xref: /petsc/src/mat/impls/sbaij/seq/sbaijfact.c (revision 81bfdfe8f062de6d040b794b1069c3423f23b916)
1 /* Using Modified Sparse Row (MSR) storage.
2 See page 85, "Iterative Methods ..." by Saad. */
3 
4 /*$Id: sbaijfact.c,v 1.11 2000/08/01 14:14:52 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 perm,PetscReal f,Mat *B)
16 {
17   Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b;
18   IS          iperm;
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 
24   PetscFunctionBegin;
25   PetscValidHeaderSpecific(perm,IS_COOKIE);
26   if (A->M != A->N) SETERRQ(PETSC_ERR_ARG_WRONG,0,"matrix must be square");
27   ierr = ISInvertPermutation(perm,PETSC_DECIDE,&iperm);CHKERRQ(ierr);
28   ierr = ISGetIndices(perm,&rip);CHKERRQ(ierr);
29   ierr = ISGetIndices(iperm,&riip);CHKERRQ(ierr);
30 
31   /* initialization */
32   /* Don't know how many column pointers are needed so estimate.
33      Use Modified Sparse Row storage for u and ju, see Sasd pp.85 */
34   iu   = (int*)PetscMalloc((mbs+1)*sizeof(int));CHKPTRQ(iu);
35   umax = (int)(f*ai[mbs] + 1); umax += mbs + 1;
36   ju   = (int*)PetscMalloc(umax*sizeof(int));CHKPTRQ(ju);
37   iu[0] = mbs+1;
38   juptr = mbs;
39   jl =  (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl);
40   q  =  (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(q);
41   for (i=0; i<mbs; i++){
42     jl[i] = mbs; q[i] = 0;
43   }
44 
45   /* for each row k */
46   for (k=0; k<mbs; k++){
47     nzk = 0; /* num. of nz blocks in k-th block row with diagonal block excluded */
48     q[k] = mbs;
49     /* initialize nonzero structure of k-th row to row rip[k] of A */
50     jmin = ai[rip[k]];
51     jmax = ai[rip[k]+1];
52     for (j=jmin; j<jmax; j++){
53       vj = riip[aj[j]]; /* col. value */
54       if(vj > k){
55         qm = k;
56         do {
57           m  = qm; qm = q[m];
58         } while(qm < vj);
59         if (qm == vj) {
60           printf(" error: duplicate entry in A\n"); break;
61         }
62         nzk++;
63         q[m] = vj;
64         q[vj] = qm;
65       } /* if(vj > k) */
66     } /* for (j=jmin; j<jmax; j++) */
67 
68     /* modify nonzero structure of k-th row by computing fill-in
69        for each row i to be merged in */
70     i = k;
71     i = jl[i]; /* next pivot row (== mbs for symbolic factorization) */
72     /* printf(" next pivot row i=%d\n",i); */
73     while (i < mbs){
74       /* merge row i into k-th row */
75       nzi = iu[i+1] - (iu[i]+1);
76       jmin = iu[i] + 1; jmax = iu[i] + nzi;
77       qm = k;
78       for (j=jmin; j<jmax+1; j++){
79         vj = ju[j];
80         do {
81           m = qm; qm = q[m];
82         } while (qm < vj);
83         if (qm != vj){
84          nzk++; q[m] = vj; q[vj] = qm; qm = vj;
85         }
86       }
87       i = jl[i]; /* next pivot row */
88     }
89 
90     /* add k to row list for first nonzero element in k-th row */
91     if (nzk > 0){
92       i = q[k]; /* col value of first nonzero element in U(k, k+1:mbs-1) */
93       jl[k] = jl[i]; jl[i] = k;
94     }
95     iu[k+1] = iu[k] + nzk;   /* printf(" iu[%d]=%d, umax=%d\n", k+1, iu[k+1],umax);*/
96 
97     /* allocate more space to ju if needed */
98     if (iu[k+1] > umax) { printf("allocate more space, iu[%d]=%d > umax=%d\n",k+1, iu[k+1],umax);
99       /* estimate how much additional space we will need */
100       /* use the strategy suggested by David Hysom <hysom@perch-t.icase.edu> */
101       /* just double the memory each time */
102       maxadd = umax;
103       if (maxadd < nzk) maxadd = (mbs-k)*(nzk+1)/2;
104       umax += maxadd;
105 
106       /* allocate a longer ju */
107       jutmp = (int*)PetscMalloc(umax*sizeof(int));CHKPTRQ(jutmp);
108       ierr  = PetscMemcpy(jutmp,ju,iu[k]*sizeof(int));CHKERRQ(ierr);
109       ierr  = PetscFree(ju);CHKERRQ(ierr);
110       ju    = jutmp;
111       realloc++; /* count how many times we realloc */
112     }
113 
114     /* save nonzero structure of k-th row in ju */
115     i=k;
116     jumin = juptr + 1; juptr += nzk;
117     for (j=jumin; j<juptr+1; j++){
118       i=q[i];
119       ju[j]=i;
120     }
121   }
122 
123   if (ai[mbs] != 0) {
124     PetscReal af = ((PetscReal)iu[mbs])/((PetscReal)ai[mbs]);
125     PLogInfo(A,"MatCholeskyFactorSymbolic_SeqSBAIJ:Reallocs %d Fill ratio:given %g needed %g\n",realloc,f,af);
126     PLogInfo(A,"MatCholeskyFactorSymbolic_SeqSBAIJ:Run with -pc_lu_fill %g or use \n",af);
127     PLogInfo(A,"MatCholeskyFactorSymbolic_SeqSBAIJ:PCLUSetFill(pc,%g);\n",af);
128     PLogInfo(A,"MatCholeskyFactorSymbolic_SeqSBAIJ:for best performance.\n");
129   } else {
130      PLogInfo(A,"MatCholeskyFactorSymbolic_SeqSBAIJ:Empty matrix.\n");
131   }
132 
133   ierr = ISRestoreIndices(perm,&rip);CHKERRQ(ierr);
134   ierr = ISRestoreIndices(iperm,&riip);CHKERRQ(ierr);
135 
136   ierr = PetscFree(q);CHKERRQ(ierr);
137   ierr = PetscFree(jl);CHKERRQ(ierr);
138 
139   /* put together the new matrix */
140   ierr = MatCreateSeqSBAIJ(A->comm,bs,bs*mbs,bs*mbs,0,PETSC_NULL,B);CHKERRQ(ierr);
141   PLogObjectParent(*B,iperm);
142   b = (Mat_SeqSBAIJ*)(*B)->data;
143   ierr = PetscFree(b->imax);CHKERRQ(ierr);
144   b->singlemalloc = PETSC_FALSE;
145   /* the next line frees the default space generated by the Create() */
146   ierr = PetscFree(b->a);CHKERRQ(ierr);
147   ierr = PetscFree(b->ilen);CHKERRQ(ierr);
148   b->a          = (MatScalar*)PetscMalloc((iu[mbs]+1)*sizeof(MatScalar)*bs2);CHKPTRQ(b->a);
149   b->j          = ju;
150   b->i          = iu;
151   b->diag       = 0;
152   b->ilen       = 0;
153   b->imax       = 0;
154   b->row        = perm;
155   ierr          = PetscObjectReference((PetscObject)perm);CHKERRQ(ierr);
156   b->icol       = iperm;
157   b->solve_work = (Scalar*)PetscMalloc((bs*mbs+bs)*sizeof(Scalar));CHKPTRQ(b->solve_work);
158   /* In b structure:  Free imax, ilen, old a, old j.
159      Allocate idnew, solve_work, new a, new j */
160   PLogObjectMemory(*B,(iu[mbs]-mbs)*(sizeof(int)+sizeof(MatScalar)));
161   b->s_maxnz = b->s_nz = iu[mbs];
162 
163   (*B)->factor                 = FACTOR_LU;
164   (*B)->info.factor_mallocs    = realloc;
165   (*B)->info.fill_ratio_given  = f;
166   if (ai[mbs] != 0) {
167     (*B)->info.fill_ratio_needed = ((PetscReal)iu[mbs])/((PetscReal)ai[mbs]);
168   } else {
169     (*B)->info.fill_ratio_needed = 0.0;
170   }
171 
172 
173   PetscFunctionReturn(0);
174 }
175 
176 #undef __FUNC__
177 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_N"
178 int MatCholeskyFactorNumeric_SeqSBAIJ_N(Mat A,Mat *B)
179 {
180   Mat                C = *B;
181   Mat_SeqBAIJ        *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
182   IS                 isrow = b->row,isicol = b->icol;
183   int                *r,*ic,ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
184   int                *ajtmpold,*ajtmp,nz,row,bslog,*ai=a->i,*aj=a->j,k,flg;
185   int                *diag_offset=b->diag,diag,bs=a->bs,bs2 = a->bs2,*v_pivots,*pj;
186   MatScalar          *ba = b->a,*aa = a->a,*pv,*v,*rtmp,*multiplier,*v_work,*pc,*w;
187 
188   PetscFunctionBegin;
189   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
190   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
191   rtmp = (MatScalar*)PetscMalloc(bs2*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
192   ierr = PetscMemzero(rtmp,bs2*(n+1)*sizeof(MatScalar));CHKERRQ(ierr);
193   /* generate work space needed by dense LU factorization */
194   v_work     = (MatScalar*)PetscMalloc(bs*sizeof(int) + (bs+bs2)*sizeof(MatScalar));CHKPTRQ(v_work);
195   multiplier = v_work + bs;
196   v_pivots   = (int*)(multiplier + bs2);
197 
198   /* flops in while loop */
199   bslog = 2*bs*bs2;
200 
201   for (i=0; i<n; i++) {
202     nz    = bi[i+1] - bi[i];
203     ajtmp = bj + bi[i];
204     for  (j=0; j<nz; j++) {
205       ierr = PetscMemzero(rtmp+bs2*ajtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
206     }
207     /* load in initial (unfactored row) */
208     nz       = ai[r[i]+1] - ai[r[i]];
209     ajtmpold = aj + ai[r[i]];
210     v        = aa + bs2*ai[r[i]];
211     for (j=0; j<nz; j++) {
212       ierr = PetscMemcpy(rtmp+bs2*ic[ajtmpold[j]],v+bs2*j,bs2*sizeof(MatScalar));CHKERRQ(ierr);
213     }
214     row = *ajtmp++;
215     while (row < i) {
216       pc = rtmp + bs2*row;
217 /*      if (*pc) { */
218       for (flg=0,k=0; k<bs2; k++) { if (pc[k]!=0.0) { flg =1; break; }}
219       if (flg) {
220         pv = ba + bs2*diag_offset[row];
221         pj = bj + diag_offset[row] + 1;
222         Kernel_A_gets_A_times_B(bs,pc,pv,multiplier);
223         nz = bi[row+1] - diag_offset[row] - 1;
224         pv += bs2;
225         for (j=0; j<nz; j++) {
226           Kernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j);
227         }
228         PLogFlops(bslog*(nz+1)-bs);
229       }
230         row = *ajtmp++;
231     }
232     /* finished row so stick it into b->a */
233     pv = ba + bs2*bi[i];
234     pj = bj + bi[i];
235     nz = bi[i+1] - bi[i];
236     for (j=0; j<nz; j++) {
237       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
238     }
239     diag = diag_offset[i] - bi[i];
240     /* invert diagonal block */
241     w = pv + bs2*diag;
242     Kernel_A_gets_inverse_A(bs,w,v_pivots,v_work);
243   }
244 
245   ierr = PetscFree(rtmp);CHKERRQ(ierr);
246   ierr = PetscFree(v_work);CHKERRQ(ierr);
247   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
248   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
249   C->factor = FACTOR_LU;
250   C->assembled = PETSC_TRUE;
251   PLogFlops(1.3333*bs*bs2*b->mbs); /* from inverting diagonal blocks */
252   PetscFunctionReturn(0);
253 }
254 
255 /*
256       Version for when blocks are 7 by 7
257 */
258 #undef __FUNC__
259 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_7"
260 int MatCholeskyFactorNumeric_SeqSBAIJ_7(Mat A,Mat *B)
261 {
262   Mat         C = *B;
263   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
264   IS          isrow = b->row,isicol = b->icol;
265   int         *r,*ic,ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
266   int         *ajtmpold,*ajtmp,nz,row;
267   int         *diag_offset = b->diag,idx,*ai=a->i,*aj=a->j,*pj;
268   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
269   MatScalar   p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
270   MatScalar   p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
271   MatScalar   x17,x18,x19,x20,x21,x22,x23,x24,x25,p10,p11,p12,p13,p14;
272   MatScalar   p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,m10,m11,m12;
273   MatScalar   m13,m14,m15,m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
274   MatScalar   p26,p27,p28,p29,p30,p31,p32,p33,p34,p35,p36;
275   MatScalar   p37,p38,p39,p40,p41,p42,p43,p44,p45,p46,p47,p48,p49;
276   MatScalar   x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36;
277   MatScalar   x37,x38,x39,x40,x41,x42,x43,x44,x45,x46,x47,x48,x49;
278   MatScalar   m26,m27,m28,m29,m30,m31,m32,m33,m34,m35,m36;
279   MatScalar   m37,m38,m39,m40,m41,m42,m43,m44,m45,m46,m47,m48,m49;
280   MatScalar   *ba = b->a,*aa = a->a;
281 
282   PetscFunctionBegin;
283   ierr  = ISGetIndices(isrow,&r);CHKERRQ(ierr);
284   ierr  = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
285   rtmp  = (MatScalar*)PetscMalloc(49*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
286 
287   for (i=0; i<n; i++) {
288     nz    = bi[i+1] - bi[i];
289     ajtmp = bj + bi[i];
290     for  (j=0; j<nz; j++) {
291       x = rtmp+49*ajtmp[j];
292       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
293       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
294       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = x[25] = 0.0 ;
295       x[26] = x[27] = x[28] = x[29] = x[30] = x[31] = x[32] = x[33] = 0.0 ;
296       x[34] = x[35] = x[36] = x[37] = x[38] = x[39] = x[40] = x[41] = 0.0 ;
297       x[42] = x[43] = x[44] = x[45] = x[46] = x[47] = x[48] = 0.0 ;
298     }
299     /* load in initial (unfactored row) */
300     idx      = r[i];
301     nz       = ai[idx+1] - ai[idx];
302     ajtmpold = aj + ai[idx];
303     v        = aa + 49*ai[idx];
304     for (j=0; j<nz; j++) {
305       x    = rtmp+49*ic[ajtmpold[j]];
306       x[0] =  v[0];  x[1] =  v[1];  x[2] =  v[2];  x[3] =  v[3];
307       x[4] =  v[4];  x[5] =  v[5];  x[6] =  v[6];  x[7] =  v[7];
308       x[8] =  v[8];  x[9] =  v[9];  x[10] = v[10]; x[11] = v[11];
309       x[12] = v[12]; x[13] = v[13]; x[14] = v[14]; x[15] = v[15];
310       x[16] = v[16]; x[17] = v[17]; x[18] = v[18]; x[19] = v[19];
311       x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23];
312       x[24] = v[24]; x[25] = v[25]; x[26] = v[26]; x[27] = v[27];
313       x[28] = v[28]; x[29] = v[29]; x[30] = v[30]; x[31] = v[31];
314       x[32] = v[32]; x[33] = v[33]; x[34] = v[34]; x[35] = v[35];
315       x[36] = v[36]; x[37] = v[37]; x[38] = v[38]; x[39] = v[39];
316       x[40] = v[40]; x[41] = v[41]; x[42] = v[42]; x[43] = v[43];
317       x[44] = v[44]; x[45] = v[45]; x[46] = v[46]; x[47] = v[47];
318       x[48] = v[48];
319       v    += 49;
320     }
321     row = *ajtmp++;
322     while (row < i) {
323       pc  =  rtmp + 49*row;
324       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
325       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];
326       p9  = pc[8];  p10 = pc[9];  p11 = pc[10]; p12 = pc[11];
327       p13 = pc[12]; p14 = pc[13]; p15 = pc[14]; p16 = pc[15];
328       p17 = pc[16]; p18 = pc[17]; p19 = pc[18]; p20 = pc[19];
329       p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
330       p25 = pc[24]; p26 = pc[25]; p27 = pc[26]; p28 = pc[27];
331       p29 = pc[28]; p30 = pc[29]; p31 = pc[30]; p32 = pc[31];
332       p33 = pc[32]; p34 = pc[33]; p35 = pc[34]; p36 = pc[35];
333       p37 = pc[36]; p38 = pc[37]; p39 = pc[38]; p40 = pc[39];
334       p41 = pc[40]; p42 = pc[41]; p43 = pc[42]; p44 = pc[43];
335       p45 = pc[44]; p46 = pc[45]; p47 = pc[46]; p48 = pc[47];
336       p49 = pc[48];
337       if (p1  != 0.0 || p2  != 0.0 || p3  != 0.0 || p4  != 0.0 ||
338           p5  != 0.0 || p6  != 0.0 || p7  != 0.0 || p8  != 0.0 ||
339           p9  != 0.0 || p10 != 0.0 || p11 != 0.0 || p12 != 0.0 ||
340           p13 != 0.0 || p14 != 0.0 || p15 != 0.0 || p16 != 0.0 ||
341           p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 ||
342           p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 ||
343           p25 != 0.0 || p26 != 0.0 || p27 != 0.0 || p28 != 0.0 ||
344           p29 != 0.0 || p30 != 0.0 || p31 != 0.0 || p32 != 0.0 ||
345           p33 != 0.0 || p34 != 0.0 || p35 != 0.0 || p36 != 0.0 ||
346           p37 != 0.0 || p38 != 0.0 || p39 != 0.0 || p40 != 0.0 ||
347           p41 != 0.0 || p42 != 0.0 || p43 != 0.0 || p44 != 0.0 ||
348           p45 != 0.0 || p46 != 0.0 || p47 != 0.0 || p48 != 0.0 ||
349           p49 != 0.0) {
350         pv = ba + 49*diag_offset[row];
351         pj = bj + diag_offset[row] + 1;
352 	x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
353 	x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
354 	x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
355 	x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
356 	x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
357 	x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
358 	x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
359 	x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
360 	x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
361 	x37 = pv[36]; x38 = pv[37]; x39 = pv[38]; x40 = pv[39];
362 	x41 = pv[40]; x42 = pv[41]; x43 = pv[42]; x44 = pv[43];
363 	x45 = pv[44]; x46 = pv[45]; x47 = pv[46]; x48 = pv[47];
364 	x49 = pv[48];
365         pc[0]  = m1  = p1*x1  + p8*x2   + p15*x3  + p22*x4  + p29*x5  + p36*x6 + p43*x7;
366         pc[1]  = m2  = p2*x1  + p9*x2   + p16*x3  + p23*x4  + p30*x5  + p37*x6 + p44*x7;
367         pc[2]  = m3  = p3*x1  + p10*x2  + p17*x3  + p24*x4  + p31*x5  + p38*x6 + p45*x7;
368         pc[3]  = m4  = p4*x1  + p11*x2  + p18*x3  + p25*x4  + p32*x5  + p39*x6 + p46*x7;
369         pc[4]  = m5  = p5*x1  + p12*x2  + p19*x3  + p26*x4  + p33*x5  + p40*x6 + p47*x7;
370         pc[5]  = m6  = p6*x1  + p13*x2  + p20*x3  + p27*x4  + p34*x5  + p41*x6 + p48*x7;
371         pc[6]  = m7  = p7*x1  + p14*x2  + p21*x3  + p28*x4  + p35*x5  + p42*x6 + p49*x7;
372 
373         pc[7]  = m8  = p1*x8  + p8*x9   + p15*x10 + p22*x11 + p29*x12 + p36*x13 + p43*x14;
374         pc[8]  = m9  = p2*x8  + p9*x9   + p16*x10 + p23*x11 + p30*x12 + p37*x13 + p44*x14;
375         pc[9]  = m10 = p3*x8  + p10*x9  + p17*x10 + p24*x11 + p31*x12 + p38*x13 + p45*x14;
376         pc[10] = m11 = p4*x8  + p11*x9  + p18*x10 + p25*x11 + p32*x12 + p39*x13 + p46*x14;
377         pc[11] = m12 = p5*x8  + p12*x9  + p19*x10 + p26*x11 + p33*x12 + p40*x13 + p47*x14;
378         pc[12] = m13 = p6*x8  + p13*x9  + p20*x10 + p27*x11 + p34*x12 + p41*x13 + p48*x14;
379         pc[13] = m14 = p7*x8  + p14*x9  + p21*x10 + p28*x11 + p35*x12 + p42*x13 + p49*x14;
380 
381         pc[14] = m15 = p1*x15 + p8*x16  + p15*x17 + p22*x18 + p29*x19 + p36*x20 + p43*x21;
382         pc[15] = m16 = p2*x15 + p9*x16  + p16*x17 + p23*x18 + p30*x19 + p37*x20 + p44*x21;
383         pc[16] = m17 = p3*x15 + p10*x16 + p17*x17 + p24*x18 + p31*x19 + p38*x20 + p45*x21;
384         pc[17] = m18 = p4*x15 + p11*x16 + p18*x17 + p25*x18 + p32*x19 + p39*x20 + p46*x21;
385         pc[18] = m19 = p5*x15 + p12*x16 + p19*x17 + p26*x18 + p33*x19 + p40*x20 + p47*x21;
386         pc[19] = m20 = p6*x15 + p13*x16 + p20*x17 + p27*x18 + p34*x19 + p41*x20 + p48*x21;
387         pc[20] = m21 = p7*x15 + p14*x16 + p21*x17 + p28*x18 + p35*x19 + p42*x20 + p49*x21;
388 
389         pc[21] = m22 = p1*x22 + p8*x23  + p15*x24 + p22*x25 + p29*x26 + p36*x27 + p43*x28;
390         pc[22] = m23 = p2*x22 + p9*x23  + p16*x24 + p23*x25 + p30*x26 + p37*x27 + p44*x28;
391         pc[23] = m24 = p3*x22 + p10*x23 + p17*x24 + p24*x25 + p31*x26 + p38*x27 + p45*x28;
392         pc[24] = m25 = p4*x22 + p11*x23 + p18*x24 + p25*x25 + p32*x26 + p39*x27 + p46*x28;
393         pc[25] = m26 = p5*x22 + p12*x23 + p19*x24 + p26*x25 + p33*x26 + p40*x27 + p47*x28;
394         pc[26] = m27 = p6*x22 + p13*x23 + p20*x24 + p27*x25 + p34*x26 + p41*x27 + p48*x28;
395         pc[27] = m28 = p7*x22 + p14*x23 + p21*x24 + p28*x25 + p35*x26 + p42*x27 + p49*x28;
396 
397         pc[28] = m29 = p1*x29 + p8*x30  + p15*x31 + p22*x32 + p29*x33 + p36*x34 + p43*x35;
398         pc[29] = m30 = p2*x29 + p9*x30  + p16*x31 + p23*x32 + p30*x33 + p37*x34 + p44*x35;
399         pc[30] = m31 = p3*x29 + p10*x30 + p17*x31 + p24*x32 + p31*x33 + p38*x34 + p45*x35;
400         pc[31] = m32 = p4*x29 + p11*x30 + p18*x31 + p25*x32 + p32*x33 + p39*x34 + p46*x35;
401         pc[32] = m33 = p5*x29 + p12*x30 + p19*x31 + p26*x32 + p33*x33 + p40*x34 + p47*x35;
402         pc[33] = m34 = p6*x29 + p13*x30 + p20*x31 + p27*x32 + p34*x33 + p41*x34 + p48*x35;
403         pc[34] = m35 = p7*x29 + p14*x30 + p21*x31 + p28*x32 + p35*x33 + p42*x34 + p49*x35;
404 
405         pc[35] = m36 = p1*x36 + p8*x37  + p15*x38 + p22*x39 + p29*x40 + p36*x41 + p43*x42;
406         pc[36] = m37 = p2*x36 + p9*x37  + p16*x38 + p23*x39 + p30*x40 + p37*x41 + p44*x42;
407         pc[37] = m38 = p3*x36 + p10*x37 + p17*x38 + p24*x39 + p31*x40 + p38*x41 + p45*x42;
408         pc[38] = m39 = p4*x36 + p11*x37 + p18*x38 + p25*x39 + p32*x40 + p39*x41 + p46*x42;
409         pc[39] = m40 = p5*x36 + p12*x37 + p19*x38 + p26*x39 + p33*x40 + p40*x41 + p47*x42;
410         pc[40] = m41 = p6*x36 + p13*x37 + p20*x38 + p27*x39 + p34*x40 + p41*x41 + p48*x42;
411         pc[41] = m42 = p7*x36 + p14*x37 + p21*x38 + p28*x39 + p35*x40 + p42*x41 + p49*x42;
412 
413         pc[42] = m43 = p1*x43 + p8*x44  + p15*x45 + p22*x46 + p29*x47 + p36*x48 + p43*x49;
414         pc[43] = m44 = p2*x43 + p9*x44  + p16*x45 + p23*x46 + p30*x47 + p37*x48 + p44*x49;
415         pc[44] = m45 = p3*x43 + p10*x44 + p17*x45 + p24*x46 + p31*x47 + p38*x48 + p45*x49;
416         pc[45] = m46 = p4*x43 + p11*x44 + p18*x45 + p25*x46 + p32*x47 + p39*x48 + p46*x49;
417         pc[46] = m47 = p5*x43 + p12*x44 + p19*x45 + p26*x46 + p33*x47 + p40*x48 + p47*x49;
418         pc[47] = m48 = p6*x43 + p13*x44 + p20*x45 + p27*x46 + p34*x47 + p41*x48 + p48*x49;
419         pc[48] = m49 = p7*x43 + p14*x44 + p21*x45 + p28*x46 + p35*x47 + p42*x48 + p49*x49;
420 
421         nz = bi[row+1] - diag_offset[row] - 1;
422         pv += 49;
423         for (j=0; j<nz; j++) {
424 	  x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
425 	  x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
426 	  x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
427 	  x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
428 	  x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
429 	  x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
430 	  x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
431 	  x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
432 	  x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
433 	  x37 = pv[36]; x38 = pv[37]; x39 = pv[38]; x40 = pv[39];
434 	  x41 = pv[40]; x42 = pv[41]; x43 = pv[42]; x44 = pv[43];
435 	  x45 = pv[44]; x46 = pv[45]; x47 = pv[46]; x48 = pv[47];
436 	  x49 = pv[48];
437 	  x    = rtmp + 49*pj[j];
438 	  x[0]  -= m1*x1  + m8*x2   + m15*x3  + m22*x4  + m29*x5  + m36*x6 + m43*x7;
439 	  x[1]  -= m2*x1  + m9*x2   + m16*x3  + m23*x4  + m30*x5  + m37*x6 + m44*x7;
440 	  x[2]  -= m3*x1  + m10*x2  + m17*x3  + m24*x4  + m31*x5  + m38*x6 + m45*x7;
441 	  x[3]  -= m4*x1  + m11*x2  + m18*x3  + m25*x4  + m32*x5  + m39*x6 + m46*x7;
442 	  x[4]  -= m5*x1  + m12*x2  + m19*x3  + m26*x4  + m33*x5  + m40*x6 + m47*x7;
443 	  x[5]  -= m6*x1  + m13*x2  + m20*x3  + m27*x4  + m34*x5  + m41*x6 + m48*x7;
444 	  x[6]  -= m7*x1  + m14*x2  + m21*x3  + m28*x4  + m35*x5  + m42*x6 + m49*x7;
445 
446 	  x[7]  -= m1*x8  + m8*x9   + m15*x10 + m22*x11 + m29*x12 + m36*x13 + m43*x14;
447 	  x[8]  -= m2*x8  + m9*x9   + m16*x10 + m23*x11 + m30*x12 + m37*x13 + m44*x14;
448 	  x[9]  -= m3*x8  + m10*x9  + m17*x10 + m24*x11 + m31*x12 + m38*x13 + m45*x14;
449 	  x[10] -= m4*x8  + m11*x9  + m18*x10 + m25*x11 + m32*x12 + m39*x13 + m46*x14;
450 	  x[11] -= m5*x8  + m12*x9  + m19*x10 + m26*x11 + m33*x12 + m40*x13 + m47*x14;
451 	  x[12] -= m6*x8  + m13*x9  + m20*x10 + m27*x11 + m34*x12 + m41*x13 + m48*x14;
452 	  x[13] -= m7*x8  + m14*x9  + m21*x10 + m28*x11 + m35*x12 + m42*x13 + m49*x14;
453 
454 	  x[14] -= m1*x15 + m8*x16  + m15*x17 + m22*x18 + m29*x19 + m36*x20 + m43*x21;
455 	  x[15] -= m2*x15 + m9*x16  + m16*x17 + m23*x18 + m30*x19 + m37*x20 + m44*x21;
456 	  x[16] -= m3*x15 + m10*x16 + m17*x17 + m24*x18 + m31*x19 + m38*x20 + m45*x21;
457 	  x[17] -= m4*x15 + m11*x16 + m18*x17 + m25*x18 + m32*x19 + m39*x20 + m46*x21;
458 	  x[18] -= m5*x15 + m12*x16 + m19*x17 + m26*x18 + m33*x19 + m40*x20 + m47*x21;
459 	  x[19] -= m6*x15 + m13*x16 + m20*x17 + m27*x18 + m34*x19 + m41*x20 + m48*x21;
460 	  x[20] -= m7*x15 + m14*x16 + m21*x17 + m28*x18 + m35*x19 + m42*x20 + m49*x21;
461 
462 	  x[21] -= m1*x22 + m8*x23  + m15*x24 + m22*x25 + m29*x26 + m36*x27 + m43*x28;
463 	  x[22] -= m2*x22 + m9*x23  + m16*x24 + m23*x25 + m30*x26 + m37*x27 + m44*x28;
464 	  x[23] -= m3*x22 + m10*x23 + m17*x24 + m24*x25 + m31*x26 + m38*x27 + m45*x28;
465 	  x[24] -= m4*x22 + m11*x23 + m18*x24 + m25*x25 + m32*x26 + m39*x27 + m46*x28;
466 	  x[25] -= m5*x22 + m12*x23 + m19*x24 + m26*x25 + m33*x26 + m40*x27 + m47*x28;
467 	  x[26] -= m6*x22 + m13*x23 + m20*x24 + m27*x25 + m34*x26 + m41*x27 + m48*x28;
468 	  x[27] -= m7*x22 + m14*x23 + m21*x24 + m28*x25 + m35*x26 + m42*x27 + m49*x28;
469 
470 	  x[28] -= m1*x29 + m8*x30  + m15*x31 + m22*x32 + m29*x33 + m36*x34 + m43*x35;
471 	  x[29] -= m2*x29 + m9*x30  + m16*x31 + m23*x32 + m30*x33 + m37*x34 + m44*x35;
472 	  x[30] -= m3*x29 + m10*x30 + m17*x31 + m24*x32 + m31*x33 + m38*x34 + m45*x35;
473 	  x[31] -= m4*x29 + m11*x30 + m18*x31 + m25*x32 + m32*x33 + m39*x34 + m46*x35;
474 	  x[32] -= m5*x29 + m12*x30 + m19*x31 + m26*x32 + m33*x33 + m40*x34 + m47*x35;
475 	  x[33] -= m6*x29 + m13*x30 + m20*x31 + m27*x32 + m34*x33 + m41*x34 + m48*x35;
476 	  x[34] -= m7*x29 + m14*x30 + m21*x31 + m28*x32 + m35*x33 + m42*x34 + m49*x35;
477 
478 	  x[35] -= m1*x36 + m8*x37  + m15*x38 + m22*x39 + m29*x40 + m36*x41 + m43*x42;
479 	  x[36] -= m2*x36 + m9*x37  + m16*x38 + m23*x39 + m30*x40 + m37*x41 + m44*x42;
480 	  x[37] -= m3*x36 + m10*x37 + m17*x38 + m24*x39 + m31*x40 + m38*x41 + m45*x42;
481 	  x[38] -= m4*x36 + m11*x37 + m18*x38 + m25*x39 + m32*x40 + m39*x41 + m46*x42;
482 	  x[39] -= m5*x36 + m12*x37 + m19*x38 + m26*x39 + m33*x40 + m40*x41 + m47*x42;
483 	  x[40] -= m6*x36 + m13*x37 + m20*x38 + m27*x39 + m34*x40 + m41*x41 + m48*x42;
484 	  x[41] -= m7*x36 + m14*x37 + m21*x38 + m28*x39 + m35*x40 + m42*x41 + m49*x42;
485 
486 	  x[42] -= m1*x43 + m8*x44  + m15*x45 + m22*x46 + m29*x47 + m36*x48 + m43*x49;
487 	  x[43] -= m2*x43 + m9*x44  + m16*x45 + m23*x46 + m30*x47 + m37*x48 + m44*x49;
488 	  x[44] -= m3*x43 + m10*x44 + m17*x45 + m24*x46 + m31*x47 + m38*x48 + m45*x49;
489 	  x[45] -= m4*x43 + m11*x44 + m18*x45 + m25*x46 + m32*x47 + m39*x48 + m46*x49;
490 	  x[46] -= m5*x43 + m12*x44 + m19*x45 + m26*x46 + m33*x47 + m40*x48 + m47*x49;
491 	  x[47] -= m6*x43 + m13*x44 + m20*x45 + m27*x46 + m34*x47 + m41*x48 + m48*x49;
492 	  x[48] -= m7*x43 + m14*x44 + m21*x45 + m28*x46 + m35*x47 + m42*x48 + m49*x49;
493           pv   += 49;
494         }
495         PLogFlops(686*nz+637);
496       }
497       row = *ajtmp++;
498     }
499     /* finished row so stick it into b->a */
500     pv = ba + 49*bi[i];
501     pj = bj + bi[i];
502     nz = bi[i+1] - bi[i];
503     for (j=0; j<nz; j++) {
504       x      = rtmp+49*pj[j];
505       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
506       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7];
507       pv[8]  = x[8];  pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11];
508       pv[12] = x[12]; pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
509       pv[16] = x[16]; pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19];
510       pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23];
511       pv[24] = x[24]; pv[25] = x[25]; pv[26] = x[26]; pv[27] = x[27];
512       pv[28] = x[28]; pv[29] = x[29]; pv[30] = x[30]; pv[31] = x[31];
513       pv[32] = x[32]; pv[33] = x[33]; pv[34] = x[34]; pv[35] = x[35];
514       pv[36] = x[36]; pv[37] = x[37]; pv[38] = x[38]; pv[39] = x[39];
515       pv[40] = x[40]; pv[41] = x[41]; pv[42] = x[42]; pv[43] = x[43];
516       pv[44] = x[44]; pv[45] = x[45]; pv[46] = x[46]; pv[47] = x[47];
517       pv[48] = x[48];
518       pv   += 49;
519     }
520     /* invert diagonal block */
521     w = ba + 49*diag_offset[i];
522     ierr = Kernel_A_gets_inverse_A_7(w);CHKERRQ(ierr);
523   }
524 
525   ierr = PetscFree(rtmp);CHKERRQ(ierr);
526   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
527   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
528   C->factor = FACTOR_LU;
529   C->assembled = PETSC_TRUE;
530   PLogFlops(1.3333*343*b->mbs); /* from inverting diagonal blocks */
531   PetscFunctionReturn(0);
532 }
533 
534 /*
535       Version for when blocks are 7 by 7 Using natural ordering
536 */
537 #undef __FUNC__
538 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_7_NaturalOrdering"
539 int MatCholeskyFactorNumeric_SeqSBAIJ_7_NaturalOrdering(Mat A,Mat *B)
540 {
541   Mat          C = *B;
542   Mat_SeqBAIJ  *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
543   int          ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
544   int          *ajtmpold,*ajtmp,nz,row;
545   int          *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
546   MatScalar    *pv,*v,*rtmp,*pc,*w,*x;
547   MatScalar    x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15;
548   MatScalar    x16,x17,x18,x19,x20,x21,x22,x23,x24,x25;
549   MatScalar    p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15;
550   MatScalar    p16,p17,p18,p19,p20,p21,p22,p23,p24,p25;
551   MatScalar    m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12,m13,m14,m15;
552   MatScalar    m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
553   MatScalar    p26,p27,p28,p29,p30,p31,p32,p33,p34,p35,p36;
554   MatScalar    p37,p38,p39,p40,p41,p42,p43,p44,p45,p46,p47,p48,p49;
555   MatScalar    x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36;
556   MatScalar    x37,x38,x39,x40,x41,x42,x43,x44,x45,x46,x47,x48,x49;
557   MatScalar    m26,m27,m28,m29,m30,m31,m32,m33,m34,m35,m36;
558   MatScalar    m37,m38,m39,m40,m41,m42,m43,m44,m45,m46,m47,m48,m49;
559   MatScalar    *ba = b->a,*aa = a->a;
560 
561   PetscFunctionBegin;
562   rtmp  = (MatScalar*)PetscMalloc(49*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
563   for (i=0; i<n; i++) {
564     nz    = bi[i+1] - bi[i];
565     ajtmp = bj + bi[i];
566     for  (j=0; j<nz; j++) {
567       x = rtmp+49*ajtmp[j];
568       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
569       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
570       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = x[25] = 0.0 ;
571       x[26] = x[27] = x[28] = x[29] = x[30] = x[31] = x[32] = x[33] = 0.0 ;
572       x[34] = x[35] = x[36] = x[37] = x[38] = x[39] = x[40] = x[41] = 0.0 ;
573       x[42] = x[43] = x[44] = x[45] = x[46] = x[47] = x[48] = 0.0 ;
574     }
575     /* load in initial (unfactored row) */
576     nz       = ai[i+1] - ai[i];
577     ajtmpold = aj + ai[i];
578     v        = aa + 49*ai[i];
579     for (j=0; j<nz; j++) {
580       x    = rtmp+49*ajtmpold[j];
581       x[0] =  v[0];  x[1] =  v[1];  x[2] =  v[2];  x[3] =  v[3];
582       x[4] =  v[4];  x[5] =  v[5];  x[6] =  v[6];  x[7] =  v[7];
583       x[8] =  v[8];  x[9] =  v[9];  x[10] = v[10]; x[11] = v[11];
584       x[12] = v[12]; x[13] = v[13]; x[14] = v[14]; x[15] = v[15];
585       x[16] = v[16]; x[17] = v[17]; x[18] = v[18]; x[19] = v[19];
586       x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23];
587       x[24] = v[24]; x[25] = v[25]; x[26] = v[26]; x[27] = v[27];
588       x[28] = v[28]; x[29] = v[29]; x[30] = v[30]; x[31] = v[31];
589       x[32] = v[32]; x[33] = v[33]; x[34] = v[34]; x[35] = v[35];
590       x[36] = v[36]; x[37] = v[37]; x[38] = v[38]; x[39] = v[39];
591       x[40] = v[40]; x[41] = v[41]; x[42] = v[42]; x[43] = v[43];
592       x[44] = v[44]; x[45] = v[45]; x[46] = v[46]; x[47] = v[47];
593       x[48] = v[48];
594       v    += 49;
595     }
596     row = *ajtmp++;
597     while (row < i) {
598       pc  = rtmp + 49*row;
599       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
600       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];
601       p9  = pc[8];  p10 = pc[9];  p11 = pc[10]; p12 = pc[11];
602       p13 = pc[12]; p14 = pc[13]; p15 = pc[14]; p16 = pc[15];
603       p17 = pc[16]; p18 = pc[17]; p19 = pc[18]; p20 = pc[19];
604       p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
605       p25 = pc[24]; p26 = pc[25]; p27 = pc[26]; p28 = pc[27];
606       p29 = pc[28]; p30 = pc[29]; p31 = pc[30]; p32 = pc[31];
607       p33 = pc[32]; p34 = pc[33]; p35 = pc[34]; p36 = pc[35];
608       p37 = pc[36]; p38 = pc[37]; p39 = pc[38]; p40 = pc[39];
609       p41 = pc[40]; p42 = pc[41]; p43 = pc[42]; p44 = pc[43];
610       p45 = pc[44]; p46 = pc[45]; p47 = pc[46]; p48 = pc[47];
611       p49 = pc[48];
612       if (p1  != 0.0 || p2  != 0.0 || p3  != 0.0 || p4  != 0.0 ||
613           p5  != 0.0 || p6  != 0.0 || p7  != 0.0 || p8  != 0.0 ||
614           p9  != 0.0 || p10 != 0.0 || p11 != 0.0 || p12 != 0.0 ||
615           p13 != 0.0 || p14 != 0.0 || p15 != 0.0 || p16 != 0.0 ||
616           p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 ||
617           p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 ||
618           p25 != 0.0 || p26 != 0.0 || p27 != 0.0 || p28 != 0.0 ||
619           p29 != 0.0 || p30 != 0.0 || p31 != 0.0 || p32 != 0.0 ||
620           p33 != 0.0 || p34 != 0.0 || p35 != 0.0 || p36 != 0.0 ||
621           p37 != 0.0 || p38 != 0.0 || p39 != 0.0 || p40 != 0.0 ||
622           p41 != 0.0 || p42 != 0.0 || p43 != 0.0 || p44 != 0.0 ||
623           p45 != 0.0 || p46 != 0.0 || p47 != 0.0 || p48 != 0.0 ||
624           p49 != 0.0) {
625         pv = ba + 49*diag_offset[row];
626         pj = bj + diag_offset[row] + 1;
627 	x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
628 	x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
629 	x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
630 	x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
631 	x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
632 	x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
633 	x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
634 	x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
635 	x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
636 	x37 = pv[36]; x38 = pv[37]; x39 = pv[38]; x40 = pv[39];
637 	x41 = pv[40]; x42 = pv[41]; x43 = pv[42]; x44 = pv[43];
638 	x45 = pv[44]; x46 = pv[45]; x47 = pv[46]; x48 = pv[47];
639         x49 = pv[48];
640         pc[0]  = m1  = p1*x1  + p8*x2   + p15*x3  + p22*x4  + p29*x5  + p36*x6 + p43*x7;
641         pc[1]  = m2  = p2*x1  + p9*x2   + p16*x3  + p23*x4  + p30*x5  + p37*x6 + p44*x7;
642         pc[2]  = m3  = p3*x1  + p10*x2  + p17*x3  + p24*x4  + p31*x5  + p38*x6 + p45*x7;
643         pc[3]  = m4  = p4*x1  + p11*x2  + p18*x3  + p25*x4  + p32*x5  + p39*x6 + p46*x7;
644         pc[4]  = m5  = p5*x1  + p12*x2  + p19*x3  + p26*x4  + p33*x5  + p40*x6 + p47*x7;
645         pc[5]  = m6  = p6*x1  + p13*x2  + p20*x3  + p27*x4  + p34*x5  + p41*x6 + p48*x7;
646         pc[6]  = m7  = p7*x1  + p14*x2  + p21*x3  + p28*x4  + p35*x5  + p42*x6 + p49*x7;
647 
648         pc[7]  = m8  = p1*x8  + p8*x9   + p15*x10 + p22*x11 + p29*x12 + p36*x13 + p43*x14;
649         pc[8]  = m9  = p2*x8  + p9*x9   + p16*x10 + p23*x11 + p30*x12 + p37*x13 + p44*x14;
650         pc[9]  = m10 = p3*x8  + p10*x9  + p17*x10 + p24*x11 + p31*x12 + p38*x13 + p45*x14;
651         pc[10] = m11 = p4*x8  + p11*x9  + p18*x10 + p25*x11 + p32*x12 + p39*x13 + p46*x14;
652         pc[11] = m12 = p5*x8  + p12*x9  + p19*x10 + p26*x11 + p33*x12 + p40*x13 + p47*x14;
653         pc[12] = m13 = p6*x8  + p13*x9  + p20*x10 + p27*x11 + p34*x12 + p41*x13 + p48*x14;
654         pc[13] = m14 = p7*x8  + p14*x9  + p21*x10 + p28*x11 + p35*x12 + p42*x13 + p49*x14;
655 
656         pc[14] = m15 = p1*x15 + p8*x16  + p15*x17 + p22*x18 + p29*x19 + p36*x20 + p43*x21;
657         pc[15] = m16 = p2*x15 + p9*x16  + p16*x17 + p23*x18 + p30*x19 + p37*x20 + p44*x21;
658         pc[16] = m17 = p3*x15 + p10*x16 + p17*x17 + p24*x18 + p31*x19 + p38*x20 + p45*x21;
659         pc[17] = m18 = p4*x15 + p11*x16 + p18*x17 + p25*x18 + p32*x19 + p39*x20 + p46*x21;
660         pc[18] = m19 = p5*x15 + p12*x16 + p19*x17 + p26*x18 + p33*x19 + p40*x20 + p47*x21;
661         pc[19] = m20 = p6*x15 + p13*x16 + p20*x17 + p27*x18 + p34*x19 + p41*x20 + p48*x21;
662         pc[20] = m21 = p7*x15 + p14*x16 + p21*x17 + p28*x18 + p35*x19 + p42*x20 + p49*x21;
663 
664         pc[21] = m22 = p1*x22 + p8*x23  + p15*x24 + p22*x25 + p29*x26 + p36*x27 + p43*x28;
665         pc[22] = m23 = p2*x22 + p9*x23  + p16*x24 + p23*x25 + p30*x26 + p37*x27 + p44*x28;
666         pc[23] = m24 = p3*x22 + p10*x23 + p17*x24 + p24*x25 + p31*x26 + p38*x27 + p45*x28;
667         pc[24] = m25 = p4*x22 + p11*x23 + p18*x24 + p25*x25 + p32*x26 + p39*x27 + p46*x28;
668         pc[25] = m26 = p5*x22 + p12*x23 + p19*x24 + p26*x25 + p33*x26 + p40*x27 + p47*x28;
669         pc[26] = m27 = p6*x22 + p13*x23 + p20*x24 + p27*x25 + p34*x26 + p41*x27 + p48*x28;
670         pc[27] = m28 = p7*x22 + p14*x23 + p21*x24 + p28*x25 + p35*x26 + p42*x27 + p49*x28;
671 
672         pc[28] = m29 = p1*x29 + p8*x30  + p15*x31 + p22*x32 + p29*x33 + p36*x34 + p43*x35;
673         pc[29] = m30 = p2*x29 + p9*x30  + p16*x31 + p23*x32 + p30*x33 + p37*x34 + p44*x35;
674         pc[30] = m31 = p3*x29 + p10*x30 + p17*x31 + p24*x32 + p31*x33 + p38*x34 + p45*x35;
675         pc[31] = m32 = p4*x29 + p11*x30 + p18*x31 + p25*x32 + p32*x33 + p39*x34 + p46*x35;
676         pc[32] = m33 = p5*x29 + p12*x30 + p19*x31 + p26*x32 + p33*x33 + p40*x34 + p47*x35;
677         pc[33] = m34 = p6*x29 + p13*x30 + p20*x31 + p27*x32 + p34*x33 + p41*x34 + p48*x35;
678         pc[34] = m35 = p7*x29 + p14*x30 + p21*x31 + p28*x32 + p35*x33 + p42*x34 + p49*x35;
679 
680         pc[35] = m36 = p1*x36 + p8*x37  + p15*x38 + p22*x39 + p29*x40 + p36*x41 + p43*x42;
681         pc[36] = m37 = p2*x36 + p9*x37  + p16*x38 + p23*x39 + p30*x40 + p37*x41 + p44*x42;
682         pc[37] = m38 = p3*x36 + p10*x37 + p17*x38 + p24*x39 + p31*x40 + p38*x41 + p45*x42;
683         pc[38] = m39 = p4*x36 + p11*x37 + p18*x38 + p25*x39 + p32*x40 + p39*x41 + p46*x42;
684         pc[39] = m40 = p5*x36 + p12*x37 + p19*x38 + p26*x39 + p33*x40 + p40*x41 + p47*x42;
685         pc[40] = m41 = p6*x36 + p13*x37 + p20*x38 + p27*x39 + p34*x40 + p41*x41 + p48*x42;
686         pc[41] = m42 = p7*x36 + p14*x37 + p21*x38 + p28*x39 + p35*x40 + p42*x41 + p49*x42;
687 
688         pc[42] = m43 = p1*x43 + p8*x44  + p15*x45 + p22*x46 + p29*x47 + p36*x48 + p43*x49;
689         pc[43] = m44 = p2*x43 + p9*x44  + p16*x45 + p23*x46 + p30*x47 + p37*x48 + p44*x49;
690         pc[44] = m45 = p3*x43 + p10*x44 + p17*x45 + p24*x46 + p31*x47 + p38*x48 + p45*x49;
691         pc[45] = m46 = p4*x43 + p11*x44 + p18*x45 + p25*x46 + p32*x47 + p39*x48 + p46*x49;
692         pc[46] = m47 = p5*x43 + p12*x44 + p19*x45 + p26*x46 + p33*x47 + p40*x48 + p47*x49;
693         pc[47] = m48 = p6*x43 + p13*x44 + p20*x45 + p27*x46 + p34*x47 + p41*x48 + p48*x49;
694         pc[48] = m49 = p7*x43 + p14*x44 + p21*x45 + p28*x46 + p35*x47 + p42*x48 + p49*x49;
695 
696         nz = bi[row+1] - diag_offset[row] - 1;
697         pv += 49;
698         for (j=0; j<nz; j++) {
699 	  x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
700 	  x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
701 	  x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
702 	  x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
703 	  x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
704 	  x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
705 	  x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
706 	  x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
707 	  x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
708 	  x37 = pv[36]; x38 = pv[37]; x39 = pv[38]; x40 = pv[39];
709 	  x41 = pv[40]; x42 = pv[41]; x43 = pv[42]; x44 = pv[43];
710 	  x45 = pv[44]; x46 = pv[45]; x47 = pv[46]; x48 = pv[47];
711 	  x49 = pv[48];
712 	  x    = rtmp + 49*pj[j];
713 	  x[0]  -= m1*x1  + m8*x2   + m15*x3  + m22*x4  + m29*x5  + m36*x6 + m43*x7;
714 	  x[1]  -= m2*x1  + m9*x2   + m16*x3  + m23*x4  + m30*x5  + m37*x6 + m44*x7;
715 	  x[2]  -= m3*x1  + m10*x2  + m17*x3  + m24*x4  + m31*x5  + m38*x6 + m45*x7;
716 	  x[3]  -= m4*x1  + m11*x2  + m18*x3  + m25*x4  + m32*x5  + m39*x6 + m46*x7;
717 	  x[4]  -= m5*x1  + m12*x2  + m19*x3  + m26*x4  + m33*x5  + m40*x6 + m47*x7;
718 	  x[5]  -= m6*x1  + m13*x2  + m20*x3  + m27*x4  + m34*x5  + m41*x6 + m48*x7;
719 	  x[6]  -= m7*x1  + m14*x2  + m21*x3  + m28*x4  + m35*x5  + m42*x6 + m49*x7;
720 
721 	  x[7]  -= m1*x8  + m8*x9   + m15*x10 + m22*x11 + m29*x12 + m36*x13 + m43*x14;
722 	  x[8]  -= m2*x8  + m9*x9   + m16*x10 + m23*x11 + m30*x12 + m37*x13 + m44*x14;
723 	  x[9]  -= m3*x8  + m10*x9  + m17*x10 + m24*x11 + m31*x12 + m38*x13 + m45*x14;
724 	  x[10] -= m4*x8  + m11*x9  + m18*x10 + m25*x11 + m32*x12 + m39*x13 + m46*x14;
725 	  x[11] -= m5*x8  + m12*x9  + m19*x10 + m26*x11 + m33*x12 + m40*x13 + m47*x14;
726 	  x[12] -= m6*x8  + m13*x9  + m20*x10 + m27*x11 + m34*x12 + m41*x13 + m48*x14;
727 	  x[13] -= m7*x8  + m14*x9  + m21*x10 + m28*x11 + m35*x12 + m42*x13 + m49*x14;
728 
729 	  x[14] -= m1*x15 + m8*x16  + m15*x17 + m22*x18 + m29*x19 + m36*x20 + m43*x21;
730 	  x[15] -= m2*x15 + m9*x16  + m16*x17 + m23*x18 + m30*x19 + m37*x20 + m44*x21;
731 	  x[16] -= m3*x15 + m10*x16 + m17*x17 + m24*x18 + m31*x19 + m38*x20 + m45*x21;
732 	  x[17] -= m4*x15 + m11*x16 + m18*x17 + m25*x18 + m32*x19 + m39*x20 + m46*x21;
733 	  x[18] -= m5*x15 + m12*x16 + m19*x17 + m26*x18 + m33*x19 + m40*x20 + m47*x21;
734 	  x[19] -= m6*x15 + m13*x16 + m20*x17 + m27*x18 + m34*x19 + m41*x20 + m48*x21;
735 	  x[20] -= m7*x15 + m14*x16 + m21*x17 + m28*x18 + m35*x19 + m42*x20 + m49*x21;
736 
737 	  x[21] -= m1*x22 + m8*x23  + m15*x24 + m22*x25 + m29*x26 + m36*x27 + m43*x28;
738 	  x[22] -= m2*x22 + m9*x23  + m16*x24 + m23*x25 + m30*x26 + m37*x27 + m44*x28;
739 	  x[23] -= m3*x22 + m10*x23 + m17*x24 + m24*x25 + m31*x26 + m38*x27 + m45*x28;
740 	  x[24] -= m4*x22 + m11*x23 + m18*x24 + m25*x25 + m32*x26 + m39*x27 + m46*x28;
741 	  x[25] -= m5*x22 + m12*x23 + m19*x24 + m26*x25 + m33*x26 + m40*x27 + m47*x28;
742 	  x[26] -= m6*x22 + m13*x23 + m20*x24 + m27*x25 + m34*x26 + m41*x27 + m48*x28;
743 	  x[27] -= m7*x22 + m14*x23 + m21*x24 + m28*x25 + m35*x26 + m42*x27 + m49*x28;
744 
745 	  x[28] -= m1*x29 + m8*x30  + m15*x31 + m22*x32 + m29*x33 + m36*x34 + m43*x35;
746 	  x[29] -= m2*x29 + m9*x30  + m16*x31 + m23*x32 + m30*x33 + m37*x34 + m44*x35;
747 	  x[30] -= m3*x29 + m10*x30 + m17*x31 + m24*x32 + m31*x33 + m38*x34 + m45*x35;
748 	  x[31] -= m4*x29 + m11*x30 + m18*x31 + m25*x32 + m32*x33 + m39*x34 + m46*x35;
749 	  x[32] -= m5*x29 + m12*x30 + m19*x31 + m26*x32 + m33*x33 + m40*x34 + m47*x35;
750 	  x[33] -= m6*x29 + m13*x30 + m20*x31 + m27*x32 + m34*x33 + m41*x34 + m48*x35;
751 	  x[34] -= m7*x29 + m14*x30 + m21*x31 + m28*x32 + m35*x33 + m42*x34 + m49*x35;
752 
753 	  x[35] -= m1*x36 + m8*x37  + m15*x38 + m22*x39 + m29*x40 + m36*x41 + m43*x42;
754 	  x[36] -= m2*x36 + m9*x37  + m16*x38 + m23*x39 + m30*x40 + m37*x41 + m44*x42;
755 	  x[37] -= m3*x36 + m10*x37 + m17*x38 + m24*x39 + m31*x40 + m38*x41 + m45*x42;
756 	  x[38] -= m4*x36 + m11*x37 + m18*x38 + m25*x39 + m32*x40 + m39*x41 + m46*x42;
757 	  x[39] -= m5*x36 + m12*x37 + m19*x38 + m26*x39 + m33*x40 + m40*x41 + m47*x42;
758 	  x[40] -= m6*x36 + m13*x37 + m20*x38 + m27*x39 + m34*x40 + m41*x41 + m48*x42;
759 	  x[41] -= m7*x36 + m14*x37 + m21*x38 + m28*x39 + m35*x40 + m42*x41 + m49*x42;
760 
761 	  x[42] -= m1*x43 + m8*x44  + m15*x45 + m22*x46 + m29*x47 + m36*x48 + m43*x49;
762 	  x[43] -= m2*x43 + m9*x44  + m16*x45 + m23*x46 + m30*x47 + m37*x48 + m44*x49;
763 	  x[44] -= m3*x43 + m10*x44 + m17*x45 + m24*x46 + m31*x47 + m38*x48 + m45*x49;
764 	  x[45] -= m4*x43 + m11*x44 + m18*x45 + m25*x46 + m32*x47 + m39*x48 + m46*x49;
765 	  x[46] -= m5*x43 + m12*x44 + m19*x45 + m26*x46 + m33*x47 + m40*x48 + m47*x49;
766 	  x[47] -= m6*x43 + m13*x44 + m20*x45 + m27*x46 + m34*x47 + m41*x48 + m48*x49;
767 	  x[48] -= m7*x43 + m14*x44 + m21*x45 + m28*x46 + m35*x47 + m42*x48 + m49*x49;
768           pv   += 49;
769         }
770         PLogFlops(686*nz+637);
771       }
772       row = *ajtmp++;
773     }
774     /* finished row so stick it into b->a */
775     pv = ba + 49*bi[i];
776     pj = bj + bi[i];
777     nz = bi[i+1] - bi[i];
778     for (j=0; j<nz; j++) {
779       x      = rtmp+49*pj[j];
780       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
781       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7];
782       pv[8]  = x[8];  pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11];
783       pv[12] = x[12]; pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
784       pv[16] = x[16]; pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19];
785       pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23];
786       pv[24] = x[24]; pv[25] = x[25]; pv[26] = x[26]; pv[27] = x[27];
787       pv[28] = x[28]; pv[29] = x[29]; pv[30] = x[30]; pv[31] = x[31];
788       pv[32] = x[32]; pv[33] = x[33]; pv[34] = x[34]; pv[35] = x[35];
789       pv[36] = x[36]; pv[37] = x[37]; pv[38] = x[38]; pv[39] = x[39];
790       pv[40] = x[40]; pv[41] = x[41]; pv[42] = x[42]; pv[43] = x[43];
791       pv[44] = x[44]; pv[45] = x[45]; pv[46] = x[46]; pv[47] = x[47];
792       pv[48] = x[48];
793       pv   += 49;
794     }
795     /* invert diagonal block */
796     w = ba + 49*diag_offset[i];
797     ierr = Kernel_A_gets_inverse_A_7(w);CHKERRQ(ierr);
798   }
799 
800   ierr = PetscFree(rtmp);CHKERRQ(ierr);
801   C->factor    = FACTOR_LU;
802   C->assembled = PETSC_TRUE;
803   PLogFlops(1.3333*343*b->mbs); /* from inverting diagonal blocks */
804   PetscFunctionReturn(0);
805 }
806 
807 /* ------------------------------------------------------------*/
808 /*
809       Version for when blocks are 6 by 6
810 */
811 #undef __FUNC__
812 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_6"
813 int MatCholeskyFactorNumeric_SeqSBAIJ_6(Mat A,Mat *B)
814 {
815   Mat          C = *B;
816   Mat_SeqBAIJ  *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
817   IS           isrow = b->row,isicol = b->icol;
818   int          *r,*ic,ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
819   int          *ajtmpold,*ajtmp,nz,row;
820   int          *diag_offset = b->diag,idx,*ai=a->i,*aj=a->j,*pj;
821   MatScalar    *pv,*v,*rtmp,*pc,*w,*x;
822   MatScalar    p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
823   MatScalar    p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
824   MatScalar    x17,x18,x19,x20,x21,x22,x23,x24,x25,p10,p11,p12,p13,p14;
825   MatScalar    p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,m10,m11,m12;
826   MatScalar    m13,m14,m15,m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
827   MatScalar    p26,p27,p28,p29,p30,p31,p32,p33,p34,p35,p36;
828   MatScalar    x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36;
829   MatScalar    m26,m27,m28,m29,m30,m31,m32,m33,m34,m35,m36;
830   MatScalar    *ba = b->a,*aa = a->a;
831 
832   PetscFunctionBegin;
833   ierr  = ISGetIndices(isrow,&r);CHKERRQ(ierr);
834   ierr  = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
835   rtmp  = (MatScalar*)PetscMalloc(36*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
836 
837   for (i=0; i<n; i++) {
838     nz    = bi[i+1] - bi[i];
839     ajtmp = bj + bi[i];
840     for  (j=0; j<nz; j++) {
841       x = rtmp+36*ajtmp[j];
842       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
843       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
844       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = x[25] = 0.0 ;
845       x[26] = x[27] = x[28] = x[29] = x[30] = x[31] = x[32] = x[33] = 0.0 ;
846       x[34] = x[35] = 0.0 ;
847     }
848     /* load in initial (unfactored row) */
849     idx      = r[i];
850     nz       = ai[idx+1] - ai[idx];
851     ajtmpold = aj + ai[idx];
852     v        = aa + 36*ai[idx];
853     for (j=0; j<nz; j++) {
854       x    = rtmp+36*ic[ajtmpold[j]];
855       x[0] =  v[0];  x[1] =  v[1];  x[2] =  v[2];  x[3] =  v[3];
856       x[4] =  v[4];  x[5] =  v[5];  x[6] =  v[6];  x[7] =  v[7];
857       x[8] =  v[8];  x[9] =  v[9];  x[10] = v[10]; x[11] = v[11];
858       x[12] = v[12]; x[13] = v[13]; x[14] = v[14]; x[15] = v[15];
859       x[16] = v[16]; x[17] = v[17]; x[18] = v[18]; x[19] = v[19];
860       x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23];
861       x[24] = v[24]; x[25] = v[25]; x[26] = v[26]; x[27] = v[27];
862       x[28] = v[28]; x[29] = v[29]; x[30] = v[30]; x[31] = v[31];
863       x[32] = v[32]; x[33] = v[33]; x[34] = v[34]; x[35] = v[35];
864       v    += 36;
865     }
866     row = *ajtmp++;
867     while (row < i) {
868       pc  =  rtmp + 36*row;
869       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
870       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];
871       p9  = pc[8];  p10 = pc[9];  p11 = pc[10]; p12 = pc[11];
872       p13 = pc[12]; p14 = pc[13]; p15 = pc[14]; p16 = pc[15];
873       p17 = pc[16]; p18 = pc[17]; p19 = pc[18]; p20 = pc[19];
874       p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
875       p25 = pc[24]; p26 = pc[25]; p27 = pc[26]; p28 = pc[27];
876       p29 = pc[28]; p30 = pc[29]; p31 = pc[30]; p32 = pc[31];
877       p33 = pc[32]; p34 = pc[33]; p35 = pc[34]; p36 = pc[35];
878       if (p1  != 0.0 || p2  != 0.0 || p3  != 0.0 || p4  != 0.0 ||
879           p5  != 0.0 || p6  != 0.0 || p7  != 0.0 || p8  != 0.0 ||
880           p9  != 0.0 || p10 != 0.0 || p11 != 0.0 || p12 != 0.0 ||
881           p13 != 0.0 || p14 != 0.0 || p15 != 0.0 || p16 != 0.0 ||
882           p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 ||
883           p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 ||
884           p25 != 0.0 || p26 != 0.0 || p27 != 0.0 || p28 != 0.0 ||
885           p29 != 0.0 || p30 != 0.0 || p31 != 0.0 || p32 != 0.0 ||
886           p33 != 0.0 || p34 != 0.0 || p35 != 0.0 || p36 != 0.0) {
887         pv = ba + 36*diag_offset[row];
888         pj = bj + diag_offset[row] + 1;
889 	x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
890 	x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
891 	x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
892 	x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
893 	x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
894 	x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
895 	x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
896 	x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
897 	x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
898         pc[0]  = m1  = p1*x1  + p7*x2   + p13*x3  + p19*x4  + p25*x5  + p31*x6;
899         pc[1]  = m2  = p2*x1  + p8*x2   + p14*x3  + p20*x4  + p26*x5  + p32*x6;
900         pc[2]  = m3  = p3*x1  + p9*x2   + p15*x3  + p21*x4  + p27*x5  + p33*x6;
901         pc[3]  = m4  = p4*x1  + p10*x2  + p16*x3  + p22*x4  + p28*x5  + p34*x6;
902         pc[4]  = m5  = p5*x1  + p11*x2  + p17*x3  + p23*x4  + p29*x5  + p35*x6;
903         pc[5]  = m6  = p6*x1  + p12*x2  + p18*x3  + p24*x4  + p30*x5  + p36*x6;
904 
905         pc[6]  = m7  = p1*x7  + p7*x8   + p13*x9  + p19*x10 + p25*x11 + p31*x12;
906         pc[7]  = m8  = p2*x7  + p8*x8   + p14*x9  + p20*x10 + p26*x11 + p32*x12;
907         pc[8]  = m9  = p3*x7  + p9*x8   + p15*x9  + p21*x10 + p27*x11 + p33*x12;
908         pc[9]  = m10 = p4*x7  + p10*x8  + p16*x9  + p22*x10 + p28*x11 + p34*x12;
909         pc[10] = m11 = p5*x7  + p11*x8  + p17*x9  + p23*x10 + p29*x11 + p35*x12;
910         pc[11] = m12 = p6*x7  + p12*x8  + p18*x9  + p24*x10 + p30*x11 + p36*x12;
911 
912         pc[12] = m13 = p1*x13 + p7*x14  + p13*x15 + p19*x16 + p25*x17 + p31*x18;
913         pc[13] = m14 = p2*x13 + p8*x14  + p14*x15 + p20*x16 + p26*x17 + p32*x18;
914         pc[14] = m15 = p3*x13 + p9*x14  + p15*x15 + p21*x16 + p27*x17 + p33*x18;
915         pc[15] = m16 = p4*x13 + p10*x14 + p16*x15 + p22*x16 + p28*x17 + p34*x18;
916         pc[16] = m17 = p5*x13 + p11*x14 + p17*x15 + p23*x16 + p29*x17 + p35*x18;
917         pc[17] = m18 = p6*x13 + p12*x14 + p18*x15 + p24*x16 + p30*x17 + p36*x18;
918 
919         pc[18] = m19 = p1*x19 + p7*x20  + p13*x21 + p19*x22 + p25*x23 + p31*x24;
920         pc[19] = m20 = p2*x19 + p8*x20  + p14*x21 + p20*x22 + p26*x23 + p32*x24;
921         pc[20] = m21 = p3*x19 + p9*x20  + p15*x21 + p21*x22 + p27*x23 + p33*x24;
922         pc[21] = m22 = p4*x19 + p10*x20 + p16*x21 + p22*x22 + p28*x23 + p34*x24;
923         pc[22] = m23 = p5*x19 + p11*x20 + p17*x21 + p23*x22 + p29*x23 + p35*x24;
924         pc[23] = m24 = p6*x19 + p12*x20 + p18*x21 + p24*x22 + p30*x23 + p36*x24;
925 
926         pc[24] = m25 = p1*x25 + p7*x26  + p13*x27 + p19*x28 + p25*x29 + p31*x30;
927         pc[25] = m26 = p2*x25 + p8*x26  + p14*x27 + p20*x28 + p26*x29 + p32*x30;
928         pc[26] = m27 = p3*x25 + p9*x26  + p15*x27 + p21*x28 + p27*x29 + p33*x30;
929         pc[27] = m28 = p4*x25 + p10*x26 + p16*x27 + p22*x28 + p28*x29 + p34*x30;
930         pc[28] = m29 = p5*x25 + p11*x26 + p17*x27 + p23*x28 + p29*x29 + p35*x30;
931         pc[29] = m30 = p6*x25 + p12*x26 + p18*x27 + p24*x28 + p30*x29 + p36*x30;
932 
933         pc[30] = m31 = p1*x31 + p7*x32  + p13*x33 + p19*x34 + p25*x35 + p31*x36;
934         pc[31] = m32 = p2*x31 + p8*x32  + p14*x33 + p20*x34 + p26*x35 + p32*x36;
935         pc[32] = m33 = p3*x31 + p9*x32  + p15*x33 + p21*x34 + p27*x35 + p33*x36;
936         pc[33] = m34 = p4*x31 + p10*x32 + p16*x33 + p22*x34 + p28*x35 + p34*x36;
937         pc[34] = m35 = p5*x31 + p11*x32 + p17*x33 + p23*x34 + p29*x35 + p35*x36;
938         pc[35] = m36 = p6*x31 + p12*x32 + p18*x33 + p24*x34 + p30*x35 + p36*x36;
939 
940         nz = bi[row+1] - diag_offset[row] - 1;
941         pv += 36;
942         for (j=0; j<nz; j++) {
943 	  x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
944 	  x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
945 	  x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
946 	  x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
947 	  x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
948 	  x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
949 	  x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
950 	  x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
951 	  x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
952 	  x    = rtmp + 36*pj[j];
953           x[0]  -= m1*x1  + m7*x2   + m13*x3  + m19*x4  + m25*x5  + m31*x6;
954           x[1]  -= m2*x1  + m8*x2   + m14*x3  + m20*x4  + m26*x5  + m32*x6;
955           x[2]  -= m3*x1  + m9*x2   + m15*x3  + m21*x4  + m27*x5  + m33*x6;
956           x[3]  -= m4*x1  + m10*x2  + m16*x3  + m22*x4  + m28*x5  + m34*x6;
957           x[4]  -= m5*x1  + m11*x2  + m17*x3  + m23*x4  + m29*x5  + m35*x6;
958           x[5]  -= m6*x1  + m12*x2  + m18*x3  + m24*x4  + m30*x5  + m36*x6;
959 
960 	  x[6]  -= m1*x7  + m7*x8   + m13*x9  + m19*x10 + m25*x11 + m31*x12;
961 	  x[7]  -= m2*x7  + m8*x8   + m14*x9  + m20*x10 + m26*x11 + m32*x12;
962 	  x[8]  -= m3*x7  + m9*x8   + m15*x9  + m21*x10 + m27*x11 + m33*x12;
963 	  x[9]  -= m4*x7  + m10*x8  + m16*x9  + m22*x10 + m28*x11 + m34*x12;
964 	  x[10] -= m5*x7  + m11*x8  + m17*x9  + m23*x10 + m29*x11 + m35*x12;
965 	  x[11] -= m6*x7  + m12*x8  + m18*x9  + m24*x10 + m30*x11 + m36*x12;
966 
967 	  x[12] -= m1*x13 + m7*x14  + m13*x15 + m19*x16 + m25*x17 + m31*x18;
968 	  x[13] -= m2*x13 + m8*x14  + m14*x15 + m20*x16 + m26*x17 + m32*x18;
969 	  x[14] -= m3*x13 + m9*x14  + m15*x15 + m21*x16 + m27*x17 + m33*x18;
970 	  x[15] -= m4*x13 + m10*x14 + m16*x15 + m22*x16 + m28*x17 + m34*x18;
971 	  x[16] -= m5*x13 + m11*x14 + m17*x15 + m23*x16 + m29*x17 + m35*x18;
972 	  x[17] -= m6*x13 + m12*x14 + m18*x15 + m24*x16 + m30*x17 + m36*x18;
973 
974 	  x[18] -= m1*x19 + m7*x20  + m13*x21 + m19*x22 + m25*x23 + m31*x24;
975 	  x[19] -= m2*x19 + m8*x20  + m14*x21 + m20*x22 + m26*x23 + m32*x24;
976 	  x[20] -= m3*x19 + m9*x20  + m15*x21 + m21*x22 + m27*x23 + m33*x24;
977 	  x[21] -= m4*x19 + m10*x20 + m16*x21 + m22*x22 + m28*x23 + m34*x24;
978 	  x[22] -= m5*x19 + m11*x20 + m17*x21 + m23*x22 + m29*x23 + m35*x24;
979 	  x[23] -= m6*x19 + m12*x20 + m18*x21 + m24*x22 + m30*x23 + m36*x24;
980 
981 	  x[24] -= m1*x25 + m7*x26  + m13*x27 + m19*x28 + m25*x29 + m31*x30;
982 	  x[25] -= m2*x25 + m8*x26  + m14*x27 + m20*x28 + m26*x29 + m32*x30;
983 	  x[26] -= m3*x25 + m9*x26  + m15*x27 + m21*x28 + m27*x29 + m33*x30;
984 	  x[27] -= m4*x25 + m10*x26 + m16*x27 + m22*x28 + m28*x29 + m34*x30;
985 	  x[28] -= m5*x25 + m11*x26 + m17*x27 + m23*x28 + m29*x29 + m35*x30;
986 	  x[29] -= m6*x25 + m12*x26 + m18*x27 + m24*x28 + m30*x29 + m36*x30;
987 
988 	  x[30] -= m1*x31 + m7*x32  + m13*x33 + m19*x34 + m25*x35 + m31*x36;
989 	  x[31] -= m2*x31 + m8*x32  + m14*x33 + m20*x34 + m26*x35 + m32*x36;
990 	  x[32] -= m3*x31 + m9*x32  + m15*x33 + m21*x34 + m27*x35 + m33*x36;
991 	  x[33] -= m4*x31 + m10*x32 + m16*x33 + m22*x34 + m28*x35 + m34*x36;
992 	  x[34] -= m5*x31 + m11*x32 + m17*x33 + m23*x34 + m29*x35 + m35*x36;
993 	  x[35] -= m6*x31 + m12*x32 + m18*x33 + m24*x34 + m30*x35 + m36*x36;
994 
995           pv   += 36;
996         }
997         PLogFlops(432*nz+396);
998       }
999       row = *ajtmp++;
1000     }
1001     /* finished row so stick it into b->a */
1002     pv = ba + 36*bi[i];
1003     pj = bj + bi[i];
1004     nz = bi[i+1] - bi[i];
1005     for (j=0; j<nz; j++) {
1006       x      = rtmp+36*pj[j];
1007       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
1008       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7];
1009       pv[8]  = x[8];  pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11];
1010       pv[12] = x[12]; pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
1011       pv[16] = x[16]; pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19];
1012       pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23];
1013       pv[24] = x[24]; pv[25] = x[25]; pv[26] = x[26]; pv[27] = x[27];
1014       pv[28] = x[28]; pv[29] = x[29]; pv[30] = x[30]; pv[31] = x[31];
1015       pv[32] = x[32]; pv[33] = x[33]; pv[34] = x[34]; pv[35] = x[35];
1016       pv   += 36;
1017     }
1018     /* invert diagonal block */
1019     w = ba + 36*diag_offset[i];
1020     ierr = Kernel_A_gets_inverse_A_6(w);CHKERRQ(ierr);
1021   }
1022 
1023   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1024   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
1025   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
1026   C->factor = FACTOR_LU;
1027   C->assembled = PETSC_TRUE;
1028   PLogFlops(1.3333*216*b->mbs); /* from inverting diagonal blocks */
1029   PetscFunctionReturn(0);
1030 }
1031 /*
1032       Version for when blocks are 6 by 6 Using natural ordering
1033 */
1034 #undef __FUNC__
1035 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_6_NaturalOrdering"
1036 int MatCholeskyFactorNumeric_SeqSBAIJ_6_NaturalOrdering(Mat A,Mat *B)
1037 {
1038   Mat         C = *B;
1039   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
1040   int         ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
1041   int         *ajtmpold,*ajtmp,nz,row;
1042   int         *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
1043   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
1044   MatScalar   x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15;
1045   MatScalar   x16,x17,x18,x19,x20,x21,x22,x23,x24,x25;
1046   MatScalar   p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15;
1047   MatScalar   p16,p17,p18,p19,p20,p21,p22,p23,p24,p25;
1048   MatScalar   m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12,m13,m14,m15;
1049   MatScalar   m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
1050   MatScalar   p26,p27,p28,p29,p30,p31,p32,p33,p34,p35,p36;
1051   MatScalar   x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36;
1052   MatScalar   m26,m27,m28,m29,m30,m31,m32,m33,m34,m35,m36;
1053   MatScalar   *ba = b->a,*aa = a->a;
1054 
1055   PetscFunctionBegin;
1056   rtmp  = (MatScalar*)PetscMalloc(36*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
1057   for (i=0; i<n; i++) {
1058     nz    = bi[i+1] - bi[i];
1059     ajtmp = bj + bi[i];
1060     for  (j=0; j<nz; j++) {
1061       x = rtmp+36*ajtmp[j];
1062       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
1063       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
1064       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = x[25] = 0.0 ;
1065       x[26] = x[27] = x[28] = x[29] = x[30] = x[31] = x[32] = x[33] = 0.0 ;
1066       x[34] = x[35] = 0.0 ;
1067     }
1068     /* load in initial (unfactored row) */
1069     nz       = ai[i+1] - ai[i];
1070     ajtmpold = aj + ai[i];
1071     v        = aa + 36*ai[i];
1072     for (j=0; j<nz; j++) {
1073       x    = rtmp+36*ajtmpold[j];
1074       x[0] =  v[0];  x[1] =  v[1];  x[2] =  v[2];  x[3] =  v[3];
1075       x[4] =  v[4];  x[5] =  v[5];  x[6] =  v[6];  x[7] =  v[7];
1076       x[8] =  v[8];  x[9] =  v[9];  x[10] = v[10]; x[11] = v[11];
1077       x[12] = v[12]; x[13] = v[13]; x[14] = v[14]; x[15] = v[15];
1078       x[16] = v[16]; x[17] = v[17]; x[18] = v[18]; x[19] = v[19];
1079       x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23];
1080       x[24] = v[24]; x[25] = v[25]; x[26] = v[26]; x[27] = v[27];
1081       x[28] = v[28]; x[29] = v[29]; x[30] = v[30]; x[31] = v[31];
1082       x[32] = v[32]; x[33] = v[33]; x[34] = v[34]; x[35] = v[35];
1083       v    += 36;
1084     }
1085     row = *ajtmp++;
1086     while (row < i) {
1087       pc  = rtmp + 36*row;
1088       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
1089       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];
1090       p9  = pc[8];  p10 = pc[9];  p11 = pc[10]; p12 = pc[11];
1091       p13 = pc[12]; p14 = pc[13]; p15 = pc[14]; p16 = pc[15];
1092       p17 = pc[16]; p18 = pc[17]; p19 = pc[18]; p20 = pc[19];
1093       p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
1094       p25 = pc[24]; p26 = pc[25]; p27 = pc[26]; p28 = pc[27];
1095       p29 = pc[28]; p30 = pc[29]; p31 = pc[30]; p32 = pc[31];
1096       p33 = pc[32]; p34 = pc[33]; p35 = pc[34]; p36 = pc[35];
1097       if (p1  != 0.0 || p2  != 0.0 || p3  != 0.0 || p4  != 0.0 ||
1098           p5  != 0.0 || p6  != 0.0 || p7  != 0.0 || p8  != 0.0 ||
1099           p9  != 0.0 || p10 != 0.0 || p11 != 0.0 || p12 != 0.0 ||
1100           p13 != 0.0 || p14 != 0.0 || p15 != 0.0 || p16 != 0.0 ||
1101           p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 ||
1102           p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 ||
1103           p25 != 0.0 || p26 != 0.0 || p27 != 0.0 || p28 != 0.0 ||
1104           p29 != 0.0 || p30 != 0.0 || p31 != 0.0 || p32 != 0.0 ||
1105           p33 != 0.0 || p34 != 0.0 || p35 != 0.0 || p36 != 0.0) {
1106         pv = ba + 36*diag_offset[row];
1107         pj = bj + diag_offset[row] + 1;
1108 	x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
1109 	x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
1110 	x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
1111 	x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
1112 	x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
1113 	x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
1114 	x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
1115 	x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
1116 	x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
1117         pc[0]  = m1  = p1*x1  + p7*x2   + p13*x3  + p19*x4  + p25*x5  + p31*x6;
1118         pc[1]  = m2  = p2*x1  + p8*x2   + p14*x3  + p20*x4  + p26*x5  + p32*x6;
1119         pc[2]  = m3  = p3*x1  + p9*x2   + p15*x3  + p21*x4  + p27*x5  + p33*x6;
1120         pc[3]  = m4  = p4*x1  + p10*x2  + p16*x3  + p22*x4  + p28*x5  + p34*x6;
1121         pc[4]  = m5  = p5*x1  + p11*x2  + p17*x3  + p23*x4  + p29*x5  + p35*x6;
1122         pc[5]  = m6  = p6*x1  + p12*x2  + p18*x3  + p24*x4  + p30*x5  + p36*x6;
1123 
1124         pc[6]  = m7  = p1*x7  + p7*x8   + p13*x9  + p19*x10 + p25*x11 + p31*x12;
1125         pc[7]  = m8  = p2*x7  + p8*x8   + p14*x9  + p20*x10 + p26*x11 + p32*x12;
1126         pc[8]  = m9  = p3*x7  + p9*x8   + p15*x9  + p21*x10 + p27*x11 + p33*x12;
1127         pc[9]  = m10 = p4*x7  + p10*x8  + p16*x9  + p22*x10 + p28*x11 + p34*x12;
1128         pc[10] = m11 = p5*x7  + p11*x8  + p17*x9  + p23*x10 + p29*x11 + p35*x12;
1129         pc[11] = m12 = p6*x7  + p12*x8  + p18*x9  + p24*x10 + p30*x11 + p36*x12;
1130 
1131         pc[12] = m13 = p1*x13 + p7*x14  + p13*x15 + p19*x16 + p25*x17 + p31*x18;
1132         pc[13] = m14 = p2*x13 + p8*x14  + p14*x15 + p20*x16 + p26*x17 + p32*x18;
1133         pc[14] = m15 = p3*x13 + p9*x14  + p15*x15 + p21*x16 + p27*x17 + p33*x18;
1134         pc[15] = m16 = p4*x13 + p10*x14 + p16*x15 + p22*x16 + p28*x17 + p34*x18;
1135         pc[16] = m17 = p5*x13 + p11*x14 + p17*x15 + p23*x16 + p29*x17 + p35*x18;
1136         pc[17] = m18 = p6*x13 + p12*x14 + p18*x15 + p24*x16 + p30*x17 + p36*x18;
1137 
1138         pc[18] = m19 = p1*x19 + p7*x20  + p13*x21 + p19*x22 + p25*x23 + p31*x24;
1139         pc[19] = m20 = p2*x19 + p8*x20  + p14*x21 + p20*x22 + p26*x23 + p32*x24;
1140         pc[20] = m21 = p3*x19 + p9*x20  + p15*x21 + p21*x22 + p27*x23 + p33*x24;
1141         pc[21] = m22 = p4*x19 + p10*x20 + p16*x21 + p22*x22 + p28*x23 + p34*x24;
1142         pc[22] = m23 = p5*x19 + p11*x20 + p17*x21 + p23*x22 + p29*x23 + p35*x24;
1143         pc[23] = m24 = p6*x19 + p12*x20 + p18*x21 + p24*x22 + p30*x23 + p36*x24;
1144 
1145         pc[24] = m25 = p1*x25 + p7*x26  + p13*x27 + p19*x28 + p25*x29 + p31*x30;
1146         pc[25] = m26 = p2*x25 + p8*x26  + p14*x27 + p20*x28 + p26*x29 + p32*x30;
1147         pc[26] = m27 = p3*x25 + p9*x26  + p15*x27 + p21*x28 + p27*x29 + p33*x30;
1148         pc[27] = m28 = p4*x25 + p10*x26 + p16*x27 + p22*x28 + p28*x29 + p34*x30;
1149         pc[28] = m29 = p5*x25 + p11*x26 + p17*x27 + p23*x28 + p29*x29 + p35*x30;
1150         pc[29] = m30 = p6*x25 + p12*x26 + p18*x27 + p24*x28 + p30*x29 + p36*x30;
1151 
1152         pc[30] = m31 = p1*x31 + p7*x32  + p13*x33 + p19*x34 + p25*x35 + p31*x36;
1153         pc[31] = m32 = p2*x31 + p8*x32  + p14*x33 + p20*x34 + p26*x35 + p32*x36;
1154         pc[32] = m33 = p3*x31 + p9*x32  + p15*x33 + p21*x34 + p27*x35 + p33*x36;
1155         pc[33] = m34 = p4*x31 + p10*x32 + p16*x33 + p22*x34 + p28*x35 + p34*x36;
1156         pc[34] = m35 = p5*x31 + p11*x32 + p17*x33 + p23*x34 + p29*x35 + p35*x36;
1157         pc[35] = m36 = p6*x31 + p12*x32 + p18*x33 + p24*x34 + p30*x35 + p36*x36;
1158 
1159         nz = bi[row+1] - diag_offset[row] - 1;
1160         pv += 36;
1161         for (j=0; j<nz; j++) {
1162 	  x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
1163 	  x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
1164 	  x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
1165 	  x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
1166 	  x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
1167 	  x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
1168 	  x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
1169 	  x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
1170 	  x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
1171 	  x    = rtmp + 36*pj[j];
1172           x[0]  -= m1*x1  + m7*x2   + m13*x3  + m19*x4  + m25*x5  + m31*x6;
1173           x[1]  -= m2*x1  + m8*x2   + m14*x3  + m20*x4  + m26*x5  + m32*x6;
1174           x[2]  -= m3*x1  + m9*x2   + m15*x3  + m21*x4  + m27*x5  + m33*x6;
1175           x[3]  -= m4*x1  + m10*x2  + m16*x3  + m22*x4  + m28*x5  + m34*x6;
1176           x[4]  -= m5*x1  + m11*x2  + m17*x3  + m23*x4  + m29*x5  + m35*x6;
1177           x[5]  -= m6*x1  + m12*x2  + m18*x3  + m24*x4  + m30*x5  + m36*x6;
1178 
1179 	  x[6]  -= m1*x7  + m7*x8   + m13*x9  + m19*x10 + m25*x11 + m31*x12;
1180 	  x[7]  -= m2*x7  + m8*x8   + m14*x9  + m20*x10 + m26*x11 + m32*x12;
1181 	  x[8]  -= m3*x7  + m9*x8   + m15*x9  + m21*x10 + m27*x11 + m33*x12;
1182 	  x[9]  -= m4*x7  + m10*x8  + m16*x9  + m22*x10 + m28*x11 + m34*x12;
1183 	  x[10] -= m5*x7  + m11*x8  + m17*x9  + m23*x10 + m29*x11 + m35*x12;
1184 	  x[11] -= m6*x7  + m12*x8  + m18*x9  + m24*x10 + m30*x11 + m36*x12;
1185 
1186 	  x[12] -= m1*x13 + m7*x14  + m13*x15 + m19*x16 + m25*x17 + m31*x18;
1187 	  x[13] -= m2*x13 + m8*x14  + m14*x15 + m20*x16 + m26*x17 + m32*x18;
1188 	  x[14] -= m3*x13 + m9*x14  + m15*x15 + m21*x16 + m27*x17 + m33*x18;
1189 	  x[15] -= m4*x13 + m10*x14 + m16*x15 + m22*x16 + m28*x17 + m34*x18;
1190 	  x[16] -= m5*x13 + m11*x14 + m17*x15 + m23*x16 + m29*x17 + m35*x18;
1191 	  x[17] -= m6*x13 + m12*x14 + m18*x15 + m24*x16 + m30*x17 + m36*x18;
1192 
1193 	  x[18] -= m1*x19 + m7*x20  + m13*x21 + m19*x22 + m25*x23 + m31*x24;
1194 	  x[19] -= m2*x19 + m8*x20  + m14*x21 + m20*x22 + m26*x23 + m32*x24;
1195 	  x[20] -= m3*x19 + m9*x20  + m15*x21 + m21*x22 + m27*x23 + m33*x24;
1196 	  x[21] -= m4*x19 + m10*x20 + m16*x21 + m22*x22 + m28*x23 + m34*x24;
1197 	  x[22] -= m5*x19 + m11*x20 + m17*x21 + m23*x22 + m29*x23 + m35*x24;
1198 	  x[23] -= m6*x19 + m12*x20 + m18*x21 + m24*x22 + m30*x23 + m36*x24;
1199 
1200 	  x[24] -= m1*x25 + m7*x26  + m13*x27 + m19*x28 + m25*x29 + m31*x30;
1201 	  x[25] -= m2*x25 + m8*x26  + m14*x27 + m20*x28 + m26*x29 + m32*x30;
1202 	  x[26] -= m3*x25 + m9*x26  + m15*x27 + m21*x28 + m27*x29 + m33*x30;
1203 	  x[27] -= m4*x25 + m10*x26 + m16*x27 + m22*x28 + m28*x29 + m34*x30;
1204 	  x[28] -= m5*x25 + m11*x26 + m17*x27 + m23*x28 + m29*x29 + m35*x30;
1205 	  x[29] -= m6*x25 + m12*x26 + m18*x27 + m24*x28 + m30*x29 + m36*x30;
1206 
1207 	  x[30] -= m1*x31 + m7*x32  + m13*x33 + m19*x34 + m25*x35 + m31*x36;
1208 	  x[31] -= m2*x31 + m8*x32  + m14*x33 + m20*x34 + m26*x35 + m32*x36;
1209 	  x[32] -= m3*x31 + m9*x32  + m15*x33 + m21*x34 + m27*x35 + m33*x36;
1210 	  x[33] -= m4*x31 + m10*x32 + m16*x33 + m22*x34 + m28*x35 + m34*x36;
1211 	  x[34] -= m5*x31 + m11*x32 + m17*x33 + m23*x34 + m29*x35 + m35*x36;
1212 	  x[35] -= m6*x31 + m12*x32 + m18*x33 + m24*x34 + m30*x35 + m36*x36;
1213 
1214           pv   += 36;
1215         }
1216         PLogFlops(432*nz+396);
1217       }
1218       row = *ajtmp++;
1219     }
1220     /* finished row so stick it into b->a */
1221     pv = ba + 36*bi[i];
1222     pj = bj + bi[i];
1223     nz = bi[i+1] - bi[i];
1224     for (j=0; j<nz; j++) {
1225       x      = rtmp+36*pj[j];
1226       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
1227       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7];
1228       pv[8]  = x[8];  pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11];
1229       pv[12] = x[12]; pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
1230       pv[16] = x[16]; pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19];
1231       pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23];
1232       pv[24] = x[24]; pv[25] = x[25]; pv[26] = x[26]; pv[27] = x[27];
1233       pv[28] = x[28]; pv[29] = x[29]; pv[30] = x[30]; pv[31] = x[31];
1234       pv[32] = x[32]; pv[33] = x[33]; pv[34] = x[34]; pv[35] = x[35];
1235       pv   += 36;
1236     }
1237     /* invert diagonal block */
1238     w = ba + 36*diag_offset[i];
1239     ierr = Kernel_A_gets_inverse_A_6(w);CHKERRQ(ierr);
1240   }
1241 
1242   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1243   C->factor    = FACTOR_LU;
1244   C->assembled = PETSC_TRUE;
1245   PLogFlops(1.3333*216*b->mbs); /* from inverting diagonal blocks */
1246   PetscFunctionReturn(0);
1247 }
1248 
1249 /*
1250       Version for when blocks are 5 by 5
1251 */
1252 #undef __FUNC__
1253 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_5"
1254 int MatCholeskyFactorNumeric_SeqSBAIJ_5(Mat A,Mat *B)
1255 {
1256   Mat         C = *B;
1257   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
1258   IS          isrow = b->row,isicol = b->icol;
1259   int         *r,*ic,ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
1260   int         *ajtmpold,*ajtmp,nz,row;
1261   int         *diag_offset = b->diag,idx,*ai=a->i,*aj=a->j,*pj;
1262   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
1263   MatScalar   p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
1264   MatScalar   p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
1265   MatScalar   x17,x18,x19,x20,x21,x22,x23,x24,x25,p10,p11,p12,p13,p14;
1266   MatScalar   p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,m10,m11,m12;
1267   MatScalar   m13,m14,m15,m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
1268   MatScalar   *ba = b->a,*aa = a->a;
1269 
1270   PetscFunctionBegin;
1271   ierr  = ISGetIndices(isrow,&r);CHKERRQ(ierr);
1272   ierr  = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
1273   rtmp  = (MatScalar*)PetscMalloc(25*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
1274 
1275   for (i=0; i<n; i++) {
1276     nz    = bi[i+1] - bi[i];
1277     ajtmp = bj + bi[i];
1278     for  (j=0; j<nz; j++) {
1279       x = rtmp+25*ajtmp[j];
1280       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
1281       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
1282       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0;
1283     }
1284     /* load in initial (unfactored row) */
1285     idx      = r[i];
1286     nz       = ai[idx+1] - ai[idx];
1287     ajtmpold = aj + ai[idx];
1288     v        = aa + 25*ai[idx];
1289     for (j=0; j<nz; j++) {
1290       x    = rtmp+25*ic[ajtmpold[j]];
1291       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
1292       x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
1293       x[9] = v[9]; x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
1294       x[14] = v[14]; x[15] = v[15]; x[16] = v[16]; x[17] = v[17];
1295       x[18] = v[18]; x[19] = v[19]; x[20] = v[20]; x[21] = v[21];
1296       x[22] = v[22]; x[23] = v[23]; x[24] = v[24];
1297       v    += 25;
1298     }
1299     row = *ajtmp++;
1300     while (row < i) {
1301       pc = rtmp + 25*row;
1302       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
1303       p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
1304       p10 = pc[9]; p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
1305       p15 = pc[14]; p16 = pc[15]; p17 = pc[16]; p18 = pc[17]; p19 = pc[18];
1306       p20 = pc[19]; p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
1307       p25 = pc[24];
1308       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
1309           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
1310           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
1311           || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 ||
1312           p20 != 0.0 || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 ||
1313           p24 != 0.0 || p25 != 0.0) {
1314         pv = ba + 25*diag_offset[row];
1315         pj = bj + diag_offset[row] + 1;
1316         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
1317         x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
1318         x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
1319         x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17];
1320         x19 = pv[18]; x20 = pv[19]; x21 = pv[20]; x22 = pv[21];
1321         x23 = pv[22]; x24 = pv[23]; x25 = pv[24];
1322         pc[0] = m1 = p1*x1 + p6*x2  + p11*x3 + p16*x4 + p21*x5;
1323         pc[1] = m2 = p2*x1 + p7*x2  + p12*x3 + p17*x4 + p22*x5;
1324         pc[2] = m3 = p3*x1 + p8*x2  + p13*x3 + p18*x4 + p23*x5;
1325         pc[3] = m4 = p4*x1 + p9*x2  + p14*x3 + p19*x4 + p24*x5;
1326         pc[4] = m5 = p5*x1 + p10*x2 + p15*x3 + p20*x4 + p25*x5;
1327 
1328         pc[5] = m6 = p1*x6 + p6*x7  + p11*x8 + p16*x9 + p21*x10;
1329         pc[6] = m7 = p2*x6 + p7*x7  + p12*x8 + p17*x9 + p22*x10;
1330         pc[7] = m8 = p3*x6 + p8*x7  + p13*x8 + p18*x9 + p23*x10;
1331         pc[8] = m9 = p4*x6 + p9*x7  + p14*x8 + p19*x9 + p24*x10;
1332         pc[9] = m10 = p5*x6 + p10*x7 + p15*x8 + p20*x9 + p25*x10;
1333 
1334         pc[10] = m11 = p1*x11 + p6*x12  + p11*x13 + p16*x14 + p21*x15;
1335         pc[11] = m12 = p2*x11 + p7*x12  + p12*x13 + p17*x14 + p22*x15;
1336         pc[12] = m13 = p3*x11 + p8*x12  + p13*x13 + p18*x14 + p23*x15;
1337         pc[13] = m14 = p4*x11 + p9*x12  + p14*x13 + p19*x14 + p24*x15;
1338         pc[14] = m15 = p5*x11 + p10*x12 + p15*x13 + p20*x14 + p25*x15;
1339 
1340         pc[15] = m16 = p1*x16 + p6*x17  + p11*x18 + p16*x19 + p21*x20;
1341         pc[16] = m17 = p2*x16 + p7*x17  + p12*x18 + p17*x19 + p22*x20;
1342         pc[17] = m18 = p3*x16 + p8*x17  + p13*x18 + p18*x19 + p23*x20;
1343         pc[18] = m19 = p4*x16 + p9*x17  + p14*x18 + p19*x19 + p24*x20;
1344         pc[19] = m20 = p5*x16 + p10*x17 + p15*x18 + p20*x19 + p25*x20;
1345 
1346         pc[20] = m21 = p1*x21 + p6*x22  + p11*x23 + p16*x24 + p21*x25;
1347         pc[21] = m22 = p2*x21 + p7*x22  + p12*x23 + p17*x24 + p22*x25;
1348         pc[22] = m23 = p3*x21 + p8*x22  + p13*x23 + p18*x24 + p23*x25;
1349         pc[23] = m24 = p4*x21 + p9*x22  + p14*x23 + p19*x24 + p24*x25;
1350         pc[24] = m25 = p5*x21 + p10*x22 + p15*x23 + p20*x24 + p25*x25;
1351 
1352         nz = bi[row+1] - diag_offset[row] - 1;
1353         pv += 25;
1354         for (j=0; j<nz; j++) {
1355           x1   = pv[0];  x2 = pv[1];   x3  = pv[2];  x4  = pv[3];
1356           x5   = pv[4];  x6 = pv[5];   x7  = pv[6];  x8  = pv[7]; x9 = pv[8];
1357           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
1358           x14  = pv[13]; x15 = pv[14]; x16 = pv[15]; x17 = pv[16];
1359           x18  = pv[17]; x19 = pv[18]; x20 = pv[19]; x21 = pv[20];
1360           x22  = pv[21]; x23 = pv[22]; x24 = pv[23]; x25 = pv[24];
1361           x    = rtmp + 25*pj[j];
1362           x[0] -= m1*x1 + m6*x2  + m11*x3 + m16*x4 + m21*x5;
1363           x[1] -= m2*x1 + m7*x2  + m12*x3 + m17*x4 + m22*x5;
1364           x[2] -= m3*x1 + m8*x2  + m13*x3 + m18*x4 + m23*x5;
1365           x[3] -= m4*x1 + m9*x2  + m14*x3 + m19*x4 + m24*x5;
1366           x[4] -= m5*x1 + m10*x2 + m15*x3 + m20*x4 + m25*x5;
1367 
1368           x[5] -= m1*x6 + m6*x7  + m11*x8 + m16*x9 + m21*x10;
1369           x[6] -= m2*x6 + m7*x7  + m12*x8 + m17*x9 + m22*x10;
1370           x[7] -= m3*x6 + m8*x7  + m13*x8 + m18*x9 + m23*x10;
1371           x[8] -= m4*x6 + m9*x7  + m14*x8 + m19*x9 + m24*x10;
1372           x[9] -= m5*x6 + m10*x7 + m15*x8 + m20*x9 + m25*x10;
1373 
1374           x[10] -= m1*x11 + m6*x12  + m11*x13 + m16*x14 + m21*x15;
1375           x[11] -= m2*x11 + m7*x12  + m12*x13 + m17*x14 + m22*x15;
1376           x[12] -= m3*x11 + m8*x12  + m13*x13 + m18*x14 + m23*x15;
1377           x[13] -= m4*x11 + m9*x12  + m14*x13 + m19*x14 + m24*x15;
1378           x[14] -= m5*x11 + m10*x12 + m15*x13 + m20*x14 + m25*x15;
1379 
1380           x[15] -= m1*x16 + m6*x17  + m11*x18 + m16*x19 + m21*x20;
1381           x[16] -= m2*x16 + m7*x17  + m12*x18 + m17*x19 + m22*x20;
1382           x[17] -= m3*x16 + m8*x17  + m13*x18 + m18*x19 + m23*x20;
1383           x[18] -= m4*x16 + m9*x17  + m14*x18 + m19*x19 + m24*x20;
1384           x[19] -= m5*x16 + m10*x17 + m15*x18 + m20*x19 + m25*x20;
1385 
1386           x[20] -= m1*x21 + m6*x22  + m11*x23 + m16*x24 + m21*x25;
1387           x[21] -= m2*x21 + m7*x22  + m12*x23 + m17*x24 + m22*x25;
1388           x[22] -= m3*x21 + m8*x22  + m13*x23 + m18*x24 + m23*x25;
1389           x[23] -= m4*x21 + m9*x22  + m14*x23 + m19*x24 + m24*x25;
1390           x[24] -= m5*x21 + m10*x22 + m15*x23 + m20*x24 + m25*x25;
1391 
1392           pv   += 25;
1393         }
1394         PLogFlops(250*nz+225);
1395       }
1396       row = *ajtmp++;
1397     }
1398     /* finished row so stick it into b->a */
1399     pv = ba + 25*bi[i];
1400     pj = bj + bi[i];
1401     nz = bi[i+1] - bi[i];
1402     for (j=0; j<nz; j++) {
1403       x     = rtmp+25*pj[j];
1404       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
1405       pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
1406       pv[9] = x[9]; pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
1407       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; pv[16] = x[16];
1408       pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19]; pv[20] = x[20];
1409       pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23]; pv[24] = x[24];
1410       pv   += 25;
1411     }
1412     /* invert diagonal block */
1413     w = ba + 25*diag_offset[i];
1414     ierr = Kernel_A_gets_inverse_A_5(w);CHKERRQ(ierr);
1415   }
1416 
1417   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1418   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
1419   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
1420   C->factor = FACTOR_LU;
1421   C->assembled = PETSC_TRUE;
1422   PLogFlops(1.3333*125*b->mbs); /* from inverting diagonal blocks */
1423   PetscFunctionReturn(0);
1424 }
1425 /*
1426       Version for when blocks are 5 by 5 Using natural ordering
1427 */
1428 #undef __FUNC__
1429 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_5_NaturalOrdering"
1430 int MatCholeskyFactorNumeric_SeqSBAIJ_5_NaturalOrdering(Mat A,Mat *B)
1431 {
1432   Mat         C = *B;
1433   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
1434   int         ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
1435   int         *ajtmpold,*ajtmp,nz,row;
1436   int         *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
1437   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
1438   MatScalar   x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15;
1439   MatScalar   x16,x17,x18,x19,x20,x21,x22,x23,x24,x25;
1440   MatScalar   p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15;
1441   MatScalar   p16,p17,p18,p19,p20,p21,p22,p23,p24,p25;
1442   MatScalar   m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12,m13,m14,m15;
1443   MatScalar   m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
1444   MatScalar   *ba = b->a,*aa = a->a;
1445 
1446   PetscFunctionBegin;
1447   rtmp  = (MatScalar*)PetscMalloc(25*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
1448   for (i=0; i<n; i++) {
1449     nz    = bi[i+1] - bi[i];
1450     ajtmp = bj + bi[i];
1451     for  (j=0; j<nz; j++) {
1452       x = rtmp+25*ajtmp[j];
1453       x[0]  = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = x[9] = 0.0;
1454       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
1455       x[16] = x[17] = x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0;
1456     }
1457     /* load in initial (unfactored row) */
1458     nz       = ai[i+1] - ai[i];
1459     ajtmpold = aj + ai[i];
1460     v        = aa + 25*ai[i];
1461     for (j=0; j<nz; j++) {
1462       x    = rtmp+25*ajtmpold[j];
1463       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
1464       x[4]  = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
1465       x[9]  = v[9];  x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
1466       x[14] = v[14]; x[15] = v[15]; x[16] = v[16]; x[17] = v[17]; x[18] = v[18];
1467       x[19] = v[19]; x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23];
1468       x[24] = v[24];
1469       v    += 25;
1470     }
1471     row = *ajtmp++;
1472     while (row < i) {
1473       pc  = rtmp + 25*row;
1474       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
1475       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
1476       p10 = pc[9];  p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
1477       p15 = pc[14]; p16 = pc[15]; p17 = pc[16]; p18 = pc[17];
1478       p19 = pc[18]; p20 = pc[19]; p21 = pc[20]; p22 = pc[21]; p23 = pc[22];
1479       p24 = pc[23]; p25 = pc[24];
1480       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
1481           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
1482           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
1483           || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0
1484           || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 || p25 != 0.0) {
1485         pv = ba + 25*diag_offset[row];
1486         pj = bj + diag_offset[row] + 1;
1487         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
1488         x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
1489         x10 = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
1490         x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17]; x19 = pv[18];
1491         x20 = pv[19]; x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
1492         x25 = pv[24];
1493         pc[0] = m1 = p1*x1 + p6*x2  + p11*x3 + p16*x4 + p21*x5;
1494         pc[1] = m2 = p2*x1 + p7*x2  + p12*x3 + p17*x4 + p22*x5;
1495         pc[2] = m3 = p3*x1 + p8*x2  + p13*x3 + p18*x4 + p23*x5;
1496         pc[3] = m4 = p4*x1 + p9*x2  + p14*x3 + p19*x4 + p24*x5;
1497         pc[4] = m5 = p5*x1 + p10*x2 + p15*x3 + p20*x4 + p25*x5;
1498 
1499         pc[5]  = m6  = p1*x6 + p6*x7  + p11*x8 + p16*x9 + p21*x10;
1500         pc[6]  = m7  = p2*x6 + p7*x7  + p12*x8 + p17*x9 + p22*x10;
1501         pc[7]  = m8  = p3*x6 + p8*x7  + p13*x8 + p18*x9 + p23*x10;
1502         pc[8]  = m9  = p4*x6 + p9*x7  + p14*x8 + p19*x9 + p24*x10;
1503         pc[9]  = m10 = p5*x6 + p10*x7 + p15*x8 + p20*x9 + p25*x10;
1504 
1505         pc[10] = m11 = p1*x11 + p6*x12  + p11*x13 + p16*x14 + p21*x15;
1506         pc[11] = m12 = p2*x11 + p7*x12  + p12*x13 + p17*x14 + p22*x15;
1507         pc[12] = m13 = p3*x11 + p8*x12  + p13*x13 + p18*x14 + p23*x15;
1508         pc[13] = m14 = p4*x11 + p9*x12  + p14*x13 + p19*x14 + p24*x15;
1509         pc[14] = m15 = p5*x11 + p10*x12 + p15*x13 + p20*x14 + p25*x15;
1510 
1511         pc[15] = m16 = p1*x16 + p6*x17  + p11*x18 + p16*x19 + p21*x20;
1512         pc[16] = m17 = p2*x16 + p7*x17  + p12*x18 + p17*x19 + p22*x20;
1513         pc[17] = m18 = p3*x16 + p8*x17  + p13*x18 + p18*x19 + p23*x20;
1514         pc[18] = m19 = p4*x16 + p9*x17  + p14*x18 + p19*x19 + p24*x20;
1515         pc[19] = m20 = p5*x16 + p10*x17 + p15*x18 + p20*x19 + p25*x20;
1516 
1517         pc[20] = m21 = p1*x21 + p6*x22  + p11*x23 + p16*x24 + p21*x25;
1518         pc[21] = m22 = p2*x21 + p7*x22  + p12*x23 + p17*x24 + p22*x25;
1519         pc[22] = m23 = p3*x21 + p8*x22  + p13*x23 + p18*x24 + p23*x25;
1520         pc[23] = m24 = p4*x21 + p9*x22  + p14*x23 + p19*x24 + p24*x25;
1521         pc[24] = m25 = p5*x21 + p10*x22 + p15*x23 + p20*x24 + p25*x25;
1522 
1523         nz = bi[row+1] - diag_offset[row] - 1;
1524         pv += 25;
1525         for (j=0; j<nz; j++) {
1526           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
1527           x5   = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
1528           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
1529           x14  = pv[13]; x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17];
1530           x19 = pv[18];  x20 = pv[19]; x21 = pv[20]; x22 = pv[21]; x23 = pv[22];
1531           x24 = pv[23];  x25 = pv[24];
1532           x    = rtmp + 25*pj[j];
1533           x[0] -= m1*x1 + m6*x2   + m11*x3  + m16*x4 + m21*x5;
1534           x[1] -= m2*x1 + m7*x2   + m12*x3  + m17*x4 + m22*x5;
1535           x[2] -= m3*x1 + m8*x2   + m13*x3  + m18*x4 + m23*x5;
1536           x[3] -= m4*x1 + m9*x2   + m14*x3  + m19*x4 + m24*x5;
1537           x[4] -= m5*x1 + m10*x2  + m15*x3  + m20*x4 + m25*x5;
1538 
1539           x[5] -= m1*x6 + m6*x7   + m11*x8  + m16*x9 + m21*x10;
1540           x[6] -= m2*x6 + m7*x7   + m12*x8  + m17*x9 + m22*x10;
1541           x[7] -= m3*x6 + m8*x7   + m13*x8  + m18*x9 + m23*x10;
1542           x[8] -= m4*x6 + m9*x7   + m14*x8  + m19*x9 + m24*x10;
1543           x[9] -= m5*x6 + m10*x7  + m15*x8  + m20*x9 + m25*x10;
1544 
1545           x[10] -= m1*x11 + m6*x12  + m11*x13 + m16*x14 + m21*x15;
1546           x[11] -= m2*x11 + m7*x12  + m12*x13 + m17*x14 + m22*x15;
1547           x[12] -= m3*x11 + m8*x12  + m13*x13 + m18*x14 + m23*x15;
1548           x[13] -= m4*x11 + m9*x12  + m14*x13 + m19*x14 + m24*x15;
1549           x[14] -= m5*x11 + m10*x12 + m15*x13 + m20*x14 + m25*x15;
1550 
1551           x[15] -= m1*x16 + m6*x17  + m11*x18 + m16*x19 + m21*x20;
1552           x[16] -= m2*x16 + m7*x17  + m12*x18 + m17*x19 + m22*x20;
1553           x[17] -= m3*x16 + m8*x17  + m13*x18 + m18*x19 + m23*x20;
1554           x[18] -= m4*x16 + m9*x17  + m14*x18 + m19*x19 + m24*x20;
1555           x[19] -= m5*x16 + m10*x17 + m15*x18 + m20*x19 + m25*x20;
1556 
1557           x[20] -= m1*x21 + m6*x22  + m11*x23 + m16*x24 + m21*x25;
1558           x[21] -= m2*x21 + m7*x22  + m12*x23 + m17*x24 + m22*x25;
1559           x[22] -= m3*x21 + m8*x22  + m13*x23 + m18*x24 + m23*x25;
1560           x[23] -= m4*x21 + m9*x22  + m14*x23 + m19*x24 + m24*x25;
1561           x[24] -= m5*x21 + m10*x22 + m15*x23 + m20*x24 + m25*x25;
1562           pv   += 25;
1563         }
1564         PLogFlops(250*nz+225);
1565       }
1566       row = *ajtmp++;
1567     }
1568     /* finished row so stick it into b->a */
1569     pv = ba + 25*bi[i];
1570     pj = bj + bi[i];
1571     nz = bi[i+1] - bi[i];
1572     for (j=0; j<nz; j++) {
1573       x      = rtmp+25*pj[j];
1574       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
1575       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
1576       pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
1577       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; pv[16] = x[16]; pv[17] = x[17];
1578       pv[18] = x[18]; pv[19] = x[19]; pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22];
1579       pv[23] = x[23]; pv[24] = x[24];
1580       pv   += 25;
1581     }
1582     /* invert diagonal block */
1583     w = ba + 25*diag_offset[i];
1584     ierr = Kernel_A_gets_inverse_A_5(w);CHKERRQ(ierr);
1585   }
1586 
1587   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1588   C->factor    = FACTOR_LU;
1589   C->assembled = PETSC_TRUE;
1590   PLogFlops(1.3333*125*b->mbs); /* from inverting diagonal blocks */
1591   PetscFunctionReturn(0);
1592 }
1593 
1594 /*
1595       Version for when blocks are 4 by 4
1596 */
1597 #undef __FUNC__
1598 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_4"
1599 int MatCholeskyFactorNumeric_SeqSBAIJ_4(Mat A,Mat *B)
1600 {
1601   Mat         C = *B;
1602   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
1603   IS          isrow = b->row,isicol = b->icol;
1604   int         *r,*ic,ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
1605   int         *ajtmpold,*ajtmp,nz,row;
1606   int         *diag_offset = b->diag,idx,*ai=a->i,*aj=a->j,*pj;
1607   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
1608   MatScalar   p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
1609   MatScalar   p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
1610   MatScalar   p10,p11,p12,p13,p14,p15,p16,m10,m11,m12;
1611   MatScalar   m13,m14,m15,m16;
1612   MatScalar   *ba = b->a,*aa = a->a;
1613 
1614   PetscFunctionBegin;
1615   ierr  = ISGetIndices(isrow,&r);CHKERRQ(ierr);
1616   ierr  = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
1617   rtmp  = (MatScalar*)PetscMalloc(16*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
1618 
1619   for (i=0; i<n; i++) {
1620     nz    = bi[i+1] - bi[i];
1621     ajtmp = bj + bi[i];
1622     for  (j=0; j<nz; j++) {
1623       x = rtmp+16*ajtmp[j];
1624       x[0]  = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = x[9] = 0.0;
1625       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
1626     }
1627     /* load in initial (unfactored row) */
1628     idx      = r[i];
1629     nz       = ai[idx+1] - ai[idx];
1630     ajtmpold = aj + ai[idx];
1631     v        = aa + 16*ai[idx];
1632     for (j=0; j<nz; j++) {
1633       x    = rtmp+16*ic[ajtmpold[j]];
1634       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
1635       x[4]  = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
1636       x[9]  = v[9];  x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
1637       x[14] = v[14]; x[15] = v[15];
1638       v    += 16;
1639     }
1640     row = *ajtmp++;
1641     while (row < i) {
1642       pc  = rtmp + 16*row;
1643       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
1644       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
1645       p10 = pc[9];  p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
1646       p15 = pc[14]; p16 = pc[15];
1647       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
1648           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
1649           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
1650           || p16 != 0.0) {
1651         pv = ba + 16*diag_offset[row];
1652         pj = bj + diag_offset[row] + 1;
1653         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
1654         x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
1655         x10 = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
1656         x15 = pv[14]; x16 = pv[15];
1657         pc[0] = m1 = p1*x1 + p5*x2  + p9*x3  + p13*x4;
1658         pc[1] = m2 = p2*x1 + p6*x2  + p10*x3 + p14*x4;
1659         pc[2] = m3 = p3*x1 + p7*x2  + p11*x3 + p15*x4;
1660         pc[3] = m4 = p4*x1 + p8*x2  + p12*x3 + p16*x4;
1661 
1662         pc[4] = m5 = p1*x5 + p5*x6  + p9*x7  + p13*x8;
1663         pc[5] = m6 = p2*x5 + p6*x6  + p10*x7 + p14*x8;
1664         pc[6] = m7 = p3*x5 + p7*x6  + p11*x7 + p15*x8;
1665         pc[7] = m8 = p4*x5 + p8*x6  + p12*x7 + p16*x8;
1666 
1667         pc[8]  = m9  = p1*x9 + p5*x10  + p9*x11  + p13*x12;
1668         pc[9]  = m10 = p2*x9 + p6*x10  + p10*x11 + p14*x12;
1669         pc[10] = m11 = p3*x9 + p7*x10  + p11*x11 + p15*x12;
1670         pc[11] = m12 = p4*x9 + p8*x10  + p12*x11 + p16*x12;
1671 
1672         pc[12] = m13 = p1*x13 + p5*x14  + p9*x15  + p13*x16;
1673         pc[13] = m14 = p2*x13 + p6*x14  + p10*x15 + p14*x16;
1674         pc[14] = m15 = p3*x13 + p7*x14  + p11*x15 + p15*x16;
1675         pc[15] = m16 = p4*x13 + p8*x14  + p12*x15 + p16*x16;
1676 
1677         nz = bi[row+1] - diag_offset[row] - 1;
1678         pv += 16;
1679         for (j=0; j<nz; j++) {
1680           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
1681           x5   = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
1682           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
1683           x14  = pv[13]; x15 = pv[14]; x16 = pv[15];
1684           x    = rtmp + 16*pj[j];
1685           x[0] -= m1*x1 + m5*x2  + m9*x3  + m13*x4;
1686           x[1] -= m2*x1 + m6*x2  + m10*x3 + m14*x4;
1687           x[2] -= m3*x1 + m7*x2  + m11*x3 + m15*x4;
1688           x[3] -= m4*x1 + m8*x2  + m12*x3 + m16*x4;
1689 
1690           x[4] -= m1*x5 + m5*x6  + m9*x7  + m13*x8;
1691           x[5] -= m2*x5 + m6*x6  + m10*x7 + m14*x8;
1692           x[6] -= m3*x5 + m7*x6  + m11*x7 + m15*x8;
1693           x[7] -= m4*x5 + m8*x6  + m12*x7 + m16*x8;
1694 
1695           x[8]  -= m1*x9 + m5*x10 + m9*x11  + m13*x12;
1696           x[9]  -= m2*x9 + m6*x10 + m10*x11 + m14*x12;
1697           x[10] -= m3*x9 + m7*x10 + m11*x11 + m15*x12;
1698           x[11] -= m4*x9 + m8*x10 + m12*x11 + m16*x12;
1699 
1700           x[12] -= m1*x13 + m5*x14  + m9*x15  + m13*x16;
1701           x[13] -= m2*x13 + m6*x14  + m10*x15 + m14*x16;
1702           x[14] -= m3*x13 + m7*x14  + m11*x15 + m15*x16;
1703           x[15] -= m4*x13 + m8*x14  + m12*x15 + m16*x16;
1704 
1705           pv   += 16;
1706         }
1707         PLogFlops(128*nz+112);
1708       }
1709       row = *ajtmp++;
1710     }
1711     /* finished row so stick it into b->a */
1712     pv = ba + 16*bi[i];
1713     pj = bj + bi[i];
1714     nz = bi[i+1] - bi[i];
1715     for (j=0; j<nz; j++) {
1716       x      = rtmp+16*pj[j];
1717       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
1718       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
1719       pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
1720       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
1721       pv   += 16;
1722     }
1723     /* invert diagonal block */
1724     w = ba + 16*diag_offset[i];
1725     ierr = Kernel_A_gets_inverse_A_4(w);CHKERRQ(ierr);
1726   }
1727 
1728   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1729   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
1730   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
1731   C->factor = FACTOR_LU;
1732   C->assembled = PETSC_TRUE;
1733   PLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */
1734   PetscFunctionReturn(0);
1735 }
1736 /*
1737       Version for when blocks are 4 by 4 Using natural ordering
1738 */
1739 #undef __FUNC__
1740 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_4_NaturalOrdering"
1741 int MatCholeskyFactorNumeric_SeqSBAIJ_4_NaturalOrdering(Mat A,Mat *B)
1742 {
1743   Mat         C = *B;
1744   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
1745   int         ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
1746   int         *ajtmpold,*ajtmp,nz,row;
1747   int         *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
1748   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
1749   MatScalar   p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
1750   MatScalar   p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
1751   MatScalar   p10,p11,p12,p13,p14,p15,p16,m10,m11,m12;
1752   MatScalar   m13,m14,m15,m16;
1753   MatScalar   *ba = b->a,*aa = a->a;
1754 
1755   PetscFunctionBegin;
1756   rtmp  = (MatScalar*)PetscMalloc(16*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
1757 
1758   for (i=0; i<n; i++) {
1759     nz    = bi[i+1] - bi[i];
1760     ajtmp = bj + bi[i];
1761     for  (j=0; j<nz; j++) {
1762       x = rtmp+16*ajtmp[j];
1763       x[0]  = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = x[9] = 0.0;
1764       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
1765     }
1766     /* load in initial (unfactored row) */
1767     nz       = ai[i+1] - ai[i];
1768     ajtmpold = aj + ai[i];
1769     v        = aa + 16*ai[i];
1770     for (j=0; j<nz; j++) {
1771       x    = rtmp+16*ajtmpold[j];
1772       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
1773       x[4]  = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
1774       x[9]  = v[9];  x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
1775       x[14] = v[14]; x[15] = v[15];
1776       v    += 16;
1777     }
1778     row = *ajtmp++;
1779     while (row < i) {
1780       pc  = rtmp + 16*row;
1781       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
1782       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
1783       p10 = pc[9];  p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
1784       p15 = pc[14]; p16 = pc[15];
1785       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
1786           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
1787           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
1788           || p16 != 0.0) {
1789         pv = ba + 16*diag_offset[row];
1790         pj = bj + diag_offset[row] + 1;
1791         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
1792         x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
1793         x10 = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
1794         x15 = pv[14]; x16 = pv[15];
1795         pc[0] = m1 = p1*x1 + p5*x2  + p9*x3  + p13*x4;
1796         pc[1] = m2 = p2*x1 + p6*x2  + p10*x3 + p14*x4;
1797         pc[2] = m3 = p3*x1 + p7*x2  + p11*x3 + p15*x4;
1798         pc[3] = m4 = p4*x1 + p8*x2  + p12*x3 + p16*x4;
1799 
1800         pc[4] = m5 = p1*x5 + p5*x6  + p9*x7  + p13*x8;
1801         pc[5] = m6 = p2*x5 + p6*x6  + p10*x7 + p14*x8;
1802         pc[6] = m7 = p3*x5 + p7*x6  + p11*x7 + p15*x8;
1803         pc[7] = m8 = p4*x5 + p8*x6  + p12*x7 + p16*x8;
1804 
1805         pc[8]  = m9  = p1*x9 + p5*x10  + p9*x11  + p13*x12;
1806         pc[9]  = m10 = p2*x9 + p6*x10  + p10*x11 + p14*x12;
1807         pc[10] = m11 = p3*x9 + p7*x10  + p11*x11 + p15*x12;
1808         pc[11] = m12 = p4*x9 + p8*x10  + p12*x11 + p16*x12;
1809 
1810         pc[12] = m13 = p1*x13 + p5*x14  + p9*x15  + p13*x16;
1811         pc[13] = m14 = p2*x13 + p6*x14  + p10*x15 + p14*x16;
1812         pc[14] = m15 = p3*x13 + p7*x14  + p11*x15 + p15*x16;
1813         pc[15] = m16 = p4*x13 + p8*x14  + p12*x15 + p16*x16;
1814 
1815         nz = bi[row+1] - diag_offset[row] - 1;
1816         pv += 16;
1817         for (j=0; j<nz; j++) {
1818           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
1819           x5   = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
1820           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
1821           x14  = pv[13]; x15 = pv[14]; x16 = pv[15];
1822           x    = rtmp + 16*pj[j];
1823           x[0] -= m1*x1 + m5*x2  + m9*x3  + m13*x4;
1824           x[1] -= m2*x1 + m6*x2  + m10*x3 + m14*x4;
1825           x[2] -= m3*x1 + m7*x2  + m11*x3 + m15*x4;
1826           x[3] -= m4*x1 + m8*x2  + m12*x3 + m16*x4;
1827 
1828           x[4] -= m1*x5 + m5*x6  + m9*x7  + m13*x8;
1829           x[5] -= m2*x5 + m6*x6  + m10*x7 + m14*x8;
1830           x[6] -= m3*x5 + m7*x6  + m11*x7 + m15*x8;
1831           x[7] -= m4*x5 + m8*x6  + m12*x7 + m16*x8;
1832 
1833           x[8]  -= m1*x9 + m5*x10 + m9*x11  + m13*x12;
1834           x[9]  -= m2*x9 + m6*x10 + m10*x11 + m14*x12;
1835           x[10] -= m3*x9 + m7*x10 + m11*x11 + m15*x12;
1836           x[11] -= m4*x9 + m8*x10 + m12*x11 + m16*x12;
1837 
1838           x[12] -= m1*x13 + m5*x14  + m9*x15  + m13*x16;
1839           x[13] -= m2*x13 + m6*x14  + m10*x15 + m14*x16;
1840           x[14] -= m3*x13 + m7*x14  + m11*x15 + m15*x16;
1841           x[15] -= m4*x13 + m8*x14  + m12*x15 + m16*x16;
1842 
1843           pv   += 16;
1844         }
1845         PLogFlops(128*nz+112);
1846       }
1847       row = *ajtmp++;
1848     }
1849     /* finished row so stick it into b->a */
1850     pv = ba + 16*bi[i];
1851     pj = bj + bi[i];
1852     nz = bi[i+1] - bi[i];
1853     for (j=0; j<nz; j++) {
1854       x      = rtmp+16*pj[j];
1855       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
1856       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
1857       pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
1858       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
1859       pv   += 16;
1860     }
1861     /* invert diagonal block */
1862     w = ba + 16*diag_offset[i];
1863     ierr = Kernel_A_gets_inverse_A_4(w);CHKERRQ(ierr);
1864   }
1865 
1866   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1867   C->factor    = FACTOR_LU;
1868   C->assembled = PETSC_TRUE;
1869   PLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */
1870   PetscFunctionReturn(0);
1871 }
1872 
1873 /*
1874       Version for when blocks are 3 by 3
1875 */
1876 #undef __FUNC__
1877 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_3"
1878 int MatCholeskyFactorNumeric_SeqSBAIJ_3(Mat A,Mat *B)
1879 {
1880   Mat         C = *B;
1881   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
1882   IS          isrow = b->row,isicol = b->icol;
1883   int         *r,*ic,ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
1884   int         *ajtmpold,*ajtmp,nz,row,*ai=a->i,*aj=a->j;
1885   int         *diag_offset = b->diag,idx,*pj;
1886   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
1887   MatScalar   p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
1888   MatScalar   p5,p6,p7,p8,p9,x5,x6,x7,x8,x9;
1889   MatScalar   *ba = b->a,*aa = a->a;
1890 
1891   PetscFunctionBegin;
1892   ierr  = ISGetIndices(isrow,&r);CHKERRQ(ierr);
1893   ierr  = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
1894   rtmp  = (MatScalar*)PetscMalloc(9*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
1895 
1896   for (i=0; i<n; i++) {
1897     nz    = bi[i+1] - bi[i];
1898     ajtmp = bj + bi[i];
1899     for  (j=0; j<nz; j++) {
1900       x = rtmp + 9*ajtmp[j];
1901       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = 0.0;
1902     }
1903     /* load in initial (unfactored row) */
1904     idx      = r[i];
1905     nz       = ai[idx+1] - ai[idx];
1906     ajtmpold = aj + ai[idx];
1907     v        = aa + 9*ai[idx];
1908     for (j=0; j<nz; j++) {
1909       x    = rtmp + 9*ic[ajtmpold[j]];
1910       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
1911       x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
1912       v    += 9;
1913     }
1914     row = *ajtmp++;
1915     while (row < i) {
1916       pc = rtmp + 9*row;
1917       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
1918       p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
1919       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
1920           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0) {
1921         pv = ba + 9*diag_offset[row];
1922         pj = bj + diag_offset[row] + 1;
1923         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
1924         x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
1925         pc[0] = m1 = p1*x1 + p4*x2 + p7*x3;
1926         pc[1] = m2 = p2*x1 + p5*x2 + p8*x3;
1927         pc[2] = m3 = p3*x1 + p6*x2 + p9*x3;
1928 
1929         pc[3] = m4 = p1*x4 + p4*x5 + p7*x6;
1930         pc[4] = m5 = p2*x4 + p5*x5 + p8*x6;
1931         pc[5] = m6 = p3*x4 + p6*x5 + p9*x6;
1932 
1933         pc[6] = m7 = p1*x7 + p4*x8 + p7*x9;
1934         pc[7] = m8 = p2*x7 + p5*x8 + p8*x9;
1935         pc[8] = m9 = p3*x7 + p6*x8 + p9*x9;
1936         nz = bi[row+1] - diag_offset[row] - 1;
1937         pv += 9;
1938         for (j=0; j<nz; j++) {
1939           x1   = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
1940           x5   = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
1941           x    = rtmp + 9*pj[j];
1942           x[0] -= m1*x1 + m4*x2 + m7*x3;
1943           x[1] -= m2*x1 + m5*x2 + m8*x3;
1944           x[2] -= m3*x1 + m6*x2 + m9*x3;
1945 
1946           x[3] -= m1*x4 + m4*x5 + m7*x6;
1947           x[4] -= m2*x4 + m5*x5 + m8*x6;
1948           x[5] -= m3*x4 + m6*x5 + m9*x6;
1949 
1950           x[6] -= m1*x7 + m4*x8 + m7*x9;
1951           x[7] -= m2*x7 + m5*x8 + m8*x9;
1952           x[8] -= m3*x7 + m6*x8 + m9*x9;
1953           pv   += 9;
1954         }
1955         PLogFlops(54*nz+36);
1956       }
1957       row = *ajtmp++;
1958     }
1959     /* finished row so stick it into b->a */
1960     pv = ba + 9*bi[i];
1961     pj = bj + bi[i];
1962     nz = bi[i+1] - bi[i];
1963     for (j=0; j<nz; j++) {
1964       x     = rtmp + 9*pj[j];
1965       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
1966       pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
1967       pv   += 9;
1968     }
1969     /* invert diagonal block */
1970     w = ba + 9*diag_offset[i];
1971     ierr = Kernel_A_gets_inverse_A_3(w);CHKERRQ(ierr);
1972   }
1973 
1974   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1975   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
1976   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
1977   C->factor = FACTOR_LU;
1978   C->assembled = PETSC_TRUE;
1979   PLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */
1980   PetscFunctionReturn(0);
1981 }
1982 /*
1983       Version for when blocks are 3 by 3 Using natural ordering
1984 */
1985 #undef __FUNC__
1986 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_3_NaturalOrdering"
1987 int MatCholeskyFactorNumeric_SeqSBAIJ_3_NaturalOrdering(Mat A,Mat *B)
1988 {
1989   Mat                C = *B;
1990   Mat_SeqBAIJ        *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
1991   int                ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
1992   int                *ajtmpold,*ajtmp,nz,row;
1993   int                *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
1994   MatScalar          *pv,*v,*rtmp,*pc,*w,*x;
1995   MatScalar          p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
1996   MatScalar          p5,p6,p7,p8,p9,x5,x6,x7,x8,x9;
1997   MatScalar          *ba = b->a,*aa = a->a;
1998 
1999   PetscFunctionBegin;
2000   rtmp  = (MatScalar*)PetscMalloc(9*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
2001 
2002   for (i=0; i<n; i++) {
2003     nz    = bi[i+1] - bi[i];
2004     ajtmp = bj + bi[i];
2005     for  (j=0; j<nz; j++) {
2006       x = rtmp+9*ajtmp[j];
2007       x[0]  = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = 0.0;
2008     }
2009     /* load in initial (unfactored row) */
2010     nz       = ai[i+1] - ai[i];
2011     ajtmpold = aj + ai[i];
2012     v        = aa + 9*ai[i];
2013     for (j=0; j<nz; j++) {
2014       x    = rtmp+9*ajtmpold[j];
2015       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
2016       x[4]  = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
2017       v    += 9;
2018     }
2019     row = *ajtmp++;
2020     while (row < i) {
2021       pc  = rtmp + 9*row;
2022       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
2023       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
2024       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
2025           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0) {
2026         pv = ba + 9*diag_offset[row];
2027         pj = bj + diag_offset[row] + 1;
2028         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
2029         x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
2030         pc[0] = m1 = p1*x1 + p4*x2 + p7*x3;
2031         pc[1] = m2 = p2*x1 + p5*x2 + p8*x3;
2032         pc[2] = m3 = p3*x1 + p6*x2 + p9*x3;
2033 
2034         pc[3] = m4 = p1*x4 + p4*x5 + p7*x6;
2035         pc[4] = m5 = p2*x4 + p5*x5 + p8*x6;
2036         pc[5] = m6 = p3*x4 + p6*x5 + p9*x6;
2037 
2038         pc[6] = m7 = p1*x7 + p4*x8 + p7*x9;
2039         pc[7] = m8 = p2*x7 + p5*x8 + p8*x9;
2040         pc[8] = m9 = p3*x7 + p6*x8 + p9*x9;
2041 
2042         nz = bi[row+1] - diag_offset[row] - 1;
2043         pv += 9;
2044         for (j=0; j<nz; j++) {
2045           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
2046           x5   = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
2047           x    = rtmp + 9*pj[j];
2048           x[0] -= m1*x1 + m4*x2 + m7*x3;
2049           x[1] -= m2*x1 + m5*x2 + m8*x3;
2050           x[2] -= m3*x1 + m6*x2 + m9*x3;
2051 
2052           x[3] -= m1*x4 + m4*x5 + m7*x6;
2053           x[4] -= m2*x4 + m5*x5 + m8*x6;
2054           x[5] -= m3*x4 + m6*x5 + m9*x6;
2055 
2056           x[6] -= m1*x7 + m4*x8 + m7*x9;
2057           x[7] -= m2*x7 + m5*x8 + m8*x9;
2058           x[8] -= m3*x7 + m6*x8 + m9*x9;
2059           pv   += 9;
2060         }
2061         PLogFlops(54*nz+36);
2062       }
2063       row = *ajtmp++;
2064     }
2065     /* finished row so stick it into b->a */
2066     pv = ba + 9*bi[i];
2067     pj = bj + bi[i];
2068     nz = bi[i+1] - bi[i];
2069     for (j=0; j<nz; j++) {
2070       x      = rtmp+9*pj[j];
2071       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
2072       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
2073       pv   += 9;
2074     }
2075     /* invert diagonal block */
2076     w = ba + 9*diag_offset[i];
2077     ierr = Kernel_A_gets_inverse_A_3(w);CHKERRQ(ierr);
2078   }
2079 
2080   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2081   C->factor    = FACTOR_LU;
2082   C->assembled = PETSC_TRUE;
2083   PLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */
2084   PetscFunctionReturn(0);
2085 }
2086 
2087 /*
2088       Version for when blocks are 2 by 2
2089 */
2090 #undef __FUNC__
2091 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_2"
2092 int MatCholeskyFactorNumeric_SeqSBAIJ_2(Mat A,Mat *B)
2093 {
2094   Mat                C = *B;
2095   Mat_SeqBAIJ        *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
2096   IS                 isrow = b->row,isicol = b->icol;
2097   int                *r,*ic,ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
2098   int                *ajtmpold,*ajtmp,nz,row;
2099   int                *diag_offset=b->diag,idx,*ai=a->i,*aj=a->j,*pj;
2100   MatScalar          *pv,*v,*rtmp,m1,m2,m3,m4,*pc,*w,*x,x1,x2,x3,x4;
2101   MatScalar          p1,p2,p3,p4;
2102   MatScalar          *ba = b->a,*aa = a->a;
2103 
2104   PetscFunctionBegin;
2105   ierr  = ISGetIndices(isrow,&r);CHKERRQ(ierr);
2106   ierr  = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
2107   rtmp  = (MatScalar*)PetscMalloc(4*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
2108 
2109   for (i=0; i<n; i++) {
2110     nz    = bi[i+1] - bi[i];
2111     ajtmp = bj + bi[i];
2112     for  (j=0; j<nz; j++) {
2113       x = rtmp+4*ajtmp[j]; x[0] = x[1] = x[2] = x[3] = 0.0;
2114     }
2115     /* load in initial (unfactored row) */
2116     idx      = r[i];
2117     nz       = ai[idx+1] - ai[idx];
2118     ajtmpold = aj + ai[idx];
2119     v        = aa + 4*ai[idx];
2120     for (j=0; j<nz; j++) {
2121       x    = rtmp+4*ic[ajtmpold[j]];
2122       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
2123       v    += 4;
2124     }
2125     row = *ajtmp++;
2126     while (row < i) {
2127       pc = rtmp + 4*row;
2128       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
2129       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0) {
2130         pv = ba + 4*diag_offset[row];
2131         pj = bj + diag_offset[row] + 1;
2132         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
2133         pc[0] = m1 = p1*x1 + p3*x2;
2134         pc[1] = m2 = p2*x1 + p4*x2;
2135         pc[2] = m3 = p1*x3 + p3*x4;
2136         pc[3] = m4 = p2*x3 + p4*x4;
2137         nz = bi[row+1] - diag_offset[row] - 1;
2138         pv += 4;
2139         for (j=0; j<nz; j++) {
2140           x1   = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
2141           x    = rtmp + 4*pj[j];
2142           x[0] -= m1*x1 + m3*x2;
2143           x[1] -= m2*x1 + m4*x2;
2144           x[2] -= m1*x3 + m3*x4;
2145           x[3] -= m2*x3 + m4*x4;
2146           pv   += 4;
2147         }
2148         PLogFlops(16*nz+12);
2149       }
2150       row = *ajtmp++;
2151     }
2152     /* finished row so stick it into b->a */
2153     pv = ba + 4*bi[i];
2154     pj = bj + bi[i];
2155     nz = bi[i+1] - bi[i];
2156     for (j=0; j<nz; j++) {
2157       x     = rtmp+4*pj[j];
2158       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
2159       pv   += 4;
2160     }
2161     /* invert diagonal block */
2162     w = ba + 4*diag_offset[i];
2163     ierr = Kernel_A_gets_inverse_A_2(w);CHKERRQ(ierr);
2164     /*Kernel_A_gets_inverse_A(bs,w,v_pivots,v_work);*/
2165   }
2166 
2167   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2168   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
2169   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
2170   C->factor = FACTOR_LU;
2171   C->assembled = PETSC_TRUE;
2172   PLogFlops(1.3333*8*b->mbs); /* from inverting diagonal blocks */
2173   PetscFunctionReturn(0);
2174 }
2175 /*
2176       Version for when blocks are 2 by 2 Using natural ordering
2177 */
2178 #undef __FUNC__
2179 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_2_NaturalOrdering"
2180 int MatCholeskyFactorNumeric_SeqSBAIJ_2_NaturalOrdering(Mat A,Mat *B)
2181 {
2182   Mat                C = *B;
2183   Mat_SeqBAIJ        *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
2184   int                ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
2185   int                *ajtmpold,*ajtmp,nz,row;
2186   int                *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
2187   MatScalar          *pv,*v,*rtmp,*pc,*w,*x;
2188   MatScalar          p1,p2,p3,p4,m1,m2,m3,m4,x1,x2,x3,x4;
2189   MatScalar          *ba = b->a,*aa = a->a;
2190 
2191   PetscFunctionBegin;
2192   rtmp  = (MatScalar*)PetscMalloc(4*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
2193 
2194   for (i=0; i<n; i++) {
2195     nz    = bi[i+1] - bi[i];
2196     ajtmp = bj + bi[i];
2197     for  (j=0; j<nz; j++) {
2198       x = rtmp+4*ajtmp[j];
2199       x[0]  = x[1]  = x[2]  = x[3]  = 0.0;
2200     }
2201     /* load in initial (unfactored row) */
2202     nz       = ai[i+1] - ai[i];
2203     ajtmpold = aj + ai[i];
2204     v        = aa + 4*ai[i];
2205     for (j=0; j<nz; j++) {
2206       x    = rtmp+4*ajtmpold[j];
2207       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
2208       v    += 4;
2209     }
2210     row = *ajtmp++;
2211     while (row < i) {
2212       pc  = rtmp + 4*row;
2213       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
2214       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0) {
2215         pv = ba + 4*diag_offset[row];
2216         pj = bj + diag_offset[row] + 1;
2217         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
2218         pc[0] = m1 = p1*x1 + p3*x2;
2219         pc[1] = m2 = p2*x1 + p4*x2;
2220         pc[2] = m3 = p1*x3 + p3*x4;
2221         pc[3] = m4 = p2*x3 + p4*x4;
2222         nz = bi[row+1] - diag_offset[row] - 1;
2223         pv += 4;
2224         for (j=0; j<nz; j++) {
2225           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
2226           x    = rtmp + 4*pj[j];
2227           x[0] -= m1*x1 + m3*x2;
2228           x[1] -= m2*x1 + m4*x2;
2229           x[2] -= m1*x3 + m3*x4;
2230           x[3] -= m2*x3 + m4*x4;
2231           pv   += 4;
2232         }
2233         PLogFlops(16*nz+12);
2234       }
2235       row = *ajtmp++;
2236     }
2237     /* finished row so stick it into b->a */
2238     pv = ba + 4*bi[i];
2239     pj = bj + bi[i];
2240     nz = bi[i+1] - bi[i];
2241     for (j=0; j<nz; j++) {
2242       x      = rtmp+4*pj[j];
2243       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
2244       pv   += 4;
2245     }
2246     /* invert diagonal block */
2247     w = ba + 4*diag_offset[i];
2248     ierr = Kernel_A_gets_inverse_A_2(w);CHKERRQ(ierr);
2249     /*Kernel_A_gets_inverse_A(bs,w,v_pivots,v_work);*/
2250   }
2251 
2252   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2253   C->factor    = FACTOR_LU;
2254   C->assembled = PETSC_TRUE;
2255   PLogFlops(1.3333*8*b->mbs); /* from inverting diagonal blocks */
2256   PetscFunctionReturn(0);
2257 }
2258 
2259 /*
2260      Version for when blocks are 1 by 1.
2261 */
2262 #undef __FUNC__
2263 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_1"
2264 int MatCholeskyFactorNumeric_SeqSBAIJ_1(Mat A,Mat *B)
2265 {
2266   Mat                C = *B;
2267   Mat_SeqSBAIJ       *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data;
2268   IS                 ip = b->row;
2269   int                *rip,*riip,ierr,i,j,mbs = a->mbs,*bi = b->i,*bj = b->j;
2270   int                *ai = a->i,*aj = a->j;
2271   MatScalar          *rtmp;
2272   MatScalar          *ba = b->a,*aa = a->a;
2273   MatScalar          dk,uikdi;
2274   int                k,jmin,jmax,*jl,*il,vj,nexti,juj,ili;
2275 
2276   PetscFunctionBegin;
2277   ierr  = ISGetIndices(ip,&rip);CHKERRQ(ierr);
2278   riip = rip;
2279 
2280   /* INITIALIZATION */
2281   /* il and jl record the first nonzero element in each row of the accessing
2282      window U(0:k, k:mbs-1).
2283      jl:    list of rows to be added to uneliminated rows
2284             i>= k: jl(i) is the first row to be added to row i
2285             i<  k: jl(i) is the row following row i in some list of rows
2286             jl(i) = mbs indicates the end of a list
2287      il(i): points to the first nonzero element in columns k,...,mbs-1 of
2288             row i of U */
2289   rtmp  = (MatScalar*)PetscMalloc(mbs*sizeof(MatScalar));CHKPTRQ(rtmp);
2290   il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il);
2291   jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl);
2292   for (i=0; i<mbs; i++) {
2293     rtmp[i] = 0.0; jl[i] = mbs; il[0] = 0;
2294   }
2295 
2296   /* FOR EACH ROW K */
2297   for (k = 0; k<mbs; k++){
2298 
2299     /* INITIALIZE K-TH ROW WITH ELEMENTS NONZERO IN ROW P(K) OF A */
2300     jmin = ai[rip[k]]; jmax = ai[rip[k]+1];
2301     if (jmin < jmax) {
2302       for (j = jmin; j < jmax; j++){
2303         vj = riip[aj[j]];
2304         if (k <= vj) rtmp[vj] = aa[j];
2305       }
2306     }
2307 
2308     /* MODIFY K-TH ROW BY ADDING IN THOSE ROWS I WITH U(I,K) NE 0
2309        FOR EACH ROW I TO BE ADDED IN */
2310     dk = rtmp[k];
2311     i = jl[k]; /* first row to be added to k_th row  */
2312     /* printf(" k=%d, pivot row = %d\n",k,i); */
2313 
2314     while (i < mbs){
2315       nexti = jl[i]; /* next row to be added to k_th row */
2316       /* printf("      pivot row = %d\n", nexti); */
2317 
2318       /* COMPUTE MULTIPLIER AND UPDATE DIAGONAL ELEMENT */
2319       ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
2320       uikdi = - ba[ili]*ba[i];
2321       dk += uikdi*ba[ili];
2322       ba[ili] = uikdi; /* update U(i,k) */
2323 
2324       /* ADD MULTIPLE OF ROW I TO K-TH ROW ... */
2325       jmin = ili + 1; jmax = bi[i+1];
2326       if (jmin < jmax){
2327         for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j];
2328         /* ... AND ADD I TO ROW LIST FOR NEXT NONZERO ENTRY */
2329          il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
2330          j     = bj[jmin];
2331          jl[i] = jl[j]; jl[j] = i; /* update jl */
2332       }
2333       i = nexti;
2334       /* printf("                  pivot row i=%d\n",i);  */
2335     }
2336 
2337     /* CHECK FOR ZERO PIVOT AND SAVE DIAGONAL ELEMENT */
2338     if (dk == 0.0){
2339       SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,0,"Zero pivot");
2340     }
2341 
2342     /* SAVE NONZERO ENTRIES IN K-TH ROW OF U ... */
2343     ba[k] = 1.0/dk;
2344     jmin = bi[k]; jmax = bi[k+1];
2345     if (jmin < jmax) {
2346       for (j=jmin; j<jmax; j++){
2347          juj = bj[j]; ba[j] = rtmp[juj]; rtmp[juj] = 0.0;
2348       }
2349 
2350       /* ... AND ADD K TO ROW LIST FOR FIRST NONZERO ENTRY IN K-TH ROW */
2351       il[k] = jmin;
2352       i     = bj[jmin];
2353       jl[k] = jl[i]; jl[i] = k;
2354     }
2355   }
2356 
2357   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2358   ierr = PetscFree(il);CHKERRQ(ierr);
2359   ierr = PetscFree(jl);CHKERRQ(ierr);
2360 
2361   ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr);
2362   C->factor    = FACTOR_LU;
2363   C->assembled = PETSC_TRUE;
2364   PLogFlops(b->mbs);
2365   PetscFunctionReturn(0);
2366 }
2367 
2368 #undef __FUNC__
2369 #define __FUNC__ "MatCholeskyFactor_SeqSBAIJ"
2370 int MatCholeskyFactor_SeqSBAIJ(Mat A,IS perm,PetscReal f)
2371 {
2372   Mat_SeqSBAIJ    *mat = (Mat_SeqSBAIJ*)A->data;
2373   int            ierr,refct;
2374   Mat            C;
2375   PetscOps *Abops;
2376   MatOps   Aops;
2377 
2378   PetscFunctionBegin;
2379   ierr = MatCholeskyFactorSymbolic(A,perm,f,&C);CHKERRQ(ierr);
2380   ierr = MatCholeskyFactorNumeric(A,&C);CHKERRQ(ierr);
2381 
2382   /* free all the data structures from mat */
2383   ierr = PetscFree(mat->a);CHKERRQ(ierr);
2384   if (!mat->singlemalloc) {
2385     ierr = PetscFree(mat->i);CHKERRQ(ierr);
2386     ierr = PetscFree(mat->j);CHKERRQ(ierr);
2387   }
2388   if (mat->diag) {ierr = PetscFree(mat->diag);CHKERRQ(ierr);}
2389   if (mat->ilen) {ierr = PetscFree(mat->ilen);CHKERRQ(ierr);}
2390   if (mat->imax) {ierr = PetscFree(mat->imax);CHKERRQ(ierr);}
2391   if (mat->solve_work) {ierr = PetscFree(mat->solve_work);CHKERRQ(ierr);}
2392   if (mat->mult_work) {ierr = PetscFree(mat->mult_work);CHKERRQ(ierr);}
2393   if (mat->icol) {ierr = ISDestroy(mat->icol);CHKERRQ(ierr);}
2394   ierr = PetscFree(mat);CHKERRQ(ierr);
2395 
2396   ierr = MapDestroy(A->rmap);CHKERRQ(ierr);
2397   ierr = MapDestroy(A->cmap);CHKERRQ(ierr);
2398 
2399   /*
2400        This is horrible,horrible code. We need to keep the
2401     A pointers for the bops and ops but copy everything
2402     else from C.
2403   */
2404   Abops = A->bops;
2405   Aops  = A->ops;
2406   refct = A->refct;
2407   ierr  = PetscMemcpy(A,C,sizeof(struct _p_Mat));CHKERRQ(ierr);
2408   mat   = (Mat_SeqSBAIJ*)A->data;
2409   PLogObjectParent(A,mat->icol);
2410 
2411   A->bops  = Abops;
2412   A->ops   = Aops;
2413   A->qlist = 0;
2414   A->refct = refct;
2415   /* copy over the type_name and name */
2416   ierr     = PetscStrallocpy(C->type_name,&A->type_name);CHKERRQ(ierr);
2417   ierr     = PetscStrallocpy(C->name,&A->name);CHKERRQ(ierr);
2418 
2419   PetscHeaderDestroy(C);
2420   PetscFunctionReturn(0);
2421 }
2422 
2423 
2424