xref: /petsc/src/mat/impls/baij/seq/baijfact.c (revision da045f9d91f20b1a7a2fc0b3eba9f8bde746c5b7)
1 #ifndef lint
2 static char vcid[] = "$Id: baijfact.c,v 1.20 1996/04/28 02:09:52 bsmith Exp balay $";
3 #endif
4 /*
5     Factorization code for BAIJ format.
6 */
7 
8 #include "baij.h"
9 #include "src/inline/ilu.h"
10 
11 /*
12     The symbolic factorization code is identical to that for AIJ format,
13   except for very small changes since this is now a SeqBAIJ datastructure.
14   NOT good code reuse.
15 */
16 int MatLUFactorSymbolic_SeqBAIJ(Mat A,IS isrow,IS iscol,double f,Mat *B)
17 {
18   Mat_SeqBAIJ *a = (Mat_SeqBAIJ *) A->data, *b;
19   IS          isicol;
20   int         *r,*ic, ierr, i, n = a->mbs, *ai = a->i, *aj = a->j;
21   int         *ainew,*ajnew, jmax,*fill, *ajtmp, nz, bs = a->bs, bs2=a->bs2;
22   int         *idnew, idx, row,m,fm, nnz, nzi,len, realloc = 0,nzbd,*im;
23 
24   if (a->m != a->n) SETERRQ(1,"MatLUFactorSymbolic_SeqBAIJ:Must be square");
25   if (!isrow) SETERRQ(1,"MatLUFactorSymbolic_SeqBAIJ:Must have row permutation");
26   if (!iscol) SETERRQ(1,"MatLUFactorSymbolic_SeqBAIJ:Must have col. permutation");
27 
28   ierr = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
29   ISGetIndices(isrow,&r); ISGetIndices(isicol,&ic);
30 
31   /* get new row pointers */
32   ainew = (int *) PetscMalloc( (n+1)*sizeof(int) ); CHKPTRQ(ainew);
33   ainew[0] = 0;
34   /* don't know how many column pointers are needed so estimate */
35   jmax = (int) (f*ai[n] + 1);
36   ajnew = (int *) PetscMalloc( (jmax)*sizeof(int) ); CHKPTRQ(ajnew);
37   /* fill is a linked list of nonzeros in active row */
38   fill = (int *) PetscMalloc( (2*n+1)*sizeof(int)); CHKPTRQ(fill);
39   im = fill + n + 1;
40   /* idnew is location of diagonal in factor */
41   idnew = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(idnew);
42   idnew[0] = 0;
43 
44   for ( i=0; i<n; i++ ) {
45     /* first copy previous fill into linked list */
46     nnz     = nz    = ai[r[i]+1] - ai[r[i]];
47     ajtmp   = aj + ai[r[i]];
48     fill[n] = n;
49     while (nz--) {
50       fm  = n;
51       idx = ic[*ajtmp++];
52       do {
53         m  = fm;
54         fm = fill[m];
55       } while (fm < idx);
56       fill[m]   = idx;
57       fill[idx] = fm;
58     }
59     row = fill[n];
60     while ( row < i ) {
61       ajtmp = ajnew + idnew[row] + 1;
62       nzbd  = 1 + idnew[row] - ainew[row];
63       nz    = im[row] - nzbd;
64       fm    = row;
65       while (nz-- > 0) {
66         idx = *ajtmp++;
67         nzbd++;
68         if (idx == i) im[row] = nzbd;
69         do {
70           m  = fm;
71           fm = fill[m];
72         } while (fm < idx);
73         if (fm != idx) {
74           fill[m]   = idx;
75           fill[idx] = fm;
76           fm        = idx;
77           nnz++;
78         }
79       }
80       row = fill[row];
81     }
82     /* copy new filled row into permanent storage */
83     ainew[i+1] = ainew[i] + nnz;
84     if (ainew[i+1] > jmax) {
85       /* allocate a longer ajnew */
86       int maxadd;
87       maxadd = (int) ((f*(ai[n]+1)*(n-i+5))/n);
88       if (maxadd < nnz) maxadd = (n-i)*(nnz+1);
89       jmax += maxadd;
90       ajtmp = (int *) PetscMalloc( jmax*sizeof(int) );CHKPTRQ(ajtmp);
91       PetscMemcpy(ajtmp,ajnew,ainew[i]*sizeof(int));
92       PetscFree(ajnew);
93       ajnew = ajtmp;
94       realloc++; /* count how many times we realloc */
95     }
96     ajtmp = ajnew + ainew[i];
97     fm    = fill[n];
98     nzi   = 0;
99     im[i] = nnz;
100     while (nnz--) {
101       if (fm < i) nzi++;
102       *ajtmp++ = fm;
103       fm       = fill[fm];
104     }
105     idnew[i] = ainew[i] + nzi;
106   }
107 
108   PLogInfo(A,
109     "Info:MatLUFactorSymbolic_SeqBAIJ:Reallocs %d Fill ratio:given %g needed %g\n",
110                              realloc,f,((double)ainew[n])/((double)ai[i]));
111 
112   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
113   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
114 
115   PetscFree(fill);
116 
117   /* put together the new matrix */
118   ierr = MatCreateSeqBAIJ(A->comm,bs,bs*n,bs*n,0,PETSC_NULL,B); CHKERRQ(ierr);
119   PLogObjectParent(*B,isicol);
120   ierr = ISDestroy(isicol); CHKERRQ(ierr);
121   b = (Mat_SeqBAIJ *) (*B)->data;
122   PetscFree(b->imax);
123   b->singlemalloc = 0;
124   len             = ainew[n]*sizeof(Scalar);
125   /* the next line frees the default space generated by the Create() */
126   PetscFree(b->a); PetscFree(b->ilen);
127   b->a          = (Scalar *) PetscMalloc( len*bs2 ); CHKPTRQ(b->a);
128   b->j          = ajnew;
129   b->i          = ainew;
130   b->diag       = idnew;
131   b->ilen       = 0;
132   b->imax       = 0;
133   b->row        = isrow;
134   b->col        = iscol;
135   b->solve_work = (Scalar *) PetscMalloc( (bs*n+bs)*sizeof(Scalar));
136   CHKPTRQ(b->solve_work);
137   /* In b structure:  Free imax, ilen, old a, old j.
138      Allocate idnew, solve_work, new a, new j */
139   PLogObjectMemory(*B,(ainew[n]-n)*(sizeof(int)+sizeof(Scalar)));
140   b->maxnz = b->nz = ainew[n];
141 
142   return 0;
143 }
144 
145 /* ----------------------------------------------------------- */
146 int MatLUFactorNumeric_SeqBAIJ_N(Mat A,Mat *B)
147 {
148   Mat             C = *B;
149   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data,*b = (Mat_SeqBAIJ *)C->data;
150   IS              iscol = b->col, isrow = b->row, isicol;
151   int             *r,*ic, ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
152   int             *ajtmpold, *ajtmp, nz, row, bslog,*ai=a->i,*aj=a->j;
153   int             *diag_offset=b->diag,diag,bs=a->bs,bs2 = bs*bs,*v_pivots;
154   Scalar          *ba = b->a,*aa = a->a;
155   register Scalar *pv,*v,*rtmp,*multiplier,*v_work,*pc,*w;
156   register int    *pj;
157 
158   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
159   PLogObjectParent(*B,isicol);
160   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
161   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
162   rtmp  = (Scalar *) PetscMalloc(bs2*(n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
163 
164   /* generate work space needed by dense LU factorization */
165   v_work     = (Scalar *) PetscMalloc(bs*sizeof(int) + (bs+bs2)*sizeof(Scalar));
166                CHKPTRQ(v_work);
167   multiplier = v_work + bs;
168   v_pivots   = (int *) (multiplier + bs2);
169 
170   /* flops in while loop */
171   bslog = 2*bs*bs2;
172 
173   for ( i=0; i<n; i++ ) {
174     nz    = bi[i+1] - bi[i];
175     ajtmp = bj + bi[i];
176     for  ( j=0; j<nz; j++ ) {
177       PetscMemzero(rtmp+bs2*ajtmp[j],bs2*sizeof(Scalar));
178     }
179     /* load in initial (unfactored row) */
180     nz       = ai[r[i]+1] - ai[r[i]];
181     ajtmpold = aj + ai[r[i]];
182     v        = aa + bs2*ai[r[i]];
183     for ( j=0; j<nz; j++ ) {
184       PetscMemcpy(rtmp+bs2*ic[ajtmpold[j]],v+bs2*j,bs2*sizeof(Scalar));
185     }
186     row = *ajtmp++;
187     while (row < i) {
188       pc = rtmp + bs2*row;
189 /*      if (*pc) { */
190         pv = ba + bs2*diag_offset[row];
191         pj = bj + diag_offset[row] + 1;
192         /*
193           BLgemm_("N","N",&bs,&bs,&bs,&one,pc,&bs,pv,&bs,&zero,
194                 multiplier,&bs);
195           PetscMemcpy(pc,multiplier,bs2*sizeof(Scalar));
196 	*/
197         Kernel_A_gets_A_times_B(bs,pc,pv,multiplier);
198         nz = bi[row+1] - diag_offset[row] - 1;
199         pv += bs2;
200         for (j=0; j<nz; j++) {
201           /*
202             BLgemm_("N","N",&bs,&bs,&bs,&mone,pc,&bs,pv+bs2*j,&bs,
203                     &one,rtmp+bs2*pj[j],&bs);
204 	  */
205           Kernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j);
206         }
207         PLogFlops(bslog*(nz+1)-bs);
208 /*      } */
209         row = *ajtmp++;
210     }
211     /* finished row so stick it into b->a */
212     pv = ba + bs2*bi[i];
213     pj = bj + bi[i];
214     nz = bi[i+1] - bi[i];
215     for ( j=0; j<nz; j++ ) {
216       PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(Scalar));
217     }
218     diag = diag_offset[i] - bi[i];
219     /* invert diagonal block */
220     w = pv + bs2*diag;
221     /*
222       ierr = Linpack_DGEFA(w,bs,v_pivots); CHKERRQ(ierr);
223       ierr = Linpack_DGEDI(w,bs,v_pivots,v_work); CHKERRQ(ierr);
224     */
225     Kernel_A_gets_inverse_A(bs,w,v_pivots,v_work);
226   }
227 
228   PetscFree(rtmp); PetscFree(v_work);
229   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
230   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
231   ierr = ISDestroy(isicol); CHKERRQ(ierr);
232   C->factor = FACTOR_LU;
233   C->assembled = PETSC_TRUE;
234   PLogFlops(1.3333*bs*bs2*b->mbs); /* from inverting diagonal blocks */
235   return 0;
236 }
237 /* ------------------------------------------------------------*/
238 /*
239       Version for when blocks are 5 by 5
240 */
241 int MatLUFactorNumeric_SeqBAIJ_5(Mat A,Mat *B)
242 {
243   Mat             C = *B;
244   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data,*b = (Mat_SeqBAIJ *)C->data;
245   IS              iscol = b->col, isrow = b->row, isicol;
246   int             *r,*ic, ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
247   int             *ajtmpold, *ajtmp, nz, row, v_pivots[5];
248   int             *diag_offset = b->diag,bs = 5,idx,*ai=a->i,*aj=a->j;
249   register Scalar *pv,*v,*rtmp,*pc,*w,*x;
250   Scalar          p1,p2,p3,p4,v_work[5],m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
251   Scalar          p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
252   Scalar          x17,x18,x19,x20,x21,x22,x23,x24,x25,p10,p11,p12,p13,p14;
253   Scalar          p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,m10,m11,m12;
254   Scalar          m13,m14,m15,m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
255   Scalar          *ba = b->a,*aa = a->a;
256   register int    *pj;
257 
258   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
259   PLogObjectParent(*B,isicol);
260   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
261   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
262   rtmp  = (Scalar *) PetscMalloc(25*(n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
263 
264   for ( i=0; i<n; i++ ) {
265     nz    = bi[i+1] - bi[i];
266     ajtmp = bj + bi[i];
267     for  ( j=0; j<nz; j++ ) {
268       x = rtmp+25*ajtmp[j];
269       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
270       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
271       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0;
272     }
273     /* load in initial (unfactored row) */
274     idx      = r[i];
275     nz       = ai[idx+1] - ai[idx];
276     ajtmpold = aj + ai[idx];
277     v        = aa + 25*ai[idx];
278     for ( j=0; j<nz; j++ ) {
279       x    = rtmp+25*ic[ajtmpold[j]];
280       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
281       x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
282       x[9] = v[9]; x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
283       x[14] = v[14]; x[15] = v[15]; x[16] = v[16]; x[17] = v[17];
284       x[18] = v[18]; x[19] = v[19]; x[20] = v[20]; x[21] = v[21];
285       x[22] = v[22]; x[23] = v[23]; x[24] = v[24];
286       v    += 25;
287     }
288     row = *ajtmp++;
289     while (row < i) {
290       pc = rtmp + 25*row;
291       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
292       p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
293       p10 = pc[9]; p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
294       p15 = pc[14]; p16 = pc[15]; p17 = pc[16]; p18 = pc[17]; p19 = pc[18];
295       p20 = pc[19]; p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
296       p25 = pc[24];
297       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
298           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
299           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
300           || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 ||
301           p20 != 0.0 || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 ||
302           p24 != 0.0 || p25 != 0.0) {
303         pv = ba + 25*diag_offset[row];
304         pj = bj + diag_offset[row] + 1;
305         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
306         x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
307         x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
308         x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17];
309         x19 = pv[18]; x20 = pv[19]; x21 = pv[20]; x22 = pv[21];
310         x23 = pv[22]; x24 = pv[23]; x25 = pv[24];
311         pc[0] = m1 = p1*x1 + p6*x2  + p11*x3 + p16*x4 + p21*x5;
312         pc[1] = m2 = p2*x1 + p7*x2  + p12*x3 + p17*x4 + p22*x5;
313         pc[2] = m3 = p3*x1 + p8*x2  + p13*x3 + p18*x4 + p23*x5;
314         pc[3] = m4 = p4*x1 + p9*x2  + p14*x3 + p19*x4 + p24*x5;
315         pc[4] = m5 = p5*x1 + p10*x2 + p15*x3 + p20*x4 + p25*x5;
316 
317         pc[5] = m6 = p1*x6 + p6*x7  + p11*x8 + p16*x9 + p21*x10;
318         pc[6] = m7 = p2*x6 + p7*x7  + p12*x8 + p17*x9 + p22*x10;
319         pc[7] = m8 = p3*x6 + p8*x7  + p13*x8 + p18*x9 + p23*x10;
320         pc[8] = m9 = p4*x6 + p9*x7  + p14*x8 + p19*x9 + p24*x10;
321         pc[9] = m10 = p5*x6 + p10*x7 + p15*x8 + p20*x9 + p25*x10;
322 
323         pc[10] = m11 = p1*x11 + p6*x12  + p11*x13 + p16*x14 + p21*x15;
324         pc[11] = m12 = p2*x11 + p7*x12  + p12*x13 + p17*x14 + p22*x15;
325         pc[12] = m13 = p3*x11 + p8*x12  + p13*x13 + p18*x14 + p23*x15;
326         pc[13] = m14 = p4*x11 + p9*x12  + p14*x13 + p19*x14 + p24*x15;
327         pc[14] = m15 = p5*x11 + p10*x12 + p15*x13 + p20*x14 + p25*x15;
328 
329         pc[15] = m16 = p1*x16 + p6*x17  + p11*x18 + p16*x19 + p21*x20;
330         pc[16] = m17 = p2*x16 + p7*x17  + p12*x18 + p17*x19 + p22*x20;
331         pc[17] = m18 = p3*x16 + p8*x17  + p13*x18 + p18*x19 + p23*x20;
332         pc[18] = m19 = p4*x16 + p9*x17  + p14*x18 + p19*x19 + p24*x20;
333         pc[19] = m20 = p5*x16 + p10*x17 + p15*x18 + p20*x19 + p25*x20;
334 
335         pc[20] = m21 = p1*x21 + p6*x22  + p11*x23 + p16*x24 + p21*x25;
336         pc[21] = m22 = p2*x21 + p7*x22  + p12*x23 + p17*x24 + p22*x25;
337         pc[22] = m23 = p3*x21 + p8*x22  + p13*x23 + p18*x24 + p23*x25;
338         pc[23] = m24 = p4*x21 + p9*x22  + p14*x23 + p19*x24 + p24*x25;
339         pc[24] = m25 = p5*x21 + p10*x22 + p15*x23 + p20*x24 + p25*x25;
340 
341         nz = bi[row+1] - diag_offset[row] - 1;
342         pv += 25;
343         for (j=0; j<nz; j++) {
344           x1   = pv[0];  x2 = pv[1];   x3  = pv[2];  x4  = pv[3];
345           x5   = pv[4];  x6 = pv[5];   x7  = pv[6];  x8  = pv[7]; x9 = pv[8];
346           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
347           x14  = pv[13]; x15 = pv[14]; x16 = pv[15]; x17 = pv[16];
348           x18  = pv[17]; x19 = pv[18]; x20 = pv[19]; x21 = pv[20];
349           x22  = pv[21]; x23 = pv[22]; x24 = pv[23]; x25 = pv[24];
350           x    = rtmp + 25*pj[j];
351           x[0] -= m1*x1 + m6*x2  + m11*x3 + m16*x4 + m21*x5;
352           x[1] -= m2*x1 + m7*x2  + m12*x3 + m17*x4 + m22*x5;
353           x[2] -= m3*x1 + m8*x2  + m13*x3 + m18*x4 + m23*x5;
354           x[3] -= m4*x1 + m9*x2  + m14*x3 + m19*x4 + m24*x5;
355           x[4] -= m5*x1 + m10*x2 + m15*x3 + m20*x4 + m25*x5;
356 
357           x[5] -= m1*x6 + m6*x7  + m11*x8 + m16*x9 + m21*x10;
358           x[6] -= m2*x6 + m7*x7  + m12*x8 + m17*x9 + m22*x10;
359           x[7] -= m3*x6 + m8*x7  + m13*x8 + m18*x9 + m23*x10;
360           x[8] -= m4*x6 + m9*x7  + m14*x8 + m19*x9 + m24*x10;
361           x[9] -= m5*x6 + m10*x7 + m15*x8 + m20*x9 + m25*x10;
362 
363           x[10] -= m1*x11 + m6*x12  + m11*x13 + m16*x14 + m21*x15;
364           x[11] -= m2*x11 + m7*x12  + m12*x13 + m17*x14 + m22*x15;
365           x[12] -= m3*x11 + m8*x12  + m13*x13 + m18*x14 + m23*x15;
366           x[13] -= m4*x11 + m9*x12  + m14*x13 + m19*x14 + m24*x15;
367           x[14] -= m5*x11 + m10*x12 + m15*x13 + m20*x14 + m25*x15;
368 
369           x[15] -= m1*x16 + m6*x17  + m11*x18 + m16*x19 + m21*x20;
370           x[16] -= m2*x16 + m7*x17  + m12*x18 + m17*x19 + m22*x20;
371           x[17] -= m3*x16 + m8*x17  + m13*x18 + m18*x19 + m23*x20;
372           x[18] -= m4*x16 + m9*x17  + m14*x18 + m19*x19 + m24*x20;
373           x[19] -= m5*x16 + m10*x17 + m15*x18 + m20*x19 + m25*x20;
374 
375           x[20] -= m1*x21 + m6*x22  + m11*x23 + m16*x24 + m21*x25;
376           x[21] -= m2*x21 + m7*x22  + m12*x23 + m17*x24 + m22*x25;
377           x[22] -= m3*x21 + m8*x22  + m13*x23 + m18*x24 + m23*x25;
378           x[23] -= m4*x21 + m9*x22  + m14*x23 + m19*x24 + m24*x25;
379           x[24] -= m5*x21 + m10*x22 + m15*x23 + m20*x24 + m25*x25;
380 
381           pv   += 25;
382         }
383         PLogFlops(250*nz+225);
384       }
385       row = *ajtmp++;
386     }
387     /* finished row so stick it into b->a */
388     pv = ba + 25*bi[i];
389     pj = bj + bi[i];
390     nz = bi[i+1] - bi[i];
391     for ( j=0; j<nz; j++ ) {
392       x     = rtmp+25*pj[j];
393       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
394       pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
395       pv[9] = x[9]; pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
396       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; pv[16] = x[16];
397       pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19]; pv[20] = x[20];
398       pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23]; pv[24] = x[24];
399       pv   += 25;
400     }
401     /* invert diagonal block */
402     w = ba + 25*diag_offset[i];
403     /*
404       ierr = Linpack_DGEFA(w,bs,v_pivots); CHKERRQ(ierr);
405       ierr = Linpack_DGEDI(w,bs,v_pivots,v_work); CHKERRQ(ierr);
406     */
407     Kernel_A_gets_inverse_A(bs,w,v_pivots,v_work);
408   }
409 
410   PetscFree(rtmp);
411   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
412   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
413   ierr = ISDestroy(isicol); CHKERRQ(ierr);
414   C->factor = FACTOR_LU;
415   C->assembled = PETSC_TRUE;
416   PLogFlops(1.3333*125*b->mbs); /* from inverting diagonal blocks */
417   return 0;
418 }
419 
420 /* ------------------------------------------------------------*/
421 /*
422       Version for when blocks are 4 by 4
423 */
424 int MatLUFactorNumeric_SeqBAIJ_4(Mat A,Mat *B)
425 {
426   Mat             C = *B;
427   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data,*b = (Mat_SeqBAIJ *)C->data;
428   IS              iscol = b->col, isrow = b->row, isicol;
429   int             *r,*ic, ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
430   int             *ajtmpold, *ajtmp, nz, row, v_pivots[4];
431   int             *diag_offset = b->diag,bs = 4,idx,*ai=a->i,*aj=a->j;
432   register Scalar *pv,*v,*rtmp,*pc,*w,*x;
433   Scalar          p1,p2,p3,p4,v_work[4],m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
434   Scalar          p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
435   Scalar          p10,p11,p12,p13,p14,p15,p16,m10,m11,m12;
436   Scalar          m13,m14,m15,m16;
437   Scalar          *ba = b->a,*aa = a->a;
438   register int    *pj;
439 
440   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
441   PLogObjectParent(*B,isicol);
442   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
443   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
444   rtmp  = (Scalar *) PetscMalloc(16*(n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
445 
446   for ( i=0; i<n; i++ ) {
447     nz    = bi[i+1] - bi[i];
448     ajtmp = bj + bi[i];
449     for  ( j=0; j<nz; j++ ) {
450       x = rtmp+16*ajtmp[j];
451       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
452       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
453     }
454     /* load in initial (unfactored row) */
455     idx      = r[i];
456     nz       = ai[idx+1] - ai[idx];
457     ajtmpold = aj + ai[idx];
458     v        = aa + 16*ai[idx];
459     for ( j=0; j<nz; j++ ) {
460       x    = rtmp+16*ic[ajtmpold[j]];
461       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
462       x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
463       x[9] = v[9]; x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
464       x[14] = v[14]; x[15] = v[15];
465       v    += 16;
466     }
467     row = *ajtmp++;
468     while (row < i) {
469       pc = rtmp + 16*row;
470       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
471       p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
472       p10 = pc[9]; p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
473       p15 = pc[14]; p16 = pc[15];
474       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
475           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
476           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
477           || p16 != 0.0) {
478         pv = ba + 16*diag_offset[row];
479         pj = bj + diag_offset[row] + 1;
480         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
481         x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
482         x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
483         x15 = pv[14]; x16 = pv[15];
484         pc[0] = m1 = p1*x1 + p5*x2  + p9*x3  + p13*x4;
485         pc[1] = m2 = p2*x1 + p6*x2  + p10*x3 + p14*x4;
486         pc[2] = m3 = p3*x1 + p7*x2  + p11*x3 + p15*x4;
487         pc[3] = m4 = p4*x1 + p8*x2  + p12*x3 + p16*x4;
488 
489         pc[4] = m5 = p1*x5 + p5*x6  + p9*x7  + p13*x8;
490         pc[5] = m6 = p2*x5 + p6*x6  + p10*x7 + p14*x8;
491         pc[6] = m7 = p3*x5 + p7*x6  + p11*x7 + p15*x8;
492         pc[7] = m8 = p4*x5 + p8*x6  + p12*x7 + p16*x8;
493 
494         pc[8]  = m9  = p1*x9 + p5*x10  + p9*x11  + p13*x12;
495         pc[9]  = m10 = p2*x9 + p6*x10  + p10*x11 + p14*x12;
496         pc[10] = m11 = p3*x9 + p7*x10  + p11*x11 + p15*x12;
497         pc[11] = m12 = p4*x9 + p8*x10  + p12*x11 + p16*x12;
498 
499         pc[12] = m13 = p1*x13 + p5*x14  + p9*x15  + p13*x16;
500         pc[13] = m14 = p2*x13 + p6*x14  + p10*x15 + p14*x16;
501         pc[14] = m15 = p3*x13 + p7*x14  + p11*x15 + p15*x16;
502         pc[15] = m16 = p4*x13 + p8*x14  + p12*x15 + p16*x16;
503 
504         nz = bi[row+1] - diag_offset[row] - 1;
505         pv += 16;
506         for (j=0; j<nz; j++) {
507           x1   = pv[0];  x2 = pv[1];   x3  = pv[2];  x4  = pv[3];
508           x5   = pv[4];  x6 = pv[5];   x7  = pv[6];  x8  = pv[7]; x9 = pv[8];
509           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
510           x14  = pv[13]; x15 = pv[14]; x16 = pv[15];
511           x    = rtmp + 16*pj[j];
512           x[0] -= m1*x1 + m5*x2  + m9*x3 + m13*x4;
513           x[1] -= m2*x1 + m6*x2  + m10*x3 + m14*x4;
514           x[2] -= m3*x1 + m7*x2  + m11*x3 + m15*x4;
515           x[3] -= m4*x1 + m8*x2  + m12*x3 + m16*x4;
516 
517           x[4] -= m1*x5 + m5*x6  + m9*x7  + m13*x8;
518           x[5] -= m2*x5 + m6*x6  + m10*x7 + m14*x8;
519           x[6] -= m3*x5 + m7*x6  + m11*x7 + m15*x8;
520           x[7] -= m4*x5 + m8*x6  + m12*x7 + m16*x8;
521 
522           x[8] -= m1*x9  + m5*x10  + m9*x11 + m13*x12;
523           x[9] -= m2*x9  + m6*x10  + m10*x11 + m14*x12;
524           x[10] -= m3*x9 + m7*x10  + m11*x11 + m15*x12;
525           x[11] -= m4*x9 + m8*x10  + m12*x11 + m16*x12;
526 
527           x[12] -= m1*x13 + m5*x14  + m9*x15 + m13*x16;
528           x[13] -= m2*x13 + m6*x14  + m10*x15 + m14*x16;
529           x[14] -= m3*x13 + m7*x14  + m11*x15 + m15*x16;
530           x[15] -= m4*x13 + m8*x14  + m12*x15 + m16*x16;
531 
532           pv   += 16;
533         }
534         PLogFlops(128*nz+112);
535       }
536       row = *ajtmp++;
537     }
538     /* finished row so stick it into b->a */
539     pv = ba + 16*bi[i];
540     pj = bj + bi[i];
541     nz = bi[i+1] - bi[i];
542     for ( j=0; j<nz; j++ ) {
543       x     = rtmp+16*pj[j];
544       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
545       pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
546       pv[9] = x[9]; pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
547       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
548       pv   += 16;
549     }
550     /* invert diagonal block */
551     w = ba + 16*diag_offset[i];
552     /*
553       ierr = Linpack_DGEFA(w,bs,v_pivots); CHKERRQ(ierr);
554       ierr = Linpack_DGEDI(w,bs,v_pivots,v_work); CHKERRQ(ierr);
555     */
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 int MatLUFactorNumeric_SeqBAIJ_3(Mat A,Mat *B)
573 {
574   Mat             C = *B;
575   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data,*b = (Mat_SeqBAIJ *)C->data;
576   IS              iscol = b->col, isrow = b->row, isicol;
577   int             *r,*ic, ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
578   int             *ajtmpold, *ajtmp, nz, row, v_pivots[3],*ai=a->i,*aj=a->j;
579   int             *diag_offset = b->diag,bs = 3,idx;
580   register Scalar *pv,*v,*rtmp,*pc,*w,*x;
581   Scalar          p1,p2,p3,p4,v_work[3],m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
582   Scalar          p5,p6,p7,p8,p9,x5,x6,x7,x8,x9;
583   Scalar          *ba = b->a,*aa = a->a;
584   register int    *pj;
585 
586   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
587   PLogObjectParent(*B,isicol);
588   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
589   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
590   rtmp  = (Scalar *) PetscMalloc(9*(n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
591 
592   for ( i=0; i<n; i++ ) {
593     nz    = bi[i+1] - bi[i];
594     ajtmp = bj + bi[i];
595     for  ( j=0; j<nz; j++ ) {
596       x = rtmp + 9*ajtmp[j];
597       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
598     }
599     /* load in initial (unfactored row) */
600     idx      = r[i];
601     nz       = ai[idx+1] - ai[idx];
602     ajtmpold = aj + ai[idx];
603     v        = aa + 9*ai[idx];
604     for ( j=0; j<nz; j++ ) {
605       x    = rtmp + 9*ic[ajtmpold[j]];
606       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
607       x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
608       v    += 9;
609     }
610     row = *ajtmp++;
611     while (row < i) {
612       pc = rtmp + 9*row;
613       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
614       p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
615       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
616           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0) {
617         pv = ba + 9*diag_offset[row];
618         pj = bj + diag_offset[row] + 1;
619         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
620         x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
621         pc[0] = m1 = p1*x1 + p4*x2 + p7*x3;
622         pc[1] = m2 = p2*x1 + p5*x2 + p8*x3;
623         pc[2] = m3 = p3*x1 + p6*x2 + p9*x3;
624 
625         pc[3] = m4 = p1*x4 + p4*x5 + p7*x6;
626         pc[4] = m5 = p2*x4 + p5*x5 + p8*x6;
627         pc[5] = m6 = p3*x4 + p6*x5 + p9*x6;
628 
629         pc[6] = m7 = p1*x7 + p4*x8 + p7*x9;
630         pc[7] = m8 = p2*x7 + p5*x8 + p8*x9;
631         pc[8] = m9 = p3*x7 + p6*x8 + p9*x9;
632         nz = bi[row+1] - diag_offset[row] - 1;
633         pv += 9;
634         for (j=0; j<nz; j++) {
635           x1   = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
636           x5   = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
637           x    = rtmp + 9*pj[j];
638           x[0] -= m1*x1 + m4*x2 + m7*x3;
639           x[1] -= m2*x1 + m5*x2 + m8*x3;
640           x[2] -= m3*x1 + m6*x2 + m9*x3;
641 
642           x[3] -= m1*x4 + m4*x5 + m7*x6;
643           x[4] -= m2*x4 + m5*x5 + m8*x6;
644           x[5] -= m3*x4 + m6*x5 + m9*x6;
645 
646           x[6] -= m1*x7 + m4*x8 + m7*x9;
647           x[7] -= m2*x7 + m5*x8 + m8*x9;
648           x[8] -= m3*x7 + m6*x8 + m9*x9;
649           pv   += 9;
650         }
651         PLogFlops(54*nz+36);
652       }
653       row = *ajtmp++;
654     }
655     /* finished row so stick it into b->a */
656     pv = ba + 9*bi[i];
657     pj = bj + bi[i];
658     nz = bi[i+1] - bi[i];
659     for ( j=0; j<nz; j++ ) {
660       x     = rtmp + 9*pj[j];
661       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
662       pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
663       pv   += 9;
664     }
665     /* invert diagonal block */
666     w = ba + 9*diag_offset[i];
667     ierr = Kernel_A_gets_inverse_A_3(w); CHKERRQ(ierr);
668     /* Kernel_A_gets_inverse_A(bs,w,v_pivots,v_work); */
669   }
670 
671   PetscFree(rtmp);
672   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
673   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
674   ierr = ISDestroy(isicol); CHKERRQ(ierr);
675   C->factor = FACTOR_LU;
676   C->assembled = PETSC_TRUE;
677   PLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */
678   return 0;
679 }
680 
681 /* ------------------------------------------------------------*/
682 /*
683       Version for when blocks are 2 by 2
684 */
685 int MatLUFactorNumeric_SeqBAIJ_2(Mat A,Mat *B)
686 {
687   Mat             C = *B;
688   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data,*b = (Mat_SeqBAIJ *)C->data;
689   IS              iscol = b->col, isrow = b->row, isicol;
690   int             *r,*ic, ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
691   int             *ajtmpold, *ajtmp, nz, row, v_pivots[2];
692   int             *diag_offset=b->diag,bs = 2,idx,*ai=a->i,*aj=a->j;
693   register Scalar *pv,*v,*rtmp,m1,m2,m3,m4,*pc,*w,*x,x1,x2,x3,x4;
694   Scalar          p1,p2,p3,p4,v_work[2];
695   Scalar          *ba = b->a,*aa = a->a;
696   register int    *pj;
697 
698   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
699   PLogObjectParent(*B,isicol);
700   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
701   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
702   rtmp  = (Scalar *) PetscMalloc(4*(n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
703 
704   for ( i=0; i<n; i++ ) {
705     nz    = bi[i+1] - bi[i];
706     ajtmp = bj + bi[i];
707     for  ( j=0; j<nz; j++ ) {
708       x = rtmp+4*ajtmp[j]; x[0] = x[1] = x[2] = x[3] = 0.0;
709     }
710     /* load in initial (unfactored row) */
711     idx      = r[i];
712     nz       = ai[idx+1] - ai[idx];
713     ajtmpold = aj + ai[idx];
714     v        = aa + 4*ai[idx];
715     for ( j=0; j<nz; j++ ) {
716       x    = rtmp+4*ic[ajtmpold[j]];
717       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
718       v    += 4;
719     }
720     row = *ajtmp++;
721     while (row < i) {
722       pc = rtmp + 4*row;
723       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
724       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0) {
725         pv = ba + 4*diag_offset[row];
726         pj = bj + diag_offset[row] + 1;
727         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
728         pc[0] = m1 = p1*x1 + p3*x2;
729         pc[1] = m2 = p2*x1 + p4*x2;
730         pc[2] = m3 = p1*x3 + p3*x4;
731         pc[3] = m4 = p2*x3 + p4*x4;
732         nz = bi[row+1] - diag_offset[row] - 1;
733         pv += 4;
734         for (j=0; j<nz; j++) {
735           x1   = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
736           x    = rtmp + 4*pj[j];
737           x[0] -= m1*x1 + m3*x2;
738           x[1] -= m2*x1 + m4*x2;
739           x[2] -= m1*x3 + m3*x4;
740           x[3] -= m2*x3 + m4*x4;
741           pv   += 4;
742         }
743         PLogFlops(16*nz+12);
744       }
745       row = *ajtmp++;
746     }
747     /* finished row so stick it into b->a */
748     pv = ba + 4*bi[i];
749     pj = bj + bi[i];
750     nz = bi[i+1] - bi[i];
751     for ( j=0; j<nz; j++ ) {
752       x     = rtmp+4*pj[j];
753       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
754       pv   += 4;
755     }
756     /* invert diagonal block */
757     w = ba + 4*diag_offset[i];
758     /*
759       ierr = Linpack_DGEFA(w,bs,v_pivots); CHKERRQ(ierr);
760       ierr = Linpack_DGEDI(w,bs,v_pivots,v_work); CHKERRQ(ierr);
761     */
762     Kernel_A_gets_inverse_A(bs,w,v_pivots,v_work);
763   }
764 
765   PetscFree(rtmp);
766   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
767   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
768   ierr = ISDestroy(isicol); CHKERRQ(ierr);
769   C->factor = FACTOR_LU;
770   C->assembled = PETSC_TRUE;
771   PLogFlops(1.3333*8*b->mbs); /* from inverting diagonal blocks */
772   return 0;
773 }
774 
775 /* ----------------------------------------------------------- */
776 /*
777      Version for when blocks are 1 by 1.
778 */
779 int MatLUFactorNumeric_SeqBAIJ_1(Mat A,Mat *B)
780 {
781   Mat             C = *B;
782   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data, *b = (Mat_SeqBAIJ *)C->data;
783   IS              iscol = b->col, isrow = b->row, isicol;
784   int             *r,*ic, ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
785   int             *ajtmpold, *ajtmp, nz, row,*ai = a->i,*aj = a->j;
786   int             *diag_offset = b->diag,diag;
787   register Scalar *pv,*v,*rtmp,multiplier,*pc;
788   Scalar          *ba = b->a,*aa = a->a;
789   register int    *pj;
790 
791   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
792   PLogObjectParent(*B,isicol);
793   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
794   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
795   rtmp  = (Scalar *) PetscMalloc((n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
796 
797   for ( i=0; i<n; i++ ) {
798     nz    = bi[i+1] - bi[i];
799     ajtmp = bj + bi[i];
800     for  ( j=0; j<nz; j++ ) rtmp[ajtmp[j]] = 0.0;
801 
802     /* load in initial (unfactored row) */
803     nz       = ai[r[i]+1] - ai[r[i]];
804     ajtmpold = aj + ai[r[i]];
805     v        = aa + ai[r[i]];
806     for ( j=0; j<nz; j++ ) rtmp[ic[ajtmpold[j]]] =  v[j];
807 
808     row = *ajtmp++;
809     while (row < i) {
810       pc = rtmp + row;
811       if (*pc != 0.0) {
812         pv         = ba + diag_offset[row];
813         pj         = bj + diag_offset[row] + 1;
814         multiplier = *pc * *pv++;
815         *pc        = multiplier;
816         nz         = bi[row+1] - diag_offset[row] - 1;
817         for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
818         PLogFlops(1+2*nz);
819       }
820       row = *ajtmp++;
821     }
822     /* finished row so stick it into b->a */
823     pv = ba + bi[i];
824     pj = bj + bi[i];
825     nz = bi[i+1] - bi[i];
826     for ( j=0; j<nz; j++ ) {pv[j] = rtmp[pj[j]];}
827     diag = diag_offset[i] - bi[i];
828     /* check pivot entry for current row */
829     if (pv[diag] == 0.0) {
830       SETERRQ(1,"MatLUFactorNumeric_SeqAIJ:Zero pivot");
831     }
832     pv[diag] = 1.0/pv[diag];
833   }
834 
835   PetscFree(rtmp);
836   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
837   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
838   ierr = ISDestroy(isicol); CHKERRQ(ierr);
839   C->factor    = FACTOR_LU;
840   C->assembled = PETSC_TRUE;
841   PLogFlops(b->n);
842   return 0;
843 }
844 
845 /* ----------------------------------------------------------- */
846 int MatLUFactor_SeqBAIJ(Mat A,IS row,IS col,double f)
847 {
848   Mat_SeqBAIJ *mat = (Mat_SeqBAIJ *) A->data;
849   int         ierr;
850   Mat         C;
851 
852   ierr = MatLUFactorSymbolic_SeqBAIJ(A,row,col,f,&C); CHKERRQ(ierr);
853   ierr = MatLUFactorNumeric(A,&C); CHKERRQ(ierr);
854 
855   /* free all the data structures from mat */
856   PetscFree(mat->a);
857   if (!mat->singlemalloc) {PetscFree(mat->i); PetscFree(mat->j);}
858   if (mat->diag) PetscFree(mat->diag);
859   if (mat->ilen) PetscFree(mat->ilen);
860   if (mat->imax) PetscFree(mat->imax);
861   if (mat->solve_work) PetscFree(mat->solve_work);
862   if (mat->mult_work) PetscFree(mat->mult_work);
863   PetscFree(mat);
864 
865   PetscMemcpy(A,C,sizeof(struct _Mat));
866   PetscHeaderDestroy(C);
867   return 0;
868 }
869 /* ----------------------------------------------------------- */
870 int MatSolve_SeqBAIJ_N(Mat A,Vec bb,Vec xx)
871 {
872   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
873   IS              iscol=a->col,isrow=a->row;
874   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j;
875   int             nz,bs=a->bs,bs2=a->bs2,_One=1;
876   Scalar          *xa,*ba,*aa=a->a,*sum,_DOne=1.0,_DMOne=-1.0,_DZero=0.0;
877   register Scalar *x,*b,*lsum,*tmp,*v;
878 
879   ierr = VecGetArray(bb,&ba); CHKERRQ(ierr); b = ba;
880   ierr = VecGetArray(xx,&xa); CHKERRQ(ierr); x = xa;
881   tmp  = a->solve_work;
882 
883   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
884   ierr = ISGetIndices(iscol,&c);CHKERRQ(ierr); c = c + (n-1);
885 
886   /* forward solve the lower triangular */
887   PetscMemcpy(tmp,b + bs*(*r++), bs*sizeof(Scalar));
888   for ( i=1; i<n; i++ ) {
889     v   = aa + bs2*ai[i];
890     vi  = aj + ai[i];
891     nz  = a->diag[i] - ai[i];
892     sum = tmp + bs*i;
893     PetscMemcpy(sum,b+bs*(*r++),bs*sizeof(Scalar));
894     while (nz--) {
895       LAgemv_("N",&bs,&bs,&_DMOne,v,&bs,tmp+bs*(*vi++),&_One,&_DOne,sum,&_One);
896       v += bs2;
897     }
898   }
899   /* backward solve the upper triangular */
900   lsum = a->solve_work + a->n;
901   for ( i=n-1; i>=0; i-- ){
902     v   = aa + bs2*(a->diag[i] + 1);
903     vi  = aj + a->diag[i] + 1;
904     nz  = ai[i+1] - a->diag[i] - 1;
905     PetscMemcpy(lsum,tmp+i*bs,bs*sizeof(Scalar));
906     while (nz--) {
907       LAgemv_("N",&bs,&bs,&_DMOne,v,&bs,tmp+bs*(*vi++),&_One,&_DOne,lsum,&_One);
908       v += bs2;
909     }
910     LAgemv_("N",&bs,&bs,&_DOne,aa+bs2*a->diag[i],&bs,lsum,&_One,&_DZero,
911                 tmp+i*bs,&_One);
912     PetscMemcpy(x + bs*(*c--),tmp+i*bs,bs*sizeof(Scalar));
913   }
914 
915   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
916   ierr = ISRestoreIndices(iscol,&c); CHKERRQ(ierr);
917   PLogFlops(2*(a->bs2)*(a->nz) - a->n);
918   return 0;
919 }
920 
921 int MatSolve_SeqBAIJ_5(Mat A,Vec bb,Vec xx)
922 {
923   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
924   IS              iscol=a->col,isrow=a->row;
925   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc;
926   Scalar          *xa,*ba,*aa=a->a,sum1,sum2,sum3,sum4,sum5,x1,x2,x3,x4,x5;
927   register Scalar *x,*b,*tmp,*v;
928 
929   ierr = VecGetArray(bb,&ba); CHKERRQ(ierr); b = ba;
930   ierr = VecGetArray(xx,&xa); CHKERRQ(ierr); x = xa;
931   tmp  = a->solve_work;
932 
933   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
934   ierr = ISGetIndices(iscol,&c);CHKERRQ(ierr); c = c + (n-1);
935 
936   /* forward solve the lower triangular */
937   idx    = 5*(*r++);
938   tmp[0] = b[idx];   tmp[1] = b[1+idx];
939   tmp[2] = b[2+idx]; tmp[3] = b[3+idx]; tmp[4] = b[4+idx];
940   for ( i=1; i<n; i++ ) {
941     v     = aa + 25*ai[i];
942     vi    = aj + ai[i];
943     nz    = a->diag[i] - ai[i];
944     idx   = 5*(*r++);
945     sum1  = b[idx];sum2 = b[1+idx];sum3 = b[2+idx];sum4 = b[3+idx];
946     sum5  = b[4+idx];
947     while (nz--) {
948       idx   = 5*(*vi++);
949       x1    = tmp[idx];  x2 = tmp[1+idx];x3 = tmp[2+idx];
950       x4    = tmp[3+idx];x5 = tmp[4+idx];
951       sum1 -= v[0]*x1 + v[5]*x2 + v[10]*x3 + v[15]*x4 + v[20]*x5;
952       sum2 -= v[1]*x1 + v[6]*x2 + v[11]*x3 + v[16]*x4 + v[21]*x5;
953       sum3 -= v[2]*x1 + v[7]*x2 + v[12]*x3 + v[17]*x4 + v[22]*x5;
954       sum4 -= v[3]*x1 + v[8]*x2 + v[13]*x3 + v[18]*x4 + v[23]*x5;
955       sum5 -= v[4]*x1 + v[9]*x2 + v[14]*x3 + v[19]*x4 + v[24]*x5;
956       v += 25;
957     }
958     idx = 5*i;
959     tmp[idx]   = sum1;tmp[1+idx] = sum2;
960     tmp[2+idx] = sum3;tmp[3+idx] = sum4; tmp[4+idx] = sum5;
961   }
962   /* backward solve the upper triangular */
963   for ( i=n-1; i>=0; i-- ){
964     v    = aa + 25*a->diag[i] + 25;
965     vi   = aj + a->diag[i] + 1;
966     nz   = ai[i+1] - a->diag[i] - 1;
967     idt  = 5*i;
968     sum1 = tmp[idt];  sum2 = tmp[1+idt];
969     sum3 = tmp[2+idt];sum4 = tmp[3+idt]; sum5 = tmp[4+idt];
970     while (nz--) {
971       idx   = 5*(*vi++);
972       x1    = tmp[idx];   x2 = tmp[1+idx];
973       x3    = tmp[2+idx]; x4 = tmp[3+idx]; x5 = tmp[4+idx];
974       sum1 -= v[0]*x1 + v[5]*x2 + v[10]*x3 + v[15]*x4 + v[20]*x5;
975       sum2 -= v[1]*x1 + v[6]*x2 + v[11]*x3 + v[16]*x4 + v[21]*x5;
976       sum3 -= v[2]*x1 + v[7]*x2 + v[12]*x3 + v[17]*x4 + v[22]*x5;
977       sum4 -= v[3]*x1 + v[8]*x2 + v[13]*x3 + v[18]*x4 + v[23]*x5;
978       sum5 -= v[4]*x1 + v[9]*x2 + v[14]*x3 + v[19]*x4 + v[24]*x5;
979       v += 25;
980     }
981     idc = 5*(*c--);
982     v   = aa + 25*a->diag[i];
983     x[idc]   = tmp[idt]   = v[0]*sum1+v[5]*sum2+v[10]*sum3+
984                                  v[15]*sum4+v[20]*sum5;
985     x[1+idc] = tmp[1+idt] = v[1]*sum1+v[6]*sum2+v[11]*sum3+
986                                  v[16]*sum4+v[21]*sum5;
987     x[2+idc] = tmp[2+idt] = v[2]*sum1+v[7]*sum2+v[12]*sum3+
988                                  v[17]*sum4+v[22]*sum5;
989     x[3+idc] = tmp[3+idt] = v[3]*sum1+v[8]*sum2+v[13]*sum3+
990                                  v[18]*sum4+v[23]*sum5;
991     x[4+idc] = tmp[4+idt] = v[4]*sum1+v[9]*sum2+v[14]*sum3+
992                                  v[19]*sum4+v[24]*sum5;
993   }
994 
995   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
996   ierr = ISRestoreIndices(iscol,&c); CHKERRQ(ierr);
997   PLogFlops(2*25*(a->nz) - a->n);
998   return 0;
999 }
1000 
1001 int MatSolve_SeqBAIJ_4(Mat A,Vec bb,Vec xx)
1002 {
1003   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
1004   IS              iscol=a->col,isrow=a->row;
1005   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc;
1006   Scalar          *xa,*ba,*aa=a->a,sum1,sum2,sum3,sum4,x1,x2,x3,x4;
1007   register Scalar *x,*b,*tmp,*v;
1008 
1009   ierr = VecGetArray(bb,&ba); CHKERRQ(ierr); b = ba;
1010   ierr = VecGetArray(xx,&xa); CHKERRQ(ierr); x = xa;
1011   tmp  = a->solve_work;
1012 
1013   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
1014   ierr = ISGetIndices(iscol,&c);CHKERRQ(ierr); c = c + (n-1);
1015 
1016   /* forward solve the lower triangular */
1017   idx    = 4*(*r++);
1018   tmp[0] = b[idx];   tmp[1] = b[1+idx];
1019   tmp[2] = b[2+idx]; tmp[3] = b[3+idx];
1020   for ( i=1; i<n; i++ ) {
1021     v     = aa + 16*ai[i];
1022     vi    = aj + ai[i];
1023     nz    = a->diag[i] - ai[i];
1024     idx   = 4*(*r++);
1025     sum1  = b[idx];sum2 = b[1+idx];sum3 = b[2+idx];sum4 = b[3+idx];
1026     while (nz--) {
1027       idx   = 4*(*vi++);
1028       x1    = tmp[idx];x2 = tmp[1+idx];x3 = tmp[2+idx];x4 = tmp[3+idx];
1029       sum1 -= v[0]*x1 + v[4]*x2 + v[8]*x3  + v[12]*x4;
1030       sum2 -= v[1]*x1 + v[5]*x2 + v[9]*x3  + v[13]*x4;
1031       sum3 -= v[2]*x1 + v[6]*x2 + v[10]*x3 + v[14]*x4;
1032       sum4 -= v[3]*x1 + v[7]*x2 + v[11]*x3 + v[15]*x4;
1033       v += 16;
1034     }
1035     idx = 4*i;
1036     tmp[idx]   = sum1;tmp[1+idx] = sum2;
1037     tmp[2+idx] = sum3;tmp[3+idx] = sum4;
1038   }
1039   /* backward solve the upper triangular */
1040   for ( i=n-1; i>=0; i-- ){
1041     v    = aa + 16*a->diag[i] + 16;
1042     vi   = aj + a->diag[i] + 1;
1043     nz   = ai[i+1] - a->diag[i] - 1;
1044     idt  = 4*i;
1045     sum1 = tmp[idt];  sum2 = tmp[1+idt];
1046     sum3 = tmp[2+idt];sum4 = tmp[3+idt];
1047     while (nz--) {
1048       idx   = 4*(*vi++);
1049       x1    = tmp[idx];   x2 = tmp[1+idx];
1050       x3    = tmp[2+idx]; x4 = tmp[3+idx];
1051       sum1 -= v[0]*x1 + v[4]*x2 + v[8]*x3   + v[12]*x4;
1052       sum2 -= v[1]*x1 + v[5]*x2 + v[9]*x3   + v[13]*x4;
1053       sum3 -= v[2]*x1 + v[6]*x2 + v[10]*x3  + v[14]*x4;
1054       sum4 -= v[3]*x1 + v[7]*x2 + v[11]*x3  + v[15]*x4;
1055       v += 16;
1056     }
1057     idc = 4*(*c--);
1058     v   = aa + 16*a->diag[i];
1059     x[idc]   = tmp[idt]   = v[0]*sum1+v[4]*sum2+v[8]*sum3+v[12]*sum4;
1060     x[1+idc] = tmp[1+idt] = v[1]*sum1+v[5]*sum2+v[9]*sum3+v[13]*sum4;
1061     x[2+idc] = tmp[2+idt] = v[2]*sum1+v[6]*sum2+v[10]*sum3+v[14]*sum4;
1062     x[3+idc] = tmp[3+idt] = v[3]*sum1+v[7]*sum2+v[11]*sum3+v[15]*sum4;
1063   }
1064 
1065   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
1066   ierr = ISRestoreIndices(iscol,&c); CHKERRQ(ierr);
1067   PLogFlops(2*16*(a->nz) - a->n);
1068   return 0;
1069 }
1070 
1071 
1072 int MatSolve_SeqBAIJ_3(Mat A,Vec bb,Vec xx)
1073 {
1074   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
1075   IS              iscol=a->col,isrow=a->row;
1076   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc;
1077   Scalar          *xa,*ba,*aa=a->a,sum1,sum2,sum3,x1,x2,x3;
1078   register Scalar *x,*b,*tmp,*v;
1079 
1080   ierr = VecGetArray(bb,&ba); CHKERRQ(ierr); b = ba;
1081   ierr = VecGetArray(xx,&xa); CHKERRQ(ierr); x = xa;
1082   tmp  = a->solve_work;
1083 
1084   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
1085   ierr = ISGetIndices(iscol,&c);CHKERRQ(ierr); c = c + (n-1);
1086 
1087   /* forward solve the lower triangular */
1088   idx    = 3*(*r++);
1089   tmp[0] = b[idx]; tmp[1] = b[1+idx]; tmp[2] = b[2+idx];
1090   for ( i=1; i<n; i++ ) {
1091     v     = aa + 9*ai[i];
1092     vi    = aj + ai[i];
1093     nz    = a->diag[i] - ai[i];
1094     idx   = 3*(*r++);
1095     sum1  = b[idx]; sum2 = b[1+idx]; sum3 = b[2+idx];
1096     while (nz--) {
1097       idx   = 3*(*vi++);
1098       x1    = tmp[idx]; x2 = tmp[1+idx]; x3 = tmp[2+idx];
1099       sum1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
1100       sum2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
1101       sum3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
1102       v += 9;
1103     }
1104     idx = 3*i;
1105     tmp[idx] = sum1; tmp[1+idx] = sum2; tmp[2+idx] = sum3;
1106   }
1107   /* backward solve the upper triangular */
1108   for ( i=n-1; i>=0; i-- ){
1109     v    = aa + 9*a->diag[i] + 9;
1110     vi   = aj + a->diag[i] + 1;
1111     nz   = ai[i+1] - a->diag[i] - 1;
1112     idt  = 3*i;
1113     sum1 = tmp[idt]; sum2 = tmp[1+idt]; sum3 = tmp[2+idt];
1114     while (nz--) {
1115       idx   = 3*(*vi++);
1116       x1    = tmp[idx]; x2 = tmp[1+idx]; x3 = tmp[2+idx];
1117       sum1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
1118       sum2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
1119       sum3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
1120       v += 9;
1121     }
1122     idc = 3*(*c--);
1123     v   = aa + 9*a->diag[i];
1124     x[idc]   = tmp[idt]   = v[0]*sum1 + v[3]*sum2 + v[6]*sum3;
1125     x[1+idc] = tmp[1+idt] = v[1]*sum1 + v[4]*sum2 + v[7]*sum3;
1126     x[2+idc] = tmp[2+idt] = v[2]*sum1 + v[5]*sum2 + v[8]*sum3;
1127   }
1128   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
1129   ierr = ISRestoreIndices(iscol,&c); CHKERRQ(ierr);
1130   PLogFlops(2*9*(a->nz) - a->n);
1131   return 0;
1132 }
1133 
1134 int MatSolve_SeqBAIJ_2(Mat A,Vec bb,Vec xx)
1135 {
1136   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
1137   IS              iscol=a->col,isrow=a->row;
1138   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc;
1139   Scalar          *xa,*ba,*aa=a->a,sum1,sum2,x1,x2;
1140   register Scalar *x,*b,*tmp,*v;
1141 
1142   ierr = VecGetArray(bb,&ba); CHKERRQ(ierr); b = ba;
1143   ierr = VecGetArray(xx,&xa); CHKERRQ(ierr); x = xa;
1144   tmp  = a->solve_work;
1145 
1146   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
1147   ierr = ISGetIndices(iscol,&c);CHKERRQ(ierr); c = c + (n-1);
1148 
1149   /* forward solve the lower triangular */
1150   idx    = 2*(*r++);
1151   tmp[0] = b[idx]; tmp[1] = b[1+idx];
1152   for ( i=1; i<n; i++ ) {
1153     v     = aa + 4*ai[i];
1154     vi    = aj + ai[i];
1155     nz    = a->diag[i] - ai[i];
1156     idx   = 2*(*r++);
1157     sum1  = b[idx]; sum2 = b[1+idx];
1158     while (nz--) {
1159       idx   = 2*(*vi++);
1160       x1    = tmp[idx]; x2 = tmp[1+idx];
1161       sum1 -= v[0]*x1 + v[2]*x2;
1162       sum2 -= v[1]*x1 + v[3]*x2;
1163       v += 4;
1164     }
1165     idx = 2*i;
1166     tmp[idx] = sum1; tmp[1+idx] = sum2;
1167   }
1168   /* backward solve the upper triangular */
1169   for ( i=n-1; i>=0; i-- ){
1170     v    = aa + 4*a->diag[i] + 4;
1171     vi   = aj + a->diag[i] + 1;
1172     nz   = ai[i+1] - a->diag[i] - 1;
1173     idt  = 2*i;
1174     sum1 = tmp[idt]; sum2 = tmp[1+idt];
1175     while (nz--) {
1176       idx   = 2*(*vi++);
1177       x1    = tmp[idx]; x2 = tmp[1+idx];
1178       sum1 -= v[0]*x1 + v[2]*x2;
1179       sum2 -= v[1]*x1 + v[3]*x2;
1180       v += 4;
1181     }
1182     idc = 2*(*c--);
1183     v   = aa + 4*a->diag[i];
1184     x[idc]   = tmp[idt]   = v[0]*sum1 + v[2]*sum2;
1185     x[1+idc] = tmp[1+idt] = v[1]*sum1 + v[3]*sum2;
1186   }
1187   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
1188   ierr = ISRestoreIndices(iscol,&c); CHKERRQ(ierr);
1189   PLogFlops(2*4*(a->nz) - a->n);
1190   return 0;
1191 }
1192 
1193 
1194 int MatSolve_SeqBAIJ_1(Mat A,Vec bb,Vec xx)
1195 {
1196   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
1197   IS              iscol=a->col,isrow=a->row;
1198   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz;
1199   Scalar          *xa,*ba,*aa=a->a,sum1;
1200   register Scalar *x,*b,*tmp,*v;
1201 
1202   ierr = VecGetArray(bb,&ba); CHKERRQ(ierr); b = ba;
1203   ierr = VecGetArray(xx,&xa); CHKERRQ(ierr); x = xa;
1204   tmp  = a->solve_work;
1205 
1206   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
1207   ierr = ISGetIndices(iscol,&c);CHKERRQ(ierr); c = c + (n-1);
1208 
1209   /* forward solve the lower triangular */
1210   tmp[0] = b[*r++];
1211   for ( i=1; i<n; i++ ) {
1212     v     = aa + ai[i];
1213     vi    = aj + ai[i];
1214     nz    = a->diag[i] - ai[i];
1215     sum1  = b[*r++];
1216     while (nz--) {
1217       sum1 -= (*v++)*tmp[*vi++];
1218     }
1219     tmp[i] = sum1;
1220   }
1221   /* backward solve the upper triangular */
1222   for ( i=n-1; i>=0; i-- ){
1223     v    = aa + a->diag[i] + 1;
1224     vi   = aj + a->diag[i] + 1;
1225     nz   = ai[i+1] - a->diag[i] - 1;
1226     sum1 = tmp[i];
1227     while (nz--) {
1228       sum1 -= (*v++)*tmp[*vi++];
1229     }
1230     x[*c--] = tmp[i] = aa[a->diag[i]]*sum1;
1231   }
1232 
1233   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
1234   ierr = ISRestoreIndices(iscol,&c); CHKERRQ(ierr);
1235   PLogFlops(2*1*(a->nz) - a->n);
1236   return 0;
1237 }
1238 
1239 /* ----------------------------------------------------------------*/
1240 /*
1241      This code is virtually identical to MatILUFactorSymbolic_SeqAIJ
1242    except that the data structure of Mat_SeqAIJ is slightly different.
1243    Not a good example of code reuse.
1244 */
1245 int MatILUFactorSymbolic_SeqBAIJ(Mat A,IS isrow,IS iscol,double f,int levels,
1246                                  Mat *fact)
1247 {
1248   Mat_SeqBAIJ *a = (Mat_SeqBAIJ *) A->data, *b;
1249   IS          isicol;
1250   int         *r,*ic, ierr, prow, n = a->mbs, *ai = a->i, *aj = a->j;
1251   int         *ainew,*ajnew, jmax,*fill, *xi, nz, *im,*ajfill,*flev;
1252   int         *dloc, idx, row,m,fm, nzf, nzi,len,  realloc = 0;
1253   int         incrlev,nnz,i,bs = a->bs,bs2 = a->bs2;
1254   PetscTruth  col_identity, row_identity;
1255 
1256   if (a->m != a->n) SETERRQ(1,"MatILUFactorSymbolic_SeqBAIJ:Matrix must be square");
1257   if (!isrow) SETERRQ(1,"MatILUFactorSymbolic_SeqBAIJ:Must have row permutation");
1258   if (!iscol) SETERRQ(1,"MatILUFactorSymbolic_SeqBAIJ:Must have column permutation");
1259 
1260   /* special case that simply copies fill pattern */
1261   ISIdentity(isrow,&row_identity); ISIdentity(iscol,&col_identity);
1262   if (levels == 0 && row_identity && col_identity) {
1263     ierr = MatConvertSameType_SeqBAIJ(A,fact,DO_NOT_COPY_VALUES); CHKERRQ(ierr);
1264     (*fact)->factor = FACTOR_LU;
1265     b               = (Mat_SeqBAIJ *) (*fact)->data;
1266     if (!b->diag) {
1267       ierr = MatMarkDiag_SeqBAIJ(*fact); CHKERRQ(ierr);
1268     }
1269     b->row        = isrow;
1270     b->col        = iscol;
1271     b->solve_work = (Scalar *) PetscMalloc((b->m+1+b->bs)*sizeof(Scalar));CHKPTRQ(b->solve_work);
1272     return 0;
1273   }
1274 
1275   ierr = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
1276   ierr = ISGetIndices(isrow,&r); CHKERRQ(ierr);
1277   ierr = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
1278 
1279   /* get new row pointers */
1280   ainew = (int *) PetscMalloc( (n+1)*sizeof(int) ); CHKPTRQ(ainew);
1281   ainew[0] = 0;
1282   /* don't know how many column pointers are needed so estimate */
1283   jmax = (int) (f*ai[n] + 1);
1284   ajnew = (int *) PetscMalloc( (jmax)*sizeof(int) ); CHKPTRQ(ajnew);
1285   /* ajfill is level of fill for each fill entry */
1286   ajfill = (int *) PetscMalloc( (jmax)*sizeof(int) ); CHKPTRQ(ajfill);
1287   /* fill is a linked list of nonzeros in active row */
1288   fill = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(fill);
1289   /* im is level for each filled value */
1290   im = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(im);
1291   /* dloc is location of diagonal in factor */
1292   dloc = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(dloc);
1293   dloc[0]  = 0;
1294   for ( prow=0; prow<n; prow++ ) {
1295     /* first copy previous fill into linked list */
1296     nzf     = nz  = ai[r[prow]+1] - ai[r[prow]];
1297     xi      = aj + ai[r[prow]];
1298     fill[n] = n;
1299     while (nz--) {
1300       fm  = n;
1301       idx = ic[*xi++];
1302       do {
1303         m  = fm;
1304         fm = fill[m];
1305       } while (fm < idx);
1306       fill[m]   = idx;
1307       fill[idx] = fm;
1308       im[idx]   = 0;
1309     }
1310     nzi = 0;
1311     row = fill[n];
1312     while ( row < prow ) {
1313       incrlev = im[row] + 1;
1314       nz      = dloc[row];
1315       xi      = ajnew  + ainew[row] + nz;
1316       flev    = ajfill + ainew[row] + nz + 1;
1317       nnz     = ainew[row+1] - ainew[row] - nz - 1;
1318       if (*xi++ != row) {
1319         SETERRQ(1,"MatILUFactorSymbolic_SeqBAIJ:zero pivot");
1320       }
1321       fm      = row;
1322       while (nnz-- > 0) {
1323         idx = *xi++;
1324         if (*flev + incrlev > levels) {
1325           flev++;
1326           continue;
1327         }
1328         do {
1329           m  = fm;
1330           fm = fill[m];
1331         } while (fm < idx);
1332         if (fm != idx) {
1333           im[idx]   = *flev + incrlev;
1334           fill[m]   = idx;
1335           fill[idx] = fm;
1336           fm        = idx;
1337           nzf++;
1338         }
1339         else {
1340           if (im[idx] > *flev + incrlev) im[idx] = *flev+incrlev;
1341         }
1342         flev++;
1343       }
1344       row = fill[row];
1345       nzi++;
1346     }
1347     /* copy new filled row into permanent storage */
1348     ainew[prow+1] = ainew[prow] + nzf;
1349     if (ainew[prow+1] > jmax) {
1350       /* allocate a longer ajnew */
1351       int maxadd;
1352       maxadd = (int) (((f*ai[n]+1)*(n-prow+5))/n);
1353       if (maxadd < nzf) maxadd = (n-prow)*(nzf+1);
1354       jmax += maxadd;
1355       xi = (int *) PetscMalloc( jmax*sizeof(int) );CHKPTRQ(xi);
1356       PetscMemcpy(xi,ajnew,ainew[prow]*sizeof(int));
1357       PetscFree(ajnew);
1358       ajnew = xi;
1359       /* allocate a longer ajfill */
1360       xi = (int *) PetscMalloc( jmax*sizeof(int) );CHKPTRQ(xi);
1361       PetscMemcpy(xi,ajfill,ainew[prow]*sizeof(int));
1362       PetscFree(ajfill);
1363       ajfill = xi;
1364       realloc++;
1365     }
1366     xi          = ajnew + ainew[prow];
1367     flev        = ajfill + ainew[prow];
1368     dloc[prow]  = nzi;
1369     fm          = fill[n];
1370     while (nzf--) {
1371       *xi++   = fm;
1372       *flev++ = im[fm];
1373       fm      = fill[fm];
1374     }
1375   }
1376   PetscFree(ajfill);
1377   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
1378   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
1379   ierr = ISDestroy(isicol); CHKERRQ(ierr);
1380   PetscFree(fill); PetscFree(im);
1381 
1382   PLogInfo(A,
1383     "Info:MatILUFactorSymbolic_SeqBAIJ:Realloc %d Fill ratio:given %g needed %g\n",
1384                              realloc,f,((double)ainew[n])/((double)ai[prow]));
1385 
1386   /* put together the new matrix */
1387   ierr = MatCreateSeqBAIJ(A->comm,bs,bs*n,bs*n,0,PETSC_NULL,fact);CHKERRQ(ierr);
1388   b = (Mat_SeqBAIJ *) (*fact)->data;
1389   PetscFree(b->imax);
1390   b->singlemalloc = 0;
1391   len = bs2*ainew[n]*sizeof(Scalar);
1392   /* the next line frees the default space generated by the Create() */
1393   PetscFree(b->a); PetscFree(b->ilen);
1394   b->a          = (Scalar *) PetscMalloc( len ); CHKPTRQ(b->a);
1395   b->j          = ajnew;
1396   b->i          = ainew;
1397   for ( i=0; i<n; i++ ) dloc[i] += ainew[i];
1398   b->diag       = dloc;
1399   b->ilen       = 0;
1400   b->imax       = 0;
1401   b->row        = isrow;
1402   b->col        = iscol;
1403   b->solve_work = (Scalar *) PetscMalloc( (bs*n+bs)*sizeof(Scalar));
1404   CHKPTRQ(b->solve_work);
1405   /* In b structure:  Free imax, ilen, old a, old j.
1406      Allocate dloc, solve_work, new a, new j */
1407   PLogObjectMemory(*fact,(ainew[n]-n)*(sizeof(int))+bs2*ainew[n]*sizeof(Scalar));
1408   b->maxnz          = b->nz = ainew[n];
1409   (*fact)->factor   = FACTOR_LU;
1410   return 0;
1411 }
1412 
1413 
1414 
1415 
1416