p38*x34 + p45*x35;
703         pc[31] = m32 = p4*x29 + p11*x30 + p18*x31 + p25*x32 + p32*x33 + p39*x34 + p46*x35;
704         pc[32] = m33 = p5*x29 + p12*x30 + p19*x31 + p26*x32 + p33*x33 + p40*x34 + p47*x35;
705         pc[33] = m34 = p6*x29 + p13*x30 + p20*x31 + p27*x32 + p34*x33 + p41*x34 + p48*x35;
706         pc[34] = m35 = p7*x29 + p14*x30 + p21*x31 + p28*x32 + p35*x33 + p42*x34 + p49*x35;
707 
708         pc[35] = m36 = p1*x36 + p8*x37  + p15*x38 + p22*x39 + p29*x40 + p36*x41 + p43*x42;
709         pc[36] = m37 = p2*x36 + p9*x37  + p16*x38 + p23*x39 + p30*x40 + p37*x41 + p44*x42;
710         pc[37] = m38 = p3*x36 + p10*x37 + p17*x38 + p24*x39 + p31*x40 + p38*x41 + p45*x42;
711         pc[38] = m39 = p4*x36 + p11*x37 + p18*x38 + p25*x39 + p32*x40 + p39*x41 + p46*x42;
712         pc[39] = m40 = p5*x36 + p12*x37 + p19*x38 + p26*x39 + p33*x40 + p40*x41 + p47*x42;
713         pc[40] = m41 = p6*x36 + p13*x37 + p20*x38 + p27*x39 + p34*x40 + p41*x41 + p48*x42;
714         pc[41] = m42 = p7*x36 + p14*x37 + p21*x38 + p28*x39 + p35*x40 + p42*x41 + p49*x42;
715 
716         pc[42] = m43 = p1*x43 + p8*x44  + p15*x45 + p22*x46 + p29*x47 + p36*x48 + p43*x49;
717         pc[43] = m44 = p2*x43 + p9*x44  + p16*x45 + p23*x46 + p30*x47 + p37*x48 + p44*x49;
718         pc[44] = m45 = p3*x43 + p10*x44 + p17*x45 + p24*x46 + p31*x47 + p38*x48 + p45*x49;
719         pc[45] = m46 = p4*x43 + p11*x44 + p18*x45 + p25*x46 + p32*x47 + p39*x48 + p46*x49;
720         pc[46] = m47 = p5*x43 + p12*x44 + p19*x45 + p26*x46 + p33*x47 + p40*x48 + p47*x49;
721         pc[47] = m48 = p6*x43 + p13*x44 + p20*x45 + p27*x46 + p34*x47 + p41*x48 + p48*x49;
722         pc[48] = m49 = p7*x43 + p14*x44 + p21*x45 + p28*x46 + p35*x47 + p42*x48 + p49*x49;
723 
724         nz = bi[row+1] - diag_offset[row] - 1;
725         pv += 49;
726         for (j=0; j<nz; j++) {
727 	  x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
728 	  x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
729 	  x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
730 	  x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
731 	  x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
732 	  x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
733 	  x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
734 	  x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
735 	  x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
736 	  x37 = pv[36]; x38 = pv[37]; x39 = pv[38]; x40 = pv[39];
737 	  x41 = pv[40]; x42 = pv[41]; x43 = pv[42]; x44 = pv[43];
738 	  x45 = pv[44]; x46 = pv[45]; x47 = pv[46]; x48 = pv[47];
739 	  x49 = pv[48];
740 	  x    = rtmp + 49*pj[j];
741 	  x[0]  -= m1*x1  + m8*x2   + m15*x3  + m22*x4  + m29*x5  + m36*x6 + m43*x7;
742 	  x[1]  -= m2*x1  + m9*x2   + m16*x3  + m23*x4  + m30*x5  + m37*x6 + m44*x7;
743 	  x[2]  -= m3*x1  + m10*x2  + m17*x3  + m24*x4  + m31*x5  + m38*x6 + m45*x7;
744 	  x[3]  -= m4*x1  + m11*x2  + m18*x3  + m25*x4  + m32*x5  + m39*x6 + m46*x7;
745 	  x[4]  -= m5*x1  + m12*x2  + m19*x3  + m26*x4  + m33*x5  + m40*x6 + m47*x7;
746 	  x[5]  -= m6*x1  + m13*x2  + m20*x3  + m27*x4  + m34*x5  + m41*x6 + m48*x7;
747 	  x[6]  -= m7*x1  + m14*x2  + m21*x3  + m28*x4  + m35*x5  + m42*x6 + m49*x7;
748 
749 	  x[7]  -= m1*x8  + m8*x9   + m15*x10 + m22*x11 + m29*x12 + m36*x13 + m43*x14;
750 	  x[8]  -= m2*x8  + m9*x9   + m16*x10 + m23*x11 + m30*x12 + m37*x13 + m44*x14;
751 	  x[9]  -= m3*x8  + m10*x9  + m17*x10 + m24*x11 + m31*x12 + m38*x13 + m45*x14;
752 	  x[10] -= m4*x8  + m11*x9  + m18*x10 + m25*x11 + m32*x12 + m39*x13 + m46*x14;
753 	  x[11] -= m5*x8  + m12*x9  + m19*x10 + m26*x11 + m33*x12 + m40*x13 + m47*x14;
754 	  x[12] -= m6*x8  + m13*x9  + m20*x10 + m27*x11 + m34*x12 + m41*x13 + m48*x14;
755 	  x[13] -= m7*x8  + m14*x9  + m21*x10 + m28*x11 + m35*x12 + m42*x13 + m49*x14;
756 
757 	  x[14] -= m1*x15 + m8*x16  + m15*x17 + m22*x18 + m29*x19 + m36*x20 + m43*x21;
758 	  x[15] -= m2*x15 + m9*x16  + m16*x17 + m23*x18 + m30*x19 + m37*x20 + m44*x21;
759 	  x[16] -= m3*x15 + m10*x16 + m17*x17 + m24*x18 + m31*x19 + m38*x20 + m45*x21;
760 	  x[17] -= m4*x15 + m11*x16 + m18*x17 + m25*x18 + m32*x19 + m39*x20 + m46*x21;
761 	  x[18] -= m5*x15 + m12*x16 + m19*x17 + m26*x18 + m33*x19 + m40*x20 + m47*x21;
762 	  x[19] -= m6*x15 + m13*x16 + m20*x17 + m27*x18 + m34*x19 + m41*x20 + m48*x21;
763 	  x[20] -= m7*x15 + m14*x16 + m21*x17 + m28*x18 + m35*x19 + m42*x20 + m49*x21;
764 
765 	  x[21] -= m1*x22 + m8*x23  + m15*x24 + m22*x25 + m29*x26 + m36*x27 + m43*x28;
766 	  x[22] -= m2*x22 + m9*x23  + m16*x24 + m23*x25 + m30*x26 + m37*x27 + m44*x28;
767 	  x[23] -= m3*x22 + m10*x23 + m17*x24 + m24*x25 + m31*x26 + m38*x27 + m45*x28;
768 	  x[24] -= m4*x22 + m11*x23 + m18*x24 + m25*x25 + m32*x26 + m39*x27 + m46*x28;
769 	  x[25] -= m5*x22 + m12*x23 + m19*x24 + m26*x25 + m33*x26 + m40*x27 + m47*x28;
770 	  x[26] -= m6*x22 + m13*x23 + m20*x24 + m27*x25 + m34*x26 + m41*x27 + m48*x28;
771 	  x[27] -= m7*x22 + m14*x23 + m21*x24 + m28*x25 + m35*x26 + m42*x27 + m49*x28;
772 
773 	  x[28] -= m1*x29 + m8*x30  + m15*x31 + m22*x32 + m29*x33 + m36*x34 + m43*x35;
774 	  x[29] -= m2*x29 + m9*x30  + m16*x31 + m23*x32 + m30*x33 + m37*x34 + m44*x35;
775 	  x[30] -= m3*x29 + m10*x30 + m17*x31 + m24*x32 + m31*x33 + m38*x34 + m45*x35;
776 	  x[31] -= m4*x29 + m11*x30 + m18*x31 + m25*x32 + m32*x33 + m39*x34 + m46*x35;
777 	  x[32] -= m5*x29 + m12*x30 + m19*x31 + m26*x32 + m33*x33 + m40*x34 + m47*x35;
778 	  x[33] -= m6*x29 + m13*x30 + m20*x31 + m27*x32 + m34*x33 + m41*x34 + m48*x35;
779 	  x[34] -= m7*x29 + m14*x30 + m21*x31 + m28*x32 + m35*x33 + m42*x34 + m49*x35;
780 
781 	  x[35] -= m1*x36 + m8*x37  + m15*x38 + m22*x39 + m29*x40 + m36*x41 + m43*x42;
782 	  x[36] -= m2*x36 + m9*x37  + m16*x38 + m23*x39 + m30*x40 + m37*x41 + m44*x42;
783 	  x[37] -= m3*x36 + m10*x37 + m17*x38 + m24*x39 + m31*x40 + m38*x41 + m45*x42;
784 	  x[38] -= m4*x36 + m11*x37 + m18*x38 + m25*x39 + m32*x40 + m39*x41 + m46*x42;
785 	  x[39] -= m5*x36 + m12*x37 + m19*x38 + m26*x39 + m33*x40 + m40*x41 + m47*x42;
786 	  x[40] -= m6*x36 + m13*x37 + m20*x38 + m27*x39 + m34*x40 + m41*x41 + m48*x42;
787 	  x[41] -= m7*x36 + m14*x37 + m21*x38 + m28*x39 + m35*x40 + m42*x41 + m49*x42;
788 
789 	  x[42] -= m1*x43 + m8*x44  + m15*x45 + m22*x46 + m29*x47 + m36*x48 + m43*x49;
790 	  x[43] -= m2*x43 + m9*x44  + m16*x45 + m23*x46 + m30*x47 + m37*x48 + m44*x49;
791 	  x[44] -= m3*x43 + m10*x44 + m17*x45 + m24*x46 + m31*x47 + m38*x48 + m45*x49;
792 	  x[45] -= m4*x43 + m11*x44 + m18*x45 + m25*x46 + m32*x47 + m39*x48 + m46*x49;
793 	  x[46] -= m5*x43 + m12*x44 + m19*x45 + m26*x46 + m33*x47 + m40*x48 + m47*x49;
794 	  x[47] -= m6*x43 + m13*x44 + m20*x45 + m27*x46 + m34*x47 + m41*x48 + m48*x49;
795 	  x[48] -= m7*x43 + m14*x44 + m21*x45 + m28*x46 + m35*x47 + m42*x48 + m49*x49;
796           pv   += 49;
797         }
798         PLogFlops(686*nz+637);
799       }
800       row = *ajtmp++;
801     }
802     /* finished row so stick it into b->a */
803     pv = ba + 49*bi[i];
804     pj = bj + bi[i];
805     nz = bi[i+1] - bi[i];
806     for (j=0; j<nz; j++) {
807       x      = rtmp+49*pj[j];
808       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
809       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7];
810       pv[8]  = x[8];  pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11];
811       pv[12] = x[12]; pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
812       pv[16] = x[16]; pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19];
813       pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23];
814       pv[24] = x[24]; pv[25] = x[25]; pv[26] = x[26]; pv[27] = x[27];
815       pv[28] = x[28]; pv[29] = x[29]; pv[30] = x[30]; pv[31] = x[31];
816       pv[32] = x[32]; pv[33] = x[33]; pv[34] = x[34]; pv[35] = x[35];
817       pv[36] = x[36]; pv[37] = x[37]; pv[38] = x[38]; pv[39] = x[39];
818       pv[40] = x[40]; pv[41] = x[41]; pv[42] = x[42]; pv[43] = x[43];
819       pv[44] = x[44]; pv[45] = x[45]; pv[46] = x[46]; pv[47] = x[47];
820       pv[48] = x[48];
821       pv   += 49;
822     }
823     /* invert diagonal block */
824     w = ba + 49*diag_offset[i];
825     ierr = Kernel_A_gets_inverse_A_7(w);CHKERRQ(ierr);
826   }
827 
828   ierr = PetscFree(rtmp);CHKERRQ(ierr);
829   C->factor    = FACTOR_LU;
830   C->assembled = PETSC_TRUE;
831   PLogFlops(1.3333*343*b->mbs); /* from inverting diagonal blocks */
832   PetscFunctionReturn(0);
833 }
834 
835 /* ------------------------------------------------------------*/
836 /*
837       Version for when blocks are 6 by 6
838 */
839 #undef __FUNC__
840 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_6"
841 int MatCholeskyFactorNumeric_SeqSBAIJ_6(Mat A,Mat *B)
842 {
843   Mat          C = *B;
844   Mat_SeqBAIJ  *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
845   IS           isrow = b->row,isicol = b->icol;
846   int          *r,*ic,ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
847   int          *ajtmpold,*ajtmp,nz,row;
848   int          *diag_offset = b->diag,idx,*ai=a->i,*aj=a->j,*pj;
849   MatScalar    *pv,*v,*rtmp,*pc,*w,*x;
850   MatScalar    p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
851   MatScalar    p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
852   MatScalar    x17,x18,x19,x20,x21,x22,x23,x24,x25,p10,p11,p12,p13,p14;
853   MatScalar    p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,m10,m11,m12;
854   MatScalar    m13,m14,m15,m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
855   MatScalar    p26,p27,p28,p29,p30,p31,p32,p33,p34,p35,p36;
856   MatScalar    x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36;
857   MatScalar    m26,m27,m28,m29,m30,m31,m32,m33,m34,m35,m36;
858   MatScalar    *ba = b->a,*aa = a->a;
859 
860   PetscFunctionBegin;
861   ierr  = ISGetIndices(isrow,&r);CHKERRQ(ierr);
862   ierr  = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
863   rtmp  = (MatScalar*)PetscMalloc(36*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
864 
865   for (i=0; i<n; i++) {
866     nz    = bi[i+1] - bi[i];
867     ajtmp = bj + bi[i];
868     for  (j=0; j<nz; j++) {
869       x = rtmp+36*ajtmp[j];
870       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
871       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
872       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = x[25] = 0.0 ;
873       x[26] = x[27] = x[28] = x[29] = x[30] = x[31] = x[32] = x[33] = 0.0 ;
874       x[34] = x[35] = 0.0 ;
875     }
876     /* load in initial (unfactored row) */
877     idx      = r[i];
878     nz       = ai[idx+1] - ai[idx];
879     ajtmpold = aj + ai[idx];
880     v        = aa + 36*ai[idx];
881     for (j=0; j<nz; j++) {
882       x    = rtmp+36*ic[ajtmpold[j]];
883       x[0] =  v[0];  x[1] =  v[1];  x[2] =  v[2];  x[3] =  v[3];
884       x[4] =  v[4];  x[5] =  v[5];  x[6] =  v[6];  x[7] =  v[7];
885       x[8] =  v[8];  x[9] =  v[9];  x[10] = v[10]; x[11] = v[11];
886       x[12] = v[12]; x[13] = v[13]; x[14] = v[14]; x[15] = v[15];
887       x[16] = v[16]; x[17] = v[17]; x[18] = v[18]; x[19] = v[19];
888       x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23];
889       x[24] = v[24]; x[25] = v[25]; x[26] = v[26]; x[27] = v[27];
890       x[28] = v[28]; x[29] = v[29]; x[30] = v[30]; x[31] = v[31];
891       x[32] = v[32]; x[33] = v[33]; x[34] = v[34]; x[35] = v[35];
892       v    += 36;
893     }
894     row = *ajtmp++;
895     while (row < i) {
896       pc  =  rtmp + 36*row;
897       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
898       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];
899       p9  = pc[8];  p10 = pc[9];  p11 = pc[10]; p12 = pc[11];
900       p13 = pc[12]; p14 = pc[13]; p15 = pc[14]; p16 = pc[15];
901       p17 = pc[16]; p18 = pc[17]; p19 = pc[18]; p20 = pc[19];
902       p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
903       p25 = pc[24]; p26 = pc[25]; p27 = pc[26]; p28 = pc[27];
904       p29 = pc[28]; p30 = pc[29]; p31 = pc[30]; p32 = pc[31];
905       p33 = pc[32]; p34 = pc[33]; p35 = pc[34]; p36 = pc[35];
906       if (p1  != 0.0 || p2  != 0.0 || p3  != 0.0 || p4  != 0.0 ||
907           p5  != 0.0 || p6  != 0.0 || p7  != 0.0 || p8  != 0.0 ||
908           p9  != 0.0 || p10 != 0.0 || p11 != 0.0 || p12 != 0.0 ||
909           p13 != 0.0 || p14 != 0.0 || p15 != 0.0 || p16 != 0.0 ||
910           p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 ||
911           p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 ||
912           p25 != 0.0 || p26 != 0.0 || p27 != 0.0 || p28 != 0.0 ||
913           p29 != 0.0 || p30 != 0.0 || p31 != 0.0 || p32 != 0.0 ||
914           p33 != 0.0 || p34 != 0.0 || p35 != 0.0 || p36 != 0.0) {
915         pv = ba + 36*diag_offset[row];
916         pj = bj + diag_offset[row] + 1;
917 	x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
918 	x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
919 	x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
920 	x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
921 	x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
922 	x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
923 	x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
924 	x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
925 	x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
926         pc[0]  = m1  = p1*x1  + p7*x2   + p13*x3  + p19*x4  + p25*x5  + p31*x6;
927         pc[1]  = m2  = p2*x1  + p8*x2   + p14*x3  + p20*x4  + p26*x5  + p32*x6;
928         pc[2]  = m3  = p3*x1  + p9*x2   + p15*x3  + p21*x4  + p27*x5  + p33*x6;
929         pc[3]  = m4  = p4*x1  + p10*x2  + p16*x3  + p22*x4  + p28*x5  + p34*x6;
930         pc[4]  = m5  = p5*x1  + p11*x2  + p17*x3  + p23*x4  + p29*x5  + p35*x6;
931         pc[5]  = m6  = p6*x1  + p12*x2  + p18*x3  + p24*x4  + p30*x5  + p36*x6;
932 
933         pc[6]  = m7  = p1*x7  + p7*x8   + p13*x9  + p19*x10 + p25*x11 + p31*x12;
934         pc[7]  = m8  = p2*x7  + p8*x8   + p14*x9  + p20*x10 + p26*x11 + p32*x12;
935         pc[8]  = m9  = p3*x7  + p9*x8   + p15*x9  + p21*x10 + p27*x11 + p33*x12;
936         pc[9]  = m10 = p4*x7  + p10*x8  + p16*x9  + p22*x10 + p28*x11 + p34*x12;
937         pc[10] = m11 = p5*x7  + p11*x8  + p17*x9  + p23*x10 + p29*x11 + p35*x12;
938         pc[11] = m12 = p6*x7  + p12*x8  + p18*x9  + p24*x10 + p30*x11 + p36*x12;
939 
940         pc[12] = m13 = p1*x13 + p7*x14  + p13*x15 + p19*x16 + p25*x17 + p31*x18;
941         pc[13] = m14 = p2*x13 + p8*x14  + p14*x15 + p20*x16 + p26*x17 + p32*x18;
942         pc[14] = m15 = p3*x13 + p9*x14  + p15*x15 + p21*x16 + p27*x17 + p33*x18;
943         pc[15] = m16 = p4*x13 + p10*x14 + p16*x15 + p22*x16 + p28*x17 + p34*x18;
944         pc[16] = m17 = p5*x13 + p11*x14 + p17*x15 + p23*x16 + p29*x17 + p35*x18;
945         pc[17] = m18 = p6*x13 + p12*x14 + p18*x15 + p24*x16 + p30*x17 + p36*x18;
946 
947         pc[18] = m19 = p1*x19 + p7*x20  + p13*x21 + p19*x22 + p25*x23 + p31*x24;
948         pc[19] = m20 = p2*x19 + p8*x20  + p14*x21 + p20*x22 + p26*x23 + p32*x24;
949         pc[20] = m21 = p3*x19 + p9*x20  + p15*x21 + p21*x22 + p27*x23 + p33*x24;
950         pc[21] = m22 = p4*x19 + p10*x20 + p16*x21 + p22*x22 + p28*x23 + p34*x24;
951         pc[22] = m23 = p5*x19 + p11*x20 + p17*x21 + p23*x22 + p29*x23 + p35*x24;
952         pc[23] = m24 = p6*x19 + p12*x20 + p18*x21 + p24*x22 + p30*x23 + p36*x24;
953 
954         pc[24] = m25 = p1*x25 + p7*x26  + p13*x27 + p19*x28 + p25*x29 + p31*x30;
955         pc[25] = m26 = p2*x25 + p8*x26  + p14*x27 + p20*x28 + p26*x29 + p32*x30;
956         pc[26] = m27 = p3*x25 + p9*x26  + p15*x27 + p21*x28 + p27*x29 + p33*x30;
957         pc[27] = m28 = p4*x25 + p10*x26 + p16*x27 + p22*x28 + p28*x29 + p34*x30;
958         pc[28] = m29 = p5*x25 + p11*x26 + p17*x27 + p23*x28 + p29*x29 + p35*x30;
959         pc[29] = m30 = p6*x25 + p12*x26 + p18*x27 + p24*x28 + p30*x29 + p36*x30;
960 
961         pc[30] = m31 = p1*x31 + p7*x32  + p13*x33 + p19*x34 + p25*x35 + p31*x36;
962         pc[31] = m32 = p2*x31 + p8*x32  + p14*x33 + p20*x34 + p26*x35 + p32*x36;
963         pc[32] = m33 = p3*x31 + p9*x32  + p15*x33 + p21*x34 + p27*x35 + p33*x36;
964         pc[33] = m34 = p4*x31 + p10*x32 + p16*x33 + p22*x34 + p28*x35 + p34*x36;
965         pc[34] = m35 = p5*x31 + p11*x32 + p17*x33 + p23*x34 + p29*x35 + p35*x36;
966         pc[35] = m36 = p6*x31 + p12*x32 + p18*x33 + p24*x34 + p30*x35 + p36*x36;
967 
968         nz = bi[row+1] - diag_offset[row] - 1;
969         pv += 36;
970         for (j=0; j<nz; j++) {
971 	  x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
972 	  x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
973 	  x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
974 	  x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
975 	  x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
976 	  x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
977 	  x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
978 	  x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
979 	  x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
980 	  x    = rtmp + 36*pj[j];
981           x[0]  -= m1*x1  + m7*x2   + m13*x3  + m19*x4  + m25*x5  + m31*x6;
982           x[1]  -= m2*x1  + m8*x2   + m14*x3  + m20*x4  + m26*x5  + m32*x6;
983           x[2]  -= m3*x1  + m9*x2   + m15*x3  + m21*x4  + m27*x5  + m33*x6;
984           x[3]  -= m4*x1  + m10*x2  + m16*x3  + m22*x4  + m28*x5  + m34*x6;
985           x[4]  -= m5*x1  + m11*x2  + m17*x3  + m23*x4  + m29*x5  + m35*x6;
986           x[5]  -= m6*x1  + m12*x2  + m18*x3  + m24*x4  + m30*x5  + m36*x6;
987 
988 	  x[6]  -= m1*x7  + m7*x8   + m13*x9  + m19*x10 + m25*x11 + m31*x12;
989 	  x[7]  -= m2*x7  + m8*x8   + m14*x9  + m20*x10 + m26*x11 + m32*x12;
990 	  x[8]  -= m3*x7  + m9*x8   + m15*x9  + m21*x10 + m27*x11 + m33*x12;
991 	  x[9]  -= m4*x7  + m10*x8  + m16*x9  + m22*x10 + m28*x11 + m34*x12;
992 	  x[10] -= m5*x7  + m11*x8  + m17*x9  + m23*x10 + m29*x11 + m35*x12;
993 	  x[11] -= m6*x7  + m12*x8  + m18*x9  + m24*x10 + m30*x11 + m36*x12;
994 
995 	  x[12] -= m1*x13 + m7*x14  + m13*x15 + m19*x16 + m25*x17 + m31*x18;
996 	  x[13] -= m2*x13 + m8*x14  + m14*x15 + m20*x16 + m26*x17 + m32*x18;
997 	  x[14] -= m3*x13 + m9*x14  + m15*x15 + m21*x16 + m27*x17 + m33*x18;
998 	  x[15] -= m4*x13 + m10*x14 + m16*x15 + m22*x16 + m28*x17 + m34*x18;
999 	  x[16] -= m5*x13 + m11*x14 + m17*x15 + m23*x16 + m29*x17 + m35*x18;
1000 	  x[17] -= m6*x13 + m12*x14 + m18*x15 + m24*x16 + m30*x17 + m36*x18;
1001 
1002 	  x[18] -= m1*x19 + m7*x20  + m13*x21 + m19*x22 + m25*x23 + m31*x24;
1003 	  x[19] -= m2*x19 + m8*x20  + m14*x21 + m20*x22 + m26*x23 + m32*x24;
1004 	  x[20] -= m3*x19 + m9*x20  + m15*x21 + m21*x22 + m27*x23 + m33*x24;
1005 	  x[21] -= m4*x19 + m10*x20 + m16*x21 + m22*x22 + m28*x23 + m34*x24;
1006 	  x[22] -= m5*x19 + m11*x20 + m17*x21 + m23*x22 + m29*x23 + m35*x24;
1007 	  x[23] -= m6*x19 + m12*x20 + m18*x21 + m24*x22 + m30*x23 + m36*x24;
1008 
1009 	  x[24] -= m1*x25 + m7*x26  + m13*x27 + m19*x28 + m25*x29 + m31*x30;
1010 	  x[25] -= m2*x25 + m8*x26  + m14*x27 + m20*x28 + m26*x29 + m32*x30;
1011 	  x[26] -= m3*x25 + m9*x26  + m15*x27 + m21*x28 + m27*x29 + m33*x30;
1012 	  x[27] -= m4*x25 + m10*x26 + m16*x27 + m22*x28 + m28*x29 + m34*x30;
1013 	  x[28] -= m5*x25 + m11*x26 + m17*x27 + m23*x28 + m29*x29 + m35*x30;
1014 	  x[29] -= m6*x25 + m12*x26 + m18*x27 + m24*x28 + m30*x29 + m36*x30;
1015 
1016 	  x[30] -= m1*x31 + m7*x32  + m13*x33 + m19*x34 + m25*x35 + m31*x36;
1017 	  x[31] -= m2*x31 + m8*x32  + m14*x33 + m20*x34 + m26*x35 + m32*x36;
1018 	  x[32] -= m3*x31 + m9*x32  + m15*x33 + m21*x34 + m27*x35 + m33*x36;
1019 	  x[33] -= m4*x31 + m10*x32 + m16*x33 + m22*x34 + m28*x35 + m34*x36;
1020 	  x[34] -= m5*x31 + m11*x32 + m17*x33 + m23*x34 + m29*x35 + m35*x36;
1021 	  x[35] -= m6*x31 + m12*x32 + m18*x33 + m24*x34 + m30*x35 + m36*x36;
1022 
1023           pv   += 36;
1024         }
1025         PLogFlops(432*nz+396);
1026       }
1027       row = *ajtmp++;
1028     }
1029     /* finished row so stick it into b->a */
1030     pv = ba + 36*bi[i];
1031     pj = bj + bi[i];
1032     nz = bi[i+1] - bi[i];
1033     for (j=0; j<nz; j++) {
1034       x      = rtmp+36*pj[j];
1035       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
1036       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7];
1037       pv[8]  = x[8];  pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11];
1038       pv[12] = x[12]; pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
1039       pv[16] = x[16]; pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19];
1040       pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23];
1041       pv[24] = x[24]; pv[25] = x[25]; pv[26] = x[26]; pv[27] = x[27];
1042       pv[28] = x[28]; pv[29] = x[29]; pv[30] = x[30]; pv[31] = x[31];
1043       pv[32] = x[32]; pv[33] = x[33]; pv[34] = x[34]; pv[35] = x[35];
1044       pv   += 36;
1045     }
1046     /* invert diagonal block */
1047     w = ba + 36*diag_offset[i];
1048     ierr = Kernel_A_gets_inverse_A_6(w);CHKERRQ(ierr);
1049   }
1050 
1051   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1052   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
1053   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
1054   C->factor = FACTOR_LU;
1055   C->assembled = PETSC_TRUE;
1056   PLogFlops(1.3333*216*b->mbs); /* from inverting diagonal blocks */
1057   PetscFunctionReturn(0);
1058 }
1059 /*
1060       Version for when blocks are 6 by 6 Using natural ordering
1061 */
1062 #undef __FUNC__
1063 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_6_NaturalOrdering"
1064 int MatCholeskyFactorNumeric_SeqSBAIJ_6_NaturalOrdering(Mat A,Mat *B)
1065 {
1066   Mat         C = *B;
1067   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
1068   int         ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
1069   int         *ajtmpold,*ajtmp,nz,row;
1070   int         *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
1071   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
1072   MatScalar   x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15;
1073   MatScalar   x16,x17,x18,x19,x20,x21,x22,x23,x24,x25;
1074   MatScalar   p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15;
1075   MatScalar   p16,p17,p18,p19,p20,p21,p22,p23,p24,p25;
1076   MatScalar   m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12,m13,m14,m15;
1077   MatScalar   m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
1078   MatScalar   p26,p27,p28,p29,p30,p31,p32,p33,p34,p35,p36;
1079   MatScalar   x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36;
1080   MatScalar   m26,m27,m28,m29,m30,m31,m32,m33,m34,m35,m36;
1081   MatScalar   *ba = b->a,*aa = a->a;
1082 
1083   PetscFunctionBegin;
1084   rtmp  = (MatScalar*)PetscMalloc(36*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
1085   for (i=0; i<n; i++) {
1086     nz    = bi[i+1] - bi[i];
1087     ajtmp = bj + bi[i];
1088     for  (j=0; j<nz; j++) {
1089       x = rtmp+36*ajtmp[j];
1090       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
1091       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
1092       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = x[25] = 0.0 ;
1093       x[26] = x[27] = x[28] = x[29] = x[30] = x[31] = x[32] = x[33] = 0.0 ;
1094       x[34] = x[35] = 0.0 ;
1095     }
1096     /* load in initial (unfactored row) */
1097     nz       = ai[i+1] - ai[i];
1098     ajtmpold = aj + ai[i];
1099     v        = aa + 36*ai[i];
1100     for (j=0; j<nz; j++) {
1101       x    = rtmp+36*ajtmpold[j];
1102       x[0] =  v[0];  x[1] =  v[1];  x[2] =  v[2];  x[3] =  v[3];
1103       x[4] =  v[4];  x[5] =  v[5];  x[6] =  v[6];  x[7] =  v[7];
1104       x[8] =  v[8];  x[9] =  v[9];  x[10] = v[10]; x[11] = v[11];
1105       x[12] = v[12]; x[13] = v[13]; x[14] = v[14]; x[15] = v[15];
1106       x[16] = v[16]; x[17] = v[17]; x[18] = v[18]; x[19] = v[19];
1107       x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23];
1108       x[24] = v[24]; x[25] = v[25]; x[26] = v[26]; x[27] = v[27];
1109       x[28] = v[28]; x[29] = v[29]; x[30] = v[30]; x[31] = v[31];
1110       x[32] = v[32]; x[33] = v[33]; x[34] = v[34]; x[35] = v[35];
1111       v    += 36;
1112     }
1113     row = *ajtmp++;
1114     while (row < i) {
1115       pc  = rtmp + 36*row;
1116       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
1117       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];
1118       p9  = pc[8];  p10 = pc[9];  p11 = pc[10]; p12 = pc[11];
1119       p13 = pc[12]; p14 = pc[13]; p15 = pc[14]; p16 = pc[15];
1120       p17 = pc[16]; p18 = pc[17]; p19 = pc[18]; p20 = pc[19];
1121       p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
1122       p25 = pc[24]; p26 = pc[25]; p27 = pc[26]; p28 = pc[27];
1123       p29 = pc[28]; p30 = pc[29]; p31 = pc[30]; p32 = pc[31];
1124       p33 = pc[32]; p34 = pc[33]; p35 = pc[34]; p36 = pc[35];
1125       if (p1  != 0.0 || p2  != 0.0 || p3  != 0.0 || p4  != 0.0 ||
1126           p5  != 0.0 || p6  != 0.0 || p7  != 0.0 || p8  != 0.0 ||
1127           p9  != 0.0 || p10 != 0.0 || p11 != 0.0 || p12 != 0.0 ||
1128           p13 != 0.0 || p14 != 0.0 || p15 != 0.0 || p16 != 0.0 ||
1129           p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 ||
1130           p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 ||
1131           p25 != 0.0 || p26 != 0.0 || p27 != 0.0 || p28 != 0.0 ||
1132           p29 != 0.0 || p30 != 0.0 || p31 != 0.0 || p32 != 0.0 ||
1133           p33 != 0.0 || p34 != 0.0 || p35 != 0.0 || p36 != 0.0) {
1134         pv = ba + 36*diag_offset[row];
1135         pj = bj + diag_offset[row] + 1;
1136 	x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
1137 	x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
1138 	x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
1139 	x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
1140 	x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
1141 	x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
1142 	x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
1143 	x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
1144 	x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
1145         pc[0]  = m1  = p1*x1  + p7*x2   + p13*x3  + p19*x4  + p25*x5  + p31*x6;
1146         pc[1]  = m2  = p2*x1  + p8*x2   + p14*x3  + p20*x4  + p26*x5  + p32*x6;
1147         pc[2]  = m3  = p3*x1  + p9*x2   + p15*x3  + p21*x4  + p27*x5  + p33*x6;
1148         pc[3]  = m4  = p4*x1  + p10*x2  + p16*x3  + p22*x4  + p28*x5  + p34*x6;
1149         pc[4]  = m5  = p5*x1  + p11*x2  + p17*x3  + p23*x4  + p29*x5  + p35*x6;
1150         pc[5]  = m6  = p6*x1  + p12*x2  + p18*x3  + p24*x4  + p30*x5  + p36*x6;
1151 
1152         pc[6]  = m7  = p1*x7  + p7*x8   + p13*x9  + p19*x10 + p25*x11 + p31*x12;
1153         pc[7]  = m8  = p2*x7  + p8*x8   + p14*x9  + p20*x10 + p26*x11 + p32*x12;
1154         pc[8]  = m9  = p3*x7  + p9*x8   + p15*x9  + p21*x10 + p27*x11 + p33*x12;
1155         pc[9]  = m10 = p4*x7  + p10*x8  + p16*x9  + p22*x10 + p28*x11 + p34*x12;
1156         pc[10] = m11 = p5*x7  + p11*x8  + p17*x9  + p23*x10 + p29*x11 + p35*x12;
1157         pc[11] = m12 = p6*x7  + p12*x8  + p18*x9  + p24*x10 + p30*x11 + p36*x12;
1158 
1159         pc[12] = m13 = p1*x13 + p7*x14  + p13*x15 + p19*x16 + p25*x17 + p31*x18;
1160         pc[13] = m14 = p2*x13 + p8*x14  + p14*x15 + p20*x16 + p26*x17 + p32*x18;
1161         pc[14] = m15 = p3*x13 + p9*x14  + p15*x15 + p21*x16 + p27*x17 + p33*x18;
1162         pc[15] = m16 = p4*x13 + p10*x14 + p16*x15 + p22*x16 + p28*x17 + p34*x18;
1163         pc[16] = m17 = p5*x13 + p11*x14 + p17*x15 + p23*x16 + p29*x17 + p35*x18;
1164         pc[17] = m18 = p6*x13 + p12*x14 + p18*x15 + p24*x16 + p30*x17 + p36*x18;
1165 
1166         pc[18] = m19 = p1*x19 + p7*x20  + p13*x21 + p19*x22 + p25*x23 + p31*x24;
1167         pc[19] = m20 = p2*x19 + p8*x20  + p14*x21 + p20*x22 + p26*x23 + p32*x24;
1168         pc[20] = m21 = p3*x19 + p9*x20  + p15*x21 + p21*x22 + p27*x23 + p33*x24;
1169         pc[21] = m22 = p4*x19 + p10*x20 + p16*x21 + p22*x22 + p28*x23 + p34*x24;
1170         pc[22] = m23 = p5*x19 + p11*x20 + p17*x21 + p23*x22 + p29*x23 + p35*x24;
1171         pc[23] = m24 = p6*x19 + p12*x20 + p18*x21 + p24*x22 + p30*x23 + p36*x24;
1172 
1173         pc[24] = m25 = p1*x25 + p7*x26  + p13*x27 + p19*x28 + p25*x29 + p31*x30;
1174         pc[25] = m26 = p2*x25 + p8*x26  + p14*x27 + p20*x28 + p26*x29 + p32*x30;
1175         pc[26] = m27 = p3*x25 + p9*x26  + p15*x27 + p21*x28 + p27*x29 + p33*x30;
1176         pc[27] = m28 = p4*x25 + p10*x26 + p16*x27 + p22*x28 + p28*x29 + p34*x30;
1177         pc[28] = m29 = p5*x25 + p11*x26 + p17*x27 + p23*x28 + p29*x29 + p35*x30;
1178         pc[29] = m30 = p6*x25 + p12*x26 + p18*x27 + p24*x28 + p30*x29 + p36*x30;
1179 
1180         pc[30] = m31 = p1*x31 + p7*x32  + p13*x33 + p19*x34 + p25*x35 + p31*x36;
1181         pc[31] = m32 = p2*x31 + p8*x32  + p14*x33 + p20*x34 + p26*x35 + p32*x36;
1182         pc[32] = m33 = p3*x31 + p9*x32  + p15*x33 + p21*x34 + p27*x35 + p33*x36;
1183         pc[33] = m34 = p4*x31 + p10*x32 + p16*x33 + p22*x34 + p28*x35 + p34*x36;
1184         pc[34] = m35 = p5*x31 + p11*x32 + p17*x33 + p23*x34 + p29*x35 + p35*x36;
1185         pc[35] = m36 = p6*x31 + p12*x32 + p18*x33 + p24*x34 + p30*x35 + p36*x36;
1186 
1187         nz = bi[row+1] - diag_offset[row] - 1;
1188         pv += 36;
1189         for (j=0; j<nz; j++) {
1190 	  x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
1191 	  x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
1192 	  x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
1193 	  x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
1194 	  x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
1195 	  x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
1196 	  x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
1197 	  x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
1198 	  x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
1199 	  x    = rtmp + 36*pj[j];
1200           x[0]  -= m1*x1  + m7*x2   + m13*x3  + m19*x4  + m25*x5  + m31*x6;
1201           x[1]  -= m2*x1  + m8*x2   + m14*x3  + m20*x4  + m26*x5  + m32*x6;
1202           x[2]  -= m3*x1  + m9*x2   + m15*x3  + m21*x4  + m27*x5  + m33*x6;
1203           x[3]  -= m4*x1  + m10*x2  + m16*x3  + m22*x4  + m28*x5  + m34*x6;
1204           x[4]  -= m5*x1  + m11*x2  + m17*x3  + m23*x4  + m29*x5  + m35*x6;
1205           x[5]  -= m6*x1  + m12*x2  + m18*x3  + m24*x4  + m30*x5  + m36*x6;
1206 
1207 	  x[6]  -= m1*x7  + m7*x8   + m13*x9  + m19*x10 + m25*x11 + m31*x12;
1208 	  x[7]  -= m2*x7  + m8*x8   + m14*x9  + m20*x10 + m26*x11 + m32*x12;
1209 	  x[8]  -= m3*x7  + m9*x8   + m15*x9  + m21*x10 + m27*x11 + m33*x12;
1210 	  x[9]  -= m4*x7  + m10*x8  + m16*x9  + m22*x10 + m28*x11 + m34*x12;
1211 	  x[10] -= m5*x7  + m11*x8  + m17*x9  + m23*x10 + m29*x11 + m35*x12;
1212 	  x[11] -= m6*x7  + m12*x8  + m18*x9  + m24*x10 + m30*x11 + m36*x12;
1213 
1214 	  x[12] -= m1*x13 + m7*x14  + m13*x15 + m19*x16 + m25*x17 + m31*x18;
1215 	  x[13] -= m2*x13 + m8*x14  + m14*x15 + m20*x16 + m26*x17 + m32*x18;
1216 	  x[14] -= m3*x13 + m9*x14  + m15*x15 + m21*x16 + m27*x17 + m33*x18;
1217 	  x[15] -= m4*x13 + m10*x14 + m16*x15 + m22*x16 + m28*x17 + m34*x18;
1218 	  x[16] -= m5*x13 + m11*x14 + m17*x15 + m23*x16 + m29*x17 + m35*x18;
1219 	  x[17] -= m6*x13 + m12*x14 + m18*x15 + m24*x16 + m30*x17 + m36*x18;
1220 
1221 	  x[18] -= m1*x19 + m7*x20  + m13*x21 + m19*x22 + m25*x23 + m31*x24;
1222 	  x[19] -= m2*x19 + m8*x20  + m14*x21 + m20*x22 + m26*x23 + m32*x24;
1223 	  x[20] -= m3*x19 + m9*x20  + m15*x21 + m21*x22 + m27*x23 + m33*x24;
1224 	  x[21] -= m4*x19 + m10*x20 + m16*x21 + m22*x22 + m28*x23 + m34*x24;
1225 	  x[22] -= m5*x19 + m11*x20 + m17*x21 + m23*x22 + m29*x23 + m35*x24;
1226 	  x[23] -= m6*x19 + m12*x20 + m18*x21 + m24*x22 + m30*x23 + m36*x24;
1227 
1228 	  x[24] -= m1*x25 + m7*x26  + m13*x27 + m19*x28 + m25*x29 + m31*x30;
1229 	  x[25] -= m2*x25 + m8*x26  + m14*x27 + m20*x28 + m26*x29 + m32*x30;
1230 	  x[26] -= m3*x25 + m9*x26  + m15*x27 + m21*x28 + m27*x29 + m33*x30;
1231 	  x[27] -= m4*x25 + m10*x26 + m16*x27 + m22*x28 + m28*x29 + m34*x30;
1232 	  x[28] -= m5*x25 + m11*x26 + m17*x27 + m23*x28 + m29*x29 + m35*x30;
1233 	  x[29] -= m6*x25 + m12*x26 + m18*x27 + m24*x28 + m30*x29 + m36*x30;
1234 
1235 	  x[30] -= m1*x31 + m7*x32  + m13*x33 + m19*x34 + m25*x35 + m31*x36;
1236 	  x[31] -= m2*x31 + m8*x32  + m14*x33 + m20*x34 + m26*x35 + m32*x36;
1237 	  x[32] -= m3*x31 + m9*x32  + m15*x33 + m21*x34 + m27*x35 + m33*x36;
1238 	  x[33] -= m4*x31 + m10*x32 + m16*x33 + m22*x34 + m28*x35 + m34*x36;
1239 	  x[34] -= m5*x31 + m11*x32 + m17*x33 + m23*x34 + m29*x35 + m35*x36;
1240 	  x[35] -= m6*x31 + m12*x32 + m18*x33 + m24*x34 + m30*x35 + m36*x36;
1241 
1242           pv   += 36;
1243         }
1244         PLogFlops(432*nz+396);
1245       }
1246       row = *ajtmp++;
1247     }
1248     /* finished row so stick it into b->a */
1249     pv = ba + 36*bi[i];
1250     pj = bj + bi[i];
1251     nz = bi[i+1] - bi[i];
1252     for (j=0; j<nz; j++) {
1253       x      = rtmp+36*pj[j];
1254       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
1255       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7];
1256       pv[8]  = x[8];  pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11];
1257       pv[12] = x[12]; pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
1258       pv[16] = x[16]; pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19];
1259       pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23];
1260       pv[24] = x[24]; pv[25] = x[25]; pv[26] = x[26]; pv[27] = x[27];
1261       pv[28] = x[28]; pv[29] = x[29]; pv[30] = x[30]; pv[31] = x[31];
1262       pv[32] = x[32]; pv[33] = x[33]; pv[34] = x[34]; pv[35] = x[35];
1263       pv   += 36;
1264     }
1265     /* invert diagonal block */
1266     w = ba + 36*diag_offset[i];
1267     ierr = Kernel_A_gets_inverse_A_6(w);CHKERRQ(ierr);
1268   }
1269 
1270   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1271   C->factor    = FACTOR_LU;
1272   C->assembled = PETSC_TRUE;
1273   PLogFlops(1.3333*216*b->mbs); /* from inverting diagonal blocks */
1274   PetscFunctionReturn(0);
1275 }
1276 
1277 /*
1278       Version for when blocks are 5 by 5
1279 */
1280 #undef __FUNC__
1281 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_5"
1282 int MatCholeskyFactorNumeric_SeqSBAIJ_5(Mat A,Mat *B)
1283 {
1284   Mat         C = *B;
1285   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
1286   IS          isrow = b->row,isicol = b->icol;
1287   int         *r,*ic,ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
1288   int         *ajtmpold,*ajtmp,nz,row;
1289   int         *diag_offset = b->diag,idx,*ai=a->i,*aj=a->j,*pj;
1290   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
1291   MatScalar   p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
1292   MatScalar   p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
1293   MatScalar   x17,x18,x19,x20,x21,x22,x23,x24,x25,p10,p11,p12,p13,p14;
1294   MatScalar   p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,m10,m11,m12;
1295   MatScalar   m13,m14,m15,m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
1296   MatScalar   *ba = b->a,*aa = a->a;
1297 
1298   PetscFunctionBegin;
1299   ierr  = ISGetIndices(isrow,&r);CHKERRQ(ierr);
1300   ierr  = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
1301   rtmp  = (MatScalar*)PetscMalloc(25*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
1302 
1303   for (i=0; i<n; i++) {
1304     nz    = bi[i+1] - bi[i];
1305     ajtmp = bj + bi[i];
1306     for  (j=0; j<nz; j++) {
1307       x = rtmp+25*ajtmp[j];
1308       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
1309       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
1310       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0;
1311     }
1312     /* load in initial (unfactored row) */
1313     idx      = r[i];
1314     nz       = ai[idx+1] - ai[idx];
1315     ajtmpold = aj + ai[idx];
1316     v        = aa + 25*ai[idx];
1317     for (j=0; j<nz; j++) {
1318       x    = rtmp+25*ic[ajtmpold[j]];
1319       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
1320       x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
1321       x[9] = v[9]; x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
1322       x[14] = v[14]; x[15] = v[15]; x[16] = v[16]; x[17] = v[17];
1323       x[18] = v[18]; x[19] = v[19]; x[20] = v[20]; x[21] = v[21];
1324       x[22] = v[22]; x[23] = v[23]; x[24] = v[24];
1325       v    += 25;
1326     }
1327     row = *ajtmp++;
1328     while (row < i) {
1329       pc = rtmp + 25*row;
1330       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
1331       p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
1332       p10 = pc[9]; p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
1333       p15 = pc[14]; p16 = pc[15]; p17 = pc[16]; p18 = pc[17]; p19 = pc[18];
1334       p20 = pc[19]; p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
1335       p25 = pc[24];
1336       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
1337           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
1338           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
1339           || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 ||
1340           p20 != 0.0 || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 ||
1341           p24 != 0.0 || p25 != 0.0) {
1342         pv = ba + 25*diag_offset[row];
1343         pj = bj + diag_offset[row] + 1;
1344         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
1345         x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
1346         x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
1347         x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17];
1348         x19 = pv[18]; x20 = pv[19]; x21 = pv[20]; x22 = pv[21];
1349         x23 = pv[22]; x24 = pv[23]; x25 = pv[24];
1350         pc[0] = m1 = p1*x1 + p6*x2  + p11*x3 + p16*x4 + p21*x5;
1351         pc[1] = m2 = p2*x1 + p7*x2  + p12*x3 + p17*x4 + p22*x5;
1352         pc[2] = m3 = p3*x1 + p8*x2  + p13*x3 + p18*x4 + p23*x5;
1353         pc[3] = m4 = p4*x1 + p9*x2  + p14*x3 + p19*x4 + p24*x5;
1354         pc[4] = m5 = p5*x1 + p10*x2 + p15*x3 + p20*x4 + p25*x5;
1355 
1356         pc[5] = m6 = p1*x6 + p6*x7  + p11*x8 + p16*x9 + p21*x10;
1357         pc[6] = m7 = p2*x6 + p7*x7  + p12*x8 + p17*x9 + p22*x10;
1358         pc[7] = m8 = p3*x6 + p8*x7  + p13*x8 + p18*x9 + p23*x10;
1359         pc[8] = m9 = p4*x6 + p9*x7  + p14*x8 + p19*x9 + p24*x10;
1360         pc[9] = m10 = p5*x6 + p10*x7 + p15*x8 + p20*x9 + p25*x10;
1361 
1362         pc[10] = m11 = p1*x11 + p6*x12  + p11*x13 + p16*x14 + p21*x15;
1363         pc[11] = m12 = p2*x11 + p7*x12  + p12*x13 + p17*x14 + p22*x15;
1364         pc[12] = m13 = p3*x11 + p8*x12  + p13*x13 + p18*x14 + p23*x15;
1365         pc[13] = m14 = p4*x11 + p9*x12  + p14*x13 + p19*x14 + p24*x15;
1366         pc[14] = m15 = p5*x11 + p10*x12 + p15*x13 + p20*x14 + p25*x15;
1367 
1368         pc[15] = m16 = p1*x16 + p6*x17  + p11*x18 + p16*x19 + p21*x20;
1369         pc[16] = m17 = p2*x16 + p7*x17  + p12*x18 + p17*x19 + p22*x20;
1370         pc[17] = m18 = p3*x16 + p8*x17  + p13*x18 + p18*x19 + p23*x20;
1371         pc[18] = m19 = p4*x16 + p9*x17  + p14*x18 + p19*x19 + p24*x20;
1372         pc[19] = m20 = p5*x16 + p10*x17 + p15*x18 + p20*x19 + p25*x20;
1373 
1374         pc[20] = m21 = p1*x21 + p6*x22  + p11*x23 + p16*x24 + p21*x25;
1375         pc[21] = m22 = p2*x21 + p7*x22  + p12*x23 + p17*x24 + p22*x25;
1376         pc[22] = m23 = p3*x21 + p8*x22  + p13*x23 + p18*x24 + p23*x25;
1377         pc[23] = m24 = p4*x21 + p9*x22  + p14*x23 + p19*x24 + p24*x25;
1378         pc[24] = m25 = p5*x21 + p10*x22 + p15*x23 + p20*x24 + p25*x25;
1379 
1380         nz = bi[row+1] - diag_offset[row] - 1;
1381         pv += 25;
1382         for (j=0; j<nz; j++) {
1383           x1   = pv[0];  x2 = pv[1];   x3  = pv[2];  x4  = pv[3];
1384           x5   = pv[4];  x6 = pv[5];   x7  = pv[6];  x8  = pv[7]; x9 = pv[8];
1385           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
1386           x14  = pv[13]; x15 = pv[14]; x16 = pv[15]; x17 = pv[16];
1387           x18  = pv[17]; x19 = pv[18]; x20 = pv[19]; x21 = pv[20];
1388           x22  = pv[21]; x23 = pv[22]; x24 = pv[23]; x25 = pv[24];
1389           x    = rtmp + 25*pj[j];
1390           x[0] -= m1*x1 + m6*x2  + m11*x3 + m16*x4 + m21*x5;
1391           x[1] -= m2*x1 + m7*x2  + m12*x3 + m17*x4 + m22*x5;
1392           x[2] -= m3*x1 + m8*x2  + m13*x3 + m18*x4 + m23*x5;
1393           x[3] -= m4*x1 + m9*x2  + m14*x3 + m19*x4 + m24*x5;
1394           x[4] -= m5*x1 + m10*x2 + m15*x3 + m20*x4 + m25*x5;
1395 
1396           x[5] -= m1*x6 + m6*x7  + m11*x8 + m16*x9 + m21*x10;
1397           x[6] -= m2*x6 + m7*x7  + m12*x8 + m17*x9 + m22*x10;
1398           x[7] -= m3*x6 + m8*x7  + m13*x8 + m18*x9 + m23*x10;
1399           x[8] -= m4*x6 + m9*x7  + m14*x8 + m19*x9 + m24*x10;
1400           x[9] -= m5*x6 + m10*x7 + m15*x8 + m20*x9 + m25*x10;
1401 
1402           x[10] -= m1*x11 + m6*x12  + m11*x13 + m16*x14 + m21*x15;
1403           x[11] -= m2*x11 + m7*x12  + m12*x13 + m17*x14 + m22*x15;
1404           x[12] -= m3*x11 + m8*x12  + m13*x13 + m18*x14 + m23*x15;
1405           x[13] -= m4*x11 + m9*x12  + m14*x13 + m19*x14 + m24*x15;
1406           x[14] -= m5*x11 + m10*x12 + m15*x13 + m20*x14 + m25*x15;
1407 
1408           x[15] -= m1*x16 + m6*x17  + m11*x18 + m16*x19 + m21*x20;
1409           x[16] -= m2*x16 + m7*x17  + m12*x18 + m17*x19 + m22*x20;
1410           x[17] -= m3*x16 + m8*x17  + m13*x18 + m18*x19 + m23*x20;
1411           x[18] -= m4*x16 + m9*x17  + m14*x18 + m19*x19 + m24*x20;
1412           x[19] -= m5*x16 + m10*x17 + m15*x18 + m20*x19 + m25*x20;
1413 
1414           x[20] -= m1*x21 + m6*x22  + m11*x23 + m16*x24 + m21*x25;
1415           x[21] -= m2*x21 + m7*x22  + m12*x23 + m17*x24 + m22*x25;
1416           x[22] -= m3*x21 + m8*x22  + m13*x23 + m18*x24 + m23*x25;
1417           x[23] -= m4*x21 + m9*x22  + m14*x23 + m19*x24 + m24*x25;
1418           x[24] -= m5*x21 + m10*x22 + m15*x23 + m20*x24 + m25*x25;
1419 
1420           pv   += 25;
1421         }
1422         PLogFlops(250*nz+225);
1423       }
1424       row = *ajtmp++;
1425     }
1426     /* finished row so stick it into b->a */
1427     pv = ba + 25*bi[i];
1428     pj = bj + bi[i];
1429     nz = bi[i+1] - bi[i];
1430     for (j=0; j<nz; j++) {
1431       x     = rtmp+25*pj[j];
1432       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
1433       pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
1434       pv[9] = x[9]; pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
1435       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; pv[16] = x[16];
1436       pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19]; pv[20] = x[20];
1437       pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23]; pv[24] = x[24];
1438       pv   += 25;
1439     }
1440     /* invert diagonal block */
1441     w = ba + 25*diag_offset[i];
1442     ierr = Kernel_A_gets_inverse_A_5(w);CHKERRQ(ierr);
1443   }
1444 
1445   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1446   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
1447   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
1448   C->factor = FACTOR_LU;
1449   C->assembled = PETSC_TRUE;
1450   PLogFlops(1.3333*125*b->mbs); /* from inverting diagonal blocks */
1451   PetscFunctionReturn(0);
1452 }
1453 /*
1454       Version for when blocks are 5 by 5 Using natural ordering
1455 */
1456 #undef __FUNC__
1457 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_5_NaturalOrdering"
1458 int MatCholeskyFactorNumeric_SeqSBAIJ_5_NaturalOrdering(Mat A,Mat *B)
1459 {
1460   Mat         C = *B;
1461   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
1462   int         ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
1463   int         *ajtmpold,*ajtmp,nz,row;
1464   int         *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
1465   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
1466   MatScalar   x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15;
1467   MatScalar   x16,x17,x18,x19,x20,x21,x22,x23,x24,x25;
1468   MatScalar   p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15;
1469   MatScalar   p16,p17,p18,p19,p20,p21,p22,p23,p24,p25;
1470   MatScalar   m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12,m13,m14,m15;
1471   MatScalar   m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
1472   MatScalar   *ba = b->a,*aa = a->a;
1473 
1474   PetscFunctionBegin;
1475   rtmp  = (MatScalar*)PetscMalloc(25*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
1476   for (i=0; i<n; i++) {
1477     nz    = bi[i+1] - bi[i];
1478     ajtmp = bj + bi[i];
1479     for  (j=0; j<nz; j++) {
1480       x = rtmp+25*ajtmp[j];
1481       x[0]  = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = x[9] = 0.0;
1482       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
1483       x[16] = x[17] = x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0;
1484     }
1485     /* load in initial (unfactored row) */
1486     nz       = ai[i+1] - ai[i];
1487     ajtmpold = aj + ai[i];
1488     v        = aa + 25*ai[i];
1489     for (j=0; j<nz; j++) {
1490       x    = rtmp+25*ajtmpold[j];
1491       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
1492       x[4]  = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
1493       x[9]  = v[9];  x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
1494       x[14] = v[14]; x[15] = v[15]; x[16] = v[16]; x[17] = v[17]; x[18] = v[18];
1495       x[19] = v[19]; x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23];
1496       x[24] = v[24];
1497       v    += 25;
1498     }
1499     row = *ajtmp++;
1500     while (row < i) {
1501       pc  = rtmp + 25*row;
1502       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
1503       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
1504       p10 = pc[9];  p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
1505       p15 = pc[14]; p16 = pc[15]; p17 = pc[16]; p18 = pc[17];
1506       p19 = pc[18]; p20 = pc[19]; p21 = pc[20]; p22 = pc[21]; p23 = pc[22];
1507       p24 = pc[23]; p25 = pc[24];
1508       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
1509           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
1510           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
1511           || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0
1512           || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 || p25 != 0.0) {
1513         pv = ba + 25*diag_offset[row];
1514         pj = bj + diag_offset[row] + 1;
1515         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
1516         x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
1517         x10 = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
1518         x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17]; x19 = pv[18];
1519         x20 = pv[19]; x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
1520         x25 = pv[24];
1521         pc[0] = m1 = p1*x1 + p6*x2  + p11*x3 + p16*x4 + p21*x5;
1522         pc[1] = m2 = p2*x1 + p7*x2  + p12*x3 + p17*x4 + p22*x5;
1523         pc[2] = m3 = p3*x1 + p8*x2  + p13*x3 + p18*x4 + p23*x5;
1524         pc[3] = m4 = p4*x1 + p9*x2  + p14*x3 + p19*x4 + p24*x5;
1525         pc[4] = m5 = p5*x1 + p10*x2 + p15*x3 + p20*x4 + p25*x5;
1526 
1527         pc[5]  = m6  = p1*x6 + p6*x7  + p11*x8 + p16*x9 + p21*x10;
1528         pc[6]  = m7  = p2*x6 + p7*x7  + p12*x8 + p17*x9 + p22*x10;
1529         pc[7]  = m8  = p3*x6 + p8*x7  + p13*x8 + p18*x9 + p23*x10;
1530         pc[8]  = m9  = p4*x6 + p9*x7  + p14*x8 + p19*x9 + p24*x10;
1531         pc[9]  = m10 = p5*x6 + p10*x7 + p15*x8 + p20*x9 + p25*x10;
1532 
1533         pc[10] = m11 = p1*x11 + p6*x12  + p11*x13 + p16*x14 + p21*x15;
1534         pc[11] = m12 = p2*x11 + p7*x12  + p12*x13 + p17*x14 + p22*x15;
1535         pc[12] = m13 = p3*x11 + p8*x12  + p13*x13 + p18*x14 + p23*x15;
1536         pc[13] = m14 = p4*x11 + p9*x12  + p14*x13 + p19*x14 + p24*x15;
1537         pc[14] = m15 = p5*x11 + p10*x12 + p15*x13 + p20*x14 + p25*x15;
1538 
1539         pc[15] = m16 = p1*x16 + p6*x17  + p11*x18 + p16*x19 + p21*x20;
1540         pc[16] = m17 = p2*x16 + p7*x17  + p12*x18 + p17*x19 + p22*x20;
1541         pc[17] = m18 = p3*x16 + p8*x17  + p13*x18 + p18*x19 + p23*x20;
1542         pc[18] = m19 = p4*x16 + p9*x17  + p14*x18 + p19*x19 + p24*x20;
1543         pc[19] = m20 = p5*x16 + p10*x17 + p15*x18 + p20*x19 + p25*x20;
1544 
1545         pc[20] = m21 = p1*x21 + p6*x22  + p11*x23 + p16*x24 + p21*x25;
1546         pc[21] = m22 = p2*x21 + p7*x22  + p12*x23 + p17*x24 + p22*x25;
1547         pc[22] = m23 = p3*x21 + p8*x22  + p13*x23 + p18*x24 + p23*x25;
1548         pc[23] = m24 = p4*x21 + p9*x22  + p14*x23 + p19*x24 + p24*x25;
1549         pc[24] = m25 = p5*x21 + p10*x22 + p15*x23 + p20*x24 + p25*x25;
1550 
1551         nz = bi[row+1] - diag_offset[row] - 1;
1552         pv += 25;
1553         for (j=0; j<nz; j++) {
1554           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
1555           x5   = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
1556           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
1557           x14  = pv[13]; x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17];
1558           x19 = pv[18];  x20 = pv[19]; x21 = pv[20]; x22 = pv[21]; x23 = pv[22];
1559           x24 = pv[23];  x25 = pv[24];
1560           x    = rtmp + 25*pj[j];
1561           x[0] -= m1*x1 + m6*x2   + m11*x3  + m16*x4 + m21*x5;
1562           x[1] -= m2*x1 + m7*x2   + m12*x3  + m17*x4 + m22*x5;
1563           x[2] -= m3*x1 + m8*x2   + m13*x3  + m18*x4 + m23*x5;
1564           x[3] -= m4*x1 + m9*x2   + m14*x3  + m19*x4 + m24*x5;
1565           x[4] -= m5*x1 + m10*x2  + m15*x3  + m20*x4 + m25*x5;
1566 
1567           x[5] -= m1*x6 + m6*x7   + m11*x8  + m16*x9 + m21*x10;
1568           x[6] -= m2*x6 + m7*x7   + m12*x8  + m17*x9 + m22*x10;
1569           x[7] -= m3*x6 + m8*x7   + m13*x8  + m18*x9 + m23*x10;
1570           x[8] -= m4*x6 + m9*x7   + m14*x8  + m19*x9 + m24*x10;
1571           x[9] -= m5*x6 + m10*x7  + m15*x8  + m20*x9 + m25*x10;
1572 
1573           x[10] -= m1*x11 + m6*x12  + m11*x13 + m16*x14 + m21*x15;
1574           x[11] -= m2*x11 + m7*x12  + m12*x13 + m17*x14 + m22*x15;
1575           x[12] -= m3*x11 + m8*x12  + m13*x13 + m18*x14 + m23*x15;
1576           x[13] -= m4*x11 + m9*x12  + m14*x13 + m19*x14 + m24*x15;
1577           x[14] -= m5*x11 + m10*x12 + m15*x13 + m20*x14 + m25*x15;
1578 
1579           x[15] -= m1*x16 + m6*x17  + m11*x18 + m16*x19 + m21*x20;
1580           x[16] -= m2*x16 + m7*x17  + m12*x18 + m17*x19 + m22*x20;
1581           x[17] -= m3*x16 + m8*x17  + m13*x18 + m18*x19 + m23*x20;
1582           x[18] -= m4*x16 + m9*x17  + m14*x18 + m19*x19 + m24*x20;
1583           x[19] -= m5*x16 + m10*x17 + m15*x18 + m20*x19 + m25*x20;
1584 
1585           x[20] -= m1*x21 + m6*x22  + m11*x23 + m16*x24 + m21*x25;
1586           x[21] -= m2*x21 + m7*x22  + m12*x23 + m17*x24 + m22*x25;
1587           x[22] -= m3*x21 + m8*x22  + m13*x23 + m18*x24 + m23*x25;
1588           x[23] -= m4*x21 + m9*x22  + m14*x23 + m19*x24 + m24*x25;
1589           x[24] -= m5*x21 + m10*x22 + m15*x23 + m20*x24 + m25*x25;
1590           pv   += 25;
1591         }
1592         PLogFlops(250*nz+225);
1593       }
1594       row = *ajtmp++;
1595     }
1596     /* finished row so stick it into b->a */
1597     pv = ba + 25*bi[i];
1598     pj = bj + bi[i];
1599     nz = bi[i+1] - bi[i];
1600     for (j=0; j<nz; j++) {
1601       x      = rtmp+25*pj[j];
1602       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
1603       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
1604       pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
1605       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; pv[16] = x[16]; pv[17] = x[17];
1606       pv[18] = x[18]; pv[19] = x[19]; pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22];
1607       pv[23] = x[23]; pv[24] = x[24];
1608       pv   += 25;
1609     }
1610     /* invert diagonal block */
1611     w = ba + 25*diag_offset[i];
1612     ierr = Kernel_A_gets_inverse_A_5(w);CHKERRQ(ierr);
1613   }
1614 
1615   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1616   C->factor    = FACTOR_LU;
1617   C->assembled = PETSC_TRUE;
1618   PLogFlops(1.3333*125*b->mbs); /* from inverting diagonal blocks */
1619   PetscFunctionReturn(0);
1620 }
1621 
1622 /*
1623       Version for when blocks are 4 by 4
1624 */
1625 #undef __FUNC__
1626 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_4"
1627 int MatCholeskyFactorNumeric_SeqSBAIJ_4(Mat A,Mat *B)
1628 {
1629   Mat         C = *B;
1630   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
1631   IS          isrow = b->row,isicol = b->icol;
1632   int         *r,*ic,ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
1633   int         *ajtmpold,*ajtmp,nz,row;
1634   int         *diag_offset = b->diag,idx,*ai=a->i,*aj=a->j,*pj;
1635   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
1636   MatScalar   p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
1637   MatScalar   p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
1638   MatScalar   p10,p11,p12,p13,p14,p15,p16,m10,m11,m12;
1639   MatScalar   m13,m14,m15,m16;
1640   MatScalar   *ba = b->a,*aa = a->a;
1641 
1642   PetscFunctionBegin;
1643   ierr  = ISGetIndices(isrow,&r);CHKERRQ(ierr);
1644   ierr  = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
1645   rtmp  = (MatScalar*)PetscMalloc(16*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
1646 
1647   for (i=0; i<n; i++) {
1648     nz    = bi[i+1] - bi[i];
1649     ajtmp = bj + bi[i];
1650     for  (j=0; j<nz; j++) {
1651       x = rtmp+16*ajtmp[j];
1652       x[0]  = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = x[9] = 0.0;
1653       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
1654     }
1655     /* load in initial (unfactored row) */
1656     idx      = r[i];
1657     nz       = ai[idx+1] - ai[idx];
1658     ajtmpold = aj + ai[idx];
1659     v        = aa + 16*ai[idx];
1660     for (j=0; j<nz; j++) {
1661       x    = rtmp+16*ic[ajtmpold[j]];
1662       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
1663       x[4]  = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
1664       x[9]  = v[9];  x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
1665       x[14] = v[14]; x[15] = v[15];
1666       v    += 16;
1667     }
1668     row = *ajtmp++;
1669     while (row < i) {
1670       pc  = rtmp + 16*row;
1671       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
1672       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
1673       p10 = pc[9];  p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
1674       p15 = pc[14]; p16 = pc[15];
1675       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
1676           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
1677           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
1678           || p16 != 0.0) {
1679         pv = ba + 16*diag_offset[row];
1680         pj = bj + diag_offset[row] + 1;
1681         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
1682         x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
1683         x10 = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
1684         x15 = pv[14]; x16 = pv[15];
1685         pc[0] = m1 = p1*x1 + p5*x2  + p9*x3  + p13*x4;
1686         pc[1] = m2 = p2*x1 + p6*x2  + p10*x3 + p14*x4;
1687         pc[2] = m3 = p3*x1 + p7*x2  + p11*x3 + p15*x4;
1688         pc[3] = m4 = p4*x1 + p8*x2  + p12*x3 + p16*x4;
1689 
1690         pc[4] = m5 = p1*x5 + p5*x6  + p9*x7  + p13*x8;
1691         pc[5] = m6 = p2*x5 + p6*x6  + p10*x7 + p14*x8;
1692         pc[6] = m7 = p3*x5 + p7*x6  + p11*x7 + p15*x8;
1693         pc[7] = m8 = p4*x5 + p8*x6  + p12*x7 + p16*x8;
1694 
1695         pc[8]  = m9  = p1*x9 + p5*x10  + p9*x11  + p13*x12;
1696         pc[9]  = m10 = p2*x9 + p6*x10  + p10*x11 + p14*x12;
1697         pc[10] = m11 = p3*x9 + p7*x10  + p11*x11 + p15*x12;
1698         pc[11] = m12 = p4*x9 + p8*x10  + p12*x11 + p16*x12;
1699 
1700         pc[12] = m13 = p1*x13 + p5*x14  + p9*x15  + p13*x16;
1701         pc[13] = m14 = p2*x13 + p6*x14  + p10*x15 + p14*x16;
1702         pc[14] = m15 = p3*x13 + p7*x14  + p11*x15 + p15*x16;
1703         pc[15] = m16 = p4*x13 + p8*x14  + p12*x15 + p16*x16;
1704 
1705         nz = bi[row+1] - diag_offset[row] - 1;
1706         pv += 16;
1707         for (j=0; j<nz; j++) {
1708           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
1709           x5   = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
1710           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
1711           x14  = pv[13]; x15 = pv[14]; x16 = pv[15];
1712           x    = rtmp + 16*pj[j];
1713           x[0] -= m1*x1 + m5*x2  + m9*x3  + m13*x4;
1714           x[1] -= m2*x1 + m6*x2  + m10*x3 + m14*x4;
1715           x[2] -= m3*x1 + m7*x2  + m11*x3 + m15*x4;
1716           x[3] -= m4*x1 + m8*x2  + m12*x3 + m16*x4;
1717 
1718           x[4] -= m1*x5 + m5*x6  + m9*x7  + m13*x8;
1719           x[5] -= m2*x5 + m6*x6  + m10*x7 + m14*x8;
1720           x[6] -= m3*x5 + m7*x6  + m11*x7 + m15*x8;
1721           x[7] -= m4*x5 + m8*x6  + m12*x7 + m16*x8;
1722 
1723           x[8]  -= m1*x9 + m5*x10 + m9*x11  + m13*x12;
1724           x[9]  -= m2*x9 + m6*x10 + m10*x11 + m14*x12;
1725           x[10] -= m3*x9 + m7*x10 + m11*x11 + m15*x12;
1726           x[11] -= m4*x9 + m8*x10 + m12*x11 + m16*x12;
1727 
1728           x[12] -= m1*x13 + m5*x14  + m9*x15  + m13*x16;
1729           x[13] -= m2*x13 + m6*x14  + m10*x15 + m14*x16;
1730           x[14] -= m3*x13 + m7*x14  + m11*x15 + m15*x16;
1731           x[15] -= m4*x13 + m8*x14  + m12*x15 + m16*x16;
1732 
1733           pv   += 16;
1734         }
1735         PLogFlops(128*nz+112);
1736       }
1737       row = *ajtmp++;
1738     }
1739     /* finished row so stick it into b->a */
1740     pv = ba + 16*bi[i];
1741     pj = bj + bi[i];
1742     nz = bi[i+1] - bi[i];
1743     for (j=0; j<nz; j++) {
1744       x      = rtmp+16*pj[j];
1745       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
1746       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
1747       pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
1748       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
1749       pv   += 16;
1750     }
1751     /* invert diagonal block */
1752     w = ba + 16*diag_offset[i];
1753     ierr = Kernel_A_gets_inverse_A_4(w);CHKERRQ(ierr);
1754   }
1755 
1756   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1757   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
1758   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
1759   C->factor = FACTOR_LU;
1760   C->assembled = PETSC_TRUE;
1761   PLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */
1762   PetscFunctionReturn(0);
1763 }
1764 /*
1765       Version for when blocks are 4 by 4 Using natural ordering
1766 */
1767 #undef __FUNC__
1768 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_4_NaturalOrdering"
1769 int MatCholeskyFactorNumeric_SeqSBAIJ_4_NaturalOrdering(Mat A,Mat *B)
1770 {
1771   Mat         C = *B;
1772   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
1773   int         ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
1774   int         *ajtmpold,*ajtmp,nz,row;
1775   int         *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
1776   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
1777   MatScalar   p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
1778   MatScalar   p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
1779   MatScalar   p10,p11,p12,p13,p14,p15,p16,m10,m11,m12;
1780   MatScalar   m13,m14,m15,m16;
1781   MatScalar   *ba = b->a,*aa = a->a;
1782 
1783   PetscFunctionBegin;
1784   rtmp  = (MatScalar*)PetscMalloc(16*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
1785 
1786   for (i=0; i<n; i++) {
1787     nz    = bi[i+1] - bi[i];
1788     ajtmp = bj + bi[i];
1789     for  (j=0; j<nz; j++) {
1790       x = rtmp+16*ajtmp[j];
1791       x[0]  = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = x[9] = 0.0;
1792       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
1793     }
1794     /* load in initial (unfactored row) */
1795     nz       = ai[i+1] - ai[i];
1796     ajtmpold = aj + ai[i];
1797     v        = aa + 16*ai[i];
1798     for (j=0; j<nz; j++) {
1799       x    = rtmp+16*ajtmpold[j];
1800       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
1801       x[4]  = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
1802       x[9]  = v[9];  x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
1803       x[14] = v[14]; x[15] = v[15];
1804       v    += 16;
1805     }
1806     row = *ajtmp++;
1807     while (row < i) {
1808       pc  = rtmp + 16*row;
1809       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
1810       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
1811       p10 = pc[9];  p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
1812       p15 = pc[14]; p16 = pc[15];
1813       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
1814           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
1815           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
1816           || p16 != 0.0) {
1817         pv = ba + 16*diag_offset[row];
1818         pj = bj + diag_offset[row] + 1;
1819         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
1820         x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
1821         x10 = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
1822         x15 = pv[14]; x16 = pv[15];
1823         pc[0] = m1 = p1*x1 + p5*x2  + p9*x3  + p13*x4;
1824         pc[1] = m2 = p2*x1 + p6*x2  + p10*x3 + p14*x4;
1825         pc[2] = m3 = p3*x1 + p7*x2  + p11*x3 + p15*x4;
1826         pc[3] = m4 = p4*x1 + p8*x2  + p12*x3 + p16*x4;
1827 
1828         pc[4] = m5 = p1*x5 + p5*x6  + p9*x7  + p13*x8;
1829         pc[5] = m6 = p2*x5 + p6*x6  + p10*x7 + p14*x8;
1830         pc[6] = m7 = p3*x5 + p7*x6  + p11*x7 + p15*x8;
1831         pc[7] = m8 = p4*x5 + p8*x6  + p12*x7 + p16*x8;
1832 
1833         pc[8]  = m9  = p1*x9 + p5*x10  + p9*x11  + p13*x12;
1834         pc[9]  = m10 = p2*x9 + p6*x10  + p10*x11 + p14*x12;
1835         pc[10] = m11 = p3*x9 + p7*x10  + p11*x11 + p15*x12;
1836         pc[11] = m12 = p4*x9 + p8*x10  + p12*x11 + p16*x12;
1837 
1838         pc[12] = m13 = p1*x13 + p5*x14  + p9*x15  + p13*x16;
1839         pc[13] = m14 = p2*x13 + p6*x14  + p10*x15 + p14*x16;
1840         pc[14] = m15 = p3*x13 + p7*x14  + p11*x15 + p15*x16;
1841         pc[15] = m16 = p4*x13 + p8*x14  + p12*x15 + p16*x16;
1842 
1843         nz = bi[row+1] - diag_offset[row] - 1;
1844         pv += 16;
1845         for (j=0; j<nz; j++) {
1846           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
1847           x5   = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
1848           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
1849           x14  = pv[13]; x15 = pv[14]; x16 = pv[15];
1850           x    = rtmp + 16*pj[j];
1851           x[0] -= m1*x1 + m5*x2  + m9*x3  + m13*x4;
1852           x[1] -= m2*x1 + m6*x2  + m10*x3 + m14*x4;
1853           x[2] -= m3*x1 + m7*x2  + m11*x3 + m15*x4;
1854           x[3] -= m4*x1 + m8*x2  + m12*x3 + m16*x4;
1855 
1856           x[4] -= m1*x5 + m5*x6  + m9*x7  + m13*x8;
1857           x[5] -= m2*x5 + m6*x6  + m10*x7 + m14*x8;
1858           x[6] -= m3*x5 + m7*x6  + m11*x7 + m15*x8;
1859           x[7] -= m4*x5 + m8*x6  + m12*x7 + m16*x8;
1860 
1861           x[8]  -= m1*x9 + m5*x10 + m9*x11  + m13*x12;
1862           x[9]  -= m2*x9 + m6*x10 + m10*x11 + m14*x12;
1863           x[10] -= m3*x9 + m7*x10 + m11*x11 + m15*x12;
1864           x[11] -= m4*x9 + m8*x10 + m12*x11 + m16*x12;
1865 
1866           x[12] -= m1*x13 + m5*x14  + m9*x15  + m13*x16;
1867           x[13] -= m2*x13 + m6*x14  + m10*x15 + m14*x16;
1868           x[14] -= m3*x13 + m7*x14  + m11*x15 + m15*x16;
1869           x[15] -= m4*x13 + m8*x14  + m12*x15 + m16*x16;
1870 
1871           pv   += 16;
1872         }
1873         PLogFlops(128*nz+112);
1874       }
1875       row = *ajtmp++;
1876     }
1877     /* finished row so stick it into b->a */
1878     pv = ba + 16*bi[i];
1879     pj = bj + bi[i];
1880     nz = bi[i+1] - bi[i];
1881     for (j=0; j<nz; j++) {
1882       x      = rtmp+16*pj[j];
1883       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
1884       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
1885       pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
1886       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
1887       pv   += 16;
1888     }
1889     /* invert diagonal block */
1890     w = ba + 16*diag_offset[i];
1891     ierr = Kernel_A_gets_inverse_A_4(w);CHKERRQ(ierr);
1892   }
1893 
1894   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1895   C->factor    = FACTOR_LU;
1896   C->assembled = PETSC_TRUE;
1897   PLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */
1898   PetscFunctionReturn(0);
1899 }
1900 
1901 /*
1902       Version for when blocks are 3 by 3
1903 */
1904 #undef __FUNC__
1905 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_3"
1906 int MatCholeskyFactorNumeric_SeqSBAIJ_3(Mat A,Mat *B)
1907 {
1908   Mat         C = *B;
1909   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
1910   IS          isrow = b->row,isicol = b->icol;
1911   int         *r,*ic,ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
1912   int         *ajtmpold,*ajtmp,nz,row,*ai=a->i,*aj=a->j;
1913   int         *diag_offset = b->diag,idx,*pj;
1914   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
1915   MatScalar   p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
1916   MatScalar   p5,p6,p7,p8,p9,x5,x6,x7,x8,x9;
1917   MatScalar   *ba = b->a,*aa = a->a;
1918 
1919   PetscFunctionBegin;
1920   ierr  = ISGetIndices(isrow,&r);CHKERRQ(ierr);
1921   ierr  = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
1922   rtmp  = (MatScalar*)PetscMalloc(9*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
1923 
1924   for (i=0; i<n; i++) {
1925     nz    = bi[i+1] - bi[i];
1926     ajtmp = bj + bi[i];
1927     for  (j=0; j<nz; j++) {
1928       x = rtmp + 9*ajtmp[j];
1929       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = 0.0;
1930     }
1931     /* load in initial (unfactored row) */
1932     idx      = r[i];
1933     nz       = ai[idx+1] - ai[idx];
1934     ajtmpold = aj + ai[idx];
1935     v        = aa + 9*ai[idx];
1936     for (j=0; j<nz; j++) {
1937       x    = rtmp + 9*ic[ajtmpold[j]];
1938       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
1939       x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
1940       v    += 9;
1941     }
1942     row = *ajtmp++;
1943     while (row < i) {
1944       pc = rtmp + 9*row;
1945       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
1946       p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
1947       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
1948           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0) {
1949         pv = ba + 9*diag_offset[row];
1950         pj = bj + diag_offset[row] + 1;
1951         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
1952         x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
1953         pc[0] = m1 = p1*x1 + p4*x2 + p7*x3;
1954         pc[1] = m2 = p2*x1 + p5*x2 + p8*x3;
1955         pc[2] = m3 = p3*x1 + p6*x2 + p9*x3;
1956 
1957         pc[3] = m4 = p1*x4 + p4*x5 + p7*x6;
1958         pc[4] = m5 = p2*x4 + p5*x5 + p8*x6;
1959         pc[5] = m6 = p3*x4 + p6*x5 + p9*x6;
1960 
1961         pc[6] = m7 = p1*x7 + p4*x8 + p7*x9;
1962         pc[7] = m8 = p2*x7 + p5*x8 + p8*x9;
1963         pc[8] = m9 = p3*x7 + p6*x8 + p9*x9;
1964         nz = bi[row+1] - diag_offset[row] - 1;
1965         pv += 9;
1966         for (j=0; j<nz; j++) {
1967           x1   = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
1968           x5   = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
1969           x    = rtmp + 9*pj[j];
1970           x[0] -= m1*x1 + m4*x2 + m7*x3;
1971           x[1] -= m2*x1 + m5*x2 + m8*x3;
1972           x[2] -= m3*x1 + m6*x2 + m9*x3;
1973 
1974           x[3] -= m1*x4 + m4*x5 + m7*x6;
1975           x[4] -= m2*x4 + m5*x5 + m8*x6;
1976           x[5] -= m3*x4 + m6*x5 + m9*x6;
1977 
1978           x[6] -= m1*x7 + m4*x8 + m7*x9;
1979           x[7] -= m2*x7 + m5*x8 + m8*x9;
1980           x[8] -= m3*x7 + m6*x8 + m9*x9;
1981           pv   += 9;
1982         }
1983         PLogFlops(54*nz+36);
1984       }
1985       row = *ajtmp++;
1986     }
1987     /* finished row so stick it into b->a */
1988     pv = ba + 9*bi[i];
1989     pj = bj + bi[i];
1990     nz = bi[i+1] - bi[i];
1991     for (j=0; j<nz; j++) {
1992       x     = rtmp + 9*pj[j];
1993       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
1994       pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
1995       pv   += 9;
1996     }
1997     /* invert diagonal block */
1998     w = ba + 9*diag_offset[i];
1999     ierr = Kernel_A_gets_inverse_A_3(w);CHKERRQ(ierr);
2000   }
2001 
2002   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2003   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
2004   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
2005   C->factor = FACTOR_LU;
2006   C->assembled = PETSC_TRUE;
2007   PLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */
2008   PetscFunctionReturn(0);
2009 }
2010 /*
2011       Version for when blocks are 3 by 3 Using natural ordering
2012 */
2013 #undef __FUNC__
2014 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_3_NaturalOrdering"
2015 int MatCholeskyFactorNumeric_SeqSBAIJ_3_NaturalOrdering(Mat A,Mat *B)
2016 {
2017   Mat                C = *B;
2018   Mat_SeqBAIJ        *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
2019   int                ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
2020   int                *ajtmpold,*ajtmp,nz,row;
2021   int                *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
2022   MatScalar          *pv,*v,*rtmp,*pc,*w,*x;
2023   MatScalar          p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
2024   MatScalar          p5,p6,p7,p8,p9,x5,x6,x7,x8,x9;
2025   MatScalar          *ba = b->a,*aa = a->a;
2026 
2027   PetscFunctionBegin;
2028   rtmp  = (MatScalar*)PetscMalloc(9*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
2029 
2030   for (i=0; i<n; i++) {
2031     nz    = bi[i+1] - bi[i];
2032     ajtmp = bj + bi[i];
2033     for  (j=0; j<nz; j++) {
2034       x = rtmp+9*ajtmp[j];
2035       x[0]  = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = 0.0;
2036     }
2037     /* load in initial (unfactored row) */
2038     nz       = ai[i+1] - ai[i];
2039     ajtmpold = aj + ai[i];
2040     v        = aa + 9*ai[i];
2041     for (j=0; j<nz; j++) {
2042       x    = rtmp+9*ajtmpold[j];
2043       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
2044       x[4]  = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
2045       v    += 9;
2046     }
2047     row = *ajtmp++;
2048     while (row < i) {
2049       pc  = rtmp + 9*row;
2050       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
2051       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
2052       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
2053           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0) {
2054         pv = ba + 9*diag_offset[row];
2055         pj = bj + diag_offset[row] + 1;
2056         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
2057         x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
2058         pc[0] = m1 = p1*x1 + p4*x2 + p7*x3;
2059         pc[1] = m2 = p2*x1 + p5*x2 + p8*x3;
2060         pc[2] = m3 = p3*x1 + p6*x2 + p9*x3;
2061 
2062         pc[3] = m4 = p1*x4 + p4*x5 + p7*x6;
2063         pc[4] = m5 = p2*x4 + p5*x5 + p8*x6;
2064         pc[5] = m6 = p3*x4 + p6*x5 + p9*x6;
2065 
2066         pc[6] = m7 = p1*x7 + p4*x8 + p7*x9;
2067         pc[7] = m8 = p2*x7 + p5*x8 + p8*x9;
2068         pc[8] = m9 = p3*x7 + p6*x8 + p9*x9;
2069 
2070         nz = bi[row+1] - diag_offset[row] - 1;
2071         pv += 9;
2072         for (j=0; j<nz; j++) {
2073           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
2074           x5   = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
2075           x    = rtmp + 9*pj[j];
2076           x[0] -= m1*x1 + m4*x2 + m7*x3;
2077           x[1] -= m2*x1 + m5*x2 + m8*x3;
2078           x[2] -= m3*x1 + m6*x2 + m9*x3;
2079 
2080           x[3] -= m1*x4 + m4*x5 + m7*x6;
2081           x[4] -= m2*x4 + m5*x5 + m8*x6;
2082           x[5] -= m3*x4 + m6*x5 + m9*x6;
2083 
2084           x[6] -= m1*x7 + m4*x8 + m7*x9;
2085           x[7] -= m2*x7 + m5*x8 + m8*x9;
2086           x[8] -= m3*x7 + m6*x8 + m9*x9;
2087           pv   += 9;
2088         }
2089         PLogFlops(54*nz+36);
2090       }
2091       row = *ajtmp++;
2092     }
2093     /* finished row so stick it into b->a */
2094     pv = ba + 9*bi[i];
2095     pj = bj + bi[i];
2096     nz = bi[i+1] - bi[i];
2097     for (j=0; j<nz; j++) {
2098       x      = rtmp+9*pj[j];
2099       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
2100       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
2101       pv   += 9;
2102     }
2103     /* invert diagonal block */
2104     w = ba + 9*diag_offset[i];
2105     ierr = Kernel_A_gets_inverse_A_3(w);CHKERRQ(ierr);
2106   }
2107 
2108   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2109   C->factor    = FACTOR_LU;
2110   C->assembled = PETSC_TRUE;
2111   PLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */
2112   PetscFunctionReturn(0);
2113 }
2114 
2115 /*
2116       Version for when blocks are 2 by 2
2117 */
2118 #undef __FUNC__
2119 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_2"
2120 int MatCholeskyFactorNumeric_SeqSBAIJ_2(Mat A,Mat *B)
2121 {
2122   Mat                C = *B;
2123   Mat_SeqBAIJ        *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
2124   IS                 isrow = b->row,isicol = b->icol;
2125   int                *r,*ic,ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
2126   int                *ajtmpold,*ajtmp,nz,row;
2127   int                *diag_offset=b->diag,idx,*ai=a->i,*aj=a->j,*pj;
2128   MatScalar          *pv,*v,*rtmp,m1,m2,m3,m4,*pc,*w,*x,x1,x2,x3,x4;
2129   MatScalar          p1,p2,p3,p4;
2130   MatScalar          *ba = b->a,*aa = a->a;
2131 
2132   PetscFunctionBegin;
2133   ierr  = ISGetIndices(isrow,&r);CHKERRQ(ierr);
2134   ierr  = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
2135   rtmp  = (MatScalar*)PetscMalloc(4*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
2136 
2137   for (i=0; i<n; i++) {
2138     nz    = bi[i+1] - bi[i];
2139     ajtmp = bj + bi[i];
2140     for  (j=0; j<nz; j++) {
2141       x = rtmp+4*ajtmp[j]; x[0] = x[1] = x[2] = x[3] = 0.0;
2142     }
2143     /* load in initial (unfactored row) */
2144     idx      = r[i];
2145     nz       = ai[idx+1] - ai[idx];
2146     ajtmpold = aj + ai[idx];
2147     v        = aa + 4*ai[idx];
2148     for (j=0; j<nz; j++) {
2149       x    = rtmp+4*ic[ajtmpold[j]];
2150       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
2151       v    += 4;
2152     }
2153     row = *ajtmp++;
2154     while (row < i) {
2155       pc = rtmp + 4*row;
2156       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
2157       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0) {
2158         pv = ba + 4*diag_offset[row];
2159         pj = bj + diag_offset[row] + 1;
2160         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
2161         pc[0] = m1 = p1*x1 + p3*x2;
2162         pc[1] = m2 = p2*x1 + p4*x2;
2163         pc[2] = m3 = p1*x3 + p3*x4;
2164         pc[3] = m4 = p2*x3 + p4*x4;
2165         nz = bi[row+1] - diag_offset[row] - 1;
2166         pv += 4;
2167         for (j=0; j<nz; j++) {
2168           x1   = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
2169           x    = rtmp + 4*pj[j];
2170           x[0] -= m1*x1 + m3*x2;
2171           x[1] -= m2*x1 + m4*x2;
2172           x[2] -= m1*x3 + m3*x4;
2173           x[3] -= m2*x3 + m4*x4;
2174           pv   += 4;
2175         }
2176         PLogFlops(16*nz+12);
2177       }
2178       row = *ajtmp++;
2179     }
2180     /* finished row so stick it into b->a */
2181     pv = ba + 4*bi[i];
2182     pj = bj + bi[i];
2183     nz = bi[i+1] - bi[i];
2184     for (j=0; j<nz; j++) {
2185       x     = rtmp+4*pj[j];
2186       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
2187       pv   += 4;
2188     }
2189     /* invert diagonal block */
2190     w = ba + 4*diag_offset[i];
2191     ierr = Kernel_A_gets_inverse_A_2(w);CHKERRQ(ierr);
2192     /*Kernel_A_gets_inverse_A(bs,w,v_pivots,v_work);*/
2193   }
2194 
2195   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2196   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
2197   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
2198   C->factor = FACTOR_LU;
2199   C->assembled = PETSC_TRUE;
2200   PLogFlops(1.3333*8*b->mbs); /* from inverting diagonal blocks */
2201   PetscFunctionReturn(0);
2202 }
2203 /*
2204       Version for when blocks are 2 by 2 Using natural ordering
2205 */
2206 #undef __FUNC__
2207 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_2_NaturalOrdering"
2208 int MatCholeskyFactorNumeric_SeqSBAIJ_2_NaturalOrdering(Mat A,Mat *B)
2209 {
2210   Mat                C = *B;
2211   Mat_SeqBAIJ        *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
2212   int                ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
2213   int                *ajtmpold,*ajtmp,nz,row;
2214   int                *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
2215   MatScalar          *pv,*v,*rtmp,*pc,*w,*x;
2216   MatScalar          p1,p2,p3,p4,m1,m2,m3,m4,x1,x2,x3,x4;
2217   MatScalar          *ba = b->a,*aa = a->a;
2218 
2219   PetscFunctionBegin;
2220   rtmp  = (MatScalar*)PetscMalloc(4*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
2221 
2222   for (i=0; i<n; i++) {
2223     nz    = bi[i+1] - bi[i];
2224     ajtmp = bj + bi[i];
2225     for  (j=0; j<nz; j++) {
2226       x = rtmp+4*ajtmp[j];
2227       x[0]  = x[1]  = x[2]  = x[3]  = 0.0;
2228     }
2229     /* load in initial (unfactored row) */
2230     nz       = ai[i+1] - ai[i];
2231     ajtmpold = aj + ai[i];
2232     v        = aa + 4*ai[i];
2233     for (j=0; j<nz; j++) {
2234       x    = rtmp+4*ajtmpold[j];
2235       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
2236       v    += 4;
2237     }
2238     row = *ajtmp++;
2239     while (row < i) {
2240       pc  = rtmp + 4*row;
2241       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
2242       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0) {
2243         pv = ba + 4*diag_offset[row];
2244         pj = bj + diag_offset[row] + 1;
2245         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
2246         pc[0] = m1 = p1*x1 + p3*x2;
2247         pc[1] = m2 = p2*x1 + p4*x2;
2248         pc[2] = m3 = p1*x3 + p3*x4;
2249         pc[3] = m4 = p2*x3 + p4*x4;
2250         nz = bi[row+1] - diag_offset[row] - 1;
2251         pv += 4;
2252         for (j=0; j<nz; j++) {
2253           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
2254           x    = rtmp + 4*pj[j];
2255           x[0] -= m1*x1 + m3*x2;
2256           x[1] -= m2*x1 + m4*x2;
2257           x[2] -= m1*x3 + m3*x4;
2258           x[3] -= m2*x3 + m4*x4;
2259           pv   += 4;
2260         }
2261         PLogFlops(16*nz+12);
2262       }
2263       row = *ajtmp++;
2264     }
2265     /* finished row so stick it into b->a */
2266     pv = ba + 4*bi[i];
2267     pj = bj + bi[i];
2268     nz = bi[i+1] - bi[i];
2269     for (j=0; j<nz; j++) {
2270       x      = rtmp+4*pj[j];
2271       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
2272       pv   += 4;
2273     }
2274     /* invert diagonal block */
2275     w = ba + 4*diag_offset[i];
2276     ierr = Kernel_A_gets_inverse_A_2(w);CHKERRQ(ierr);
2277     /*Kernel_A_gets_inverse_A(bs,w,v_pivots,v_work);*/
2278   }
2279 
2280   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2281   C->factor    = FACTOR_LU;
2282   C->assembled = PETSC_TRUE;
2283   PLogFlops(1.3333*8*b->mbs); /* from inverting diagonal blocks */
2284   PetscFunctionReturn(0);
2285 }
2286 
2287 /*
2288      Version for when blocks are 1 by 1.
2289 */
2290 #undef __FUNC__
2291 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_1"
2292 int MatCholeskyFactorNumeric_SeqSBAIJ_1(Mat A,Mat *B)
2293 {
2294   Mat                C = *B;
2295   Mat_SeqSBAIJ       *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data;
2296   IS                 ip = b->row;
2297   int                *rip,*riip,ierr,i,j,mbs = a->mbs,*bi = b->i,*bj = b->j;
2298   int                *ai,*aj,*a2anew,*r;
2299   MatScalar          *rtmp;
2300   MatScalar          *ba = b->a,*aa,ak;
2301   MatScalar          dk,uikdi;
2302   int                k,jmin,jmax,*jl,*il,vj,nexti,juj,ili;
2303   PetscTruth flg_perm = PETSC_FALSE; /* non-trivial permutation */
2304 
2305   PetscFunctionBegin;
2306   ierr  = ISGetIndices(ip,&rip);CHKERRQ(ierr);
2307   riip = rip;
2308 
2309   if (!flg_perm){
2310     ai = a->i; aj = a->j; aa = a->a;
2311   } else {
2312 
2313     ai = a->inew; aj = a->jnew;
2314 
2315     aa = (MatScalar*)PetscMalloc(ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa);
2316     ierr = PetscMemcpy(aa,a->a,(ai[mbs])*sizeof(MatScalar));CHKERRQ(ierr);
2317 
2318     r   = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(r);
2319     ierr= PetscMemcpy(r,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr);
2320 
2321     jmin = ai[0]; jmax = ai[mbs];
2322     for (j=jmin; j<jmax; j++){
2323       while (a2anew[j] != j){
2324         k = r[j]; r[j] = r[k]; r[k] = k;
2325         ak = aa[k]; aa[k] = aa[j]; aa[j] = ak;
2326       }
2327     }
2328     a->anew = aa;
2329     ierr = PetscFree(r);CHKERRA(ierr);
2330   }
2331 
2332   /* INITIALIZATION */
2333   /* il and jl record the first nonzero element in each row of the accessing
2334      window U(0:k, k:mbs-1).
2335      jl:    list of rows to be added to uneliminated rows
2336             i>= k: jl(i) is the first row to be added to row i
2337             i<  k: jl(i) is the row following row i in some list of rows
2338             jl(i) = mbs indicates the end of a list
2339      il(i): points to the first nonzero element in columns k,...,mbs-1 of
2340             row i of U */
2341   rtmp  = (MatScalar*)PetscMalloc(mbs*sizeof(MatScalar));CHKPTRQ(rtmp);
2342   il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il);
2343   jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl);
2344   for (i=0; i<mbs; i++) {
2345     rtmp[i] = 0.0; jl[i] = mbs; il[0] = 0;
2346   }
2347 
2348   /* FOR EACH ROW K */
2349   for (k = 0; k<mbs; k++){
2350 
2351     /* INITIALIZE K-TH ROW WITH ELEMENTS NONZERO IN ROW P(K) OF A */
2352     jmin = ai[rip[k]]; jmax = ai[rip[k]+1];
2353     if (jmin < jmax) {
2354       for (j = jmin; j < jmax; j++){
2355         vj = riip[aj[j]];
2356         if (k <= vj) rtmp[vj] = aa[j];
2357       }
2358     }
2359 
2360     /* MODIFY K-TH ROW BY ADDING IN THOSE ROWS I WITH U(I,K) NE 0
2361        FOR EACH ROW I TO BE ADDED IN */
2362     dk = rtmp[k];
2363     i = jl[k]; /* first row to be added to k_th row  */
2364     /* printf(" k=%d, pivot row = %d\n",k,i); */
2365 
2366     while (i < mbs){
2367       nexti = jl[i]; /* next row to be added to k_th row */
2368       /* printf("      pivot row = %d\n", nexti); */
2369 
2370       /* COMPUTE MULTIPLIER AND UPDATE DIAGONAL ELEMENT */
2371       ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
2372       uikdi = - ba[ili]*ba[i];
2373       dk += uikdi*ba[ili];
2374       ba[ili] = uikdi; /* update U(i,k) */
2375 
2376       /* ADD MULTIPLE OF ROW I TO K-TH ROW ... */
2377       jmin = ili + 1; jmax = bi[i+1];
2378       if (jmin < jmax){
2379         for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j];
2380         /* ... AND ADD I TO ROW LIST FOR NEXT NONZERO ENTRY */
2381          il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
2382          j     = bj[jmin];
2383          jl[i] = jl[j]; jl[j] = i; /* update jl */
2384       }
2385       i = nexti;
2386       /* printf("                  pivot row i=%d\n",i);  */
2387     }
2388 
2389     /* CHECK FOR ZERO PIVOT AND SAVE DIAGONAL ELEMENT */
2390     if (dk == 0.0){
2391       SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,0,"Zero pivot");
2392     }
2393 
2394     /* SAVE NONZERO ENTRIES IN K-TH ROW OF U ... */
2395     ba[k] = 1.0/dk;
2396     jmin = bi[k]; jmax = bi[k+1];
2397     if (jmin < jmax) {
2398       for (j=jmin; j<jmax; j++){
2399          juj = bj[j]; ba[j] = rtmp[juj]; rtmp[juj] = 0.0;
2400       }
2401 
2402       /* ... AND ADD K TO ROW LIST FOR FIRST NONZERO ENTRY IN K-TH ROW */
2403       il[k] = jmin;
2404       i     = bj[jmin];
2405       jl[k] = jl[i]; jl[i] = k;
2406     }
2407   }
2408 
2409   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2410   ierr = PetscFree(il);CHKERRQ(ierr);
2411   ierr = PetscFree(jl);CHKERRQ(ierr);
2412 
2413   ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr);
2414   C->factor    = FACTOR_LU;
2415   C->assembled = PETSC_TRUE;
2416   PLogFlops(b->mbs);
2417   PetscFunctionReturn(0);
2418 }
2419 
2420 #undef __FUNC__
2421 #define __FUNC__ "MatCholeskyFactor_SeqSBAIJ"
2422 int MatCholeskyFactor_SeqSBAIJ(Mat A,IS perm,PetscReal f)
2423 {
2424   Mat_SeqSBAIJ    *mat = (Mat_SeqSBAIJ*)A->data;
2425   int            ierr,refct;
2426   Mat            C;
2427   PetscOps *Abops;
2428   MatOps   Aops;
2429 
2430   PetscFunctionBegin;
2431   ierr = MatCholeskyFactorSymbolic(A,perm,f,&C);CHKERRQ(ierr);
2432   ierr = MatCholeskyFactorNumeric(A,&C);CHKERRQ(ierr);
2433 
2434   /* free all the data structures from mat */
2435   ierr = PetscFree(mat->a);CHKERRQ(ierr);
2436   if (!mat->singlemalloc) {
2437     ierr = PetscFree(mat->i);CHKERRQ(ierr);
2438     ierr = PetscFree(mat->j);CHKERRQ(ierr);
2439   }
2440   if (mat->diag) {ierr = PetscFree(mat->diag);CHKERRQ(ierr);}
2441   if (mat->ilen) {ierr = PetscFree(mat->ilen);CHKERRQ(ierr);}
2442   if (mat->imax) {ierr = PetscFree(mat->imax);CHKERRQ(ierr);}
2443   if (mat->solve_work) {ierr = PetscFree(mat->solve_work);CHKERRQ(ierr);}
2444   if (mat->mult_work) {ierr = PetscFree(mat->mult_work);CHKERRQ(ierr);}
2445   if (mat->icol) {ierr = ISDestroy(mat->icol);CHKERRQ(ierr);}
2446   ierr = PetscFree(mat);CHKERRQ(ierr);
2447 
2448   ierr = MapDestroy(A->rmap);CHKERRQ(ierr);
2449   ierr = MapDestroy(A->cmap);CHKERRQ(ierr);
2450 
2451   /*
2452        This is horrible,horrible code. We need to keep the
2453     A pointers for the bops and ops but copy everything
2454     else from C.
2455   */
2456   Abops = A->bops;
2457   Aops  = A->ops;
2458   refct = A->refct;
2459   ierr  = PetscMemcpy(A,C,sizeof(struct _p_Mat));CHKERRQ(ierr);
2460   mat   = (Mat_SeqSBAIJ*)A->data;
2461   PLogObjectParent(A,mat->icol);
2462 
2463   A->bops  = Abops;
2464   A->ops   = Aops;
2465   A->qlist = 0;
2466   A->refct = refct;
2467   /* copy over the type_name and name */
2468   ierr     = PetscStrallocpy(C->type_name,&A->type_name);CHKERRQ(ierr);
2469   ierr     = PetscStrallocpy(C->name,&A->name);CHKERRQ(ierr);
2470 
2471   PetscHeaderDestroy(C);
2472   PetscFunctionReturn(0);
2473 }
2474 
2475 
2476