xref: /petsc/src/mat/impls/baij/seq/baijfact2.c (revision 74c49fae86232ee8d4cedab0aa791f2687f7bef6)
1 #ifdef PETSC_RCS_HEADER
2 static char vcid[] = "$Id: baijfact2.c,v 1.14 1998/10/13 02:11:28 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 #include "src/inline/dot.h"
12 
13 /* ----------------------------------------------------------- */
14 #undef __FUNC__
15 #define __FUNC__ "MatSolve_SeqBAIJ_N"
16 int MatSolve_SeqBAIJ_N(Mat A,Vec bb,Vec xx)
17 {
18   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
19   IS              iscol=a->col,isrow=a->row;
20   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j;
21   int             nz,bs=a->bs,bs2=a->bs2,*rout,*cout;
22   Scalar          *aa=a->a,*sum;
23   Scalar *x,*b,*lsum,*tmp,*v;
24 
25   PetscFunctionBegin;
26   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
27   ierr = VecGetArray(xx,&x); CHKERRQ(ierr);
28   tmp  = a->solve_work;
29 
30   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
31   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
32 
33   /* forward solve the lower triangular */
34   PetscMemcpy(tmp,b + bs*(*r++), bs*sizeof(Scalar));
35   for ( i=1; i<n; i++ ) {
36     v   = aa + bs2*ai[i];
37     vi  = aj + ai[i];
38     nz  = a->diag[i] - ai[i];
39     sum = tmp + bs*i;
40     PetscMemcpy(sum,b+bs*(*r++),bs*sizeof(Scalar));
41     while (nz--) {
42       Kernel_v_gets_v_minus_A_times_w(bs,sum,v,tmp+bs*(*vi++));
43       v += bs2;
44     }
45   }
46   /* backward solve the upper triangular */
47   lsum = a->solve_work + a->n;
48   for ( i=n-1; i>=0; i-- ){
49     v   = aa + bs2*(a->diag[i] + 1);
50     vi  = aj + a->diag[i] + 1;
51     nz  = ai[i+1] - a->diag[i] - 1;
52     PetscMemcpy(lsum,tmp+i*bs,bs*sizeof(Scalar));
53     while (nz--) {
54       Kernel_v_gets_v_minus_A_times_w(bs,lsum,v,tmp+bs*(*vi++));
55       v += bs2;
56     }
57     Kernel_w_gets_A_times_v(bs,lsum,aa+bs2*a->diag[i],tmp+i*bs);
58     PetscMemcpy(x + bs*(*c--),tmp+i*bs,bs*sizeof(Scalar));
59   }
60 
61   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
62   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
63   ierr = VecRestoreArray(bb,&b); CHKERRQ(ierr);
64   ierr = VecRestoreArray(xx,&x); CHKERRQ(ierr);
65   PLogFlops(2*(a->bs2)*(a->nz) - a->n);
66   PetscFunctionReturn(0);
67 }
68 
69 #undef __FUNC__
70 #define __FUNC__ "MatSolve_SeqBAIJ_7"
71 int MatSolve_SeqBAIJ_7(Mat A,Vec bb,Vec xx)
72 {
73   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
74   IS              iscol=a->col,isrow=a->row;
75   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout;
76   int             *diag = a->diag;
77   Scalar          *aa=a->a,sum1,sum2,sum3,sum4,sum5,sum6,sum7,x1,x2,x3,x4,x5,x6,x7;
78   Scalar *x,*b,*tmp,*v;
79 
80   PetscFunctionBegin;
81   ierr = VecGetArray(bb,&b); CHKERRQ(ierr);
82   ierr = VecGetArray(xx,&x); CHKERRQ(ierr);
83   tmp  = a->solve_work;
84 
85   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
86   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
87 
88   /* forward solve the lower triangular */
89   idx    = 7*(*r++);
90   tmp[0] = b[idx];   tmp[1] = b[1+idx];
91   tmp[2] = b[2+idx]; tmp[3] = b[3+idx]; tmp[4] = b[4+idx];
92   tmp[5] = b[5+idx]; tmp[6] = b[6+idx];
93 
94   for ( i=1; i<n; i++ ) {
95     v     = aa + 49*ai[i];
96     vi    = aj + ai[i];
97     nz    = diag[i] - ai[i];
98     idx   = 7*(*r++);
99     sum1  = b[idx];sum2 = b[1+idx];sum3 = b[2+idx];sum4 = b[3+idx];
100     sum5  = b[4+idx];sum6 = b[5+idx];sum7 = b[6+idx];
101     while (nz--) {
102       idx   = 7*(*vi++);
103       x1    = tmp[idx];  x2 = tmp[1+idx];x3 = tmp[2+idx];
104       x4    = tmp[3+idx];x5 = tmp[4+idx];
105       x6    = tmp[5+idx];x7 = tmp[6+idx];
106       sum1 -= v[0]*x1 + v[7]*x2  + v[14]*x3 + v[21]*x4 + v[28]*x5 + v[35]*x6 + v[42]*x7;
107       sum2 -= v[1]*x1 + v[8]*x2  + v[15]*x3 + v[22]*x4 + v[29]*x5 + v[36]*x6 + v[43]*x7;
108       sum3 -= v[2]*x1 + v[9]*x2  + v[16]*x3 + v[23]*x4 + v[30]*x5 + v[37]*x6 + v[44]*x7;
109       sum4 -= v[3]*x1 + v[10]*x2 + v[17]*x3 + v[24]*x4 + v[31]*x5 + v[38]*x6 + v[45]*x7;
110       sum5 -= v[4]*x1 + v[11]*x2 + v[18]*x3 + v[25]*x4 + v[32]*x5 + v[39]*x6 + v[46]*x7;
111       sum6 -= v[5]*x1 + v[12]*x2 + v[19]*x3 + v[26]*x4 + v[33]*x5 + v[40]*x6 + v[47]*x7;
112       sum7 -= v[6]*x1 + v[13]*x2 + v[20]*x3 + v[27]*x4 + v[34]*x5 + v[41]*x6 + v[48]*x7;
113       v += 49;
114     }
115     idx = 7*i;
116     tmp[idx]   = sum1;tmp[1+idx] = sum2;
117     tmp[2+idx] = sum3;tmp[3+idx] = sum4; tmp[4+idx] = sum5;
118     tmp[5+idx] = sum6;tmp[6+idx] = sum7;
119   }
120   /* backward solve the upper triangular */
121   for ( i=n-1; i>=0; i-- ){
122     v    = aa + 49*diag[i] + 49;
123     vi   = aj + diag[i] + 1;
124     nz   = ai[i+1] - diag[i] - 1;
125     idt  = 7*i;
126     sum1 = tmp[idt];  sum2 = tmp[1+idt];
127     sum3 = tmp[2+idt];sum4 = tmp[3+idt]; sum5 = tmp[4+idt];
128     sum6 = tmp[5+idt];sum7 = tmp[6+idt];
129     while (nz--) {
130       idx   = 7*(*vi++);
131       x1    = tmp[idx];   x2 = tmp[1+idx];
132       x3    = tmp[2+idx]; x4 = tmp[3+idx]; x5 = tmp[4+idx];
133       x6    = tmp[5+idx]; x7 = tmp[6+idx];
134       sum1 -= v[0]*x1 + v[7]*x2  + v[14]*x3 + v[21]*x4 + v[28]*x5 + v[35]*x6 + v[42]*x7;
135       sum2 -= v[1]*x1 + v[8]*x2  + v[15]*x3 + v[22]*x4 + v[29]*x5 + v[36]*x6 + v[43]*x7;
136       sum3 -= v[2]*x1 + v[9]*x2  + v[16]*x3 + v[23]*x4 + v[30]*x5 + v[37]*x6 + v[44]*x7;
137       sum4 -= v[3]*x1 + v[10]*x2 + v[17]*x3 + v[24]*x4 + v[31]*x5 + v[38]*x6 + v[45]*x7;
138       sum5 -= v[4]*x1 + v[11]*x2 + v[18]*x3 + v[25]*x4 + v[32]*x5 + v[39]*x6 + v[46]*x7;
139       sum6 -= v[5]*x1 + v[12]*x2 + v[19]*x3 + v[26]*x4 + v[33]*x5 + v[40]*x6 + v[47]*x7;
140       sum7 -= v[6]*x1 + v[13]*x2 + v[20]*x3 + v[27]*x4 + v[34]*x5 + v[41]*x6 + v[48]*x7;
141       v += 49;
142     }
143     idc = 7*(*c--);
144     v   = aa + 49*diag[i];
145     x[idc]   = tmp[idt]   = v[0]*sum1+v[7]*sum2+v[14]*sum3+
146                                  v[21]*sum4+v[28]*sum5+v[35]*sum6+v[42]*sum7;
147     x[1+idc] = tmp[1+idt] = v[1]*sum1+v[8]*sum2+v[15]*sum3+
148                                  v[22]*sum4+v[29]*sum5+v[36]*sum6+v[43]*sum7;
149     x[2+idc] = tmp[2+idt] = v[2]*sum1+v[9]*sum2+v[16]*sum3+
150                                  v[23]*sum4+v[30]*sum5+v[37]*sum6+v[44]*sum7;
151     x[3+idc] = tmp[3+idt] = v[3]*sum1+v[10]*sum2+v[17]*sum3+
152                                  v[24]*sum4+v[31]*sum5+v[38]*sum6+v[45]*sum7;
153     x[4+idc] = tmp[4+idt] = v[4]*sum1+v[11]*sum2+v[18]*sum3+
154                                  v[25]*sum4+v[32]*sum5+v[39]*sum6+v[46]*sum7;
155     x[5+idc] = tmp[5+idt] = v[5]*sum1+v[12]*sum2+v[19]*sum3+
156                                  v[26]*sum4+v[33]*sum5+v[40]*sum6+v[47]*sum7;
157     x[6+idc] = tmp[6+idt] = v[6]*sum1+v[13]*sum2+v[20]*sum3+
158                                  v[27]*sum4+v[34]*sum5+v[41]*sum6+v[48]*sum7;
159   }
160 
161   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
162   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
163   ierr = VecRestoreArray(bb,&b); CHKERRQ(ierr);
164   ierr = VecRestoreArray(xx,&x); CHKERRQ(ierr);
165   PLogFlops(2*49*(a->nz) - a->n);
166   PetscFunctionReturn(0);
167 }
168 
169 #undef __FUNC__
170 #define __FUNC__ "MatSolve_SeqBAIJ_5"
171 int MatSolve_SeqBAIJ_5(Mat A,Vec bb,Vec xx)
172 {
173   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
174   IS              iscol=a->col,isrow=a->row;
175   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout;
176   int             *diag = a->diag;
177   Scalar          *aa=a->a,sum1,sum2,sum3,sum4,sum5,x1,x2,x3,x4,x5;
178   Scalar *x,*b,*tmp,*v;
179 
180   PetscFunctionBegin;
181   ierr = VecGetArray(bb,&b); CHKERRQ(ierr);
182   ierr = VecGetArray(xx,&x); CHKERRQ(ierr);
183   tmp  = a->solve_work;
184 
185   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
186   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
187 
188   /* forward solve the lower triangular */
189   idx    = 5*(*r++);
190   tmp[0] = b[idx];   tmp[1] = b[1+idx];
191   tmp[2] = b[2+idx]; tmp[3] = b[3+idx]; tmp[4] = b[4+idx];
192   for ( i=1; i<n; i++ ) {
193     v     = aa + 25*ai[i];
194     vi    = aj + ai[i];
195     nz    = diag[i] - ai[i];
196     idx   = 5*(*r++);
197     sum1  = b[idx];sum2 = b[1+idx];sum3 = b[2+idx];sum4 = b[3+idx];
198     sum5  = b[4+idx];
199     while (nz--) {
200       idx   = 5*(*vi++);
201       x1    = tmp[idx];  x2 = tmp[1+idx];x3 = tmp[2+idx];
202       x4    = tmp[3+idx];x5 = tmp[4+idx];
203       sum1 -= v[0]*x1 + v[5]*x2 + v[10]*x3 + v[15]*x4 + v[20]*x5;
204       sum2 -= v[1]*x1 + v[6]*x2 + v[11]*x3 + v[16]*x4 + v[21]*x5;
205       sum3 -= v[2]*x1 + v[7]*x2 + v[12]*x3 + v[17]*x4 + v[22]*x5;
206       sum4 -= v[3]*x1 + v[8]*x2 + v[13]*x3 + v[18]*x4 + v[23]*x5;
207       sum5 -= v[4]*x1 + v[9]*x2 + v[14]*x3 + v[19]*x4 + v[24]*x5;
208       v += 25;
209     }
210     idx = 5*i;
211     tmp[idx]   = sum1;tmp[1+idx] = sum2;
212     tmp[2+idx] = sum3;tmp[3+idx] = sum4; tmp[4+idx] = sum5;
213   }
214   /* backward solve the upper triangular */
215   for ( i=n-1; i>=0; i-- ){
216     v    = aa + 25*diag[i] + 25;
217     vi   = aj + diag[i] + 1;
218     nz   = ai[i+1] - diag[i] - 1;
219     idt  = 5*i;
220     sum1 = tmp[idt];  sum2 = tmp[1+idt];
221     sum3 = tmp[2+idt];sum4 = tmp[3+idt]; sum5 = tmp[4+idt];
222     while (nz--) {
223       idx   = 5*(*vi++);
224       x1    = tmp[idx];   x2 = tmp[1+idx];
225       x3    = tmp[2+idx]; x4 = tmp[3+idx]; x5 = tmp[4+idx];
226       sum1 -= v[0]*x1 + v[5]*x2 + v[10]*x3 + v[15]*x4 + v[20]*x5;
227       sum2 -= v[1]*x1 + v[6]*x2 + v[11]*x3 + v[16]*x4 + v[21]*x5;
228       sum3 -= v[2]*x1 + v[7]*x2 + v[12]*x3 + v[17]*x4 + v[22]*x5;
229       sum4 -= v[3]*x1 + v[8]*x2 + v[13]*x3 + v[18]*x4 + v[23]*x5;
230       sum5 -= v[4]*x1 + v[9]*x2 + v[14]*x3 + v[19]*x4 + v[24]*x5;
231       v += 25;
232     }
233     idc = 5*(*c--);
234     v   = aa + 25*diag[i];
235     x[idc]   = tmp[idt]   = v[0]*sum1+v[5]*sum2+v[10]*sum3+
236                                  v[15]*sum4+v[20]*sum5;
237     x[1+idc] = tmp[1+idt] = v[1]*sum1+v[6]*sum2+v[11]*sum3+
238                                  v[16]*sum4+v[21]*sum5;
239     x[2+idc] = tmp[2+idt] = v[2]*sum1+v[7]*sum2+v[12]*sum3+
240                                  v[17]*sum4+v[22]*sum5;
241     x[3+idc] = tmp[3+idt] = v[3]*sum1+v[8]*sum2+v[13]*sum3+
242                                  v[18]*sum4+v[23]*sum5;
243     x[4+idc] = tmp[4+idt] = v[4]*sum1+v[9]*sum2+v[14]*sum3+
244                                  v[19]*sum4+v[24]*sum5;
245   }
246 
247   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
248   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
249   ierr = VecRestoreArray(bb,&b); CHKERRQ(ierr);
250   ierr = VecRestoreArray(xx,&x); CHKERRQ(ierr);
251   PLogFlops(2*25*(a->nz) - a->n);
252   PetscFunctionReturn(0);
253 }
254 
255 #undef __FUNC__
256 #define __FUNC__ "MatSolve_SeqBAIJ_4"
257 int MatSolve_SeqBAIJ_4(Mat A,Vec bb,Vec xx)
258 {
259   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *)A->data;
260   IS              iscol=a->col,isrow=a->row;
261   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout;
262   int             *diag = a->diag;
263   Scalar          *aa=a->a,sum1,sum2,sum3,sum4,x1,x2,x3,x4;
264   Scalar          *x,*b,*tmp,*v;
265 
266   PetscFunctionBegin;
267   ierr = VecGetArray(bb,&b); CHKERRQ(ierr);
268   ierr = VecGetArray(xx,&x); CHKERRQ(ierr);
269   tmp  = a->solve_work;
270 
271   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
272   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
273 
274   /* forward solve the lower triangular */
275   idx    = 4*(*r++);
276   tmp[0] = b[idx];   tmp[1] = b[1+idx];
277   tmp[2] = b[2+idx]; tmp[3] = b[3+idx];
278   for ( i=1; i<n; i++ ) {
279     v     = aa + 16*ai[i];
280     vi    = aj + ai[i];
281     nz    = diag[i] - ai[i];
282     idx   = 4*(*r++);
283     sum1  = b[idx];sum2 = b[1+idx];sum3 = b[2+idx];sum4 = b[3+idx];
284     while (nz--) {
285       idx   = 4*(*vi++);
286       x1    = tmp[idx];x2 = tmp[1+idx];x3 = tmp[2+idx];x4 = tmp[3+idx];
287       sum1 -= v[0]*x1 + v[4]*x2 + v[8]*x3  + v[12]*x4;
288       sum2 -= v[1]*x1 + v[5]*x2 + v[9]*x3  + v[13]*x4;
289       sum3 -= v[2]*x1 + v[6]*x2 + v[10]*x3 + v[14]*x4;
290       sum4 -= v[3]*x1 + v[7]*x2 + v[11]*x3 + v[15]*x4;
291       v    += 16;
292     }
293     idx        = 4*i;
294     tmp[idx]   = sum1;tmp[1+idx] = sum2;
295     tmp[2+idx] = sum3;tmp[3+idx] = sum4;
296   }
297   /* backward solve the upper triangular */
298   for ( i=n-1; i>=0; i-- ){
299     v    = aa + 16*diag[i] + 16;
300     vi   = aj + diag[i] + 1;
301     nz   = ai[i+1] - diag[i] - 1;
302     idt  = 4*i;
303     sum1 = tmp[idt];  sum2 = tmp[1+idt];
304     sum3 = tmp[2+idt];sum4 = tmp[3+idt];
305     while (nz--) {
306       idx   = 4*(*vi++);
307       x1    = tmp[idx];   x2 = tmp[1+idx];
308       x3    = tmp[2+idx]; x4 = tmp[3+idx];
309       sum1 -= v[0]*x1 + v[4]*x2 + v[8]*x3   + v[12]*x4;
310       sum2 -= v[1]*x1 + v[5]*x2 + v[9]*x3   + v[13]*x4;
311       sum3 -= v[2]*x1 + v[6]*x2 + v[10]*x3  + v[14]*x4;
312       sum4 -= v[3]*x1 + v[7]*x2 + v[11]*x3  + v[15]*x4;
313       v += 16;
314     }
315     idc      = 4*(*c--);
316     v        = aa + 16*diag[i];
317     x[idc]   = tmp[idt]   = v[0]*sum1+v[4]*sum2+v[8]*sum3+v[12]*sum4;
318     x[1+idc] = tmp[1+idt] = v[1]*sum1+v[5]*sum2+v[9]*sum3+v[13]*sum4;
319     x[2+idc] = tmp[2+idt] = v[2]*sum1+v[6]*sum2+v[10]*sum3+v[14]*sum4;
320     x[3+idc] = tmp[3+idt] = v[3]*sum1+v[7]*sum2+v[11]*sum3+v[15]*sum4;
321   }
322 
323   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
324   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
325   ierr = VecRestoreArray(bb,&b); CHKERRQ(ierr);
326   ierr = VecRestoreArray(xx,&x); CHKERRQ(ierr);
327   PLogFlops(2*16*(a->nz) - a->n);
328   PetscFunctionReturn(0);
329 }
330 
331 /*
332       Special case where the matrix was ILU(0) factored in the natural
333    ordering. This eliminates the need for the column and row permutation.
334 */
335 #undef __FUNC__
336 #define __FUNC__ "MatSolve_SeqBAIJ_4_NaturalOrdering"
337 int MatSolve_SeqBAIJ_4_NaturalOrdering(Mat A,Vec bb,Vec xx)
338 {
339   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *)A->data;
340   int             n=a->mbs,*ai=a->i,*aj=a->j;
341   int             ierr,*diag = a->diag;
342   Scalar          *aa=a->a;
343   Scalar          *x,*b;
344 
345   PetscFunctionBegin;
346   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
347   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
348 
349 #if defined(USE_FORTRAN_KERNEL_SOLVEBAIJBLAS)
350   {
351     static Scalar w[2000]; /* very BAD need to fix */
352     fortransolvebaij4blas_(&n,x,ai,aj,diag,aa,b,w);
353   }
354 #elif defined(USE_FORTRAN_KERNEL_SOLVEBAIJ)
355   {
356     static Scalar w[2000]; /* very BAD need to fix */
357     fortransolvebaij4_(&n,x,ai,aj,diag,aa,b,w);
358   }
359 #elif defined(USE_FORTRAN_KERNEL_SOLVEBAIJUNROLL)
360   fortransolvebaij4unroll_(&n,x,ai,aj,diag,aa,b);
361 #else
362   {
363     Scalar sum1,sum2,sum3,sum4,x1,x2,x3,x4,*v;
364     int    jdx,idt,idx,nz,*vi,i;
365 
366   /* forward solve the lower triangular */
367   idx    = 0;
368   x[0]   = b[0]; x[1] = b[1]; x[2] = b[2]; x[3] = b[3];
369   for ( i=1; i<n; i++ ) {
370     v     =  aa      + 16*ai[i];
371     vi    =  aj      + ai[i];
372     nz    =  diag[i] - ai[i];
373     idx   +=  4;
374     sum1  =  b[idx];sum2 = b[1+idx];sum3 = b[2+idx];sum4 = b[3+idx];
375     while (nz--) {
376       jdx   = 4*(*vi++);
377       x1    = x[jdx];x2 = x[1+jdx];x3 = x[2+jdx];x4 = x[3+jdx];
378       sum1 -= v[0]*x1 + v[4]*x2 + v[8]*x3  + v[12]*x4;
379       sum2 -= v[1]*x1 + v[5]*x2 + v[9]*x3  + v[13]*x4;
380       sum3 -= v[2]*x1 + v[6]*x2 + v[10]*x3 + v[14]*x4;
381       sum4 -= v[3]*x1 + v[7]*x2 + v[11]*x3 + v[15]*x4;
382       v    += 16;
383     }
384     x[idx]   = sum1;
385     x[1+idx] = sum2;
386     x[2+idx] = sum3;
387     x[3+idx] = sum4;
388   }
389   /* backward solve the upper triangular */
390   for ( i=n-1; i>=0; i-- ){
391     v    = aa + 16*diag[i] + 16;
392     vi   = aj + diag[i] + 1;
393     nz   = ai[i+1] - diag[i] - 1;
394     idt  = 4*i;
395     sum1 = x[idt];  sum2 = x[1+idt];
396     sum3 = x[2+idt];sum4 = x[3+idt];
397     while (nz--) {
398       idx   = 4*(*vi++);
399       x1    = x[idx];   x2 = x[1+idx];x3    = x[2+idx]; x4 = x[3+idx];
400       sum1 -= v[0]*x1 + v[4]*x2 + v[8]*x3   + v[12]*x4;
401       sum2 -= v[1]*x1 + v[5]*x2 + v[9]*x3   + v[13]*x4;
402       sum3 -= v[2]*x1 + v[6]*x2 + v[10]*x3  + v[14]*x4;
403       sum4 -= v[3]*x1 + v[7]*x2 + v[11]*x3  + v[15]*x4;
404       v    += 16;
405     }
406     v        = aa + 16*diag[i];
407     x[idt]   = v[0]*sum1 + v[4]*sum2 + v[8]*sum3  + v[12]*sum4;
408     x[1+idt] = v[1]*sum1 + v[5]*sum2 + v[9]*sum3  + v[13]*sum4;
409     x[2+idt] = v[2]*sum1 + v[6]*sum2 + v[10]*sum3 + v[14]*sum4;
410     x[3+idt] = v[3]*sum1 + v[7]*sum2 + v[11]*sum3 + v[15]*sum4;
411   }
412   }
413 #endif
414 
415   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
416   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
417   PLogFlops(2*16*(a->nz) - a->n);
418   PetscFunctionReturn(0);
419 }
420 
421 
422 #undef __FUNC__
423 #define __FUNC__ "MatSolve_SeqBAIJ_3"
424 int MatSolve_SeqBAIJ_3(Mat A,Vec bb,Vec xx)
425 {
426   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
427   IS              iscol=a->col,isrow=a->row;
428   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout;
429   int             *diag = a->diag;
430   Scalar          *aa=a->a,sum1,sum2,sum3,x1,x2,x3;
431   Scalar *x,*b,*tmp,*v;
432 
433   PetscFunctionBegin;
434   ierr = VecGetArray(bb,&b); CHKERRQ(ierr);
435   ierr = VecGetArray(xx,&x); CHKERRQ(ierr);
436   tmp  = a->solve_work;
437 
438   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
439   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
440 
441   /* forward solve the lower triangular */
442   idx    = 3*(*r++);
443   tmp[0] = b[idx]; tmp[1] = b[1+idx]; tmp[2] = b[2+idx];
444   for ( i=1; i<n; i++ ) {
445     v     = aa + 9*ai[i];
446     vi    = aj + ai[i];
447     nz    = diag[i] - ai[i];
448     idx   = 3*(*r++);
449     sum1  = b[idx]; sum2 = b[1+idx]; sum3 = b[2+idx];
450     while (nz--) {
451       idx   = 3*(*vi++);
452       x1    = tmp[idx]; x2 = tmp[1+idx]; x3 = tmp[2+idx];
453       sum1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
454       sum2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
455       sum3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
456       v += 9;
457     }
458     idx = 3*i;
459     tmp[idx] = sum1; tmp[1+idx] = sum2; tmp[2+idx] = sum3;
460   }
461   /* backward solve the upper triangular */
462   for ( i=n-1; i>=0; i-- ){
463     v    = aa + 9*diag[i] + 9;
464     vi   = aj + diag[i] + 1;
465     nz   = ai[i+1] - diag[i] - 1;
466     idt  = 3*i;
467     sum1 = tmp[idt]; sum2 = tmp[1+idt]; sum3 = tmp[2+idt];
468     while (nz--) {
469       idx   = 3*(*vi++);
470       x1    = tmp[idx]; x2 = tmp[1+idx]; x3 = tmp[2+idx];
471       sum1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
472       sum2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
473       sum3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
474       v += 9;
475     }
476     idc = 3*(*c--);
477     v   = aa + 9*diag[i];
478     x[idc]   = tmp[idt]   = v[0]*sum1 + v[3]*sum2 + v[6]*sum3;
479     x[1+idc] = tmp[1+idt] = v[1]*sum1 + v[4]*sum2 + v[7]*sum3;
480     x[2+idc] = tmp[2+idt] = v[2]*sum1 + v[5]*sum2 + v[8]*sum3;
481   }
482   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
483   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
484   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
485   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
486   PLogFlops(2*9*(a->nz) - a->n);
487   PetscFunctionReturn(0);
488 }
489 
490 #undef __FUNC__
491 #define __FUNC__ "MatSolve_SeqBAIJ_2"
492 int MatSolve_SeqBAIJ_2(Mat A,Vec bb,Vec xx)
493 {
494   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
495   IS              iscol=a->col,isrow=a->row;
496   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,*rout,*cout;
497   int             *diag = a->diag;
498   Scalar          *aa=a->a,sum1,sum2,x1,x2;
499   Scalar *x,*b,*tmp,*v;
500 
501   PetscFunctionBegin;
502   ierr = VecGetArray(bb,&b); CHKERRQ(ierr);
503   ierr = VecGetArray(xx,&x); CHKERRQ(ierr);
504   tmp  = a->solve_work;
505 
506   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
507   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
508 
509   /* forward solve the lower triangular */
510   idx    = 2*(*r++);
511   tmp[0] = b[idx]; tmp[1] = b[1+idx];
512   for ( i=1; i<n; i++ ) {
513     v     = aa + 4*ai[i];
514     vi    = aj + ai[i];
515     nz    = diag[i] - ai[i];
516     idx   = 2*(*r++);
517     sum1  = b[idx]; sum2 = b[1+idx];
518     while (nz--) {
519       idx   = 2*(*vi++);
520       x1    = tmp[idx]; x2 = tmp[1+idx];
521       sum1 -= v[0]*x1 + v[2]*x2;
522       sum2 -= v[1]*x1 + v[3]*x2;
523       v += 4;
524     }
525     idx = 2*i;
526     tmp[idx] = sum1; tmp[1+idx] = sum2;
527   }
528   /* backward solve the upper triangular */
529   for ( i=n-1; i>=0; i-- ){
530     v    = aa + 4*diag[i] + 4;
531     vi   = aj + diag[i] + 1;
532     nz   = ai[i+1] - diag[i] - 1;
533     idt  = 2*i;
534     sum1 = tmp[idt]; sum2 = tmp[1+idt];
535     while (nz--) {
536       idx   = 2*(*vi++);
537       x1    = tmp[idx]; x2 = tmp[1+idx];
538       sum1 -= v[0]*x1 + v[2]*x2;
539       sum2 -= v[1]*x1 + v[3]*x2;
540       v += 4;
541     }
542     idc = 2*(*c--);
543     v   = aa + 4*diag[i];
544     x[idc]   = tmp[idt]   = v[0]*sum1 + v[2]*sum2;
545     x[1+idc] = tmp[1+idt] = v[1]*sum1 + v[3]*sum2;
546   }
547   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
548   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
549   ierr = VecRestoreArray(bb,&b); CHKERRQ(ierr);
550   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
551   PLogFlops(2*4*(a->nz) - a->n);
552   PetscFunctionReturn(0);
553 }
554 
555 
556 #undef __FUNC__
557 #define __FUNC__ "MatSolve_SeqBAIJ_1"
558 int MatSolve_SeqBAIJ_1(Mat A,Vec bb,Vec xx)
559 {
560   Mat_SeqBAIJ     *a=(Mat_SeqBAIJ *)A->data;
561   IS              iscol=a->col,isrow=a->row;
562   int             *r,*c,ierr,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,*rout,*cout;
563   int             *diag = a->diag;
564   Scalar          *aa=a->a,sum1;
565   Scalar *x,*b,*tmp,*v;
566 
567   PetscFunctionBegin;
568   if (!n) PetscFunctionReturn(0);
569 
570   ierr = VecGetArray(bb,&b); CHKERRQ(ierr);
571   ierr = VecGetArray(xx,&x); CHKERRQ(ierr);
572   tmp  = a->solve_work;
573 
574   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
575   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
576 
577   /* forward solve the lower triangular */
578   tmp[0] = b[*r++];
579   for ( i=1; i<n; i++ ) {
580     v     = aa + ai[i];
581     vi    = aj + ai[i];
582     nz    = diag[i] - ai[i];
583     sum1  = b[*r++];
584     while (nz--) {
585       sum1 -= (*v++)*tmp[*vi++];
586     }
587     tmp[i] = sum1;
588   }
589   /* backward solve the upper triangular */
590   for ( i=n-1; i>=0; i-- ){
591     v    = aa + diag[i] + 1;
592     vi   = aj + diag[i] + 1;
593     nz   = ai[i+1] - diag[i] - 1;
594     sum1 = tmp[i];
595     while (nz--) {
596       sum1 -= (*v++)*tmp[*vi++];
597     }
598     x[*c--] = tmp[i] = aa[diag[i]]*sum1;
599   }
600 
601   ierr = ISRestoreIndices(isrow,&rout); CHKERRQ(ierr);
602   ierr = ISRestoreIndices(iscol,&cout); CHKERRQ(ierr);
603   ierr = VecRestoreArray(bb,&b); CHKERRQ(ierr);
604   ierr = VecRestoreArray(xx,&x); CHKERRQ(ierr);
605   PLogFlops(2*1*(a->nz) - a->n);
606   PetscFunctionReturn(0);
607 }
608 
609 extern int MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering(Mat,Mat*);
610 extern int MatSolve_SeqBAIJ_4_NaturalOrdering(Mat,Vec,Vec);
611 /* ----------------------------------------------------------------*/
612 /*
613      This code is virtually identical to MatILUFactorSymbolic_SeqAIJ
614    except that the data structure of Mat_SeqAIJ is slightly different.
615    Not a good example of code reuse.
616 */
617 #undef __FUNC__
618 #define __FUNC__ "MatILUFactorSymbolic_SeqBAIJ"
619 int MatILUFactorSymbolic_SeqBAIJ(Mat A,IS isrow,IS iscol,double f,int levels,
620                                  Mat *fact)
621 {
622   Mat_SeqBAIJ *a = (Mat_SeqBAIJ *) A->data, *b;
623   IS          isicol;
624   int         *r,*ic, ierr, prow, n = a->mbs, *ai = a->i, *aj = a->j;
625   int         *ainew,*ajnew, jmax,*fill, *xi, nz, *im,*ajfill,*flev;
626   int         *dloc, idx, row,m,fm, nzf, nzi,len,  realloc = 0;
627   int         incrlev,nnz,i,bs = a->bs,bs2 = a->bs2;
628   PetscTruth  col_identity, row_identity;
629 
630   PetscFunctionBegin;
631   ierr = ISInvertPermutation(iscol,&isicol); CHKERRQ(ierr);
632 
633   /* special case that simply copies fill pattern */
634   PetscValidHeaderSpecific(isrow,IS_COOKIE);
635   PetscValidHeaderSpecific(iscol,IS_COOKIE);
636   ISIdentity(isrow,&row_identity); ISIdentity(iscol,&col_identity);
637   if (levels == 0 && row_identity && col_identity) {
638     ierr = MatDuplicate_SeqBAIJ(A,MAT_DO_NOT_COPY_VALUES,fact); CHKERRQ(ierr);
639     (*fact)->factor = FACTOR_LU;
640     b               = (Mat_SeqBAIJ *) (*fact)->data;
641     if (!b->diag) {
642       ierr = MatMarkDiag_SeqBAIJ(*fact); CHKERRQ(ierr);
643     }
644     b->row        = isrow;
645     b->col        = iscol;
646     b->icol       = isicol;
647     b->solve_work = (Scalar *) PetscMalloc((b->m+1+b->bs)*sizeof(Scalar));CHKPTRQ(b->solve_work);
648     /*
649         Blocksize 4 has a special faster solver for ILU(0) factorization
650         with natural ordering
651     */
652     if (b->bs == 4) {
653       (*fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqBAIJ_4_NaturalOrdering;
654       (*fact)->ops->solve           = MatSolve_SeqBAIJ_4_NaturalOrdering;
655     }
656     PetscFunctionReturn(0);
657   }
658 
659   ierr = ISGetIndices(isrow,&r); CHKERRQ(ierr);
660   ierr = ISGetIndices(isicol,&ic); CHKERRQ(ierr);
661 
662   /* get new row pointers */
663   ainew = (int *) PetscMalloc( (n+1)*sizeof(int) ); CHKPTRQ(ainew);
664   ainew[0] = 0;
665   /* don't know how many column pointers are needed so estimate */
666   jmax = (int) (f*ai[n] + 1);
667   ajnew = (int *) PetscMalloc( (jmax)*sizeof(int) ); CHKPTRQ(ajnew);
668   /* ajfill is level of fill for each fill entry */
669   ajfill = (int *) PetscMalloc( (jmax)*sizeof(int) ); CHKPTRQ(ajfill);
670   /* fill is a linked list of nonzeros in active row */
671   fill = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(fill);
672   /* im is level for each filled value */
673   im = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(im);
674   /* dloc is location of diagonal in factor */
675   dloc = (int *) PetscMalloc( (n+1)*sizeof(int)); CHKPTRQ(dloc);
676   dloc[0]  = 0;
677   for ( prow=0; prow<n; prow++ ) {
678     /* first copy previous fill into linked list */
679     nzf     = nz  = ai[r[prow]+1] - ai[r[prow]];
680     if (!nz) SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,1,"Empty row in matrix");
681     xi      = aj + ai[r[prow]];
682     fill[n] = n;
683     while (nz--) {
684       fm  = n;
685       idx = ic[*xi++];
686       do {
687         m  = fm;
688         fm = fill[m];
689       } while (fm < idx);
690       fill[m]   = idx;
691       fill[idx] = fm;
692       im[idx]   = 0;
693     }
694     nzi = 0;
695     row = fill[n];
696     while ( row < prow ) {
697       incrlev = im[row] + 1;
698       nz      = dloc[row];
699       xi      = ajnew  + ainew[row] + nz;
700       flev    = ajfill + ainew[row] + nz + 1;
701       nnz     = ainew[row+1] - ainew[row] - nz - 1;
702       if (*xi++ != row) {
703         SETERRQ(PETSC_ERR_MAT_LU_ZRPVT,0,"Zero pivot: try running with -pc_ilu_nonzeros_along_diagonal");
704       }
705       fm      = row;
706       while (nnz-- > 0) {
707         idx = *xi++;
708         if (*flev + incrlev > levels) {
709           flev++;
710           continue;
711         }
712         do {
713           m  = fm;
714           fm = fill[m];
715         } while (fm < idx);
716         if (fm != idx) {
717           im[idx]   = *flev + incrlev;
718           fill[m]   = idx;
719           fill[idx] = fm;
720           fm        = idx;
721           nzf++;
722         } else {
723           if (im[idx] > *flev + incrlev) im[idx] = *flev+incrlev;
724         }
725         flev++;
726       }
727       row = fill[row];
728       nzi++;
729     }
730     /* copy new filled row into permanent storage */
731     ainew[prow+1] = ainew[prow] + nzf;
732     if (ainew[prow+1] > jmax) {
733 
734       /* estimate how much additional space we will need */
735       /* use the strategy suggested by David Hysom <hysom@perch-t.icase.edu> */
736       /* just double the memory each time */
737       int maxadd = jmax;
738       /* maxadd = (int) (((f*ai[n]+1)*(n-prow+5))/n); */
739       if (maxadd < nzf) maxadd = (n-prow)*(nzf+1);
740       jmax += maxadd;
741 
742       /* allocate a longer ajnew and ajfill */
743       xi = (int *) PetscMalloc( jmax*sizeof(int) );CHKPTRQ(xi);
744       PetscMemcpy(xi,ajnew,ainew[prow]*sizeof(int));
745       PetscFree(ajnew);
746       ajnew = xi;
747       xi = (int *) PetscMalloc( jmax*sizeof(int) );CHKPTRQ(xi);
748       PetscMemcpy(xi,ajfill,ainew[prow]*sizeof(int));
749       PetscFree(ajfill);
750       ajfill = xi;
751       realloc++; /* count how many reallocations are needed */
752     }
753     xi          = ajnew + ainew[prow];
754     flev        = ajfill + ainew[prow];
755     dloc[prow]  = nzi;
756     fm          = fill[n];
757     while (nzf--) {
758       *xi++   = fm;
759       *flev++ = im[fm];
760       fm      = fill[fm];
761     }
762   }
763   PetscFree(ajfill);
764   ierr = ISRestoreIndices(isrow,&r); CHKERRQ(ierr);
765   ierr = ISRestoreIndices(isicol,&ic); CHKERRQ(ierr);
766   PetscFree(fill); PetscFree(im);
767 
768   {
769     double af = ((double)ainew[n])/((double)ai[n]);
770     PLogInfo(A,"MatILUFactorSymbolic_SeqBAIJ:Reallocs %d Fill ratio:given %g needed %g\n",
771              realloc,f,af);
772     PLogInfo(A,"MatILUFactorSymbolic_SeqBAIJ:Run with -pc_ilu_fill %g or use \n",af);
773     PLogInfo(A,"MatILUFactorSymbolic_SeqBAIJ:PCILUSetFill(pc,%g);\n",af);
774     PLogInfo(A,"MatILUFactorSymbolic_SeqBAIJ:for best performance.\n");
775   }
776 
777   /* put together the new matrix */
778   ierr = MatCreateSeqBAIJ(A->comm,bs,bs*n,bs*n,0,PETSC_NULL,fact);CHKERRQ(ierr);
779   PLogObjectParent(*fact,isicol);
780   b = (Mat_SeqBAIJ *) (*fact)->data;
781   PetscFree(b->imax);
782   b->singlemalloc = 0;
783   len = bs2*ainew[n]*sizeof(Scalar);
784   /* the next line frees the default space generated by the Create() */
785   PetscFree(b->a); PetscFree(b->ilen);
786   b->a          = (Scalar *) PetscMalloc( len ); CHKPTRQ(b->a);
787   b->j          = ajnew;
788   b->i          = ainew;
789   for ( i=0; i<n; i++ ) dloc[i] += ainew[i];
790   b->diag       = dloc;
791   b->ilen       = 0;
792   b->imax       = 0;
793   b->row        = isrow;
794   b->col        = iscol;
795   b->icol       = isicol;
796   b->solve_work = (Scalar *) PetscMalloc( (bs*n+bs)*sizeof(Scalar));CHKPTRQ(b->solve_work);
797   /* In b structure:  Free imax, ilen, old a, old j.
798      Allocate dloc, solve_work, new a, new j */
799   PLogObjectMemory(*fact,(ainew[n]-n)*(sizeof(int))+bs2*ainew[n]*sizeof(Scalar));
800   b->maxnz          = b->nz = ainew[n];
801   (*fact)->factor   = FACTOR_LU;
802 
803   (*fact)->info.factor_mallocs    = realloc;
804   (*fact)->info.fill_ratio_given  = f;
805   (*fact)->info.fill_ratio_needed = ((double)ainew[n])/((double)ai[prow]);
806 
807   PetscFunctionReturn(0);
808 }
809 
810 
811 
812 
813