xref: /petsc/src/mat/impls/sbaij/seq/sbaijfact.c (revision 5d1a10b1e93e00413872aeb7c1118d31f04cd00a)
1 /* Using Modified Sparse Row (MSR) storage.
2 See page 85, "Iterative Methods ..." by Saad. */
3 
4 /*$Id: sbaijfact.c,v 1.7 2000/07/25 13:47:46 hzhang Exp hzhang $*/
5 /*
6     Factorization code for SBAIJ format.
7 */
8 #include "sbaij.h"
9 #include "src/mat/impls/baij/seq/baij.h"
10 #include "src/vec/vecimpl.h"
11 #include "src/inline/ilu.h"
12 
13 #undef __FUNC__
14 #define __FUNC__ "MatCholeskyFactorSymbolic_SeqSBAIJ"
15 int MatCholeskyFactorSymbolic_SeqSBAIJ(Mat A,IS iscol,PetscReal f,Mat *B)
16 {
17   Mat_SeqSBAIJ *a = (Mat_SeqSBAIJ*)A->data,*b;
18   IS          isicol,isrow;
19   int         *rip,*riip,ierr,i,mbs = a->mbs,*ai = a->i,*aj = a->j;
20   int         *jutmp,bs = a->bs,bs2=a->bs2;
21   int         m,nzi,realloc = 0;
22   int         *jl,*q,jumin,jmin,jmax,juptr,nzk,qm,*iu,*ju,k,j,vj,umax,maxadd;
23   /* PetscReal   f = 1.0; */
24 
25   PetscFunctionBegin;
26   isrow = iscol;   /* remove isrow later! */
27   PetscValidHeaderSpecific(isrow,IS_COOKIE);
28   PetscValidHeaderSpecific(iscol,IS_COOKIE);
29   /* if (A->M != A->N) SETERRQ(PETSC_ERR_ARG_WRONG,0,"matrix must be square");*/
30   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
31   ierr = ISGetIndices(isrow,&rip);CHKERRQ(ierr);
32   ierr = ISGetIndices(isicol,&riip);CHKERRQ(ierr);
33 
34   for (k=0; k<mbs; k++) {
35     if ( rip[k] - riip[k] != 0 ) {
36       printf("Non-symm. permutation, use symm. permutation or general matrix format\n");
37       break;
38     }
39   }
40 
41   /* initialization */
42   /* Don't know how many column pointers are needed so estimate.
43      Use Modified Sparse Row storage for u and ju, see Sasd pp.85 */
44   /* if (info) f = info->fill; */
45   umax = (int)(f*ai[mbs] + 1); umax += mbs + 1;
46   ju = iu = (int*)PetscMalloc(umax*sizeof(int));CHKPTRQ(ju);
47   iu[0] = mbs+1;
48   juptr = mbs;
49   jl =  (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl);
50   q  =  (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(q);
51   for (i=0; i<mbs; i++){
52     jl[i] = mbs; q[i] = 0;
53   }
54 
55   /* for each row k */
56   for (k=0; k<mbs; k++){
57     nzk = 0; /* num. of nz blocks in k-th block row with diagonal block excluded */
58     q[k] = mbs;
59     /* initialize nonzero structure of k-th row to row rip[k] of A */
60     jmin = ai[rip[k]];
61     jmax = ai[rip[k]+1];
62     for (j=jmin; j<jmax; j++){
63       vj = riip[aj[j]]; /* col. value */
64       if(vj > k){
65         qm = k;
66         do {
67           m  = qm; qm = q[m];
68         } while(qm < vj);
69         if (qm == vj) {
70           printf(" error: duplicate entry in A\n"); break;
71         }
72         nzk++;
73         q[m] = vj;
74         q[vj] = qm;
75       } /* if(vj > k) */
76     } /* for (j=jmin; j<jmax; j++) */
77 
78     /* modify nonzero structure of k-th row by computing fill-in
79        for each row i to be merged in */
80     i = k;
81     i = jl[i]; /* next pivot row (== mbs for symbolic factorization) */
82     /* printf(" next pivot row i=%d\n",i); */
83     while (i < mbs){
84       /* merge row i into k-th row */
85       nzi = iu[i+1] - (iu[i]+1);
86       jmin = iu[i] + 1; jmax = iu[i] + nzi;
87       qm = k;
88       for (j=jmin; j<jmax+1; j++){
89         vj = ju[j];
90         do {
91           m = qm; qm = q[m];
92         } while (qm < vj);
93         if (qm != vj){
94          nzk++; q[m] = vj; q[vj] = qm; qm = vj;
95         }
96       }
97       i = jl[i]; /* next pivot row */
98     }
99 
100     /* add k to row list for first nonzero element in k-th row */
101     if (nzk > 0){
102       i = q[k]; /* col value of first nonzero element in U(k, k+1:mbs-1) */
103       jl[k] = jl[i]; jl[i] = k;
104     }
105     iu[k+1] = iu[k] + nzk;   /* printf(" iu[%d]=%d, umax=%d\n", k+1, iu[k+1],umax);*/
106 
107     /* allocate more space to ju if needed */
108     if (iu[k+1] > umax) { printf("allocate more space, iu[%d]=%d > umax=%d\n",k+1, iu[k+1],umax);
109       /* estimate how much additional space we will need */
110       /* use the strategy suggested by David Hysom <hysom@perch-t.icase.edu> */
111       /* just double the memory each time */
112       maxadd = umax;
113       if (maxadd < nzk) maxadd = (mbs-k)*(nzk+1)/2;
114       umax += maxadd;
115 
116       /* allocate a longer ju (NOTE: iu poits to the beginning of ju) */
117       jutmp = (int*)PetscMalloc(umax*sizeof(int));CHKPTRQ(jutmp);
118       ierr  = PetscMemcpy(jutmp,ju,iu[k]*sizeof(int));CHKERRQ(ierr);
119       ierr = PetscFree(ju);CHKERRQ(ierr);
120       ju = iu = jutmp;
121       realloc++; /* count how many times we realloc */
122     }
123 
124     /* save nonzero structure of k-th row in ju */
125     i=k;
126     jumin = juptr + 1; juptr += nzk;
127     for (j=jumin; j<juptr+1; j++){
128       i=q[i];
129       ju[j]=i;
130       /* printf(" k=%d, ju[%d]=%d\n",k,j,ju[j]);*/
131     }
132     /* printf("\n");  */
133   } /* for (k=0; k<mbs; k++) */
134 
135   if (ai[mbs] != 0) {
136     PetscReal af = ((PetscReal)iu[mbs])/((PetscReal)ai[mbs]);
137     PLogInfo(A,"MatCholeskyFactorSymbolic_SeqSBAIJ:Reallocs %d Fill ratio:given %g needed %g\n",realloc,f,af);
138     PLogInfo(A,"MatCholeskyFactorSymbolic_SeqSBAIJ:Run with -pc_lu_fill %g or use \n",af);
139     PLogInfo(A,"MatCholeskyFactorSymbolic_SeqSBAIJ:PCLUSetFill(pc,%g);\n",af);
140     PLogInfo(A,"MatCholeskyFactorSymbolic_SeqSBAIJ:for best performance.\n");
141   } else {
142      PLogInfo(A,"MatCholeskyFactorSymbolic_SeqSBAIJ:Empty matrix.\n");
143   }
144 
145   ierr = ISRestoreIndices(isrow,&rip);CHKERRQ(ierr);
146   ierr = ISRestoreIndices(isicol,&riip);CHKERRQ(ierr);
147 
148   ierr = PetscFree(q);CHKERRQ(ierr);
149   ierr = PetscFree(jl);CHKERRQ(ierr);
150 
151   /* put together the new matrix */
152   ierr = MatCreateSeqSBAIJ(A->comm,bs,bs*mbs,bs*mbs,0,PETSC_NULL,B);CHKERRQ(ierr);
153   PLogObjectParent(*B,isicol);
154   b = (Mat_SeqSBAIJ*)(*B)->data;
155   ierr = PetscFree(b->imax);CHKERRQ(ierr);
156   b->singlemalloc = PETSC_FALSE;
157   /* the next line frees the default space generated by the Create() */
158   ierr = PetscFree(b->a);CHKERRQ(ierr);
159   ierr = PetscFree(b->ilen);CHKERRQ(ierr);
160   b->a          = (MatScalar*)PetscMalloc((iu[mbs]+1)*sizeof(MatScalar)*bs2);CHKPTRQ(b->a);
161   b->j          = ju;
162   b->i          = iu;
163   b->diag       = 0;
164   b->ilen       = 0;
165   b->imax       = 0;
166   b->row        = isrow;
167   b->col        = iscol;
168   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
169   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
170   b->icol       = isicol;
171   b->solve_work = (Scalar*)PetscMalloc((bs*mbs+bs)*sizeof(Scalar));CHKPTRQ(b->solve_work);
172   /* In b structure:  Free imax, ilen, old a, old j.
173      Allocate idnew, solve_work, new a, new j */
174   PLogObjectMemory(*B,(iu[mbs]-mbs)*(sizeof(int)+sizeof(MatScalar)));
175   b->s_maxnz = b->s_nz = iu[mbs];
176 
177   (*B)->factor                 = FACTOR_LU;
178   (*B)->info.factor_mallocs    = realloc;
179   (*B)->info.fill_ratio_given  = f;
180   if (ai[mbs] != 0) {
181     (*B)->info.fill_ratio_needed = ((PetscReal)iu[mbs])/((PetscReal)ai[mbs]);
182   } else {
183     (*B)->info.fill_ratio_needed = 0.0;
184   }
185 
186 
187   PetscFunctionReturn(0);
188 }
189 
190 /* ----------------------------------------------------------- */
191 #undef __FUNC__
192 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_N"
193 int MatCholeskyFactorNumeric_SeqSBAIJ_N(Mat A,Mat *B)
194 {
195   Mat                C = *B;
196   Mat_SeqBAIJ        *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
197   IS                 isrow = b->row,isicol = b->icol;
198   int                *r,*ic,ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
199   int                *ajtmpold,*ajtmp,nz,row,bslog,*ai=a->i,*aj=a->j,k,flg;
200   int                *diag_offset=b->diag,diag,bs=a->bs,bs2 = a->bs2,*v_pivots,*pj;
201   MatScalar          *ba = b->a,*aa = a->a,*pv,*v,*rtmp,*multiplier,*v_work,*pc,*w;
202 
203   PetscFunctionBegin;
204   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
205   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
206   rtmp = (MatScalar*)PetscMalloc(bs2*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
207   ierr = PetscMemzero(rtmp,bs2*(n+1)*sizeof(MatScalar));CHKERRQ(ierr);
208   /* generate work space needed by dense LU factorization */
209   v_work     = (MatScalar*)PetscMalloc(bs*sizeof(int) + (bs+bs2)*sizeof(MatScalar));CHKPTRQ(v_work);
210   multiplier = v_work + bs;
211   v_pivots   = (int*)(multiplier + bs2);
212 
213   /* flops in while loop */
214   bslog = 2*bs*bs2;
215 
216   for (i=0; i<n; i++) {
217     nz    = bi[i+1] - bi[i];
218     ajtmp = bj + bi[i];
219     for  (j=0; j<nz; j++) {
220       ierr = PetscMemzero(rtmp+bs2*ajtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
221     }
222     /* load in initial (unfactored row) */
223     nz       = ai[r[i]+1] - ai[r[i]];
224     ajtmpold = aj + ai[r[i]];
225     v        = aa + bs2*ai[r[i]];
226     for (j=0; j<nz; j++) {
227       ierr = PetscMemcpy(rtmp+bs2*ic[ajtmpold[j]],v+bs2*j,bs2*sizeof(MatScalar));CHKERRQ(ierr);
228     }
229     row = *ajtmp++;
230     while (row < i) {
231       pc = rtmp + bs2*row;
232 /*      if (*pc) { */
233       for (flg=0,k=0; k<bs2; k++) { if (pc[k]!=0.0) { flg =1; break; }}
234       if (flg) {
235         pv = ba + bs2*diag_offset[row];
236         pj = bj + diag_offset[row] + 1;
237         Kernel_A_gets_A_times_B(bs,pc,pv,multiplier);
238         nz = bi[row+1] - diag_offset[row] - 1;
239         pv += bs2;
240         for (j=0; j<nz; j++) {
241           Kernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j);
242         }
243         PLogFlops(bslog*(nz+1)-bs);
244       }
245         row = *ajtmp++;
246     }
247     /* finished row so stick it into b->a */
248     pv = ba + bs2*bi[i];
249     pj = bj + bi[i];
250     nz = bi[i+1] - bi[i];
251     for (j=0; j<nz; j++) {
252       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
253     }
254     diag = diag_offset[i] - bi[i];
255     /* invert diagonal block */
256     w = pv + bs2*diag;
257     Kernel_A_gets_inverse_A(bs,w,v_pivots,v_work);
258   }
259 
260   ierr = PetscFree(rtmp);CHKERRQ(ierr);
261   ierr = PetscFree(v_work);CHKERRQ(ierr);
262   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
263   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
264   C->factor = FACTOR_LU;
265   C->assembled = PETSC_TRUE;
266   PLogFlops(1.3333*bs*bs2*b->mbs); /* from inverting diagonal blocks */
267   PetscFunctionReturn(0);
268 }
269 /* ------------------------------------------------------------*/
270 /*
271       Version for when blocks are 7 by 7
272 */
273 #undef __FUNC__
274 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_7"
275 int MatCholeskyFactorNumeric_SeqSBAIJ_7(Mat A,Mat *B)
276 {
277   Mat         C = *B;
278   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
279   IS          isrow = b->row,isicol = b->icol;
280   int         *r,*ic,ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
281   int         *ajtmpold,*ajtmp,nz,row;
282   int         *diag_offset = b->diag,idx,*ai=a->i,*aj=a->j,*pj;
283   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
284   MatScalar   p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
285   MatScalar   p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
286   MatScalar   x17,x18,x19,x20,x21,x22,x23,x24,x25,p10,p11,p12,p13,p14;
287   MatScalar   p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,m10,m11,m12;
288   MatScalar   m13,m14,m15,m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
289   MatScalar   p26,p27,p28,p29,p30,p31,p32,p33,p34,p35,p36;
290   MatScalar   p37,p38,p39,p40,p41,p42,p43,p44,p45,p46,p47,p48,p49;
291   MatScalar   x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36;
292   MatScalar   x37,x38,x39,x40,x41,x42,x43,x44,x45,x46,x47,x48,x49;
293   MatScalar   m26,m27,m28,m29,m30,m31,m32,m33,m34,m35,m36;
294   MatScalar   m37,m38,m39,m40,m41,m42,m43,m44,m45,m46,m47,m48,m49;
295   MatScalar   *ba = b->a,*aa = a->a;
296 
297   PetscFunctionBegin;
298   ierr  = ISGetIndices(isrow,&r);CHKERRQ(ierr);
299   ierr  = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
300   rtmp  = (MatScalar*)PetscMalloc(49*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
301 
302   for (i=0; i<n; i++) {
303     nz    = bi[i+1] - bi[i];
304     ajtmp = bj + bi[i];
305     for  (j=0; j<nz; j++) {
306       x = rtmp+49*ajtmp[j];
307       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
308       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
309       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = x[25] = 0.0 ;
310       x[26] = x[27] = x[28] = x[29] = x[30] = x[31] = x[32] = x[33] = 0.0 ;
311       x[34] = x[35] = x[36] = x[37] = x[38] = x[39] = x[40] = x[41] = 0.0 ;
312       x[42] = x[43] = x[44] = x[45] = x[46] = x[47] = x[48] = 0.0 ;
313     }
314     /* load in initial (unfactored row) */
315     idx      = r[i];
316     nz       = ai[idx+1] - ai[idx];
317     ajtmpold = aj + ai[idx];
318     v        = aa + 49*ai[idx];
319     for (j=0; j<nz; j++) {
320       x    = rtmp+49*ic[ajtmpold[j]];
321       x[0] =  v[0];  x[1] =  v[1];  x[2] =  v[2];  x[3] =  v[3];
322       x[4] =  v[4];  x[5] =  v[5];  x[6] =  v[6];  x[7] =  v[7];
323       x[8] =  v[8];  x[9] =  v[9];  x[10] = v[10]; x[11] = v[11];
324       x[12] = v[12]; x[13] = v[13]; x[14] = v[14]; x[15] = v[15];
325       x[16] = v[16]; x[17] = v[17]; x[18] = v[18]; x[19] = v[19];
326       x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23];
327       x[24] = v[24]; x[25] = v[25]; x[26] = v[26]; x[27] = v[27];
328       x[28] = v[28]; x[29] = v[29]; x[30] = v[30]; x[31] = v[31];
329       x[32] = v[32]; x[33] = v[33]; x[34] = v[34]; x[35] = v[35];
330       x[36] = v[36]; x[37] = v[37]; x[38] = v[38]; x[39] = v[39];
331       x[40] = v[40]; x[41] = v[41]; x[42] = v[42]; x[43] = v[43];
332       x[44] = v[44]; x[45] = v[45]; x[46] = v[46]; x[47] = v[47];
333       x[48] = v[48];
334       v    += 49;
335     }
336     row = *ajtmp++;
337     while (row < i) {
338       pc  =  rtmp + 49*row;
339       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
340       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];
341       p9  = pc[8];  p10 = pc[9];  p11 = pc[10]; p12 = pc[11];
342       p13 = pc[12]; p14 = pc[13]; p15 = pc[14]; p16 = pc[15];
343       p17 = pc[16]; p18 = pc[17]; p19 = pc[18]; p20 = pc[19];
344       p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
345       p25 = pc[24]; p26 = pc[25]; p27 = pc[26]; p28 = pc[27];
346       p29 = pc[28]; p30 = pc[29]; p31 = pc[30]; p32 = pc[31];
347       p33 = pc[32]; p34 = pc[33]; p35 = pc[34]; p36 = pc[35];
348       p37 = pc[36]; p38 = pc[37]; p39 = pc[38]; p40 = pc[39];
349       p41 = pc[40]; p42 = pc[41]; p43 = pc[42]; p44 = pc[43];
350       p45 = pc[44]; p46 = pc[45]; p47 = pc[46]; p48 = pc[47];
351       p49 = pc[48];
352       if (p1  != 0.0 || p2  != 0.0 || p3  != 0.0 || p4  != 0.0 ||
353           p5  != 0.0 || p6  != 0.0 || p7  != 0.0 || p8  != 0.0 ||
354           p9  != 0.0 || p10 != 0.0 || p11 != 0.0 || p12 != 0.0 ||
355           p13 != 0.0 || p14 != 0.0 || p15 != 0.0 || p16 != 0.0 ||
356           p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 ||
357           p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 ||
358           p25 != 0.0 || p26 != 0.0 || p27 != 0.0 || p28 != 0.0 ||
359           p29 != 0.0 || p30 != 0.0 || p31 != 0.0 || p32 != 0.0 ||
360           p33 != 0.0 || p34 != 0.0 || p35 != 0.0 || p36 != 0.0 ||
361           p37 != 0.0 || p38 != 0.0 || p39 != 0.0 || p40 != 0.0 ||
362           p41 != 0.0 || p42 != 0.0 || p43 != 0.0 || p44 != 0.0 ||
363           p45 != 0.0 || p46 != 0.0 || p47 != 0.0 || p48 != 0.0 ||
364           p49 != 0.0) {
365         pv = ba + 49*diag_offset[row];
366         pj = bj + diag_offset[row] + 1;
367 	x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
368 	x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
369 	x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
370 	x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
371 	x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
372 	x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
373 	x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
374 	x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
375 	x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
376 	x37 = pv[36]; x38 = pv[37]; x39 = pv[38]; x40 = pv[39];
377 	x41 = pv[40]; x42 = pv[41]; x43 = pv[42]; x44 = pv[43];
378 	x45 = pv[44]; x46 = pv[45]; x47 = pv[46]; x48 = pv[47];
379 	x49 = pv[48];
380         pc[0]  = m1  = p1*x1  + p8*x2   + p15*x3  + p22*x4  + p29*x5  + p36*x6 + p43*x7;
381         pc[1]  = m2  = p2*x1  + p9*x2   + p16*x3  + p23*x4  + p30*x5  + p37*x6 + p44*x7;
382         pc[2]  = m3  = p3*x1  + p10*x2  + p17*x3  + p24*x4  + p31*x5  + p38*x6 + p45*x7;
383         pc[3]  = m4  = p4*x1  + p11*x2  + p18*x3  + p25*x4  + p32*x5  + p39*x6 + p46*x7;
384         pc[4]  = m5  = p5*x1  + p12*x2  + p19*x3  + p26*x4  + p33*x5  + p40*x6 + p47*x7;
385         pc[5]  = m6  = p6*x1  + p13*x2  + p20*x3  + p27*x4  + p34*x5  + p41*x6 + p48*x7;
386         pc[6]  = m7  = p7*x1  + p14*x2  + p21*x3  + p28*x4  + p35*x5  + p42*x6 + p49*x7;
387 
388         pc[7]  = m8  = p1*x8  + p8*x9   + p15*x10 + p22*x11 + p29*x12 + p36*x13 + p43*x14;
389         pc[8]  = m9  = p2*x8  + p9*x9   + p16*x10 + p23*x11 + p30*x12 + p37*x13 + p44*x14;
390         pc[9]  = m10 = p3*x8  + p10*x9  + p17*x10 + p24*x11 + p31*x12 + p38*x13 + p45*x14;
391         pc[10] = m11 = p4*x8  + p11*x9  + p18*x10 + p25*x11 + p32*x12 + p39*x13 + p46*x14;
392         pc[11] = m12 = p5*x8  + p12*x9  + p19*x10 + p26*x11 + p33*x12 + p40*x13 + p47*x14;
393         pc[12] = m13 = p6*x8  + p13*x9  + p20*x10 + p27*x11 + p34*x12 + p41*x13 + p48*x14;
394         pc[13] = m14 = p7*x8  + p14*x9  + p21*x10 + p28*x11 + p35*x12 + p42*x13 + p49*x14;
395 
396         pc[14] = m15 = p1*x15 + p8*x16  + p15*x17 + p22*x18 + p29*x19 + p36*x20 + p43*x21;
397         pc[15] = m16 = p2*x15 + p9*x16  + p16*x17 + p23*x18 + p30*x19 + p37*x20 + p44*x21;
398         pc[16] = m17 = p3*x15 + p10*x16 + p17*x17 + p24*x18 + p31*x19 + p38*x20 + p45*x21;
399         pc[17] = m18 = p4*x15 + p11*x16 + p18*x17 + p25*x18 + p32*x19 + p39*x20 + p46*x21;
400         pc[18] = m19 = p5*x15 + p12*x16 + p19*x17 + p26*x18 + p33*x19 + p40*x20 + p47*x21;
401         pc[19] = m20 = p6*x15 + p13*x16 + p20*x17 + p27*x18 + p34*x19 + p41*x20 + p48*x21;
402         pc[20] = m21 = p7*x15 + p14*x16 + p21*x17 + p28*x18 + p35*x19 + p42*x20 + p49*x21;
403 
404         pc[21] = m22 = p1*x22 + p8*x23  + p15*x24 + p22*x25 + p29*x26 + p36*x27 + p43*x28;
405         pc[22] = m23 = p2*x22 + p9*x23  + p16*x24 + p23*x25 + p30*x26 + p37*x27 + p44*x28;
406         pc[23] = m24 = p3*x22 + p10*x23 + p17*x24 + p24*x25 + p31*x26 + p38*x27 + p45*x28;
407         pc[24] = m25 = p4*x22 + p11*x23 + p18*x24 + p25*x25 + p32*x26 + p39*x27 + p46*x28;
408         pc[25] = m26 = p5*x22 + p12*x23 + p19*x24 + p26*x25 + p33*x26 + p40*x27 + p47*x28;
409         pc[26] = m27 = p6*x22 + p13*x23 + p20*x24 + p27*x25 + p34*x26 + p41*x27 + p48*x28;
410         pc[27] = m28 = p7*x22 + p14*x23 + p21*x24 + p28*x25 + p35*x26 + p42*x27 + p49*x28;
411 
412         pc[28] = m29 = p1*x29 + p8*x30  + p15*x31 + p22*x32 + p29*x33 + p36*x34 + p43*x35;
413         pc[29] = m30 = p2*x29 + p9*x30  + p16*x31 + p23*x32 + p30*x33 + p37*x34 + p44*x35;
414         pc[30] = m31 = p3*x29 + p10*x30 + p17*x31 + p24*x32 + p31*x33 + p38*x34 + p45*x35;
415         pc[31] = m32 = p4*x29 + p11*x30 + p18*x31 + p25*x32 + p32*x33 + p39*x34 + p46*x35;
416         pc[32] = m33 = p5*x29 + p12*x30 + p19*x31 + p26*x32 + p33*x33 + p40*x34 + p47*x35;
417         pc[33] = m34 = p6*x29 + p13*x30 + p20*x31 + p27*x32 + p34*x33 + p41*x34 + p48*x35;
418         pc[34] = m35 = p7*x29 + p14*x30 + p21*x31 + p28*x32 + p35*x33 + p42*x34 + p49*x35;
419 
420         pc[35] = m36 = p1*x36 + p8*x37  + p15*x38 + p22*x39 + p29*x40 + p36*x41 + p43*x42;
421         pc[36] = m37 = p2*x36 + p9*x37  + p16*x38 + p23*x39 + p30*x40 + p37*x41 + p44*x42;
422         pc[37] = m38 = p3*x36 + p10*x37 + p17*x38 + p24*x39 + p31*x40 + p38*x41 + p45*x42;
423         pc[38] = m39 = p4*x36 + p11*x37 + p18*x38 + p25*x39 + p32*x40 + p39*x41 + p46*x42;
424         pc[39] = m40 = p5*x36 + p12*x37 + p19*x38 + p26*x39 + p33*x40 + p40*x41 + p47*x42;
425         pc[40] = m41 = p6*x36 + p13*x37 + p20*x38 + p27*x39 + p34*x40 + p41*x41 + p48*x42;
426         pc[41] = m42 = p7*x36 + p14*x37 + p21*x38 + p28*x39 + p35*x40 + p42*x41 + p49*x42;
427 
428         pc[42] = m43 = p1*x43 + p8*x44  + p15*x45 + p22*x46 + p29*x47 + p36*x48 + p43*x49;
429         pc[43] = m44 = p2*x43 + p9*x44  + p16*x45 + p23*x46 + p30*x47 + p37*x48 + p44*x49;
430         pc[44] = m45 = p3*x43 + p10*x44 + p17*x45 + p24*x46 + p31*x47 + p38*x48 + p45*x49;
431         pc[45] = m46 = p4*x43 + p11*x44 + p18*x45 + p25*x46 + p32*x47 + p39*x48 + p46*x49;
432         pc[46] = m47 = p5*x43 + p12*x44 + p19*x45 + p26*x46 + p33*x47 + p40*x48 + p47*x49;
433         pc[47] = m48 = p6*x43 + p13*x44 + p20*x45 + p27*x46 + p34*x47 + p41*x48 + p48*x49;
434         pc[48] = m49 = p7*x43 + p14*x44 + p21*x45 + p28*x46 + p35*x47 + p42*x48 + p49*x49;
435 
436         nz = bi[row+1] - diag_offset[row] - 1;
437         pv += 49;
438         for (j=0; j<nz; j++) {
439 	  x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
440 	  x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
441 	  x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
442 	  x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
443 	  x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
444 	  x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
445 	  x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
446 	  x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
447 	  x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
448 	  x37 = pv[36]; x38 = pv[37]; x39 = pv[38]; x40 = pv[39];
449 	  x41 = pv[40]; x42 = pv[41]; x43 = pv[42]; x44 = pv[43];
450 	  x45 = pv[44]; x46 = pv[45]; x47 = pv[46]; x48 = pv[47];
451 	  x49 = pv[48];
452 	  x    = rtmp + 49*pj[j];
453 	  x[0]  -= m1*x1  + m8*x2   + m15*x3  + m22*x4  + m29*x5  + m36*x6 + m43*x7;
454 	  x[1]  -= m2*x1  + m9*x2   + m16*x3  + m23*x4  + m30*x5  + m37*x6 + m44*x7;
455 	  x[2]  -= m3*x1  + m10*x2  + m17*x3  + m24*x4  + m31*x5  + m38*x6 + m45*x7;
456 	  x[3]  -= m4*x1  + m11*x2  + m18*x3  + m25*x4  + m32*x5  + m39*x6 + m46*x7;
457 	  x[4]  -= m5*x1  + m12*x2  + m19*x3  + m26*x4  + m33*x5  + m40*x6 + m47*x7;
458 	  x[5]  -= m6*x1  + m13*x2  + m20*x3  + m27*x4  + m34*x5  + m41*x6 + m48*x7;
459 	  x[6]  -= m7*x1  + m14*x2  + m21*x3  + m28*x4  + m35*x5  + m42*x6 + m49*x7;
460 
461 	  x[7]  -= m1*x8  + m8*x9   + m15*x10 + m22*x11 + m29*x12 + m36*x13 + m43*x14;
462 	  x[8]  -= m2*x8  + m9*x9   + m16*x10 + m23*x11 + m30*x12 + m37*x13 + m44*x14;
463 	  x[9]  -= m3*x8  + m10*x9  + m17*x10 + m24*x11 + m31*x12 + m38*x13 + m45*x14;
464 	  x[10] -= m4*x8  + m11*x9  + m18*x10 + m25*x11 + m32*x12 + m39*x13 + m46*x14;
465 	  x[11] -= m5*x8  + m12*x9  + m19*x10 + m26*x11 + m33*x12 + m40*x13 + m47*x14;
466 	  x[12] -= m6*x8  + m13*x9  + m20*x10 + m27*x11 + m34*x12 + m41*x13 + m48*x14;
467 	  x[13] -= m7*x8  + m14*x9  + m21*x10 + m28*x11 + m35*x12 + m42*x13 + m49*x14;
468 
469 	  x[14] -= m1*x15 + m8*x16  + m15*x17 + m22*x18 + m29*x19 + m36*x20 + m43*x21;
470 	  x[15] -= m2*x15 + m9*x16  + m16*x17 + m23*x18 + m30*x19 + m37*x20 + m44*x21;
471 	  x[16] -= m3*x15 + m10*x16 + m17*x17 + m24*x18 + m31*x19 + m38*x20 + m45*x21;
472 	  x[17] -= m4*x15 + m11*x16 + m18*x17 + m25*x18 + m32*x19 + m39*x20 + m46*x21;
473 	  x[18] -= m5*x15 + m12*x16 + m19*x17 + m26*x18 + m33*x19 + m40*x20 + m47*x21;
474 	  x[19] -= m6*x15 + m13*x16 + m20*x17 + m27*x18 + m34*x19 + m41*x20 + m48*x21;
475 	  x[20] -= m7*x15 + m14*x16 + m21*x17 + m28*x18 + m35*x19 + m42*x20 + m49*x21;
476 
477 	  x[21] -= m1*x22 + m8*x23  + m15*x24 + m22*x25 + m29*x26 + m36*x27 + m43*x28;
478 	  x[22] -= m2*x22 + m9*x23  + m16*x24 + m23*x25 + m30*x26 + m37*x27 + m44*x28;
479 	  x[23] -= m3*x22 + m10*x23 + m17*x24 + m24*x25 + m31*x26 + m38*x27 + m45*x28;
480 	  x[24] -= m4*x22 + m11*x23 + m18*x24 + m25*x25 + m32*x26 + m39*x27 + m46*x28;
481 	  x[25] -= m5*x22 + m12*x23 + m19*x24 + m26*x25 + m33*x26 + m40*x27 + m47*x28;
482 	  x[26] -= m6*x22 + m13*x23 + m20*x24 + m27*x25 + m34*x26 + m41*x27 + m48*x28;
483 	  x[27] -= m7*x22 + m14*x23 + m21*x24 + m28*x25 + m35*x26 + m42*x27 + m49*x28;
484 
485 	  x[28] -= m1*x29 + m8*x30  + m15*x31 + m22*x32 + m29*x33 + m36*x34 + m43*x35;
486 	  x[29] -= m2*x29 + m9*x30  + m16*x31 + m23*x32 + m30*x33 + m37*x34 + m44*x35;
487 	  x[30] -= m3*x29 + m10*x30 + m17*x31 + m24*x32 + m31*x33 + m38*x34 + m45*x35;
488 	  x[31] -= m4*x29 + m11*x30 + m18*x31 + m25*x32 + m32*x33 + m39*x34 + m46*x35;
489 	  x[32] -= m5*x29 + m12*x30 + m19*x31 + m26*x32 + m33*x33 + m40*x34 + m47*x35;
490 	  x[33] -= m6*x29 + m13*x30 + m20*x31 + m27*x32 + m34*x33 + m41*x34 + m48*x35;
491 	  x[34] -= m7*x29 + m14*x30 + m21*x31 + m28*x32 + m35*x33 + m42*x34 + m49*x35;
492 
493 	  x[35] -= m1*x36 + m8*x37  + m15*x38 + m22*x39 + m29*x40 + m36*x41 + m43*x42;
494 	  x[36] -= m2*x36 + m9*x37  + m16*x38 + m23*x39 + m30*x40 + m37*x41 + m44*x42;
495 	  x[37] -= m3*x36 + m10*x37 + m17*x38 + m24*x39 + m31*x40 + m38*x41 + m45*x42;
496 	  x[38] -= m4*x36 + m11*x37 + m18*x38 + m25*x39 + m32*x40 + m39*x41 + m46*x42;
497 	  x[39] -= m5*x36 + m12*x37 + m19*x38 + m26*x39 + m33*x40 + m40*x41 + m47*x42;
498 	  x[40] -= m6*x36 + m13*x37 + m20*x38 + m27*x39 + m34*x40 + m41*x41 + m48*x42;
499 	  x[41] -= m7*x36 + m14*x37 + m21*x38 + m28*x39 + m35*x40 + m42*x41 + m49*x42;
500 
501 	  x[42] -= m1*x43 + m8*x44  + m15*x45 + m22*x46 + m29*x47 + m36*x48 + m43*x49;
502 	  x[43] -= m2*x43 + m9*x44  + m16*x45 + m23*x46 + m30*x47 + m37*x48 + m44*x49;
503 	  x[44] -= m3*x43 + m10*x44 + m17*x45 + m24*x46 + m31*x47 + m38*x48 + m45*x49;
504 	  x[45] -= m4*x43 + m11*x44 + m18*x45 + m25*x46 + m32*x47 + m39*x48 + m46*x49;
505 	  x[46] -= m5*x43 + m12*x44 + m19*x45 + m26*x46 + m33*x47 + m40*x48 + m47*x49;
506 	  x[47] -= m6*x43 + m13*x44 + m20*x45 + m27*x46 + m34*x47 + m41*x48 + m48*x49;
507 	  x[48] -= m7*x43 + m14*x44 + m21*x45 + m28*x46 + m35*x47 + m42*x48 + m49*x49;
508           pv   += 49;
509         }
510         PLogFlops(686*nz+637);
511       }
512       row = *ajtmp++;
513     }
514     /* finished row so stick it into b->a */
515     pv = ba + 49*bi[i];
516     pj = bj + bi[i];
517     nz = bi[i+1] - bi[i];
518     for (j=0; j<nz; j++) {
519       x      = rtmp+49*pj[j];
520       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
521       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7];
522       pv[8]  = x[8];  pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11];
523       pv[12] = x[12]; pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
524       pv[16] = x[16]; pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19];
525       pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23];
526       pv[24] = x[24]; pv[25] = x[25]; pv[26] = x[26]; pv[27] = x[27];
527       pv[28] = x[28]; pv[29] = x[29]; pv[30] = x[30]; pv[31] = x[31];
528       pv[32] = x[32]; pv[33] = x[33]; pv[34] = x[34]; pv[35] = x[35];
529       pv[36] = x[36]; pv[37] = x[37]; pv[38] = x[38]; pv[39] = x[39];
530       pv[40] = x[40]; pv[41] = x[41]; pv[42] = x[42]; pv[43] = x[43];
531       pv[44] = x[44]; pv[45] = x[45]; pv[46] = x[46]; pv[47] = x[47];
532       pv[48] = x[48];
533       pv   += 49;
534     }
535     /* invert diagonal block */
536     w = ba + 49*diag_offset[i];
537     ierr = Kernel_A_gets_inverse_A_7(w);CHKERRQ(ierr);
538   }
539 
540   ierr = PetscFree(rtmp);CHKERRQ(ierr);
541   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
542   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
543   C->factor = FACTOR_LU;
544   C->assembled = PETSC_TRUE;
545   PLogFlops(1.3333*343*b->mbs); /* from inverting diagonal blocks */
546   PetscFunctionReturn(0);
547 }
548 
549 /*
550       Version for when blocks are 7 by 7 Using natural ordering
551 */
552 #undef __FUNC__
553 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_7_NaturalOrdering"
554 int MatCholeskyFactorNumeric_SeqSBAIJ_7_NaturalOrdering(Mat A,Mat *B)
555 {
556   Mat          C = *B;
557   Mat_SeqBAIJ  *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
558   int          ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
559   int          *ajtmpold,*ajtmp,nz,row;
560   int          *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
561   MatScalar    *pv,*v,*rtmp,*pc,*w,*x;
562   MatScalar    x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15;
563   MatScalar    x16,x17,x18,x19,x20,x21,x22,x23,x24,x25;
564   MatScalar    p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15;
565   MatScalar    p16,p17,p18,p19,p20,p21,p22,p23,p24,p25;
566   MatScalar    m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12,m13,m14,m15;
567   MatScalar    m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
568   MatScalar    p26,p27,p28,p29,p30,p31,p32,p33,p34,p35,p36;
569   MatScalar    p37,p38,p39,p40,p41,p42,p43,p44,p45,p46,p47,p48,p49;
570   MatScalar    x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36;
571   MatScalar    x37,x38,x39,x40,x41,x42,x43,x44,x45,x46,x47,x48,x49;
572   MatScalar    m26,m27,m28,m29,m30,m31,m32,m33,m34,m35,m36;
573   MatScalar    m37,m38,m39,m40,m41,m42,m43,m44,m45,m46,m47,m48,m49;
574   MatScalar    *ba = b->a,*aa = a->a;
575 
576   PetscFunctionBegin;
577   rtmp  = (MatScalar*)PetscMalloc(49*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
578   for (i=0; i<n; i++) {
579     nz    = bi[i+1] - bi[i];
580     ajtmp = bj + bi[i];
581     for  (j=0; j<nz; j++) {
582       x = rtmp+49*ajtmp[j];
583       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
584       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
585       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = x[25] = 0.0 ;
586       x[26] = x[27] = x[28] = x[29] = x[30] = x[31] = x[32] = x[33] = 0.0 ;
587       x[34] = x[35] = x[36] = x[37] = x[38] = x[39] = x[40] = x[41] = 0.0 ;
588       x[42] = x[43] = x[44] = x[45] = x[46] = x[47] = x[48] = 0.0 ;
589     }
590     /* load in initial (unfactored row) */
591     nz       = ai[i+1] - ai[i];
592     ajtmpold = aj + ai[i];
593     v        = aa + 49*ai[i];
594     for (j=0; j<nz; j++) {
595       x    = rtmp+49*ajtmpold[j];
596       x[0] =  v[0];  x[1] =  v[1];  x[2] =  v[2];  x[3] =  v[3];
597       x[4] =  v[4];  x[5] =  v[5];  x[6] =  v[6];  x[7] =  v[7];
598       x[8] =  v[8];  x[9] =  v[9];  x[10] = v[10]; x[11] = v[11];
599       x[12] = v[12]; x[13] = v[13]; x[14] = v[14]; x[15] = v[15];
600       x[16] = v[16]; x[17] = v[17]; x[18] = v[18]; x[19] = v[19];
601       x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23];
602       x[24] = v[24]; x[25] = v[25]; x[26] = v[26]; x[27] = v[27];
603       x[28] = v[28]; x[29] = v[29]; x[30] = v[30]; x[31] = v[31];
604       x[32] = v[32]; x[33] = v[33]; x[34] = v[34]; x[35] = v[35];
605       x[36] = v[36]; x[37] = v[37]; x[38] = v[38]; x[39] = v[39];
606       x[40] = v[40]; x[41] = v[41]; x[42] = v[42]; x[43] = v[43];
607       x[44] = v[44]; x[45] = v[45]; x[46] = v[46]; x[47] = v[47];
608       x[48] = v[48];
609       v    += 49;
610     }
611     row = *ajtmp++;
612     while (row < i) {
613       pc  = rtmp + 49*row;
614       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
615       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];
616       p9  = pc[8];  p10 = pc[9];  p11 = pc[10]; p12 = pc[11];
617       p13 = pc[12]; p14 = pc[13]; p15 = pc[14]; p16 = pc[15];
618       p17 = pc[16]; p18 = pc[17]; p19 = pc[18]; p20 = pc[19];
619       p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
620       p25 = pc[24]; p26 = pc[25]; p27 = pc[26]; p28 = pc[27];
621       p29 = pc[28]; p30 = pc[29]; p31 = pc[30]; p32 = pc[31];
622       p33 = pc[32]; p34 = pc[33]; p35 = pc[34]; p36 = pc[35];
623       p37 = pc[36]; p38 = pc[37]; p39 = pc[38]; p40 = pc[39];
624       p41 = pc[40]; p42 = pc[41]; p43 = pc[42]; p44 = pc[43];
625       p45 = pc[44]; p46 = pc[45]; p47 = pc[46]; p48 = pc[47];
626       p49 = pc[48];
627       if (p1  != 0.0 || p2  != 0.0 || p3  != 0.0 || p4  != 0.0 ||
628           p5  != 0.0 || p6  != 0.0 || p7  != 0.0 || p8  != 0.0 ||
629           p9  != 0.0 || p10 != 0.0 || p11 != 0.0 || p12 != 0.0 ||
630           p13 != 0.0 || p14 != 0.0 || p15 != 0.0 || p16 != 0.0 ||
631           p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 ||
632           p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 ||
633           p25 != 0.0 || p26 != 0.0 || p27 != 0.0 || p28 != 0.0 ||
634           p29 != 0.0 || p30 != 0.0 || p31 != 0.0 || p32 != 0.0 ||
635           p33 != 0.0 || p34 != 0.0 || p35 != 0.0 || p36 != 0.0 ||
636           p37 != 0.0 || p38 != 0.0 || p39 != 0.0 || p40 != 0.0 ||
637           p41 != 0.0 || p42 != 0.0 || p43 != 0.0 || p44 != 0.0 ||
638           p45 != 0.0 || p46 != 0.0 || p47 != 0.0 || p48 != 0.0 ||
639           p49 != 0.0) {
640         pv = ba + 49*diag_offset[row];
641         pj = bj + diag_offset[row] + 1;
642 	x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
643 	x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
644 	x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
645 	x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
646 	x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
647 	x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
648 	x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
649 	x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
650 	x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
651 	x37 = pv[36]; x38 = pv[37]; x39 = pv[38]; x40 = pv[39];
652 	x41 = pv[40]; x42 = pv[41]; x43 = pv[42]; x44 = pv[43];
653 	x45 = pv[44]; x46 = pv[45]; x47 = pv[46]; x48 = pv[47];
654         x49 = pv[48];
655         pc[0]  = m1  = p1*x1  + p8*x2   + p15*x3  + p22*x4  + p29*x5  + p36*x6 + p43*x7;
656         pc[1]  = m2  = p2*x1  + p9*x2   + p16*x3  + p23*x4  + p30*x5  + p37*x6 + p44*x7;
657         pc[2]  = m3  = p3*x1  + p10*x2  + p17*x3  + p24*x4  + p31*x5  + p38*x6 + p45*x7;
658         pc[3]  = m4  = p4*x1  + p11*x2  + p18*x3  + p25*x4  + p32*x5  + p39*x6 + p46*x7;
659         pc[4]  = m5  = p5*x1  + p12*x2  + p19*x3  + p26*x4  + p33*x5  + p40*x6 + p47*x7;
660         pc[5]  = m6  = p6*x1  + p13*x2  + p20*x3  + p27*x4  + p34*x5  + p41*x6 + p48*x7;
661         pc[6]  = m7  = p7*x1  + p14*x2  + p21*x3  + p28*x4  + p35*x5  + p42*x6 + p49*x7;
662 
663         pc[7]  = m8  = p1*x8  + p8*x9   + p15*x10 + p22*x11 + p29*x12 + p36*x13 + p43*x14;
664         pc[8]  = m9  = p2*x8  + p9*x9   + p16*x10 + p23*x11 + p30*x12 + p37*x13 + p44*x14;
665         pc[9]  = m10 = p3*x8  + p10*x9  + p17*x10 + p24*x11 + p31*x12 + p38*x13 + p45*x14;
666         pc[10] = m11 = p4*x8  + p11*x9  + p18*x10 + p25*x11 + p32*x12 + p39*x13 + p46*x14;
667         pc[11] = m12 = p5*x8  + p12*x9  + p19*x10 + p26*x11 + p33*x12 + p40*x13 + p47*x14;
668         pc[12] = m13 = p6*x8  + p13*x9  + p20*x10 + p27*x11 + p34*x12 + p41*x13 + p48*x14;
669         pc[13] = m14 = p7*x8  + p14*x9  + p21*x10 + p28*x11 + p35*x12 + p42*x13 + p49*x14;
670 
671         pc[14] = m15 = p1*x15 + p8*x16  + p15*x17 + p22*x18 + p29*x19 + p36*x20 + p43*x21;
672         pc[15] = m16 = p2*x15 + p9*x16  + p16*x17 + p23*x18 + p30*x19 + p37*x20 + p44*x21;
673         pc[16] = m17 = p3*x15 + p10*x16 + p17*x17 + p24*x18 + p31*x19 + p38*x20 + p45*x21;
674         pc[17] = m18 = p4*x15 + p11*x16 + p18*x17 + p25*x18 + p32*x19 + p39*x20 + p46*x21;
675         pc[18] = m19 = p5*x15 + p12*x16 + p19*x17 + p26*x18 + p33*x19 + p40*x20 + p47*x21;
676         pc[19] = m20 = p6*x15 + p13*x16 + p20*x17 + p27*x18 + p34*x19 + p41*x20 + p48*x21;
677         pc[20] = m21 = p7*x15 + p14*x16 + p21*x17 + p28*x18 + p35*x19 + p42*x20 + p49*x21;
678 
679         pc[21] = m22 = p1*x22 + p8*x23  + p15*x24 + p22*x25 + p29*x26 + p36*x27 + p43*x28;
680         pc[22] = m23 = p2*x22 + p9*x23  + p16*x24 + p23*x25 + p30*x26 + p37*x27 + p44*x28;
681         pc[23] = m24 = p3*x22 + p10*x23 + p17*x24 + p24*x25 + p31*x26 + p38*x27 + p45*x28;
682         pc[24] = m25 = p4*x22 + p11*x23 + p18*x24 + p25*x25 + p32*x26 + p39*x27 + p46*x28;
683         pc[25] = m26 = p5*x22 + p12*x23 + p19*x24 + p26*x25 + p33*x26 + p40*x27 + p47*x28;
684         pc[26] = m27 = p6*x22 + p13*x23 + p20*x24 + p27*x25 + p34*x26 + p41*x27 + p48*x28;
685         pc[27] = m28 = p7*x22 + p14*x23 + p21*x24 + p28*x25 + p35*x26 + p42*x27 + p49*x28;
686 
687         pc[28] = m29 = p1*x29 + p8*x30  + p15*x31 + p22*x32 + p29*x33 + p36*x34 + p43*x35;
688         pc[29] = m30 = p2*x29 + p9*x30  + p16*x31 + p23*x32 + p30*x33 + p37*x34 + p44*x35;
689         pc[30] = m31 = p3*x29 + p10*x30 + p17*x31 + p24*x32 + p31*x33 + p38*x34 + p45*x35;
690         pc[31] = m32 = p4*x29 + p11*x30 + p18*x31 + p25*x32 + p32*x33 + p39*x34 + p46*x35;
691         pc[32] = m33 = p5*x29 + p12*x30 + p19*x31 + p26*x32 + p33*x33 + p40*x34 + p47*x35;
692         pc[33] = m34 = p6*x29 + p13*x30 + p20*x31 + p27*x32 + p34*x33 + p41*x34 + p48*x35;
693         pc[34] = m35 = p7*x29 + p14*x30 + p21*x31 + p28*x32 + p35*x33 + p42*x34 + p49*x35;
694 
695         pc[35] = m36 = p1*x36 + p8*x37  + p15*x38 + p22*x39 + p29*x40 + p36*x41 + p43*x42;
696         pc[36] = m37 = p2*x36 + p9*x37  + p16*x38 + p23*x39 + p30*x40 + p37*x41 + p44*x42;
697         pc[37] = m38 = p3*x36 + p10*x37 + p17*x38 + p24*x39 + p31*x40 + p38*x41 + p45*x42;
698         pc[38] = m39 = p4*x36 + p11*x37 + p18*x38 + p25*x39 + p32*x40 + p39*x41 + p46*x42;
699         pc[39] = m40 = p5*x36 + p12*x37 + p19*x38 + p26*x39 + p33*x40 + p40*x41 + p47*x42;
700         pc[40] = m41 = p6*x36 + p13*x37 + p20*x38 + p27*x39 + p34*x40 + p41*x41 + p48*x42;
701         pc[41] = m42 = p7*x36 + p14*x37 + p21*x38 + p28*x39 + p35*x40 + p42*x41 + p49*x42;
702 
703         pc[42] = m43 = p1*x43 + p8*x44  + p15*x45 + p22*x46 + p29*x47 + p36*x48 + p43*x49;
704         pc[43] = m44 = p2*x43 + p9*x44  + p16*x45 + p23*x46 + p30*x47 + p37*x48 + p44*x49;
705         pc[44] = m45 = p3*x43 + p10*x44 + p17*x45 + p24*x46 + p31*x47 + p38*x48 + p45*x49;
706         pc[45] = m46 = p4*x43 + p11*x44 + p18*x45 + p25*x46 + p32*x47 + p39*x48 + p46*x49;
707         pc[46] = m47 = p5*x43 + p12*x44 + p19*x45 + p26*x46 + p33*x47 + p40*x48 + p47*x49;
708         pc[47] = m48 = p6*x43 + p13*x44 + p20*x45 + p27*x46 + p34*x47 + p41*x48 + p48*x49;
709         pc[48] = m49 = p7*x43 + p14*x44 + p21*x45 + p28*x46 + p35*x47 + p42*x48 + p49*x49;
710 
711         nz = bi[row+1] - diag_offset[row] - 1;
712         pv += 49;
713         for (j=0; j<nz; j++) {
714 	  x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
715 	  x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
716 	  x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
717 	  x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
718 	  x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
719 	  x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
720 	  x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
721 	  x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
722 	  x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
723 	  x37 = pv[36]; x38 = pv[37]; x39 = pv[38]; x40 = pv[39];
724 	  x41 = pv[40]; x42 = pv[41]; x43 = pv[42]; x44 = pv[43];
725 	  x45 = pv[44]; x46 = pv[45]; x47 = pv[46]; x48 = pv[47];
726 	  x49 = pv[48];
727 	  x    = rtmp + 49*pj[j];
728 	  x[0]  -= m1*x1  + m8*x2   + m15*x3  + m22*x4  + m29*x5  + m36*x6 + m43*x7;
729 	  x[1]  -= m2*x1  + m9*x2   + m16*x3  + m23*x4  + m30*x5  + m37*x6 + m44*x7;
730 	  x[2]  -= m3*x1  + m10*x2  + m17*x3  + m24*x4  + m31*x5  + m38*x6 + m45*x7;
731 	  x[3]  -= m4*x1  + m11*x2  + m18*x3  + m25*x4  + m32*x5  + m39*x6 + m46*x7;
732 	  x[4]  -= m5*x1  + m12*x2  + m19*x3  + m26*x4  + m33*x5  + m40*x6 + m47*x7;
733 	  x[5]  -= m6*x1  + m13*x2  + m20*x3  + m27*x4  + m34*x5  + m41*x6 + m48*x7;
734 	  x[6]  -= m7*x1  + m14*x2  + m21*x3  + m28*x4  + m35*x5  + m42*x6 + m49*x7;
735 
736 	  x[7]  -= m1*x8  + m8*x9   + m15*x10 + m22*x11 + m29*x12 + m36*x13 + m43*x14;
737 	  x[8]  -= m2*x8  + m9*x9   + m16*x10 + m23*x11 + m30*x12 + m37*x13 + m44*x14;
738 	  x[9]  -= m3*x8  + m10*x9  + m17*x10 + m24*x11 + m31*x12 + m38*x13 + m45*x14;
739 	  x[10] -= m4*x8  + m11*x9  + m18*x10 + m25*x11 + m32*x12 + m39*x13 + m46*x14;
740 	  x[11] -= m5*x8  + m12*x9  + m19*x10 + m26*x11 + m33*x12 + m40*x13 + m47*x14;
741 	  x[12] -= m6*x8  + m13*x9  + m20*x10 + m27*x11 + m34*x12 + m41*x13 + m48*x14;
742 	  x[13] -= m7*x8  + m14*x9  + m21*x10 + m28*x11 + m35*x12 + m42*x13 + m49*x14;
743 
744 	  x[14] -= m1*x15 + m8*x16  + m15*x17 + m22*x18 + m29*x19 + m36*x20 + m43*x21;
745 	  x[15] -= m2*x15 + m9*x16  + m16*x17 + m23*x18 + m30*x19 + m37*x20 + m44*x21;
746 	  x[16] -= m3*x15 + m10*x16 + m17*x17 + m24*x18 + m31*x19 + m38*x20 + m45*x21;
747 	  x[17] -= m4*x15 + m11*x16 + m18*x17 + m25*x18 + m32*x19 + m39*x20 + m46*x21;
748 	  x[18] -= m5*x15 + m12*x16 + m19*x17 + m26*x18 + m33*x19 + m40*x20 + m47*x21;
749 	  x[19] -= m6*x15 + m13*x16 + m20*x17 + m27*x18 + m34*x19 + m41*x20 + m48*x21;
750 	  x[20] -= m7*x15 + m14*x16 + m21*x17 + m28*x18 + m35*x19 + m42*x20 + m49*x21;
751 
752 	  x[21] -= m1*x22 + m8*x23  + m15*x24 + m22*x25 + m29*x26 + m36*x27 + m43*x28;
753 	  x[22] -= m2*x22 + m9*x23  + m16*x24 + m23*x25 + m30*x26 + m37*x27 + m44*x28;
754 	  x[23] -= m3*x22 + m10*x23 + m17*x24 + m24*x25 + m31*x26 + m38*x27 + m45*x28;
755 	  x[24] -= m4*x22 + m11*x23 + m18*x24 + m25*x25 + m32*x26 + m39*x27 + m46*x28;
756 	  x[25] -= m5*x22 + m12*x23 + m19*x24 + m26*x25 + m33*x26 + m40*x27 + m47*x28;
757 	  x[26] -= m6*x22 + m13*x23 + m20*x24 + m27*x25 + m34*x26 + m41*x27 + m48*x28;
758 	  x[27] -= m7*x22 + m14*x23 + m21*x24 + m28*x25 + m35*x26 + m42*x27 + m49*x28;
759 
760 	  x[28] -= m1*x29 + m8*x30  + m15*x31 + m22*x32 + m29*x33 + m36*x34 + m43*x35;
761 	  x[29] -= m2*x29 + m9*x30  + m16*x31 + m23*x32 + m30*x33 + m37*x34 + m44*x35;
762 	  x[30] -= m3*x29 + m10*x30 + m17*x31 + m24*x32 + m31*x33 + m38*x34 + m45*x35;
763 	  x[31] -= m4*x29 + m11*x30 + m18*x31 + m25*x32 + m32*x33 + m39*x34 + m46*x35;
764 	  x[32] -= m5*x29 + m12*x30 + m19*x31 + m26*x32 + m33*x33 + m40*x34 + m47*x35;
765 	  x[33] -= m6*x29 + m13*x30 + m20*x31 + m27*x32 + m34*x33 + m41*x34 + m48*x35;
766 	  x[34] -= m7*x29 + m14*x30 + m21*x31 + m28*x32 + m35*x33 + m42*x34 + m49*x35;
767 
768 	  x[35] -= m1*x36 + m8*x37  + m15*x38 + m22*x39 + m29*x40 + m36*x41 + m43*x42;
769 	  x[36] -= m2*x36 + m9*x37  + m16*x38 + m23*x39 + m30*x40 + m37*x41 + m44*x42;
770 	  x[37] -= m3*x36 + m10*x37 + m17*x38 + m24*x39 + m31*x40 + m38*x41 + m45*x42;
771 	  x[38] -= m4*x36 + m11*x37 + m18*x38 + m25*x39 + m32*x40 + m39*x41 + m46*x42;
772 	  x[39] -= m5*x36 + m12*x37 + m19*x38 + m26*x39 + m33*x40 + m40*x41 + m47*x42;
773 	  x[40] -= m6*x36 + m13*x37 + m20*x38 + m27*x39 + m34*x40 + m41*x41 + m48*x42;
774 	  x[41] -= m7*x36 + m14*x37 + m21*x38 + m28*x39 + m35*x40 + m42*x41 + m49*x42;
775 
776 	  x[42] -= m1*x43 + m8*x44  + m15*x45 + m22*x46 + m29*x47 + m36*x48 + m43*x49;
777 	  x[43] -= m2*x43 + m9*x44  + m16*x45 + m23*x46 + m30*x47 + m37*x48 + m44*x49;
778 	  x[44] -= m3*x43 + m10*x44 + m17*x45 + m24*x46 + m31*x47 + m38*x48 + m45*x49;
779 	  x[45] -= m4*x43 + m11*x44 + m18*x45 + m25*x46 + m32*x47 + m39*x48 + m46*x49;
780 	  x[46] -= m5*x43 + m12*x44 + m19*x45 + m26*x46 + m33*x47 + m40*x48 + m47*x49;
781 	  x[47] -= m6*x43 + m13*x44 + m20*x45 + m27*x46 + m34*x47 + m41*x48 + m48*x49;
782 	  x[48] -= m7*x43 + m14*x44 + m21*x45 + m28*x46 + m35*x47 + m42*x48 + m49*x49;
783           pv   += 49;
784         }
785         PLogFlops(686*nz+637);
786       }
787       row = *ajtmp++;
788     }
789     /* finished row so stick it into b->a */
790     pv = ba + 49*bi[i];
791     pj = bj + bi[i];
792     nz = bi[i+1] - bi[i];
793     for (j=0; j<nz; j++) {
794       x      = rtmp+49*pj[j];
795       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
796       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7];
797       pv[8]  = x[8];  pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11];
798       pv[12] = x[12]; pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
799       pv[16] = x[16]; pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19];
800       pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23];
801       pv[24] = x[24]; pv[25] = x[25]; pv[26] = x[26]; pv[27] = x[27];
802       pv[28] = x[28]; pv[29] = x[29]; pv[30] = x[30]; pv[31] = x[31];
803       pv[32] = x[32]; pv[33] = x[33]; pv[34] = x[34]; pv[35] = x[35];
804       pv[36] = x[36]; pv[37] = x[37]; pv[38] = x[38]; pv[39] = x[39];
805       pv[40] = x[40]; pv[41] = x[41]; pv[42] = x[42]; pv[43] = x[43];
806       pv[44] = x[44]; pv[45] = x[45]; pv[46] = x[46]; pv[47] = x[47];
807       pv[48] = x[48];
808       pv   += 49;
809     }
810     /* invert diagonal block */
811     w = ba + 49*diag_offset[i];
812     ierr = Kernel_A_gets_inverse_A_7(w);CHKERRQ(ierr);
813   }
814 
815   ierr = PetscFree(rtmp);CHKERRQ(ierr);
816   C->factor    = FACTOR_LU;
817   C->assembled = PETSC_TRUE;
818   PLogFlops(1.3333*343*b->mbs); /* from inverting diagonal blocks */
819   PetscFunctionReturn(0);
820 }
821 
822 /* ------------------------------------------------------------*/
823 /*
824       Version for when blocks are 6 by 6
825 */
826 #undef __FUNC__
827 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_6"
828 int MatCholeskyFactorNumeric_SeqSBAIJ_6(Mat A,Mat *B)
829 {
830   Mat          C = *B;
831   Mat_SeqBAIJ  *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
832   IS           isrow = b->row,isicol = b->icol;
833   int          *r,*ic,ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
834   int          *ajtmpold,*ajtmp,nz,row;
835   int          *diag_offset = b->diag,idx,*ai=a->i,*aj=a->j,*pj;
836   MatScalar    *pv,*v,*rtmp,*pc,*w,*x;
837   MatScalar    p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
838   MatScalar    p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
839   MatScalar    x17,x18,x19,x20,x21,x22,x23,x24,x25,p10,p11,p12,p13,p14;
840   MatScalar    p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,m10,m11,m12;
841   MatScalar    m13,m14,m15,m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
842   MatScalar    p26,p27,p28,p29,p30,p31,p32,p33,p34,p35,p36;
843   MatScalar    x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36;
844   MatScalar    m26,m27,m28,m29,m30,m31,m32,m33,m34,m35,m36;
845   MatScalar    *ba = b->a,*aa = a->a;
846 
847   PetscFunctionBegin;
848   ierr  = ISGetIndices(isrow,&r);CHKERRQ(ierr);
849   ierr  = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
850   rtmp  = (MatScalar*)PetscMalloc(36*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
851 
852   for (i=0; i<n; i++) {
853     nz    = bi[i+1] - bi[i];
854     ajtmp = bj + bi[i];
855     for  (j=0; j<nz; j++) {
856       x = rtmp+36*ajtmp[j];
857       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
858       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
859       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = x[25] = 0.0 ;
860       x[26] = x[27] = x[28] = x[29] = x[30] = x[31] = x[32] = x[33] = 0.0 ;
861       x[34] = x[35] = 0.0 ;
862     }
863     /* load in initial (unfactored row) */
864     idx      = r[i];
865     nz       = ai[idx+1] - ai[idx];
866     ajtmpold = aj + ai[idx];
867     v        = aa + 36*ai[idx];
868     for (j=0; j<nz; j++) {
869       x    = rtmp+36*ic[ajtmpold[j]];
870       x[0] =  v[0];  x[1] =  v[1];  x[2] =  v[2];  x[3] =  v[3];
871       x[4] =  v[4];  x[5] =  v[5];  x[6] =  v[6];  x[7] =  v[7];
872       x[8] =  v[8];  x[9] =  v[9];  x[10] = v[10]; x[11] = v[11];
873       x[12] = v[12]; x[13] = v[13]; x[14] = v[14]; x[15] = v[15];
874       x[16] = v[16]; x[17] = v[17]; x[18] = v[18]; x[19] = v[19];
875       x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23];
876       x[24] = v[24]; x[25] = v[25]; x[26] = v[26]; x[27] = v[27];
877       x[28] = v[28]; x[29] = v[29]; x[30] = v[30]; x[31] = v[31];
878       x[32] = v[32]; x[33] = v[33]; x[34] = v[34]; x[35] = v[35];
879       v    += 36;
880     }
881     row = *ajtmp++;
882     while (row < i) {
883       pc  =  rtmp + 36*row;
884       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
885       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];
886       p9  = pc[8];  p10 = pc[9];  p11 = pc[10]; p12 = pc[11];
887       p13 = pc[12]; p14 = pc[13]; p15 = pc[14]; p16 = pc[15];
888       p17 = pc[16]; p18 = pc[17]; p19 = pc[18]; p20 = pc[19];
889       p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
890       p25 = pc[24]; p26 = pc[25]; p27 = pc[26]; p28 = pc[27];
891       p29 = pc[28]; p30 = pc[29]; p31 = pc[30]; p32 = pc[31];
892       p33 = pc[32]; p34 = pc[33]; p35 = pc[34]; p36 = pc[35];
893       if (p1  != 0.0 || p2  != 0.0 || p3  != 0.0 || p4  != 0.0 ||
894           p5  != 0.0 || p6  != 0.0 || p7  != 0.0 || p8  != 0.0 ||
895           p9  != 0.0 || p10 != 0.0 || p11 != 0.0 || p12 != 0.0 ||
896           p13 != 0.0 || p14 != 0.0 || p15 != 0.0 || p16 != 0.0 ||
897           p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 ||
898           p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 ||
899           p25 != 0.0 || p26 != 0.0 || p27 != 0.0 || p28 != 0.0 ||
900           p29 != 0.0 || p30 != 0.0 || p31 != 0.0 || p32 != 0.0 ||
901           p33 != 0.0 || p34 != 0.0 || p35 != 0.0 || p36 != 0.0) {
902         pv = ba + 36*diag_offset[row];
903         pj = bj + diag_offset[row] + 1;
904 	x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
905 	x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
906 	x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
907 	x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
908 	x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
909 	x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
910 	x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
911 	x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
912 	x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
913         pc[0]  = m1  = p1*x1  + p7*x2   + p13*x3  + p19*x4  + p25*x5  + p31*x6;
914         pc[1]  = m2  = p2*x1  + p8*x2   + p14*x3  + p20*x4  + p26*x5  + p32*x6;
915         pc[2]  = m3  = p3*x1  + p9*x2   + p15*x3  + p21*x4  + p27*x5  + p33*x6;
916         pc[3]  = m4  = p4*x1  + p10*x2  + p16*x3  + p22*x4  + p28*x5  + p34*x6;
917         pc[4]  = m5  = p5*x1  + p11*x2  + p17*x3  + p23*x4  + p29*x5  + p35*x6;
918         pc[5]  = m6  = p6*x1  + p12*x2  + p18*x3  + p24*x4  + p30*x5  + p36*x6;
919 
920         pc[6]  = m7  = p1*x7  + p7*x8   + p13*x9  + p19*x10 + p25*x11 + p31*x12;
921         pc[7]  = m8  = p2*x7  + p8*x8   + p14*x9  + p20*x10 + p26*x11 + p32*x12;
922         pc[8]  = m9  = p3*x7  + p9*x8   + p15*x9  + p21*x10 + p27*x11 + p33*x12;
923         pc[9]  = m10 = p4*x7  + p10*x8  + p16*x9  + p22*x10 + p28*x11 + p34*x12;
924         pc[10] = m11 = p5*x7  + p11*x8  + p17*x9  + p23*x10 + p29*x11 + p35*x12;
925         pc[11] = m12 = p6*x7  + p12*x8  + p18*x9  + p24*x10 + p30*x11 + p36*x12;
926 
927         pc[12] = m13 = p1*x13 + p7*x14  + p13*x15 + p19*x16 + p25*x17 + p31*x18;
928         pc[13] = m14 = p2*x13 + p8*x14  + p14*x15 + p20*x16 + p26*x17 + p32*x18;
929         pc[14] = m15 = p3*x13 + p9*x14  + p15*x15 + p21*x16 + p27*x17 + p33*x18;
930         pc[15] = m16 = p4*x13 + p10*x14 + p16*x15 + p22*x16 + p28*x17 + p34*x18;
931         pc[16] = m17 = p5*x13 + p11*x14 + p17*x15 + p23*x16 + p29*x17 + p35*x18;
932         pc[17] = m18 = p6*x13 + p12*x14 + p18*x15 + p24*x16 + p30*x17 + p36*x18;
933 
934         pc[18] = m19 = p1*x19 + p7*x20  + p13*x21 + p19*x22 + p25*x23 + p31*x24;
935         pc[19] = m20 = p2*x19 + p8*x20  + p14*x21 + p20*x22 + p26*x23 + p32*x24;
936         pc[20] = m21 = p3*x19 + p9*x20  + p15*x21 + p21*x22 + p27*x23 + p33*x24;
937         pc[21] = m22 = p4*x19 + p10*x20 + p16*x21 + p22*x22 + p28*x23 + p34*x24;
938         pc[22] = m23 = p5*x19 + p11*x20 + p17*x21 + p23*x22 + p29*x23 + p35*x24;
939         pc[23] = m24 = p6*x19 + p12*x20 + p18*x21 + p24*x22 + p30*x23 + p36*x24;
940 
941         pc[24] = m25 = p1*x25 + p7*x26  + p13*x27 + p19*x28 + p25*x29 + p31*x30;
942         pc[25] = m26 = p2*x25 + p8*x26  + p14*x27 + p20*x28 + p26*x29 + p32*x30;
943         pc[26] = m27 = p3*x25 + p9*x26  + p15*x27 + p21*x28 + p27*x29 + p33*x30;
944         pc[27] = m28 = p4*x25 + p10*x26 + p16*x27 + p22*x28 + p28*x29 + p34*x30;
945         pc[28] = m29 = p5*x25 + p11*x26 + p17*x27 + p23*x28 + p29*x29 + p35*x30;
946         pc[29] = m30 = p6*x25 + p12*x26 + p18*x27 + p24*x28 + p30*x29 + p36*x30;
947 
948         pc[30] = m31 = p1*x31 + p7*x32  + p13*x33 + p19*x34 + p25*x35 + p31*x36;
949         pc[31] = m32 = p2*x31 + p8*x32  + p14*x33 + p20*x34 + p26*x35 + p32*x36;
950         pc[32] = m33 = p3*x31 + p9*x32  + p15*x33 + p21*x34 + p27*x35 + p33*x36;
951         pc[33] = m34 = p4*x31 + p10*x32 + p16*x33 + p22*x34 + p28*x35 + p34*x36;
952         pc[34] = m35 = p5*x31 + p11*x32 + p17*x33 + p23*x34 + p29*x35 + p35*x36;
953         pc[35] = m36 = p6*x31 + p12*x32 + p18*x33 + p24*x34 + p30*x35 + p36*x36;
954 
955         nz = bi[row+1] - diag_offset[row] - 1;
956         pv += 36;
957         for (j=0; j<nz; j++) {
958 	  x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
959 	  x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
960 	  x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
961 	  x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
962 	  x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
963 	  x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
964 	  x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
965 	  x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
966 	  x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
967 	  x    = rtmp + 36*pj[j];
968           x[0]  -= m1*x1  + m7*x2   + m13*x3  + m19*x4  + m25*x5  + m31*x6;
969           x[1]  -= m2*x1  + m8*x2   + m14*x3  + m20*x4  + m26*x5  + m32*x6;
970           x[2]  -= m3*x1  + m9*x2   + m15*x3  + m21*x4  + m27*x5  + m33*x6;
971           x[3]  -= m4*x1  + m10*x2  + m16*x3  + m22*x4  + m28*x5  + m34*x6;
972           x[4]  -= m5*x1  + m11*x2  + m17*x3  + m23*x4  + m29*x5  + m35*x6;
973           x[5]  -= m6*x1  + m12*x2  + m18*x3  + m24*x4  + m30*x5  + m36*x6;
974 
975 	  x[6]  -= m1*x7  + m7*x8   + m13*x9  + m19*x10 + m25*x11 + m31*x12;
976 	  x[7]  -= m2*x7  + m8*x8   + m14*x9  + m20*x10 + m26*x11 + m32*x12;
977 	  x[8]  -= m3*x7  + m9*x8   + m15*x9  + m21*x10 + m27*x11 + m33*x12;
978 	  x[9]  -= m4*x7  + m10*x8  + m16*x9  + m22*x10 + m28*x11 + m34*x12;
979 	  x[10] -= m5*x7  + m11*x8  + m17*x9  + m23*x10 + m29*x11 + m35*x12;
980 	  x[11] -= m6*x7  + m12*x8  + m18*x9  + m24*x10 + m30*x11 + m36*x12;
981 
982 	  x[12] -= m1*x13 + m7*x14  + m13*x15 + m19*x16 + m25*x17 + m31*x18;
983 	  x[13] -= m2*x13 + m8*x14  + m14*x15 + m20*x16 + m26*x17 + m32*x18;
984 	  x[14] -= m3*x13 + m9*x14  + m15*x15 + m21*x16 + m27*x17 + m33*x18;
985 	  x[15] -= m4*x13 + m10*x14 + m16*x15 + m22*x16 + m28*x17 + m34*x18;
986 	  x[16] -= m5*x13 + m11*x14 + m17*x15 + m23*x16 + m29*x17 + m35*x18;
987 	  x[17] -= m6*x13 + m12*x14 + m18*x15 + m24*x16 + m30*x17 + m36*x18;
988 
989 	  x[18] -= m1*x19 + m7*x20  + m13*x21 + m19*x22 + m25*x23 + m31*x24;
990 	  x[19] -= m2*x19 + m8*x20  + m14*x21 + m20*x22 + m26*x23 + m32*x24;
991 	  x[20] -= m3*x19 + m9*x20  + m15*x21 + m21*x22 + m27*x23 + m33*x24;
992 	  x[21] -= m4*x19 + m10*x20 + m16*x21 + m22*x22 + m28*x23 + m34*x24;
993 	  x[22] -= m5*x19 + m11*x20 + m17*x21 + m23*x22 + m29*x23 + m35*x24;
994 	  x[23] -= m6*x19 + m12*x20 + m18*x21 + m24*x22 + m30*x23 + m36*x24;
995 
996 	  x[24] -= m1*x25 + m7*x26  + m13*x27 + m19*x28 + m25*x29 + m31*x30;
997 	  x[25] -= m2*x25 + m8*x26  + m14*x27 + m20*x28 + m26*x29 + m32*x30;
998 	  x[26] -= m3*x25 + m9*x26  + m15*x27 + m21*x28 + m27*x29 + m33*x30;
999 	  x[27] -= m4*x25 + m10*x26 + m16*x27 + m22*x28 + m28*x29 + m34*x30;
1000 	  x[28] -= m5*x25 + m11*x26 + m17*x27 + m23*x28 + m29*x29 + m35*x30;
1001 	  x[29] -= m6*x25 + m12*x26 + m18*x27 + m24*x28 + m30*x29 + m36*x30;
1002 
1003 	  x[30] -= m1*x31 + m7*x32  + m13*x33 + m19*x34 + m25*x35 + m31*x36;
1004 	  x[31] -= m2*x31 + m8*x32  + m14*x33 + m20*x34 + m26*x35 + m32*x36;
1005 	  x[32] -= m3*x31 + m9*x32  + m15*x33 + m21*x34 + m27*x35 + m33*x36;
1006 	  x[33] -= m4*x31 + m10*x32 + m16*x33 + m22*x34 + m28*x35 + m34*x36;
1007 	  x[34] -= m5*x31 + m11*x32 + m17*x33 + m23*x34 + m29*x35 + m35*x36;
1008 	  x[35] -= m6*x31 + m12*x32 + m18*x33 + m24*x34 + m30*x35 + m36*x36;
1009 
1010           pv   += 36;
1011         }
1012         PLogFlops(432*nz+396);
1013       }
1014       row = *ajtmp++;
1015     }
1016     /* finished row so stick it into b->a */
1017     pv = ba + 36*bi[i];
1018     pj = bj + bi[i];
1019     nz = bi[i+1] - bi[i];
1020     for (j=0; j<nz; j++) {
1021       x      = rtmp+36*pj[j];
1022       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
1023       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7];
1024       pv[8]  = x[8];  pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11];
1025       pv[12] = x[12]; pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
1026       pv[16] = x[16]; pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19];
1027       pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23];
1028       pv[24] = x[24]; pv[25] = x[25]; pv[26] = x[26]; pv[27] = x[27];
1029       pv[28] = x[28]; pv[29] = x[29]; pv[30] = x[30]; pv[31] = x[31];
1030       pv[32] = x[32]; pv[33] = x[33]; pv[34] = x[34]; pv[35] = x[35];
1031       pv   += 36;
1032     }
1033     /* invert diagonal block */
1034     w = ba + 36*diag_offset[i];
1035     ierr = Kernel_A_gets_inverse_A_6(w);CHKERRQ(ierr);
1036   }
1037 
1038   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1039   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
1040   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
1041   C->factor = FACTOR_LU;
1042   C->assembled = PETSC_TRUE;
1043   PLogFlops(1.3333*216*b->mbs); /* from inverting diagonal blocks */
1044   PetscFunctionReturn(0);
1045 }
1046 /*
1047       Version for when blocks are 6 by 6 Using natural ordering
1048 */
1049 #undef __FUNC__
1050 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_6_NaturalOrdering"
1051 int MatCholeskyFactorNumeric_SeqSBAIJ_6_NaturalOrdering(Mat A,Mat *B)
1052 {
1053   Mat         C = *B;
1054   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
1055   int         ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
1056   int         *ajtmpold,*ajtmp,nz,row;
1057   int         *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
1058   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
1059   MatScalar   x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15;
1060   MatScalar   x16,x17,x18,x19,x20,x21,x22,x23,x24,x25;
1061   MatScalar   p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15;
1062   MatScalar   p16,p17,p18,p19,p20,p21,p22,p23,p24,p25;
1063   MatScalar   m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12,m13,m14,m15;
1064   MatScalar   m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
1065   MatScalar   p26,p27,p28,p29,p30,p31,p32,p33,p34,p35,p36;
1066   MatScalar   x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36;
1067   MatScalar   m26,m27,m28,m29,m30,m31,m32,m33,m34,m35,m36;
1068   MatScalar   *ba = b->a,*aa = a->a;
1069 
1070   PetscFunctionBegin;
1071   rtmp  = (MatScalar*)PetscMalloc(36*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
1072   for (i=0; i<n; i++) {
1073     nz    = bi[i+1] - bi[i];
1074     ajtmp = bj + bi[i];
1075     for  (j=0; j<nz; j++) {
1076       x = rtmp+36*ajtmp[j];
1077       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
1078       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
1079       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = x[25] = 0.0 ;
1080       x[26] = x[27] = x[28] = x[29] = x[30] = x[31] = x[32] = x[33] = 0.0 ;
1081       x[34] = x[35] = 0.0 ;
1082     }
1083     /* load in initial (unfactored row) */
1084     nz       = ai[i+1] - ai[i];
1085     ajtmpold = aj + ai[i];
1086     v        = aa + 36*ai[i];
1087     for (j=0; j<nz; j++) {
1088       x    = rtmp+36*ajtmpold[j];
1089       x[0] =  v[0];  x[1] =  v[1];  x[2] =  v[2];  x[3] =  v[3];
1090       x[4] =  v[4];  x[5] =  v[5];  x[6] =  v[6];  x[7] =  v[7];
1091       x[8] =  v[8];  x[9] =  v[9];  x[10] = v[10]; x[11] = v[11];
1092       x[12] = v[12]; x[13] = v[13]; x[14] = v[14]; x[15] = v[15];
1093       x[16] = v[16]; x[17] = v[17]; x[18] = v[18]; x[19] = v[19];
1094       x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23];
1095       x[24] = v[24]; x[25] = v[25]; x[26] = v[26]; x[27] = v[27];
1096       x[28] = v[28]; x[29] = v[29]; x[30] = v[30]; x[31] = v[31];
1097       x[32] = v[32]; x[33] = v[33]; x[34] = v[34]; x[35] = v[35];
1098       v    += 36;
1099     }
1100     row = *ajtmp++;
1101     while (row < i) {
1102       pc  = rtmp + 36*row;
1103       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
1104       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];
1105       p9  = pc[8];  p10 = pc[9];  p11 = pc[10]; p12 = pc[11];
1106       p13 = pc[12]; p14 = pc[13]; p15 = pc[14]; p16 = pc[15];
1107       p17 = pc[16]; p18 = pc[17]; p19 = pc[18]; p20 = pc[19];
1108       p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
1109       p25 = pc[24]; p26 = pc[25]; p27 = pc[26]; p28 = pc[27];
1110       p29 = pc[28]; p30 = pc[29]; p31 = pc[30]; p32 = pc[31];
1111       p33 = pc[32]; p34 = pc[33]; p35 = pc[34]; p36 = pc[35];
1112       if (p1  != 0.0 || p2  != 0.0 || p3  != 0.0 || p4  != 0.0 ||
1113           p5  != 0.0 || p6  != 0.0 || p7  != 0.0 || p8  != 0.0 ||
1114           p9  != 0.0 || p10 != 0.0 || p11 != 0.0 || p12 != 0.0 ||
1115           p13 != 0.0 || p14 != 0.0 || p15 != 0.0 || p16 != 0.0 ||
1116           p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 ||
1117           p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 ||
1118           p25 != 0.0 || p26 != 0.0 || p27 != 0.0 || p28 != 0.0 ||
1119           p29 != 0.0 || p30 != 0.0 || p31 != 0.0 || p32 != 0.0 ||
1120           p33 != 0.0 || p34 != 0.0 || p35 != 0.0 || p36 != 0.0) {
1121         pv = ba + 36*diag_offset[row];
1122         pj = bj + diag_offset[row] + 1;
1123 	x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
1124 	x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
1125 	x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
1126 	x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
1127 	x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
1128 	x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
1129 	x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
1130 	x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
1131 	x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
1132         pc[0]  = m1  = p1*x1  + p7*x2   + p13*x3  + p19*x4  + p25*x5  + p31*x6;
1133         pc[1]  = m2  = p2*x1  + p8*x2   + p14*x3  + p20*x4  + p26*x5  + p32*x6;
1134         pc[2]  = m3  = p3*x1  + p9*x2   + p15*x3  + p21*x4  + p27*x5  + p33*x6;
1135         pc[3]  = m4  = p4*x1  + p10*x2  + p16*x3  + p22*x4  + p28*x5  + p34*x6;
1136         pc[4]  = m5  = p5*x1  + p11*x2  + p17*x3  + p23*x4  + p29*x5  + p35*x6;
1137         pc[5]  = m6  = p6*x1  + p12*x2  + p18*x3  + p24*x4  + p30*x5  + p36*x6;
1138 
1139         pc[6]  = m7  = p1*x7  + p7*x8   + p13*x9  + p19*x10 + p25*x11 + p31*x12;
1140         pc[7]  = m8  = p2*x7  + p8*x8   + p14*x9  + p20*x10 + p26*x11 + p32*x12;
1141         pc[8]  = m9  = p3*x7  + p9*x8   + p15*x9  + p21*x10 + p27*x11 + p33*x12;
1142         pc[9]  = m10 = p4*x7  + p10*x8  + p16*x9  + p22*x10 + p28*x11 + p34*x12;
1143         pc[10] = m11 = p5*x7  + p11*x8  + p17*x9  + p23*x10 + p29*x11 + p35*x12;
1144         pc[11] = m12 = p6*x7  + p12*x8  + p18*x9  + p24*x10 + p30*x11 + p36*x12;
1145 
1146         pc[12] = m13 = p1*x13 + p7*x14  + p13*x15 + p19*x16 + p25*x17 + p31*x18;
1147         pc[13] = m14 = p2*x13 + p8*x14  + p14*x15 + p20*x16 + p26*x17 + p32*x18;
1148         pc[14] = m15 = p3*x13 + p9*x14  + p15*x15 + p21*x16 + p27*x17 + p33*x18;
1149         pc[15] = m16 = p4*x13 + p10*x14 + p16*x15 + p22*x16 + p28*x17 + p34*x18;
1150         pc[16] = m17 = p5*x13 + p11*x14 + p17*x15 + p23*x16 + p29*x17 + p35*x18;
1151         pc[17] = m18 = p6*x13 + p12*x14 + p18*x15 + p24*x16 + p30*x17 + p36*x18;
1152 
1153         pc[18] = m19 = p1*x19 + p7*x20  + p13*x21 + p19*x22 + p25*x23 + p31*x24;
1154         pc[19] = m20 = p2*x19 + p8*x20  + p14*x21 + p20*x22 + p26*x23 + p32*x24;
1155         pc[20] = m21 = p3*x19 + p9*x20  + p15*x21 + p21*x22 + p27*x23 + p33*x24;
1156         pc[21] = m22 = p4*x19 + p10*x20 + p16*x21 + p22*x22 + p28*x23 + p34*x24;
1157         pc[22] = m23 = p5*x19 + p11*x20 + p17*x21 + p23*x22 + p29*x23 + p35*x24;
1158         pc[23] = m24 = p6*x19 + p12*x20 + p18*x21 + p24*x22 + p30*x23 + p36*x24;
1159 
1160         pc[24] = m25 = p1*x25 + p7*x26  + p13*x27 + p19*x28 + p25*x29 + p31*x30;
1161         pc[25] = m26 = p2*x25 + p8*x26  + p14*x27 + p20*x28 + p26*x29 + p32*x30;
1162         pc[26] = m27 = p3*x25 + p9*x26  + p15*x27 + p21*x28 + p27*x29 + p33*x30;
1163         pc[27] = m28 = p4*x25 + p10*x26 + p16*x27 + p22*x28 + p28*x29 + p34*x30;
1164         pc[28] = m29 = p5*x25 + p11*x26 + p17*x27 + p23*x28 + p29*x29 + p35*x30;
1165         pc[29] = m30 = p6*x25 + p12*x26 + p18*x27 + p24*x28 + p30*x29 + p36*x30;
1166 
1167         pc[30] = m31 = p1*x31 + p7*x32  + p13*x33 + p19*x34 + p25*x35 + p31*x36;
1168         pc[31] = m32 = p2*x31 + p8*x32  + p14*x33 + p20*x34 + p26*x35 + p32*x36;
1169         pc[32] = m33 = p3*x31 + p9*x32  + p15*x33 + p21*x34 + p27*x35 + p33*x36;
1170         pc[33] = m34 = p4*x31 + p10*x32 + p16*x33 + p22*x34 + p28*x35 + p34*x36;
1171         pc[34] = m35 = p5*x31 + p11*x32 + p17*x33 + p23*x34 + p29*x35 + p35*x36;
1172         pc[35] = m36 = p6*x31 + p12*x32 + p18*x33 + p24*x34 + p30*x35 + p36*x36;
1173 
1174         nz = bi[row+1] - diag_offset[row] - 1;
1175         pv += 36;
1176         for (j=0; j<nz; j++) {
1177 	  x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
1178 	  x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
1179 	  x9  = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
1180 	  x13 = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
1181 	  x17 = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
1182 	  x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
1183 	  x25 = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
1184 	  x29 = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
1185 	  x33 = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
1186 	  x    = rtmp + 36*pj[j];
1187           x[0]  -= m1*x1  + m7*x2   + m13*x3  + m19*x4  + m25*x5  + m31*x6;
1188           x[1]  -= m2*x1  + m8*x2   + m14*x3  + m20*x4  + m26*x5  + m32*x6;
1189           x[2]  -= m3*x1  + m9*x2   + m15*x3  + m21*x4  + m27*x5  + m33*x6;
1190           x[3]  -= m4*x1  + m10*x2  + m16*x3  + m22*x4  + m28*x5  + m34*x6;
1191           x[4]  -= m5*x1  + m11*x2  + m17*x3  + m23*x4  + m29*x5  + m35*x6;
1192           x[5]  -= m6*x1  + m12*x2  + m18*x3  + m24*x4  + m30*x5  + m36*x6;
1193 
1194 	  x[6]  -= m1*x7  + m7*x8   + m13*x9  + m19*x10 + m25*x11 + m31*x12;
1195 	  x[7]  -= m2*x7  + m8*x8   + m14*x9  + m20*x10 + m26*x11 + m32*x12;
1196 	  x[8]  -= m3*x7  + m9*x8   + m15*x9  + m21*x10 + m27*x11 + m33*x12;
1197 	  x[9]  -= m4*x7  + m10*x8  + m16*x9  + m22*x10 + m28*x11 + m34*x12;
1198 	  x[10] -= m5*x7  + m11*x8  + m17*x9  + m23*x10 + m29*x11 + m35*x12;
1199 	  x[11] -= m6*x7  + m12*x8  + m18*x9  + m24*x10 + m30*x11 + m36*x12;
1200 
1201 	  x[12] -= m1*x13 + m7*x14  + m13*x15 + m19*x16 + m25*x17 + m31*x18;
1202 	  x[13] -= m2*x13 + m8*x14  + m14*x15 + m20*x16 + m26*x17 + m32*x18;
1203 	  x[14] -= m3*x13 + m9*x14  + m15*x15 + m21*x16 + m27*x17 + m33*x18;
1204 	  x[15] -= m4*x13 + m10*x14 + m16*x15 + m22*x16 + m28*x17 + m34*x18;
1205 	  x[16] -= m5*x13 + m11*x14 + m17*x15 + m23*x16 + m29*x17 + m35*x18;
1206 	  x[17] -= m6*x13 + m12*x14 + m18*x15 + m24*x16 + m30*x17 + m36*x18;
1207 
1208 	  x[18] -= m1*x19 + m7*x20  + m13*x21 + m19*x22 + m25*x23 + m31*x24;
1209 	  x[19] -= m2*x19 + m8*x20  + m14*x21 + m20*x22 + m26*x23 + m32*x24;
1210 	  x[20] -= m3*x19 + m9*x20  + m15*x21 + m21*x22 + m27*x23 + m33*x24;
1211 	  x[21] -= m4*x19 + m10*x20 + m16*x21 + m22*x22 + m28*x23 + m34*x24;
1212 	  x[22] -= m5*x19 + m11*x20 + m17*x21 + m23*x22 + m29*x23 + m35*x24;
1213 	  x[23] -= m6*x19 + m12*x20 + m18*x21 + m24*x22 + m30*x23 + m36*x24;
1214 
1215 	  x[24] -= m1*x25 + m7*x26  + m13*x27 + m19*x28 + m25*x29 + m31*x30;
1216 	  x[25] -= m2*x25 + m8*x26  + m14*x27 + m20*x28 + m26*x29 + m32*x30;
1217 	  x[26] -= m3*x25 + m9*x26  + m15*x27 + m21*x28 + m27*x29 + m33*x30;
1218 	  x[27] -= m4*x25 + m10*x26 + m16*x27 + m22*x28 + m28*x29 + m34*x30;
1219 	  x[28] -= m5*x25 + m11*x26 + m17*x27 + m23*x28 + m29*x29 + m35*x30;
1220 	  x[29] -= m6*x25 + m12*x26 + m18*x27 + m24*x28 + m30*x29 + m36*x30;
1221 
1222 	  x[30] -= m1*x31 + m7*x32  + m13*x33 + m19*x34 + m25*x35 + m31*x36;
1223 	  x[31] -= m2*x31 + m8*x32  + m14*x33 + m20*x34 + m26*x35 + m32*x36;
1224 	  x[32] -= m3*x31 + m9*x32  + m15*x33 + m21*x34 + m27*x35 + m33*x36;
1225 	  x[33] -= m4*x31 + m10*x32 + m16*x33 + m22*x34 + m28*x35 + m34*x36;
1226 	  x[34] -= m5*x31 + m11*x32 + m17*x33 + m23*x34 + m29*x35 + m35*x36;
1227 	  x[35] -= m6*x31 + m12*x32 + m18*x33 + m24*x34 + m30*x35 + m36*x36;
1228 
1229           pv   += 36;
1230         }
1231         PLogFlops(432*nz+396);
1232       }
1233       row = *ajtmp++;
1234     }
1235     /* finished row so stick it into b->a */
1236     pv = ba + 36*bi[i];
1237     pj = bj + bi[i];
1238     nz = bi[i+1] - bi[i];
1239     for (j=0; j<nz; j++) {
1240       x      = rtmp+36*pj[j];
1241       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
1242       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7];
1243       pv[8]  = x[8];  pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11];
1244       pv[12] = x[12]; pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
1245       pv[16] = x[16]; pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19];
1246       pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23];
1247       pv[24] = x[24]; pv[25] = x[25]; pv[26] = x[26]; pv[27] = x[27];
1248       pv[28] = x[28]; pv[29] = x[29]; pv[30] = x[30]; pv[31] = x[31];
1249       pv[32] = x[32]; pv[33] = x[33]; pv[34] = x[34]; pv[35] = x[35];
1250       pv   += 36;
1251     }
1252     /* invert diagonal block */
1253     w = ba + 36*diag_offset[i];
1254     ierr = Kernel_A_gets_inverse_A_6(w);CHKERRQ(ierr);
1255   }
1256 
1257   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1258   C->factor    = FACTOR_LU;
1259   C->assembled = PETSC_TRUE;
1260   PLogFlops(1.3333*216*b->mbs); /* from inverting diagonal blocks */
1261   PetscFunctionReturn(0);
1262 }
1263 
1264 /* ------------------------------------------------------------*/
1265 /*
1266       Version for when blocks are 5 by 5
1267 */
1268 #undef __FUNC__
1269 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_5"
1270 int MatCholeskyFactorNumeric_SeqSBAIJ_5(Mat A,Mat *B)
1271 {
1272   Mat         C = *B;
1273   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
1274   IS          isrow = b->row,isicol = b->icol;
1275   int         *r,*ic,ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
1276   int         *ajtmpold,*ajtmp,nz,row;
1277   int         *diag_offset = b->diag,idx,*ai=a->i,*aj=a->j,*pj;
1278   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
1279   MatScalar   p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
1280   MatScalar   p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
1281   MatScalar   x17,x18,x19,x20,x21,x22,x23,x24,x25,p10,p11,p12,p13,p14;
1282   MatScalar   p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,m10,m11,m12;
1283   MatScalar   m13,m14,m15,m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
1284   MatScalar   *ba = b->a,*aa = a->a;
1285 
1286   PetscFunctionBegin;
1287   ierr  = ISGetIndices(isrow,&r);CHKERRQ(ierr);
1288   ierr  = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
1289   rtmp  = (MatScalar*)PetscMalloc(25*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
1290 
1291   for (i=0; i<n; i++) {
1292     nz    = bi[i+1] - bi[i];
1293     ajtmp = bj + bi[i];
1294     for  (j=0; j<nz; j++) {
1295       x = rtmp+25*ajtmp[j];
1296       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
1297       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
1298       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0;
1299     }
1300     /* load in initial (unfactored row) */
1301     idx      = r[i];
1302     nz       = ai[idx+1] - ai[idx];
1303     ajtmpold = aj + ai[idx];
1304     v        = aa + 25*ai[idx];
1305     for (j=0; j<nz; j++) {
1306       x    = rtmp+25*ic[ajtmpold[j]];
1307       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
1308       x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
1309       x[9] = v[9]; x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
1310       x[14] = v[14]; x[15] = v[15]; x[16] = v[16]; x[17] = v[17];
1311       x[18] = v[18]; x[19] = v[19]; x[20] = v[20]; x[21] = v[21];
1312       x[22] = v[22]; x[23] = v[23]; x[24] = v[24];
1313       v    += 25;
1314     }
1315     row = *ajtmp++;
1316     while (row < i) {
1317       pc = rtmp + 25*row;
1318       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
1319       p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
1320       p10 = pc[9]; p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
1321       p15 = pc[14]; p16 = pc[15]; p17 = pc[16]; p18 = pc[17]; p19 = pc[18];
1322       p20 = pc[19]; p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
1323       p25 = pc[24];
1324       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
1325           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
1326           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
1327           || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 ||
1328           p20 != 0.0 || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 ||
1329           p24 != 0.0 || p25 != 0.0) {
1330         pv = ba + 25*diag_offset[row];
1331         pj = bj + diag_offset[row] + 1;
1332         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
1333         x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
1334         x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
1335         x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17];
1336         x19 = pv[18]; x20 = pv[19]; x21 = pv[20]; x22 = pv[21];
1337         x23 = pv[22]; x24 = pv[23]; x25 = pv[24];
1338         pc[0] = m1 = p1*x1 + p6*x2  + p11*x3 + p16*x4 + p21*x5;
1339         pc[1] = m2 = p2*x1 + p7*x2  + p12*x3 + p17*x4 + p22*x5;
1340         pc[2] = m3 = p3*x1 + p8*x2  + p13*x3 + p18*x4 + p23*x5;
1341         pc[3] = m4 = p4*x1 + p9*x2  + p14*x3 + p19*x4 + p24*x5;
1342         pc[4] = m5 = p5*x1 + p10*x2 + p15*x3 + p20*x4 + p25*x5;
1343 
1344         pc[5] = m6 = p1*x6 + p6*x7  + p11*x8 + p16*x9 + p21*x10;
1345         pc[6] = m7 = p2*x6 + p7*x7  + p12*x8 + p17*x9 + p22*x10;
1346         pc[7] = m8 = p3*x6 + p8*x7  + p13*x8 + p18*x9 + p23*x10;
1347         pc[8] = m9 = p4*x6 + p9*x7  + p14*x8 + p19*x9 + p24*x10;
1348         pc[9] = m10 = p5*x6 + p10*x7 + p15*x8 + p20*x9 + p25*x10;
1349 
1350         pc[10] = m11 = p1*x11 + p6*x12  + p11*x13 + p16*x14 + p21*x15;
1351         pc[11] = m12 = p2*x11 + p7*x12  + p12*x13 + p17*x14 + p22*x15;
1352         pc[12] = m13 = p3*x11 + p8*x12  + p13*x13 + p18*x14 + p23*x15;
1353         pc[13] = m14 = p4*x11 + p9*x12  + p14*x13 + p19*x14 + p24*x15;
1354         pc[14] = m15 = p5*x11 + p10*x12 + p15*x13 + p20*x14 + p25*x15;
1355 
1356         pc[15] = m16 = p1*x16 + p6*x17  + p11*x18 + p16*x19 + p21*x20;
1357         pc[16] = m17 = p2*x16 + p7*x17  + p12*x18 + p17*x19 + p22*x20;
1358         pc[17] = m18 = p3*x16 + p8*x17  + p13*x18 + p18*x19 + p23*x20;
1359         pc[18] = m19 = p4*x16 + p9*x17  + p14*x18 + p19*x19 + p24*x20;
1360         pc[19] = m20 = p5*x16 + p10*x17 + p15*x18 + p20*x19 + p25*x20;
1361 
1362         pc[20] = m21 = p1*x21 + p6*x22  + p11*x23 + p16*x24 + p21*x25;
1363         pc[21] = m22 = p2*x21 + p7*x22  + p12*x23 + p17*x24 + p22*x25;
1364         pc[22] = m23 = p3*x21 + p8*x22  + p13*x23 + p18*x24 + p23*x25;
1365         pc[23] = m24 = p4*x21 + p9*x22  + p14*x23 + p19*x24 + p24*x25;
1366         pc[24] = m25 = p5*x21 + p10*x22 + p15*x23 + p20*x24 + p25*x25;
1367 
1368         nz = bi[row+1] - diag_offset[row] - 1;
1369         pv += 25;
1370         for (j=0; j<nz; j++) {
1371           x1   = pv[0];  x2 = pv[1];   x3  = pv[2];  x4  = pv[3];
1372           x5   = pv[4];  x6 = pv[5];   x7  = pv[6];  x8  = pv[7]; x9 = pv[8];
1373           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
1374           x14  = pv[13]; x15 = pv[14]; x16 = pv[15]; x17 = pv[16];
1375           x18  = pv[17]; x19 = pv[18]; x20 = pv[19]; x21 = pv[20];
1376           x22  = pv[21]; x23 = pv[22]; x24 = pv[23]; x25 = pv[24];
1377           x    = rtmp + 25*pj[j];
1378           x[0] -= m1*x1 + m6*x2  + m11*x3 + m16*x4 + m21*x5;
1379           x[1] -= m2*x1 + m7*x2  + m12*x3 + m17*x4 + m22*x5;
1380           x[2] -= m3*x1 + m8*x2  + m13*x3 + m18*x4 + m23*x5;
1381           x[3] -= m4*x1 + m9*x2  + m14*x3 + m19*x4 + m24*x5;
1382           x[4] -= m5*x1 + m10*x2 + m15*x3 + m20*x4 + m25*x5;
1383 
1384           x[5] -= m1*x6 + m6*x7  + m11*x8 + m16*x9 + m21*x10;
1385           x[6] -= m2*x6 + m7*x7  + m12*x8 + m17*x9 + m22*x10;
1386           x[7] -= m3*x6 + m8*x7  + m13*x8 + m18*x9 + m23*x10;
1387           x[8] -= m4*x6 + m9*x7  + m14*x8 + m19*x9 + m24*x10;
1388           x[9] -= m5*x6 + m10*x7 + m15*x8 + m20*x9 + m25*x10;
1389 
1390           x[10] -= m1*x11 + m6*x12  + m11*x13 + m16*x14 + m21*x15;
1391           x[11] -= m2*x11 + m7*x12  + m12*x13 + m17*x14 + m22*x15;
1392           x[12] -= m3*x11 + m8*x12  + m13*x13 + m18*x14 + m23*x15;
1393           x[13] -= m4*x11 + m9*x12  + m14*x13 + m19*x14 + m24*x15;
1394           x[14] -= m5*x11 + m10*x12 + m15*x13 + m20*x14 + m25*x15;
1395 
1396           x[15] -= m1*x16 + m6*x17  + m11*x18 + m16*x19 + m21*x20;
1397           x[16] -= m2*x16 + m7*x17  + m12*x18 + m17*x19 + m22*x20;
1398           x[17] -= m3*x16 + m8*x17  + m13*x18 + m18*x19 + m23*x20;
1399           x[18] -= m4*x16 + m9*x17  + m14*x18 + m19*x19 + m24*x20;
1400           x[19] -= m5*x16 + m10*x17 + m15*x18 + m20*x19 + m25*x20;
1401 
1402           x[20] -= m1*x21 + m6*x22  + m11*x23 + m16*x24 + m21*x25;
1403           x[21] -= m2*x21 + m7*x22  + m12*x23 + m17*x24 + m22*x25;
1404           x[22] -= m3*x21 + m8*x22  + m13*x23 + m18*x24 + m23*x25;
1405           x[23] -= m4*x21 + m9*x22  + m14*x23 + m19*x24 + m24*x25;
1406           x[24] -= m5*x21 + m10*x22 + m15*x23 + m20*x24 + m25*x25;
1407 
1408           pv   += 25;
1409         }
1410         PLogFlops(250*nz+225);
1411       }
1412       row = *ajtmp++;
1413     }
1414     /* finished row so stick it into b->a */
1415     pv = ba + 25*bi[i];
1416     pj = bj + bi[i];
1417     nz = bi[i+1] - bi[i];
1418     for (j=0; j<nz; j++) {
1419       x     = rtmp+25*pj[j];
1420       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
1421       pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
1422       pv[9] = x[9]; pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
1423       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; pv[16] = x[16];
1424       pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19]; pv[20] = x[20];
1425       pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23]; pv[24] = x[24];
1426       pv   += 25;
1427     }
1428     /* invert diagonal block */
1429     w = ba + 25*diag_offset[i];
1430     ierr = Kernel_A_gets_inverse_A_5(w);CHKERRQ(ierr);
1431   }
1432 
1433   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1434   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
1435   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
1436   C->factor = FACTOR_LU;
1437   C->assembled = PETSC_TRUE;
1438   PLogFlops(1.3333*125*b->mbs); /* from inverting diagonal blocks */
1439   PetscFunctionReturn(0);
1440 }
1441 /*
1442       Version for when blocks are 5 by 5 Using natural ordering
1443 */
1444 #undef __FUNC__
1445 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_5_NaturalOrdering"
1446 int MatCholeskyFactorNumeric_SeqSBAIJ_5_NaturalOrdering(Mat A,Mat *B)
1447 {
1448   Mat         C = *B;
1449   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
1450   int         ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
1451   int         *ajtmpold,*ajtmp,nz,row;
1452   int         *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
1453   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
1454   MatScalar   x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15;
1455   MatScalar   x16,x17,x18,x19,x20,x21,x22,x23,x24,x25;
1456   MatScalar   p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15;
1457   MatScalar   p16,p17,p18,p19,p20,p21,p22,p23,p24,p25;
1458   MatScalar   m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12,m13,m14,m15;
1459   MatScalar   m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
1460   MatScalar   *ba = b->a,*aa = a->a;
1461 
1462   PetscFunctionBegin;
1463   rtmp  = (MatScalar*)PetscMalloc(25*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
1464   for (i=0; i<n; i++) {
1465     nz    = bi[i+1] - bi[i];
1466     ajtmp = bj + bi[i];
1467     for  (j=0; j<nz; j++) {
1468       x = rtmp+25*ajtmp[j];
1469       x[0]  = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = x[9] = 0.0;
1470       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
1471       x[16] = x[17] = x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0;
1472     }
1473     /* load in initial (unfactored row) */
1474     nz       = ai[i+1] - ai[i];
1475     ajtmpold = aj + ai[i];
1476     v        = aa + 25*ai[i];
1477     for (j=0; j<nz; j++) {
1478       x    = rtmp+25*ajtmpold[j];
1479       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
1480       x[4]  = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
1481       x[9]  = v[9];  x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
1482       x[14] = v[14]; x[15] = v[15]; x[16] = v[16]; x[17] = v[17]; x[18] = v[18];
1483       x[19] = v[19]; x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23];
1484       x[24] = v[24];
1485       v    += 25;
1486     }
1487     row = *ajtmp++;
1488     while (row < i) {
1489       pc  = rtmp + 25*row;
1490       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
1491       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
1492       p10 = pc[9];  p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
1493       p15 = pc[14]; p16 = pc[15]; p17 = pc[16]; p18 = pc[17];
1494       p19 = pc[18]; p20 = pc[19]; p21 = pc[20]; p22 = pc[21]; p23 = pc[22];
1495       p24 = pc[23]; p25 = pc[24];
1496       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
1497           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
1498           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
1499           || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0
1500           || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 || p25 != 0.0) {
1501         pv = ba + 25*diag_offset[row];
1502         pj = bj + diag_offset[row] + 1;
1503         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
1504         x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
1505         x10 = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
1506         x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17]; x19 = pv[18];
1507         x20 = pv[19]; x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
1508         x25 = pv[24];
1509         pc[0] = m1 = p1*x1 + p6*x2  + p11*x3 + p16*x4 + p21*x5;
1510         pc[1] = m2 = p2*x1 + p7*x2  + p12*x3 + p17*x4 + p22*x5;
1511         pc[2] = m3 = p3*x1 + p8*x2  + p13*x3 + p18*x4 + p23*x5;
1512         pc[3] = m4 = p4*x1 + p9*x2  + p14*x3 + p19*x4 + p24*x5;
1513         pc[4] = m5 = p5*x1 + p10*x2 + p15*x3 + p20*x4 + p25*x5;
1514 
1515         pc[5]  = m6  = p1*x6 + p6*x7  + p11*x8 + p16*x9 + p21*x10;
1516         pc[6]  = m7  = p2*x6 + p7*x7  + p12*x8 + p17*x9 + p22*x10;
1517         pc[7]  = m8  = p3*x6 + p8*x7  + p13*x8 + p18*x9 + p23*x10;
1518         pc[8]  = m9  = p4*x6 + p9*x7  + p14*x8 + p19*x9 + p24*x10;
1519         pc[9]  = m10 = p5*x6 + p10*x7 + p15*x8 + p20*x9 + p25*x10;
1520 
1521         pc[10] = m11 = p1*x11 + p6*x12  + p11*x13 + p16*x14 + p21*x15;
1522         pc[11] = m12 = p2*x11 + p7*x12  + p12*x13 + p17*x14 + p22*x15;
1523         pc[12] = m13 = p3*x11 + p8*x12  + p13*x13 + p18*x14 + p23*x15;
1524         pc[13] = m14 = p4*x11 + p9*x12  + p14*x13 + p19*x14 + p24*x15;
1525         pc[14] = m15 = p5*x11 + p10*x12 + p15*x13 + p20*x14 + p25*x15;
1526 
1527         pc[15] = m16 = p1*x16 + p6*x17  + p11*x18 + p16*x19 + p21*x20;
1528         pc[16] = m17 = p2*x16 + p7*x17  + p12*x18 + p17*x19 + p22*x20;
1529         pc[17] = m18 = p3*x16 + p8*x17  + p13*x18 + p18*x19 + p23*x20;
1530         pc[18] = m19 = p4*x16 + p9*x17  + p14*x18 + p19*x19 + p24*x20;
1531         pc[19] = m20 = p5*x16 + p10*x17 + p15*x18 + p20*x19 + p25*x20;
1532 
1533         pc[20] = m21 = p1*x21 + p6*x22  + p11*x23 + p16*x24 + p21*x25;
1534         pc[21] = m22 = p2*x21 + p7*x22  + p12*x23 + p17*x24 + p22*x25;
1535         pc[22] = m23 = p3*x21 + p8*x22  + p13*x23 + p18*x24 + p23*x25;
1536         pc[23] = m24 = p4*x21 + p9*x22  + p14*x23 + p19*x24 + p24*x25;
1537         pc[24] = m25 = p5*x21 + p10*x22 + p15*x23 + p20*x24 + p25*x25;
1538 
1539         nz = bi[row+1] - diag_offset[row] - 1;
1540         pv += 25;
1541         for (j=0; j<nz; j++) {
1542           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
1543           x5   = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
1544           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
1545           x14  = pv[13]; x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17];
1546           x19 = pv[18];  x20 = pv[19]; x21 = pv[20]; x22 = pv[21]; x23 = pv[22];
1547           x24 = pv[23];  x25 = pv[24];
1548           x    = rtmp + 25*pj[j];
1549           x[0] -= m1*x1 + m6*x2   + m11*x3  + m16*x4 + m21*x5;
1550           x[1] -= m2*x1 + m7*x2   + m12*x3  + m17*x4 + m22*x5;
1551           x[2] -= m3*x1 + m8*x2   + m13*x3  + m18*x4 + m23*x5;
1552           x[3] -= m4*x1 + m9*x2   + m14*x3  + m19*x4 + m24*x5;
1553           x[4] -= m5*x1 + m10*x2  + m15*x3  + m20*x4 + m25*x5;
1554 
1555           x[5] -= m1*x6 + m6*x7   + m11*x8  + m16*x9 + m21*x10;
1556           x[6] -= m2*x6 + m7*x7   + m12*x8  + m17*x9 + m22*x10;
1557           x[7] -= m3*x6 + m8*x7   + m13*x8  + m18*x9 + m23*x10;
1558           x[8] -= m4*x6 + m9*x7   + m14*x8  + m19*x9 + m24*x10;
1559           x[9] -= m5*x6 + m10*x7  + m15*x8  + m20*x9 + m25*x10;
1560 
1561           x[10] -= m1*x11 + m6*x12  + m11*x13 + m16*x14 + m21*x15;
1562           x[11] -= m2*x11 + m7*x12  + m12*x13 + m17*x14 + m22*x15;
1563           x[12] -= m3*x11 + m8*x12  + m13*x13 + m18*x14 + m23*x15;
1564           x[13] -= m4*x11 + m9*x12  + m14*x13 + m19*x14 + m24*x15;
1565           x[14] -= m5*x11 + m10*x12 + m15*x13 + m20*x14 + m25*x15;
1566 
1567           x[15] -= m1*x16 + m6*x17  + m11*x18 + m16*x19 + m21*x20;
1568           x[16] -= m2*x16 + m7*x17  + m12*x18 + m17*x19 + m22*x20;
1569           x[17] -= m3*x16 + m8*x17  + m13*x18 + m18*x19 + m23*x20;
1570           x[18] -= m4*x16 + m9*x17  + m14*x18 + m19*x19 + m24*x20;
1571           x[19] -= m5*x16 + m10*x17 + m15*x18 + m20*x19 + m25*x20;
1572 
1573           x[20] -= m1*x21 + m6*x22  + m11*x23 + m16*x24 + m21*x25;
1574           x[21] -= m2*x21 + m7*x22  + m12*x23 + m17*x24 + m22*x25;
1575           x[22] -= m3*x21 + m8*x22  + m13*x23 + m18*x24 + m23*x25;
1576           x[23] -= m4*x21 + m9*x22  + m14*x23 + m19*x24 + m24*x25;
1577           x[24] -= m5*x21 + m10*x22 + m15*x23 + m20*x24 + m25*x25;
1578           pv   += 25;
1579         }
1580         PLogFlops(250*nz+225);
1581       }
1582       row = *ajtmp++;
1583     }
1584     /* finished row so stick it into b->a */
1585     pv = ba + 25*bi[i];
1586     pj = bj + bi[i];
1587     nz = bi[i+1] - bi[i];
1588     for (j=0; j<nz; j++) {
1589       x      = rtmp+25*pj[j];
1590       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
1591       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
1592       pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
1593       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; pv[16] = x[16]; pv[17] = x[17];
1594       pv[18] = x[18]; pv[19] = x[19]; pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22];
1595       pv[23] = x[23]; pv[24] = x[24];
1596       pv   += 25;
1597     }
1598     /* invert diagonal block */
1599     w = ba + 25*diag_offset[i];
1600     ierr = Kernel_A_gets_inverse_A_5(w);CHKERRQ(ierr);
1601   }
1602 
1603   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1604   C->factor    = FACTOR_LU;
1605   C->assembled = PETSC_TRUE;
1606   PLogFlops(1.3333*125*b->mbs); /* from inverting diagonal blocks */
1607   PetscFunctionReturn(0);
1608 }
1609 
1610 /* ------------------------------------------------------------*/
1611 /*
1612       Version for when blocks are 4 by 4
1613 */
1614 #undef __FUNC__
1615 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_4"
1616 int MatCholeskyFactorNumeric_SeqSBAIJ_4(Mat A,Mat *B)
1617 {
1618   Mat         C = *B;
1619   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
1620   IS          isrow = b->row,isicol = b->icol;
1621   int         *r,*ic,ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
1622   int         *ajtmpold,*ajtmp,nz,row;
1623   int         *diag_offset = b->diag,idx,*ai=a->i,*aj=a->j,*pj;
1624   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
1625   MatScalar   p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
1626   MatScalar   p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
1627   MatScalar   p10,p11,p12,p13,p14,p15,p16,m10,m11,m12;
1628   MatScalar   m13,m14,m15,m16;
1629   MatScalar   *ba = b->a,*aa = a->a;
1630 
1631   PetscFunctionBegin;
1632   ierr  = ISGetIndices(isrow,&r);CHKERRQ(ierr);
1633   ierr  = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
1634   rtmp  = (MatScalar*)PetscMalloc(16*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
1635 
1636   for (i=0; i<n; i++) {
1637     nz    = bi[i+1] - bi[i];
1638     ajtmp = bj + bi[i];
1639     for  (j=0; j<nz; j++) {
1640       x = rtmp+16*ajtmp[j];
1641       x[0]  = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = x[9] = 0.0;
1642       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
1643     }
1644     /* load in initial (unfactored row) */
1645     idx      = r[i];
1646     nz       = ai[idx+1] - ai[idx];
1647     ajtmpold = aj + ai[idx];
1648     v        = aa + 16*ai[idx];
1649     for (j=0; j<nz; j++) {
1650       x    = rtmp+16*ic[ajtmpold[j]];
1651       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
1652       x[4]  = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
1653       x[9]  = v[9];  x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
1654       x[14] = v[14]; x[15] = v[15];
1655       v    += 16;
1656     }
1657     row = *ajtmp++;
1658     while (row < i) {
1659       pc  = rtmp + 16*row;
1660       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
1661       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
1662       p10 = pc[9];  p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
1663       p15 = pc[14]; p16 = pc[15];
1664       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
1665           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
1666           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
1667           || p16 != 0.0) {
1668         pv = ba + 16*diag_offset[row];
1669         pj = bj + diag_offset[row] + 1;
1670         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
1671         x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
1672         x10 = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
1673         x15 = pv[14]; x16 = pv[15];
1674         pc[0] = m1 = p1*x1 + p5*x2  + p9*x3  + p13*x4;
1675         pc[1] = m2 = p2*x1 + p6*x2  + p10*x3 + p14*x4;
1676         pc[2] = m3 = p3*x1 + p7*x2  + p11*x3 + p15*x4;
1677         pc[3] = m4 = p4*x1 + p8*x2  + p12*x3 + p16*x4;
1678 
1679         pc[4] = m5 = p1*x5 + p5*x6  + p9*x7  + p13*x8;
1680         pc[5] = m6 = p2*x5 + p6*x6  + p10*x7 + p14*x8;
1681         pc[6] = m7 = p3*x5 + p7*x6  + p11*x7 + p15*x8;
1682         pc[7] = m8 = p4*x5 + p8*x6  + p12*x7 + p16*x8;
1683 
1684         pc[8]  = m9  = p1*x9 + p5*x10  + p9*x11  + p13*x12;
1685         pc[9]  = m10 = p2*x9 + p6*x10  + p10*x11 + p14*x12;
1686         pc[10] = m11 = p3*x9 + p7*x10  + p11*x11 + p15*x12;
1687         pc[11] = m12 = p4*x9 + p8*x10  + p12*x11 + p16*x12;
1688 
1689         pc[12] = m13 = p1*x13 + p5*x14  + p9*x15  + p13*x16;
1690         pc[13] = m14 = p2*x13 + p6*x14  + p10*x15 + p14*x16;
1691         pc[14] = m15 = p3*x13 + p7*x14  + p11*x15 + p15*x16;
1692         pc[15] = m16 = p4*x13 + p8*x14  + p12*x15 + p16*x16;
1693 
1694         nz = bi[row+1] - diag_offset[row] - 1;
1695         pv += 16;
1696         for (j=0; j<nz; j++) {
1697           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
1698           x5   = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
1699           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
1700           x14  = pv[13]; x15 = pv[14]; x16 = pv[15];
1701           x    = rtmp + 16*pj[j];
1702           x[0] -= m1*x1 + m5*x2  + m9*x3  + m13*x4;
1703           x[1] -= m2*x1 + m6*x2  + m10*x3 + m14*x4;
1704           x[2] -= m3*x1 + m7*x2  + m11*x3 + m15*x4;
1705           x[3] -= m4*x1 + m8*x2  + m12*x3 + m16*x4;
1706 
1707           x[4] -= m1*x5 + m5*x6  + m9*x7  + m13*x8;
1708           x[5] -= m2*x5 + m6*x6  + m10*x7 + m14*x8;
1709           x[6] -= m3*x5 + m7*x6  + m11*x7 + m15*x8;
1710           x[7] -= m4*x5 + m8*x6  + m12*x7 + m16*x8;
1711 
1712           x[8]  -= m1*x9 + m5*x10 + m9*x11  + m13*x12;
1713           x[9]  -= m2*x9 + m6*x10 + m10*x11 + m14*x12;
1714           x[10] -= m3*x9 + m7*x10 + m11*x11 + m15*x12;
1715           x[11] -= m4*x9 + m8*x10 + m12*x11 + m16*x12;
1716 
1717           x[12] -= m1*x13 + m5*x14  + m9*x15  + m13*x16;
1718           x[13] -= m2*x13 + m6*x14  + m10*x15 + m14*x16;
1719           x[14] -= m3*x13 + m7*x14  + m11*x15 + m15*x16;
1720           x[15] -= m4*x13 + m8*x14  + m12*x15 + m16*x16;
1721 
1722           pv   += 16;
1723         }
1724         PLogFlops(128*nz+112);
1725       }
1726       row = *ajtmp++;
1727     }
1728     /* finished row so stick it into b->a */
1729     pv = ba + 16*bi[i];
1730     pj = bj + bi[i];
1731     nz = bi[i+1] - bi[i];
1732     for (j=0; j<nz; j++) {
1733       x      = rtmp+16*pj[j];
1734       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
1735       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
1736       pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
1737       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
1738       pv   += 16;
1739     }
1740     /* invert diagonal block */
1741     w = ba + 16*diag_offset[i];
1742     ierr = Kernel_A_gets_inverse_A_4(w);CHKERRQ(ierr);
1743   }
1744 
1745   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1746   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
1747   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
1748   C->factor = FACTOR_LU;
1749   C->assembled = PETSC_TRUE;
1750   PLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */
1751   PetscFunctionReturn(0);
1752 }
1753 /*
1754       Version for when blocks are 4 by 4 Using natural ordering
1755 */
1756 #undef __FUNC__
1757 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_4_NaturalOrdering"
1758 int MatCholeskyFactorNumeric_SeqSBAIJ_4_NaturalOrdering(Mat A,Mat *B)
1759 {
1760   Mat         C = *B;
1761   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
1762   int         ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
1763   int         *ajtmpold,*ajtmp,nz,row;
1764   int         *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
1765   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
1766   MatScalar   p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
1767   MatScalar   p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
1768   MatScalar   p10,p11,p12,p13,p14,p15,p16,m10,m11,m12;
1769   MatScalar   m13,m14,m15,m16;
1770   MatScalar   *ba = b->a,*aa = a->a;
1771 
1772   PetscFunctionBegin;
1773   rtmp  = (MatScalar*)PetscMalloc(16*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
1774 
1775   for (i=0; i<n; i++) {
1776     nz    = bi[i+1] - bi[i];
1777     ajtmp = bj + bi[i];
1778     for  (j=0; j<nz; j++) {
1779       x = rtmp+16*ajtmp[j];
1780       x[0]  = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = x[9] = 0.0;
1781       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
1782     }
1783     /* load in initial (unfactored row) */
1784     nz       = ai[i+1] - ai[i];
1785     ajtmpold = aj + ai[i];
1786     v        = aa + 16*ai[i];
1787     for (j=0; j<nz; j++) {
1788       x    = rtmp+16*ajtmpold[j];
1789       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
1790       x[4]  = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
1791       x[9]  = v[9];  x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
1792       x[14] = v[14]; x[15] = v[15];
1793       v    += 16;
1794     }
1795     row = *ajtmp++;
1796     while (row < i) {
1797       pc  = rtmp + 16*row;
1798       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
1799       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
1800       p10 = pc[9];  p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
1801       p15 = pc[14]; p16 = pc[15];
1802       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
1803           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
1804           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
1805           || p16 != 0.0) {
1806         pv = ba + 16*diag_offset[row];
1807         pj = bj + diag_offset[row] + 1;
1808         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
1809         x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
1810         x10 = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
1811         x15 = pv[14]; x16 = pv[15];
1812         pc[0] = m1 = p1*x1 + p5*x2  + p9*x3  + p13*x4;
1813         pc[1] = m2 = p2*x1 + p6*x2  + p10*x3 + p14*x4;
1814         pc[2] = m3 = p3*x1 + p7*x2  + p11*x3 + p15*x4;
1815         pc[3] = m4 = p4*x1 + p8*x2  + p12*x3 + p16*x4;
1816 
1817         pc[4] = m5 = p1*x5 + p5*x6  + p9*x7  + p13*x8;
1818         pc[5] = m6 = p2*x5 + p6*x6  + p10*x7 + p14*x8;
1819         pc[6] = m7 = p3*x5 + p7*x6  + p11*x7 + p15*x8;
1820         pc[7] = m8 = p4*x5 + p8*x6  + p12*x7 + p16*x8;
1821 
1822         pc[8]  = m9  = p1*x9 + p5*x10  + p9*x11  + p13*x12;
1823         pc[9]  = m10 = p2*x9 + p6*x10  + p10*x11 + p14*x12;
1824         pc[10] = m11 = p3*x9 + p7*x10  + p11*x11 + p15*x12;
1825         pc[11] = m12 = p4*x9 + p8*x10  + p12*x11 + p16*x12;
1826 
1827         pc[12] = m13 = p1*x13 + p5*x14  + p9*x15  + p13*x16;
1828         pc[13] = m14 = p2*x13 + p6*x14  + p10*x15 + p14*x16;
1829         pc[14] = m15 = p3*x13 + p7*x14  + p11*x15 + p15*x16;
1830         pc[15] = m16 = p4*x13 + p8*x14  + p12*x15 + p16*x16;
1831 
1832         nz = bi[row+1] - diag_offset[row] - 1;
1833         pv += 16;
1834         for (j=0; j<nz; j++) {
1835           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
1836           x5   = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
1837           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
1838           x14  = pv[13]; x15 = pv[14]; x16 = pv[15];
1839           x    = rtmp + 16*pj[j];
1840           x[0] -= m1*x1 + m5*x2  + m9*x3  + m13*x4;
1841           x[1] -= m2*x1 + m6*x2  + m10*x3 + m14*x4;
1842           x[2] -= m3*x1 + m7*x2  + m11*x3 + m15*x4;
1843           x[3] -= m4*x1 + m8*x2  + m12*x3 + m16*x4;
1844 
1845           x[4] -= m1*x5 + m5*x6  + m9*x7  + m13*x8;
1846           x[5] -= m2*x5 + m6*x6  + m10*x7 + m14*x8;
1847           x[6] -= m3*x5 + m7*x6  + m11*x7 + m15*x8;
1848           x[7] -= m4*x5 + m8*x6  + m12*x7 + m16*x8;
1849 
1850           x[8]  -= m1*x9 + m5*x10 + m9*x11  + m13*x12;
1851           x[9]  -= m2*x9 + m6*x10 + m10*x11 + m14*x12;
1852           x[10] -= m3*x9 + m7*x10 + m11*x11 + m15*x12;
1853           x[11] -= m4*x9 + m8*x10 + m12*x11 + m16*x12;
1854 
1855           x[12] -= m1*x13 + m5*x14  + m9*x15  + m13*x16;
1856           x[13] -= m2*x13 + m6*x14  + m10*x15 + m14*x16;
1857           x[14] -= m3*x13 + m7*x14  + m11*x15 + m15*x16;
1858           x[15] -= m4*x13 + m8*x14  + m12*x15 + m16*x16;
1859 
1860           pv   += 16;
1861         }
1862         PLogFlops(128*nz+112);
1863       }
1864       row = *ajtmp++;
1865     }
1866     /* finished row so stick it into b->a */
1867     pv = ba + 16*bi[i];
1868     pj = bj + bi[i];
1869     nz = bi[i+1] - bi[i];
1870     for (j=0; j<nz; j++) {
1871       x      = rtmp+16*pj[j];
1872       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
1873       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
1874       pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
1875       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
1876       pv   += 16;
1877     }
1878     /* invert diagonal block */
1879     w = ba + 16*diag_offset[i];
1880     ierr = Kernel_A_gets_inverse_A_4(w);CHKERRQ(ierr);
1881   }
1882 
1883   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1884   C->factor    = FACTOR_LU;
1885   C->assembled = PETSC_TRUE;
1886   PLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */
1887   PetscFunctionReturn(0);
1888 }
1889 
1890 
1891 /* ------------------------------------------------------------*/
1892 /*
1893       Version for when blocks are 3 by 3
1894 */
1895 #undef __FUNC__
1896 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_3"
1897 int MatCholeskyFactorNumeric_SeqSBAIJ_3(Mat A,Mat *B)
1898 {
1899   Mat         C = *B;
1900   Mat_SeqBAIJ *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
1901   IS          isrow = b->row,isicol = b->icol;
1902   int         *r,*ic,ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
1903   int         *ajtmpold,*ajtmp,nz,row,*ai=a->i,*aj=a->j;
1904   int         *diag_offset = b->diag,idx,*pj;
1905   MatScalar   *pv,*v,*rtmp,*pc,*w,*x;
1906   MatScalar   p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
1907   MatScalar   p5,p6,p7,p8,p9,x5,x6,x7,x8,x9;
1908   MatScalar   *ba = b->a,*aa = a->a;
1909 
1910   PetscFunctionBegin;
1911   ierr  = ISGetIndices(isrow,&r);CHKERRQ(ierr);
1912   ierr  = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
1913   rtmp  = (MatScalar*)PetscMalloc(9*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
1914 
1915   for (i=0; i<n; i++) {
1916     nz    = bi[i+1] - bi[i];
1917     ajtmp = bj + bi[i];
1918     for  (j=0; j<nz; j++) {
1919       x = rtmp + 9*ajtmp[j];
1920       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = 0.0;
1921     }
1922     /* load in initial (unfactored row) */
1923     idx      = r[i];
1924     nz       = ai[idx+1] - ai[idx];
1925     ajtmpold = aj + ai[idx];
1926     v        = aa + 9*ai[idx];
1927     for (j=0; j<nz; j++) {
1928       x    = rtmp + 9*ic[ajtmpold[j]];
1929       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
1930       x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
1931       v    += 9;
1932     }
1933     row = *ajtmp++;
1934     while (row < i) {
1935       pc = rtmp + 9*row;
1936       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
1937       p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
1938       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
1939           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0) {
1940         pv = ba + 9*diag_offset[row];
1941         pj = bj + diag_offset[row] + 1;
1942         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
1943         x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
1944         pc[0] = m1 = p1*x1 + p4*x2 + p7*x3;
1945         pc[1] = m2 = p2*x1 + p5*x2 + p8*x3;
1946         pc[2] = m3 = p3*x1 + p6*x2 + p9*x3;
1947 
1948         pc[3] = m4 = p1*x4 + p4*x5 + p7*x6;
1949         pc[4] = m5 = p2*x4 + p5*x5 + p8*x6;
1950         pc[5] = m6 = p3*x4 + p6*x5 + p9*x6;
1951 
1952         pc[6] = m7 = p1*x7 + p4*x8 + p7*x9;
1953         pc[7] = m8 = p2*x7 + p5*x8 + p8*x9;
1954         pc[8] = m9 = p3*x7 + p6*x8 + p9*x9;
1955         nz = bi[row+1] - diag_offset[row] - 1;
1956         pv += 9;
1957         for (j=0; j<nz; j++) {
1958           x1   = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
1959           x5   = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
1960           x    = rtmp + 9*pj[j];
1961           x[0] -= m1*x1 + m4*x2 + m7*x3;
1962           x[1] -= m2*x1 + m5*x2 + m8*x3;
1963           x[2] -= m3*x1 + m6*x2 + m9*x3;
1964 
1965           x[3] -= m1*x4 + m4*x5 + m7*x6;
1966           x[4] -= m2*x4 + m5*x5 + m8*x6;
1967           x[5] -= m3*x4 + m6*x5 + m9*x6;
1968 
1969           x[6] -= m1*x7 + m4*x8 + m7*x9;
1970           x[7] -= m2*x7 + m5*x8 + m8*x9;
1971           x[8] -= m3*x7 + m6*x8 + m9*x9;
1972           pv   += 9;
1973         }
1974         PLogFlops(54*nz+36);
1975       }
1976       row = *ajtmp++;
1977     }
1978     /* finished row so stick it into b->a */
1979     pv = ba + 9*bi[i];
1980     pj = bj + bi[i];
1981     nz = bi[i+1] - bi[i];
1982     for (j=0; j<nz; j++) {
1983       x     = rtmp + 9*pj[j];
1984       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
1985       pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
1986       pv   += 9;
1987     }
1988     /* invert diagonal block */
1989     w = ba + 9*diag_offset[i];
1990     ierr = Kernel_A_gets_inverse_A_3(w);CHKERRQ(ierr);
1991   }
1992 
1993   ierr = PetscFree(rtmp);CHKERRQ(ierr);
1994   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
1995   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
1996   C->factor = FACTOR_LU;
1997   C->assembled = PETSC_TRUE;
1998   PLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */
1999   PetscFunctionReturn(0);
2000 }
2001 /*
2002       Version for when blocks are 3 by 3 Using natural ordering
2003 */
2004 #undef __FUNC__
2005 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_3_NaturalOrdering"
2006 int MatCholeskyFactorNumeric_SeqSBAIJ_3_NaturalOrdering(Mat A,Mat *B)
2007 {
2008   Mat                C = *B;
2009   Mat_SeqBAIJ        *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
2010   int                ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
2011   int                *ajtmpold,*ajtmp,nz,row;
2012   int                *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
2013   MatScalar          *pv,*v,*rtmp,*pc,*w,*x;
2014   MatScalar          p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
2015   MatScalar          p5,p6,p7,p8,p9,x5,x6,x7,x8,x9;
2016   MatScalar          *ba = b->a,*aa = a->a;
2017 
2018   PetscFunctionBegin;
2019   rtmp  = (MatScalar*)PetscMalloc(9*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
2020 
2021   for (i=0; i<n; i++) {
2022     nz    = bi[i+1] - bi[i];
2023     ajtmp = bj + bi[i];
2024     for  (j=0; j<nz; j++) {
2025       x = rtmp+9*ajtmp[j];
2026       x[0]  = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = 0.0;
2027     }
2028     /* load in initial (unfactored row) */
2029     nz       = ai[i+1] - ai[i];
2030     ajtmpold = aj + ai[i];
2031     v        = aa + 9*ai[i];
2032     for (j=0; j<nz; j++) {
2033       x    = rtmp+9*ajtmpold[j];
2034       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
2035       x[4]  = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
2036       v    += 9;
2037     }
2038     row = *ajtmp++;
2039     while (row < i) {
2040       pc  = rtmp + 9*row;
2041       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
2042       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
2043       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
2044           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0) {
2045         pv = ba + 9*diag_offset[row];
2046         pj = bj + diag_offset[row] + 1;
2047         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
2048         x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
2049         pc[0] = m1 = p1*x1 + p4*x2 + p7*x3;
2050         pc[1] = m2 = p2*x1 + p5*x2 + p8*x3;
2051         pc[2] = m3 = p3*x1 + p6*x2 + p9*x3;
2052 
2053         pc[3] = m4 = p1*x4 + p4*x5 + p7*x6;
2054         pc[4] = m5 = p2*x4 + p5*x5 + p8*x6;
2055         pc[5] = m6 = p3*x4 + p6*x5 + p9*x6;
2056 
2057         pc[6] = m7 = p1*x7 + p4*x8 + p7*x9;
2058         pc[7] = m8 = p2*x7 + p5*x8 + p8*x9;
2059         pc[8] = m9 = p3*x7 + p6*x8 + p9*x9;
2060 
2061         nz = bi[row+1] - diag_offset[row] - 1;
2062         pv += 9;
2063         for (j=0; j<nz; j++) {
2064           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
2065           x5   = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
2066           x    = rtmp + 9*pj[j];
2067           x[0] -= m1*x1 + m4*x2 + m7*x3;
2068           x[1] -= m2*x1 + m5*x2 + m8*x3;
2069           x[2] -= m3*x1 + m6*x2 + m9*x3;
2070 
2071           x[3] -= m1*x4 + m4*x5 + m7*x6;
2072           x[4] -= m2*x4 + m5*x5 + m8*x6;
2073           x[5] -= m3*x4 + m6*x5 + m9*x6;
2074 
2075           x[6] -= m1*x7 + m4*x8 + m7*x9;
2076           x[7] -= m2*x7 + m5*x8 + m8*x9;
2077           x[8] -= m3*x7 + m6*x8 + m9*x9;
2078           pv   += 9;
2079         }
2080         PLogFlops(54*nz+36);
2081       }
2082       row = *ajtmp++;
2083     }
2084     /* finished row so stick it into b->a */
2085     pv = ba + 9*bi[i];
2086     pj = bj + bi[i];
2087     nz = bi[i+1] - bi[i];
2088     for (j=0; j<nz; j++) {
2089       x      = rtmp+9*pj[j];
2090       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
2091       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
2092       pv   += 9;
2093     }
2094     /* invert diagonal block */
2095     w = ba + 9*diag_offset[i];
2096     ierr = Kernel_A_gets_inverse_A_3(w);CHKERRQ(ierr);
2097   }
2098 
2099   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2100   C->factor    = FACTOR_LU;
2101   C->assembled = PETSC_TRUE;
2102   PLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */
2103   PetscFunctionReturn(0);
2104 }
2105 
2106 /* ------------------------------------------------------------*/
2107 /*
2108       Version for when blocks are 2 by 2
2109 */
2110 #undef __FUNC__
2111 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_2"
2112 int MatCholeskyFactorNumeric_SeqSBAIJ_2(Mat A,Mat *B)
2113 {
2114   Mat                C = *B;
2115   Mat_SeqBAIJ        *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
2116   IS                 isrow = b->row,isicol = b->icol;
2117   int                *r,*ic,ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
2118   int                *ajtmpold,*ajtmp,nz,row;
2119   int                *diag_offset=b->diag,idx,*ai=a->i,*aj=a->j,*pj;
2120   MatScalar          *pv,*v,*rtmp,m1,m2,m3,m4,*pc,*w,*x,x1,x2,x3,x4;
2121   MatScalar          p1,p2,p3,p4;
2122   MatScalar          *ba = b->a,*aa = a->a;
2123 
2124   PetscFunctionBegin;
2125   ierr  = ISGetIndices(isrow,&r);CHKERRQ(ierr);
2126   ierr  = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
2127   rtmp  = (MatScalar*)PetscMalloc(4*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
2128 
2129   for (i=0; i<n; i++) {
2130     nz    = bi[i+1] - bi[i];
2131     ajtmp = bj + bi[i];
2132     for  (j=0; j<nz; j++) {
2133       x = rtmp+4*ajtmp[j]; x[0] = x[1] = x[2] = x[3] = 0.0;
2134     }
2135     /* load in initial (unfactored row) */
2136     idx      = r[i];
2137     nz       = ai[idx+1] - ai[idx];
2138     ajtmpold = aj + ai[idx];
2139     v        = aa + 4*ai[idx];
2140     for (j=0; j<nz; j++) {
2141       x    = rtmp+4*ic[ajtmpold[j]];
2142       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
2143       v    += 4;
2144     }
2145     row = *ajtmp++;
2146     while (row < i) {
2147       pc = rtmp + 4*row;
2148       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
2149       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0) {
2150         pv = ba + 4*diag_offset[row];
2151         pj = bj + diag_offset[row] + 1;
2152         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
2153         pc[0] = m1 = p1*x1 + p3*x2;
2154         pc[1] = m2 = p2*x1 + p4*x2;
2155         pc[2] = m3 = p1*x3 + p3*x4;
2156         pc[3] = m4 = p2*x3 + p4*x4;
2157         nz = bi[row+1] - diag_offset[row] - 1;
2158         pv += 4;
2159         for (j=0; j<nz; j++) {
2160           x1   = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
2161           x    = rtmp + 4*pj[j];
2162           x[0] -= m1*x1 + m3*x2;
2163           x[1] -= m2*x1 + m4*x2;
2164           x[2] -= m1*x3 + m3*x4;
2165           x[3] -= m2*x3 + m4*x4;
2166           pv   += 4;
2167         }
2168         PLogFlops(16*nz+12);
2169       }
2170       row = *ajtmp++;
2171     }
2172     /* finished row so stick it into b->a */
2173     pv = ba + 4*bi[i];
2174     pj = bj + bi[i];
2175     nz = bi[i+1] - bi[i];
2176     for (j=0; j<nz; j++) {
2177       x     = rtmp+4*pj[j];
2178       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
2179       pv   += 4;
2180     }
2181     /* invert diagonal block */
2182     w = ba + 4*diag_offset[i];
2183     ierr = Kernel_A_gets_inverse_A_2(w);CHKERRQ(ierr);
2184     /*Kernel_A_gets_inverse_A(bs,w,v_pivots,v_work);*/
2185   }
2186 
2187   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2188   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
2189   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
2190   C->factor = FACTOR_LU;
2191   C->assembled = PETSC_TRUE;
2192   PLogFlops(1.3333*8*b->mbs); /* from inverting diagonal blocks */
2193   PetscFunctionReturn(0);
2194 }
2195 /*
2196       Version for when blocks are 2 by 2 Using natural ordering
2197 */
2198 #undef __FUNC__
2199 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_2_NaturalOrdering"
2200 int MatCholeskyFactorNumeric_SeqSBAIJ_2_NaturalOrdering(Mat A,Mat *B)
2201 {
2202   Mat                C = *B;
2203   Mat_SeqBAIJ        *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
2204   int                ierr,i,j,n = a->mbs,*bi = b->i,*bj = b->j;
2205   int                *ajtmpold,*ajtmp,nz,row;
2206   int                *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
2207   MatScalar          *pv,*v,*rtmp,*pc,*w,*x;
2208   MatScalar          p1,p2,p3,p4,m1,m2,m3,m4,x1,x2,x3,x4;
2209   MatScalar          *ba = b->a,*aa = a->a;
2210 
2211   PetscFunctionBegin;
2212   rtmp  = (MatScalar*)PetscMalloc(4*(n+1)*sizeof(MatScalar));CHKPTRQ(rtmp);
2213 
2214   for (i=0; i<n; i++) {
2215     nz    = bi[i+1] - bi[i];
2216     ajtmp = bj + bi[i];
2217     for  (j=0; j<nz; j++) {
2218       x = rtmp+4*ajtmp[j];
2219       x[0]  = x[1]  = x[2]  = x[3]  = 0.0;
2220     }
2221     /* load in initial (unfactored row) */
2222     nz       = ai[i+1] - ai[i];
2223     ajtmpold = aj + ai[i];
2224     v        = aa + 4*ai[i];
2225     for (j=0; j<nz; j++) {
2226       x    = rtmp+4*ajtmpold[j];
2227       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
2228       v    += 4;
2229     }
2230     row = *ajtmp++;
2231     while (row < i) {
2232       pc  = rtmp + 4*row;
2233       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
2234       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0) {
2235         pv = ba + 4*diag_offset[row];
2236         pj = bj + diag_offset[row] + 1;
2237         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
2238         pc[0] = m1 = p1*x1 + p3*x2;
2239         pc[1] = m2 = p2*x1 + p4*x2;
2240         pc[2] = m3 = p1*x3 + p3*x4;
2241         pc[3] = m4 = p2*x3 + p4*x4;
2242         nz = bi[row+1] - diag_offset[row] - 1;
2243         pv += 4;
2244         for (j=0; j<nz; j++) {
2245           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
2246           x    = rtmp + 4*pj[j];
2247           x[0] -= m1*x1 + m3*x2;
2248           x[1] -= m2*x1 + m4*x2;
2249           x[2] -= m1*x3 + m3*x4;
2250           x[3] -= m2*x3 + m4*x4;
2251           pv   += 4;
2252         }
2253         PLogFlops(16*nz+12);
2254       }
2255       row = *ajtmp++;
2256     }
2257     /* finished row so stick it into b->a */
2258     pv = ba + 4*bi[i];
2259     pj = bj + bi[i];
2260     nz = bi[i+1] - bi[i];
2261     for (j=0; j<nz; j++) {
2262       x      = rtmp+4*pj[j];
2263       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
2264       pv   += 4;
2265     }
2266     /* invert diagonal block */
2267     w = ba + 4*diag_offset[i];
2268     ierr = Kernel_A_gets_inverse_A_2(w);CHKERRQ(ierr);
2269     /*Kernel_A_gets_inverse_A(bs,w,v_pivots,v_work);*/
2270   }
2271 
2272   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2273   C->factor    = FACTOR_LU;
2274   C->assembled = PETSC_TRUE;
2275   PLogFlops(1.3333*8*b->mbs); /* from inverting diagonal blocks */
2276   PetscFunctionReturn(0);
2277 }
2278 
2279 /* ----------------------------------------------------------- */
2280 /*
2281      Version for when blocks are 1 by 1.
2282 */
2283 #undef __FUNC__
2284 #define __FUNC__ "MatCholeskyFactorNumeric_SeqSBAIJ_1"
2285 int MatCholeskyFactorNumeric_SeqSBAIJ_1(Mat A,Mat *B)
2286 {
2287   Mat                C = *B;
2288   Mat_SeqSBAIJ       *a = (Mat_SeqSBAIJ*)A->data,*b = (Mat_SeqSBAIJ *)C->data;
2289   IS                 ip = b->row;
2290   int                *rip,*riip,ierr,i,j,mbs = a->mbs,*bi = b->i,*bj = b->j;
2291   int                *ai = a->i,*aj = a->j;
2292   MatScalar          *rtmp;
2293   MatScalar          *ba = b->a,*aa = a->a;
2294   MatScalar          dk,uikdi;
2295   int                k,jmin,jmax,*jl,*il,vj,nexti,juj,ili;
2296 
2297   PetscFunctionBegin;
2298   ierr  = ISGetIndices(ip,&rip);CHKERRQ(ierr);
2299   riip = rip;
2300 
2301   /* INITIALIZATION */
2302   /* il and jl record the first nonzero element in each row of the accessing
2303      window U(0:k, k:mbs-1).
2304      jl:    list of rows to be added to uneliminated rows
2305             i>= k: jl(i) is the first row to be added to row i
2306             i<  k: jl(i) is the row following row i in some list of rows
2307             jl(i) = mbs indicates the end of a list
2308      il(i): points to the first nonzero element in columns k,...,mbs-1 of
2309             row i of U */
2310   rtmp  = (MatScalar*)PetscMalloc(mbs*sizeof(MatScalar));CHKPTRQ(rtmp);
2311   il = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(il);
2312   jl = (int*)PetscMalloc(mbs*sizeof(int));CHKPTRQ(jl);
2313   for (i=0; i<mbs; i++) {
2314     rtmp[i] = 0.0; jl[i] = mbs; il[0] = 0;
2315   }
2316 
2317   /* FOR EACH ROW K */
2318   for (k = 0; k<mbs; k++){
2319 
2320     /* INITIALIZE K-TH ROW WITH ELEMENTS NONZERO IN ROW P(K) OF A */
2321     jmin = ai[rip[k]]; jmax = ai[rip[k]+1];
2322     if (jmin < jmax) {
2323       for (j = jmin; j < jmax; j++){
2324         vj = riip[aj[j]];
2325         if (k <= vj) rtmp[vj] = aa[j];
2326       }
2327     }
2328 
2329     /* MODIFY K-TH ROW BY ADDING IN THOSE ROWS I WITH U(I,K) NE 0
2330        FOR EACH ROW I TO BE ADDED IN */
2331     dk = rtmp[k];
2332     i = jl[k]; /* first row to be added to k_th row  */
2333     /* printf(" k=%d, pivot row = %d\n",k,i); */
2334 
2335     while (i < mbs){
2336       nexti = jl[i]; /* next row to be added to k_th row */
2337       /* printf("      pivot row = %d\n", nexti); */
2338 
2339       /* COMPUTE MULTIPLIER AND UPDATE DIAGONAL ELEMENT */
2340       ili = il[i];  /* index of first nonzero element in U(i,k:bms-1) */
2341       uikdi = - ba[ili]*ba[i];
2342       dk += uikdi*ba[ili];
2343       ba[ili] = uikdi; /* update U(i,k) */
2344 
2345       /* ADD MULTIPLE OF ROW I TO K-TH ROW ... */
2346       jmin = ili + 1; jmax = bi[i+1];
2347       if (jmin < jmax){
2348         for (j=jmin; j<jmax; j++) rtmp[bj[j]] += uikdi*ba[j];
2349         /* ... AND ADD I TO ROW LIST FOR NEXT NONZERO ENTRY */
2350          il[i] = jmin;             /* update il(i) in column k+1, ... mbs-1 */
2351          j     = bj[jmin];
2352          jl[i] = jl[j]; jl[j] = i; /* update jl */
2353       }
2354       i = nexti;
2355       /* printf("                  pivot row i=%d\n",i);  */
2356     }
2357 
2358     /* CHECK FOR ZERO PIVOT AND SAVE DIAGONAL ELEMENT */
2359     if (dk == 0.0){
2360       SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,0,"Zero pivot");
2361     }
2362 
2363     /* SAVE NONZERO ENTRIES IN K-TH ROW OF U ... */
2364     ba[k] = 1.0/dk;
2365     jmin = bi[k]; jmax = bi[k+1];
2366     if (jmin < jmax) {
2367       for (j=jmin; j<jmax; j++){
2368          juj = bj[j]; ba[j] = rtmp[juj]; rtmp[juj] = 0.0;
2369       }
2370 
2371       /* ... AND ADD K TO ROW LIST FOR FIRST NONZERO ENTRY IN K-TH ROW */
2372       il[k] = jmin;
2373       i     = bj[jmin];
2374       jl[k] = jl[i]; jl[i] = k;
2375     }
2376   }
2377 
2378   ierr = PetscFree(rtmp);CHKERRQ(ierr);
2379   ierr = PetscFree(il);CHKERRQ(ierr);
2380   ierr = PetscFree(jl);CHKERRQ(ierr);
2381 
2382   ierr = ISRestoreIndices(ip,&rip);CHKERRQ(ierr);
2383   C->factor    = FACTOR_LU;
2384   C->assembled = PETSC_TRUE;
2385   PLogFlops(b->mbs);
2386   PetscFunctionReturn(0);
2387 }
2388 
2389 #undef __FUNC__
2390 #define __FUNC__ "MatCholeskyFactor_SeqSBAIJ"
2391 int MatCholeskyFactor_SeqSBAIJ(Mat A,IS perm,PetscReal f)
2392 {
2393   Mat_SeqSBAIJ    *mat = (Mat_SeqSBAIJ*)A->data;
2394   int            ierr,refct;
2395   Mat            C;
2396   PetscOps *Abops;
2397   MatOps   Aops;
2398 
2399   PetscFunctionBegin;
2400   ierr = MatCholeskyFactorSymbolic(A,perm,f,&C);CHKERRQ(ierr);
2401   ierr = MatCholeskyFactorNumeric(A,&C);CHKERRQ(ierr);
2402 
2403   /* free all the data structures from mat */
2404   ierr = PetscFree(mat->a);CHKERRQ(ierr);
2405   if (!mat->singlemalloc) {
2406     ierr = PetscFree(mat->i);CHKERRQ(ierr);
2407     ierr = PetscFree(mat->j);CHKERRQ(ierr);
2408   }
2409   if (mat->diag) {ierr = PetscFree(mat->diag);CHKERRQ(ierr);}
2410   if (mat->ilen) {ierr = PetscFree(mat->ilen);CHKERRQ(ierr);}
2411   if (mat->imax) {ierr = PetscFree(mat->imax);CHKERRQ(ierr);}
2412   if (mat->solve_work) {ierr = PetscFree(mat->solve_work);CHKERRQ(ierr);}
2413   if (mat->mult_work) {ierr = PetscFree(mat->mult_work);CHKERRQ(ierr);}
2414   if (mat->icol) {ierr = ISDestroy(mat->icol);CHKERRQ(ierr);}
2415   ierr = PetscFree(mat);CHKERRQ(ierr);
2416 
2417   ierr = MapDestroy(A->rmap);CHKERRQ(ierr);
2418   ierr = MapDestroy(A->cmap);CHKERRQ(ierr);
2419 
2420   /*
2421        This is horrible,horrible code. We need to keep the
2422     A pointers for the bops and ops but copy everything
2423     else from C.
2424   */
2425   Abops = A->bops;
2426   Aops  = A->ops;
2427   refct = A->refct;
2428   ierr  = PetscMemcpy(A,C,sizeof(struct _p_Mat));CHKERRQ(ierr);
2429   mat   = (Mat_SeqSBAIJ*)A->data;
2430   PLogObjectParent(A,mat->icol);
2431 
2432   A->bops  = Abops;
2433   A->ops   = Aops;
2434   A->qlist = 0;
2435   A->refct = refct;
2436   /* copy over the type_name and name */
2437   ierr     = PetscStrallocpy(C->type_name,&A->type_name);CHKERRQ(ierr);
2438   ierr     = PetscStrallocpy(C->name,&A->name);CHKERRQ(ierr);
2439 
2440   PetscHeaderDestroy(C);
2441   PetscFunctionReturn(0);
2442 }
2443 
2444 
2445