xref: /petsc/src/mat/impls/baij/seq/baijfact.c (revision 8ba3a721c9105e9240dbd90dceddbf8833cabcd1)
1 #ifndef lint
2 static char vcid[] = "$Id: baijfact.c,v 1.39 1997/02/04 01:21:08 balay 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 __FUNC__
19 #define __FUNC__ "MatLUFactorSymbolic_SeqBAIJ"
20 int MatLUFactorSymbolic_SeqBAIJ(Mat A,IS isrow,IS iscol,double f,Mat *B)
21 {
22   Mat_SeqBAIJ *a = (Mat_SeqBAIJ *) A->data, *b;
23   IS          isicol;
24   int         *r,*ic, ierr, i, n = a->mbs, *ai = a->i, *aj = a->j;
25   int         *ainew,*ajnew, jmax,*fill, *ajtmp, nz, bs = a->bs, bs2=a->bs2;
26   int         *idnew, idx, row,m,fm, nnz, nzi,realloc = 0,nzbd,*im;
27 
28   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     if (!nz) SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,1,"Empty row in matrix");
50     ajtmp   = aj + ai[r[i]];
51     fill[n] = n;
52     while (nz--) {
53       fm  = n;
54       idx = ic[*ajtmp++];
55       do {
56         m  = fm;
57         fm = fill[m];
58       } while (fm < idx);
59       fill[m]   = idx;
60       fill[idx] = fm;
61     }
62     row = fill[n];
63     while ( row < i ) {
64       ajtmp = ajnew + idnew[row] + 1;
65       nzbd  = 1 + idnew[row] - ainew[row];
66       nz    = im[row] - nzbd;
67       fm    = row;
68       while (nz-- > 0) {
69         idx = *ajtmp++;
70         nzbd++;
71         if (idx == i) im[row] = nzbd;
72         do {
73           m  = fm;
74           fm = fill[m];
75         } while (fm < idx);
76         if (fm != idx) {
77           fill[m]   = idx;
78           fill[idx] = fm;
79           fm        = idx;
80           nnz++;
81         }
82       }
83       row = fill[row];
84     }
85     /* copy new filled row into permanent storage */
86     ainew[i+1] = ainew[i] + nnz;
87     if (ainew[i+1] > jmax) {
88       /* allocate a longer ajnew */
89       int maxadd;
90       maxadd = (int) ((f*(ai[n]+1)*(n-i+5))/n);
91       if (maxadd < nnz) maxadd = (n-i)*(nnz+1);
92       jmax += maxadd;
93       ajtmp = (int *) PetscMalloc( jmax*sizeof(int) );CHKPTRQ(ajtmp);
94       PetscMemcpy(ajtmp,ajnew,ainew[i]*sizeof(int));
95       PetscFree(ajnew);
96       ajnew = ajtmp;
97       realloc++; /* count how many times we realloc */
98     }
99     ajtmp = ajnew + ainew[i];
100     fm    = fill[n];
101     nzi   = 0;
102     im[i] = nnz;
103     while (nnz--) {
104       if (fm < i) nzi++;
105       *ajtmp++ = fm;
106       fm       = fill[fm];
107     }
108     idnew[i] = ainew[i] + nzi;
109   }
110 
111   PLogInfo(A,
112     "Info:MatLUFactorSymbolic_SeqBAIJ:Reallocs %d Fill ratio:given %g needed %g\n",
113                              realloc,f,((double)ainew[n])/((double)ai[i]));
114 
115   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
116   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
117 
118   PetscFree(fill);
119 
120   /* put together the new matrix */
121   ierr = MatCreateSeqBAIJ(A->comm,bs,bs*n,bs*n,0,PETSC_NULL,B); CHKERRQ(ierr);
122   PLogObjectParent(*B,isicol);
123   ierr = ISDestroy(isicol); CHKERRQ(ierr);
124   b = (Mat_SeqBAIJ *) (*B)->data;
125   PetscFree(b->imax);
126   b->singlemalloc = 0;
127   /* the next line frees the default space generated by the Create() */
128   PetscFree(b->a); PetscFree(b->ilen);
129   b->a          = (Scalar *) PetscMalloc((ainew[n]+1)*sizeof(Scalar)*bs2);CHKPTRQ(b->a);
130   b->j          = ajnew;
131   b->i          = ainew;
132   b->diag       = idnew;
133   b->ilen       = 0;
134   b->imax       = 0;
135   b->row        = isrow;
136   b->col        = iscol;
137   b->solve_work = (Scalar *) PetscMalloc( (bs*n+bs)*sizeof(Scalar));
138   CHKPTRQ(b->solve_work);
139   /* In b structure:  Free imax, ilen, old a, old j.
140      Allocate idnew, solve_work, new a, new j */
141   PLogObjectMemory(*B,(ainew[n]-n)*(sizeof(int)+sizeof(Scalar)));
142   b->maxnz = b->nz = ainew[n];
143 
144   (*B)->info.factor_mallocs    = realloc;
145   (*B)->info.fill_ratio_given  = f;
146   (*B)->info.fill_ratio_needed = ((double)ainew[n])/((double)ai[i]);
147 
148   return 0;
149 }
150 
151 /* ----------------------------------------------------------- */
152 #undef __FUNC__
153 #define __FUNC__ "MatLUFactorNumeric_SeqBAIJ_N"
154 int MatLUFactorNumeric_SeqBAIJ_N(Mat A,Mat *B)
155 {
156   Mat             C = *B;
157   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data,*b = (Mat_SeqBAIJ *)C->data;
158   IS              iscol = b->col, isrow = b->row, isicol;
159   int             *r,*ic, ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
160   int             *ajtmpold, *ajtmp, nz, row, bslog,*ai=a->i,*aj=a->j,k,flg;
161   int             *diag_offset=b->diag,diag,bs=a->bs,bs2 = a->bs2,*v_pivots;
162   Scalar          *ba = b->a,*aa = a->a;
163   register Scalar *pv,*v,*rtmp,*multiplier,*v_work,*pc,*w;
164   register int    *pj;
165 
166   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
167   PLogObjectParent(*B,isicol);
168   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
169   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
170   rtmp  = (Scalar *) PetscMalloc(bs2*(n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
171   PetscMemzero(rtmp,bs2*(n+1)*sizeof(Scalar));
172   /* generate work space needed by dense LU factorization */
173   v_work     = (Scalar *) PetscMalloc(bs*sizeof(int) + (bs+bs2)*sizeof(Scalar));
174                CHKPTRQ(v_work);
175   multiplier = v_work + bs;
176   v_pivots   = (int *) (multiplier + bs2);
177 
178   /* flops in while loop */
179   bslog = 2*bs*bs2;
180 
181   for ( i=0; i<n; i++ ) {
182     nz    = bi[i+1] - bi[i];
183     ajtmp = bj + bi[i];
184     for  ( j=0; j<nz; j++ ) {
185       PetscMemzero(rtmp+bs2*ajtmp[j],bs2*sizeof(Scalar));
186     }
187     /* load in initial (unfactored row) */
188     nz       = ai[r[i]+1] - ai[r[i]];
189     ajtmpold = aj + ai[r[i]];
190     v        = aa + bs2*ai[r[i]];
191     for ( j=0; j<nz; j++ ) {
192       PetscMemcpy(rtmp+bs2*ic[ajtmpold[j]],v+bs2*j,bs2*sizeof(Scalar));
193     }
194     row = *ajtmp++;
195     while (row < i) {
196       pc = rtmp + bs2*row;
197 /*      if (*pc) { */
198       for ( flg=0,k=0; k<bs2; k++ ) { if (pc[k]!=0.0) { flg =1; break; }}
199       if (flg) {
200         pv = ba + bs2*diag_offset[row];
201         pj = bj + diag_offset[row] + 1;
202         Kernel_A_gets_A_times_B(bs,pc,pv,multiplier);
203         nz = bi[row+1] - diag_offset[row] - 1;
204         pv += bs2;
205         for (j=0; j<nz; j++) {
206           Kernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j);
207         }
208         PLogFlops(bslog*(nz+1)-bs);
209       }
210         row = *ajtmp++;
211     }
212     /* finished row so stick it into b->a */
213     pv = ba + bs2*bi[i];
214     pj = bj + bi[i];
215     nz = bi[i+1] - bi[i];
216     for ( j=0; j<nz; j++ ) {
217       PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(Scalar));
218     }
219     diag = diag_offset[i] - bi[i];
220     /* invert diagonal block */
221     w = pv + bs2*diag;
222     Kernel_A_gets_inverse_A(bs,w,v_pivots,v_work);
223   }
224 
225   PetscFree(rtmp); PetscFree(v_work);
226   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
227   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
228   ierr = ISDestroy(isicol); CHKERRQ(ierr);
229   C->factor = FACTOR_LU;
230   C->assembled = PETSC_TRUE;
231   PLogFlops(1.3333*bs*bs2*b->mbs); /* from inverting diagonal blocks */
232   return 0;
233 }
234 /* ------------------------------------------------------------*/
235 /*
236       Version for when blocks are 5 by 5
237 */
238 #undef __FUNC__
239 #define __FUNC__ "MatLUFactorNumeric_SeqBAIJ_5"
240 int MatLUFactorNumeric_SeqBAIJ_5(Mat A,Mat *B)
241 {
242   Mat             C = *B;
243   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data,*b = (Mat_SeqBAIJ *)C->data;
244   IS              iscol = b->col, isrow = b->row, isicol;
245   int             *r,*ic, ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
246   int             *ajtmpold, *ajtmp, nz, row, v_pivots[5];
247   int             *diag_offset = b->diag,bs = 5,idx,*ai=a->i,*aj=a->j;
248   register Scalar *pv,*v,*rtmp,*pc,*w,*x;
249   Scalar          p1,p2,p3,p4,v_work[5],m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
250   Scalar          p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
251   Scalar          x17,x18,x19,x20,x21,x22,x23,x24,x25,p10,p11,p12,p13,p14;
252   Scalar          p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,m10,m11,m12;
253   Scalar          m13,m14,m15,m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
254   Scalar          *ba = b->a,*aa = a->a;
255   register int    *pj;
256 
257   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
258   PLogObjectParent(*B,isicol);
259   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
260   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
261   rtmp  = (Scalar *) PetscMalloc(25*(n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
262 
263   for ( i=0; i<n; i++ ) {
264     nz    = bi[i+1] - bi[i];
265     ajtmp = bj + bi[i];
266     for  ( j=0; j<nz; j++ ) {
267       x = rtmp+25*ajtmp[j];
268       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
269       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
270       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0;
271     }
272     /* load in initial (unfactored row) */
273     idx      = r[i];
274     nz       = ai[idx+1] - ai[idx];
275     ajtmpold = aj + ai[idx];
276     v        = aa + 25*ai[idx];
277     for ( j=0; j<nz; j++ ) {
278       x    = rtmp+25*ic[ajtmpold[j]];
279       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
280       x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
281       x[9] = v[9]; x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
282       x[14] = v[14]; x[15] = v[15]; x[16] = v[16]; x[17] = v[17];
283       x[18] = v[18]; x[19] = v[19]; x[20] = v[20]; x[21] = v[21];
284       x[22] = v[22]; x[23] = v[23]; x[24] = v[24];
285       v    += 25;
286     }
287     row = *ajtmp++;
288     while (row < i) {
289       pc = rtmp + 25*row;
290       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
291       p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
292       p10 = pc[9]; p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
293       p15 = pc[14]; p16 = pc[15]; p17 = pc[16]; p18 = pc[17]; p19 = pc[18];
294       p20 = pc[19]; p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
295       p25 = pc[24];
296       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
297           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
298           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
299           || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 ||
300           p20 != 0.0 || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 ||
301           p24 != 0.0 || p25 != 0.0) {
302         pv = ba + 25*diag_offset[row];
303         pj = bj + diag_offset[row] + 1;
304         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
305         x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
306         x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
307         x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17];
308         x19 = pv[18]; x20 = pv[19]; x21 = pv[20]; x22 = pv[21];
309         x23 = pv[22]; x24 = pv[23]; x25 = pv[24];
310         pc[0] = m1 = p1*x1 + p6*x2  + p11*x3 + p16*x4 + p21*x5;
311         pc[1] = m2 = p2*x1 + p7*x2  + p12*x3 + p17*x4 + p22*x5;
312         pc[2] = m3 = p3*x1 + p8*x2  + p13*x3 + p18*x4 + p23*x5;
313         pc[3] = m4 = p4*x1 + p9*x2  + p14*x3 + p19*x4 + p24*x5;
314         pc[4] = m5 = p5*x1 + p10*x2 + p15*x3 + p20*x4 + p25*x5;
315 
316         pc[5] = m6 = p1*x6 + p6*x7  + p11*x8 + p16*x9 + p21*x10;
317         pc[6] = m7 = p2*x6 + p7*x7  + p12*x8 + p17*x9 + p22*x10;
318         pc[7] = m8 = p3*x6 + p8*x7  + p13*x8 + p18*x9 + p23*x10;
319         pc[8] = m9 = p4*x6 + p9*x7  + p14*x8 + p19*x9 + p24*x10;
320         pc[9] = m10 = p5*x6 + p10*x7 + p15*x8 + p20*x9 + p25*x10;
321 
322         pc[10] = m11 = p1*x11 + p6*x12  + p11*x13 + p16*x14 + p21*x15;
323         pc[11] = m12 = p2*x11 + p7*x12  + p12*x13 + p17*x14 + p22*x15;
324         pc[12] = m13 = p3*x11 + p8*x12  + p13*x13 + p18*x14 + p23*x15;
325         pc[13] = m14 = p4*x11 + p9*x12  + p14*x13 + p19*x14 + p24*x15;
326         pc[14] = m15 = p5*x11 + p10*x12 + p15*x13 + p20*x14 + p25*x15;
327 
328         pc[15] = m16 = p1*x16 + p6*x17  + p11*x18 + p16*x19 + p21*x20;
329         pc[16] = m17 = p2*x16 + p7*x17  + p12*x18 + p17*x19 + p22*x20;
330         pc[17] = m18 = p3*x16 + p8*x17  + p13*x18 + p18*x19 + p23*x20;
331         pc[18] = m19 = p4*x16 + p9*x17  + p14*x18 + p19*x19 + p24*x20;
332         pc[19] = m20 = p5*x16 + p10*x17 + p15*x18 + p20*x19 + p25*x20;
333 
334         pc[20] = m21 = p1*x21 + p6*x22  + p11*x23 + p16*x24 + p21*x25;
335         pc[21] = m22 = p2*x21 + p7*x22  + p12*x23 + p17*x24 + p22*x25;
336         pc[22] = m23 = p3*x21 + p8*x22  + p13*x23 + p18*x24 + p23*x25;
337         pc[23] = m24 = p4*x21 + p9*x22  + p14*x23 + p19*x24 + p24*x25;
338         pc[24] = m25 = p5*x21 + p10*x22 + p15*x23 + p20*x24 + p25*x25;
339 
340         nz = bi[row+1] - diag_offset[row] - 1;
341         pv += 25;
342         for (j=0; j<nz; j++) {
343           x1   = pv[0];  x2 = pv[1];   x3  = pv[2];  x4  = pv[3];
344           x5   = pv[4];  x6 = pv[5];   x7  = pv[6];  x8  = pv[7]; x9 = pv[8];
345           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
346           x14  = pv[13]; x15 = pv[14]; x16 = pv[15]; x17 = pv[16];
347           x18  = pv[17]; x19 = pv[18]; x20 = pv[19]; x21 = pv[20];
348           x22  = pv[21]; x23 = pv[22]; x24 = pv[23]; x25 = pv[24];
349           x    = rtmp + 25*pj[j];
350           x[0] -= m1*x1 + m6*x2  + m11*x3 + m16*x4 + m21*x5;
351           x[1] -= m2*x1 + m7*x2  + m12*x3 + m17*x4 + m22*x5;
352           x[2] -= m3*x1 + m8*x2  + m13*x3 + m18*x4 + m23*x5;
353           x[3] -= m4*x1 + m9*x2  + m14*x3 + m19*x4 + m24*x5;
354           x[4] -= m5*x1 + m10*x2 + m15*x3 + m20*x4 + m25*x5;
355 
356           x[5] -= m1*x6 + m6*x7  + m11*x8 + m16*x9 + m21*x10;
357           x[6] -= m2*x6 + m7*x7  + m12*x8 + m17*x9 + m22*x10;
358           x[7] -= m3*x6 + m8*x7  + m13*x8 + m18*x9 + m23*x10;
359           x[8] -= m4*x6 + m9*x7  + m14*x8 + m19*x9 + m24*x10;
360           x[9] -= m5*x6 + m10*x7 + m15*x8 + m20*x9 + m25*x10;
361 
362           x[10] -= m1*x11 + m6*x12  + m11*x13 + m16*x14 + m21*x15;
363           x[11] -= m2*x11 + m7*x12  + m12*x13 + m17*x14 + m22*x15;
364           x[12] -= m3*x11 + m8*x12  + m13*x13 + m18*x14 + m23*x15;
365           x[13] -= m4*x11 + m9*x12  + m14*x13 + m19*x14 + m24*x15;
366           x[14] -= m5*x11 + m10*x12 + m15*x13 + m20*x14 + m25*x15;
367 
368           x[15] -= m1*x16 + m6*x17  + m11*x18 + m16*x19 + m21*x20;
369           x[16] -= m2*x16 + m7*x17  + m12*x18 + m17*x19 + m22*x20;
370           x[17] -= m3*x16 + m8*x17  + m13*x18 + m18*x19 + m23*x20;
371           x[18] -= m4*x16 + m9*x17  + m14*x18 + m19*x19 + m24*x20;
372           x[19] -= m5*x16 + m10*x17 + m15*x18 + m20*x19 + m25*x20;
373 
374           x[20] -= m1*x21 + m6*x22  + m11*x23 + m16*x24 + m21*x25;
375           x[21] -= m2*x21 + m7*x22  + m12*x23 + m17*x24 + m22*x25;
376           x[22] -= m3*x21 + m8*x22  + m13*x23 + m18*x24 + m23*x25;
377           x[23] -= m4*x21 + m9*x22  + m14*x23 + m19*x24 + m24*x25;
378           x[24] -= m5*x21 + m10*x22 + m15*x23 + m20*x24 + m25*x25;
379 
380           pv   += 25;
381         }
382         PLogFlops(250*nz+225);
383       }
384       row = *ajtmp++;
385     }
386     /* finished row so stick it into b->a */
387     pv = ba + 25*bi[i];
388     pj = bj + bi[i];
389     nz = bi[i+1] - bi[i];
390     for ( j=0; j<nz; j++ ) {
391       x     = rtmp+25*pj[j];
392       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
393       pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
394       pv[9] = x[9]; pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
395       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; pv[16] = x[16];
396       pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19]; pv[20] = x[20];
397       pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23]; pv[24] = x[24];
398       pv   += 25;
399     }
400     /* invert diagonal block */
401     w = ba + 25*diag_offset[i];
402     Kernel_A_gets_inverse_A(bs,w,v_pivots,v_work);
403   }
404 
405   PetscFree(rtmp);
406   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
407   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
408   ierr = ISDestroy(isicol); CHKERRQ(ierr);
409   C->factor = FACTOR_LU;
410   C->assembled = PETSC_TRUE;
411   PLogFlops(1.3333*125*b->mbs); /* from inverting diagonal blocks */
412   return 0;
413 }
414 
415 /* ------------------------------------------------------------*/
416 /*
417       Version for when blocks are 4 by 4
418 */
419 #undef __FUNC__
420 #define __FUNC__ "MatLUFactorNumeric_SeqBAIJ_4"
421 int MatLUFactorNumeric_SeqBAIJ_4(Mat A,Mat *B)
422 {
423   Mat             C = *B;
424   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data,*b = (Mat_SeqBAIJ *)C->data;
425   IS              iscol = b->col, isrow = b->row, isicol;
426   int             *r,*ic, ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
427   int             *ajtmpold, *ajtmp, nz, row, v_pivots[4];
428   int             *diag_offset = b->diag,bs = 4,idx,*ai=a->i,*aj=a->j;
429   register Scalar *pv,*v,*rtmp,*pc,*w,*x;
430   Scalar          p1,p2,p3,p4,v_work[4],m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
431   Scalar          p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
432   Scalar          p10,p11,p12,p13,p14,p15,p16,m10,m11,m12;
433   Scalar          m13,m14,m15,m16;
434   Scalar          *ba = b->a,*aa = a->a;
435   register int    *pj;
436 
437   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
438   PLogObjectParent(*B,isicol);
439   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
440   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
441   rtmp  = (Scalar *) PetscMalloc(16*(n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
442 
443   for ( i=0; i<n; i++ ) {
444     nz    = bi[i+1] - bi[i];
445     ajtmp = bj + bi[i];
446     for  ( j=0; j<nz; j++ ) {
447       x = rtmp+16*ajtmp[j];
448       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
449       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
450     }
451     /* load in initial (unfactored row) */
452     idx      = r[i];
453     nz       = ai[idx+1] - ai[idx];
454     ajtmpold = aj + ai[idx];
455     v        = aa + 16*ai[idx];
456     for ( j=0; j<nz; j++ ) {
457       x    = rtmp+16*ic[ajtmpold[j]];
458       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
459       x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
460       x[9] = v[9]; x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
461       x[14] = v[14]; x[15] = v[15];
462       v    += 16;
463     }
464     row = *ajtmp++;
465     while (row < i) {
466       pc = rtmp + 16*row;
467       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
468       p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
469       p10 = pc[9]; p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
470       p15 = pc[14]; p16 = pc[15];
471       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
472           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
473           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
474           || p16 != 0.0) {
475         pv = ba + 16*diag_offset[row];
476         pj = bj + diag_offset[row] + 1;
477         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
478         x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
479         x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
480         x15 = pv[14]; x16 = pv[15];
481         pc[0] = m1 = p1*x1 + p5*x2  + p9*x3  + p13*x4;
482         pc[1] = m2 = p2*x1 + p6*x2  + p10*x3 + p14*x4;
483         pc[2] = m3 = p3*x1 + p7*x2  + p11*x3 + p15*x4;
484         pc[3] = m4 = p4*x1 + p8*x2  + p12*x3 + p16*x4;
485 
486         pc[4] = m5 = p1*x5 + p5*x6  + p9*x7  + p13*x8;
487         pc[5] = m6 = p2*x5 + p6*x6  + p10*x7 + p14*x8;
488         pc[6] = m7 = p3*x5 + p7*x6  + p11*x7 + p15*x8;
489         pc[7] = m8 = p4*x5 + p8*x6  + p12*x7 + p16*x8;
490 
491         pc[8]  = m9  = p1*x9 + p5*x10  + p9*x11  + p13*x12;
492         pc[9]  = m10 = p2*x9 + p6*x10  + p10*x11 + p14*x12;
493         pc[10] = m11 = p3*x9 + p7*x10  + p11*x11 + p15*x12;
494         pc[11] = m12 = p4*x9 + p8*x10  + p12*x11 + p16*x12;
495 
496         pc[12] = m13 = p1*x13 + p5*x14  + p9*x15  + p13*x16;
497         pc[13] = m14 = p2*x13 + p6*x14  + p10*x15 + p14*x16;
498         pc[14] = m15 = p3*x13 + p7*x14  + p11*x15 + p15*x16;
499         pc[15] = m16 = p4*x13 + p8*x14  + p12*x15 + p16*x16;
500 
501         nz = bi[row+1] - diag_offset[row] - 1;
502         pv += 16;
503         for (j=0; j<nz; j++) {
504           x1   = pv[0];  x2 = pv[1];   x3  = pv[2];  x4  = pv[3];
505           x5   = pv[4];  x6 = pv[5];   x7  = pv[6];  x8  = pv[7]; x9 = pv[8];
506           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
507           x14  = pv[13]; x15 = pv[14]; x16 = pv[15];
508           x    = rtmp + 16*pj[j];
509           x[0] -= m1*x1 + m5*x2  + m9*x3 + m13*x4;
510           x[1] -= m2*x1 + m6*x2  + m10*x3 + m14*x4;
511           x[2] -= m3*x1 + m7*x2  + m11*x3 + m15*x4;
512           x[3] -= m4*x1 + m8*x2  + m12*x3 + m16*x4;
513 
514           x[4] -= m1*x5 + m5*x6  + m9*x7  + m13*x8;
515           x[5] -= m2*x5 + m6*x6  + m10*x7 + m14*x8;
516           x[6] -= m3*x5 + m7*x6  + m11*x7 + m15*x8;
517           x[7] -= m4*x5 + m8*x6  + m12*x7 + m16*x8;
518 
519           x[8] -= m1*x9  + m5*x10  + m9*x11 + m13*x12;
520           x[9] -= m2*x9  + m6*x10  + m10*x11 + m14*x12;
521           x[10] -= m3*x9 + m7*x10  + m11*x11 + m15*x12;
522           x[11] -= m4*x9 + m8*x10  + m12*x11 + m16*x12;
523 
524           x[12] -= m1*x13 + m5*x14  + m9*x15 + m13*x16;
525           x[13] -= m2*x13 + m6*x14  + m10*x15 + m14*x16;
526           x[14] -= m3*x13 + m7*x14  + m11*x15 + m15*x16;
527           x[15] -= m4*x13 + m8*x14  + m12*x15 + m16*x16;
528 
529           pv   += 16;
530         }
531         PLogFlops(128*nz+112);
532       }
533       row = *ajtmp++;
534     }
535     /* finished row so stick it into b->a */
536     pv = ba + 16*bi[i];
537     pj = bj + bi[i];
538     nz = bi[i+1] - bi[i];
539     for ( j=0; j<nz; j++ ) {
540       x     = rtmp+16*pj[j];
541       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
542       pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
543       pv[9] = x[9]; pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
544       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
545       pv   += 16;
546     }
547     /* invert diagonal block */
548     w = ba + 16*diag_offset[i];
549     Kernel_A_gets_inverse_A(bs,w,v_pivots,v_work);
550   }
551 
552   PetscFree(rtmp);
553   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
554   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
555   ierr = ISDestroy(isicol); CHKERRQ(ierr);
556   C->factor = FACTOR_LU;
557   C->assembled = PETSC_TRUE;
558   PLogFlops(1.3333*64*b->mbs); /* from inverting diagonal blocks */
559   return 0;
560 }
561 /* ------------------------------------------------------------*/
562 /*
563       Version for when blocks are 3 by 3
564 */
565 #undef __FUNC__
566 #define __FUNC__ "MatLUFactorNumeric_SeqBAIJ_3"
567 int MatLUFactorNumeric_SeqBAIJ_3(Mat A,Mat *B)
568 {
569   Mat             C = *B;
570   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data,*b = (Mat_SeqBAIJ *)C->data;
571   IS              iscol = b->col, isrow = b->row, isicol;
572   int             *r,*ic, ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
573   int             *ajtmpold, *ajtmp, nz, row, *ai=a->i,*aj=a->j;
574   int             *diag_offset = b->diag,idx;
575   register Scalar *pv,*v,*rtmp,*pc,*w,*x;
576   Scalar          p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
577   Scalar          p5,p6,p7,p8,p9,x5,x6,x7,x8,x9;
578   Scalar          *ba = b->a,*aa = a->a;
579   register int    *pj;
580 
581   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
582   PLogObjectParent(*B,isicol);
583   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
584   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
585   rtmp  = (Scalar *) PetscMalloc(9*(n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
586 
587   for ( i=0; i<n; i++ ) {
588     nz    = bi[i+1] - bi[i];
589     ajtmp = bj + bi[i];
590     for  ( j=0; j<nz; j++ ) {
591       x = rtmp + 9*ajtmp[j];
592       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
593     }
594     /* load in initial (unfactored row) */
595     idx      = r[i];
596     nz       = ai[idx+1] - ai[idx];
597     ajtmpold = aj + ai[idx];
598     v        = aa + 9*ai[idx];
599     for ( j=0; j<nz; j++ ) {
600       x    = rtmp + 9*ic[ajtmpold[j]];
601       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
602       x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
603       v    += 9;
604     }
605     row = *ajtmp++;
606     while (row < i) {
607       pc = rtmp + 9*row;
608       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
609       p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
610       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
611           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0) {
612         pv = ba + 9*diag_offset[row];
613         pj = bj + diag_offset[row] + 1;
614         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
615         x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
616         pc[0] = m1 = p1*x1 + p4*x2 + p7*x3;
617         pc[1] = m2 = p2*x1 + p5*x2 + p8*x3;
618         pc[2] = m3 = p3*x1 + p6*x2 + p9*x3;
619 
620         pc[3] = m4 = p1*x4 + p4*x5 + p7*x6;
621         pc[4] = m5 = p2*x4 + p5*x5 + p8*x6;
622         pc[5] = m6 = p3*x4 + p6*x5 + p9*x6;
623 
624         pc[6] = m7 = p1*x7 + p4*x8 + p7*x9;
625         pc[7] = m8 = p2*x7 + p5*x8 + p8*x9;
626         pc[8] = m9 = p3*x7 + p6*x8 + p9*x9;
627         nz = bi[row+1] - diag_offset[row] - 1;
628         pv += 9;
629         for (j=0; j<nz; j++) {
630           x1   = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
631           x5   = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
632           x    = rtmp + 9*pj[j];
633           x[0] -= m1*x1 + m4*x2 + m7*x3;
634           x[1] -= m2*x1 + m5*x2 + m8*x3;
635           x[2] -= m3*x1 + m6*x2 + m9*x3;
636 
637           x[3] -= m1*x4 + m4*x5 + m7*x6;
638           x[4] -= m2*x4 + m5*x5 + m8*x6;
639           x[5] -= m3*x4 + m6*x5 + m9*x6;
640 
641           x[6] -= m1*x7 + m4*x8 + m7*x9;
642           x[7] -= m2*x7 + m5*x8 + m8*x9;
643           x[8] -= m3*x7 + m6*x8 + m9*x9;
644           pv   += 9;
645         }
646         PLogFlops(54*nz+36);
647       }
648       row = *ajtmp++;
649     }
650     /* finished row so stick it into b->a */
651     pv = ba + 9*bi[i];
652     pj = bj + bi[i];
653     nz = bi[i+1] - bi[i];
654     for ( j=0; j<nz; j++ ) {
655       x     = rtmp + 9*pj[j];
656       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
657       pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
658       pv   += 9;
659     }
660     /* invert diagonal block */
661     w = ba + 9*diag_offset[i];
662     ierr = Kernel_A_gets_inverse_A_3(w); CHKERRQ(ierr);
663   }
664 
665   PetscFree(rtmp);
666   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
667   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
668   ierr = ISDestroy(isicol); CHKERRQ(ierr);
669   C->factor = FACTOR_LU;
670   C->assembled = PETSC_TRUE;
671   PLogFlops(1.3333*27*b->mbs); /* from inverting diagonal blocks */
672   return 0;
673 }
674 
675 /* ------------------------------------------------------------*/
676 /*
677       Version for when blocks are 2 by 2
678 */
679 #undef __FUNC__
680 #define __FUNC__ "MatLUFactorNumeric_SeqBAIJ_2"
681 int MatLUFactorNumeric_SeqBAIJ_2(Mat A,Mat *B)
682 {
683   Mat             C = *B;
684   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data,*b = (Mat_SeqBAIJ *)C->data;
685   IS              iscol = b->col, isrow = b->row, isicol;
686   int             *r,*ic, ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
687   int             *ajtmpold, *ajtmp, nz, row, v_pivots[2];
688   int             *diag_offset=b->diag,bs = 2,idx,*ai=a->i,*aj=a->j;
689   register Scalar *pv,*v,*rtmp,m1,m2,m3,m4,*pc,*w,*x,x1,x2,x3,x4;
690   Scalar          p1,p2,p3,p4,v_work[2];
691   Scalar          *ba = b->a,*aa = a->a;
692   register int    *pj;
693 
694   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
695   PLogObjectParent(*B,isicol);
696   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
697   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
698   rtmp  = (Scalar *) PetscMalloc(4*(n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
699 
700   for ( i=0; i<n; i++ ) {
701     nz    = bi[i+1] - bi[i];
702     ajtmp = bj + bi[i];
703     for  ( j=0; j<nz; j++ ) {
704       x = rtmp+4*ajtmp[j]; x[0] = x[1] = x[2] = x[3] = 0.0;
705     }
706     /* load in initial (unfactored row) */
707     idx      = r[i];
708     nz       = ai[idx+1] - ai[idx];
709     ajtmpold = aj + ai[idx];
710     v        = aa + 4*ai[idx];
711     for ( j=0; j<nz; j++ ) {
712       x    = rtmp+4*ic[ajtmpold[j]];
713       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
714       v    += 4;
715     }
716     row = *ajtmp++;
717     while (row < i) {
718       pc = rtmp + 4*row;
719       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
720       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0) {
721         pv = ba + 4*diag_offset[row];
722         pj = bj + diag_offset[row] + 1;
723         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
724         pc[0] = m1 = p1*x1 + p3*x2;
725         pc[1] = m2 = p2*x1 + p4*x2;
726         pc[2] = m3 = p1*x3 + p3*x4;
727         pc[3] = m4 = p2*x3 + p4*x4;
728         nz = bi[row+1] - diag_offset[row] - 1;
729         pv += 4;
730         for (j=0; j<nz; j++) {
731           x1   = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
732           x    = rtmp + 4*pj[j];
733           x[0] -= m1*x1 + m3*x2;
734           x[1] -= m2*x1 + m4*x2;
735           x[2] -= m1*x3 + m3*x4;
736           x[3] -= m2*x3 + m4*x4;
737           pv   += 4;
738         }
739         PLogFlops(16*nz+12);
740       }
741       row = *ajtmp++;
742     }
743     /* finished row so stick it into b->a */
744     pv = ba + 4*bi[i];
745     pj = bj + bi[i];
746     nz = bi[i+1] - bi[i];
747     for ( j=0; j<nz; j++ ) {
748       x     = rtmp+4*pj[j];
749       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
750       pv   += 4;
751     }
752     /* invert diagonal block */
753     w = ba + 4*diag_offset[i];
754     Kernel_A_gets_inverse_A(bs,w,v_pivots,v_work);
755   }
756 
757   PetscFree(rtmp);
758   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
759   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
760   ierr = ISDestroy(isicol); CHKERRQ(ierr);
761   C->factor = FACTOR_LU;
762   C->assembled = PETSC_TRUE;
763   PLogFlops(1.3333*8*b->mbs); /* from inverting diagonal blocks */
764   return 0;
765 }
766 
767 /* ----------------------------------------------------------- */
768 /*
769      Version for when blocks are 1 by 1.
770 */
771 #undef __FUNC__
772 #define __FUNC__ "MatLUFactorNumeric_SeqBAIJ_1"
773 int MatLUFactorNumeric_SeqBAIJ_1(Mat A,Mat *B)
774 {
775   Mat             C = *B;
776   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *) A->data, *b = (Mat_SeqBAIJ *)C->data;
777   IS              iscol = b->col, isrow = b->row, isicol;
778   int             *r,*ic, ierr, i, j, n = a->mbs, *bi = b->i, *bj = b->j;
779   int             *ajtmpold, *ajtmp, nz, row,*ai = a->i,*aj = a->j;
780   int             *diag_offset = b->diag,diag;
781   register Scalar *pv,*v,*rtmp,multiplier,*pc;
782   Scalar          *ba = b->a,*aa = a->a;
783   register int    *pj;
784 
785   ierr  = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
786   PLogObjectParent(*B,isicol);
787   ierr  = ISGetIndices(isrow,&r); CHKERRQ(ierr);
788   ierr  = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
789   rtmp  = (Scalar *) PetscMalloc((n+1)*sizeof(Scalar));CHKPTRQ(rtmp);
790 
791   for ( i=0; i<n; i++ ) {
792     nz    = bi[i+1] - bi[i];
793     ajtmp = bj + bi[i];
794     for  ( j=0; j<nz; j++ ) rtmp[ajtmp[j]] = 0.0;
795 
796     /* load in initial (unfactored row) */
797     nz       = ai[r[i]+1] - ai[r[i]];
798     ajtmpold = aj + ai[r[i]];
799     v        = aa + ai[r[i]];
800     for ( j=0; j<nz; j++ ) rtmp[ic[ajtmpold[j]]] =  v[j];
801 
802     row = *ajtmp++;
803     while (row < i) {
804       pc = rtmp + row;
805       if (*pc != 0.0) {
806         pv         = ba + diag_offset[row];
807         pj         = bj + diag_offset[row] + 1;
808         multiplier = *pc * *pv++;
809         *pc        = multiplier;
810         nz         = bi[row+1] - diag_offset[row] - 1;
811         for (j=0; j<nz; j++) rtmp[pj[j]] -= multiplier * pv[j];
812         PLogFlops(1+2*nz);
813       }
814       row = *ajtmp++;
815     }
816     /* finished row so stick it into b->a */
817     pv = ba + bi[i];
818     pj = bj + bi[i];
819     nz = bi[i+1] - bi[i];
820     for ( j=0; j<nz; j++ ) {pv[j] = rtmp[pj[j]];}
821     diag = diag_offset[i] - bi[i];
822     /* check pivot entry for current row */
823     if (pv[diag] == 0.0) {
824       SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,0,"Zero pivot");
825     }
826     pv[diag] = 1.0/pv[diag];
827   }
828 
829   PetscFree(rtmp);
830   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
831   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
832   ierr = ISDestroy(isicol); CHKERRQ(ierr);
833   C->factor    = FACTOR_LU;
834   C->assembled = PETSC_TRUE;
835   PLogFlops(b->n);
836   return 0;
837 }
838 
839 /* ----------------------------------------------------------- */
840 #undef __FUNC__
841 #define __FUNC__ "MatLUFactor_SeqBAIJ"
842 int MatLUFactor_SeqBAIJ(Mat A,IS row,IS col,double f)
843 {
844   Mat_SeqBAIJ *mat = (Mat_SeqBAIJ *) A->data;
845   int         ierr;
846   Mat         C;
847 
848   ierr = MatLUFactorSymbolic(A,row,col,f,&C); CHKERRQ(ierr);
849   ierr = MatLUFactorNumeric(A,&C); CHKERRQ(ierr);
850 
851   /* free all the data structures from mat */
852   PetscFree(mat->a);
853   if (!mat->singlemalloc) {PetscFree(mat->i); PetscFree(mat->j);}
854   if (mat->diag) PetscFree(mat->diag);
855   if (mat->ilen) PetscFree(mat->ilen);
856   if (mat->imax) PetscFree(mat->imax);
857   if (mat->solve_work) PetscFree(mat->solve_work);
858   if (mat->mult_work) PetscFree(mat->mult_work);
859   PetscFree(mat);
860 
861   PetscMemcpy(A,C,sizeof(struct _Mat));
862   PetscHeaderDestroy(C);
863   return 0;
864 }
865 /* ----------------------------------------------------------- */
866 #undef __FUNC__
867 #define __FUNC__ "MatSolve_SeqBAIJ_N"
868 int MatSolve_SeqBAIJ_N(Mat A,Vec bb,Vec xx)
869 {
870   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
871   IS              iscol=a->col,isrow=a->row;
872   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j;
873   int             nz,bs=a->bs,bs2=a->bs2,*rout,*cout;
874   Scalar          *aa=a->a,*sum;
875   register Scalar *x,*b,*lsum,*tmp,*v;
876 
877   VecGetArray_Fast(bb,b);
878   VecGetArray_Fast(xx,x);
879   tmp  = a->solve_work;
880 
881   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
882   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
883 
884   /* forward solve the lower triangular */
885   PetscMemcpy(tmp,b + bs*(*r++), bs*sizeof(Scalar));
886   for ( i=1; i<n; i++ ) {
887     v   = aa + bs2*ai[i];
888     vi  = aj + ai[i];
889     nz  = a->diag[i] - ai[i];
890     sum = tmp + bs*i;
891     PetscMemcpy(sum,b+bs*(*r++),bs*sizeof(Scalar));
892     while (nz--) {
893       Kernel_v_gets_v_minus_A_times_w(bs,sum,v,tmp+bs*(*vi++));
894       v += bs2;
895     }
896   }
897   /* backward solve the upper triangular */
898   lsum = a->solve_work + a->n;
899   for ( i=n-1; i>=0; i-- ){
900     v   = aa + bs2*(a->diag[i] + 1);
901     vi  = aj + a->diag[i] + 1;
902     nz  = ai[i+1] - a->diag[i] - 1;
903     PetscMemcpy(lsum,tmp+i*bs,bs*sizeof(Scalar));
904     while (nz--) {
905       Kernel_v_gets_v_minus_A_times_w(bs,lsum,v,tmp+bs*(*vi++));
906       v += bs2;
907     }
908     Kernel_w_gets_A_times_v(bs,lsum,aa+bs2*a->diag[i],tmp+i*bs);
909     PetscMemcpy(x + bs*(*c--),tmp+i*bs,bs*sizeof(Scalar));
910   }
911 
912   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
913   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
914   VecRestoreArray_Fast(bb,b);
915   VecRestoreArray_Fast(xx,x);
916   PLogFlops(2*(a->bs2)*(a->nz) - a->n);
917   return 0;
918 }
919 
920 #undef __FUNC__
921 #define __FUNC__ "MatSolve_SeqBAIJ_7"
922 int MatSolve_SeqBAIJ_7(Mat A,Vec bb,Vec xx)
923 {
924   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
925   IS              iscol=a->col,isrow=a->row;
926   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout;
927   Scalar          *aa=a->a,sum1,sum2,sum3,sum4,sum5,sum6,sum7,x1,x2,x3,x4,x5,x6,x7;
928   register Scalar *x,*b,*tmp,*v;
929 
930   VecGetArray_Fast(bb,b);
931   VecGetArray_Fast(xx,x);
932   tmp  = a->solve_work;
933 
934   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
935   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
936 
937   /* forward solve the lower triangular */
938   idx    = 7*(*r++);
939   tmp[0] = b[idx];   tmp[1] = b[1+idx];
940   tmp[2] = b[2+idx]; tmp[3] = b[3+idx]; tmp[4] = b[4+idx];
941   tmp[5] = b[5+idx]; tmp[6] = b[6+idx];
942 
943   for ( i=1; i<n; i++ ) {
944     v     = aa + 49*ai[i];
945     vi    = aj + ai[i];
946     nz    = a->diag[i] - ai[i];
947     idx   = 7*(*r++);
948     sum1  = b[idx];sum2 = b[1+idx];sum3 = b[2+idx];sum4 = b[3+idx];
949     sum5  = b[4+idx];sum6 = b[5+idx];sum7 = b[6+idx];
950     while (nz--) {
951       idx   = 7*(*vi++);
952       x1    = tmp[idx];  x2 = tmp[1+idx];x3 = tmp[2+idx];
953       x4    = tmp[3+idx];x5 = tmp[4+idx];
954       x6    = tmp[5+idx];x7 = tmp[6+idx];
955       sum1 -= v[0]*x1 + v[7]*x2  + v[14]*x3 + v[21]*x4 + v[28]*x5 + v[35]*x6 + v[42]*x7;
956       sum2 -= v[1]*x1 + v[8]*x2  + v[15]*x3 + v[22]*x4 + v[29]*x5 + v[36]*x6 + v[43]*x7;
957       sum3 -= v[2]*x1 + v[9]*x2  + v[16]*x3 + v[23]*x4 + v[30]*x5 + v[37]*x6 + v[44]*x7;
958       sum4 -= v[3]*x1 + v[10]*x2 + v[17]*x3 + v[24]*x4 + v[31]*x5 + v[38]*x6 + v[45]*x7;
959       sum5 -= v[4]*x1 + v[11]*x2 + v[18]*x3 + v[25]*x4 + v[32]*x5 + v[39]*x6 + v[46]*x7;
960       sum6 -= v[5]*x1 + v[12]*x2 + v[19]*x3 + v[26]*x4 + v[33]*x5 + v[40]*x6 + v[47]*x7;
961       sum7 -= v[6]*x1 + v[13]*x2 + v[20]*x3 + v[27]*x4 + v[34]*x5 + v[41]*x6 + v[48]*x7;
962       v += 49;
963     }
964     idx = 7*i;
965     tmp[idx]   = sum1;tmp[1+idx] = sum2;
966     tmp[2+idx] = sum3;tmp[3+idx] = sum4; tmp[4+idx] = sum5;
967     tmp[5+idx] = sum6;tmp[6+idx] = sum7;
968   }
969   /* backward solve the upper triangular */
970   for ( i=n-1; i>=0; i-- ){
971     v    = aa + 49*a->diag[i] + 49;
972     vi   = aj + a->diag[i] + 1;
973     nz   = ai[i+1] - a->diag[i] - 1;
974     idt  = 7*i;
975     sum1 = tmp[idt];  sum2 = tmp[1+idt];
976     sum3 = tmp[2+idt];sum4 = tmp[3+idt]; sum5 = tmp[4+idt];
977     sum6 = tmp[5+idt];sum7 = tmp[6+idt];
978     while (nz--) {
979       idx   = 7*(*vi++);
980       x1    = tmp[idx];   x2 = tmp[1+idx];
981       x3    = tmp[2+idx]; x4 = tmp[3+idx]; x5 = tmp[4+idx];
982       x6    = tmp[5+idx]; x7 = tmp[6+idx];
983       sum1 -= v[0]*x1 + v[7]*x2  + v[14]*x3 + v[21]*x4 + v[28]*x5 + v[35]*x6 + v[42]*x7;
984       sum2 -= v[1]*x1 + v[8]*x2  + v[15]*x3 + v[22]*x4 + v[29]*x5 + v[36]*x6 + v[43]*x7;
985       sum3 -= v[2]*x1 + v[9]*x2  + v[16]*x3 + v[23]*x4 + v[30]*x5 + v[37]*x6 + v[44]*x7;
986       sum4 -= v[3]*x1 + v[10]*x2 + v[17]*x3 + v[24]*x4 + v[31]*x5 + v[38]*x6 + v[45]*x7;
987       sum5 -= v[4]*x1 + v[11]*x2 + v[18]*x3 + v[25]*x4 + v[32]*x5 + v[39]*x6 + v[46]*x7;
988       sum6 -= v[5]*x1 + v[12]*x2 + v[19]*x3 + v[26]*x4 + v[33]*x5 + v[40]*x6 + v[47]*x7;
989       sum7 -= v[6]*x1 + v[13]*x2 + v[20]*x3 + v[27]*x4 + v[34]*x5 + v[41]*x6 + v[48]*x7;
990       v += 49;
991     }
992     idc = 7*(*c--);
993     v   = aa + 49*a->diag[i];
994     x[idc]   = tmp[idt]   = v[0]*sum1+v[7]*sum2+v[14]*sum3+
995                                  v[21]*sum4+v[28]*sum5+v[35]*sum6+v[42]*sum7;
996     x[1+idc] = tmp[1+idt] = v[1]*sum1+v[8]*sum2+v[15]*sum3+
997                                  v[22]*sum4+v[29]*sum5+v[36]*sum6+v[43]*sum7;
998     x[2+idc] = tmp[2+idt] = v[2]*sum1+v[9]*sum2+v[16]*sum3+
999                                  v[23]*sum4+v[30]*sum5+v[37]*sum6+v[44]*sum7;
1000     x[3+idc] = tmp[3+idt] = v[3]*sum1+v[10]*sum2+v[17]*sum3+
1001                                  v[24]*sum4+v[31]*sum5+v[38]*sum6+v[45]*sum7;
1002     x[4+idc] = tmp[4+idt] = v[4]*sum1+v[11]*sum2+v[18]*sum3+
1003                                  v[25]*sum4+v[32]*sum5+v[39]*sum6+v[46]*sum7;
1004     x[5+idc] = tmp[5+idt] = v[5]*sum1+v[12]*sum2+v[19]*sum3+
1005                                  v[26]*sum4+v[33]*sum5+v[40]*sum6+v[47]*sum7;
1006     x[6+idc] = tmp[6+idt] = v[6]*sum1+v[13]*sum2+v[20]*sum3+
1007                                  v[27]*sum4+v[34]*sum5+v[41]*sum6+v[48]*sum7;
1008   }
1009 
1010   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
1011   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
1012   VecRestoreArray_Fast(bb,b);
1013   VecRestoreArray_Fast(xx,x);
1014   PLogFlops(2*49*(a->nz) - a->n);
1015   return 0;
1016 }
1017 
1018 #undef __FUNC__
1019 #define __FUNC__ "MatSolve_SeqBAIJ_5"
1020 int MatSolve_SeqBAIJ_5(Mat A,Vec bb,Vec xx)
1021 {
1022   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
1023   IS              iscol=a->col,isrow=a->row;
1024   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout;
1025   Scalar          *aa=a->a,sum1,sum2,sum3,sum4,sum5,x1,x2,x3,x4,x5;
1026   register Scalar *x,*b,*tmp,*v;
1027 
1028   VecGetArray_Fast(bb,b);
1029   VecGetArray_Fast(xx,x);
1030   tmp  = a->solve_work;
1031 
1032   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1033   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1034 
1035   /* forward solve the lower triangular */
1036   idx    = 5*(*r++);
1037   tmp[0] = b[idx];   tmp[1] = b[1+idx];
1038   tmp[2] = b[2+idx]; tmp[3] = b[3+idx]; tmp[4] = b[4+idx];
1039   for ( i=1; i<n; i++ ) {
1040     v     = aa + 25*ai[i];
1041     vi    = aj + ai[i];
1042     nz    = a->diag[i] - ai[i];
1043     idx   = 5*(*r++);
1044     sum1  = b[idx];sum2 = b[1+idx];sum3 = b[2+idx];sum4 = b[3+idx];
1045     sum5  = b[4+idx];
1046     while (nz--) {
1047       idx   = 5*(*vi++);
1048       x1    = tmp[idx];  x2 = tmp[1+idx];x3 = tmp[2+idx];
1049       x4    = tmp[3+idx];x5 = tmp[4+idx];
1050       sum1 -= v[0]*x1 + v[5]*x2 + v[10]*x3 + v[15]*x4 + v[20]*x5;
1051       sum2 -= v[1]*x1 + v[6]*x2 + v[11]*x3 + v[16]*x4 + v[21]*x5;
1052       sum3 -= v[2]*x1 + v[7]*x2 + v[12]*x3 + v[17]*x4 + v[22]*x5;
1053       sum4 -= v[3]*x1 + v[8]*x2 + v[13]*x3 + v[18]*x4 + v[23]*x5;
1054       sum5 -= v[4]*x1 + v[9]*x2 + v[14]*x3 + v[19]*x4 + v[24]*x5;
1055       v += 25;
1056     }
1057     idx = 5*i;
1058     tmp[idx]   = sum1;tmp[1+idx] = sum2;
1059     tmp[2+idx] = sum3;tmp[3+idx] = sum4; tmp[4+idx] = sum5;
1060   }
1061   /* backward solve the upper triangular */
1062   for ( i=n-1; i>=0; i-- ){
1063     v    = aa + 25*a->diag[i] + 25;
1064     vi   = aj + a->diag[i] + 1;
1065     nz   = ai[i+1] - a->diag[i] - 1;
1066     idt  = 5*i;
1067     sum1 = tmp[idt];  sum2 = tmp[1+idt];
1068     sum3 = tmp[2+idt];sum4 = tmp[3+idt]; sum5 = tmp[4+idt];
1069     while (nz--) {
1070       idx   = 5*(*vi++);
1071       x1    = tmp[idx];   x2 = tmp[1+idx];
1072       x3    = tmp[2+idx]; x4 = tmp[3+idx]; x5 = tmp[4+idx];
1073       sum1 -= v[0]*x1 + v[5]*x2 + v[10]*x3 + v[15]*x4 + v[20]*x5;
1074       sum2 -= v[1]*x1 + v[6]*x2 + v[11]*x3 + v[16]*x4 + v[21]*x5;
1075       sum3 -= v[2]*x1 + v[7]*x2 + v[12]*x3 + v[17]*x4 + v[22]*x5;
1076       sum4 -= v[3]*x1 + v[8]*x2 + v[13]*x3 + v[18]*x4 + v[23]*x5;
1077       sum5 -= v[4]*x1 + v[9]*x2 + v[14]*x3 + v[19]*x4 + v[24]*x5;
1078       v += 25;
1079     }
1080     idc = 5*(*c--);
1081     v   = aa + 25*a->diag[i];
1082     x[idc]   = tmp[idt]   = v[0]*sum1+v[5]*sum2+v[10]*sum3+
1083                                  v[15]*sum4+v[20]*sum5;
1084     x[1+idc] = tmp[1+idt] = v[1]*sum1+v[6]*sum2+v[11]*sum3+
1085                                  v[16]*sum4+v[21]*sum5;
1086     x[2+idc] = tmp[2+idt] = v[2]*sum1+v[7]*sum2+v[12]*sum3+
1087                                  v[17]*sum4+v[22]*sum5;
1088     x[3+idc] = tmp[3+idt] = v[3]*sum1+v[8]*sum2+v[13]*sum3+
1089                                  v[18]*sum4+v[23]*sum5;
1090     x[4+idc] = tmp[4+idt] = v[4]*sum1+v[9]*sum2+v[14]*sum3+
1091                                  v[19]*sum4+v[24]*sum5;
1092   }
1093 
1094   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
1095   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
1096   VecRestoreArray_Fast(bb,b);
1097   VecRestoreArray_Fast(xx,x);
1098   PLogFlops(2*25*(a->nz) - a->n);
1099   return 0;
1100 }
1101 
1102 #undef __FUNC__
1103 #define __FUNC__ "MatSolve_SeqBAIJ_4"
1104 int MatSolve_SeqBAIJ_4(Mat A,Vec bb,Vec xx)
1105 {
1106   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
1107   IS              iscol=a->col,isrow=a->row;
1108   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout;
1109   Scalar          *aa=a->a,sum1,sum2,sum3,sum4,x1,x2,x3,x4;
1110   register Scalar *x,*b,*tmp,*v;
1111 
1112   VecGetArray_Fast(bb,b);
1113   VecGetArray_Fast(xx,x);
1114   tmp  = a->solve_work;
1115 
1116   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1117   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1118 
1119   /* forward solve the lower triangular */
1120   idx    = 4*(*r++);
1121   tmp[0] = b[idx];   tmp[1] = b[1+idx];
1122   tmp[2] = b[2+idx]; tmp[3] = b[3+idx];
1123   for ( i=1; i<n; i++ ) {
1124     v     = aa + 16*ai[i];
1125     vi    = aj + ai[i];
1126     nz    = a->diag[i] - ai[i];
1127     idx   = 4*(*r++);
1128     sum1  = b[idx];sum2 = b[1+idx];sum3 = b[2+idx];sum4 = b[3+idx];
1129     while (nz--) {
1130       idx   = 4*(*vi++);
1131       x1    = tmp[idx];x2 = tmp[1+idx];x3 = tmp[2+idx];x4 = tmp[3+idx];
1132       sum1 -= v[0]*x1 + v[4]*x2 + v[8]*x3  + v[12]*x4;
1133       sum2 -= v[1]*x1 + v[5]*x2 + v[9]*x3  + v[13]*x4;
1134       sum3 -= v[2]*x1 + v[6]*x2 + v[10]*x3 + v[14]*x4;
1135       sum4 -= v[3]*x1 + v[7]*x2 + v[11]*x3 + v[15]*x4;
1136       v += 16;
1137     }
1138     idx = 4*i;
1139     tmp[idx]   = sum1;tmp[1+idx] = sum2;
1140     tmp[2+idx] = sum3;tmp[3+idx] = sum4;
1141   }
1142   /* backward solve the upper triangular */
1143   for ( i=n-1; i>=0; i-- ){
1144     v    = aa + 16*a->diag[i] + 16;
1145     vi   = aj + a->diag[i] + 1;
1146     nz   = ai[i+1] - a->diag[i] - 1;
1147     idt  = 4*i;
1148     sum1 = tmp[idt];  sum2 = tmp[1+idt];
1149     sum3 = tmp[2+idt];sum4 = tmp[3+idt];
1150     while (nz--) {
1151       idx   = 4*(*vi++);
1152       x1    = tmp[idx];   x2 = tmp[1+idx];
1153       x3    = tmp[2+idx]; x4 = tmp[3+idx];
1154       sum1 -= v[0]*x1 + v[4]*x2 + v[8]*x3   + v[12]*x4;
1155       sum2 -= v[1]*x1 + v[5]*x2 + v[9]*x3   + v[13]*x4;
1156       sum3 -= v[2]*x1 + v[6]*x2 + v[10]*x3  + v[14]*x4;
1157       sum4 -= v[3]*x1 + v[7]*x2 + v[11]*x3  + v[15]*x4;
1158       v += 16;
1159     }
1160     idc = 4*(*c--);
1161     v   = aa + 16*a->diag[i];
1162     x[idc]   = tmp[idt]   = v[0]*sum1+v[4]*sum2+v[8]*sum3+v[12]*sum4;
1163     x[1+idc] = tmp[1+idt] = v[1]*sum1+v[5]*sum2+v[9]*sum3+v[13]*sum4;
1164     x[2+idc] = tmp[2+idt] = v[2]*sum1+v[6]*sum2+v[10]*sum3+v[14]*sum4;
1165     x[3+idc] = tmp[3+idt] = v[3]*sum1+v[7]*sum2+v[11]*sum3+v[15]*sum4;
1166   }
1167 
1168   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
1169   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
1170   VecRestoreArray_Fast(bb,b);
1171   VecRestoreArray_Fast(xx,x);
1172   PLogFlops(2*16*(a->nz) - a->n);
1173   return 0;
1174 }
1175 
1176 
1177 #undef __FUNC__
1178 #define __FUNC__ "MatSolve_SeqBAIJ_3"
1179 int MatSolve_SeqBAIJ_3(Mat A,Vec bb,Vec xx)
1180 {
1181   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
1182   IS              iscol=a->col,isrow=a->row;
1183   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout;
1184   Scalar          *aa=a->a,sum1,sum2,sum3,x1,x2,x3;
1185   register Scalar *x,*b,*tmp,*v;
1186 
1187   VecGetArray_Fast(bb,b);
1188   VecGetArray_Fast(xx,x);
1189   tmp  = a->solve_work;
1190 
1191   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1192   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1193 
1194   /* forward solve the lower triangular */
1195   idx    = 3*(*r++);
1196   tmp[0] = b[idx]; tmp[1] = b[1+idx]; tmp[2] = b[2+idx];
1197   for ( i=1; i<n; i++ ) {
1198     v     = aa + 9*ai[i];
1199     vi    = aj + ai[i];
1200     nz    = a->diag[i] - ai[i];
1201     idx   = 3*(*r++);
1202     sum1  = b[idx]; sum2 = b[1+idx]; sum3 = b[2+idx];
1203     while (nz--) {
1204       idx   = 3*(*vi++);
1205       x1    = tmp[idx]; x2 = tmp[1+idx]; x3 = tmp[2+idx];
1206       sum1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
1207       sum2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
1208       sum3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
1209       v += 9;
1210     }
1211     idx = 3*i;
1212     tmp[idx] = sum1; tmp[1+idx] = sum2; tmp[2+idx] = sum3;
1213   }
1214   /* backward solve the upper triangular */
1215   for ( i=n-1; i>=0; i-- ){
1216     v    = aa + 9*a->diag[i] + 9;
1217     vi   = aj + a->diag[i] + 1;
1218     nz   = ai[i+1] - a->diag[i] - 1;
1219     idt  = 3*i;
1220     sum1 = tmp[idt]; sum2 = tmp[1+idt]; sum3 = tmp[2+idt];
1221     while (nz--) {
1222       idx   = 3*(*vi++);
1223       x1    = tmp[idx]; x2 = tmp[1+idx]; x3 = tmp[2+idx];
1224       sum1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
1225       sum2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
1226       sum3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
1227       v += 9;
1228     }
1229     idc = 3*(*c--);
1230     v   = aa + 9*a->diag[i];
1231     x[idc]   = tmp[idt]   = v[0]*sum1 + v[3]*sum2 + v[6]*sum3;
1232     x[1+idc] = tmp[1+idt] = v[1]*sum1 + v[4]*sum2 + v[7]*sum3;
1233     x[2+idc] = tmp[2+idt] = v[2]*sum1 + v[5]*sum2 + v[8]*sum3;
1234   }
1235   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
1236   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
1237   VecRestoreArray_Fast(bb,b);
1238   VecRestoreArray_Fast(xx,x);
1239   PLogFlops(2*9*(a->nz) - a->n);
1240   return 0;
1241 }
1242 
1243 #undef __FUNC__
1244 #define __FUNC__ "MatSolve_SeqBAIJ_2"
1245 int MatSolve_SeqBAIJ_2(Mat A,Vec bb,Vec xx)
1246 {
1247   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
1248   IS              iscol=a->col,isrow=a->row;
1249   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout;
1250   Scalar          *aa=a->a,sum1,sum2,x1,x2;
1251   register Scalar *x,*b,*tmp,*v;
1252 
1253   VecGetArray_Fast(bb,b);
1254   VecGetArray_Fast(xx,x);
1255   tmp  = a->solve_work;
1256 
1257   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1258   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1259 
1260   /* forward solve the lower triangular */
1261   idx    = 2*(*r++);
1262   tmp[0] = b[idx]; tmp[1] = b[1+idx];
1263   for ( i=1; i<n; i++ ) {
1264     v     = aa + 4*ai[i];
1265     vi    = aj + ai[i];
1266     nz    = a->diag[i] - ai[i];
1267     idx   = 2*(*r++);
1268     sum1  = b[idx]; sum2 = b[1+idx];
1269     while (nz--) {
1270       idx   = 2*(*vi++);
1271       x1    = tmp[idx]; x2 = tmp[1+idx];
1272       sum1 -= v[0]*x1 + v[2]*x2;
1273       sum2 -= v[1]*x1 + v[3]*x2;
1274       v += 4;
1275     }
1276     idx = 2*i;
1277     tmp[idx] = sum1; tmp[1+idx] = sum2;
1278   }
1279   /* backward solve the upper triangular */
1280   for ( i=n-1; i>=0; i-- ){
1281     v    = aa + 4*a->diag[i] + 4;
1282     vi   = aj + a->diag[i] + 1;
1283     nz   = ai[i+1] - a->diag[i] - 1;
1284     idt  = 2*i;
1285     sum1 = tmp[idt]; sum2 = tmp[1+idt];
1286     while (nz--) {
1287       idx   = 2*(*vi++);
1288       x1    = tmp[idx]; x2 = tmp[1+idx];
1289       sum1 -= v[0]*x1 + v[2]*x2;
1290       sum2 -= v[1]*x1 + v[3]*x2;
1291       v += 4;
1292     }
1293     idc = 2*(*c--);
1294     v   = aa + 4*a->diag[i];
1295     x[idc]   = tmp[idt]   = v[0]*sum1 + v[2]*sum2;
1296     x[1+idc] = tmp[1+idt] = v[1]*sum1 + v[3]*sum2;
1297   }
1298   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
1299   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
1300   VecRestoreArray_Fast(bb,b);
1301   VecRestoreArray_Fast(xx,x);
1302   PLogFlops(2*4*(a->nz) - a->n);
1303   return 0;
1304 }
1305 
1306 
1307 #undef __FUNC__
1308 #define __FUNC__ "MatSolve_SeqBAIJ_1"
1309 int MatSolve_SeqBAIJ_1(Mat A,Vec bb,Vec xx)
1310 {
1311   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
1312   IS              iscol=a->col,isrow=a->row;
1313   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,*rout,*cout;
1314   Scalar          *aa=a->a,sum1;
1315   register Scalar *x,*b,*tmp,*v;
1316 
1317   if (!n) return 0;
1318 
1319   VecGetArray_Fast(bb,b);
1320   VecGetArray_Fast(xx,x);
1321   tmp  = a->solve_work;
1322 
1323   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1324   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1325 
1326   /* forward solve the lower triangular */
1327   tmp[0] = b[*r++];
1328   for ( i=1; i<n; i++ ) {
1329     v     = aa + ai[i];
1330     vi    = aj + ai[i];
1331     nz    = a->diag[i] - ai[i];
1332     sum1  = b[*r++];
1333     while (nz--) {
1334       sum1 -= (*v++)*tmp[*vi++];
1335     }
1336     tmp[i] = sum1;
1337   }
1338   /* backward solve the upper triangular */
1339   for ( i=n-1; i>=0; i-- ){
1340     v    = aa + a->diag[i] + 1;
1341     vi   = aj + a->diag[i] + 1;
1342     nz   = ai[i+1] - a->diag[i] - 1;
1343     sum1 = tmp[i];
1344     while (nz--) {
1345       sum1 -= (*v++)*tmp[*vi++];
1346     }
1347     x[*c--] = tmp[i] = aa[a->diag[i]]*sum1;
1348   }
1349 
1350   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
1351   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
1352   VecRestoreArray_Fast(bb,b);
1353   VecRestoreArray_Fast(xx,x);
1354   PLogFlops(2*1*(a->nz) - a->n);
1355   return 0;
1356 }
1357 
1358 /* ----------------------------------------------------------------*/
1359 /*
1360      This code is virtually identical to MatILUFactorSymbolic_SeqAIJ
1361    except that the data structure of Mat_SeqAIJ is slightly different.
1362    Not a good example of code reuse.
1363 */
1364 #undef __FUNC__
1365 #define __FUNC__ "MatILUFactorSymbolic_SeqBAIJ"
1366 int MatILUFactorSymbolic_SeqBAIJ(Mat A,IS isrow,IS iscol,double f,int levels,
1367                                  Mat *fact)
1368 {
1369   Mat_SeqBAIJ *a = (Mat_SeqBAIJ *) A->data, *b;
1370   IS          isicol;
1371   int         *r,*ic, ierr, prow, n = a->mbs, *ai = a->i, *aj = a->j;
1372   int         *ainew,*ajnew, jmax,*fill, *xi, nz, *im,*ajfill,*flev;
1373   int         *dloc, idx, row,m,fm, nzf, nzi,len,  realloc = 0;
1374   int         incrlev,nnz,i,bs = a->bs,bs2 = a->bs2;
1375   PetscTruth  col_identity, row_identity;
1376 
1377   /* special case that simply copies fill pattern */
1378   PetscValidHeaderSpecific(isrow,IS_COOKIE);
1379   PetscValidHeaderSpecific(iscol,IS_COOKIE);
1380   ISIdentity(isrow,&row_identity); ISIdentity(iscol,&col_identity);
1381   if (levels == 0 && row_identity && col_identity) {
1382     ierr = MatConvertSameType_SeqBAIJ(A,fact,DO_NOT_COPY_VALUES); CHKERRQ(ierr);
1383     (*fact)->factor = FACTOR_LU;
1384     b               = (Mat_SeqBAIJ *) (*fact)->data;
1385     if (!b->diag) {
1386       ierr = MatMarkDiag_SeqBAIJ(*fact); CHKERRQ(ierr);
1387     }
1388     b->row        = isrow;
1389     b->col        = iscol;
1390     b->solve_work = (Scalar *) PetscMalloc((b->m+1+b->bs)*sizeof(Scalar));CHKPTRQ(b->solve_work);
1391     return 0;
1392   }
1393 
1394   ierr = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
1395   ierr = ISGetIndices(isrow,&r); CHKERRQ(ierr);
1396   ierr = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
1397 
1398   /* get new row pointers */
1399   ainew = (int *) PetscMalloc( (n+1)*sizeof(int) ); CHKPTRQ(ainew);
1400   ainew[0] = 0;
1401   /* don't know how many column pointers are needed so estimate */
1402   jmax = (int) (f*ai[n] + 1);
1403   ajnew = (int *) PetscMalloc( (jmax)*sizeof(int) ); CHKPTRQ(ajnew);
1404   /* ajfill is level of fill for each fill entry */
1405   ajfill = (int *) PetscMalloc( (jmax)*sizeof(int) ); CHKPTRQ(ajfill);
1406   /* fill is a linked list of nonzeros in active row */
1407   fill = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(fill);
1408   /* im is level for each filled value */
1409   im = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(im);
1410   /* dloc is location of diagonal in factor */
1411   dloc = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(dloc);
1412   dloc[0]  = 0;
1413   for ( prow=0; prow<n; prow++ ) {
1414     /* first copy previous fill into linked list */
1415     nzf     = nz  = ai[r[prow]+1] - ai[r[prow]];
1416     if (!nz) SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,1,"Empty row in matrix");
1417     xi      = aj + ai[r[prow]];
1418     fill[n] = n;
1419     while (nz--) {
1420       fm  = n;
1421       idx = ic[*xi++];
1422       do {
1423         m  = fm;
1424         fm = fill[m];
1425       } while (fm < idx);
1426       fill[m]   = idx;
1427       fill[idx] = fm;
1428       im[idx]   = 0;
1429     }
1430     nzi = 0;
1431     row = fill[n];
1432     while ( row < prow ) {
1433       incrlev = im[row] + 1;
1434       nz      = dloc[row];
1435       xi      = ajnew  + ainew[row] + nz;
1436       flev    = ajfill + ainew[row] + nz + 1;
1437       nnz     = ainew[row+1] - ainew[row] - nz - 1;
1438       if (*xi++ != row) {
1439         SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,0,"zero pivot");
1440       }
1441       fm      = row;
1442       while (nnz-- > 0) {
1443         idx = *xi++;
1444         if (*flev + incrlev > levels) {
1445           flev++;
1446           continue;
1447         }
1448         do {
1449           m  = fm;
1450           fm = fill[m];
1451         } while (fm < idx);
1452         if (fm != idx) {
1453           im[idx]   = *flev + incrlev;
1454           fill[m]   = idx;
1455           fill[idx] = fm;
1456           fm        = idx;
1457           nzf++;
1458         }
1459         else {
1460           if (im[idx] > *flev + incrlev) im[idx] = *flev+incrlev;
1461         }
1462         flev++;
1463       }
1464       row = fill[row];
1465       nzi++;
1466     }
1467     /* copy new filled row into permanent storage */
1468     ainew[prow+1] = ainew[prow] + nzf;
1469     if (ainew[prow+1] > jmax) {
1470       /* allocate a longer ajnew */
1471       int maxadd;
1472       maxadd = (int) (((f*ai[n]+1)*(n-prow+5))/n);
1473       if (maxadd < nzf) maxadd = (n-prow)*(nzf+1);
1474       jmax += maxadd;
1475       xi = (int *) PetscMalloc( jmax*sizeof(int) );CHKPTRQ(xi);
1476       PetscMemcpy(xi,ajnew,ainew[prow]*sizeof(int));
1477       PetscFree(ajnew);
1478       ajnew = xi;
1479       /* allocate a longer ajfill */
1480       xi = (int *) PetscMalloc( jmax*sizeof(int) );CHKPTRQ(xi);
1481       PetscMemcpy(xi,ajfill,ainew[prow]*sizeof(int));
1482       PetscFree(ajfill);
1483       ajfill = xi;
1484       realloc++;
1485     }
1486     xi          = ajnew + ainew[prow];
1487     flev        = ajfill + ainew[prow];
1488     dloc[prow]  = nzi;
1489     fm          = fill[n];
1490     while (nzf--) {
1491       *xi++   = fm;
1492       *flev++ = im[fm];
1493       fm      = fill[fm];
1494     }
1495   }
1496   PetscFree(ajfill);
1497   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
1498   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
1499   ierr = ISDestroy(isicol); CHKERRQ(ierr);
1500   PetscFree(fill); PetscFree(im);
1501 
1502   PLogInfo(A,
1503     "Info:MatILUFactorSymbolic_SeqBAIJ:Realloc %d Fill ratio:given %g needed %g\n",
1504                              realloc,f,((double)ainew[n])/((double)ai[prow]));
1505 
1506   /* put together the new matrix */
1507   ierr = MatCreateSeqBAIJ(A->comm,bs,bs*n,bs*n,0,PETSC_NULL,fact);CHKERRQ(ierr);
1508   b = (Mat_SeqBAIJ *) (*fact)->data;
1509   PetscFree(b->imax);
1510   b->singlemalloc = 0;
1511   len = bs2*ainew[n]*sizeof(Scalar);
1512   /* the next line frees the default space generated by the Create() */
1513   PetscFree(b->a); PetscFree(b->ilen);
1514   b->a          = (Scalar *) PetscMalloc( len ); CHKPTRQ(b->a);
1515   b->j          = ajnew;
1516   b->i          = ainew;
1517   for ( i=0; i<n; i++ ) dloc[i] += ainew[i];
1518   b->diag       = dloc;
1519   b->ilen       = 0;
1520   b->imax       = 0;
1521   b->row        = isrow;
1522   b->col        = iscol;
1523   b->solve_work = (Scalar *) PetscMalloc( (bs*n+bs)*sizeof(Scalar));
1524   CHKPTRQ(b->solve_work);
1525   /* In b structure:  Free imax, ilen, old a, old j.
1526      Allocate dloc, solve_work, new a, new j */
1527   PLogObjectMemory(*fact,(ainew[n]-n)*(sizeof(int))+bs2*ainew[n]*sizeof(Scalar));
1528   b->maxnz          = b->nz = ainew[n];
1529   (*fact)->factor   = FACTOR_LU;
1530 
1531   (*fact)->info.factor_mallocs    = realloc;
1532   (*fact)->info.fill_ratio_given  = f;
1533   (*fact)->info.fill_ratio_needed = ((double)ainew[n])/((double)ai[prow]);
1534 
1535   return 0;
1536 }
1537 
1538 
1539 
1540 
1541