xref: /petsc/src/mat/impls/sbaij/seq/sbaijfact.c (revision 9f9cb213d6e537a5d6b4dcd99979fb301675b5d1)
1 /* Using Modified Sparse Row (MSR) storage.
2 See page 85, "Iterative Methods ..." by Saad. */
3 
4 /*$Id: sbaijfact.c,v 1.8 2000/07/26 15:42:02 hzhang Exp hzhang $*/
5 /*
6     Factorization code for SBAIJ format.
7 */
8 #include "sbaij.h"
9 #include "src/mat/impls/baij/seq/baij.h"
10 #include "src/vec/vecimpl.h"
11 #include "src/inline/ilu.h"
12 
13 #undef __FUNC__
14 #define __FUNC__ "MatCholeskyFactorSymbolic_SeqSBAIJ"
15 int MatCholeskyFactorSymbolic_SeqSBAIJ(Mat A,IS iscol,PetscReal f,Mat *B)
16 {
17   Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b;
18   IS          isicol,isrow;
19   int         *rip,*riip,ierr,i,mbs = a->mbs,*ai = a->i,*aj = a->j;
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   /* PetscReal   f = 1.0; */
24 
25   PetscFunctionBegin;
26   isrow = iscol;   /* remove isrow later! */
27   PetscValidHeaderSpecific(isrow,IS_COOKIE);
28   PetscValidHeaderSpecific(iscol,IS_COOKIE);
29   /* if (A->M != A->N) SETERRQ(PETSC_ERR_ARG_WRONG,0,"matrix must be square");*/
30   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
31   ierr = ISGetIndices(isrow,&rip);CHKERRQ(ierr);
32   ierr = ISGetIndices(isicol,&riip);CHKERRQ(ierr);
33 
34   for (k=0; k<mbs; k++) {
35     if ( rip[k] - riip[k] != 0 ) {
36       printf("Non-symm. permutation, use symm. permutation or general matrix format\n");
37       break;
38     }
39   }
40 
41   /* initialization */
42   /* Don't know how many column pointers are needed so estimate.
43      Use Modified Sparse Row storage for u and ju, see Sasd pp.85 */
44   /* if (info) f = info->fill; */
45   iu   = (int*)PetscMalloc((mbs+1)*sizeof(int));CHKPTRQ(iu);
46   umax = (int)(f*ai[mbs] + 1); umax += mbs + 1;
47   ju   = (int*)PetscMalloc(umax*sizeof(int));CHKPTRQ(ju);
48   iu[0] = mbs+1;
49   juptr = mbs;
50   jl =  (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl);
51   q  =  (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(q);
52   for (i=0; i<mbs; i++){
53     jl[i] = mbs; q[i] = 0;
54   }
55 
56   /* for each row k */
57   for (k=0; k<mbs; k++){
58     nzk = 0; /* num. of nz blocks in k-th block row with diagonal block excluded */
59     q[k] = mbs;
60     /* initialize nonzero structure of k-th row to row rip[k] of A */
61     jmin = ai[rip[k]];
62     jmax = ai[rip[k]+1];
63     for (j=jmin; j<jmax; j++){
64       vj = riip[aj[j]]; /* col. value */
65       if(vj > k){
66         qm = k;
67         do {
68           m  = qm; qm = q[m];
69         } while(qm < vj);
70         if (qm == vj) {
71           printf(" error: duplicate entry in A\n"); break;
72         }
73         nzk++;
74         q[m] = vj;
75         q[vj] = qm;
76       } /* if(vj > k) */
77     } /* for (j=jmin; j<jmax; j++) */
78 
79     /* modify nonzero structure of k-th row by computing fill-in
80        for each row i to be merged in */
81     i = k;
82     i = jl[i]; /* next pivot row (== mbs for symbolic factorization) */
83     /* printf(" next pivot row i=%d\n",i); */
84     while (i < mbs){
85       /* merge row i into k-th row */
86       nzi = iu[i+1] - (iu[i]+1);
87       jmin = iu[i] + 1; jmax = iu[i] + nzi;
88       qm = k;
89       for (j=jmin; j<jmax+1; j++){
90         vj = ju[j];
91         do {
92           m = qm; qm = q[m];
93         } while (qm < vj);
94         if (qm != vj){
95          nzk++; q[m] = vj; q[vj] = qm; qm = vj;
96         }
97       }
98       i = jl[i]; /* next pivot row */
99     }
100 
101     /* add k to row list for first nonzero element in k-th row */
102     if (nzk > 0){
103       i = q[k]; /* col value of first nonzero element in U(k, k+1:mbs-1) */
104       jl[k] = jl[i]; jl[i] = k;
105     }
106     iu[k+1] = iu[k] + nzk;   /* printf(" iu[%d]=%d, umax=%d\n", k+1, iu[k+1],umax);*/
107 
108     /* allocate more space to ju if needed */
109     if (iu[k+1] > umax) { printf("allocate more space, iu[%d]=%d > umax=%d\n",k+1, iu[k+1],umax);
110       /* estimate how much additional space we will need */
111       /* use the strategy suggested by David Hysom <hysom@perch-t.icase.edu> */
112       /* just double the memory each time */
113       maxadd = umax;
114       if (maxadd < nzk) maxadd = (mbs-k)*(nzk+1)/2;
115       umax += maxadd;
116 
117       /* allocate a longer ju */
118       jutmp = (int*)PetscMalloc(umax*sizeof(int));CHKPTRQ(jutmp);
119       ierr  = PetscMemcpy(jutmp,ju,iu[k]*sizeof(int));CHKERRQ(ierr);
120       ierr  = PetscFree(ju);CHKERRQ(ierr);
121       ju    = jutmp;
122       realloc++; /* count how many times we realloc */
123     }
124 
125     /* save nonzero structure of k-th row in ju */
126     i=k;
127     jumin = juptr + 1; juptr += nzk;
128     for (j=jumin; j<juptr+1; j++){
129       i=q[i];
130       ju[j]=i;
131       /* printf(" k=%d, ju[%d]=%d\n",k,j,ju[j]);*/
132     }
133     /* printf("\n");  */
134   } /* for (k=0; k<mbs; k++) */
135 
136   if (ai[mbs] != 0) {
137     PetscReal af = ((PetscReal)iu[mbs])/((PetscReal)ai[mbs]);
138     PLogInfo(A,"MatCholeskyFactorSymbolic_SeqSBAIJ:Reallocs %d Fill ratio:given %g needed %g\n",realloc,f,af);
139     PLogInfo(A,"MatCholeskyFactorSymbolic_SeqSBAIJ:Run with -pc_lu_fill %g or use \n",af);
140     PLogInfo(A,"MatCholeskyFactorSymbolic_SeqSBAIJ:PCLUSetFill(pc,%g);\n",af);
141     PLogInfo(A,"MatCholeskyFactorSymbolic_SeqSBAIJ:for best performance.\n");
142   } else {
143      PLogInfo(A,"MatCholeskyFactorSymbolic_SeqSBAIJ:Empty matrix.\n");
144   }
145 
146   ierr = ISRestoreIndices(isrow,&rip);CHKERRQ(ierr);
147   ierr = ISRestoreIndices(isicol,&riip);CHKERRQ(ierr);
148 
149   ierr = PetscFree(q);CHKERRQ(ierr);
150   ierr = PetscFree(jl);CHKERRQ(ierr);
151 
152   /* put together the new matrix */
153   ierr = MatCreateSeqSBAIJ(A->comm,bs,bs*mbs,bs*mbs,0,PETSC_NULL,B);CHKERRQ(ierr);
154   PLogObjectParent(*B,isicol);
155   b = (Mat_SeqSBAIJ*)(*B)->data;
156   ierr = PetscFree(b->imax);CHKERRQ(ierr);
157   b->singlemalloc = PETSC_FALSE;
158   /* the next line frees the default space generated by the Create() */
159   ierr = PetscFree(b->a);CHKERRQ(ierr);
160   ierr = PetscFree(b->ilen);CHKERRQ(ierr);
161   b->a          = (MatScalar*)PetscMalloc((iu[mbs]+1)*sizeof(MatScalar)*bs2);CHKPTRQ(b->a);
162   b->j          = ju;
163   b->i          = iu;
164   b->diag       = 0;
165   b->ilen       = 0;
166   b->imax       = 0;
167   b->row        = isrow;
168   b->col        = iscol;
169   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
170   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
171   b->icol       = isicol;
172   b->solve_work = (Scalar*)PetscMalloc((bs*mbs+bs)*sizeof(Scalar));CHKPTRQ(b->solve_work);
173   /* In b structure:  Free imax, ilen, old a, old j.
174      Allocate idnew, solve_work, new a, new j */
175   PLogObjectMemory(*B,(iu[mbs]-mbs)*(sizeof(int)+sizeof(MatScalar)));
176   b->s_maxnz = b->s_nz = iu[mbs];
177 
178   (*B)->factor                 = FACTOR_LU;
179   (*B)->info.factor_mallocs    = realloc;
180   (*B)->info.fill_ratio_given  = f;
181   if (ai[mbs] != 0) {
182     (*B)->info.fill_ratio_needed = ((PetscReal)iu[mbs])/((PetscReal)ai[mbs]);
183   } else {
184     (*B)->info.fill_ratio_needed = 0.0;
185   }
186 
187 
188   PetscFunctionReturn(0);
189 }
190 
191 /* ----------------------------------------------------------- */
192 #undef __FUNC__
193 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_N"
194 int MatCholeskyFactorNumeric_SeqSBAIJ_N(Mat A,Mat *B)
195 {
196   Mat                C = *B;
197   Mat_SeqBAIJ        *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
198   IS                 isrow = b->row,isicol = b->icol;
199   int                *r,*ic,ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
200   int                *ajtmpold,*ajtmp,nz,row,bslog,*ai=a->i,*aj=a->j,k,flg;
201   int                *diag_offset=b->diag,diag,bs=a->bs,bs2 = a->bs2,*v_pivots,*pj;
202   MatScalar          *ba = b->a,*aa = a->a,*pv,*v,*rtmp,*multiplier,*v_work,*pc,*w;
203 
204   PetscFunctionBegin;
205   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
206   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
207   rtmp = (MatScalar*)PetscMalloc(bs2*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
208   ierr = PetscMemzero(rtmp,bs2*(n+1)*sizeof(MatScalar));CHKERRQ(ierr);
209   /* generate work space needed by dense LU factorization */
210   v_work     = (MatScalar*)PetscMalloc(bs*sizeof(int) + (bs+bs2)*sizeof(MatScalar));CHKPTRQ(v_work);
211   multiplier = v_work + bs;
212   v_pivots   = (int*)(multiplier + bs2);
213 
214   /* flops in while loop */
215   bslog = 2*bs*bs2;
216 
217   for (i=0; i<n; i++) {
218     nz    = bi[i+1] - bi[i];
219     ajtmp = bj + bi[i];
220     for  (j=0; j<nz; j++) {
221       ierr = PetscMemzero(rtmp+bs2*ajtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
222     }
223     /* load in initial (unfactored row) */
224     nz       = ai[r[i]+1] - ai[r[i]];
225     ajtmpold = aj + ai[r[i]];
226     v        = aa + bs2*ai[r[i]];
227     for (j=0; j<nz; j++) {
228       ierr = PetscMemcpy(rtmp+bs2*ic[ajtmpold[j]],v+bs2*j,bs2*sizeof(MatScalar));CHKERRQ(ierr);
229     }
230     row = *ajtmp++;
231     while (row < i) {
232       pc = rtmp + bs2*row;
233 /*      if (*pc) { */
234       for (flg=0,k=0; k<bs2; k++) { if (pc[k]!=0.0) { flg =1; break; }}
235       if (flg) {
236         pv = ba + bs2*diag_offset[row];
237         pj = bj + diag_offset[row] + 1;
238         Kernel_A_gets_A_times_B(bs,pc,pv,multiplier);
239         nz = bi[row+1] - diag_offset[row] - 1;
240         pv += bs2;
241         for (j=0; j<nz; j++) {
242           Kernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j);
243         }
244         PLogFlops(bslog*(nz+1)-bs);
245       }
246         row = *ajtmp++;
247     }
248     /* finished row so stick it into b->a */
249     pv = ba + bs2*bi[i];
250     pj = bj + bi[i];
251     nz = bi[i+1] - bi[i];
252     for (j=0; j<nz; j++) {
253       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
254     }
255     diag = diag_offset[i] - bi[i];
256     /* invert diagonal block */
257     w = pv + bs2*diag;
258     Kernel_A_gets_inverse_A(bs,w,v_pivots,v_work);
259   }
260 
261   ierr = PetscFree(rtmp);CHKERRQ(ierr);
262   ierr = PetscFree(v_work);CHKERRQ(ierr);
263   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
264   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
265   C->factor = FACTOR_LU;
266   C->assembled = PETSC_TRUE;
267   PLogFlops(1.3333*bs*bs2*b->mbs); /* from inverting diagonal blocks */
268   PetscFunctionReturn(0);
269 }
270 /* ------------------------------------------------------------*/
271 /*
272       Version for when blocks are 7 by 7
273 */
274 #undef __FUNC__
275 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_7"
276 int MatCholeskyFactorNumeric_SeqSBAIJ_7(Mat A,Mat *B)
277 {
278   Mat         C = *B;
279   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
280   IS          isrow = b->row,isicol = b->icol;
281   int         *r,*ic,ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
282   int         *ajtmpold,*ajtmp,nz,row;
283   int         *diag_offset = b->diag,idx,*ai=a->i,*aj=a->j,*pj;
284   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
285   MatScalar   p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
286   MatScalar   p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
287   MatScalar   x17,x18,x19,x20,x21,x22,x23,x24,x25,p10,p11,p12,p13,p14;
288   MatScalar   p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,m10,m11,m12;
289   MatScalar   m13,m14,m15,m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
290   MatScalar   p26,p27,p28,p29,p30,p31,p32,p33,p34,p35,p36;
291   MatScalar   p37,p38,p39,p40,p41,p42,p43,p44,p45,p46,p47,p48,p49;
292   MatScalar   x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36;
293   MatScalar   x37,x38,x39,x40,x41,x42,x43,x44,x45,x46,x47,x48,x49;
294   MatScalar   m26,m27,m28,m29,m30,m31,m32,m33,m34,m35,m36;
295   MatScalar   m37,m38,m39,m40,m41,m42,m43,m44,m45,m46,m47,m48,m49;
296   MatScalar   *ba = b->a,*aa = a->a;
297 
298   PetscFunctionBegin;
299   ierr  = ISGetIndices(isrow,&r);CHKERRQ(ierr);
300   ierr  = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
301   rtmp  = (MatScalar*)PetscMalloc(49*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
302 
303   for (i=0; i<n; i++) {
304     nz    = bi[i+1] - bi[i];
305     ajtmp = bj + bi[i];
306     for  (j=0; j<nz; j++) {
307       x = rtmp+49*ajtmp[j];
308       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
309       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
310       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = x[25] = 0.0 ;
311       x[26] = x[27] = x[28] = x[29] = x[30] = x[31] = x[32] = x[33] = 0.0 ;
312       x[34] = x[35] = x[36] = x[37] = x[38] = x[39] = x[40] = x[41] = 0.0 ;
313       x[42] = x[43] = x[44] = x[45] = x[46] = x[47] = x[48] = 0.0 ;
314     }
315     /* load in initial (unfactored row) */
316     idx      = r[i];
317     nz       = ai[idx+1] - ai[idx];
318     ajtmpold = aj + ai[idx];
319     v        = aa + 49*ai[idx];
320     for (j=0; j<nz; j++) {
321       x    = rtmp+49*ic[ajtmpold[j]];
322       x[0] =  v[0];  x[1] =  v[1];  x[2] =  v[2];  x[3] =  v[3];
323       x[4] =  v[4];  x[5] =  v[5];  x[6] =  v[6];  x[7] =  v[7];
324       x[8] =  v[8];  x[9] =  v[9];  x[10] = v[10]; x[11] = v[11];
325       x[12] = v[12]; x[13] = v[13]; x[14] = v[14]; x[15] = v[15];
326       x[16] = v[16]; x[17] = v[17]; x[18] = v[18]; x[19] = v[19];
327       x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23];
328       x[24] = v[24]; x[25] = v[25]; x[26] = v[26]; x[27] = v[27];
329       x[28] = v[28]; x[29] = v[29]; x[30] = v[30]; x[31] = v[31];
330       x[32] = v[32]; x[33] = v[33]; x[34] = v[34]; x[35] = v[35];
331       x[36] = v[36]; x[37] = v[37]; x[38] = v[38]; x[39] = v[39];
332       x[40] = v[40]; x[41] = v[41]; x[42] = v[42]; x[43] = v[43];
333       x[44] = v[44]; x[45] = v[45]; x[46] = v[46]; x[47] = v[47];
334       x[48] = v[48];
335       v    += 49;
336     }
337     row = *ajtmp++;
338     while (row < i) {
339       pc  =  rtmp + 49*row;
340       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
341       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];
342       p9  = pc[8];  p10 = pc[9];  p11 = pc[10]; p12 = pc[11];
343       p13 = pc[12]; p14 = pc[13]; p15 = pc[14]; p16 = pc[15];
344       p17 = pc[16]; p18 = pc[17]; p19 = pc[18]; p20 = pc[19];
345       p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
346       p25 = pc[24]; p26 = pc[25]; p27 = pc[26]; p28 = pc[27];
347       p29 = pc[28]; p30 = pc[29]; p31 = pc[30]; p32 = pc[31];
348       p33 = pc[32]; p34 = pc[33]; p35 = pc[34]; p36 = pc[35];
349       p37 = pc[36]; p38 = pc[37]; p39 = pc[38]; p40 = pc[39];
350       p41 = pc[40]; p42 = pc[41]; p43 = pc[42]; p44 = pc[43];
351       p45 = pc[44]; p46 = pc[45]; p47 = pc[46]; p48 = pc[47];
352       p49 = pc[48];
353       if (p1  != 0.0 || p2  != 0.0 || p3  != 0.0 || p4  != 0.0 ||
354           p5  != 0.0 || p6  != 0.0 || p7  != 0.0 || p8  != 0.0 ||
355           p9  != 0.0 || p10 != 0.0 || p11 != 0.0 || p12 != 0.0 ||
356           p13 != 0.0 || p14 != 0.0 || p15 != 0.0 || p16 != 0.0 ||
357           p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 ||
358           p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 ||
359           p25 != 0.0 || p26 != 0.0 || p27 != 0.0 || p28 != 0.0 ||
360           p29 != 0.0 || p30 != 0.0 || p31 != 0.0 || p32 != 0.0 ||
361           p33 != 0.0 || p34 != 0.0 || p35 != 0.0 || p36 != 0.0 ||
362           p37 != 0.0 || p38 != 0.0 || p39 != 0.0 || p40 != 0.0 ||
363           p41 != 0.0 || p42 != 0.0 || p43 != 0.0 || p44 != 0.0 ||
364           p45 != 0.0 || p46 != 0.0 || p47 != 0.0 || p48 != 0.0 ||
365           p49 != 0.0) {
366         pv = ba + 49*diag_offset[row];
367         pj = bj + diag_offset[row] + 1;
368 	x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
369 	x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
370 	x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
371 	x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
372 	x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
373 	x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
374 	x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
375 	x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
376 	x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
377 	x37 = pv[36]; x38 = pv[37]; x39 = pv[38]; x40 = pv[39];
378 	x41 = pv[40]; x42 = pv[41]; x43 = pv[42]; x44 = pv[43];
379 	x45 = pv[44]; x46 = pv[45]; x47 = pv[46]; x48 = pv[47];
380 	x49 = pv[48];
381         pc[0]  = m1  = p1*x1  + p8*x2   + p15*x3  + p22*x4  + p29*x5  + p36*x6 + p43*x7;
382         pc[1]  = m2  = p2*x1  + p9*x2   + p16*x3  + p23*x4  + p30*x5  + p37*x6 + p44*x7;
383         pc[2]  = m3  = p3*x1  + p10*x2  + p17*x3  + p24*x4  + p31*x5  + p38*x6 + p45*x7;
384         pc[3]  = m4  = p4*x1  + p11*x2  + p18*x3  + p25*x4  + p32*x5  + p39*x6 + p46*x7;
385         pc[4]  = m5  = p5*x1  + p12*x2  + p19*x3  + p26*x4  + p33*x5  + p40*x6 + p47*x7;
386         pc[5]  = m6  = p6*x1  + p13*x2  + p20*x3  + p27*x4  + p34*x5  + p41*x6 + p48*x7;
387         pc[6]  = m7  = p7*x1  + p14*x2  + p21*x3  + p28*x4  + p35*x5  + p42*x6 + p49*x7;
388 
389         pc[7]  = m8  = p1*x8  + p8*x9   + p15*x10 + p22*x11 + p29*x12 + p36*x13 + p43*x14;
390         pc[8]  = m9  = p2*x8  + p9*x9   + p16*x10 + p23*x11 + p30*x12 + p37*x13 + p44*x14;
391         pc[9]  = m10 = p3*x8  + p10*x9  + p17*x10 + p24*x11 + p31*x12 + p38*x13 + p45*x14;
392         pc[10] = m11 = p4*x8  + p11*x9  + p18*x10 + p25*x11 + p32*x12 + p39*x13 + p46*x14;
393         pc[11] = m12 = p5*x8  + p12*x9  + p19*x10 + p26*x11 + p33*x12 + p40*x13 + p47*x14;
394         pc[12] = m13 = p6*x8  + p13*x9  + p20*x10 + p27*x11 + p34*x12 + p41*x13 + p48*x14;
395         pc[13] = m14 = p7*x8  + p14*x9  + p21*x10 + p28*x11 + p35*x12 + p42*x13 + p49*x14;
396 
397         pc[14] = m15 = p1*x15 + p8*x16  + p15*x17 + p22*x18 + p29*x19 + p36*x20 + p43*x21;
398         pc[15] = m16 = p2*x15 + p9*x16  + p16*x17 + p23*x18 + p30*x19 + p37*x20 + p44*x21;
399         pc[16] = m17 = p3*x15 + p10*x16 + p17*x17 + p24*x18 + p31*x19 + p38*x20 + p45*x21;
400         pc[17] = m18 = p4*x15 + p11*x16 + p18*x17 + p25*x18 + p32*x19 + p39*x20 + p46*x21;
401         pc[18] = m19 = p5*x15 + p12*x16 + p19*x17 + p26*x18 + p33*x19 + p40*x20 + p47*x21;
402         pc[19] = m20 = p6*x15 + p13*x16 + p20*x17 + p27*x18 + p34*x19 + p41*x20 + p48*x21;
403         pc[20] = m21 = p7*x15 + p14*x16 + p21*x17 + p28*x18 + p35*x19 + p42*x20 + p49*x21;
404 
405         pc[21] = m22 = p1*x22 + p8*x23  + p15*x24 + p22*x25 + p29*x26 + p36*x27 + p43*x28;
406         pc[22] = m23 = p2*x22 + p9*x23  + p16*x24 + p23*x25 + p30*x26 + p37*x27 + p44*x28;
407         pc[23] = m24 = p3*x22 + p10*x23 + p17*x24 + p24*x25 + p31*x26 + p38*x27 + p45*x28;
408         pc[24] = m25 = p4*x22 + p11*x23 + p18*x24 + p25*x25 + p32*x26 + p39*x27 + p46*x28;
409         pc[25] = m26 = p5*x22 + p12*x23 + p19*x24 + p26*x25 + p33*x26 + p40*x27 + p47*x28;
410         pc[26] = m27 = p6*x22 + p13*x23 + p20*x24 + p27*x25 + p34*x26 + p41*x27 + p48*x28;
411         pc[27] = m28 = p7*x22 + p14*x23 + p21*x24 + p28*x25 + p35*x26 + p42*x27 + p49*x28;
412 
413         pc[28] = m29 = p1*x29 + p8*x30  + p15*x31 + p22*x32 + p29*x33 + p36*x34 + p43*x35;
414         pc[29] = m30 = p2*x29 + p9*x30  + p16*x31 + p23*x32 + p30*x33 + p37*x34 + p44*x35;
415         pc[30] = m31 = p3*x29 + p10*x30 + p17*x31 + p24*x32 + p31*x33 + p38*x34 + p45*x35;
416         pc[31] = m32 = p4*x29 + p11*x30 + p18*x31 + p25*x32 + p32*x33 + p39*x34 + p46*x35;
417         pc[32] = m33 = p5*x29 + p12*x30 + p19*x31 + p26*x32 + p33*x33 + p40*x34 + p47*x35;
418         pc[33] = m34 = p6*x29 + p13*x30 + p20*x31 + p27*x32 + p34*x33 + p41*x34 + p48*x35;
419         pc[34] = m35 = p7*x29 + p14*x30 + p21*x31 + p28*x32 + p35*x33 + p42*x34 + p49*x35;
420 
421         pc[35] = m36 = p1*x36 + p8*x37  + p15*x38 + p22*x39 + p29*x40 + p36*x41 + p43*x42;
422         pc[36] = m37 = p2*x36 + p9*x37  + p16*x38 + p23*x39 + p30*x40 + p37*x41 + p44*x42;
423         pc[37] = m38 = p3*x36 + p10*x37 + p17*x38 + p24*x39 + p31*x40 + p38*x41 + p45*x42;
424         pc[38] = m39 = p4*x36 + p11*x37 + p18*x38 + p25*x39 + p32*x40 + p39*x41 + p46*x42;
425         pc[39] = m40 = p5*x36 + p12*x37 + p19*x38 + p26*x39 + p33*x40 + p40*x41 + p47*x42;
426         pc[40] = m41 = p6*x36 + p13*x37 + p20*x38 + p27*x39 + p34*x40 + p41*x41 + p48*x42;
427         pc[41] = m42 = p7*x36 + p14*x37 + p21*x38 + p28*x39 + p35*x40 + p42*x41 + p49*x42;
428 
429         pc[42] = m43 = p1*x43 + p8*x44  + p15*x45 + p22*x46 + p29*x47 + p36*x48 + p43*x49;
430         pc[43] = m44 = p2*x43 + p9*x44  + p16*x45 + p23*x46 + p30*x47 + p37*x48 + p44*x49;
431         pc[44] = m45 = p3*x43 + p10*x44 + p17*x45 + p24*x46 + p31*x47 + p38*x48 + p45*x49;
432         pc[45] = m46 = p4*x43 + p11*x44 + p18*x45 + p25*x46 + p32*x47 + p39*x48 + p46*x49;
433         pc[46] = m47 = p5*x43 + p12*x44 + p19*x45 + p26*x46 + p33*x47 + p40*x48 + p47*x49;
434         pc[47] = m48 = p6*x43 + p13*x44 + p20*x45 + p27*x46 + p34*x47 + p41*x48 + p48*x49;
435         pc[48] = m49 = p7*x43 + p14*x44 + p21*x45 + p28*x46 + p35*x47 + p42*x48 + p49*x49;
436 
437         nz = bi[row+1] - diag_offset[row] - 1;
438         pv += 49;
439         for (j=0; j<nz; j++) {
440 	  x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
441 	  x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
442 	  x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
443 	  x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
444 	  x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
445 	  x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
446 	  x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
447 	  x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
448 	  x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
449 	  x37 = pv[36]; x38 = pv[37]; x39 = pv[38]; x40 = pv[39];
450 	  x41 = pv[40]; x42 = pv[41]; x43 = pv[42]; x44 = pv[43];
451 	  x45 = pv[44]; x46 = pv[45]; x47 = pv[46]; x48 = pv[47];
452 	  x49 = pv[48];
453 	  x    = rtmp + 49*pj[j];
454 	  x[0]  -= m1*x1  + m8*x2   + m15*x3  + m22*x4  + m29*x5  + m36*x6 + m43*x7;
455 	  x[1]  -= m2*x1  + m9*x2   + m16*x3  + m23*x4  + m30*x5  + m37*x6 + m44*x7;
456 	  x[2]  -= m3*x1  + m10*x2  + m17*x3  + m24*x4  + m31*x5  + m38*x6 + m45*x7;
457 	  x[3]  -= m4*x1  + m11*x2  + m18*x3  + m25*x4  + m32*x5  + m39*x6 + m46*x7;
458 	  x[4]  -= m5*x1  + m12*x2  + m19*x3  + m26*x4  + m33*x5  + m40*x6 + m47*x7;
459 	  x[5]  -= m6*x1  + m13*x2  + m20*x3  + m27*x4  + m34*x5  + m41*x6 + m48*x7;
460 	  x[6]  -= m7*x1  + m14*x2  + m21*x3  + m28*x4  + m35*x5  + m42*x6 + m49*x7;
461 
462 	  x[7]  -= m1*x8  + m8*x9   + m15*x10 + m22*x11 + m29*x12 + m36*x13 + m43*x14;
463 	  x[8]  -= m2*x8  + m9*x9   + m16*x10 + m23*x11 + m30*x12 + m37*x13 + m44*x14;
464 	  x[9]  -= m3*x8  + m10*x9  + m17*x10 + m24*x11 + m31*x12 + m38*x13 + m45*x14;
465 	  x[10] -= m4*x8  + m11*x9  + m18*x10 + m25*x11 + m32*x12 + m39*x13 + m46*x14;
466 	  x[11] -= m5*x8  + m12*x9  + m19*x10 + m26*x11 + m33*x12 + m40*x13 + m47*x14;
467 	  x[12] -= m6*x8  + m13*x9  + m20*x10 + m27*x11 + m34*x12 + m41*x13 + m48*x14;
468 	  x[13] -= m7*x8  + m14*x9  + m21*x10 + m28*x11 + m35*x12 + m42*x13 + m49*x14;
469 
470 	  x[14] -= m1*x15 + m8*x16  + m15*x17 + m22*x18 + m29*x19 + m36*x20 + m43*x21;
471 	  x[15] -= m2*x15 + m9*x16  + m16*x17 + m23*x18 + m30*x19 + m37*x20 + m44*x21;
472 	  x[16] -= m3*x15 + m10*x16 + m17*x17 + m24*x18 + m31*x19 + m38*x20 + m45*x21;
473 	  x[17] -= m4*x15 + m11*x16 + m18*x17 + m25*x18 + m32*x19 + m39*x20 + m46*x21;
474 	  x[18] -= m5*x15 + m12*x16 + m19*x17 + m26*x18 + m33*x19 + m40*x20 + m47*x21;
475 	  x[19] -= m6*x15 + m13*x16 + m20*x17 + m27*x18 + m34*x19 + m41*x20 + m48*x21;
476 	  x[20] -= m7*x15 + m14*x16 + m21*x17 + m28*x18 + m35*x19 + m42*x20 + m49*x21;
477 
478 	  x[21] -= m1*x22 + m8*x23  + m15*x24 + m22*x25 + m29*x26 + m36*x27 + m43*x28;
479 	  x[22] -= m2*x22 + m9*x23  + m16*x24 + m23*x25 + m30*x26 + m37*x27 + m44*x28;
480 	  x[23] -= m3*x22 + m10*x23 + m17*x24 + m24*x25 + m31*x26 + m38*x27 + m45*x28;
481 	  x[24] -= m4*x22 + m11*x23 + m18*x24 + m25*x25 + m32*x26 + m39*x27 + m46*x28;
482 	  x[25] -= m5*x22 + m12*x23 + m19*x24 + m26*x25 + m33*x26 + m40*x27 + m47*x28;
483 	  x[26] -= m6*x22 + m13*x23 + m20*x24 + m27*x25 + m34*x26 + m41*x27 + m48*x28;
484 	  x[27] -= m7*x22 + m14*x23 + m21*x24 + m28*x25 + m35*x26 + m42*x27 + m49*x28;
485 
486 	  x[28] -= m1*x29 + m8*x30  + m15*x31 + m22*x32 + m29*x33 + m36*x34 + m43*x35;
487 	  x[29] -= m2*x29 + m9*x30  + m16*x31 + m23*x32 + m30*x33 + m37*x34 + m44*x35;
488 	  x[30] -= m3*x29 + m10*x30 + m17*x31 + m24*x32 + m31*x33 + m38*x34 + m45*x35;
489 	  x[31] -= m4*x29 + m11*x30 + m18*x31 + m25*x32 + m32*x33 + m39*x34 + m46*x35;
490 	  x[32] -= m5*x29 + m12*x30 + m19*x31 + m26*x32 + m33*x33 + m40*x34 + m47*x35;
491 	  x[33] -= m6*x29 + m13*x30 + m20*x31 + m27*x32 + m34*x33 + m41*x34 + m48*x35;
492 	  x[34] -= m7*x29 + m14*x30 + m21*x31 + m28*x32 + m35*x33 + m42*x34 + m49*x35;
493 
494 	  x[35] -= m1*x36 + m8*x37  + m15*x38 + m22*x39 + m29*x40 + m36*x41 + m43*x42;
495 	  x[36] -= m2*x36 + m9*x37  + m16*x38 + m23*x39 + m30*x40 + m37*x41 + m44*x42;
496 	  x[37] -= m3*x36 + m10*x37 + m17*x38 + m24*x39 + m31*x40 + m38*x41 + m45*x42;
497 	  x[38] -= m4*x36 + m11*x37 + m18*x38 + m25*x39 + m32*x40 + m39*x41 + m46*x42;
498 	  x[39] -= m5*x36 + m12*x37 + m19*x38 + m26*x39 + m33*x40 + m40*x41 + m47*x42;
499 	  x[40] -= m6*x36 + m13*x37 + m20*x38 + m27*x39 + m34*x40 + m41*x41 + m48*x42;
500 	  x[41] -= m7*x36 + m14*x37 + m21*x38 + m28*x39 + m35*x40 + m42*x41 + m49*x42;
501 
502 	  x[42] -= m1*x43 + m8*x44  + m15*x45 + m22*x46 + m29*x47 + m36*x48 + m43*x49;
503 	  x[43] -= m2*x43 + m9*x44  + m16*x45 + m23*x46 + m30*x47 + m37*x48 + m44*x49;
504 	  x[44] -= m3*x43 + m10*x44 + m17*x45 + m24*x46 + m31*x47 + m38*x48 + m45*x49;
505 	  x[45] -= m4*x43 + m11*x44 + m18*x45 + m25*x46 + m32*x47 + m39*x48 + m46*x49;
506 	  x[46] -= m5*x43 + m12*x44 + m19*x45 + m26*x46 + m33*x47 + m40*x48 + m47*x49;
507 	  x[47] -= m6*x43 + m13*x44 + m20*x45 + m27*x46 + m34*x47 + m41*x48 + m48*x49;
508 	  x[48] -= m7*x43 + m14*x44 + m21*x45 + m28*x46 + m35*x47 + m42*x48 + m49*x49;
509           pv   += 49;
510         }
511         PLogFlops(686*nz+637);
512       }
513       row = *ajtmp++;
514     }
515     /* finished row so stick it into b->a */
516     pv = ba + 49*bi[i];
517     pj = bj + bi[i];
518     nz = bi[i+1] - bi[i];
519     for (j=0; j<nz; j++) {
520       x      = rtmp+49*pj[j];
521       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
522       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7];
523       pv[8]  = x[8];  pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11];
524       pv[12] = x[12]; pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
525       pv[16] = x[16]; pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19];
526       pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23];
527       pv[24] = x[24]; pv[25] = x[25]; pv[26] = x[26]; pv[27] = x[27];
528       pv[28] = x[28]; pv[29] = x[29]; pv[30] = x[30]; pv[31] = x[31];
529       pv[32] = x[32]; pv[33] = x[33]; pv[34] = x[34]; pv[35] = x[35];
530       pv[36] = x[36]; pv[37] = x[37]; pv[38] = x[38]; pv[39] = x[39];
531       pv[40] = x[40]; pv[41] = x[41]; pv[42] = x[42]; pv[43] = x[43];
532       pv[44] = x[44]; pv[45] = x[45]; pv[46] = x[46]; pv[47] = x[47];
533       pv[48] = x[48];
534       pv   += 49;
535     }
536     /* invert diagonal block */
537     w = ba + 49*diag_offset[i];
538     ierr = Kernel_A_gets_inverse_A_7(w);CHKERRQ(ierr);
539   }
540 
541   ierr = PetscFree(rtmp);CHKERRQ(ierr);
542   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
543   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
544   C->factor = FACTOR_LU;
545   C->assembled = PETSC_TRUE;
546   PLogFlops(1.3333*343*b->mbs); /* from inverting diagonal blocks */
547   PetscFunctionReturn(0);
548 }
549 
550 /*
551       Version for when blocks are 7 by 7 Using natural ordering
552 */
553 #undef __FUNC__
554 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_7_NaturalOrdering"
555 int MatCholeskyFactorNumeric_SeqSBAIJ_7_NaturalOrdering(Mat A,Mat *B)
556 {
557   Mat          C = *B;
558   Mat_SeqBAIJ  *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
559   int          ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
560   int          *ajtmpold,*ajtmp,nz,row;
561   int          *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
562   MatScalar    *pv,*v,*rtmp,*pc,*w,*x;
563   MatScalar    x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15;
564   MatScalar    x16,x17,x18,x19,x20,x21,x22,x23,x24,x25;
565   MatScalar    p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15;
566   MatScalar    p16,p17,p18,p19,p20,p21,p22,p23,p24,p25;
567   MatScalar    m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12,m13,m14,m15;
568   MatScalar    m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
569   MatScalar    p26,p27,p28,p29,p30,p31,p32,p33,p34,p35,p36;
570   MatScalar    p37,p38,p39,p40,p41,p42,p43,p44,p45,p46,p47,p48,p49;
571   MatScalar    x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36;
572   MatScalar    x37,x38,x39,x40,x41,x42,x43,x44,x45,x46,x47,x48,x49;
573   MatScalar    m26,m27,m28,m29,m30,m31,m32,m33,m34,m35,m36;
574   MatScalar    m37,m38,m39,m40,m41,m42,m43,m44,m45,m46,m47,m48,m49;
575   MatScalar    *ba = b->a,*aa = a->a;
576 
577   PetscFunctionBegin;
578   rtmp  = (MatScalar*)PetscMalloc(49*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
579   for (i=0; i<n; i++) {
580     nz    = bi[i+1] - bi[i];
581     ajtmp = bj + bi[i];
582     for  (j=0; j<nz; j++) {
583       x = rtmp+49*ajtmp[j];
584       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
585       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
586       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = x[25] = 0.0 ;
587       x[26] = x[27] = x[28] = x[29] = x[30] = x[31] = x[32] = x[33] = 0.0 ;
588       x[34] = x[35] = x[36] = x[37] = x[38] = x[39] = x[40] = x[41] = 0.0 ;
589       x[42] = x[43] = x[44] = x[45] = x[46] = x[47] = x[48] = 0.0 ;
590     }
591     /* load in initial (unfactored row) */
592     nz       = ai[i+1] - ai[i];
593     ajtmpold = aj + ai[i];
594     v        = aa + 49*ai[i];
595     for (j=0; j<nz; j++) {
596       x    = rtmp+49*ajtmpold[j];
597       x[0] =  v[0];  x[1] =  v[1];  x[2] =  v[2];  x[3] =  v[3];
598       x[4] =  v[4];  x[5] =  v[5];  x[6] =  v[6];  x[7] =  v[7];
599       x[8] =  v[8];  x[9] =  v[9];  x[10] = v[10]; x[11] = v[11];
600       x[12] = v[12]; x[13] = v[13]; x[14] = v[14]; x[15] = v[15];
601       x[16] = v[16]; x[17] = v[17]; x[18] = v[18]; x[19] = v[19];
602       x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23];
603       x[24] = v[24]; x[25] = v[25]; x[26] = v[26]; x[27] = v[27];
604       x[28] = v[28]; x[29] = v[29]; x[30] = v[30]; x[31] = v[31];
605       x[32] = v[32]; x[33] = v[33]; x[34] = v[34]; x[35] = v[35];
606       x[36] = v[36]; x[37] = v[37]; x[38] = v[38]; x[39] = v[39];
607       x[40] = v[40]; x[41] = v[41]; x[42] = v[42]; x[43] = v[43];
608       x[44] = v[44]; x[45] = v[45]; x[46] = v[46]; x[47] = v[47];
609       x[48] = v[48];
610       v    += 49;
611     }
612     row = *ajtmp++;
613     while (row < i) {
614       pc  = rtmp + 49*row;
615       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
616       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];
617       p9  = pc[8];  p10 = pc[9];  p11 = pc[10]; p12 = pc[11];
618       p13 = pc[12]; p14 = pc[13]; p15 = pc[14]; p16 = pc[15];
619       p17 = pc[16]; p18 = pc[17]; p19 = pc[18]; p20 = pc[19];
620       p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
621       p25 = pc[24]; p26 = pc[25]; p27 = pc[26]; p28 = pc[27];
622       p29 = pc[28]; p30 = pc[29]; p31 = pc[30]; p32 = pc[31];
623       p33 = pc[32]; p34 = pc[33]; p35 = pc[34]; p36 = pc[35];
624       p37 = pc[36]; p38 = pc[37]; p39 = pc[38]; p40 = pc[39];
625       p41 = pc[40]; p42 = pc[41]; p43 = pc[42]; p44 = pc[43];
626       p45 = pc[44]; p46 = pc[45]; p47 = pc[46]; p48 = pc[47];
627       p49 = pc[48];
628       if (p1  != 0.0 || p2  != 0.0 || p3  != 0.0 || p4  != 0.0 ||
629           p5  != 0.0 || p6  != 0.0 || p7  != 0.0 || p8  != 0.0 ||
630           p9  != 0.0 || p10 != 0.0 || p11 != 0.0 || p12 != 0.0 ||
631           p13 != 0.0 || p14 != 0.0 || p15 != 0.0 || p16 != 0.0 ||
632           p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 ||
633           p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 ||
634           p25 != 0.0 || p26 != 0.0 || p27 != 0.0 || p28 != 0.0 ||
635           p29 != 0.0 || p30 != 0.0 || p31 != 0.0 || p32 != 0.0 ||
636           p33 != 0.0 || p34 != 0.0 || p35 != 0.0 || p36 != 0.0 ||
637           p37 != 0.0 || p38 != 0.0 || p39 != 0.0 || p40 != 0.0 ||
638           p41 != 0.0 || p42 != 0.0 || p43 != 0.0 || p44 != 0.0 ||
639           p45 != 0.0 || p46 != 0.0 || p47 != 0.0 || p48 != 0.0 ||
640           p49 != 0.0) {
641         pv = ba + 49*diag_offset[row];
642         pj = bj + diag_offset[row] + 1;
643 	x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
644 	x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
645 	x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
646 	x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
647 	x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
648 	x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
649 	x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
650 	x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
651 	x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
652 	x37 = pv[36]; x38 = pv[37]; x39 = pv[38]; x40 = pv[39];
653 	x41 = pv[40]; x42 = pv[41]; x43 = pv[42]; x44 = pv[43];
654 	x45 = pv[44]; x46 = pv[45]; x47 = pv[46]; x48 = pv[47];
655         x49 = pv[48];
656         pc[0]  = m1  = p1*x1  + p8*x2   + p15*x3  + p22*x4  + p29*x5  + p36*x6 + p43*x7;
657         pc[1]  = m2  = p2*x1  + p9*x2   + p16*x3  + p23*x4  + p30*x5  + p37*x6 + p44*x7;
658         pc[2]  = m3  = p3*x1  + p10*x2  + p17*x3  + p24*x4  + p31*x5  + p38*x6 + p45*x7;
659         pc[3]  = m4  = p4*x1  + p11*x2  + p18*x3  + p25*x4  + p32*x5  + p39*x6 + p46*x7;
660         pc[4]  = m5  = p5*x1  + p12*x2  + p19*x3  + p26*x4  + p33*x5  + p40*x6 + p47*x7;
661         pc[5]  = m6  = p6*x1  + p13*x2  + p20*x3  + p27*x4  + p34*x5  + p41*x6 + p48*x7;
662         pc[6]  = m7  = p7*x1  + p14*x2  + p21*x3  + p28*x4  + p35*x5  + p42*x6 + p49*x7;
663 
664         pc[7]  = m8  = p1*x8  + p8*x9   + p15*x10 + p22*x11 + p29*x12 + p36*x13 + p43*x14;
665         pc[8]  = m9  = p2*x8  + p9*x9   + p16*x10 + p23*x11 + p30*x12 + p37*x13 + p44*x14;
666         pc[9]  = m10 = p3*x8  + p10*x9  + p17*x10 + p24*x11 + p31*x12 + p38*x13 + p45*x14;
667         pc[10] = m11 = p4*x8  + p11*x9  + p18*x10 + p25*x11 + p32*x12 + p39*x13 + p46*x14;
668         pc[11] = m12 = p5*x8  + p12*x9  + p19*x10 + p26*x11 + p33*x12 + p40*x13 + p47*x14;
669         pc[12] = m13 = p6*x8  + p13*x9  + p20*x10 + p27*x11 + p34*x12 + p41*x13 + p48*x14;
670         pc[13] = m14 = p7*x8  + p14*x9  + p21*x10 + p28*x11 + p35*x12 + p42*x13 + p49*x14;
671 
672         pc[14] = m15 = p1*x15 + p8*x16  + p15*x17 + p22*x18 + p29*x19 + p36*x20 + p43*x21;
673         pc[15] = m16 = p2*x15 + p9*x16  + p16*x17 + p23*x18 + p30*x19 + p37*x20 + p44*x21;
674         pc[16] = m17 = p3*x15 + p10*x16 + p17*x17 + p24*x18 + p31*x19 + p38*x20 + p45*x21;
675         pc[17] = m18 = p4*x15 + p11*x16 + p18*x17 + p25*x18 + p32*x19 + p39*x20 + p46*x21;
676         pc[18] = m19 = p5*x15 + p12*x16 + p19*x17 + p26*x18 + p33*x19 + p40*x20 + p47*x21;
677         pc[19] = m20 = p6*x15 + p13*x16 + p20*x17 + p27*x18 + p34*x19 + p41*x20 + p48*x21;
678         pc[20] = m21 = p7*x15 + p14*x16 + p21*x17 + p28*x18 + p35*x19 + p42*x20 + p49*x21;
679 
680         pc[21] = m22 = p1*x22 + p8*x23  + p15*x24 + p22*x25 + p29*x26 + p36*x27 + p43*x28;
681         pc[22] = m23 = p2*x22 + p9*x23  + p16*x24 + p23*x25 + p30*x26 + p37*x27 + p44*x28;
682         pc[23] = m24 = p3*x22 + p10*x23 + p17*x24 + p24*x25 + p31*x26 + p38*x27 + p45*x28;
683         pc[24] = m25 = p4*x22 + p11*x23 + p18*x24 + p25*x25 + p32*x26 + p39*x27 + p46*x28;
684         pc[25] = m26 = p5*x22 + p12*x23 + p19*x24 + p26*x25 + p33*x26 + p40*x27 + p47*x28;
685         pc[26] = m27 = p6*x22 + p13*x23 + p20*x24 + p27*x25 + p34*x26 + p41*x27 + p48*x28;
686         pc[27] = m28 = p7*x22 + p14*x23 + p21*x24 + p28*x25 + p35*x26 + p42*x27 + p49*x28;
687 
688         pc[28] = m29 = p1*x29 + p8*x30  + p15*x31 + p22*x32 + p29*x33 + p36*x34 + p43*x35;
689         pc[29] = m30 = p2*x29 + p9*x30  + p16*x31 + p23*x32 + p30*x33 + p37*x34 + p44*x35;
690         pc[30] = m31 = p3*x29 + p10*x30 + p17*x31 + p24*x32 + p31*x33 + p38*x34 + p45*x35;
691         pc[31] = m32 = p4*x29 + p11*x30 + p18*x31 + p25*x32 + p32*x33 + p39*x34 + p46*x35;
692         pc[32] = m33 = p5*x29 + p12*x30 + p19*x31 + p26*x32 + p33*x33 + p40*x34 + p47*x35;
693         pc[33] = m34 = p6*x29 + p13*x30 + p20*x31 + p27*x32 + p34*x33 + p41*x34 + p48*x35;
694         pc[34] = m35 = p7*x29 + p14*x30 + p21*x31 + p28*x32 + p35*x33 + p42*x34 + p49*x35;
695 
696         pc[35] = m36 = p1*x36 + p8*x37  + p15*x38 + p22*x39 + p29*x40 + p36*x41 + p43*x42;
697         pc[36] = m37 = p2*x36 + p9*x37  + p16*x38 + p23*x39 + p30*x40 + p37*x41 + p44*x42;
698         pc[37] = m38 = p3*x36 + p10*x37 + p17*x38 + p24*x39 + p31*x40 + p38*x41 + p45*x42;
699         pc[38] = m39 = p4*x36 + p11*x37 + p18*x38 + p25*x39 + p32*x40 + p39*x41 + p46*x42;
700         pc[39] = m40 = p5*x36 + p12*x37 + p19*x38 + p26*x39 + p33*x40 + p40*x41 + p47*x42;
701         pc[40] = m41 = p6*x36 + p13*x37 + p20*x38 + p27*x39 + p34*x40 + p41*x41 + p48*x42;
702         pc[41] = m42 = p7*x36 + p14*x37 + p21*x38 + p28*x39 + p35*x40 + p42*x41 + p49*x42;
703 
704         pc[42] = m43 = p1*x43 + p8*x44  + p15*x45 + p22*x46 + p29*x47 + p36*x48 + p43*x49;
705         pc[43] = m44 = p2*x43 + p9*x44  + p16*x45 + p23*x46 + p30*x47 + p37*x48 + p44*x49;
706         pc[44] = m45 = p3*x43 + p10*x44 + p17*x45 + p24*x46 + p31*x47 + p38*x48 + p45*x49;
707         pc[45] = m46 = p4*x43 + p11*x44 + p18*x45 + p25*x46 + p32*x47 + p39*x48 + p46*x49;
708         pc[46] = m47 = p5*x43 + p12*x44 + p19*x45 + p26*x46 + p33*x47 + p40*x48 + p47*x49;
709         pc[47] = m48 = p6*x43 + p13*x44 + p20*x45 + p27*x46 + p34*x47 + p41*x48 + p48*x49;
710         pc[48] = m49 = p7*x43 + p14*x44 + p21*x45 + p28*x46 + p35*x47 + p42*x48 + p49*x49;
711 
712         nz = bi[row+1] - diag_offset[row] - 1;
713         pv += 49;
714         for (j=0; j<nz; j++) {
715 	  x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
716 	  x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
717 	  x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
718 	  x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
719 	  x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
720 	  x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
721 	  x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
722 	  x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
723 	  x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
724 	  x37 = pv[36]; x38 = pv[37]; x39 = pv[38]; x40 = pv[39];
725 	  x41 = pv[40]; x42 = pv[41]; x43 = pv[42]; x44 = pv[43];
726 	  x45 = pv[44]; x46 = pv[45]; x47 = pv[46]; x48 = pv[47];
727 	  x49 = pv[48];
728 	  x    = rtmp + 49*pj[j];
729 	  x[0]  -= m1*x1  + m8*x2   + m15*x3  + m22*x4  + m29*x5  + m36*x6 + m43*x7;
730 	  x[1]  -= m2*x1  + m9*x2   + m16*x3  + m23*x4  + m30*x5  + m37*x6 + m44*x7;
731 	  x[2]  -= m3*x1  + m10*x2  + m17*x3  + m24*x4  + m31*x5  + m38*x6 + m45*x7;
732 	  x[3]  -= m4*x1  + m11*x2  + m18*x3  + m25*x4  + m32*x5  + m39*x6 + m46*x7;
733 	  x[4]  -= m5*x1  + m12*x2  + m19*x3  + m26*x4  + m33*x5  + m40*x6 + m47*x7;
734 	  x[5]  -= m6*x1  + m13*x2  + m20*x3  + m27*x4  + m34*x5  + m41*x6 + m48*x7;
735 	  x[6]  -= m7*x1  + m14*x2  + m21*x3  + m28*x4  + m35*x5  + m42*x6 + m49*x7;
736 
737 	  x[7]  -= m1*x8  + m8*x9   + m15*x10 + m22*x11 + m29*x12 + m36*x13 + m43*x14;
738 	  x[8]  -= m2*x8  + m9*x9   + m16*x10 + m23*x11 + m30*x12 + m37*x13 + m44*x14;
739 	  x[9]  -= m3*x8  + m10*x9  + m17*x10 + m24*x11 + m31*x12 + m38*x13 + m45*x14;
740 	  x[10] -= m4*x8  + m11*x9  + m18*x10 + m25*x11 + m32*x12 + m39*x13 + m46*x14;
741 	  x[11] -= m5*x8  + m12*x9  + m19*x10 + m26*x11 + m33*x12 + m40*x13 + m47*x14;
742 	  x[12] -= m6*x8  + m13*x9  + m20*x10 + m27*x11 + m34*x12 + m41*x13 + m48*x14;
743 	  x[13] -= m7*x8  + m14*x9  + m21*x10 + m28*x11 + m35*x12 + m42*x13 + m49*x14;
744 
745 	  x[14] -= m1*x15 + m8*x16  + m15*x17 + m22*x18 + m29*x19 + m36*x20 + m43*x21;
746 	  x[15] -= m2*x15 + m9*x16  + m16*x17 + m23*x18 + m30*x19 + m37*x20 + m44*x21;
747 	  x[16] -= m3*x15 + m10*x16 + m17*x17 + m24*x18 + m31*x19 + m38*x20 + m45*x21;
748 	  x[17] -= m4*x15 + m11*x16 + m18*x17 + m25*x18 + m32*x19 + m39*x20 + m46*x21;
749 	  x[18] -= m5*x15 + m12*x16 + m19*x17 + m26*x18 + m33*x19 + m40*x20 + m47*x21;
750 	  x[19] -= m6*x15 + m13*x16 + m20*x17 + m27*x18 + m34*x19 + m41*x20 + m48*x21;
751 	  x[20] -= m7*x15 + m14*x16 + m21*x17 + m28*x18 + m35*x19 + m42*x20 + m49*x21;
752 
753 	  x[21] -= m1*x22 + m8*x23  + m15*x24 + m22*x25 + m29*x26 + m36*x27 + m43*x28;
754 	  x[22] -= m2*x22 + m9*x23  + m16*x24 + m23*x25 + m30*x26 + m37*x27 + m44*x28;
755 	  x[23] -= m3*x22 + m10*x23 + m17*x24 + m24*x25 + m31*x26 + m38*x27 + m45*x28;
756 	  x[24] -= m4*x22 + m11*x23 + m18*x24 + m25*x25 + m32*x26 + m39*x27 + m46*x28;
757 	  x[25] -= m5*x22 + m12*x23 + m19*x24 + m26*x25 + m33*x26 + m40*x27 + m47*x28;
758 	  x[26] -= m6*x22 + m13*x23 + m20*x24 + m27*x25 + m34*x26 + m41*x27 + m48*x28;
759 	  x[27] -= m7*x22 + m14*x23 + m21*x24 + m28*x25 + m35*x26 + m42*x27 + m49*x28;
760 
761 	  x[28] -= m1*x29 + m8*x30  + m15*x31 + m22*x32 + m29*x33 + m36*x34 + m43*x35;
762 	  x[29] -= m2*x29 + m9*x30  + m16*x31 + m23*x32 + m30*x33 + m37*x34 + m44*x35;
763 	  x[30] -= m3*x29 + m10*x30 + m17*x31 + m24*x32 + m31*x33 + m38*x34 + m45*x35;
764 	  x[31] -= m4*x29 + m11*x30 + m18*x31 + m25*x32 + m32*x33 + m39*x34 + m46*x35;
765 	  x[32] -= m5*x29 + m12*x30 + m19*x31 + m26*x32 + m33*x33 + m40*x34 + m47*x35;
766 	  x[33] -= m6*x29 + m13*x30 + m20*x31 + m27*x32 + m34*x33 + m41*x34 + m48*x35;
767 	  x[34] -= m7*x29 + m14*x30 + m21*x31 + m28*x32 + m35*x33 + m42*x34 + m49*x35;
768 
769 	  x[35] -= m1*x36 + m8*x37  + m15*x38 + m22*x39 + m29*x40 + m36*x41 + m43*x42;
770 	  x[36] -= m2*x36 + m9*x37  + m16*x38 + m23*x39 + m30*x40 + m37*x41 + m44*x42;
771 	  x[37] -= m3*x36 + m10*x37 + m17*x38 + m24*x39 + m31*x40 + m38*x41 + m45*x42;
772 	  x[38] -= m4*x36 + m11*x37 + m18*x38 + m25*x39 + m32*x40 + m39*x41 + m46*x42;
773 	  x[39] -= m5*x36 + m12*x37 + m19*x38 + m26*x39 + m33*x40 + m40*x41 + m47*x42;
774 	  x[40] -= m6*x36 + m13*x37 + m20*x38 + m27*x39 + m34*x40 + m41*x41 + m48*x42;
775 	  x[41] -= m7*x36 + m14*x37 + m21*x38 + m28*x39 + m35*x40 + m42*x41 + m49*x42;
776 
777 	  x[42] -= m1*x43 + m8*x44  + m15*x45 + m22*x46 + m29*x47 + m36*x48 + m43*x49;
778 	  x[43] -= m2*x43 + m9*x44  + m16*x45 + m23*x46 + m30*x47 + m37*x48 + m44*x49;
779 	  x[44] -= m3*x43 + m10*x44 + m17*x45 + m24*x46 + m31*x47 + m38*x48 + m45*x49;
780 	  x[45] -= m4*x43 + m11*x44 + m18*x45 + m25*x46 + m32*x47 + m39*x48 + m46*x49;
781 	  x[46] -= m5*x43 + m12*x44 + m19*x45 + m26*x46 + m33*x47 + m40*x48 + m47*x49;
782 	  x[47] -= m6*x43 + m13*x44 + m20*x45 + m27*x46 + m34*x47 + m41*x48 + m48*x49;
783 	  x[48] -= m7*x43 + m14*x44 + m21*x45 + m28*x46 + m35*x47 + m42*x48 + m49*x49;
784           pv   += 49;
785         }
786         PLogFlops(686*nz+637);
787       }
788       row = *ajtmp++;
789     }
790     /* finished row so stick it into b->a */
791     pv = ba + 49*bi[i];
792     pj = bj + bi[i];
793     nz = bi[i+1] - bi[i];
794     for (j=0; j<nz; j++) {
795       x      = rtmp+49*pj[j];
796       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
797       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7];
798       pv[8]  = x[8];  pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11];
799       pv[12] = x[12]; pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
800       pv[16] = x[16]; pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19];
801       pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23];
802       pv[24] = x[24]; pv[25] = x[25]; pv[26] = x[26]; pv[27] = x[27];
803       pv[28] = x[28]; pv[29] = x[29]; pv[30] = x[30]; pv[31] = x[31];
804       pv[32] = x[32]; pv[33] = x[33]; pv[34] = x[34]; pv[35] = x[35];
805       pv[36] = x[36]; pv[37] = x[37]; pv[38] = x[38]; pv[39] = x[39];
806       pv[40] = x[40]; pv[41] = x[41]; pv[42] = x[42]; pv[43] = x[43];
807       pv[44] = x[44]; pv[45] = x[45]; pv[46] = x[46]; pv[47] = x[47];
808       pv[48] = x[48];
809       pv   += 49;
810     }
811     /* invert diagonal block */
812     w = ba + 49*diag_offset[i];
813     ierr = Kernel_A_gets_inverse_A_7(w);CHKERRQ(ierr);
814   }
815 
816   ierr = PetscFree(rtmp);CHKERRQ(ierr);
817   C->factor    = FACTOR_LU;
818   C->assembled = PETSC_TRUE;
819   PLogFlops(1.3333*343*b->mbs); /* from inverting diagonal blocks */
820   PetscFunctionReturn(0);
821 }
822 
823 /* ------------------------------------------------------------*/
824 /*
825       Version for when blocks are 6 by 6
826 */
827 #undef __FUNC__
828 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_6"
829 int MatCholeskyFactorNumeric_SeqSBAIJ_6(Mat A,Mat *B)
830 {
831   Mat          C = *B;
832   Mat_SeqBAIJ  *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
833   IS           isrow = b->row,isicol = b->icol;
834   int          *r,*ic,ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
835   int          *ajtmpold,*ajtmp,nz,row;
836   int          *diag_offset = b->diag,idx,*ai=a->i,*aj=a->j,*pj;
837   MatScalar    *pv,*v,*rtmp,*pc,*w,*x;
838   MatScalar    p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
839   MatScalar    p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
840   MatScalar    x17,x18,x19,x20,x21,x22,x23,x24,x25,p10,p11,p12,p13,p14;
841   MatScalar    p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,m10,m11,m12;
842   MatScalar    m13,m14,m15,m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
843   MatScalar    p26,p27,p28,p29,p30,p31,p32,p33,p34,p35,p36;
844   MatScalar    x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36;
845   MatScalar    m26,m27,m28,m29,m30,m31,m32,m33,m34,m35,m36;
846   MatScalar    *ba = b->a,*aa = a->a;
847 
848   PetscFunctionBegin;
849   ierr  = ISGetIndices(isrow,&r);CHKERRQ(ierr);
850   ierr  = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
851   rtmp  = (MatScalar*)PetscMalloc(36*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
852 
853   for (i=0; i<n; i++) {
854     nz    = bi[i+1] - bi[i];
855     ajtmp = bj + bi[i];
856     for  (j=0; j<nz; j++) {
857       x = rtmp+36*ajtmp[j];
858       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
859       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
860       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = x[25] = 0.0 ;
861       x[26] = x[27] = x[28] = x[29] = x[30] = x[31] = x[32] = x[33] = 0.0 ;
862       x[34] = x[35] = 0.0 ;
863     }
864     /* load in initial (unfactored row) */
865     idx      = r[i];
866     nz       = ai[idx+1] - ai[idx];
867     ajtmpold = aj + ai[idx];
868     v        = aa + 36*ai[idx];
869     for (j=0; j<nz; j++) {
870       x    = rtmp+36*ic[ajtmpold[j]];
871       x[0] =  v[0];  x[1] =  v[1];  x[2] =  v[2];  x[3] =  v[3];
872       x[4] =  v[4];  x[5] =  v[5];  x[6] =  v[6];  x[7] =  v[7];
873       x[8] =  v[8];  x[9] =  v[9];  x[10] = v[10]; x[11] = v[11];
874       x[12] = v[12]; x[13] = v[13]; x[14] = v[14]; x[15] = v[15];
875       x[16] = v[16]; x[17] = v[17]; x[18] = v[18]; x[19] = v[19];
876       x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23];
877       x[24] = v[24]; x[25] = v[25]; x[26] = v[26]; x[27] = v[27];
878       x[28] = v[28]; x[29] = v[29]; x[30] = v[30]; x[31] = v[31];
879       x[32] = v[32]; x[33] = v[33]; x[34] = v[34]; x[35] = v[35];
880       v    += 36;
881     }
882     row = *ajtmp++;
883     while (row < i) {
884       pc  =  rtmp + 36*row;
885       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
886       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];
887       p9  = pc[8];  p10 = pc[9];  p11 = pc[10]; p12 = pc[11];
888       p13 = pc[12]; p14 = pc[13]; p15 = pc[14]; p16 = pc[15];
889       p17 = pc[16]; p18 = pc[17]; p19 = pc[18]; p20 = pc[19];
890       p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
891       p25 = pc[24]; p26 = pc[25]; p27 = pc[26]; p28 = pc[27];
892       p29 = pc[28]; p30 = pc[29]; p31 = pc[30]; p32 = pc[31];
893       p33 = pc[32]; p34 = pc[33]; p35 = pc[34]; p36 = pc[35];
894       if (p1  != 0.0 || p2  != 0.0 || p3  != 0.0 || p4  != 0.0 ||
895           p5  != 0.0 || p6  != 0.0 || p7  != 0.0 || p8  != 0.0 ||
896           p9  != 0.0 || p10 != 0.0 || p11 != 0.0 || p12 != 0.0 ||
897           p13 != 0.0 || p14 != 0.0 || p15 != 0.0 || p16 != 0.0 ||
898           p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 ||
899           p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 ||
900           p25 != 0.0 || p26 != 0.0 || p27 != 0.0 || p28 != 0.0 ||
901           p29 != 0.0 || p30 != 0.0 || p31 != 0.0 || p32 != 0.0 ||
902           p33 != 0.0 || p34 != 0.0 || p35 != 0.0 || p36 != 0.0) {
903         pv = ba + 36*diag_offset[row];
904         pj = bj + diag_offset[row] + 1;
905 	x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
906 	x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
907 	x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
908 	x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
909 	x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
910 	x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
911 	x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
912 	x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
913 	x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
914         pc[0]  = m1  = p1*x1  + p7*x2   + p13*x3  + p19*x4  + p25*x5  + p31*x6;
915         pc[1]  = m2  = p2*x1  + p8*x2   + p14*x3  + p20*x4  + p26*x5  + p32*x6;
916         pc[2]  = m3  = p3*x1  + p9*x2   + p15*x3  + p21*x4  + p27*x5  + p33*x6;
917         pc[3]  = m4  = p4*x1  + p10*x2  + p16*x3  + p22*x4  + p28*x5  + p34*x6;
918         pc[4]  = m5  = p5*x1  + p11*x2  + p17*x3  + p23*x4  + p29*x5  + p35*x6;
919         pc[5]  = m6  = p6*x1  + p12*x2  + p18*x3  + p24*x4  + p30*x5  + p36*x6;
920 
921         pc[6]  = m7  = p1*x7  + p7*x8   + p13*x9  + p19*x10 + p25*x11 + p31*x12;
922         pc[7]  = m8  = p2*x7  + p8*x8   + p14*x9  + p20*x10 + p26*x11 + p32*x12;
923         pc[8]  = m9  = p3*x7  + p9*x8   + p15*x9  + p21*x10 + p27*x11 + p33*x12;
924         pc[9]  = m10 = p4*x7  + p10*x8  + p16*x9  + p22*x10 + p28*x11 + p34*x12;
925         pc[10] = m11 = p5*x7  + p11*x8  + p17*x9  + p23*x10 + p29*x11 + p35*x12;
926         pc[11] = m12 = p6*x7  + p12*x8  + p18*x9  + p24*x10 + p30*x11 + p36*x12;
927 
928         pc[12] = m13 = p1*x13 + p7*x14  + p13*x15 + p19*x16 + p25*x17 + p31*x18;
929         pc[13] = m14 = p2*x13 + p8*x14  + p14*x15 + p20*x16 + p26*x17 + p32*x18;
930         pc[14] = m15 = p3*x13 + p9*x14  + p15*x15 + p21*x16 + p27*x17 + p33*x18;
931         pc[15] = m16 = p4*x13 + p10*x14 + p16*x15 + p22*x16 + p28*x17 + p34*x18;
932         pc[16] = m17 = p5*x13 + p11*x14 + p17*x15 + p23*x16 + p29*x17 + p35*x18;
933         pc[17] = m18 = p6*x13 + p12*x14 + p18*x15 + p24*x16 + p30*x17 + p36*x18;
934 
935         pc[18] = m19 = p1*x19 + p7*x20  + p13*x21 + p19*x22 + p25*x23 + p31*x24;
936         pc[19] = m20 = p2*x19 + p8*x20  + p14*x21 + p20*x22 + p26*x23 + p32*x24;
937         pc[20] = m21 = p3*x19 + p9*x20  + p15*x21 + p21*x22 + p27*x23 + p33*x24;
938         pc[21] = m22 = p4*x19 + p10*x20 + p16*x21 + p22*x22 + p28*x23 + p34*x24;
939         pc[22] = m23 = p5*x19 + p11*x20 + p17*x21 + p23*x22 + p29*x23 + p35*x24;
940         pc[23] = m24 = p6*x19 + p12*x20 + p18*x21 + p24*x22 + p30*x23 + p36*x24;
941 
942         pc[24] = m25 = p1*x25 + p7*x26  + p13*x27 + p19*x28 + p25*x29 + p31*x30;
943         pc[25] = m26 = p2*x25 + p8*x26  + p14*x27 + p20*x28 + p26*x29 + p32*x30;
944         pc[26] = m27 = p3*x25 + p9*x26  + p15*x27 + p21*x28 + p27*x29 + p33*x30;
945         pc[27] = m28 = p4*x25 + p10*x26 + p16*x27 + p22*x28 + p28*x29 + p34*x30;
946         pc[28] = m29 = p5*x25 + p11*x26 + p17*x27 + p23*x28 + p29*x29 + p35*x30;
947         pc[29] = m30 = p6*x25 + p12*x26 + p18*x27 + p24*x28 + p30*x29 + p36*x30;
948 
949         pc[30] = m31 = p1*x31 + p7*x32  + p13*x33 + p19*x34 + p25*x35 + p31*x36;
950         pc[31] = m32 = p2*x31 + p8*x32  + p14*x33 + p20*x34 + p26*x35 + p32*x36;
951         pc[32] = m33 = p3*x31 + p9*x32  + p15*x33 + p21*x34 + p27*x35 + p33*x36;
952         pc[33] = m34 = p4*x31 + p10*x32 + p16*x33 + p22*x34 + p28*x35 + p34*x36;
953         pc[34] = m35 = p5*x31 + p11*x32 + p17*x33 + p23*x34 + p29*x35 + p35*x36;
954         pc[35] = m36 = p6*x31 + p12*x32 + p18*x33 + p24*x34 + p30*x35 + p36*x36;
955 
956         nz = bi[row+1] - diag_offset[row] - 1;
957         pv += 36;
958         for (j=0; j<nz; j++) {
959 	  x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
960 	  x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
961 	  x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
962 	  x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
963 	  x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
964 	  x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
965 	  x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
966 	  x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
967 	  x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
968 	  x    = rtmp + 36*pj[j];
969           x[0]  -= m1*x1  + m7*x2   + m13*x3  + m19*x4  + m25*x5  + m31*x6;
970           x[1]  -= m2*x1  + m8*x2   + m14*x3  + m20*x4  + m26*x5  + m32*x6;
971           x[2]  -= m3*x1  + m9*x2   + m15*x3  + m21*x4  + m27*x5  + m33*x6;
972           x[3]  -= m4*x1  + m10*x2  + m16*x3  + m22*x4  + m28*x5  + m34*x6;
973           x[4]  -= m5*x1  + m11*x2  + m17*x3  + m23*x4  + m29*x5  + m35*x6;
974           x[5]  -= m6*x1  + m12*x2  + m18*x3  + m24*x4  + m30*x5  + m36*x6;
975 
976 	  x[6]  -= m1*x7  + m7*x8   + m13*x9  + m19*x10 + m25*x11 + m31*x12;
977 	  x[7]  -= m2*x7  + m8*x8   + m14*x9  + m20*x10 + m26*x11 + m32*x12;
978 	  x[8]  -= m3*x7  + m9*x8   + m15*x9  + m21*x10 + m27*x11 + m33*x12;
979 	  x[9]  -= m4*x7  + m10*x8  + m16*x9  + m22*x10 + m28*x11 + m34*x12;
980 	  x[10] -= m5*x7  + m11*x8  + m17*x9  + m23*x10 + m29*x11 + m35*x12;
981 	  x[11] -= m6*x7  + m12*x8  + m18*x9  + m24*x10 + m30*x11 + m36*x12;
982 
983 	  x[12] -= m1*x13 + m7*x14  + m13*x15 + m19*x16 + m25*x17 + m31*x18;
984 	  x[13] -= m2*x13 + m8*x14  + m14*x15 + m20*x16 + m26*x17 + m32*x18;
985 	  x[14] -= m3*x13 + m9*x14  + m15*x15 + m21*x16 + m27*x17 + m33*x18;
986 	  x[15] -= m4*x13 + m10*x14 + m16*x15 + m22*x16 + m28*x17 + m34*x18;
987 	  x[16] -= m5*x13 + m11*x14 + m17*x15 + m23*x16 + m29*x17 + m35*x18;
988 	  x[17] -= m6*x13 + m12*x14 + m18*x15 + m24*x16 + m30*x17 + m36*x18;
989 
990 	  x[18] -= m1*x19 + m7*x20  + m13*x21 + m19*x22 + m25*x23 + m31*x24;
991 	  x[19] -= m2*x19 + m8*x20  + m14*x21 + m20*x22 + m26*x23 + m32*x24;
992 	  x[20] -= m3*x19 + m9*x20  + m15*x21 + m21*x22 + m27*x23 + m33*x24;
993 	  x[21] -= m4*x19 + m10*x20 + m16*x21 + m22*x22 + m28*x23 + m34*x24;
994 	  x[22] -= m5*x19 + m11*x20 + m17*x21 + m23*x22 + m29*x23 + m35*x24;
995 	  x[23] -= m6*x19 + m12*x20 + m18*x21 + m24*x22 + m30*x23 + m36*x24;
996 
997 	  x[24] -= m1*x25 + m7*x26  + m13*x27 + m19*x28 + m25*x29 + m31*x30;
998 	  x[25] -= m2*x25 + m8*x26  + m14*x27 + m20*x28 + m26*x29 + m32*x30;
999 	  x[26] -= m3*x25 + m9*x26  + m15*x27 + m21*x28 + m27*x29 + m33*x30;
1000 	  x[27] -= m4*x25 + m10*x26 + m16*x27 + m22*x28 + m28*x29 + m34*x30;
1001 	  x[28] -= m5*x25 + m11*x26 + m17*x27 + m23*x28 + m29*x29 + m35*x30;
1002 	  x[29] -= m6*x25 + m12*x26 + m18*x27 + m24*x28 + m30*x29 + m36*x30;
1003 
1004 	  x[30] -= m1*x31 + m7*x32  + m13*x33 + m19*x34 + m25*x35 + m31*x36;
1005 	  x[31] -= m2*x31 + m8*x32  + m14*x33 + m20*x34 + m26*x35 + m32*x36;
1006 	  x[32] -= m3*x31 + m9*x32  + m15*x33 + m21*x34 + m27*x35 + m33*x36;
1007 	  x[33] -= m4*x31 + m10*x32 + m16*x33 + m22*x34 + m28*x35 + m34*x36;
1008 	  x[34] -= m5*x31 + m11*x32 + m17*x33 + m23*x34 + m29*x35 + m35*x36;
1009 	  x[35] -= m6*x31 + m12*x32 + m18*x33 + m24*x34 + m30*x35 + m36*x36;
1010 
1011           pv   += 36;
1012         }
1013         PLogFlops(432*nz+396);
1014       }
1015       row = *ajtmp++;
1016     }
1017     /* finished row so stick it into b->a */
1018     pv = ba + 36*bi[i];
1019     pj = bj + bi[i];
1020     nz = bi[i+1] - bi[i];
1021     for (j=0; j<nz; j++) {
1022       x      = rtmp+36*pj[j];
1023       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
1024       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7];
1025       pv[8]  = x[8];  pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11];
1026       pv[12] = x[12]; pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
1027       pv[16] = x[16]; pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19];
1028       pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23];
1029       pv[24] = x[24]; pv[25] = x[25]; pv[26] = x[26]; pv[27] = x[27];
1030       pv[28] = x[28]; pv[29] = x[29]; pv[30] = x[30]; pv[31] = x[31];
1031       pv[32] = x[32]; pv[33] = x[33]; pv[34] = x[34]; pv[35] = x[35];
1032       pv   += 36;
1033     }
1034     /* invert diagonal block */
1035     w = ba + 36*diag_offset[i];
1036     ierr = Kernel_A_gets_inverse_A_6(w);CHKERRQ(ierr);
1037   }
1038 
1039   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1040   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
1041   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
1042   C->factor = FACTOR_LU;
1043   C->assembled = PETSC_TRUE;
1044   PLogFlops(1.3333*216*b->mbs); /* from inverting diagonal blocks */
1045   PetscFunctionReturn(0);
1046 }
1047 /*
1048       Version for when blocks are 6 by 6 Using natural ordering
1049 */
1050 #undef __FUNC__
1051 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_6_NaturalOrdering"
1052 int MatCholeskyFactorNumeric_SeqSBAIJ_6_NaturalOrdering(Mat A,Mat *B)
1053 {
1054   Mat         C = *B;
1055   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
1056   int         ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
1057   int         *ajtmpold,*ajtmp,nz,row;
1058   int         *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
1059   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
1060   MatScalar   x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15;
1061   MatScalar   x16,x17,x18,x19,x20,x21,x22,x23,x24,x25;
1062   MatScalar   p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15;
1063   MatScalar   p16,p17,p18,p19,p20,p21,p22,p23,p24,p25;
1064   MatScalar   m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12,m13,m14,m15;
1065   MatScalar   m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
1066   MatScalar   p26,p27,p28,p29,p30,p31,p32,p33,p34,p35,p36;
1067   MatScalar   x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36;
1068   MatScalar   m26,m27,m28,m29,m30,m31,m32,m33,m34,m35,m36;
1069   MatScalar   *ba = b->a,*aa = a->a;
1070 
1071   PetscFunctionBegin;
1072   rtmp  = (MatScalar*)PetscMalloc(36*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
1073   for (i=0; i<n; i++) {
1074     nz    = bi[i+1] - bi[i];
1075     ajtmp = bj + bi[i];
1076     for  (j=0; j<nz; j++) {
1077       x = rtmp+36*ajtmp[j];
1078       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
1079       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
1080       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = x[25] = 0.0 ;
1081       x[26] = x[27] = x[28] = x[29] = x[30] = x[31] = x[32] = x[33] = 0.0 ;
1082       x[34] = x[35] = 0.0 ;
1083     }
1084     /* load in initial (unfactored row) */
1085     nz       = ai[i+1] - ai[i];
1086     ajtmpold = aj + ai[i];
1087     v        = aa + 36*ai[i];
1088     for (j=0; j<nz; j++) {
1089       x    = rtmp+36*ajtmpold[j];
1090       x[0] =  v[0];  x[1] =  v[1];  x[2] =  v[2];  x[3] =  v[3];
1091       x[4] =  v[4];  x[5] =  v[5];  x[6] =  v[6];  x[7] =  v[7];
1092       x[8] =  v[8];  x[9] =  v[9];  x[10] = v[10]; x[11] = v[11];
1093       x[12] = v[12]; x[13] = v[13]; x[14] = v[14]; x[15] = v[15];
1094       x[16] = v[16]; x[17] = v[17]; x[18] = v[18]; x[19] = v[19];
1095       x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23];
1096       x[24] = v[24]; x[25] = v[25]; x[26] = v[26]; x[27] = v[27];
1097       x[28] = v[28]; x[29] = v[29]; x[30] = v[30]; x[31] = v[31];
1098       x[32] = v[32]; x[33] = v[33]; x[34] = v[34]; x[35] = v[35];
1099       v    += 36;
1100     }
1101     row = *ajtmp++;
1102     while (row < i) {
1103       pc  = rtmp + 36*row;
1104       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
1105       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];
1106       p9  = pc[8];  p10 = pc[9];  p11 = pc[10]; p12 = pc[11];
1107       p13 = pc[12]; p14 = pc[13]; p15 = pc[14]; p16 = pc[15];
1108       p17 = pc[16]; p18 = pc[17]; p19 = pc[18]; p20 = pc[19];
1109       p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
1110       p25 = pc[24]; p26 = pc[25]; p27 = pc[26]; p28 = pc[27];
1111       p29 = pc[28]; p30 = pc[29]; p31 = pc[30]; p32 = pc[31];
1112       p33 = pc[32]; p34 = pc[33]; p35 = pc[34]; p36 = pc[35];
1113       if (p1  != 0.0 || p2  != 0.0 || p3  != 0.0 || p4  != 0.0 ||
1114           p5  != 0.0 || p6  != 0.0 || p7  != 0.0 || p8  != 0.0 ||
1115           p9  != 0.0 || p10 != 0.0 || p11 != 0.0 || p12 != 0.0 ||
1116           p13 != 0.0 || p14 != 0.0 || p15 != 0.0 || p16 != 0.0 ||
1117           p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 ||
1118           p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 ||
1119           p25 != 0.0 || p26 != 0.0 || p27 != 0.0 || p28 != 0.0 ||
1120           p29 != 0.0 || p30 != 0.0 || p31 != 0.0 || p32 != 0.0 ||
1121           p33 != 0.0 || p34 != 0.0 || p35 != 0.0 || p36 != 0.0) {
1122         pv = ba + 36*diag_offset[row];
1123         pj = bj + diag_offset[row] + 1;
1124 	x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
1125 	x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
1126 	x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
1127 	x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
1128 	x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
1129 	x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
1130 	x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
1131 	x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
1132 	x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
1133         pc[0]  = m1  = p1*x1  + p7*x2   + p13*x3  + p19*x4  + p25*x5  + p31*x6;
1134         pc[1]  = m2  = p2*x1  + p8*x2   + p14*x3  + p20*x4  + p26*x5  + p32*x6;
1135         pc[2]  = m3  = p3*x1  + p9*x2   + p15*x3  + p21*x4  + p27*x5  + p33*x6;
1136         pc[3]  = m4  = p4*x1  + p10*x2  + p16*x3  + p22*x4  + p28*x5  + p34*x6;
1137         pc[4]  = m5  = p5*x1  + p11*x2  + p17*x3  + p23*x4  + p29*x5  + p35*x6;
1138         pc[5]  = m6  = p6*x1  + p12*x2  + p18*x3  + p24*x4  + p30*x5  + p36*x6;
1139 
1140         pc[6]  = m7  = p1*x7  + p7*x8   + p13*x9  + p19*x10 + p25*x11 + p31*x12;
1141         pc[7]  = m8  = p2*x7  + p8*x8   + p14*x9  + p20*x10 + p26*x11 + p32*x12;
1142         pc[8]  = m9  = p3*x7  + p9*x8   + p15*x9  + p21*x10 + p27*x11 + p33*x12;
1143         pc[9]  = m10 = p4*x7  + p10*x8  + p16*x9  + p22*x10 + p28*x11 + p34*x12;
1144         pc[10] = m11 = p5*x7  + p11*x8  + p17*x9  + p23*x10 + p29*x11 + p35*x12;
1145         pc[11] = m12 = p6*x7  + p12*x8  + p18*x9  + p24*x10 + p30*x11 + p36*x12;
1146 
1147         pc[12] = m13 = p1*x13 + p7*x14  + p13*x15 + p19*x16 + p25*x17 + p31*x18;
1148         pc[13] = m14 = p2*x13 + p8*x14  + p14*x15 + p20*x16 + p26*x17 + p32*x18;
1149         pc[14] = m15 = p3*x13 + p9*x14  + p15*x15 + p21*x16 + p27*x17 + p33*x18;
1150         pc[15] = m16 = p4*x13 + p10*x14 + p16*x15 + p22*x16 + p28*x17 + p34*x18;
1151         pc[16] = m17 = p5*x13 + p11*x14 + p17*x15 + p23*x16 + p29*x17 + p35*x18;
1152         pc[17] = m18 = p6*x13 + p12*x14 + p18*x15 + p24*x16 + p30*x17 + p36*x18;
1153 
1154         pc[18] = m19 = p1*x19 + p7*x20  + p13*x21 + p19*x22 + p25*x23 + p31*x24;
1155         pc[19] = m20 = p2*x19 + p8*x20  + p14*x21 + p20*x22 + p26*x23 + p32*x24;
1156         pc[20] = m21 = p3*x19 + p9*x20  + p15*x21 + p21*x22 + p27*x23 + p33*x24;
1157         pc[21] = m22 = p4*x19 + p10*x20 + p16*x21 + p22*x22 + p28*x23 + p34*x24;
1158         pc[22] = m23 = p5*x19 + p11*x20 + p17*x21 + p23*x22 + p29*x23 + p35*x24;
1159         pc[23] = m24 = p6*x19 + p12*x20 + p18*x21 + p24*x22 + p30*x23 + p36*x24;
1160 
1161         pc[24] = m25 = p1*x25 + p7*x26  + p13*x27 + p19*x28 + p25*x29 + p31*x30;
1162         pc[25] = m26 = p2*x25 + p8*x26  + p14*x27 + p20*x28 + p26*x29 + p32*x30;
1163         pc[26] = m27 = p3*x25 + p9*x26  + p15*x27 + p21*x28 + p27*x29 + p33*x30;
1164         pc[27] = m28 = p4*x25 + p10*x26 + p16*x27 + p22*x28 + p28*x29 + p34*x30;
1165         pc[28] = m29 = p5*x25 + p11*x26 + p17*x27 + p23*x28 + p29*x29 + p35*x30;
1166         pc[29] = m30 = p6*x25 + p12*x26 + p18*x27 + p24*x28 + p30*x29 + p36*x30;
1167 
1168         pc[30] = m31 = p1*x31 + p7*x32  + p13*x33 + p19*x34 + p25*x35 + p31*x36;
1169         pc[31] = m32 = p2*x31 + p8*x32  + p14*x33 + p20*x34 + p26*x35 + p32*x36;
1170         pc[32] = m33 = p3*x31 + p9*x32  + p15*x33 + p21*x34 + p27*x35 + p33*x36;
1171         pc[33] = m34 = p4*x31 + p10*x32 + p16*x33 + p22*x34 + p28*x35 + p34*x36;
1172         pc[34] = m35 = p5*x31 + p11*x32 + p17*x33 + p23*x34 + p29*x35 + p35*x36;
1173         pc[35] = m36 = p6*x31 + p12*x32 + p18*x33 + p24*x34 + p30*x35 + p36*x36;
1174 
1175         nz = bi[row+1] - diag_offset[row] - 1;
1176         pv += 36;
1177         for (j=0; j<nz; j++) {
1178 	  x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
1179 	  x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
1180 	  x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
1181 	  x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
1182 	  x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
1183 	  x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
1184 	  x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
1185 	  x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
1186 	  x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
1187 	  x    = rtmp + 36*pj[j];
1188           x[0]  -= m1*x1  + m7*x2   + m13*x3  + m19*x4  + m25*x5  + m31*x6;
1189           x[1]  -= m2*x1  + m8*x2   + m14*x3  + m20*x4  + m26*x5  + m32*x6;
1190           x[2]  -= m3*x1  + m9*x2   + m15*x3  + m21*x4  + m27*x5  + m33*x6;
1191           x[3]  -= m4*x1  + m10*x2  + m16*x3  + m22*x4  + m28*x5  + m34*x6;
1192           x[4]  -= m5*x1  + m11*x2  + m17*x3  + m23*x4  + m29*x5  + m35*x6;
1193           x[5]  -= m6*x1  + m12*x2  + m18*x3  + m24*x4  + m30*x5  + m36*x6;
1194 
1195 	  x[6]  -= m1*x7  + m7*x8   + m13*x9  + m19*x10 + m25*x11 + m31*x12;
1196 	  x[7]  -= m2*x7  + m8*x8   + m14*x9  + m20*x10 + m26*x11 + m32*x12;
1197 	  x[8]  -= m3*x7  + m9*x8   + m15*x9  + m21*x10 + m27*x11 + m33*x12;
1198 	  x[9]  -= m4*x7  + m10*x8  + m16*x9  + m22*x10 + m28*x11 + m34*x12;
1199 	  x[10] -= m5*x7  + m11*x8  + m17*x9  + m23*x10 + m29*x11 + m35*x12;
1200 	  x[11] -= m6*x7  + m12*x8  + m18*x9  + m24*x10 + m30*x11 + m36*x12;
1201 
1202 	  x[12] -= m1*x13 + m7*x14  + m13*x15 + m19*x16 + m25*x17 + m31*x18;
1203 	  x[13] -= m2*x13 + m8*x14  + m14*x15 + m20*x16 + m26*x17 + m32*x18;
1204 	  x[14] -= m3*x13 + m9*x14  + m15*x15 + m21*x16 + m27*x17 + m33*x18;
1205 	  x[15] -= m4*x13 + m10*x14 + m16*x15 + m22*x16 + m28*x17 + m34*x18;
1206 	  x[16] -= m5*x13 + m11*x14 + m17*x15 + m23*x16 + m29*x17 + m35*x18;
1207 	  x[17] -= m6*x13 + m12*x14 + m18*x15 + m24*x16 + m30*x17 + m36*x18;
1208 
1209 	  x[18] -= m1*x19 + m7*x20  + m13*x21 + m19*x22 + m25*x23 + m31*x24;
1210 	  x[19] -= m2*x19 + m8*x20  + m14*x21 + m20*x22 + m26*x23 + m32*x24;
1211 	  x[20] -= m3*x19 + m9*x20  + m15*x21 + m21*x22 + m27*x23 + m33*x24;
1212 	  x[21] -= m4*x19 + m10*x20 + m16*x21 + m22*x22 + m28*x23 + m34*x24;
1213 	  x[22] -= m5*x19 + m11*x20 + m17*x21 + m23*x22 + m29*x23 + m35*x24;
1214 	  x[23] -= m6*x19 + m12*x20 + m18*x21 + m24*x22 + m30*x23 + m36*x24;
1215 
1216 	  x[24] -= m1*x25 + m7*x26  + m13*x27 + m19*x28 + m25*x29 + m31*x30;
1217 	  x[25] -= m2*x25 + m8*x26  + m14*x27 + m20*x28 + m26*x29 + m32*x30;
1218 	  x[26] -= m3*x25 + m9*x26  + m15*x27 + m21*x28 + m27*x29 + m33*x30;
1219 	  x[27] -= m4*x25 + m10*x26 + m16*x27 + m22*x28 + m28*x29 + m34*x30;
1220 	  x[28] -= m5*x25 + m11*x26 + m17*x27 + m23*x28 + m29*x29 + m35*x30;
1221 	  x[29] -= m6*x25 + m12*x26 + m18*x27 + m24*x28 + m30*x29 + m36*x30;
1222 
1223 	  x[30] -= m1*x31 + m7*x32  + m13*x33 + m19*x34 + m25*x35 + m31*x36;
1224 	  x[31] -= m2*x31 + m8*x32  + m14*x33 + m20*x34 + m26*x35 + m32*x36;
1225 	  x[32] -= m3*x31 + m9*x32  + m15*x33 + m21*x34 + m27*x35 + m33*x36;
1226 	  x[33] -= m4*x31 + m10*x32 + m16*x33 + m22*x34 + m28*x35 + m34*x36;
1227 	  x[34] -= m5*x31 + m11*x32 + m17*x33 + m23*x34 + m29*x35 + m35*x36;
1228 	  x[35] -= m6*x31 + m12*x32 + m18*x33 + m24*x34 + m30*x35 + m36*x36;
1229 
1230           pv   += 36;
1231         }
1232         PLogFlops(432*nz+396);
1233       }
1234       row = *ajtmp++;
1235     }
1236     /* finished row so stick it into b->a */
1237     pv = ba + 36*bi[i];
1238     pj = bj + bi[i];
1239     nz = bi[i+1] - bi[i];
1240     for (j=0; j<nz; j++) {
1241       x      = rtmp+36*pj[j];
1242       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
1243       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7];
1244       pv[8]  = x[8];  pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11];
1245       pv[12] = x[12]; pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
1246       pv[16] = x[16]; pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19];
1247       pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23];
1248       pv[24] = x[24]; pv[25] = x[25]; pv[26] = x[26]; pv[27] = x[27];
1249       pv[28] = x[28]; pv[29] = x[29]; pv[30] = x[30]; pv[31] = x[31];
1250       pv[32] = x[32]; pv[33] = x[33]; pv[34] = x[34]; pv[35] = x[35];
1251       pv   += 36;
1252     }
1253     /* invert diagonal block */
1254     w = ba + 36*diag_offset[i];
1255     ierr = Kernel_A_gets_inverse_A_6(w);CHKERRQ(ierr);
1256   }
1257 
1258   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1259   C->factor    = FACTOR_LU;
1260   C->assembled = PETSC_TRUE;
1261   PLogFlops(1.3333*216*b->mbs); /* from inverting diagonal blocks */
1262   PetscFunctionReturn(0);
1263 }
1264 
1265 /* ------------------------------------------------------------*/
1266 /*
1267       Version for when blocks are 5 by 5
1268 */
1269 #undef __FUNC__
1270 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_5"
1271 int MatCholeskyFactorNumeric_SeqSBAIJ_5(Mat A,Mat *B)
1272 {
1273   Mat         C = *B;
1274   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
1275   IS          isrow = b->row,isicol = b->icol;
1276   int         *r,*ic,ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
1277   int         *ajtmpold,*ajtmp,nz,row;
1278   int         *diag_offset = b->diag,idx,*ai=a->i,*aj=a->j,*pj;
1279   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
1280   MatScalar   p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
1281   MatScalar   p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
1282   MatScalar   x17,x18,x19,x20,x21,x22,x23,x24,x25,p10,p11,p12,p13,p14;
1283   MatScalar   p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,m10,m11,m12;
1284   MatScalar   m13,m14,m15,m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
1285   MatScalar   *ba = b->a,*aa = a->a;
1286 
1287   PetscFunctionBegin;
1288   ierr  = ISGetIndices(isrow,&r);CHKERRQ(ierr);
1289   ierr  = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
1290   rtmp  = (MatScalar*)PetscMalloc(25*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
1291 
1292   for (i=0; i<n; i++) {
1293     nz    = bi[i+1] - bi[i];
1294     ajtmp = bj + bi[i];
1295     for  (j=0; j<nz; j++) {
1296       x = rtmp+25*ajtmp[j];
1297       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
1298       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
1299       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0;
1300     }
1301     /* load in initial (unfactored row) */
1302     idx      = r[i];
1303     nz       = ai[idx+1] - ai[idx];
1304     ajtmpold = aj + ai[idx];
1305     v        = aa + 25*ai[idx];
1306     for (j=0; j<nz; j++) {
1307       x    = rtmp+25*ic[ajtmpold[j]];
1308       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
1309       x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
1310       x[9] = v[9]; x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
1311       x[14] = v[14]; x[15] = v[15]; x[16] = v[16]; x[17] = v[17];
1312       x[18] = v[18]; x[19] = v[19]; x[20] = v[20]; x[21] = v[21];
1313       x[22] = v[22]; x[23] = v[23]; x[24] = v[24];
1314       v    += 25;
1315     }
1316     row = *ajtmp++;
1317     while (row < i) {
1318       pc = rtmp + 25*row;
1319       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
1320       p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
1321       p10 = pc[9]; p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
1322       p15 = pc[14]; p16 = pc[15]; p17 = pc[16]; p18 = pc[17]; p19 = pc[18];
1323       p20 = pc[19]; p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
1324       p25 = pc[24];
1325       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
1326           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
1327           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
1328           || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 ||
1329           p20 != 0.0 || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 ||
1330           p24 != 0.0 || p25 != 0.0) {
1331         pv = ba + 25*diag_offset[row];
1332         pj = bj + diag_offset[row] + 1;
1333         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
1334         x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
1335         x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
1336         x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17];
1337         x19 = pv[18]; x20 = pv[19]; x21 = pv[20]; x22 = pv[21];
1338         x23 = pv[22]; x24 = pv[23]; x25 = pv[24];
1339         pc[0] = m1 = p1*x1 + p6*x2  + p11*x3 + p16*x4 + p21*x5;
1340         pc[1] = m2 = p2*x1 + p7*x2  + p12*x3 + p17*x4 + p22*x5;
1341         pc[2] = m3 = p3*x1 + p8*x2  + p13*x3 + p18*x4 + p23*x5;
1342         pc[3] = m4 = p4*x1 + p9*x2  + p14*x3 + p19*x4 + p24*x5;
1343         pc[4] = m5 = p5*x1 + p10*x2 + p15*x3 + p20*x4 + p25*x5;
1344 
1345         pc[5] = m6 = p1*x6 + p6*x7  + p11*x8 + p16*x9 + p21*x10;
1346         pc[6] = m7 = p2*x6 + p7*x7  + p12*x8 + p17*x9 + p22*x10;
1347         pc[7] = m8 = p3*x6 + p8*x7  + p13*x8 + p18*x9 + p23*x10;
1348         pc[8] = m9 = p4*x6 + p9*x7  + p14*x8 + p19*x9 + p24*x10;
1349         pc[9] = m10 = p5*x6 + p10*x7 + p15*x8 + p20*x9 + p25*x10;
1350 
1351         pc[10] = m11 = p1*x11 + p6*x12  + p11*x13 + p16*x14 + p21*x15;
1352         pc[11] = m12 = p2*x11 + p7*x12  + p12*x13 + p17*x14 + p22*x15;
1353         pc[12] = m13 = p3*x11 + p8*x12  + p13*x13 + p18*x14 + p23*x15;
1354         pc[13] = m14 = p4*x11 + p9*x12  + p14*x13 + p19*x14 + p24*x15;
1355         pc[14] = m15 = p5*x11 + p10*x12 + p15*x13 + p20*x14 + p25*x15;
1356 
1357         pc[15] = m16 = p1*x16 + p6*x17  + p11*x18 + p16*x19 + p21*x20;
1358         pc[16] = m17 = p2*x16 + p7*x17  + p12*x18 + p17*x19 + p22*x20;
1359         pc[17] = m18 = p3*x16 + p8*x17  + p13*x18 + p18*x19 + p23*x20;
1360         pc[18] = m19 = p4*x16 + p9*x17  + p14*x18 + p19*x19 + p24*x20;
1361         pc[19] = m20 = p5*x16 + p10*x17 + p15*x18 + p20*x19 + p25*x20;
1362 
1363         pc[20] = m21 = p1*x21 + p6*x22  + p11*x23 + p16*x24 + p21*x25;
1364         pc[21] = m22 = p2*x21 + p7*x22  + p12*x23 + p17*x24 + p22*x25;
1365         pc[22] = m23 = p3*x21 + p8*x22  + p13*x23 + p18*x24 + p23*x25;
1366         pc[23] = m24 = p4*x21 + p9*x22  + p14*x23 + p19*x24 + p24*x25;
1367         pc[24] = m25 = p5*x21 + p10*x22 + p15*x23 + p20*x24 + p25*x25;
1368 
1369         nz = bi[row+1] - diag_offset[row] - 1;
1370         pv += 25;
1371         for (j=0; j<nz; j++) {
1372           x1   = pv[0];  x2 = pv[1];   x3  = pv[2];  x4  = pv[3];
1373           x5   = pv[4];  x6 = pv[5];   x7  = pv[6];  x8  = pv[7]; x9 = pv[8];
1374           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
1375           x14  = pv[13]; x15 = pv[14]; x16 = pv[15]; x17 = pv[16];
1376           x18  = pv[17]; x19 = pv[18]; x20 = pv[19]; x21 = pv[20];
1377           x22  = pv[21]; x23 = pv[22]; x24 = pv[23]; x25 = pv[24];
1378           x    = rtmp + 25*pj[j];
1379           x[0] -= m1*x1 + m6*x2  + m11*x3 + m16*x4 + m21*x5;
1380           x[1] -= m2*x1 + m7*x2  + m12*x3 + m17*x4 + m22*x5;
1381           x[2] -= m3*x1 + m8*x2  + m13*x3 + m18*x4 + m23*x5;
1382           x[3] -= m4*x1 + m9*x2  + m14*x3 + m19*x4 + m24*x5;
1383           x[4] -= m5*x1 + m10*x2 + m15*x3 + m20*x4 + m25*x5;
1384 
1385           x[5] -= m1*x6 + m6*x7  + m11*x8 + m16*x9 + m21*x10;
1386           x[6] -= m2*x6 + m7*x7  + m12*x8 + m17*x9 + m22*x10;
1387           x[7] -= m3*x6 + m8*x7  + m13*x8 + m18*x9 + m23*x10;
1388           x[8] -= m4*x6 + m9*x7  + m14*x8 + m19*x9 + m24*x10;
1389           x[9] -= m5*x6 + m10*x7 + m15*x8 + m20*x9 + m25*x10;
1390 
1391           x[10] -= m1*x11 + m6*x12  + m11*x13 + m16*x14 + m21*x15;
1392           x[11] -= m2*x11 + m7*x12  + m12*x13 + m17*x14 + m22*x15;
1393           x[12] -= m3*x11 + m8*x12  + m13*x13 + m18*x14 + m23*x15;
1394           x[13] -= m4*x11 + m9*x12  + m14*x13 + m19*x14 + m24*x15;
1395           x[14] -= m5*x11 + m10*x12 + m15*x13 + m20*x14 + m25*x15;
1396 
1397           x[15] -= m1*x16 + m6*x17  + m11*x18 + m16*x19 + m21*x20;
1398           x[16] -= m2*x16 + m7*x17  + m12*x18 + m17*x19 + m22*x20;
1399           x[17] -= m3*x16 + m8*x17  + m13*x18 + m18*x19 + m23*x20;
1400           x[18] -= m4*x16 + m9*x17  + m14*x18 + m19*x19 + m24*x20;
1401           x[19] -= m5*x16 + m10*x17 + m15*x18 + m20*x19 + m25*x20;
1402 
1403           x[20] -= m1*x21 + m6*x22  + m11*x23 + m16*x24 + m21*x25;
1404           x[21] -= m2*x21 + m7*x22  + m12*x23 + m17*x24 + m22*x25;
1405           x[22] -= m3*x21 + m8*x22  + m13*x23 + m18*x24 + m23*x25;
1406           x[23] -= m4*x21 + m9*x22  + m14*x23 + m19*x24 + m24*x25;
1407           x[24] -= m5*x21 + m10*x22 + m15*x23 + m20*x24 + m25*x25;
1408 
1409           pv   += 25;
1410         }
1411         PLogFlops(250*nz+225);
1412       }
1413       row = *ajtmp++;
1414     }
1415     /* finished row so stick it into b->a */
1416     pv = ba + 25*bi[i];
1417     pj = bj + bi[i];
1418     nz = bi[i+1] - bi[i];
1419     for (j=0; j<nz; j++) {
1420       x     = rtmp+25*pj[j];
1421       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
1422       pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
1423       pv[9] = x[9]; pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
1424       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; pv[16] = x[16];
1425       pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19]; pv[20] = x[20];
1426       pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23]; pv[24] = x[24];
1427       pv   += 25;
1428     }
1429     /* invert diagonal block */
1430     w = ba + 25*diag_offset[i];
1431     ierr = Kernel_A_gets_inverse_A_5(w);CHKERRQ(ierr);
1432   }
1433 
1434   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1435   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
1436   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
1437   C->factor = FACTOR_LU;
1438   C->assembled = PETSC_TRUE;
1439   PLogFlops(1.3333*125*b->mbs); /* from inverting diagonal blocks */
1440   PetscFunctionReturn(0);
1441 }
1442 /*
1443       Version for when blocks are 5 by 5 Using natural ordering
1444 */
1445 #undef __FUNC__
1446 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_5_NaturalOrdering"
1447 int MatCholeskyFactorNumeric_SeqSBAIJ_5_NaturalOrdering(Mat A,Mat *B)
1448 {
1449   Mat         C = *B;
1450   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
1451   int         ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
1452   int         *ajtmpold,*ajtmp,nz,row;
1453   int         *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
1454   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
1455   MatScalar   x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15;
1456   MatScalar   x16,x17,x18,x19,x20,x21,x22,x23,x24,x25;
1457   MatScalar   p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15;
1458   MatScalar   p16,p17,p18,p19,p20,p21,p22,p23,p24,p25;
1459   MatScalar   m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12,m13,m14,m15;
1460   MatScalar   m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
1461   MatScalar   *ba = b->a,*aa = a->a;
1462 
1463   PetscFunctionBegin;
1464   rtmp  = (MatScalar*)PetscMalloc(25*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
1465   for (i=0; i<n; i++) {
1466     nz    = bi[i+1] - bi[i];
1467     ajtmp = bj + bi[i];
1468     for  (j=0; j<nz; j++) {
1469       x = rtmp+25*ajtmp[j];
1470       x[0]  = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = x[9] = 0.0;
1471       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
1472       x[16] = x[17] = x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0;
1473     }
1474     /* load in initial (unfactored row) */
1475     nz       = ai[i+1] - ai[i];
1476     ajtmpold = aj + ai[i];
1477     v        = aa + 25*ai[i];
1478     for (j=0; j<nz; j++) {
1479       x    = rtmp+25*ajtmpold[j];
1480       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
1481       x[4]  = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
1482       x[9]  = v[9];  x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
1483       x[14] = v[14]; x[15] = v[15]; x[16] = v[16]; x[17] = v[17]; x[18] = v[18];
1484       x[19] = v[19]; x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23];
1485       x[24] = v[24];
1486       v    += 25;
1487     }
1488     row = *ajtmp++;
1489     while (row < i) {
1490       pc  = rtmp + 25*row;
1491       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
1492       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
1493       p10 = pc[9];  p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
1494       p15 = pc[14]; p16 = pc[15]; p17 = pc[16]; p18 = pc[17];
1495       p19 = pc[18]; p20 = pc[19]; p21 = pc[20]; p22 = pc[21]; p23 = pc[22];
1496       p24 = pc[23]; p25 = pc[24];
1497       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
1498           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
1499           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
1500           || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0
1501           || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 || p25 != 0.0) {
1502         pv = ba + 25*diag_offset[row];
1503         pj = bj + diag_offset[row] + 1;
1504         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
1505         x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
1506         x10 = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
1507         x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17]; x19 = pv[18];
1508         x20 = pv[19]; x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
1509         x25 = pv[24];
1510         pc[0] = m1 = p1*x1 + p6*x2  + p11*x3 + p16*x4 + p21*x5;
1511         pc[1] = m2 = p2*x1 + p7*x2  + p12*x3 + p17*x4 + p22*x5;
1512         pc[2] = m3 = p3*x1 + p8*x2  + p13*x3 + p18*x4 + p23*x5;
1513         pc[3] = m4 = p4*x1 + p9*x2  + p14*x3 + p19*x4 + p24*x5;
1514         pc[4] = m5 = p5*x1 + p10*x2 + p15*x3 + p20*x4 + p25*x5;
1515 
1516         pc[5]  = m6  = p1*x6 + p6*x7  + p11*x8 + p16*x9 + p21*x10;
1517         pc[6]  = m7  = p2*x6 + p7*x7  + p12*x8 + p17*x9 + p22*x10;
1518         pc[7]  = m8  = p3*x6 + p8*x7  + p13*x8 + p18*x9 + p23*x10;
1519         pc[8]  = m9  = p4*x6 + p9*x7  + p14*x8 + p19*x9 + p24*x10;
1520         pc[9]  = m10 = p5*x6 + p10*x7 + p15*x8 + p20*x9 + p25*x10;
1521 
1522         pc[10] = m11 = p1*x11 + p6*x12  + p11*x13 + p16*x14 + p21*x15;
1523         pc[11] = m12 = p2*x11 + p7*x12  + p12*x13 + p17*x14 + p22*x15;
1524         pc[12] = m13 = p3*x11 + p8*x12  + p13*x13 + p18*x14 + p23*x15;
1525         pc[13] = m14 = p4*x11 + p9*x12  + p14*x13 + p19*x14 + p24*x15;
1526         pc[14] = m15 = p5*x11 + p10*x12 + p15*x13 + p20*x14 + p25*x15;
1527 
1528         pc[15] = m16 = p1*x16 + p6*x17  + p11*x18 + p16*x19 + p21*x20;
1529         pc[16] = m17 = p2*x16 + p7*x17  + p12*x18 + p17*x19 + p22*x20;
1530         pc[17] = m18 = p3*x16 + p8*x17  + p13*x18 + p18*x19 + p23*x20;
1531         pc[18] = m19 = p4*x16 + p9*x17  + p14*x18 + p19*x19 + p24*x20;
1532         pc[19] = m20 = p5*x16 + p10*x17 + p15*x18 + p20*x19 + p25*x20;
1533 
1534         pc[20] = m21 = p1*x21 + p6*x22  + p11*x23 + p16*x24 + p21*x25;
1535         pc[21] = m22 = p2*x21 + p7*x22  + p12*x23 + p17*x24 + p22*x25;
1536         pc[22] = m23 = p3*x21 + p8*x22  + p13*x23 + p18*x24 + p23*x25;
1537         pc[23] = m24 = p4*x21 + p9*x22  + p14*x23 + p19*x24 + p24*x25;
1538         pc[24] = m25 = p5*x21 + p10*x22 + p15*x23 + p20*x24 + p25*x25;
1539 
1540         nz = bi[row+1] - diag_offset[row] - 1;
1541         pv += 25;
1542         for (j=0; j<nz; j++) {
1543           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
1544           x5   = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
1545           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
1546           x14  = pv[13]; x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17];
1547           x19 = pv[18];  x20 = pv[19]; x21 = pv[20]; x22 = pv[21]; x23 = pv[22];
1548           x24 = pv[23];  x25 = pv[24];
1549           x    = rtmp + 25*pj[j];
1550           x[0] -= m1*x1 + m6*x2   + m11*x3  + m16*x4 + m21*x5;
1551           x[1] -= m2*x1 + m7*x2   + m12*x3  + m17*x4 + m22*x5;
1552           x[2] -= m3*x1 + m8*x2   + m13*x3  + m18*x4 + m23*x5;
1553           x[3] -= m4*x1 + m9*x2   + m14*x3  + m19*x4 + m24*x5;
1554           x[4] -= m5*x1 + m10*x2  + m15*x3  + m20*x4 + m25*x5;
1555 
1556           x[5] -= m1*x6 + m6*x7   + m11*x8  + m16*x9 + m21*x10;
1557           x[6] -= m2*x6 + m7*x7   + m12*x8  + m17*x9 + m22*x10;
1558           x[7] -= m3*x6 + m8*x7   + m13*x8  + m18*x9 + m23*x10;
1559           x[8] -= m4*x6 + m9*x7   + m14*x8  + m19*x9 + m24*x10;
1560           x[9] -= m5*x6 + m10*x7  + m15*x8  + m20*x9 + m25*x10;
1561 
1562           x[10] -= m1*x11 + m6*x12  + m11*x13 + m16*x14 + m21*x15;
1563           x[11] -= m2*x11 + m7*x12  + m12*x13 + m17*x14 + m22*x15;
1564           x[12] -= m3*x11 + m8*x12  + m13*x13 + m18*x14 + m23*x15;
1565           x[13] -= m4*x11 + m9*x12  + m14*x13 + m19*x14 + m24*x15;
1566           x[14] -= m5*x11 + m10*x12 + m15*x13 + m20*x14 + m25*x15;
1567 
1568           x[15] -= m1*x16 + m6*x17  + m11*x18 + m16*x19 + m21*x20;
1569           x[16] -= m2*x16 + m7*x17  + m12*x18 + m17*x19 + m22*x20;
1570           x[17] -= m3*x16 + m8*x17  + m13*x18 + m18*x19 + m23*x20;
1571           x[18] -= m4*x16 + m9*x17  + m14*x18 + m19*x19 + m24*x20;
1572           x[19] -= m5*x16 + m10*x17 + m15*x18 + m20*x19 + m25*x20;
1573 
1574           x[20] -= m1*x21 + m6*x22  + m11*x23 + m16*x24 + m21*x25;
1575           x[21] -= m2*x21 + m7*x22  + m12*x23 + m17*x24 + m22*x25;
1576           x[22] -= m3*x21 + m8*x22  + m13*x23 + m18*x24 + m23*x25;
1577           x[23] -= m4*x21 + m9*x22  + m14*x23 + m19*x24 + m24*x25;
1578           x[24] -= m5*x21 + m10*x22 + m15*x23 + m20*x24 + m25*x25;
1579           pv   += 25;
1580         }
1581         PLogFlops(250*nz+225);
1582       }
1583       row = *ajtmp++;
1584     }
1585     /* finished row so stick it into b->a */
1586     pv = ba + 25*bi[i];
1587     pj = bj + bi[i];
1588     nz = bi[i+1] - bi[i];
1589     for (j=0; j<nz; j++) {
1590       x      = rtmp+25*pj[j];
1591       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
1592       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
1593       pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
1594       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; pv[16] = x[16]; pv[17] = x[17];
1595       pv[18] = x[18]; pv[19] = x[19]; pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22];
1596       pv[23] = x[23]; pv[24] = x[24];
1597       pv   += 25;
1598     }
1599     /* invert diagonal block */
1600     w = ba + 25*diag_offset[i];
1601     ierr = Kernel_A_gets_inverse_A_5(w);CHKERRQ(ierr);
1602   }
1603 
1604   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1605   C->factor    = FACTOR_LU;
1606   C->assembled = PETSC_TRUE;
1607   PLogFlops(1.3333*125*b->mbs); /* from inverting diagonal blocks */
1608   PetscFunctionReturn(0);
1609 }
1610 
1611 /* ------------------------------------------------------------*/
1612 /*
1613       Version for when blocks are 4 by 4
1614 */
1615 #undef __FUNC__
1616 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_4"
1617 int MatCholeskyFactorNumeric_SeqSBAIJ_4(Mat A,Mat *B)
1618 {
1619   Mat         C = *B;
1620   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
1621   IS          isrow = b->row,isicol = b->icol;
1622   int         *r,*ic,ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
1623   int         *ajtmpold,*ajtmp,nz,row;
1624   int         *diag_offset = b->diag,idx,*ai=a->i,*aj=a->j,*pj;
1625   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
1626   MatScalar   p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
1627   MatScalar   p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
1628   MatScalar   p10,p11,p12,p13,p14,p15,p16,m10,m11,m12;
1629   MatScalar   m13,m14,m15,m16;
1630   MatScalar   *ba = b->a,*aa = a->a;
1631 
1632   PetscFunctionBegin;
1633   ierr  = ISGetIndices(isrow,&r);CHKERRQ(ierr);
1634   ierr  = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
1635   rtmp  = (MatScalar*)PetscMalloc(16*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
1636 
1637   for (i=0; i<n; i++) {
1638     nz    = bi[i+1] - bi[i];
1639     ajtmp = bj + bi[i];
1640     for  (j=0; j<nz; j++) {
1641       x = rtmp+16*ajtmp[j];
1642       x[0]  = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = x[9] = 0.0;
1643       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
1644     }
1645     /* load in initial (unfactored row) */
1646     idx      = r[i];
1647     nz       = ai[idx+1] - ai[idx];
1648     ajtmpold = aj + ai[idx];
1649     v        = aa + 16*ai[idx];
1650     for (j=0; j<nz; j++) {
1651       x    = rtmp+16*ic[ajtmpold[j]];
1652       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
1653       x[4]  = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
1654       x[9]  = v[9];  x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
1655       x[14] = v[14]; x[15] = v[15];
1656       v    += 16;
1657     }
1658     row = *ajtmp++;
1659     while (row < i) {
1660       pc  = rtmp + 16*row;
1661       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
1662       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
1663       p10 = pc[9];  p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
1664       p15 = pc[14]; p16 = pc[15];
1665       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
1666           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
1667           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
1668           || p16 != 0.0) {
1669         pv = ba + 16*diag_offset[row];
1670         pj = bj + diag_offset[row] + 1;
1671         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
1672         x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
1673         x10 = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
1674         x15 = pv[14]; x16 = pv[15];
1675         pc[0] = m1 = p1*x1 + p5*x2  + p9*x3  + p13*x4;
1676         pc[1] = m2 = p2*x1 + p6*x2  + p10*x3 + p14*x4;
1677         pc[2] = m3 = p3*x1 + p7*x2  + p11*x3 + p15*x4;
1678         pc[3] = m4 = p4*x1 + p8*x2  + p12*x3 + p16*x4;
1679 
1680         pc[4] = m5 = p1*x5 + p5*x6  + p9*x7  + p13*x8;
1681         pc[5] = m6 = p2*x5 + p6*x6  + p10*x7 + p14*x8;
1682         pc[6] = m7 = p3*x5 + p7*x6  + p11*x7 + p15*x8;
1683         pc[7] = m8 = p4*x5 + p8*x6  + p12*x7 + p16*x8;
1684 
1685         pc[8]  = m9  = p1*x9 + p5*x10  + p9*x11  + p13*x12;
1686         pc[9]  = m10 = p2*x9 + p6*x10  + p10*x11 + p14*x12;
1687         pc[10] = m11 = p3*x9 + p7*x10  + p11*x11 + p15*x12;
1688         pc[11] = m12 = p4*x9 + p8*x10  + p12*x11 + p16*x12;
1689 
1690         pc[12] = m13 = p1*x13 + p5*x14  + p9*x15  + p13*x16;
1691         pc[13] = m14 = p2*x13 + p6*x14  + p10*x15 + p14*x16;
1692         pc[14] = m15 = p3*x13 + p7*x14  + p11*x15 + p15*x16;
1693         pc[15] = m16 = p4*x13 + p8*x14  + p12*x15 + p16*x16;
1694 
1695         nz = bi[row+1] - diag_offset[row] - 1;
1696         pv += 16;
1697         for (j=0; j<nz; j++) {
1698           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
1699           x5   = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
1700           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
1701           x14  = pv[13]; x15 = pv[14]; x16 = pv[15];
1702           x    = rtmp + 16*pj[j];
1703           x[0] -= m1*x1 + m5*x2  + m9*x3  + m13*x4;
1704           x[1] -= m2*x1 + m6*x2  + m10*x3 + m14*x4;
1705           x[2] -= m3*x1 + m7*x2  + m11*x3 + m15*x4;
1706           x[3] -= m4*x1 + m8*x2  + m12*x3 + m16*x4;
1707 
1708           x[4] -= m1*x5 + m5*x6  + m9*x7  + m13*x8;
1709           x[5] -= m2*x5 + m6*x6  + m10*x7 + m14*x8;
1710           x[6] -= m3*x5 + m7*x6  + m11*x7 + m15*x8;
1711           x[7] -= m4*x5 + m8*x6  + m12*x7 + m16*x8;
1712 
1713           x[8]  -= m1*x9 + m5*x10 + m9*x11  + m13*x12;
1714           x[9]  -= m2*x9 + m6*x10 + m10*x11 + m14*x12;
1715           x[10] -= m3*x9 + m7*x10 + m11*x11 + m15*x12;
1716           x[11] -= m4*x9 + m8*x10 + m12*x11 + m16*x12;
1717 
1718           x[12] -= m1*x13 + m5*x14  + m9*x15  + m13*x16;
1719           x[13] -= m2*x13 + m6*x14  + m10*x15 + m14*x16;
1720           x[14] -= m3*x13 + m7*x14  + m11*x15 + m15*x16;
1721           x[15] -= m4*x13 + m8*x14  + m12*x15 + m16*x16;
1722 
1723           pv   += 16;
1724         }
1725         PLogFlops(128*nz+112);
1726       }
1727       row = *ajtmp++;
1728     }
1729     /* finished row so stick it into b->a */
1730     pv = ba + 16*bi[i];
1731     pj = bj + bi[i];
1732     nz = bi[i+1] - bi[i];
1733     for (j=0; j<nz; j++) {
1734       x      = rtmp+16*pj[j];
1735       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
1736       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
1737       pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
1738       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
1739       pv   += 16;
1740     }
1741     /* invert diagonal block */
1742     w = ba + 16*diag_offset[i];
1743     ierr = Kernel_A_gets_inverse_A_4(w);CHKERRQ(ierr);
1744   }
1745 
1746   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1747   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
1748   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
1749   C->factor = FACTOR_LU;
1750   C->assembled = PETSC_TRUE;
1751   PLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */
1752   PetscFunctionReturn(0);
1753 }
1754 /*
1755       Version for when blocks are 4 by 4 Using natural ordering
1756 */
1757 #undef __FUNC__
1758 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_4_NaturalOrdering"
1759 int MatCholeskyFactorNumeric_SeqSBAIJ_4_NaturalOrdering(Mat A,Mat *B)
1760 {
1761   Mat         C = *B;
1762   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
1763   int         ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
1764   int         *ajtmpold,*ajtmp,nz,row;
1765   int         *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
1766   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
1767   MatScalar   p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
1768   MatScalar   p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
1769   MatScalar   p10,p11,p12,p13,p14,p15,p16,m10,m11,m12;
1770   MatScalar   m13,m14,m15,m16;
1771   MatScalar   *ba = b->a,*aa = a->a;
1772 
1773   PetscFunctionBegin;
1774   rtmp  = (MatScalar*)PetscMalloc(16*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
1775 
1776   for (i=0; i<n; i++) {
1777     nz    = bi[i+1] - bi[i];
1778     ajtmp = bj + bi[i];
1779     for  (j=0; j<nz; j++) {
1780       x = rtmp+16*ajtmp[j];
1781       x[0]  = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = x[9] = 0.0;
1782       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
1783     }
1784     /* load in initial (unfactored row) */
1785     nz       = ai[i+1] - ai[i];
1786     ajtmpold = aj + ai[i];
1787     v        = aa + 16*ai[i];
1788     for (j=0; j<nz; j++) {
1789       x    = rtmp+16*ajtmpold[j];
1790       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
1791       x[4]  = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
1792       x[9]  = v[9];  x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
1793       x[14] = v[14]; x[15] = v[15];
1794       v    += 16;
1795     }
1796     row = *ajtmp++;
1797     while (row < i) {
1798       pc  = rtmp + 16*row;
1799       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
1800       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
1801       p10 = pc[9];  p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
1802       p15 = pc[14]; p16 = pc[15];
1803       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
1804           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
1805           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
1806           || p16 != 0.0) {
1807         pv = ba + 16*diag_offset[row];
1808         pj = bj + diag_offset[row] + 1;
1809         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
1810         x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
1811         x10 = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
1812         x15 = pv[14]; x16 = pv[15];
1813         pc[0] = m1 = p1*x1 + p5*x2  + p9*x3  + p13*x4;
1814         pc[1] = m2 = p2*x1 + p6*x2  + p10*x3 + p14*x4;
1815         pc[2] = m3 = p3*x1 + p7*x2  + p11*x3 + p15*x4;
1816         pc[3] = m4 = p4*x1 + p8*x2  + p12*x3 + p16*x4;
1817 
1818         pc[4] = m5 = p1*x5 + p5*x6  + p9*x7  + p13*x8;
1819         pc[5] = m6 = p2*x5 + p6*x6  + p10*x7 + p14*x8;
1820         pc[6] = m7 = p3*x5 + p7*x6  + p11*x7 + p15*x8;
1821         pc[7] = m8 = p4*x5 + p8*x6  + p12*x7 + p16*x8;
1822 
1823         pc[8]  = m9  = p1*x9 + p5*x10  + p9*x11  + p13*x12;
1824         pc[9]  = m10 = p2*x9 + p6*x10  + p10*x11 + p14*x12;
1825         pc[10] = m11 = p3*x9 + p7*x10  + p11*x11 + p15*x12;
1826         pc[11] = m12 = p4*x9 + p8*x10  + p12*x11 + p16*x12;
1827 
1828         pc[12] = m13 = p1*x13 + p5*x14  + p9*x15  + p13*x16;
1829         pc[13] = m14 = p2*x13 + p6*x14  + p10*x15 + p14*x16;
1830         pc[14] = m15 = p3*x13 + p7*x14  + p11*x15 + p15*x16;
1831         pc[15] = m16 = p4*x13 + p8*x14  + p12*x15 + p16*x16;
1832 
1833         nz = bi[row+1] - diag_offset[row] - 1;
1834         pv += 16;
1835         for (j=0; j<nz; j++) {
1836           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
1837           x5   = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
1838           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
1839           x14  = pv[13]; x15 = pv[14]; x16 = pv[15];
1840           x    = rtmp + 16*pj[j];
1841           x[0] -= m1*x1 + m5*x2  + m9*x3  + m13*x4;
1842           x[1] -= m2*x1 + m6*x2  + m10*x3 + m14*x4;
1843           x[2] -= m3*x1 + m7*x2  + m11*x3 + m15*x4;
1844           x[3] -= m4*x1 + m8*x2  + m12*x3 + m16*x4;
1845 
1846           x[4] -= m1*x5 + m5*x6  + m9*x7  + m13*x8;
1847           x[5] -= m2*x5 + m6*x6  + m10*x7 + m14*x8;
1848           x[6] -= m3*x5 + m7*x6  + m11*x7 + m15*x8;
1849           x[7] -= m4*x5 + m8*x6  + m12*x7 + m16*x8;
1850 
1851           x[8]  -= m1*x9 + m5*x10 + m9*x11  + m13*x12;
1852           x[9]  -= m2*x9 + m6*x10 + m10*x11 + m14*x12;
1853           x[10] -= m3*x9 + m7*x10 + m11*x11 + m15*x12;
1854           x[11] -= m4*x9 + m8*x10 + m12*x11 + m16*x12;
1855 
1856           x[12] -= m1*x13 + m5*x14  + m9*x15  + m13*x16;
1857           x[13] -= m2*x13 + m6*x14  + m10*x15 + m14*x16;
1858           x[14] -= m3*x13 + m7*x14  + m11*x15 + m15*x16;
1859           x[15] -= m4*x13 + m8*x14  + m12*x15 + m16*x16;
1860 
1861           pv   += 16;
1862         }
1863         PLogFlops(128*nz+112);
1864       }
1865       row = *ajtmp++;
1866     }
1867     /* finished row so stick it into b->a */
1868     pv = ba + 16*bi[i];
1869     pj = bj + bi[i];
1870     nz = bi[i+1] - bi[i];
1871     for (j=0; j<nz; j++) {
1872       x      = rtmp+16*pj[j];
1873       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
1874       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
1875       pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
1876       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
1877       pv   += 16;
1878     }
1879     /* invert diagonal block */
1880     w = ba + 16*diag_offset[i];
1881     ierr = Kernel_A_gets_inverse_A_4(w);CHKERRQ(ierr);
1882   }
1883 
1884   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1885   C->factor    = FACTOR_LU;
1886   C->assembled = PETSC_TRUE;
1887   PLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */
1888   PetscFunctionReturn(0);
1889 }
1890 
1891 
1892 /* ------------------------------------------------------------*/
1893 /*
1894       Version for when blocks are 3 by 3
1895 */
1896 #undef __FUNC__
1897 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_3"
1898 int MatCholeskyFactorNumeric_SeqSBAIJ_3(Mat A,Mat *B)
1899 {
1900   Mat         C = *B;
1901   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
1902   IS          isrow = b->row,isicol = b->icol;
1903   int         *r,*ic,ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
1904   int         *ajtmpold,*ajtmp,nz,row,*ai=a->i,*aj=a->j;
1905   int         *diag_offset = b->diag,idx,*pj;
1906   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
1907   MatScalar   p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
1908   MatScalar   p5,p6,p7,p8,p9,x5,x6,x7,x8,x9;
1909   MatScalar   *ba = b->a,*aa = a->a;
1910 
1911   PetscFunctionBegin;
1912   ierr  = ISGetIndices(isrow,&r);CHKERRQ(ierr);
1913   ierr  = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
1914   rtmp  = (MatScalar*)PetscMalloc(9*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
1915 
1916   for (i=0; i<n; i++) {
1917     nz    = bi[i+1] - bi[i];
1918     ajtmp = bj + bi[i];
1919     for  (j=0; j<nz; j++) {
1920       x = rtmp + 9*ajtmp[j];
1921       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = 0.0;
1922     }
1923     /* load in initial (unfactored row) */
1924     idx      = r[i];
1925     nz       = ai[idx+1] - ai[idx];
1926     ajtmpold = aj + ai[idx];
1927     v        = aa + 9*ai[idx];
1928     for (j=0; j<nz; j++) {
1929       x    = rtmp + 9*ic[ajtmpold[j]];
1930       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
1931       x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
1932       v    += 9;
1933     }
1934     row = *ajtmp++;
1935     while (row < i) {
1936       pc = rtmp + 9*row;
1937       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
1938       p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
1939       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
1940           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0) {
1941         pv = ba + 9*diag_offset[row];
1942         pj = bj + diag_offset[row] + 1;
1943         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
1944         x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
1945         pc[0] = m1 = p1*x1 + p4*x2 + p7*x3;
1946         pc[1] = m2 = p2*x1 + p5*x2 + p8*x3;
1947         pc[2] = m3 = p3*x1 + p6*x2 + p9*x3;
1948 
1949         pc[3] = m4 = p1*x4 + p4*x5 + p7*x6;
1950         pc[4] = m5 = p2*x4 + p5*x5 + p8*x6;
1951         pc[5] = m6 = p3*x4 + p6*x5 + p9*x6;
1952 
1953         pc[6] = m7 = p1*x7 + p4*x8 + p7*x9;
1954         pc[7] = m8 = p2*x7 + p5*x8 + p8*x9;
1955         pc[8] = m9 = p3*x7 + p6*x8 + p9*x9;
1956         nz = bi[row+1] - diag_offset[row] - 1;
1957         pv += 9;
1958         for (j=0; j<nz; j++) {
1959           x1   = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
1960           x5   = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
1961           x    = rtmp + 9*pj[j];
1962           x[0] -= m1*x1 + m4*x2 + m7*x3;
1963           x[1] -= m2*x1 + m5*x2 + m8*x3;
1964           x[2] -= m3*x1 + m6*x2 + m9*x3;
1965 
1966           x[3] -= m1*x4 + m4*x5 + m7*x6;
1967           x[4] -= m2*x4 + m5*x5 + m8*x6;
1968           x[5] -= m3*x4 + m6*x5 + m9*x6;
1969 
1970           x[6] -= m1*x7 + m4*x8 + m7*x9;
1971           x[7] -= m2*x7 + m5*x8 + m8*x9;
1972           x[8] -= m3*x7 + m6*x8 + m9*x9;
1973           pv   += 9;
1974         }
1975         PLogFlops(54*nz+36);
1976       }
1977       row = *ajtmp++;
1978     }
1979     /* finished row so stick it into b->a */
1980     pv = ba + 9*bi[i];
1981     pj = bj + bi[i];
1982     nz = bi[i+1] - bi[i];
1983     for (j=0; j<nz; j++) {
1984       x     = rtmp + 9*pj[j];
1985       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
1986       pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
1987       pv   += 9;
1988     }
1989     /* invert diagonal block */
1990     w = ba + 9*diag_offset[i];
1991     ierr = Kernel_A_gets_inverse_A_3(w);CHKERRQ(ierr);
1992   }
1993 
1994   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1995   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
1996   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
1997   C->factor = FACTOR_LU;
1998   C->assembled = PETSC_TRUE;
1999   PLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */
2000   PetscFunctionReturn(0);
2001 }
2002 /*
2003       Version for when blocks are 3 by 3 Using natural ordering
2004 */
2005 #undef __FUNC__
2006 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_3_NaturalOrdering"
2007 int MatCholeskyFactorNumeric_SeqSBAIJ_3_NaturalOrdering(Mat A,Mat *B)
2008 {
2009   Mat                C = *B;
2010   Mat_SeqBAIJ        *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
2011   int                ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
2012   int                *ajtmpold,*ajtmp,nz,row;
2013   int                *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
2014   MatScalar          *pv,*v,*rtmp,*pc,*w,*x;
2015   MatScalar          p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
2016   MatScalar          p5,p6,p7,p8,p9,x5,x6,x7,x8,x9;
2017   MatScalar          *ba = b->a,*aa = a->a;
2018 
2019   PetscFunctionBegin;
2020   rtmp  = (MatScalar*)PetscMalloc(9*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
2021 
2022   for (i=0; i<n; i++) {
2023     nz    = bi[i+1] - bi[i];
2024     ajtmp = bj + bi[i];
2025     for  (j=0; j<nz; j++) {
2026       x = rtmp+9*ajtmp[j];
2027       x[0]  = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = 0.0;
2028     }
2029     /* load in initial (unfactored row) */
2030     nz       = ai[i+1] - ai[i];
2031     ajtmpold = aj + ai[i];
2032     v        = aa + 9*ai[i];
2033     for (j=0; j<nz; j++) {
2034       x    = rtmp+9*ajtmpold[j];
2035       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
2036       x[4]  = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
2037       v    += 9;
2038     }
2039     row = *ajtmp++;
2040     while (row < i) {
2041       pc  = rtmp + 9*row;
2042       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
2043       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
2044       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
2045           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0) {
2046         pv = ba + 9*diag_offset[row];
2047         pj = bj + diag_offset[row] + 1;
2048         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
2049         x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
2050         pc[0] = m1 = p1*x1 + p4*x2 + p7*x3;
2051         pc[1] = m2 = p2*x1 + p5*x2 + p8*x3;
2052         pc[2] = m3 = p3*x1 + p6*x2 + p9*x3;
2053 
2054         pc[3] = m4 = p1*x4 + p4*x5 + p7*x6;
2055         pc[4] = m5 = p2*x4 + p5*x5 + p8*x6;
2056         pc[5] = m6 = p3*x4 + p6*x5 + p9*x6;
2057 
2058         pc[6] = m7 = p1*x7 + p4*x8 + p7*x9;
2059         pc[7] = m8 = p2*x7 + p5*x8 + p8*x9;
2060         pc[8] = m9 = p3*x7 + p6*x8 + p9*x9;
2061 
2062         nz = bi[row+1] - diag_offset[row] - 1;
2063         pv += 9;
2064         for (j=0; j<nz; j++) {
2065           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
2066           x5   = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
2067           x    = rtmp + 9*pj[j];
2068           x[0] -= m1*x1 + m4*x2 + m7*x3;
2069           x[1] -= m2*x1 + m5*x2 + m8*x3;
2070           x[2] -= m3*x1 + m6*x2 + m9*x3;
2071 
2072           x[3] -= m1*x4 + m4*x5 + m7*x6;
2073           x[4] -= m2*x4 + m5*x5 + m8*x6;
2074           x[5] -= m3*x4 + m6*x5 + m9*x6;
2075 
2076           x[6] -= m1*x7 + m4*x8 + m7*x9;
2077           x[7] -= m2*x7 + m5*x8 + m8*x9;
2078           x[8] -= m3*x7 + m6*x8 + m9*x9;
2079           pv   += 9;
2080         }
2081         PLogFlops(54*nz+36);
2082       }
2083       row = *ajtmp++;
2084     }
2085     /* finished row so stick it into b->a */
2086     pv = ba + 9*bi[i];
2087     pj = bj + bi[i];
2088     nz = bi[i+1] - bi[i];
2089     for (j=0; j<nz; j++) {
2090       x      = rtmp+9*pj[j];
2091       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
2092       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
2093       pv   += 9;
2094     }
2095     /* invert diagonal block */
2096     w = ba + 9*diag_offset[i];
2097     ierr = Kernel_A_gets_inverse_A_3(w);CHKERRQ(ierr);
2098   }
2099 
2100   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2101   C->factor    = FACTOR_LU;
2102   C->assembled = PETSC_TRUE;
2103   PLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */
2104   PetscFunctionReturn(0);
2105 }
2106 
2107 /* ------------------------------------------------------------*/
2108 /*
2109       Version for when blocks are 2 by 2
2110 */
2111 #undef __FUNC__
2112 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_2"
2113 int MatCholeskyFactorNumeric_SeqSBAIJ_2(Mat A,Mat *B)
2114 {
2115   Mat                C = *B;
2116   Mat_SeqBAIJ        *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
2117   IS                 isrow = b->row,isicol = b->icol;
2118   int                *r,*ic,ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
2119   int                *ajtmpold,*ajtmp,nz,row;
2120   int                *diag_offset=b->diag,idx,*ai=a->i,*aj=a->j,*pj;
2121   MatScalar          *pv,*v,*rtmp,m1,m2,m3,m4,*pc,*w,*x,x1,x2,x3,x4;
2122   MatScalar          p1,p2,p3,p4;
2123   MatScalar          *ba = b->a,*aa = a->a;
2124 
2125   PetscFunctionBegin;
2126   ierr  = ISGetIndices(isrow,&r);CHKERRQ(ierr);
2127   ierr  = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
2128   rtmp  = (MatScalar*)PetscMalloc(4*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
2129 
2130   for (i=0; i<n; i++) {
2131     nz    = bi[i+1] - bi[i];
2132     ajtmp = bj + bi[i];
2133     for  (j=0; j<nz; j++) {
2134       x = rtmp+4*ajtmp[j]; x[0] = x[1] = x[2] = x[3] = 0.0;
2135     }
2136     /* load in initial (unfactored row) */
2137     idx      = r[i];
2138     nz       = ai[idx+1] - ai[idx];
2139     ajtmpold = aj + ai[idx];
2140     v        = aa + 4*ai[idx];
2141     for (j=0; j<nz; j++) {
2142       x    = rtmp+4*ic[ajtmpold[j]];
2143       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
2144       v    += 4;
2145     }
2146     row = *ajtmp++;
2147     while (row < i) {
2148       pc = rtmp + 4*row;
2149       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
2150       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0) {
2151         pv = ba + 4*diag_offset[row];
2152         pj = bj + diag_offset[row] + 1;
2153         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
2154         pc[0] = m1 = p1*x1 + p3*x2;
2155         pc[1] = m2 = p2*x1 + p4*x2;
2156         pc[2] = m3 = p1*x3 + p3*x4;
2157         pc[3] = m4 = p2*x3 + p4*x4;
2158         nz = bi[row+1] - diag_offset[row] - 1;
2159         pv += 4;
2160         for (j=0; j<nz; j++) {
2161           x1   = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
2162           x    = rtmp + 4*pj[j];
2163           x[0] -= m1*x1 + m3*x2;
2164           x[1] -= m2*x1 + m4*x2;
2165           x[2] -= m1*x3 + m3*x4;
2166           x[3] -= m2*x3 + m4*x4;
2167           pv   += 4;
2168         }
2169         PLogFlops(16*nz+12);
2170       }
2171       row = *ajtmp++;
2172     }
2173     /* finished row so stick it into b->a */
2174     pv = ba + 4*bi[i];
2175     pj = bj + bi[i];
2176     nz = bi[i+1] - bi[i];
2177     for (j=0; j<nz; j++) {
2178       x     = rtmp+4*pj[j];
2179       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
2180       pv   += 4;
2181     }
2182     /* invert diagonal block */
2183     w = ba + 4*diag_offset[i];
2184     ierr = Kernel_A_gets_inverse_A_2(w);CHKERRQ(ierr);
2185     /*Kernel_A_gets_inverse_A(bs,w,v_pivots,v_work);*/
2186   }
2187 
2188   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2189   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
2190   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
2191   C->factor = FACTOR_LU;
2192   C->assembled = PETSC_TRUE;
2193   PLogFlops(1.3333*8*b->mbs); /* from inverting diagonal blocks */
2194   PetscFunctionReturn(0);
2195 }
2196 /*
2197       Version for when blocks are 2 by 2 Using natural ordering
2198 */
2199 #undef __FUNC__
2200 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_2_NaturalOrdering"
2201 int MatCholeskyFactorNumeric_SeqSBAIJ_2_NaturalOrdering(Mat A,Mat *B)
2202 {
2203   Mat                C = *B;
2204   Mat_SeqBAIJ        *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
2205   int                ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
2206   int                *ajtmpold,*ajtmp,nz,row;
2207   int                *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
2208   MatScalar          *pv,*v,*rtmp,*pc,*w,*x;
2209   MatScalar          p1,p2,p3,p4,m1,m2,m3,m4,x1,x2,x3,x4;
2210   MatScalar          *ba = b->a,*aa = a->a;
2211 
2212   PetscFunctionBegin;
2213   rtmp  = (MatScalar*)PetscMalloc(4*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
2214 
2215   for (i=0; i<n; i++) {
2216     nz    = bi[i+1] - bi[i];
2217     ajtmp = bj + bi[i];
2218     for  (j=0; j<nz; j++) {
2219       x = rtmp+4*ajtmp[j];
2220       x[0]  = x[1]  = x[2]  = x[3]  = 0.0;
2221     }
2222     /* load in initial (unfactored row) */
2223     nz       = ai[i+1] - ai[i];
2224     ajtmpold = aj + ai[i];
2225     v        = aa + 4*ai[i];
2226     for (j=0; j<nz; j++) {
2227       x    = rtmp+4*ajtmpold[j];
2228       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
2229       v    += 4;
2230     }
2231     row = *ajtmp++;
2232     while (row < i) {
2233       pc  = rtmp + 4*row;
2234       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
2235       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0) {
2236         pv = ba + 4*diag_offset[row];
2237         pj = bj + diag_offset[row] + 1;
2238         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
2239         pc[0] = m1 = p1*x1 + p3*x2;
2240         pc[1] = m2 = p2*x1 + p4*x2;
2241         pc[2] = m3 = p1*x3 + p3*x4;
2242         pc[3] = m4 = p2*x3 + p4*x4;
2243         nz = bi[row+1] - diag_offset[row] - 1;
2244         pv += 4;
2245         for (j=0; j<nz; j++) {
2246           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
2247           x    = rtmp + 4*pj[j];
2248           x[0] -= m1*x1 + m3*x2;
2249           x[1] -= m2*x1 + m4*x2;
2250           x[2] -= m1*x3 + m3*x4;
2251           x[3] -= m2*x3 + m4*x4;
2252           pv   += 4;
2253         }
2254         PLogFlops(16*nz+12);
2255       }
2256       row = *ajtmp++;
2257     }
2258     /* finished row so stick it into b->a */
2259     pv = ba + 4*bi[i];
2260     pj = bj + bi[i];
2261     nz = bi[i+1] - bi[i];
2262     for (j=0; j<nz; j++) {
2263       x      = rtmp+4*pj[j];
2264       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
2265       pv   += 4;
2266     }
2267     /* invert diagonal block */
2268     w = ba + 4*diag_offset[i];
2269     ierr = Kernel_A_gets_inverse_A_2(w);CHKERRQ(ierr);
2270     /*Kernel_A_gets_inverse_A(bs,w,v_pivots,v_work);*/
2271   }
2272 
2273   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2274   C->factor    = FACTOR_LU;
2275   C->assembled = PETSC_TRUE;
2276   PLogFlops(1.3333*8*b->mbs); /* from inverting diagonal blocks */
2277   PetscFunctionReturn(0);
2278 }
2279 
2280 /* ----------------------------------------------------------- */
2281 /*
2282      Version for when blocks are 1 by 1.
2283 */
2284 #undef __FUNC__
2285 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_1"
2286 int MatCholeskyFactorNumeric_SeqSBAIJ_1(Mat A,Mat *B)
2287 {
2288   Mat                C = *B;
2289   Mat_SeqSBAIJ       *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data;
2290   IS                 ip = b->row;
2291   int                *rip,*riip,ierr,i,j,mbs = a->mbs,*bi = b->i,*bj = b->j;
2292   int                *ai = a->i,*aj = a->j;
2293   MatScalar          *rtmp;
2294   MatScalar          *ba = b->a,*aa = a->a;
2295   MatScalar          dk,uikdi;
2296   int                k,jmin,jmax,*jl,*il,vj,nexti,juj,ili;
2297 
2298   PetscFunctionBegin;
2299   ierr  = ISGetIndices(ip,&rip);CHKERRQ(ierr);
2300   riip = rip;
2301 
2302   /* INITIALIZATION */
2303   /* il and jl record the first nonzero element in each row of the accessing
2304      window U(0:k, k:mbs-1).
2305      jl:    list of rows to be added to uneliminated rows
2306             i>= k: jl(i) is the first row to be added to row i
2307             i<  k: jl(i) is the row following row i in some list of rows
2308             jl(i) = mbs indicates the end of a list
2309      il(i): points to the first nonzero element in columns k,...,mbs-1 of
2310             row i of U */
2311   rtmp  = (MatScalar*)PetscMalloc(mbs*sizeof(MatScalar));CHKPTRQ(rtmp);
2312   il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il);
2313   jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl);
2314   for (i=0; i<mbs; i++) {
2315     rtmp[i] = 0.0; jl[i] = mbs; il[0] = 0;
2316   }
2317 
2318   /* FOR EACH ROW K */
2319   for (k = 0; k<mbs; k++){
2320 
2321     /* INITIALIZE K-TH ROW WITH ELEMENTS NONZERO IN ROW P(K) OF A */
2322     jmin = ai[rip[k]]; jmax = ai[rip[k]+1];
2323     if (jmin < jmax) {
2324       for (j = jmin; j < jmax; j++){
2325         vj = riip[aj[j]];
2326         if (k <= vj) rtmp[vj] = aa[j];
2327       }
2328     }
2329 
2330     /* MODIFY K-TH ROW BY ADDING IN THOSE ROWS I WITH U(I,K) NE 0
2331        FOR EACH ROW I TO BE ADDED IN */
2332     dk = rtmp[k];
2333     i = jl[k]; /* first row to be added to k_th row  */
2334     /* printf(" k=%d, pivot row = %d\n",k,i); */
2335 
2336     while (i < mbs){
2337       nexti = jl[i]; /* next row to be added to k_th row */
2338       /* printf("      pivot row = %d\n", nexti); */
2339 
2340       /* COMPUTE MULTIPLIER AND UPDATE DIAGONAL ELEMENT */
2341       ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
2342       uikdi = - ba[ili]*ba[i];
2343       dk += uikdi*ba[ili];
2344       ba[ili] = uikdi; /* update U(i,k) */
2345 
2346       /* ADD MULTIPLE OF ROW I TO K-TH ROW ... */
2347       jmin = ili + 1; jmax = bi[i+1];
2348       if (jmin < jmax){
2349         for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j];
2350         /* ... AND ADD I TO ROW LIST FOR NEXT NONZERO ENTRY */
2351          il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
2352          j     = bj[jmin];
2353          jl[i] = jl[j]; jl[j] = i; /* update jl */
2354       }
2355       i = nexti;
2356       /* printf("                  pivot row i=%d\n",i);  */
2357     }
2358 
2359     /* CHECK FOR ZERO PIVOT AND SAVE DIAGONAL ELEMENT */
2360     if (dk == 0.0){
2361       SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,0,"Zero pivot");
2362     }
2363 
2364     /* SAVE NONZERO ENTRIES IN K-TH ROW OF U ... */
2365     ba[k] = 1.0/dk;
2366     jmin = bi[k]; jmax = bi[k+1];
2367     if (jmin < jmax) {
2368       for (j=jmin; j<jmax; j++){
2369          juj = bj[j]; ba[j] = rtmp[juj]; rtmp[juj] = 0.0;
2370       }
2371 
2372       /* ... AND ADD K TO ROW LIST FOR FIRST NONZERO ENTRY IN K-TH ROW */
2373       il[k] = jmin;
2374       i     = bj[jmin];
2375       jl[k] = jl[i]; jl[i] = k;
2376     }
2377   }
2378 
2379   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2380   ierr = PetscFree(il);CHKERRQ(ierr);
2381   ierr = PetscFree(jl);CHKERRQ(ierr);
2382 
2383   ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr);
2384   C->factor    = FACTOR_LU;
2385   C->assembled = PETSC_TRUE;
2386   PLogFlops(b->mbs);
2387   PetscFunctionReturn(0);
2388 }
2389 
2390 #undef __FUNC__
2391 #define __FUNC__ "MatCholeskyFactor_SeqSBAIJ"
2392 int MatCholeskyFactor_SeqSBAIJ(Mat A,IS perm,PetscReal f)
2393 {
2394   Mat_SeqSBAIJ    *mat = (Mat_SeqSBAIJ*)A->data;
2395   int            ierr,refct;
2396   Mat            C;
2397   PetscOps *Abops;
2398   MatOps   Aops;
2399 
2400   PetscFunctionBegin;
2401   ierr = MatCholeskyFactorSymbolic(A,perm,f,&C);CHKERRQ(ierr);
2402   ierr = MatCholeskyFactorNumeric(A,&C);CHKERRQ(ierr);
2403 
2404   /* free all the data structures from mat */
2405   ierr = PetscFree(mat->a);CHKERRQ(ierr);
2406   if (!mat->singlemalloc) {
2407     ierr = PetscFree(mat->i);CHKERRQ(ierr);
2408     ierr = PetscFree(mat->j);CHKERRQ(ierr);
2409   }
2410   if (mat->diag) {ierr = PetscFree(mat->diag);CHKERRQ(ierr);}
2411   if (mat->ilen) {ierr = PetscFree(mat->ilen);CHKERRQ(ierr);}
2412   if (mat->imax) {ierr = PetscFree(mat->imax);CHKERRQ(ierr);}
2413   if (mat->solve_work) {ierr = PetscFree(mat->solve_work);CHKERRQ(ierr);}
2414   if (mat->mult_work) {ierr = PetscFree(mat->mult_work);CHKERRQ(ierr);}
2415   if (mat->icol) {ierr = ISDestroy(mat->icol);CHKERRQ(ierr);}
2416   ierr = PetscFree(mat);CHKERRQ(ierr);
2417 
2418   ierr = MapDestroy(A->rmap);CHKERRQ(ierr);
2419   ierr = MapDestroy(A->cmap);CHKERRQ(ierr);
2420 
2421   /*
2422        This is horrible,horrible code. We need to keep the
2423     A pointers for the bops and ops but copy everything
2424     else from C.
2425   */
2426   Abops = A->bops;
2427   Aops  = A->ops;
2428   refct = A->refct;
2429   ierr  = PetscMemcpy(A,C,sizeof(struct _p_Mat));CHKERRQ(ierr);
2430   mat   = (Mat_SeqSBAIJ*)A->data;
2431   PLogObjectParent(A,mat->icol);
2432 
2433   A->bops  = Abops;
2434   A->ops   = Aops;
2435   A->qlist = 0;
2436   A->refct = refct;
2437   /* copy over the type_name and name */
2438   ierr     = PetscStrallocpy(C->type_name,&A->type_name);CHKERRQ(ierr);
2439   ierr     = PetscStrallocpy(C->name,&A->name);CHKERRQ(ierr);
2440 
2441   PetscHeaderDestroy(C);
2442   PetscFunctionReturn(0);
2443 }
2444 
2445 
2446