xref: /petsc/src/mat/impls/baij/seq/baijfact.c (revision 05bf559cbb56c1096253c7feaa733587ece3e0bd)
1 
2 #ifndef lint
3 static char vcid[] = "$Id: baijfact.c,v 1.41 1997/03/26 01:36:13 bsmith Exp balay $";
4 #endif
5 /*
6     Factorization code for BAIJ format.
7 */
8 
9 #include "src/mat/impls/baij/seq/baij.h"
10 #include "src/vec/vecimpl.h"
11 #include "src/inline/ilu.h"
12 
13 
14 /*
15     The symbolic factorization code is identical to that for AIJ format,
16   except for very small changes since this is now a SeqBAIJ datastructure.
17   NOT good code reuse.
18 */
19 #undef __FUNC__
20 #define __FUNC__ "MatLUFactorSymbolic_SeqBAIJ"
21 int MatLUFactorSymbolic_SeqBAIJ(Mat A,IS isrow,IS iscol,double f,Mat *B)
22 {
23   Mat_SeqBAIJ *a = (Mat_SeqBAIJ *) A->data, *b;
24   IS          isicol;
25   int         *r,*ic, ierr, i, n = a->mbs, *ai = a->i, *aj = a->j;
26   int         *ainew,*ajnew, jmax,*fill, *ajtmp, nz, bs = a->bs, bs2=a->bs2;
27   int         *idnew, idx, row,m,fm, nnz, nzi,realloc = 0,nzbd,*im;
28 
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       /* allocate a longer ajnew */
90       int maxadd;
91       maxadd = (int) ((f*(ai[n]+1)*(n-i+5))/n);
92       if (maxadd < nnz) maxadd = (n-i)*(nnz+1);
93       jmax += maxadd;
94       ajtmp = (int *) PetscMalloc( jmax*sizeof(int) );CHKPTRQ(ajtmp);
95       PetscMemcpy(ajtmp,ajnew,ainew[i]*sizeof(int));
96       PetscFree(ajnew);
97       ajnew = ajtmp;
98       realloc++; /* count how many times we realloc */
99     }
100     ajtmp = ajnew + ainew[i];
101     fm    = fill[n];
102     nzi   = 0;
103     im[i] = nnz;
104     while (nnz--) {
105       if (fm < i) nzi++;
106       *ajtmp++ = fm;
107       fm       = fill[fm];
108     }
109     idnew[i] = ainew[i] + nzi;
110   }
111 
112   if (ai[i] != 0) {
113   PLogInfo(A,
114     "Info:MatLUFactorSymbolic_SeqBAIJ:Reallocs %d Fill ratio:given %g needed %g\n",
115                              realloc,f,((double)ainew[n])/((double)ai[i]));
116   } else {
117      PLogInfo(A,"Info:MatLUFactorSymbolic_SeqBAIJ:Empty matrix.\n");
118   }
119 
120 
121 
122   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
123   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
124 
125   PetscFree(fill);
126 
127   /* put together the new matrix */
128   ierr = MatCreateSeqBAIJ(A->comm,bs,bs*n,bs*n,0,PETSC_NULL,B); CHKERRQ(ierr);
129   PLogObjectParent(*B,isicol);
130   ierr = ISDestroy(isicol); CHKERRQ(ierr);
131   b = (Mat_SeqBAIJ *) (*B)->data;
132   PetscFree(b->imax);
133   b->singlemalloc = 0;
134   /* the next line frees the default space generated by the Create() */
135   PetscFree(b->a); PetscFree(b->ilen);
136   b->a          = (Scalar *) PetscMalloc((ainew[n]+1)*sizeof(Scalar)*bs2);CHKPTRQ(b->a);
137   b->j          = ajnew;
138   b->i          = ainew;
139   b->diag       = idnew;
140   b->ilen       = 0;
141   b->imax       = 0;
142   b->row        = isrow;
143   b->col        = iscol;
144   b->solve_work = (Scalar *) PetscMalloc( (bs*n+bs)*sizeof(Scalar));
145   CHKPTRQ(b->solve_work);
146   /* In b structure:  Free imax, ilen, old a, old j.
147      Allocate idnew, solve_work, new a, new j */
148   PLogObjectMemory(*B,(ainew[n]-n)*(sizeof(int)+sizeof(Scalar)));
149   b->maxnz = b->nz = ainew[n];
150 
151   (*B)->info.factor_mallocs    = realloc;
152   (*B)->info.fill_ratio_given  = f;
153   (*B)->info.fill_ratio_needed = ((double)ainew[n])/((double)ai[i]);
154 
155   return 0;
156 }
157 
158 /* ----------------------------------------------------------- */
159 #undef __FUNC__
160 #define __FUNC__ "MatLUFactorNumeric_SeqBAIJ_N"
161 int MatLUFactorNumeric_SeqBAIJ_N(Mat A,Mat *B)
162 {
163   Mat             C = *B;
164   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data,*b = (Mat_SeqBAIJ *)C->data;
165   IS              iscol = b->col, isrow = b->row, isicol;
166   int             *r,*ic, ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
167   int             *ajtmpold, *ajtmp, nz, row, bslog,*ai=a->i,*aj=a->j,k,flg;
168   int             *diag_offset=b->diag,diag,bs=a->bs,bs2 = a->bs2,*v_pivots;
169   Scalar          *ba = b->a,*aa = a->a;
170   register Scalar *pv,*v,*rtmp,*multiplier,*v_work,*pc,*w;
171   register int    *pj;
172 
173   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
174   PLogObjectParent(*B,isicol);
175   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
176   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
177   rtmp  = (Scalar *) PetscMalloc(bs2*(n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
178   PetscMemzero(rtmp,bs2*(n+1)*sizeof(Scalar));
179   /* generate work space needed by dense LU factorization */
180   v_work     = (Scalar *) PetscMalloc(bs*sizeof(int) + (bs+bs2)*sizeof(Scalar));
181                CHKPTRQ(v_work);
182   multiplier = v_work + bs;
183   v_pivots   = (int *) (multiplier + bs2);
184 
185   /* flops in while loop */
186   bslog = 2*bs*bs2;
187 
188   for ( i=0; i<n; i++ ) {
189     nz    = bi[i+1] - bi[i];
190     ajtmp = bj + bi[i];
191     for  ( j=0; j<nz; j++ ) {
192       PetscMemzero(rtmp+bs2*ajtmp[j],bs2*sizeof(Scalar));
193     }
194     /* load in initial (unfactored row) */
195     nz       = ai[r[i]+1] - ai[r[i]];
196     ajtmpold = aj + ai[r[i]];
197     v        = aa + bs2*ai[r[i]];
198     for ( j=0; j<nz; j++ ) {
199       PetscMemcpy(rtmp+bs2*ic[ajtmpold[j]],v+bs2*j,bs2*sizeof(Scalar));
200     }
201     row = *ajtmp++;
202     while (row < i) {
203       pc = rtmp + bs2*row;
204 /*      if (*pc) { */
205       for ( flg=0,k=0; k<bs2; k++ ) { if (pc[k]!=0.0) { flg =1; break; }}
206       if (flg) {
207         pv = ba + bs2*diag_offset[row];
208         pj = bj + diag_offset[row] + 1;
209         Kernel_A_gets_A_times_B(bs,pc,pv,multiplier);
210         nz = bi[row+1] - diag_offset[row] - 1;
211         pv += bs2;
212         for (j=0; j<nz; j++) {
213           Kernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j);
214         }
215         PLogFlops(bslog*(nz+1)-bs);
216       }
217         row = *ajtmp++;
218     }
219     /* finished row so stick it into b->a */
220     pv = ba + bs2*bi[i];
221     pj = bj + bi[i];
222     nz = bi[i+1] - bi[i];
223     for ( j=0; j<nz; j++ ) {
224       PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(Scalar));
225     }
226     diag = diag_offset[i] - bi[i];
227     /* invert diagonal block */
228     w = pv + bs2*diag;
229     Kernel_A_gets_inverse_A(bs,w,v_pivots,v_work);
230   }
231 
232   PetscFree(rtmp); PetscFree(v_work);
233   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
234   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
235   ierr = ISDestroy(isicol); CHKERRQ(ierr);
236   C->factor = FACTOR_LU;
237   C->assembled = PETSC_TRUE;
238   PLogFlops(1.3333*bs*bs2*b->mbs); /* from inverting diagonal blocks */
239   return 0;
240 }
241 /* ------------------------------------------------------------*/
242 /*
243       Version for when blocks are 5 by 5
244 */
245 #undef __FUNC__
246 #define __FUNC__ "MatLUFactorNumeric_SeqBAIJ_5"
247 int MatLUFactorNumeric_SeqBAIJ_5(Mat A,Mat *B)
248 {
249   Mat             C = *B;
250   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data,*b = (Mat_SeqBAIJ *)C->data;
251   IS              iscol = b->col, isrow = b->row, isicol;
252   int             *r,*ic, ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
253   int             *ajtmpold, *ajtmp, nz, row, v_pivots[5];
254   int             *diag_offset = b->diag,bs = 5,idx,*ai=a->i,*aj=a->j;
255   register Scalar *pv,*v,*rtmp,*pc,*w,*x;
256   Scalar          p1,p2,p3,p4,v_work[5],m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
257   Scalar          p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
258   Scalar          x17,x18,x19,x20,x21,x22,x23,x24,x25,p10,p11,p12,p13,p14;
259   Scalar          p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,m10,m11,m12;
260   Scalar          m13,m14,m15,m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
261   Scalar          *ba = b->a,*aa = a->a;
262   register int    *pj;
263 
264   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
265   PLogObjectParent(*B,isicol);
266   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
267   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
268   rtmp  = (Scalar *) PetscMalloc(25*(n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
269 
270   for ( i=0; i<n; i++ ) {
271     nz    = bi[i+1] - bi[i];
272     ajtmp = bj + bi[i];
273     for  ( j=0; j<nz; j++ ) {
274       x = rtmp+25*ajtmp[j];
275       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
276       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
277       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0;
278     }
279     /* load in initial (unfactored row) */
280     idx      = r[i];
281     nz       = ai[idx+1] - ai[idx];
282     ajtmpold = aj + ai[idx];
283     v        = aa + 25*ai[idx];
284     for ( j=0; j<nz; j++ ) {
285       x    = rtmp+25*ic[ajtmpold[j]];
286       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
287       x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
288       x[9] = v[9]; x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
289       x[14] = v[14]; x[15] = v[15]; x[16] = v[16]; x[17] = v[17];
290       x[18] = v[18]; x[19] = v[19]; x[20] = v[20]; x[21] = v[21];
291       x[22] = v[22]; x[23] = v[23]; x[24] = v[24];
292       v    += 25;
293     }
294     row = *ajtmp++;
295     while (row < i) {
296       pc = rtmp + 25*row;
297       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
298       p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
299       p10 = pc[9]; p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
300       p15 = pc[14]; p16 = pc[15]; p17 = pc[16]; p18 = pc[17]; p19 = pc[18];
301       p20 = pc[19]; p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
302       p25 = pc[24];
303       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
304           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
305           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
306           || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 ||
307           p20 != 0.0 || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 ||
308           p24 != 0.0 || p25 != 0.0) {
309         pv = ba + 25*diag_offset[row];
310         pj = bj + diag_offset[row] + 1;
311         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
312         x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
313         x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
314         x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17];
315         x19 = pv[18]; x20 = pv[19]; x21 = pv[20]; x22 = pv[21];
316         x23 = pv[22]; x24 = pv[23]; x25 = pv[24];
317         pc[0] = m1 = p1*x1 + p6*x2  + p11*x3 + p16*x4 + p21*x5;
318         pc[1] = m2 = p2*x1 + p7*x2  + p12*x3 + p17*x4 + p22*x5;
319         pc[2] = m3 = p3*x1 + p8*x2  + p13*x3 + p18*x4 + p23*x5;
320         pc[3] = m4 = p4*x1 + p9*x2  + p14*x3 + p19*x4 + p24*x5;
321         pc[4] = m5 = p5*x1 + p10*x2 + p15*x3 + p20*x4 + p25*x5;
322 
323         pc[5] = m6 = p1*x6 + p6*x7  + p11*x8 + p16*x9 + p21*x10;
324         pc[6] = m7 = p2*x6 + p7*x7  + p12*x8 + p17*x9 + p22*x10;
325         pc[7] = m8 = p3*x6 + p8*x7  + p13*x8 + p18*x9 + p23*x10;
326         pc[8] = m9 = p4*x6 + p9*x7  + p14*x8 + p19*x9 + p24*x10;
327         pc[9] = m10 = p5*x6 + p10*x7 + p15*x8 + p20*x9 + p25*x10;
328 
329         pc[10] = m11 = p1*x11 + p6*x12  + p11*x13 + p16*x14 + p21*x15;
330         pc[11] = m12 = p2*x11 + p7*x12  + p12*x13 + p17*x14 + p22*x15;
331         pc[12] = m13 = p3*x11 + p8*x12  + p13*x13 + p18*x14 + p23*x15;
332         pc[13] = m14 = p4*x11 + p9*x12  + p14*x13 + p19*x14 + p24*x15;
333         pc[14] = m15 = p5*x11 + p10*x12 + p15*x13 + p20*x14 + p25*x15;
334 
335         pc[15] = m16 = p1*x16 + p6*x17  + p11*x18 + p16*x19 + p21*x20;
336         pc[16] = m17 = p2*x16 + p7*x17  + p12*x18 + p17*x19 + p22*x20;
337         pc[17] = m18 = p3*x16 + p8*x17  + p13*x18 + p18*x19 + p23*x20;
338         pc[18] = m19 = p4*x16 + p9*x17  + p14*x18 + p19*x19 + p24*x20;
339         pc[19] = m20 = p5*x16 + p10*x17 + p15*x18 + p20*x19 + p25*x20;
340 
341         pc[20] = m21 = p1*x21 + p6*x22  + p11*x23 + p16*x24 + p21*x25;
342         pc[21] = m22 = p2*x21 + p7*x22  + p12*x23 + p17*x24 + p22*x25;
343         pc[22] = m23 = p3*x21 + p8*x22  + p13*x23 + p18*x24 + p23*x25;
344         pc[23] = m24 = p4*x21 + p9*x22  + p14*x23 + p19*x24 + p24*x25;
345         pc[24] = m25 = p5*x21 + p10*x22 + p15*x23 + p20*x24 + p25*x25;
346 
347         nz = bi[row+1] - diag_offset[row] - 1;
348         pv += 25;
349         for (j=0; j<nz; j++) {
350           x1   = pv[0];  x2 = pv[1];   x3  = pv[2];  x4  = pv[3];
351           x5   = pv[4];  x6 = pv[5];   x7  = pv[6];  x8  = pv[7]; x9 = pv[8];
352           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
353           x14  = pv[13]; x15 = pv[14]; x16 = pv[15]; x17 = pv[16];
354           x18  = pv[17]; x19 = pv[18]; x20 = pv[19]; x21 = pv[20];
355           x22  = pv[21]; x23 = pv[22]; x24 = pv[23]; x25 = pv[24];
356           x    = rtmp + 25*pj[j];
357           x[0] -= m1*x1 + m6*x2  + m11*x3 + m16*x4 + m21*x5;
358           x[1] -= m2*x1 + m7*x2  + m12*x3 + m17*x4 + m22*x5;
359           x[2] -= m3*x1 + m8*x2  + m13*x3 + m18*x4 + m23*x5;
360           x[3] -= m4*x1 + m9*x2  + m14*x3 + m19*x4 + m24*x5;
361           x[4] -= m5*x1 + m10*x2 + m15*x3 + m20*x4 + m25*x5;
362 
363           x[5] -= m1*x6 + m6*x7  + m11*x8 + m16*x9 + m21*x10;
364           x[6] -= m2*x6 + m7*x7  + m12*x8 + m17*x9 + m22*x10;
365           x[7] -= m3*x6 + m8*x7  + m13*x8 + m18*x9 + m23*x10;
366           x[8] -= m4*x6 + m9*x7  + m14*x8 + m19*x9 + m24*x10;
367           x[9] -= m5*x6 + m10*x7 + m15*x8 + m20*x9 + m25*x10;
368 
369           x[10] -= m1*x11 + m6*x12  + m11*x13 + m16*x14 + m21*x15;
370           x[11] -= m2*x11 + m7*x12  + m12*x13 + m17*x14 + m22*x15;
371           x[12] -= m3*x11 + m8*x12  + m13*x13 + m18*x14 + m23*x15;
372           x[13] -= m4*x11 + m9*x12  + m14*x13 + m19*x14 + m24*x15;
373           x[14] -= m5*x11 + m10*x12 + m15*x13 + m20*x14 + m25*x15;
374 
375           x[15] -= m1*x16 + m6*x17  + m11*x18 + m16*x19 + m21*x20;
376           x[16] -= m2*x16 + m7*x17  + m12*x18 + m17*x19 + m22*x20;
377           x[17] -= m3*x16 + m8*x17  + m13*x18 + m18*x19 + m23*x20;
378           x[18] -= m4*x16 + m9*x17  + m14*x18 + m19*x19 + m24*x20;
379           x[19] -= m5*x16 + m10*x17 + m15*x18 + m20*x19 + m25*x20;
380 
381           x[20] -= m1*x21 + m6*x22  + m11*x23 + m16*x24 + m21*x25;
382           x[21] -= m2*x21 + m7*x22  + m12*x23 + m17*x24 + m22*x25;
383           x[22] -= m3*x21 + m8*x22  + m13*x23 + m18*x24 + m23*x25;
384           x[23] -= m4*x21 + m9*x22  + m14*x23 + m19*x24 + m24*x25;
385           x[24] -= m5*x21 + m10*x22 + m15*x23 + m20*x24 + m25*x25;
386 
387           pv   += 25;
388         }
389         PLogFlops(250*nz+225);
390       }
391       row = *ajtmp++;
392     }
393     /* finished row so stick it into b->a */
394     pv = ba + 25*bi[i];
395     pj = bj + bi[i];
396     nz = bi[i+1] - bi[i];
397     for ( j=0; j<nz; j++ ) {
398       x     = rtmp+25*pj[j];
399       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
400       pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
401       pv[9] = x[9]; pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
402       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; pv[16] = x[16];
403       pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19]; pv[20] = x[20];
404       pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23]; pv[24] = x[24];
405       pv   += 25;
406     }
407     /* invert diagonal block */
408     w = ba + 25*diag_offset[i];
409     Kernel_A_gets_inverse_A(bs,w,v_pivots,v_work);
410   }
411 
412   PetscFree(rtmp);
413   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
414   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
415   ierr = ISDestroy(isicol); CHKERRQ(ierr);
416   C->factor = FACTOR_LU;
417   C->assembled = PETSC_TRUE;
418   PLogFlops(1.3333*125*b->mbs); /* from inverting diagonal blocks */
419   return 0;
420 }
421 
422 /* ------------------------------------------------------------*/
423 /*
424       Version for when blocks are 4 by 4
425 */
426 #undef __FUNC__
427 #define __FUNC__ "MatLUFactorNumeric_SeqBAIJ_4"
428 int MatLUFactorNumeric_SeqBAIJ_4(Mat A,Mat *B)
429 {
430   Mat             C = *B;
431   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data,*b = (Mat_SeqBAIJ *)C->data;
432   IS              iscol = b->col, isrow = b->row, isicol;
433   int             *r,*ic, ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
434   int             *ajtmpold, *ajtmp, nz, row, v_pivots[4];
435   int             *diag_offset = b->diag,bs = 4,idx,*ai=a->i,*aj=a->j;
436   register Scalar *pv,*v,*rtmp,*pc,*w,*x;
437   Scalar          p1,p2,p3,p4,v_work[4],m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
438   Scalar          p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
439   Scalar          p10,p11,p12,p13,p14,p15,p16,m10,m11,m12;
440   Scalar          m13,m14,m15,m16;
441   Scalar          *ba = b->a,*aa = a->a;
442   register int    *pj;
443 
444   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
445   PLogObjectParent(*B,isicol);
446   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
447   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
448   rtmp  = (Scalar *) PetscMalloc(16*(n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
449 
450   for ( i=0; i<n; i++ ) {
451     nz    = bi[i+1] - bi[i];
452     ajtmp = bj + bi[i];
453     for  ( j=0; j<nz; j++ ) {
454       x = rtmp+16*ajtmp[j];
455       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
456       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
457     }
458     /* load in initial (unfactored row) */
459     idx      = r[i];
460     nz       = ai[idx+1] - ai[idx];
461     ajtmpold = aj + ai[idx];
462     v        = aa + 16*ai[idx];
463     for ( j=0; j<nz; j++ ) {
464       x    = rtmp+16*ic[ajtmpold[j]];
465       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
466       x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
467       x[9] = v[9]; x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
468       x[14] = v[14]; x[15] = v[15];
469       v    += 16;
470     }
471     row = *ajtmp++;
472     while (row < i) {
473       pc = rtmp + 16*row;
474       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
475       p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
476       p10 = pc[9]; p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
477       p15 = pc[14]; p16 = pc[15];
478       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
479           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
480           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
481           || p16 != 0.0) {
482         pv = ba + 16*diag_offset[row];
483         pj = bj + diag_offset[row] + 1;
484         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
485         x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
486         x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
487         x15 = pv[14]; x16 = pv[15];
488         pc[0] = m1 = p1*x1 + p5*x2  + p9*x3  + p13*x4;
489         pc[1] = m2 = p2*x1 + p6*x2  + p10*x3 + p14*x4;
490         pc[2] = m3 = p3*x1 + p7*x2  + p11*x3 + p15*x4;
491         pc[3] = m4 = p4*x1 + p8*x2  + p12*x3 + p16*x4;
492 
493         pc[4] = m5 = p1*x5 + p5*x6  + p9*x7  + p13*x8;
494         pc[5] = m6 = p2*x5 + p6*x6  + p10*x7 + p14*x8;
495         pc[6] = m7 = p3*x5 + p7*x6  + p11*x7 + p15*x8;
496         pc[7] = m8 = p4*x5 + p8*x6  + p12*x7 + p16*x8;
497 
498         pc[8]  = m9  = p1*x9 + p5*x10  + p9*x11  + p13*x12;
499         pc[9]  = m10 = p2*x9 + p6*x10  + p10*x11 + p14*x12;
500         pc[10] = m11 = p3*x9 + p7*x10  + p11*x11 + p15*x12;
501         pc[11] = m12 = p4*x9 + p8*x10  + p12*x11 + p16*x12;
502 
503         pc[12] = m13 = p1*x13 + p5*x14  + p9*x15  + p13*x16;
504         pc[13] = m14 = p2*x13 + p6*x14  + p10*x15 + p14*x16;
505         pc[14] = m15 = p3*x13 + p7*x14  + p11*x15 + p15*x16;
506         pc[15] = m16 = p4*x13 + p8*x14  + p12*x15 + p16*x16;
507 
508         nz = bi[row+1] - diag_offset[row] - 1;
509         pv += 16;
510         for (j=0; j<nz; j++) {
511           x1   = pv[0];  x2 = pv[1];   x3  = pv[2];  x4  = pv[3];
512           x5   = pv[4];  x6 = pv[5];   x7  = pv[6];  x8  = pv[7]; x9 = pv[8];
513           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
514           x14  = pv[13]; x15 = pv[14]; x16 = pv[15];
515           x    = rtmp + 16*pj[j];
516           x[0] -= m1*x1 + m5*x2  + m9*x3 + m13*x4;
517           x[1] -= m2*x1 + m6*x2  + m10*x3 + m14*x4;
518           x[2] -= m3*x1 + m7*x2  + m11*x3 + m15*x4;
519           x[3] -= m4*x1 + m8*x2  + m12*x3 + m16*x4;
520 
521           x[4] -= m1*x5 + m5*x6  + m9*x7  + m13*x8;
522           x[5] -= m2*x5 + m6*x6  + m10*x7 + m14*x8;
523           x[6] -= m3*x5 + m7*x6  + m11*x7 + m15*x8;
524           x[7] -= m4*x5 + m8*x6  + m12*x7 + m16*x8;
525 
526           x[8] -= m1*x9  + m5*x10  + m9*x11 + m13*x12;
527           x[9] -= m2*x9  + m6*x10  + m10*x11 + m14*x12;
528           x[10] -= m3*x9 + m7*x10  + m11*x11 + m15*x12;
529           x[11] -= m4*x9 + m8*x10  + m12*x11 + m16*x12;
530 
531           x[12] -= m1*x13 + m5*x14  + m9*x15 + m13*x16;
532           x[13] -= m2*x13 + m6*x14  + m10*x15 + m14*x16;
533           x[14] -= m3*x13 + m7*x14  + m11*x15 + m15*x16;
534           x[15] -= m4*x13 + m8*x14  + m12*x15 + m16*x16;
535 
536           pv   += 16;
537         }
538         PLogFlops(128*nz+112);
539       }
540       row = *ajtmp++;
541     }
542     /* finished row so stick it into b->a */
543     pv = ba + 16*bi[i];
544     pj = bj + bi[i];
545     nz = bi[i+1] - bi[i];
546     for ( j=0; j<nz; j++ ) {
547       x     = rtmp+16*pj[j];
548       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
549       pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
550       pv[9] = x[9]; pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
551       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
552       pv   += 16;
553     }
554     /* invert diagonal block */
555     w = ba + 16*diag_offset[i];
556     Kernel_A_gets_inverse_A(bs,w,v_pivots,v_work);
557   }
558 
559   PetscFree(rtmp);
560   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
561   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
562   ierr = ISDestroy(isicol); CHKERRQ(ierr);
563   C->factor = FACTOR_LU;
564   C->assembled = PETSC_TRUE;
565   PLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */
566   return 0;
567 }
568 /* ------------------------------------------------------------*/
569 /*
570       Version for when blocks are 3 by 3
571 */
572 #undef __FUNC__
573 #define __FUNC__ "MatLUFactorNumeric_SeqBAIJ_3"
574 int MatLUFactorNumeric_SeqBAIJ_3(Mat A,Mat *B)
575 {
576   Mat             C = *B;
577   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data,*b = (Mat_SeqBAIJ *)C->data;
578   IS              iscol = b->col, isrow = b->row, isicol;
579   int             *r,*ic, ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
580   int             *ajtmpold, *ajtmp, nz, row, *ai=a->i,*aj=a->j;
581   int             *diag_offset = b->diag,idx;
582   register Scalar *pv,*v,*rtmp,*pc,*w,*x;
583   Scalar          p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
584   Scalar          p5,p6,p7,p8,p9,x5,x6,x7,x8,x9;
585   Scalar          *ba = b->a,*aa = a->a;
586   register int    *pj;
587 
588   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
589   PLogObjectParent(*B,isicol);
590   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
591   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
592   rtmp  = (Scalar *) PetscMalloc(9*(n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
593 
594   for ( i=0; i<n; i++ ) {
595     nz    = bi[i+1] - bi[i];
596     ajtmp = bj + bi[i];
597     for  ( j=0; j<nz; j++ ) {
598       x = rtmp + 9*ajtmp[j];
599       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
600     }
601     /* load in initial (unfactored row) */
602     idx      = r[i];
603     nz       = ai[idx+1] - ai[idx];
604     ajtmpold = aj + ai[idx];
605     v        = aa + 9*ai[idx];
606     for ( j=0; j<nz; j++ ) {
607       x    = rtmp + 9*ic[ajtmpold[j]];
608       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
609       x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
610       v    += 9;
611     }
612     row = *ajtmp++;
613     while (row < i) {
614       pc = rtmp + 9*row;
615       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
616       p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
617       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
618           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0) {
619         pv = ba + 9*diag_offset[row];
620         pj = bj + diag_offset[row] + 1;
621         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
622         x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
623         pc[0] = m1 = p1*x1 + p4*x2 + p7*x3;
624         pc[1] = m2 = p2*x1 + p5*x2 + p8*x3;
625         pc[2] = m3 = p3*x1 + p6*x2 + p9*x3;
626 
627         pc[3] = m4 = p1*x4 + p4*x5 + p7*x6;
628         pc[4] = m5 = p2*x4 + p5*x5 + p8*x6;
629         pc[5] = m6 = p3*x4 + p6*x5 + p9*x6;
630 
631         pc[6] = m7 = p1*x7 + p4*x8 + p7*x9;
632         pc[7] = m8 = p2*x7 + p5*x8 + p8*x9;
633         pc[8] = m9 = p3*x7 + p6*x8 + p9*x9;
634         nz = bi[row+1] - diag_offset[row] - 1;
635         pv += 9;
636         for (j=0; j<nz; j++) {
637           x1   = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
638           x5   = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
639           x    = rtmp + 9*pj[j];
640           x[0] -= m1*x1 + m4*x2 + m7*x3;
641           x[1] -= m2*x1 + m5*x2 + m8*x3;
642           x[2] -= m3*x1 + m6*x2 + m9*x3;
643 
644           x[3] -= m1*x4 + m4*x5 + m7*x6;
645           x[4] -= m2*x4 + m5*x5 + m8*x6;
646           x[5] -= m3*x4 + m6*x5 + m9*x6;
647 
648           x[6] -= m1*x7 + m4*x8 + m7*x9;
649           x[7] -= m2*x7 + m5*x8 + m8*x9;
650           x[8] -= m3*x7 + m6*x8 + m9*x9;
651           pv   += 9;
652         }
653         PLogFlops(54*nz+36);
654       }
655       row = *ajtmp++;
656     }
657     /* finished row so stick it into b->a */
658     pv = ba + 9*bi[i];
659     pj = bj + bi[i];
660     nz = bi[i+1] - bi[i];
661     for ( j=0; j<nz; j++ ) {
662       x     = rtmp + 9*pj[j];
663       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
664       pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
665       pv   += 9;
666     }
667     /* invert diagonal block */
668     w = ba + 9*diag_offset[i];
669     ierr = Kernel_A_gets_inverse_A_3(w); CHKERRQ(ierr);
670   }
671 
672   PetscFree(rtmp);
673   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
674   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
675   ierr = ISDestroy(isicol); CHKERRQ(ierr);
676   C->factor = FACTOR_LU;
677   C->assembled = PETSC_TRUE;
678   PLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */
679   return 0;
680 }
681 
682 /* ------------------------------------------------------------*/
683 /*
684       Version for when blocks are 2 by 2
685 */
686 #undef __FUNC__
687 #define __FUNC__ "MatLUFactorNumeric_SeqBAIJ_2"
688 int MatLUFactorNumeric_SeqBAIJ_2(Mat A,Mat *B)
689 {
690   Mat             C = *B;
691   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data,*b = (Mat_SeqBAIJ *)C->data;
692   IS              iscol = b->col, isrow = b->row, isicol;
693   int             *r,*ic, ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
694   int             *ajtmpold, *ajtmp, nz, row, v_pivots[2];
695   int             *diag_offset=b->diag,bs = 2,idx,*ai=a->i,*aj=a->j;
696   register Scalar *pv,*v,*rtmp,m1,m2,m3,m4,*pc,*w,*x,x1,x2,x3,x4;
697   Scalar          p1,p2,p3,p4,v_work[2];
698   Scalar          *ba = b->a,*aa = a->a;
699   register int    *pj;
700 
701   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
702   PLogObjectParent(*B,isicol);
703   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
704   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
705   rtmp  = (Scalar *) PetscMalloc(4*(n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
706 
707   for ( i=0; i<n; i++ ) {
708     nz    = bi[i+1] - bi[i];
709     ajtmp = bj + bi[i];
710     for  ( j=0; j<nz; j++ ) {
711       x = rtmp+4*ajtmp[j]; x[0] = x[1] = x[2] = x[3] = 0.0;
712     }
713     /* load in initial (unfactored row) */
714     idx      = r[i];
715     nz       = ai[idx+1] - ai[idx];
716     ajtmpold = aj + ai[idx];
717     v        = aa + 4*ai[idx];
718     for ( j=0; j<nz; j++ ) {
719       x    = rtmp+4*ic[ajtmpold[j]];
720       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
721       v    += 4;
722     }
723     row = *ajtmp++;
724     while (row < i) {
725       pc = rtmp + 4*row;
726       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
727       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0) {
728         pv = ba + 4*diag_offset[row];
729         pj = bj + diag_offset[row] + 1;
730         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
731         pc[0] = m1 = p1*x1 + p3*x2;
732         pc[1] = m2 = p2*x1 + p4*x2;
733         pc[2] = m3 = p1*x3 + p3*x4;
734         pc[3] = m4 = p2*x3 + p4*x4;
735         nz = bi[row+1] - diag_offset[row] - 1;
736         pv += 4;
737         for (j=0; j<nz; j++) {
738           x1   = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
739           x    = rtmp + 4*pj[j];
740           x[0] -= m1*x1 + m3*x2;
741           x[1] -= m2*x1 + m4*x2;
742           x[2] -= m1*x3 + m3*x4;
743           x[3] -= m2*x3 + m4*x4;
744           pv   += 4;
745         }
746         PLogFlops(16*nz+12);
747       }
748       row = *ajtmp++;
749     }
750     /* finished row so stick it into b->a */
751     pv = ba + 4*bi[i];
752     pj = bj + bi[i];
753     nz = bi[i+1] - bi[i];
754     for ( j=0; j<nz; j++ ) {
755       x     = rtmp+4*pj[j];
756       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
757       pv   += 4;
758     }
759     /* invert diagonal block */
760     w = ba + 4*diag_offset[i];
761     Kernel_A_gets_inverse_A(bs,w,v_pivots,v_work);
762   }
763 
764   PetscFree(rtmp);
765   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
766   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
767   ierr = ISDestroy(isicol); CHKERRQ(ierr);
768   C->factor = FACTOR_LU;
769   C->assembled = PETSC_TRUE;
770   PLogFlops(1.3333*8*b->mbs); /* from inverting diagonal blocks */
771   return 0;
772 }
773 
774 /* ----------------------------------------------------------- */
775 /*
776      Version for when blocks are 1 by 1.
777 */
778 #undef __FUNC__
779 #define __FUNC__ "MatLUFactorNumeric_SeqBAIJ_1"
780 int MatLUFactorNumeric_SeqBAIJ_1(Mat A,Mat *B)
781 {
782   Mat             C = *B;
783   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data, *b = (Mat_SeqBAIJ *)C->data;
784   IS              iscol = b->col, isrow = b->row, isicol;
785   int             *r,*ic, ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
786   int             *ajtmpold, *ajtmp, nz, row,*ai = a->i,*aj = a->j;
787   int             *diag_offset = b->diag,diag;
788   register Scalar *pv,*v,*rtmp,multiplier,*pc;
789   Scalar          *ba = b->a,*aa = a->a;
790   register int    *pj;
791 
792   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
793   PLogObjectParent(*B,isicol);
794   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
795   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
796   rtmp  = (Scalar *) PetscMalloc((n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
797 
798   for ( i=0; i<n; i++ ) {
799     nz    = bi[i+1] - bi[i];
800     ajtmp = bj + bi[i];
801     for  ( j=0; j<nz; j++ ) rtmp[ajtmp[j]] = 0.0;
802 
803     /* load in initial (unfactored row) */
804     nz       = ai[r[i]+1] - ai[r[i]];
805     ajtmpold = aj + ai[r[i]];
806     v        = aa + ai[r[i]];
807     for ( j=0; j<nz; j++ ) rtmp[ic[ajtmpold[j]]] =  v[j];
808 
809     row = *ajtmp++;
810     while (row < i) {
811       pc = rtmp + row;
812       if (*pc != 0.0) {
813         pv         = ba + diag_offset[row];
814         pj         = bj + diag_offset[row] + 1;
815         multiplier = *pc * *pv++;
816         *pc        = multiplier;
817         nz         = bi[row+1] - diag_offset[row] - 1;
818         for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
819         PLogFlops(1+2*nz);
820       }
821       row = *ajtmp++;
822     }
823     /* finished row so stick it into b->a */
824     pv = ba + bi[i];
825     pj = bj + bi[i];
826     nz = bi[i+1] - bi[i];
827     for ( j=0; j<nz; j++ ) {pv[j] = rtmp[pj[j]];}
828     diag = diag_offset[i] - bi[i];
829     /* check pivot entry for current row */
830     if (pv[diag] == 0.0) {
831       SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,0,"Zero pivot");
832     }
833     pv[diag] = 1.0/pv[diag];
834   }
835 
836   PetscFree(rtmp);
837   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
838   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
839   ierr = ISDestroy(isicol); CHKERRQ(ierr);
840   C->factor    = FACTOR_LU;
841   C->assembled = PETSC_TRUE;
842   PLogFlops(b->n);
843   return 0;
844 }
845 
846 /* ----------------------------------------------------------- */
847 #undef __FUNC__
848 #define __FUNC__ "MatLUFactor_SeqBAIJ"
849 int MatLUFactor_SeqBAIJ(Mat A,IS row,IS col,double f)
850 {
851   Mat_SeqBAIJ *mat = (Mat_SeqBAIJ *) A->data;
852   int         ierr;
853   Mat         C;
854 
855   ierr = MatLUFactorSymbolic(A,row,col,f,&C); CHKERRQ(ierr);
856   ierr = MatLUFactorNumeric(A,&C); CHKERRQ(ierr);
857 
858   /* free all the data structures from mat */
859   PetscFree(mat->a);
860   if (!mat->singlemalloc) {PetscFree(mat->i); PetscFree(mat->j);}
861   if (mat->diag) PetscFree(mat->diag);
862   if (mat->ilen) PetscFree(mat->ilen);
863   if (mat->imax) PetscFree(mat->imax);
864   if (mat->solve_work) PetscFree(mat->solve_work);
865   if (mat->mult_work) PetscFree(mat->mult_work);
866   PetscFree(mat);
867 
868   PetscMemcpy(A,C,sizeof(struct _Mat));
869   PetscHeaderDestroy(C);
870   return 0;
871 }
872 /* ----------------------------------------------------------- */
873 #undef __FUNC__
874 #define __FUNC__ "MatSolve_SeqBAIJ_N"
875 int MatSolve_SeqBAIJ_N(Mat A,Vec bb,Vec xx)
876 {
877   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
878   IS              iscol=a->col,isrow=a->row;
879   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j;
880   int             nz,bs=a->bs,bs2=a->bs2,*rout,*cout;
881   Scalar          *aa=a->a,*sum;
882   register Scalar *x,*b,*lsum,*tmp,*v;
883 
884   VecGetArray_Fast(bb,b);
885   VecGetArray_Fast(xx,x);
886   tmp  = a->solve_work;
887 
888   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
889   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
890 
891   /* forward solve the lower triangular */
892   PetscMemcpy(tmp,b + bs*(*r++), bs*sizeof(Scalar));
893   for ( i=1; i<n; i++ ) {
894     v   = aa + bs2*ai[i];
895     vi  = aj + ai[i];
896     nz  = a->diag[i] - ai[i];
897     sum = tmp + bs*i;
898     PetscMemcpy(sum,b+bs*(*r++),bs*sizeof(Scalar));
899     while (nz--) {
900       Kernel_v_gets_v_minus_A_times_w(bs,sum,v,tmp+bs*(*vi++));
901       v += bs2;
902     }
903   }
904   /* backward solve the upper triangular */
905   lsum = a->solve_work + a->n;
906   for ( i=n-1; i>=0; i-- ){
907     v   = aa + bs2*(a->diag[i] + 1);
908     vi  = aj + a->diag[i] + 1;
909     nz  = ai[i+1] - a->diag[i] - 1;
910     PetscMemcpy(lsum,tmp+i*bs,bs*sizeof(Scalar));
911     while (nz--) {
912       Kernel_v_gets_v_minus_A_times_w(bs,lsum,v,tmp+bs*(*vi++));
913       v += bs2;
914     }
915     Kernel_w_gets_A_times_v(bs,lsum,aa+bs2*a->diag[i],tmp+i*bs);
916     PetscMemcpy(x + bs*(*c--),tmp+i*bs,bs*sizeof(Scalar));
917   }
918 
919   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
920   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
921   VecRestoreArray_Fast(bb,b);
922   VecRestoreArray_Fast(xx,x);
923   PLogFlops(2*(a->bs2)*(a->nz) - a->n);
924   return 0;
925 }
926 
927 #undef __FUNC__
928 #define __FUNC__ "MatSolve_SeqBAIJ_7"
929 int MatSolve_SeqBAIJ_7(Mat A,Vec bb,Vec xx)
930 {
931   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
932   IS              iscol=a->col,isrow=a->row;
933   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout;
934   Scalar          *aa=a->a,sum1,sum2,sum3,sum4,sum5,sum6,sum7,x1,x2,x3,x4,x5,x6,x7;
935   register Scalar *x,*b,*tmp,*v;
936 
937   VecGetArray_Fast(bb,b);
938   VecGetArray_Fast(xx,x);
939   tmp  = a->solve_work;
940 
941   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
942   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
943 
944   /* forward solve the lower triangular */
945   idx    = 7*(*r++);
946   tmp[0] = b[idx];   tmp[1] = b[1+idx];
947   tmp[2] = b[2+idx]; tmp[3] = b[3+idx]; tmp[4] = b[4+idx];
948   tmp[5] = b[5+idx]; tmp[6] = b[6+idx];
949 
950   for ( i=1; i<n; i++ ) {
951     v     = aa + 49*ai[i];
952     vi    = aj + ai[i];
953     nz    = a->diag[i] - ai[i];
954     idx   = 7*(*r++);
955     sum1  = b[idx];sum2 = b[1+idx];sum3 = b[2+idx];sum4 = b[3+idx];
956     sum5  = b[4+idx];sum6 = b[5+idx];sum7 = b[6+idx];
957     while (nz--) {
958       idx   = 7*(*vi++);
959       x1    = tmp[idx];  x2 = tmp[1+idx];x3 = tmp[2+idx];
960       x4    = tmp[3+idx];x5 = tmp[4+idx];
961       x6    = tmp[5+idx];x7 = tmp[6+idx];
962       sum1 -= v[0]*x1 + v[7]*x2  + v[14]*x3 + v[21]*x4 + v[28]*x5 + v[35]*x6 + v[42]*x7;
963       sum2 -= v[1]*x1 + v[8]*x2  + v[15]*x3 + v[22]*x4 + v[29]*x5 + v[36]*x6 + v[43]*x7;
964       sum3 -= v[2]*x1 + v[9]*x2  + v[16]*x3 + v[23]*x4 + v[30]*x5 + v[37]*x6 + v[44]*x7;
965       sum4 -= v[3]*x1 + v[10]*x2 + v[17]*x3 + v[24]*x4 + v[31]*x5 + v[38]*x6 + v[45]*x7;
966       sum5 -= v[4]*x1 + v[11]*x2 + v[18]*x3 + v[25]*x4 + v[32]*x5 + v[39]*x6 + v[46]*x7;
967       sum6 -= v[5]*x1 + v[12]*x2 + v[19]*x3 + v[26]*x4 + v[33]*x5 + v[40]*x6 + v[47]*x7;
968       sum7 -= v[6]*x1 + v[13]*x2 + v[20]*x3 + v[27]*x4 + v[34]*x5 + v[41]*x6 + v[48]*x7;
969       v += 49;
970     }
971     idx = 7*i;
972     tmp[idx]   = sum1;tmp[1+idx] = sum2;
973     tmp[2+idx] = sum3;tmp[3+idx] = sum4; tmp[4+idx] = sum5;
974     tmp[5+idx] = sum6;tmp[6+idx] = sum7;
975   }
976   /* backward solve the upper triangular */
977   for ( i=n-1; i>=0; i-- ){
978     v    = aa + 49*a->diag[i] + 49;
979     vi   = aj + a->diag[i] + 1;
980     nz   = ai[i+1] - a->diag[i] - 1;
981     idt  = 7*i;
982     sum1 = tmp[idt];  sum2 = tmp[1+idt];
983     sum3 = tmp[2+idt];sum4 = tmp[3+idt]; sum5 = tmp[4+idt];
984     sum6 = tmp[5+idt];sum7 = tmp[6+idt];
985     while (nz--) {
986       idx   = 7*(*vi++);
987       x1    = tmp[idx];   x2 = tmp[1+idx];
988       x3    = tmp[2+idx]; x4 = tmp[3+idx]; x5 = tmp[4+idx];
989       x6    = tmp[5+idx]; x7 = tmp[6+idx];
990       sum1 -= v[0]*x1 + v[7]*x2  + v[14]*x3 + v[21]*x4 + v[28]*x5 + v[35]*x6 + v[42]*x7;
991       sum2 -= v[1]*x1 + v[8]*x2  + v[15]*x3 + v[22]*x4 + v[29]*x5 + v[36]*x6 + v[43]*x7;
992       sum3 -= v[2]*x1 + v[9]*x2  + v[16]*x3 + v[23]*x4 + v[30]*x5 + v[37]*x6 + v[44]*x7;
993       sum4 -= v[3]*x1 + v[10]*x2 + v[17]*x3 + v[24]*x4 + v[31]*x5 + v[38]*x6 + v[45]*x7;
994       sum5 -= v[4]*x1 + v[11]*x2 + v[18]*x3 + v[25]*x4 + v[32]*x5 + v[39]*x6 + v[46]*x7;
995       sum6 -= v[5]*x1 + v[12]*x2 + v[19]*x3 + v[26]*x4 + v[33]*x5 + v[40]*x6 + v[47]*x7;
996       sum7 -= v[6]*x1 + v[13]*x2 + v[20]*x3 + v[27]*x4 + v[34]*x5 + v[41]*x6 + v[48]*x7;
997       v += 49;
998     }
999     idc = 7*(*c--);
1000     v   = aa + 49*a->diag[i];
1001     x[idc]   = tmp[idt]   = v[0]*sum1+v[7]*sum2+v[14]*sum3+
1002                                  v[21]*sum4+v[28]*sum5+v[35]*sum6+v[42]*sum7;
1003     x[1+idc] = tmp[1+idt] = v[1]*sum1+v[8]*sum2+v[15]*sum3+
1004                                  v[22]*sum4+v[29]*sum5+v[36]*sum6+v[43]*sum7;
1005     x[2+idc] = tmp[2+idt] = v[2]*sum1+v[9]*sum2+v[16]*sum3+
1006                                  v[23]*sum4+v[30]*sum5+v[37]*sum6+v[44]*sum7;
1007     x[3+idc] = tmp[3+idt] = v[3]*sum1+v[10]*sum2+v[17]*sum3+
1008                                  v[24]*sum4+v[31]*sum5+v[38]*sum6+v[45]*sum7;
1009     x[4+idc] = tmp[4+idt] = v[4]*sum1+v[11]*sum2+v[18]*sum3+
1010                                  v[25]*sum4+v[32]*sum5+v[39]*sum6+v[46]*sum7;
1011     x[5+idc] = tmp[5+idt] = v[5]*sum1+v[12]*sum2+v[19]*sum3+
1012                                  v[26]*sum4+v[33]*sum5+v[40]*sum6+v[47]*sum7;
1013     x[6+idc] = tmp[6+idt] = v[6]*sum1+v[13]*sum2+v[20]*sum3+
1014                                  v[27]*sum4+v[34]*sum5+v[41]*sum6+v[48]*sum7;
1015   }
1016 
1017   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
1018   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
1019   VecRestoreArray_Fast(bb,b);
1020   VecRestoreArray_Fast(xx,x);
1021   PLogFlops(2*49*(a->nz) - a->n);
1022   return 0;
1023 }
1024 
1025 #undef __FUNC__
1026 #define __FUNC__ "MatSolve_SeqBAIJ_5"
1027 int MatSolve_SeqBAIJ_5(Mat A,Vec bb,Vec xx)
1028 {
1029   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
1030   IS              iscol=a->col,isrow=a->row;
1031   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout;
1032   Scalar          *aa=a->a,sum1,sum2,sum3,sum4,sum5,x1,x2,x3,x4,x5;
1033   register Scalar *x,*b,*tmp,*v;
1034 
1035   VecGetArray_Fast(bb,b);
1036   VecGetArray_Fast(xx,x);
1037   tmp  = a->solve_work;
1038 
1039   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1040   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1041 
1042   /* forward solve the lower triangular */
1043   idx    = 5*(*r++);
1044   tmp[0] = b[idx];   tmp[1] = b[1+idx];
1045   tmp[2] = b[2+idx]; tmp[3] = b[3+idx]; tmp[4] = b[4+idx];
1046   for ( i=1; i<n; i++ ) {
1047     v     = aa + 25*ai[i];
1048     vi    = aj + ai[i];
1049     nz    = a->diag[i] - ai[i];
1050     idx   = 5*(*r++);
1051     sum1  = b[idx];sum2 = b[1+idx];sum3 = b[2+idx];sum4 = b[3+idx];
1052     sum5  = b[4+idx];
1053     while (nz--) {
1054       idx   = 5*(*vi++);
1055       x1    = tmp[idx];  x2 = tmp[1+idx];x3 = tmp[2+idx];
1056       x4    = tmp[3+idx];x5 = tmp[4+idx];
1057       sum1 -= v[0]*x1 + v[5]*x2 + v[10]*x3 + v[15]*x4 + v[20]*x5;
1058       sum2 -= v[1]*x1 + v[6]*x2 + v[11]*x3 + v[16]*x4 + v[21]*x5;
1059       sum3 -= v[2]*x1 + v[7]*x2 + v[12]*x3 + v[17]*x4 + v[22]*x5;
1060       sum4 -= v[3]*x1 + v[8]*x2 + v[13]*x3 + v[18]*x4 + v[23]*x5;
1061       sum5 -= v[4]*x1 + v[9]*x2 + v[14]*x3 + v[19]*x4 + v[24]*x5;
1062       v += 25;
1063     }
1064     idx = 5*i;
1065     tmp[idx]   = sum1;tmp[1+idx] = sum2;
1066     tmp[2+idx] = sum3;tmp[3+idx] = sum4; tmp[4+idx] = sum5;
1067   }
1068   /* backward solve the upper triangular */
1069   for ( i=n-1; i>=0; i-- ){
1070     v    = aa + 25*a->diag[i] + 25;
1071     vi   = aj + a->diag[i] + 1;
1072     nz   = ai[i+1] - a->diag[i] - 1;
1073     idt  = 5*i;
1074     sum1 = tmp[idt];  sum2 = tmp[1+idt];
1075     sum3 = tmp[2+idt];sum4 = tmp[3+idt]; sum5 = tmp[4+idt];
1076     while (nz--) {
1077       idx   = 5*(*vi++);
1078       x1    = tmp[idx];   x2 = tmp[1+idx];
1079       x3    = tmp[2+idx]; x4 = tmp[3+idx]; x5 = tmp[4+idx];
1080       sum1 -= v[0]*x1 + v[5]*x2 + v[10]*x3 + v[15]*x4 + v[20]*x5;
1081       sum2 -= v[1]*x1 + v[6]*x2 + v[11]*x3 + v[16]*x4 + v[21]*x5;
1082       sum3 -= v[2]*x1 + v[7]*x2 + v[12]*x3 + v[17]*x4 + v[22]*x5;
1083       sum4 -= v[3]*x1 + v[8]*x2 + v[13]*x3 + v[18]*x4 + v[23]*x5;
1084       sum5 -= v[4]*x1 + v[9]*x2 + v[14]*x3 + v[19]*x4 + v[24]*x5;
1085       v += 25;
1086     }
1087     idc = 5*(*c--);
1088     v   = aa + 25*a->diag[i];
1089     x[idc]   = tmp[idt]   = v[0]*sum1+v[5]*sum2+v[10]*sum3+
1090                                  v[15]*sum4+v[20]*sum5;
1091     x[1+idc] = tmp[1+idt] = v[1]*sum1+v[6]*sum2+v[11]*sum3+
1092                                  v[16]*sum4+v[21]*sum5;
1093     x[2+idc] = tmp[2+idt] = v[2]*sum1+v[7]*sum2+v[12]*sum3+
1094                                  v[17]*sum4+v[22]*sum5;
1095     x[3+idc] = tmp[3+idt] = v[3]*sum1+v[8]*sum2+v[13]*sum3+
1096                                  v[18]*sum4+v[23]*sum5;
1097     x[4+idc] = tmp[4+idt] = v[4]*sum1+v[9]*sum2+v[14]*sum3+
1098                                  v[19]*sum4+v[24]*sum5;
1099   }
1100 
1101   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
1102   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
1103   VecRestoreArray_Fast(bb,b);
1104   VecRestoreArray_Fast(xx,x);
1105   PLogFlops(2*25*(a->nz) - a->n);
1106   return 0;
1107 }
1108 
1109 #undef __FUNC__
1110 #define __FUNC__ "MatSolve_SeqBAIJ_4"
1111 int MatSolve_SeqBAIJ_4(Mat A,Vec bb,Vec xx)
1112 {
1113   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
1114   IS              iscol=a->col,isrow=a->row;
1115   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout;
1116   Scalar          *aa=a->a,sum1,sum2,sum3,sum4,x1,x2,x3,x4;
1117   register Scalar *x,*b,*tmp,*v;
1118 
1119   VecGetArray_Fast(bb,b);
1120   VecGetArray_Fast(xx,x);
1121   tmp  = a->solve_work;
1122 
1123   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1124   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1125 
1126   /* forward solve the lower triangular */
1127   idx    = 4*(*r++);
1128   tmp[0] = b[idx];   tmp[1] = b[1+idx];
1129   tmp[2] = b[2+idx]; tmp[3] = b[3+idx];
1130   for ( i=1; i<n; i++ ) {
1131     v     = aa + 16*ai[i];
1132     vi    = aj + ai[i];
1133     nz    = a->diag[i] - ai[i];
1134     idx   = 4*(*r++);
1135     sum1  = b[idx];sum2 = b[1+idx];sum3 = b[2+idx];sum4 = b[3+idx];
1136     while (nz--) {
1137       idx   = 4*(*vi++);
1138       x1    = tmp[idx];x2 = tmp[1+idx];x3 = tmp[2+idx];x4 = tmp[3+idx];
1139       sum1 -= v[0]*x1 + v[4]*x2 + v[8]*x3  + v[12]*x4;
1140       sum2 -= v[1]*x1 + v[5]*x2 + v[9]*x3  + v[13]*x4;
1141       sum3 -= v[2]*x1 + v[6]*x2 + v[10]*x3 + v[14]*x4;
1142       sum4 -= v[3]*x1 + v[7]*x2 + v[11]*x3 + v[15]*x4;
1143       v += 16;
1144     }
1145     idx = 4*i;
1146     tmp[idx]   = sum1;tmp[1+idx] = sum2;
1147     tmp[2+idx] = sum3;tmp[3+idx] = sum4;
1148   }
1149   /* backward solve the upper triangular */
1150   for ( i=n-1; i>=0; i-- ){
1151     v    = aa + 16*a->diag[i] + 16;
1152     vi   = aj + a->diag[i] + 1;
1153     nz   = ai[i+1] - a->diag[i] - 1;
1154     idt  = 4*i;
1155     sum1 = tmp[idt];  sum2 = tmp[1+idt];
1156     sum3 = tmp[2+idt];sum4 = tmp[3+idt];
1157     while (nz--) {
1158       idx   = 4*(*vi++);
1159       x1    = tmp[idx];   x2 = tmp[1+idx];
1160       x3    = tmp[2+idx]; x4 = tmp[3+idx];
1161       sum1 -= v[0]*x1 + v[4]*x2 + v[8]*x3   + v[12]*x4;
1162       sum2 -= v[1]*x1 + v[5]*x2 + v[9]*x3   + v[13]*x4;
1163       sum3 -= v[2]*x1 + v[6]*x2 + v[10]*x3  + v[14]*x4;
1164       sum4 -= v[3]*x1 + v[7]*x2 + v[11]*x3  + v[15]*x4;
1165       v += 16;
1166     }
1167     idc = 4*(*c--);
1168     v   = aa + 16*a->diag[i];
1169     x[idc]   = tmp[idt]   = v[0]*sum1+v[4]*sum2+v[8]*sum3+v[12]*sum4;
1170     x[1+idc] = tmp[1+idt] = v[1]*sum1+v[5]*sum2+v[9]*sum3+v[13]*sum4;
1171     x[2+idc] = tmp[2+idt] = v[2]*sum1+v[6]*sum2+v[10]*sum3+v[14]*sum4;
1172     x[3+idc] = tmp[3+idt] = v[3]*sum1+v[7]*sum2+v[11]*sum3+v[15]*sum4;
1173   }
1174 
1175   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
1176   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
1177   VecRestoreArray_Fast(bb,b);
1178   VecRestoreArray_Fast(xx,x);
1179   PLogFlops(2*16*(a->nz) - a->n);
1180   return 0;
1181 }
1182 
1183 
1184 #undef __FUNC__
1185 #define __FUNC__ "MatSolve_SeqBAIJ_3"
1186 int MatSolve_SeqBAIJ_3(Mat A,Vec bb,Vec xx)
1187 {
1188   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
1189   IS              iscol=a->col,isrow=a->row;
1190   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout;
1191   Scalar          *aa=a->a,sum1,sum2,sum3,x1,x2,x3;
1192   register Scalar *x,*b,*tmp,*v;
1193 
1194   VecGetArray_Fast(bb,b);
1195   VecGetArray_Fast(xx,x);
1196   tmp  = a->solve_work;
1197 
1198   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1199   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1200 
1201   /* forward solve the lower triangular */
1202   idx    = 3*(*r++);
1203   tmp[0] = b[idx]; tmp[1] = b[1+idx]; tmp[2] = b[2+idx];
1204   for ( i=1; i<n; i++ ) {
1205     v     = aa + 9*ai[i];
1206     vi    = aj + ai[i];
1207     nz    = a->diag[i] - ai[i];
1208     idx   = 3*(*r++);
1209     sum1  = b[idx]; sum2 = b[1+idx]; sum3 = b[2+idx];
1210     while (nz--) {
1211       idx   = 3*(*vi++);
1212       x1    = tmp[idx]; x2 = tmp[1+idx]; x3 = tmp[2+idx];
1213       sum1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
1214       sum2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
1215       sum3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
1216       v += 9;
1217     }
1218     idx = 3*i;
1219     tmp[idx] = sum1; tmp[1+idx] = sum2; tmp[2+idx] = sum3;
1220   }
1221   /* backward solve the upper triangular */
1222   for ( i=n-1; i>=0; i-- ){
1223     v    = aa + 9*a->diag[i] + 9;
1224     vi   = aj + a->diag[i] + 1;
1225     nz   = ai[i+1] - a->diag[i] - 1;
1226     idt  = 3*i;
1227     sum1 = tmp[idt]; sum2 = tmp[1+idt]; sum3 = tmp[2+idt];
1228     while (nz--) {
1229       idx   = 3*(*vi++);
1230       x1    = tmp[idx]; x2 = tmp[1+idx]; x3 = tmp[2+idx];
1231       sum1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
1232       sum2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
1233       sum3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
1234       v += 9;
1235     }
1236     idc = 3*(*c--);
1237     v   = aa + 9*a->diag[i];
1238     x[idc]   = tmp[idt]   = v[0]*sum1 + v[3]*sum2 + v[6]*sum3;
1239     x[1+idc] = tmp[1+idt] = v[1]*sum1 + v[4]*sum2 + v[7]*sum3;
1240     x[2+idc] = tmp[2+idt] = v[2]*sum1 + v[5]*sum2 + v[8]*sum3;
1241   }
1242   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
1243   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
1244   VecRestoreArray_Fast(bb,b);
1245   VecRestoreArray_Fast(xx,x);
1246   PLogFlops(2*9*(a->nz) - a->n);
1247   return 0;
1248 }
1249 
1250 #undef __FUNC__
1251 #define __FUNC__ "MatSolve_SeqBAIJ_2"
1252 int MatSolve_SeqBAIJ_2(Mat A,Vec bb,Vec xx)
1253 {
1254   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
1255   IS              iscol=a->col,isrow=a->row;
1256   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout;
1257   Scalar          *aa=a->a,sum1,sum2,x1,x2;
1258   register Scalar *x,*b,*tmp,*v;
1259 
1260   VecGetArray_Fast(bb,b);
1261   VecGetArray_Fast(xx,x);
1262   tmp  = a->solve_work;
1263 
1264   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1265   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1266 
1267   /* forward solve the lower triangular */
1268   idx    = 2*(*r++);
1269   tmp[0] = b[idx]; tmp[1] = b[1+idx];
1270   for ( i=1; i<n; i++ ) {
1271     v     = aa + 4*ai[i];
1272     vi    = aj + ai[i];
1273     nz    = a->diag[i] - ai[i];
1274     idx   = 2*(*r++);
1275     sum1  = b[idx]; sum2 = b[1+idx];
1276     while (nz--) {
1277       idx   = 2*(*vi++);
1278       x1    = tmp[idx]; x2 = tmp[1+idx];
1279       sum1 -= v[0]*x1 + v[2]*x2;
1280       sum2 -= v[1]*x1 + v[3]*x2;
1281       v += 4;
1282     }
1283     idx = 2*i;
1284     tmp[idx] = sum1; tmp[1+idx] = sum2;
1285   }
1286   /* backward solve the upper triangular */
1287   for ( i=n-1; i>=0; i-- ){
1288     v    = aa + 4*a->diag[i] + 4;
1289     vi   = aj + a->diag[i] + 1;
1290     nz   = ai[i+1] - a->diag[i] - 1;
1291     idt  = 2*i;
1292     sum1 = tmp[idt]; sum2 = tmp[1+idt];
1293     while (nz--) {
1294       idx   = 2*(*vi++);
1295       x1    = tmp[idx]; x2 = tmp[1+idx];
1296       sum1 -= v[0]*x1 + v[2]*x2;
1297       sum2 -= v[1]*x1 + v[3]*x2;
1298       v += 4;
1299     }
1300     idc = 2*(*c--);
1301     v   = aa + 4*a->diag[i];
1302     x[idc]   = tmp[idt]   = v[0]*sum1 + v[2]*sum2;
1303     x[1+idc] = tmp[1+idt] = v[1]*sum1 + v[3]*sum2;
1304   }
1305   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
1306   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
1307   VecRestoreArray_Fast(bb,b);
1308   VecRestoreArray_Fast(xx,x);
1309   PLogFlops(2*4*(a->nz) - a->n);
1310   return 0;
1311 }
1312 
1313 
1314 #undef __FUNC__
1315 #define __FUNC__ "MatSolve_SeqBAIJ_1"
1316 int MatSolve_SeqBAIJ_1(Mat A,Vec bb,Vec xx)
1317 {
1318   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
1319   IS              iscol=a->col,isrow=a->row;
1320   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,*rout,*cout;
1321   Scalar          *aa=a->a,sum1;
1322   register Scalar *x,*b,*tmp,*v;
1323 
1324   if (!n) return 0;
1325 
1326   VecGetArray_Fast(bb,b);
1327   VecGetArray_Fast(xx,x);
1328   tmp  = a->solve_work;
1329 
1330   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1331   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1332 
1333   /* forward solve the lower triangular */
1334   tmp[0] = b[*r++];
1335   for ( i=1; i<n; i++ ) {
1336     v     = aa + ai[i];
1337     vi    = aj + ai[i];
1338     nz    = a->diag[i] - ai[i];
1339     sum1  = b[*r++];
1340     while (nz--) {
1341       sum1 -= (*v++)*tmp[*vi++];
1342     }
1343     tmp[i] = sum1;
1344   }
1345   /* backward solve the upper triangular */
1346   for ( i=n-1; i>=0; i-- ){
1347     v    = aa + a->diag[i] + 1;
1348     vi   = aj + a->diag[i] + 1;
1349     nz   = ai[i+1] - a->diag[i] - 1;
1350     sum1 = tmp[i];
1351     while (nz--) {
1352       sum1 -= (*v++)*tmp[*vi++];
1353     }
1354     x[*c--] = tmp[i] = aa[a->diag[i]]*sum1;
1355   }
1356 
1357   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
1358   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
1359   VecRestoreArray_Fast(bb,b);
1360   VecRestoreArray_Fast(xx,x);
1361   PLogFlops(2*1*(a->nz) - a->n);
1362   return 0;
1363 }
1364 
1365 /* ----------------------------------------------------------------*/
1366 /*
1367      This code is virtually identical to MatILUFactorSymbolic_SeqAIJ
1368    except that the data structure of Mat_SeqAIJ is slightly different.
1369    Not a good example of code reuse.
1370 */
1371 #undef __FUNC__
1372 #define __FUNC__ "MatILUFactorSymbolic_SeqBAIJ"
1373 int MatILUFactorSymbolic_SeqBAIJ(Mat A,IS isrow,IS iscol,double f,int levels,
1374                                  Mat *fact)
1375 {
1376   Mat_SeqBAIJ *a = (Mat_SeqBAIJ *) A->data, *b;
1377   IS          isicol;
1378   int         *r,*ic, ierr, prow, n = a->mbs, *ai = a->i, *aj = a->j;
1379   int         *ainew,*ajnew, jmax,*fill, *xi, nz, *im,*ajfill,*flev;
1380   int         *dloc, idx, row,m,fm, nzf, nzi,len,  realloc = 0;
1381   int         incrlev,nnz,i,bs = a->bs,bs2 = a->bs2;
1382   PetscTruth  col_identity, row_identity;
1383 
1384   /* special case that simply copies fill pattern */
1385   PetscValidHeaderSpecific(isrow,IS_COOKIE);
1386   PetscValidHeaderSpecific(iscol,IS_COOKIE);
1387   ISIdentity(isrow,&row_identity); ISIdentity(iscol,&col_identity);
1388   if (levels == 0 && row_identity && col_identity) {
1389     ierr = MatConvertSameType_SeqBAIJ(A,fact,DO_NOT_COPY_VALUES); CHKERRQ(ierr);
1390     (*fact)->factor = FACTOR_LU;
1391     b               = (Mat_SeqBAIJ *) (*fact)->data;
1392     if (!b->diag) {
1393       ierr = MatMarkDiag_SeqBAIJ(*fact); CHKERRQ(ierr);
1394     }
1395     b->row        = isrow;
1396     b->col        = iscol;
1397     b->solve_work = (Scalar *) PetscMalloc((b->m+1+b->bs)*sizeof(Scalar));CHKPTRQ(b->solve_work);
1398     return 0;
1399   }
1400 
1401   ierr = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
1402   ierr = ISGetIndices(isrow,&r); CHKERRQ(ierr);
1403   ierr = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
1404 
1405   /* get new row pointers */
1406   ainew = (int *) PetscMalloc( (n+1)*sizeof(int) ); CHKPTRQ(ainew);
1407   ainew[0] = 0;
1408   /* don't know how many column pointers are needed so estimate */
1409   jmax = (int) (f*ai[n] + 1);
1410   ajnew = (int *) PetscMalloc( (jmax)*sizeof(int) ); CHKPTRQ(ajnew);
1411   /* ajfill is level of fill for each fill entry */
1412   ajfill = (int *) PetscMalloc( (jmax)*sizeof(int) ); CHKPTRQ(ajfill);
1413   /* fill is a linked list of nonzeros in active row */
1414   fill = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(fill);
1415   /* im is level for each filled value */
1416   im = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(im);
1417   /* dloc is location of diagonal in factor */
1418   dloc = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(dloc);
1419   dloc[0]  = 0;
1420   for ( prow=0; prow<n; prow++ ) {
1421     /* first copy previous fill into linked list */
1422     nzf     = nz  = ai[r[prow]+1] - ai[r[prow]];
1423     if (!nz) SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,1,"Empty row in matrix");
1424     xi      = aj + ai[r[prow]];
1425     fill[n] = n;
1426     while (nz--) {
1427       fm  = n;
1428       idx = ic[*xi++];
1429       do {
1430         m  = fm;
1431         fm = fill[m];
1432       } while (fm < idx);
1433       fill[m]   = idx;
1434       fill[idx] = fm;
1435       im[idx]   = 0;
1436     }
1437     nzi = 0;
1438     row = fill[n];
1439     while ( row < prow ) {
1440       incrlev = im[row] + 1;
1441       nz      = dloc[row];
1442       xi      = ajnew  + ainew[row] + nz;
1443       flev    = ajfill + ainew[row] + nz + 1;
1444       nnz     = ainew[row+1] - ainew[row] - nz - 1;
1445       if (*xi++ != row) {
1446         SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,0,"zero pivot");
1447       }
1448       fm      = row;
1449       while (nnz-- > 0) {
1450         idx = *xi++;
1451         if (*flev + incrlev > levels) {
1452           flev++;
1453           continue;
1454         }
1455         do {
1456           m  = fm;
1457           fm = fill[m];
1458         } while (fm < idx);
1459         if (fm != idx) {
1460           im[idx]   = *flev + incrlev;
1461           fill[m]   = idx;
1462           fill[idx] = fm;
1463           fm        = idx;
1464           nzf++;
1465         }
1466         else {
1467           if (im[idx] > *flev + incrlev) im[idx] = *flev+incrlev;
1468         }
1469         flev++;
1470       }
1471       row = fill[row];
1472       nzi++;
1473     }
1474     /* copy new filled row into permanent storage */
1475     ainew[prow+1] = ainew[prow] + nzf;
1476     if (ainew[prow+1] > jmax) {
1477       /* allocate a longer ajnew */
1478       int maxadd;
1479       maxadd = (int) (((f*ai[n]+1)*(n-prow+5))/n);
1480       if (maxadd < nzf) maxadd = (n-prow)*(nzf+1);
1481       jmax += maxadd;
1482       xi = (int *) PetscMalloc( jmax*sizeof(int) );CHKPTRQ(xi);
1483       PetscMemcpy(xi,ajnew,ainew[prow]*sizeof(int));
1484       PetscFree(ajnew);
1485       ajnew = xi;
1486       /* allocate a longer ajfill */
1487       xi = (int *) PetscMalloc( jmax*sizeof(int) );CHKPTRQ(xi);
1488       PetscMemcpy(xi,ajfill,ainew[prow]*sizeof(int));
1489       PetscFree(ajfill);
1490       ajfill = xi;
1491       realloc++;
1492     }
1493     xi          = ajnew + ainew[prow];
1494     flev        = ajfill + ainew[prow];
1495     dloc[prow]  = nzi;
1496     fm          = fill[n];
1497     while (nzf--) {
1498       *xi++   = fm;
1499       *flev++ = im[fm];
1500       fm      = fill[fm];
1501     }
1502   }
1503   PetscFree(ajfill);
1504   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
1505   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
1506   ierr = ISDestroy(isicol); CHKERRQ(ierr);
1507   PetscFree(fill); PetscFree(im);
1508 
1509   PLogInfo(A,
1510     "Info:MatILUFactorSymbolic_SeqBAIJ:Realloc %d Fill ratio:given %g needed %g\n",
1511                              realloc,f,((double)ainew[n])/((double)ai[prow]));
1512 
1513   /* put together the new matrix */
1514   ierr = MatCreateSeqBAIJ(A->comm,bs,bs*n,bs*n,0,PETSC_NULL,fact);CHKERRQ(ierr);
1515   b = (Mat_SeqBAIJ *) (*fact)->data;
1516   PetscFree(b->imax);
1517   b->singlemalloc = 0;
1518   len = bs2*ainew[n]*sizeof(Scalar);
1519   /* the next line frees the default space generated by the Create() */
1520   PetscFree(b->a); PetscFree(b->ilen);
1521   b->a          = (Scalar *) PetscMalloc( len ); CHKPTRQ(b->a);
1522   b->j          = ajnew;
1523   b->i          = ainew;
1524   for ( i=0; i<n; i++ ) dloc[i] += ainew[i];
1525   b->diag       = dloc;
1526   b->ilen       = 0;
1527   b->imax       = 0;
1528   b->row        = isrow;
1529   b->col        = iscol;
1530   b->solve_work = (Scalar *) PetscMalloc( (bs*n+bs)*sizeof(Scalar));
1531   CHKPTRQ(b->solve_work);
1532   /* In b structure:  Free imax, ilen, old a, old j.
1533      Allocate dloc, solve_work, new a, new j */
1534   PLogObjectMemory(*fact,(ainew[n]-n)*(sizeof(int))+bs2*ainew[n]*sizeof(Scalar));
1535   b->maxnz          = b->nz = ainew[n];
1536   (*fact)->factor   = FACTOR_LU;
1537 
1538   (*fact)->info.factor_mallocs    = realloc;
1539   (*fact)->info.fill_ratio_given  = f;
1540   (*fact)->info.fill_ratio_needed = ((double)ainew[n])/((double)ai[prow]);
1541 
1542   return 0;
1543 }
1544 
1545 
1546 
1547 
1548