xref: /petsc/src/mat/impls/baij/seq/baijfact.c (revision 34cea2960b8f49dcd4d13b4c98b9c083dc8262fd)
1 #ifndef lint
2 static char vcid[] = "$Id: baijfact.c,v 1.31 1996/12/08 20:09:19 bsmith Exp balay $";
3 #endif
4 /*
5     Factorization code for BAIJ format.
6 */
7 
8 #include "src/mat/impls/baij/seq/baij.h"
9 #include "src/vec/vecimpl.h"
10 #include "src/inline/ilu.h"
11 
12 
13 /*
14     The symbolic factorization code is identical to that for AIJ format,
15   except for very small changes since this is now a SeqBAIJ datastructure.
16   NOT good code reuse.
17 */
18 #undef __FUNCTION__
19 #define __FUNCTION__ "MatLUFactorSymbolic_SeqBAIJ"
20 int MatLUFactorSymbolic_SeqBAIJ(Mat A,IS isrow,IS iscol,double f,Mat *B)
21 {
22   Mat_SeqBAIJ *a = (Mat_SeqBAIJ *) A->data, *b;
23   IS          isicol;
24   int         *r,*ic, ierr, i, n = a->mbs, *ai = a->i, *aj = a->j;
25   int         *ainew,*ajnew, jmax,*fill, *ajtmp, nz, bs = a->bs, bs2=a->bs2;
26   int         *idnew, idx, row,m,fm, nnz, nzi,realloc = 0,nzbd,*im;
27 
28   PetscValidHeaderSpecific(isrow,IS_COOKIE);
29   PetscValidHeaderSpecific(iscol,IS_COOKIE);
30   ierr = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
31   ISGetIndices(isrow,&r); ISGetIndices(isicol,&ic);
32 
33   /* get new row pointers */
34   ainew = (int *) PetscMalloc( (n+1)*sizeof(int) ); CHKPTRQ(ainew);
35   ainew[0] = 0;
36   /* don't know how many column pointers are needed so estimate */
37   jmax = (int) (f*ai[n] + 1);
38   ajnew = (int *) PetscMalloc( (jmax)*sizeof(int) ); CHKPTRQ(ajnew);
39   /* fill is a linked list of nonzeros in active row */
40   fill = (int *) PetscMalloc( (2*n+1)*sizeof(int)); CHKPTRQ(fill);
41   im = fill + n + 1;
42   /* idnew is location of diagonal in factor */
43   idnew = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(idnew);
44   idnew[0] = 0;
45 
46   for ( i=0; i<n; i++ ) {
47     /* first copy previous fill into linked list */
48     nnz     = nz    = ai[r[i]+1] - ai[r[i]];
49     ajtmp   = aj + ai[r[i]];
50     fill[n] = n;
51     while (nz--) {
52       fm  = n;
53       idx = ic[*ajtmp++];
54       do {
55         m  = fm;
56         fm = fill[m];
57       } while (fm < idx);
58       fill[m]   = idx;
59       fill[idx] = fm;
60     }
61     row = fill[n];
62     while ( row < i ) {
63       ajtmp = ajnew + idnew[row] + 1;
64       nzbd  = 1 + idnew[row] - ainew[row];
65       nz    = im[row] - nzbd;
66       fm    = row;
67       while (nz-- > 0) {
68         idx = *ajtmp++;
69         nzbd++;
70         if (idx == i) im[row] = nzbd;
71         do {
72           m  = fm;
73           fm = fill[m];
74         } while (fm < idx);
75         if (fm != idx) {
76           fill[m]   = idx;
77           fill[idx] = fm;
78           fm        = idx;
79           nnz++;
80         }
81       }
82       row = fill[row];
83     }
84     /* copy new filled row into permanent storage */
85     ainew[i+1] = ainew[i] + nnz;
86     if (ainew[i+1] > jmax) {
87       /* allocate a longer ajnew */
88       int maxadd;
89       maxadd = (int) ((f*(ai[n]+1)*(n-i+5))/n);
90       if (maxadd < nnz) maxadd = (n-i)*(nnz+1);
91       jmax += maxadd;
92       ajtmp = (int *) PetscMalloc( jmax*sizeof(int) );CHKPTRQ(ajtmp);
93       PetscMemcpy(ajtmp,ajnew,ainew[i]*sizeof(int));
94       PetscFree(ajnew);
95       ajnew = ajtmp;
96       realloc++; /* count how many times we realloc */
97     }
98     ajtmp = ajnew + ainew[i];
99     fm    = fill[n];
100     nzi   = 0;
101     im[i] = nnz;
102     while (nnz--) {
103       if (fm < i) nzi++;
104       *ajtmp++ = fm;
105       fm       = fill[fm];
106     }
107     idnew[i] = ainew[i] + nzi;
108   }
109 
110   PLogInfo(A,
111     "Info:MatLUFactorSymbolic_SeqBAIJ:Reallocs %d Fill ratio:given %g needed %g\n",
112                              realloc,f,((double)ainew[n])/((double)ai[i]));
113 
114   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
115   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
116 
117   PetscFree(fill);
118 
119   /* put together the new matrix */
120   ierr = MatCreateSeqBAIJ(A->comm,bs,bs*n,bs*n,0,PETSC_NULL,B); CHKERRQ(ierr);
121   PLogObjectParent(*B,isicol);
122   ierr = ISDestroy(isicol); CHKERRQ(ierr);
123   b = (Mat_SeqBAIJ *) (*B)->data;
124   PetscFree(b->imax);
125   b->singlemalloc = 0;
126   /* the next line frees the default space generated by the Create() */
127   PetscFree(b->a); PetscFree(b->ilen);
128   b->a          = (Scalar *) PetscMalloc((ainew[n]+1)*sizeof(Scalar)*bs2);CHKPTRQ(b->a);
129   b->j          = ajnew;
130   b->i          = ainew;
131   b->diag       = idnew;
132   b->ilen       = 0;
133   b->imax       = 0;
134   b->row        = isrow;
135   b->col        = iscol;
136   b->solve_work = (Scalar *) PetscMalloc( (bs*n+bs)*sizeof(Scalar));
137   CHKPTRQ(b->solve_work);
138   /* In b structure:  Free imax, ilen, old a, old j.
139      Allocate idnew, solve_work, new a, new j */
140   PLogObjectMemory(*B,(ainew[n]-n)*(sizeof(int)+sizeof(Scalar)));
141   b->maxnz = b->nz = ainew[n];
142 
143   (*B)->info.factor_mallocs    = realloc;
144   (*B)->info.fill_ratio_given  = f;
145   (*B)->info.fill_ratio_needed = ((double)ainew[n])/((double)ai[i]);
146 
147   return 0;
148 }
149 
150 /* ----------------------------------------------------------- */
151 #undef __FUNCTION__
152 #define __FUNCTION__ "MatLUFactorNumeric_SeqBAIJ_N"
153 int MatLUFactorNumeric_SeqBAIJ_N(Mat A,Mat *B)
154 {
155   Mat             C = *B;
156   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data,*b = (Mat_SeqBAIJ *)C->data;
157   IS              iscol = b->col, isrow = b->row, isicol;
158   int             *r,*ic, ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
159   int             *ajtmpold, *ajtmp, nz, row, bslog,*ai=a->i,*aj=a->j;
160   int             *diag_offset=b->diag,diag,bs=a->bs,bs2 = bs*bs,*v_pivots;
161   Scalar          *ba = b->a,*aa = a->a;
162   register Scalar *pv,*v,*rtmp,*multiplier,*v_work,*pc,*w;
163   register int    *pj;
164 
165   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
166   PLogObjectParent(*B,isicol);
167   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
168   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
169   rtmp  = (Scalar *) PetscMalloc(bs2*(n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
170   PetscMemzero(rtmp,bs2*(n+1)*sizeof(Scalar));
171   /* generate work space needed by dense LU factorization */
172   v_work     = (Scalar *) PetscMalloc(bs*sizeof(int) + (bs+bs2)*sizeof(Scalar));
173                CHKPTRQ(v_work);
174   multiplier = v_work + bs;
175   v_pivots   = (int *) (multiplier + bs2);
176 
177   /* flops in while loop */
178   bslog = 2*bs*bs2;
179 
180   for ( i=0; i<n; i++ ) {
181     nz    = bi[i+1] - bi[i];
182     ajtmp = bj + bi[i];
183     for  ( j=0; j<nz; j++ ) {
184       PetscMemzero(rtmp+bs2*ajtmp[j],bs2*sizeof(Scalar));
185     }
186     /* load in initial (unfactored row) */
187     nz       = ai[r[i]+1] - ai[r[i]];
188     ajtmpold = aj + ai[r[i]];
189     v        = aa + bs2*ai[r[i]];
190     for ( j=0; j<nz; j++ ) {
191       PetscMemcpy(rtmp+bs2*ic[ajtmpold[j]],v+bs2*j,bs2*sizeof(Scalar));
192     }
193     row = *ajtmp++;
194     while (row < i) {
195       pc = rtmp + bs2*row;
196 /*      if (*pc) { */
197         pv = ba + bs2*diag_offset[row];
198         pj = bj + diag_offset[row] + 1;
199         Kernel_A_gets_A_times_B(bs,pc,pv,multiplier);
200         nz = bi[row+1] - diag_offset[row] - 1;
201         pv += bs2;
202         for (j=0; j<nz; j++) {
203           Kernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j);
204         }
205         PLogFlops(bslog*(nz+1)-bs);
206 /*      } */
207         row = *ajtmp++;
208     }
209     /* finished row so stick it into b->a */
210     pv = ba + bs2*bi[i];
211     pj = bj + bi[i];
212     nz = bi[i+1] - bi[i];
213     for ( j=0; j<nz; j++ ) {
214       PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(Scalar));
215     }
216     diag = diag_offset[i] - bi[i];
217     /* invert diagonal block */
218     w = pv + bs2*diag;
219     Kernel_A_gets_inverse_A(bs,w,v_pivots,v_work);
220   }
221 
222   PetscFree(rtmp); PetscFree(v_work);
223   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
224   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
225   ierr = ISDestroy(isicol); CHKERRQ(ierr);
226   C->factor = FACTOR_LU;
227   C->assembled = PETSC_TRUE;
228   PLogFlops(1.3333*bs*bs2*b->mbs); /* from inverting diagonal blocks */
229   return 0;
230 }
231 /* ------------------------------------------------------------*/
232 /*
233       Version for when blocks are 5 by 5
234 */
235 #undef __FUNCTION__
236 #define __FUNCTION__ "MatLUFactorNumeric_SeqBAIJ_5"
237 int MatLUFactorNumeric_SeqBAIJ_5(Mat A,Mat *B)
238 {
239   Mat             C = *B;
240   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data,*b = (Mat_SeqBAIJ *)C->data;
241   IS              iscol = b->col, isrow = b->row, isicol;
242   int             *r,*ic, ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
243   int             *ajtmpold, *ajtmp, nz, row, v_pivots[5];
244   int             *diag_offset = b->diag,bs = 5,idx,*ai=a->i,*aj=a->j;
245   register Scalar *pv,*v,*rtmp,*pc,*w,*x;
246   Scalar          p1,p2,p3,p4,v_work[5],m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
247   Scalar          p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
248   Scalar          x17,x18,x19,x20,x21,x22,x23,x24,x25,p10,p11,p12,p13,p14;
249   Scalar          p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,m10,m11,m12;
250   Scalar          m13,m14,m15,m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
251   Scalar          *ba = b->a,*aa = a->a;
252   register int    *pj;
253 
254   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
255   PLogObjectParent(*B,isicol);
256   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
257   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
258   rtmp  = (Scalar *) PetscMalloc(25*(n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
259 
260   for ( i=0; i<n; i++ ) {
261     nz    = bi[i+1] - bi[i];
262     ajtmp = bj + bi[i];
263     for  ( j=0; j<nz; j++ ) {
264       x = rtmp+25*ajtmp[j];
265       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
266       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
267       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0;
268     }
269     /* load in initial (unfactored row) */
270     idx      = r[i];
271     nz       = ai[idx+1] - ai[idx];
272     ajtmpold = aj + ai[idx];
273     v        = aa + 25*ai[idx];
274     for ( j=0; j<nz; j++ ) {
275       x    = rtmp+25*ic[ajtmpold[j]];
276       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
277       x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
278       x[9] = v[9]; x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
279       x[14] = v[14]; x[15] = v[15]; x[16] = v[16]; x[17] = v[17];
280       x[18] = v[18]; x[19] = v[19]; x[20] = v[20]; x[21] = v[21];
281       x[22] = v[22]; x[23] = v[23]; x[24] = v[24];
282       v    += 25;
283     }
284     row = *ajtmp++;
285     while (row < i) {
286       pc = rtmp + 25*row;
287       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
288       p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
289       p10 = pc[9]; p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
290       p15 = pc[14]; p16 = pc[15]; p17 = pc[16]; p18 = pc[17]; p19 = pc[18];
291       p20 = pc[19]; p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
292       p25 = pc[24];
293       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
294           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
295           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
296           || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 ||
297           p20 != 0.0 || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 ||
298           p24 != 0.0 || p25 != 0.0) {
299         pv = ba + 25*diag_offset[row];
300         pj = bj + diag_offset[row] + 1;
301         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
302         x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
303         x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
304         x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17];
305         x19 = pv[18]; x20 = pv[19]; x21 = pv[20]; x22 = pv[21];
306         x23 = pv[22]; x24 = pv[23]; x25 = pv[24];
307         pc[0] = m1 = p1*x1 + p6*x2  + p11*x3 + p16*x4 + p21*x5;
308         pc[1] = m2 = p2*x1 + p7*x2  + p12*x3 + p17*x4 + p22*x5;
309         pc[2] = m3 = p3*x1 + p8*x2  + p13*x3 + p18*x4 + p23*x5;
310         pc[3] = m4 = p4*x1 + p9*x2  + p14*x3 + p19*x4 + p24*x5;
311         pc[4] = m5 = p5*x1 + p10*x2 + p15*x3 + p20*x4 + p25*x5;
312 
313         pc[5] = m6 = p1*x6 + p6*x7  + p11*x8 + p16*x9 + p21*x10;
314         pc[6] = m7 = p2*x6 + p7*x7  + p12*x8 + p17*x9 + p22*x10;
315         pc[7] = m8 = p3*x6 + p8*x7  + p13*x8 + p18*x9 + p23*x10;
316         pc[8] = m9 = p4*x6 + p9*x7  + p14*x8 + p19*x9 + p24*x10;
317         pc[9] = m10 = p5*x6 + p10*x7 + p15*x8 + p20*x9 + p25*x10;
318 
319         pc[10] = m11 = p1*x11 + p6*x12  + p11*x13 + p16*x14 + p21*x15;
320         pc[11] = m12 = p2*x11 + p7*x12  + p12*x13 + p17*x14 + p22*x15;
321         pc[12] = m13 = p3*x11 + p8*x12  + p13*x13 + p18*x14 + p23*x15;
322         pc[13] = m14 = p4*x11 + p9*x12  + p14*x13 + p19*x14 + p24*x15;
323         pc[14] = m15 = p5*x11 + p10*x12 + p15*x13 + p20*x14 + p25*x15;
324 
325         pc[15] = m16 = p1*x16 + p6*x17  + p11*x18 + p16*x19 + p21*x20;
326         pc[16] = m17 = p2*x16 + p7*x17  + p12*x18 + p17*x19 + p22*x20;
327         pc[17] = m18 = p3*x16 + p8*x17  + p13*x18 + p18*x19 + p23*x20;
328         pc[18] = m19 = p4*x16 + p9*x17  + p14*x18 + p19*x19 + p24*x20;
329         pc[19] = m20 = p5*x16 + p10*x17 + p15*x18 + p20*x19 + p25*x20;
330 
331         pc[20] = m21 = p1*x21 + p6*x22  + p11*x23 + p16*x24 + p21*x25;
332         pc[21] = m22 = p2*x21 + p7*x22  + p12*x23 + p17*x24 + p22*x25;
333         pc[22] = m23 = p3*x21 + p8*x22  + p13*x23 + p18*x24 + p23*x25;
334         pc[23] = m24 = p4*x21 + p9*x22  + p14*x23 + p19*x24 + p24*x25;
335         pc[24] = m25 = p5*x21 + p10*x22 + p15*x23 + p20*x24 + p25*x25;
336 
337         nz = bi[row+1] - diag_offset[row] - 1;
338         pv += 25;
339         for (j=0; j<nz; j++) {
340           x1   = pv[0];  x2 = pv[1];   x3  = pv[2];  x4  = pv[3];
341           x5   = pv[4];  x6 = pv[5];   x7  = pv[6];  x8  = pv[7]; x9 = pv[8];
342           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
343           x14  = pv[13]; x15 = pv[14]; x16 = pv[15]; x17 = pv[16];
344           x18  = pv[17]; x19 = pv[18]; x20 = pv[19]; x21 = pv[20];
345           x22  = pv[21]; x23 = pv[22]; x24 = pv[23]; x25 = pv[24];
346           x    = rtmp + 25*pj[j];
347           x[0] -= m1*x1 + m6*x2  + m11*x3 + m16*x4 + m21*x5;
348           x[1] -= m2*x1 + m7*x2  + m12*x3 + m17*x4 + m22*x5;
349           x[2] -= m3*x1 + m8*x2  + m13*x3 + m18*x4 + m23*x5;
350           x[3] -= m4*x1 + m9*x2  + m14*x3 + m19*x4 + m24*x5;
351           x[4] -= m5*x1 + m10*x2 + m15*x3 + m20*x4 + m25*x5;
352 
353           x[5] -= m1*x6 + m6*x7  + m11*x8 + m16*x9 + m21*x10;
354           x[6] -= m2*x6 + m7*x7  + m12*x8 + m17*x9 + m22*x10;
355           x[7] -= m3*x6 + m8*x7  + m13*x8 + m18*x9 + m23*x10;
356           x[8] -= m4*x6 + m9*x7  + m14*x8 + m19*x9 + m24*x10;
357           x[9] -= m5*x6 + m10*x7 + m15*x8 + m20*x9 + m25*x10;
358 
359           x[10] -= m1*x11 + m6*x12  + m11*x13 + m16*x14 + m21*x15;
360           x[11] -= m2*x11 + m7*x12  + m12*x13 + m17*x14 + m22*x15;
361           x[12] -= m3*x11 + m8*x12  + m13*x13 + m18*x14 + m23*x15;
362           x[13] -= m4*x11 + m9*x12  + m14*x13 + m19*x14 + m24*x15;
363           x[14] -= m5*x11 + m10*x12 + m15*x13 + m20*x14 + m25*x15;
364 
365           x[15] -= m1*x16 + m6*x17  + m11*x18 + m16*x19 + m21*x20;
366           x[16] -= m2*x16 + m7*x17  + m12*x18 + m17*x19 + m22*x20;
367           x[17] -= m3*x16 + m8*x17  + m13*x18 + m18*x19 + m23*x20;
368           x[18] -= m4*x16 + m9*x17  + m14*x18 + m19*x19 + m24*x20;
369           x[19] -= m5*x16 + m10*x17 + m15*x18 + m20*x19 + m25*x20;
370 
371           x[20] -= m1*x21 + m6*x22  + m11*x23 + m16*x24 + m21*x25;
372           x[21] -= m2*x21 + m7*x22  + m12*x23 + m17*x24 + m22*x25;
373           x[22] -= m3*x21 + m8*x22  + m13*x23 + m18*x24 + m23*x25;
374           x[23] -= m4*x21 + m9*x22  + m14*x23 + m19*x24 + m24*x25;
375           x[24] -= m5*x21 + m10*x22 + m15*x23 + m20*x24 + m25*x25;
376 
377           pv   += 25;
378         }
379         PLogFlops(250*nz+225);
380       }
381       row = *ajtmp++;
382     }
383     /* finished row so stick it into b->a */
384     pv = ba + 25*bi[i];
385     pj = bj + bi[i];
386     nz = bi[i+1] - bi[i];
387     for ( j=0; j<nz; j++ ) {
388       x     = rtmp+25*pj[j];
389       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
390       pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
391       pv[9] = x[9]; pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
392       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; pv[16] = x[16];
393       pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19]; pv[20] = x[20];
394       pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23]; pv[24] = x[24];
395       pv   += 25;
396     }
397     /* invert diagonal block */
398     w = ba + 25*diag_offset[i];
399     Kernel_A_gets_inverse_A(bs,w,v_pivots,v_work);
400   }
401 
402   PetscFree(rtmp);
403   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
404   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
405   ierr = ISDestroy(isicol); CHKERRQ(ierr);
406   C->factor = FACTOR_LU;
407   C->assembled = PETSC_TRUE;
408   PLogFlops(1.3333*125*b->mbs); /* from inverting diagonal blocks */
409   return 0;
410 }
411 
412 /* ------------------------------------------------------------*/
413 /*
414       Version for when blocks are 4 by 4
415 */
416 #undef __FUNCTION__
417 #define __FUNCTION__ "MatLUFactorNumeric_SeqBAIJ_4"
418 int MatLUFactorNumeric_SeqBAIJ_4(Mat A,Mat *B)
419 {
420   Mat             C = *B;
421   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data,*b = (Mat_SeqBAIJ *)C->data;
422   IS              iscol = b->col, isrow = b->row, isicol;
423   int             *r,*ic, ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
424   int             *ajtmpold, *ajtmp, nz, row, v_pivots[4];
425   int             *diag_offset = b->diag,bs = 4,idx,*ai=a->i,*aj=a->j;
426   register Scalar *pv,*v,*rtmp,*pc,*w,*x;
427   Scalar          p1,p2,p3,p4,v_work[4],m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
428   Scalar          p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
429   Scalar          p10,p11,p12,p13,p14,p15,p16,m10,m11,m12;
430   Scalar          m13,m14,m15,m16;
431   Scalar          *ba = b->a,*aa = a->a;
432   register int    *pj;
433 
434   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
435   PLogObjectParent(*B,isicol);
436   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
437   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
438   rtmp  = (Scalar *) PetscMalloc(16*(n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
439 
440   for ( i=0; i<n; i++ ) {
441     nz    = bi[i+1] - bi[i];
442     ajtmp = bj + bi[i];
443     for  ( j=0; j<nz; j++ ) {
444       x = rtmp+16*ajtmp[j];
445       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
446       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
447     }
448     /* load in initial (unfactored row) */
449     idx      = r[i];
450     nz       = ai[idx+1] - ai[idx];
451     ajtmpold = aj + ai[idx];
452     v        = aa + 16*ai[idx];
453     for ( j=0; j<nz; j++ ) {
454       x    = rtmp+16*ic[ajtmpold[j]];
455       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
456       x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
457       x[9] = v[9]; x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
458       x[14] = v[14]; x[15] = v[15];
459       v    += 16;
460     }
461     row = *ajtmp++;
462     while (row < i) {
463       pc = rtmp + 16*row;
464       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
465       p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
466       p10 = pc[9]; p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
467       p15 = pc[14]; p16 = pc[15];
468       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
469           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
470           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
471           || p16 != 0.0) {
472         pv = ba + 16*diag_offset[row];
473         pj = bj + diag_offset[row] + 1;
474         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
475         x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
476         x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
477         x15 = pv[14]; x16 = pv[15];
478         pc[0] = m1 = p1*x1 + p5*x2  + p9*x3  + p13*x4;
479         pc[1] = m2 = p2*x1 + p6*x2  + p10*x3 + p14*x4;
480         pc[2] = m3 = p3*x1 + p7*x2  + p11*x3 + p15*x4;
481         pc[3] = m4 = p4*x1 + p8*x2  + p12*x3 + p16*x4;
482 
483         pc[4] = m5 = p1*x5 + p5*x6  + p9*x7  + p13*x8;
484         pc[5] = m6 = p2*x5 + p6*x6  + p10*x7 + p14*x8;
485         pc[6] = m7 = p3*x5 + p7*x6  + p11*x7 + p15*x8;
486         pc[7] = m8 = p4*x5 + p8*x6  + p12*x7 + p16*x8;
487 
488         pc[8]  = m9  = p1*x9 + p5*x10  + p9*x11  + p13*x12;
489         pc[9]  = m10 = p2*x9 + p6*x10  + p10*x11 + p14*x12;
490         pc[10] = m11 = p3*x9 + p7*x10  + p11*x11 + p15*x12;
491         pc[11] = m12 = p4*x9 + p8*x10  + p12*x11 + p16*x12;
492 
493         pc[12] = m13 = p1*x13 + p5*x14  + p9*x15  + p13*x16;
494         pc[13] = m14 = p2*x13 + p6*x14  + p10*x15 + p14*x16;
495         pc[14] = m15 = p3*x13 + p7*x14  + p11*x15 + p15*x16;
496         pc[15] = m16 = p4*x13 + p8*x14  + p12*x15 + p16*x16;
497 
498         nz = bi[row+1] - diag_offset[row] - 1;
499         pv += 16;
500         for (j=0; j<nz; j++) {
501           x1   = pv[0];  x2 = pv[1];   x3  = pv[2];  x4  = pv[3];
502           x5   = pv[4];  x6 = pv[5];   x7  = pv[6];  x8  = pv[7]; x9 = pv[8];
503           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
504           x14  = pv[13]; x15 = pv[14]; x16 = pv[15];
505           x    = rtmp + 16*pj[j];
506           x[0] -= m1*x1 + m5*x2  + m9*x3 + m13*x4;
507           x[1] -= m2*x1 + m6*x2  + m10*x3 + m14*x4;
508           x[2] -= m3*x1 + m7*x2  + m11*x3 + m15*x4;
509           x[3] -= m4*x1 + m8*x2  + m12*x3 + m16*x4;
510 
511           x[4] -= m1*x5 + m5*x6  + m9*x7  + m13*x8;
512           x[5] -= m2*x5 + m6*x6  + m10*x7 + m14*x8;
513           x[6] -= m3*x5 + m7*x6  + m11*x7 + m15*x8;
514           x[7] -= m4*x5 + m8*x6  + m12*x7 + m16*x8;
515 
516           x[8] -= m1*x9  + m5*x10  + m9*x11 + m13*x12;
517           x[9] -= m2*x9  + m6*x10  + m10*x11 + m14*x12;
518           x[10] -= m3*x9 + m7*x10  + m11*x11 + m15*x12;
519           x[11] -= m4*x9 + m8*x10  + m12*x11 + m16*x12;
520 
521           x[12] -= m1*x13 + m5*x14  + m9*x15 + m13*x16;
522           x[13] -= m2*x13 + m6*x14  + m10*x15 + m14*x16;
523           x[14] -= m3*x13 + m7*x14  + m11*x15 + m15*x16;
524           x[15] -= m4*x13 + m8*x14  + m12*x15 + m16*x16;
525 
526           pv   += 16;
527         }
528         PLogFlops(128*nz+112);
529       }
530       row = *ajtmp++;
531     }
532     /* finished row so stick it into b->a */
533     pv = ba + 16*bi[i];
534     pj = bj + bi[i];
535     nz = bi[i+1] - bi[i];
536     for ( j=0; j<nz; j++ ) {
537       x     = rtmp+16*pj[j];
538       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
539       pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
540       pv[9] = x[9]; pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
541       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
542       pv   += 16;
543     }
544     /* invert diagonal block */
545     w = ba + 16*diag_offset[i];
546     Kernel_A_gets_inverse_A(bs,w,v_pivots,v_work);
547   }
548 
549   PetscFree(rtmp);
550   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
551   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
552   ierr = ISDestroy(isicol); CHKERRQ(ierr);
553   C->factor = FACTOR_LU;
554   C->assembled = PETSC_TRUE;
555   PLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */
556   return 0;
557 }
558 /* ------------------------------------------------------------*/
559 /*
560       Version for when blocks are 3 by 3
561 */
562 #undef __FUNCTION__
563 #define __FUNCTION__ "MatLUFactorNumeric_SeqBAIJ_3"
564 int MatLUFactorNumeric_SeqBAIJ_3(Mat A,Mat *B)
565 {
566   Mat             C = *B;
567   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data,*b = (Mat_SeqBAIJ *)C->data;
568   IS              iscol = b->col, isrow = b->row, isicol;
569   int             *r,*ic, ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
570   int             *ajtmpold, *ajtmp, nz, row, *ai=a->i,*aj=a->j;
571   int             *diag_offset = b->diag,idx;
572   register Scalar *pv,*v,*rtmp,*pc,*w,*x;
573   Scalar          p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
574   Scalar          p5,p6,p7,p8,p9,x5,x6,x7,x8,x9;
575   Scalar          *ba = b->a,*aa = a->a;
576   register int    *pj;
577 
578   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
579   PLogObjectParent(*B,isicol);
580   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
581   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
582   rtmp  = (Scalar *) PetscMalloc(9*(n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
583 
584   for ( i=0; i<n; i++ ) {
585     nz    = bi[i+1] - bi[i];
586     ajtmp = bj + bi[i];
587     for  ( j=0; j<nz; j++ ) {
588       x = rtmp + 9*ajtmp[j];
589       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
590     }
591     /* load in initial (unfactored row) */
592     idx      = r[i];
593     nz       = ai[idx+1] - ai[idx];
594     ajtmpold = aj + ai[idx];
595     v        = aa + 9*ai[idx];
596     for ( j=0; j<nz; j++ ) {
597       x    = rtmp + 9*ic[ajtmpold[j]];
598       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
599       x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
600       v    += 9;
601     }
602     row = *ajtmp++;
603     while (row < i) {
604       pc = rtmp + 9*row;
605       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
606       p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
607       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
608           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0) {
609         pv = ba + 9*diag_offset[row];
610         pj = bj + diag_offset[row] + 1;
611         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
612         x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
613         pc[0] = m1 = p1*x1 + p4*x2 + p7*x3;
614         pc[1] = m2 = p2*x1 + p5*x2 + p8*x3;
615         pc[2] = m3 = p3*x1 + p6*x2 + p9*x3;
616 
617         pc[3] = m4 = p1*x4 + p4*x5 + p7*x6;
618         pc[4] = m5 = p2*x4 + p5*x5 + p8*x6;
619         pc[5] = m6 = p3*x4 + p6*x5 + p9*x6;
620 
621         pc[6] = m7 = p1*x7 + p4*x8 + p7*x9;
622         pc[7] = m8 = p2*x7 + p5*x8 + p8*x9;
623         pc[8] = m9 = p3*x7 + p6*x8 + p9*x9;
624         nz = bi[row+1] - diag_offset[row] - 1;
625         pv += 9;
626         for (j=0; j<nz; j++) {
627           x1   = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
628           x5   = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
629           x    = rtmp + 9*pj[j];
630           x[0] -= m1*x1 + m4*x2 + m7*x3;
631           x[1] -= m2*x1 + m5*x2 + m8*x3;
632           x[2] -= m3*x1 + m6*x2 + m9*x3;
633 
634           x[3] -= m1*x4 + m4*x5 + m7*x6;
635           x[4] -= m2*x4 + m5*x5 + m8*x6;
636           x[5] -= m3*x4 + m6*x5 + m9*x6;
637 
638           x[6] -= m1*x7 + m4*x8 + m7*x9;
639           x[7] -= m2*x7 + m5*x8 + m8*x9;
640           x[8] -= m3*x7 + m6*x8 + m9*x9;
641           pv   += 9;
642         }
643         PLogFlops(54*nz+36);
644       }
645       row = *ajtmp++;
646     }
647     /* finished row so stick it into b->a */
648     pv = ba + 9*bi[i];
649     pj = bj + bi[i];
650     nz = bi[i+1] - bi[i];
651     for ( j=0; j<nz; j++ ) {
652       x     = rtmp + 9*pj[j];
653       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
654       pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
655       pv   += 9;
656     }
657     /* invert diagonal block */
658     w = ba + 9*diag_offset[i];
659     ierr = Kernel_A_gets_inverse_A_3(w); CHKERRQ(ierr);
660   }
661 
662   PetscFree(rtmp);
663   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
664   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
665   ierr = ISDestroy(isicol); CHKERRQ(ierr);
666   C->factor = FACTOR_LU;
667   C->assembled = PETSC_TRUE;
668   PLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */
669   return 0;
670 }
671 
672 /* ------------------------------------------------------------*/
673 /*
674       Version for when blocks are 2 by 2
675 */
676 #undef __FUNCTION__
677 #define __FUNCTION__ "MatLUFactorNumeric_SeqBAIJ_2"
678 int MatLUFactorNumeric_SeqBAIJ_2(Mat A,Mat *B)
679 {
680   Mat             C = *B;
681   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data,*b = (Mat_SeqBAIJ *)C->data;
682   IS              iscol = b->col, isrow = b->row, isicol;
683   int             *r,*ic, ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
684   int             *ajtmpold, *ajtmp, nz, row, v_pivots[2];
685   int             *diag_offset=b->diag,bs = 2,idx,*ai=a->i,*aj=a->j;
686   register Scalar *pv,*v,*rtmp,m1,m2,m3,m4,*pc,*w,*x,x1,x2,x3,x4;
687   Scalar          p1,p2,p3,p4,v_work[2];
688   Scalar          *ba = b->a,*aa = a->a;
689   register int    *pj;
690 
691   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
692   PLogObjectParent(*B,isicol);
693   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
694   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
695   rtmp  = (Scalar *) PetscMalloc(4*(n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
696 
697   for ( i=0; i<n; i++ ) {
698     nz    = bi[i+1] - bi[i];
699     ajtmp = bj + bi[i];
700     for  ( j=0; j<nz; j++ ) {
701       x = rtmp+4*ajtmp[j]; x[0] = x[1] = x[2] = x[3] = 0.0;
702     }
703     /* load in initial (unfactored row) */
704     idx      = r[i];
705     nz       = ai[idx+1] - ai[idx];
706     ajtmpold = aj + ai[idx];
707     v        = aa + 4*ai[idx];
708     for ( j=0; j<nz; j++ ) {
709       x    = rtmp+4*ic[ajtmpold[j]];
710       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
711       v    += 4;
712     }
713     row = *ajtmp++;
714     while (row < i) {
715       pc = rtmp + 4*row;
716       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
717       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0) {
718         pv = ba + 4*diag_offset[row];
719         pj = bj + diag_offset[row] + 1;
720         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
721         pc[0] = m1 = p1*x1 + p3*x2;
722         pc[1] = m2 = p2*x1 + p4*x2;
723         pc[2] = m3 = p1*x3 + p3*x4;
724         pc[3] = m4 = p2*x3 + p4*x4;
725         nz = bi[row+1] - diag_offset[row] - 1;
726         pv += 4;
727         for (j=0; j<nz; j++) {
728           x1   = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
729           x    = rtmp + 4*pj[j];
730           x[0] -= m1*x1 + m3*x2;
731           x[1] -= m2*x1 + m4*x2;
732           x[2] -= m1*x3 + m3*x4;
733           x[3] -= m2*x3 + m4*x4;
734           pv   += 4;
735         }
736         PLogFlops(16*nz+12);
737       }
738       row = *ajtmp++;
739     }
740     /* finished row so stick it into b->a */
741     pv = ba + 4*bi[i];
742     pj = bj + bi[i];
743     nz = bi[i+1] - bi[i];
744     for ( j=0; j<nz; j++ ) {
745       x     = rtmp+4*pj[j];
746       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
747       pv   += 4;
748     }
749     /* invert diagonal block */
750     w = ba + 4*diag_offset[i];
751     Kernel_A_gets_inverse_A(bs,w,v_pivots,v_work);
752   }
753 
754   PetscFree(rtmp);
755   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
756   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
757   ierr = ISDestroy(isicol); CHKERRQ(ierr);
758   C->factor = FACTOR_LU;
759   C->assembled = PETSC_TRUE;
760   PLogFlops(1.3333*8*b->mbs); /* from inverting diagonal blocks */
761   return 0;
762 }
763 
764 /* ----------------------------------------------------------- */
765 /*
766      Version for when blocks are 1 by 1.
767 */
768 #undef __FUNCTION__
769 #define __FUNCTION__ "MatLUFactorNumeric_SeqBAIJ_1"
770 int MatLUFactorNumeric_SeqBAIJ_1(Mat A,Mat *B)
771 {
772   Mat             C = *B;
773   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data, *b = (Mat_SeqBAIJ *)C->data;
774   IS              iscol = b->col, isrow = b->row, isicol;
775   int             *r,*ic, ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
776   int             *ajtmpold, *ajtmp, nz, row,*ai = a->i,*aj = a->j;
777   int             *diag_offset = b->diag,diag;
778   register Scalar *pv,*v,*rtmp,multiplier,*pc;
779   Scalar          *ba = b->a,*aa = a->a;
780   register int    *pj;
781 
782   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
783   PLogObjectParent(*B,isicol);
784   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
785   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
786   rtmp  = (Scalar *) PetscMalloc((n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
787 
788   for ( i=0; i<n; i++ ) {
789     nz    = bi[i+1] - bi[i];
790     ajtmp = bj + bi[i];
791     for  ( j=0; j<nz; j++ ) rtmp[ajtmp[j]] = 0.0;
792 
793     /* load in initial (unfactored row) */
794     nz       = ai[r[i]+1] - ai[r[i]];
795     ajtmpold = aj + ai[r[i]];
796     v        = aa + ai[r[i]];
797     for ( j=0; j<nz; j++ ) rtmp[ic[ajtmpold[j]]] =  v[j];
798 
799     row = *ajtmp++;
800     while (row < i) {
801       pc = rtmp + row;
802       if (*pc != 0.0) {
803         pv         = ba + diag_offset[row];
804         pj         = bj + diag_offset[row] + 1;
805         multiplier = *pc * *pv++;
806         *pc        = multiplier;
807         nz         = bi[row+1] - diag_offset[row] - 1;
808         for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
809         PLogFlops(1+2*nz);
810       }
811       row = *ajtmp++;
812     }
813     /* finished row so stick it into b->a */
814     pv = ba + bi[i];
815     pj = bj + bi[i];
816     nz = bi[i+1] - bi[i];
817     for ( j=0; j<nz; j++ ) {pv[j] = rtmp[pj[j]];}
818     diag = diag_offset[i] - bi[i];
819     /* check pivot entry for current row */
820     if (pv[diag] == 0.0) {
821       SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,"MatLUFactorNumeric_SeqBAIJ_1:Zero pivot");
822     }
823     pv[diag] = 1.0/pv[diag];
824   }
825 
826   PetscFree(rtmp);
827   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
828   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
829   ierr = ISDestroy(isicol); CHKERRQ(ierr);
830   C->factor    = FACTOR_LU;
831   C->assembled = PETSC_TRUE;
832   PLogFlops(b->n);
833   return 0;
834 }
835 
836 /* ----------------------------------------------------------- */
837 #undef __FUNCTION__
838 #define __FUNCTION__ "MatLUFactor_SeqBAIJ"
839 int MatLUFactor_SeqBAIJ(Mat A,IS row,IS col,double f)
840 {
841   Mat_SeqBAIJ *mat = (Mat_SeqBAIJ *) A->data;
842   int         ierr;
843   Mat         C;
844 
845   ierr = MatLUFactorSymbolic_SeqBAIJ(A,row,col,f,&C); CHKERRQ(ierr);
846   ierr = MatLUFactorNumeric(A,&C); CHKERRQ(ierr);
847 
848   /* free all the data structures from mat */
849   PetscFree(mat->a);
850   if (!mat->singlemalloc) {PetscFree(mat->i); PetscFree(mat->j);}
851   if (mat->diag) PetscFree(mat->diag);
852   if (mat->ilen) PetscFree(mat->ilen);
853   if (mat->imax) PetscFree(mat->imax);
854   if (mat->solve_work) PetscFree(mat->solve_work);
855   if (mat->mult_work) PetscFree(mat->mult_work);
856   PetscFree(mat);
857 
858   PetscMemcpy(A,C,sizeof(struct _Mat));
859   PetscHeaderDestroy(C);
860   return 0;
861 }
862 /* ----------------------------------------------------------- */
863 #undef __FUNCTION__
864 #define __FUNCTION__ "MatSolve_SeqBAIJ_N"
865 int MatSolve_SeqBAIJ_N(Mat A,Vec bb,Vec xx)
866 {
867   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
868   IS              iscol=a->col,isrow=a->row;
869   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j;
870   int             nz,bs=a->bs,bs2=a->bs2,*rout,*cout;
871   Scalar          *aa=a->a,*sum;
872   register Scalar *x,*b,*lsum,*tmp,*v;
873 
874   VecGetArray_Fast(bb,b);
875   VecGetArray_Fast(xx,x);
876   tmp  = a->solve_work;
877 
878   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
879   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
880 
881   /* forward solve the lower triangular */
882   PetscMemcpy(tmp,b + bs*(*r++), bs*sizeof(Scalar));
883   for ( i=1; i<n; i++ ) {
884     v   = aa + bs2*ai[i];
885     vi  = aj + ai[i];
886     nz  = a->diag[i] - ai[i];
887     sum = tmp + bs*i;
888     PetscMemcpy(sum,b+bs*(*r++),bs*sizeof(Scalar));
889     while (nz--) {
890       Kernel_v_gets_v_minus_A_times_w(bs,sum,v,tmp+bs*(*vi++));
891       v += bs2;
892     }
893   }
894   /* backward solve the upper triangular */
895   lsum = a->solve_work + a->n;
896   for ( i=n-1; i>=0; i-- ){
897     v   = aa + bs2*(a->diag[i] + 1);
898     vi  = aj + a->diag[i] + 1;
899     nz  = ai[i+1] - a->diag[i] - 1;
900     PetscMemcpy(lsum,tmp+i*bs,bs*sizeof(Scalar));
901     while (nz--) {
902       Kernel_v_gets_v_minus_A_times_w(bs,lsum,v,tmp+bs*(*vi++));
903       v += bs2;
904     }
905     Kernel_w_gets_A_times_v(bs,lsum,aa+bs2*a->diag[i],tmp+i*bs);
906     PetscMemcpy(x + bs*(*c--),tmp+i*bs,bs*sizeof(Scalar));
907   }
908 
909   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
910   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
911   VecRestoreArray_Fast(bb,b);
912   VecRestoreArray_Fast(xx,x);
913   PLogFlops(2*(a->bs2)*(a->nz) - a->n);
914   return 0;
915 }
916 
917 #undef __FUNCTION__
918 #define __FUNCTION__ "MatSolve_SeqBAIJ_5"
919 int MatSolve_SeqBAIJ_5(Mat A,Vec bb,Vec xx)
920 {
921   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
922   IS              iscol=a->col,isrow=a->row;
923   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout;
924   Scalar          *aa=a->a,sum1,sum2,sum3,sum4,sum5,x1,x2,x3,x4,x5;
925   register Scalar *x,*b,*tmp,*v;
926 
927   VecGetArray_Fast(bb,b);
928   VecGetArray_Fast(xx,x);
929   tmp  = a->solve_work;
930 
931   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
932   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
933 
934   /* forward solve the lower triangular */
935   idx    = 5*(*r++);
936   tmp[0] = b[idx];   tmp[1] = b[1+idx];
937   tmp[2] = b[2+idx]; tmp[3] = b[3+idx]; tmp[4] = b[4+idx];
938   for ( i=1; i<n; i++ ) {
939     v     = aa + 25*ai[i];
940     vi    = aj + ai[i];
941     nz    = a->diag[i] - ai[i];
942     idx   = 5*(*r++);
943     sum1  = b[idx];sum2 = b[1+idx];sum3 = b[2+idx];sum4 = b[3+idx];
944     sum5  = b[4+idx];
945     while (nz--) {
946       idx   = 5*(*vi++);
947       x1    = tmp[idx];  x2 = tmp[1+idx];x3 = tmp[2+idx];
948       x4    = tmp[3+idx];x5 = tmp[4+idx];
949       sum1 -= v[0]*x1 + v[5]*x2 + v[10]*x3 + v[15]*x4 + v[20]*x5;
950       sum2 -= v[1]*x1 + v[6]*x2 + v[11]*x3 + v[16]*x4 + v[21]*x5;
951       sum3 -= v[2]*x1 + v[7]*x2 + v[12]*x3 + v[17]*x4 + v[22]*x5;
952       sum4 -= v[3]*x1 + v[8]*x2 + v[13]*x3 + v[18]*x4 + v[23]*x5;
953       sum5 -= v[4]*x1 + v[9]*x2 + v[14]*x3 + v[19]*x4 + v[24]*x5;
954       v += 25;
955     }
956     idx = 5*i;
957     tmp[idx]   = sum1;tmp[1+idx] = sum2;
958     tmp[2+idx] = sum3;tmp[3+idx] = sum4; tmp[4+idx] = sum5;
959   }
960   /* backward solve the upper triangular */
961   for ( i=n-1; i>=0; i-- ){
962     v    = aa + 25*a->diag[i] + 25;
963     vi   = aj + a->diag[i] + 1;
964     nz   = ai[i+1] - a->diag[i] - 1;
965     idt  = 5*i;
966     sum1 = tmp[idt];  sum2 = tmp[1+idt];
967     sum3 = tmp[2+idt];sum4 = tmp[3+idt]; sum5 = tmp[4+idt];
968     while (nz--) {
969       idx   = 5*(*vi++);
970       x1    = tmp[idx];   x2 = tmp[1+idx];
971       x3    = tmp[2+idx]; x4 = tmp[3+idx]; x5 = tmp[4+idx];
972       sum1 -= v[0]*x1 + v[5]*x2 + v[10]*x3 + v[15]*x4 + v[20]*x5;
973       sum2 -= v[1]*x1 + v[6]*x2 + v[11]*x3 + v[16]*x4 + v[21]*x5;
974       sum3 -= v[2]*x1 + v[7]*x2 + v[12]*x3 + v[17]*x4 + v[22]*x5;
975       sum4 -= v[3]*x1 + v[8]*x2 + v[13]*x3 + v[18]*x4 + v[23]*x5;
976       sum5 -= v[4]*x1 + v[9]*x2 + v[14]*x3 + v[19]*x4 + v[24]*x5;
977       v += 25;
978     }
979     idc = 5*(*c--);
980     v   = aa + 25*a->diag[i];
981     x[idc]   = tmp[idt]   = v[0]*sum1+v[5]*sum2+v[10]*sum3+
982                                  v[15]*sum4+v[20]*sum5;
983     x[1+idc] = tmp[1+idt] = v[1]*sum1+v[6]*sum2+v[11]*sum3+
984                                  v[16]*sum4+v[21]*sum5;
985     x[2+idc] = tmp[2+idt] = v[2]*sum1+v[7]*sum2+v[12]*sum3+
986                                  v[17]*sum4+v[22]*sum5;
987     x[3+idc] = tmp[3+idt] = v[3]*sum1+v[8]*sum2+v[13]*sum3+
988                                  v[18]*sum4+v[23]*sum5;
989     x[4+idc] = tmp[4+idt] = v[4]*sum1+v[9]*sum2+v[14]*sum3+
990                                  v[19]*sum4+v[24]*sum5;
991   }
992 
993   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
994   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
995   VecRestoreArray_Fast(bb,b);
996   VecRestoreArray_Fast(xx,x);
997   PLogFlops(2*25*(a->nz) - a->n);
998   return 0;
999 }
1000 
1001 #undef __FUNCTION__
1002 #define __FUNCTION__ "MatSolve_SeqBAIJ_4"
1003 int MatSolve_SeqBAIJ_4(Mat A,Vec bb,Vec xx)
1004 {
1005   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
1006   IS              iscol=a->col,isrow=a->row;
1007   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout;
1008   Scalar          *aa=a->a,sum1,sum2,sum3,sum4,x1,x2,x3,x4;
1009   register Scalar *x,*b,*tmp,*v;
1010 
1011   VecGetArray_Fast(bb,b);
1012   VecGetArray_Fast(xx,x);
1013   tmp  = a->solve_work;
1014 
1015   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1016   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1017 
1018   /* forward solve the lower triangular */
1019   idx    = 4*(*r++);
1020   tmp[0] = b[idx];   tmp[1] = b[1+idx];
1021   tmp[2] = b[2+idx]; tmp[3] = b[3+idx];
1022   for ( i=1; i<n; i++ ) {
1023     v     = aa + 16*ai[i];
1024     vi    = aj + ai[i];
1025     nz    = a->diag[i] - ai[i];
1026     idx   = 4*(*r++);
1027     sum1  = b[idx];sum2 = b[1+idx];sum3 = b[2+idx];sum4 = b[3+idx];
1028     while (nz--) {
1029       idx   = 4*(*vi++);
1030       x1    = tmp[idx];x2 = tmp[1+idx];x3 = tmp[2+idx];x4 = tmp[3+idx];
1031       sum1 -= v[0]*x1 + v[4]*x2 + v[8]*x3  + v[12]*x4;
1032       sum2 -= v[1]*x1 + v[5]*x2 + v[9]*x3  + v[13]*x4;
1033       sum3 -= v[2]*x1 + v[6]*x2 + v[10]*x3 + v[14]*x4;
1034       sum4 -= v[3]*x1 + v[7]*x2 + v[11]*x3 + v[15]*x4;
1035       v += 16;
1036     }
1037     idx = 4*i;
1038     tmp[idx]   = sum1;tmp[1+idx] = sum2;
1039     tmp[2+idx] = sum3;tmp[3+idx] = sum4;
1040   }
1041   /* backward solve the upper triangular */
1042   for ( i=n-1; i>=0; i-- ){
1043     v    = aa + 16*a->diag[i] + 16;
1044     vi   = aj + a->diag[i] + 1;
1045     nz   = ai[i+1] - a->diag[i] - 1;
1046     idt  = 4*i;
1047     sum1 = tmp[idt];  sum2 = tmp[1+idt];
1048     sum3 = tmp[2+idt];sum4 = tmp[3+idt];
1049     while (nz--) {
1050       idx   = 4*(*vi++);
1051       x1    = tmp[idx];   x2 = tmp[1+idx];
1052       x3    = tmp[2+idx]; x4 = tmp[3+idx];
1053       sum1 -= v[0]*x1 + v[4]*x2 + v[8]*x3   + v[12]*x4;
1054       sum2 -= v[1]*x1 + v[5]*x2 + v[9]*x3   + v[13]*x4;
1055       sum3 -= v[2]*x1 + v[6]*x2 + v[10]*x3  + v[14]*x4;
1056       sum4 -= v[3]*x1 + v[7]*x2 + v[11]*x3  + v[15]*x4;
1057       v += 16;
1058     }
1059     idc = 4*(*c--);
1060     v   = aa + 16*a->diag[i];
1061     x[idc]   = tmp[idt]   = v[0]*sum1+v[4]*sum2+v[8]*sum3+v[12]*sum4;
1062     x[1+idc] = tmp[1+idt] = v[1]*sum1+v[5]*sum2+v[9]*sum3+v[13]*sum4;
1063     x[2+idc] = tmp[2+idt] = v[2]*sum1+v[6]*sum2+v[10]*sum3+v[14]*sum4;
1064     x[3+idc] = tmp[3+idt] = v[3]*sum1+v[7]*sum2+v[11]*sum3+v[15]*sum4;
1065   }
1066 
1067   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
1068   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
1069   VecRestoreArray_Fast(bb,b);
1070   VecRestoreArray_Fast(xx,x);
1071   PLogFlops(2*16*(a->nz) - a->n);
1072   return 0;
1073 }
1074 
1075 
1076 #undef __FUNCTION__
1077 #define __FUNCTION__ "MatSolve_SeqBAIJ_3"
1078 int MatSolve_SeqBAIJ_3(Mat A,Vec bb,Vec xx)
1079 {
1080   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
1081   IS              iscol=a->col,isrow=a->row;
1082   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout;
1083   Scalar          *aa=a->a,sum1,sum2,sum3,x1,x2,x3;
1084   register Scalar *x,*b,*tmp,*v;
1085 
1086   VecGetArray_Fast(bb,b);
1087   VecGetArray_Fast(xx,x);
1088   tmp  = a->solve_work;
1089 
1090   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1091   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1092 
1093   /* forward solve the lower triangular */
1094   idx    = 3*(*r++);
1095   tmp[0] = b[idx]; tmp[1] = b[1+idx]; tmp[2] = b[2+idx];
1096   for ( i=1; i<n; i++ ) {
1097     v     = aa + 9*ai[i];
1098     vi    = aj + ai[i];
1099     nz    = a->diag[i] - ai[i];
1100     idx   = 3*(*r++);
1101     sum1  = b[idx]; sum2 = b[1+idx]; sum3 = b[2+idx];
1102     while (nz--) {
1103       idx   = 3*(*vi++);
1104       x1    = tmp[idx]; x2 = tmp[1+idx]; x3 = tmp[2+idx];
1105       sum1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
1106       sum2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
1107       sum3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
1108       v += 9;
1109     }
1110     idx = 3*i;
1111     tmp[idx] = sum1; tmp[1+idx] = sum2; tmp[2+idx] = sum3;
1112   }
1113   /* backward solve the upper triangular */
1114   for ( i=n-1; i>=0; i-- ){
1115     v    = aa + 9*a->diag[i] + 9;
1116     vi   = aj + a->diag[i] + 1;
1117     nz   = ai[i+1] - a->diag[i] - 1;
1118     idt  = 3*i;
1119     sum1 = tmp[idt]; sum2 = tmp[1+idt]; sum3 = tmp[2+idt];
1120     while (nz--) {
1121       idx   = 3*(*vi++);
1122       x1    = tmp[idx]; x2 = tmp[1+idx]; x3 = tmp[2+idx];
1123       sum1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
1124       sum2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
1125       sum3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
1126       v += 9;
1127     }
1128     idc = 3*(*c--);
1129     v   = aa + 9*a->diag[i];
1130     x[idc]   = tmp[idt]   = v[0]*sum1 + v[3]*sum2 + v[6]*sum3;
1131     x[1+idc] = tmp[1+idt] = v[1]*sum1 + v[4]*sum2 + v[7]*sum3;
1132     x[2+idc] = tmp[2+idt] = v[2]*sum1 + v[5]*sum2 + v[8]*sum3;
1133   }
1134   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
1135   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
1136   VecRestoreArray_Fast(bb,b);
1137   VecRestoreArray_Fast(xx,x);
1138   PLogFlops(2*9*(a->nz) - a->n);
1139   return 0;
1140 }
1141 
1142 #undef __FUNCTION__
1143 #define __FUNCTION__ "MatSolve_SeqBAIJ_2"
1144 int MatSolve_SeqBAIJ_2(Mat A,Vec bb,Vec xx)
1145 {
1146   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
1147   IS              iscol=a->col,isrow=a->row;
1148   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout;
1149   Scalar          *aa=a->a,sum1,sum2,x1,x2;
1150   register Scalar *x,*b,*tmp,*v;
1151 
1152   VecGetArray_Fast(bb,b);
1153   VecGetArray_Fast(xx,x);
1154   tmp  = a->solve_work;
1155 
1156   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1157   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1158 
1159   /* forward solve the lower triangular */
1160   idx    = 2*(*r++);
1161   tmp[0] = b[idx]; tmp[1] = b[1+idx];
1162   for ( i=1; i<n; i++ ) {
1163     v     = aa + 4*ai[i];
1164     vi    = aj + ai[i];
1165     nz    = a->diag[i] - ai[i];
1166     idx   = 2*(*r++);
1167     sum1  = b[idx]; sum2 = b[1+idx];
1168     while (nz--) {
1169       idx   = 2*(*vi++);
1170       x1    = tmp[idx]; x2 = tmp[1+idx];
1171       sum1 -= v[0]*x1 + v[2]*x2;
1172       sum2 -= v[1]*x1 + v[3]*x2;
1173       v += 4;
1174     }
1175     idx = 2*i;
1176     tmp[idx] = sum1; tmp[1+idx] = sum2;
1177   }
1178   /* backward solve the upper triangular */
1179   for ( i=n-1; i>=0; i-- ){
1180     v    = aa + 4*a->diag[i] + 4;
1181     vi   = aj + a->diag[i] + 1;
1182     nz   = ai[i+1] - a->diag[i] - 1;
1183     idt  = 2*i;
1184     sum1 = tmp[idt]; sum2 = tmp[1+idt];
1185     while (nz--) {
1186       idx   = 2*(*vi++);
1187       x1    = tmp[idx]; x2 = tmp[1+idx];
1188       sum1 -= v[0]*x1 + v[2]*x2;
1189       sum2 -= v[1]*x1 + v[3]*x2;
1190       v += 4;
1191     }
1192     idc = 2*(*c--);
1193     v   = aa + 4*a->diag[i];
1194     x[idc]   = tmp[idt]   = v[0]*sum1 + v[2]*sum2;
1195     x[1+idc] = tmp[1+idt] = v[1]*sum1 + v[3]*sum2;
1196   }
1197   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
1198   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
1199   VecRestoreArray_Fast(bb,b);
1200   VecRestoreArray_Fast(xx,x);
1201   PLogFlops(2*4*(a->nz) - a->n);
1202   return 0;
1203 }
1204 
1205 
1206 #undef __FUNCTION__
1207 #define __FUNCTION__ "MatSolve_SeqBAIJ_1"
1208 int MatSolve_SeqBAIJ_1(Mat A,Vec bb,Vec xx)
1209 {
1210   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
1211   IS              iscol=a->col,isrow=a->row;
1212   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,*rout,*cout;
1213   Scalar          *aa=a->a,sum1;
1214   register Scalar *x,*b,*tmp,*v;
1215 
1216   if (!n) return 0;
1217 
1218   VecGetArray_Fast(bb,b);
1219   VecGetArray_Fast(xx,x);
1220   tmp  = a->solve_work;
1221 
1222   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1223   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1224 
1225   /* forward solve the lower triangular */
1226   tmp[0] = b[*r++];
1227   for ( i=1; i<n; i++ ) {
1228     v     = aa + ai[i];
1229     vi    = aj + ai[i];
1230     nz    = a->diag[i] - ai[i];
1231     sum1  = b[*r++];
1232     while (nz--) {
1233       sum1 -= (*v++)*tmp[*vi++];
1234     }
1235     tmp[i] = sum1;
1236   }
1237   /* backward solve the upper triangular */
1238   for ( i=n-1; i>=0; i-- ){
1239     v    = aa + a->diag[i] + 1;
1240     vi   = aj + a->diag[i] + 1;
1241     nz   = ai[i+1] - a->diag[i] - 1;
1242     sum1 = tmp[i];
1243     while (nz--) {
1244       sum1 -= (*v++)*tmp[*vi++];
1245     }
1246     x[*c--] = tmp[i] = aa[a->diag[i]]*sum1;
1247   }
1248 
1249   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
1250   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
1251   VecRestoreArray_Fast(bb,b);
1252   VecRestoreArray_Fast(xx,x);
1253   PLogFlops(2*1*(a->nz) - a->n);
1254   return 0;
1255 }
1256 
1257 /* ----------------------------------------------------------------*/
1258 /*
1259      This code is virtually identical to MatILUFactorSymbolic_SeqAIJ
1260    except that the data structure of Mat_SeqAIJ is slightly different.
1261    Not a good example of code reuse.
1262 */
1263 #undef __FUNCTION__
1264 #define __FUNCTION__ "MatILUFactorSymbolic_SeqBAIJ"
1265 int MatILUFactorSymbolic_SeqBAIJ(Mat A,IS isrow,IS iscol,double f,int levels,
1266                                  Mat *fact)
1267 {
1268   Mat_SeqBAIJ *a = (Mat_SeqBAIJ *) A->data, *b;
1269   IS          isicol;
1270   int         *r,*ic, ierr, prow, n = a->mbs, *ai = a->i, *aj = a->j;
1271   int         *ainew,*ajnew, jmax,*fill, *xi, nz, *im,*ajfill,*flev;
1272   int         *dloc, idx, row,m,fm, nzf, nzi,len,  realloc = 0;
1273   int         incrlev,nnz,i,bs = a->bs,bs2 = a->bs2;
1274   PetscTruth  col_identity, row_identity;
1275 
1276   /* special case that simply copies fill pattern */
1277   PetscValidHeaderSpecific(isrow,IS_COOKIE);
1278   PetscValidHeaderSpecific(iscol,IS_COOKIE);
1279   ISIdentity(isrow,&row_identity); ISIdentity(iscol,&col_identity);
1280   if (levels == 0 && row_identity && col_identity) {
1281     ierr = MatConvertSameType_SeqBAIJ(A,fact,DO_NOT_COPY_VALUES); CHKERRQ(ierr);
1282     (*fact)->factor = FACTOR_LU;
1283     b               = (Mat_SeqBAIJ *) (*fact)->data;
1284     if (!b->diag) {
1285       ierr = MatMarkDiag_SeqBAIJ(*fact); CHKERRQ(ierr);
1286     }
1287     b->row        = isrow;
1288     b->col        = iscol;
1289     b->solve_work = (Scalar *) PetscMalloc((b->m+1+b->bs)*sizeof(Scalar));CHKPTRQ(b->solve_work);
1290     return 0;
1291   }
1292 
1293   ierr = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
1294   ierr = ISGetIndices(isrow,&r); CHKERRQ(ierr);
1295   ierr = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
1296 
1297   /* get new row pointers */
1298   ainew = (int *) PetscMalloc( (n+1)*sizeof(int) ); CHKPTRQ(ainew);
1299   ainew[0] = 0;
1300   /* don't know how many column pointers are needed so estimate */
1301   jmax = (int) (f*ai[n] + 1);
1302   ajnew = (int *) PetscMalloc( (jmax)*sizeof(int) ); CHKPTRQ(ajnew);
1303   /* ajfill is level of fill for each fill entry */
1304   ajfill = (int *) PetscMalloc( (jmax)*sizeof(int) ); CHKPTRQ(ajfill);
1305   /* fill is a linked list of nonzeros in active row */
1306   fill = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(fill);
1307   /* im is level for each filled value */
1308   im = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(im);
1309   /* dloc is location of diagonal in factor */
1310   dloc = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(dloc);
1311   dloc[0]  = 0;
1312   for ( prow=0; prow<n; prow++ ) {
1313     /* first copy previous fill into linked list */
1314     nzf     = nz  = ai[r[prow]+1] - ai[r[prow]];
1315     xi      = aj + ai[r[prow]];
1316     fill[n] = n;
1317     while (nz--) {
1318       fm  = n;
1319       idx = ic[*xi++];
1320       do {
1321         m  = fm;
1322         fm = fill[m];
1323       } while (fm < idx);
1324       fill[m]   = idx;
1325       fill[idx] = fm;
1326       im[idx]   = 0;
1327     }
1328     nzi = 0;
1329     row = fill[n];
1330     while ( row < prow ) {
1331       incrlev = im[row] + 1;
1332       nz      = dloc[row];
1333       xi      = ajnew  + ainew[row] + nz;
1334       flev    = ajfill + ainew[row] + nz + 1;
1335       nnz     = ainew[row+1] - ainew[row] - nz - 1;
1336       if (*xi++ != row) {
1337         SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,"MatILUFactorSymbolic_SeqBAIJ:zero pivot");
1338       }
1339       fm      = row;
1340       while (nnz-- > 0) {
1341         idx = *xi++;
1342         if (*flev + incrlev > levels) {
1343           flev++;
1344           continue;
1345         }
1346         do {
1347           m  = fm;
1348           fm = fill[m];
1349         } while (fm < idx);
1350         if (fm != idx) {
1351           im[idx]   = *flev + incrlev;
1352           fill[m]   = idx;
1353           fill[idx] = fm;
1354           fm        = idx;
1355           nzf++;
1356         }
1357         else {
1358           if (im[idx] > *flev + incrlev) im[idx] = *flev+incrlev;
1359         }
1360         flev++;
1361       }
1362       row = fill[row];
1363       nzi++;
1364     }
1365     /* copy new filled row into permanent storage */
1366     ainew[prow+1] = ainew[prow] + nzf;
1367     if (ainew[prow+1] > jmax) {
1368       /* allocate a longer ajnew */
1369       int maxadd;
1370       maxadd = (int) (((f*ai[n]+1)*(n-prow+5))/n);
1371       if (maxadd < nzf) maxadd = (n-prow)*(nzf+1);
1372       jmax += maxadd;
1373       xi = (int *) PetscMalloc( jmax*sizeof(int) );CHKPTRQ(xi);
1374       PetscMemcpy(xi,ajnew,ainew[prow]*sizeof(int));
1375       PetscFree(ajnew);
1376       ajnew = xi;
1377       /* allocate a longer ajfill */
1378       xi = (int *) PetscMalloc( jmax*sizeof(int) );CHKPTRQ(xi);
1379       PetscMemcpy(xi,ajfill,ainew[prow]*sizeof(int));
1380       PetscFree(ajfill);
1381       ajfill = xi;
1382       realloc++;
1383     }
1384     xi          = ajnew + ainew[prow];
1385     flev        = ajfill + ainew[prow];
1386     dloc[prow]  = nzi;
1387     fm          = fill[n];
1388     while (nzf--) {
1389       *xi++   = fm;
1390       *flev++ = im[fm];
1391       fm      = fill[fm];
1392     }
1393   }
1394   PetscFree(ajfill);
1395   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
1396   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
1397   ierr = ISDestroy(isicol); CHKERRQ(ierr);
1398   PetscFree(fill); PetscFree(im);
1399 
1400   PLogInfo(A,
1401     "Info:MatILUFactorSymbolic_SeqBAIJ:Realloc %d Fill ratio:given %g needed %g\n",
1402                              realloc,f,((double)ainew[n])/((double)ai[prow]));
1403 
1404   /* put together the new matrix */
1405   ierr = MatCreateSeqBAIJ(A->comm,bs,bs*n,bs*n,0,PETSC_NULL,fact);CHKERRQ(ierr);
1406   b = (Mat_SeqBAIJ *) (*fact)->data;
1407   PetscFree(b->imax);
1408   b->singlemalloc = 0;
1409   len = bs2*ainew[n]*sizeof(Scalar);
1410   /* the next line frees the default space generated by the Create() */
1411   PetscFree(b->a); PetscFree(b->ilen);
1412   b->a          = (Scalar *) PetscMalloc( len ); CHKPTRQ(b->a);
1413   b->j          = ajnew;
1414   b->i          = ainew;
1415   for ( i=0; i<n; i++ ) dloc[i] += ainew[i];
1416   b->diag       = dloc;
1417   b->ilen       = 0;
1418   b->imax       = 0;
1419   b->row        = isrow;
1420   b->col        = iscol;
1421   b->solve_work = (Scalar *) PetscMalloc( (bs*n+bs)*sizeof(Scalar));
1422   CHKPTRQ(b->solve_work);
1423   /* In b structure:  Free imax, ilen, old a, old j.
1424      Allocate dloc, solve_work, new a, new j */
1425   PLogObjectMemory(*fact,(ainew[n]-n)*(sizeof(int))+bs2*ainew[n]*sizeof(Scalar));
1426   b->maxnz          = b->nz = ainew[n];
1427   (*fact)->factor   = FACTOR_LU;
1428 
1429   (*fact)->info.factor_mallocs    = realloc;
1430   (*fact)->info.fill_ratio_given  = f;
1431   (*fact)->info.fill_ratio_needed = ((double)ainew[n])/((double)ai[prow]);
1432 
1433   return 0;
1434 }
1435 
1436 
1437 
1438 
1439