xref: /petsc/src/mat/impls/baij/seq/baijfact.c (revision 2b36279985d181bf1ae28d424577ae2c2fbebdf4)
1 
2 #ifndef lint
3 static char vcid[] = "$Id: baijfact.c,v 1.40 1997/02/04 16:28:38 balay Exp bsmith $";
4 #endif
5 /*
6     Factorization code for BAIJ format.
7 */
8 
9 #include "src/mat/impls/baij/seq/baij.h"
10 #include "src/vec/vecimpl.h"
11 #include "src/inline/ilu.h"
12 
13 
14 /*
15     The symbolic factorization code is identical to that for AIJ format,
16   except for very small changes since this is now a SeqBAIJ datastructure.
17   NOT good code reuse.
18 */
19 #undef __FUNC__
20 #define __FUNC__ "MatLUFactorSymbolic_SeqBAIJ"
21 int MatLUFactorSymbolic_SeqBAIJ(Mat A,IS isrow,IS iscol,double f,Mat *B)
22 {
23   Mat_SeqBAIJ *a = (Mat_SeqBAIJ *) A->data, *b;
24   IS          isicol;
25   int         *r,*ic, ierr, i, n = a->mbs, *ai = a->i, *aj = a->j;
26   int         *ainew,*ajnew, jmax,*fill, *ajtmp, nz, bs = a->bs, bs2=a->bs2;
27   int         *idnew, idx, row,m,fm, nnz, nzi,realloc = 0,nzbd,*im;
28 
29   PetscValidHeaderSpecific(isrow,IS_COOKIE);
30   PetscValidHeaderSpecific(iscol,IS_COOKIE);
31   ierr = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
32   ISGetIndices(isrow,&r); ISGetIndices(isicol,&ic);
33 
34   /* get new row pointers */
35   ainew = (int *) PetscMalloc( (n+1)*sizeof(int) ); CHKPTRQ(ainew);
36   ainew[0] = 0;
37   /* don't know how many column pointers are needed so estimate */
38   jmax = (int) (f*ai[n] + 1);
39   ajnew = (int *) PetscMalloc( (jmax)*sizeof(int) ); CHKPTRQ(ajnew);
40   /* fill is a linked list of nonzeros in active row */
41   fill = (int *) PetscMalloc( (2*n+1)*sizeof(int)); CHKPTRQ(fill);
42   im = fill + n + 1;
43   /* idnew is location of diagonal in factor */
44   idnew = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(idnew);
45   idnew[0] = 0;
46 
47   for ( i=0; i<n; i++ ) {
48     /* first copy previous fill into linked list */
49     nnz     = nz    = ai[r[i]+1] - ai[r[i]];
50     if (!nz) SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,1,"Empty row in matrix");
51     ajtmp   = aj + ai[r[i]];
52     fill[n] = n;
53     while (nz--) {
54       fm  = n;
55       idx = ic[*ajtmp++];
56       do {
57         m  = fm;
58         fm = fill[m];
59       } while (fm < idx);
60       fill[m]   = idx;
61       fill[idx] = fm;
62     }
63     row = fill[n];
64     while ( row < i ) {
65       ajtmp = ajnew + idnew[row] + 1;
66       nzbd  = 1 + idnew[row] - ainew[row];
67       nz    = im[row] - nzbd;
68       fm    = row;
69       while (nz-- > 0) {
70         idx = *ajtmp++;
71         nzbd++;
72         if (idx == i) im[row] = nzbd;
73         do {
74           m  = fm;
75           fm = fill[m];
76         } while (fm < idx);
77         if (fm != idx) {
78           fill[m]   = idx;
79           fill[idx] = fm;
80           fm        = idx;
81           nnz++;
82         }
83       }
84       row = fill[row];
85     }
86     /* copy new filled row into permanent storage */
87     ainew[i+1] = ainew[i] + nnz;
88     if (ainew[i+1] > jmax) {
89       /* allocate a longer ajnew */
90       int maxadd;
91       maxadd = (int) ((f*(ai[n]+1)*(n-i+5))/n);
92       if (maxadd < nnz) maxadd = (n-i)*(nnz+1);
93       jmax += maxadd;
94       ajtmp = (int *) PetscMalloc( jmax*sizeof(int) );CHKPTRQ(ajtmp);
95       PetscMemcpy(ajtmp,ajnew,ainew[i]*sizeof(int));
96       PetscFree(ajnew);
97       ajnew = ajtmp;
98       realloc++; /* count how many times we realloc */
99     }
100     ajtmp = ajnew + ainew[i];
101     fm    = fill[n];
102     nzi   = 0;
103     im[i] = nnz;
104     while (nnz--) {
105       if (fm < i) nzi++;
106       *ajtmp++ = fm;
107       fm       = fill[fm];
108     }
109     idnew[i] = ainew[i] + nzi;
110   }
111 
112   PLogInfo(A,
113     "Info:MatLUFactorSymbolic_SeqBAIJ:Reallocs %d Fill ratio:given %g needed %g\n",
114                              realloc,f,((double)ainew[n])/((double)ai[i]));
115 
116   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
117   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
118 
119   PetscFree(fill);
120 
121   /* put together the new matrix */
122   ierr = MatCreateSeqBAIJ(A->comm,bs,bs*n,bs*n,0,PETSC_NULL,B); CHKERRQ(ierr);
123   PLogObjectParent(*B,isicol);
124   ierr = ISDestroy(isicol); CHKERRQ(ierr);
125   b = (Mat_SeqBAIJ *) (*B)->data;
126   PetscFree(b->imax);
127   b->singlemalloc = 0;
128   /* the next line frees the default space generated by the Create() */
129   PetscFree(b->a); PetscFree(b->ilen);
130   b->a          = (Scalar *) PetscMalloc((ainew[n]+1)*sizeof(Scalar)*bs2);CHKPTRQ(b->a);
131   b->j          = ajnew;
132   b->i          = ainew;
133   b->diag       = idnew;
134   b->ilen       = 0;
135   b->imax       = 0;
136   b->row        = isrow;
137   b->col        = iscol;
138   b->solve_work = (Scalar *) PetscMalloc( (bs*n+bs)*sizeof(Scalar));
139   CHKPTRQ(b->solve_work);
140   /* In b structure:  Free imax, ilen, old a, old j.
141      Allocate idnew, solve_work, new a, new j */
142   PLogObjectMemory(*B,(ainew[n]-n)*(sizeof(int)+sizeof(Scalar)));
143   b->maxnz = b->nz = ainew[n];
144 
145   (*B)->info.factor_mallocs    = realloc;
146   (*B)->info.fill_ratio_given  = f;
147   (*B)->info.fill_ratio_needed = ((double)ainew[n])/((double)ai[i]);
148 
149   return 0;
150 }
151 
152 /* ----------------------------------------------------------- */
153 #undef __FUNC__
154 #define __FUNC__ "MatLUFactorNumeric_SeqBAIJ_N"
155 int MatLUFactorNumeric_SeqBAIJ_N(Mat A,Mat *B)
156 {
157   Mat             C = *B;
158   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data,*b = (Mat_SeqBAIJ *)C->data;
159   IS              iscol = b->col, isrow = b->row, isicol;
160   int             *r,*ic, ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
161   int             *ajtmpold, *ajtmp, nz, row, bslog,*ai=a->i,*aj=a->j,k,flg;
162   int             *diag_offset=b->diag,diag,bs=a->bs,bs2 = a->bs2,*v_pivots;
163   Scalar          *ba = b->a,*aa = a->a;
164   register Scalar *pv,*v,*rtmp,*multiplier,*v_work,*pc,*w;
165   register int    *pj;
166 
167   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
168   PLogObjectParent(*B,isicol);
169   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
170   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
171   rtmp  = (Scalar *) PetscMalloc(bs2*(n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
172   PetscMemzero(rtmp,bs2*(n+1)*sizeof(Scalar));
173   /* generate work space needed by dense LU factorization */
174   v_work     = (Scalar *) PetscMalloc(bs*sizeof(int) + (bs+bs2)*sizeof(Scalar));
175                CHKPTRQ(v_work);
176   multiplier = v_work + bs;
177   v_pivots   = (int *) (multiplier + bs2);
178 
179   /* flops in while loop */
180   bslog = 2*bs*bs2;
181 
182   for ( i=0; i<n; i++ ) {
183     nz    = bi[i+1] - bi[i];
184     ajtmp = bj + bi[i];
185     for  ( j=0; j<nz; j++ ) {
186       PetscMemzero(rtmp+bs2*ajtmp[j],bs2*sizeof(Scalar));
187     }
188     /* load in initial (unfactored row) */
189     nz       = ai[r[i]+1] - ai[r[i]];
190     ajtmpold = aj + ai[r[i]];
191     v        = aa + bs2*ai[r[i]];
192     for ( j=0; j<nz; j++ ) {
193       PetscMemcpy(rtmp+bs2*ic[ajtmpold[j]],v+bs2*j,bs2*sizeof(Scalar));
194     }
195     row = *ajtmp++;
196     while (row < i) {
197       pc = rtmp + bs2*row;
198 /*      if (*pc) { */
199       for ( flg=0,k=0; k<bs2; k++ ) { if (pc[k]!=0.0) { flg =1; break; }}
200       if (flg) {
201         pv = ba + bs2*diag_offset[row];
202         pj = bj + diag_offset[row] + 1;
203         Kernel_A_gets_A_times_B(bs,pc,pv,multiplier);
204         nz = bi[row+1] - diag_offset[row] - 1;
205         pv += bs2;
206         for (j=0; j<nz; j++) {
207           Kernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j);
208         }
209         PLogFlops(bslog*(nz+1)-bs);
210       }
211         row = *ajtmp++;
212     }
213     /* finished row so stick it into b->a */
214     pv = ba + bs2*bi[i];
215     pj = bj + bi[i];
216     nz = bi[i+1] - bi[i];
217     for ( j=0; j<nz; j++ ) {
218       PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(Scalar));
219     }
220     diag = diag_offset[i] - bi[i];
221     /* invert diagonal block */
222     w = pv + bs2*diag;
223     Kernel_A_gets_inverse_A(bs,w,v_pivots,v_work);
224   }
225 
226   PetscFree(rtmp); PetscFree(v_work);
227   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
228   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
229   ierr = ISDestroy(isicol); CHKERRQ(ierr);
230   C->factor = FACTOR_LU;
231   C->assembled = PETSC_TRUE;
232   PLogFlops(1.3333*bs*bs2*b->mbs); /* from inverting diagonal blocks */
233   return 0;
234 }
235 /* ------------------------------------------------------------*/
236 /*
237       Version for when blocks are 5 by 5
238 */
239 #undef __FUNC__
240 #define __FUNC__ "MatLUFactorNumeric_SeqBAIJ_5"
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     Kernel_A_gets_inverse_A(bs,w,v_pivots,v_work);
404   }
405 
406   PetscFree(rtmp);
407   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
408   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
409   ierr = ISDestroy(isicol); CHKERRQ(ierr);
410   C->factor = FACTOR_LU;
411   C->assembled = PETSC_TRUE;
412   PLogFlops(1.3333*125*b->mbs); /* from inverting diagonal blocks */
413   return 0;
414 }
415 
416 /* ------------------------------------------------------------*/
417 /*
418       Version for when blocks are 4 by 4
419 */
420 #undef __FUNC__
421 #define __FUNC__ "MatLUFactorNumeric_SeqBAIJ_4"
422 int MatLUFactorNumeric_SeqBAIJ_4(Mat A,Mat *B)
423 {
424   Mat             C = *B;
425   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data,*b = (Mat_SeqBAIJ *)C->data;
426   IS              iscol = b->col, isrow = b->row, isicol;
427   int             *r,*ic, ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
428   int             *ajtmpold, *ajtmp, nz, row, v_pivots[4];
429   int             *diag_offset = b->diag,bs = 4,idx,*ai=a->i,*aj=a->j;
430   register Scalar *pv,*v,*rtmp,*pc,*w,*x;
431   Scalar          p1,p2,p3,p4,v_work[4],m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
432   Scalar          p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
433   Scalar          p10,p11,p12,p13,p14,p15,p16,m10,m11,m12;
434   Scalar          m13,m14,m15,m16;
435   Scalar          *ba = b->a,*aa = a->a;
436   register int    *pj;
437 
438   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
439   PLogObjectParent(*B,isicol);
440   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
441   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
442   rtmp  = (Scalar *) PetscMalloc(16*(n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
443 
444   for ( i=0; i<n; i++ ) {
445     nz    = bi[i+1] - bi[i];
446     ajtmp = bj + bi[i];
447     for  ( j=0; j<nz; j++ ) {
448       x = rtmp+16*ajtmp[j];
449       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
450       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
451     }
452     /* load in initial (unfactored row) */
453     idx      = r[i];
454     nz       = ai[idx+1] - ai[idx];
455     ajtmpold = aj + ai[idx];
456     v        = aa + 16*ai[idx];
457     for ( j=0; j<nz; j++ ) {
458       x    = rtmp+16*ic[ajtmpold[j]];
459       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
460       x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
461       x[9] = v[9]; x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
462       x[14] = v[14]; x[15] = v[15];
463       v    += 16;
464     }
465     row = *ajtmp++;
466     while (row < i) {
467       pc = rtmp + 16*row;
468       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
469       p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
470       p10 = pc[9]; p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
471       p15 = pc[14]; p16 = pc[15];
472       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
473           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
474           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
475           || p16 != 0.0) {
476         pv = ba + 16*diag_offset[row];
477         pj = bj + diag_offset[row] + 1;
478         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
479         x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
480         x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
481         x15 = pv[14]; x16 = pv[15];
482         pc[0] = m1 = p1*x1 + p5*x2  + p9*x3  + p13*x4;
483         pc[1] = m2 = p2*x1 + p6*x2  + p10*x3 + p14*x4;
484         pc[2] = m3 = p3*x1 + p7*x2  + p11*x3 + p15*x4;
485         pc[3] = m4 = p4*x1 + p8*x2  + p12*x3 + p16*x4;
486 
487         pc[4] = m5 = p1*x5 + p5*x6  + p9*x7  + p13*x8;
488         pc[5] = m6 = p2*x5 + p6*x6  + p10*x7 + p14*x8;
489         pc[6] = m7 = p3*x5 + p7*x6  + p11*x7 + p15*x8;
490         pc[7] = m8 = p4*x5 + p8*x6  + p12*x7 + p16*x8;
491 
492         pc[8]  = m9  = p1*x9 + p5*x10  + p9*x11  + p13*x12;
493         pc[9]  = m10 = p2*x9 + p6*x10  + p10*x11 + p14*x12;
494         pc[10] = m11 = p3*x9 + p7*x10  + p11*x11 + p15*x12;
495         pc[11] = m12 = p4*x9 + p8*x10  + p12*x11 + p16*x12;
496 
497         pc[12] = m13 = p1*x13 + p5*x14  + p9*x15  + p13*x16;
498         pc[13] = m14 = p2*x13 + p6*x14  + p10*x15 + p14*x16;
499         pc[14] = m15 = p3*x13 + p7*x14  + p11*x15 + p15*x16;
500         pc[15] = m16 = p4*x13 + p8*x14  + p12*x15 + p16*x16;
501 
502         nz = bi[row+1] - diag_offset[row] - 1;
503         pv += 16;
504         for (j=0; j<nz; j++) {
505           x1   = pv[0];  x2 = pv[1];   x3  = pv[2];  x4  = pv[3];
506           x5   = pv[4];  x6 = pv[5];   x7  = pv[6];  x8  = pv[7]; x9 = pv[8];
507           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
508           x14  = pv[13]; x15 = pv[14]; x16 = pv[15];
509           x    = rtmp + 16*pj[j];
510           x[0] -= m1*x1 + m5*x2  + m9*x3 + m13*x4;
511           x[1] -= m2*x1 + m6*x2  + m10*x3 + m14*x4;
512           x[2] -= m3*x1 + m7*x2  + m11*x3 + m15*x4;
513           x[3] -= m4*x1 + m8*x2  + m12*x3 + m16*x4;
514 
515           x[4] -= m1*x5 + m5*x6  + m9*x7  + m13*x8;
516           x[5] -= m2*x5 + m6*x6  + m10*x7 + m14*x8;
517           x[6] -= m3*x5 + m7*x6  + m11*x7 + m15*x8;
518           x[7] -= m4*x5 + m8*x6  + m12*x7 + m16*x8;
519 
520           x[8] -= m1*x9  + m5*x10  + m9*x11 + m13*x12;
521           x[9] -= m2*x9  + m6*x10  + m10*x11 + m14*x12;
522           x[10] -= m3*x9 + m7*x10  + m11*x11 + m15*x12;
523           x[11] -= m4*x9 + m8*x10  + m12*x11 + m16*x12;
524 
525           x[12] -= m1*x13 + m5*x14  + m9*x15 + m13*x16;
526           x[13] -= m2*x13 + m6*x14  + m10*x15 + m14*x16;
527           x[14] -= m3*x13 + m7*x14  + m11*x15 + m15*x16;
528           x[15] -= m4*x13 + m8*x14  + m12*x15 + m16*x16;
529 
530           pv   += 16;
531         }
532         PLogFlops(128*nz+112);
533       }
534       row = *ajtmp++;
535     }
536     /* finished row so stick it into b->a */
537     pv = ba + 16*bi[i];
538     pj = bj + bi[i];
539     nz = bi[i+1] - bi[i];
540     for ( j=0; j<nz; j++ ) {
541       x     = rtmp+16*pj[j];
542       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
543       pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
544       pv[9] = x[9]; pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
545       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
546       pv   += 16;
547     }
548     /* invert diagonal block */
549     w = ba + 16*diag_offset[i];
550     Kernel_A_gets_inverse_A(bs,w,v_pivots,v_work);
551   }
552 
553   PetscFree(rtmp);
554   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
555   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
556   ierr = ISDestroy(isicol); CHKERRQ(ierr);
557   C->factor = FACTOR_LU;
558   C->assembled = PETSC_TRUE;
559   PLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */
560   return 0;
561 }
562 /* ------------------------------------------------------------*/
563 /*
564       Version for when blocks are 3 by 3
565 */
566 #undef __FUNC__
567 #define __FUNC__ "MatLUFactorNumeric_SeqBAIJ_3"
568 int MatLUFactorNumeric_SeqBAIJ_3(Mat A,Mat *B)
569 {
570   Mat             C = *B;
571   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data,*b = (Mat_SeqBAIJ *)C->data;
572   IS              iscol = b->col, isrow = b->row, isicol;
573   int             *r,*ic, ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
574   int             *ajtmpold, *ajtmp, nz, row, *ai=a->i,*aj=a->j;
575   int             *diag_offset = b->diag,idx;
576   register Scalar *pv,*v,*rtmp,*pc,*w,*x;
577   Scalar          p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
578   Scalar          p5,p6,p7,p8,p9,x5,x6,x7,x8,x9;
579   Scalar          *ba = b->a,*aa = a->a;
580   register int    *pj;
581 
582   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
583   PLogObjectParent(*B,isicol);
584   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
585   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
586   rtmp  = (Scalar *) PetscMalloc(9*(n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
587 
588   for ( i=0; i<n; i++ ) {
589     nz    = bi[i+1] - bi[i];
590     ajtmp = bj + bi[i];
591     for  ( j=0; j<nz; j++ ) {
592       x = rtmp + 9*ajtmp[j];
593       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
594     }
595     /* load in initial (unfactored row) */
596     idx      = r[i];
597     nz       = ai[idx+1] - ai[idx];
598     ajtmpold = aj + ai[idx];
599     v        = aa + 9*ai[idx];
600     for ( j=0; j<nz; j++ ) {
601       x    = rtmp + 9*ic[ajtmpold[j]];
602       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
603       x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
604       v    += 9;
605     }
606     row = *ajtmp++;
607     while (row < i) {
608       pc = rtmp + 9*row;
609       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
610       p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
611       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
612           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0) {
613         pv = ba + 9*diag_offset[row];
614         pj = bj + diag_offset[row] + 1;
615         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
616         x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
617         pc[0] = m1 = p1*x1 + p4*x2 + p7*x3;
618         pc[1] = m2 = p2*x1 + p5*x2 + p8*x3;
619         pc[2] = m3 = p3*x1 + p6*x2 + p9*x3;
620 
621         pc[3] = m4 = p1*x4 + p4*x5 + p7*x6;
622         pc[4] = m5 = p2*x4 + p5*x5 + p8*x6;
623         pc[5] = m6 = p3*x4 + p6*x5 + p9*x6;
624 
625         pc[6] = m7 = p1*x7 + p4*x8 + p7*x9;
626         pc[7] = m8 = p2*x7 + p5*x8 + p8*x9;
627         pc[8] = m9 = p3*x7 + p6*x8 + p9*x9;
628         nz = bi[row+1] - diag_offset[row] - 1;
629         pv += 9;
630         for (j=0; j<nz; j++) {
631           x1   = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
632           x5   = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
633           x    = rtmp + 9*pj[j];
634           x[0] -= m1*x1 + m4*x2 + m7*x3;
635           x[1] -= m2*x1 + m5*x2 + m8*x3;
636           x[2] -= m3*x1 + m6*x2 + m9*x3;
637 
638           x[3] -= m1*x4 + m4*x5 + m7*x6;
639           x[4] -= m2*x4 + m5*x5 + m8*x6;
640           x[5] -= m3*x4 + m6*x5 + m9*x6;
641 
642           x[6] -= m1*x7 + m4*x8 + m7*x9;
643           x[7] -= m2*x7 + m5*x8 + m8*x9;
644           x[8] -= m3*x7 + m6*x8 + m9*x9;
645           pv   += 9;
646         }
647         PLogFlops(54*nz+36);
648       }
649       row = *ajtmp++;
650     }
651     /* finished row so stick it into b->a */
652     pv = ba + 9*bi[i];
653     pj = bj + bi[i];
654     nz = bi[i+1] - bi[i];
655     for ( j=0; j<nz; j++ ) {
656       x     = rtmp + 9*pj[j];
657       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
658       pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
659       pv   += 9;
660     }
661     /* invert diagonal block */
662     w = ba + 9*diag_offset[i];
663     ierr = Kernel_A_gets_inverse_A_3(w); CHKERRQ(ierr);
664   }
665 
666   PetscFree(rtmp);
667   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
668   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
669   ierr = ISDestroy(isicol); CHKERRQ(ierr);
670   C->factor = FACTOR_LU;
671   C->assembled = PETSC_TRUE;
672   PLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */
673   return 0;
674 }
675 
676 /* ------------------------------------------------------------*/
677 /*
678       Version for when blocks are 2 by 2
679 */
680 #undef __FUNC__
681 #define __FUNC__ "MatLUFactorNumeric_SeqBAIJ_2"
682 int MatLUFactorNumeric_SeqBAIJ_2(Mat A,Mat *B)
683 {
684   Mat             C = *B;
685   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data,*b = (Mat_SeqBAIJ *)C->data;
686   IS              iscol = b->col, isrow = b->row, isicol;
687   int             *r,*ic, ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
688   int             *ajtmpold, *ajtmp, nz, row, v_pivots[2];
689   int             *diag_offset=b->diag,bs = 2,idx,*ai=a->i,*aj=a->j;
690   register Scalar *pv,*v,*rtmp,m1,m2,m3,m4,*pc,*w,*x,x1,x2,x3,x4;
691   Scalar          p1,p2,p3,p4,v_work[2];
692   Scalar          *ba = b->a,*aa = a->a;
693   register int    *pj;
694 
695   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
696   PLogObjectParent(*B,isicol);
697   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
698   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
699   rtmp  = (Scalar *) PetscMalloc(4*(n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
700 
701   for ( i=0; i<n; i++ ) {
702     nz    = bi[i+1] - bi[i];
703     ajtmp = bj + bi[i];
704     for  ( j=0; j<nz; j++ ) {
705       x = rtmp+4*ajtmp[j]; x[0] = x[1] = x[2] = x[3] = 0.0;
706     }
707     /* load in initial (unfactored row) */
708     idx      = r[i];
709     nz       = ai[idx+1] - ai[idx];
710     ajtmpold = aj + ai[idx];
711     v        = aa + 4*ai[idx];
712     for ( j=0; j<nz; j++ ) {
713       x    = rtmp+4*ic[ajtmpold[j]];
714       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
715       v    += 4;
716     }
717     row = *ajtmp++;
718     while (row < i) {
719       pc = rtmp + 4*row;
720       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
721       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0) {
722         pv = ba + 4*diag_offset[row];
723         pj = bj + diag_offset[row] + 1;
724         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
725         pc[0] = m1 = p1*x1 + p3*x2;
726         pc[1] = m2 = p2*x1 + p4*x2;
727         pc[2] = m3 = p1*x3 + p3*x4;
728         pc[3] = m4 = p2*x3 + p4*x4;
729         nz = bi[row+1] - diag_offset[row] - 1;
730         pv += 4;
731         for (j=0; j<nz; j++) {
732           x1   = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
733           x    = rtmp + 4*pj[j];
734           x[0] -= m1*x1 + m3*x2;
735           x[1] -= m2*x1 + m4*x2;
736           x[2] -= m1*x3 + m3*x4;
737           x[3] -= m2*x3 + m4*x4;
738           pv   += 4;
739         }
740         PLogFlops(16*nz+12);
741       }
742       row = *ajtmp++;
743     }
744     /* finished row so stick it into b->a */
745     pv = ba + 4*bi[i];
746     pj = bj + bi[i];
747     nz = bi[i+1] - bi[i];
748     for ( j=0; j<nz; j++ ) {
749       x     = rtmp+4*pj[j];
750       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
751       pv   += 4;
752     }
753     /* invert diagonal block */
754     w = ba + 4*diag_offset[i];
755     Kernel_A_gets_inverse_A(bs,w,v_pivots,v_work);
756   }
757 
758   PetscFree(rtmp);
759   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
760   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
761   ierr = ISDestroy(isicol); CHKERRQ(ierr);
762   C->factor = FACTOR_LU;
763   C->assembled = PETSC_TRUE;
764   PLogFlops(1.3333*8*b->mbs); /* from inverting diagonal blocks */
765   return 0;
766 }
767 
768 /* ----------------------------------------------------------- */
769 /*
770      Version for when blocks are 1 by 1.
771 */
772 #undef __FUNC__
773 #define __FUNC__ "MatLUFactorNumeric_SeqBAIJ_1"
774 int MatLUFactorNumeric_SeqBAIJ_1(Mat A,Mat *B)
775 {
776   Mat             C = *B;
777   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data, *b = (Mat_SeqBAIJ *)C->data;
778   IS              iscol = b->col, isrow = b->row, isicol;
779   int             *r,*ic, ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
780   int             *ajtmpold, *ajtmp, nz, row,*ai = a->i,*aj = a->j;
781   int             *diag_offset = b->diag,diag;
782   register Scalar *pv,*v,*rtmp,multiplier,*pc;
783   Scalar          *ba = b->a,*aa = a->a;
784   register int    *pj;
785 
786   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
787   PLogObjectParent(*B,isicol);
788   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
789   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
790   rtmp  = (Scalar *) PetscMalloc((n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
791 
792   for ( i=0; i<n; i++ ) {
793     nz    = bi[i+1] - bi[i];
794     ajtmp = bj + bi[i];
795     for  ( j=0; j<nz; j++ ) rtmp[ajtmp[j]] = 0.0;
796 
797     /* load in initial (unfactored row) */
798     nz       = ai[r[i]+1] - ai[r[i]];
799     ajtmpold = aj + ai[r[i]];
800     v        = aa + ai[r[i]];
801     for ( j=0; j<nz; j++ ) rtmp[ic[ajtmpold[j]]] =  v[j];
802 
803     row = *ajtmp++;
804     while (row < i) {
805       pc = rtmp + row;
806       if (*pc != 0.0) {
807         pv         = ba + diag_offset[row];
808         pj         = bj + diag_offset[row] + 1;
809         multiplier = *pc * *pv++;
810         *pc        = multiplier;
811         nz         = bi[row+1] - diag_offset[row] - 1;
812         for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
813         PLogFlops(1+2*nz);
814       }
815       row = *ajtmp++;
816     }
817     /* finished row so stick it into b->a */
818     pv = ba + bi[i];
819     pj = bj + bi[i];
820     nz = bi[i+1] - bi[i];
821     for ( j=0; j<nz; j++ ) {pv[j] = rtmp[pj[j]];}
822     diag = diag_offset[i] - bi[i];
823     /* check pivot entry for current row */
824     if (pv[diag] == 0.0) {
825       SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,0,"Zero pivot");
826     }
827     pv[diag] = 1.0/pv[diag];
828   }
829 
830   PetscFree(rtmp);
831   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
832   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
833   ierr = ISDestroy(isicol); CHKERRQ(ierr);
834   C->factor    = FACTOR_LU;
835   C->assembled = PETSC_TRUE;
836   PLogFlops(b->n);
837   return 0;
838 }
839 
840 /* ----------------------------------------------------------- */
841 #undef __FUNC__
842 #define __FUNC__ "MatLUFactor_SeqBAIJ"
843 int MatLUFactor_SeqBAIJ(Mat A,IS row,IS col,double f)
844 {
845   Mat_SeqBAIJ *mat = (Mat_SeqBAIJ *) A->data;
846   int         ierr;
847   Mat         C;
848 
849   ierr = MatLUFactorSymbolic(A,row,col,f,&C); CHKERRQ(ierr);
850   ierr = MatLUFactorNumeric(A,&C); CHKERRQ(ierr);
851 
852   /* free all the data structures from mat */
853   PetscFree(mat->a);
854   if (!mat->singlemalloc) {PetscFree(mat->i); PetscFree(mat->j);}
855   if (mat->diag) PetscFree(mat->diag);
856   if (mat->ilen) PetscFree(mat->ilen);
857   if (mat->imax) PetscFree(mat->imax);
858   if (mat->solve_work) PetscFree(mat->solve_work);
859   if (mat->mult_work) PetscFree(mat->mult_work);
860   PetscFree(mat);
861 
862   PetscMemcpy(A,C,sizeof(struct _Mat));
863   PetscHeaderDestroy(C);
864   return 0;
865 }
866 /* ----------------------------------------------------------- */
867 #undef __FUNC__
868 #define __FUNC__ "MatSolve_SeqBAIJ_N"
869 int MatSolve_SeqBAIJ_N(Mat A,Vec bb,Vec xx)
870 {
871   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
872   IS              iscol=a->col,isrow=a->row;
873   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j;
874   int             nz,bs=a->bs,bs2=a->bs2,*rout,*cout;
875   Scalar          *aa=a->a,*sum;
876   register Scalar *x,*b,*lsum,*tmp,*v;
877 
878   VecGetArray_Fast(bb,b);
879   VecGetArray_Fast(xx,x);
880   tmp  = a->solve_work;
881 
882   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
883   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
884 
885   /* forward solve the lower triangular */
886   PetscMemcpy(tmp,b + bs*(*r++), bs*sizeof(Scalar));
887   for ( i=1; i<n; i++ ) {
888     v   = aa + bs2*ai[i];
889     vi  = aj + ai[i];
890     nz  = a->diag[i] - ai[i];
891     sum = tmp + bs*i;
892     PetscMemcpy(sum,b+bs*(*r++),bs*sizeof(Scalar));
893     while (nz--) {
894       Kernel_v_gets_v_minus_A_times_w(bs,sum,v,tmp+bs*(*vi++));
895       v += bs2;
896     }
897   }
898   /* backward solve the upper triangular */
899   lsum = a->solve_work + a->n;
900   for ( i=n-1; i>=0; i-- ){
901     v   = aa + bs2*(a->diag[i] + 1);
902     vi  = aj + a->diag[i] + 1;
903     nz  = ai[i+1] - a->diag[i] - 1;
904     PetscMemcpy(lsum,tmp+i*bs,bs*sizeof(Scalar));
905     while (nz--) {
906       Kernel_v_gets_v_minus_A_times_w(bs,lsum,v,tmp+bs*(*vi++));
907       v += bs2;
908     }
909     Kernel_w_gets_A_times_v(bs,lsum,aa+bs2*a->diag[i],tmp+i*bs);
910     PetscMemcpy(x + bs*(*c--),tmp+i*bs,bs*sizeof(Scalar));
911   }
912 
913   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
914   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
915   VecRestoreArray_Fast(bb,b);
916   VecRestoreArray_Fast(xx,x);
917   PLogFlops(2*(a->bs2)*(a->nz) - a->n);
918   return 0;
919 }
920 
921 #undef __FUNC__
922 #define __FUNC__ "MatSolve_SeqBAIJ_7"
923 int MatSolve_SeqBAIJ_7(Mat A,Vec bb,Vec xx)
924 {
925   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
926   IS              iscol=a->col,isrow=a->row;
927   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout;
928   Scalar          *aa=a->a,sum1,sum2,sum3,sum4,sum5,sum6,sum7,x1,x2,x3,x4,x5,x6,x7;
929   register Scalar *x,*b,*tmp,*v;
930 
931   VecGetArray_Fast(bb,b);
932   VecGetArray_Fast(xx,x);
933   tmp  = a->solve_work;
934 
935   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
936   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
937 
938   /* forward solve the lower triangular */
939   idx    = 7*(*r++);
940   tmp[0] = b[idx];   tmp[1] = b[1+idx];
941   tmp[2] = b[2+idx]; tmp[3] = b[3+idx]; tmp[4] = b[4+idx];
942   tmp[5] = b[5+idx]; tmp[6] = b[6+idx];
943 
944   for ( i=1; i<n; i++ ) {
945     v     = aa + 49*ai[i];
946     vi    = aj + ai[i];
947     nz    = a->diag[i] - ai[i];
948     idx   = 7*(*r++);
949     sum1  = b[idx];sum2 = b[1+idx];sum3 = b[2+idx];sum4 = b[3+idx];
950     sum5  = b[4+idx];sum6 = b[5+idx];sum7 = b[6+idx];
951     while (nz--) {
952       idx   = 7*(*vi++);
953       x1    = tmp[idx];  x2 = tmp[1+idx];x3 = tmp[2+idx];
954       x4    = tmp[3+idx];x5 = tmp[4+idx];
955       x6    = tmp[5+idx];x7 = tmp[6+idx];
956       sum1 -= v[0]*x1 + v[7]*x2  + v[14]*x3 + v[21]*x4 + v[28]*x5 + v[35]*x6 + v[42]*x7;
957       sum2 -= v[1]*x1 + v[8]*x2  + v[15]*x3 + v[22]*x4 + v[29]*x5 + v[36]*x6 + v[43]*x7;
958       sum3 -= v[2]*x1 + v[9]*x2  + v[16]*x3 + v[23]*x4 + v[30]*x5 + v[37]*x6 + v[44]*x7;
959       sum4 -= v[3]*x1 + v[10]*x2 + v[17]*x3 + v[24]*x4 + v[31]*x5 + v[38]*x6 + v[45]*x7;
960       sum5 -= v[4]*x1 + v[11]*x2 + v[18]*x3 + v[25]*x4 + v[32]*x5 + v[39]*x6 + v[46]*x7;
961       sum6 -= v[5]*x1 + v[12]*x2 + v[19]*x3 + v[26]*x4 + v[33]*x5 + v[40]*x6 + v[47]*x7;
962       sum7 -= v[6]*x1 + v[13]*x2 + v[20]*x3 + v[27]*x4 + v[34]*x5 + v[41]*x6 + v[48]*x7;
963       v += 49;
964     }
965     idx = 7*i;
966     tmp[idx]   = sum1;tmp[1+idx] = sum2;
967     tmp[2+idx] = sum3;tmp[3+idx] = sum4; tmp[4+idx] = sum5;
968     tmp[5+idx] = sum6;tmp[6+idx] = sum7;
969   }
970   /* backward solve the upper triangular */
971   for ( i=n-1; i>=0; i-- ){
972     v    = aa + 49*a->diag[i] + 49;
973     vi   = aj + a->diag[i] + 1;
974     nz   = ai[i+1] - a->diag[i] - 1;
975     idt  = 7*i;
976     sum1 = tmp[idt];  sum2 = tmp[1+idt];
977     sum3 = tmp[2+idt];sum4 = tmp[3+idt]; sum5 = tmp[4+idt];
978     sum6 = tmp[5+idt];sum7 = tmp[6+idt];
979     while (nz--) {
980       idx   = 7*(*vi++);
981       x1    = tmp[idx];   x2 = tmp[1+idx];
982       x3    = tmp[2+idx]; x4 = tmp[3+idx]; x5 = tmp[4+idx];
983       x6    = tmp[5+idx]; x7 = tmp[6+idx];
984       sum1 -= v[0]*x1 + v[7]*x2  + v[14]*x3 + v[21]*x4 + v[28]*x5 + v[35]*x6 + v[42]*x7;
985       sum2 -= v[1]*x1 + v[8]*x2  + v[15]*x3 + v[22]*x4 + v[29]*x5 + v[36]*x6 + v[43]*x7;
986       sum3 -= v[2]*x1 + v[9]*x2  + v[16]*x3 + v[23]*x4 + v[30]*x5 + v[37]*x6 + v[44]*x7;
987       sum4 -= v[3]*x1 + v[10]*x2 + v[17]*x3 + v[24]*x4 + v[31]*x5 + v[38]*x6 + v[45]*x7;
988       sum5 -= v[4]*x1 + v[11]*x2 + v[18]*x3 + v[25]*x4 + v[32]*x5 + v[39]*x6 + v[46]*x7;
989       sum6 -= v[5]*x1 + v[12]*x2 + v[19]*x3 + v[26]*x4 + v[33]*x5 + v[40]*x6 + v[47]*x7;
990       sum7 -= v[6]*x1 + v[13]*x2 + v[20]*x3 + v[27]*x4 + v[34]*x5 + v[41]*x6 + v[48]*x7;
991       v += 49;
992     }
993     idc = 7*(*c--);
994     v   = aa + 49*a->diag[i];
995     x[idc]   = tmp[idt]   = v[0]*sum1+v[7]*sum2+v[14]*sum3+
996                                  v[21]*sum4+v[28]*sum5+v[35]*sum6+v[42]*sum7;
997     x[1+idc] = tmp[1+idt] = v[1]*sum1+v[8]*sum2+v[15]*sum3+
998                                  v[22]*sum4+v[29]*sum5+v[36]*sum6+v[43]*sum7;
999     x[2+idc] = tmp[2+idt] = v[2]*sum1+v[9]*sum2+v[16]*sum3+
1000                                  v[23]*sum4+v[30]*sum5+v[37]*sum6+v[44]*sum7;
1001     x[3+idc] = tmp[3+idt] = v[3]*sum1+v[10]*sum2+v[17]*sum3+
1002                                  v[24]*sum4+v[31]*sum5+v[38]*sum6+v[45]*sum7;
1003     x[4+idc] = tmp[4+idt] = v[4]*sum1+v[11]*sum2+v[18]*sum3+
1004                                  v[25]*sum4+v[32]*sum5+v[39]*sum6+v[46]*sum7;
1005     x[5+idc] = tmp[5+idt] = v[5]*sum1+v[12]*sum2+v[19]*sum3+
1006                                  v[26]*sum4+v[33]*sum5+v[40]*sum6+v[47]*sum7;
1007     x[6+idc] = tmp[6+idt] = v[6]*sum1+v[13]*sum2+v[20]*sum3+
1008                                  v[27]*sum4+v[34]*sum5+v[41]*sum6+v[48]*sum7;
1009   }
1010 
1011   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
1012   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
1013   VecRestoreArray_Fast(bb,b);
1014   VecRestoreArray_Fast(xx,x);
1015   PLogFlops(2*49*(a->nz) - a->n);
1016   return 0;
1017 }
1018 
1019 #undef __FUNC__
1020 #define __FUNC__ "MatSolve_SeqBAIJ_5"
1021 int MatSolve_SeqBAIJ_5(Mat A,Vec bb,Vec xx)
1022 {
1023   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
1024   IS              iscol=a->col,isrow=a->row;
1025   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout;
1026   Scalar          *aa=a->a,sum1,sum2,sum3,sum4,sum5,x1,x2,x3,x4,x5;
1027   register Scalar *x,*b,*tmp,*v;
1028 
1029   VecGetArray_Fast(bb,b);
1030   VecGetArray_Fast(xx,x);
1031   tmp  = a->solve_work;
1032 
1033   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1034   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1035 
1036   /* forward solve the lower triangular */
1037   idx    = 5*(*r++);
1038   tmp[0] = b[idx];   tmp[1] = b[1+idx];
1039   tmp[2] = b[2+idx]; tmp[3] = b[3+idx]; tmp[4] = b[4+idx];
1040   for ( i=1; i<n; i++ ) {
1041     v     = aa + 25*ai[i];
1042     vi    = aj + ai[i];
1043     nz    = a->diag[i] - ai[i];
1044     idx   = 5*(*r++);
1045     sum1  = b[idx];sum2 = b[1+idx];sum3 = b[2+idx];sum4 = b[3+idx];
1046     sum5  = b[4+idx];
1047     while (nz--) {
1048       idx   = 5*(*vi++);
1049       x1    = tmp[idx];  x2 = tmp[1+idx];x3 = tmp[2+idx];
1050       x4    = tmp[3+idx];x5 = tmp[4+idx];
1051       sum1 -= v[0]*x1 + v[5]*x2 + v[10]*x3 + v[15]*x4 + v[20]*x5;
1052       sum2 -= v[1]*x1 + v[6]*x2 + v[11]*x3 + v[16]*x4 + v[21]*x5;
1053       sum3 -= v[2]*x1 + v[7]*x2 + v[12]*x3 + v[17]*x4 + v[22]*x5;
1054       sum4 -= v[3]*x1 + v[8]*x2 + v[13]*x3 + v[18]*x4 + v[23]*x5;
1055       sum5 -= v[4]*x1 + v[9]*x2 + v[14]*x3 + v[19]*x4 + v[24]*x5;
1056       v += 25;
1057     }
1058     idx = 5*i;
1059     tmp[idx]   = sum1;tmp[1+idx] = sum2;
1060     tmp[2+idx] = sum3;tmp[3+idx] = sum4; tmp[4+idx] = sum5;
1061   }
1062   /* backward solve the upper triangular */
1063   for ( i=n-1; i>=0; i-- ){
1064     v    = aa + 25*a->diag[i] + 25;
1065     vi   = aj + a->diag[i] + 1;
1066     nz   = ai[i+1] - a->diag[i] - 1;
1067     idt  = 5*i;
1068     sum1 = tmp[idt];  sum2 = tmp[1+idt];
1069     sum3 = tmp[2+idt];sum4 = tmp[3+idt]; sum5 = tmp[4+idt];
1070     while (nz--) {
1071       idx   = 5*(*vi++);
1072       x1    = tmp[idx];   x2 = tmp[1+idx];
1073       x3    = tmp[2+idx]; x4 = tmp[3+idx]; x5 = tmp[4+idx];
1074       sum1 -= v[0]*x1 + v[5]*x2 + v[10]*x3 + v[15]*x4 + v[20]*x5;
1075       sum2 -= v[1]*x1 + v[6]*x2 + v[11]*x3 + v[16]*x4 + v[21]*x5;
1076       sum3 -= v[2]*x1 + v[7]*x2 + v[12]*x3 + v[17]*x4 + v[22]*x5;
1077       sum4 -= v[3]*x1 + v[8]*x2 + v[13]*x3 + v[18]*x4 + v[23]*x5;
1078       sum5 -= v[4]*x1 + v[9]*x2 + v[14]*x3 + v[19]*x4 + v[24]*x5;
1079       v += 25;
1080     }
1081     idc = 5*(*c--);
1082     v   = aa + 25*a->diag[i];
1083     x[idc]   = tmp[idt]   = v[0]*sum1+v[5]*sum2+v[10]*sum3+
1084                                  v[15]*sum4+v[20]*sum5;
1085     x[1+idc] = tmp[1+idt] = v[1]*sum1+v[6]*sum2+v[11]*sum3+
1086                                  v[16]*sum4+v[21]*sum5;
1087     x[2+idc] = tmp[2+idt] = v[2]*sum1+v[7]*sum2+v[12]*sum3+
1088                                  v[17]*sum4+v[22]*sum5;
1089     x[3+idc] = tmp[3+idt] = v[3]*sum1+v[8]*sum2+v[13]*sum3+
1090                                  v[18]*sum4+v[23]*sum5;
1091     x[4+idc] = tmp[4+idt] = v[4]*sum1+v[9]*sum2+v[14]*sum3+
1092                                  v[19]*sum4+v[24]*sum5;
1093   }
1094 
1095   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
1096   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
1097   VecRestoreArray_Fast(bb,b);
1098   VecRestoreArray_Fast(xx,x);
1099   PLogFlops(2*25*(a->nz) - a->n);
1100   return 0;
1101 }
1102 
1103 #undef __FUNC__
1104 #define __FUNC__ "MatSolve_SeqBAIJ_4"
1105 int MatSolve_SeqBAIJ_4(Mat A,Vec bb,Vec xx)
1106 {
1107   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
1108   IS              iscol=a->col,isrow=a->row;
1109   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout;
1110   Scalar          *aa=a->a,sum1,sum2,sum3,sum4,x1,x2,x3,x4;
1111   register Scalar *x,*b,*tmp,*v;
1112 
1113   VecGetArray_Fast(bb,b);
1114   VecGetArray_Fast(xx,x);
1115   tmp  = a->solve_work;
1116 
1117   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1118   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1119 
1120   /* forward solve the lower triangular */
1121   idx    = 4*(*r++);
1122   tmp[0] = b[idx];   tmp[1] = b[1+idx];
1123   tmp[2] = b[2+idx]; tmp[3] = b[3+idx];
1124   for ( i=1; i<n; i++ ) {
1125     v     = aa + 16*ai[i];
1126     vi    = aj + ai[i];
1127     nz    = a->diag[i] - ai[i];
1128     idx   = 4*(*r++);
1129     sum1  = b[idx];sum2 = b[1+idx];sum3 = b[2+idx];sum4 = b[3+idx];
1130     while (nz--) {
1131       idx   = 4*(*vi++);
1132       x1    = tmp[idx];x2 = tmp[1+idx];x3 = tmp[2+idx];x4 = tmp[3+idx];
1133       sum1 -= v[0]*x1 + v[4]*x2 + v[8]*x3  + v[12]*x4;
1134       sum2 -= v[1]*x1 + v[5]*x2 + v[9]*x3  + v[13]*x4;
1135       sum3 -= v[2]*x1 + v[6]*x2 + v[10]*x3 + v[14]*x4;
1136       sum4 -= v[3]*x1 + v[7]*x2 + v[11]*x3 + v[15]*x4;
1137       v += 16;
1138     }
1139     idx = 4*i;
1140     tmp[idx]   = sum1;tmp[1+idx] = sum2;
1141     tmp[2+idx] = sum3;tmp[3+idx] = sum4;
1142   }
1143   /* backward solve the upper triangular */
1144   for ( i=n-1; i>=0; i-- ){
1145     v    = aa + 16*a->diag[i] + 16;
1146     vi   = aj + a->diag[i] + 1;
1147     nz   = ai[i+1] - a->diag[i] - 1;
1148     idt  = 4*i;
1149     sum1 = tmp[idt];  sum2 = tmp[1+idt];
1150     sum3 = tmp[2+idt];sum4 = tmp[3+idt];
1151     while (nz--) {
1152       idx   = 4*(*vi++);
1153       x1    = tmp[idx];   x2 = tmp[1+idx];
1154       x3    = tmp[2+idx]; x4 = tmp[3+idx];
1155       sum1 -= v[0]*x1 + v[4]*x2 + v[8]*x3   + v[12]*x4;
1156       sum2 -= v[1]*x1 + v[5]*x2 + v[9]*x3   + v[13]*x4;
1157       sum3 -= v[2]*x1 + v[6]*x2 + v[10]*x3  + v[14]*x4;
1158       sum4 -= v[3]*x1 + v[7]*x2 + v[11]*x3  + v[15]*x4;
1159       v += 16;
1160     }
1161     idc = 4*(*c--);
1162     v   = aa + 16*a->diag[i];
1163     x[idc]   = tmp[idt]   = v[0]*sum1+v[4]*sum2+v[8]*sum3+v[12]*sum4;
1164     x[1+idc] = tmp[1+idt] = v[1]*sum1+v[5]*sum2+v[9]*sum3+v[13]*sum4;
1165     x[2+idc] = tmp[2+idt] = v[2]*sum1+v[6]*sum2+v[10]*sum3+v[14]*sum4;
1166     x[3+idc] = tmp[3+idt] = v[3]*sum1+v[7]*sum2+v[11]*sum3+v[15]*sum4;
1167   }
1168 
1169   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
1170   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
1171   VecRestoreArray_Fast(bb,b);
1172   VecRestoreArray_Fast(xx,x);
1173   PLogFlops(2*16*(a->nz) - a->n);
1174   return 0;
1175 }
1176 
1177 
1178 #undef __FUNC__
1179 #define __FUNC__ "MatSolve_SeqBAIJ_3"
1180 int MatSolve_SeqBAIJ_3(Mat A,Vec bb,Vec xx)
1181 {
1182   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
1183   IS              iscol=a->col,isrow=a->row;
1184   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout;
1185   Scalar          *aa=a->a,sum1,sum2,sum3,x1,x2,x3;
1186   register Scalar *x,*b,*tmp,*v;
1187 
1188   VecGetArray_Fast(bb,b);
1189   VecGetArray_Fast(xx,x);
1190   tmp  = a->solve_work;
1191 
1192   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1193   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1194 
1195   /* forward solve the lower triangular */
1196   idx    = 3*(*r++);
1197   tmp[0] = b[idx]; tmp[1] = b[1+idx]; tmp[2] = b[2+idx];
1198   for ( i=1; i<n; i++ ) {
1199     v     = aa + 9*ai[i];
1200     vi    = aj + ai[i];
1201     nz    = a->diag[i] - ai[i];
1202     idx   = 3*(*r++);
1203     sum1  = b[idx]; sum2 = b[1+idx]; sum3 = b[2+idx];
1204     while (nz--) {
1205       idx   = 3*(*vi++);
1206       x1    = tmp[idx]; x2 = tmp[1+idx]; x3 = tmp[2+idx];
1207       sum1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
1208       sum2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
1209       sum3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
1210       v += 9;
1211     }
1212     idx = 3*i;
1213     tmp[idx] = sum1; tmp[1+idx] = sum2; tmp[2+idx] = sum3;
1214   }
1215   /* backward solve the upper triangular */
1216   for ( i=n-1; i>=0; i-- ){
1217     v    = aa + 9*a->diag[i] + 9;
1218     vi   = aj + a->diag[i] + 1;
1219     nz   = ai[i+1] - a->diag[i] - 1;
1220     idt  = 3*i;
1221     sum1 = tmp[idt]; sum2 = tmp[1+idt]; sum3 = tmp[2+idt];
1222     while (nz--) {
1223       idx   = 3*(*vi++);
1224       x1    = tmp[idx]; x2 = tmp[1+idx]; x3 = tmp[2+idx];
1225       sum1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
1226       sum2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
1227       sum3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
1228       v += 9;
1229     }
1230     idc = 3*(*c--);
1231     v   = aa + 9*a->diag[i];
1232     x[idc]   = tmp[idt]   = v[0]*sum1 + v[3]*sum2 + v[6]*sum3;
1233     x[1+idc] = tmp[1+idt] = v[1]*sum1 + v[4]*sum2 + v[7]*sum3;
1234     x[2+idc] = tmp[2+idt] = v[2]*sum1 + v[5]*sum2 + v[8]*sum3;
1235   }
1236   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
1237   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
1238   VecRestoreArray_Fast(bb,b);
1239   VecRestoreArray_Fast(xx,x);
1240   PLogFlops(2*9*(a->nz) - a->n);
1241   return 0;
1242 }
1243 
1244 #undef __FUNC__
1245 #define __FUNC__ "MatSolve_SeqBAIJ_2"
1246 int MatSolve_SeqBAIJ_2(Mat A,Vec bb,Vec xx)
1247 {
1248   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
1249   IS              iscol=a->col,isrow=a->row;
1250   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout;
1251   Scalar          *aa=a->a,sum1,sum2,x1,x2;
1252   register Scalar *x,*b,*tmp,*v;
1253 
1254   VecGetArray_Fast(bb,b);
1255   VecGetArray_Fast(xx,x);
1256   tmp  = a->solve_work;
1257 
1258   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1259   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1260 
1261   /* forward solve the lower triangular */
1262   idx    = 2*(*r++);
1263   tmp[0] = b[idx]; tmp[1] = b[1+idx];
1264   for ( i=1; i<n; i++ ) {
1265     v     = aa + 4*ai[i];
1266     vi    = aj + ai[i];
1267     nz    = a->diag[i] - ai[i];
1268     idx   = 2*(*r++);
1269     sum1  = b[idx]; sum2 = b[1+idx];
1270     while (nz--) {
1271       idx   = 2*(*vi++);
1272       x1    = tmp[idx]; x2 = tmp[1+idx];
1273       sum1 -= v[0]*x1 + v[2]*x2;
1274       sum2 -= v[1]*x1 + v[3]*x2;
1275       v += 4;
1276     }
1277     idx = 2*i;
1278     tmp[idx] = sum1; tmp[1+idx] = sum2;
1279   }
1280   /* backward solve the upper triangular */
1281   for ( i=n-1; i>=0; i-- ){
1282     v    = aa + 4*a->diag[i] + 4;
1283     vi   = aj + a->diag[i] + 1;
1284     nz   = ai[i+1] - a->diag[i] - 1;
1285     idt  = 2*i;
1286     sum1 = tmp[idt]; sum2 = tmp[1+idt];
1287     while (nz--) {
1288       idx   = 2*(*vi++);
1289       x1    = tmp[idx]; x2 = tmp[1+idx];
1290       sum1 -= v[0]*x1 + v[2]*x2;
1291       sum2 -= v[1]*x1 + v[3]*x2;
1292       v += 4;
1293     }
1294     idc = 2*(*c--);
1295     v   = aa + 4*a->diag[i];
1296     x[idc]   = tmp[idt]   = v[0]*sum1 + v[2]*sum2;
1297     x[1+idc] = tmp[1+idt] = v[1]*sum1 + v[3]*sum2;
1298   }
1299   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
1300   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
1301   VecRestoreArray_Fast(bb,b);
1302   VecRestoreArray_Fast(xx,x);
1303   PLogFlops(2*4*(a->nz) - a->n);
1304   return 0;
1305 }
1306 
1307 
1308 #undef __FUNC__
1309 #define __FUNC__ "MatSolve_SeqBAIJ_1"
1310 int MatSolve_SeqBAIJ_1(Mat A,Vec bb,Vec xx)
1311 {
1312   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
1313   IS              iscol=a->col,isrow=a->row;
1314   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,*rout,*cout;
1315   Scalar          *aa=a->a,sum1;
1316   register Scalar *x,*b,*tmp,*v;
1317 
1318   if (!n) return 0;
1319 
1320   VecGetArray_Fast(bb,b);
1321   VecGetArray_Fast(xx,x);
1322   tmp  = a->solve_work;
1323 
1324   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1325   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1326 
1327   /* forward solve the lower triangular */
1328   tmp[0] = b[*r++];
1329   for ( i=1; i<n; i++ ) {
1330     v     = aa + ai[i];
1331     vi    = aj + ai[i];
1332     nz    = a->diag[i] - ai[i];
1333     sum1  = b[*r++];
1334     while (nz--) {
1335       sum1 -= (*v++)*tmp[*vi++];
1336     }
1337     tmp[i] = sum1;
1338   }
1339   /* backward solve the upper triangular */
1340   for ( i=n-1; i>=0; i-- ){
1341     v    = aa + a->diag[i] + 1;
1342     vi   = aj + a->diag[i] + 1;
1343     nz   = ai[i+1] - a->diag[i] - 1;
1344     sum1 = tmp[i];
1345     while (nz--) {
1346       sum1 -= (*v++)*tmp[*vi++];
1347     }
1348     x[*c--] = tmp[i] = aa[a->diag[i]]*sum1;
1349   }
1350 
1351   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
1352   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
1353   VecRestoreArray_Fast(bb,b);
1354   VecRestoreArray_Fast(xx,x);
1355   PLogFlops(2*1*(a->nz) - a->n);
1356   return 0;
1357 }
1358 
1359 /* ----------------------------------------------------------------*/
1360 /*
1361      This code is virtually identical to MatILUFactorSymbolic_SeqAIJ
1362    except that the data structure of Mat_SeqAIJ is slightly different.
1363    Not a good example of code reuse.
1364 */
1365 #undef __FUNC__
1366 #define __FUNC__ "MatILUFactorSymbolic_SeqBAIJ"
1367 int MatILUFactorSymbolic_SeqBAIJ(Mat A,IS isrow,IS iscol,double f,int levels,
1368                                  Mat *fact)
1369 {
1370   Mat_SeqBAIJ *a = (Mat_SeqBAIJ *) A->data, *b;
1371   IS          isicol;
1372   int         *r,*ic, ierr, prow, n = a->mbs, *ai = a->i, *aj = a->j;
1373   int         *ainew,*ajnew, jmax,*fill, *xi, nz, *im,*ajfill,*flev;
1374   int         *dloc, idx, row,m,fm, nzf, nzi,len,  realloc = 0;
1375   int         incrlev,nnz,i,bs = a->bs,bs2 = a->bs2;
1376   PetscTruth  col_identity, row_identity;
1377 
1378   /* special case that simply copies fill pattern */
1379   PetscValidHeaderSpecific(isrow,IS_COOKIE);
1380   PetscValidHeaderSpecific(iscol,IS_COOKIE);
1381   ISIdentity(isrow,&row_identity); ISIdentity(iscol,&col_identity);
1382   if (levels == 0 && row_identity && col_identity) {
1383     ierr = MatConvertSameType_SeqBAIJ(A,fact,DO_NOT_COPY_VALUES); CHKERRQ(ierr);
1384     (*fact)->factor = FACTOR_LU;
1385     b               = (Mat_SeqBAIJ *) (*fact)->data;
1386     if (!b->diag) {
1387       ierr = MatMarkDiag_SeqBAIJ(*fact); CHKERRQ(ierr);
1388     }
1389     b->row        = isrow;
1390     b->col        = iscol;
1391     b->solve_work = (Scalar *) PetscMalloc((b->m+1+b->bs)*sizeof(Scalar));CHKPTRQ(b->solve_work);
1392     return 0;
1393   }
1394 
1395   ierr = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
1396   ierr = ISGetIndices(isrow,&r); CHKERRQ(ierr);
1397   ierr = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
1398 
1399   /* get new row pointers */
1400   ainew = (int *) PetscMalloc( (n+1)*sizeof(int) ); CHKPTRQ(ainew);
1401   ainew[0] = 0;
1402   /* don't know how many column pointers are needed so estimate */
1403   jmax = (int) (f*ai[n] + 1);
1404   ajnew = (int *) PetscMalloc( (jmax)*sizeof(int) ); CHKPTRQ(ajnew);
1405   /* ajfill is level of fill for each fill entry */
1406   ajfill = (int *) PetscMalloc( (jmax)*sizeof(int) ); CHKPTRQ(ajfill);
1407   /* fill is a linked list of nonzeros in active row */
1408   fill = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(fill);
1409   /* im is level for each filled value */
1410   im = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(im);
1411   /* dloc is location of diagonal in factor */
1412   dloc = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(dloc);
1413   dloc[0]  = 0;
1414   for ( prow=0; prow<n; prow++ ) {
1415     /* first copy previous fill into linked list */
1416     nzf     = nz  = ai[r[prow]+1] - ai[r[prow]];
1417     if (!nz) SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,1,"Empty row in matrix");
1418     xi      = aj + ai[r[prow]];
1419     fill[n] = n;
1420     while (nz--) {
1421       fm  = n;
1422       idx = ic[*xi++];
1423       do {
1424         m  = fm;
1425         fm = fill[m];
1426       } while (fm < idx);
1427       fill[m]   = idx;
1428       fill[idx] = fm;
1429       im[idx]   = 0;
1430     }
1431     nzi = 0;
1432     row = fill[n];
1433     while ( row < prow ) {
1434       incrlev = im[row] + 1;
1435       nz      = dloc[row];
1436       xi      = ajnew  + ainew[row] + nz;
1437       flev    = ajfill + ainew[row] + nz + 1;
1438       nnz     = ainew[row+1] - ainew[row] - nz - 1;
1439       if (*xi++ != row) {
1440         SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,0,"zero pivot");
1441       }
1442       fm      = row;
1443       while (nnz-- > 0) {
1444         idx = *xi++;
1445         if (*flev + incrlev > levels) {
1446           flev++;
1447           continue;
1448         }
1449         do {
1450           m  = fm;
1451           fm = fill[m];
1452         } while (fm < idx);
1453         if (fm != idx) {
1454           im[idx]   = *flev + incrlev;
1455           fill[m]   = idx;
1456           fill[idx] = fm;
1457           fm        = idx;
1458           nzf++;
1459         }
1460         else {
1461           if (im[idx] > *flev + incrlev) im[idx] = *flev+incrlev;
1462         }
1463         flev++;
1464       }
1465       row = fill[row];
1466       nzi++;
1467     }
1468     /* copy new filled row into permanent storage */
1469     ainew[prow+1] = ainew[prow] + nzf;
1470     if (ainew[prow+1] > jmax) {
1471       /* allocate a longer ajnew */
1472       int maxadd;
1473       maxadd = (int) (((f*ai[n]+1)*(n-prow+5))/n);
1474       if (maxadd < nzf) maxadd = (n-prow)*(nzf+1);
1475       jmax += maxadd;
1476       xi = (int *) PetscMalloc( jmax*sizeof(int) );CHKPTRQ(xi);
1477       PetscMemcpy(xi,ajnew,ainew[prow]*sizeof(int));
1478       PetscFree(ajnew);
1479       ajnew = xi;
1480       /* allocate a longer ajfill */
1481       xi = (int *) PetscMalloc( jmax*sizeof(int) );CHKPTRQ(xi);
1482       PetscMemcpy(xi,ajfill,ainew[prow]*sizeof(int));
1483       PetscFree(ajfill);
1484       ajfill = xi;
1485       realloc++;
1486     }
1487     xi          = ajnew + ainew[prow];
1488     flev        = ajfill + ainew[prow];
1489     dloc[prow]  = nzi;
1490     fm          = fill[n];
1491     while (nzf--) {
1492       *xi++   = fm;
1493       *flev++ = im[fm];
1494       fm      = fill[fm];
1495     }
1496   }
1497   PetscFree(ajfill);
1498   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
1499   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
1500   ierr = ISDestroy(isicol); CHKERRQ(ierr);
1501   PetscFree(fill); PetscFree(im);
1502 
1503   PLogInfo(A,
1504     "Info:MatILUFactorSymbolic_SeqBAIJ:Realloc %d Fill ratio:given %g needed %g\n",
1505                              realloc,f,((double)ainew[n])/((double)ai[prow]));
1506 
1507   /* put together the new matrix */
1508   ierr = MatCreateSeqBAIJ(A->comm,bs,bs*n,bs*n,0,PETSC_NULL,fact);CHKERRQ(ierr);
1509   b = (Mat_SeqBAIJ *) (*fact)->data;
1510   PetscFree(b->imax);
1511   b->singlemalloc = 0;
1512   len = bs2*ainew[n]*sizeof(Scalar);
1513   /* the next line frees the default space generated by the Create() */
1514   PetscFree(b->a); PetscFree(b->ilen);
1515   b->a          = (Scalar *) PetscMalloc( len ); CHKPTRQ(b->a);
1516   b->j          = ajnew;
1517   b->i          = ainew;
1518   for ( i=0; i<n; i++ ) dloc[i] += ainew[i];
1519   b->diag       = dloc;
1520   b->ilen       = 0;
1521   b->imax       = 0;
1522   b->row        = isrow;
1523   b->col        = iscol;
1524   b->solve_work = (Scalar *) PetscMalloc( (bs*n+bs)*sizeof(Scalar));
1525   CHKPTRQ(b->solve_work);
1526   /* In b structure:  Free imax, ilen, old a, old j.
1527      Allocate dloc, solve_work, new a, new j */
1528   PLogObjectMemory(*fact,(ainew[n]-n)*(sizeof(int))+bs2*ainew[n]*sizeof(Scalar));
1529   b->maxnz          = b->nz = ainew[n];
1530   (*fact)->factor   = FACTOR_LU;
1531 
1532   (*fact)->info.factor_mallocs    = realloc;
1533   (*fact)->info.fill_ratio_given  = f;
1534   (*fact)->info.fill_ratio_needed = ((double)ainew[n])/((double)ai[prow]);
1535 
1536   return 0;
1537 }
1538 
1539 
1540 
1541 
1542