xref: /petsc/src/mat/impls/sbaij/seq/sbaijfact.c (revision b59abe41f7046795d52ee5645eea94fb5259d4d3)
1 /* Using Modified Sparse Row (MSR) storage.
2 See page 85, "Iterative Methods ..." by Saad. */
3 
4 /*$Id: sbaijfact.c,v 1.35 2000/10/30 19:58:55 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) */  /* undone yet! */
1397       dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3];
1398       dk[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3];
1399       dk[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3];
1400       dk[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3];
1401 
1402       dk[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7];
1403       dk[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7];
1404       dk[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7];
1405       dk[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7];
1406 
1407       dk[8] += uik[0]*u[8] + uik[1]*u[9] + uik[2]*u[10] + uik[3]*u[11];
1408       dk[9] += uik[4]*u[8] + uik[5]*u[9] + uik[6]*u[10] + uik[7]*u[11];
1409       dk[10]+= uik[8]*u[8] + uik[9]*u[9] + uik[10]*u[10]+ uik[11]*u[11];
1410       dk[11]+= uik[12]*u[8]+ uik[13]*u[9]+ uik[14]*u[10]+ uik[15]*u[11];
1411 
1412       dk[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15];
1413       dk[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15];
1414       dk[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15];
1415       dk[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15];
1416 
1417       /* update -U(i,k) */
1418       ierr = PetscMemcpy(ba+ili*25,uik,25*sizeof(MatScalar));CHKERRQ(ierr);
1419 
1420       /* add multiple of row i to k-th row ... */
1421       jmin = ili + 1; jmax = bi[i+1];
1422       if (jmin < jmax){
1423         for (j=jmin; j<jmax; j++) {
1424           /* rtmp += -U(i,k)^T * U_bar(i,j) */
1425           rtmp_ptr = rtmp + bj[j]*25;
1426           u = ba + j*25;
1427           rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3];
1428           rtmp_ptr[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3];
1429           rtmp_ptr[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3];
1430           rtmp_ptr[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3];
1431 
1432           rtmp_ptr[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7];
1433           rtmp_ptr[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7];
1434           rtmp_ptr[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7];
1435           rtmp_ptr[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7];
1436 
1437           rtmp_ptr[8] += uik[0]*u[8] + uik[1]*u[9] + uik[2]*u[10] + uik[3]*u[11];
1438           rtmp_ptr[9] += uik[4]*u[8] + uik[5]*u[9] + uik[6]*u[10] + uik[7]*u[11];
1439           rtmp_ptr[10]+= uik[8]*u[8] + uik[9]*u[9] + uik[10]*u[10]+ uik[11]*u[11];
1440           rtmp_ptr[11]+= uik[12]*u[8]+ uik[13]*u[9]+ uik[14]*u[10]+ uik[15]*u[11];
1441 
1442           rtmp_ptr[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15];
1443           rtmp_ptr[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15];
1444           rtmp_ptr[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15];
1445           rtmp_ptr[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15];
1446         }
1447 
1448         /* ... add i to row list for next nonzero entry */
1449         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
1450         j     = bj[jmin];
1451         jl[i] = jl[j]; jl[j] = i; /* update jl */
1452       }
1453       i = nexti;
1454     }
1455 
1456     /* save nonzero entries in k-th row of U ... */
1457 
1458     /* invert diagonal block */
1459     d = ba+k*25;
1460     ierr = PetscMemcpy(d,dk,25*sizeof(MatScalar));CHKERRQ(ierr);
1461     ierr = Kernel_A_gets_inverse_A_5(d);CHKERRQ(ierr);
1462 
1463     jmin = bi[k]; jmax = bi[k+1];
1464     if (jmin < jmax) {
1465       for (j=jmin; j<jmax; j++){
1466          vj = bj[j];           /* block col. index of U */
1467          u   = ba + j*25;
1468          rtmp_ptr = rtmp + vj*25;
1469          for (k1=0; k1<25; k1++){
1470            *u++        = *rtmp_ptr;
1471            *rtmp_ptr++ = 0.0;
1472          }
1473       }
1474 
1475       /* ... add k to row list for first nonzero entry in k-th row */
1476       il[k] = jmin;
1477       i     = bj[jmin];
1478       jl[k] = jl[i]; jl[i] = k;
1479     }
1480   }
1481 
1482   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1483   ierr = PetscFree(il);CHKERRQ(ierr);
1484   ierr = PetscFree(jl);CHKERRQ(ierr);
1485   ierr = PetscFree(dk);CHKERRQ(ierr);
1486   ierr = PetscFree(uik);CHKERRQ(ierr);
1487   if (a->permute){
1488     ierr = PetscFree(aa);CHKERRQ(ierr);
1489   }
1490 
1491   ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr);
1492   C->factor    = FACTOR_CHOLESKY;
1493   C->assembled = PETSC_TRUE;
1494   C->preallocated = PETSC_TRUE;
1495   PLogFlops(1.3333*125*b->mbs); /* from inverting diagonal blocks */
1496   PetscFunctionReturn(0);
1497 }
1498 #ifdef OLD
1499 /*
1500       Version for when blocks are 5 by 5
1501 */
1502 #undef __FUNC__
1503 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_5"
1504 int MatCholeskyFactorNumeric_SeqSBAIJ_5(Mat A,Mat *B)
1505 {
1506   Mat         C = *B;
1507   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
1508   IS          isrow = b->row,isicol = b->icol;
1509   int         *r,*ic,ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
1510   int         *ajtmpold,*ajtmp,nz,row;
1511   int         *diag_offset = b->diag,idx,*ai=a->i,*aj=a->j,*pj;
1512   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
1513   MatScalar   p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
1514   MatScalar   p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
1515   MatScalar   x17,x18,x19,x20,x21,x22,x23,x24,x25,p10,p11,p12,p13,p14;
1516   MatScalar   p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,m10,m11,m12;
1517   MatScalar   m13,m14,m15,m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
1518   MatScalar   *ba = b->a,*aa = a->a;
1519 
1520   PetscFunctionBegin;
1521   ierr  = ISGetIndices(isrow,&r);CHKERRQ(ierr);
1522   ierr  = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
1523   rtmp  = (MatScalar*)PetscMalloc(25*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
1524 
1525   for (i=0; i<n; i++) {
1526     nz    = bi[i+1] - bi[i];
1527     ajtmp = bj + bi[i];
1528     for  (j=0; j<nz; j++) {
1529       x = rtmp+25*ajtmp[j];
1530       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
1531       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
1532       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0;
1533     }
1534     /* load in initial (unfactored row) */
1535     idx      = r[i];
1536     nz       = ai[idx+1] - ai[idx];
1537     ajtmpold = aj + ai[idx];
1538     v        = aa + 25*ai[idx];
1539     for (j=0; j<nz; j++) {
1540       x    = rtmp+25*ic[ajtmpold[j]];
1541       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
1542       x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
1543       x[9] = v[9]; x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
1544       x[14] = v[14]; x[15] = v[15]; x[16] = v[16]; x[17] = v[17];
1545       x[18] = v[18]; x[19] = v[19]; x[20] = v[20]; x[21] = v[21];
1546       x[22] = v[22]; x[23] = v[23]; x[24] = v[24];
1547       v    += 25;
1548     }
1549     row = *ajtmp++;
1550     while (row < i) {
1551       pc = rtmp + 25*row;
1552       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
1553       p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
1554       p10 = pc[9]; p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
1555       p15 = pc[14]; p16 = pc[15]; p17 = pc[16]; p18 = pc[17]; p19 = pc[18];
1556       p20 = pc[19]; p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
1557       p25 = pc[24];
1558       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
1559           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
1560           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
1561           || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 ||
1562           p20 != 0.0 || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 ||
1563           p24 != 0.0 || p25 != 0.0) {
1564         pv = ba + 25*diag_offset[row];
1565         pj = bj + diag_offset[row] + 1;
1566         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
1567         x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
1568         x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
1569         x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17];
1570         x19 = pv[18]; x20 = pv[19]; x21 = pv[20]; x22 = pv[21];
1571         x23 = pv[22]; x24 = pv[23]; x25 = pv[24];
1572         pc[0] = m1 = p1*x1 + p6*x2  + p11*x3 + p16*x4 + p21*x5;
1573         pc[1] = m2 = p2*x1 + p7*x2  + p12*x3 + p17*x4 + p22*x5;
1574         pc[2] = m3 = p3*x1 + p8*x2  + p13*x3 + p18*x4 + p23*x5;
1575         pc[3] = m4 = p4*x1 + p9*x2  + p14*x3 + p19*x4 + p24*x5;
1576         pc[4] = m5 = p5*x1 + p10*x2 + p15*x3 + p20*x4 + p25*x5;
1577 
1578         pc[5] = m6 = p1*x6 + p6*x7  + p11*x8 + p16*x9 + p21*x10;
1579         pc[6] = m7 = p2*x6 + p7*x7  + p12*x8 + p17*x9 + p22*x10;
1580         pc[7] = m8 = p3*x6 + p8*x7  + p13*x8 + p18*x9 + p23*x10;
1581         pc[8] = m9 = p4*x6 + p9*x7  + p14*x8 + p19*x9 + p24*x10;
1582         pc[9] = m10 = p5*x6 + p10*x7 + p15*x8 + p20*x9 + p25*x10;
1583 
1584         pc[10] = m11 = p1*x11 + p6*x12  + p11*x13 + p16*x14 + p21*x15;
1585         pc[11] = m12 = p2*x11 + p7*x12  + p12*x13 + p17*x14 + p22*x15;
1586         pc[12] = m13 = p3*x11 + p8*x12  + p13*x13 + p18*x14 + p23*x15;
1587         pc[13] = m14 = p4*x11 + p9*x12  + p14*x13 + p19*x14 + p24*x15;
1588         pc[14] = m15 = p5*x11 + p10*x12 + p15*x13 + p20*x14 + p25*x15;
1589 
1590         pc[15] = m16 = p1*x16 + p6*x17  + p11*x18 + p16*x19 + p21*x20;
1591         pc[16] = m17 = p2*x16 + p7*x17  + p12*x18 + p17*x19 + p22*x20;
1592         pc[17] = m18 = p3*x16 + p8*x17  + p13*x18 + p18*x19 + p23*x20;
1593         pc[18] = m19 = p4*x16 + p9*x17  + p14*x18 + p19*x19 + p24*x20;
1594         pc[19] = m20 = p5*x16 + p10*x17 + p15*x18 + p20*x19 + p25*x20;
1595 
1596         pc[20] = m21 = p1*x21 + p6*x22  + p11*x23 + p16*x24 + p21*x25;
1597         pc[21] = m22 = p2*x21 + p7*x22  + p12*x23 + p17*x24 + p22*x25;
1598         pc[22] = m23 = p3*x21 + p8*x22  + p13*x23 + p18*x24 + p23*x25;
1599         pc[23] = m24 = p4*x21 + p9*x22  + p14*x23 + p19*x24 + p24*x25;
1600         pc[24] = m25 = p5*x21 + p10*x22 + p15*x23 + p20*x24 + p25*x25;
1601 
1602         nz = bi[row+1] - diag_offset[row] - 1;
1603         pv += 25;
1604         for (j=0; j<nz; j++) {
1605           x1   = pv[0];  x2 = pv[1];   x3  = pv[2];  x4  = pv[3];
1606           x5   = pv[4];  x6 = pv[5];   x7  = pv[6];  x8  = pv[7]; x9 = pv[8];
1607           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
1608           x14  = pv[13]; x15 = pv[14]; x16 = pv[15]; x17 = pv[16];
1609           x18  = pv[17]; x19 = pv[18]; x20 = pv[19]; x21 = pv[20];
1610           x22  = pv[21]; x23 = pv[22]; x24 = pv[23]; x25 = pv[24];
1611           x    = rtmp + 25*pj[j];
1612           x[0] -= m1*x1 + m6*x2  + m11*x3 + m16*x4 + m21*x5;
1613           x[1] -= m2*x1 + m7*x2  + m12*x3 + m17*x4 + m22*x5;
1614           x[2] -= m3*x1 + m8*x2  + m13*x3 + m18*x4 + m23*x5;
1615           x[3] -= m4*x1 + m9*x2  + m14*x3 + m19*x4 + m24*x5;
1616           x[4] -= m5*x1 + m10*x2 + m15*x3 + m20*x4 + m25*x5;
1617 
1618           x[5] -= m1*x6 + m6*x7  + m11*x8 + m16*x9 + m21*x10;
1619           x[6] -= m2*x6 + m7*x7  + m12*x8 + m17*x9 + m22*x10;
1620           x[7] -= m3*x6 + m8*x7  + m13*x8 + m18*x9 + m23*x10;
1621           x[8] -= m4*x6 + m9*x7  + m14*x8 + m19*x9 + m24*x10;
1622           x[9] -= m5*x6 + m10*x7 + m15*x8 + m20*x9 + m25*x10;
1623 
1624           x[10] -= m1*x11 + m6*x12  + m11*x13 + m16*x14 + m21*x15;
1625           x[11] -= m2*x11 + m7*x12  + m12*x13 + m17*x14 + m22*x15;
1626           x[12] -= m3*x11 + m8*x12  + m13*x13 + m18*x14 + m23*x15;
1627           x[13] -= m4*x11 + m9*x12  + m14*x13 + m19*x14 + m24*x15;
1628           x[14] -= m5*x11 + m10*x12 + m15*x13 + m20*x14 + m25*x15;
1629 
1630           x[15] -= m1*x16 + m6*x17  + m11*x18 + m16*x19 + m21*x20;
1631           x[16] -= m2*x16 + m7*x17  + m12*x18 + m17*x19 + m22*x20;
1632           x[17] -= m3*x16 + m8*x17  + m13*x18 + m18*x19 + m23*x20;
1633           x[18] -= m4*x16 + m9*x17  + m14*x18 + m19*x19 + m24*x20;
1634           x[19] -= m5*x16 + m10*x17 + m15*x18 + m20*x19 + m25*x20;
1635 
1636           x[20] -= m1*x21 + m6*x22  + m11*x23 + m16*x24 + m21*x25;
1637           x[21] -= m2*x21 + m7*x22  + m12*x23 + m17*x24 + m22*x25;
1638           x[22] -= m3*x21 + m8*x22  + m13*x23 + m18*x24 + m23*x25;
1639           x[23] -= m4*x21 + m9*x22  + m14*x23 + m19*x24 + m24*x25;
1640           x[24] -= m5*x21 + m10*x22 + m15*x23 + m20*x24 + m25*x25;
1641 
1642           pv   += 25;
1643         }
1644         PLogFlops(250*nz+225);
1645       }
1646       row = *ajtmp++;
1647     }
1648     /* finished row so stick it into b->a */
1649     pv = ba + 25*bi[i];
1650     pj = bj + bi[i];
1651     nz = bi[i+1] - bi[i];
1652     for (j=0; j<nz; j++) {
1653       x     = rtmp+25*pj[j];
1654       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
1655       pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
1656       pv[9] = x[9]; pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
1657       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; pv[16] = x[16];
1658       pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19]; pv[20] = x[20];
1659       pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23]; pv[24] = x[24];
1660       pv   += 25;
1661     }
1662     /* invert diagonal block */
1663     w = ba + 25*diag_offset[i];
1664     ierr = Kernel_A_gets_inverse_A_5(w);CHKERRQ(ierr);
1665   }
1666 
1667   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1668   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
1669   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
1670   C->factor = FACTOR_LU;
1671   C->assembled = PETSC_TRUE;
1672   PLogFlops(1.3333*125*b->mbs); /* from inverting diagonal blocks */
1673   PetscFunctionReturn(0);
1674 }
1675 #endif
1676 /*
1677       Version for when blocks are 5 by 5 Using natural ordering
1678 */
1679 #undef __FUNC__
1680 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_5_NaturalOrdering"
1681 int MatCholeskyFactorNumeric_SeqSBAIJ_5_NaturalOrdering(Mat A,Mat *B)
1682 {
1683   Mat         C = *B;
1684   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
1685   int         ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
1686   int         *ajtmpold,*ajtmp,nz,row;
1687   int         *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
1688   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
1689   MatScalar   x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15;
1690   MatScalar   x16,x17,x18,x19,x20,x21,x22,x23,x24,x25;
1691   MatScalar   p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15;
1692   MatScalar   p16,p17,p18,p19,p20,p21,p22,p23,p24,p25;
1693   MatScalar   m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12,m13,m14,m15;
1694   MatScalar   m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
1695   MatScalar   *ba = b->a,*aa = a->a;
1696 
1697   PetscFunctionBegin;
1698   rtmp  = (MatScalar*)PetscMalloc(25*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
1699   for (i=0; i<n; i++) {
1700     nz    = bi[i+1] - bi[i];
1701     ajtmp = bj + bi[i];
1702     for  (j=0; j<nz; j++) {
1703       x = rtmp+25*ajtmp[j];
1704       x[0]  = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = x[9] = 0.0;
1705       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
1706       x[16] = x[17] = x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0;
1707     }
1708     /* load in initial (unfactored row) */
1709     nz       = ai[i+1] - ai[i];
1710     ajtmpold = aj + ai[i];
1711     v        = aa + 25*ai[i];
1712     for (j=0; j<nz; j++) {
1713       x    = rtmp+25*ajtmpold[j];
1714       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
1715       x[4]  = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
1716       x[9]  = v[9];  x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
1717       x[14] = v[14]; x[15] = v[15]; x[16] = v[16]; x[17] = v[17]; x[18] = v[18];
1718       x[19] = v[19]; x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23];
1719       x[24] = v[24];
1720       v    += 25;
1721     }
1722     row = *ajtmp++;
1723     while (row < i) {
1724       pc  = rtmp + 25*row;
1725       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
1726       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
1727       p10 = pc[9];  p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
1728       p15 = pc[14]; p16 = pc[15]; p17 = pc[16]; p18 = pc[17];
1729       p19 = pc[18]; p20 = pc[19]; p21 = pc[20]; p22 = pc[21]; p23 = pc[22];
1730       p24 = pc[23]; p25 = pc[24];
1731       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
1732           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
1733           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
1734           || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0
1735           || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 || p25 != 0.0) {
1736         pv = ba + 25*diag_offset[row];
1737         pj = bj + diag_offset[row] + 1;
1738         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
1739         x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
1740         x10 = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
1741         x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17]; x19 = pv[18];
1742         x20 = pv[19]; x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
1743         x25 = pv[24];
1744         pc[0] = m1 = p1*x1 + p6*x2  + p11*x3 + p16*x4 + p21*x5;
1745         pc[1] = m2 = p2*x1 + p7*x2  + p12*x3 + p17*x4 + p22*x5;
1746         pc[2] = m3 = p3*x1 + p8*x2  + p13*x3 + p18*x4 + p23*x5;
1747         pc[3] = m4 = p4*x1 + p9*x2  + p14*x3 + p19*x4 + p24*x5;
1748         pc[4] = m5 = p5*x1 + p10*x2 + p15*x3 + p20*x4 + p25*x5;
1749 
1750         pc[5]  = m6  = p1*x6 + p6*x7  + p11*x8 + p16*x9 + p21*x10;
1751         pc[6]  = m7  = p2*x6 + p7*x7  + p12*x8 + p17*x9 + p22*x10;
1752         pc[7]  = m8  = p3*x6 + p8*x7  + p13*x8 + p18*x9 + p23*x10;
1753         pc[8]  = m9  = p4*x6 + p9*x7  + p14*x8 + p19*x9 + p24*x10;
1754         pc[9]  = m10 = p5*x6 + p10*x7 + p15*x8 + p20*x9 + p25*x10;
1755 
1756         pc[10] = m11 = p1*x11 + p6*x12  + p11*x13 + p16*x14 + p21*x15;
1757         pc[11] = m12 = p2*x11 + p7*x12  + p12*x13 + p17*x14 + p22*x15;
1758         pc[12] = m13 = p3*x11 + p8*x12  + p13*x13 + p18*x14 + p23*x15;
1759         pc[13] = m14 = p4*x11 + p9*x12  + p14*x13 + p19*x14 + p24*x15;
1760         pc[14] = m15 = p5*x11 + p10*x12 + p15*x13 + p20*x14 + p25*x15;
1761 
1762         pc[15] = m16 = p1*x16 + p6*x17  + p11*x18 + p16*x19 + p21*x20;
1763         pc[16] = m17 = p2*x16 + p7*x17  + p12*x18 + p17*x19 + p22*x20;
1764         pc[17] = m18 = p3*x16 + p8*x17  + p13*x18 + p18*x19 + p23*x20;
1765         pc[18] = m19 = p4*x16 + p9*x17  + p14*x18 + p19*x19 + p24*x20;
1766         pc[19] = m20 = p5*x16 + p10*x17 + p15*x18 + p20*x19 + p25*x20;
1767 
1768         pc[20] = m21 = p1*x21 + p6*x22  + p11*x23 + p16*x24 + p21*x25;
1769         pc[21] = m22 = p2*x21 + p7*x22  + p12*x23 + p17*x24 + p22*x25;
1770         pc[22] = m23 = p3*x21 + p8*x22  + p13*x23 + p18*x24 + p23*x25;
1771         pc[23] = m24 = p4*x21 + p9*x22  + p14*x23 + p19*x24 + p24*x25;
1772         pc[24] = m25 = p5*x21 + p10*x22 + p15*x23 + p20*x24 + p25*x25;
1773 
1774         nz = bi[row+1] - diag_offset[row] - 1;
1775         pv += 25;
1776         for (j=0; j<nz; j++) {
1777           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
1778           x5   = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
1779           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
1780           x14  = pv[13]; x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17];
1781           x19 = pv[18];  x20 = pv[19]; x21 = pv[20]; x22 = pv[21]; x23 = pv[22];
1782           x24 = pv[23];  x25 = pv[24];
1783           x    = rtmp + 25*pj[j];
1784           x[0] -= m1*x1 + m6*x2   + m11*x3  + m16*x4 + m21*x5;
1785           x[1] -= m2*x1 + m7*x2   + m12*x3  + m17*x4 + m22*x5;
1786           x[2] -= m3*x1 + m8*x2   + m13*x3  + m18*x4 + m23*x5;
1787           x[3] -= m4*x1 + m9*x2   + m14*x3  + m19*x4 + m24*x5;
1788           x[4] -= m5*x1 + m10*x2  + m15*x3  + m20*x4 + m25*x5;
1789 
1790           x[5] -= m1*x6 + m6*x7   + m11*x8  + m16*x9 + m21*x10;
1791           x[6] -= m2*x6 + m7*x7   + m12*x8  + m17*x9 + m22*x10;
1792           x[7] -= m3*x6 + m8*x7   + m13*x8  + m18*x9 + m23*x10;
1793           x[8] -= m4*x6 + m9*x7   + m14*x8  + m19*x9 + m24*x10;
1794           x[9] -= m5*x6 + m10*x7  + m15*x8  + m20*x9 + m25*x10;
1795 
1796           x[10] -= m1*x11 + m6*x12  + m11*x13 + m16*x14 + m21*x15;
1797           x[11] -= m2*x11 + m7*x12  + m12*x13 + m17*x14 + m22*x15;
1798           x[12] -= m3*x11 + m8*x12  + m13*x13 + m18*x14 + m23*x15;
1799           x[13] -= m4*x11 + m9*x12  + m14*x13 + m19*x14 + m24*x15;
1800           x[14] -= m5*x11 + m10*x12 + m15*x13 + m20*x14 + m25*x15;
1801 
1802           x[15] -= m1*x16 + m6*x17  + m11*x18 + m16*x19 + m21*x20;
1803           x[16] -= m2*x16 + m7*x17  + m12*x18 + m17*x19 + m22*x20;
1804           x[17] -= m3*x16 + m8*x17  + m13*x18 + m18*x19 + m23*x20;
1805           x[18] -= m4*x16 + m9*x17  + m14*x18 + m19*x19 + m24*x20;
1806           x[19] -= m5*x16 + m10*x17 + m15*x18 + m20*x19 + m25*x20;
1807 
1808           x[20] -= m1*x21 + m6*x22  + m11*x23 + m16*x24 + m21*x25;
1809           x[21] -= m2*x21 + m7*x22  + m12*x23 + m17*x24 + m22*x25;
1810           x[22] -= m3*x21 + m8*x22  + m13*x23 + m18*x24 + m23*x25;
1811           x[23] -= m4*x21 + m9*x22  + m14*x23 + m19*x24 + m24*x25;
1812           x[24] -= m5*x21 + m10*x22 + m15*x23 + m20*x24 + m25*x25;
1813           pv   += 25;
1814         }
1815         PLogFlops(250*nz+225);
1816       }
1817       row = *ajtmp++;
1818     }
1819     /* finished row so stick it into b->a */
1820     pv = ba + 25*bi[i];
1821     pj = bj + bi[i];
1822     nz = bi[i+1] - bi[i];
1823     for (j=0; j<nz; j++) {
1824       x      = rtmp+25*pj[j];
1825       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
1826       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
1827       pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
1828       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; pv[16] = x[16]; pv[17] = x[17];
1829       pv[18] = x[18]; pv[19] = x[19]; pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22];
1830       pv[23] = x[23]; pv[24] = x[24];
1831       pv   += 25;
1832     }
1833     /* invert diagonal block */
1834     w = ba + 25*diag_offset[i];
1835     ierr = Kernel_A_gets_inverse_A_5(w);CHKERRQ(ierr);
1836   }
1837 
1838   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1839   C->factor    = FACTOR_LU;
1840   C->assembled = PETSC_TRUE;
1841   PLogFlops(1.3333*125*b->mbs); /* from inverting diagonal blocks */
1842   PetscFunctionReturn(0);
1843 }
1844 
1845 /*
1846       Version for when blocks are 4 by 4 Using natural ordering
1847 */
1848 #undef __FUNC__
1849 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_4_NaturalOrdering"
1850 int MatCholeskyFactorNumeric_SeqSBAIJ_4_NaturalOrdering(Mat A,Mat *B)
1851 {
1852   Mat         C = *B;
1853   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
1854   int         ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
1855   int         *ajtmpold,*ajtmp,nz,row;
1856   int         *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
1857   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
1858   MatScalar   p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
1859   MatScalar   p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
1860   MatScalar   p10,p11,p12,p13,p14,p15,p16,m10,m11,m12;
1861   MatScalar   m13,m14,m15,m16;
1862   MatScalar   *ba = b->a,*aa = a->a;
1863 
1864   PetscFunctionBegin;
1865   rtmp  = (MatScalar*)PetscMalloc(16*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
1866 
1867   for (i=0; i<n; i++) {
1868     nz    = bi[i+1] - bi[i];
1869     ajtmp = bj + bi[i];
1870     for  (j=0; j<nz; j++) {
1871       x = rtmp+16*ajtmp[j];
1872       x[0]  = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = x[9] = 0.0;
1873       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
1874     }
1875     /* load in initial (unfactored row) */
1876     nz       = ai[i+1] - ai[i];
1877     ajtmpold = aj + ai[i];
1878     v        = aa + 16*ai[i];
1879     for (j=0; j<nz; j++) {
1880       x    = rtmp+16*ajtmpold[j];
1881       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
1882       x[4]  = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
1883       x[9]  = v[9];  x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
1884       x[14] = v[14]; x[15] = v[15];
1885       v    += 16;
1886     }
1887     row = *ajtmp++;
1888     while (row < i) {
1889       pc  = rtmp + 16*row;
1890       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
1891       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
1892       p10 = pc[9];  p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
1893       p15 = pc[14]; p16 = pc[15];
1894       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
1895           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
1896           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
1897           || p16 != 0.0) {
1898         pv = ba + 16*diag_offset[row];
1899         pj = bj + diag_offset[row] + 1;
1900         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
1901         x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
1902         x10 = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
1903         x15 = pv[14]; x16 = pv[15];
1904         pc[0] = m1 = p1*x1 + p5*x2  + p9*x3  + p13*x4;
1905         pc[1] = m2 = p2*x1 + p6*x2  + p10*x3 + p14*x4;
1906         pc[2] = m3 = p3*x1 + p7*x2  + p11*x3 + p15*x4;
1907         pc[3] = m4 = p4*x1 + p8*x2  + p12*x3 + p16*x4;
1908 
1909         pc[4] = m5 = p1*x5 + p5*x6  + p9*x7  + p13*x8;
1910         pc[5] = m6 = p2*x5 + p6*x6  + p10*x7 + p14*x8;
1911         pc[6] = m7 = p3*x5 + p7*x6  + p11*x7 + p15*x8;
1912         pc[7] = m8 = p4*x5 + p8*x6  + p12*x7 + p16*x8;
1913 
1914         pc[8]  = m9  = p1*x9 + p5*x10  + p9*x11  + p13*x12;
1915         pc[9]  = m10 = p2*x9 + p6*x10  + p10*x11 + p14*x12;
1916         pc[10] = m11 = p3*x9 + p7*x10  + p11*x11 + p15*x12;
1917         pc[11] = m12 = p4*x9 + p8*x10  + p12*x11 + p16*x12;
1918 
1919         pc[12] = m13 = p1*x13 + p5*x14  + p9*x15  + p13*x16;
1920         pc[13] = m14 = p2*x13 + p6*x14  + p10*x15 + p14*x16;
1921         pc[14] = m15 = p3*x13 + p7*x14  + p11*x15 + p15*x16;
1922         pc[15] = m16 = p4*x13 + p8*x14  + p12*x15 + p16*x16;
1923 
1924         nz = bi[row+1] - diag_offset[row] - 1;
1925         pv += 16;
1926         for (j=0; j<nz; j++) {
1927           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
1928           x5   = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
1929           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
1930           x14  = pv[13]; x15 = pv[14]; x16 = pv[15];
1931           x    = rtmp + 16*pj[j];
1932           x[0] -= m1*x1 + m5*x2  + m9*x3  + m13*x4;
1933           x[1] -= m2*x1 + m6*x2  + m10*x3 + m14*x4;
1934           x[2] -= m3*x1 + m7*x2  + m11*x3 + m15*x4;
1935           x[3] -= m4*x1 + m8*x2  + m12*x3 + m16*x4;
1936 
1937           x[4] -= m1*x5 + m5*x6  + m9*x7  + m13*x8;
1938           x[5] -= m2*x5 + m6*x6  + m10*x7 + m14*x8;
1939           x[6] -= m3*x5 + m7*x6  + m11*x7 + m15*x8;
1940           x[7] -= m4*x5 + m8*x6  + m12*x7 + m16*x8;
1941 
1942           x[8]  -= m1*x9 + m5*x10 + m9*x11  + m13*x12;
1943           x[9]  -= m2*x9 + m6*x10 + m10*x11 + m14*x12;
1944           x[10] -= m3*x9 + m7*x10 + m11*x11 + m15*x12;
1945           x[11] -= m4*x9 + m8*x10 + m12*x11 + m16*x12;
1946 
1947           x[12] -= m1*x13 + m5*x14  + m9*x15  + m13*x16;
1948           x[13] -= m2*x13 + m6*x14  + m10*x15 + m14*x16;
1949           x[14] -= m3*x13 + m7*x14  + m11*x15 + m15*x16;
1950           x[15] -= m4*x13 + m8*x14  + m12*x15 + m16*x16;
1951 
1952           pv   += 16;
1953         }
1954         PLogFlops(128*nz+112);
1955       }
1956       row = *ajtmp++;
1957     }
1958     /* finished row so stick it into b->a */
1959     pv = ba + 16*bi[i];
1960     pj = bj + bi[i];
1961     nz = bi[i+1] - bi[i];
1962     for (j=0; j<nz; j++) {
1963       x      = rtmp+16*pj[j];
1964       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
1965       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
1966       pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
1967       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
1968       pv   += 16;
1969     }
1970     /* invert diagonal block */
1971     w = ba + 16*diag_offset[i];
1972     ierr = Kernel_A_gets_inverse_A_4(w);CHKERRQ(ierr);
1973   }
1974 
1975   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1976   C->factor    = FACTOR_LU;
1977   C->assembled = PETSC_TRUE;
1978   C->preallocated = PETSC_TRUE;
1979   PLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */
1980   PetscFunctionReturn(0);
1981 }
1982 
1983 /* Version for when blocks are 4 by 4  */
1984 #undef __FUNC__
1985 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_4"
1986 int MatCholeskyFactorNumeric_SeqSBAIJ_4(Mat A,Mat *B)
1987 {
1988   Mat                C = *B;
1989   Mat_SeqSBAIJ       *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data;
1990   IS                 perm = b->row;
1991   int                *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
1992   int                *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
1993   MatScalar          *ba = b->a,*aa,*ap,*dk,*uik;
1994   MatScalar          *u,*diag,*rtmp,*rtmp_ptr;
1995 
1996   PetscFunctionBegin;
1997   /* initialization */
1998   rtmp  = (MatScalar*)PetscMalloc(16*mbs*sizeof(MatScalar));CHKPTRQ(rtmp);
1999   ierr = PetscMemzero(rtmp,16*mbs*sizeof(MatScalar));CHKERRQ(ierr);
2000   il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il);
2001   jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl);
2002   for (i=0; i<mbs; i++) {
2003     jl[i] = mbs; il[0] = 0;
2004   }
2005   dk    = (MatScalar*)PetscMalloc(16*sizeof(MatScalar));CHKPTRQ(dk);
2006   uik   = (MatScalar*)PetscMalloc(16*sizeof(MatScalar));CHKPTRQ(uik);
2007   ierr  = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr);
2008 
2009   /* check permutation */
2010   if (!a->permute){
2011     ai = a->i; aj = a->j; aa = a->a;
2012   } else {
2013     ai = a->inew; aj = a->jnew;
2014     aa = (MatScalar*)PetscMalloc(16*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa);
2015     ierr = PetscMemcpy(aa,a->a,16*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr);
2016     a2anew  = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew);
2017     ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr);
2018 
2019     for (i=0; i<mbs; i++){
2020       jmin = ai[i]; jmax = ai[i+1];
2021       for (j=jmin; j<jmax; j++){
2022         while (a2anew[j] != j){
2023           k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k;
2024           for (k1=0; k1<16; k1++){
2025             dk[k1]       = aa[k*16+k1];
2026             aa[k*16+k1] = aa[j*16+k1];
2027             aa[j*16+k1] = dk[k1];
2028           }
2029         }
2030         /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */
2031         if (i > aj[j]){
2032           /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */
2033           ap = aa + j*16;                     /* ptr to the beginning of j-th block of aa */
2034           for (k=0; k<16; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */
2035           for (k=0; k<4; k++){               /* j-th block of aa <- dk^T */
2036             for (k1=0; k1<4; k1++) *ap++ = dk[k + 4*k1];
2037           }
2038         }
2039       }
2040     }
2041     ierr = PetscFree(a2anew);CHKERRA(ierr);
2042   }
2043 
2044   /* for each row k */
2045   for (k = 0; k<mbs; k++){
2046 
2047     /*initialize k-th row with elements nonzero in row perm(k) of A */
2048     jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1];
2049     if (jmin < jmax) {
2050       ap = aa + jmin*16;
2051       for (j = jmin; j < jmax; j++){
2052         vj = perm_ptr[aj[j]];         /* block col. index */
2053         rtmp_ptr = rtmp + vj*16;
2054         for (i=0; i<16; i++) *rtmp_ptr++ = *ap++;
2055       }
2056     }
2057 
2058     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
2059     ierr = PetscMemcpy(dk,rtmp+k*16,16*sizeof(MatScalar));CHKERRQ(ierr);
2060     i = jl[k]; /* first row to be added to k_th row  */
2061 
2062     while (i < mbs){
2063       nexti = jl[i]; /* next row to be added to k_th row */
2064 
2065       /* compute multiplier */
2066       ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
2067 
2068       /* uik = -inv(Di)*U_bar(i,k) */
2069       diag = ba + i*16;
2070       u    = ba + ili*16;
2071 
2072       uik[0] = -(diag[0]*u[0] + diag[4]*u[1] + diag[8]*u[2] + diag[12]*u[3]);
2073       uik[1] = -(diag[1]*u[0] + diag[5]*u[1] + diag[9]*u[2] + diag[13]*u[3]);
2074       uik[2] = -(diag[2]*u[0] + diag[6]*u[1] + diag[10]*u[2]+ diag[14]*u[3]);
2075       uik[3] = -(diag[3]*u[0] + diag[7]*u[1] + diag[11]*u[2]+ diag[15]*u[3]);
2076 
2077       uik[4] = -(diag[0]*u[4] + diag[4]*u[5] + diag[8]*u[6] + diag[12]*u[7]);
2078       uik[5] = -(diag[1]*u[4] + diag[5]*u[5] + diag[9]*u[6] + diag[13]*u[7]);
2079       uik[6] = -(diag[2]*u[4] + diag[6]*u[5] + diag[10]*u[6]+ diag[14]*u[7]);
2080       uik[7] = -(diag[3]*u[4] + diag[7]*u[5] + diag[11]*u[6]+ diag[15]*u[7]);
2081 
2082       uik[8] = -(diag[0]*u[8] + diag[4]*u[9] + diag[8]*u[10] + diag[12]*u[11]);
2083       uik[9] = -(diag[1]*u[8] + diag[5]*u[9] + diag[9]*u[10] + diag[13]*u[11]);
2084       uik[10]= -(diag[2]*u[8] + diag[6]*u[9] + diag[10]*u[10]+ diag[14]*u[11]);
2085       uik[11]= -(diag[3]*u[8] + diag[7]*u[9] + diag[11]*u[10]+ diag[15]*u[11]);
2086 
2087       uik[12]= -(diag[0]*u[12] + diag[4]*u[13] + diag[8]*u[14] + diag[12]*u[15]);
2088       uik[13]= -(diag[1]*u[12] + diag[5]*u[13] + diag[9]*u[14] + diag[13]*u[15]);
2089       uik[14]= -(diag[2]*u[12] + diag[6]*u[13] + diag[10]*u[14]+ diag[14]*u[15]);
2090       uik[15]= -(diag[3]*u[12] + diag[7]*u[13] + diag[11]*u[14]+ diag[15]*u[15]);
2091 
2092       /* update D(k) += -U(i,k)^T * U_bar(i,k) */
2093       dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3];
2094       dk[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3];
2095       dk[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3];
2096       dk[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3];
2097 
2098       dk[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7];
2099       dk[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7];
2100       dk[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7];
2101       dk[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7];
2102 
2103       dk[8] += uik[0]*u[8] + uik[1]*u[9] + uik[2]*u[10] + uik[3]*u[11];
2104       dk[9] += uik[4]*u[8] + uik[5]*u[9] + uik[6]*u[10] + uik[7]*u[11];
2105       dk[10]+= uik[8]*u[8] + uik[9]*u[9] + uik[10]*u[10]+ uik[11]*u[11];
2106       dk[11]+= uik[12]*u[8]+ uik[13]*u[9]+ uik[14]*u[10]+ uik[15]*u[11];
2107 
2108       dk[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15];
2109       dk[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15];
2110       dk[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15];
2111       dk[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15];
2112 
2113       /* update -U(i,k) */
2114       ierr = PetscMemcpy(ba+ili*16,uik,16*sizeof(MatScalar));CHKERRQ(ierr);
2115 
2116       /* add multiple of row i to k-th row ... */
2117       jmin = ili + 1; jmax = bi[i+1];
2118       if (jmin < jmax){
2119         for (j=jmin; j<jmax; j++) {
2120           /* rtmp += -U(i,k)^T * U_bar(i,j) */
2121           rtmp_ptr = rtmp + bj[j]*16;
2122           u = ba + j*16;
2123           rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2] + uik[3]*u[3];
2124           rtmp_ptr[1] += uik[4]*u[0] + uik[5]*u[1] + uik[6]*u[2] + uik[7]*u[3];
2125           rtmp_ptr[2] += uik[8]*u[0] + uik[9]*u[1] + uik[10]*u[2]+ uik[11]*u[3];
2126           rtmp_ptr[3] += uik[12]*u[0]+ uik[13]*u[1]+ uik[14]*u[2]+ uik[15]*u[3];
2127 
2128           rtmp_ptr[4] += uik[0]*u[4] + uik[1]*u[5] + uik[2]*u[6] + uik[3]*u[7];
2129           rtmp_ptr[5] += uik[4]*u[4] + uik[5]*u[5] + uik[6]*u[6] + uik[7]*u[7];
2130           rtmp_ptr[6] += uik[8]*u[4] + uik[9]*u[5] + uik[10]*u[6]+ uik[11]*u[7];
2131           rtmp_ptr[7] += uik[12]*u[4]+ uik[13]*u[5]+ uik[14]*u[6]+ uik[15]*u[7];
2132 
2133           rtmp_ptr[8] += uik[0]*u[8] + uik[1]*u[9] + uik[2]*u[10] + uik[3]*u[11];
2134           rtmp_ptr[9] += uik[4]*u[8] + uik[5]*u[9] + uik[6]*u[10] + uik[7]*u[11];
2135           rtmp_ptr[10]+= uik[8]*u[8] + uik[9]*u[9] + uik[10]*u[10]+ uik[11]*u[11];
2136           rtmp_ptr[11]+= uik[12]*u[8]+ uik[13]*u[9]+ uik[14]*u[10]+ uik[15]*u[11];
2137 
2138           rtmp_ptr[12]+= uik[0]*u[12] + uik[1]*u[13] + uik[2]*u[14] + uik[3]*u[15];
2139           rtmp_ptr[13]+= uik[4]*u[12] + uik[5]*u[13] + uik[6]*u[14] + uik[7]*u[15];
2140           rtmp_ptr[14]+= uik[8]*u[12] + uik[9]*u[13] + uik[10]*u[14]+ uik[11]*u[15];
2141           rtmp_ptr[15]+= uik[12]*u[12]+ uik[13]*u[13]+ uik[14]*u[14]+ uik[15]*u[15];
2142         }
2143 
2144         /* ... add i to row list for next nonzero entry */
2145         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
2146         j     = bj[jmin];
2147         jl[i] = jl[j]; jl[j] = i; /* update jl */
2148       }
2149       i = nexti;
2150     }
2151 
2152     /* save nonzero entries in k-th row of U ... */
2153 
2154     /* invert diagonal block */
2155     diag = ba+k*16;
2156     ierr = PetscMemcpy(diag,dk,16*sizeof(MatScalar));CHKERRQ(ierr);
2157     ierr = Kernel_A_gets_inverse_A_4(diag);CHKERRQ(ierr);
2158 
2159     jmin = bi[k]; jmax = bi[k+1];
2160     if (jmin < jmax) {
2161       for (j=jmin; j<jmax; j++){
2162          vj = bj[j];           /* block col. index of U */
2163          u   = ba + j*16;
2164          rtmp_ptr = rtmp + vj*16;
2165          for (k1=0; k1<16; k1++){
2166            *u++        = *rtmp_ptr;
2167            *rtmp_ptr++ = 0.0;
2168          }
2169       }
2170 
2171       /* ... add k to row list for first nonzero entry in k-th row */
2172       il[k] = jmin;
2173       i     = bj[jmin];
2174       jl[k] = jl[i]; jl[i] = k;
2175     }
2176   }
2177 
2178   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2179   ierr = PetscFree(il);CHKERRQ(ierr);
2180   ierr = PetscFree(jl);CHKERRQ(ierr);
2181   ierr = PetscFree(dk);CHKERRQ(ierr);
2182   ierr = PetscFree(uik);CHKERRQ(ierr);
2183   if (a->permute){
2184     ierr = PetscFree(aa);CHKERRQ(ierr);
2185   }
2186 
2187   ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr);
2188   C->factor    = FACTOR_CHOLESKY;
2189   C->assembled = PETSC_TRUE;
2190   C->preallocated = PETSC_TRUE;
2191   PLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */
2192   PetscFunctionReturn(0);
2193 }
2194 
2195 /* Version for when blocks are 3 by 3  */
2196 #undef __FUNC__
2197 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_3"
2198 int MatCholeskyFactorNumeric_SeqSBAIJ_3(Mat A,Mat *B)
2199 {
2200   Mat                C = *B;
2201   Mat_SeqSBAIJ       *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data;
2202   IS                 perm = b->row;
2203   int                *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
2204   int                *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
2205   MatScalar          *ba = b->a,*aa,*ap,*dk,*uik;
2206   MatScalar          *u,*diag,*rtmp,*rtmp_ptr;
2207 
2208   PetscFunctionBegin;
2209   /* initialization */
2210   rtmp  = (MatScalar*)PetscMalloc(9*mbs*sizeof(MatScalar));CHKPTRQ(rtmp);
2211   ierr = PetscMemzero(rtmp,9*mbs*sizeof(MatScalar));CHKERRQ(ierr);
2212   il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il);
2213   jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl);
2214   for (i=0; i<mbs; i++) {
2215     jl[i] = mbs; il[0] = 0;
2216   }
2217   dk  = (MatScalar*)PetscMalloc(9*sizeof(MatScalar));CHKPTRQ(dk);
2218   uik = (MatScalar*)PetscMalloc(9*sizeof(MatScalar));CHKPTRQ(uik);
2219   ierr  = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr);
2220 
2221   /* check permutation */
2222   if (!a->permute){
2223     ai = a->i; aj = a->j; aa = a->a;
2224   } else {
2225     ai = a->inew; aj = a->jnew;
2226     aa = (MatScalar*)PetscMalloc(9*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa);
2227     ierr = PetscMemcpy(aa,a->a,9*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr);
2228     a2anew  = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew);
2229     ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr);
2230 
2231     for (i=0; i<mbs; i++){
2232       jmin = ai[i]; jmax = ai[i+1];
2233       for (j=jmin; j<jmax; j++){
2234         while (a2anew[j] != j){
2235           k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k;
2236           for (k1=0; k1<9; k1++){
2237             dk[k1]       = aa[k*9+k1];
2238             aa[k*9+k1] = aa[j*9+k1];
2239             aa[j*9+k1] = dk[k1];
2240           }
2241         }
2242         /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */
2243         if (i > aj[j]){
2244           /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */
2245           ap = aa + j*9;                     /* ptr to the beginning of j-th block of aa */
2246           for (k=0; k<9; k++) dk[k] = ap[k]; /* dk <- j-th block of aa */
2247           for (k=0; k<3; k++){               /* j-th block of aa <- dk^T */
2248             for (k1=0; k1<3; k1++) *ap++ = dk[k + 3*k1];
2249           }
2250         }
2251       }
2252     }
2253     ierr = PetscFree(a2anew);CHKERRA(ierr);
2254   }
2255 
2256   /* for each row k */
2257   for (k = 0; k<mbs; k++){
2258 
2259     /*initialize k-th row with elements nonzero in row perm(k) of A */
2260     jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1];
2261     if (jmin < jmax) {
2262       ap = aa + jmin*9;
2263       for (j = jmin; j < jmax; j++){
2264         vj = perm_ptr[aj[j]];         /* block col. index */
2265         rtmp_ptr = rtmp + vj*9;
2266         for (i=0; i<9; i++) *rtmp_ptr++ = *ap++;
2267       }
2268     }
2269 
2270     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
2271     ierr = PetscMemcpy(dk,rtmp+k*9,9*sizeof(MatScalar));CHKERRQ(ierr);
2272     i = jl[k]; /* first row to be added to k_th row  */
2273 
2274     while (i < mbs){
2275       nexti = jl[i]; /* next row to be added to k_th row */
2276 
2277       /* compute multiplier */
2278       ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
2279 
2280       /* uik = -inv(Di)*U_bar(i,k) */
2281       diag = ba + i*9;
2282       u    = ba + ili*9;
2283 
2284       uik[0] = -(diag[0]*u[0] + diag[3]*u[1] + diag[6]*u[2]);
2285       uik[1] = -(diag[1]*u[0] + diag[4]*u[1] + diag[7]*u[2]);
2286       uik[2] = -(diag[2]*u[0] + diag[5]*u[1] + diag[8]*u[2]);
2287 
2288       uik[3] = -(diag[0]*u[3] + diag[3]*u[4] + diag[6]*u[5]);
2289       uik[4] = -(diag[1]*u[3] + diag[4]*u[4] + diag[7]*u[5]);
2290       uik[5] = -(diag[2]*u[3] + diag[5]*u[4] + diag[8]*u[5]);
2291 
2292       uik[6] = -(diag[0]*u[6] + diag[3]*u[7] + diag[6]*u[8]);
2293       uik[7] = -(diag[1]*u[6] + diag[4]*u[7] + diag[7]*u[8]);
2294       uik[8] = -(diag[2]*u[6] + diag[5]*u[7] + diag[8]*u[8]);
2295 
2296       /* update D(k) += -U(i,k)^T * U_bar(i,k) */
2297       dk[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2];
2298       dk[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2];
2299       dk[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2];
2300 
2301       dk[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5];
2302       dk[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5];
2303       dk[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5];
2304 
2305       dk[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8];
2306       dk[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8];
2307       dk[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8];
2308 
2309       /* update -U(i,k) */
2310       ierr = PetscMemcpy(ba+ili*9,uik,9*sizeof(MatScalar));CHKERRQ(ierr);
2311 
2312       /* add multiple of row i to k-th row ... */
2313       jmin = ili + 1; jmax = bi[i+1];
2314       if (jmin < jmax){
2315         for (j=jmin; j<jmax; j++) {
2316           /* rtmp += -U(i,k)^T * U_bar(i,j) */
2317           rtmp_ptr = rtmp + bj[j]*9;
2318           u = ba + j*9;
2319           rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1] + uik[2]*u[2];
2320           rtmp_ptr[1] += uik[3]*u[0] + uik[4]*u[1] + uik[5]*u[2];
2321           rtmp_ptr[2] += uik[6]*u[0] + uik[7]*u[1] + uik[8]*u[2];
2322 
2323           rtmp_ptr[3] += uik[0]*u[3] + uik[1]*u[4] + uik[2]*u[5];
2324           rtmp_ptr[4] += uik[3]*u[3] + uik[4]*u[4] + uik[5]*u[5];
2325           rtmp_ptr[5] += uik[6]*u[3] + uik[7]*u[4] + uik[8]*u[5];
2326 
2327           rtmp_ptr[6] += uik[0]*u[6] + uik[1]*u[7] + uik[2]*u[8];
2328           rtmp_ptr[7] += uik[3]*u[6] + uik[4]*u[7] + uik[5]*u[8];
2329           rtmp_ptr[8] += uik[6]*u[6] + uik[7]*u[7] + uik[8]*u[8];
2330         }
2331 
2332         /* ... add i to row list for next nonzero entry */
2333         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
2334         j     = bj[jmin];
2335         jl[i] = jl[j]; jl[j] = i; /* update jl */
2336       }
2337       i = nexti;
2338     }
2339 
2340     /* save nonzero entries in k-th row of U ... */
2341 
2342     /* invert diagonal block */
2343     diag = ba+k*9;
2344     ierr = PetscMemcpy(diag,dk,9*sizeof(MatScalar));CHKERRQ(ierr);
2345     ierr = Kernel_A_gets_inverse_A_3(diag);CHKERRQ(ierr);
2346 
2347     jmin = bi[k]; jmax = bi[k+1];
2348     if (jmin < jmax) {
2349       for (j=jmin; j<jmax; j++){
2350          vj = bj[j];           /* block col. index of U */
2351          u   = ba + j*9;
2352          rtmp_ptr = rtmp + vj*9;
2353          for (k1=0; k1<9; k1++){
2354            *u++        = *rtmp_ptr;
2355            *rtmp_ptr++ = 0.0;
2356          }
2357       }
2358 
2359       /* ... add k to row list for first nonzero entry in k-th row */
2360       il[k] = jmin;
2361       i     = bj[jmin];
2362       jl[k] = jl[i]; jl[i] = k;
2363     }
2364   }
2365 
2366   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2367   ierr = PetscFree(il);CHKERRQ(ierr);
2368   ierr = PetscFree(jl);CHKERRQ(ierr);
2369   ierr = PetscFree(dk);CHKERRQ(ierr);
2370   ierr = PetscFree(uik);CHKERRQ(ierr);
2371   if (a->permute){
2372     ierr = PetscFree(aa);CHKERRQ(ierr);
2373   }
2374 
2375   ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr);
2376   C->factor    = FACTOR_CHOLESKY;
2377   C->assembled = PETSC_TRUE;
2378   C->preallocated = PETSC_TRUE;
2379   PLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */
2380   PetscFunctionReturn(0);
2381 }
2382 
2383 /*
2384       Version for when blocks are 3 by 3 Using natural ordering
2385 */
2386 #undef __FUNC__
2387 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_3_NaturalOrdering"
2388 int MatCholeskyFactorNumeric_SeqSBAIJ_3_NaturalOrdering(Mat A,Mat *B)
2389 {
2390   Mat                C = *B;
2391   Mat_SeqBAIJ        *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
2392   int                ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
2393   int                *ajtmpold,*ajtmp,nz,row;
2394   int                *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
2395   MatScalar          *pv,*v,*rtmp,*pc,*w,*x;
2396   MatScalar          p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
2397   MatScalar          p5,p6,p7,p8,p9,x5,x6,x7,x8,x9;
2398   MatScalar          *ba = b->a,*aa = a->a;
2399 
2400   PetscFunctionBegin;
2401   rtmp  = (MatScalar*)PetscMalloc(9*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
2402 
2403   for (i=0; i<n; i++) {
2404     nz    = bi[i+1] - bi[i];
2405     ajtmp = bj + bi[i];
2406     for  (j=0; j<nz; j++) {
2407       x = rtmp+9*ajtmp[j];
2408       x[0]  = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = 0.0;
2409     }
2410     /* load in initial (unfactored row) */
2411     nz       = ai[i+1] - ai[i];
2412     ajtmpold = aj + ai[i];
2413     v        = aa + 9*ai[i];
2414     for (j=0; j<nz; j++) {
2415       x    = rtmp+9*ajtmpold[j];
2416       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
2417       x[4]  = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
2418       v    += 9;
2419     }
2420     row = *ajtmp++;
2421     while (row < i) {
2422       pc  = rtmp + 9*row;
2423       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
2424       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
2425       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
2426           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0) {
2427         pv = ba + 9*diag_offset[row];
2428         pj = bj + diag_offset[row] + 1;
2429         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
2430         x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
2431         pc[0] = m1 = p1*x1 + p4*x2 + p7*x3;
2432         pc[1] = m2 = p2*x1 + p5*x2 + p8*x3;
2433         pc[2] = m3 = p3*x1 + p6*x2 + p9*x3;
2434 
2435         pc[3] = m4 = p1*x4 + p4*x5 + p7*x6;
2436         pc[4] = m5 = p2*x4 + p5*x5 + p8*x6;
2437         pc[5] = m6 = p3*x4 + p6*x5 + p9*x6;
2438 
2439         pc[6] = m7 = p1*x7 + p4*x8 + p7*x9;
2440         pc[7] = m8 = p2*x7 + p5*x8 + p8*x9;
2441         pc[8] = m9 = p3*x7 + p6*x8 + p9*x9;
2442 
2443         nz = bi[row+1] - diag_offset[row] - 1;
2444         pv += 9;
2445         for (j=0; j<nz; j++) {
2446           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
2447           x5   = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
2448           x    = rtmp + 9*pj[j];
2449           x[0] -= m1*x1 + m4*x2 + m7*x3;
2450           x[1] -= m2*x1 + m5*x2 + m8*x3;
2451           x[2] -= m3*x1 + m6*x2 + m9*x3;
2452 
2453           x[3] -= m1*x4 + m4*x5 + m7*x6;
2454           x[4] -= m2*x4 + m5*x5 + m8*x6;
2455           x[5] -= m3*x4 + m6*x5 + m9*x6;
2456 
2457           x[6] -= m1*x7 + m4*x8 + m7*x9;
2458           x[7] -= m2*x7 + m5*x8 + m8*x9;
2459           x[8] -= m3*x7 + m6*x8 + m9*x9;
2460           pv   += 9;
2461         }
2462         PLogFlops(54*nz+36);
2463       }
2464       row = *ajtmp++;
2465     }
2466     /* finished row so stick it into b->a */
2467     pv = ba + 9*bi[i];
2468     pj = bj + bi[i];
2469     nz = bi[i+1] - bi[i];
2470     for (j=0; j<nz; j++) {
2471       x      = rtmp+9*pj[j];
2472       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
2473       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
2474       pv   += 9;
2475     }
2476     /* invert diagonal block */
2477     w = ba + 9*diag_offset[i];
2478     ierr = Kernel_A_gets_inverse_A_3(w);CHKERRQ(ierr);
2479   }
2480 
2481   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2482   C->factor    = FACTOR_CHOLESKY;
2483   C->assembled = PETSC_TRUE;
2484   C->preallocated = PETSC_TRUE;
2485   PLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */
2486   PetscFunctionReturn(0);
2487 }
2488 
2489 /*
2490     Numeric U^T*D*U factorization for SBAIJ format. Modified from SNF of YSMP.
2491     Version for blocks 2 by 2.
2492 */
2493 #undef __FUNC__
2494 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_2"
2495 int MatCholeskyFactorNumeric_SeqSBAIJ_2(Mat A,Mat *B)
2496 {
2497   Mat                C = *B;
2498   Mat_SeqSBAIJ       *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data;
2499   IS                 perm = b->row;
2500   int                *perm_ptr,ierr,i,j,mbs=a->mbs,*bi=b->i,*bj=b->j;
2501   int                *ai,*aj,*a2anew,k,k1,jmin,jmax,*jl,*il,vj,nexti,ili;
2502   MatScalar          *ba = b->a,*aa,*ap,*dk,*uik;
2503   MatScalar          *u,*diag,*rtmp,*rtmp_ptr;
2504 
2505   PetscFunctionBegin;
2506 
2507   /* initialization */
2508   /* il and jl record the first nonzero element in each row of the accessing
2509      window U(0:k, k:mbs-1).
2510      jl:    list of rows to be added to uneliminated rows
2511             i>= k: jl(i) is the first row to be added to row i
2512             i<  k: jl(i) is the row following row i in some list of rows
2513             jl(i) = mbs indicates the end of a list
2514      il(i): points to the first nonzero element in columns k,...,mbs-1 of
2515             row i of U */
2516   rtmp  = (MatScalar*)PetscMalloc(4*mbs*sizeof(MatScalar));CHKPTRQ(rtmp);
2517   ierr = PetscMemzero(rtmp,4*mbs*sizeof(MatScalar));CHKERRQ(ierr);
2518   il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il);
2519   jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl);
2520   for (i=0; i<mbs; i++) {
2521     jl[i] = mbs; il[0] = 0;
2522   }
2523   dk  = (MatScalar*)PetscMalloc(4*sizeof(MatScalar));CHKPTRQ(dk);
2524   uik = (MatScalar*)PetscMalloc(4*sizeof(MatScalar));CHKPTRQ(uik);
2525   ierr  = ISGetIndices(perm,&perm_ptr);CHKERRQ(ierr);
2526 
2527   /* check permutation */
2528   if (!a->permute){
2529     ai = a->i; aj = a->j; aa = a->a;
2530   } else {
2531     ai = a->inew; aj = a->jnew;
2532     aa = (MatScalar*)PetscMalloc(4*ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa);
2533     ierr = PetscMemcpy(aa,a->a,4*ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr);
2534     a2anew  = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(a2anew);
2535     ierr= PetscMemcpy(a2anew,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr);
2536 
2537     for (i=0; i<mbs; i++){
2538       jmin = ai[i]; jmax = ai[i+1];
2539       for (j=jmin; j<jmax; j++){
2540         while (a2anew[j] != j){
2541           k = a2anew[j]; a2anew[j] = a2anew[k]; a2anew[k] = k;
2542           for (k1=0; k1<4; k1++){
2543             dk[k1]       = aa[k*4+k1];
2544             aa[k*4+k1] = aa[j*4+k1];
2545             aa[j*4+k1] = dk[k1];
2546           }
2547         }
2548         /* transform columnoriented blocks that lie in the lower triangle to roworiented blocks */
2549         if (i > aj[j]){
2550           /* printf("change orientation, row: %d, col: %d\n",i,aj[j]); */
2551           ap = aa + j*4;     /* ptr to the beginning of the block */
2552           dk[1] = ap[1];     /* swap ap[1] and ap[2] */
2553           ap[1] = ap[2];
2554           ap[2] = dk[1];
2555         }
2556       }
2557     }
2558     ierr = PetscFree(a2anew);CHKERRA(ierr);
2559   }
2560 
2561   /* for each row k */
2562   for (k = 0; k<mbs; k++){
2563 
2564     /*initialize k-th row with elements nonzero in row perm(k) of A */
2565     jmin = ai[perm_ptr[k]]; jmax = ai[perm_ptr[k]+1];
2566     if (jmin < jmax) {
2567       ap = aa + jmin*4;
2568       for (j = jmin; j < jmax; j++){
2569         vj = perm_ptr[aj[j]];         /* block col. index */
2570         rtmp_ptr = rtmp + vj*4;
2571         for (i=0; i<4; i++) *rtmp_ptr++ = *ap++;
2572       }
2573     }
2574 
2575     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
2576     ierr = PetscMemcpy(dk,rtmp+k*4,4*sizeof(MatScalar));CHKERRQ(ierr);
2577     i = jl[k]; /* first row to be added to k_th row  */
2578 
2579     while (i < mbs){
2580       nexti = jl[i]; /* next row to be added to k_th row */
2581 
2582       /* compute multiplier */
2583       ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
2584 
2585       /* uik = -inv(Di)*U_bar(i,k): - ba[ili]*ba[i] */
2586       diag = ba + i*4;
2587       u    = ba + ili*4;
2588       uik[0] = -(diag[0]*u[0] + diag[2]*u[1]);
2589       uik[1] = -(diag[1]*u[0] + diag[3]*u[1]);
2590       uik[2] = -(diag[0]*u[2] + diag[2]*u[3]);
2591       uik[3] = -(diag[1]*u[2] + diag[3]*u[3]);
2592 
2593       /* update D(k) += -U(i,k)^T * U_bar(i,k): dk += uik*ba[ili] */
2594       dk[0] += uik[0]*u[0] + uik[1]*u[1];
2595       dk[1] += uik[2]*u[0] + uik[3]*u[1];
2596       dk[2] += uik[0]*u[2] + uik[1]*u[3];
2597       dk[3] += uik[2]*u[2] + uik[3]*u[3];
2598 
2599       /* update -U(i,k): ba[ili] = uik */
2600       ierr = PetscMemcpy(ba+ili*4,uik,4*sizeof(MatScalar));CHKERRQ(ierr);
2601 
2602       /* add multiple of row i to k-th row ... */
2603       jmin = ili + 1; jmax = bi[i+1];
2604       if (jmin < jmax){
2605         for (j=jmin; j<jmax; j++) {
2606           /* rtmp += -U(i,k)^T * U_bar(i,j): rtmp[bj[j]] += uik*ba[j]; */
2607           rtmp_ptr = rtmp + bj[j]*4;
2608           u = ba + j*4;
2609           rtmp_ptr[0] += uik[0]*u[0] + uik[1]*u[1];
2610           rtmp_ptr[1] += uik[2]*u[0] + uik[3]*u[1];
2611           rtmp_ptr[2] += uik[0]*u[2] + uik[1]*u[3];
2612           rtmp_ptr[3] += uik[2]*u[2] + uik[3]*u[3];
2613         }
2614 
2615         /* ... add i to row list for next nonzero entry */
2616         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
2617         j     = bj[jmin];
2618         jl[i] = jl[j]; jl[j] = i; /* update jl */
2619       }
2620       i = nexti;
2621     }
2622 
2623     /* save nonzero entries in k-th row of U ... */
2624 
2625     /* invert diagonal block */
2626     diag = ba+k*4;
2627     ierr = PetscMemcpy(diag,dk,4*sizeof(MatScalar));CHKERRQ(ierr);
2628     ierr = Kernel_A_gets_inverse_A_2(diag);CHKERRQ(ierr);
2629 
2630     jmin = bi[k]; jmax = bi[k+1];
2631     if (jmin < jmax) {
2632       for (j=jmin; j<jmax; j++){
2633          vj = bj[j];           /* block col. index of U */
2634          u   = ba + j*4;
2635          rtmp_ptr = rtmp + vj*4;
2636          for (k1=0; k1<4; k1++){
2637            *u++        = *rtmp_ptr;
2638            *rtmp_ptr++ = 0.0;
2639          }
2640       }
2641 
2642       /* ... add k to row list for first nonzero entry in k-th row */
2643       il[k] = jmin;
2644       i     = bj[jmin];
2645       jl[k] = jl[i]; jl[i] = k;
2646     }
2647   }
2648 
2649   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2650   ierr = PetscFree(il);CHKERRQ(ierr);
2651   ierr = PetscFree(jl);CHKERRQ(ierr);
2652   ierr = PetscFree(dk);CHKERRQ(ierr);
2653   ierr = PetscFree(uik);CHKERRQ(ierr);
2654   if (a->permute){
2655     ierr = PetscFree(aa);CHKERRQ(ierr);
2656   }
2657 
2658   ierr = ISRestoreIndices(perm,&perm_ptr);CHKERRQ(ierr);
2659   C->factor    = FACTOR_CHOLESKY;
2660   C->assembled = PETSC_TRUE;
2661   C->preallocated = PETSC_TRUE;
2662   PLogFlops(1.3333*8*b->mbs); /* from inverting diagonal blocks */
2663   PetscFunctionReturn(0);
2664 }
2665 
2666 /*
2667       Version for when blocks are 2 by 2 Using natural ordering
2668 */
2669 #undef __FUNC__
2670 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_2_NaturalOrdering"
2671 int MatCholeskyFactorNumeric_SeqSBAIJ_2_NaturalOrdering(Mat A,Mat *B)
2672 {
2673   Mat                C = *B;
2674   Mat_SeqBAIJ        *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
2675   int                ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
2676   int                *ajtmpold,*ajtmp,nz,row;
2677   int                *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
2678   MatScalar          *pv,*v,*rtmp,*pc,*w,*x;
2679   MatScalar          p1,p2,p3,p4,m1,m2,m3,m4,x1,x2,x3,x4;
2680   MatScalar          *ba = b->a,*aa = a->a;
2681 
2682   PetscFunctionBegin;
2683   rtmp  = (MatScalar*)PetscMalloc(4*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
2684 
2685   for (i=0; i<n; i++) {
2686     nz    = bi[i+1] - bi[i];
2687     ajtmp = bj + bi[i];
2688     for  (j=0; j<nz; j++) {
2689       x = rtmp+4*ajtmp[j];
2690       x[0]  = x[1]  = x[2]  = x[3]  = 0.0;
2691     }
2692     /* load in initial (unfactored row) */
2693     nz       = ai[i+1] - ai[i];
2694     ajtmpold = aj + ai[i];
2695     v        = aa + 4*ai[i];
2696     for (j=0; j<nz; j++) {
2697       x    = rtmp+4*ajtmpold[j];
2698       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
2699       v    += 4;
2700     }
2701     row = *ajtmp++;
2702     while (row < i) {
2703       pc  = rtmp + 4*row;
2704       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
2705       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0) {
2706         pv = ba + 4*diag_offset[row];
2707         pj = bj + diag_offset[row] + 1;
2708         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
2709         pc[0] = m1 = p1*x1 + p3*x2;
2710         pc[1] = m2 = p2*x1 + p4*x2;
2711         pc[2] = m3 = p1*x3 + p3*x4;
2712         pc[3] = m4 = p2*x3 + p4*x4;
2713         nz = bi[row+1] - diag_offset[row] - 1;
2714         pv += 4;
2715         for (j=0; j<nz; j++) {
2716           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
2717           x    = rtmp + 4*pj[j];
2718           x[0] -= m1*x1 + m3*x2;
2719           x[1] -= m2*x1 + m4*x2;
2720           x[2] -= m1*x3 + m3*x4;
2721           x[3] -= m2*x3 + m4*x4;
2722           pv   += 4;
2723         }
2724         PLogFlops(16*nz+12);
2725       }
2726       row = *ajtmp++;
2727     }
2728     /* finished row so stick it into b->a */
2729     pv = ba + 4*bi[i];
2730     pj = bj + bi[i];
2731     nz = bi[i+1] - bi[i];
2732     for (j=0; j<nz; j++) {
2733       x      = rtmp+4*pj[j];
2734       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
2735       pv   += 4;
2736     }
2737     /* invert diagonal block */
2738     w = ba + 4*diag_offset[i];
2739     ierr = Kernel_A_gets_inverse_A_2(w);CHKERRQ(ierr);
2740     /*Kernel_A_gets_inverse_A(bs,w,v_pivots,v_work);*/
2741   }
2742 
2743   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2744   C->factor    = FACTOR_LU;
2745   C->assembled = PETSC_TRUE;
2746   C->preallocated = PETSC_TRUE;
2747   PLogFlops(1.3333*8*b->mbs); /* from inverting diagonal blocks */
2748   PetscFunctionReturn(0);
2749 }
2750 
2751 /*
2752     Numeric U^T*D*U factorization for SBAIJ format. Modified from SNF of YSMP.
2753     Version for blocks are 1 by 1.
2754 */
2755 #undef __FUNC__
2756 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_1"
2757 int MatCholeskyFactorNumeric_SeqSBAIJ_1(Mat A,Mat *B)
2758 {
2759   Mat                C = *B;
2760   Mat_SeqSBAIJ       *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data;
2761   IS                 ip = b->row;
2762   int                *rip,ierr,i,j,mbs = a->mbs,*bi = b->i,*bj = b->j;
2763   int                *ai,*aj,*r;
2764   MatScalar          *rtmp;
2765   MatScalar          *ba = b->a,*aa,ak;
2766   MatScalar          dk,uikdi;
2767   int                k,jmin,jmax,*jl,*il,vj,nexti,ili;
2768 
2769   PetscFunctionBegin;
2770   ierr  = ISGetIndices(ip,&rip);CHKERRQ(ierr);
2771   if (!a->permute){
2772     ai = a->i; aj = a->j; aa = a->a;
2773   } else {
2774     ai = a->inew; aj = a->jnew;
2775     aa = (MatScalar*)PetscMalloc(ai[mbs]*sizeof(MatScalar));CHKPTRQ(aa);
2776     ierr = PetscMemcpy(aa,a->a,ai[mbs]*sizeof(MatScalar));CHKERRQ(ierr);
2777     r   = (int*)PetscMalloc(ai[mbs]*sizeof(int));CHKPTRQ(r);
2778     ierr= PetscMemcpy(r,a->a2anew,(ai[mbs])*sizeof(int));CHKERRQ(ierr);
2779 
2780     jmin = ai[0]; jmax = ai[mbs];
2781     for (j=jmin; j<jmax; j++){
2782       while (r[j] != j){
2783         k = r[j]; r[j] = r[k]; r[k] = k;
2784         ak = aa[k]; aa[k] = aa[j]; aa[j] = ak;
2785       }
2786     }
2787     ierr = PetscFree(r);CHKERRA(ierr);
2788   }
2789 
2790   /* initialization */
2791   /* il and jl record the first nonzero element in each row of the accessing
2792      window U(0:k, k:mbs-1).
2793      jl:    list of rows to be added to uneliminated rows
2794             i>= k: jl(i) is the first row to be added to row i
2795             i<  k: jl(i) is the row following row i in some list of rows
2796             jl(i) = mbs indicates the end of a list
2797      il(i): points to the first nonzero element in columns k,...,mbs-1 of
2798             row i of U */
2799   rtmp  = (MatScalar*)PetscMalloc(mbs*sizeof(MatScalar));CHKPTRQ(rtmp);
2800   il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il);
2801   jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl);
2802   for (i=0; i<mbs; i++) {
2803     rtmp[i] = 0.0; jl[i] = mbs; il[0] = 0;
2804   }
2805 
2806   /* for each row k */
2807   for (k = 0; k<mbs; k++){
2808 
2809     /*initialize k-th row with elements nonzero in row perm(k) of A */
2810     jmin = ai[rip[k]]; jmax = ai[rip[k]+1];
2811     if (jmin < jmax) {
2812       for (j = jmin; j < jmax; j++){
2813         vj = rip[aj[j]];
2814         /* if (k <= vj)*/ rtmp[vj] = aa[j];
2815       }
2816     }
2817 
2818     /* modify k-th row by adding in those rows i with U(i,k) != 0 */
2819     dk = rtmp[k];
2820     i = jl[k]; /* first row to be added to k_th row  */
2821     /* printf(" k=%d, pivot row = %d\n",k,i); */
2822 
2823     while (i < mbs){
2824       nexti = jl[i]; /* next row to be added to k_th row */
2825 
2826       /* compute multiplier, update D(k) and U(i,k) */
2827       ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
2828       uikdi = - ba[ili]*ba[i];
2829       dk += uikdi*ba[ili];
2830       ba[ili] = uikdi; /* -U(i,k) */
2831 
2832       /* add multiple of row i to k-th row ... */
2833       jmin = ili + 1; jmax = bi[i+1];
2834       if (jmin < jmax){
2835         for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j];
2836         /* ... add i to row list for next nonzero entry */
2837         il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
2838         j     = bj[jmin];
2839         jl[i] = jl[j]; jl[j] = i; /* update jl */
2840       }
2841       i = nexti; /* printf("                  pivot row i=%d\n",i);  */
2842     }
2843 
2844     /* check for zero pivot and save diagoanl element */
2845     if (dk == 0.0){
2846       SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot");
2847     }else if (PetscRealPart(dk) < 0){
2848       ierr = PetscPrintf(PETSC_COMM_SELF,"Negative pivot: d[%d] = %g\n",k,dk);
2849     }
2850 
2851     /* save nonzero entries in k-th row of U ... */
2852     ba[k] = 1.0/dk;
2853     jmin = bi[k]; jmax = bi[k+1];
2854     if (jmin < jmax) {
2855       for (j=jmin; j<jmax; j++){
2856          vj = bj[j]; ba[j] = rtmp[vj]; rtmp[vj] = 0.0;
2857       }
2858       /* ... add k to row list for first nonzero entry in k-th row */
2859       il[k] = jmin;
2860       i     = bj[jmin];
2861       jl[k] = jl[i]; jl[i] = k;
2862     }
2863   }
2864 
2865   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2866   ierr = PetscFree(il);CHKERRQ(ierr);
2867   ierr = PetscFree(jl);CHKERRQ(ierr);
2868   if (a->permute){
2869     ierr = PetscFree(aa);CHKERRQ(ierr);
2870   }
2871 
2872   ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr);
2873   C->factor    = FACTOR_CHOLESKY;
2874   C->assembled = PETSC_TRUE;
2875   C->preallocated = PETSC_TRUE;
2876   PLogFlops(b->mbs);
2877 #ifdef TEMP
2878   printf("in factnum_1\n");
2879   for (k=0; k<mbs; k++){
2880     i = b->i[k+1] - b->i[k];
2881     printf("\n b->i[%d]: %d, nzk: %d, diag: %g\n",k,b->i[k],i,b->a[k]);
2882     jmin = b->i[k]; jmax = b->i[k+1];
2883     for (j=jmin; j<jmax; j++){
2884       printf(" %d %g, ",b->j[j],b->a[j]);
2885     }
2886   }
2887 #endif
2888   PetscFunctionReturn(0);
2889 }
2890 
2891 #undef __FUNC__
2892 #define __FUNC__ "MatCholeskyFactor_SeqSBAIJ"
2893 int MatCholeskyFactor_SeqSBAIJ(Mat A,IS perm,PetscReal f)
2894 {
2895   int ierr;
2896   Mat C;
2897 
2898   PetscFunctionBegin;
2899   ierr = MatCholeskyFactorSymbolic(A,perm,f,&C);CHKERRQ(ierr);
2900   ierr = MatCholeskyFactorNumeric(A,&C);CHKERRQ(ierr);
2901   ierr = MatHeaderCopy(A,C);CHKERRQ(ierr);
2902   PetscFunctionReturn(0);
2903 }
2904 
2905 
2906