xref: /petsc/src/mat/impls/baij/seq/baijfact2.c (revision e12933850baf6ee5ed30d09cb860fcc862df920c)
1 #ifdef PETSC_RCS_HEADER
2 static char vcid[] = "$Id: baijfact2.c,v 1.9 1998/04/03 23:15:34 bsmith Exp bsmith $";
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 #undef __FUNC__
14 #define __FUNC__ "MatSolve_SeqBAIJ_N"
15 int MatSolve_SeqBAIJ_N(Mat A,Vec bb,Vec xx)
16 {
17   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
18   IS              iscol=a->col,isrow=a->row;
19   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j;
20   int             nz,bs=a->bs,bs2=a->bs2,*rout,*cout;
21   Scalar          *aa=a->a,*sum;
22   Scalar *x,*b,*lsum,*tmp,*v;
23 
24   PetscFunctionBegin;
25   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
26   ierr = VecGetArray(xx,&x); CHKERRQ(ierr);
27   tmp  = a->solve_work;
28 
29   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
30   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
31 
32   /* forward solve the lower triangular */
33   PetscMemcpy(tmp,b + bs*(*r++), bs*sizeof(Scalar));
34   for ( i=1; i<n; i++ ) {
35     v   = aa + bs2*ai[i];
36     vi  = aj + ai[i];
37     nz  = a->diag[i] - ai[i];
38     sum = tmp + bs*i;
39     PetscMemcpy(sum,b+bs*(*r++),bs*sizeof(Scalar));
40     while (nz--) {
41       Kernel_v_gets_v_minus_A_times_w(bs,sum,v,tmp+bs*(*vi++));
42       v += bs2;
43     }
44   }
45   /* backward solve the upper triangular */
46   lsum = a->solve_work + a->n;
47   for ( i=n-1; i>=0; i-- ){
48     v   = aa + bs2*(a->diag[i] + 1);
49     vi  = aj + a->diag[i] + 1;
50     nz  = ai[i+1] - a->diag[i] - 1;
51     PetscMemcpy(lsum,tmp+i*bs,bs*sizeof(Scalar));
52     while (nz--) {
53       Kernel_v_gets_v_minus_A_times_w(bs,lsum,v,tmp+bs*(*vi++));
54       v += bs2;
55     }
56     Kernel_w_gets_A_times_v(bs,lsum,aa+bs2*a->diag[i],tmp+i*bs);
57     PetscMemcpy(x + bs*(*c--),tmp+i*bs,bs*sizeof(Scalar));
58   }
59 
60   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
61   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
62   ierr = VecRestoreArray(bb,&b); CHKERRQ(ierr);
63   ierr = VecRestoreArray(xx,&x); CHKERRQ(ierr);
64   PLogFlops(2*(a->bs2)*(a->nz) - a->n);
65   PetscFunctionReturn(0);
66 }
67 
68 #undef __FUNC__
69 #define __FUNC__ "MatSolve_SeqBAIJ_7"
70 int MatSolve_SeqBAIJ_7(Mat A,Vec bb,Vec xx)
71 {
72   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
73   IS              iscol=a->col,isrow=a->row;
74   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout;
75   int             *diag = a->diag;
76   Scalar          *aa=a->a,sum1,sum2,sum3,sum4,sum5,sum6,sum7,x1,x2,x3,x4,x5,x6,x7;
77   Scalar *x,*b,*tmp,*v;
78 
79   PetscFunctionBegin;
80   ierr = VecGetArray(bb,&b); CHKERRQ(ierr);
81   ierr = VecGetArray(xx,&x); CHKERRQ(ierr);
82   tmp  = a->solve_work;
83 
84   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
85   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
86 
87   /* forward solve the lower triangular */
88   idx    = 7*(*r++);
89   tmp[0] = b[idx];   tmp[1] = b[1+idx];
90   tmp[2] = b[2+idx]; tmp[3] = b[3+idx]; tmp[4] = b[4+idx];
91   tmp[5] = b[5+idx]; tmp[6] = b[6+idx];
92 
93   for ( i=1; i<n; i++ ) {
94     v     = aa + 49*ai[i];
95     vi    = aj + ai[i];
96     nz    = diag[i] - ai[i];
97     idx   = 7*(*r++);
98     sum1  = b[idx];sum2 = b[1+idx];sum3 = b[2+idx];sum4 = b[3+idx];
99     sum5  = b[4+idx];sum6 = b[5+idx];sum7 = b[6+idx];
100     while (nz--) {
101       idx   = 7*(*vi++);
102       x1    = tmp[idx];  x2 = tmp[1+idx];x3 = tmp[2+idx];
103       x4    = tmp[3+idx];x5 = tmp[4+idx];
104       x6    = tmp[5+idx];x7 = tmp[6+idx];
105       sum1 -= v[0]*x1 + v[7]*x2  + v[14]*x3 + v[21]*x4 + v[28]*x5 + v[35]*x6 + v[42]*x7;
106       sum2 -= v[1]*x1 + v[8]*x2  + v[15]*x3 + v[22]*x4 + v[29]*x5 + v[36]*x6 + v[43]*x7;
107       sum3 -= v[2]*x1 + v[9]*x2  + v[16]*x3 + v[23]*x4 + v[30]*x5 + v[37]*x6 + v[44]*x7;
108       sum4 -= v[3]*x1 + v[10]*x2 + v[17]*x3 + v[24]*x4 + v[31]*x5 + v[38]*x6 + v[45]*x7;
109       sum5 -= v[4]*x1 + v[11]*x2 + v[18]*x3 + v[25]*x4 + v[32]*x5 + v[39]*x6 + v[46]*x7;
110       sum6 -= v[5]*x1 + v[12]*x2 + v[19]*x3 + v[26]*x4 + v[33]*x5 + v[40]*x6 + v[47]*x7;
111       sum7 -= v[6]*x1 + v[13]*x2 + v[20]*x3 + v[27]*x4 + v[34]*x5 + v[41]*x6 + v[48]*x7;
112       v += 49;
113     }
114     idx = 7*i;
115     tmp[idx]   = sum1;tmp[1+idx] = sum2;
116     tmp[2+idx] = sum3;tmp[3+idx] = sum4; tmp[4+idx] = sum5;
117     tmp[5+idx] = sum6;tmp[6+idx] = sum7;
118   }
119   /* backward solve the upper triangular */
120   for ( i=n-1; i>=0; i-- ){
121     v    = aa + 49*diag[i] + 49;
122     vi   = aj + diag[i] + 1;
123     nz   = ai[i+1] - diag[i] - 1;
124     idt  = 7*i;
125     sum1 = tmp[idt];  sum2 = tmp[1+idt];
126     sum3 = tmp[2+idt];sum4 = tmp[3+idt]; sum5 = tmp[4+idt];
127     sum6 = tmp[5+idt];sum7 = tmp[6+idt];
128     while (nz--) {
129       idx   = 7*(*vi++);
130       x1    = tmp[idx];   x2 = tmp[1+idx];
131       x3    = tmp[2+idx]; x4 = tmp[3+idx]; x5 = tmp[4+idx];
132       x6    = tmp[5+idx]; x7 = tmp[6+idx];
133       sum1 -= v[0]*x1 + v[7]*x2  + v[14]*x3 + v[21]*x4 + v[28]*x5 + v[35]*x6 + v[42]*x7;
134       sum2 -= v[1]*x1 + v[8]*x2  + v[15]*x3 + v[22]*x4 + v[29]*x5 + v[36]*x6 + v[43]*x7;
135       sum3 -= v[2]*x1 + v[9]*x2  + v[16]*x3 + v[23]*x4 + v[30]*x5 + v[37]*x6 + v[44]*x7;
136       sum4 -= v[3]*x1 + v[10]*x2 + v[17]*x3 + v[24]*x4 + v[31]*x5 + v[38]*x6 + v[45]*x7;
137       sum5 -= v[4]*x1 + v[11]*x2 + v[18]*x3 + v[25]*x4 + v[32]*x5 + v[39]*x6 + v[46]*x7;
138       sum6 -= v[5]*x1 + v[12]*x2 + v[19]*x3 + v[26]*x4 + v[33]*x5 + v[40]*x6 + v[47]*x7;
139       sum7 -= v[6]*x1 + v[13]*x2 + v[20]*x3 + v[27]*x4 + v[34]*x5 + v[41]*x6 + v[48]*x7;
140       v += 49;
141     }
142     idc = 7*(*c--);
143     v   = aa + 49*diag[i];
144     x[idc]   = tmp[idt]   = v[0]*sum1+v[7]*sum2+v[14]*sum3+
145                                  v[21]*sum4+v[28]*sum5+v[35]*sum6+v[42]*sum7;
146     x[1+idc] = tmp[1+idt] = v[1]*sum1+v[8]*sum2+v[15]*sum3+
147                                  v[22]*sum4+v[29]*sum5+v[36]*sum6+v[43]*sum7;
148     x[2+idc] = tmp[2+idt] = v[2]*sum1+v[9]*sum2+v[16]*sum3+
149                                  v[23]*sum4+v[30]*sum5+v[37]*sum6+v[44]*sum7;
150     x[3+idc] = tmp[3+idt] = v[3]*sum1+v[10]*sum2+v[17]*sum3+
151                                  v[24]*sum4+v[31]*sum5+v[38]*sum6+v[45]*sum7;
152     x[4+idc] = tmp[4+idt] = v[4]*sum1+v[11]*sum2+v[18]*sum3+
153                                  v[25]*sum4+v[32]*sum5+v[39]*sum6+v[46]*sum7;
154     x[5+idc] = tmp[5+idt] = v[5]*sum1+v[12]*sum2+v[19]*sum3+
155                                  v[26]*sum4+v[33]*sum5+v[40]*sum6+v[47]*sum7;
156     x[6+idc] = tmp[6+idt] = v[6]*sum1+v[13]*sum2+v[20]*sum3+
157                                  v[27]*sum4+v[34]*sum5+v[41]*sum6+v[48]*sum7;
158   }
159 
160   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
161   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
162   ierr = VecRestoreArray(bb,&b); CHKERRQ(ierr);
163   ierr = VecRestoreArray(xx,&x); CHKERRQ(ierr);
164   PLogFlops(2*49*(a->nz) - a->n);
165   PetscFunctionReturn(0);
166 }
167 
168 #undef __FUNC__
169 #define __FUNC__ "MatSolve_SeqBAIJ_5"
170 int MatSolve_SeqBAIJ_5(Mat A,Vec bb,Vec xx)
171 {
172   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
173   IS              iscol=a->col,isrow=a->row;
174   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout;
175   int             *diag = a->diag;
176   Scalar          *aa=a->a,sum1,sum2,sum3,sum4,sum5,x1,x2,x3,x4,x5;
177   Scalar *x,*b,*tmp,*v;
178 
179   PetscFunctionBegin;
180   ierr = VecGetArray(bb,&b); CHKERRQ(ierr);
181   ierr = VecGetArray(xx,&x); CHKERRQ(ierr);
182   tmp  = a->solve_work;
183 
184   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
185   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
186 
187   /* forward solve the lower triangular */
188   idx    = 5*(*r++);
189   tmp[0] = b[idx];   tmp[1] = b[1+idx];
190   tmp[2] = b[2+idx]; tmp[3] = b[3+idx]; tmp[4] = b[4+idx];
191   for ( i=1; i<n; i++ ) {
192     v     = aa + 25*ai[i];
193     vi    = aj + ai[i];
194     nz    = diag[i] - ai[i];
195     idx   = 5*(*r++);
196     sum1  = b[idx];sum2 = b[1+idx];sum3 = b[2+idx];sum4 = b[3+idx];
197     sum5  = b[4+idx];
198     while (nz--) {
199       idx   = 5*(*vi++);
200       x1    = tmp[idx];  x2 = tmp[1+idx];x3 = tmp[2+idx];
201       x4    = tmp[3+idx];x5 = tmp[4+idx];
202       sum1 -= v[0]*x1 + v[5]*x2 + v[10]*x3 + v[15]*x4 + v[20]*x5;
203       sum2 -= v[1]*x1 + v[6]*x2 + v[11]*x3 + v[16]*x4 + v[21]*x5;
204       sum3 -= v[2]*x1 + v[7]*x2 + v[12]*x3 + v[17]*x4 + v[22]*x5;
205       sum4 -= v[3]*x1 + v[8]*x2 + v[13]*x3 + v[18]*x4 + v[23]*x5;
206       sum5 -= v[4]*x1 + v[9]*x2 + v[14]*x3 + v[19]*x4 + v[24]*x5;
207       v += 25;
208     }
209     idx = 5*i;
210     tmp[idx]   = sum1;tmp[1+idx] = sum2;
211     tmp[2+idx] = sum3;tmp[3+idx] = sum4; tmp[4+idx] = sum5;
212   }
213   /* backward solve the upper triangular */
214   for ( i=n-1; i>=0; i-- ){
215     v    = aa + 25*diag[i] + 25;
216     vi   = aj + diag[i] + 1;
217     nz   = ai[i+1] - diag[i] - 1;
218     idt  = 5*i;
219     sum1 = tmp[idt];  sum2 = tmp[1+idt];
220     sum3 = tmp[2+idt];sum4 = tmp[3+idt]; sum5 = tmp[4+idt];
221     while (nz--) {
222       idx   = 5*(*vi++);
223       x1    = tmp[idx];   x2 = tmp[1+idx];
224       x3    = tmp[2+idx]; x4 = tmp[3+idx]; x5 = tmp[4+idx];
225       sum1 -= v[0]*x1 + v[5]*x2 + v[10]*x3 + v[15]*x4 + v[20]*x5;
226       sum2 -= v[1]*x1 + v[6]*x2 + v[11]*x3 + v[16]*x4 + v[21]*x5;
227       sum3 -= v[2]*x1 + v[7]*x2 + v[12]*x3 + v[17]*x4 + v[22]*x5;
228       sum4 -= v[3]*x1 + v[8]*x2 + v[13]*x3 + v[18]*x4 + v[23]*x5;
229       sum5 -= v[4]*x1 + v[9]*x2 + v[14]*x3 + v[19]*x4 + v[24]*x5;
230       v += 25;
231     }
232     idc = 5*(*c--);
233     v   = aa + 25*diag[i];
234     x[idc]   = tmp[idt]   = v[0]*sum1+v[5]*sum2+v[10]*sum3+
235                                  v[15]*sum4+v[20]*sum5;
236     x[1+idc] = tmp[1+idt] = v[1]*sum1+v[6]*sum2+v[11]*sum3+
237                                  v[16]*sum4+v[21]*sum5;
238     x[2+idc] = tmp[2+idt] = v[2]*sum1+v[7]*sum2+v[12]*sum3+
239                                  v[17]*sum4+v[22]*sum5;
240     x[3+idc] = tmp[3+idt] = v[3]*sum1+v[8]*sum2+v[13]*sum3+
241                                  v[18]*sum4+v[23]*sum5;
242     x[4+idc] = tmp[4+idt] = v[4]*sum1+v[9]*sum2+v[14]*sum3+
243                                  v[19]*sum4+v[24]*sum5;
244   }
245 
246   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
247   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
248   ierr = VecRestoreArray(bb,&b); CHKERRQ(ierr);
249   ierr = VecRestoreArray(xx,&x); CHKERRQ(ierr);
250   PLogFlops(2*25*(a->nz) - a->n);
251   PetscFunctionReturn(0);
252 }
253 
254 #undef __FUNC__
255 #define __FUNC__ "MatSolve_SeqBAIJ_4"
256 int MatSolve_SeqBAIJ_4(Mat A,Vec bb,Vec xx)
257 {
258   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *)A->data;
259   IS              iscol=a->col,isrow=a->row;
260   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout;
261   int             *diag = a->diag;
262   Scalar          *aa=a->a,sum1,sum2,sum3,sum4,x1,x2,x3,x4;
263   Scalar          *x,*b,*tmp,*v;
264 
265   PetscFunctionBegin;
266   ierr = VecGetArray(bb,&b); CHKERRQ(ierr);
267   ierr = VecGetArray(xx,&x); CHKERRQ(ierr);
268   tmp  = a->solve_work;
269 
270   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
271   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
272 
273   /* forward solve the lower triangular */
274   idx    = 4*(*r++);
275   tmp[0] = b[idx];   tmp[1] = b[1+idx];
276   tmp[2] = b[2+idx]; tmp[3] = b[3+idx];
277   for ( i=1; i<n; i++ ) {
278     v     = aa + 16*ai[i];
279     vi    = aj + ai[i];
280     nz    = diag[i] - ai[i];
281     idx   = 4*(*r++);
282     sum1  = b[idx];sum2 = b[1+idx];sum3 = b[2+idx];sum4 = b[3+idx];
283     while (nz--) {
284       idx   = 4*(*vi++);
285       x1    = tmp[idx];x2 = tmp[1+idx];x3 = tmp[2+idx];x4 = tmp[3+idx];
286       sum1 -= v[0]*x1 + v[4]*x2 + v[8]*x3  + v[12]*x4;
287       sum2 -= v[1]*x1 + v[5]*x2 + v[9]*x3  + v[13]*x4;
288       sum3 -= v[2]*x1 + v[6]*x2 + v[10]*x3 + v[14]*x4;
289       sum4 -= v[3]*x1 + v[7]*x2 + v[11]*x3 + v[15]*x4;
290       v    += 16;
291     }
292     idx        = 4*i;
293     tmp[idx]   = sum1;tmp[1+idx] = sum2;
294     tmp[2+idx] = sum3;tmp[3+idx] = sum4;
295   }
296   /* backward solve the upper triangular */
297   for ( i=n-1; i>=0; i-- ){
298     v    = aa + 16*diag[i] + 16;
299     vi   = aj + diag[i] + 1;
300     nz   = ai[i+1] - diag[i] - 1;
301     idt  = 4*i;
302     sum1 = tmp[idt];  sum2 = tmp[1+idt];
303     sum3 = tmp[2+idt];sum4 = tmp[3+idt];
304     while (nz--) {
305       idx   = 4*(*vi++);
306       x1    = tmp[idx];   x2 = tmp[1+idx];
307       x3    = tmp[2+idx]; x4 = tmp[3+idx];
308       sum1 -= v[0]*x1 + v[4]*x2 + v[8]*x3   + v[12]*x4;
309       sum2 -= v[1]*x1 + v[5]*x2 + v[9]*x3   + v[13]*x4;
310       sum3 -= v[2]*x1 + v[6]*x2 + v[10]*x3  + v[14]*x4;
311       sum4 -= v[3]*x1 + v[7]*x2 + v[11]*x3  + v[15]*x4;
312       v += 16;
313     }
314     idc      = 4*(*c--);
315     v        = aa + 16*diag[i];
316     x[idc]   = tmp[idt]   = v[0]*sum1+v[4]*sum2+v[8]*sum3+v[12]*sum4;
317     x[1+idc] = tmp[1+idt] = v[1]*sum1+v[5]*sum2+v[9]*sum3+v[13]*sum4;
318     x[2+idc] = tmp[2+idt] = v[2]*sum1+v[6]*sum2+v[10]*sum3+v[14]*sum4;
319     x[3+idc] = tmp[3+idt] = v[3]*sum1+v[7]*sum2+v[11]*sum3+v[15]*sum4;
320   }
321 
322   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
323   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
324   ierr = VecRestoreArray(bb,&b); CHKERRQ(ierr);
325   ierr = VecRestoreArray(xx,&x); CHKERRQ(ierr);
326   PLogFlops(2*16*(a->nz) - a->n);
327   PetscFunctionReturn(0);
328 }
329 
330 /*
331       Special case where the matrix was ILU(0) factored in the natural
332    ordering. This eliminates the need for the column and row permutation.
333 */
334 #undef __FUNC__
335 #define __FUNC__ "MatSolve_SeqBAIJ_4_NaturalOrdering"
336 int MatSolve_SeqBAIJ_4_NaturalOrdering(Mat A,Vec bb,Vec xx)
337 {
338   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *)A->data;
339   int             i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt;
340   int             ierr,*diag = a->diag,jdx;
341   Scalar          *aa=a->a,sum1,sum2,sum3,sum4,x1,x2,x3,x4;
342   Scalar          *x,*b,*v;
343 
344   PetscFunctionBegin;
345   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
346   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
347 
348 #if defined(USE_FORTRAN_KERNEL_SOLVEBAIJ)
349   fortransolvebaij4_(&n,x,ai,aj,adiag,aa,b);
350 #else
351 
352   /* forward solve the lower triangular */
353   idx    = 0;
354   x[0]   = b[0]; x[1] = b[1]; x[2] = b[2]; x[3] = b[3];
355   for ( i=1; i<n; i++ ) {
356     v     =  aa      + 16*ai[i];
357     vi    =  aj      + ai[i];
358     nz    =  diag[i] - ai[i];
359     idx   +=  4;
360     sum1  =  b[idx];sum2 = b[1+idx];sum3 = b[2+idx];sum4 = b[3+idx];
361     while (nz--) {
362       jdx   = 4*(*vi++);
363       x1    = x[jdx];x2 = x[1+jdx];x3 = x[2+jdx];x4 = x[3+jdx];
364       sum1 -= v[0]*x1 + v[4]*x2 + v[8]*x3  + v[12]*x4;
365       sum2 -= v[1]*x1 + v[5]*x2 + v[9]*x3  + v[13]*x4;
366       sum3 -= v[2]*x1 + v[6]*x2 + v[10]*x3 + v[14]*x4;
367       sum4 -= v[3]*x1 + v[7]*x2 + v[11]*x3 + v[15]*x4;
368       v    += 16;
369     }
370     x[idx]   = sum1;
371     x[1+idx] = sum2;
372     x[2+idx] = sum3;
373     x[3+idx] = sum4;
374   }
375   /* backward solve the upper triangular */
376   for ( i=n-1; i>=0; i-- ){
377     v    = aa + 16*diag[i] + 16;
378     vi   = aj + diag[i] + 1;
379     nz   = ai[i+1] - diag[i] - 1;
380     idt  = 4*i;
381     sum1 = x[idt];  sum2 = x[1+idt];
382     sum3 = x[2+idt];sum4 = x[3+idt];
383     while (nz--) {
384       idx   = 4*(*vi++);
385       x1    = x[idx];   x2 = x[1+idx];x3    = x[2+idx]; x4 = x[3+idx];
386       sum1 -= v[0]*x1 + v[4]*x2 + v[8]*x3   + v[12]*x4;
387       sum2 -= v[1]*x1 + v[5]*x2 + v[9]*x3   + v[13]*x4;
388       sum3 -= v[2]*x1 + v[6]*x2 + v[10]*x3  + v[14]*x4;
389       sum4 -= v[3]*x1 + v[7]*x2 + v[11]*x3  + v[15]*x4;
390       v    += 16;
391     }
392     v        = aa + 16*diag[i];
393     x[idt]   = v[0]*sum1 + v[4]*sum2 + v[8]*sum3  + v[12]*sum4;
394     x[1+idt] = v[1]*sum1 + v[5]*sum2 + v[9]*sum3  + v[13]*sum4;
395     x[2+idt] = v[2]*sum1 + v[6]*sum2 + v[10]*sum3 + v[14]*sum4;
396     x[3+idt] = v[3]*sum1 + v[7]*sum2 + v[11]*sum3 + v[15]*sum4;
397   }
398 #endif
399 
400   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
401   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
402   PLogFlops(2*16*(a->nz) - a->n);
403   PetscFunctionReturn(0);
404 }
405 
406 
407 #undef __FUNC__
408 #define __FUNC__ "MatSolve_SeqBAIJ_3"
409 int MatSolve_SeqBAIJ_3(Mat A,Vec bb,Vec xx)
410 {
411   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
412   IS              iscol=a->col,isrow=a->row;
413   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout;
414   int             *diag = a->diag;
415   Scalar          *aa=a->a,sum1,sum2,sum3,x1,x2,x3;
416   Scalar *x,*b,*tmp,*v;
417 
418   PetscFunctionBegin;
419   ierr = VecGetArray(bb,&b); CHKERRQ(ierr);
420   ierr = VecGetArray(xx,&x); CHKERRQ(ierr);
421   tmp  = a->solve_work;
422 
423   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
424   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
425 
426   /* forward solve the lower triangular */
427   idx    = 3*(*r++);
428   tmp[0] = b[idx]; tmp[1] = b[1+idx]; tmp[2] = b[2+idx];
429   for ( i=1; i<n; i++ ) {
430     v     = aa + 9*ai[i];
431     vi    = aj + ai[i];
432     nz    = diag[i] - ai[i];
433     idx   = 3*(*r++);
434     sum1  = b[idx]; sum2 = b[1+idx]; sum3 = b[2+idx];
435     while (nz--) {
436       idx   = 3*(*vi++);
437       x1    = tmp[idx]; x2 = tmp[1+idx]; x3 = tmp[2+idx];
438       sum1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
439       sum2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
440       sum3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
441       v += 9;
442     }
443     idx = 3*i;
444     tmp[idx] = sum1; tmp[1+idx] = sum2; tmp[2+idx] = sum3;
445   }
446   /* backward solve the upper triangular */
447   for ( i=n-1; i>=0; i-- ){
448     v    = aa + 9*diag[i] + 9;
449     vi   = aj + diag[i] + 1;
450     nz   = ai[i+1] - diag[i] - 1;
451     idt  = 3*i;
452     sum1 = tmp[idt]; sum2 = tmp[1+idt]; sum3 = tmp[2+idt];
453     while (nz--) {
454       idx   = 3*(*vi++);
455       x1    = tmp[idx]; x2 = tmp[1+idx]; x3 = tmp[2+idx];
456       sum1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
457       sum2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
458       sum3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
459       v += 9;
460     }
461     idc = 3*(*c--);
462     v   = aa + 9*diag[i];
463     x[idc]   = tmp[idt]   = v[0]*sum1 + v[3]*sum2 + v[6]*sum3;
464     x[1+idc] = tmp[1+idt] = v[1]*sum1 + v[4]*sum2 + v[7]*sum3;
465     x[2+idc] = tmp[2+idt] = v[2]*sum1 + v[5]*sum2 + v[8]*sum3;
466   }
467   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
468   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
469   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
470   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
471   PLogFlops(2*9*(a->nz) - a->n);
472   PetscFunctionReturn(0);
473 }
474 
475 #undef __FUNC__
476 #define __FUNC__ "MatSolve_SeqBAIJ_2"
477 int MatSolve_SeqBAIJ_2(Mat A,Vec bb,Vec xx)
478 {
479   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
480   IS              iscol=a->col,isrow=a->row;
481   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout;
482   int             *diag = a->diag;
483   Scalar          *aa=a->a,sum1,sum2,x1,x2;
484   Scalar *x,*b,*tmp,*v;
485 
486   PetscFunctionBegin;
487   ierr = VecGetArray(bb,&b); CHKERRQ(ierr);
488   ierr = VecGetArray(xx,&x); CHKERRQ(ierr);
489   tmp  = a->solve_work;
490 
491   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
492   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
493 
494   /* forward solve the lower triangular */
495   idx    = 2*(*r++);
496   tmp[0] = b[idx]; tmp[1] = b[1+idx];
497   for ( i=1; i<n; i++ ) {
498     v     = aa + 4*ai[i];
499     vi    = aj + ai[i];
500     nz    = diag[i] - ai[i];
501     idx   = 2*(*r++);
502     sum1  = b[idx]; sum2 = b[1+idx];
503     while (nz--) {
504       idx   = 2*(*vi++);
505       x1    = tmp[idx]; x2 = tmp[1+idx];
506       sum1 -= v[0]*x1 + v[2]*x2;
507       sum2 -= v[1]*x1 + v[3]*x2;
508       v += 4;
509     }
510     idx = 2*i;
511     tmp[idx] = sum1; tmp[1+idx] = sum2;
512   }
513   /* backward solve the upper triangular */
514   for ( i=n-1; i>=0; i-- ){
515     v    = aa + 4*diag[i] + 4;
516     vi   = aj + diag[i] + 1;
517     nz   = ai[i+1] - diag[i] - 1;
518     idt  = 2*i;
519     sum1 = tmp[idt]; sum2 = tmp[1+idt];
520     while (nz--) {
521       idx   = 2*(*vi++);
522       x1    = tmp[idx]; x2 = tmp[1+idx];
523       sum1 -= v[0]*x1 + v[2]*x2;
524       sum2 -= v[1]*x1 + v[3]*x2;
525       v += 4;
526     }
527     idc = 2*(*c--);
528     v   = aa + 4*diag[i];
529     x[idc]   = tmp[idt]   = v[0]*sum1 + v[2]*sum2;
530     x[1+idc] = tmp[1+idt] = v[1]*sum1 + v[3]*sum2;
531   }
532   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
533   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
534   ierr = VecRestoreArray(bb,&b); CHKERRQ(ierr);
535   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
536   PLogFlops(2*4*(a->nz) - a->n);
537   PetscFunctionReturn(0);
538 }
539 
540 
541 #undef __FUNC__
542 #define __FUNC__ "MatSolve_SeqBAIJ_1"
543 int MatSolve_SeqBAIJ_1(Mat A,Vec bb,Vec xx)
544 {
545   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
546   IS              iscol=a->col,isrow=a->row;
547   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,*rout,*cout;
548   int             *diag = a->diag;
549   Scalar          *aa=a->a,sum1;
550   Scalar *x,*b,*tmp,*v;
551 
552   PetscFunctionBegin;
553   if (!n) PetscFunctionReturn(0);
554 
555   ierr = VecGetArray(bb,&b); CHKERRQ(ierr);
556   ierr = VecGetArray(xx,&x); CHKERRQ(ierr);
557   tmp  = a->solve_work;
558 
559   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
560   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
561 
562   /* forward solve the lower triangular */
563   tmp[0] = b[*r++];
564   for ( i=1; i<n; i++ ) {
565     v     = aa + ai[i];
566     vi    = aj + ai[i];
567     nz    = diag[i] - ai[i];
568     sum1  = b[*r++];
569     while (nz--) {
570       sum1 -= (*v++)*tmp[*vi++];
571     }
572     tmp[i] = sum1;
573   }
574   /* backward solve the upper triangular */
575   for ( i=n-1; i>=0; i-- ){
576     v    = aa + diag[i] + 1;
577     vi   = aj + diag[i] + 1;
578     nz   = ai[i+1] - diag[i] - 1;
579     sum1 = tmp[i];
580     while (nz--) {
581       sum1 -= (*v++)*tmp[*vi++];
582     }
583     x[*c--] = tmp[i] = aa[diag[i]]*sum1;
584   }
585 
586   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
587   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
588   ierr = VecRestoreArray(bb,&b); CHKERRQ(ierr);
589   ierr = VecRestoreArray(xx,&x); CHKERRQ(ierr);
590   PLogFlops(2*1*(a->nz) - a->n);
591   PetscFunctionReturn(0);
592 }
593 
594 extern int MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering(Mat,Mat*);
595 extern int MatSolve_SeqBAIJ_4_NaturalOrdering(Mat,Vec,Vec);
596 /* ----------------------------------------------------------------*/
597 /*
598      This code is virtually identical to MatILUFactorSymbolic_SeqAIJ
599    except that the data structure of Mat_SeqAIJ is slightly different.
600    Not a good example of code reuse.
601 */
602 #undef __FUNC__
603 #define __FUNC__ "MatILUFactorSymbolic_SeqBAIJ"
604 int MatILUFactorSymbolic_SeqBAIJ(Mat A,IS isrow,IS iscol,double f,int levels,
605                                  Mat *fact)
606 {
607   Mat_SeqBAIJ *a = (Mat_SeqBAIJ *) A->data, *b;
608   IS          isicol;
609   int         *r,*ic, ierr, prow, n = a->mbs, *ai = a->i, *aj = a->j;
610   int         *ainew,*ajnew, jmax,*fill, *xi, nz, *im,*ajfill,*flev;
611   int         *dloc, idx, row,m,fm, nzf, nzi,len,  realloc = 0;
612   int         incrlev,nnz,i,bs = a->bs,bs2 = a->bs2;
613   PetscTruth  col_identity, row_identity;
614 
615   PetscFunctionBegin;
616   ierr = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
617 
618   /* special case that simply copies fill pattern */
619   PetscValidHeaderSpecific(isrow,IS_COOKIE);
620   PetscValidHeaderSpecific(iscol,IS_COOKIE);
621   ISIdentity(isrow,&row_identity); ISIdentity(iscol,&col_identity);
622   if (levels == 0 && row_identity && col_identity) {
623     ierr = MatDuplicate_SeqBAIJ(A,MAT_DO_NOT_COPY_VALUES,fact); CHKERRQ(ierr);
624     (*fact)->factor = FACTOR_LU;
625     b               = (Mat_SeqBAIJ *) (*fact)->data;
626     if (!b->diag) {
627       ierr = MatMarkDiag_SeqBAIJ(*fact); CHKERRQ(ierr);
628     }
629     b->row        = isrow;
630     b->col        = iscol;
631     b->icol       = isicol;
632     b->solve_work = (Scalar *) PetscMalloc((b->m+1+b->bs)*sizeof(Scalar));CHKPTRQ(b->solve_work);
633     /*
634         Blocksize 4 has a special faster solver for ILU(0) factorization
635         with natural ordering
636     */
637     if (b->bs == 4) {
638       (*fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering;
639       (*fact)->ops->solve           = MatSolve_SeqBAIJ_4_NaturalOrdering;
640     }
641     PetscFunctionReturn(0);
642   }
643 
644   ierr = ISGetIndices(isrow,&r); CHKERRQ(ierr);
645   ierr = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
646 
647   /* get new row pointers */
648   ainew = (int *) PetscMalloc( (n+1)*sizeof(int) ); CHKPTRQ(ainew);
649   ainew[0] = 0;
650   /* don't know how many column pointers are needed so estimate */
651   jmax = (int) (f*ai[n] + 1);
652   ajnew = (int *) PetscMalloc( (jmax)*sizeof(int) ); CHKPTRQ(ajnew);
653   /* ajfill is level of fill for each fill entry */
654   ajfill = (int *) PetscMalloc( (jmax)*sizeof(int) ); CHKPTRQ(ajfill);
655   /* fill is a linked list of nonzeros in active row */
656   fill = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(fill);
657   /* im is level for each filled value */
658   im = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(im);
659   /* dloc is location of diagonal in factor */
660   dloc = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(dloc);
661   dloc[0]  = 0;
662   for ( prow=0; prow<n; prow++ ) {
663     /* first copy previous fill into linked list */
664     nzf     = nz  = ai[r[prow]+1] - ai[r[prow]];
665     if (!nz) SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,1,"Empty row in matrix");
666     xi      = aj + ai[r[prow]];
667     fill[n] = n;
668     while (nz--) {
669       fm  = n;
670       idx = ic[*xi++];
671       do {
672         m  = fm;
673         fm = fill[m];
674       } while (fm < idx);
675       fill[m]   = idx;
676       fill[idx] = fm;
677       im[idx]   = 0;
678     }
679     nzi = 0;
680     row = fill[n];
681     while ( row < prow ) {
682       incrlev = im[row] + 1;
683       nz      = dloc[row];
684       xi      = ajnew  + ainew[row] + nz;
685       flev    = ajfill + ainew[row] + nz + 1;
686       nnz     = ainew[row+1] - ainew[row] - nz - 1;
687       if (*xi++ != row) {
688         SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,0,"Zero pivot: try running with -pc_ilu_nonzeros_along_diagonal");
689       }
690       fm      = row;
691       while (nnz-- > 0) {
692         idx = *xi++;
693         if (*flev + incrlev > levels) {
694           flev++;
695           continue;
696         }
697         do {
698           m  = fm;
699           fm = fill[m];
700         } while (fm < idx);
701         if (fm != idx) {
702           im[idx]   = *flev + incrlev;
703           fill[m]   = idx;
704           fill[idx] = fm;
705           fm        = idx;
706           nzf++;
707         } else {
708           if (im[idx] > *flev + incrlev) im[idx] = *flev+incrlev;
709         }
710         flev++;
711       }
712       row = fill[row];
713       nzi++;
714     }
715     /* copy new filled row into permanent storage */
716     ainew[prow+1] = ainew[prow] + nzf;
717     if (ainew[prow+1] > jmax) {
718 
719       /* estimate how much additional space we will need */
720       /* use the strategy suggested by David Hysom <hysom@perch-t.icase.edu> */
721       /* just double the memory each time */
722       int maxadd = jmax;
723       /* maxadd = (int) (((f*ai[n]+1)*(n-prow+5))/n); */
724       if (maxadd < nzf) maxadd = (n-prow)*(nzf+1);
725       jmax += maxadd;
726 
727       /* allocate a longer ajnew and ajfill */
728       xi = (int *) PetscMalloc( jmax*sizeof(int) );CHKPTRQ(xi);
729       PetscMemcpy(xi,ajnew,ainew[prow]*sizeof(int));
730       PetscFree(ajnew);
731       ajnew = xi;
732       xi = (int *) PetscMalloc( jmax*sizeof(int) );CHKPTRQ(xi);
733       PetscMemcpy(xi,ajfill,ainew[prow]*sizeof(int));
734       PetscFree(ajfill);
735       ajfill = xi;
736       realloc++; /* count how many reallocations are needed */
737     }
738     xi          = ajnew + ainew[prow];
739     flev        = ajfill + ainew[prow];
740     dloc[prow]  = nzi;
741     fm          = fill[n];
742     while (nzf--) {
743       *xi++   = fm;
744       *flev++ = im[fm];
745       fm      = fill[fm];
746     }
747   }
748   PetscFree(ajfill);
749   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
750   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
751   PetscFree(fill); PetscFree(im);
752 
753   {
754     double af = ((double)ainew[n])/((double)ai[n]);
755     PLogInfo(A,"MatILUFactorSymbolic_SeqBAIJ:Reallocs %d Fill ratio:given %g needed %g\n",
756              realloc,f,af);
757     PLogInfo(A,"MatILUFactorSymbolic_SeqBAIJ:Run with -pc_ilu_fill %g or use \n",af);
758     PLogInfo(A,"MatILUFactorSymbolic_SeqBAIJ:PCILUSetFill(pc,%g);\n",af);
759     PLogInfo(A,"MatILUFactorSymbolic_SeqBAIJ:for best performance.\n");
760   }
761 
762   /* put together the new matrix */
763   ierr = MatCreateSeqBAIJ(A->comm,bs,bs*n,bs*n,0,PETSC_NULL,fact);CHKERRQ(ierr);
764   PLogObjectParent(*fact,isicol);
765   b = (Mat_SeqBAIJ *) (*fact)->data;
766   PetscFree(b->imax);
767   b->singlemalloc = 0;
768   len = bs2*ainew[n]*sizeof(Scalar);
769   /* the next line frees the default space generated by the Create() */
770   PetscFree(b->a); PetscFree(b->ilen);
771   b->a          = (Scalar *) PetscMalloc( len ); CHKPTRQ(b->a);
772   b->j          = ajnew;
773   b->i          = ainew;
774   for ( i=0; i<n; i++ ) dloc[i] += ainew[i];
775   b->diag       = dloc;
776   b->ilen       = 0;
777   b->imax       = 0;
778   b->row        = isrow;
779   b->col        = iscol;
780   b->icol       = isicol;
781   b->solve_work = (Scalar *) PetscMalloc( (bs*n+bs)*sizeof(Scalar));CHKPTRQ(b->solve_work);
782   /* In b structure:  Free imax, ilen, old a, old j.
783      Allocate dloc, solve_work, new a, new j */
784   PLogObjectMemory(*fact,(ainew[n]-n)*(sizeof(int))+bs2*ainew[n]*sizeof(Scalar));
785   b->maxnz          = b->nz = ainew[n];
786   (*fact)->factor   = FACTOR_LU;
787 
788   (*fact)->info.factor_mallocs    = realloc;
789   (*fact)->info.fill_ratio_given  = f;
790   (*fact)->info.fill_ratio_needed = ((double)ainew[n])/((double)ai[prow]);
791 
792   PetscFunctionReturn(0);
793 }
794 
795 
796 
797 
798