xref: /petsc/src/mat/impls/sbaij/seq/sbaijfact.c (revision 4445dded8dfd2806566eb2c814a9ca3a02a8f3a3)
1 /* Using Modified Sparse Row (MSR) storage.
2 See page 85, "Iterative Methods ..." by Saad. */
3 
4 /*$Id: sbaijfact.c,v 1.25 2000/10/20 19:21:01 hzhang Exp bsmith $*/
5 /*
6     Symbolic (-UT)*D*(-U) factorization for SBAIJ format. Modified from SSF of YSMP.
7 */
8 #include "sbaij.h"
9 #include "src/mat/impls/baij/seq/baij.h"
10 #include "src/vec/vecimpl.h"
11 #include "src/inline/ilu.h"
12 #include "include/petscis.h"
13 
14 #undef __FUNC__
15 #define __FUNC__ "MatCholeskyFactorSymbolic_SeqSBAIJ"
16 int MatCholeskyFactorSymbolic_SeqSBAIJ(Mat A,IS perm,PetscReal f,Mat *B)
17 {
18   Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b;
19   int         *rip,ierr,i,mbs = a->mbs,*ai,*aj;
20   int         *jutmp,bs = a->bs,bs2=a->bs2;
21   int         m,nzi,realloc = 0;
22   int         *jl,*q,jumin,jmin,jmax,juptr,nzk,qm,*iu,*ju,k,j,vj,umax,maxadd;
23   /* PetscTruth  ident; */
24 
25   PetscFunctionBegin;
26   PetscValidHeaderSpecific(perm,IS_COOKIE);
27   if (A->M != A->N) SETERRQ(PETSC_ERR_ARG_WRONG,"matrix must be square");
28 
29   /* check whether perm is the identity mapping */
30   /*
31   ierr = ISView(perm, VIEWER_STDOUT_SELF);CHKERRA(ierr);
32   ierr = ISIdentity(perm,&ident);CHKERRQ(ierr);
33   printf("ident = %d\n", ident);
34   */
35   ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
36   for (i=0; i<mbs; i++){
37     if (rip[i] != i){
38       a->permute = PETSC_TRUE;
39       /* printf("non-trivial perm\n"); */
40       break;
41     }
42   }
43 
44   if (!a->permute){ /* without permutation */
45     ai = a->i; aj = a->j;
46   } else {       /* non-trivial permutation */
47     ierr = MatReorderingSeqSBAIJ(A, perm);CHKERRA(ierr);
48     ai = a->inew; aj = a->jnew;
49   }
50 
51   /* initialization */
52   /* Don't know how many column pointers are needed so estimate.
53      Use Modified Sparse Row storage for u and ju, see Sasd pp.85 */
54   iu   = (int*)PetscMalloc((mbs+1)*sizeof(int));CHKPTRQ(iu);
55   umax = (int)(f*ai[mbs] + 1); umax += mbs + 1;
56   ju   = (int*)PetscMalloc(umax*sizeof(int));CHKPTRQ(ju);
57   iu[0] = mbs+1;
58   juptr = mbs;
59   jl =  (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl);
60   q  =  (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(q);
61   for (i=0; i<mbs; i++){
62     jl[i] = mbs; q[i] = 0;
63   }
64 
65   /* for each row k */
66   for (k=0; k<mbs; k++){
67     nzk = 0; /* num. of nz blocks in k-th block row with diagonal block excluded */
68     q[k] = mbs;
69     /* initialize nonzero structure of k-th row to row rip[k] of A */
70     jmin = ai[rip[k]];
71     jmax = ai[rip[k]+1];
72     for (j=jmin; j<jmax; j++){
73       vj = rip[aj[j]]; /* col. value */
74       if(vj > k){
75         qm = k;
76         do {
77           m  = qm; qm = q[m];
78         } while(qm < vj);
79         if (qm == vj) {
80           printf(" error: duplicate entry in A\n"); break;
81         }
82         nzk++;
83         q[m] = vj;
84         q[vj] = qm;
85       } /* if(vj > k) */
86     } /* for (j=jmin; j<jmax; j++) */
87 
88     /* modify nonzero structure of k-th row by computing fill-in
89        for each row i to be merged in */
90     i = k;
91     i = jl[i]; /* next pivot row (== mbs for symbolic factorization) */
92     /* printf(" next pivot row i=%d\n",i); */
93     while (i < mbs){
94       /* merge row i into k-th row */
95       nzi = iu[i+1] - (iu[i]+1);
96       jmin = iu[i] + 1; jmax = iu[i] + nzi;
97       qm = k;
98       for (j=jmin; j<jmax+1; j++){
99         vj = ju[j];
100         do {
101           m = qm; qm = q[m];
102         } while (qm < vj);
103         if (qm != vj){
104          nzk++; q[m] = vj; q[vj] = qm; qm = vj;
105         }
106       }
107       i = jl[i]; /* next pivot row */
108     }
109 
110     /* add k to row list for first nonzero element in k-th row */
111     if (nzk > 0){
112       i = q[k]; /* col value of first nonzero element in U(k, k+1:mbs-1) */
113       jl[k] = jl[i]; jl[i] = k;
114     }
115     iu[k+1] = iu[k] + nzk;   /* printf(" iu[%d]=%d, umax=%d\n", k+1, iu[k+1],umax);*/
116 
117     /* allocate more space to ju if needed */
118     if (iu[k+1] > umax) { printf("allocate more space, iu[%d]=%d > umax=%d\n",k+1, iu[k+1],umax);
119       /* estimate how much additional space we will need */
120       /* use the strategy suggested by David Hysom <hysom@perch-t.icase.edu> */
121       /* just double the memory each time */
122       maxadd = umax;
123       if (maxadd < nzk) maxadd = (mbs-k)*(nzk+1)/2;
124       umax += maxadd;
125 
126       /* allocate a longer ju */
127       jutmp = (int*)PetscMalloc(umax*sizeof(int));CHKPTRQ(jutmp);
128       ierr  = PetscMemcpy(jutmp,ju,iu[k]*sizeof(int));CHKERRQ(ierr);
129       ierr  = PetscFree(ju);CHKERRQ(ierr);
130       ju    = jutmp;
131       realloc++; /* count how many times we realloc */
132     }
133 
134     /* save nonzero structure of k-th row in ju */
135     i=k;
136     jumin = juptr + 1; juptr += nzk;
137     for (j=jumin; j<juptr+1; j++){
138       i=q[i];
139       ju[j]=i;
140     }
141   }
142 
143   if (ai[mbs] != 0) {
144     PetscReal af = ((PetscReal)iu[mbs])/((PetscReal)ai[mbs]);
145     PLogInfo(A,"MatCholeskyFactorSymbolic_SeqSBAIJ:Reallocs %d Fill ratio:given %g needed %g\n",realloc,f,af);
146     PLogInfo(A,"MatCholeskyFactorSymbolic_SeqSBAIJ:Run with -pc_lu_fill %g or use \n",af);
147     PLogInfo(A,"MatCholeskyFactorSymbolic_SeqSBAIJ:PCLUSetFill(pc,%g);\n",af);
148     PLogInfo(A,"MatCholeskyFactorSymbolic_SeqSBAIJ:for best performance.\n");
149   } else {
150      PLogInfo(A,"MatCholeskyFactorSymbolic_SeqSBAIJ:Empty matrix.\n");
151   }
152 
153   ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
154   ierr = PetscFree(q);CHKERRQ(ierr);
155   ierr = PetscFree(jl);CHKERRQ(ierr);
156 
157   /* put together the new matrix */
158   ierr = MatCreateSeqSBAIJ(A->comm,bs,bs*mbs,bs*mbs,0,PETSC_NULL,B);CHKERRQ(ierr);
159   /* PLogObjectParent(*B,iperm); */
160   b = (Mat_SeqSBAIJ*)(*B)->data;
161   ierr = PetscFree(b->imax);CHKERRQ(ierr);
162   b->singlemalloc = PETSC_FALSE;
163   /* the next line frees the default space generated by the Create() */
164   ierr = PetscFree(b->a);CHKERRQ(ierr);
165   ierr = PetscFree(b->ilen);CHKERRQ(ierr);
166   b->a          = (MatScalar*)PetscMalloc((iu[mbs]+1)*sizeof(MatScalar)*bs2);CHKPTRQ(b->a);
167   b->j          = ju;
168   b->i          = iu;
169   b->diag       = 0;
170   b->ilen       = 0;
171   b->imax       = 0;
172   b->row        = perm;
173   ierr          = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
174   b->icol       = perm;
175   ierr          = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
176   b->solve_work = (Scalar*)PetscMalloc((bs*mbs+bs)*sizeof(Scalar));CHKPTRQ(b->solve_work);
177   /* In b structure:  Free imax, ilen, old a, old j.
178      Allocate idnew, solve_work, new a, new j */
179   PLogObjectMemory(*B,(iu[mbs]-mbs)*(sizeof(int)+sizeof(MatScalar)));
180   b->s_maxnz = b->s_nz = iu[mbs];
181 
182   (*B)->factor                 = FACTOR_LU;
183   (*B)->info.factor_mallocs    = realloc;
184   (*B)->info.fill_ratio_given  = f;
185   if (ai[mbs] != 0) {
186     (*B)->info.fill_ratio_needed = ((PetscReal)iu[mbs])/((PetscReal)ai[mbs]);
187   } else {
188     (*B)->info.fill_ratio_needed = 0.0;
189   }
190   PetscFunctionReturn(0);
191 }
192 
193 #undef __FUNC__
194 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_N"
195 int MatCholeskyFactorNumeric_SeqSBAIJ_N(Mat A,Mat *B)
196 {
197   Mat                C = *B;
198   Mat_SeqBAIJ        *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
199   IS                 isrow = b->row,isicol = b->icol;
200   int                *r,*ic,ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
201   int                *ajtmpold,*ajtmp,nz,row,bslog,*ai=a->i,*aj=a->j,k,flg;
202   int                *diag_offset=b->diag,diag,bs=a->bs,bs2 = a->bs2,*v_pivots,*pj;
203   MatScalar          *ba = b->a,*aa = a->a,*pv,*v,*rtmp,*multiplier,*v_work,*pc,*w;
204 
205   PetscFunctionBegin;
206   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
207   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
208   rtmp = (MatScalar*)PetscMalloc(bs2*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
209   ierr = PetscMemzero(rtmp,bs2*(n+1)*sizeof(MatScalar));CHKERRQ(ierr);
210   /* generate work space needed by dense LU factorization */
211   v_work     = (MatScalar*)PetscMalloc(bs*sizeof(int) + (bs+bs2)*sizeof(MatScalar));CHKPTRQ(v_work);
212   multiplier = v_work + bs;
213   v_pivots   = (int*)(multiplier + bs2);
214 
215   /* flops in while loop */
216   bslog = 2*bs*bs2;
217 
218   for (i=0; i<n; i++) {
219     nz    = bi[i+1] - bi[i];
220     ajtmp = bj + bi[i];
221     for  (j=0; j<nz; j++) {
222       ierr = PetscMemzero(rtmp+bs2*ajtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
223     }
224     /* load in initial (unfactored row) */
225     nz       = ai[r[i]+1] - ai[r[i]];
226     ajtmpold = aj + ai[r[i]];
227     v        = aa + bs2*ai[r[i]];
228     for (j=0; j<nz; j++) {
229       ierr = PetscMemcpy(rtmp+bs2*ic[ajtmpold[j]],v+bs2*j,bs2*sizeof(MatScalar));CHKERRQ(ierr);
230     }
231     row = *ajtmp++;
232     while (row < i) {
233       pc = rtmp + bs2*row;
234 /*      if (*pc) { */
235       for (flg=0,k=0; k<bs2; k++) { if (pc[k]!=0.0) { flg =1; break; }}
236       if (flg) {
237         pv = ba + bs2*diag_offset[row];
238         pj = bj + diag_offset[row] + 1;
239         Kernel_A_gets_A_times_B(bs,pc,pv,multiplier);
240         nz = bi[row+1] - diag_offset[row] - 1;
241         pv += bs2;
242         for (j=0; j<nz; j++) {
243           Kernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j);
244         }
245         PLogFlops(bslog*(nz+1)-bs);
246       }
247         row = *ajtmp++;
248     }
249     /* finished row so stick it into b->a */
250     pv = ba + bs2*bi[i];
251     pj = bj + bi[i];
252     nz = bi[i+1] - bi[i];
253     for (j=0; j<nz; j++) {
254       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
255     }
256     diag = diag_offset[i] - bi[i];
257     /* invert diagonal block */
258     w = pv + bs2*diag;
259     Kernel_A_gets_inverse_A(bs,w,v_pivots,v_work);
260   }
261 
262   ierr = PetscFree(rtmp);CHKERRQ(ierr);
263   ierr = PetscFree(v_work);CHKERRQ(ierr);
264   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
265   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
266   C->factor = FACTOR_LU;
267   C->assembled = PETSC_TRUE;
268   PLogFlops(1.3333*bs*bs2*b->mbs); /* from inverting diagonal blocks */
269   PetscFunctionReturn(0);
270 }
271 
272 /*
273       Version for when blocks are 7 by 7
274 */
275 #undef __FUNC__
276 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_7"
277 int MatCholeskyFactorNumeric_SeqSBAIJ_7(Mat A,Mat *B)
278 {
279   Mat         C = *B;
280   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
281   IS          isrow = b->row,isicol = b->icol;
282   int         *r,*ic,ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
283   int         *ajtmpold,*ajtmp,nz,row;
284   int         *diag_offset = b->diag,idx,*ai=a->i,*aj=a->j,*pj;
285   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
286   MatScalar   p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
287   MatScalar   p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
288   MatScalar   x17,x18,x19,x20,x21,x22,x23,x24,x25,p10,p11,p12,p13,p14;
289   MatScalar   p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,m10,m11,m12;
290   MatScalar   m13,m14,m15,m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
291   MatScalar   p26,p27,p28,p29,p30,p31,p32,p33,p34,p35,p36;
292   MatScalar   p37,p38,p39,p40,p41,p42,p43,p44,p45,p46,p47,p48,p49;
293   MatScalar   x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36;
294   MatScalar   x37,x38,x39,x40,x41,x42,x43,x44,x45,x46,x47,x48,x49;
295   MatScalar   m26,m27,m28,m29,m30,m31,m32,m33,m34,m35,m36;
296   MatScalar   m37,m38,m39,m40,m41,m42,m43,m44,m45,m46,m47,m48,m49;
297   MatScalar   *ba = b->a,*aa = a->a;
298 
299   PetscFunctionBegin;
300   ierr  = ISGetIndices(isrow,&r);CHKERRQ(ierr);
301   ierr  = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
302   rtmp  = (MatScalar*)PetscMalloc(49*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
303 
304   for (i=0; i<n; i++) {
305     nz    = bi[i+1] - bi[i];
306     ajtmp = bj + bi[i];
307     for  (j=0; j<nz; j++) {
308       x = rtmp+49*ajtmp[j];
309       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
310       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
311       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = x[25] = 0.0 ;
312       x[26] = x[27] = x[28] = x[29] = x[30] = x[31] = x[32] = x[33] = 0.0 ;
313       x[34] = x[35] = x[36] = x[37] = x[38] = x[39] = x[40] = x[41] = 0.0 ;
314       x[42] = x[43] = x[44] = x[45] = x[46] = x[47] = x[48] = 0.0 ;
315     }
316     /* load in initial (unfactored row) */
317     idx      = r[i];
318     nz       = ai[idx+1] - ai[idx];
319     ajtmpold = aj + ai[idx];
320     v        = aa + 49*ai[idx];
321     for (j=0; j<nz; j++) {
322       x    = rtmp+49*ic[ajtmpold[j]];
323       x[0] =  v[0];  x[1] =  v[1];  x[2] =  v[2];  x[3] =  v[3];
324       x[4] =  v[4];  x[5] =  v[5];  x[6] =  v[6];  x[7] =  v[7];
325       x[8] =  v[8];  x[9] =  v[9];  x[10] = v[10]; x[11] = v[11];
326       x[12] = v[12]; x[13] = v[13]; x[14] = v[14]; x[15] = v[15];
327       x[16] = v[16]; x[17] = v[17]; x[18] = v[18]; x[19] = v[19];
328       x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23];
329       x[24] = v[24]; x[25] = v[25]; x[26] = v[26]; x[27] = v[27];
330       x[28] = v[28]; x[29] = v[29]; x[30] = v[30]; x[31] = v[31];
331       x[32] = v[32]; x[33] = v[33]; x[34] = v[34]; x[35] = v[35];
332       x[36] = v[36]; x[37] = v[37]; x[38] = v[38]; x[39] = v[39];
333       x[40] = v[40]; x[41] = v[41]; x[42] = v[42]; x[43] = v[43];
334       x[44] = v[44]; x[45] = v[45]; x[46] = v[46]; x[47] = v[47];
335       x[48] = v[48];
336       v    += 49;
337     }
338     row = *ajtmp++;
339     while (row < i) {
340       pc  =  rtmp + 49*row;
341       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
342       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];
343       p9  = pc[8];  p10 = pc[9];  p11 = pc[10]; p12 = pc[11];
344       p13 = pc[12]; p14 = pc[13]; p15 = pc[14]; p16 = pc[15];
345       p17 = pc[16]; p18 = pc[17]; p19 = pc[18]; p20 = pc[19];
346       p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
347       p25 = pc[24]; p26 = pc[25]; p27 = pc[26]; p28 = pc[27];
348       p29 = pc[28]; p30 = pc[29]; p31 = pc[30]; p32 = pc[31];
349       p33 = pc[32]; p34 = pc[33]; p35 = pc[34]; p36 = pc[35];
350       p37 = pc[36]; p38 = pc[37]; p39 = pc[38]; p40 = pc[39];
351       p41 = pc[40]; p42 = pc[41]; p43 = pc[42]; p44 = pc[43];
352       p45 = pc[44]; p46 = pc[45]; p47 = pc[46]; p48 = pc[47];
353       p49 = pc[48];
354       if (p1  != 0.0 || p2  != 0.0 || p3  != 0.0 || p4  != 0.0 ||
355           p5  != 0.0 || p6  != 0.0 || p7  != 0.0 || p8  != 0.0 ||
356           p9  != 0.0 || p10 != 0.0 || p11 != 0.0 || p12 != 0.0 ||
357           p13 != 0.0 || p14 != 0.0 || p15 != 0.0 || p16 != 0.0 ||
358           p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 ||
359           p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 ||
360           p25 != 0.0 || p26 != 0.0 || p27 != 0.0 || p28 != 0.0 ||
361           p29 != 0.0 || p30 != 0.0 || p31 != 0.0 || p32 != 0.0 ||
362           p33 != 0.0 || p34 != 0.0 || p35 != 0.0 || p36 != 0.0 ||
363           p37 != 0.0 || p38 != 0.0 || p39 != 0.0 || p40 != 0.0 ||
364           p41 != 0.0 || p42 != 0.0 || p43 != 0.0 || p44 != 0.0 ||
365           p45 != 0.0 || p46 != 0.0 || p47 != 0.0 || p48 != 0.0 ||
366           p49 != 0.0) {
367         pv = ba + 49*diag_offset[row];
368         pj = bj + diag_offset[row] + 1;
369 	x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
370 	x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
371 	x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
372 	x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
373 	x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
374 	x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
375 	x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
376 	x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
377 	x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
378 	x37 = pv[36]; x38 = pv[37]; x39 = pv[38]; x40 = pv[39];
379 	x41 = pv[40]; x42 = pv[41]; x43 = pv[42]; x44 = pv[43];
380 	x45 = pv[44]; x46 = pv[45]; x47 = pv[46]; x48 = pv[47];
381 	x49 = pv[48];
382         pc[0]  = m1  = p1*x1  + p8*x2   + p15*x3  + p22*x4  + p29*x5  + p36*x6 + p43*x7;
383         pc[1]  = m2  = p2*x1  + p9*x2   + p16*x3  + p23*x4  + p30*x5  + p37*x6 + p44*x7;
384         pc[2]  = m3  = p3*x1  + p10*x2  + p17*x3  + p24*x4  + p31*x5  + p38*x6 + p45*x7;
385         pc[3]  = m4  = p4*x1  + p11*x2  + p18*x3  + p25*x4  + p32*x5  + p39*x6 + p46*x7;
386         pc[4]  = m5  = p5*x1  + p12*x2  + p19*x3  + p26*x4  + p33*x5  + p40*x6 + p47*x7;
387         pc[5]  = m6  = p6*x1  + p13*x2  + p20*x3  + p27*x4  + p34*x5  + p41*x6 + p48*x7;
388         pc[6]  = m7  = p7*x1  + p14*x2  + p21*x3  + p28*x4  + p35*x5  + p42*x6 + p49*x7;
389 
390         pc[7]  = m8  = p1*x8  + p8*x9   + p15*x10 + p22*x11 + p29*x12 + p36*x13 + p43*x14;
391         pc[8]  = m9  = p2*x8  + p9*x9   + p16*x10 + p23*x11 + p30*x12 + p37*x13 + p44*x14;
392         pc[9]  = m10 = p3*x8  + p10*x9  + p17*x10 + p24*x11 + p31*x12 + p38*x13 + p45*x14;
393         pc[10] = m11 = p4*x8  + p11*x9  + p18*x10 + p25*x11 + p32*x12 + p39*x13 + p46*x14;
394         pc[11] = m12 = p5*x8  + p12*x9  + p19*x10 + p26*x11 + p33*x12 + p40*x13 + p47*x14;
395         pc[12] = m13 = p6*x8  + p13*x9  + p20*x10 + p27*x11 + p34*x12 + p41*x13 + p48*x14;
396         pc[13] = m14 = p7*x8  + p14*x9  + p21*x10 + p28*x11 + p35*x12 + p42*x13 + p49*x14;
397 
398         pc[14] = m15 = p1*x15 + p8*x16  + p15*x17 + p22*x18 + p29*x19 + p36*x20 + p43*x21;
399         pc[15] = m16 = p2*x15 + p9*x16  + p16*x17 + p23*x18 + p30*x19 + p37*x20 + p44*x21;
400         pc[16] = m17 = p3*x15 + p10*x16 + p17*x17 + p24*x18 + p31*x19 + p38*x20 + p45*x21;
401         pc[17] = m18 = p4*x15 + p11*x16 + p18*x17 + p25*x18 + p32*x19 + p39*x20 + p46*x21;
402         pc[18] = m19 = p5*x15 + p12*x16 + p19*x17 + p26*x18 + p33*x19 + p40*x20 + p47*x21;
403         pc[19] = m20 = p6*x15 + p13*x16 + p20*x17 + p27*x18 + p34*x19 + p41*x20 + p48*x21;
404         pc[20] = m21 = p7*x15 + p14*x16 + p21*x17 + p28*x18 + p35*x19 + p42*x20 + p49*x21;
405 
406         pc[21] = m22 = p1*x22 + p8*x23  + p15*x24 + p22*x25 + p29*x26 + p36*x27 + p43*x28;
407         pc[22] = m23 = p2*x22 + p9*x23  + p16*x24 + p23*x25 + p30*x26 + p37*x27 + p44*x28;
408         pc[23] = m24 = p3*x22 + p10*x23 + p17*x24 + p24*x25 + p31*x26 + p38*x27 + p45*x28;
409         pc[24] = m25 = p4*x22 + p11*x23 + p18*x24 + p25*x25 + p32*x26 + p39*x27 + p46*x28;
410         pc[25] = m26 = p5*x22 + p12*x23 + p19*x24 + p26*x25 + p33*x26 + p40*x27 + p47*x28;
411         pc[26] = m27 = p6*x22 + p13*x23 + p20*x24 + p27*x25 + p34*x26 + p41*x27 + p48*x28;
412         pc[27] = m28 = p7*x22 + p14*x23 + p21*x24 + p28*x25 + p35*x26 + p42*x27 + p49*x28;
413 
414         pc[28] = m29 = p1*x29 + p8*x30  + p15*x31 + p22*x32 + p29*x33 + p36*x34 + p43*x35;
415         pc[29] = m30 = p2*x29 + p9*x30  + p16*x31 + p23*x32 + p30*x33 + p37*x34 + p44*x35;
416         pc[30] = m31 = p3*x29 + p10*x30 + p17*x31 + p24*x32 + p31*x33 + p38*x34 + p45*x35;
417         pc[31] = m32 = p4*x29 + p11*x30 + p18*x31 + p25*x32 + p32*x33 + p39*x34 + p46*x35;
418         pc[32] = m33 = p5*x29 + p12*x30 + p19*x31 + p26*x32 + p33*x33 + p40*x34 + p47*x35;
419         pc[33] = m34 = p6*x29 + p13*x30 + p20*x31 + p27*x32 + p34*x33 + p41*x34 + p48*x35;
420         pc[34] = m35 = p7*x29 + p14*x30 + p21*x31 + p28*x32 + p35*x33 + p42*x34 + p49*x35;
421 
422         pc[35] = m36 = p1*x36 + p8*x37  + p15*x38 + p22*x39 + p29*x40 + p36*x41 + p43*x42;
423         pc[36] = m37 = p2*x36 + p9*x37  + p16*x38 + p23*x39 + p30*x40 + p37*x41 + p44*x42;
424         pc[37] = m38 = p3*x36 + p10*x37 + p17*x38 + p24*x39 + p31*x40 + p38*x41 + p45*x42;
425         pc[38] = m39 = p4*x36 + p11*x37 + p18*x38 + p25*x39 + p32*x40 + p39*x41 + p46*x42;
426         pc[39] = m40 = p5*x36 + p12*x37 + p19*x38 + p26*x39 + p33*x40 + p40*x41 + p47*x42;
427         pc[40] = m41 = p6*x36 + p13*x37 + p20*x38 + p27*x39 + p34*x40 + p41*x41 + p48*x42;
428         pc[41] = m42 = p7*x36 + p14*x37 + p21*x38 + p28*x39 + p35*x40 + p42*x41 + p49*x42;
429 
430         pc[42] = m43 = p1*x43 + p8*x44  + p15*x45 + p22*x46 + p29*x47 + p36*x48 + p43*x49;
431         pc[43] = m44 = p2*x43 + p9*x44  + p16*x45 + p23*x46 + p30*x47 + p37*x48 + p44*x49;
432         pc[44] = m45 = p3*x43 + p10*x44 + p17*x45 + p24*x46 + p31*x47 + p38*x48 + p45*x49;
433         pc[45] = m46 = p4*x43 + p11*x44 + p18*x45 + p25*x46 + p32*x47 + p39*x48 + p46*x49;
434         pc[46] = m47 = p5*x43 + p12*x44 + p19*x45 + p26*x46 + p33*x47 + p40*x48 + p47*x49;
435         pc[47] = m48 = p6*x43 + p13*x44 + p20*x45 + p27*x46 + p34*x47 + p41*x48 + p48*x49;
436         pc[48] = m49 = p7*x43 + p14*x44 + p21*x45 + p28*x46 + p35*x47 + p42*x48 + p49*x49;
437 
438         nz = bi[row+1] - diag_offset[row] - 1;
439         pv += 49;
440         for (j=0; j<nz; j++) {
441 	  x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
442 	  x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
443 	  x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
444 	  x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
445 	  x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
446 	  x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
447 	  x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
448 	  x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
449 	  x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
450 	  x37 = pv[36]; x38 = pv[37]; x39 = pv[38]; x40 = pv[39];
451 	  x41 = pv[40]; x42 = pv[41]; x43 = pv[42]; x44 = pv[43];
452 	  x45 = pv[44]; x46 = pv[45]; x47 = pv[46]; x48 = pv[47];
453 	  x49 = pv[48];
454 	  x    = rtmp + 49*pj[j];
455 	  x[0]  -= m1*x1  + m8*x2   + m15*x3  + m22*x4  + m29*x5  + m36*x6 + m43*x7;
456 	  x[1]  -= m2*x1  + m9*x2   + m16*x3  + m23*x4  + m30*x5  + m37*x6 + m44*x7;
457 	  x[2]  -= m3*x1  + m10*x2  + m17*x3  + m24*x4  + m31*x5  + m38*x6 + m45*x7;
458 	  x[3]  -= m4*x1  + m11*x2  + m18*x3  + m25*x4  + m32*x5  + m39*x6 + m46*x7;
459 	  x[4]  -= m5*x1  + m12*x2  + m19*x3  + m26*x4  + m33*x5  + m40*x6 + m47*x7;
460 	  x[5]  -= m6*x1  + m13*x2  + m20*x3  + m27*x4  + m34*x5  + m41*x6 + m48*x7;
461 	  x[6]  -= m7*x1  + m14*x2  + m21*x3  + m28*x4  + m35*x5  + m42*x6 + m49*x7;
462 
463 	  x[7]  -= m1*x8  + m8*x9   + m15*x10 + m22*x11 + m29*x12 + m36*x13 + m43*x14;
464 	  x[8]  -= m2*x8  + m9*x9   + m16*x10 + m23*x11 + m30*x12 + m37*x13 + m44*x14;
465 	  x[9]  -= m3*x8  + m10*x9  + m17*x10 + m24*x11 + m31*x12 + m38*x13 + m45*x14;
466 	  x[10] -= m4*x8  + m11*x9  + m18*x10 + m25*x11 + m32*x12 + m39*x13 + m46*x14;
467 	  x[11] -= m5*x8  + m12*x9  + m19*x10 + m26*x11 + m33*x12 + m40*x13 + m47*x14;
468 	  x[12] -= m6*x8  + m13*x9  + m20*x10 + m27*x11 + m34*x12 + m41*x13 + m48*x14;
469 	  x[13] -= m7*x8  + m14*x9  + m21*x10 + m28*x11 + m35*x12 + m42*x13 + m49*x14;
470 
471 	  x[14] -= m1*x15 + m8*x16  + m15*x17 + m22*x18 + m29*x19 + m36*x20 + m43*x21;
472 	  x[15] -= m2*x15 + m9*x16  + m16*x17 + m23*x18 + m30*x19 + m37*x20 + m44*x21;
473 	  x[16] -= m3*x15 + m10*x16 + m17*x17 + m24*x18 + m31*x19 + m38*x20 + m45*x21;
474 	  x[17] -= m4*x15 + m11*x16 + m18*x17 + m25*x18 + m32*x19 + m39*x20 + m46*x21;
475 	  x[18] -= m5*x15 + m12*x16 + m19*x17 + m26*x18 + m33*x19 + m40*x20 + m47*x21;
476 	  x[19] -= m6*x15 + m13*x16 + m20*x17 + m27*x18 + m34*x19 + m41*x20 + m48*x21;
477 	  x[20] -= m7*x15 + m14*x16 + m21*x17 + m28*x18 + m35*x19 + m42*x20 + m49*x21;
478 
479 	  x[21] -= m1*x22 + m8*x23  + m15*x24 + m22*x25 + m29*x26 + m36*x27 + m43*x28;
480 	  x[22] -= m2*x22 + m9*x23  + m16*x24 + m23*x25 + m30*x26 + m37*x27 + m44*x28;
481 	  x[23] -= m3*x22 + m10*x23 + m17*x24 + m24*x25 + m31*x26 + m38*x27 + m45*x28;
482 	  x[24] -= m4*x22 + m11*x23 + m18*x24 + m25*x25 + m32*x26 + m39*x27 + m46*x28;
483 	  x[25] -= m5*x22 + m12*x23 + m19*x24 + m26*x25 + m33*x26 + m40*x27 + m47*x28;
484 	  x[26] -= m6*x22 + m13*x23 + m20*x24 + m27*x25 + m34*x26 + m41*x27 + m48*x28;
485 	  x[27] -= m7*x22 + m14*x23 + m21*x24 + m28*x25 + m35*x26 + m42*x27 + m49*x28;
486 
487 	  x[28] -= m1*x29 + m8*x30  + m15*x31 + m22*x32 + m29*x33 + m36*x34 + m43*x35;
488 	  x[29] -= m2*x29 + m9*x30  + m16*x31 + m23*x32 + m30*x33 + m37*x34 + m44*x35;
489 	  x[30] -= m3*x29 + m10*x30 + m17*x31 + m24*x32 + m31*x33 + m38*x34 + m45*x35;
490 	  x[31] -= m4*x29 + m11*x30 + m18*x31 + m25*x32 + m32*x33 + m39*x34 + m46*x35;
491 	  x[32] -= m5*x29 + m12*x30 + m19*x31 + m26*x32 + m33*x33 + m40*x34 + m47*x35;
492 	  x[33] -= m6*x29 + m13*x30 + m20*x31 + m27*x32 + m34*x33 + m41*x34 + m48*x35;
493 	  x[34] -= m7*x29 + m14*x30 + m21*x31 + m28*x32 + m35*x33 + m42*x34 + m49*x35;
494 
495 	  x[35] -= m1*x36 + m8*x37  + m15*x38 + m22*x39 + m29*x40 + m36*x41 + m43*x42;
496 	  x[36] -= m2*x36 + m9*x37  + m16*x38 + m23*x39 + m30*x40 + m37*x41 + m44*x42;
497 	  x[37] -= m3*x36 + m10*x37 + m17*x38 + m24*x39 + m31*x40 + m38*x41 + m45*x42;
498 	  x[38] -= m4*x36 + m11*x37 + m18*x38 + m25*x39 + m32*x40 + m39*x41 + m46*x42;
499 	  x[39] -= m5*x36 + m12*x37 + m19*x38 + m26*x39 + m33*x40 + m40*x41 + m47*x42;
500 	  x[40] -= m6*x36 + m13*x37 + m20*x38 + m27*x39 + m34*x40 + m41*x41 + m48*x42;
501 	  x[41] -= m7*x36 + m14*x37 + m21*x38 + m28*x39 + m35*x40 + m42*x41 + m49*x42;
502 
503 	  x[42] -= m1*x43 + m8*x44  + m15*x45 + m22*x46 + m29*x47 + m36*x48 + m43*x49;
504 	  x[43] -= m2*x43 + m9*x44  + m16*x45 + m23*x46 + m30*x47 + m37*x48 + m44*x49;
505 	  x[44] -= m3*x43 + m10*x44 + m17*x45 + m24*x46 + m31*x47 + m38*x48 + m45*x49;
506 	  x[45] -= m4*x43 + m11*x44 + m18*x45 + m25*x46 + m32*x47 + m39*x48 + m46*x49;
507 	  x[46] -= m5*x43 + m12*x44 + m19*x45 + m26*x46 + m33*x47 + m40*x48 + m47*x49;
508 	  x[47] -= m6*x43 + m13*x44 + m20*x45 + m27*x46 + m34*x47 + m41*x48 + m48*x49;
509 	  x[48] -= m7*x43 + m14*x44 + m21*x45 + m28*x46 + m35*x47 + m42*x48 + m49*x49;
510           pv   += 49;
511         }
512         PLogFlops(686*nz+637);
513       }
514       row = *ajtmp++;
515     }
516     /* finished row so stick it into b->a */
517     pv = ba + 49*bi[i];
518     pj = bj + bi[i];
519     nz = bi[i+1] - bi[i];
520     for (j=0; j<nz; j++) {
521       x      = rtmp+49*pj[j];
522       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
523       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7];
524       pv[8]  = x[8];  pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11];
525       pv[12] = x[12]; pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
526       pv[16] = x[16]; pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19];
527       pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23];
528       pv[24] = x[24]; pv[25] = x[25]; pv[26] = x[26]; pv[27] = x[27];
529       pv[28] = x[28]; pv[29] = x[29]; pv[30] = x[30]; pv[31] = x[31];
530       pv[32] = x[32]; pv[33] = x[33]; pv[34] = x[34]; pv[35] = x[35];
531       pv[36] = x[36]; pv[37] = x[37]; pv[38] = x[38]; pv[39] = x[39];
532       pv[40] = x[40]; pv[41] = x[41]; pv[42] = x[42]; pv[43] = x[43];
533       pv[44] = x[44]; pv[45] = x[45]; pv[46] = x[46]; pv[47] = x[47];
534       pv[48] = x[48];
535       pv   += 49;
536     }
537     /* invert diagonal block */
538     w = ba + 49*diag_offset[i];
539     ierr = Kernel_A_gets_inverse_A_7(w);CHKERRQ(ierr);
540   }
541 
542   ierr = PetscFree(rtmp);CHKERRQ(ierr);
543   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
544   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
545   C->factor = FACTOR_LU;
546   C->assembled = PETSC_TRUE;
547   PLogFlops(1.3333*343*b->mbs); /* from inverting diagonal blocks */
548   PetscFunctionReturn(0);
549 }
550 
551 /*
552       Version for when blocks are 7 by 7 Using natural ordering
553 */
554 #undef __FUNC__
555 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_7_NaturalOrdering"
556 int MatCholeskyFactorNumeric_SeqSBAIJ_7_NaturalOrdering(Mat A,Mat *B)
557 {
558   Mat          C = *B;
559   Mat_SeqBAIJ  *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
560   int          ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
561   int          *ajtmpold,*ajtmp,nz,row;
562   int          *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
563   MatScalar    *pv,*v,*rtmp,*pc,*w,*x;
564   MatScalar    x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15;
565   MatScalar    x16,x17,x18,x19,x20,x21,x22,x23,x24,x25;
566   MatScalar    p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15;
567   MatScalar    p16,p17,p18,p19,p20,p21,p22,p23,p24,p25;
568   MatScalar    m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12,m13,m14,m15;
569   MatScalar    m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
570   MatScalar    p26,p27,p28,p29,p30,p31,p32,p33,p34,p35,p36;
571   MatScalar    p37,p38,p39,p40,p41,p42,p43,p44,p45,p46,p47,p48,p49;
572   MatScalar    x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36;
573   MatScalar    x37,x38,x39,x40,x41,x42,x43,x44,x45,x46,x47,x48,x49;
574   MatScalar    m26,m27,m28,m29,m30,m31,m32,m33,m34,m35,m36;
575   MatScalar    m37,m38,m39,m40,m41,m42,m43,m44,m45,m46,m47,m48,m49;
576   MatScalar    *ba = b->a,*aa = a->a;
577 
578   PetscFunctionBegin;
579   rtmp  = (MatScalar*)PetscMalloc(49*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
580   for (i=0; i<n; i++) {
581     nz    = bi[i+1] - bi[i];
582     ajtmp = bj + bi[i];
583     for  (j=0; j<nz; j++) {
584       x = rtmp+49*ajtmp[j];
585       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
586       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
587       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = x[25] = 0.0 ;
588       x[26] = x[27] = x[28] = x[29] = x[30] = x[31] = x[32] = x[33] = 0.0 ;
589       x[34] = x[35] = x[36] = x[37] = x[38] = x[39] = x[40] = x[41] = 0.0 ;
590       x[42] = x[43] = x[44] = x[45] = x[46] = x[47] = x[48] = 0.0 ;
591     }
592     /* load in initial (unfactored row) */
593     nz       = ai[i+1] - ai[i];
594     ajtmpold = aj + ai[i];
595     v        = aa + 49*ai[i];
596     for (j=0; j<nz; j++) {
597       x    = rtmp+49*ajtmpold[j];
598       x[0] =  v[0];  x[1] =  v[1];  x[2] =  v[2];  x[3] =  v[3];
599       x[4] =  v[4];  x[5] =  v[5];  x[6] =  v[6];  x[7] =  v[7];
600       x[8] =  v[8];  x[9] =  v[9];  x[10] = v[10]; x[11] = v[11];
601       x[12] = v[12]; x[13] = v[13]; x[14] = v[14]; x[15] = v[15];
602       x[16] = v[16]; x[17] = v[17]; x[18] = v[18]; x[19] = v[19];
603       x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23];
604       x[24] = v[24]; x[25] = v[25]; x[26] = v[26]; x[27] = v[27];
605       x[28] = v[28]; x[29] = v[29]; x[30] = v[30]; x[31] = v[31];
606       x[32] = v[32]; x[33] = v[33]; x[34] = v[34]; x[35] = v[35];
607       x[36] = v[36]; x[37] = v[37]; x[38] = v[38]; x[39] = v[39];
608       x[40] = v[40]; x[41] = v[41]; x[42] = v[42]; x[43] = v[43];
609       x[44] = v[44]; x[45] = v[45]; x[46] = v[46]; x[47] = v[47];
610       x[48] = v[48];
611       v    += 49;
612     }
613     row = *ajtmp++;
614     while (row < i) {
615       pc  = rtmp + 49*row;
616       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
617       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];
618       p9  = pc[8];  p10 = pc[9];  p11 = pc[10]; p12 = pc[11];
619       p13 = pc[12]; p14 = pc[13]; p15 = pc[14]; p16 = pc[15];
620       p17 = pc[16]; p18 = pc[17]; p19 = pc[18]; p20 = pc[19];
621       p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
622       p25 = pc[24]; p26 = pc[25]; p27 = pc[26]; p28 = pc[27];
623       p29 = pc[28]; p30 = pc[29]; p31 = pc[30]; p32 = pc[31];
624       p33 = pc[32]; p34 = pc[33]; p35 = pc[34]; p36 = pc[35];
625       p37 = pc[36]; p38 = pc[37]; p39 = pc[38]; p40 = pc[39];
626       p41 = pc[40]; p42 = pc[41]; p43 = pc[42]; p44 = pc[43];
627       p45 = pc[44]; p46 = pc[45]; p47 = pc[46]; p48 = pc[47];
628       p49 = pc[48];
629       if (p1  != 0.0 || p2  != 0.0 || p3  != 0.0 || p4  != 0.0 ||
630           p5  != 0.0 || p6  != 0.0 || p7  != 0.0 || p8  != 0.0 ||
631           p9  != 0.0 || p10 != 0.0 || p11 != 0.0 || p12 != 0.0 ||
632           p13 != 0.0 || p14 != 0.0 || p15 != 0.0 || p16 != 0.0 ||
633           p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 ||
634           p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 ||
635           p25 != 0.0 || p26 != 0.0 || p27 != 0.0 || p28 != 0.0 ||
636           p29 != 0.0 || p30 != 0.0 || p31 != 0.0 || p32 != 0.0 ||
637           p33 != 0.0 || p34 != 0.0 || p35 != 0.0 || p36 != 0.0 ||
638           p37 != 0.0 || p38 != 0.0 || p39 != 0.0 || p40 != 0.0 ||
639           p41 != 0.0 || p42 != 0.0 || p43 != 0.0 || p44 != 0.0 ||
640           p45 != 0.0 || p46 != 0.0 || p47 != 0.0 || p48 != 0.0 ||
641           p49 != 0.0) {
642         pv = ba + 49*diag_offset[row];
643         pj = bj + diag_offset[row] + 1;
644 	x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
645 	x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
646 	x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
647 	x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
648 	x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
649 	x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
650 	x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
651 	x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
652 	x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
653 	x37 = pv[36]; x38 = pv[37]; x39 = pv[38]; x40 = pv[39];
654 	x41 = pv[40]; x42 = pv[41]; x43 = pv[42]; x44 = pv[43];
655 	x45 = pv[44]; x46 = pv[45]; x47 = pv[46]; x48 = pv[47];
656         x49 = pv[48];
657         pc[0]  = m1  = p1*x1  + p8*x2   + p15*x3  + p22*x4  + p29*x5  + p36*x6 + p43*x7;
658         pc[1]  = m2  = p2*x1  + p9*x2   + p16*x3  + p23*x4  + p30*x5  + p37*x6 + p44*x7;
659         pc[2]  = m3  = p3*x1  + p10*x2  + p17*x3  + p24*x4  + p31*x5  + p38*x6 + p45*x7;
660         pc[3]  = m4  = p4*x1  + p11*x2  + p18*x3  + p25*x4  + p32*x5  + p39*x6 + p46*x7;
661         pc[4]  = m5  = p5*x1  + p12*x2  + p19*x3  + p26*x4  + p33*x5  + p40*x6 + p47*x7;
662         pc[5]  = m6  = p6*x1  + p13*x2  + p20*x3  + p27*x4  + p34*x5  + p41*x6 + p48*x7;
663         pc[6]  = m7  = p7*x1  + p14*x2  + p21*x3  + p28*x4  + p35*x5  + p42*x6 + p49*x7;
664 
665         pc[7]  = m8  = p1*x8  + p8*x9   + p15*x10 + p22*x11 + p29*x12 + p36*x13 + p43*x14;
666         pc[8]  = m9  = p2*x8  + p9*x9   + p16*x10 + p23*x11 + p30*x12 + p37*x13 + p44*x14;
667         pc[9]  = m10 = p3*x8  + p10*x9  + p17*x10 + p24*x11 + p31*x12 + p38*x13 + p45*x14;
668         pc[10] = m11 = p4*x8  + p11*x9  + p18*x10 + p25*x11 + p32*x12 + p39*x13 + p46*x14;
669         pc[11] = m12 = p5*x8  + p12*x9  + p19*x10 + p26*x11 + p33*x12 + p40*x13 + p47*x14;
670         pc[12] = m13 = p6*x8  + p13*x9  + p20*x10 + p27*x11 + p34*x12 + p41*x13 + p48*x14;
671         pc[13] = m14 = p7*x8  + p14*x9  + p21*x10 + p28*x11 + p35*x12 + p42*x13 + p49*x14;
672 
673         pc[14] = m15 = p1*x15 + p8*x16  + p15*x17 + p22*x18 + p29*x19 + p36*x20 + p43*x21;
674         pc[15] = m16 = p2*x15 + p9*x16  + p16*x17 + p23*x18 + p30*x19 + p37*x20 + p44*x21;
675         pc[16] = m17 = p3*x15 + p10*x16 + p17*x17 + p24*x18 + p31*x19 + p38*x20 + p45*x21;
676         pc[17] = m18 = p4*x15 + p11*x16 + p18*x17 + p25*x18 + p32*x19 + p39*x20 + p46*x21;
677         pc[18] = m19 = p5*x15 + p12*x16 + p19*x17 + p26*x18 + p33*x19 + p40*x20 + p47*x21;
678         pc[19] = m20 = p6*x15 + p13*x16 + p20*x17 + p27*x18 + p34*x19 + p41*x20 + p48*x21;
679         pc[20] = m21 = p7*x15 + p14*x16 + p21*x17 + p28*x18 + p35*x19 + p42*x20 + p49*x21;
680 
681         pc[21] = m22 = p1*x22 + p8*x23  + p15*x24 + p22*x25 + p29*x26 + p36*x27 + p43*x28;
682         pc[22] = m23 = p2*x22 + p9*x23  + p16*x24 + p23*x25 + p30*x26 + p37*x27 + p44*x28;
683         pc[23] = m24 = p3*x22 + p10*x23 + p17*x24 + p24*x25 + p31*x26 + p38*x27 + p45*x28;
684         pc[24] = m25 = p4*x22 + p11*x23 + p18*x24 + p25*x25 + p32*x26 + p39*x27 + p46*x28;
685         pc[25] = m26 = p5*x22 + p12*x23 + p19*x24 + p26*x25 + p33*x26 + p40*x27 + p47*x28;
686         pc[26] = m27 = p6*x22 + p13*x23 + p20*x24 + p27*x25 + p34*x26 + p41*x27 + p48*x28;
687         pc[27] = m28 = p7*x22 + p14*x23 + p21*x24 + p28*x25 + p35*x26 + p42*x27 + p49*x28;
688 
689         pc[28] = m29 = p1*x29 + p8*x30  + p15*x31 + p22*x32 + p29*x33 + p36*x34 + p43*x35;
690         pc[29] = m30 = p2*x29 + p9*x30  + p16*x31 + p23*x32 + p30*x33 + p37*x34 + p44*x35;
691         pc[30] = m31 = p3*x29 + p10*x30 + p17*x31 + p24*x32 + p31*x33 + p38*x34 + p45*x35;
692         pc[31] = m32 = p4*x29 + p11*x30 + p18*x31 + p25*x32 + p32*x33 + p39*x34 + p46*x35;
693         pc[32] = m33 = p5*x29 + p12*x30 + p19*x31 + p26*x32 + p33*x33 + p40*x34 + p47*x35;
694         pc[33] = m34 = p6*x29 + p13*x30 + p20*x31 + p27*x32 + p34*x33 + p41*x34 + p48*x35;
695         pc[34] = m35 = p7*x29 + p14*x30 + p21*x31 + p28*x32 + p35*x33 + p42*x34 + p49*x35;
696 
697         pc[35] = m36 = p1*x36 + p8*x37  + p15*x38 + p22*x39 + p29*x40 + p36*x41 + p43*x42;
698         pc[36] = m37 = p2*x36 + p9*x37  + p16*x38 + p23*x39 + p30*x40 + p37*x41 + p44*x42;
699         pc[37] = m38 = p3*x36 + p10*x37 + p17*x38 + p24*x39 + p31*x40 + p38*x41 + p45*x42;
700         pc[38] = m39 = p4*x36 + p11*x37 + p18*x38 + p25*x39 + p32*x40 + p39*x41 + p46*x42;
701         pc[39] = m40 = p5*x36 + p12*x37 + p19*x38 + p26*x39 + p33*x40 + p40*x41 + p47*x42;
702         pc[40] = m41 = p6*x36 + p13*x37 + p20*x38 + p27*x39 + p34*x40 + p41*x41 + p48*x42;
703         pc[41] = m42 = p7*x36 + p14*x37 + p21*x38 + p28*x39 + p35*x40 + p42*x41 + p49*x42;
704 
705         pc[42] = m43 = p1*x43 + p8*x44  + p15*x45 + p22*x46 + p29*x47 + p36*x48 + p43*x49;
706         pc[43] = m44 = p2*x43 + p9*x44  + p16*x45 + p23*x46 + p30*x47 + p37*x48 + p44*x49;
707         pc[44] = m45 = p3*x43 + p10*x44 + p17*x45 + p24*x46 + p31*x47 + p38*x48 + p45*x49;
708         pc[45] = m46 = p4*x43 + p11*x44 + p18*x45 + p25*x46 + p32*x47 + p39*x48 + p46*x49;
709         pc[46] = m47 = p5*x43 + p12*x44 + p19*x45 + p26*x46 + p33*x47 + p40*x48 + p47*x49;
710         pc[47] = m48 = p6*x43 + p13*x44 + p20*x45 + p27*x46 + p34*x47 + p41*x48 + p48*x49;
711         pc[48] = m49 = p7*x43 + p14*x44 + p21*x45 + p28*x46 + p35*x47 + p42*x48 + p49*x49;
712 
713         nz = bi[row+1] - diag_offset[row] - 1;
714         pv += 49;
715         for (j=0; j<nz; j++) {
716 	  x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
717 	  x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
718 	  x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
719 	  x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
720 	  x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
721 	  x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
722 	  x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
723 	  x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
724 	  x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
725 	  x37 = pv[36]; x38 = pv[37]; x39 = pv[38]; x40 = pv[39];
726 	  x41 = pv[40]; x42 = pv[41]; x43 = pv[42]; x44 = pv[43];
727 	  x45 = pv[44]; x46 = pv[45]; x47 = pv[46]; x48 = pv[47];
728 	  x49 = pv[48];
729 	  x    = rtmp + 49*pj[j];
730 	  x[0]  -= m1*x1  + m8*x2   + m15*x3  + m22*x4  + m29*x5  + m36*x6 + m43*x7;
731 	  x[1]  -= m2*x1  + m9*x2   + m16*x3  + m23*x4  + m30*x5  + m37*x6 + m44*x7;
732 	  x[2]  -= m3*x1  + m10*x2  + m17*x3  + m24*x4  + m31*x5  + m38*x6 + m45*x7;
733 	  x[3]  -= m4*x1  + m11*x2  + m18*x3  + m25*x4  + m32*x5  + m39*x6 + m46*x7;
734 	  x[4]  -= m5*x1  + m12*x2  + m19*x3  + m26*x4  + m33*x5  + m40*x6 + m47*x7;
735 	  x[5]  -= m6*x1  + m13*x2  + m20*x3  + m27*x4  + m34*x5  + m41*x6 + m48*x7;
736 	  x[6]  -= m7*x1  + m14*x2  + m21*x3  + m28*x4  + m35*x5  + m42*x6 + m49*x7;
737 
738 	  x[7]  -= m1*x8  + m8*x9   + m15*x10 + m22*x11 + m29*x12 + m36*x13 + m43*x14;
739 	  x[8]  -= m2*x8  + m9*x9   + m16*x10 + m23*x11 + m30*x12 + m37*x13 + m44*x14;
740 	  x[9]  -= m3*x8  + m10*x9  + m17*x10 + m24*x11 + m31*x12 + m38*x13 + m45*x14;
741 	  x[10] -= m4*x8  + m11*x9  + m18*x10 + m25*x11 + m32*x12 + m39*x13 + m46*x14;
742 	  x[11] -= m5*x8  + m12*x9  + m19*x10 + m26*x11 + m33*x12 + m40*x13 + m47*x14;
743 	  x[12] -= m6*x8  + m13*x9  + m20*x10 + m27*x11 + m34*x12 + m41*x13 + m48*x14;
744 	  x[13] -= m7*x8  + m14*x9  + m21*x10 + m28*x11 + m35*x12 + m42*x13 + m49*x14;
745 
746 	  x[14] -= m1*x15 + m8*x16  + m15*x17 + m22*x18 + m29*x19 + m36*x20 + m43*x21;
747 	  x[15] -= m2*x15 + m9*x16  + m16*x17 + m23*x18 + m30*x19 + m37*x20 + m44*x21;
748 	  x[16] -= m3*x15 + m10*x16 + m17*x17 + m24*x18 + m31*x19 + m38*x20 + m45*x21;
749 	  x[17] -= m4*x15 + m11*x16 + m18*x17 + m25*x18 + m32*x19 + m39*x20 + m46*x21;
750 	  x[18] -= m5*x15 + m12*x16 + m19*x17 + m26*x18 + m33*x19 + m40*x20 + m47*x21;
751 	  x[19] -= m6*x15 + m13*x16 + m20*x17 + m27*x18 + m34*x19 + m41*x20 + m48*x21;
752 	  x[20] -= m7*x15 + m14*x16 + m21*x17 + m28*x18 + m35*x19 + m42*x20 + m49*x21;
753 
754 	  x[21] -= m1*x22 + m8*x23  + m15*x24 + m22*x25 + m29*x26 + m36*x27 + m43*x28;
755 	  x[22] -= m2*x22 + m9*x23  + m16*x24 + m23*x25 + m30*x26 + m37*x27 + m44*x28;
756 	  x[23] -= m3*x22 + m10*x23 + m17*x24 + m24*x25 + m31*x26 + m38*x27 + m45*x28;
757 	  x[24] -= m4*x22 + m11*x23 + m18*x24 + m25*x25 + m32*x26 + m39*x27 + m46*x28;
758 	  x[25] -= m5*x22 + m12*x23 + m19*x24 + m26*x25 + m33*x26 + m40*x27 + m47*x28;
759 	  x[26] -= m6*x22 + m13*x23 + m20*x24 + m27*x25 + m34*x26 + m41*x27 + m48*x28;
760 	  x[27] -= m7*x22 + m14*x23 + m21*x24 + m28*x25 + m35*x26 + m42*x27 + m49*x28;
761 
762 	  x[28] -= m1*x29 + m8*x30  + m15*x31 + m22*x32 + m29*x33 + m36*x34 + m43*x35;
763 	  x[29] -= m2*x29 + m9*x30  + m16*x31 + m23*x32 + m30*x33 + m37*x34 + m44*x35;
764 	  x[30] -= m3*x29 + m10*x30 + m17*x31 + m24*x32 + m31*x33 + m38*x34 + m45*x35;
765 	  x[31] -= m4*x29 + m11*x30 + m18*x31 + m25*x32 + m32*x33 + m39*x34 + m46*x35;
766 	  x[32] -= m5*x29 + m12*x30 + m19*x31 + m26*x32 + m33*x33 + m40*x34 + m47*x35;
767 	  x[33] -= m6*x29 + m13*x30 + m20*x31 + m27*x32 + m34*x33 + m41*x34 + m48*x35;
768 	  x[34] -= m7*x29 + m14*x30 + m21*x31 + m28*x32 + m35*x33 + m42*x34 + m49*x35;
769 
770 	  x[35] -= m1*x36 + m8*x37  + m15*x38 + m22*x39 + m29*x40 + m36*x41 + m43*x42;
771 	  x[36] -= m2*x36 + m9*x37  + m16*x38 + m23*x39 + m30*x40 + m37*x41 + m44*x42;
772 	  x[37] -= m3*x36 + m10*x37 + m17*x38 + m24*x39 + m31*x40 + m38*x41 + m45*x42;
773 	  x[38] -= m4*x36 + m11*x37 + m18*x38 + m25*x39 + m32*x40 + m39*x41 + m46*x42;
774 	  x[39] -= m5*x36 + m12*x37 + m19*x38 + m26*x39 + m33*x40 + m40*x41 + m47*x42;
775 	  x[40] -= m6*x36 + m13*x37 + m20*x38 + m27*x39 + m34*x40 + m41*x41 + m48*x42;
776 	  x[41] -= m7*x36 + m14*x37 + m21*x38 + m28*x39 + m35*x40 + m42*x41 + m49*x42;
777 
778 	  x[42] -= m1*x43 + m8*x44  + m15*x45 + m22*x46 + m29*x47 + m36*x48 + m43*x49;
779 	  x[43] -= m2*x43 + m9*x44  + m16*x45 + m23*x46 + m30*x47 + m37*x48 + m44*x49;
780 	  x[44] -= m3*x43 + m10*x44 + m17*x45 + m24*x46 + m31*x47 + m38*x48 + m45*x49;
781 	  x[45] -= m4*x43 + m11*x44 + m18*x45 + m25*x46 + m32*x47 + m39*x48 + m46*x49;
782 	  x[46] -= m5*x43 + m12*x44 + m19*x45 + m26*x46 + m33*x47 + m40*x48 + m47*x49;
783 	  x[47] -= m6*x43 + m13*x44 + m20*x45 + m27*x46 + m34*x47 + m41*x48 + m48*x49;
784 	  x[48] -= m7*x43 + m14*x44 + m21*x45 + m28*x46 + m35*x47 + m42*x48 + m49*x49;
785           pv   += 49;
786         }
787         PLogFlops(686*nz+637);
788       }
789       row = *ajtmp++;
790     }
791     /* finished row so stick it into b->a */
792     pv = ba + 49*bi[i];
793     pj = bj + bi[i];
794     nz = bi[i+1] - bi[i];
795     for (j=0; j<nz; j++) {
796       x      = rtmp+49*pj[j];
797       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
798       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7];
799       pv[8]  = x[8];  pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11];
800       pv[12] = x[12]; pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
801       pv[16] = x[16]; pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19];
802       pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23];
803       pv[24] = x[24]; pv[25] = x[25]; pv[26] = x[26]; pv[27] = x[27];
804       pv[28] = x[28]; pv[29] = x[29]; pv[30] = x[30]; pv[31] = x[31];
805       pv[32] = x[32]; pv[33] = x[33]; pv[34] = x[34]; pv[35] = x[35];
806       pv[36] = x[36]; pv[37] = x[37]; pv[38] = x[38]; pv[39] = x[39];
807       pv[40] = x[40]; pv[41] = x[41]; pv[42] = x[42]; pv[43] = x[43];
808       pv[44] = x[44]; pv[45] = x[45]; pv[46] = x[46]; pv[47] = x[47];
809       pv[48] = x[48];
810       pv   += 49;
811     }
812     /* invert diagonal block */
813     w = ba + 49*diag_offset[i];
814     ierr = Kernel_A_gets_inverse_A_7(w);CHKERRQ(ierr);
815   }
816 
817   ierr = PetscFree(rtmp);CHKERRQ(ierr);
818   C->factor    = FACTOR_LU;
819   C->assembled = PETSC_TRUE;
820   PLogFlops(1.3333*343*b->mbs); /* from inverting diagonal blocks */
821   PetscFunctionReturn(0);
822 }
823 
824 /* ------------------------------------------------------------*/
825 /*
826       Version for when blocks are 6 by 6
827 */
828 #undef __FUNC__
829 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_6"
830 int MatCholeskyFactorNumeric_SeqSBAIJ_6(Mat A,Mat *B)
831 {
832   Mat          C = *B;
833   Mat_SeqBAIJ  *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
834   IS           isrow = b->row,isicol = b->icol;
835   int          *r,*ic,ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
836   int          *ajtmpold,*ajtmp,nz,row;
837   int          *diag_offset = b->diag,idx,*ai=a->i,*aj=a->j,*pj;
838   MatScalar    *pv,*v,*rtmp,*pc,*w,*x;
839   MatScalar    p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
840   MatScalar    p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
841   MatScalar    x17,x18,x19,x20,x21,x22,x23,x24,x25,p10,p11,p12,p13,p14;
842   MatScalar    p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,m10,m11,m12;
843   MatScalar    m13,m14,m15,m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
844   MatScalar    p26,p27,p28,p29,p30,p31,p32,p33,p34,p35,p36;
845   MatScalar    x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36;
846   MatScalar    m26,m27,m28,m29,m30,m31,m32,m33,m34,m35,m36;
847   MatScalar    *ba = b->a,*aa = a->a;
848 
849   PetscFunctionBegin;
850   ierr  = ISGetIndices(isrow,&r);CHKERRQ(ierr);
851   ierr  = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
852   rtmp  = (MatScalar*)PetscMalloc(36*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
853 
854   for (i=0; i<n; i++) {
855     nz    = bi[i+1] - bi[i];
856     ajtmp = bj + bi[i];
857     for  (j=0; j<nz; j++) {
858       x = rtmp+36*ajtmp[j];
859       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
860       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
861       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = x[25] = 0.0 ;
862       x[26] = x[27] = x[28] = x[29] = x[30] = x[31] = x[32] = x[33] = 0.0 ;
863       x[34] = x[35] = 0.0 ;
864     }
865     /* load in initial (unfactored row) */
866     idx      = r[i];
867     nz       = ai[idx+1] - ai[idx];
868     ajtmpold = aj + ai[idx];
869     v        = aa + 36*ai[idx];
870     for (j=0; j<nz; j++) {
871       x    = rtmp+36*ic[ajtmpold[j]];
872       x[0] =  v[0];  x[1] =  v[1];  x[2] =  v[2];  x[3] =  v[3];
873       x[4] =  v[4];  x[5] =  v[5];  x[6] =  v[6];  x[7] =  v[7];
874       x[8] =  v[8];  x[9] =  v[9];  x[10] = v[10]; x[11] = v[11];
875       x[12] = v[12]; x[13] = v[13]; x[14] = v[14]; x[15] = v[15];
876       x[16] = v[16]; x[17] = v[17]; x[18] = v[18]; x[19] = v[19];
877       x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23];
878       x[24] = v[24]; x[25] = v[25]; x[26] = v[26]; x[27] = v[27];
879       x[28] = v[28]; x[29] = v[29]; x[30] = v[30]; x[31] = v[31];
880       x[32] = v[32]; x[33] = v[33]; x[34] = v[34]; x[35] = v[35];
881       v    += 36;
882     }
883     row = *ajtmp++;
884     while (row < i) {
885       pc  =  rtmp + 36*row;
886       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
887       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];
888       p9  = pc[8];  p10 = pc[9];  p11 = pc[10]; p12 = pc[11];
889       p13 = pc[12]; p14 = pc[13]; p15 = pc[14]; p16 = pc[15];
890       p17 = pc[16]; p18 = pc[17]; p19 = pc[18]; p20 = pc[19];
891       p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
892       p25 = pc[24]; p26 = pc[25]; p27 = pc[26]; p28 = pc[27];
893       p29 = pc[28]; p30 = pc[29]; p31 = pc[30]; p32 = pc[31];
894       p33 = pc[32]; p34 = pc[33]; p35 = pc[34]; p36 = pc[35];
895       if (p1  != 0.0 || p2  != 0.0 || p3  != 0.0 || p4  != 0.0 ||
896           p5  != 0.0 || p6  != 0.0 || p7  != 0.0 || p8  != 0.0 ||
897           p9  != 0.0 || p10 != 0.0 || p11 != 0.0 || p12 != 0.0 ||
898           p13 != 0.0 || p14 != 0.0 || p15 != 0.0 || p16 != 0.0 ||
899           p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 ||
900           p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 ||
901           p25 != 0.0 || p26 != 0.0 || p27 != 0.0 || p28 != 0.0 ||
902           p29 != 0.0 || p30 != 0.0 || p31 != 0.0 || p32 != 0.0 ||
903           p33 != 0.0 || p34 != 0.0 || p35 != 0.0 || p36 != 0.0) {
904         pv = ba + 36*diag_offset[row];
905         pj = bj + diag_offset[row] + 1;
906 	x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
907 	x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
908 	x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
909 	x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
910 	x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
911 	x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
912 	x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
913 	x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
914 	x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
915         pc[0]  = m1  = p1*x1  + p7*x2   + p13*x3  + p19*x4  + p25*x5  + p31*x6;
916         pc[1]  = m2  = p2*x1  + p8*x2   + p14*x3  + p20*x4  + p26*x5  + p32*x6;
917         pc[2]  = m3  = p3*x1  + p9*x2   + p15*x3  + p21*x4  + p27*x5  + p33*x6;
918         pc[3]  = m4  = p4*x1  + p10*x2  + p16*x3  + p22*x4  + p28*x5  + p34*x6;
919         pc[4]  = m5  = p5*x1  + p11*x2  + p17*x3  + p23*x4  + p29*x5  + p35*x6;
920         pc[5]  = m6  = p6*x1  + p12*x2  + p18*x3  + p24*x4  + p30*x5  + p36*x6;
921 
922         pc[6]  = m7  = p1*x7  + p7*x8   + p13*x9  + p19*x10 + p25*x11 + p31*x12;
923         pc[7]  = m8  = p2*x7  + p8*x8   + p14*x9  + p20*x10 + p26*x11 + p32*x12;
924         pc[8]  = m9  = p3*x7  + p9*x8   + p15*x9  + p21*x10 + p27*x11 + p33*x12;
925         pc[9]  = m10 = p4*x7  + p10*x8  + p16*x9  + p22*x10 + p28*x11 + p34*x12;
926         pc[10] = m11 = p5*x7  + p11*x8  + p17*x9  + p23*x10 + p29*x11 + p35*x12;
927         pc[11] = m12 = p6*x7  + p12*x8  + p18*x9  + p24*x10 + p30*x11 + p36*x12;
928 
929         pc[12] = m13 = p1*x13 + p7*x14  + p13*x15 + p19*x16 + p25*x17 + p31*x18;
930         pc[13] = m14 = p2*x13 + p8*x14  + p14*x15 + p20*x16 + p26*x17 + p32*x18;
931         pc[14] = m15 = p3*x13 + p9*x14  + p15*x15 + p21*x16 + p27*x17 + p33*x18;
932         pc[15] = m16 = p4*x13 + p10*x14 + p16*x15 + p22*x16 + p28*x17 + p34*x18;
933         pc[16] = m17 = p5*x13 + p11*x14 + p17*x15 + p23*x16 + p29*x17 + p35*x18;
934         pc[17] = m18 = p6*x13 + p12*x14 + p18*x15 + p24*x16 + p30*x17 + p36*x18;
935 
936         pc[18] = m19 = p1*x19 + p7*x20  + p13*x21 + p19*x22 + p25*x23 + p31*x24;
937         pc[19] = m20 = p2*x19 + p8*x20  + p14*x21 + p20*x22 + p26*x23 + p32*x24;
938         pc[20] = m21 = p3*x19 + p9*x20  + p15*x21 + p21*x22 + p27*x23 + p33*x24;
939         pc[21] = m22 = p4*x19 + p10*x20 + p16*x21 + p22*x22 + p28*x23 + p34*x24;
940         pc[22] = m23 = p5*x19 + p11*x20 + p17*x21 + p23*x22 + p29*x23 + p35*x24;
941         pc[23] = m24 = p6*x19 + p12*x20 + p18*x21 + p24*x22 + p30*x23 + p36*x24;
942 
943         pc[24] = m25 = p1*x25 + p7*x26  + p13*x27 + p19*x28 + p25*x29 + p31*x30;
944         pc[25] = m26 = p2*x25 + p8*x26  + p14*x27 + p20*x28 + p26*x29 + p32*x30;
945         pc[26] = m27 = p3*x25 + p9*x26  + p15*x27 + p21*x28 + p27*x29 + p33*x30;
946         pc[27] = m28 = p4*x25 + p10*x26 + p16*x27 + p22*x28 + p28*x29 + p34*x30;
947         pc[28] = m29 = p5*x25 + p11*x26 + p17*x27 + p23*x28 + p29*x29 + p35*x30;
948         pc[29] = m30 = p6*x25 + p12*x26 + p18*x27 + p24*x28 + p30*x29 + p36*x30;
949 
950         pc[30] = m31 = p1*x31 + p7*x32  + p13*x33 + p19*x34 + p25*x35 + p31*x36;
951         pc[31] = m32 = p2*x31 + p8*x32  + p14*x33 + p20*x34 + p26*x35 + p32*x36;
952         pc[32] = m33 = p3*x31 + p9*x32  + p15*x33 + p21*x34 + p27*x35 + p33*x36;
953         pc[33] = m34 = p4*x31 + p10*x32 + p16*x33 + p22*x34 + p28*x35 + p34*x36;
954         pc[34] = m35 = p5*x31 + p11*x32 + p17*x33 + p23*x34 + p29*x35 + p35*x36;
955         pc[35] = m36 = p6*x31 + p12*x32 + p18*x33 + p24*x34 + p30*x35 + p36*x36;
956 
957         nz = bi[row+1] - diag_offset[row] - 1;
958         pv += 36;
959         for (j=0; j<nz; j++) {
960 	  x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
961 	  x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
962 	  x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
963 	  x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
964 	  x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
965 	  x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
966 	  x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
967 	  x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
968 	  x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
969 	  x    = rtmp + 36*pj[j];
970           x[0]  -= m1*x1  + m7*x2   + m13*x3  + m19*x4  + m25*x5  + m31*x6;
971           x[1]  -= m2*x1  + m8*x2   + m14*x3  + m20*x4  + m26*x5  + m32*x6;
972           x[2]  -= m3*x1  + m9*x2   + m15*x3  + m21*x4  + m27*x5  + m33*x6;
973           x[3]  -= m4*x1  + m10*x2  + m16*x3  + m22*x4  + m28*x5  + m34*x6;
974           x[4]  -= m5*x1  + m11*x2  + m17*x3  + m23*x4  + m29*x5  + m35*x6;
975           x[5]  -= m6*x1  + m12*x2  + m18*x3  + m24*x4  + m30*x5  + m36*x6;
976 
977 	  x[6]  -= m1*x7  + m7*x8   + m13*x9  + m19*x10 + m25*x11 + m31*x12;
978 	  x[7]  -= m2*x7  + m8*x8   + m14*x9  + m20*x10 + m26*x11 + m32*x12;
979 	  x[8]  -= m3*x7  + m9*x8   + m15*x9  + m21*x10 + m27*x11 + m33*x12;
980 	  x[9]  -= m4*x7  + m10*x8  + m16*x9  + m22*x10 + m28*x11 + m34*x12;
981 	  x[10] -= m5*x7  + m11*x8  + m17*x9  + m23*x10 + m29*x11 + m35*x12;
982 	  x[11] -= m6*x7  + m12*x8  + m18*x9  + m24*x10 + m30*x11 + m36*x12;
983 
984 	  x[12] -= m1*x13 + m7*x14  + m13*x15 + m19*x16 + m25*x17 + m31*x18;
985 	  x[13] -= m2*x13 + m8*x14  + m14*x15 + m20*x16 + m26*x17 + m32*x18;
986 	  x[14] -= m3*x13 + m9*x14  + m15*x15 + m21*x16 + m27*x17 + m33*x18;
987 	  x[15] -= m4*x13 + m10*x14 + m16*x15 + m22*x16 + m28*x17 + m34*x18;
988 	  x[16] -= m5*x13 + m11*x14 + m17*x15 + m23*x16 + m29*x17 + m35*x18;
989 	  x[17] -= m6*x13 + m12*x14 + m18*x15 + m24*x16 + m30*x17 + m36*x18;
990 
991 	  x[18] -= m1*x19 + m7*x20  + m13*x21 + m19*x22 + m25*x23 + m31*x24;
992 	  x[19] -= m2*x19 + m8*x20  + m14*x21 + m20*x22 + m26*x23 + m32*x24;
993 	  x[20] -= m3*x19 + m9*x20  + m15*x21 + m21*x22 + m27*x23 + m33*x24;
994 	  x[21] -= m4*x19 + m10*x20 + m16*x21 + m22*x22 + m28*x23 + m34*x24;
995 	  x[22] -= m5*x19 + m11*x20 + m17*x21 + m23*x22 + m29*x23 + m35*x24;
996 	  x[23] -= m6*x19 + m12*x20 + m18*x21 + m24*x22 + m30*x23 + m36*x24;
997 
998 	  x[24] -= m1*x25 + m7*x26  + m13*x27 + m19*x28 + m25*x29 + m31*x30;
999 	  x[25] -= m2*x25 + m8*x26  + m14*x27 + m20*x28 + m26*x29 + m32*x30;
1000 	  x[26] -= m3*x25 + m9*x26  + m15*x27 + m21*x28 + m27*x29 + m33*x30;
1001 	  x[27] -= m4*x25 + m10*x26 + m16*x27 + m22*x28 + m28*x29 + m34*x30;
1002 	  x[28] -= m5*x25 + m11*x26 + m17*x27 + m23*x28 + m29*x29 + m35*x30;
1003 	  x[29] -= m6*x25 + m12*x26 + m18*x27 + m24*x28 + m30*x29 + m36*x30;
1004 
1005 	  x[30] -= m1*x31 + m7*x32  + m13*x33 + m19*x34 + m25*x35 + m31*x36;
1006 	  x[31] -= m2*x31 + m8*x32  + m14*x33 + m20*x34 + m26*x35 + m32*x36;
1007 	  x[32] -= m3*x31 + m9*x32  + m15*x33 + m21*x34 + m27*x35 + m33*x36;
1008 	  x[33] -= m4*x31 + m10*x32 + m16*x33 + m22*x34 + m28*x35 + m34*x36;
1009 	  x[34] -= m5*x31 + m11*x32 + m17*x33 + m23*x34 + m29*x35 + m35*x36;
1010 	  x[35] -= m6*x31 + m12*x32 + m18*x33 + m24*x34 + m30*x35 + m36*x36;
1011 
1012           pv   += 36;
1013         }
1014         PLogFlops(432*nz+396);
1015       }
1016       row = *ajtmp++;
1017     }
1018     /* finished row so stick it into b->a */
1019     pv = ba + 36*bi[i];
1020     pj = bj + bi[i];
1021     nz = bi[i+1] - bi[i];
1022     for (j=0; j<nz; j++) {
1023       x      = rtmp+36*pj[j];
1024       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
1025       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7];
1026       pv[8]  = x[8];  pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11];
1027       pv[12] = x[12]; pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
1028       pv[16] = x[16]; pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19];
1029       pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23];
1030       pv[24] = x[24]; pv[25] = x[25]; pv[26] = x[26]; pv[27] = x[27];
1031       pv[28] = x[28]; pv[29] = x[29]; pv[30] = x[30]; pv[31] = x[31];
1032       pv[32] = x[32]; pv[33] = x[33]; pv[34] = x[34]; pv[35] = x[35];
1033       pv   += 36;
1034     }
1035     /* invert diagonal block */
1036     w = ba + 36*diag_offset[i];
1037     ierr = Kernel_A_gets_inverse_A_6(w);CHKERRQ(ierr);
1038   }
1039 
1040   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1041   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
1042   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
1043   C->factor = FACTOR_LU;
1044   C->assembled = PETSC_TRUE;
1045   PLogFlops(1.3333*216*b->mbs); /* from inverting diagonal blocks */
1046   PetscFunctionReturn(0);
1047 }
1048 /*
1049       Version for when blocks are 6 by 6 Using natural ordering
1050 */
1051 #undef __FUNC__
1052 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_6_NaturalOrdering"
1053 int MatCholeskyFactorNumeric_SeqSBAIJ_6_NaturalOrdering(Mat A,Mat *B)
1054 {
1055   Mat         C = *B;
1056   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
1057   int         ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
1058   int         *ajtmpold,*ajtmp,nz,row;
1059   int         *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
1060   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
1061   MatScalar   x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15;
1062   MatScalar   x16,x17,x18,x19,x20,x21,x22,x23,x24,x25;
1063   MatScalar   p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15;
1064   MatScalar   p16,p17,p18,p19,p20,p21,p22,p23,p24,p25;
1065   MatScalar   m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12,m13,m14,m15;
1066   MatScalar   m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
1067   MatScalar   p26,p27,p28,p29,p30,p31,p32,p33,p34,p35,p36;
1068   MatScalar   x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36;
1069   MatScalar   m26,m27,m28,m29,m30,m31,m32,m33,m34,m35,m36;
1070   MatScalar   *ba = b->a,*aa = a->a;
1071 
1072   PetscFunctionBegin;
1073   rtmp  = (MatScalar*)PetscMalloc(36*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
1074   for (i=0; i<n; i++) {
1075     nz    = bi[i+1] - bi[i];
1076     ajtmp = bj + bi[i];
1077     for  (j=0; j<nz; j++) {
1078       x = rtmp+36*ajtmp[j];
1079       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
1080       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
1081       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = x[25] = 0.0 ;
1082       x[26] = x[27] = x[28] = x[29] = x[30] = x[31] = x[32] = x[33] = 0.0 ;
1083       x[34] = x[35] = 0.0 ;
1084     }
1085     /* load in initial (unfactored row) */
1086     nz       = ai[i+1] - ai[i];
1087     ajtmpold = aj + ai[i];
1088     v        = aa + 36*ai[i];
1089     for (j=0; j<nz; j++) {
1090       x    = rtmp+36*ajtmpold[j];
1091       x[0] =  v[0];  x[1] =  v[1];  x[2] =  v[2];  x[3] =  v[3];
1092       x[4] =  v[4];  x[5] =  v[5];  x[6] =  v[6];  x[7] =  v[7];
1093       x[8] =  v[8];  x[9] =  v[9];  x[10] = v[10]; x[11] = v[11];
1094       x[12] = v[12]; x[13] = v[13]; x[14] = v[14]; x[15] = v[15];
1095       x[16] = v[16]; x[17] = v[17]; x[18] = v[18]; x[19] = v[19];
1096       x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23];
1097       x[24] = v[24]; x[25] = v[25]; x[26] = v[26]; x[27] = v[27];
1098       x[28] = v[28]; x[29] = v[29]; x[30] = v[30]; x[31] = v[31];
1099       x[32] = v[32]; x[33] = v[33]; x[34] = v[34]; x[35] = v[35];
1100       v    += 36;
1101     }
1102     row = *ajtmp++;
1103     while (row < i) {
1104       pc  = rtmp + 36*row;
1105       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
1106       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];
1107       p9  = pc[8];  p10 = pc[9];  p11 = pc[10]; p12 = pc[11];
1108       p13 = pc[12]; p14 = pc[13]; p15 = pc[14]; p16 = pc[15];
1109       p17 = pc[16]; p18 = pc[17]; p19 = pc[18]; p20 = pc[19];
1110       p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
1111       p25 = pc[24]; p26 = pc[25]; p27 = pc[26]; p28 = pc[27];
1112       p29 = pc[28]; p30 = pc[29]; p31 = pc[30]; p32 = pc[31];
1113       p33 = pc[32]; p34 = pc[33]; p35 = pc[34]; p36 = pc[35];
1114       if (p1  != 0.0 || p2  != 0.0 || p3  != 0.0 || p4  != 0.0 ||
1115           p5  != 0.0 || p6  != 0.0 || p7  != 0.0 || p8  != 0.0 ||
1116           p9  != 0.0 || p10 != 0.0 || p11 != 0.0 || p12 != 0.0 ||
1117           p13 != 0.0 || p14 != 0.0 || p15 != 0.0 || p16 != 0.0 ||
1118           p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 ||
1119           p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 ||
1120           p25 != 0.0 || p26 != 0.0 || p27 != 0.0 || p28 != 0.0 ||
1121           p29 != 0.0 || p30 != 0.0 || p31 != 0.0 || p32 != 0.0 ||
1122           p33 != 0.0 || p34 != 0.0 || p35 != 0.0 || p36 != 0.0) {
1123         pv = ba + 36*diag_offset[row];
1124         pj = bj + diag_offset[row] + 1;
1125 	x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
1126 	x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
1127 	x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
1128 	x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
1129 	x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
1130 	x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
1131 	x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
1132 	x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
1133 	x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
1134         pc[0]  = m1  = p1*x1  + p7*x2   + p13*x3  + p19*x4  + p25*x5  + p31*x6;
1135         pc[1]  = m2  = p2*x1  + p8*x2   + p14*x3  + p20*x4  + p26*x5  + p32*x6;
1136         pc[2]  = m3  = p3*x1  + p9*x2   + p15*x3  + p21*x4  + p27*x5  + p33*x6;
1137         pc[3]  = m4  = p4*x1  + p10*x2  + p16*x3  + p22*x4  + p28*x5  + p34*x6;
1138         pc[4]  = m5  = p5*x1  + p11*x2  + p17*x3  + p23*x4  + p29*x5  + p35*x6;
1139         pc[5]  = m6  = p6*x1  + p12*x2  + p18*x3  + p24*x4  + p30*x5  + p36*x6;
1140 
1141         pc[6]  = m7  = p1*x7  + p7*x8   + p13*x9  + p19*x10 + p25*x11 + p31*x12;
1142         pc[7]  = m8  = p2*x7  + p8*x8   + p14*x9  + p20*x10 + p26*x11 + p32*x12;
1143         pc[8]  = m9  = p3*x7  + p9*x8   + p15*x9  + p21*x10 + p27*x11 + p33*x12;
1144         pc[9]  = m10 = p4*x7  + p10*x8  + p16*x9  + p22*x10 + p28*x11 + p34*x12;
1145         pc[10] = m11 = p5*x7  + p11*x8  + p17*x9  + p23*x10 + p29*x11 + p35*x12;
1146         pc[11] = m12 = p6*x7  + p12*x8  + p18*x9  + p24*x10 + p30*x11 + p36*x12;
1147 
1148         pc[12] = m13 = p1*x13 + p7*x14  + p13*x15 + p19*x16 + p25*x17 + p31*x18;
1149         pc[13] = m14 = p2*x13 + p8*x14  + p14*x15 + p20*x16 + p26*x17 + p32*x18;
1150         pc[14] = m15 = p3*x13 + p9*x14  + p15*x15 + p21*x16 + p27*x17 + p33*x18;
1151         pc[15] = m16 = p4*x13 + p10*x14 + p16*x15 + p22*x16 + p28*x17 + p34*x18;
1152         pc[16] = m17 = p5*x13 + p11*x14 + p17*x15 + p23*x16 + p29*x17 + p35*x18;
1153         pc[17] = m18 = p6*x13 + p12*x14 + p18*x15 + p24*x16 + p30*x17 + p36*x18;
1154 
1155         pc[18] = m19 = p1*x19 + p7*x20  + p13*x21 + p19*x22 + p25*x23 + p31*x24;
1156         pc[19] = m20 = p2*x19 + p8*x20  + p14*x21 + p20*x22 + p26*x23 + p32*x24;
1157         pc[20] = m21 = p3*x19 + p9*x20  + p15*x21 + p21*x22 + p27*x23 + p33*x24;
1158         pc[21] = m22 = p4*x19 + p10*x20 + p16*x21 + p22*x22 + p28*x23 + p34*x24;
1159         pc[22] = m23 = p5*x19 + p11*x20 + p17*x21 + p23*x22 + p29*x23 + p35*x24;
1160         pc[23] = m24 = p6*x19 + p12*x20 + p18*x21 + p24*x22 + p30*x23 + p36*x24;
1161 
1162         pc[24] = m25 = p1*x25 + p7*x26  + p13*x27 + p19*x28 + p25*x29 + p31*x30;
1163         pc[25] = m26 = p2*x25 + p8*x26  + p14*x27 + p20*x28 + p26*x29 + p32*x30;
1164         pc[26] = m27 = p3*x25 + p9*x26  + p15*x27 + p21*x28 + p27*x29 + p33*x30;
1165         pc[27] = m28 = p4*x25 + p10*x26 + p16*x27 + p22*x28 + p28*x29 + p34*x30;
1166         pc[28] = m29 = p5*x25 + p11*x26 + p17*x27 + p23*x28 + p29*x29 + p35*x30;
1167         pc[29] = m30 = p6*x25 + p12*x26 + p18*x27 + p24*x28 + p30*x29 + p36*x30;
1168 
1169         pc[30] = m31 = p1*x31 + p7*x32  + p13*x33 + p19*x34 + p25*x35 + p31*x36;
1170         pc[31] = m32 = p2*x31 + p8*x32  + p14*x33 + p20*x34 + p26*x35 + p32*x36;
1171         pc[32] = m33 = p3*x31 + p9*x32  + p15*x33 + p21*x34 + p27*x35 + p33*x36;
1172         pc[33] = m34 = p4*x31 + p10*x32 + p16*x33 + p22*x34 + p28*x35 + p34*x36;
1173         pc[34] = m35 = p5*x31 + p11*x32 + p17*x33 + p23*x34 + p29*x35 + p35*x36;
1174         pc[35] = m36 = p6*x31 + p12*x32 + p18*x33 + p24*x34 + p30*x35 + p36*x36;
1175 
1176         nz = bi[row+1] - diag_offset[row] - 1;
1177         pv += 36;
1178         for (j=0; j<nz; j++) {
1179 	  x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
1180 	  x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
1181 	  x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
1182 	  x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
1183 	  x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
1184 	  x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
1185 	  x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
1186 	  x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
1187 	  x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
1188 	  x    = rtmp + 36*pj[j];
1189           x[0]  -= m1*x1  + m7*x2   + m13*x3  + m19*x4  + m25*x5  + m31*x6;
1190           x[1]  -= m2*x1  + m8*x2   + m14*x3  + m20*x4  + m26*x5  + m32*x6;
1191           x[2]  -= m3*x1  + m9*x2   + m15*x3  + m21*x4  + m27*x5  + m33*x6;
1192           x[3]  -= m4*x1  + m10*x2  + m16*x3  + m22*x4  + m28*x5  + m34*x6;
1193           x[4]  -= m5*x1  + m11*x2  + m17*x3  + m23*x4  + m29*x5  + m35*x6;
1194           x[5]  -= m6*x1  + m12*x2  + m18*x3  + m24*x4  + m30*x5  + m36*x6;
1195 
1196 	  x[6]  -= m1*x7  + m7*x8   + m13*x9  + m19*x10 + m25*x11 + m31*x12;
1197 	  x[7]  -= m2*x7  + m8*x8   + m14*x9  + m20*x10 + m26*x11 + m32*x12;
1198 	  x[8]  -= m3*x7  + m9*x8   + m15*x9  + m21*x10 + m27*x11 + m33*x12;
1199 	  x[9]  -= m4*x7  + m10*x8  + m16*x9  + m22*x10 + m28*x11 + m34*x12;
1200 	  x[10] -= m5*x7  + m11*x8  + m17*x9  + m23*x10 + m29*x11 + m35*x12;
1201 	  x[11] -= m6*x7  + m12*x8  + m18*x9  + m24*x10 + m30*x11 + m36*x12;
1202 
1203 	  x[12] -= m1*x13 + m7*x14  + m13*x15 + m19*x16 + m25*x17 + m31*x18;
1204 	  x[13] -= m2*x13 + m8*x14  + m14*x15 + m20*x16 + m26*x17 + m32*x18;
1205 	  x[14] -= m3*x13 + m9*x14  + m15*x15 + m21*x16 + m27*x17 + m33*x18;
1206 	  x[15] -= m4*x13 + m10*x14 + m16*x15 + m22*x16 + m28*x17 + m34*x18;
1207 	  x[16] -= m5*x13 + m11*x14 + m17*x15 + m23*x16 + m29*x17 + m35*x18;
1208 	  x[17] -= m6*x13 + m12*x14 + m18*x15 + m24*x16 + m30*x17 + m36*x18;
1209 
1210 	  x[18] -= m1*x19 + m7*x20  + m13*x21 + m19*x22 + m25*x23 + m31*x24;
1211 	  x[19] -= m2*x19 + m8*x20  + m14*x21 + m20*x22 + m26*x23 + m32*x24;
1212 	  x[20] -= m3*x19 + m9*x20  + m15*x21 + m21*x22 + m27*x23 + m33*x24;
1213 	  x[21] -= m4*x19 + m10*x20 + m16*x21 + m22*x22 + m28*x23 + m34*x24;
1214 	  x[22] -= m5*x19 + m11*x20 + m17*x21 + m23*x22 + m29*x23 + m35*x24;
1215 	  x[23] -= m6*x19 + m12*x20 + m18*x21 + m24*x22 + m30*x23 + m36*x24;
1216 
1217 	  x[24] -= m1*x25 + m7*x26  + m13*x27 + m19*x28 + m25*x29 + m31*x30;
1218 	  x[25] -= m2*x25 + m8*x26  + m14*x27 + m20*x28 + m26*x29 + m32*x30;
1219 	  x[26] -= m3*x25 + m9*x26  + m15*x27 + m21*x28 + m27*x29 + m33*x30;
1220 	  x[27] -= m4*x25 + m10*x26 + m16*x27 + m22*x28 + m28*x29 + m34*x30;
1221 	  x[28] -= m5*x25 + m11*x26 + m17*x27 + m23*x28 + m29*x29 + m35*x30;
1222 	  x[29] -= m6*x25 + m12*x26 + m18*x27 + m24*x28 + m30*x29 + m36*x30;
1223 
1224 	  x[30] -= m1*x31 + m7*x32  + m13*x33 + m19*x34 + m25*x35 + m31*x36;
1225 	  x[31] -= m2*x31 + m8*x32  + m14*x33 + m20*x34 + m26*x35 + m32*x36;
1226 	  x[32] -= m3*x31 + m9*x32  + m15*x33 + m21*x34 + m27*x35 + m33*x36;
1227 	  x[33] -= m4*x31 + m10*x32 + m16*x33 + m22*x34 + m28*x35 + m34*x36;
1228 	  x[34] -= m5*x31 + m11*x32 + m17*x33 + m23*x34 + m29*x35 + m35*x36;
1229 	  x[35] -= m6*x31 + m12*x32 + m18*x33 + m24*x34 + m30*x35 + m36*x36;
1230 
1231           pv   += 36;
1232         }
1233         PLogFlops(432*nz+396);
1234       }
1235       row = *ajtmp++;
1236     }
1237     /* finished row so stick it into b->a */
1238     pv = ba + 36*bi[i];
1239     pj = bj + bi[i];
1240     nz = bi[i+1] - bi[i];
1241     for (j=0; j<nz; j++) {
1242       x      = rtmp+36*pj[j];
1243       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
1244       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7];
1245       pv[8]  = x[8];  pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11];
1246       pv[12] = x[12]; pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
1247       pv[16] = x[16]; pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19];
1248       pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23];
1249       pv[24] = x[24]; pv[25] = x[25]; pv[26] = x[26]; pv[27] = x[27];
1250       pv[28] = x[28]; pv[29] = x[29]; pv[30] = x[30]; pv[31] = x[31];
1251       pv[32] = x[32]; pv[33] = x[33]; pv[34] = x[34]; pv[35] = x[35];
1252       pv   += 36;
1253     }
1254     /* invert diagonal block */
1255     w = ba + 36*diag_offset[i];
1256     ierr = Kernel_A_gets_inverse_A_6(w);CHKERRQ(ierr);
1257   }
1258 
1259   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1260   C->factor    = FACTOR_LU;
1261   C->assembled = PETSC_TRUE;
1262   PLogFlops(1.3333*216*b->mbs); /* from inverting diagonal blocks */
1263   PetscFunctionReturn(0);
1264 }
1265 
1266 /*
1267       Version for when blocks are 5 by 5
1268 */
1269 #undef __FUNC__
1270 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_5"
1271 int MatCholeskyFactorNumeric_SeqSBAIJ_5(Mat A,Mat *B)
1272 {
1273   Mat         C = *B;
1274   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
1275   IS          isrow = b->row,isicol = b->icol;
1276   int         *r,*ic,ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
1277   int         *ajtmpold,*ajtmp,nz,row;
1278   int         *diag_offset = b->diag,idx,*ai=a->i,*aj=a->j,*pj;
1279   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
1280   MatScalar   p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
1281   MatScalar   p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
1282   MatScalar   x17,x18,x19,x20,x21,x22,x23,x24,x25,p10,p11,p12,p13,p14;
1283   MatScalar   p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,m10,m11,m12;
1284   MatScalar   m13,m14,m15,m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
1285   MatScalar   *ba = b->a,*aa = a->a;
1286 
1287   PetscFunctionBegin;
1288   ierr  = ISGetIndices(isrow,&r);CHKERRQ(ierr);
1289   ierr  = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
1290   rtmp  = (MatScalar*)PetscMalloc(25*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
1291 
1292   for (i=0; i<n; i++) {
1293     nz    = bi[i+1] - bi[i];
1294     ajtmp = bj + bi[i];
1295     for  (j=0; j<nz; j++) {
1296       x = rtmp+25*ajtmp[j];
1297       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
1298       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
1299       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0;
1300     }
1301     /* load in initial (unfactored row) */
1302     idx      = r[i];
1303     nz       = ai[idx+1] - ai[idx];
1304     ajtmpold = aj + ai[idx];
1305     v        = aa + 25*ai[idx];
1306     for (j=0; j<nz; j++) {
1307       x    = rtmp+25*ic[ajtmpold[j]];
1308       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
1309       x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
1310       x[9] = v[9]; x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
1311       x[14] = v[14]; x[15] = v[15]; x[16] = v[16]; x[17] = v[17];
1312       x[18] = v[18]; x[19] = v[19]; x[20] = v[20]; x[21] = v[21];
1313       x[22] = v[22]; x[23] = v[23]; x[24] = v[24];
1314       v    += 25;
1315     }
1316     row = *ajtmp++;
1317     while (row < i) {
1318       pc = rtmp + 25*row;
1319       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
1320       p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
1321       p10 = pc[9]; p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
1322       p15 = pc[14]; p16 = pc[15]; p17 = pc[16]; p18 = pc[17]; p19 = pc[18];
1323       p20 = pc[19]; p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
1324       p25 = pc[24];
1325       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
1326           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
1327           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
1328           || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 ||
1329           p20 != 0.0 || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 ||
1330           p24 != 0.0 || p25 != 0.0) {
1331         pv = ba + 25*diag_offset[row];
1332         pj = bj + diag_offset[row] + 1;
1333         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
1334         x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
1335         x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
1336         x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17];
1337         x19 = pv[18]; x20 = pv[19]; x21 = pv[20]; x22 = pv[21];
1338         x23 = pv[22]; x24 = pv[23]; x25 = pv[24];
1339         pc[0] = m1 = p1*x1 + p6*x2  + p11*x3 + p16*x4 + p21*x5;
1340         pc[1] = m2 = p2*x1 + p7*x2  + p12*x3 + p17*x4 + p22*x5;
1341         pc[2] = m3 = p3*x1 + p8*x2  + p13*x3 + p18*x4 + p23*x5;
1342         pc[3] = m4 = p4*x1 + p9*x2  + p14*x3 + p19*x4 + p24*x5;
1343         pc[4] = m5 = p5*x1 + p10*x2 + p15*x3 + p20*x4 + p25*x5;
1344 
1345         pc[5] = m6 = p1*x6 + p6*x7  + p11*x8 + p16*x9 + p21*x10;
1346         pc[6] = m7 = p2*x6 + p7*x7  + p12*x8 + p17*x9 + p22*x10;
1347         pc[7] = m8 = p3*x6 + p8*x7  + p13*x8 + p18*x9 + p23*x10;
1348         pc[8] = m9 = p4*x6 + p9*x7  + p14*x8 + p19*x9 + p24*x10;
1349         pc[9] = m10 = p5*x6 + p10*x7 + p15*x8 + p20*x9 + p25*x10;
1350 
1351         pc[10] = m11 = p1*x11 + p6*x12  + p11*x13 + p16*x14 + p21*x15;
1352         pc[11] = m12 = p2*x11 + p7*x12  + p12*x13 + p17*x14 + p22*x15;
1353         pc[12] = m13 = p3*x11 + p8*x12  + p13*x13 + p18*x14 + p23*x15;
1354         pc[13] = m14 = p4*x11 + p9*x12  + p14*x13 + p19*x14 + p24*x15;
1355         pc[14] = m15 = p5*x11 + p10*x12 + p15*x13 + p20*x14 + p25*x15;
1356 
1357         pc[15] = m16 = p1*x16 + p6*x17  + p11*x18 + p16*x19 + p21*x20;
1358         pc[16] = m17 = p2*x16 + p7*x17  + p12*x18 + p17*x19 + p22*x20;
1359         pc[17] = m18 = p3*x16 + p8*x17  + p13*x18 + p18*x19 + p23*x20;
1360         pc[18] = m19 = p4*x16 + p9*x17  + p14*x18 + p19*x19 + p24*x20;
1361         pc[19] = m20 = p5*x16 + p10*x17 + p15*x18 + p20*x19 + p25*x20;
1362 
1363         pc[20] = m21 = p1*x21 + p6*x22  + p11*x23 + p16*x24 + p21*x25;
1364         pc[21] = m22 = p2*x21 + p7*x22  + p12*x23 + p17*x24 + p22*x25;
1365         pc[22] = m23 = p3*x21 + p8*x22  + p13*x23 + p18*x24 + p23*x25;
1366         pc[23] = m24 = p4*x21 + p9*x22  + p14*x23 + p19*x24 + p24*x25;
1367         pc[24] = m25 = p5*x21 + p10*x22 + p15*x23 + p20*x24 + p25*x25;
1368 
1369         nz = bi[row+1] - diag_offset[row] - 1;
1370         pv += 25;
1371         for (j=0; j<nz; j++) {
1372           x1   = pv[0];  x2 = pv[1];   x3  = pv[2];  x4  = pv[3];
1373           x5   = pv[4];  x6 = pv[5];   x7  = pv[6];  x8  = pv[7]; x9 = pv[8];
1374           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
1375           x14  = pv[13]; x15 = pv[14]; x16 = pv[15]; x17 = pv[16];
1376           x18  = pv[17]; x19 = pv[18]; x20 = pv[19]; x21 = pv[20];
1377           x22  = pv[21]; x23 = pv[22]; x24 = pv[23]; x25 = pv[24];
1378           x    = rtmp + 25*pj[j];
1379           x[0] -= m1*x1 + m6*x2  + m11*x3 + m16*x4 + m21*x5;
1380           x[1] -= m2*x1 + m7*x2  + m12*x3 + m17*x4 + m22*x5;
1381           x[2] -= m3*x1 + m8*x2  + m13*x3 + m18*x4 + m23*x5;
1382           x[3] -= m4*x1 + m9*x2  + m14*x3 + m19*x4 + m24*x5;
1383           x[4] -= m5*x1 + m10*x2 + m15*x3 + m20*x4 + m25*x5;
1384 
1385           x[5] -= m1*x6 + m6*x7  + m11*x8 + m16*x9 + m21*x10;
1386           x[6] -= m2*x6 + m7*x7  + m12*x8 + m17*x9 + m22*x10;
1387           x[7] -= m3*x6 + m8*x7  + m13*x8 + m18*x9 + m23*x10;
1388           x[8] -= m4*x6 + m9*x7  + m14*x8 + m19*x9 + m24*x10;
1389           x[9] -= m5*x6 + m10*x7 + m15*x8 + m20*x9 + m25*x10;
1390 
1391           x[10] -= m1*x11 + m6*x12  + m11*x13 + m16*x14 + m21*x15;
1392           x[11] -= m2*x11 + m7*x12  + m12*x13 + m17*x14 + m22*x15;
1393           x[12] -= m3*x11 + m8*x12  + m13*x13 + m18*x14 + m23*x15;
1394           x[13] -= m4*x11 + m9*x12  + m14*x13 + m19*x14 + m24*x15;
1395           x[14] -= m5*x11 + m10*x12 + m15*x13 + m20*x14 + m25*x15;
1396 
1397           x[15] -= m1*x16 + m6*x17  + m11*x18 + m16*x19 + m21*x20;
1398           x[16] -= m2*x16 + m7*x17  + m12*x18 + m17*x19 + m22*x20;
1399           x[17] -= m3*x16 + m8*x17  + m13*x18 + m18*x19 + m23*x20;
1400           x[18] -= m4*x16 + m9*x17  + m14*x18 + m19*x19 + m24*x20;
1401           x[19] -= m5*x16 + m10*x17 + m15*x18 + m20*x19 + m25*x20;
1402 
1403           x[20] -= m1*x21 + m6*x22  + m11*x23 + m16*x24 + m21*x25;
1404           x[21] -= m2*x21 + m7*x22  + m12*x23 + m17*x24 + m22*x25;
1405           x[22] -= m3*x21 + m8*x22  + m13*x23 + m18*x24 + m23*x25;
1406           x[23] -= m4*x21 + m9*x22  + m14*x23 + m19*x24 + m24*x25;
1407           x[24] -= m5*x21 + m10*x22 + m15*x23 + m20*x24 + m25*x25;
1408 
1409           pv   += 25;
1410         }
1411         PLogFlops(250*nz+225);
1412       }
1413       row = *ajtmp++;
1414     }
1415     /* finished row so stick it into b->a */
1416     pv = ba + 25*bi[i];
1417     pj = bj + bi[i];
1418     nz = bi[i+1] - bi[i];
1419     for (j=0; j<nz; j++) {
1420       x     = rtmp+25*pj[j];
1421       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
1422       pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
1423       pv[9] = x[9]; pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
1424       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; pv[16] = x[16];
1425       pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19]; pv[20] = x[20];
1426       pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23]; pv[24] = x[24];
1427       pv   += 25;
1428     }
1429     /* invert diagonal block */
1430     w = ba + 25*diag_offset[i];
1431     ierr = Kernel_A_gets_inverse_A_5(w);CHKERRQ(ierr);
1432   }
1433 
1434   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1435   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
1436   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
1437   C->factor = FACTOR_LU;
1438   C->assembled = PETSC_TRUE;
1439   PLogFlops(1.3333*125*b->mbs); /* from inverting diagonal blocks */
1440   PetscFunctionReturn(0);
1441 }
1442 /*
1443       Version for when blocks are 5 by 5 Using natural ordering
1444 */
1445 #undef __FUNC__
1446 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_5_NaturalOrdering"
1447 int MatCholeskyFactorNumeric_SeqSBAIJ_5_NaturalOrdering(Mat A,Mat *B)
1448 {
1449   Mat         C = *B;
1450   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
1451   int         ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
1452   int         *ajtmpold,*ajtmp,nz,row;
1453   int         *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
1454   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
1455   MatScalar   x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15;
1456   MatScalar   x16,x17,x18,x19,x20,x21,x22,x23,x24,x25;
1457   MatScalar   p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15;
1458   MatScalar   p16,p17,p18,p19,p20,p21,p22,p23,p24,p25;
1459   MatScalar   m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12,m13,m14,m15;
1460   MatScalar   m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
1461   MatScalar   *ba = b->a,*aa = a->a;
1462 
1463   PetscFunctionBegin;
1464   rtmp  = (MatScalar*)PetscMalloc(25*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
1465   for (i=0; i<n; i++) {
1466     nz    = bi[i+1] - bi[i];
1467     ajtmp = bj + bi[i];
1468     for  (j=0; j<nz; j++) {
1469       x = rtmp+25*ajtmp[j];
1470       x[0]  = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = x[9] = 0.0;
1471       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
1472       x[16] = x[17] = x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0;
1473     }
1474     /* load in initial (unfactored row) */
1475     nz       = ai[i+1] - ai[i];
1476     ajtmpold = aj + ai[i];
1477     v        = aa + 25*ai[i];
1478     for (j=0; j<nz; j++) {
1479       x    = rtmp+25*ajtmpold[j];
1480       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
1481       x[4]  = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
1482       x[9]  = v[9];  x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
1483       x[14] = v[14]; x[15] = v[15]; x[16] = v[16]; x[17] = v[17]; x[18] = v[18];
1484       x[19] = v[19]; x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23];
1485       x[24] = v[24];
1486       v    += 25;
1487     }
1488     row = *ajtmp++;
1489     while (row < i) {
1490       pc  = rtmp + 25*row;
1491       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
1492       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
1493       p10 = pc[9];  p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
1494       p15 = pc[14]; p16 = pc[15]; p17 = pc[16]; p18 = pc[17];
1495       p19 = pc[18]; p20 = pc[19]; p21 = pc[20]; p22 = pc[21]; p23 = pc[22];
1496       p24 = pc[23]; p25 = pc[24];
1497       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
1498           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
1499           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
1500           || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0
1501           || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 || p25 != 0.0) {
1502         pv = ba + 25*diag_offset[row];
1503         pj = bj + diag_offset[row] + 1;
1504         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
1505         x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
1506         x10 = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
1507         x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17]; x19 = pv[18];
1508         x20 = pv[19]; x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
1509         x25 = pv[24];
1510         pc[0] = m1 = p1*x1 + p6*x2  + p11*x3 + p16*x4 + p21*x5;
1511         pc[1] = m2 = p2*x1 + p7*x2  + p12*x3 + p17*x4 + p22*x5;
1512         pc[2] = m3 = p3*x1 + p8*x2  + p13*x3 + p18*x4 + p23*x5;
1513         pc[3] = m4 = p4*x1 + p9*x2  + p14*x3 + p19*x4 + p24*x5;
1514         pc[4] = m5 = p5*x1 + p10*x2 + p15*x3 + p20*x4 + p25*x5;
1515 
1516         pc[5]  = m6  = p1*x6 + p6*x7  + p11*x8 + p16*x9 + p21*x10;
1517         pc[6]  = m7  = p2*x6 + p7*x7  + p12*x8 + p17*x9 + p22*x10;
1518         pc[7]  = m8  = p3*x6 + p8*x7  + p13*x8 + p18*x9 + p23*x10;
1519         pc[8]  = m9  = p4*x6 + p9*x7  + p14*x8 + p19*x9 + p24*x10;
1520         pc[9]  = m10 = p5*x6 + p10*x7 + p15*x8 + p20*x9 + p25*x10;
1521 
1522         pc[10] = m11 = p1*x11 + p6*x12  + p11*x13 + p16*x14 + p21*x15;
1523         pc[11] = m12 = p2*x11 + p7*x12  + p12*x13 + p17*x14 + p22*x15;
1524         pc[12] = m13 = p3*x11 + p8*x12  + p13*x13 + p18*x14 + p23*x15;
1525         pc[13] = m14 = p4*x11 + p9*x12  + p14*x13 + p19*x14 + p24*x15;
1526         pc[14] = m15 = p5*x11 + p10*x12 + p15*x13 + p20*x14 + p25*x15;
1527 
1528         pc[15] = m16 = p1*x16 + p6*x17  + p11*x18 + p16*x19 + p21*x20;
1529         pc[16] = m17 = p2*x16 + p7*x17  + p12*x18 + p17*x19 + p22*x20;
1530         pc[17] = m18 = p3*x16 + p8*x17  + p13*x18 + p18*x19 + p23*x20;
1531         pc[18] = m19 = p4*x16 + p9*x17  + p14*x18 + p19*x19 + p24*x20;
1532         pc[19] = m20 = p5*x16 + p10*x17 + p15*x18 + p20*x19 + p25*x20;
1533 
1534         pc[20] = m21 = p1*x21 + p6*x22  + p11*x23 + p16*x24 + p21*x25;
1535         pc[21] = m22 = p2*x21 + p7*x22  + p12*x23 + p17*x24 + p22*x25;
1536         pc[22] = m23 = p3*x21 + p8*x22  + p13*x23 + p18*x24 + p23*x25;
1537         pc[23] = m24 = p4*x21 + p9*x22  + p14*x23 + p19*x24 + p24*x25;
1538         pc[24] = m25 = p5*x21 + p10*x22 + p15*x23 + p20*x24 + p25*x25;
1539 
1540         nz = bi[row+1] - diag_offset[row] - 1;
1541         pv += 25;
1542         for (j=0; j<nz; j++) {
1543           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
1544           x5   = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
1545           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
1546           x14  = pv[13]; x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17];
1547           x19 = pv[18];  x20 = pv[19]; x21 = pv[20]; x22 = pv[21]; x23 = pv[22];
1548           x24 = pv[23];  x25 = pv[24];
1549           x    = rtmp + 25*pj[j];
1550           x[0] -= m1*x1 + m6*x2   + m11*x3  + m16*x4 + m21*x5;
1551           x[1] -= m2*x1 + m7*x2   + m12*x3  + m17*x4 + m22*x5;
1552           x[2] -= m3*x1 + m8*x2   + m13*x3  + m18*x4 + m23*x5;
1553           x[3] -= m4*x1 + m9*x2   + m14*x3  + m19*x4 + m24*x5;
1554           x[4] -= m5*x1 + m10*x2  + m15*x3  + m20*x4 + m25*x5;
1555 
1556           x[5] -= m1*x6 + m6*x7   + m11*x8  + m16*x9 + m21*x10;
1557           x[6] -= m2*x6 + m7*x7   + m12*x8  + m17*x9 + m22*x10;
1558           x[7] -= m3*x6 + m8*x7   + m13*x8  + m18*x9 + m23*x10;
1559           x[8] -= m4*x6 + m9*x7   + m14*x8  + m19*x9 + m24*x10;
1560           x[9] -= m5*x6 + m10*x7  + m15*x8  + m20*x9 + m25*x10;
1561 
1562           x[10] -= m1*x11 + m6*x12  + m11*x13 + m16*x14 + m21*x15;
1563           x[11] -= m2*x11 + m7*x12  + m12*x13 + m17*x14 + m22*x15;
1564           x[12] -= m3*x11 + m8*x12  + m13*x13 + m18*x14 + m23*x15;
1565           x[13] -= m4*x11 + m9*x12  + m14*x13 + m19*x14 + m24*x15;
1566           x[14] -= m5*x11 + m10*x12 + m15*x13 + m20*x14 + m25*x15;
1567 
1568           x[15] -= m1*x16 + m6*x17  + m11*x18 + m16*x19 + m21*x20;
1569           x[16] -= m2*x16 + m7*x17  + m12*x18 + m17*x19 + m22*x20;
1570           x[17] -= m3*x16 + m8*x17  + m13*x18 + m18*x19 + m23*x20;
1571           x[18] -= m4*x16 + m9*x17  + m14*x18 + m19*x19 + m24*x20;
1572           x[19] -= m5*x16 + m10*x17 + m15*x18 + m20*x19 + m25*x20;
1573 
1574           x[20] -= m1*x21 + m6*x22  + m11*x23 + m16*x24 + m21*x25;
1575           x[21] -= m2*x21 + m7*x22  + m12*x23 + m17*x24 + m22*x25;
1576           x[22] -= m3*x21 + m8*x22  + m13*x23 + m18*x24 + m23*x25;
1577           x[23] -= m4*x21 + m9*x22  + m14*x23 + m19*x24 + m24*x25;
1578           x[24] -= m5*x21 + m10*x22 + m15*x23 + m20*x24 + m25*x25;
1579           pv   += 25;
1580         }
1581         PLogFlops(250*nz+225);
1582       }
1583       row = *ajtmp++;
1584     }
1585     /* finished row so stick it into b->a */
1586     pv = ba + 25*bi[i];
1587     pj = bj + bi[i];
1588     nz = bi[i+1] - bi[i];
1589     for (j=0; j<nz; j++) {
1590       x      = rtmp+25*pj[j];
1591       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
1592       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
1593       pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
1594       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; pv[16] = x[16]; pv[17] = x[17];
1595       pv[18] = x[18]; pv[19] = x[19]; pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22];
1596       pv[23] = x[23]; pv[24] = x[24];
1597       pv   += 25;
1598     }
1599     /* invert diagonal block */
1600     w = ba + 25*diag_offset[i];
1601     ierr = Kernel_A_gets_inverse_A_5(w);CHKERRQ(ierr);
1602   }
1603 
1604   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1605   C->factor    = FACTOR_LU;
1606   C->assembled = PETSC_TRUE;
1607   PLogFlops(1.3333*125*b->mbs); /* from inverting diagonal blocks */
1608   PetscFunctionReturn(0);
1609 }
1610 
1611 /*
1612       Version for when blocks are 4 by 4
1613 */
1614 #undef __FUNC__
1615 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_4"
1616 int MatCholeskyFactorNumeric_SeqSBAIJ_4(Mat A,Mat *B)
1617 {
1618   Mat         C = *B;
1619   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
1620   IS          isrow = b->row,isicol = b->icol;
1621   int         *r,*ic,ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
1622   int         *ajtmpold,*ajtmp,nz,row;
1623   int         *diag_offset = b->diag,idx,*ai=a->i,*aj=a->j,*pj;
1624   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
1625   MatScalar   p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
1626   MatScalar   p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
1627   MatScalar   p10,p11,p12,p13,p14,p15,p16,m10,m11,m12;
1628   MatScalar   m13,m14,m15,m16;
1629   MatScalar   *ba = b->a,*aa = a->a;
1630 
1631   PetscFunctionBegin;
1632   ierr  = ISGetIndices(isrow,&r);CHKERRQ(ierr);
1633   ierr  = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
1634   rtmp  = (MatScalar*)PetscMalloc(16*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
1635 
1636   for (i=0; i<n; i++) {
1637     nz    = bi[i+1] - bi[i];
1638     ajtmp = bj + bi[i];
1639     for  (j=0; j<nz; j++) {
1640       x = rtmp+16*ajtmp[j];
1641       x[0]  = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = x[9] = 0.0;
1642       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
1643     }
1644     /* load in initial (unfactored row) */
1645     idx      = r[i];
1646     nz       = ai[idx+1] - ai[idx];
1647     ajtmpold = aj + ai[idx];
1648     v        = aa + 16*ai[idx];
1649     for (j=0; j<nz; j++) {
1650       x    = rtmp+16*ic[ajtmpold[j]];
1651       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
1652       x[4]  = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
1653       x[9]  = v[9];  x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
1654       x[14] = v[14]; x[15] = v[15];
1655       v    += 16;
1656     }
1657     row = *ajtmp++;
1658     while (row < i) {
1659       pc  = rtmp + 16*row;
1660       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
1661       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
1662       p10 = pc[9];  p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
1663       p15 = pc[14]; p16 = pc[15];
1664       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
1665           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
1666           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
1667           || p16 != 0.0) {
1668         pv = ba + 16*diag_offset[row];
1669         pj = bj + diag_offset[row] + 1;
1670         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
1671         x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
1672         x10 = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
1673         x15 = pv[14]; x16 = pv[15];
1674         pc[0] = m1 = p1*x1 + p5*x2  + p9*x3  + p13*x4;
1675         pc[1] = m2 = p2*x1 + p6*x2  + p10*x3 + p14*x4;
1676         pc[2] = m3 = p3*x1 + p7*x2  + p11*x3 + p15*x4;
1677         pc[3] = m4 = p4*x1 + p8*x2  + p12*x3 + p16*x4;
1678 
1679         pc[4] = m5 = p1*x5 + p5*x6  + p9*x7  + p13*x8;
1680         pc[5] = m6 = p2*x5 + p6*x6  + p10*x7 + p14*x8;
1681         pc[6] = m7 = p3*x5 + p7*x6  + p11*x7 + p15*x8;
1682         pc[7] = m8 = p4*x5 + p8*x6  + p12*x7 + p16*x8;
1683 
1684         pc[8]  = m9  = p1*x9 + p5*x10  + p9*x11  + p13*x12;
1685         pc[9]  = m10 = p2*x9 + p6*x10  + p10*x11 + p14*x12;
1686         pc[10] = m11 = p3*x9 + p7*x10  + p11*x11 + p15*x12;
1687         pc[11] = m12 = p4*x9 + p8*x10  + p12*x11 + p16*x12;
1688 
1689         pc[12] = m13 = p1*x13 + p5*x14  + p9*x15  + p13*x16;
1690         pc[13] = m14 = p2*x13 + p6*x14  + p10*x15 + p14*x16;
1691         pc[14] = m15 = p3*x13 + p7*x14  + p11*x15 + p15*x16;
1692         pc[15] = m16 = p4*x13 + p8*x14  + p12*x15 + p16*x16;
1693 
1694         nz = bi[row+1] - diag_offset[row] - 1;
1695         pv += 16;
1696         for (j=0; j<nz; j++) {
1697           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
1698           x5   = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
1699           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
1700           x14  = pv[13]; x15 = pv[14]; x16 = pv[15];
1701           x    = rtmp + 16*pj[j];
1702           x[0] -= m1*x1 + m5*x2  + m9*x3  + m13*x4;
1703           x[1] -= m2*x1 + m6*x2  + m10*x3 + m14*x4;
1704           x[2] -= m3*x1 + m7*x2  + m11*x3 + m15*x4;
1705           x[3] -= m4*x1 + m8*x2  + m12*x3 + m16*x4;
1706 
1707           x[4] -= m1*x5 + m5*x6  + m9*x7  + m13*x8;
1708           x[5] -= m2*x5 + m6*x6  + m10*x7 + m14*x8;
1709           x[6] -= m3*x5 + m7*x6  + m11*x7 + m15*x8;
1710           x[7] -= m4*x5 + m8*x6  + m12*x7 + m16*x8;
1711 
1712           x[8]  -= m1*x9 + m5*x10 + m9*x11  + m13*x12;
1713           x[9]  -= m2*x9 + m6*x10 + m10*x11 + m14*x12;
1714           x[10] -= m3*x9 + m7*x10 + m11*x11 + m15*x12;
1715           x[11] -= m4*x9 + m8*x10 + m12*x11 + m16*x12;
1716 
1717           x[12] -= m1*x13 + m5*x14  + m9*x15  + m13*x16;
1718           x[13] -= m2*x13 + m6*x14  + m10*x15 + m14*x16;
1719           x[14] -= m3*x13 + m7*x14  + m11*x15 + m15*x16;
1720           x[15] -= m4*x13 + m8*x14  + m12*x15 + m16*x16;
1721 
1722           pv   += 16;
1723         }
1724         PLogFlops(128*nz+112);
1725       }
1726       row = *ajtmp++;
1727     }
1728     /* finished row so stick it into b->a */
1729     pv = ba + 16*bi[i];
1730     pj = bj + bi[i];
1731     nz = bi[i+1] - bi[i];
1732     for (j=0; j<nz; j++) {
1733       x      = rtmp+16*pj[j];
1734       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
1735       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
1736       pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
1737       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
1738       pv   += 16;
1739     }
1740     /* invert diagonal block */
1741     w = ba + 16*diag_offset[i];
1742     ierr = Kernel_A_gets_inverse_A_4(w);CHKERRQ(ierr);
1743   }
1744 
1745   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1746   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
1747   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
1748   C->factor = FACTOR_LU;
1749   C->assembled = PETSC_TRUE;
1750   PLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */
1751   PetscFunctionReturn(0);
1752 }
1753 /*
1754       Version for when blocks are 4 by 4 Using natural ordering
1755 */
1756 #undef __FUNC__
1757 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_4_NaturalOrdering"
1758 int MatCholeskyFactorNumeric_SeqSBAIJ_4_NaturalOrdering(Mat A,Mat *B)
1759 {
1760   Mat         C = *B;
1761   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
1762   int         ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
1763   int         *ajtmpold,*ajtmp,nz,row;
1764   int         *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
1765   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
1766   MatScalar   p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
1767   MatScalar   p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
1768   MatScalar   p10,p11,p12,p13,p14,p15,p16,m10,m11,m12;
1769   MatScalar   m13,m14,m15,m16;
1770   MatScalar   *ba = b->a,*aa = a->a;
1771 
1772   PetscFunctionBegin;
1773   rtmp  = (MatScalar*)PetscMalloc(16*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
1774 
1775   for (i=0; i<n; i++) {
1776     nz    = bi[i+1] - bi[i];
1777     ajtmp = bj + bi[i];
1778     for  (j=0; j<nz; j++) {
1779       x = rtmp+16*ajtmp[j];
1780       x[0]  = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = x[9] = 0.0;
1781       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
1782     }
1783     /* load in initial (unfactored row) */
1784     nz       = ai[i+1] - ai[i];
1785     ajtmpold = aj + ai[i];
1786     v        = aa + 16*ai[i];
1787     for (j=0; j<nz; j++) {
1788       x    = rtmp+16*ajtmpold[j];
1789       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
1790       x[4]  = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
1791       x[9]  = v[9];  x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
1792       x[14] = v[14]; x[15] = v[15];
1793       v    += 16;
1794     }
1795     row = *ajtmp++;
1796     while (row < i) {
1797       pc  = rtmp + 16*row;
1798       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
1799       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
1800       p10 = pc[9];  p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
1801       p15 = pc[14]; p16 = pc[15];
1802       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
1803           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
1804           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
1805           || p16 != 0.0) {
1806         pv = ba + 16*diag_offset[row];
1807         pj = bj + diag_offset[row] + 1;
1808         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
1809         x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
1810         x10 = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
1811         x15 = pv[14]; x16 = pv[15];
1812         pc[0] = m1 = p1*x1 + p5*x2  + p9*x3  + p13*x4;
1813         pc[1] = m2 = p2*x1 + p6*x2  + p10*x3 + p14*x4;
1814         pc[2] = m3 = p3*x1 + p7*x2  + p11*x3 + p15*x4;
1815         pc[3] = m4 = p4*x1 + p8*x2  + p12*x3 + p16*x4;
1816 
1817         pc[4] = m5 = p1*x5 + p5*x6  + p9*x7  + p13*x8;
1818         pc[5] = m6 = p2*x5 + p6*x6  + p10*x7 + p14*x8;
1819         pc[6] = m7 = p3*x5 + p7*x6  + p11*x7 + p15*x8;
1820         pc[7] = m8 = p4*x5 + p8*x6  + p12*x7 + p16*x8;
1821 
1822         pc[8]  = m9  = p1*x9 + p5*x10  + p9*x11  + p13*x12;
1823         pc[9]  = m10 = p2*x9 + p6*x10  + p10*x11 + p14*x12;
1824         pc[10] = m11 = p3*x9 + p7*x10  + p11*x11 + p15*x12;
1825         pc[11] = m12 = p4*x9 + p8*x10  + p12*x11 + p16*x12;
1826 
1827         pc[12] = m13 = p1*x13 + p5*x14  + p9*x15  + p13*x16;
1828         pc[13] = m14 = p2*x13 + p6*x14  + p10*x15 + p14*x16;
1829         pc[14] = m15 = p3*x13 + p7*x14  + p11*x15 + p15*x16;
1830         pc[15] = m16 = p4*x13 + p8*x14  + p12*x15 + p16*x16;
1831 
1832         nz = bi[row+1] - diag_offset[row] - 1;
1833         pv += 16;
1834         for (j=0; j<nz; j++) {
1835           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
1836           x5   = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
1837           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
1838           x14  = pv[13]; x15 = pv[14]; x16 = pv[15];
1839           x    = rtmp + 16*pj[j];
1840           x[0] -= m1*x1 + m5*x2  + m9*x3  + m13*x4;
1841           x[1] -= m2*x1 + m6*x2  + m10*x3 + m14*x4;
1842           x[2] -= m3*x1 + m7*x2  + m11*x3 + m15*x4;
1843           x[3] -= m4*x1 + m8*x2  + m12*x3 + m16*x4;
1844 
1845           x[4] -= m1*x5 + m5*x6  + m9*x7  + m13*x8;
1846           x[5] -= m2*x5 + m6*x6  + m10*x7 + m14*x8;
1847           x[6] -= m3*x5 + m7*x6  + m11*x7 + m15*x8;
1848           x[7] -= m4*x5 + m8*x6  + m12*x7 + m16*x8;
1849 
1850           x[8]  -= m1*x9 + m5*x10 + m9*x11  + m13*x12;
1851           x[9]  -= m2*x9 + m6*x10 + m10*x11 + m14*x12;
1852           x[10] -= m3*x9 + m7*x10 + m11*x11 + m15*x12;
1853           x[11] -= m4*x9 + m8*x10 + m12*x11 + m16*x12;
1854 
1855           x[12] -= m1*x13 + m5*x14  + m9*x15  + m13*x16;
1856           x[13] -= m2*x13 + m6*x14  + m10*x15 + m14*x16;
1857           x[14] -= m3*x13 + m7*x14  + m11*x15 + m15*x16;
1858           x[15] -= m4*x13 + m8*x14  + m12*x15 + m16*x16;
1859 
1860           pv   += 16;
1861         }
1862         PLogFlops(128*nz+112);
1863       }
1864       row = *ajtmp++;
1865     }
1866     /* finished row so stick it into b->a */
1867     pv = ba + 16*bi[i];
1868     pj = bj + bi[i];
1869     nz = bi[i+1] - bi[i];
1870     for (j=0; j<nz; j++) {
1871       x      = rtmp+16*pj[j];
1872       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
1873       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
1874       pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
1875       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
1876       pv   += 16;
1877     }
1878     /* invert diagonal block */
1879     w = ba + 16*diag_offset[i];
1880     ierr = Kernel_A_gets_inverse_A_4(w);CHKERRQ(ierr);
1881   }
1882 
1883   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1884   C->factor    = FACTOR_LU;
1885   C->assembled = PETSC_TRUE;
1886   PLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */
1887   PetscFunctionReturn(0);
1888 }
1889 
1890 /*
1891       Version for when blocks are 3 by 3
1892 */
1893 #undef __FUNC__
1894 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_3"
1895 int MatCholeskyFactorNumeric_SeqSBAIJ_3(Mat A,Mat *B)
1896 {
1897   Mat         C = *B;
1898   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
1899   IS          isrow = b->row,isicol = b->icol;
1900   int         *r,*ic,ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
1901   int         *ajtmpold,*ajtmp,nz,row,*ai=a->i,*aj=a->j;
1902   int         *diag_offset = b->diag,idx,*pj;
1903   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
1904   MatScalar   p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
1905   MatScalar   p5,p6,p7,p8,p9,x5,x6,x7,x8,x9;
1906   MatScalar   *ba = b->a,*aa = a->a;
1907 
1908   PetscFunctionBegin;
1909   ierr  = ISGetIndices(isrow,&r);CHKERRQ(ierr);
1910   ierr  = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
1911   rtmp  = (MatScalar*)PetscMalloc(9*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
1912 
1913   for (i=0; i<n; i++) {
1914     nz    = bi[i+1] - bi[i];
1915     ajtmp = bj + bi[i];
1916     for  (j=0; j<nz; j++) {
1917       x = rtmp + 9*ajtmp[j];
1918       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = 0.0;
1919     }
1920     /* load in initial (unfactored row) */
1921     idx      = r[i];
1922     nz       = ai[idx+1] - ai[idx];
1923     ajtmpold = aj + ai[idx];
1924     v        = aa + 9*ai[idx];
1925     for (j=0; j<nz; j++) {
1926       x    = rtmp + 9*ic[ajtmpold[j]];
1927       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
1928       x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
1929       v    += 9;
1930     }
1931     row = *ajtmp++;
1932     while (row < i) {
1933       pc = rtmp + 9*row;
1934       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
1935       p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
1936       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
1937           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0) {
1938         pv = ba + 9*diag_offset[row];
1939         pj = bj + diag_offset[row] + 1;
1940         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
1941         x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
1942         pc[0] = m1 = p1*x1 + p4*x2 + p7*x3;
1943         pc[1] = m2 = p2*x1 + p5*x2 + p8*x3;
1944         pc[2] = m3 = p3*x1 + p6*x2 + p9*x3;
1945 
1946         pc[3] = m4 = p1*x4 + p4*x5 + p7*x6;
1947         pc[4] = m5 = p2*x4 + p5*x5 + p8*x6;
1948         pc[5] = m6 = p3*x4 + p6*x5 + p9*x6;
1949 
1950         pc[6] = m7 = p1*x7 + p4*x8 + p7*x9;
1951         pc[7] = m8 = p2*x7 + p5*x8 + p8*x9;
1952         pc[8] = m9 = p3*x7 + p6*x8 + p9*x9;
1953         nz = bi[row+1] - diag_offset[row] - 1;
1954         pv += 9;
1955         for (j=0; j<nz; j++) {
1956           x1   = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
1957           x5   = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
1958           x    = rtmp + 9*pj[j];
1959           x[0] -= m1*x1 + m4*x2 + m7*x3;
1960           x[1] -= m2*x1 + m5*x2 + m8*x3;
1961           x[2] -= m3*x1 + m6*x2 + m9*x3;
1962 
1963           x[3] -= m1*x4 + m4*x5 + m7*x6;
1964           x[4] -= m2*x4 + m5*x5 + m8*x6;
1965           x[5] -= m3*x4 + m6*x5 + m9*x6;
1966 
1967           x[6] -= m1*x7 + m4*x8 + m7*x9;
1968           x[7] -= m2*x7 + m5*x8 + m8*x9;
1969           x[8] -= m3*x7 + m6*x8 + m9*x9;
1970           pv   += 9;
1971         }
1972         PLogFlops(54*nz+36);
1973       }
1974       row = *ajtmp++;
1975     }
1976     /* finished row so stick it into b->a */
1977     pv = ba + 9*bi[i];
1978     pj = bj + bi[i];
1979     nz = bi[i+1] - bi[i];
1980     for (j=0; j<nz; j++) {
1981       x     = rtmp + 9*pj[j];
1982       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
1983       pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
1984       pv   += 9;
1985     }
1986     /* invert diagonal block */
1987     w = ba + 9*diag_offset[i];
1988     ierr = Kernel_A_gets_inverse_A_3(w);CHKERRQ(ierr);
1989   }
1990 
1991   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1992   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
1993   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
1994   C->factor = FACTOR_LU;
1995   C->assembled = PETSC_TRUE;
1996   PLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */
1997   PetscFunctionReturn(0);
1998 }
1999 /*
2000       Version for when blocks are 3 by 3 Using natural ordering
2001 */
2002 #undef __FUNC__
2003 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_3_NaturalOrdering"
2004 int MatCholeskyFactorNumeric_SeqSBAIJ_3_NaturalOrdering(Mat A,Mat *B)
2005 {
2006   Mat                C = *B;
2007   Mat_SeqBAIJ        *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
2008   int                ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
2009   int                *ajtmpold,*ajtmp,nz,row;
2010   int                *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
2011   MatScalar          *pv,*v,*rtmp,*pc,*w,*x;
2012   MatScalar          p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
2013   MatScalar          p5,p6,p7,p8,p9,x5,x6,x7,x8,x9;
2014   MatScalar          *ba = b->a,*aa = a->a;
2015 
2016   PetscFunctionBegin;
2017   rtmp  = (MatScalar*)PetscMalloc(9*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
2018 
2019   for (i=0; i<n; i++) {
2020     nz    = bi[i+1] - bi[i];
2021     ajtmp = bj + bi[i];
2022     for  (j=0; j<nz; j++) {
2023       x = rtmp+9*ajtmp[j];
2024       x[0]  = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = 0.0;
2025     }
2026     /* load in initial (unfactored row) */
2027     nz       = ai[i+1] - ai[i];
2028     ajtmpold = aj + ai[i];
2029     v        = aa + 9*ai[i];
2030     for (j=0; j<nz; j++) {
2031       x    = rtmp+9*ajtmpold[j];
2032       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
2033       x[4]  = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
2034       v    += 9;
2035     }
2036     row = *ajtmp++;
2037     while (row < i) {
2038       pc  = rtmp + 9*row;
2039       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
2040       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
2041       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
2042           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0) {
2043         pv = ba + 9*diag_offset[row];
2044         pj = bj + diag_offset[row] + 1;
2045         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
2046         x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
2047         pc[0] = m1 = p1*x1 + p4*x2 + p7*x3;
2048         pc[1] = m2 = p2*x1 + p5*x2 + p8*x3;
2049         pc[2] = m3 = p3*x1 + p6*x2 + p9*x3;
2050 
2051         pc[3] = m4 = p1*x4 + p4*x5 + p7*x6;
2052         pc[4] = m5 = p2*x4 + p5*x5 + p8*x6;
2053         pc[5] = m6 = p3*x4 + p6*x5 + p9*x6;
2054 
2055         pc[6] = m7 = p1*x7 + p4*x8 + p7*x9;
2056         pc[7] = m8 = p2*x7 + p5*x8 + p8*x9;
2057         pc[8] = m9 = p3*x7 + p6*x8 + p9*x9;
2058 
2059         nz = bi[row+1] - diag_offset[row] - 1;
2060         pv += 9;
2061         for (j=0; j<nz; j++) {
2062           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
2063           x5   = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
2064           x    = rtmp + 9*pj[j];
2065           x[0] -= m1*x1 + m4*x2 + m7*x3;
2066           x[1] -= m2*x1 + m5*x2 + m8*x3;
2067           x[2] -= m3*x1 + m6*x2 + m9*x3;
2068 
2069           x[3] -= m1*x4 + m4*x5 + m7*x6;
2070           x[4] -= m2*x4 + m5*x5 + m8*x6;
2071           x[5] -= m3*x4 + m6*x5 + m9*x6;
2072 
2073           x[6] -= m1*x7 + m4*x8 + m7*x9;
2074           x[7] -= m2*x7 + m5*x8 + m8*x9;
2075           x[8] -= m3*x7 + m6*x8 + m9*x9;
2076           pv   += 9;
2077         }
2078         PLogFlops(54*nz+36);
2079       }
2080       row = *ajtmp++;
2081     }
2082     /* finished row so stick it into b->a */
2083     pv = ba + 9*bi[i];
2084     pj = bj + bi[i];
2085     nz = bi[i+1] - bi[i];
2086     for (j=0; j<nz; j++) {
2087       x      = rtmp+9*pj[j];
2088       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
2089       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
2090       pv   += 9;
2091     }
2092     /* invert diagonal block */
2093     w = ba + 9*diag_offset[i];
2094     ierr = Kernel_A_gets_inverse_A_3(w);CHKERRQ(ierr);
2095   }
2096 
2097   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2098   C->factor    = FACTOR_LU;
2099   C->assembled = PETSC_TRUE;
2100   PLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */
2101   PetscFunctionReturn(0);
2102 }
2103 
2104 /*
2105     Numeric (-UT)*D*(-U) factorization for SBAIJ format. Modified from SNF of YSMP.
2106     Version for blocks are 2 by 2.
2107 */
2108 #undef __FUNC__
2109 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_2"
2110 int MatCholeskyFactorNumeric_SeqSBAIJ_2(Mat A,Mat *B)
2111 {
2112   Mat                C = *B;
2113   Mat_SeqSBAIJ       *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data;
2114   IS                 ip = b->row;
2115   int                *rip,ierr,i,j,mbs = a->mbs,*bi = b->i,*bj = b->j;
2116   int                *ai,*aj,*r,bs2 = a->bs2;
2117   MatScalar          *rtmp;
2118   MatScalar          *ba = b->a,*aa,*ak,*ap;
2119   MatScalar          *dk,*uik;
2120   int                k,jmin,jmax,*jl,*il,vj,nexti,juj,ili;
2121   int                k1;
2122   MatScalar          *up,*diag,*rtmp_ptr;
2123 
2124   PetscFunctionBegin;
2125   printf("called factornum_2, bs2: %d\n",bs2);
2126   ierr  = ISGetIndices(ip,&rip);CHKERRQ(ierr);
2127 
2128   if (!a->permute){
2129     ai = a->i; aj = a->j; aa = a->a;
2130   } else {
2131     ai = a->inew; aj = a->jnew;
2132     aa = (MatScalar*)PetscMalloc(bs2*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa);
2133     ierr = PetscMemcpy(aa,a->a,bs2*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr);
2134     r   = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(r);
2135     ierr= PetscMemcpy(r,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr);
2136 
2137     ak = (MatScalar*)PetscMalloc(bs2*sizeof(MatScalar));CHKPTRQ(ak);
2138 
2139     for (i=0; i<mbs; i++){
2140       jmin = ai[i]; jmax = ai[i+1];
2141       for (j=jmin; j<jmax; j++){
2142         while (r[j] != j){
2143           k = r[j]; r[j] = r[k]; r[k] = k;
2144           for (k1=0; k1<bs2; k1++){
2145             ak[k1]       = aa[k*bs2+k1];
2146             aa[k*bs2+k1] = aa[j*bs2+k1];
2147             aa[j*bs2+k1] = ak[k1];
2148           }
2149         }
2150       }
2151     }
2152 
2153     /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks.
2154        should be combined into the above loops */
2155     for (i=0; i<mbs; i++){
2156       jmin = ai[i]; jmax = ai[i+1];
2157       for (j=jmin; j<jmax; j++){
2158         if (i > aj[j]){
2159           ap = aa + j*bs2;     /* ptr to the beginning of the block */
2160           ak[1] = ap[1];       /* swap ap[1] and ap[2] */
2161           ap[1] = ap[2];
2162           ap[2] = ak[1];
2163         }
2164       }
2165     }
2166     ierr = PetscFree(r);CHKERRA(ierr);
2167     ierr = PetscFree(ak);CHKERRA(ierr);
2168   }
2169 
2170   /* initialization */
2171   /* il and jl record the first nonzero element in each row of the accessing
2172      window U(0:k, k:mbs-1).
2173      jl:    list of rows to be added to uneliminated rows
2174             i>= k: jl(i) is the first row to be added to row i
2175             i<  k: jl(i) is the row following row i in some list of rows
2176             jl(i) = mbs indicates the end of a list
2177      il(i): points to the first nonzero element in columns k,...,mbs-1 of
2178             row i of U */
2179   rtmp  = (MatScalar*)PetscMalloc(bs2*mbs*sizeof(MatScalar));CHKPTRQ(rtmp);
2180   ierr = PetscMemzero(rtmp,bs2*sizeof(MatScalar));CHKERRQ(ierr);
2181   il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il);
2182   jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl);
2183   dk = (MatScalar*)PetscMalloc(bs2*sizeof(MatScalar));CHKPTRQ(dk);
2184   uik= (MatScalar*)PetscMalloc(bs2*sizeof(MatScalar));CHKPTRQ(uik);
2185 
2186   for (i=0; i<mbs; i++) {
2187     jl[i] = mbs; il[0] = 0;
2188   }
2189 
2190   /* for each row k */
2191   for (k = 0; k<mbs; k++){
2192 
2193     /*initialize k-th row with elements nonzero in row perm(k) of A */
2194     jmin = ai[rip[k]]; jmax = ai[rip[k]+1];
2195     if (jmin < jmax) {
2196       for (j = jmin; j < jmax; j++){
2197         vj = rip[aj[j]];         /* block col. index */
2198         if (k <= vj) {
2199           ap = aa + j*bs2;       /* ptr to the beginning of the block */
2200           for (i=0; i<bs2; i++){
2201             rtmp[vj*bs2 + i] = *ap; ap++;
2202           }
2203         }
2204       }
2205     }
2206 
2207     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
2208     ierr = PetscMemcpy(dk,rtmp+k*bs2,bs2*sizeof(MatScalar));CHKERRQ(ierr); /* dk = rtmp[k]; */
2209     i = jl[k]; /* first row to be added to k_th row  */
2210     /* printf(" k=%d, pivot row = %d\n",k,i); */
2211 
2212     while (i < mbs){
2213       nexti = jl[i]; /* next row to be added to k_th row */
2214 
2215       /* compute multiplier */
2216       ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
2217 
2218       /* uik = -inv(Di)*U_bar(i,k): - ba[ili]*ba[i] */
2219       diag = ba + i*bs2;
2220       up   = ba + ili*bs2;
2221       uik[0] = -(diag[0]*up[0] + diag[2]*up[1]);
2222       uik[1] = -(diag[1]*up[0] + diag[3]*up[1]);
2223       uik[2] = -(diag[0]*up[2] + diag[2]*up[3]);
2224       uik[3] = -(diag[1]*up[2] + diag[3]*up[3]);
2225 
2226       /* update D(k) += -U(i,k)^T * U_bar(i,k): dk += uik*ba[ili] */
2227       dk[0] += uik[0]*up[0] + uik[1]*up[1];
2228       dk[1] += uik[2]*up[0] + uik[3]*up[1];
2229       dk[2] += uik[0]*up[2] + uik[1]*up[3];
2230       dk[3] += uik[2]*up[2] + uik[3]*up[3];
2231 
2232       /* update -U(i,k): ba[ili] = uik */
2233       ierr = PetscMemcpy(ba+ili*bs2,uik,bs2*sizeof(MatScalar));CHKERRQ(ierr);
2234 
2235       /* add multiple of row i to k-th row ... */
2236       jmin = ili + 1; jmax = bi[i+1];
2237       if (jmin < jmax){
2238         for (j=jmin; j<jmax; j++) {
2239           /* rtmp += -U(i,k)^T * U_bar(i,j): rtmp[bj[j]] += uik*ba[j]; */
2240           rtmp_ptr = rtmp + bj[j]*bs2;
2241           up = ba + j*bs2;
2242           rtmp_ptr[0] += uik[0]*up[0] + uik[1]*up[1];
2243           rtmp_ptr[1] += uik[2]*up[0] + uik[3]*up[1];
2244           rtmp_ptr[2] += uik[0]*up[2] + uik[1]*up[3];
2245           rtmp_ptr[3] += uik[2]*up[2] + uik[3]*up[3];
2246         }
2247 
2248         /* ... add i to row list for next nonzero entry */
2249         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
2250         j     = bj[jmin];
2251         jl[i] = jl[j]; jl[j] = i; /* update jl */
2252       }
2253       i = nexti; /* printf("                  pivot row i=%d\n",i);  */
2254     }
2255 #ifdef CONT
2256     /* check for zero pivot and save diagoanl element */
2257     if (dk == 0.0){
2258       SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot");
2259     }else if (PetscRealPart(dk) < 0){
2260       ierr = PetscPrintf(PETSC_COMM_SELF,"Negative pivot: d[%d] = %g\n",k,dk);
2261     }
2262 #endif
2263     /* save nonzero entries in k-th row of U ... */
2264 
2265     /* invert diagonal block: ba[k] = 1.0/dk  */
2266     diag = ba+k*bs2;
2267     ierr = PetscMemcpy(diag,dk,bs2*sizeof(MatScalar));CHKERRQ(ierr);
2268     ierr = Kernel_A_gets_inverse_A_2(diag);CHKERRQ(ierr);
2269 
2270     jmin = bi[k]; jmax = bi[k+1];
2271     if (jmin < jmax) {
2272       for (j=jmin; j<jmax; j++){
2273          juj = bj[j];
2274 
2275          /* ba[j] = rtmp[juj]; rtmp[juj] = 0.0; */
2276          up       = ba + j*bs2;
2277          rtmp_ptr = rtmp + juj*bs2;
2278          for (k1=0; k1<bs2; k1++){
2279            *up = *rtmp_ptr; *rtmp_ptr = 0.0;
2280            up++; rtmp_ptr++;
2281          }
2282       }
2283       /* ... add k to row list for first nonzero entry in k-th row */
2284       il[k] = jmin;
2285       i     = bj[jmin];
2286       jl[k] = jl[i]; jl[i] = k;
2287     }
2288   }
2289 
2290   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2291   ierr = PetscFree(il);CHKERRQ(ierr);
2292   ierr = PetscFree(jl);CHKERRQ(ierr);
2293   ierr = PetscFree(dk);CHKERRQ(ierr);
2294   ierr = PetscFree(uik);CHKERRQ(ierr);
2295   if (a->permute){
2296     ierr = PetscFree(aa);CHKERRQ(ierr);
2297   }
2298 
2299   ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr);
2300   C->factor    = FACTOR_CHOLESKY;
2301   /* C->factor    = FACTOR_LU; */
2302   C->assembled = PETSC_TRUE;
2303   PLogFlops(b->mbs);
2304   PetscFunctionReturn(0);
2305 }
2306 
2307 /*
2308       Version for when blocks are 2 by 2 Using natural ordering
2309 */
2310 #undef __FUNC__
2311 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_2_NaturalOrdering"
2312 int MatCholeskyFactorNumeric_SeqSBAIJ_2_NaturalOrdering(Mat A,Mat *B)
2313 {
2314   Mat                C = *B;
2315   Mat_SeqBAIJ        *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
2316   int                ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
2317   int                *ajtmpold,*ajtmp,nz,row;
2318   int                *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
2319   MatScalar          *pv,*v,*rtmp,*pc,*w,*x;
2320   MatScalar          p1,p2,p3,p4,m1,m2,m3,m4,x1,x2,x3,x4;
2321   MatScalar          *ba = b->a,*aa = a->a;
2322 
2323   PetscFunctionBegin;
2324   rtmp  = (MatScalar*)PetscMalloc(4*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
2325 
2326   for (i=0; i<n; i++) {
2327     nz    = bi[i+1] - bi[i];
2328     ajtmp = bj + bi[i];
2329     for  (j=0; j<nz; j++) {
2330       x = rtmp+4*ajtmp[j];
2331       x[0]  = x[1]  = x[2]  = x[3]  = 0.0;
2332     }
2333     /* load in initial (unfactored row) */
2334     nz       = ai[i+1] - ai[i];
2335     ajtmpold = aj + ai[i];
2336     v        = aa + 4*ai[i];
2337     for (j=0; j<nz; j++) {
2338       x    = rtmp+4*ajtmpold[j];
2339       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
2340       v    += 4;
2341     }
2342     row = *ajtmp++;
2343     while (row < i) {
2344       pc  = rtmp + 4*row;
2345       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
2346       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0) {
2347         pv = ba + 4*diag_offset[row];
2348         pj = bj + diag_offset[row] + 1;
2349         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
2350         pc[0] = m1 = p1*x1 + p3*x2;
2351         pc[1] = m2 = p2*x1 + p4*x2;
2352         pc[2] = m3 = p1*x3 + p3*x4;
2353         pc[3] = m4 = p2*x3 + p4*x4;
2354         nz = bi[row+1] - diag_offset[row] - 1;
2355         pv += 4;
2356         for (j=0; j<nz; j++) {
2357           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
2358           x    = rtmp + 4*pj[j];
2359           x[0] -= m1*x1 + m3*x2;
2360           x[1] -= m2*x1 + m4*x2;
2361           x[2] -= m1*x3 + m3*x4;
2362           x[3] -= m2*x3 + m4*x4;
2363           pv   += 4;
2364         }
2365         PLogFlops(16*nz+12);
2366       }
2367       row = *ajtmp++;
2368     }
2369     /* finished row so stick it into b->a */
2370     pv = ba + 4*bi[i];
2371     pj = bj + bi[i];
2372     nz = bi[i+1] - bi[i];
2373     for (j=0; j<nz; j++) {
2374       x      = rtmp+4*pj[j];
2375       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
2376       pv   += 4;
2377     }
2378     /* invert diagonal block */
2379     w = ba + 4*diag_offset[i];
2380     ierr = Kernel_A_gets_inverse_A_2(w);CHKERRQ(ierr);
2381     /*Kernel_A_gets_inverse_A(bs,w,v_pivots,v_work);*/
2382   }
2383 
2384   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2385   C->factor    = FACTOR_LU;
2386   C->assembled = PETSC_TRUE;
2387   PLogFlops(1.3333*8*b->mbs); /* from inverting diagonal blocks */
2388   PetscFunctionReturn(0);
2389 }
2390 
2391 /*
2392     Numeric (-UT)*D*(-U) factorization for SBAIJ format. Modified from SNF of YSMP.
2393     Version for blocks are 1 by 1.
2394 */
2395 #undef __FUNC__
2396 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_1"
2397 int MatCholeskyFactorNumeric_SeqSBAIJ_1(Mat A,Mat *B)
2398 {
2399   Mat                C = *B;
2400   Mat_SeqSBAIJ       *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data;
2401   IS                 ip = b->row;
2402   int                *rip,ierr,i,j,mbs = a->mbs,*bi = b->i,*bj = b->j;
2403   int                *ai,*aj,*r;
2404   MatScalar          *rtmp;
2405   MatScalar          *ba = b->a,*aa,ak;
2406   MatScalar          dk,uikdi;
2407   int                k,jmin,jmax,*jl,*il,vj,nexti,juj,ili;
2408 
2409   PetscFunctionBegin;
2410   ierr  = ISGetIndices(ip,&rip);CHKERRQ(ierr);
2411 
2412   if (!a->permute){
2413     ai = a->i; aj = a->j; aa = a->a;
2414   } else {
2415     ai = a->inew; aj = a->jnew;
2416     aa = (MatScalar*)PetscMalloc(ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa);
2417     ierr = PetscMemcpy(aa,a->a,ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr);
2418     r   = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(r);
2419     ierr= PetscMemcpy(r,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr);
2420 
2421     jmin = ai[0]; jmax = ai[mbs];
2422     for (j=jmin; j<jmax; j++){
2423       while (r[j] != j){
2424         k = r[j]; r[j] = r[k]; r[k] = k;
2425         ak = aa[k]; aa[k] = aa[j]; aa[j] = ak;
2426       }
2427     }
2428     ierr = PetscFree(r);CHKERRA(ierr);
2429   }
2430 
2431   /* initialization */
2432   /* il and jl record the first nonzero element in each row of the accessing
2433      window U(0:k, k:mbs-1).
2434      jl:    list of rows to be added to uneliminated rows
2435             i>= k: jl(i) is the first row to be added to row i
2436             i<  k: jl(i) is the row following row i in some list of rows
2437             jl(i) = mbs indicates the end of a list
2438      il(i): points to the first nonzero element in columns k,...,mbs-1 of
2439             row i of U */
2440   rtmp  = (MatScalar*)PetscMalloc(mbs*sizeof(MatScalar));CHKPTRQ(rtmp);
2441   il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il);
2442   jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl);
2443   for (i=0; i<mbs; i++) {
2444     rtmp[i] = 0.0; jl[i] = mbs; il[0] = 0;
2445   }
2446 
2447   /* for each row k */
2448   for (k = 0; k<mbs; k++){
2449 
2450     /*initialize k-th row with elements nonzero in row perm(k) of A */
2451     jmin = ai[rip[k]]; jmax = ai[rip[k]+1];
2452     if (jmin < jmax) {
2453       for (j = jmin; j < jmax; j++){
2454         vj = rip[aj[j]];
2455         if (k <= vj) rtmp[vj] = aa[j];
2456       }
2457     }
2458 
2459     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
2460     dk = rtmp[k];
2461     i = jl[k]; /* first row to be added to k_th row  */
2462     /* printf(" k=%d, pivot row = %d\n",k,i); */
2463 
2464     while (i < mbs){
2465       nexti = jl[i]; /* next row to be added to k_th row */
2466 
2467       /* compute multiplier, update D(k) and U(i,k) */
2468       ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
2469       uikdi = - ba[ili]*ba[i];
2470       dk += uikdi*ba[ili];
2471       ba[ili] = uikdi; /* -U(i,k) */
2472 
2473       /* add multiple of row i to k-th row ... */
2474       jmin = ili + 1; jmax = bi[i+1];
2475       if (jmin < jmax){
2476         for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j];
2477         /* ... add i to row list for next nonzero entry */
2478         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
2479         j     = bj[jmin];
2480         jl[i] = jl[j]; jl[j] = i; /* update jl */
2481       }
2482       i = nexti; /* printf("                  pivot row i=%d\n",i);  */
2483     }
2484 
2485     /* check for zero pivot and save diagoanl element */
2486     if (dk == 0.0){
2487       SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot");
2488     }else if (PetscRealPart(dk) < 0){
2489       ierr = PetscPrintf(PETSC_COMM_SELF,"Negative pivot: d[%d] = %g\n",k,dk);
2490     }
2491 
2492     /* save nonzero entries in k-th row of U ... */
2493     ba[k] = 1.0/dk;
2494     jmin = bi[k]; jmax = bi[k+1];
2495     if (jmin < jmax) {
2496       for (j=jmin; j<jmax; j++){
2497          juj = bj[j]; ba[j] = rtmp[juj]; rtmp[juj] = 0.0;
2498       }
2499       /* ... add k to row list for first nonzero entry in k-th row */
2500       il[k] = jmin;
2501       i     = bj[jmin];
2502       jl[k] = jl[i]; jl[i] = k;
2503     }
2504   }
2505 
2506   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2507   ierr = PetscFree(il);CHKERRQ(ierr);
2508   ierr = PetscFree(jl);CHKERRQ(ierr);
2509   if (a->permute){
2510     ierr = PetscFree(aa);CHKERRQ(ierr);
2511   }
2512 
2513   ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr);
2514   C->factor    = FACTOR_CHOLESKY;
2515   /* C->factor    = FACTOR_LU; */
2516   C->assembled = PETSC_TRUE;
2517   PLogFlops(b->mbs);
2518   PetscFunctionReturn(0);
2519 }
2520 
2521 #undef __FUNC__
2522 #define __FUNC__ "MatCholeskyFactor_SeqSBAIJ"
2523 int MatCholeskyFactor_SeqSBAIJ(Mat A,IS perm,PetscReal f)
2524 {
2525   int ierr;
2526   Mat C;
2527 
2528   PetscFunctionBegin;
2529   ierr = MatCholeskyFactorSymbolic(A,perm,f,&C);CHKERRQ(ierr);
2530   ierr = MatCholeskyFactorNumeric(A,&C);CHKERRQ(ierr);
2531   ierr = MatHeaderCopy(A,C);CHKERRQ(ierr);
2532   PetscFunctionReturn(0);
2533 }
2534 
2535 
2536