xref: /petsc/src/mat/impls/sbaij/seq/sbaijfact.c (revision 936bb23250dc8eb56a8ec3ef019dcd05eecdd78c)
1 /* Using Modified Sparse Row (MSR) storage.
2 See page 85, "Iterative Methods ..." by Saad. */
3 
4 /*$Id: sbaijfact.c,v 1.36 2000/10/30 21:30:19 hzhang Exp hzhang $*/
5 /*
6     Symbolic U^T*D*U factorization for SBAIJ format. Modified from SSF of YSMP.
7 */
8 #include "sbaij.h"
9 #include "src/mat/impls/baij/seq/baij.h"
10 #include "src/vec/vecimpl.h"
11 #include "src/inline/ilu.h"
12 #include "include/petscis.h"
13 
14 #undef __FUNC__
15 #define __FUNC__ "MatCholeskyFactorSymbolic_SeqSBAIJ"
16 int MatCholeskyFactorSymbolic_SeqSBAIJ(Mat A,IS perm,PetscReal f,Mat *B)
17 {
18   Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b;
19   int         *rip,ierr,i,mbs = a->mbs,*ai,*aj;
20   int         *jutmp,bs = a->bs,bs2=a->bs2;
21   int         m,nzi,realloc = 0;
22   int         *jl,*q,jumin,jmin,jmax,juptr,nzk,qm,*iu,*ju,k,j,vj,umax,maxadd;
23   /* PetscTruth  ident; */
24 
25   PetscFunctionBegin;
26   PetscValidHeaderSpecific(perm,IS_COOKIE);
27   if (A->M != A->N) SETERRQ(PETSC_ERR_ARG_WRONG,"matrix must be square");
28 
29   /* check whether perm is the identity mapping */
30   /*
31   ierr = ISView(perm, VIEWER_STDOUT_SELF);CHKERRA(ierr);
32   ierr = ISIdentity(perm,&ident);CHKERRQ(ierr);
33   printf("ident = %d\n", ident);
34   */
35   ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
36   for (i=0; i<mbs; i++){
37     if (rip[i] != i){
38       a->permute = PETSC_TRUE;
39       /* printf("non-trivial perm\n"); */
40       break;
41     }
42   }
43 
44   if (!a->permute){ /* without permutation */
45     ai = a->i; aj = a->j;
46   } else {       /* non-trivial permutation */
47     ierr = MatReorderingSeqSBAIJ(A, perm);CHKERRA(ierr);
48     ai = a->inew; aj = a->jnew;
49   }
50 
51   /* initialization */
52   /* Don't know how many column pointers are needed so estimate.
53      Use Modified Sparse Row storage for u and ju, see Sasd pp.85 */
54   iu   = (int*)PetscMalloc((mbs+1)*sizeof(int));CHKPTRQ(iu);
55   umax = (int)(f*ai[mbs] + 1); umax += mbs + 1;
56   ju   = (int*)PetscMalloc(umax*sizeof(int));CHKPTRQ(ju);
57   iu[0] = mbs+1;
58   juptr = mbs;
59   jl =  (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl);
60   q  =  (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(q);
61   for (i=0; i<mbs; i++){
62     jl[i] = mbs; q[i] = 0;
63   }
64 
65   /* for each row k */
66   for (k=0; k<mbs; k++){
67     nzk = 0; /* num. of nz blocks in k-th block row with diagonal block excluded */
68     q[k] = mbs;
69     /* initialize nonzero structure of k-th row to row rip[k] of A */
70     jmin = ai[rip[k]];
71     jmax = ai[rip[k]+1];
72     for (j=jmin; j<jmax; j++){
73       vj = rip[aj[j]]; /* col. value */
74       if(vj > k){
75         qm = k;
76         do {
77           m  = qm; qm = q[m];
78         } while(qm < vj);
79         if (qm == vj) {
80           printf(" error: duplicate entry in A\n"); break;
81         }
82         nzk++;
83         q[m] = vj;
84         q[vj] = qm;
85       } /* if(vj > k) */
86     } /* for (j=jmin; j<jmax; j++) */
87 
88     /* modify nonzero structure of k-th row by computing fill-in
89        for each row i to be merged in */
90     i = k;
91     i = jl[i]; /* next pivot row (== mbs for symbolic factorization) */
92     /* printf(" next pivot row i=%d\n",i); */
93     while (i < mbs){
94       /* merge row i into k-th row */
95       nzi = iu[i+1] - (iu[i]+1);
96       jmin = iu[i] + 1; jmax = iu[i] + nzi;
97       qm = k;
98       for (j=jmin; j<jmax+1; j++){
99         vj = ju[j];
100         do {
101           m = qm; qm = q[m];
102         } while (qm < vj);
103         if (qm != vj){
104          nzk++; q[m] = vj; q[vj] = qm; qm = vj;
105         }
106       }
107       i = jl[i]; /* next pivot row */
108     }
109 
110     /* add k to row list for first nonzero element in k-th row */
111     if (nzk > 0){
112       i = q[k]; /* col value of first nonzero element in U(k, k+1:mbs-1) */
113       jl[k] = jl[i]; jl[i] = k;
114     }
115     iu[k+1] = iu[k] + nzk;   /* printf(" iu[%d]=%d, umax=%d\n", k+1, iu[k+1],umax);*/
116 
117     /* allocate more space to ju if needed */
118     if (iu[k+1] > umax) { printf("allocate more space, iu[%d]=%d > umax=%d\n",k+1, iu[k+1],umax);
119       /* estimate how much additional space we will need */
120       /* use the strategy suggested by David Hysom <hysom@perch-t.icase.edu> */
121       /* just double the memory each time */
122       maxadd = umax;
123       if (maxadd < nzk) maxadd = (mbs-k)*(nzk+1)/2;
124       umax += maxadd;
125 
126       /* allocate a longer ju */
127       jutmp = (int*)PetscMalloc(umax*sizeof(int));CHKPTRQ(jutmp);
128       ierr  = PetscMemcpy(jutmp,ju,iu[k]*sizeof(int));CHKERRQ(ierr);
129       ierr  = PetscFree(ju);CHKERRQ(ierr);
130       ju    = jutmp;
131       realloc++; /* count how many times we realloc */
132     }
133 
134     /* save nonzero structure of k-th row in ju */
135     i=k;
136     jumin = juptr + 1; juptr += nzk;
137     for (j=jumin; j<juptr+1; j++){
138       i=q[i];
139       ju[j]=i;
140     }
141   }
142 
143   if (ai[mbs] != 0) {
144     PetscReal af = ((PetscReal)iu[mbs])/((PetscReal)ai[mbs]);
145     PLogInfo(A,"MatCholeskyFactorSymbolic_SeqSBAIJ:Reallocs %d Fill ratio:given %g needed %g\n",realloc,f,af);
146     PLogInfo(A,"MatCholeskyFactorSymbolic_SeqSBAIJ:Run with -pc_lu_fill %g or use \n",af);
147     PLogInfo(A,"MatCholeskyFactorSymbolic_SeqSBAIJ:PCLUSetFill(pc,%g);\n",af);
148     PLogInfo(A,"MatCholeskyFactorSymbolic_SeqSBAIJ:for best performance.\n");
149   } else {
150      PLogInfo(A,"MatCholeskyFactorSymbolic_SeqSBAIJ:Empty matrix.\n");
151   }
152 
153   ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
154   ierr = PetscFree(q);CHKERRQ(ierr);
155   ierr = PetscFree(jl);CHKERRQ(ierr);
156 
157   /* put together the new matrix */
158   ierr = MatCreateSeqSBAIJ(A->comm,bs,bs*mbs,bs*mbs,0,PETSC_NULL,B);CHKERRQ(ierr);
159   /* PLogObjectParent(*B,iperm); */
160   b = (Mat_SeqSBAIJ*)(*B)->data;
161   ierr = PetscFree(b->imax);CHKERRQ(ierr);
162   b->singlemalloc = PETSC_FALSE;
163   /* the next line frees the default space generated by the Create() */
164   ierr = PetscFree(b->a);CHKERRQ(ierr);
165   ierr = PetscFree(b->ilen);CHKERRQ(ierr);
166   b->a          = (MatScalar*)PetscMalloc((iu[mbs]+1)*sizeof(MatScalar)*bs2);CHKPTRQ(b->a);
167   b->j          = ju;
168   b->i          = iu;
169   b->diag       = 0;
170   b->ilen       = 0;
171   b->imax       = 0;
172   b->row        = perm;
173   ierr          = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
174   b->icol       = perm;
175   ierr          = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
176   b->solve_work = (Scalar*)PetscMalloc((bs*mbs+bs)*sizeof(Scalar));CHKPTRQ(b->solve_work);
177   /* In b structure:  Free imax, ilen, old a, old j.
178      Allocate idnew, solve_work, new a, new j */
179   PLogObjectMemory(*B,(iu[mbs]-mbs)*(sizeof(int)+sizeof(MatScalar)));
180   b->s_maxnz = b->s_nz = iu[mbs];
181 
182   (*B)->factor                 = FACTOR_CHOLESKY;
183   (*B)->info.factor_mallocs    = realloc;
184   (*B)->info.fill_ratio_given  = f;
185   if (ai[mbs] != 0) {
186     (*B)->info.fill_ratio_needed = ((PetscReal)iu[mbs])/((PetscReal)ai[mbs]);
187   } else {
188     (*B)->info.fill_ratio_needed = 0.0;
189   }
190 #ifdef TEMP
191   for (k=0; k<mbs; k++){
192     nzk = b->i[k+1] - b->i[k];
193     printf("\n b->i[%d]: %d, nzk: %d\n",k,b->i[k],nzk);
194     jmin = b->i[k]; jmax = b->i[k+1];
195     for (j=jmin; j<jmax; j++){
196       printf(" %d,",b->j[j]);
197     }
198   }
199 #endif
200   PetscFunctionReturn(0);
201 }
202 
203 #undef __FUNC__
204 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_N"
205 int MatCholeskyFactorNumeric_SeqSBAIJ_N(Mat A,Mat *B)
206 {
207   Mat                C = *B;
208   Mat_SeqBAIJ        *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
209   IS                 isrow = b->row,isicol = b->icol;
210   int                *r,*ic,ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
211   int                *ajtmpold,*ajtmp,nz,row,bslog,*ai=a->i,*aj=a->j,k,flg;
212   int                *diag_offset=b->diag,diag,bs=a->bs,bs2 = a->bs2,*v_pivots,*pj;
213   MatScalar          *ba = b->a,*aa = a->a,*pv,*v,*rtmp,*multiplier,*v_work,*pc,*w;
214 
215   PetscFunctionBegin;
216   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
217   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
218   rtmp = (MatScalar*)PetscMalloc(bs2*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
219   ierr = PetscMemzero(rtmp,bs2*(n+1)*sizeof(MatScalar));CHKERRQ(ierr);
220   /* generate work space needed by dense LU factorization */
221   v_work     = (MatScalar*)PetscMalloc(bs*sizeof(int) + (bs+bs2)*sizeof(MatScalar));CHKPTRQ(v_work);
222   multiplier = v_work + bs;
223   v_pivots   = (int*)(multiplier + bs2);
224 
225   /* flops in while loop */
226   bslog = 2*bs*bs2;
227 
228   for (i=0; i<n; i++) {
229     nz    = bi[i+1] - bi[i];
230     ajtmp = bj + bi[i];
231     for  (j=0; j<nz; j++) {
232       ierr = PetscMemzero(rtmp+bs2*ajtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
233     }
234     /* load in initial (unfactored row) */
235     nz       = ai[r[i]+1] - ai[r[i]];
236     ajtmpold = aj + ai[r[i]];
237     v        = aa + bs2*ai[r[i]];
238     for (j=0; j<nz; j++) {
239       ierr = PetscMemcpy(rtmp+bs2*ic[ajtmpold[j]],v+bs2*j,bs2*sizeof(MatScalar));CHKERRQ(ierr);
240     }
241     row = *ajtmp++;
242     while (row < i) {
243       pc = rtmp + bs2*row;
244 /*      if (*pc) { */
245       for (flg=0,k=0; k<bs2; k++) { if (pc[k]!=0.0) { flg =1; break; }}
246       if (flg) {
247         pv = ba + bs2*diag_offset[row];
248         pj = bj + diag_offset[row] + 1;
249         Kernel_A_gets_A_times_B(bs,pc,pv,multiplier);
250         nz = bi[row+1] - diag_offset[row] - 1;
251         pv += bs2;
252         for (j=0; j<nz; j++) {
253           Kernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j);
254         }
255         PLogFlops(bslog*(nz+1)-bs);
256       }
257         row = *ajtmp++;
258     }
259     /* finished row so stick it into b->a */
260     pv = ba + bs2*bi[i];
261     pj = bj + bi[i];
262     nz = bi[i+1] - bi[i];
263     for (j=0; j<nz; j++) {
264       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
265     }
266     diag = diag_offset[i] - bi[i];
267     /* invert diagonal block */
268     w = pv + bs2*diag;
269     Kernel_A_gets_inverse_A(bs,w,v_pivots,v_work);
270   }
271 
272   ierr = PetscFree(rtmp);CHKERRQ(ierr);
273   ierr = PetscFree(v_work);CHKERRQ(ierr);
274   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
275   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
276   C->factor = FACTOR_LU;
277   C->assembled = PETSC_TRUE;
278   PLogFlops(1.3333*bs*bs2*b->mbs); /* from inverting diagonal blocks */
279   PetscFunctionReturn(0);
280 }
281 
282 /*
283       Version for when blocks are 7 by 7
284 */
285 #undef __FUNC__
286 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_7"
287 int MatCholeskyFactorNumeric_SeqSBAIJ_7(Mat A,Mat *B)
288 {
289   Mat         C = *B;
290   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
291   IS          isrow = b->row,isicol = b->icol;
292   int         *r,*ic,ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
293   int         *ajtmpold,*ajtmp,nz,row;
294   int         *diag_offset = b->diag,idx,*ai=a->i,*aj=a->j,*pj;
295   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
296   MatScalar   p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
297   MatScalar   p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
298   MatScalar   x17,x18,x19,x20,x21,x22,x23,x24,x25,p10,p11,p12,p13,p14;
299   MatScalar   p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,m10,m11,m12;
300   MatScalar   m13,m14,m15,m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
301   MatScalar   p26,p27,p28,p29,p30,p31,p32,p33,p34,p35,p36;
302   MatScalar   p37,p38,p39,p40,p41,p42,p43,p44,p45,p46,p47,p48,p49;
303   MatScalar   x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36;
304   MatScalar   x37,x38,x39,x40,x41,x42,x43,x44,x45,x46,x47,x48,x49;
305   MatScalar   m26,m27,m28,m29,m30,m31,m32,m33,m34,m35,m36;
306   MatScalar   m37,m38,m39,m40,m41,m42,m43,m44,m45,m46,m47,m48,m49;
307   MatScalar   *ba = b->a,*aa = a->a;
308 
309   PetscFunctionBegin;
310   ierr  = ISGetIndices(isrow,&r);CHKERRQ(ierr);
311   ierr  = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
312   rtmp  = (MatScalar*)PetscMalloc(49*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
313 
314   for (i=0; i<n; i++) {
315     nz    = bi[i+1] - bi[i];
316     ajtmp = bj + bi[i];
317     for  (j=0; j<nz; j++) {
318       x = rtmp+49*ajtmp[j];
319       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
320       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
321       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = x[25] = 0.0 ;
322       x[26] = x[27] = x[28] = x[29] = x[30] = x[31] = x[32] = x[33] = 0.0 ;
323       x[34] = x[35] = x[36] = x[37] = x[38] = x[39] = x[40] = x[41] = 0.0 ;
324       x[42] = x[43] = x[44] = x[45] = x[46] = x[47] = x[48] = 0.0 ;
325     }
326     /* load in initial (unfactored row) */
327     idx      = r[i];
328     nz       = ai[idx+1] - ai[idx];
329     ajtmpold = aj + ai[idx];
330     v        = aa + 49*ai[idx];
331     for (j=0; j<nz; j++) {
332       x    = rtmp+49*ic[ajtmpold[j]];
333       x[0] =  v[0];  x[1] =  v[1];  x[2] =  v[2];  x[3] =  v[3];
334       x[4] =  v[4];  x[5] =  v[5];  x[6] =  v[6];  x[7] =  v[7];
335       x[8] =  v[8];  x[9] =  v[9];  x[10] = v[10]; x[11] = v[11];
336       x[12] = v[12]; x[13] = v[13]; x[14] = v[14]; x[15] = v[15];
337       x[16] = v[16]; x[17] = v[17]; x[18] = v[18]; x[19] = v[19];
338       x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23];
339       x[24] = v[24]; x[25] = v[25]; x[26] = v[26]; x[27] = v[27];
340       x[28] = v[28]; x[29] = v[29]; x[30] = v[30]; x[31] = v[31];
341       x[32] = v[32]; x[33] = v[33]; x[34] = v[34]; x[35] = v[35];
342       x[36] = v[36]; x[37] = v[37]; x[38] = v[38]; x[39] = v[39];
343       x[40] = v[40]; x[41] = v[41]; x[42] = v[42]; x[43] = v[43];
344       x[44] = v[44]; x[45] = v[45]; x[46] = v[46]; x[47] = v[47];
345       x[48] = v[48];
346       v    += 49;
347     }
348     row = *ajtmp++;
349     while (row < i) {
350       pc  =  rtmp + 49*row;
351       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
352       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];
353       p9  = pc[8];  p10 = pc[9];  p11 = pc[10]; p12 = pc[11];
354       p13 = pc[12]; p14 = pc[13]; p15 = pc[14]; p16 = pc[15];
355       p17 = pc[16]; p18 = pc[17]; p19 = pc[18]; p20 = pc[19];
356       p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
357       p25 = pc[24]; p26 = pc[25]; p27 = pc[26]; p28 = pc[27];
358       p29 = pc[28]; p30 = pc[29]; p31 = pc[30]; p32 = pc[31];
359       p33 = pc[32]; p34 = pc[33]; p35 = pc[34]; p36 = pc[35];
360       p37 = pc[36]; p38 = pc[37]; p39 = pc[38]; p40 = pc[39];
361       p41 = pc[40]; p42 = pc[41]; p43 = pc[42]; p44 = pc[43];
362       p45 = pc[44]; p46 = pc[45]; p47 = pc[46]; p48 = pc[47];
363       p49 = pc[48];
364       if (p1  != 0.0 || p2  != 0.0 || p3  != 0.0 || p4  != 0.0 ||
365           p5  != 0.0 || p6  != 0.0 || p7  != 0.0 || p8  != 0.0 ||
366           p9  != 0.0 || p10 != 0.0 || p11 != 0.0 || p12 != 0.0 ||
367           p13 != 0.0 || p14 != 0.0 || p15 != 0.0 || p16 != 0.0 ||
368           p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 ||
369           p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 ||
370           p25 != 0.0 || p26 != 0.0 || p27 != 0.0 || p28 != 0.0 ||
371           p29 != 0.0 || p30 != 0.0 || p31 != 0.0 || p32 != 0.0 ||
372           p33 != 0.0 || p34 != 0.0 || p35 != 0.0 || p36 != 0.0 ||
373           p37 != 0.0 || p38 != 0.0 || p39 != 0.0 || p40 != 0.0 ||
374           p41 != 0.0 || p42 != 0.0 || p43 != 0.0 || p44 != 0.0 ||
375           p45 != 0.0 || p46 != 0.0 || p47 != 0.0 || p48 != 0.0 ||
376           p49 != 0.0) {
377         pv = ba + 49*diag_offset[row];
378         pj = bj + diag_offset[row] + 1;
379 	x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
380 	x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
381 	x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
382 	x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
383 	x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
384 	x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
385 	x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
386 	x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
387 	x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
388 	x37 = pv[36]; x38 = pv[37]; x39 = pv[38]; x40 = pv[39];
389 	x41 = pv[40]; x42 = pv[41]; x43 = pv[42]; x44 = pv[43];
390 	x45 = pv[44]; x46 = pv[45]; x47 = pv[46]; x48 = pv[47];
391 	x49 = pv[48];
392         pc[0]  = m1  = p1*x1  + p8*x2   + p15*x3  + p22*x4  + p29*x5  + p36*x6 + p43*x7;
393         pc[1]  = m2  = p2*x1  + p9*x2   + p16*x3  + p23*x4  + p30*x5  + p37*x6 + p44*x7;
394         pc[2]  = m3  = p3*x1  + p10*x2  + p17*x3  + p24*x4  + p31*x5  + p38*x6 + p45*x7;
395         pc[3]  = m4  = p4*x1  + p11*x2  + p18*x3  + p25*x4  + p32*x5  + p39*x6 + p46*x7;
396         pc[4]  = m5  = p5*x1  + p12*x2  + p19*x3  + p26*x4  + p33*x5  + p40*x6 + p47*x7;
397         pc[5]  = m6  = p6*x1  + p13*x2  + p20*x3  + p27*x4  + p34*x5  + p41*x6 + p48*x7;
398         pc[6]  = m7  = p7*x1  + p14*x2  + p21*x3  + p28*x4  + p35*x5  + p42*x6 + p49*x7;
399 
400         pc[7]  = m8  = p1*x8  + p8*x9   + p15*x10 + p22*x11 + p29*x12 + p36*x13 + p43*x14;
401         pc[8]  = m9  = p2*x8  + p9*x9   + p16*x10 + p23*x11 + p30*x12 + p37*x13 + p44*x14;
402         pc[9]  = m10 = p3*x8  + p10*x9  + p17*x10 + p24*x11 + p31*x12 + p38*x13 + p45*x14;
403         pc[10] = m11 = p4*x8  + p11*x9  + p18*x10 + p25*x11 + p32*x12 + p39*x13 + p46*x14;
404         pc[11] = m12 = p5*x8  + p12*x9  + p19*x10 + p26*x11 + p33*x12 + p40*x13 + p47*x14;
405         pc[12] = m13 = p6*x8  + p13*x9  + p20*x10 + p27*x11 + p34*x12 + p41*x13 + p48*x14;
406         pc[13] = m14 = p7*x8  + p14*x9  + p21*x10 + p28*x11 + p35*x12 + p42*x13 + p49*x14;
407 
408         pc[14] = m15 = p1*x15 + p8*x16  + p15*x17 + p22*x18 + p29*x19 + p36*x20 + p43*x21;
409         pc[15] = m16 = p2*x15 + p9*x16  + p16*x17 + p23*x18 + p30*x19 + p37*x20 + p44*x21;
410         pc[16] = m17 = p3*x15 + p10*x16 + p17*x17 + p24*x18 + p31*x19 + p38*x20 + p45*x21;
411         pc[17] = m18 = p4*x15 + p11*x16 + p18*x17 + p25*x18 + p32*x19 + p39*x20 + p46*x21;
412         pc[18] = m19 = p5*x15 + p12*x16 + p19*x17 + p26*x18 + p33*x19 + p40*x20 + p47*x21;
413         pc[19] = m20 = p6*x15 + p13*x16 + p20*x17 + p27*x18 + p34*x19 + p41*x20 + p48*x21;
414         pc[20] = m21 = p7*x15 + p14*x16 + p21*x17 + p28*x18 + p35*x19 + p42*x20 + p49*x21;
415 
416         pc[21] = m22 = p1*x22 + p8*x23  + p15*x24 + p22*x25 + p29*x26 + p36*x27 + p43*x28;
417         pc[22] = m23 = p2*x22 + p9*x23  + p16*x24 + p23*x25 + p30*x26 + p37*x27 + p44*x28;
418         pc[23] = m24 = p3*x22 + p10*x23 + p17*x24 + p24*x25 + p31*x26 + p38*x27 + p45*x28;
419         pc[24] = m25 = p4*x22 + p11*x23 + p18*x24 + p25*x25 + p32*x26 + p39*x27 + p46*x28;
420         pc[25] = m26 = p5*x22 + p12*x23 + p19*x24 + p26*x25 + p33*x26 + p40*x27 + p47*x28;
421         pc[26] = m27 = p6*x22 + p13*x23 + p20*x24 + p27*x25 + p34*x26 + p41*x27 + p48*x28;
422         pc[27] = m28 = p7*x22 + p14*x23 + p21*x24 + p28*x25 + p35*x26 + p42*x27 + p49*x28;
423 
424         pc[28] = m29 = p1*x29 + p8*x30  + p15*x31 + p22*x32 + p29*x33 + p36*x34 + p43*x35;
425         pc[29] = m30 = p2*x29 + p9*x30  + p16*x31 + p23*x32 + p30*x33 + p37*x34 + p44*x35;
426         pc[30] = m31 = p3*x29 + p10*x30 + p17*x31 + p24*x32 + p31*x33 + p38*x34 + p45*x35;
427         pc[31] = m32 = p4*x29 + p11*x30 + p18*x31 + p25*x32 + p32*x33 + p39*x34 + p46*x35;
428         pc[32] = m33 = p5*x29 + p12*x30 + p19*x31 + p26*x32 + p33*x33 + p40*x34 + p47*x35;
429         pc[33] = m34 = p6*x29 + p13*x30 + p20*x31 + p27*x32 + p34*x33 + p41*x34 + p48*x35;
430         pc[34] = m35 = p7*x29 + p14*x30 + p21*x31 + p28*x32 + p35*x33 + p42*x34 + p49*x35;
431 
432         pc[35] = m36 = p1*x36 + p8*x37  + p15*x38 + p22*x39 + p29*x40 + p36*x41 + p43*x42;
433         pc[36] = m37 = p2*x36 + p9*x37  + p16*x38 + p23*x39 + p30*x40 + p37*x41 + p44*x42;
434         pc[37] = m38 = p3*x36 + p10*x37 + p17*x38 + p24*x39 + p31*x40 + p38*x41 + p45*x42;
435         pc[38] = m39 = p4*x36 + p11*x37 + p18*x38 + p25*x39 + p32*x40 + p39*x41 + p46*x42;
436         pc[39] = m40 = p5*x36 + p12*x37 + p19*x38 + p26*x39 + p33*x40 + p40*x41 + p47*x42;
437         pc[40] = m41 = p6*x36 + p13*x37 + p20*x38 + p27*x39 + p34*x40 + p41*x41 + p48*x42;
438         pc[41] = m42 = p7*x36 + p14*x37 + p21*x38 + p28*x39 + p35*x40 + p42*x41 + p49*x42;
439 
440         pc[42] = m43 = p1*x43 + p8*x44  + p15*x45 + p22*x46 + p29*x47 + p36*x48 + p43*x49;
441         pc[43] = m44 = p2*x43 + p9*x44  + p16*x45 + p23*x46 + p30*x47 + p37*x48 + p44*x49;
442         pc[44] = m45 = p3*x43 + p10*x44 + p17*x45 + p24*x46 + p31*x47 + p38*x48 + p45*x49;
443         pc[45] = m46 = p4*x43 + p11*x44 + p18*x45 + p25*x46 + p32*x47 + p39*x48 + p46*x49;
444         pc[46] = m47 = p5*x43 + p12*x44 + p19*x45 + p26*x46 + p33*x47 + p40*x48 + p47*x49;
445         pc[47] = m48 = p6*x43 + p13*x44 + p20*x45 + p27*x46 + p34*x47 + p41*x48 + p48*x49;
446         pc[48] = m49 = p7*x43 + p14*x44 + p21*x45 + p28*x46 + p35*x47 + p42*x48 + p49*x49;
447 
448         nz = bi[row+1] - diag_offset[row] - 1;
449         pv += 49;
450         for (j=0; j<nz; j++) {
451 	  x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
452 	  x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
453 	  x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
454 	  x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
455 	  x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
456 	  x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
457 	  x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
458 	  x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
459 	  x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
460 	  x37 = pv[36]; x38 = pv[37]; x39 = pv[38]; x40 = pv[39];
461 	  x41 = pv[40]; x42 = pv[41]; x43 = pv[42]; x44 = pv[43];
462 	  x45 = pv[44]; x46 = pv[45]; x47 = pv[46]; x48 = pv[47];
463 	  x49 = pv[48];
464 	  x    = rtmp + 49*pj[j];
465 	  x[0]  -= m1*x1  + m8*x2   + m15*x3  + m22*x4  + m29*x5  + m36*x6 + m43*x7;
466 	  x[1]  -= m2*x1  + m9*x2   + m16*x3  + m23*x4  + m30*x5  + m37*x6 + m44*x7;
467 	  x[2]  -= m3*x1  + m10*x2  + m17*x3  + m24*x4  + m31*x5  + m38*x6 + m45*x7;
468 	  x[3]  -= m4*x1  + m11*x2  + m18*x3  + m25*x4  + m32*x5  + m39*x6 + m46*x7;
469 	  x[4]  -= m5*x1  + m12*x2  + m19*x3  + m26*x4  + m33*x5  + m40*x6 + m47*x7;
470 	  x[5]  -= m6*x1  + m13*x2  + m20*x3  + m27*x4  + m34*x5  + m41*x6 + m48*x7;
471 	  x[6]  -= m7*x1  + m14*x2  + m21*x3  + m28*x4  + m35*x5  + m42*x6 + m49*x7;
472 
473 	  x[7]  -= m1*x8  + m8*x9   + m15*x10 + m22*x11 + m29*x12 + m36*x13 + m43*x14;
474 	  x[8]  -= m2*x8  + m9*x9   + m16*x10 + m23*x11 + m30*x12 + m37*x13 + m44*x14;
475 	  x[9]  -= m3*x8  + m10*x9  + m17*x10 + m24*x11 + m31*x12 + m38*x13 + m45*x14;
476 	  x[10] -= m4*x8  + m11*x9  + m18*x10 + m25*x11 + m32*x12 + m39*x13 + m46*x14;
477 	  x[11] -= m5*x8  + m12*x9  + m19*x10 + m26*x11 + m33*x12 + m40*x13 + m47*x14;
478 	  x[12] -= m6*x8  + m13*x9  + m20*x10 + m27*x11 + m34*x12 + m41*x13 + m48*x14;
479 	  x[13] -= m7*x8  + m14*x9  + m21*x10 + m28*x11 + m35*x12 + m42*x13 + m49*x14;
480 
481 	  x[14] -= m1*x15 + m8*x16  + m15*x17 + m22*x18 + m29*x19 + m36*x20 + m43*x21;
482 	  x[15] -= m2*x15 + m9*x16  + m16*x17 + m23*x18 + m30*x19 + m37*x20 + m44*x21;
483 	  x[16] -= m3*x15 + m10*x16 + m17*x17 + m24*x18 + m31*x19 + m38*x20 + m45*x21;
484 	  x[17] -= m4*x15 + m11*x16 + m18*x17 + m25*x18 + m32*x19 + m39*x20 + m46*x21;
485 	  x[18] -= m5*x15 + m12*x16 + m19*x17 + m26*x18 + m33*x19 + m40*x20 + m47*x21;
486 	  x[19] -= m6*x15 + m13*x16 + m20*x17 + m27*x18 + m34*x19 + m41*x20 + m48*x21;
487 	  x[20] -= m7*x15 + m14*x16 + m21*x17 + m28*x18 + m35*x19 + m42*x20 + m49*x21;
488 
489 	  x[21] -= m1*x22 + m8*x23  + m15*x24 + m22*x25 + m29*x26 + m36*x27 + m43*x28;
490 	  x[22] -= m2*x22 + m9*x23  + m16*x24 + m23*x25 + m30*x26 + m37*x27 + m44*x28;
491 	  x[23] -= m3*x22 + m10*x23 + m17*x24 + m24*x25 + m31*x26 + m38*x27 + m45*x28;
492 	  x[24] -= m4*x22 + m11*x23 + m18*x24 + m25*x25 + m32*x26 + m39*x27 + m46*x28;
493 	  x[25] -= m5*x22 + m12*x23 + m19*x24 + m26*x25 + m33*x26 + m40*x27 + m47*x28;
494 	  x[26] -= m6*x22 + m13*x23 + m20*x24 + m27*x25 + m34*x26 + m41*x27 + m48*x28;
495 	  x[27] -= m7*x22 + m14*x23 + m21*x24 + m28*x25 + m35*x26 + m42*x27 + m49*x28;
496 
497 	  x[28] -= m1*x29 + m8*x30  + m15*x31 + m22*x32 + m29*x33 + m36*x34 + m43*x35;
498 	  x[29] -= m2*x29 + m9*x30  + m16*x31 + m23*x32 + m30*x33 + m37*x34 + m44*x35;
499 	  x[30] -= m3*x29 + m10*x30 + m17*x31 + m24*x32 + m31*x33 + m38*x34 + m45*x35;
500 	  x[31] -= m4*x29 + m11*x30 + m18*x31 + m25*x32 + m32*x33 + m39*x34 + m46*x35;
501 	  x[32] -= m5*x29 + m12*x30 + m19*x31 + m26*x32 + m33*x33 + m40*x34 + m47*x35;
502 	  x[33] -= m6*x29 + m13*x30 + m20*x31 + m27*x32 + m34*x33 + m41*x34 + m48*x35;
503 	  x[34] -= m7*x29 + m14*x30 + m21*x31 + m28*x32 + m35*x33 + m42*x34 + m49*x35;
504 
505 	  x[35] -= m1*x36 + m8*x37  + m15*x38 + m22*x39 + m29*x40 + m36*x41 + m43*x42;
506 	  x[36] -= m2*x36 + m9*x37  + m16*x38 + m23*x39 + m30*x40 + m37*x41 + m44*x42;
507 	  x[37] -= m3*x36 + m10*x37 + m17*x38 + m24*x39 + m31*x40 + m38*x41 + m45*x42;
508 	  x[38] -= m4*x36 + m11*x37 + m18*x38 + m25*x39 + m32*x40 + m39*x41 + m46*x42;
509 	  x[39] -= m5*x36 + m12*x37 + m19*x38 + m26*x39 + m33*x40 + m40*x41 + m47*x42;
510 	  x[40] -= m6*x36 + m13*x37 + m20*x38 + m27*x39 + m34*x40 + m41*x41 + m48*x42;
511 	  x[41] -= m7*x36 + m14*x37 + m21*x38 + m28*x39 + m35*x40 + m42*x41 + m49*x42;
512 
513 	  x[42] -= m1*x43 + m8*x44  + m15*x45 + m22*x46 + m29*x47 + m36*x48 + m43*x49;
514 	  x[43] -= m2*x43 + m9*x44  + m16*x45 + m23*x46 + m30*x47 + m37*x48 + m44*x49;
515 	  x[44] -= m3*x43 + m10*x44 + m17*x45 + m24*x46 + m31*x47 + m38*x48 + m45*x49;
516 	  x[45] -= m4*x43 + m11*x44 + m18*x45 + m25*x46 + m32*x47 + m39*x48 + m46*x49;
517 	  x[46] -= m5*x43 + m12*x44 + m19*x45 + m26*x46 + m33*x47 + m40*x48 + m47*x49;
518 	  x[47] -= m6*x43 + m13*x44 + m20*x45 + m27*x46 + m34*x47 + m41*x48 + m48*x49;
519 	  x[48] -= m7*x43 + m14*x44 + m21*x45 + m28*x46 + m35*x47 + m42*x48 + m49*x49;
520           pv   += 49;
521         }
522         PLogFlops(686*nz+637);
523       }
524       row = *ajtmp++;
525     }
526     /* finished row so stick it into b->a */
527     pv = ba + 49*bi[i];
528     pj = bj + bi[i];
529     nz = bi[i+1] - bi[i];
530     for (j=0; j<nz; j++) {
531       x      = rtmp+49*pj[j];
532       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
533       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7];
534       pv[8]  = x[8];  pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11];
535       pv[12] = x[12]; pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
536       pv[16] = x[16]; pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19];
537       pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23];
538       pv[24] = x[24]; pv[25] = x[25]; pv[26] = x[26]; pv[27] = x[27];
539       pv[28] = x[28]; pv[29] = x[29]; pv[30] = x[30]; pv[31] = x[31];
540       pv[32] = x[32]; pv[33] = x[33]; pv[34] = x[34]; pv[35] = x[35];
541       pv[36] = x[36]; pv[37] = x[37]; pv[38] = x[38]; pv[39] = x[39];
542       pv[40] = x[40]; pv[41] = x[41]; pv[42] = x[42]; pv[43] = x[43];
543       pv[44] = x[44]; pv[45] = x[45]; pv[46] = x[46]; pv[47] = x[47];
544       pv[48] = x[48];
545       pv   += 49;
546     }
547     /* invert diagonal block */
548     w = ba + 49*diag_offset[i];
549     ierr = Kernel_A_gets_inverse_A_7(w);CHKERRQ(ierr);
550   }
551 
552   ierr = PetscFree(rtmp);CHKERRQ(ierr);
553   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
554   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
555   C->factor = FACTOR_LU;
556   C->assembled = PETSC_TRUE;
557   PLogFlops(1.3333*343*b->mbs); /* from inverting diagonal blocks */
558   PetscFunctionReturn(0);
559 }
560 
561 /*
562       Version for when blocks are 7 by 7 Using natural ordering
563 */
564 #undef __FUNC__
565 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_7_NaturalOrdering"
566 int MatCholeskyFactorNumeric_SeqSBAIJ_7_NaturalOrdering(Mat A,Mat *B)
567 {
568   Mat          C = *B;
569   Mat_SeqBAIJ  *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
570   int          ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
571   int          *ajtmpold,*ajtmp,nz,row;
572   int          *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
573   MatScalar    *pv,*v,*rtmp,*pc,*w,*x;
574   MatScalar    x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15;
575   MatScalar    x16,x17,x18,x19,x20,x21,x22,x23,x24,x25;
576   MatScalar    p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15;
577   MatScalar    p16,p17,p18,p19,p20,p21,p22,p23,p24,p25;
578   MatScalar    m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12,m13,m14,m15;
579   MatScalar    m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
580   MatScalar    p26,p27,p28,p29,p30,p31,p32,p33,p34,p35,p36;
581   MatScalar    p37,p38,p39,p40,p41,p42,p43,p44,p45,p46,p47,p48,p49;
582   MatScalar    x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36;
583   MatScalar    x37,x38,x39,x40,x41,x42,x43,x44,x45,x46,x47,x48,x49;
584   MatScalar    m26,m27,m28,m29,m30,m31,m32,m33,m34,m35,m36;
585   MatScalar    m37,m38,m39,m40,m41,m42,m43,m44,m45,m46,m47,m48,m49;
586   MatScalar    *ba = b->a,*aa = a->a;
587 
588   PetscFunctionBegin;
589   rtmp  = (MatScalar*)PetscMalloc(49*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
590   for (i=0; i<n; i++) {
591     nz    = bi[i+1] - bi[i];
592     ajtmp = bj + bi[i];
593     for  (j=0; j<nz; j++) {
594       x = rtmp+49*ajtmp[j];
595       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
596       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
597       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = x[25] = 0.0 ;
598       x[26] = x[27] = x[28] = x[29] = x[30] = x[31] = x[32] = x[33] = 0.0 ;
599       x[34] = x[35] = x[36] = x[37] = x[38] = x[39] = x[40] = x[41] = 0.0 ;
600       x[42] = x[43] = x[44] = x[45] = x[46] = x[47] = x[48] = 0.0 ;
601     }
602     /* load in initial (unfactored row) */
603     nz       = ai[i+1] - ai[i];
604     ajtmpold = aj + ai[i];
605     v        = aa + 49*ai[i];
606     for (j=0; j<nz; j++) {
607       x    = rtmp+49*ajtmpold[j];
608       x[0] =  v[0];  x[1] =  v[1];  x[2] =  v[2];  x[3] =  v[3];
609       x[4] =  v[4];  x[5] =  v[5];  x[6] =  v[6];  x[7] =  v[7];
610       x[8] =  v[8];  x[9] =  v[9];  x[10] = v[10]; x[11] = v[11];
611       x[12] = v[12]; x[13] = v[13]; x[14] = v[14]; x[15] = v[15];
612       x[16] = v[16]; x[17] = v[17]; x[18] = v[18]; x[19] = v[19];
613       x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23];
614       x[24] = v[24]; x[25] = v[25]; x[26] = v[26]; x[27] = v[27];
615       x[28] = v[28]; x[29] = v[29]; x[30] = v[30]; x[31] = v[31];
616       x[32] = v[32]; x[33] = v[33]; x[34] = v[34]; x[35] = v[35];
617       x[36] = v[36]; x[37] = v[37]; x[38] = v[38]; x[39] = v[39];
618       x[40] = v[40]; x[41] = v[41]; x[42] = v[42]; x[43] = v[43];
619       x[44] = v[44]; x[45] = v[45]; x[46] = v[46]; x[47] = v[47];
620       x[48] = v[48];
621       v    += 49;
622     }
623     row = *ajtmp++;
624     while (row < i) {
625       pc  = rtmp + 49*row;
626       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
627       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];
628       p9  = pc[8];  p10 = pc[9];  p11 = pc[10]; p12 = pc[11];
629       p13 = pc[12]; p14 = pc[13]; p15 = pc[14]; p16 = pc[15];
630       p17 = pc[16]; p18 = pc[17]; p19 = pc[18]; p20 = pc[19];
631       p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
632       p25 = pc[24]; p26 = pc[25]; p27 = pc[26]; p28 = pc[27];
633       p29 = pc[28]; p30 = pc[29]; p31 = pc[30]; p32 = pc[31];
634       p33 = pc[32]; p34 = pc[33]; p35 = pc[34]; p36 = pc[35];
635       p37 = pc[36]; p38 = pc[37]; p39 = pc[38]; p40 = pc[39];
636       p41 = pc[40]; p42 = pc[41]; p43 = pc[42]; p44 = pc[43];
637       p45 = pc[44]; p46 = pc[45]; p47 = pc[46]; p48 = pc[47];
638       p49 = pc[48];
639       if (p1  != 0.0 || p2  != 0.0 || p3  != 0.0 || p4  != 0.0 ||
640           p5  != 0.0 || p6  != 0.0 || p7  != 0.0 || p8  != 0.0 ||
641           p9  != 0.0 || p10 != 0.0 || p11 != 0.0 || p12 != 0.0 ||
642           p13 != 0.0 || p14 != 0.0 || p15 != 0.0 || p16 != 0.0 ||
643           p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 ||
644           p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 ||
645           p25 != 0.0 || p26 != 0.0 || p27 != 0.0 || p28 != 0.0 ||
646           p29 != 0.0 || p30 != 0.0 || p31 != 0.0 || p32 != 0.0 ||
647           p33 != 0.0 || p34 != 0.0 || p35 != 0.0 || p36 != 0.0 ||
648           p37 != 0.0 || p38 != 0.0 || p39 != 0.0 || p40 != 0.0 ||
649           p41 != 0.0 || p42 != 0.0 || p43 != 0.0 || p44 != 0.0 ||
650           p45 != 0.0 || p46 != 0.0 || p47 != 0.0 || p48 != 0.0 ||
651           p49 != 0.0) {
652         pv = ba + 49*diag_offset[row];
653         pj = bj + diag_offset[row] + 1;
654 	x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
655 	x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
656 	x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
657 	x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
658 	x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
659 	x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
660 	x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
661 	x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
662 	x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
663 	x37 = pv[36]; x38 = pv[37]; x39 = pv[38]; x40 = pv[39];
664 	x41 = pv[40]; x42 = pv[41]; x43 = pv[42]; x44 = pv[43];
665 	x45 = pv[44]; x46 = pv[45]; x47 = pv[46]; x48 = pv[47];
666         x49 = pv[48];
667         pc[0]  = m1  = p1*x1  + p8*x2   + p15*x3  + p22*x4  + p29*x5  + p36*x6 + p43*x7;
668         pc[1]  = m2  = p2*x1  + p9*x2   + p16*x3  + p23*x4  + p30*x5  + p37*x6 + p44*x7;
669         pc[2]  = m3  = p3*x1  + p10*x2  + p17*x3  + p24*x4  + p31*x5  + p38*x6 + p45*x7;
670         pc[3]  = m4  = p4*x1  + p11*x2  + p18*x3  + p25*x4  + p32*x5  + p39*x6 + p46*x7;
671         pc[4]  = m5  = p5*x1  + p12*x2  + p19*x3  + p26*x4  + p33*x5  + p40*x6 + p47*x7;
672         pc[5]  = m6  = p6*x1  + p13*x2  + p20*x3  + p27*x4  + p34*x5  + p41*x6 + p48*x7;
673         pc[6]  = m7  = p7*x1  + p14*x2  + p21*x3  + p28*x4  + p35*x5  + p42*x6 + p49*x7;
674 
675         pc[7]  = m8  = p1*x8  + p8*x9   + p15*x10 + p22*x11 + p29*x12 + p36*x13 + p43*x14;
676         pc[8]  = m9  = p2*x8  + p9*x9   + p16*x10 + p23*x11 + p30*x12 + p37*x13 + p44*x14;
677         pc[9]  = m10 = p3*x8  + p10*x9  + p17*x10 + p24*x11 + p31*x12 + p38*x13 + p45*x14;
678         pc[10] = m11 = p4*x8  + p11*x9  + p18*x10 + p25*x11 + p32*x12 + p39*x13 + p46*x14;
679         pc[11] = m12 = p5*x8  + p12*x9  + p19*x10 + p26*x11 + p33*x12 + p40*x13 + p47*x14;
680         pc[12] = m13 = p6*x8  + p13*x9  + p20*x10 + p27*x11 + p34*x12 + p41*x13 + p48*x14;
681         pc[13] = m14 = p7*x8  + p14*x9  + p21*x10 + p28*x11 + p35*x12 + p42*x13 + p49*x14;
682 
683         pc[14] = m15 = p1*x15 + p8*x16  + p15*x17 + p22*x18 + p29*x19 + p36*x20 + p43*x21;
684         pc[15] = m16 = p2*x15 + p9*x16  + p16*x17 + p23*x18 + p30*x19 + p37*x20 + p44*x21;
685         pc[16] = m17 = p3*x15 + p10*x16 + p17*x17 + p24*x18 + p31*x19 + p38*x20 + p45*x21;
686         pc[17] = m18 = p4*x15 + p11*x16 + p18*x17 + p25*x18 + p32*x19 + p39*x20 + p46*x21;
687         pc[18] = m19 = p5*x15 + p12*x16 + p19*x17 + p26*x18 + p33*x19 + p40*x20 + p47*x21;
688         pc[19] = m20 = p6*x15 + p13*x16 + p20*x17 + p27*x18 + p34*x19 + p41*x20 + p48*x21;
689         pc[20] = m21 = p7*x15 + p14*x16 + p21*x17 + p28*x18 + p35*x19 + p42*x20 + p49*x21;
690 
691         pc[21] = m22 = p1*x22 + p8*x23  + p15*x24 + p22*x25 + p29*x26 + p36*x27 + p43*x28;
692         pc[22] = m23 = p2*x22 + p9*x23  + p16*x24 + p23*x25 + p30*x26 + p37*x27 + p44*x28;
693         pc[23] = m24 = p3*x22 + p10*x23 + p17*x24 + p24*x25 + p31*x26 + p38*x27 + p45*x28;
694         pc[24] = m25 = p4*x22 + p11*x23 + p18*x24 + p25*x25 + p32*x26 + p39*x27 + p46*x28;
695         pc[25] = m26 = p5*x22 + p12*x23 + p19*x24 + p26*x25 + p33*x26 + p40*x27 + p47*x28;
696         pc[26] = m27 = p6*x22 + p13*x23 + p20*x24 + p27*x25 + p34*x26 + p41*x27 + p48*x28;
697         pc[27] = m28 = p7*x22 + p14*x23 + p21*x24 + p28*x25 + p35*x26 + p42*x27 + p49*x28;
698 
699         pc[28] = m29 = p1*x29 + p8*x30  + p15*x31 + p22*x32 + p29*x33 + p36*x34 + p43*x35;
700         pc[29] = m30 = p2*x29 + p9*x30  + p16*x31 + p23*x32 + p30*x33 + p37*x34 + p44*x35;
701         pc[30] = m31 = p3*x29 + p10*x30 + p17*x31 + p24*x32 + p31*x33 + p38*x34 + p45*x35;
702         pc[31] = m32 = p4*x29 + p11*x30 + p18*x31 + p25*x32 + p32*x33 + p39*x34 + p46*x35;
703         pc[32] = m33 = p5*x29 + p12*x30 + p19*x31 + p26*x32 + p33*x33 + p40*x34 + p47*x35;
704         pc[33] = m34 = p6*x29 + p13*x30 + p20*x31 + p27*x32 + p34*x33 + p41*x34 + p48*x35;
705         pc[34] = m35 = p7*x29 + p14*x30 + p21*x31 + p28*x32 + p35*x33 + p42*x34 + p49*x35;
706 
707         pc[35] = m36 = p1*x36 + p8*x37  + p15*x38 + p22*x39 + p29*x40 + p36*x41 + p43*x42;
708         pc[36] = m37 = p2*x36 + p9*x37  + p16*x38 + p23*x39 + p30*x40 + p37*x41 + p44*x42;
709         pc[37] = m38 = p3*x36 + p10*x37 + p17*x38 + p24*x39 + p31*x40 + p38*x41 + p45*x42;
710         pc[38] = m39 = p4*x36 + p11*x37 + p18*x38 + p25*x39 + p32*x40 + p39*x41 + p46*x42;
711         pc[39] = m40 = p5*x36 + p12*x37 + p19*x38 + p26*x39 + p33*x40 + p40*x41 + p47*x42;
712         pc[40] = m41 = p6*x36 + p13*x37 + p20*x38 + p27*x39 + p34*x40 + p41*x41 + p48*x42;
713         pc[41] = m42 = p7*x36 + p14*x37 + p21*x38 + p28*x39 + p35*x40 + p42*x41 + p49*x42;
714 
715         pc[42] = m43 = p1*x43 + p8*x44  + p15*x45 + p22*x46 + p29*x47 + p36*x48 + p43*x49;
716         pc[43] = m44 = p2*x43 + p9*x44  + p16*x45 + p23*x46 + p30*x47 + p37*x48 + p44*x49;
717         pc[44] = m45 = p3*x43 + p10*x44 + p17*x45 + p24*x46 + p31*x47 + p38*x48 + p45*x49;
718         pc[45] = m46 = p4*x43 + p11*x44 + p18*x45 + p25*x46 + p32*x47 + p39*x48 + p46*x49;
719         pc[46] = m47 = p5*x43 + p12*x44 + p19*x45 + p26*x46 + p33*x47 + p40*x48 + p47*x49;
720         pc[47] = m48 = p6*x43 + p13*x44 + p20*x45 + p27*x46 + p34*x47 + p41*x48 + p48*x49;
721         pc[48] = m49 = p7*x43 + p14*x44 + p21*x45 + p28*x46 + p35*x47 + p42*x48 + p49*x49;
722 
723         nz = bi[row+1] - diag_offset[row] - 1;
724         pv += 49;
725         for (j=0; j<nz; j++) {
726 	  x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
727 	  x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
728 	  x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
729 	  x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
730 	  x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
731 	  x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
732 	  x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
733 	  x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
734 	  x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
735 	  x37 = pv[36]; x38 = pv[37]; x39 = pv[38]; x40 = pv[39];
736 	  x41 = pv[40]; x42 = pv[41]; x43 = pv[42]; x44 = pv[43];
737 	  x45 = pv[44]; x46 = pv[45]; x47 = pv[46]; x48 = pv[47];
738 	  x49 = pv[48];
739 	  x    = rtmp + 49*pj[j];
740 	  x[0]  -= m1*x1  + m8*x2   + m15*x3  + m22*x4  + m29*x5  + m36*x6 + m43*x7;
741 	  x[1]  -= m2*x1  + m9*x2   + m16*x3  + m23*x4  + m30*x5  + m37*x6 + m44*x7;
742 	  x[2]  -= m3*x1  + m10*x2  + m17*x3  + m24*x4  + m31*x5  + m38*x6 + m45*x7;
743 	  x[3]  -= m4*x1  + m11*x2  + m18*x3  + m25*x4  + m32*x5  + m39*x6 + m46*x7;
744 	  x[4]  -= m5*x1  + m12*x2  + m19*x3  + m26*x4  + m33*x5  + m40*x6 + m47*x7;
745 	  x[5]  -= m6*x1  + m13*x2  + m20*x3  + m27*x4  + m34*x5  + m41*x6 + m48*x7;
746 	  x[6]  -= m7*x1  + m14*x2  + m21*x3  + m28*x4  + m35*x5  + m42*x6 + m49*x7;
747 
748 	  x[7]  -= m1*x8  + m8*x9   + m15*x10 + m22*x11 + m29*x12 + m36*x13 + m43*x14;
749 	  x[8]  -= m2*x8  + m9*x9   + m16*x10 + m23*x11 + m30*x12 + m37*x13 + m44*x14;
750 	  x[9]  -= m3*x8  + m10*x9  + m17*x10 + m24*x11 + m31*x12 + m38*x13 + m45*x14;
751 	  x[10] -= m4*x8  + m11*x9  + m18*x10 + m25*x11 + m32*x12 + m39*x13 + m46*x14;
752 	  x[11] -= m5*x8  + m12*x9  + m19*x10 + m26*x11 + m33*x12 + m40*x13 + m47*x14;
753 	  x[12] -= m6*x8  + m13*x9  + m20*x10 + m27*x11 + m34*x12 + m41*x13 + m48*x14;
754 	  x[13] -= m7*x8  + m14*x9  + m21*x10 + m28*x11 + m35*x12 + m42*x13 + m49*x14;
755 
756 	  x[14] -= m1*x15 + m8*x16  + m15*x17 + m22*x18 + m29*x19 + m36*x20 + m43*x21;
757 	  x[15] -= m2*x15 + m9*x16  + m16*x17 + m23*x18 + m30*x19 + m37*x20 + m44*x21;
758 	  x[16] -= m3*x15 + m10*x16 + m17*x17 + m24*x18 + m31*x19 + m38*x20 + m45*x21;
759 	  x[17] -= m4*x15 + m11*x16 + m18*x17 + m25*x18 + m32*x19 + m39*x20 + m46*x21;
760 	  x[18] -= m5*x15 + m12*x16 + m19*x17 + m26*x18 + m33*x19 + m40*x20 + m47*x21;
761 	  x[19] -= m6*x15 + m13*x16 + m20*x17 + m27*x18 + m34*x19 + m41*x20 + m48*x21;
762 	  x[20] -= m7*x15 + m14*x16 + m21*x17 + m28*x18 + m35*x19 + m42*x20 + m49*x21;
763 
764 	  x[21] -= m1*x22 + m8*x23  + m15*x24 + m22*x25 + m29*x26 + m36*x27 + m43*x28;
765 	  x[22] -= m2*x22 + m9*x23  + m16*x24 + m23*x25 + m30*x26 + m37*x27 + m44*x28;
766 	  x[23] -= m3*x22 + m10*x23 + m17*x24 + m24*x25 + m31*x26 + m38*x27 + m45*x28;
767 	  x[24] -= m4*x22 + m11*x23 + m18*x24 + m25*x25 + m32*x26 + m39*x27 + m46*x28;
768 	  x[25] -= m5*x22 + m12*x23 + m19*x24 + m26*x25 + m33*x26 + m40*x27 + m47*x28;
769 	  x[26] -= m6*x22 + m13*x23 + m20*x24 + m27*x25 + m34*x26 + m41*x27 + m48*x28;
770 	  x[27] -= m7*x22 + m14*x23 + m21*x24 + m28*x25 + m35*x26 + m42*x27 + m49*x28;
771 
772 	  x[28] -= m1*x29 + m8*x30  + m15*x31 + m22*x32 + m29*x33 + m36*x34 + m43*x35;
773 	  x[29] -= m2*x29 + m9*x30  + m16*x31 + m23*x32 + m30*x33 + m37*x34 + m44*x35;
774 	  x[30] -= m3*x29 + m10*x30 + m17*x31 + m24*x32 + m31*x33 + m38*x34 + m45*x35;
775 	  x[31] -= m4*x29 + m11*x30 + m18*x31 + m25*x32 + m32*x33 + m39*x34 + m46*x35;
776 	  x[32] -= m5*x29 + m12*x30 + m19*x31 + m26*x32 + m33*x33 + m40*x34 + m47*x35;
777 	  x[33] -= m6*x29 + m13*x30 + m20*x31 + m27*x32 + m34*x33 + m41*x34 + m48*x35;
778 	  x[34] -= m7*x29 + m14*x30 + m21*x31 + m28*x32 + m35*x33 + m42*x34 + m49*x35;
779 
780 	  x[35] -= m1*x36 + m8*x37  + m15*x38 + m22*x39 + m29*x40 + m36*x41 + m43*x42;
781 	  x[36] -= m2*x36 + m9*x37  + m16*x38 + m23*x39 + m30*x40 + m37*x41 + m44*x42;
782 	  x[37] -= m3*x36 + m10*x37 + m17*x38 + m24*x39 + m31*x40 + m38*x41 + m45*x42;
783 	  x[38] -= m4*x36 + m11*x37 + m18*x38 + m25*x39 + m32*x40 + m39*x41 + m46*x42;
784 	  x[39] -= m5*x36 + m12*x37 + m19*x38 + m26*x39 + m33*x40 + m40*x41 + m47*x42;
785 	  x[40] -= m6*x36 + m13*x37 + m20*x38 + m27*x39 + m34*x40 + m41*x41 + m48*x42;
786 	  x[41] -= m7*x36 + m14*x37 + m21*x38 + m28*x39 + m35*x40 + m42*x41 + m49*x42;
787 
788 	  x[42] -= m1*x43 + m8*x44  + m15*x45 + m22*x46 + m29*x47 + m36*x48 + m43*x49;
789 	  x[43] -= m2*x43 + m9*x44  + m16*x45 + m23*x46 + m30*x47 + m37*x48 + m44*x49;
790 	  x[44] -= m3*x43 + m10*x44 + m17*x45 + m24*x46 + m31*x47 + m38*x48 + m45*x49;
791 	  x[45] -= m4*x43 + m11*x44 + m18*x45 + m25*x46 + m32*x47 + m39*x48 + m46*x49;
792 	  x[46] -= m5*x43 + m12*x44 + m19*x45 + m26*x46 + m33*x47 + m40*x48 + m47*x49;
793 	  x[47] -= m6*x43 + m13*x44 + m20*x45 + m27*x46 + m34*x47 + m41*x48 + m48*x49;
794 	  x[48] -= m7*x43 + m14*x44 + m21*x45 + m28*x46 + m35*x47 + m42*x48 + m49*x49;
795           pv   += 49;
796         }
797         PLogFlops(686*nz+637);
798       }
799       row = *ajtmp++;
800     }
801     /* finished row so stick it into b->a */
802     pv = ba + 49*bi[i];
803     pj = bj + bi[i];
804     nz = bi[i+1] - bi[i];
805     for (j=0; j<nz; j++) {
806       x      = rtmp+49*pj[j];
807       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
808       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7];
809       pv[8]  = x[8];  pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11];
810       pv[12] = x[12]; pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
811       pv[16] = x[16]; pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19];
812       pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23];
813       pv[24] = x[24]; pv[25] = x[25]; pv[26] = x[26]; pv[27] = x[27];
814       pv[28] = x[28]; pv[29] = x[29]; pv[30] = x[30]; pv[31] = x[31];
815       pv[32] = x[32]; pv[33] = x[33]; pv[34] = x[34]; pv[35] = x[35];
816       pv[36] = x[36]; pv[37] = x[37]; pv[38] = x[38]; pv[39] = x[39];
817       pv[40] = x[40]; pv[41] = x[41]; pv[42] = x[42]; pv[43] = x[43];
818       pv[44] = x[44]; pv[45] = x[45]; pv[46] = x[46]; pv[47] = x[47];
819       pv[48] = x[48];
820       pv   += 49;
821     }
822     /* invert diagonal block */
823     w = ba + 49*diag_offset[i];
824     ierr = Kernel_A_gets_inverse_A_7(w);CHKERRQ(ierr);
825   }
826 
827   ierr = PetscFree(rtmp);CHKERRQ(ierr);
828   C->factor    = FACTOR_LU;
829   C->assembled = PETSC_TRUE;
830   PLogFlops(1.3333*343*b->mbs); /* from inverting diagonal blocks */
831   PetscFunctionReturn(0);
832 }
833 
834 /* ------------------------------------------------------------*/
835 /*
836       Version for when blocks are 6 by 6
837 */
838 #undef __FUNC__
839 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_6"
840 int MatCholeskyFactorNumeric_SeqSBAIJ_6(Mat A,Mat *B)
841 {
842   Mat          C = *B;
843   Mat_SeqBAIJ  *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
844   IS           isrow = b->row,isicol = b->icol;
845   int          *r,*ic,ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
846   int          *ajtmpold,*ajtmp,nz,row;
847   int          *diag_offset = b->diag,idx,*ai=a->i,*aj=a->j,*pj;
848   MatScalar    *pv,*v,*rtmp,*pc,*w,*x;
849   MatScalar    p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
850   MatScalar    p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
851   MatScalar    x17,x18,x19,x20,x21,x22,x23,x24,x25,p10,p11,p12,p13,p14;
852   MatScalar    p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,m10,m11,m12;
853   MatScalar    m13,m14,m15,m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
854   MatScalar    p26,p27,p28,p29,p30,p31,p32,p33,p34,p35,p36;
855   MatScalar    x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36;
856   MatScalar    m26,m27,m28,m29,m30,m31,m32,m33,m34,m35,m36;
857   MatScalar    *ba = b->a,*aa = a->a;
858 
859   PetscFunctionBegin;
860   ierr  = ISGetIndices(isrow,&r);CHKERRQ(ierr);
861   ierr  = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
862   rtmp  = (MatScalar*)PetscMalloc(36*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
863 
864   for (i=0; i<n; i++) {
865     nz    = bi[i+1] - bi[i];
866     ajtmp = bj + bi[i];
867     for  (j=0; j<nz; j++) {
868       x = rtmp+36*ajtmp[j];
869       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
870       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
871       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = x[25] = 0.0 ;
872       x[26] = x[27] = x[28] = x[29] = x[30] = x[31] = x[32] = x[33] = 0.0 ;
873       x[34] = x[35] = 0.0 ;
874     }
875     /* load in initial (unfactored row) */
876     idx      = r[i];
877     nz       = ai[idx+1] - ai[idx];
878     ajtmpold = aj + ai[idx];
879     v        = aa + 36*ai[idx];
880     for (j=0; j<nz; j++) {
881       x    = rtmp+36*ic[ajtmpold[j]];
882       x[0] =  v[0];  x[1] =  v[1];  x[2] =  v[2];  x[3] =  v[3];
883       x[4] =  v[4];  x[5] =  v[5];  x[6] =  v[6];  x[7] =  v[7];
884       x[8] =  v[8];  x[9] =  v[9];  x[10] = v[10]; x[11] = v[11];
885       x[12] = v[12]; x[13] = v[13]; x[14] = v[14]; x[15] = v[15];
886       x[16] = v[16]; x[17] = v[17]; x[18] = v[18]; x[19] = v[19];
887       x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23];
888       x[24] = v[24]; x[25] = v[25]; x[26] = v[26]; x[27] = v[27];
889       x[28] = v[28]; x[29] = v[29]; x[30] = v[30]; x[31] = v[31];
890       x[32] = v[32]; x[33] = v[33]; x[34] = v[34]; x[35] = v[35];
891       v    += 36;
892     }
893     row = *ajtmp++;
894     while (row < i) {
895       pc  =  rtmp + 36*row;
896       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
897       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];
898       p9  = pc[8];  p10 = pc[9];  p11 = pc[10]; p12 = pc[11];
899       p13 = pc[12]; p14 = pc[13]; p15 = pc[14]; p16 = pc[15];
900       p17 = pc[16]; p18 = pc[17]; p19 = pc[18]; p20 = pc[19];
901       p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
902       p25 = pc[24]; p26 = pc[25]; p27 = pc[26]; p28 = pc[27];
903       p29 = pc[28]; p30 = pc[29]; p31 = pc[30]; p32 = pc[31];
904       p33 = pc[32]; p34 = pc[33]; p35 = pc[34]; p36 = pc[35];
905       if (p1  != 0.0 || p2  != 0.0 || p3  != 0.0 || p4  != 0.0 ||
906           p5  != 0.0 || p6  != 0.0 || p7  != 0.0 || p8  != 0.0 ||
907           p9  != 0.0 || p10 != 0.0 || p11 != 0.0 || p12 != 0.0 ||
908           p13 != 0.0 || p14 != 0.0 || p15 != 0.0 || p16 != 0.0 ||
909           p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 ||
910           p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 ||
911           p25 != 0.0 || p26 != 0.0 || p27 != 0.0 || p28 != 0.0 ||
912           p29 != 0.0 || p30 != 0.0 || p31 != 0.0 || p32 != 0.0 ||
913           p33 != 0.0 || p34 != 0.0 || p35 != 0.0 || p36 != 0.0) {
914         pv = ba + 36*diag_offset[row];
915         pj = bj + diag_offset[row] + 1;
916 	x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
917 	x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
918 	x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
919 	x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
920 	x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
921 	x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
922 	x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
923 	x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
924 	x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
925         pc[0]  = m1  = p1*x1  + p7*x2   + p13*x3  + p19*x4  + p25*x5  + p31*x6;
926         pc[1]  = m2  = p2*x1  + p8*x2   + p14*x3  + p20*x4  + p26*x5  + p32*x6;
927         pc[2]  = m3  = p3*x1  + p9*x2   + p15*x3  + p21*x4  + p27*x5  + p33*x6;
928         pc[3]  = m4  = p4*x1  + p10*x2  + p16*x3  + p22*x4  + p28*x5  + p34*x6;
929         pc[4]  = m5  = p5*x1  + p11*x2  + p17*x3  + p23*x4  + p29*x5  + p35*x6;
930         pc[5]  = m6  = p6*x1  + p12*x2  + p18*x3  + p24*x4  + p30*x5  + p36*x6;
931 
932         pc[6]  = m7  = p1*x7  + p7*x8   + p13*x9  + p19*x10 + p25*x11 + p31*x12;
933         pc[7]  = m8  = p2*x7  + p8*x8   + p14*x9  + p20*x10 + p26*x11 + p32*x12;
934         pc[8]  = m9  = p3*x7  + p9*x8   + p15*x9  + p21*x10 + p27*x11 + p33*x12;
935         pc[9]  = m10 = p4*x7  + p10*x8  + p16*x9  + p22*x10 + p28*x11 + p34*x12;
936         pc[10] = m11 = p5*x7  + p11*x8  + p17*x9  + p23*x10 + p29*x11 + p35*x12;
937         pc[11] = m12 = p6*x7  + p12*x8  + p18*x9  + p24*x10 + p30*x11 + p36*x12;
938 
939         pc[12] = m13 = p1*x13 + p7*x14  + p13*x15 + p19*x16 + p25*x17 + p31*x18;
940         pc[13] = m14 = p2*x13 + p8*x14  + p14*x15 + p20*x16 + p26*x17 + p32*x18;
941         pc[14] = m15 = p3*x13 + p9*x14  + p15*x15 + p21*x16 + p27*x17 + p33*x18;
942         pc[15] = m16 = p4*x13 + p10*x14 + p16*x15 + p22*x16 + p28*x17 + p34*x18;
943         pc[16] = m17 = p5*x13 + p11*x14 + p17*x15 + p23*x16 + p29*x17 + p35*x18;
944         pc[17] = m18 = p6*x13 + p12*x14 + p18*x15 + p24*x16 + p30*x17 + p36*x18;
945 
946         pc[18] = m19 = p1*x19 + p7*x20  + p13*x21 + p19*x22 + p25*x23 + p31*x24;
947         pc[19] = m20 = p2*x19 + p8*x20  + p14*x21 + p20*x22 + p26*x23 + p32*x24;
948         pc[20] = m21 = p3*x19 + p9*x20  + p15*x21 + p21*x22 + p27*x23 + p33*x24;
949         pc[21] = m22 = p4*x19 + p10*x20 + p16*x21 + p22*x22 + p28*x23 + p34*x24;
950         pc[22] = m23 = p5*x19 + p11*x20 + p17*x21 + p23*x22 + p29*x23 + p35*x24;
951         pc[23] = m24 = p6*x19 + p12*x20 + p18*x21 + p24*x22 + p30*x23 + p36*x24;
952 
953         pc[24] = m25 = p1*x25 + p7*x26  + p13*x27 + p19*x28 + p25*x29 + p31*x30;
954         pc[25] = m26 = p2*x25 + p8*x26  + p14*x27 + p20*x28 + p26*x29 + p32*x30;
955         pc[26] = m27 = p3*x25 + p9*x26  + p15*x27 + p21*x28 + p27*x29 + p33*x30;
956         pc[27] = m28 = p4*x25 + p10*x26 + p16*x27 + p22*x28 + p28*x29 + p34*x30;
957         pc[28] = m29 = p5*x25 + p11*x26 + p17*x27 + p23*x28 + p29*x29 + p35*x30;
958         pc[29] = m30 = p6*x25 + p12*x26 + p18*x27 + p24*x28 + p30*x29 + p36*x30;
959 
960         pc[30] = m31 = p1*x31 + p7*x32  + p13*x33 + p19*x34 + p25*x35 + p31*x36;
961         pc[31] = m32 = p2*x31 + p8*x32  + p14*x33 + p20*x34 + p26*x35 + p32*x36;
962         pc[32] = m33 = p3*x31 + p9*x32  + p15*x33 + p21*x34 + p27*x35 + p33*x36;
963         pc[33] = m34 = p4*x31 + p10*x32 + p16*x33 + p22*x34 + p28*x35 + p34*x36;
964         pc[34] = m35 = p5*x31 + p11*x32 + p17*x33 + p23*x34 + p29*x35 + p35*x36;
965         pc[35] = m36 = p6*x31 + p12*x32 + p18*x33 + p24*x34 + p30*x35 + p36*x36;
966 
967         nz = bi[row+1] - diag_offset[row] - 1;
968         pv += 36;
969         for (j=0; j<nz; j++) {
970 	  x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
971 	  x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
972 	  x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
973 	  x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
974 	  x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
975 	  x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
976 	  x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
977 	  x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
978 	  x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
979 	  x    = rtmp + 36*pj[j];
980           x[0]  -= m1*x1  + m7*x2   + m13*x3  + m19*x4  + m25*x5  + m31*x6;
981           x[1]  -= m2*x1  + m8*x2   + m14*x3  + m20*x4  + m26*x5  + m32*x6;
982           x[2]  -= m3*x1  + m9*x2   + m15*x3  + m21*x4  + m27*x5  + m33*x6;
983           x[3]  -= m4*x1  + m10*x2  + m16*x3  + m22*x4  + m28*x5  + m34*x6;
984           x[4]  -= m5*x1  + m11*x2  + m17*x3  + m23*x4  + m29*x5  + m35*x6;
985           x[5]  -= m6*x1  + m12*x2  + m18*x3  + m24*x4  + m30*x5  + m36*x6;
986 
987 	  x[6]  -= m1*x7  + m7*x8   + m13*x9  + m19*x10 + m25*x11 + m31*x12;
988 	  x[7]  -= m2*x7  + m8*x8   + m14*x9  + m20*x10 + m26*x11 + m32*x12;
989 	  x[8]  -= m3*x7  + m9*x8   + m15*x9  + m21*x10 + m27*x11 + m33*x12;
990 	  x[9]  -= m4*x7  + m10*x8  + m16*x9  + m22*x10 + m28*x11 + m34*x12;
991 	  x[10] -= m5*x7  + m11*x8  + m17*x9  + m23*x10 + m29*x11 + m35*x12;
992 	  x[11] -= m6*x7  + m12*x8  + m18*x9  + m24*x10 + m30*x11 + m36*x12;
993 
994 	  x[12] -= m1*x13 + m7*x14  + m13*x15 + m19*x16 + m25*x17 + m31*x18;
995 	  x[13] -= m2*x13 + m8*x14  + m14*x15 + m20*x16 + m26*x17 + m32*x18;
996 	  x[14] -= m3*x13 + m9*x14  + m15*x15 + m21*x16 + m27*x17 + m33*x18;
997 	  x[15] -= m4*x13 + m10*x14 + m16*x15 + m22*x16 + m28*x17 + m34*x18;
998 	  x[16] -= m5*x13 + m11*x14 + m17*x15 + m23*x16 + m29*x17 + m35*x18;
999 	  x[17] -= m6*x13 + m12*x14 + m18*x15 + m24*x16 + m30*x17 + m36*x18;
1000 
1001 	  x[18] -= m1*x19 + m7*x20  + m13*x21 + m19*x22 + m25*x23 + m31*x24;
1002 	  x[19] -= m2*x19 + m8*x20  + m14*x21 + m20*x22 + m26*x23 + m32*x24;
1003 	  x[20] -= m3*x19 + m9*x20  + m15*x21 + m21*x22 + m27*x23 + m33*x24;
1004 	  x[21] -= m4*x19 + m10*x20 + m16*x21 + m22*x22 + m28*x23 + m34*x24;
1005 	  x[22] -= m5*x19 + m11*x20 + m17*x21 + m23*x22 + m29*x23 + m35*x24;
1006 	  x[23] -= m6*x19 + m12*x20 + m18*x21 + m24*x22 + m30*x23 + m36*x24;
1007 
1008 	  x[24] -= m1*x25 + m7*x26  + m13*x27 + m19*x28 + m25*x29 + m31*x30;
1009 	  x[25] -= m2*x25 + m8*x26  + m14*x27 + m20*x28 + m26*x29 + m32*x30;
1010 	  x[26] -= m3*x25 + m9*x26  + m15*x27 + m21*x28 + m27*x29 + m33*x30;
1011 	  x[27] -= m4*x25 + m10*x26 + m16*x27 + m22*x28 + m28*x29 + m34*x30;
1012 	  x[28] -= m5*x25 + m11*x26 + m17*x27 + m23*x28 + m29*x29 + m35*x30;
1013 	  x[29] -= m6*x25 + m12*x26 + m18*x27 + m24*x28 + m30*x29 + m36*x30;
1014 
1015 	  x[30] -= m1*x31 + m7*x32  + m13*x33 + m19*x34 + m25*x35 + m31*x36;
1016 	  x[31] -= m2*x31 + m8*x32  + m14*x33 + m20*x34 + m26*x35 + m32*x36;
1017 	  x[32] -= m3*x31 + m9*x32  + m15*x33 + m21*x34 + m27*x35 + m33*x36;
1018 	  x[33] -= m4*x31 + m10*x32 + m16*x33 + m22*x34 + m28*x35 + m34*x36;
1019 	  x[34] -= m5*x31 + m11*x32 + m17*x33 + m23*x34 + m29*x35 + m35*x36;
1020 	  x[35] -= m6*x31 + m12*x32 + m18*x33 + m24*x34 + m30*x35 + m36*x36;
1021 
1022           pv   += 36;
1023         }
1024         PLogFlops(432*nz+396);
1025       }
1026       row = *ajtmp++;
1027     }
1028     /* finished row so stick it into b->a */
1029     pv = ba + 36*bi[i];
1030     pj = bj + bi[i];
1031     nz = bi[i+1] - bi[i];
1032     for (j=0; j<nz; j++) {
1033       x      = rtmp+36*pj[j];
1034       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
1035       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7];
1036       pv[8]  = x[8];  pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11];
1037       pv[12] = x[12]; pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
1038       pv[16] = x[16]; pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19];
1039       pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23];
1040       pv[24] = x[24]; pv[25] = x[25]; pv[26] = x[26]; pv[27] = x[27];
1041       pv[28] = x[28]; pv[29] = x[29]; pv[30] = x[30]; pv[31] = x[31];
1042       pv[32] = x[32]; pv[33] = x[33]; pv[34] = x[34]; pv[35] = x[35];
1043       pv   += 36;
1044     }
1045     /* invert diagonal block */
1046     w = ba + 36*diag_offset[i];
1047     ierr = Kernel_A_gets_inverse_A_6(w);CHKERRQ(ierr);
1048   }
1049 
1050   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1051   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
1052   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
1053   C->factor = FACTOR_LU;
1054   C->assembled = PETSC_TRUE;
1055   PLogFlops(1.3333*216*b->mbs); /* from inverting diagonal blocks */
1056   PetscFunctionReturn(0);
1057 }
1058 /*
1059       Version for when blocks are 6 by 6 Using natural ordering
1060 */
1061 #undef __FUNC__
1062 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_6_NaturalOrdering"
1063 int MatCholeskyFactorNumeric_SeqSBAIJ_6_NaturalOrdering(Mat A,Mat *B)
1064 {
1065   Mat         C = *B;
1066   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
1067   int         ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
1068   int         *ajtmpold,*ajtmp,nz,row;
1069   int         *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
1070   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
1071   MatScalar   x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15;
1072   MatScalar   x16,x17,x18,x19,x20,x21,x22,x23,x24,x25;
1073   MatScalar   p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15;
1074   MatScalar   p16,p17,p18,p19,p20,p21,p22,p23,p24,p25;
1075   MatScalar   m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12,m13,m14,m15;
1076   MatScalar   m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
1077   MatScalar   p26,p27,p28,p29,p30,p31,p32,p33,p34,p35,p36;
1078   MatScalar   x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36;
1079   MatScalar   m26,m27,m28,m29,m30,m31,m32,m33,m34,m35,m36;
1080   MatScalar   *ba = b->a,*aa = a->a;
1081 
1082   PetscFunctionBegin;
1083   rtmp  = (MatScalar*)PetscMalloc(36*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
1084   for (i=0; i<n; i++) {
1085     nz    = bi[i+1] - bi[i];
1086     ajtmp = bj + bi[i];
1087     for  (j=0; j<nz; j++) {
1088       x = rtmp+36*ajtmp[j];
1089       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
1090       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
1091       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = x[25] = 0.0 ;
1092       x[26] = x[27] = x[28] = x[29] = x[30] = x[31] = x[32] = x[33] = 0.0 ;
1093       x[34] = x[35] = 0.0 ;
1094     }
1095     /* load in initial (unfactored row) */
1096     nz       = ai[i+1] - ai[i];
1097     ajtmpold = aj + ai[i];
1098     v        = aa + 36*ai[i];
1099     for (j=0; j<nz; j++) {
1100       x    = rtmp+36*ajtmpold[j];
1101       x[0] =  v[0];  x[1] =  v[1];  x[2] =  v[2];  x[3] =  v[3];
1102       x[4] =  v[4];  x[5] =  v[5];  x[6] =  v[6];  x[7] =  v[7];
1103       x[8] =  v[8];  x[9] =  v[9];  x[10] = v[10]; x[11] = v[11];
1104       x[12] = v[12]; x[13] = v[13]; x[14] = v[14]; x[15] = v[15];
1105       x[16] = v[16]; x[17] = v[17]; x[18] = v[18]; x[19] = v[19];
1106       x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23];
1107       x[24] = v[24]; x[25] = v[25]; x[26] = v[26]; x[27] = v[27];
1108       x[28] = v[28]; x[29] = v[29]; x[30] = v[30]; x[31] = v[31];
1109       x[32] = v[32]; x[33] = v[33]; x[34] = v[34]; x[35] = v[35];
1110       v    += 36;
1111     }
1112     row = *ajtmp++;
1113     while (row < i) {
1114       pc  = rtmp + 36*row;
1115       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
1116       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];
1117       p9  = pc[8];  p10 = pc[9];  p11 = pc[10]; p12 = pc[11];
1118       p13 = pc[12]; p14 = pc[13]; p15 = pc[14]; p16 = pc[15];
1119       p17 = pc[16]; p18 = pc[17]; p19 = pc[18]; p20 = pc[19];
1120       p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
1121       p25 = pc[24]; p26 = pc[25]; p27 = pc[26]; p28 = pc[27];
1122       p29 = pc[28]; p30 = pc[29]; p31 = pc[30]; p32 = pc[31];
1123       p33 = pc[32]; p34 = pc[33]; p35 = pc[34]; p36 = pc[35];
1124       if (p1  != 0.0 || p2  != 0.0 || p3  != 0.0 || p4  != 0.0 ||
1125           p5  != 0.0 || p6  != 0.0 || p7  != 0.0 || p8  != 0.0 ||
1126           p9  != 0.0 || p10 != 0.0 || p11 != 0.0 || p12 != 0.0 ||
1127           p13 != 0.0 || p14 != 0.0 || p15 != 0.0 || p16 != 0.0 ||
1128           p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 ||
1129           p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 ||
1130           p25 != 0.0 || p26 != 0.0 || p27 != 0.0 || p28 != 0.0 ||
1131           p29 != 0.0 || p30 != 0.0 || p31 != 0.0 || p32 != 0.0 ||
1132           p33 != 0.0 || p34 != 0.0 || p35 != 0.0 || p36 != 0.0) {
1133         pv = ba + 36*diag_offset[row];
1134         pj = bj + diag_offset[row] + 1;
1135 	x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
1136 	x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
1137 	x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
1138 	x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
1139 	x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
1140 	x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
1141 	x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
1142 	x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
1143 	x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
1144         pc[0]  = m1  = p1*x1  + p7*x2   + p13*x3  + p19*x4  + p25*x5  + p31*x6;
1145         pc[1]  = m2  = p2*x1  + p8*x2   + p14*x3  + p20*x4  + p26*x5  + p32*x6;
1146         pc[2]  = m3  = p3*x1  + p9*x2   + p15*x3  + p21*x4  + p27*x5  + p33*x6;
1147         pc[3]  = m4  = p4*x1  + p10*x2  + p16*x3  + p22*x4  + p28*x5  + p34*x6;
1148         pc[4]  = m5  = p5*x1  + p11*x2  + p17*x3  + p23*x4  + p29*x5  + p35*x6;
1149         pc[5]  = m6  = p6*x1  + p12*x2  + p18*x3  + p24*x4  + p30*x5  + p36*x6;
1150 
1151         pc[6]  = m7  = p1*x7  + p7*x8   + p13*x9  + p19*x10 + p25*x11 + p31*x12;
1152         pc[7]  = m8  = p2*x7  + p8*x8   + p14*x9  + p20*x10 + p26*x11 + p32*x12;
1153         pc[8]  = m9  = p3*x7  + p9*x8   + p15*x9  + p21*x10 + p27*x11 + p33*x12;
1154         pc[9]  = m10 = p4*x7  + p10*x8  + p16*x9  + p22*x10 + p28*x11 + p34*x12;
1155         pc[10] = m11 = p5*x7  + p11*x8  + p17*x9  + p23*x10 + p29*x11 + p35*x12;
1156         pc[11] = m12 = p6*x7  + p12*x8  + p18*x9  + p24*x10 + p30*x11 + p36*x12;
1157 
1158         pc[12] = m13 = p1*x13 + p7*x14  + p13*x15 + p19*x16 + p25*x17 + p31*x18;
1159         pc[13] = m14 = p2*x13 + p8*x14  + p14*x15 + p20*x16 + p26*x17 + p32*x18;
1160         pc[14] = m15 = p3*x13 + p9*x14  + p15*x15 + p21*x16 + p27*x17 + p33*x18;
1161         pc[15] = m16 = p4*x13 + p10*x14 + p16*x15 + p22*x16 + p28*x17 + p34*x18;
1162         pc[16] = m17 = p5*x13 + p11*x14 + p17*x15 + p23*x16 + p29*x17 + p35*x18;
1163         pc[17] = m18 = p6*x13 + p12*x14 + p18*x15 + p24*x16 + p30*x17 + p36*x18;
1164 
1165         pc[18] = m19 = p1*x19 + p7*x20  + p13*x21 + p19*x22 + p25*x23 + p31*x24;
1166         pc[19] = m20 = p2*x19 + p8*x20  + p14*x21 + p20*x22 + p26*x23 + p32*x24;
1167         pc[20] = m21 = p3*x19 + p9*x20  + p15*x21 + p21*x22 + p27*x23 + p33*x24;
1168         pc[21] = m22 = p4*x19 + p10*x20 + p16*x21 + p22*x22 + p28*x23 + p34*x24;
1169         pc[22] = m23 = p5*x19 + p11*x20 + p17*x21 + p23*x22 + p29*x23 + p35*x24;
1170         pc[23] = m24 = p6*x19 + p12*x20 + p18*x21 + p24*x22 + p30*x23 + p36*x24;
1171 
1172         pc[24] = m25 = p1*x25 + p7*x26  + p13*x27 + p19*x28 + p25*x29 + p31*x30;
1173         pc[25] = m26 = p2*x25 + p8*x26  + p14*x27 + p20*x28 + p26*x29 + p32*x30;
1174         pc[26] = m27 = p3*x25 + p9*x26  + p15*x27 + p21*x28 + p27*x29 + p33*x30;
1175         pc[27] = m28 = p4*x25 + p10*x26 + p16*x27 + p22*x28 + p28*x29 + p34*x30;
1176         pc[28] = m29 = p5*x25 + p11*x26 + p17*x27 + p23*x28 + p29*x29 + p35*x30;
1177         pc[29] = m30 = p6*x25 + p12*x26 + p18*x27 + p24*x28 + p30*x29 + p36*x30;
1178 
1179         pc[30] = m31 = p1*x31 + p7*x32  + p13*x33 + p19*x34 + p25*x35 + p31*x36;
1180         pc[31] = m32 = p2*x31 + p8*x32  + p14*x33 + p20*x34 + p26*x35 + p32*x36;
1181         pc[32] = m33 = p3*x31 + p9*x32  + p15*x33 + p21*x34 + p27*x35 + p33*x36;
1182         pc[33] = m34 = p4*x31 + p10*x32 + p16*x33 + p22*x34 + p28*x35 + p34*x36;
1183         pc[34] = m35 = p5*x31 + p11*x32 + p17*x33 + p23*x34 + p29*x35 + p35*x36;
1184         pc[35] = m36 = p6*x31 + p12*x32 + p18*x33 + p24*x34 + p30*x35 + p36*x36;
1185 
1186         nz = bi[row+1] - diag_offset[row] - 1;
1187         pv += 36;
1188         for (j=0; j<nz; j++) {
1189 	  x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
1190 	  x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
1191 	  x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
1192 	  x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
1193 	  x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
1194 	  x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
1195 	  x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
1196 	  x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
1197 	  x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
1198 	  x    = rtmp + 36*pj[j];
1199           x[0]  -= m1*x1  + m7*x2   + m13*x3  + m19*x4  + m25*x5  + m31*x6;
1200           x[1]  -= m2*x1  + m8*x2   + m14*x3  + m20*x4  + m26*x5  + m32*x6;
1201           x[2]  -= m3*x1  + m9*x2   + m15*x3  + m21*x4  + m27*x5  + m33*x6;
1202           x[3]  -= m4*x1  + m10*x2  + m16*x3  + m22*x4  + m28*x5  + m34*x6;
1203           x[4]  -= m5*x1  + m11*x2  + m17*x3  + m23*x4  + m29*x5  + m35*x6;
1204           x[5]  -= m6*x1  + m12*x2  + m18*x3  + m24*x4  + m30*x5  + m36*x6;
1205 
1206 	  x[6]  -= m1*x7  + m7*x8   + m13*x9  + m19*x10 + m25*x11 + m31*x12;
1207 	  x[7]  -= m2*x7  + m8*x8   + m14*x9  + m20*x10 + m26*x11 + m32*x12;
1208 	  x[8]  -= m3*x7  + m9*x8   + m15*x9  + m21*x10 + m27*x11 + m33*x12;
1209 	  x[9]  -= m4*x7  + m10*x8  + m16*x9  + m22*x10 + m28*x11 + m34*x12;
1210 	  x[10] -= m5*x7  + m11*x8  + m17*x9  + m23*x10 + m29*x11 + m35*x12;
1211 	  x[11] -= m6*x7  + m12*x8  + m18*x9  + m24*x10 + m30*x11 + m36*x12;
1212 
1213 	  x[12] -= m1*x13 + m7*x14  + m13*x15 + m19*x16 + m25*x17 + m31*x18;
1214 	  x[13] -= m2*x13 + m8*x14  + m14*x15 + m20*x16 + m26*x17 + m32*x18;
1215 	  x[14] -= m3*x13 + m9*x14  + m15*x15 + m21*x16 + m27*x17 + m33*x18;
1216 	  x[15] -= m4*x13 + m10*x14 + m16*x15 + m22*x16 + m28*x17 + m34*x18;
1217 	  x[16] -= m5*x13 + m11*x14 + m17*x15 + m23*x16 + m29*x17 + m35*x18;
1218 	  x[17] -= m6*x13 + m12*x14 + m18*x15 + m24*x16 + m30*x17 + m36*x18;
1219 
1220 	  x[18] -= m1*x19 + m7*x20  + m13*x21 + m19*x22 + m25*x23 + m31*x24;
1221 	  x[19] -= m2*x19 + m8*x20  + m14*x21 + m20*x22 + m26*x23 + m32*x24;
1222 	  x[20] -= m3*x19 + m9*x20  + m15*x21 + m21*x22 + m27*x23 + m33*x24;
1223 	  x[21] -= m4*x19 + m10*x20 + m16*x21 + m22*x22 + m28*x23 + m34*x24;
1224 	  x[22] -= m5*x19 + m11*x20 + m17*x21 + m23*x22 + m29*x23 + m35*x24;
1225 	  x[23] -= m6*x19 + m12*x20 + m18*x21 + m24*x22 + m30*x23 + m36*x24;
1226 
1227 	  x[24] -= m1*x25 + m7*x26  + m13*x27 + m19*x28 + m25*x29 + m31*x30;
1228 	  x[25] -= m2*x25 + m8*x26  + m14*x27 + m20*x28 + m26*x29 + m32*x30;
1229 	  x[26] -= m3*x25 + m9*x26  + m15*x27 + m21*x28 + m27*x29 + m33*x30;
1230 	  x[27] -= m4*x25 + m10*x26 + m16*x27 + m22*x28 + m28*x29 + m34*x30;
1231 	  x[28] -= m5*x25 + m11*x26 + m17*x27 + m23*x28 + m29*x29 + m35*x30;
1232 	  x[29] -= m6*x25 + m12*x26 + m18*x27 + m24*x28 + m30*x29 + m36*x30;
1233 
1234 	  x[30] -= m1*x31 + m7*x32  + m13*x33 + m19*x34 + m25*x35 + m31*x36;
1235 	  x[31] -= m2*x31 + m8*x32  + m14*x33 + m20*x34 + m26*x35 + m32*x36;
1236 	  x[32] -= m3*x31 + m9*x32  + m15*x33 + m21*x34 + m27*x35 + m33*x36;
1237 	  x[33] -= m4*x31 + m10*x32 + m16*x33 + m22*x34 + m28*x35 + m34*x36;
1238 	  x[34] -= m5*x31 + m11*x32 + m17*x33 + m23*x34 + m29*x35 + m35*x36;
1239 	  x[35] -= m6*x31 + m12*x32 + m18*x33 + m24*x34 + m30*x35 + m36*x36;
1240 
1241           pv   += 36;
1242         }
1243         PLogFlops(432*nz+396);
1244       }
1245       row = *ajtmp++;
1246     }
1247     /* finished row so stick it into b->a */
1248     pv = ba + 36*bi[i];
1249     pj = bj + bi[i];
1250     nz = bi[i+1] - bi[i];
1251     for (j=0; j<nz; j++) {
1252       x      = rtmp+36*pj[j];
1253       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
1254       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7];
1255       pv[8]  = x[8];  pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11];
1256       pv[12] = x[12]; pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
1257       pv[16] = x[16]; pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19];
1258       pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23];
1259       pv[24] = x[24]; pv[25] = x[25]; pv[26] = x[26]; pv[27] = x[27];
1260       pv[28] = x[28]; pv[29] = x[29]; pv[30] = x[30]; pv[31] = x[31];
1261       pv[32] = x[32]; pv[33] = x[33]; pv[34] = x[34]; pv[35] = x[35];
1262       pv   += 36;
1263     }
1264     /* invert diagonal block */
1265     w = ba + 36*diag_offset[i];
1266     ierr = Kernel_A_gets_inverse_A_6(w);CHKERRQ(ierr);
1267   }
1268 
1269   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1270   C->factor    = FACTOR_LU;
1271   C->assembled = PETSC_TRUE;
1272   PLogFlops(1.3333*216*b->mbs); /* from inverting diagonal blocks */
1273   PetscFunctionReturn(0);
1274 }
1275 
1276 /* Version for when blocks are 5 by 5  */
1277 #undef __FUNC__
1278 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_5"
1279 int MatCholeskyFactorNumeric_SeqSBAIJ_5(Mat A,Mat *B)
1280 {
1281   Mat                C = *B;
1282   Mat_SeqSBAIJ       *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data;
1283   IS                 perm = b->row;
1284   int                *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
1285   int                *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
1286   MatScalar          *ba = b->a,*aa,*ap,*dk,*uik;
1287   MatScalar          *u,*d,*rtmp,*rtmp_ptr;
1288 
1289   PetscFunctionBegin;
1290   /* initialization */
1291   rtmp  = (MatScalar*)PetscMalloc(25*mbs*sizeof(MatScalar));CHKPTRQ(rtmp);
1292   ierr = PetscMemzero(rtmp,25*mbs*sizeof(MatScalar));CHKERRQ(ierr);
1293   il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il);
1294   jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl);
1295   for (i=0; i<mbs; i++) {
1296     jl[i] = mbs; il[0] = 0;
1297   }
1298   dk    = (MatScalar*)PetscMalloc(25*sizeof(MatScalar));CHKPTRQ(dk);
1299   uik   = (MatScalar*)PetscMalloc(25*sizeof(MatScalar));CHKPTRQ(uik);
1300   ierr  = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr);
1301 
1302   /* check permutation */
1303   if (!a->permute){
1304     ai = a->i; aj = a->j; aa = a->a;
1305   } else {
1306     ai = a->inew; aj = a->jnew;
1307     aa = (MatScalar*)PetscMalloc(25*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa);
1308     ierr = PetscMemcpy(aa,a->a,25*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr);
1309     a2anew  = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew);
1310     ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr);
1311 
1312     for (i=0; i<mbs; i++){
1313       jmin = ai[i]; jmax = ai[i+1];
1314       for (j=jmin; j<jmax; j++){
1315         while (a2anew[j] != j){
1316           k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k;
1317           for (k1=0; k1<25; k1++){
1318             dk[k1]       = aa[k*25+k1];
1319             aa[k*25+k1] = aa[j*25+k1];
1320             aa[j*25+k1] = dk[k1];
1321           }
1322         }
1323         /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */
1324         if (i > aj[j]){
1325           /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */
1326           ap = aa + j*25;                     /* ptr to the beginning of j-th block of aa */
1327           for (k=0; k<25; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */
1328           for (k=0; k<5; k++){               /* j-th block of aa <- dk^T */
1329             for (k1=0; k1<5; k1++) *ap++ = dk[k + 5*k1];
1330           }
1331         }
1332       }
1333     }
1334     ierr = PetscFree(a2anew);CHKERRA(ierr);
1335   }
1336 
1337   /* for each row k */
1338   for (k = 0; k<mbs; k++){
1339 
1340     /*initialize k-th row with elements nonzero in row perm(k) of A */
1341     jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1];
1342     if (jmin < jmax) {
1343       ap = aa + jmin*25;
1344       for (j = jmin; j < jmax; j++){
1345         vj = perm_ptr[aj[j]];         /* block col. index */
1346         rtmp_ptr = rtmp + vj*25;
1347         for (i=0; i<25; i++) *rtmp_ptr++ = *ap++;
1348       }
1349     }
1350 
1351     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
1352     ierr = PetscMemcpy(dk,rtmp+k*25,25*sizeof(MatScalar));CHKERRQ(ierr);
1353     i = jl[k]; /* first row to be added to k_th row  */
1354 
1355     while (i < mbs){
1356       nexti = jl[i]; /* next row to be added to k_th row */
1357 
1358       /* compute multiplier */
1359       ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
1360 
1361       /* uik = -inv(Di)*U_bar(i,k) */
1362       d = ba + i*25;
1363       u    = ba + ili*25;
1364 
1365       uik[0] = -(d[0]*u[0] + d[5]*u[1] + d[10]*u[2] + d[15]*u[3] + d[20]*u[4]);
1366       uik[1] = -(d[1]*u[0] + d[6]*u[1] + d[11]*u[2] + d[16]*u[3] + d[21]*u[4]);
1367       uik[2] = -(d[2]*u[0] + d[7]*u[1] + d[12]*u[2] + d[17]*u[3] + d[22]*u[4]);
1368       uik[3] = -(d[3]*u[0] + d[8]*u[1] + d[13]*u[2] + d[18]*u[3] + d[23]*u[4]);
1369       uik[4] = -(d[4]*u[0] + d[9]*u[1] + d[14]*u[2] + d[19]*u[3] + d[24]*u[4]);
1370 
1371       uik[5] = -(d[0]*u[5] + d[5]*u[6] + d[10]*u[7] + d[15]*u[8] + d[20]*u[9]);
1372       uik[6] = -(d[1]*u[5] + d[6]*u[6] + d[11]*u[7] + d[16]*u[8] + d[21]*u[9]);
1373       uik[7] = -(d[2]*u[5] + d[7]*u[6] + d[12]*u[7] + d[17]*u[8] + d[22]*u[9]);
1374       uik[8] = -(d[3]*u[5] + d[8]*u[6] + d[13]*u[7] + d[18]*u[8] + d[23]*u[9]);
1375       uik[9] = -(d[4]*u[5] + d[9]*u[6] + d[14]*u[7] + d[19]*u[8] + d[24]*u[9]);
1376 
1377       uik[10]= -(d[0]*u[10] + d[5]*u[11] + d[10]*u[12] + d[15]*u[13] + d[20]*u[14]);
1378       uik[11]= -(d[1]*u[10] + d[6]*u[11] + d[11]*u[12] + d[16]*u[13] + d[21]*u[14]);
1379       uik[12]= -(d[2]*u[10] + d[7]*u[11] + d[12]*u[12] + d[17]*u[13] + d[22]*u[14]);
1380       uik[13]= -(d[3]*u[10] + d[8]*u[11] + d[13]*u[12] + d[18]*u[13] + d[23]*u[14]);
1381       uik[14]= -(d[4]*u[10] + d[9]*u[11] + d[14]*u[12] + d[19]*u[13] + d[24]*u[14]);
1382 
1383       uik[15]= -(d[0]*u[15] + d[5]*u[16] + d[10]*u[17] + d[15]*u[18] + d[20]*u[19]);
1384       uik[16]= -(d[1]*u[15] + d[6]*u[16] + d[11]*u[17] + d[16]*u[18] + d[21]*u[19]);
1385       uik[17]= -(d[2]*u[15] + d[7]*u[16] + d[12]*u[17] + d[17]*u[18] + d[22]*u[19]);
1386       uik[18]= -(d[3]*u[15] + d[8]*u[16] + d[13]*u[17] + d[18]*u[18] + d[23]*u[19]);
1387       uik[19]= -(d[4]*u[15] + d[9]*u[16] + d[14]*u[17] + d[19]*u[18] + d[24]*u[19]);
1388 
1389       uik[20]= -(d[0]*u[20] + d[5]*u[21] + d[10]*u[22] + d[15]*u[23] + d[20]*u[24]);
1390       uik[21]= -(d[1]*u[20] + d[6]*u[21] + d[11]*u[22] + d[16]*u[23] + d[21]*u[24]);
1391       uik[22]= -(d[2]*u[20] + d[7]*u[21] + d[12]*u[22] + d[17]*u[23] + d[22]*u[24]);
1392       uik[23]= -(d[3]*u[20] + d[8]*u[21] + d[13]*u[22] + d[18]*u[23] + d[23]*u[24]);
1393       uik[24]= -(d[4]*u[20] + d[9]*u[21] + d[14]*u[22] + d[19]*u[23] + d[24]*u[24]);
1394 
1395 
1396       /* update D(k) += -U(i,k)^T * U_bar(i,k) */
1397       dk[0] +=  uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3] + uik[4]*u[4];
1398       dk[1] +=  uik[5]*u[0] + uik[6]*u[1] + uik[7]*u[2] + uik[8]*u[3] + uik[9]*u[4];
1399       dk[2] += uik[10]*u[0]+ uik[11]*u[1]+ uik[12]*u[2]+ uik[13]*u[3]+ uik[14]*u[4];
1400       dk[3] += uik[15]*u[0]+ uik[16]*u[1]+ uik[17]*u[2]+ uik[18]*u[3]+ uik[19]*u[4];
1401       dk[4] += uik[20]*u[0]+ uik[21]*u[1]+ uik[22]*u[2]+ uik[23]*u[3]+ uik[24]*u[4];
1402 
1403       dk[5] +=  uik[0]*u[5] + uik[1]*u[6] + uik[2]*u[7] + uik[3]*u[8] + uik[4]*u[9];
1404       dk[6] +=  uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8] + uik[9]*u[9];
1405       dk[7] += uik[10]*u[5]+ uik[11]*u[6]+ uik[12]*u[7]+ uik[13]*u[8]+ uik[14]*u[9];
1406       dk[8] += uik[15]*u[5]+ uik[16]*u[6]+ uik[17]*u[7]+ uik[18]*u[8]+ uik[19]*u[9];
1407       dk[9] += uik[20]*u[5]+ uik[21]*u[6]+ uik[22]*u[7]+ uik[23]*u[8]+ uik[24]*u[9];
1408 
1409       dk[10] +=  uik[0]*u[10] + uik[1]*u[11] + uik[2]*u[12] + uik[3]*u[13] + uik[4]*u[14];
1410       dk[11] +=  uik[5]*u[10] + uik[6]*u[11] + uik[7]*u[12] + uik[8]*u[13] + uik[9]*u[14];
1411       dk[12] += uik[10]*u[10]+ uik[11]*u[11]+ uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14];
1412       dk[13] += uik[15]*u[10]+ uik[16]*u[11]+ uik[17]*u[12]+ uik[18]*u[13]+ uik[19]*u[14];
1413       dk[14] += uik[20]*u[10]+ uik[21]*u[11]+ uik[22]*u[12]+ uik[23]*u[13]+ uik[24]*u[14];
1414 
1415       dk[15] +=  uik[0]*u[15] + uik[1]*u[16] + uik[2]*u[17] + uik[3]*u[18] + uik[4]*u[19];
1416       dk[16] +=  uik[5]*u[15] + uik[6]*u[16] + uik[7]*u[17] + uik[8]*u[18] + uik[9]*u[19];
1417       dk[17] += uik[10]*u[15]+ uik[11]*u[16]+ uik[12]*u[17]+ uik[13]*u[18]+ uik[14]*u[19];
1418       dk[18] += uik[15]*u[15]+ uik[16]*u[16]+ uik[17]*u[17]+ uik[18]*u[18]+ uik[19]*u[19];
1419       dk[19] += uik[20]*u[15]+ uik[21]*u[16]+ uik[22]*u[17]+ uik[23]*u[18]+ uik[24]*u[19];
1420 
1421       dk[20] +=  uik[0]*u[20] + uik[1]*u[21] + uik[2]*u[22] + uik[3]*u[23] + uik[4]*u[24];
1422       dk[21] +=  uik[5]*u[20] + uik[6]*u[21] + uik[7]*u[22] + uik[8]*u[23] + uik[9]*u[24];
1423       dk[22] += uik[10]*u[20]+ uik[11]*u[21]+ uik[12]*u[22]+ uik[13]*u[23]+ uik[14]*u[24];
1424       dk[23] += uik[15]*u[20]+ uik[16]*u[21]+ uik[17]*u[22]+ uik[18]*u[23]+ uik[19]*u[24];
1425       dk[24] += uik[20]*u[24]+ uik[21]*u[21]+ uik[22]*u[22]+ uik[23]*u[23]+ uik[24]*u[24];
1426 
1427       /* update -U(i,k) */
1428       ierr = PetscMemcpy(ba+ili*25,uik,25*sizeof(MatScalar));CHKERRQ(ierr);
1429 
1430       /* add multiple of row i to k-th row ... */
1431       jmin = ili + 1; jmax = bi[i+1];
1432       if (jmin < jmax){
1433         for (j=jmin; j<jmax; j++) {
1434           /* rtmp += -U(i,k)^T * U_bar(i,j) */
1435           rtmp_ptr = rtmp + bj[j]*25;
1436           u = ba + j*25;
1437           rtmp_ptr[0] +=  uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3] + uik[4]*u[4];
1438           rtmp_ptr[1] +=  uik[5]*u[0] + uik[6]*u[1] + uik[7]*u[2] + uik[8]*u[3] + uik[9]*u[4];
1439           rtmp_ptr[2] += uik[10]*u[0]+ uik[11]*u[1]+ uik[12]*u[2]+ uik[13]*u[3]+ uik[14]*u[4];
1440           rtmp_ptr[3] += uik[15]*u[0]+ uik[16]*u[1]+ uik[17]*u[2]+ uik[18]*u[3]+ uik[19]*u[4];
1441           rtmp_ptr[4] += uik[20]*u[0]+ uik[21]*u[1]+ uik[22]*u[2]+ uik[23]*u[3]+ uik[24]*u[4];
1442 
1443           rtmp_ptr[5] +=  uik[0]*u[5] + uik[1]*u[6] + uik[2]*u[7] + uik[3]*u[8] + uik[4]*u[9];
1444           rtmp_ptr[6] +=  uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8] + uik[9]*u[9];
1445           rtmp_ptr[7] += uik[10]*u[5]+ uik[11]*u[6]+ uik[12]*u[7]+ uik[13]*u[8]+ uik[14]*u[9];
1446           rtmp_ptr[8] += uik[15]*u[5]+ uik[16]*u[6]+ uik[17]*u[7]+ uik[18]*u[8]+ uik[19]*u[9];
1447           rtmp_ptr[9] += uik[20]*u[5]+ uik[21]*u[6]+ uik[22]*u[7]+ uik[23]*u[8]+ uik[24]*u[9];
1448 
1449           rtmp_ptr[10] +=  uik[0]*u[10] + uik[1]*u[11] + uik[2]*u[12] + uik[3]*u[13] + uik[4]*u[14];
1450           rtmp_ptr[11] +=  uik[5]*u[10] + uik[6]*u[11] + uik[7]*u[12] + uik[8]*u[13] + uik[9]*u[14];
1451           rtmp_ptr[12] += uik[10]*u[10]+ uik[11]*u[11]+ uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14];
1452           rtmp_ptr[13] += uik[15]*u[10]+ uik[16]*u[11]+ uik[17]*u[12]+ uik[18]*u[13]+ uik[19]*u[14];
1453           rtmp_ptr[14] += uik[20]*u[10]+ uik[21]*u[11]+ uik[22]*u[12]+ uik[23]*u[13]+ uik[24]*u[14];
1454 
1455           rtmp_ptr[15] +=  uik[0]*u[15] + uik[1]*u[16] + uik[2]*u[17] + uik[3]*u[18] + uik[4]*u[19];
1456           rtmp_ptr[16] +=  uik[5]*u[15] + uik[6]*u[16] + uik[7]*u[17] + uik[8]*u[18] + uik[9]*u[19];
1457           rtmp_ptr[17] += uik[10]*u[15]+ uik[11]*u[16]+ uik[12]*u[17]+ uik[13]*u[18]+ uik[14]*u[19];
1458           rtmp_ptr[18] += uik[15]*u[15]+ uik[16]*u[16]+ uik[17]*u[17]+ uik[18]*u[18]+ uik[19]*u[19];
1459           rtmp_ptr[19] += uik[20]*u[15]+ uik[21]*u[16]+ uik[22]*u[17]+ uik[23]*u[18]+ uik[24]*u[19];
1460 
1461           rtmp_ptr[20] +=  uik[0]*u[20] + uik[1]*u[21] + uik[2]*u[22] + uik[3]*u[23] + uik[4]*u[24];
1462           rtmp_ptr[21] +=  uik[5]*u[20] + uik[6]*u[21] + uik[7]*u[22] + uik[8]*u[23] + uik[9]*u[24];
1463           rtmp_ptr[22] += uik[10]*u[20]+ uik[11]*u[21]+ uik[12]*u[22]+ uik[13]*u[23]+ uik[14]*u[24];
1464           rtmp_ptr[23] += uik[15]*u[20]+ uik[16]*u[21]+ uik[17]*u[22]+ uik[18]*u[23]+ uik[19]*u[24];
1465           rtmp_ptr[24] += uik[20]*u[24]+ uik[21]*u[21]+ uik[22]*u[22]+ uik[23]*u[23]+ uik[24]*u[24];
1466         }
1467 
1468         /* ... add i to row list for next nonzero entry */
1469         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
1470         j     = bj[jmin];
1471         jl[i] = jl[j]; jl[j] = i; /* update jl */
1472       }
1473       i = nexti;
1474     }
1475 
1476     /* save nonzero entries in k-th row of U ... */
1477 
1478     /* invert diagonal block */
1479     d = ba+k*25;
1480     ierr = PetscMemcpy(d,dk,25*sizeof(MatScalar));CHKERRQ(ierr);
1481     ierr = Kernel_A_gets_inverse_A_5(d);CHKERRQ(ierr);
1482 
1483     jmin = bi[k]; jmax = bi[k+1];
1484     if (jmin < jmax) {
1485       for (j=jmin; j<jmax; j++){
1486          vj = bj[j];           /* block col. index of U */
1487          u   = ba + j*25;
1488          rtmp_ptr = rtmp + vj*25;
1489          for (k1=0; k1<25; k1++){
1490            *u++        = *rtmp_ptr;
1491            *rtmp_ptr++ = 0.0;
1492          }
1493       }
1494 
1495       /* ... add k to row list for first nonzero entry in k-th row */
1496       il[k] = jmin;
1497       i     = bj[jmin];
1498       jl[k] = jl[i]; jl[i] = k;
1499     }
1500   }
1501 
1502   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1503   ierr = PetscFree(il);CHKERRQ(ierr);
1504   ierr = PetscFree(jl);CHKERRQ(ierr);
1505   ierr = PetscFree(dk);CHKERRQ(ierr);
1506   ierr = PetscFree(uik);CHKERRQ(ierr);
1507   if (a->permute){
1508     ierr = PetscFree(aa);CHKERRQ(ierr);
1509   }
1510 
1511   ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr);
1512   C->factor    = FACTOR_CHOLESKY;
1513   C->assembled = PETSC_TRUE;
1514   C->preallocated = PETSC_TRUE;
1515   PLogFlops(1.3333*125*b->mbs); /* from inverting diagonal blocks */
1516   PetscFunctionReturn(0);
1517 }
1518 
1519 /*
1520       Version for when blocks are 5 by 5 Using natural ordering
1521 */
1522 #undef __FUNC__
1523 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_5_NaturalOrdering"
1524 int MatCholeskyFactorNumeric_SeqSBAIJ_5_NaturalOrdering(Mat A,Mat *B)
1525 {
1526   Mat         C = *B;
1527   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
1528   int         ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
1529   int         *ajtmpold,*ajtmp,nz,row;
1530   int         *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
1531   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
1532   MatScalar   x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15;
1533   MatScalar   x16,x17,x18,x19,x20,x21,x22,x23,x24,x25;
1534   MatScalar   p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15;
1535   MatScalar   p16,p17,p18,p19,p20,p21,p22,p23,p24,p25;
1536   MatScalar   m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12,m13,m14,m15;
1537   MatScalar   m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
1538   MatScalar   *ba = b->a,*aa = a->a;
1539 
1540   PetscFunctionBegin;
1541   rtmp  = (MatScalar*)PetscMalloc(25*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
1542   for (i=0; i<n; i++) {
1543     nz    = bi[i+1] - bi[i];
1544     ajtmp = bj + bi[i];
1545     for  (j=0; j<nz; j++) {
1546       x = rtmp+25*ajtmp[j];
1547       x[0]  = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = x[9] = 0.0;
1548       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
1549       x[16] = x[17] = x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0;
1550     }
1551     /* load in initial (unfactored row) */
1552     nz       = ai[i+1] - ai[i];
1553     ajtmpold = aj + ai[i];
1554     v        = aa + 25*ai[i];
1555     for (j=0; j<nz; j++) {
1556       x    = rtmp+25*ajtmpold[j];
1557       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
1558       x[4]  = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
1559       x[9]  = v[9];  x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
1560       x[14] = v[14]; x[15] = v[15]; x[16] = v[16]; x[17] = v[17]; x[18] = v[18];
1561       x[19] = v[19]; x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23];
1562       x[24] = v[24];
1563       v    += 25;
1564     }
1565     row = *ajtmp++;
1566     while (row < i) {
1567       pc  = rtmp + 25*row;
1568       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
1569       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
1570       p10 = pc[9];  p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
1571       p15 = pc[14]; p16 = pc[15]; p17 = pc[16]; p18 = pc[17];
1572       p19 = pc[18]; p20 = pc[19]; p21 = pc[20]; p22 = pc[21]; p23 = pc[22];
1573       p24 = pc[23]; p25 = pc[24];
1574       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
1575           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
1576           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
1577           || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0
1578           || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 || p25 != 0.0) {
1579         pv = ba + 25*diag_offset[row];
1580         pj = bj + diag_offset[row] + 1;
1581         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
1582         x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
1583         x10 = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
1584         x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17]; x19 = pv[18];
1585         x20 = pv[19]; x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
1586         x25 = pv[24];
1587         pc[0] = m1 = p1*x1 + p6*x2  + p11*x3 + p16*x4 + p21*x5;
1588         pc[1] = m2 = p2*x1 + p7*x2  + p12*x3 + p17*x4 + p22*x5;
1589         pc[2] = m3 = p3*x1 + p8*x2  + p13*x3 + p18*x4 + p23*x5;
1590         pc[3] = m4 = p4*x1 + p9*x2  + p14*x3 + p19*x4 + p24*x5;
1591         pc[4] = m5 = p5*x1 + p10*x2 + p15*x3 + p20*x4 + p25*x5;
1592 
1593         pc[5]  = m6  = p1*x6 + p6*x7  + p11*x8 + p16*x9 + p21*x10;
1594         pc[6]  = m7  = p2*x6 + p7*x7  + p12*x8 + p17*x9 + p22*x10;
1595         pc[7]  = m8  = p3*x6 + p8*x7  + p13*x8 + p18*x9 + p23*x10;
1596         pc[8]  = m9  = p4*x6 + p9*x7  + p14*x8 + p19*x9 + p24*x10;
1597         pc[9]  = m10 = p5*x6 + p10*x7 + p15*x8 + p20*x9 + p25*x10;
1598 
1599         pc[10] = m11 = p1*x11 + p6*x12  + p11*x13 + p16*x14 + p21*x15;
1600         pc[11] = m12 = p2*x11 + p7*x12  + p12*x13 + p17*x14 + p22*x15;
1601         pc[12] = m13 = p3*x11 + p8*x12  + p13*x13 + p18*x14 + p23*x15;
1602         pc[13] = m14 = p4*x11 + p9*x12  + p14*x13 + p19*x14 + p24*x15;
1603         pc[14] = m15 = p5*x11 + p10*x12 + p15*x13 + p20*x14 + p25*x15;
1604 
1605         pc[15] = m16 = p1*x16 + p6*x17  + p11*x18 + p16*x19 + p21*x20;
1606         pc[16] = m17 = p2*x16 + p7*x17  + p12*x18 + p17*x19 + p22*x20;
1607         pc[17] = m18 = p3*x16 + p8*x17  + p13*x18 + p18*x19 + p23*x20;
1608         pc[18] = m19 = p4*x16 + p9*x17  + p14*x18 + p19*x19 + p24*x20;
1609         pc[19] = m20 = p5*x16 + p10*x17 + p15*x18 + p20*x19 + p25*x20;
1610 
1611         pc[20] = m21 = p1*x21 + p6*x22  + p11*x23 + p16*x24 + p21*x25;
1612         pc[21] = m22 = p2*x21 + p7*x22  + p12*x23 + p17*x24 + p22*x25;
1613         pc[22] = m23 = p3*x21 + p8*x22  + p13*x23 + p18*x24 + p23*x25;
1614         pc[23] = m24 = p4*x21 + p9*x22  + p14*x23 + p19*x24 + p24*x25;
1615         pc[24] = m25 = p5*x21 + p10*x22 + p15*x23 + p20*x24 + p25*x25;
1616 
1617         nz = bi[row+1] - diag_offset[row] - 1;
1618         pv += 25;
1619         for (j=0; j<nz; j++) {
1620           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
1621           x5   = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
1622           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
1623           x14  = pv[13]; x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17];
1624           x19 = pv[18];  x20 = pv[19]; x21 = pv[20]; x22 = pv[21]; x23 = pv[22];
1625           x24 = pv[23];  x25 = pv[24];
1626           x    = rtmp + 25*pj[j];
1627           x[0] -= m1*x1 + m6*x2   + m11*x3  + m16*x4 + m21*x5;
1628           x[1] -= m2*x1 + m7*x2   + m12*x3  + m17*x4 + m22*x5;
1629           x[2] -= m3*x1 + m8*x2   + m13*x3  + m18*x4 + m23*x5;
1630           x[3] -= m4*x1 + m9*x2   + m14*x3  + m19*x4 + m24*x5;
1631           x[4] -= m5*x1 + m10*x2  + m15*x3  + m20*x4 + m25*x5;
1632 
1633           x[5] -= m1*x6 + m6*x7   + m11*x8  + m16*x9 + m21*x10;
1634           x[6] -= m2*x6 + m7*x7   + m12*x8  + m17*x9 + m22*x10;
1635           x[7] -= m3*x6 + m8*x7   + m13*x8  + m18*x9 + m23*x10;
1636           x[8] -= m4*x6 + m9*x7   + m14*x8  + m19*x9 + m24*x10;
1637           x[9] -= m5*x6 + m10*x7  + m15*x8  + m20*x9 + m25*x10;
1638 
1639           x[10] -= m1*x11 + m6*x12  + m11*x13 + m16*x14 + m21*x15;
1640           x[11] -= m2*x11 + m7*x12  + m12*x13 + m17*x14 + m22*x15;
1641           x[12] -= m3*x11 + m8*x12  + m13*x13 + m18*x14 + m23*x15;
1642           x[13] -= m4*x11 + m9*x12  + m14*x13 + m19*x14 + m24*x15;
1643           x[14] -= m5*x11 + m10*x12 + m15*x13 + m20*x14 + m25*x15;
1644 
1645           x[15] -= m1*x16 + m6*x17  + m11*x18 + m16*x19 + m21*x20;
1646           x[16] -= m2*x16 + m7*x17  + m12*x18 + m17*x19 + m22*x20;
1647           x[17] -= m3*x16 + m8*x17  + m13*x18 + m18*x19 + m23*x20;
1648           x[18] -= m4*x16 + m9*x17  + m14*x18 + m19*x19 + m24*x20;
1649           x[19] -= m5*x16 + m10*x17 + m15*x18 + m20*x19 + m25*x20;
1650 
1651           x[20] -= m1*x21 + m6*x22  + m11*x23 + m16*x24 + m21*x25;
1652           x[21] -= m2*x21 + m7*x22  + m12*x23 + m17*x24 + m22*x25;
1653           x[22] -= m3*x21 + m8*x22  + m13*x23 + m18*x24 + m23*x25;
1654           x[23] -= m4*x21 + m9*x22  + m14*x23 + m19*x24 + m24*x25;
1655           x[24] -= m5*x21 + m10*x22 + m15*x23 + m20*x24 + m25*x25;
1656           pv   += 25;
1657         }
1658         PLogFlops(250*nz+225);
1659       }
1660       row = *ajtmp++;
1661     }
1662     /* finished row so stick it into b->a */
1663     pv = ba + 25*bi[i];
1664     pj = bj + bi[i];
1665     nz = bi[i+1] - bi[i];
1666     for (j=0; j<nz; j++) {
1667       x      = rtmp+25*pj[j];
1668       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
1669       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
1670       pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
1671       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; pv[16] = x[16]; pv[17] = x[17];
1672       pv[18] = x[18]; pv[19] = x[19]; pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22];
1673       pv[23] = x[23]; pv[24] = x[24];
1674       pv   += 25;
1675     }
1676     /* invert diagonal block */
1677     w = ba + 25*diag_offset[i];
1678     ierr = Kernel_A_gets_inverse_A_5(w);CHKERRQ(ierr);
1679   }
1680 
1681   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1682   C->factor    = FACTOR_LU;
1683   C->assembled = PETSC_TRUE;
1684   PLogFlops(1.3333*125*b->mbs); /* from inverting diagonal blocks */
1685   PetscFunctionReturn(0);
1686 }
1687 
1688 /*
1689       Version for when blocks are 4 by 4 Using natural ordering
1690 */
1691 #undef __FUNC__
1692 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_4_NaturalOrdering"
1693 int MatCholeskyFactorNumeric_SeqSBAIJ_4_NaturalOrdering(Mat A,Mat *B)
1694 {
1695   Mat         C = *B;
1696   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
1697   int         ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
1698   int         *ajtmpold,*ajtmp,nz,row;
1699   int         *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
1700   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
1701   MatScalar   p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
1702   MatScalar   p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
1703   MatScalar   p10,p11,p12,p13,p14,p15,p16,m10,m11,m12;
1704   MatScalar   m13,m14,m15,m16;
1705   MatScalar   *ba = b->a,*aa = a->a;
1706 
1707   PetscFunctionBegin;
1708   rtmp  = (MatScalar*)PetscMalloc(16*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
1709 
1710   for (i=0; i<n; i++) {
1711     nz    = bi[i+1] - bi[i];
1712     ajtmp = bj + bi[i];
1713     for  (j=0; j<nz; j++) {
1714       x = rtmp+16*ajtmp[j];
1715       x[0]  = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = x[9] = 0.0;
1716       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
1717     }
1718     /* load in initial (unfactored row) */
1719     nz       = ai[i+1] - ai[i];
1720     ajtmpold = aj + ai[i];
1721     v        = aa + 16*ai[i];
1722     for (j=0; j<nz; j++) {
1723       x    = rtmp+16*ajtmpold[j];
1724       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
1725       x[4]  = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
1726       x[9]  = v[9];  x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
1727       x[14] = v[14]; x[15] = v[15];
1728       v    += 16;
1729     }
1730     row = *ajtmp++;
1731     while (row < i) {
1732       pc  = rtmp + 16*row;
1733       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
1734       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
1735       p10 = pc[9];  p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
1736       p15 = pc[14]; p16 = pc[15];
1737       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
1738           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
1739           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
1740           || p16 != 0.0) {
1741         pv = ba + 16*diag_offset[row];
1742         pj = bj + diag_offset[row] + 1;
1743         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
1744         x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
1745         x10 = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
1746         x15 = pv[14]; x16 = pv[15];
1747         pc[0] = m1 = p1*x1 + p5*x2  + p9*x3  + p13*x4;
1748         pc[1] = m2 = p2*x1 + p6*x2  + p10*x3 + p14*x4;
1749         pc[2] = m3 = p3*x1 + p7*x2  + p11*x3 + p15*x4;
1750         pc[3] = m4 = p4*x1 + p8*x2  + p12*x3 + p16*x4;
1751 
1752         pc[4] = m5 = p1*x5 + p5*x6  + p9*x7  + p13*x8;
1753         pc[5] = m6 = p2*x5 + p6*x6  + p10*x7 + p14*x8;
1754         pc[6] = m7 = p3*x5 + p7*x6  + p11*x7 + p15*x8;
1755         pc[7] = m8 = p4*x5 + p8*x6  + p12*x7 + p16*x8;
1756 
1757         pc[8]  = m9  = p1*x9 + p5*x10  + p9*x11  + p13*x12;
1758         pc[9]  = m10 = p2*x9 + p6*x10  + p10*x11 + p14*x12;
1759         pc[10] = m11 = p3*x9 + p7*x10  + p11*x11 + p15*x12;
1760         pc[11] = m12 = p4*x9 + p8*x10  + p12*x11 + p16*x12;
1761 
1762         pc[12] = m13 = p1*x13 + p5*x14  + p9*x15  + p13*x16;
1763         pc[13] = m14 = p2*x13 + p6*x14  + p10*x15 + p14*x16;
1764         pc[14] = m15 = p3*x13 + p7*x14  + p11*x15 + p15*x16;
1765         pc[15] = m16 = p4*x13 + p8*x14  + p12*x15 + p16*x16;
1766 
1767         nz = bi[row+1] - diag_offset[row] - 1;
1768         pv += 16;
1769         for (j=0; j<nz; j++) {
1770           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
1771           x5   = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
1772           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
1773           x14  = pv[13]; x15 = pv[14]; x16 = pv[15];
1774           x    = rtmp + 16*pj[j];
1775           x[0] -= m1*x1 + m5*x2  + m9*x3  + m13*x4;
1776           x[1] -= m2*x1 + m6*x2  + m10*x3 + m14*x4;
1777           x[2] -= m3*x1 + m7*x2  + m11*x3 + m15*x4;
1778           x[3] -= m4*x1 + m8*x2  + m12*x3 + m16*x4;
1779 
1780           x[4] -= m1*x5 + m5*x6  + m9*x7  + m13*x8;
1781           x[5] -= m2*x5 + m6*x6  + m10*x7 + m14*x8;
1782           x[6] -= m3*x5 + m7*x6  + m11*x7 + m15*x8;
1783           x[7] -= m4*x5 + m8*x6  + m12*x7 + m16*x8;
1784 
1785           x[8]  -= m1*x9 + m5*x10 + m9*x11  + m13*x12;
1786           x[9]  -= m2*x9 + m6*x10 + m10*x11 + m14*x12;
1787           x[10] -= m3*x9 + m7*x10 + m11*x11 + m15*x12;
1788           x[11] -= m4*x9 + m8*x10 + m12*x11 + m16*x12;
1789 
1790           x[12] -= m1*x13 + m5*x14  + m9*x15  + m13*x16;
1791           x[13] -= m2*x13 + m6*x14  + m10*x15 + m14*x16;
1792           x[14] -= m3*x13 + m7*x14  + m11*x15 + m15*x16;
1793           x[15] -= m4*x13 + m8*x14  + m12*x15 + m16*x16;
1794 
1795           pv   += 16;
1796         }
1797         PLogFlops(128*nz+112);
1798       }
1799       row = *ajtmp++;
1800     }
1801     /* finished row so stick it into b->a */
1802     pv = ba + 16*bi[i];
1803     pj = bj + bi[i];
1804     nz = bi[i+1] - bi[i];
1805     for (j=0; j<nz; j++) {
1806       x      = rtmp+16*pj[j];
1807       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
1808       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
1809       pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
1810       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
1811       pv   += 16;
1812     }
1813     /* invert diagonal block */
1814     w = ba + 16*diag_offset[i];
1815     ierr = Kernel_A_gets_inverse_A_4(w);CHKERRQ(ierr);
1816   }
1817 
1818   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1819   C->factor    = FACTOR_LU;
1820   C->assembled = PETSC_TRUE;
1821   C->preallocated = PETSC_TRUE;
1822   PLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */
1823   PetscFunctionReturn(0);
1824 }
1825 
1826 /* Version for when blocks are 4 by 4  */
1827 #undef __FUNC__
1828 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_4"
1829 int MatCholeskyFactorNumeric_SeqSBAIJ_4(Mat A,Mat *B)
1830 {
1831   Mat                C = *B;
1832   Mat_SeqSBAIJ       *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data;
1833   IS                 perm = b->row;
1834   int                *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
1835   int                *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
1836   MatScalar          *ba = b->a,*aa,*ap,*dk,*uik;
1837   MatScalar          *u,*diag,*rtmp,*rtmp_ptr;
1838 
1839   PetscFunctionBegin;
1840   /* initialization */
1841   rtmp  = (MatScalar*)PetscMalloc(16*mbs*sizeof(MatScalar));CHKPTRQ(rtmp);
1842   ierr = PetscMemzero(rtmp,16*mbs*sizeof(MatScalar));CHKERRQ(ierr);
1843   il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il);
1844   jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl);
1845   for (i=0; i<mbs; i++) {
1846     jl[i] = mbs; il[0] = 0;
1847   }
1848   dk    = (MatScalar*)PetscMalloc(16*sizeof(MatScalar));CHKPTRQ(dk);
1849   uik   = (MatScalar*)PetscMalloc(16*sizeof(MatScalar));CHKPTRQ(uik);
1850   ierr  = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr);
1851 
1852   /* check permutation */
1853   if (!a->permute){
1854     ai = a->i; aj = a->j; aa = a->a;
1855   } else {
1856     ai = a->inew; aj = a->jnew;
1857     aa = (MatScalar*)PetscMalloc(16*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa);
1858     ierr = PetscMemcpy(aa,a->a,16*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr);
1859     a2anew  = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew);
1860     ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr);
1861 
1862     for (i=0; i<mbs; i++){
1863       jmin = ai[i]; jmax = ai[i+1];
1864       for (j=jmin; j<jmax; j++){
1865         while (a2anew[j] != j){
1866           k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k;
1867           for (k1=0; k1<16; k1++){
1868             dk[k1]       = aa[k*16+k1];
1869             aa[k*16+k1] = aa[j*16+k1];
1870             aa[j*16+k1] = dk[k1];
1871           }
1872         }
1873         /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */
1874         if (i > aj[j]){
1875           /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */
1876           ap = aa + j*16;                     /* ptr to the beginning of j-th block of aa */
1877           for (k=0; k<16; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */
1878           for (k=0; k<4; k++){               /* j-th block of aa <- dk^T */
1879             for (k1=0; k1<4; k1++) *ap++ = dk[k + 4*k1];
1880           }
1881         }
1882       }
1883     }
1884     ierr = PetscFree(a2anew);CHKERRA(ierr);
1885   }
1886 
1887   /* for each row k */
1888   for (k = 0; k<mbs; k++){
1889 
1890     /*initialize k-th row with elements nonzero in row perm(k) of A */
1891     jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1];
1892     if (jmin < jmax) {
1893       ap = aa + jmin*16;
1894       for (j = jmin; j < jmax; j++){
1895         vj = perm_ptr[aj[j]];         /* block col. index */
1896         rtmp_ptr = rtmp + vj*16;
1897         for (i=0; i<16; i++) *rtmp_ptr++ = *ap++;
1898       }
1899     }
1900 
1901     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
1902     ierr = PetscMemcpy(dk,rtmp+k*16,16*sizeof(MatScalar));CHKERRQ(ierr);
1903     i = jl[k]; /* first row to be added to k_th row  */
1904 
1905     while (i < mbs){
1906       nexti = jl[i]; /* next row to be added to k_th row */
1907 
1908       /* compute multiplier */
1909       ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
1910 
1911       /* uik = -inv(Di)*U_bar(i,k) */
1912       diag = ba + i*16;
1913       u    = ba + ili*16;
1914 
1915       uik[0] = -(diag[0]*u[0] + diag[4]*u[1] + diag[8]*u[2] + diag[12]*u[3]);
1916       uik[1] = -(diag[1]*u[0] + diag[5]*u[1] + diag[9]*u[2] + diag[13]*u[3]);
1917       uik[2] = -(diag[2]*u[0] + diag[6]*u[1] + diag[10]*u[2]+ diag[14]*u[3]);
1918       uik[3] = -(diag[3]*u[0] + diag[7]*u[1] + diag[11]*u[2]+ diag[15]*u[3]);
1919 
1920       uik[4] = -(diag[0]*u[4] + diag[4]*u[5] + diag[8]*u[6] + diag[12]*u[7]);
1921       uik[5] = -(diag[1]*u[4] + diag[5]*u[5] + diag[9]*u[6] + diag[13]*u[7]);
1922       uik[6] = -(diag[2]*u[4] + diag[6]*u[5] + diag[10]*u[6]+ diag[14]*u[7]);
1923       uik[7] = -(diag[3]*u[4] + diag[7]*u[5] + diag[11]*u[6]+ diag[15]*u[7]);
1924 
1925       uik[8] = -(diag[0]*u[8] + diag[4]*u[9] + diag[8]*u[10] + diag[12]*u[11]);
1926       uik[9] = -(diag[1]*u[8] + diag[5]*u[9] + diag[9]*u[10] + diag[13]*u[11]);
1927       uik[10]= -(diag[2]*u[8] + diag[6]*u[9] + diag[10]*u[10]+ diag[14]*u[11]);
1928       uik[11]= -(diag[3]*u[8] + diag[7]*u[9] + diag[11]*u[10]+ diag[15]*u[11]);
1929 
1930       uik[12]= -(diag[0]*u[12] + diag[4]*u[13] + diag[8]*u[14] + diag[12]*u[15]);
1931       uik[13]= -(diag[1]*u[12] + diag[5]*u[13] + diag[9]*u[14] + diag[13]*u[15]);
1932       uik[14]= -(diag[2]*u[12] + diag[6]*u[13] + diag[10]*u[14]+ diag[14]*u[15]);
1933       uik[15]= -(diag[3]*u[12] + diag[7]*u[13] + diag[11]*u[14]+ diag[15]*u[15]);
1934 
1935       /* update D(k) += -U(i,k)^T * U_bar(i,k) */
1936       dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3];
1937       dk[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3];
1938       dk[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3];
1939       dk[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3];
1940 
1941       dk[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7];
1942       dk[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7];
1943       dk[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7];
1944       dk[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7];
1945 
1946       dk[8] += uik[0]*u[8] + uik[1]*u[9] + uik[2]*u[10] + uik[3]*u[11];
1947       dk[9] += uik[4]*u[8] + uik[5]*u[9] + uik[6]*u[10] + uik[7]*u[11];
1948       dk[10]+= uik[8]*u[8] + uik[9]*u[9] + uik[10]*u[10]+ uik[11]*u[11];
1949       dk[11]+= uik[12]*u[8]+ uik[13]*u[9]+ uik[14]*u[10]+ uik[15]*u[11];
1950 
1951       dk[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15];
1952       dk[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15];
1953       dk[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15];
1954       dk[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15];
1955 
1956       /* update -U(i,k) */
1957       ierr = PetscMemcpy(ba+ili*16,uik,16*sizeof(MatScalar));CHKERRQ(ierr);
1958 
1959       /* add multiple of row i to k-th row ... */
1960       jmin = ili + 1; jmax = bi[i+1];
1961       if (jmin < jmax){
1962         for (j=jmin; j<jmax; j++) {
1963           /* rtmp += -U(i,k)^T * U_bar(i,j) */
1964           rtmp_ptr = rtmp + bj[j]*16;
1965           u = ba + j*16;
1966           rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3];
1967           rtmp_ptr[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3];
1968           rtmp_ptr[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3];
1969           rtmp_ptr[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3];
1970 
1971           rtmp_ptr[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7];
1972           rtmp_ptr[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7];
1973           rtmp_ptr[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7];
1974           rtmp_ptr[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7];
1975 
1976           rtmp_ptr[8] += uik[0]*u[8] + uik[1]*u[9] + uik[2]*u[10] + uik[3]*u[11];
1977           rtmp_ptr[9] += uik[4]*u[8] + uik[5]*u[9] + uik[6]*u[10] + uik[7]*u[11];
1978           rtmp_ptr[10]+= uik[8]*u[8] + uik[9]*u[9] + uik[10]*u[10]+ uik[11]*u[11];
1979           rtmp_ptr[11]+= uik[12]*u[8]+ uik[13]*u[9]+ uik[14]*u[10]+ uik[15]*u[11];
1980 
1981           rtmp_ptr[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15];
1982           rtmp_ptr[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15];
1983           rtmp_ptr[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15];
1984           rtmp_ptr[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15];
1985         }
1986 
1987         /* ... add i to row list for next nonzero entry */
1988         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
1989         j     = bj[jmin];
1990         jl[i] = jl[j]; jl[j] = i; /* update jl */
1991       }
1992       i = nexti;
1993     }
1994 
1995     /* save nonzero entries in k-th row of U ... */
1996 
1997     /* invert diagonal block */
1998     diag = ba+k*16;
1999     ierr = PetscMemcpy(diag,dk,16*sizeof(MatScalar));CHKERRQ(ierr);
2000     ierr = Kernel_A_gets_inverse_A_4(diag);CHKERRQ(ierr);
2001 
2002     jmin = bi[k]; jmax = bi[k+1];
2003     if (jmin < jmax) {
2004       for (j=jmin; j<jmax; j++){
2005          vj = bj[j];           /* block col. index of U */
2006          u   = ba + j*16;
2007          rtmp_ptr = rtmp + vj*16;
2008          for (k1=0; k1<16; k1++){
2009            *u++        = *rtmp_ptr;
2010            *rtmp_ptr++ = 0.0;
2011          }
2012       }
2013 
2014       /* ... add k to row list for first nonzero entry in k-th row */
2015       il[k] = jmin;
2016       i     = bj[jmin];
2017       jl[k] = jl[i]; jl[i] = k;
2018     }
2019   }
2020 
2021   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2022   ierr = PetscFree(il);CHKERRQ(ierr);
2023   ierr = PetscFree(jl);CHKERRQ(ierr);
2024   ierr = PetscFree(dk);CHKERRQ(ierr);
2025   ierr = PetscFree(uik);CHKERRQ(ierr);
2026   if (a->permute){
2027     ierr = PetscFree(aa);CHKERRQ(ierr);
2028   }
2029 
2030   ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr);
2031   C->factor    = FACTOR_CHOLESKY;
2032   C->assembled = PETSC_TRUE;
2033   C->preallocated = PETSC_TRUE;
2034   PLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */
2035   PetscFunctionReturn(0);
2036 }
2037 
2038 /* Version for when blocks are 3 by 3  */
2039 #undef __FUNC__
2040 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_3"
2041 int MatCholeskyFactorNumeric_SeqSBAIJ_3(Mat A,Mat *B)
2042 {
2043   Mat                C = *B;
2044   Mat_SeqSBAIJ       *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data;
2045   IS                 perm = b->row;
2046   int                *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
2047   int                *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
2048   MatScalar          *ba = b->a,*aa,*ap,*dk,*uik;
2049   MatScalar          *u,*diag,*rtmp,*rtmp_ptr;
2050 
2051   PetscFunctionBegin;
2052   /* initialization */
2053   rtmp  = (MatScalar*)PetscMalloc(9*mbs*sizeof(MatScalar));CHKPTRQ(rtmp);
2054   ierr = PetscMemzero(rtmp,9*mbs*sizeof(MatScalar));CHKERRQ(ierr);
2055   il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il);
2056   jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl);
2057   for (i=0; i<mbs; i++) {
2058     jl[i] = mbs; il[0] = 0;
2059   }
2060   dk  = (MatScalar*)PetscMalloc(9*sizeof(MatScalar));CHKPTRQ(dk);
2061   uik = (MatScalar*)PetscMalloc(9*sizeof(MatScalar));CHKPTRQ(uik);
2062   ierr  = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr);
2063 
2064   /* check permutation */
2065   if (!a->permute){
2066     ai = a->i; aj = a->j; aa = a->a;
2067   } else {
2068     ai = a->inew; aj = a->jnew;
2069     aa = (MatScalar*)PetscMalloc(9*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa);
2070     ierr = PetscMemcpy(aa,a->a,9*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr);
2071     a2anew  = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew);
2072     ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr);
2073 
2074     for (i=0; i<mbs; i++){
2075       jmin = ai[i]; jmax = ai[i+1];
2076       for (j=jmin; j<jmax; j++){
2077         while (a2anew[j] != j){
2078           k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k;
2079           for (k1=0; k1<9; k1++){
2080             dk[k1]       = aa[k*9+k1];
2081             aa[k*9+k1] = aa[j*9+k1];
2082             aa[j*9+k1] = dk[k1];
2083           }
2084         }
2085         /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */
2086         if (i > aj[j]){
2087           /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */
2088           ap = aa + j*9;                     /* ptr to the beginning of j-th block of aa */
2089           for (k=0; k<9; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */
2090           for (k=0; k<3; k++){               /* j-th block of aa <- dk^T */
2091             for (k1=0; k1<3; k1++) *ap++ = dk[k + 3*k1];
2092           }
2093         }
2094       }
2095     }
2096     ierr = PetscFree(a2anew);CHKERRA(ierr);
2097   }
2098 
2099   /* for each row k */
2100   for (k = 0; k<mbs; k++){
2101 
2102     /*initialize k-th row with elements nonzero in row perm(k) of A */
2103     jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1];
2104     if (jmin < jmax) {
2105       ap = aa + jmin*9;
2106       for (j = jmin; j < jmax; j++){
2107         vj = perm_ptr[aj[j]];         /* block col. index */
2108         rtmp_ptr = rtmp + vj*9;
2109         for (i=0; i<9; i++) *rtmp_ptr++ = *ap++;
2110       }
2111     }
2112 
2113     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
2114     ierr = PetscMemcpy(dk,rtmp+k*9,9*sizeof(MatScalar));CHKERRQ(ierr);
2115     i = jl[k]; /* first row to be added to k_th row  */
2116 
2117     while (i < mbs){
2118       nexti = jl[i]; /* next row to be added to k_th row */
2119 
2120       /* compute multiplier */
2121       ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
2122 
2123       /* uik = -inv(Di)*U_bar(i,k) */
2124       diag = ba + i*9;
2125       u    = ba + ili*9;
2126 
2127       uik[0] = -(diag[0]*u[0] + diag[3]*u[1] + diag[6]*u[2]);
2128       uik[1] = -(diag[1]*u[0] + diag[4]*u[1] + diag[7]*u[2]);
2129       uik[2] = -(diag[2]*u[0] + diag[5]*u[1] + diag[8]*u[2]);
2130 
2131       uik[3] = -(diag[0]*u[3] + diag[3]*u[4] + diag[6]*u[5]);
2132       uik[4] = -(diag[1]*u[3] + diag[4]*u[4] + diag[7]*u[5]);
2133       uik[5] = -(diag[2]*u[3] + diag[5]*u[4] + diag[8]*u[5]);
2134 
2135       uik[6] = -(diag[0]*u[6] + diag[3]*u[7] + diag[6]*u[8]);
2136       uik[7] = -(diag[1]*u[6] + diag[4]*u[7] + diag[7]*u[8]);
2137       uik[8] = -(diag[2]*u[6] + diag[5]*u[7] + diag[8]*u[8]);
2138 
2139       /* update D(k) += -U(i,k)^T * U_bar(i,k) */
2140       dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2];
2141       dk[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2];
2142       dk[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2];
2143 
2144       dk[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5];
2145       dk[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5];
2146       dk[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5];
2147 
2148       dk[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8];
2149       dk[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8];
2150       dk[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8];
2151 
2152       /* update -U(i,k) */
2153       ierr = PetscMemcpy(ba+ili*9,uik,9*sizeof(MatScalar));CHKERRQ(ierr);
2154 
2155       /* add multiple of row i to k-th row ... */
2156       jmin = ili + 1; jmax = bi[i+1];
2157       if (jmin < jmax){
2158         for (j=jmin; j<jmax; j++) {
2159           /* rtmp += -U(i,k)^T * U_bar(i,j) */
2160           rtmp_ptr = rtmp + bj[j]*9;
2161           u = ba + j*9;
2162           rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2];
2163           rtmp_ptr[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2];
2164           rtmp_ptr[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2];
2165 
2166           rtmp_ptr[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5];
2167           rtmp_ptr[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5];
2168           rtmp_ptr[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5];
2169 
2170           rtmp_ptr[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8];
2171           rtmp_ptr[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8];
2172           rtmp_ptr[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8];
2173         }
2174 
2175         /* ... add i to row list for next nonzero entry */
2176         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
2177         j     = bj[jmin];
2178         jl[i] = jl[j]; jl[j] = i; /* update jl */
2179       }
2180       i = nexti;
2181     }
2182 
2183     /* save nonzero entries in k-th row of U ... */
2184 
2185     /* invert diagonal block */
2186     diag = ba+k*9;
2187     ierr = PetscMemcpy(diag,dk,9*sizeof(MatScalar));CHKERRQ(ierr);
2188     ierr = Kernel_A_gets_inverse_A_3(diag);CHKERRQ(ierr);
2189 
2190     jmin = bi[k]; jmax = bi[k+1];
2191     if (jmin < jmax) {
2192       for (j=jmin; j<jmax; j++){
2193          vj = bj[j];           /* block col. index of U */
2194          u   = ba + j*9;
2195          rtmp_ptr = rtmp + vj*9;
2196          for (k1=0; k1<9; k1++){
2197            *u++        = *rtmp_ptr;
2198            *rtmp_ptr++ = 0.0;
2199          }
2200       }
2201 
2202       /* ... add k to row list for first nonzero entry in k-th row */
2203       il[k] = jmin;
2204       i     = bj[jmin];
2205       jl[k] = jl[i]; jl[i] = k;
2206     }
2207   }
2208 
2209   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2210   ierr = PetscFree(il);CHKERRQ(ierr);
2211   ierr = PetscFree(jl);CHKERRQ(ierr);
2212   ierr = PetscFree(dk);CHKERRQ(ierr);
2213   ierr = PetscFree(uik);CHKERRQ(ierr);
2214   if (a->permute){
2215     ierr = PetscFree(aa);CHKERRQ(ierr);
2216   }
2217 
2218   ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr);
2219   C->factor    = FACTOR_CHOLESKY;
2220   C->assembled = PETSC_TRUE;
2221   C->preallocated = PETSC_TRUE;
2222   PLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */
2223   PetscFunctionReturn(0);
2224 }
2225 
2226 /*
2227       Version for when blocks are 3 by 3 Using natural ordering
2228 */
2229 #undef __FUNC__
2230 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_3_NaturalOrdering"
2231 int MatCholeskyFactorNumeric_SeqSBAIJ_3_NaturalOrdering(Mat A,Mat *B)
2232 {
2233   Mat                C = *B;
2234   Mat_SeqBAIJ        *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
2235   int                ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
2236   int                *ajtmpold,*ajtmp,nz,row;
2237   int                *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
2238   MatScalar          *pv,*v,*rtmp,*pc,*w,*x;
2239   MatScalar          p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
2240   MatScalar          p5,p6,p7,p8,p9,x5,x6,x7,x8,x9;
2241   MatScalar          *ba = b->a,*aa = a->a;
2242 
2243   PetscFunctionBegin;
2244   rtmp  = (MatScalar*)PetscMalloc(9*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
2245 
2246   for (i=0; i<n; i++) {
2247     nz    = bi[i+1] - bi[i];
2248     ajtmp = bj + bi[i];
2249     for  (j=0; j<nz; j++) {
2250       x = rtmp+9*ajtmp[j];
2251       x[0]  = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = 0.0;
2252     }
2253     /* load in initial (unfactored row) */
2254     nz       = ai[i+1] - ai[i];
2255     ajtmpold = aj + ai[i];
2256     v        = aa + 9*ai[i];
2257     for (j=0; j<nz; j++) {
2258       x    = rtmp+9*ajtmpold[j];
2259       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
2260       x[4]  = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
2261       v    += 9;
2262     }
2263     row = *ajtmp++;
2264     while (row < i) {
2265       pc  = rtmp + 9*row;
2266       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
2267       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
2268       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
2269           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0) {
2270         pv = ba + 9*diag_offset[row];
2271         pj = bj + diag_offset[row] + 1;
2272         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
2273         x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
2274         pc[0] = m1 = p1*x1 + p4*x2 + p7*x3;
2275         pc[1] = m2 = p2*x1 + p5*x2 + p8*x3;
2276         pc[2] = m3 = p3*x1 + p6*x2 + p9*x3;
2277 
2278         pc[3] = m4 = p1*x4 + p4*x5 + p7*x6;
2279         pc[4] = m5 = p2*x4 + p5*x5 + p8*x6;
2280         pc[5] = m6 = p3*x4 + p6*x5 + p9*x6;
2281 
2282         pc[6] = m7 = p1*x7 + p4*x8 + p7*x9;
2283         pc[7] = m8 = p2*x7 + p5*x8 + p8*x9;
2284         pc[8] = m9 = p3*x7 + p6*x8 + p9*x9;
2285 
2286         nz = bi[row+1] - diag_offset[row] - 1;
2287         pv += 9;
2288         for (j=0; j<nz; j++) {
2289           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
2290           x5   = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
2291           x    = rtmp + 9*pj[j];
2292           x[0] -= m1*x1 + m4*x2 + m7*x3;
2293           x[1] -= m2*x1 + m5*x2 + m8*x3;
2294           x[2] -= m3*x1 + m6*x2 + m9*x3;
2295 
2296           x[3] -= m1*x4 + m4*x5 + m7*x6;
2297           x[4] -= m2*x4 + m5*x5 + m8*x6;
2298           x[5] -= m3*x4 + m6*x5 + m9*x6;
2299 
2300           x[6] -= m1*x7 + m4*x8 + m7*x9;
2301           x[7] -= m2*x7 + m5*x8 + m8*x9;
2302           x[8] -= m3*x7 + m6*x8 + m9*x9;
2303           pv   += 9;
2304         }
2305         PLogFlops(54*nz+36);
2306       }
2307       row = *ajtmp++;
2308     }
2309     /* finished row so stick it into b->a */
2310     pv = ba + 9*bi[i];
2311     pj = bj + bi[i];
2312     nz = bi[i+1] - bi[i];
2313     for (j=0; j<nz; j++) {
2314       x      = rtmp+9*pj[j];
2315       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
2316       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
2317       pv   += 9;
2318     }
2319     /* invert diagonal block */
2320     w = ba + 9*diag_offset[i];
2321     ierr = Kernel_A_gets_inverse_A_3(w);CHKERRQ(ierr);
2322   }
2323 
2324   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2325   C->factor    = FACTOR_CHOLESKY;
2326   C->assembled = PETSC_TRUE;
2327   C->preallocated = PETSC_TRUE;
2328   PLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */
2329   PetscFunctionReturn(0);
2330 }
2331 
2332 /*
2333     Numeric U^T*D*U factorization for SBAIJ format. Modified from SNF of YSMP.
2334     Version for blocks 2 by 2.
2335 */
2336 #undef __FUNC__
2337 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_2"
2338 int MatCholeskyFactorNumeric_SeqSBAIJ_2(Mat A,Mat *B)
2339 {
2340   Mat                C = *B;
2341   Mat_SeqSBAIJ       *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data;
2342   IS                 perm = b->row;
2343   int                *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
2344   int                *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
2345   MatScalar          *ba = b->a,*aa,*ap,*dk,*uik;
2346   MatScalar          *u,*diag,*rtmp,*rtmp_ptr;
2347 
2348   PetscFunctionBegin;
2349 
2350   /* initialization */
2351   /* il and jl record the first nonzero element in each row of the accessing
2352      window U(0:k, k:mbs-1).
2353      jl:    list of rows to be added to uneliminated rows
2354             i>= k: jl(i) is the first row to be added to row i
2355             i<  k: jl(i) is the row following row i in some list of rows
2356             jl(i) = mbs indicates the end of a list
2357      il(i): points to the first nonzero element in columns k,...,mbs-1 of
2358             row i of U */
2359   rtmp  = (MatScalar*)PetscMalloc(4*mbs*sizeof(MatScalar));CHKPTRQ(rtmp);
2360   ierr = PetscMemzero(rtmp,4*mbs*sizeof(MatScalar));CHKERRQ(ierr);
2361   il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il);
2362   jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl);
2363   for (i=0; i<mbs; i++) {
2364     jl[i] = mbs; il[0] = 0;
2365   }
2366   dk  = (MatScalar*)PetscMalloc(4*sizeof(MatScalar));CHKPTRQ(dk);
2367   uik = (MatScalar*)PetscMalloc(4*sizeof(MatScalar));CHKPTRQ(uik);
2368   ierr  = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr);
2369 
2370   /* check permutation */
2371   if (!a->permute){
2372     ai = a->i; aj = a->j; aa = a->a;
2373   } else {
2374     ai = a->inew; aj = a->jnew;
2375     aa = (MatScalar*)PetscMalloc(4*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa);
2376     ierr = PetscMemcpy(aa,a->a,4*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr);
2377     a2anew  = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew);
2378     ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr);
2379 
2380     for (i=0; i<mbs; i++){
2381       jmin = ai[i]; jmax = ai[i+1];
2382       for (j=jmin; j<jmax; j++){
2383         while (a2anew[j] != j){
2384           k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k;
2385           for (k1=0; k1<4; k1++){
2386             dk[k1]       = aa[k*4+k1];
2387             aa[k*4+k1] = aa[j*4+k1];
2388             aa[j*4+k1] = dk[k1];
2389           }
2390         }
2391         /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */
2392         if (i > aj[j]){
2393           /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */
2394           ap = aa + j*4;     /* ptr to the beginning of the block */
2395           dk[1] = ap[1];     /* swap ap[1] and ap[2] */
2396           ap[1] = ap[2];
2397           ap[2] = dk[1];
2398         }
2399       }
2400     }
2401     ierr = PetscFree(a2anew);CHKERRA(ierr);
2402   }
2403 
2404   /* for each row k */
2405   for (k = 0; k<mbs; k++){
2406 
2407     /*initialize k-th row with elements nonzero in row perm(k) of A */
2408     jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1];
2409     if (jmin < jmax) {
2410       ap = aa + jmin*4;
2411       for (j = jmin; j < jmax; j++){
2412         vj = perm_ptr[aj[j]];         /* block col. index */
2413         rtmp_ptr = rtmp + vj*4;
2414         for (i=0; i<4; i++) *rtmp_ptr++ = *ap++;
2415       }
2416     }
2417 
2418     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
2419     ierr = PetscMemcpy(dk,rtmp+k*4,4*sizeof(MatScalar));CHKERRQ(ierr);
2420     i = jl[k]; /* first row to be added to k_th row  */
2421 
2422     while (i < mbs){
2423       nexti = jl[i]; /* next row to be added to k_th row */
2424 
2425       /* compute multiplier */
2426       ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
2427 
2428       /* uik = -inv(Di)*U_bar(i,k): - ba[ili]*ba[i] */
2429       diag = ba + i*4;
2430       u    = ba + ili*4;
2431       uik[0] = -(diag[0]*u[0] + diag[2]*u[1]);
2432       uik[1] = -(diag[1]*u[0] + diag[3]*u[1]);
2433       uik[2] = -(diag[0]*u[2] + diag[2]*u[3]);
2434       uik[3] = -(diag[1]*u[2] + diag[3]*u[3]);
2435 
2436       /* update D(k) += -U(i,k)^T * U_bar(i,k): dk += uik*ba[ili] */
2437       dk[0] += uik[0]*u[0] + uik[1]*u[1];
2438       dk[1] += uik[2]*u[0] + uik[3]*u[1];
2439       dk[2] += uik[0]*u[2] + uik[1]*u[3];
2440       dk[3] += uik[2]*u[2] + uik[3]*u[3];
2441 
2442       /* update -U(i,k): ba[ili] = uik */
2443       ierr = PetscMemcpy(ba+ili*4,uik,4*sizeof(MatScalar));CHKERRQ(ierr);
2444 
2445       /* add multiple of row i to k-th row ... */
2446       jmin = ili + 1; jmax = bi[i+1];
2447       if (jmin < jmax){
2448         for (j=jmin; j<jmax; j++) {
2449           /* rtmp += -U(i,k)^T * U_bar(i,j): rtmp[bj[j]] += uik*ba[j]; */
2450           rtmp_ptr = rtmp + bj[j]*4;
2451           u = ba + j*4;
2452           rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1];
2453           rtmp_ptr[1] += uik[2]*u[0] + uik[3]*u[1];
2454           rtmp_ptr[2] += uik[0]*u[2] + uik[1]*u[3];
2455           rtmp_ptr[3] += uik[2]*u[2] + uik[3]*u[3];
2456         }
2457 
2458         /* ... add i to row list for next nonzero entry */
2459         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
2460         j     = bj[jmin];
2461         jl[i] = jl[j]; jl[j] = i; /* update jl */
2462       }
2463       i = nexti;
2464     }
2465 
2466     /* save nonzero entries in k-th row of U ... */
2467 
2468     /* invert diagonal block */
2469     diag = ba+k*4;
2470     ierr = PetscMemcpy(diag,dk,4*sizeof(MatScalar));CHKERRQ(ierr);
2471     ierr = Kernel_A_gets_inverse_A_2(diag);CHKERRQ(ierr);
2472 
2473     jmin = bi[k]; jmax = bi[k+1];
2474     if (jmin < jmax) {
2475       for (j=jmin; j<jmax; j++){
2476          vj = bj[j];           /* block col. index of U */
2477          u   = ba + j*4;
2478          rtmp_ptr = rtmp + vj*4;
2479          for (k1=0; k1<4; k1++){
2480            *u++        = *rtmp_ptr;
2481            *rtmp_ptr++ = 0.0;
2482          }
2483       }
2484 
2485       /* ... add k to row list for first nonzero entry in k-th row */
2486       il[k] = jmin;
2487       i     = bj[jmin];
2488       jl[k] = jl[i]; jl[i] = k;
2489     }
2490   }
2491 
2492   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2493   ierr = PetscFree(il);CHKERRQ(ierr);
2494   ierr = PetscFree(jl);CHKERRQ(ierr);
2495   ierr = PetscFree(dk);CHKERRQ(ierr);
2496   ierr = PetscFree(uik);CHKERRQ(ierr);
2497   if (a->permute){
2498     ierr = PetscFree(aa);CHKERRQ(ierr);
2499   }
2500 
2501   ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr);
2502   C->factor    = FACTOR_CHOLESKY;
2503   C->assembled = PETSC_TRUE;
2504   C->preallocated = PETSC_TRUE;
2505   PLogFlops(1.3333*8*b->mbs); /* from inverting diagonal blocks */
2506   PetscFunctionReturn(0);
2507 }
2508 
2509 /*
2510       Version for when blocks are 2 by 2 Using natural ordering
2511 */
2512 #undef __FUNC__
2513 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_2_NaturalOrdering"
2514 int MatCholeskyFactorNumeric_SeqSBAIJ_2_NaturalOrdering(Mat A,Mat *B)
2515 {
2516   Mat                C = *B;
2517   Mat_SeqBAIJ        *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
2518   int                ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
2519   int                *ajtmpold,*ajtmp,nz,row;
2520   int                *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
2521   MatScalar          *pv,*v,*rtmp,*pc,*w,*x;
2522   MatScalar          p1,p2,p3,p4,m1,m2,m3,m4,x1,x2,x3,x4;
2523   MatScalar          *ba = b->a,*aa = a->a;
2524 
2525   PetscFunctionBegin;
2526   rtmp  = (MatScalar*)PetscMalloc(4*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
2527 
2528   for (i=0; i<n; i++) {
2529     nz    = bi[i+1] - bi[i];
2530     ajtmp = bj + bi[i];
2531     for  (j=0; j<nz; j++) {
2532       x = rtmp+4*ajtmp[j];
2533       x[0]  = x[1]  = x[2]  = x[3]  = 0.0;
2534     }
2535     /* load in initial (unfactored row) */
2536     nz       = ai[i+1] - ai[i];
2537     ajtmpold = aj + ai[i];
2538     v        = aa + 4*ai[i];
2539     for (j=0; j<nz; j++) {
2540       x    = rtmp+4*ajtmpold[j];
2541       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
2542       v    += 4;
2543     }
2544     row = *ajtmp++;
2545     while (row < i) {
2546       pc  = rtmp + 4*row;
2547       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
2548       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0) {
2549         pv = ba + 4*diag_offset[row];
2550         pj = bj + diag_offset[row] + 1;
2551         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
2552         pc[0] = m1 = p1*x1 + p3*x2;
2553         pc[1] = m2 = p2*x1 + p4*x2;
2554         pc[2] = m3 = p1*x3 + p3*x4;
2555         pc[3] = m4 = p2*x3 + p4*x4;
2556         nz = bi[row+1] - diag_offset[row] - 1;
2557         pv += 4;
2558         for (j=0; j<nz; j++) {
2559           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
2560           x    = rtmp + 4*pj[j];
2561           x[0] -= m1*x1 + m3*x2;
2562           x[1] -= m2*x1 + m4*x2;
2563           x[2] -= m1*x3 + m3*x4;
2564           x[3] -= m2*x3 + m4*x4;
2565           pv   += 4;
2566         }
2567         PLogFlops(16*nz+12);
2568       }
2569       row = *ajtmp++;
2570     }
2571     /* finished row so stick it into b->a */
2572     pv = ba + 4*bi[i];
2573     pj = bj + bi[i];
2574     nz = bi[i+1] - bi[i];
2575     for (j=0; j<nz; j++) {
2576       x      = rtmp+4*pj[j];
2577       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
2578       pv   += 4;
2579     }
2580     /* invert diagonal block */
2581     w = ba + 4*diag_offset[i];
2582     ierr = Kernel_A_gets_inverse_A_2(w);CHKERRQ(ierr);
2583     /*Kernel_A_gets_inverse_A(bs,w,v_pivots,v_work);*/
2584   }
2585 
2586   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2587   C->factor    = FACTOR_LU;
2588   C->assembled = PETSC_TRUE;
2589   C->preallocated = PETSC_TRUE;
2590   PLogFlops(1.3333*8*b->mbs); /* from inverting diagonal blocks */
2591   PetscFunctionReturn(0);
2592 }
2593 
2594 /*
2595     Numeric U^T*D*U factorization for SBAIJ format. Modified from SNF of YSMP.
2596     Version for blocks are 1 by 1.
2597 */
2598 #undef __FUNC__
2599 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_1"
2600 int MatCholeskyFactorNumeric_SeqSBAIJ_1(Mat A,Mat *B)
2601 {
2602   Mat                C = *B;
2603   Mat_SeqSBAIJ       *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data;
2604   IS                 ip = b->row;
2605   int                *rip,ierr,i,j,mbs = a->mbs,*bi = b->i,*bj = b->j;
2606   int                *ai,*aj,*r;
2607   MatScalar          *rtmp;
2608   MatScalar          *ba = b->a,*aa,ak;
2609   MatScalar          dk,uikdi;
2610   int                k,jmin,jmax,*jl,*il,vj,nexti,ili;
2611 
2612   PetscFunctionBegin;
2613   ierr  = ISGetIndices(ip,&rip);CHKERRQ(ierr);
2614   if (!a->permute){
2615     ai = a->i; aj = a->j; aa = a->a;
2616   } else {
2617     ai = a->inew; aj = a->jnew;
2618     aa = (MatScalar*)PetscMalloc(ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa);
2619     ierr = PetscMemcpy(aa,a->a,ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr);
2620     r   = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(r);
2621     ierr= PetscMemcpy(r,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr);
2622 
2623     jmin = ai[0]; jmax = ai[mbs];
2624     for (j=jmin; j<jmax; j++){
2625       while (r[j] != j){
2626         k = r[j]; r[j] = r[k]; r[k] = k;
2627         ak = aa[k]; aa[k] = aa[j]; aa[j] = ak;
2628       }
2629     }
2630     ierr = PetscFree(r);CHKERRA(ierr);
2631   }
2632 
2633   /* initialization */
2634   /* il and jl record the first nonzero element in each row of the accessing
2635      window U(0:k, k:mbs-1).
2636      jl:    list of rows to be added to uneliminated rows
2637             i>= k: jl(i) is the first row to be added to row i
2638             i<  k: jl(i) is the row following row i in some list of rows
2639             jl(i) = mbs indicates the end of a list
2640      il(i): points to the first nonzero element in columns k,...,mbs-1 of
2641             row i of U */
2642   rtmp  = (MatScalar*)PetscMalloc(mbs*sizeof(MatScalar));CHKPTRQ(rtmp);
2643   il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il);
2644   jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl);
2645   for (i=0; i<mbs; i++) {
2646     rtmp[i] = 0.0; jl[i] = mbs; il[0] = 0;
2647   }
2648 
2649   /* for each row k */
2650   for (k = 0; k<mbs; k++){
2651 
2652     /*initialize k-th row with elements nonzero in row perm(k) of A */
2653     jmin = ai[rip[k]]; jmax = ai[rip[k]+1];
2654     if (jmin < jmax) {
2655       for (j = jmin; j < jmax; j++){
2656         vj = rip[aj[j]];
2657         /* if (k <= vj)*/ rtmp[vj] = aa[j];
2658       }
2659     }
2660 
2661     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
2662     dk = rtmp[k];
2663     i = jl[k]; /* first row to be added to k_th row  */
2664     /* printf(" k=%d, pivot row = %d\n",k,i); */
2665 
2666     while (i < mbs){
2667       nexti = jl[i]; /* next row to be added to k_th row */
2668 
2669       /* compute multiplier, update D(k) and U(i,k) */
2670       ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
2671       uikdi = - ba[ili]*ba[i];
2672       dk += uikdi*ba[ili];
2673       ba[ili] = uikdi; /* -U(i,k) */
2674 
2675       /* add multiple of row i to k-th row ... */
2676       jmin = ili + 1; jmax = bi[i+1];
2677       if (jmin < jmax){
2678         for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j];
2679         /* ... add i to row list for next nonzero entry */
2680         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
2681         j     = bj[jmin];
2682         jl[i] = jl[j]; jl[j] = i; /* update jl */
2683       }
2684       i = nexti; /* printf("                  pivot row i=%d\n",i);  */
2685     }
2686 
2687     /* check for zero pivot and save diagoanl element */
2688     if (dk == 0.0){
2689       SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot");
2690     }else if (PetscRealPart(dk) < 0){
2691       ierr = PetscPrintf(PETSC_COMM_SELF,"Negative pivot: d[%d] = %g\n",k,dk);
2692     }
2693 
2694     /* save nonzero entries in k-th row of U ... */
2695     ba[k] = 1.0/dk;
2696     jmin = bi[k]; jmax = bi[k+1];
2697     if (jmin < jmax) {
2698       for (j=jmin; j<jmax; j++){
2699          vj = bj[j]; ba[j] = rtmp[vj]; rtmp[vj] = 0.0;
2700       }
2701       /* ... add k to row list for first nonzero entry in k-th row */
2702       il[k] = jmin;
2703       i     = bj[jmin];
2704       jl[k] = jl[i]; jl[i] = k;
2705     }
2706   }
2707 
2708   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2709   ierr = PetscFree(il);CHKERRQ(ierr);
2710   ierr = PetscFree(jl);CHKERRQ(ierr);
2711   if (a->permute){
2712     ierr = PetscFree(aa);CHKERRQ(ierr);
2713   }
2714 
2715   ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr);
2716   C->factor    = FACTOR_CHOLESKY;
2717   C->assembled = PETSC_TRUE;
2718   C->preallocated = PETSC_TRUE;
2719   PLogFlops(b->mbs);
2720 #ifdef TEMP
2721   printf("in factnum_1\n");
2722   for (k=0; k<mbs; k++){
2723     i = b->i[k+1] - b->i[k];
2724     printf("\n b->i[%d]: %d, nzk: %d, diag: %g\n",k,b->i[k],i,b->a[k]);
2725     jmin = b->i[k]; jmax = b->i[k+1];
2726     for (j=jmin; j<jmax; j++){
2727       printf(" %d %g, ",b->j[j],b->a[j]);
2728     }
2729   }
2730 #endif
2731   PetscFunctionReturn(0);
2732 }
2733 
2734 #undef __FUNC__
2735 #define __FUNC__ "MatCholeskyFactor_SeqSBAIJ"
2736 int MatCholeskyFactor_SeqSBAIJ(Mat A,IS perm,PetscReal f)
2737 {
2738   int ierr;
2739   Mat C;
2740 
2741   PetscFunctionBegin;
2742   ierr = MatCholeskyFactorSymbolic(A,perm,f,&C);CHKERRQ(ierr);
2743   ierr = MatCholeskyFactorNumeric(A,&C);CHKERRQ(ierr);
2744   ierr = MatHeaderCopy(A,C);CHKERRQ(ierr);
2745   PetscFunctionReturn(0);
2746 }
2747 
2748 
2749