xref: /petsc/src/mat/impls/baij/seq/baijfact.c (revision e80fee0d83fca2e79359165ac082b818fca7907f)
1 #ifdef PETSC_RCS_HEADER
2 static char vcid[] = "$Id: baijfact.c,v 1.62 1998/03/30 19:48:59 balay Exp bsmith $";
3 #endif
4 /*
5     Factorization code for BAIJ format.
6 */
7 
8 #include "src/mat/impls/baij/seq/baij.h"
9 #include "src/vec/vecimpl.h"
10 #include "src/inline/ilu.h"
11 
12 
13 /*
14     The symbolic factorization code is identical to that for AIJ format,
15   except for very small changes since this is now a SeqBAIJ datastructure.
16   NOT good code reuse.
17 */
18 #undef __FUNC__
19 #define __FUNC__ "MatLUFactorSymbolic_SeqBAIJ"
20 int MatLUFactorSymbolic_SeqBAIJ(Mat A,IS isrow,IS iscol,double f,Mat *B)
21 {
22   Mat_SeqBAIJ *a = (Mat_SeqBAIJ *) A->data, *b;
23   IS          isicol;
24   int         *r,*ic, ierr, i, n = a->mbs, *ai = a->i, *aj = a->j;
25   int         *ainew,*ajnew, jmax,*fill, *ajtmp, nz, bs = a->bs, bs2=a->bs2;
26   int         *idnew, idx, row,m,fm, nnz, nzi,realloc = 0,nzbd,*im;
27 
28   PetscFunctionBegin;
29   PetscValidHeaderSpecific(isrow,IS_COOKIE);
30   PetscValidHeaderSpecific(iscol,IS_COOKIE);
31   ierr = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
32   ISGetIndices(isrow,&r); ISGetIndices(isicol,&ic);
33 
34   /* get new row pointers */
35   ainew = (int *) PetscMalloc( (n+1)*sizeof(int) ); CHKPTRQ(ainew);
36   ainew[0] = 0;
37   /* don't know how many column pointers are needed so estimate */
38   jmax = (int) (f*ai[n] + 1);
39   ajnew = (int *) PetscMalloc( (jmax)*sizeof(int) ); CHKPTRQ(ajnew);
40   /* fill is a linked list of nonzeros in active row */
41   fill = (int *) PetscMalloc( (2*n+1)*sizeof(int)); CHKPTRQ(fill);
42   im = fill + n + 1;
43   /* idnew is location of diagonal in factor */
44   idnew = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(idnew);
45   idnew[0] = 0;
46 
47   for ( i=0; i<n; i++ ) {
48     /* first copy previous fill into linked list */
49     nnz     = nz    = ai[r[i]+1] - ai[r[i]];
50     if (!nz) SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,1,"Empty row in matrix");
51     ajtmp   = aj + ai[r[i]];
52     fill[n] = n;
53     while (nz--) {
54       fm  = n;
55       idx = ic[*ajtmp++];
56       do {
57         m  = fm;
58         fm = fill[m];
59       } while (fm < idx);
60       fill[m]   = idx;
61       fill[idx] = fm;
62     }
63     row = fill[n];
64     while ( row < i ) {
65       ajtmp = ajnew + idnew[row] + 1;
66       nzbd  = 1 + idnew[row] - ainew[row];
67       nz    = im[row] - nzbd;
68       fm    = row;
69       while (nz-- > 0) {
70         idx = *ajtmp++;
71         nzbd++;
72         if (idx == i) im[row] = nzbd;
73         do {
74           m  = fm;
75           fm = fill[m];
76         } while (fm < idx);
77         if (fm != idx) {
78           fill[m]   = idx;
79           fill[idx] = fm;
80           fm        = idx;
81           nnz++;
82         }
83       }
84       row = fill[row];
85     }
86     /* copy new filled row into permanent storage */
87     ainew[i+1] = ainew[i] + nnz;
88     if (ainew[i+1] > jmax) {
89 
90       /* estimate how much additional space we will need */
91       /* use the strategy suggested by David Hysom <hysom@perch-t.icase.edu> */
92       /* just double the memory each time */
93       int maxadd = jmax;
94       /* maxadd = (int) ((f*(ai[n]+1)*(n-i+5))/n); */
95       if (maxadd < nnz) maxadd = (n-i)*(nnz+1);
96       jmax += maxadd;
97 
98       /* allocate a longer ajnew */
99       ajtmp = (int *) PetscMalloc( jmax*sizeof(int) );CHKPTRQ(ajtmp);
100       PetscMemcpy(ajtmp,ajnew,ainew[i]*sizeof(int));
101       PetscFree(ajnew);
102       ajnew = ajtmp;
103       realloc++; /* count how many times we realloc */
104     }
105     ajtmp = ajnew + ainew[i];
106     fm    = fill[n];
107     nzi   = 0;
108     im[i] = nnz;
109     while (nnz--) {
110       if (fm < i) nzi++;
111       *ajtmp++ = fm;
112       fm       = fill[fm];
113     }
114     idnew[i] = ainew[i] + nzi;
115   }
116 
117   if (ai[n] != 0) {
118     double af = ((double)ainew[n])/((double)ai[n]);
119     PLogInfo(A,"MatLUFactorSymbolic_SeqBAIJ:Reallocs %d Fill ratio:given %g needed %g\n",
120              realloc,f,af);
121     PLogInfo(A,"MatLUFactorSymbolic_SeqBAIJ:Run with -pc_lu_fill %g or use \n",af);
122     PLogInfo(A,"MatLUFactorSymbolic_SeqBAIJ:PCLUSetFill(pc,%g);\n",af);
123     PLogInfo(A,"MatLUFactorSymbolic_SeqBAIJ:for best performance.\n");
124   } else {
125      PLogInfo(A,"MatLUFactorSymbolic_SeqBAIJ:Empty matrix.\n");
126   }
127 
128   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
129   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
130 
131   PetscFree(fill);
132 
133   /* put together the new matrix */
134   ierr = MatCreateSeqBAIJ(A->comm,bs,bs*n,bs*n,0,PETSC_NULL,B); CHKERRQ(ierr);
135   PLogObjectParent(*B,isicol);
136   b = (Mat_SeqBAIJ *) (*B)->data;
137   PetscFree(b->imax);
138   b->singlemalloc = 0;
139   /* the next line frees the default space generated by the Create() */
140   PetscFree(b->a); PetscFree(b->ilen);
141   b->a          = (Scalar *) PetscMalloc((ainew[n]+1)*sizeof(Scalar)*bs2);CHKPTRQ(b->a);
142   b->j          = ajnew;
143   b->i          = ainew;
144   b->diag       = idnew;
145   b->ilen       = 0;
146   b->imax       = 0;
147   b->row        = isrow;
148   b->col        = iscol;
149   b->icol       = isicol;
150   b->solve_work = (Scalar *) PetscMalloc( (bs*n+bs)*sizeof(Scalar));CHKPTRQ(b->solve_work);
151   /* In b structure:  Free imax, ilen, old a, old j.
152      Allocate idnew, solve_work, new a, new j */
153   PLogObjectMemory(*B,(ainew[n]-n)*(sizeof(int)+sizeof(Scalar)));
154   b->maxnz = b->nz = ainew[n];
155 
156   (*B)->info.factor_mallocs    = realloc;
157   (*B)->info.fill_ratio_given  = f;
158   if (ai[i] != 0) {
159     (*B)->info.fill_ratio_needed = ((double)ainew[n])/((double)ai[i]);
160   } else {
161     (*B)->info.fill_ratio_needed = 0.0;
162   }
163 
164 
165   PetscFunctionReturn(0);
166 }
167 
168 /* ----------------------------------------------------------- */
169 #undef __FUNC__
170 #define __FUNC__ "MatLUFactorNumeric_SeqBAIJ_N"
171 int MatLUFactorNumeric_SeqBAIJ_N(Mat A,Mat *B)
172 {
173   Mat             C = *B;
174   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data,*b = (Mat_SeqBAIJ *)C->data;
175   IS              isrow = b->row, isicol = b->icol;
176   int             *r,*ic, ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
177   int             *ajtmpold, *ajtmp, nz, row, bslog,*ai=a->i,*aj=a->j,k,flg;
178   int             *diag_offset=b->diag,diag,bs=a->bs,bs2 = a->bs2,*v_pivots;
179   register int    *pj;
180   register Scalar *pv,*v,*rtmp,*multiplier,*v_work,*pc,*w;
181   Scalar          *ba = b->a,*aa = a->a;
182 
183   PetscFunctionBegin;
184   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
185   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
186   rtmp  = (Scalar *) PetscMalloc(bs2*(n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
187   PetscMemzero(rtmp,bs2*(n+1)*sizeof(Scalar));
188   /* generate work space needed by dense LU factorization */
189   v_work     = (Scalar *) PetscMalloc(bs*sizeof(int) + (bs+bs2)*sizeof(Scalar));
190                CHKPTRQ(v_work);
191   multiplier = v_work + bs;
192   v_pivots   = (int *) (multiplier + bs2);
193 
194   /* flops in while loop */
195   bslog = 2*bs*bs2;
196 
197   for ( i=0; i<n; i++ ) {
198     nz    = bi[i+1] - bi[i];
199     ajtmp = bj + bi[i];
200     for  ( j=0; j<nz; j++ ) {
201       PetscMemzero(rtmp+bs2*ajtmp[j],bs2*sizeof(Scalar));
202     }
203     /* load in initial (unfactored row) */
204     nz       = ai[r[i]+1] - ai[r[i]];
205     ajtmpold = aj + ai[r[i]];
206     v        = aa + bs2*ai[r[i]];
207     for ( j=0; j<nz; j++ ) {
208       PetscMemcpy(rtmp+bs2*ic[ajtmpold[j]],v+bs2*j,bs2*sizeof(Scalar));
209     }
210     row = *ajtmp++;
211     while (row < i) {
212       pc = rtmp + bs2*row;
213 /*      if (*pc) { */
214       for ( flg=0,k=0; k<bs2; k++ ) { if (pc[k]!=0.0) { flg =1; break; }}
215       if (flg) {
216         pv = ba + bs2*diag_offset[row];
217         pj = bj + diag_offset[row] + 1;
218         Kernel_A_gets_A_times_B(bs,pc,pv,multiplier);
219         nz = bi[row+1] - diag_offset[row] - 1;
220         pv += bs2;
221         for (j=0; j<nz; j++) {
222           Kernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j);
223         }
224         PLogFlops(bslog*(nz+1)-bs);
225       }
226         row = *ajtmp++;
227     }
228     /* finished row so stick it into b->a */
229     pv = ba + bs2*bi[i];
230     pj = bj + bi[i];
231     nz = bi[i+1] - bi[i];
232     for ( j=0; j<nz; j++ ) {
233       PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(Scalar));
234     }
235     diag = diag_offset[i] - bi[i];
236     /* invert diagonal block */
237     w = pv + bs2*diag;
238     Kernel_A_gets_inverse_A(bs,w,v_pivots,v_work);
239   }
240 
241   PetscFree(rtmp); PetscFree(v_work);
242   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
243   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
244   C->factor = FACTOR_LU;
245   C->assembled = PETSC_TRUE;
246   PLogFlops(1.3333*bs*bs2*b->mbs); /* from inverting diagonal blocks */
247   PetscFunctionReturn(0);
248 }
249 /* ------------------------------------------------------------*/
250 /*
251       Version for when blocks are 5 by 5
252 */
253 #undef __FUNC__
254 #define __FUNC__ "MatLUFactorNumeric_SeqBAIJ_5"
255 int MatLUFactorNumeric_SeqBAIJ_5(Mat A,Mat *B)
256 {
257   Mat             C = *B;
258   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data,*b = (Mat_SeqBAIJ *)C->data;
259   IS              isrow = b->row, isicol = b->icol;
260   int             *r,*ic, ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
261   int             *ajtmpold, *ajtmp, nz, row;
262   int             *diag_offset = b->diag,idx,*ai=a->i,*aj=a->j;
263   register int    *pj;
264   register Scalar *pv,*v,*rtmp,*pc,*w,*x;
265   Scalar          p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
266   Scalar          p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
267   Scalar          x17,x18,x19,x20,x21,x22,x23,x24,x25,p10,p11,p12,p13,p14;
268   Scalar          p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,m10,m11,m12;
269   Scalar          m13,m14,m15,m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
270   Scalar          *ba = b->a,*aa = a->a;
271 
272   PetscFunctionBegin;
273   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
274   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
275   rtmp  = (Scalar *) PetscMalloc(25*(n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
276 
277   for ( i=0; i<n; i++ ) {
278     nz    = bi[i+1] - bi[i];
279     ajtmp = bj + bi[i];
280     for  ( j=0; j<nz; j++ ) {
281       x = rtmp+25*ajtmp[j];
282       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
283       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
284       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0;
285     }
286     /* load in initial (unfactored row) */
287     idx      = r[i];
288     nz       = ai[idx+1] - ai[idx];
289     ajtmpold = aj + ai[idx];
290     v        = aa + 25*ai[idx];
291     for ( j=0; j<nz; j++ ) {
292       x    = rtmp+25*ic[ajtmpold[j]];
293       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
294       x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
295       x[9] = v[9]; x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
296       x[14] = v[14]; x[15] = v[15]; x[16] = v[16]; x[17] = v[17];
297       x[18] = v[18]; x[19] = v[19]; x[20] = v[20]; x[21] = v[21];
298       x[22] = v[22]; x[23] = v[23]; x[24] = v[24];
299       v    += 25;
300     }
301     row = *ajtmp++;
302     while (row < i) {
303       pc = rtmp + 25*row;
304       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
305       p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
306       p10 = pc[9]; p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
307       p15 = pc[14]; p16 = pc[15]; p17 = pc[16]; p18 = pc[17]; p19 = pc[18];
308       p20 = pc[19]; p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
309       p25 = pc[24];
310       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
311           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
312           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
313           || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 ||
314           p20 != 0.0 || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 ||
315           p24 != 0.0 || p25 != 0.0) {
316         pv = ba + 25*diag_offset[row];
317         pj = bj + diag_offset[row] + 1;
318         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
319         x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
320         x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
321         x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17];
322         x19 = pv[18]; x20 = pv[19]; x21 = pv[20]; x22 = pv[21];
323         x23 = pv[22]; x24 = pv[23]; x25 = pv[24];
324         pc[0] = m1 = p1*x1 + p6*x2  + p11*x3 + p16*x4 + p21*x5;
325         pc[1] = m2 = p2*x1 + p7*x2  + p12*x3 + p17*x4 + p22*x5;
326         pc[2] = m3 = p3*x1 + p8*x2  + p13*x3 + p18*x4 + p23*x5;
327         pc[3] = m4 = p4*x1 + p9*x2  + p14*x3 + p19*x4 + p24*x5;
328         pc[4] = m5 = p5*x1 + p10*x2 + p15*x3 + p20*x4 + p25*x5;
329 
330         pc[5] = m6 = p1*x6 + p6*x7  + p11*x8 + p16*x9 + p21*x10;
331         pc[6] = m7 = p2*x6 + p7*x7  + p12*x8 + p17*x9 + p22*x10;
332         pc[7] = m8 = p3*x6 + p8*x7  + p13*x8 + p18*x9 + p23*x10;
333         pc[8] = m9 = p4*x6 + p9*x7  + p14*x8 + p19*x9 + p24*x10;
334         pc[9] = m10 = p5*x6 + p10*x7 + p15*x8 + p20*x9 + p25*x10;
335 
336         pc[10] = m11 = p1*x11 + p6*x12  + p11*x13 + p16*x14 + p21*x15;
337         pc[11] = m12 = p2*x11 + p7*x12  + p12*x13 + p17*x14 + p22*x15;
338         pc[12] = m13 = p3*x11 + p8*x12  + p13*x13 + p18*x14 + p23*x15;
339         pc[13] = m14 = p4*x11 + p9*x12  + p14*x13 + p19*x14 + p24*x15;
340         pc[14] = m15 = p5*x11 + p10*x12 + p15*x13 + p20*x14 + p25*x15;
341 
342         pc[15] = m16 = p1*x16 + p6*x17  + p11*x18 + p16*x19 + p21*x20;
343         pc[16] = m17 = p2*x16 + p7*x17  + p12*x18 + p17*x19 + p22*x20;
344         pc[17] = m18 = p3*x16 + p8*x17  + p13*x18 + p18*x19 + p23*x20;
345         pc[18] = m19 = p4*x16 + p9*x17  + p14*x18 + p19*x19 + p24*x20;
346         pc[19] = m20 = p5*x16 + p10*x17 + p15*x18 + p20*x19 + p25*x20;
347 
348         pc[20] = m21 = p1*x21 + p6*x22  + p11*x23 + p16*x24 + p21*x25;
349         pc[21] = m22 = p2*x21 + p7*x22  + p12*x23 + p17*x24 + p22*x25;
350         pc[22] = m23 = p3*x21 + p8*x22  + p13*x23 + p18*x24 + p23*x25;
351         pc[23] = m24 = p4*x21 + p9*x22  + p14*x23 + p19*x24 + p24*x25;
352         pc[24] = m25 = p5*x21 + p10*x22 + p15*x23 + p20*x24 + p25*x25;
353 
354         nz = bi[row+1] - diag_offset[row] - 1;
355         pv += 25;
356         for (j=0; j<nz; j++) {
357           x1   = pv[0];  x2 = pv[1];   x3  = pv[2];  x4  = pv[3];
358           x5   = pv[4];  x6 = pv[5];   x7  = pv[6];  x8  = pv[7]; x9 = pv[8];
359           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
360           x14  = pv[13]; x15 = pv[14]; x16 = pv[15]; x17 = pv[16];
361           x18  = pv[17]; x19 = pv[18]; x20 = pv[19]; x21 = pv[20];
362           x22  = pv[21]; x23 = pv[22]; x24 = pv[23]; x25 = pv[24];
363           x    = rtmp + 25*pj[j];
364           x[0] -= m1*x1 + m6*x2  + m11*x3 + m16*x4 + m21*x5;
365           x[1] -= m2*x1 + m7*x2  + m12*x3 + m17*x4 + m22*x5;
366           x[2] -= m3*x1 + m8*x2  + m13*x3 + m18*x4 + m23*x5;
367           x[3] -= m4*x1 + m9*x2  + m14*x3 + m19*x4 + m24*x5;
368           x[4] -= m5*x1 + m10*x2 + m15*x3 + m20*x4 + m25*x5;
369 
370           x[5] -= m1*x6 + m6*x7  + m11*x8 + m16*x9 + m21*x10;
371           x[6] -= m2*x6 + m7*x7  + m12*x8 + m17*x9 + m22*x10;
372           x[7] -= m3*x6 + m8*x7  + m13*x8 + m18*x9 + m23*x10;
373           x[8] -= m4*x6 + m9*x7  + m14*x8 + m19*x9 + m24*x10;
374           x[9] -= m5*x6 + m10*x7 + m15*x8 + m20*x9 + m25*x10;
375 
376           x[10] -= m1*x11 + m6*x12  + m11*x13 + m16*x14 + m21*x15;
377           x[11] -= m2*x11 + m7*x12  + m12*x13 + m17*x14 + m22*x15;
378           x[12] -= m3*x11 + m8*x12  + m13*x13 + m18*x14 + m23*x15;
379           x[13] -= m4*x11 + m9*x12  + m14*x13 + m19*x14 + m24*x15;
380           x[14] -= m5*x11 + m10*x12 + m15*x13 + m20*x14 + m25*x15;
381 
382           x[15] -= m1*x16 + m6*x17  + m11*x18 + m16*x19 + m21*x20;
383           x[16] -= m2*x16 + m7*x17  + m12*x18 + m17*x19 + m22*x20;
384           x[17] -= m3*x16 + m8*x17  + m13*x18 + m18*x19 + m23*x20;
385           x[18] -= m4*x16 + m9*x17  + m14*x18 + m19*x19 + m24*x20;
386           x[19] -= m5*x16 + m10*x17 + m15*x18 + m20*x19 + m25*x20;
387 
388           x[20] -= m1*x21 + m6*x22  + m11*x23 + m16*x24 + m21*x25;
389           x[21] -= m2*x21 + m7*x22  + m12*x23 + m17*x24 + m22*x25;
390           x[22] -= m3*x21 + m8*x22  + m13*x23 + m18*x24 + m23*x25;
391           x[23] -= m4*x21 + m9*x22  + m14*x23 + m19*x24 + m24*x25;
392           x[24] -= m5*x21 + m10*x22 + m15*x23 + m20*x24 + m25*x25;
393 
394           pv   += 25;
395         }
396         PLogFlops(250*nz+225);
397       }
398       row = *ajtmp++;
399     }
400     /* finished row so stick it into b->a */
401     pv = ba + 25*bi[i];
402     pj = bj + bi[i];
403     nz = bi[i+1] - bi[i];
404     for ( j=0; j<nz; j++ ) {
405       x     = rtmp+25*pj[j];
406       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
407       pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
408       pv[9] = x[9]; pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
409       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; pv[16] = x[16];
410       pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19]; pv[20] = x[20];
411       pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23]; pv[24] = x[24];
412       pv   += 25;
413     }
414     /* invert diagonal block */
415     w = ba + 25*diag_offset[i];
416     ierr = Kernel_A_gets_inverse_A_5(w); CHKERRQ(ierr);
417   }
418 
419   PetscFree(rtmp);
420   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
421   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
422   C->factor = FACTOR_LU;
423   C->assembled = PETSC_TRUE;
424   PLogFlops(1.3333*125*b->mbs); /* from inverting diagonal blocks */
425   PetscFunctionReturn(0);
426 }
427 
428 /* ------------------------------------------------------------*/
429 /*
430       Version for when blocks are 4 by 4
431 */
432 #undef __FUNC__
433 #define __FUNC__ "MatLUFactorNumeric_SeqBAIJ_4"
434 int MatLUFactorNumeric_SeqBAIJ_4(Mat A,Mat *B)
435 {
436   Mat             C = *B;
437   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data,*b = (Mat_SeqBAIJ *)C->data;
438   IS              isrow = b->row, isicol = b->icol;
439   int             *r,*ic, ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
440   int             *ajtmpold, *ajtmp, nz, row;
441   int             *diag_offset = b->diag,idx,*ai=a->i,*aj=a->j;
442   register int    *pj;
443   register Scalar *pv,*v,*rtmp,*pc,*w,*x;
444   Scalar          p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
445   Scalar          p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
446   Scalar          p10,p11,p12,p13,p14,p15,p16,m10,m11,m12;
447   Scalar          m13,m14,m15,m16;
448   Scalar          *ba = b->a,*aa = a->a;
449 
450   PetscFunctionBegin;
451   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
452   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
453   rtmp  = (Scalar *) PetscMalloc(16*(n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
454 
455   for ( i=0; i<n; i++ ) {
456     nz    = bi[i+1] - bi[i];
457     ajtmp = bj + bi[i];
458     for  ( j=0; j<nz; j++ ) {
459       x = rtmp+16*ajtmp[j];
460       x[0]  = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = x[9] = 0.0;
461       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
462     }
463     /* load in initial (unfactored row) */
464     idx      = r[i];
465     nz       = ai[idx+1] - ai[idx];
466     ajtmpold = aj + ai[idx];
467     v        = aa + 16*ai[idx];
468     for ( j=0; j<nz; j++ ) {
469       x    = rtmp+16*ic[ajtmpold[j]];
470       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
471       x[4]  = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
472       x[9]  = v[9];  x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
473       x[14] = v[14]; x[15] = v[15];
474       v    += 16;
475     }
476     row = *ajtmp++;
477     while (row < i) {
478       pc  = rtmp + 16*row;
479       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
480       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
481       p10 = pc[9];  p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
482       p15 = pc[14]; p16 = pc[15];
483       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
484           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
485           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
486           || p16 != 0.0) {
487         pv = ba + 16*diag_offset[row];
488         pj = bj + diag_offset[row] + 1;
489         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
490         x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
491         x10 = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
492         x15 = pv[14]; x16 = pv[15];
493         pc[0] = m1 = p1*x1 + p5*x2  + p9*x3  + p13*x4;
494         pc[1] = m2 = p2*x1 + p6*x2  + p10*x3 + p14*x4;
495         pc[2] = m3 = p3*x1 + p7*x2  + p11*x3 + p15*x4;
496         pc[3] = m4 = p4*x1 + p8*x2  + p12*x3 + p16*x4;
497 
498         pc[4] = m5 = p1*x5 + p5*x6  + p9*x7  + p13*x8;
499         pc[5] = m6 = p2*x5 + p6*x6  + p10*x7 + p14*x8;
500         pc[6] = m7 = p3*x5 + p7*x6  + p11*x7 + p15*x8;
501         pc[7] = m8 = p4*x5 + p8*x6  + p12*x7 + p16*x8;
502 
503         pc[8]  = m9  = p1*x9 + p5*x10  + p9*x11  + p13*x12;
504         pc[9]  = m10 = p2*x9 + p6*x10  + p10*x11 + p14*x12;
505         pc[10] = m11 = p3*x9 + p7*x10  + p11*x11 + p15*x12;
506         pc[11] = m12 = p4*x9 + p8*x10  + p12*x11 + p16*x12;
507 
508         pc[12] = m13 = p1*x13 + p5*x14  + p9*x15  + p13*x16;
509         pc[13] = m14 = p2*x13 + p6*x14  + p10*x15 + p14*x16;
510         pc[14] = m15 = p3*x13 + p7*x14  + p11*x15 + p15*x16;
511         pc[15] = m16 = p4*x13 + p8*x14  + p12*x15 + p16*x16;
512 
513         nz = bi[row+1] - diag_offset[row] - 1;
514         pv += 16;
515         for (j=0; j<nz; j++) {
516           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
517           x5   = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
518           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
519           x14  = pv[13]; x15 = pv[14]; x16 = pv[15];
520           x    = rtmp + 16*pj[j];
521           x[0] -= m1*x1 + m5*x2  + m9*x3  + m13*x4;
522           x[1] -= m2*x1 + m6*x2  + m10*x3 + m14*x4;
523           x[2] -= m3*x1 + m7*x2  + m11*x3 + m15*x4;
524           x[3] -= m4*x1 + m8*x2  + m12*x3 + m16*x4;
525 
526           x[4] -= m1*x5 + m5*x6  + m9*x7  + m13*x8;
527           x[5] -= m2*x5 + m6*x6  + m10*x7 + m14*x8;
528           x[6] -= m3*x5 + m7*x6  + m11*x7 + m15*x8;
529           x[7] -= m4*x5 + m8*x6  + m12*x7 + m16*x8;
530 
531           x[8]  -= m1*x9 + m5*x10 + m9*x11  + m13*x12;
532           x[9]  -= m2*x9 + m6*x10 + m10*x11 + m14*x12;
533           x[10] -= m3*x9 + m7*x10 + m11*x11 + m15*x12;
534           x[11] -= m4*x9 + m8*x10 + m12*x11 + m16*x12;
535 
536           x[12] -= m1*x13 + m5*x14  + m9*x15  + m13*x16;
537           x[13] -= m2*x13 + m6*x14  + m10*x15 + m14*x16;
538           x[14] -= m3*x13 + m7*x14  + m11*x15 + m15*x16;
539           x[15] -= m4*x13 + m8*x14  + m12*x15 + m16*x16;
540 
541           pv   += 16;
542         }
543         PLogFlops(128*nz+112);
544       }
545       row = *ajtmp++;
546     }
547     /* finished row so stick it into b->a */
548     pv = ba + 16*bi[i];
549     pj = bj + bi[i];
550     nz = bi[i+1] - bi[i];
551     for ( j=0; j<nz; j++ ) {
552       x      = rtmp+16*pj[j];
553       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
554       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
555       pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
556       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
557       pv   += 16;
558     }
559     /* invert diagonal block */
560     w = ba + 16*diag_offset[i];
561     ierr = Kernel_A_gets_inverse_A_4(w); CHKERRQ(ierr);
562   }
563 
564   PetscFree(rtmp);
565   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
566   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
567   C->factor = FACTOR_LU;
568   C->assembled = PETSC_TRUE;
569   PLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */
570   PetscFunctionReturn(0);
571 }
572 /*
573       Version for when blocks are 4 by 4 Using natural ordering
574 */
575 #undef __FUNC__
576 #define __FUNC__ "MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering"
577 int MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering(Mat A,Mat *B)
578 {
579   Mat             C = *B;
580   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data,*b = (Mat_SeqBAIJ *)C->data;
581   int             ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
582   int             *ajtmpold, *ajtmp, nz, row;
583   int             *diag_offset = b->diag,*ai=a->i,*aj=a->j;
584   register int    *pj;
585   register Scalar *pv,*v,*rtmp,*pc,*w,*x;
586   Scalar          p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
587   Scalar          p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
588   Scalar          p10,p11,p12,p13,p14,p15,p16,m10,m11,m12;
589   Scalar          m13,m14,m15,m16;
590   Scalar          *ba = b->a,*aa = a->a;
591 
592   PetscFunctionBegin;
593   rtmp  = (Scalar *) PetscMalloc(16*(n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
594 
595   for ( i=0; i<n; i++ ) {
596     nz    = bi[i+1] - bi[i];
597     ajtmp = bj + bi[i];
598     for  ( j=0; j<nz; j++ ) {
599       x = rtmp+16*ajtmp[j];
600       x[0]  = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = x[9] = 0.0;
601       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
602     }
603     /* load in initial (unfactored row) */
604     nz       = ai[i+1] - ai[i];
605     ajtmpold = aj + ai[i];
606     v        = aa + 16*ai[i];
607     for ( j=0; j<nz; j++ ) {
608       x    = rtmp+16*ajtmpold[j];
609       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
610       x[4]  = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
611       x[9]  = v[9];  x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
612       x[14] = v[14]; x[15] = v[15];
613       v    += 16;
614     }
615     row = *ajtmp++;
616     while (row < i) {
617       pc  = rtmp + 16*row;
618       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
619       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
620       p10 = pc[9];  p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
621       p15 = pc[14]; p16 = pc[15];
622       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
623           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
624           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
625           || p16 != 0.0) {
626         pv = ba + 16*diag_offset[row];
627         pj = bj + diag_offset[row] + 1;
628         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
629         x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
630         x10 = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
631         x15 = pv[14]; x16 = pv[15];
632         pc[0] = m1 = p1*x1 + p5*x2  + p9*x3  + p13*x4;
633         pc[1] = m2 = p2*x1 + p6*x2  + p10*x3 + p14*x4;
634         pc[2] = m3 = p3*x1 + p7*x2  + p11*x3 + p15*x4;
635         pc[3] = m4 = p4*x1 + p8*x2  + p12*x3 + p16*x4;
636 
637         pc[4] = m5 = p1*x5 + p5*x6  + p9*x7  + p13*x8;
638         pc[5] = m6 = p2*x5 + p6*x6  + p10*x7 + p14*x8;
639         pc[6] = m7 = p3*x5 + p7*x6  + p11*x7 + p15*x8;
640         pc[7] = m8 = p4*x5 + p8*x6  + p12*x7 + p16*x8;
641 
642         pc[8]  = m9  = p1*x9 + p5*x10  + p9*x11  + p13*x12;
643         pc[9]  = m10 = p2*x9 + p6*x10  + p10*x11 + p14*x12;
644         pc[10] = m11 = p3*x9 + p7*x10  + p11*x11 + p15*x12;
645         pc[11] = m12 = p4*x9 + p8*x10  + p12*x11 + p16*x12;
646 
647         pc[12] = m13 = p1*x13 + p5*x14  + p9*x15  + p13*x16;
648         pc[13] = m14 = p2*x13 + p6*x14  + p10*x15 + p14*x16;
649         pc[14] = m15 = p3*x13 + p7*x14  + p11*x15 + p15*x16;
650         pc[15] = m16 = p4*x13 + p8*x14  + p12*x15 + p16*x16;
651 
652         nz = bi[row+1] - diag_offset[row] - 1;
653         pv += 16;
654         for (j=0; j<nz; j++) {
655           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
656           x5   = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
657           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
658           x14  = pv[13]; x15 = pv[14]; x16 = pv[15];
659           x    = rtmp + 16*pj[j];
660           x[0] -= m1*x1 + m5*x2  + m9*x3  + m13*x4;
661           x[1] -= m2*x1 + m6*x2  + m10*x3 + m14*x4;
662           x[2] -= m3*x1 + m7*x2  + m11*x3 + m15*x4;
663           x[3] -= m4*x1 + m8*x2  + m12*x3 + m16*x4;
664 
665           x[4] -= m1*x5 + m5*x6  + m9*x7  + m13*x8;
666           x[5] -= m2*x5 + m6*x6  + m10*x7 + m14*x8;
667           x[6] -= m3*x5 + m7*x6  + m11*x7 + m15*x8;
668           x[7] -= m4*x5 + m8*x6  + m12*x7 + m16*x8;
669 
670           x[8]  -= m1*x9 + m5*x10 + m9*x11  + m13*x12;
671           x[9]  -= m2*x9 + m6*x10 + m10*x11 + m14*x12;
672           x[10] -= m3*x9 + m7*x10 + m11*x11 + m15*x12;
673           x[11] -= m4*x9 + m8*x10 + m12*x11 + m16*x12;
674 
675           x[12] -= m1*x13 + m5*x14  + m9*x15  + m13*x16;
676           x[13] -= m2*x13 + m6*x14  + m10*x15 + m14*x16;
677           x[14] -= m3*x13 + m7*x14  + m11*x15 + m15*x16;
678           x[15] -= m4*x13 + m8*x14  + m12*x15 + m16*x16;
679 
680           pv   += 16;
681         }
682         PLogFlops(128*nz+112);
683       }
684       row = *ajtmp++;
685     }
686     /* finished row so stick it into b->a */
687     pv = ba + 16*bi[i];
688     pj = bj + bi[i];
689     nz = bi[i+1] - bi[i];
690     for ( j=0; j<nz; j++ ) {
691       x      = rtmp+16*pj[j];
692       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
693       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
694       pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
695       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
696       pv   += 16;
697     }
698     /* invert diagonal block */
699     w = ba + 16*diag_offset[i];
700     ierr = Kernel_A_gets_inverse_A_4(w); CHKERRQ(ierr);
701   }
702 
703   PetscFree(rtmp);
704   C->factor    = FACTOR_LU;
705   C->assembled = PETSC_TRUE;
706   PLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */
707   PetscFunctionReturn(0);
708 }
709 
710 /* ------------------------------------------------------------*/
711 /*
712       Version for when blocks are 3 by 3
713 */
714 #undef __FUNC__
715 #define __FUNC__ "MatLUFactorNumeric_SeqBAIJ_3"
716 int MatLUFactorNumeric_SeqBAIJ_3(Mat A,Mat *B)
717 {
718   Mat             C = *B;
719   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data,*b = (Mat_SeqBAIJ *)C->data;
720   IS              isrow = b->row, isicol = b->icol;
721   int             *r,*ic, ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
722   int             *ajtmpold, *ajtmp, nz, row, *ai=a->i,*aj=a->j;
723   int             *diag_offset = b->diag,idx;
724   register int    *pj;
725   register Scalar *pv,*v,*rtmp,*pc,*w,*x;
726   Scalar          p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
727   Scalar          p5,p6,p7,p8,p9,x5,x6,x7,x8,x9;
728   Scalar          *ba = b->a,*aa = a->a;
729 
730   PetscFunctionBegin;
731   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
732   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
733   rtmp  = (Scalar *) PetscMalloc(9*(n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
734 
735   for ( i=0; i<n; i++ ) {
736     nz    = bi[i+1] - bi[i];
737     ajtmp = bj + bi[i];
738     for  ( j=0; j<nz; j++ ) {
739       x = rtmp + 9*ajtmp[j];
740       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
741     }
742     /* load in initial (unfactored row) */
743     idx      = r[i];
744     nz       = ai[idx+1] - ai[idx];
745     ajtmpold = aj + ai[idx];
746     v        = aa + 9*ai[idx];
747     for ( j=0; j<nz; j++ ) {
748       x    = rtmp + 9*ic[ajtmpold[j]];
749       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
750       x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
751       v    += 9;
752     }
753     row = *ajtmp++;
754     while (row < i) {
755       pc = rtmp + 9*row;
756       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
757       p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
758       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
759           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0) {
760         pv = ba + 9*diag_offset[row];
761         pj = bj + diag_offset[row] + 1;
762         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
763         x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
764         pc[0] = m1 = p1*x1 + p4*x2 + p7*x3;
765         pc[1] = m2 = p2*x1 + p5*x2 + p8*x3;
766         pc[2] = m3 = p3*x1 + p6*x2 + p9*x3;
767 
768         pc[3] = m4 = p1*x4 + p4*x5 + p7*x6;
769         pc[4] = m5 = p2*x4 + p5*x5 + p8*x6;
770         pc[5] = m6 = p3*x4 + p6*x5 + p9*x6;
771 
772         pc[6] = m7 = p1*x7 + p4*x8 + p7*x9;
773         pc[7] = m8 = p2*x7 + p5*x8 + p8*x9;
774         pc[8] = m9 = p3*x7 + p6*x8 + p9*x9;
775         nz = bi[row+1] - diag_offset[row] - 1;
776         pv += 9;
777         for (j=0; j<nz; j++) {
778           x1   = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
779           x5   = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
780           x    = rtmp + 9*pj[j];
781           x[0] -= m1*x1 + m4*x2 + m7*x3;
782           x[1] -= m2*x1 + m5*x2 + m8*x3;
783           x[2] -= m3*x1 + m6*x2 + m9*x3;
784 
785           x[3] -= m1*x4 + m4*x5 + m7*x6;
786           x[4] -= m2*x4 + m5*x5 + m8*x6;
787           x[5] -= m3*x4 + m6*x5 + m9*x6;
788 
789           x[6] -= m1*x7 + m4*x8 + m7*x9;
790           x[7] -= m2*x7 + m5*x8 + m8*x9;
791           x[8] -= m3*x7 + m6*x8 + m9*x9;
792           pv   += 9;
793         }
794         PLogFlops(54*nz+36);
795       }
796       row = *ajtmp++;
797     }
798     /* finished row so stick it into b->a */
799     pv = ba + 9*bi[i];
800     pj = bj + bi[i];
801     nz = bi[i+1] - bi[i];
802     for ( j=0; j<nz; j++ ) {
803       x     = rtmp + 9*pj[j];
804       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
805       pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
806       pv   += 9;
807     }
808     /* invert diagonal block */
809     w = ba + 9*diag_offset[i];
810     ierr = Kernel_A_gets_inverse_A_3(w); CHKERRQ(ierr);
811   }
812 
813   PetscFree(rtmp);
814   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
815   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
816   C->factor = FACTOR_LU;
817   C->assembled = PETSC_TRUE;
818   PLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */
819   PetscFunctionReturn(0);
820 }
821 
822 /* ------------------------------------------------------------*/
823 /*
824       Version for when blocks are 2 by 2
825 */
826 #undef __FUNC__
827 #define __FUNC__ "MatLUFactorNumeric_SeqBAIJ_2"
828 int MatLUFactorNumeric_SeqBAIJ_2(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, v_pivots[2];
835   int             *diag_offset=b->diag,bs = 2,idx,*ai=a->i,*aj=a->j;
836   register int    *pj;
837   register Scalar *pv,*v,*rtmp,m1,m2,m3,m4,*pc,*w,*x,x1,x2,x3,x4;
838   Scalar          p1,p2,p3,p4,v_work[2];
839   Scalar          *ba = b->a,*aa = a->a;
840 
841   PetscFunctionBegin;
842   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
843   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
844   rtmp  = (Scalar *) PetscMalloc(4*(n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
845 
846   for ( i=0; i<n; i++ ) {
847     nz    = bi[i+1] - bi[i];
848     ajtmp = bj + bi[i];
849     for  ( j=0; j<nz; j++ ) {
850       x = rtmp+4*ajtmp[j]; x[0] = x[1] = x[2] = x[3] = 0.0;
851     }
852     /* load in initial (unfactored row) */
853     idx      = r[i];
854     nz       = ai[idx+1] - ai[idx];
855     ajtmpold = aj + ai[idx];
856     v        = aa + 4*ai[idx];
857     for ( j=0; j<nz; j++ ) {
858       x    = rtmp+4*ic[ajtmpold[j]];
859       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
860       v    += 4;
861     }
862     row = *ajtmp++;
863     while (row < i) {
864       pc = rtmp + 4*row;
865       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
866       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0) {
867         pv = ba + 4*diag_offset[row];
868         pj = bj + diag_offset[row] + 1;
869         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
870         pc[0] = m1 = p1*x1 + p3*x2;
871         pc[1] = m2 = p2*x1 + p4*x2;
872         pc[2] = m3 = p1*x3 + p3*x4;
873         pc[3] = m4 = p2*x3 + p4*x4;
874         nz = bi[row+1] - diag_offset[row] - 1;
875         pv += 4;
876         for (j=0; j<nz; j++) {
877           x1   = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
878           x    = rtmp + 4*pj[j];
879           x[0] -= m1*x1 + m3*x2;
880           x[1] -= m2*x1 + m4*x2;
881           x[2] -= m1*x3 + m3*x4;
882           x[3] -= m2*x3 + m4*x4;
883           pv   += 4;
884         }
885         PLogFlops(16*nz+12);
886       }
887       row = *ajtmp++;
888     }
889     /* finished row so stick it into b->a */
890     pv = ba + 4*bi[i];
891     pj = bj + bi[i];
892     nz = bi[i+1] - bi[i];
893     for ( j=0; j<nz; j++ ) {
894       x     = rtmp+4*pj[j];
895       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
896       pv   += 4;
897     }
898     /* invert diagonal block */
899     w = ba + 4*diag_offset[i];
900     Kernel_A_gets_inverse_A(bs,w,v_pivots,v_work);
901   }
902 
903   PetscFree(rtmp);
904   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
905   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
906   C->factor = FACTOR_LU;
907   C->assembled = PETSC_TRUE;
908   PLogFlops(1.3333*8*b->mbs); /* from inverting diagonal blocks */
909   PetscFunctionReturn(0);
910 }
911 
912 /* ----------------------------------------------------------- */
913 /*
914      Version for when blocks are 1 by 1.
915 */
916 #undef __FUNC__
917 #define __FUNC__ "MatLUFactorNumeric_SeqBAIJ_1"
918 int MatLUFactorNumeric_SeqBAIJ_1(Mat A,Mat *B)
919 {
920   Mat             C = *B;
921   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data, *b = (Mat_SeqBAIJ *)C->data;
922   IS              isrow = b->row, isicol = b->icol;
923   int             *r,*ic, ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
924   int             *ajtmpold, *ajtmp, nz, row,*ai = a->i,*aj = a->j;
925   int             *diag_offset = b->diag,diag;
926   register int    *pj;
927   register Scalar *pv,*v,*rtmp,multiplier,*pc;
928   Scalar          *ba = b->a,*aa = a->a;
929 
930   PetscFunctionBegin;
931   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
932   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
933   rtmp  = (Scalar *) PetscMalloc((n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
934 
935   for ( i=0; i<n; i++ ) {
936     nz    = bi[i+1] - bi[i];
937     ajtmp = bj + bi[i];
938     for  ( j=0; j<nz; j++ ) rtmp[ajtmp[j]] = 0.0;
939 
940     /* load in initial (unfactored row) */
941     nz       = ai[r[i]+1] - ai[r[i]];
942     ajtmpold = aj + ai[r[i]];
943     v        = aa + ai[r[i]];
944     for ( j=0; j<nz; j++ ) rtmp[ic[ajtmpold[j]]] =  v[j];
945 
946     row = *ajtmp++;
947     while (row < i) {
948       pc = rtmp + row;
949       if (*pc != 0.0) {
950         pv         = ba + diag_offset[row];
951         pj         = bj + diag_offset[row] + 1;
952         multiplier = *pc * *pv++;
953         *pc        = multiplier;
954         nz         = bi[row+1] - diag_offset[row] - 1;
955         for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
956         PLogFlops(1+2*nz);
957       }
958       row = *ajtmp++;
959     }
960     /* finished row so stick it into b->a */
961     pv = ba + bi[i];
962     pj = bj + bi[i];
963     nz = bi[i+1] - bi[i];
964     for ( j=0; j<nz; j++ ) {pv[j] = rtmp[pj[j]];}
965     diag = diag_offset[i] - bi[i];
966     /* check pivot entry for current row */
967     if (pv[diag] == 0.0) {
968       SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,0,"Zero pivot");
969     }
970     pv[diag] = 1.0/pv[diag];
971   }
972 
973   PetscFree(rtmp);
974   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
975   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
976   C->factor    = FACTOR_LU;
977   C->assembled = PETSC_TRUE;
978   PLogFlops(b->n);
979   PetscFunctionReturn(0);
980 }
981 
982 /* ----------------------------------------------------------- */
983 #undef __FUNC__
984 #define __FUNC__ "MatLUFactor_SeqBAIJ"
985 int MatLUFactor_SeqBAIJ(Mat A,IS row,IS col,double f)
986 {
987   Mat_SeqBAIJ    *mat = (Mat_SeqBAIJ *) A->data;
988   int            ierr;
989   Mat            C;
990   PetscOps       *Abops;
991   struct _MatOps *Aops;
992 
993   PetscFunctionBegin;
994   ierr = MatLUFactorSymbolic(A,row,col,f,&C); CHKERRQ(ierr);
995   ierr = MatLUFactorNumeric(A,&C); CHKERRQ(ierr);
996 
997   /* free all the data structures from mat */
998   PetscFree(mat->a);
999   if (!mat->singlemalloc) {PetscFree(mat->i); PetscFree(mat->j);}
1000   if (mat->diag) PetscFree(mat->diag);
1001   if (mat->ilen) PetscFree(mat->ilen);
1002   if (mat->imax) PetscFree(mat->imax);
1003   if (mat->solve_work) PetscFree(mat->solve_work);
1004   if (mat->mult_work) PetscFree(mat->mult_work);
1005   PetscFree(mat);
1006 
1007   /*
1008        This is horrible, horrible code. We need to keep the
1009     A pointers for the bops and ops but copy everything
1010     else from C.
1011   */
1012   Abops    = A->bops;
1013   Aops     = A->ops;
1014   PetscMemcpy(A,C,sizeof(struct _p_Mat));
1015   A->bops  = Abops;
1016   A->ops   = Aops;
1017   A->qlist = 0;
1018 
1019   PetscHeaderDestroy(C);
1020   PetscFunctionReturn(0);
1021 }
1022