xref: /petsc/src/mat/impls/baij/seq/baijfact2.c (revision 07fdaae1fdcf82bbf3df981bb743e49930d8d418)
1 #ifdef PETSC_RCS_HEADER
2 static char vcid[] = "$Id: baijfact2.c,v 1.20 1998/12/21 01:00:55 bsmith Exp balay $";
3 #endif
4 /*
5     Factorization code for BAIJ format.
6 */
7 
8 
9 #include "src/mat/impls/baij/seq/baij.h"
10 #include "src/vec/vecimpl.h"
11 #include "src/inline/ilu.h"
12 #include "src/inline/dot.h"
13 
14 /* ----------------------------------------------------------- */
15 #undef __FUNC__
16 #define __FUNC__ "MatSolve_SeqBAIJ_N"
17 int MatSolve_SeqBAIJ_N(Mat A,Vec bb,Vec xx)
18 {
19   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
20   IS              iscol=a->col,isrow=a->row;
21   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j;
22   int             nz,bs=a->bs,bs2=a->bs2,*rout,*cout;
23   MatScalar       *aa=a->a,*v;
24   Scalar          *x,*b,*sum,*tmp,*lsum;
25 
26   PetscFunctionBegin;
27   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
28   ierr = VecGetArray(xx,&x); CHKERRQ(ierr);
29   tmp  = a->solve_work;
30 
31   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
32   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
33 
34   /* forward solve the lower triangular */
35   PetscMemcpy(tmp,b + bs*(*r++), bs*sizeof(Scalar));
36   for ( i=1; i<n; i++ ) {
37     v   = aa + bs2*ai[i];
38     vi  = aj + ai[i];
39     nz  = a->diag[i] - ai[i];
40     sum = tmp + bs*i;
41     PetscMemcpy(sum,b+bs*(*r++),bs*sizeof(Scalar));
42     while (nz--) {
43       Kernel_v_gets_v_minus_A_times_w(bs,sum,v,tmp+bs*(*vi++));
44       v += bs2;
45     }
46   }
47   /* backward solve the upper triangular */
48   lsum = a->solve_work + a->n;
49   for ( i=n-1; i>=0; i-- ){
50     v   = aa + bs2*(a->diag[i] + 1);
51     vi  = aj + a->diag[i] + 1;
52     nz  = ai[i+1] - a->diag[i] - 1;
53     PetscMemcpy(lsum,tmp+i*bs,bs*sizeof(Scalar));
54     while (nz--) {
55       Kernel_v_gets_v_minus_A_times_w(bs,lsum,v,tmp+bs*(*vi++));
56       v += bs2;
57     }
58     Kernel_w_gets_A_times_v(bs,lsum,aa+bs2*a->diag[i],tmp+i*bs);
59     PetscMemcpy(x + bs*(*c--),tmp+i*bs,bs*sizeof(Scalar));
60   }
61 
62   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
63   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
64   ierr = VecRestoreArray(bb,&b); CHKERRQ(ierr);
65   ierr = VecRestoreArray(xx,&x); CHKERRQ(ierr);
66   PLogFlops(2*(a->bs2)*(a->nz) - a->bs*a->n);
67   PetscFunctionReturn(0);
68 }
69 
70 #undef __FUNC__
71 #define __FUNC__ "MatSolve_SeqBAIJ_7"
72 int MatSolve_SeqBAIJ_7(Mat A,Vec bb,Vec xx)
73 {
74   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
75   IS              iscol=a->col,isrow=a->row;
76   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout;
77   int             *diag = a->diag;
78   MatScalar       *aa=a->a,*v;
79   Scalar          sum1,sum2,sum3,sum4,sum5,sum6,sum7,x1,x2,x3,x4,x5,x6,x7;
80   Scalar          *x,*b,*tmp;
81 
82   PetscFunctionBegin;
83   ierr = VecGetArray(bb,&b); CHKERRQ(ierr);
84   ierr = VecGetArray(xx,&x); CHKERRQ(ierr);
85   tmp  = a->solve_work;
86 
87   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
88   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
89 
90   /* forward solve the lower triangular */
91   idx    = 7*(*r++);
92   tmp[0] = b[idx];   tmp[1] = b[1+idx];
93   tmp[2] = b[2+idx]; tmp[3] = b[3+idx]; tmp[4] = b[4+idx];
94   tmp[5] = b[5+idx]; tmp[6] = b[6+idx];
95 
96   for ( i=1; i<n; i++ ) {
97     v     = aa + 49*ai[i];
98     vi    = aj + ai[i];
99     nz    = diag[i] - ai[i];
100     idx   = 7*(*r++);
101     sum1  = b[idx];sum2 = b[1+idx];sum3 = b[2+idx];sum4 = b[3+idx];
102     sum5  = b[4+idx];sum6 = b[5+idx];sum7 = b[6+idx];
103     while (nz--) {
104       idx   = 7*(*vi++);
105       x1    = tmp[idx];  x2 = tmp[1+idx];x3 = tmp[2+idx];
106       x4    = tmp[3+idx];x5 = tmp[4+idx];
107       x6    = tmp[5+idx];x7 = tmp[6+idx];
108       sum1 -= v[0]*x1 + v[7]*x2  + v[14]*x3 + v[21]*x4 + v[28]*x5 + v[35]*x6 + v[42]*x7;
109       sum2 -= v[1]*x1 + v[8]*x2  + v[15]*x3 + v[22]*x4 + v[29]*x5 + v[36]*x6 + v[43]*x7;
110       sum3 -= v[2]*x1 + v[9]*x2  + v[16]*x3 + v[23]*x4 + v[30]*x5 + v[37]*x6 + v[44]*x7;
111       sum4 -= v[3]*x1 + v[10]*x2 + v[17]*x3 + v[24]*x4 + v[31]*x5 + v[38]*x6 + v[45]*x7;
112       sum5 -= v[4]*x1 + v[11]*x2 + v[18]*x3 + v[25]*x4 + v[32]*x5 + v[39]*x6 + v[46]*x7;
113       sum6 -= v[5]*x1 + v[12]*x2 + v[19]*x3 + v[26]*x4 + v[33]*x5 + v[40]*x6 + v[47]*x7;
114       sum7 -= v[6]*x1 + v[13]*x2 + v[20]*x3 + v[27]*x4 + v[34]*x5 + v[41]*x6 + v[48]*x7;
115       v += 49;
116     }
117     idx = 7*i;
118     tmp[idx]   = sum1;tmp[1+idx] = sum2;
119     tmp[2+idx] = sum3;tmp[3+idx] = sum4; tmp[4+idx] = sum5;
120     tmp[5+idx] = sum6;tmp[6+idx] = sum7;
121   }
122   /* backward solve the upper triangular */
123   for ( i=n-1; i>=0; i-- ){
124     v    = aa + 49*diag[i] + 49;
125     vi   = aj + diag[i] + 1;
126     nz   = ai[i+1] - diag[i] - 1;
127     idt  = 7*i;
128     sum1 = tmp[idt];  sum2 = tmp[1+idt];
129     sum3 = tmp[2+idt];sum4 = tmp[3+idt]; sum5 = tmp[4+idt];
130     sum6 = tmp[5+idt];sum7 = tmp[6+idt];
131     while (nz--) {
132       idx   = 7*(*vi++);
133       x1    = tmp[idx];   x2 = tmp[1+idx];
134       x3    = tmp[2+idx]; x4 = tmp[3+idx]; x5 = tmp[4+idx];
135       x6    = tmp[5+idx]; x7 = tmp[6+idx];
136       sum1 -= v[0]*x1 + v[7]*x2  + v[14]*x3 + v[21]*x4 + v[28]*x5 + v[35]*x6 + v[42]*x7;
137       sum2 -= v[1]*x1 + v[8]*x2  + v[15]*x3 + v[22]*x4 + v[29]*x5 + v[36]*x6 + v[43]*x7;
138       sum3 -= v[2]*x1 + v[9]*x2  + v[16]*x3 + v[23]*x4 + v[30]*x5 + v[37]*x6 + v[44]*x7;
139       sum4 -= v[3]*x1 + v[10]*x2 + v[17]*x3 + v[24]*x4 + v[31]*x5 + v[38]*x6 + v[45]*x7;
140       sum5 -= v[4]*x1 + v[11]*x2 + v[18]*x3 + v[25]*x4 + v[32]*x5 + v[39]*x6 + v[46]*x7;
141       sum6 -= v[5]*x1 + v[12]*x2 + v[19]*x3 + v[26]*x4 + v[33]*x5 + v[40]*x6 + v[47]*x7;
142       sum7 -= v[6]*x1 + v[13]*x2 + v[20]*x3 + v[27]*x4 + v[34]*x5 + v[41]*x6 + v[48]*x7;
143       v += 49;
144     }
145     idc = 7*(*c--);
146     v   = aa + 49*diag[i];
147     x[idc]   = tmp[idt]   = v[0]*sum1+v[7]*sum2+v[14]*sum3+
148                                  v[21]*sum4+v[28]*sum5+v[35]*sum6+v[42]*sum7;
149     x[1+idc] = tmp[1+idt] = v[1]*sum1+v[8]*sum2+v[15]*sum3+
150                                  v[22]*sum4+v[29]*sum5+v[36]*sum6+v[43]*sum7;
151     x[2+idc] = tmp[2+idt] = v[2]*sum1+v[9]*sum2+v[16]*sum3+
152                                  v[23]*sum4+v[30]*sum5+v[37]*sum6+v[44]*sum7;
153     x[3+idc] = tmp[3+idt] = v[3]*sum1+v[10]*sum2+v[17]*sum3+
154                                  v[24]*sum4+v[31]*sum5+v[38]*sum6+v[45]*sum7;
155     x[4+idc] = tmp[4+idt] = v[4]*sum1+v[11]*sum2+v[18]*sum3+
156                                  v[25]*sum4+v[32]*sum5+v[39]*sum6+v[46]*sum7;
157     x[5+idc] = tmp[5+idt] = v[5]*sum1+v[12]*sum2+v[19]*sum3+
158                                  v[26]*sum4+v[33]*sum5+v[40]*sum6+v[47]*sum7;
159     x[6+idc] = tmp[6+idt] = v[6]*sum1+v[13]*sum2+v[20]*sum3+
160                                  v[27]*sum4+v[34]*sum5+v[41]*sum6+v[48]*sum7;
161   }
162 
163   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
164   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
165   ierr = VecRestoreArray(bb,&b); CHKERRQ(ierr);
166   ierr = VecRestoreArray(xx,&x); CHKERRQ(ierr);
167   PLogFlops(2*49*(a->nz) - 7*a->n);
168   PetscFunctionReturn(0);
169 }
170 
171 #undef __FUNC__
172 #define __FUNC__ "MatSolve_SeqBAIJ_5"
173 int MatSolve_SeqBAIJ_5(Mat A,Vec bb,Vec xx)
174 {
175   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
176   IS              iscol=a->col,isrow=a->row;
177   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout;
178   int             *diag = a->diag;
179   MatScalar       *aa=a->a,*v;
180   Scalar          *x,*b,sum1,sum2,sum3,sum4,sum5,x1,x2,x3,x4,x5,*tmp;
181 
182   PetscFunctionBegin;
183   ierr = VecGetArray(bb,&b); CHKERRQ(ierr);
184   ierr = VecGetArray(xx,&x); CHKERRQ(ierr);
185   tmp  = a->solve_work;
186 
187   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
188   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
189 
190   /* forward solve the lower triangular */
191   idx    = 5*(*r++);
192   tmp[0] = b[idx];   tmp[1] = b[1+idx];
193   tmp[2] = b[2+idx]; tmp[3] = b[3+idx]; tmp[4] = b[4+idx];
194   for ( i=1; i<n; i++ ) {
195     v     = aa + 25*ai[i];
196     vi    = aj + ai[i];
197     nz    = diag[i] - ai[i];
198     idx   = 5*(*r++);
199     sum1  = b[idx];sum2 = b[1+idx];sum3 = b[2+idx];sum4 = b[3+idx];
200     sum5  = b[4+idx];
201     while (nz--) {
202       idx   = 5*(*vi++);
203       x1    = tmp[idx];  x2 = tmp[1+idx];x3 = tmp[2+idx];
204       x4    = tmp[3+idx];x5 = tmp[4+idx];
205       sum1 -= v[0]*x1 + v[5]*x2 + v[10]*x3 + v[15]*x4 + v[20]*x5;
206       sum2 -= v[1]*x1 + v[6]*x2 + v[11]*x3 + v[16]*x4 + v[21]*x5;
207       sum3 -= v[2]*x1 + v[7]*x2 + v[12]*x3 + v[17]*x4 + v[22]*x5;
208       sum4 -= v[3]*x1 + v[8]*x2 + v[13]*x3 + v[18]*x4 + v[23]*x5;
209       sum5 -= v[4]*x1 + v[9]*x2 + v[14]*x3 + v[19]*x4 + v[24]*x5;
210       v += 25;
211     }
212     idx = 5*i;
213     tmp[idx]   = sum1;tmp[1+idx] = sum2;
214     tmp[2+idx] = sum3;tmp[3+idx] = sum4; tmp[4+idx] = sum5;
215   }
216   /* backward solve the upper triangular */
217   for ( i=n-1; i>=0; i-- ){
218     v    = aa + 25*diag[i] + 25;
219     vi   = aj + diag[i] + 1;
220     nz   = ai[i+1] - diag[i] - 1;
221     idt  = 5*i;
222     sum1 = tmp[idt];  sum2 = tmp[1+idt];
223     sum3 = tmp[2+idt];sum4 = tmp[3+idt]; sum5 = tmp[4+idt];
224     while (nz--) {
225       idx   = 5*(*vi++);
226       x1    = tmp[idx];   x2 = tmp[1+idx];
227       x3    = tmp[2+idx]; x4 = tmp[3+idx]; x5 = tmp[4+idx];
228       sum1 -= v[0]*x1 + v[5]*x2 + v[10]*x3 + v[15]*x4 + v[20]*x5;
229       sum2 -= v[1]*x1 + v[6]*x2 + v[11]*x3 + v[16]*x4 + v[21]*x5;
230       sum3 -= v[2]*x1 + v[7]*x2 + v[12]*x3 + v[17]*x4 + v[22]*x5;
231       sum4 -= v[3]*x1 + v[8]*x2 + v[13]*x3 + v[18]*x4 + v[23]*x5;
232       sum5 -= v[4]*x1 + v[9]*x2 + v[14]*x3 + v[19]*x4 + v[24]*x5;
233       v += 25;
234     }
235     idc = 5*(*c--);
236     v   = aa + 25*diag[i];
237     x[idc]   = tmp[idt]   = v[0]*sum1+v[5]*sum2+v[10]*sum3+
238                                  v[15]*sum4+v[20]*sum5;
239     x[1+idc] = tmp[1+idt] = v[1]*sum1+v[6]*sum2+v[11]*sum3+
240                                  v[16]*sum4+v[21]*sum5;
241     x[2+idc] = tmp[2+idt] = v[2]*sum1+v[7]*sum2+v[12]*sum3+
242                                  v[17]*sum4+v[22]*sum5;
243     x[3+idc] = tmp[3+idt] = v[3]*sum1+v[8]*sum2+v[13]*sum3+
244                                  v[18]*sum4+v[23]*sum5;
245     x[4+idc] = tmp[4+idt] = v[4]*sum1+v[9]*sum2+v[14]*sum3+
246                                  v[19]*sum4+v[24]*sum5;
247   }
248 
249   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
250   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
251   ierr = VecRestoreArray(bb,&b); CHKERRQ(ierr);
252   ierr = VecRestoreArray(xx,&x); CHKERRQ(ierr);
253   PLogFlops(2*25*(a->nz) - 5*a->n);
254   PetscFunctionReturn(0);
255 }
256 
257 #undef __FUNC__
258 #define __FUNC__ "MatSolve_SeqBAIJ_4"
259 int MatSolve_SeqBAIJ_4(Mat A,Vec bb,Vec xx)
260 {
261   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *)A->data;
262   IS              iscol=a->col,isrow=a->row;
263   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout;
264   int             *diag = a->diag;
265   MatScalar       *aa=a->a,*v;
266   Scalar          *x,*b,sum1,sum2,sum3,sum4,x1,x2,x3,x4,*tmp;
267 
268   PetscFunctionBegin;
269   ierr = VecGetArray(bb,&b); CHKERRQ(ierr);
270   ierr = VecGetArray(xx,&x); CHKERRQ(ierr);
271   tmp  = a->solve_work;
272 
273   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
274   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
275 
276   /* forward solve the lower triangular */
277   idx    = 4*(*r++);
278   tmp[0] = b[idx];   tmp[1] = b[1+idx];
279   tmp[2] = b[2+idx]; tmp[3] = b[3+idx];
280   for ( i=1; i<n; i++ ) {
281     v     = aa + 16*ai[i];
282     vi    = aj + ai[i];
283     nz    = diag[i] - ai[i];
284     idx   = 4*(*r++);
285     sum1  = b[idx];sum2 = b[1+idx];sum3 = b[2+idx];sum4 = b[3+idx];
286     while (nz--) {
287       idx   = 4*(*vi++);
288       x1    = tmp[idx];x2 = tmp[1+idx];x3 = tmp[2+idx];x4 = tmp[3+idx];
289       sum1 -= v[0]*x1 + v[4]*x2 + v[8]*x3  + v[12]*x4;
290       sum2 -= v[1]*x1 + v[5]*x2 + v[9]*x3  + v[13]*x4;
291       sum3 -= v[2]*x1 + v[6]*x2 + v[10]*x3 + v[14]*x4;
292       sum4 -= v[3]*x1 + v[7]*x2 + v[11]*x3 + v[15]*x4;
293       v    += 16;
294     }
295     idx        = 4*i;
296     tmp[idx]   = sum1;tmp[1+idx] = sum2;
297     tmp[2+idx] = sum3;tmp[3+idx] = sum4;
298   }
299   /* backward solve the upper triangular */
300   for ( i=n-1; i>=0; i-- ){
301     v    = aa + 16*diag[i] + 16;
302     vi   = aj + diag[i] + 1;
303     nz   = ai[i+1] - diag[i] - 1;
304     idt  = 4*i;
305     sum1 = tmp[idt];  sum2 = tmp[1+idt];
306     sum3 = tmp[2+idt];sum4 = tmp[3+idt];
307     while (nz--) {
308       idx   = 4*(*vi++);
309       x1    = tmp[idx];   x2 = tmp[1+idx];
310       x3    = tmp[2+idx]; x4 = tmp[3+idx];
311       sum1 -= v[0]*x1 + v[4]*x2 + v[8]*x3   + v[12]*x4;
312       sum2 -= v[1]*x1 + v[5]*x2 + v[9]*x3   + v[13]*x4;
313       sum3 -= v[2]*x1 + v[6]*x2 + v[10]*x3  + v[14]*x4;
314       sum4 -= v[3]*x1 + v[7]*x2 + v[11]*x3  + v[15]*x4;
315       v += 16;
316     }
317     idc      = 4*(*c--);
318     v        = aa + 16*diag[i];
319     x[idc]   = tmp[idt]   = v[0]*sum1+v[4]*sum2+v[8]*sum3+v[12]*sum4;
320     x[1+idc] = tmp[1+idt] = v[1]*sum1+v[5]*sum2+v[9]*sum3+v[13]*sum4;
321     x[2+idc] = tmp[2+idt] = v[2]*sum1+v[6]*sum2+v[10]*sum3+v[14]*sum4;
322     x[3+idc] = tmp[3+idt] = v[3]*sum1+v[7]*sum2+v[11]*sum3+v[15]*sum4;
323   }
324 
325   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
326   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
327   ierr = VecRestoreArray(bb,&b); CHKERRQ(ierr);
328   ierr = VecRestoreArray(xx,&x); CHKERRQ(ierr);
329   PLogFlops(2*16*(a->nz) - 4*a->n);
330   PetscFunctionReturn(0);
331 }
332 
333 
334 /*
335       Special case where the matrix was ILU(0) factored in the natural
336    ordering. This eliminates the need for the column and row permutation.
337 */
338 #undef __FUNC__
339 #define __FUNC__ "MatSolve_SeqBAIJ_4_NaturalOrdering"
340 int MatSolve_SeqBAIJ_4_NaturalOrdering(Mat A,Vec bb,Vec xx)
341 {
342   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *)A->data;
343   int             n=a->mbs,*ai=a->i,*aj=a->j;
344   int             ierr,*diag = a->diag;
345   MatScalar       *aa=a->a;
346   Scalar          *x,*b;
347 
348   PetscFunctionBegin;
349   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
350   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
351 
352 #if defined(USE_FORTRAN_KERNEL_SOLVEBAIJBLAS)
353   {
354     static Scalar w[2000]; /* very BAD need to fix */
355     fortransolvebaij4blas_(&n,x,ai,aj,diag,aa,b,w);
356   }
357 #elif defined(USE_FORTRAN_KERNEL_SOLVEBAIJ)
358   {
359     static Scalar w[2000]; /* very BAD need to fix */
360     fortransolvebaij4_(&n,x,ai,aj,diag,aa,b,w);
361   }
362 #elif defined(USE_FORTRAN_KERNEL_SOLVEBAIJUNROLL)
363   fortransolvebaij4unroll_(&n,x,ai,aj,diag,aa,b);
364 #else
365   {
366     Scalar    sum1,sum2,sum3,sum4,x1,x2,x3,x4;
367     MatScalar *v;
368     int       jdx,idt,idx,nz,*vi,i;
369 
370   /* forward solve the lower triangular */
371   idx    = 0;
372   x[0]   = b[0]; x[1] = b[1]; x[2] = b[2]; x[3] = b[3];
373   for ( i=1; i<n; i++ ) {
374     v     =  aa      + 16*ai[i];
375     vi    =  aj      + ai[i];
376     nz    =  diag[i] - ai[i];
377     idx   +=  4;
378     sum1  =  b[idx];sum2 = b[1+idx];sum3 = b[2+idx];sum4 = b[3+idx];
379     while (nz--) {
380       jdx   = 4*(*vi++);
381       x1    = x[jdx];x2 = x[1+jdx];x3 = x[2+jdx];x4 = x[3+jdx];
382       sum1 -= v[0]*x1 + v[4]*x2 + v[8]*x3  + v[12]*x4;
383       sum2 -= v[1]*x1 + v[5]*x2 + v[9]*x3  + v[13]*x4;
384       sum3 -= v[2]*x1 + v[6]*x2 + v[10]*x3 + v[14]*x4;
385       sum4 -= v[3]*x1 + v[7]*x2 + v[11]*x3 + v[15]*x4;
386       v    += 16;
387     }
388     x[idx]   = sum1;
389     x[1+idx] = sum2;
390     x[2+idx] = sum3;
391     x[3+idx] = sum4;
392   }
393   /* backward solve the upper triangular */
394   for ( i=n-1; i>=0; i-- ){
395     v    = aa + 16*diag[i] + 16;
396     vi   = aj + diag[i] + 1;
397     nz   = ai[i+1] - diag[i] - 1;
398     idt  = 4*i;
399     sum1 = x[idt];  sum2 = x[1+idt];
400     sum3 = x[2+idt];sum4 = x[3+idt];
401     while (nz--) {
402       idx   = 4*(*vi++);
403       x1    = x[idx];   x2 = x[1+idx];x3    = x[2+idx]; x4 = x[3+idx];
404       sum1 -= v[0]*x1 + v[4]*x2 + v[8]*x3   + v[12]*x4;
405       sum2 -= v[1]*x1 + v[5]*x2 + v[9]*x3   + v[13]*x4;
406       sum3 -= v[2]*x1 + v[6]*x2 + v[10]*x3  + v[14]*x4;
407       sum4 -= v[3]*x1 + v[7]*x2 + v[11]*x3  + v[15]*x4;
408       v    += 16;
409     }
410     v        = aa + 16*diag[i];
411     x[idt]   = v[0]*sum1 + v[4]*sum2 + v[8]*sum3  + v[12]*sum4;
412     x[1+idt] = v[1]*sum1 + v[5]*sum2 + v[9]*sum3  + v[13]*sum4;
413     x[2+idt] = v[2]*sum1 + v[6]*sum2 + v[10]*sum3 + v[14]*sum4;
414     x[3+idt] = v[3]*sum1 + v[7]*sum2 + v[11]*sum3 + v[15]*sum4;
415   }
416   }
417 #endif
418 
419   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
420   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
421   PLogFlops(2*16*(a->nz) - 4*a->n);
422   PetscFunctionReturn(0);
423 }
424 
425 #undef __FUNC__
426 #define __FUNC__ "MatSolve_SeqBAIJ_5_NaturalOrdering"
427 int MatSolve_SeqBAIJ_5_NaturalOrdering(Mat A,Vec bb,Vec xx)
428 {
429   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *)A->data;
430   int             i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt;
431   int             ierr,*diag = a->diag,jdx;
432   MatScalar       *aa=a->a,*v;
433   Scalar          *x,*b,sum1,sum2,sum3,sum4,sum5,x1,x2,x3,x4,x5;;
434 
435   PetscFunctionBegin;
436   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
437   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
438   /* forward solve the lower triangular */
439   idx    = 0;
440   x[0] = b[idx]; x[1] = b[1+idx]; x[2] = b[2+idx]; x[3] = b[3+idx];x[4] = b[4+idx];
441   for ( i=1; i<n; i++ ) {
442     v     =  aa + 25*ai[i];
443     vi    =  aj + ai[i];
444     nz    =  diag[i] - ai[i];
445     idx   =  5*i;
446     sum1  =  b[idx];sum2 = b[1+idx];sum3 = b[2+idx];sum4 = b[3+idx];sum5 = b[4+idx];
447     while (nz--) {
448       jdx   = 5*(*vi++);
449       x1    = x[jdx];x2 = x[1+jdx];x3 = x[2+jdx];x4 = x[3+jdx];x5 = x[4+jdx];
450       sum1 -= v[0]*x1 + v[5]*x2 + v[10]*x3  + v[15]*x4 + v[20]*x5;
451       sum2 -= v[1]*x1 + v[6]*x2 + v[11]*x3  + v[16]*x4 + v[21]*x5;
452       sum3 -= v[2]*x1 + v[7]*x2 + v[12]*x3  + v[17]*x4 + v[22]*x5;
453       sum4 -= v[3]*x1 + v[8]*x2 + v[13]*x3  + v[18]*x4 + v[23]*x5;
454       sum5 -= v[4]*x1 + v[9]*x2 + v[14]*x3  + v[19]*x4 + v[24]*x5;
455       v    += 25;
456     }
457     x[idx]   = sum1;
458     x[1+idx] = sum2;
459     x[2+idx] = sum3;
460     x[3+idx] = sum4;
461     x[4+idx] = sum5;
462   }
463   /* backward solve the upper triangular */
464   for ( i=n-1; i>=0; i-- ){
465     v    = aa + 25*diag[i] + 25;
466     vi   = aj + diag[i] + 1;
467     nz   = ai[i+1] - diag[i] - 1;
468     idt  = 5*i;
469     sum1 = x[idt];  sum2 = x[1+idt];
470     sum3 = x[2+idt];sum4 = x[3+idt]; sum5 = x[4+idt];
471     while (nz--) {
472       idx   = 5*(*vi++);
473       x1    = x[idx];   x2 = x[1+idx];x3    = x[2+idx]; x4 = x[3+idx]; x5 = x[4+idx];
474       sum1 -= v[0]*x1 + v[5]*x2 + v[10]*x3  + v[15]*x4 + v[20]*x5;
475       sum2 -= v[1]*x1 + v[6]*x2 + v[11]*x3  + v[16]*x4 + v[21]*x5;
476       sum3 -= v[2]*x1 + v[7]*x2 + v[12]*x3  + v[17]*x4 + v[22]*x5;
477       sum4 -= v[3]*x1 + v[8]*x2 + v[13]*x3  + v[18]*x4 + v[23]*x5;
478       sum5 -= v[4]*x1 + v[9]*x2 + v[14]*x3  + v[19]*x4 + v[24]*x5;
479       v    += 25;
480     }
481     v        = aa + 25*diag[i];
482     x[idt]   = v[0]*sum1 + v[5]*sum2 + v[10]*sum3  + v[15]*sum4 + v[20]*sum5;
483     x[1+idt] = v[1]*sum1 + v[6]*sum2 + v[11]*sum3  + v[16]*sum4 + v[21]*sum5;
484     x[2+idt] = v[2]*sum1 + v[7]*sum2 + v[12]*sum3  + v[17]*sum4 + v[22]*sum5;
485     x[3+idt] = v[3]*sum1 + v[8]*sum2 + v[13]*sum3  + v[18]*sum4 + v[23]*sum5;
486     x[4+idt] = v[4]*sum1 + v[9]*sum2 + v[14]*sum3  + v[19]*sum4 + v[24]*sum5;
487   }
488 
489   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
490   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
491   PLogFlops(2*25*(a->nz) - 5*a->n);
492   PetscFunctionReturn(0);
493 }
494 
495 
496 #undef __FUNC__
497 #define __FUNC__ "MatSolve_SeqBAIJ_3"
498 int MatSolve_SeqBAIJ_3(Mat A,Vec bb,Vec xx)
499 {
500   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
501   IS              iscol=a->col,isrow=a->row;
502   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout;
503   int             *diag = a->diag;
504   MatScalar       *aa=a->a,*v;
505   Scalar          *x,*b,sum1,sum2,sum3,x1,x2,x3,*tmp;
506 
507   PetscFunctionBegin;
508   ierr = VecGetArray(bb,&b); CHKERRQ(ierr);
509   ierr = VecGetArray(xx,&x); CHKERRQ(ierr);
510   tmp  = a->solve_work;
511 
512   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
513   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
514 
515   /* forward solve the lower triangular */
516   idx    = 3*(*r++);
517   tmp[0] = b[idx]; tmp[1] = b[1+idx]; tmp[2] = b[2+idx];
518   for ( i=1; i<n; i++ ) {
519     v     = aa + 9*ai[i];
520     vi    = aj + ai[i];
521     nz    = diag[i] - ai[i];
522     idx   = 3*(*r++);
523     sum1  = b[idx]; sum2 = b[1+idx]; sum3 = b[2+idx];
524     while (nz--) {
525       idx   = 3*(*vi++);
526       x1    = tmp[idx]; x2 = tmp[1+idx]; x3 = tmp[2+idx];
527       sum1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
528       sum2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
529       sum3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
530       v += 9;
531     }
532     idx = 3*i;
533     tmp[idx] = sum1; tmp[1+idx] = sum2; tmp[2+idx] = sum3;
534   }
535   /* backward solve the upper triangular */
536   for ( i=n-1; i>=0; i-- ){
537     v    = aa + 9*diag[i] + 9;
538     vi   = aj + diag[i] + 1;
539     nz   = ai[i+1] - diag[i] - 1;
540     idt  = 3*i;
541     sum1 = tmp[idt]; sum2 = tmp[1+idt]; sum3 = tmp[2+idt];
542     while (nz--) {
543       idx   = 3*(*vi++);
544       x1    = tmp[idx]; x2 = tmp[1+idx]; x3 = tmp[2+idx];
545       sum1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
546       sum2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
547       sum3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
548       v += 9;
549     }
550     idc = 3*(*c--);
551     v   = aa + 9*diag[i];
552     x[idc]   = tmp[idt]   = v[0]*sum1 + v[3]*sum2 + v[6]*sum3;
553     x[1+idc] = tmp[1+idt] = v[1]*sum1 + v[4]*sum2 + v[7]*sum3;
554     x[2+idc] = tmp[2+idt] = v[2]*sum1 + v[5]*sum2 + v[8]*sum3;
555   }
556   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
557   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
558   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
559   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
560   PLogFlops(2*9*(a->nz) - 3*a->n);
561   PetscFunctionReturn(0);
562 }
563 
564 #undef __FUNC__
565 #define __FUNC__ "MatSolve_SeqBAIJ_2"
566 int MatSolve_SeqBAIJ_2(Mat A,Vec bb,Vec xx)
567 {
568   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
569   IS              iscol=a->col,isrow=a->row;
570   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout;
571   int             *diag = a->diag;
572   MatScalar       *aa=a->a,*v;
573   Scalar          *x,*b,sum1,sum2,x1,x2,*tmp;
574 
575   PetscFunctionBegin;
576   ierr = VecGetArray(bb,&b); CHKERRQ(ierr);
577   ierr = VecGetArray(xx,&x); CHKERRQ(ierr);
578   tmp  = a->solve_work;
579 
580   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
581   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
582 
583   /* forward solve the lower triangular */
584   idx    = 2*(*r++);
585   tmp[0] = b[idx]; tmp[1] = b[1+idx];
586   for ( i=1; i<n; i++ ) {
587     v     = aa + 4*ai[i];
588     vi    = aj + ai[i];
589     nz    = diag[i] - ai[i];
590     idx   = 2*(*r++);
591     sum1  = b[idx]; sum2 = b[1+idx];
592     while (nz--) {
593       idx   = 2*(*vi++);
594       x1    = tmp[idx]; x2 = tmp[1+idx];
595       sum1 -= v[0]*x1 + v[2]*x2;
596       sum2 -= v[1]*x1 + v[3]*x2;
597       v += 4;
598     }
599     idx = 2*i;
600     tmp[idx] = sum1; tmp[1+idx] = sum2;
601   }
602   /* backward solve the upper triangular */
603   for ( i=n-1; i>=0; i-- ){
604     v    = aa + 4*diag[i] + 4;
605     vi   = aj + diag[i] + 1;
606     nz   = ai[i+1] - diag[i] - 1;
607     idt  = 2*i;
608     sum1 = tmp[idt]; sum2 = tmp[1+idt];
609     while (nz--) {
610       idx   = 2*(*vi++);
611       x1    = tmp[idx]; x2 = tmp[1+idx];
612       sum1 -= v[0]*x1 + v[2]*x2;
613       sum2 -= v[1]*x1 + v[3]*x2;
614       v += 4;
615     }
616     idc = 2*(*c--);
617     v   = aa + 4*diag[i];
618     x[idc]   = tmp[idt]   = v[0]*sum1 + v[2]*sum2;
619     x[1+idc] = tmp[1+idt] = v[1]*sum1 + v[3]*sum2;
620   }
621   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
622   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
623   ierr = VecRestoreArray(bb,&b); CHKERRQ(ierr);
624   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
625   PLogFlops(2*4*(a->nz) - 2*a->n);
626   PetscFunctionReturn(0);
627 }
628 
629 #undef __FUNC__
630 #define __FUNC__ "MatSolve_SeqBAIJ_1"
631 int MatSolve_SeqBAIJ_1(Mat A,Vec bb,Vec xx)
632 {
633   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
634   IS              iscol=a->col,isrow=a->row;
635   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,*rout,*cout;
636   int             *diag = a->diag;
637   MatScalar       *aa=a->a,*v;
638   Scalar          *x,*b,sum1,*tmp;
639 
640   PetscFunctionBegin;
641   if (!n) PetscFunctionReturn(0);
642 
643   ierr = VecGetArray(bb,&b); CHKERRQ(ierr);
644   ierr = VecGetArray(xx,&x); CHKERRQ(ierr);
645   tmp  = a->solve_work;
646 
647   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
648   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
649 
650   /* forward solve the lower triangular */
651   tmp[0] = b[*r++];
652   for ( i=1; i<n; i++ ) {
653     v     = aa + ai[i];
654     vi    = aj + ai[i];
655     nz    = diag[i] - ai[i];
656     sum1  = b[*r++];
657     while (nz--) {
658       sum1 -= (*v++)*tmp[*vi++];
659     }
660     tmp[i] = sum1;
661   }
662   /* backward solve the upper triangular */
663   for ( i=n-1; i>=0; i-- ){
664     v    = aa + diag[i] + 1;
665     vi   = aj + diag[i] + 1;
666     nz   = ai[i+1] - diag[i] - 1;
667     sum1 = tmp[i];
668     while (nz--) {
669       sum1 -= (*v++)*tmp[*vi++];
670     }
671     x[*c--] = tmp[i] = aa[diag[i]]*sum1;
672   }
673 
674   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
675   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
676   ierr = VecRestoreArray(bb,&b); CHKERRQ(ierr);
677   ierr = VecRestoreArray(xx,&x); CHKERRQ(ierr);
678   PLogFlops(2*1*(a->nz) - a->n);
679   PetscFunctionReturn(0);
680 }
681 
682 /* ----------------------------------------------------------------*/
683 /*
684      This code is virtually identical to MatILUFactorSymbolic_SeqAIJ
685    except that the data structure of Mat_SeqAIJ is slightly different.
686    Not a good example of code reuse.
687 */
688 #undef __FUNC__
689 #define __FUNC__ "MatILUFactorSymbolic_SeqBAIJ"
690 int MatILUFactorSymbolic_SeqBAIJ(Mat A,IS isrow,IS iscol,double f,int levels,Mat *fact)
691 {
692   Mat_SeqBAIJ *a = (Mat_SeqBAIJ *) A->data, *b;
693   IS          isicol;
694   int         *r,*ic, ierr, prow, n = a->mbs, *ai = a->i, *aj = a->j;
695   int         *ainew,*ajnew, jmax,*fill, *xi, nz, *im,*ajfill,*flev;
696   int         *dloc, idx, row,m,fm, nzf, nzi,len,  realloc = 0;
697   int         incrlev,nnz,i,bs = a->bs,bs2 = a->bs2;
698   PetscTruth  col_identity, row_identity;
699 
700   PetscFunctionBegin;
701   ierr = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
702 
703   /* special case that simply copies fill pattern */
704   PetscValidHeaderSpecific(isrow,IS_COOKIE);
705   PetscValidHeaderSpecific(iscol,IS_COOKIE);
706   ierr = ISIdentity(isrow,&row_identity); CHKERRQ(ierr);
707   ierr = ISIdentity(iscol,&col_identity); CHKERRQ(ierr);
708   if (levels == 0 && row_identity && col_identity) {
709     ierr = MatDuplicate_SeqBAIJ(A,MAT_DO_NOT_COPY_VALUES,fact); CHKERRQ(ierr);
710     (*fact)->factor = FACTOR_LU;
711     b               = (Mat_SeqBAIJ *) (*fact)->data;
712     if (!b->diag) {
713       ierr = MatMarkDiag_SeqBAIJ(*fact); CHKERRQ(ierr);
714     }
715     b->row        = isrow;
716     b->col        = iscol;
717     b->icol       = isicol;
718     b->solve_work = (Scalar *) PetscMalloc((b->m+1+b->bs)*sizeof(Scalar));CHKPTRQ(b->solve_work);
719     /*
720         Blocksize 4 and 5 a special faster solver for ILU(0) factorization
721         with natural ordering
722     */
723     if (b->bs == 4) {
724       (*fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering;
725       (*fact)->ops->solve           = MatSolve_SeqBAIJ_4_NaturalOrdering;
726       PLogInfo(A,"Using special natural ordering factor and solve BS=4\n");
727     } else if (b->bs == 5) {
728       (*fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqBAIJ_5_NaturalOrdering;
729       (*fact)->ops->solve           = MatSolve_SeqBAIJ_5_NaturalOrdering;
730       PLogInfo( A,"Using special natural ordering factor and solve BS=5\n");
731     }
732     PetscFunctionReturn(0);
733   }
734 
735   ierr = ISGetIndices(isrow,&r); CHKERRQ(ierr);
736   ierr = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
737 
738   /* get new row pointers */
739   ainew = (int *) PetscMalloc( (n+1)*sizeof(int) ); CHKPTRQ(ainew);
740   ainew[0] = 0;
741   /* don't know how many column pointers are needed so estimate */
742   jmax = (int) (f*ai[n] + 1);
743   ajnew = (int *) PetscMalloc( (jmax)*sizeof(int) ); CHKPTRQ(ajnew);
744   /* ajfill is level of fill for each fill entry */
745   ajfill = (int *) PetscMalloc( (jmax)*sizeof(int) ); CHKPTRQ(ajfill);
746   /* fill is a linked list of nonzeros in active row */
747   fill = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(fill);
748   /* im is level for each filled value */
749   im = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(im);
750   /* dloc is location of diagonal in factor */
751   dloc = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(dloc);
752   dloc[0]  = 0;
753   for ( prow=0; prow<n; prow++ ) {
754     /* first copy previous fill into linked list */
755     nzf     = nz  = ai[r[prow]+1] - ai[r[prow]];
756     if (!nz) SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,1,"Empty row in matrix");
757     xi      = aj + ai[r[prow]];
758     fill[n] = n;
759     while (nz--) {
760       fm  = n;
761       idx = ic[*xi++];
762       do {
763         m  = fm;
764         fm = fill[m];
765       } while (fm < idx);
766       fill[m]   = idx;
767       fill[idx] = fm;
768       im[idx]   = 0;
769     }
770     nzi = 0;
771     row = fill[n];
772     while ( row < prow ) {
773       incrlev = im[row] + 1;
774       nz      = dloc[row];
775       xi      = ajnew  + ainew[row] + nz;
776       flev    = ajfill + ainew[row] + nz + 1;
777       nnz     = ainew[row+1] - ainew[row] - nz - 1;
778       if (*xi++ != row) {
779         SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,0,"Zero pivot: try running with -pc_ilu_nonzeros_along_diagonal");
780       }
781       fm      = row;
782       while (nnz-- > 0) {
783         idx = *xi++;
784         if (*flev + incrlev > levels) {
785           flev++;
786           continue;
787         }
788         do {
789           m  = fm;
790           fm = fill[m];
791         } while (fm < idx);
792         if (fm != idx) {
793           im[idx]   = *flev + incrlev;
794           fill[m]   = idx;
795           fill[idx] = fm;
796           fm        = idx;
797           nzf++;
798         } else {
799           if (im[idx] > *flev + incrlev) im[idx] = *flev+incrlev;
800         }
801         flev++;
802       }
803       row = fill[row];
804       nzi++;
805     }
806     /* copy new filled row into permanent storage */
807     ainew[prow+1] = ainew[prow] + nzf;
808     if (ainew[prow+1] > jmax) {
809 
810       /* estimate how much additional space we will need */
811       /* use the strategy suggested by David Hysom <hysom@perch-t.icase.edu> */
812       /* just double the memory each time */
813       int maxadd = jmax;
814       /* maxadd = (int) (((f*ai[n]+1)*(n-prow+5))/n); */
815       if (maxadd < nzf) maxadd = (n-prow)*(nzf+1);
816       jmax += maxadd;
817 
818       /* allocate a longer ajnew and ajfill */
819       xi = (int *) PetscMalloc( jmax*sizeof(int) );CHKPTRQ(xi);
820       PetscMemcpy(xi,ajnew,ainew[prow]*sizeof(int));
821       PetscFree(ajnew);
822       ajnew = xi;
823       xi = (int *) PetscMalloc( jmax*sizeof(int) );CHKPTRQ(xi);
824       PetscMemcpy(xi,ajfill,ainew[prow]*sizeof(int));
825       PetscFree(ajfill);
826       ajfill = xi;
827       realloc++; /* count how many reallocations are needed */
828     }
829     xi          = ajnew + ainew[prow];
830     flev        = ajfill + ainew[prow];
831     dloc[prow]  = nzi;
832     fm          = fill[n];
833     while (nzf--) {
834       *xi++   = fm;
835       *flev++ = im[fm];
836       fm      = fill[fm];
837     }
838   }
839   PetscFree(ajfill);
840   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
841   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
842   PetscFree(fill); PetscFree(im);
843 
844   {
845     double af = ((double)ainew[n])/((double)ai[n]);
846     PLogInfo(A,"MatILUFactorSymbolic_SeqBAIJ:Reallocs %d Fill ratio:given %g needed %g\n",
847              realloc,f,af);
848     PLogInfo(A,"MatILUFactorSymbolic_SeqBAIJ:Run with -pc_ilu_fill %g or use \n",af);
849     PLogInfo(A,"MatILUFactorSymbolic_SeqBAIJ:PCILUSetFill(pc,%g);\n",af);
850     PLogInfo(A,"MatILUFactorSymbolic_SeqBAIJ:for best performance.\n");
851   }
852 
853   /* put together the new matrix */
854   ierr = MatCreateSeqBAIJ(A->comm,bs,bs*n,bs*n,0,PETSC_NULL,fact);CHKERRQ(ierr);
855   PLogObjectParent(*fact,isicol);
856   b = (Mat_SeqBAIJ *) (*fact)->data;
857   PetscFree(b->imax);
858   b->singlemalloc = 0;
859   len = bs2*ainew[n]*sizeof(MatScalar);
860   /* the next line frees the default space generated by the Create() */
861   PetscFree(b->a); PetscFree(b->ilen);
862   b->a          = (MatScalar *) PetscMalloc( len ); CHKPTRQ(b->a);
863   b->j          = ajnew;
864   b->i          = ainew;
865   for ( i=0; i<n; i++ ) dloc[i] += ainew[i];
866   b->diag       = dloc;
867   b->ilen       = 0;
868   b->imax       = 0;
869   b->row        = isrow;
870   b->col        = iscol;
871   b->icol       = isicol;
872   b->solve_work = (Scalar *) PetscMalloc( (bs*n+bs)*sizeof(Scalar));CHKPTRQ(b->solve_work);
873   /* In b structure:  Free imax, ilen, old a, old j.
874      Allocate dloc, solve_work, new a, new j */
875   PLogObjectMemory(*fact,(ainew[n]-n)*(sizeof(int))+bs2*ainew[n]*sizeof(Scalar));
876   b->maxnz          = b->nz = ainew[n];
877   (*fact)->factor   = FACTOR_LU;
878 
879   (*fact)->info.factor_mallocs    = realloc;
880   (*fact)->info.fill_ratio_given  = f;
881   (*fact)->info.fill_ratio_needed = ((double)ainew[n])/((double)ai[prow]);
882 
883   PetscFunctionReturn(0);
884 }
885 
886 
887 
888 
889