xref: /petsc/src/mat/impls/baij/seq/baijsolv.c (revision 503c0ea9b45bcfbcebbb1ea5341243bbc69f0bea) !
1 #include <../src/mat/impls/baij/seq/baij.h>
2 #include <petsc/private/kernels/blockinvert.h>
3 
4 PetscErrorCode MatSolve_SeqBAIJ_N_inplace(Mat A,Vec bb,Vec xx)
5 {
6   Mat_SeqBAIJ       *a   =(Mat_SeqBAIJ*)A->data;
7   IS                iscol=a->col,isrow=a->row;
8   const PetscInt    *r,*c,*rout,*cout;
9   const PetscInt    n=a->mbs,*ai=a->i,*aj=a->j,*vi;
10   PetscInt          i,nz;
11   const PetscInt    bs =A->rmap->bs,bs2=a->bs2;
12   const MatScalar   *aa=a->a,*v;
13   PetscScalar       *x,*s,*t,*ls;
14   const PetscScalar *b;
15 
16   PetscFunctionBegin;
17   PetscCall(VecGetArrayRead(bb,&b));
18   PetscCall(VecGetArray(xx,&x));
19   t    = a->solve_work;
20 
21   PetscCall(ISGetIndices(isrow,&rout)); r = rout;
22   PetscCall(ISGetIndices(iscol,&cout)); c = cout + (n-1);
23 
24   /* forward solve the lower triangular */
25   PetscCall(PetscArraycpy(t,b+bs*(*r++),bs));
26   for (i=1; i<n; i++) {
27     v    = aa + bs2*ai[i];
28     vi   = aj + ai[i];
29     nz   = a->diag[i] - ai[i];
30     s    = t + bs*i;
31     PetscCall(PetscArraycpy(s,b+bs*(*r++),bs));
32     while (nz--) {
33       PetscKernel_v_gets_v_minus_A_times_w(bs,s,v,t+bs*(*vi++));
34       v += bs2;
35     }
36   }
37   /* backward solve the upper triangular */
38   ls = a->solve_work + A->cmap->n;
39   for (i=n-1; i>=0; i--) {
40     v    = aa + bs2*(a->diag[i] + 1);
41     vi   = aj + a->diag[i] + 1;
42     nz   = ai[i+1] - a->diag[i] - 1;
43     PetscCall(PetscArraycpy(ls,t+i*bs,bs));
44     while (nz--) {
45       PetscKernel_v_gets_v_minus_A_times_w(bs,ls,v,t+bs*(*vi++));
46       v += bs2;
47     }
48     PetscKernel_w_gets_A_times_v(bs,ls,aa+bs2*a->diag[i],t+i*bs);
49     PetscCall(PetscArraycpy(x + bs*(*c--),t+i*bs,bs));
50   }
51 
52   PetscCall(ISRestoreIndices(isrow,&rout));
53   PetscCall(ISRestoreIndices(iscol,&cout));
54   PetscCall(VecRestoreArrayRead(bb,&b));
55   PetscCall(VecRestoreArray(xx,&x));
56   PetscCall(PetscLogFlops(2.0*(a->bs2)*(a->nz) - A->rmap->bs*A->cmap->n));
57   PetscFunctionReturn(0);
58 }
59 
60 PetscErrorCode MatSolve_SeqBAIJ_7_inplace(Mat A,Vec bb,Vec xx)
61 {
62   Mat_SeqBAIJ       *a   =(Mat_SeqBAIJ*)A->data;
63   IS                iscol=a->col,isrow=a->row;
64   const PetscInt    *r,*c,*ai=a->i,*aj=a->j;
65   const PetscInt    *rout,*cout,*diag = a->diag,*vi,n=a->mbs;
66   PetscInt          i,nz,idx,idt,idc;
67   const MatScalar   *aa=a->a,*v;
68   PetscScalar       s1,s2,s3,s4,s5,s6,s7,x1,x2,x3,x4,x5,x6,x7,*x,*t;
69   const PetscScalar *b;
70 
71   PetscFunctionBegin;
72   PetscCall(VecGetArrayRead(bb,&b));
73   PetscCall(VecGetArray(xx,&x));
74   t    = a->solve_work;
75 
76   PetscCall(ISGetIndices(isrow,&rout)); r = rout;
77   PetscCall(ISGetIndices(iscol,&cout)); c = cout + (n-1);
78 
79   /* forward solve the lower triangular */
80   idx  = 7*(*r++);
81   t[0] = b[idx];   t[1] = b[1+idx];
82   t[2] = b[2+idx]; t[3] = b[3+idx]; t[4] = b[4+idx];
83   t[5] = b[5+idx]; t[6] = b[6+idx];
84 
85   for (i=1; i<n; i++) {
86     v   = aa + 49*ai[i];
87     vi  = aj + ai[i];
88     nz  = diag[i] - ai[i];
89     idx = 7*(*r++);
90     s1  = b[idx];s2 = b[1+idx];s3 = b[2+idx];s4 = b[3+idx];
91     s5  = b[4+idx];s6 = b[5+idx];s7 = b[6+idx];
92     while (nz--) {
93       idx = 7*(*vi++);
94       x1  = t[idx];  x2 = t[1+idx];x3 = t[2+idx];
95       x4  = t[3+idx];x5 = t[4+idx];
96       x6  = t[5+idx];x7 = t[6+idx];
97       s1 -= v[0]*x1 + v[7]*x2  + v[14]*x3 + v[21]*x4 + v[28]*x5 + v[35]*x6 + v[42]*x7;
98       s2 -= v[1]*x1 + v[8]*x2  + v[15]*x3 + v[22]*x4 + v[29]*x5 + v[36]*x6 + v[43]*x7;
99       s3 -= v[2]*x1 + v[9]*x2  + v[16]*x3 + v[23]*x4 + v[30]*x5 + v[37]*x6 + v[44]*x7;
100       s4 -= v[3]*x1 + v[10]*x2 + v[17]*x3 + v[24]*x4 + v[31]*x5 + v[38]*x6 + v[45]*x7;
101       s5 -= v[4]*x1 + v[11]*x2 + v[18]*x3 + v[25]*x4 + v[32]*x5 + v[39]*x6 + v[46]*x7;
102       s6 -= v[5]*x1 + v[12]*x2 + v[19]*x3 + v[26]*x4 + v[33]*x5 + v[40]*x6 + v[47]*x7;
103       s7 -= v[6]*x1 + v[13]*x2 + v[20]*x3 + v[27]*x4 + v[34]*x5 + v[41]*x6 + v[48]*x7;
104       v  += 49;
105     }
106     idx      = 7*i;
107     t[idx]   = s1;t[1+idx] = s2;
108     t[2+idx] = s3;t[3+idx] = s4; t[4+idx] = s5;
109     t[5+idx] = s6;t[6+idx] = s7;
110   }
111   /* backward solve the upper triangular */
112   for (i=n-1; i>=0; i--) {
113     v   = aa + 49*diag[i] + 49;
114     vi  = aj + diag[i] + 1;
115     nz  = ai[i+1] - diag[i] - 1;
116     idt = 7*i;
117     s1  = t[idt];  s2 = t[1+idt];
118     s3  = t[2+idt];s4 = t[3+idt]; s5 = t[4+idt];
119     s6  = t[5+idt];s7 = t[6+idt];
120     while (nz--) {
121       idx = 7*(*vi++);
122       x1  = t[idx];   x2 = t[1+idx];
123       x3  = t[2+idx]; x4 = t[3+idx]; x5 = t[4+idx];
124       x6  = t[5+idx]; x7 = t[6+idx];
125       s1 -= v[0]*x1 + v[7]*x2  + v[14]*x3 + v[21]*x4 + v[28]*x5 + v[35]*x6 + v[42]*x7;
126       s2 -= v[1]*x1 + v[8]*x2  + v[15]*x3 + v[22]*x4 + v[29]*x5 + v[36]*x6 + v[43]*x7;
127       s3 -= v[2]*x1 + v[9]*x2  + v[16]*x3 + v[23]*x4 + v[30]*x5 + v[37]*x6 + v[44]*x7;
128       s4 -= v[3]*x1 + v[10]*x2 + v[17]*x3 + v[24]*x4 + v[31]*x5 + v[38]*x6 + v[45]*x7;
129       s5 -= v[4]*x1 + v[11]*x2 + v[18]*x3 + v[25]*x4 + v[32]*x5 + v[39]*x6 + v[46]*x7;
130       s6 -= v[5]*x1 + v[12]*x2 + v[19]*x3 + v[26]*x4 + v[33]*x5 + v[40]*x6 + v[47]*x7;
131       s7 -= v[6]*x1 + v[13]*x2 + v[20]*x3 + v[27]*x4 + v[34]*x5 + v[41]*x6 + v[48]*x7;
132       v  += 49;
133     }
134     idc    = 7*(*c--);
135     v      = aa + 49*diag[i];
136     x[idc] = t[idt]   = v[0]*s1+v[7]*s2+v[14]*s3+
137                         v[21]*s4+v[28]*s5+v[35]*s6+v[42]*s7;
138     x[1+idc] = t[1+idt] = v[1]*s1+v[8]*s2+v[15]*s3+
139                           v[22]*s4+v[29]*s5+v[36]*s6+v[43]*s7;
140     x[2+idc] = t[2+idt] = v[2]*s1+v[9]*s2+v[16]*s3+
141                           v[23]*s4+v[30]*s5+v[37]*s6+v[44]*s7;
142     x[3+idc] = t[3+idt] = v[3]*s1+v[10]*s2+v[17]*s3+
143                           v[24]*s4+v[31]*s5+v[38]*s6+v[45]*s7;
144     x[4+idc] = t[4+idt] = v[4]*s1+v[11]*s2+v[18]*s3+
145                           v[25]*s4+v[32]*s5+v[39]*s6+v[46]*s7;
146     x[5+idc] = t[5+idt] = v[5]*s1+v[12]*s2+v[19]*s3+
147                           v[26]*s4+v[33]*s5+v[40]*s6+v[47]*s7;
148     x[6+idc] = t[6+idt] = v[6]*s1+v[13]*s2+v[20]*s3+
149                           v[27]*s4+v[34]*s5+v[41]*s6+v[48]*s7;
150   }
151 
152   PetscCall(ISRestoreIndices(isrow,&rout));
153   PetscCall(ISRestoreIndices(iscol,&cout));
154   PetscCall(VecRestoreArrayRead(bb,&b));
155   PetscCall(VecRestoreArray(xx,&x));
156   PetscCall(PetscLogFlops(2.0*49*(a->nz) - 7.0*A->cmap->n));
157   PetscFunctionReturn(0);
158 }
159 
160 PetscErrorCode MatSolve_SeqBAIJ_7(Mat A,Vec bb,Vec xx)
161 {
162   Mat_SeqBAIJ       *a   =(Mat_SeqBAIJ*)A->data;
163   IS                iscol=a->col,isrow=a->row;
164   const PetscInt    *r,*c,*ai=a->i,*aj=a->j,*adiag=a->diag;
165   const PetscInt    n=a->mbs,*rout,*cout,*vi;
166   PetscInt          i,nz,idx,idt,idc,m;
167   const MatScalar   *aa=a->a,*v;
168   PetscScalar       s1,s2,s3,s4,s5,s6,s7,x1,x2,x3,x4,x5,x6,x7,*x,*t;
169   const PetscScalar *b;
170 
171   PetscFunctionBegin;
172   PetscCall(VecGetArrayRead(bb,&b));
173   PetscCall(VecGetArray(xx,&x));
174   t    = a->solve_work;
175 
176   PetscCall(ISGetIndices(isrow,&rout)); r = rout;
177   PetscCall(ISGetIndices(iscol,&cout)); c = cout;
178 
179   /* forward solve the lower triangular */
180   idx  = 7*r[0];
181   t[0] = b[idx];   t[1] = b[1+idx];
182   t[2] = b[2+idx]; t[3] = b[3+idx]; t[4] = b[4+idx];
183   t[5] = b[5+idx]; t[6] = b[6+idx];
184 
185   for (i=1; i<n; i++) {
186     v   = aa + 49*ai[i];
187     vi  = aj + ai[i];
188     nz  = ai[i+1] - ai[i];
189     idx = 7*r[i];
190     s1  = b[idx];s2 = b[1+idx];s3 = b[2+idx];s4 = b[3+idx];
191     s5  = b[4+idx];s6 = b[5+idx];s7 = b[6+idx];
192     for (m=0; m<nz; m++) {
193       idx = 7*vi[m];
194       x1  = t[idx];  x2 = t[1+idx];x3 = t[2+idx];
195       x4  = t[3+idx];x5 = t[4+idx];
196       x6  = t[5+idx];x7 = t[6+idx];
197       s1 -= v[0]*x1 + v[7]*x2  + v[14]*x3 + v[21]*x4 + v[28]*x5 + v[35]*x6 + v[42]*x7;
198       s2 -= v[1]*x1 + v[8]*x2  + v[15]*x3 + v[22]*x4 + v[29]*x5 + v[36]*x6 + v[43]*x7;
199       s3 -= v[2]*x1 + v[9]*x2  + v[16]*x3 + v[23]*x4 + v[30]*x5 + v[37]*x6 + v[44]*x7;
200       s4 -= v[3]*x1 + v[10]*x2 + v[17]*x3 + v[24]*x4 + v[31]*x5 + v[38]*x6 + v[45]*x7;
201       s5 -= v[4]*x1 + v[11]*x2 + v[18]*x3 + v[25]*x4 + v[32]*x5 + v[39]*x6 + v[46]*x7;
202       s6 -= v[5]*x1 + v[12]*x2 + v[19]*x3 + v[26]*x4 + v[33]*x5 + v[40]*x6 + v[47]*x7;
203       s7 -= v[6]*x1 + v[13]*x2 + v[20]*x3 + v[27]*x4 + v[34]*x5 + v[41]*x6 + v[48]*x7;
204       v  += 49;
205     }
206     idx      = 7*i;
207     t[idx]   = s1;t[1+idx] = s2;
208     t[2+idx] = s3;t[3+idx] = s4; t[4+idx] = s5;
209     t[5+idx] = s6;t[6+idx] = s7;
210   }
211   /* backward solve the upper triangular */
212   for (i=n-1; i>=0; i--) {
213     v   = aa + 49*(adiag[i+1]+1);
214     vi  = aj + adiag[i+1]+1;
215     nz  = adiag[i] - adiag[i+1] - 1;
216     idt = 7*i;
217     s1  = t[idt];  s2 = t[1+idt];
218     s3  = t[2+idt];s4 = t[3+idt]; s5 = t[4+idt];
219     s6  = t[5+idt];s7 = t[6+idt];
220     for (m=0; m<nz; m++) {
221       idx = 7*vi[m];
222       x1  = t[idx];   x2 = t[1+idx];
223       x3  = t[2+idx]; x4 = t[3+idx]; x5 = t[4+idx];
224       x6  = t[5+idx]; x7 = t[6+idx];
225       s1 -= v[0]*x1 + v[7]*x2  + v[14]*x3 + v[21]*x4 + v[28]*x5 + v[35]*x6 + v[42]*x7;
226       s2 -= v[1]*x1 + v[8]*x2  + v[15]*x3 + v[22]*x4 + v[29]*x5 + v[36]*x6 + v[43]*x7;
227       s3 -= v[2]*x1 + v[9]*x2  + v[16]*x3 + v[23]*x4 + v[30]*x5 + v[37]*x6 + v[44]*x7;
228       s4 -= v[3]*x1 + v[10]*x2 + v[17]*x3 + v[24]*x4 + v[31]*x5 + v[38]*x6 + v[45]*x7;
229       s5 -= v[4]*x1 + v[11]*x2 + v[18]*x3 + v[25]*x4 + v[32]*x5 + v[39]*x6 + v[46]*x7;
230       s6 -= v[5]*x1 + v[12]*x2 + v[19]*x3 + v[26]*x4 + v[33]*x5 + v[40]*x6 + v[47]*x7;
231       s7 -= v[6]*x1 + v[13]*x2 + v[20]*x3 + v[27]*x4 + v[34]*x5 + v[41]*x6 + v[48]*x7;
232       v  += 49;
233     }
234     idc    = 7*c[i];
235     x[idc] = t[idt]   = v[0]*s1+v[7]*s2+v[14]*s3+
236                         v[21]*s4+v[28]*s5+v[35]*s6+v[42]*s7;
237     x[1+idc] = t[1+idt] = v[1]*s1+v[8]*s2+v[15]*s3+
238                           v[22]*s4+v[29]*s5+v[36]*s6+v[43]*s7;
239     x[2+idc] = t[2+idt] = v[2]*s1+v[9]*s2+v[16]*s3+
240                           v[23]*s4+v[30]*s5+v[37]*s6+v[44]*s7;
241     x[3+idc] = t[3+idt] = v[3]*s1+v[10]*s2+v[17]*s3+
242                           v[24]*s4+v[31]*s5+v[38]*s6+v[45]*s7;
243     x[4+idc] = t[4+idt] = v[4]*s1+v[11]*s2+v[18]*s3+
244                           v[25]*s4+v[32]*s5+v[39]*s6+v[46]*s7;
245     x[5+idc] = t[5+idt] = v[5]*s1+v[12]*s2+v[19]*s3+
246                           v[26]*s4+v[33]*s5+v[40]*s6+v[47]*s7;
247     x[6+idc] = t[6+idt] = v[6]*s1+v[13]*s2+v[20]*s3+
248                           v[27]*s4+v[34]*s5+v[41]*s6+v[48]*s7;
249   }
250 
251   PetscCall(ISRestoreIndices(isrow,&rout));
252   PetscCall(ISRestoreIndices(iscol,&cout));
253   PetscCall(VecRestoreArrayRead(bb,&b));
254   PetscCall(VecRestoreArray(xx,&x));
255   PetscCall(PetscLogFlops(2.0*49*(a->nz) - 7.0*A->cmap->n));
256   PetscFunctionReturn(0);
257 }
258 
259 PetscErrorCode MatSolve_SeqBAIJ_6_inplace(Mat A,Vec bb,Vec xx)
260 {
261   Mat_SeqBAIJ       *a   =(Mat_SeqBAIJ*)A->data;
262   IS                iscol=a->col,isrow=a->row;
263   const PetscInt    *r,*c,*rout,*cout;
264   const PetscInt    *diag = a->diag,n=a->mbs,*vi,*ai=a->i,*aj=a->j;
265   PetscInt          i,nz,idx,idt,idc;
266   const MatScalar   *aa=a->a,*v;
267   PetscScalar       *x,s1,s2,s3,s4,s5,s6,x1,x2,x3,x4,x5,x6,*t;
268   const PetscScalar *b;
269 
270   PetscFunctionBegin;
271   PetscCall(VecGetArrayRead(bb,&b));
272   PetscCall(VecGetArray(xx,&x));
273   t    = a->solve_work;
274 
275   PetscCall(ISGetIndices(isrow,&rout)); r = rout;
276   PetscCall(ISGetIndices(iscol,&cout)); c = cout + (n-1);
277 
278   /* forward solve the lower triangular */
279   idx  = 6*(*r++);
280   t[0] = b[idx];   t[1] = b[1+idx];
281   t[2] = b[2+idx]; t[3] = b[3+idx];
282   t[4] = b[4+idx]; t[5] = b[5+idx];
283   for (i=1; i<n; i++) {
284     v   = aa + 36*ai[i];
285     vi  = aj + ai[i];
286     nz  = diag[i] - ai[i];
287     idx = 6*(*r++);
288     s1  = b[idx];s2 = b[1+idx];s3 = b[2+idx];s4 = b[3+idx];
289     s5  = b[4+idx]; s6 = b[5+idx];
290     while (nz--) {
291       idx = 6*(*vi++);
292       x1  = t[idx];   x2 = t[1+idx]; x3 = t[2+idx];
293       x4  = t[3+idx]; x5 = t[4+idx]; x6 = t[5+idx];
294       s1 -= v[0]*x1 + v[6]*x2  + v[12]*x3 + v[18]*x4 + v[24]*x5 + v[30]*x6;
295       s2 -= v[1]*x1 + v[7]*x2  + v[13]*x3 + v[19]*x4 + v[25]*x5 + v[31]*x6;
296       s3 -= v[2]*x1 + v[8]*x2  + v[14]*x3 + v[20]*x4 + v[26]*x5 + v[32]*x6;
297       s4 -= v[3]*x1 + v[9]*x2  + v[15]*x3 + v[21]*x4 + v[27]*x5 + v[33]*x6;
298       s5 -= v[4]*x1 + v[10]*x2 + v[16]*x3 + v[22]*x4 + v[28]*x5 + v[34]*x6;
299       s6 -= v[5]*x1 + v[11]*x2 + v[17]*x3 + v[23]*x4 + v[29]*x5 + v[35]*x6;
300       v  += 36;
301     }
302     idx      = 6*i;
303     t[idx]   = s1;t[1+idx] = s2;
304     t[2+idx] = s3;t[3+idx] = s4;
305     t[4+idx] = s5;t[5+idx] = s6;
306   }
307   /* backward solve the upper triangular */
308   for (i=n-1; i>=0; i--) {
309     v   = aa + 36*diag[i] + 36;
310     vi  = aj + diag[i] + 1;
311     nz  = ai[i+1] - diag[i] - 1;
312     idt = 6*i;
313     s1  = t[idt];  s2 = t[1+idt];
314     s3  = t[2+idt];s4 = t[3+idt];
315     s5  = t[4+idt];s6 = t[5+idt];
316     while (nz--) {
317       idx = 6*(*vi++);
318       x1  = t[idx];   x2 = t[1+idx];
319       x3  = t[2+idx]; x4 = t[3+idx];
320       x5  = t[4+idx]; x6 = t[5+idx];
321       s1 -= v[0]*x1 + v[6]*x2  + v[12]*x3 + v[18]*x4 + v[24]*x5 + v[30]*x6;
322       s2 -= v[1]*x1 + v[7]*x2  + v[13]*x3 + v[19]*x4 + v[25]*x5 + v[31]*x6;
323       s3 -= v[2]*x1 + v[8]*x2  + v[14]*x3 + v[20]*x4 + v[26]*x5 + v[32]*x6;
324       s4 -= v[3]*x1 + v[9]*x2  + v[15]*x3 + v[21]*x4 + v[27]*x5 + v[33]*x6;
325       s5 -= v[4]*x1 + v[10]*x2 + v[16]*x3 + v[22]*x4 + v[28]*x5 + v[34]*x6;
326       s6 -= v[5]*x1 + v[11]*x2 + v[17]*x3 + v[23]*x4 + v[29]*x5 + v[35]*x6;
327       v  += 36;
328     }
329     idc    = 6*(*c--);
330     v      = aa + 36*diag[i];
331     x[idc] = t[idt]   = v[0]*s1+v[6]*s2+v[12]*s3+
332                         v[18]*s4+v[24]*s5+v[30]*s6;
333     x[1+idc] = t[1+idt] = v[1]*s1+v[7]*s2+v[13]*s3+
334                           v[19]*s4+v[25]*s5+v[31]*s6;
335     x[2+idc] = t[2+idt] = v[2]*s1+v[8]*s2+v[14]*s3+
336                           v[20]*s4+v[26]*s5+v[32]*s6;
337     x[3+idc] = t[3+idt] = v[3]*s1+v[9]*s2+v[15]*s3+
338                           v[21]*s4+v[27]*s5+v[33]*s6;
339     x[4+idc] = t[4+idt] = v[4]*s1+v[10]*s2+v[16]*s3+
340                           v[22]*s4+v[28]*s5+v[34]*s6;
341     x[5+idc] = t[5+idt] = v[5]*s1+v[11]*s2+v[17]*s3+
342                           v[23]*s4+v[29]*s5+v[35]*s6;
343   }
344 
345   PetscCall(ISRestoreIndices(isrow,&rout));
346   PetscCall(ISRestoreIndices(iscol,&cout));
347   PetscCall(VecRestoreArrayRead(bb,&b));
348   PetscCall(VecRestoreArray(xx,&x));
349   PetscCall(PetscLogFlops(2.0*36*(a->nz) - 6.0*A->cmap->n));
350   PetscFunctionReturn(0);
351 }
352 
353 PetscErrorCode MatSolve_SeqBAIJ_6(Mat A,Vec bb,Vec xx)
354 {
355   Mat_SeqBAIJ       *a   =(Mat_SeqBAIJ*)A->data;
356   IS                iscol=a->col,isrow=a->row;
357   const PetscInt    *r,*c,*rout,*cout;
358   const PetscInt    n=a->mbs,*vi,*ai=a->i,*aj=a->j,*adiag=a->diag;
359   PetscInt          i,nz,idx,idt,idc,m;
360   const MatScalar   *aa=a->a,*v;
361   PetscScalar       *x,s1,s2,s3,s4,s5,s6,x1,x2,x3,x4,x5,x6,*t;
362   const PetscScalar *b;
363 
364   PetscFunctionBegin;
365   PetscCall(VecGetArrayRead(bb,&b));
366   PetscCall(VecGetArray(xx,&x));
367   t    = a->solve_work;
368 
369   PetscCall(ISGetIndices(isrow,&rout)); r = rout;
370   PetscCall(ISGetIndices(iscol,&cout)); c = cout;
371 
372   /* forward solve the lower triangular */
373   idx  = 6*r[0];
374   t[0] = b[idx];   t[1] = b[1+idx];
375   t[2] = b[2+idx]; t[3] = b[3+idx];
376   t[4] = b[4+idx]; t[5] = b[5+idx];
377   for (i=1; i<n; i++) {
378     v   = aa + 36*ai[i];
379     vi  = aj + ai[i];
380     nz  = ai[i+1] - ai[i];
381     idx = 6*r[i];
382     s1  = b[idx];s2 = b[1+idx];s3 = b[2+idx];s4 = b[3+idx];
383     s5  = b[4+idx]; s6 = b[5+idx];
384     for (m=0; m<nz; m++) {
385       idx = 6*vi[m];
386       x1  = t[idx];   x2 = t[1+idx]; x3 = t[2+idx];
387       x4  = t[3+idx]; x5 = t[4+idx]; x6 = t[5+idx];
388       s1 -= v[0]*x1 + v[6]*x2  + v[12]*x3 + v[18]*x4 + v[24]*x5 + v[30]*x6;
389       s2 -= v[1]*x1 + v[7]*x2  + v[13]*x3 + v[19]*x4 + v[25]*x5 + v[31]*x6;
390       s3 -= v[2]*x1 + v[8]*x2  + v[14]*x3 + v[20]*x4 + v[26]*x5 + v[32]*x6;
391       s4 -= v[3]*x1 + v[9]*x2  + v[15]*x3 + v[21]*x4 + v[27]*x5 + v[33]*x6;
392       s5 -= v[4]*x1 + v[10]*x2 + v[16]*x3 + v[22]*x4 + v[28]*x5 + v[34]*x6;
393       s6 -= v[5]*x1 + v[11]*x2 + v[17]*x3 + v[23]*x4 + v[29]*x5 + v[35]*x6;
394       v  += 36;
395     }
396     idx      = 6*i;
397     t[idx]   = s1;t[1+idx] = s2;
398     t[2+idx] = s3;t[3+idx] = s4;
399     t[4+idx] = s5;t[5+idx] = s6;
400   }
401   /* backward solve the upper triangular */
402   for (i=n-1; i>=0; i--) {
403     v   = aa + 36*(adiag[i+1]+1);
404     vi  = aj + adiag[i+1]+1;
405     nz  = adiag[i] - adiag[i+1] - 1;
406     idt = 6*i;
407     s1  = t[idt];  s2 = t[1+idt];
408     s3  = t[2+idt];s4 = t[3+idt];
409     s5  = t[4+idt];s6 = t[5+idt];
410     for (m=0; m<nz; m++) {
411       idx = 6*vi[m];
412       x1  = t[idx];   x2 = t[1+idx];
413       x3  = t[2+idx]; x4 = t[3+idx];
414       x5  = t[4+idx]; x6 = t[5+idx];
415       s1 -= v[0]*x1 + v[6]*x2  + v[12]*x3 + v[18]*x4 + v[24]*x5 + v[30]*x6;
416       s2 -= v[1]*x1 + v[7]*x2  + v[13]*x3 + v[19]*x4 + v[25]*x5 + v[31]*x6;
417       s3 -= v[2]*x1 + v[8]*x2  + v[14]*x3 + v[20]*x4 + v[26]*x5 + v[32]*x6;
418       s4 -= v[3]*x1 + v[9]*x2  + v[15]*x3 + v[21]*x4 + v[27]*x5 + v[33]*x6;
419       s5 -= v[4]*x1 + v[10]*x2 + v[16]*x3 + v[22]*x4 + v[28]*x5 + v[34]*x6;
420       s6 -= v[5]*x1 + v[11]*x2 + v[17]*x3 + v[23]*x4 + v[29]*x5 + v[35]*x6;
421       v  += 36;
422     }
423     idc    = 6*c[i];
424     x[idc] = t[idt]   = v[0]*s1+v[6]*s2+v[12]*s3+
425                         v[18]*s4+v[24]*s5+v[30]*s6;
426     x[1+idc] = t[1+idt] = v[1]*s1+v[7]*s2+v[13]*s3+
427                           v[19]*s4+v[25]*s5+v[31]*s6;
428     x[2+idc] = t[2+idt] = v[2]*s1+v[8]*s2+v[14]*s3+
429                           v[20]*s4+v[26]*s5+v[32]*s6;
430     x[3+idc] = t[3+idt] = v[3]*s1+v[9]*s2+v[15]*s3+
431                           v[21]*s4+v[27]*s5+v[33]*s6;
432     x[4+idc] = t[4+idt] = v[4]*s1+v[10]*s2+v[16]*s3+
433                           v[22]*s4+v[28]*s5+v[34]*s6;
434     x[5+idc] = t[5+idt] = v[5]*s1+v[11]*s2+v[17]*s3+
435                           v[23]*s4+v[29]*s5+v[35]*s6;
436   }
437 
438   PetscCall(ISRestoreIndices(isrow,&rout));
439   PetscCall(ISRestoreIndices(iscol,&cout));
440   PetscCall(VecRestoreArrayRead(bb,&b));
441   PetscCall(VecRestoreArray(xx,&x));
442   PetscCall(PetscLogFlops(2.0*36*(a->nz) - 6.0*A->cmap->n));
443   PetscFunctionReturn(0);
444 }
445 
446 PetscErrorCode MatSolve_SeqBAIJ_5_inplace(Mat A,Vec bb,Vec xx)
447 {
448   Mat_SeqBAIJ       *a   =(Mat_SeqBAIJ*)A->data;
449   IS                iscol=a->col,isrow=a->row;
450   const PetscInt    *r,*c,*rout,*cout,*diag = a->diag;
451   const PetscInt    n=a->mbs,*vi,*ai=a->i,*aj=a->j;
452   PetscInt          i,nz,idx,idt,idc;
453   const MatScalar   *aa=a->a,*v;
454   PetscScalar       *x,s1,s2,s3,s4,s5,x1,x2,x3,x4,x5,*t;
455   const PetscScalar *b;
456 
457   PetscFunctionBegin;
458   PetscCall(VecGetArrayRead(bb,&b));
459   PetscCall(VecGetArray(xx,&x));
460   t    = a->solve_work;
461 
462   PetscCall(ISGetIndices(isrow,&rout)); r = rout;
463   PetscCall(ISGetIndices(iscol,&cout)); c = cout + (n-1);
464 
465   /* forward solve the lower triangular */
466   idx  = 5*(*r++);
467   t[0] = b[idx];   t[1] = b[1+idx];
468   t[2] = b[2+idx]; t[3] = b[3+idx]; t[4] = b[4+idx];
469   for (i=1; i<n; i++) {
470     v   = aa + 25*ai[i];
471     vi  = aj + ai[i];
472     nz  = diag[i] - ai[i];
473     idx = 5*(*r++);
474     s1  = b[idx];s2 = b[1+idx];s3 = b[2+idx];s4 = b[3+idx];
475     s5  = b[4+idx];
476     while (nz--) {
477       idx = 5*(*vi++);
478       x1  = t[idx];  x2 = t[1+idx];x3 = t[2+idx];
479       x4  = t[3+idx];x5 = t[4+idx];
480       s1 -= v[0]*x1 + v[5]*x2 + v[10]*x3 + v[15]*x4 + v[20]*x5;
481       s2 -= v[1]*x1 + v[6]*x2 + v[11]*x3 + v[16]*x4 + v[21]*x5;
482       s3 -= v[2]*x1 + v[7]*x2 + v[12]*x3 + v[17]*x4 + v[22]*x5;
483       s4 -= v[3]*x1 + v[8]*x2 + v[13]*x3 + v[18]*x4 + v[23]*x5;
484       s5 -= v[4]*x1 + v[9]*x2 + v[14]*x3 + v[19]*x4 + v[24]*x5;
485       v  += 25;
486     }
487     idx      = 5*i;
488     t[idx]   = s1;t[1+idx] = s2;
489     t[2+idx] = s3;t[3+idx] = s4; t[4+idx] = s5;
490   }
491   /* backward solve the upper triangular */
492   for (i=n-1; i>=0; i--) {
493     v   = aa + 25*diag[i] + 25;
494     vi  = aj + diag[i] + 1;
495     nz  = ai[i+1] - diag[i] - 1;
496     idt = 5*i;
497     s1  = t[idt];  s2 = t[1+idt];
498     s3  = t[2+idt];s4 = t[3+idt]; s5 = t[4+idt];
499     while (nz--) {
500       idx = 5*(*vi++);
501       x1  = t[idx];   x2 = t[1+idx];
502       x3  = t[2+idx]; x4 = t[3+idx]; x5 = t[4+idx];
503       s1 -= v[0]*x1 + v[5]*x2 + v[10]*x3 + v[15]*x4 + v[20]*x5;
504       s2 -= v[1]*x1 + v[6]*x2 + v[11]*x3 + v[16]*x4 + v[21]*x5;
505       s3 -= v[2]*x1 + v[7]*x2 + v[12]*x3 + v[17]*x4 + v[22]*x5;
506       s4 -= v[3]*x1 + v[8]*x2 + v[13]*x3 + v[18]*x4 + v[23]*x5;
507       s5 -= v[4]*x1 + v[9]*x2 + v[14]*x3 + v[19]*x4 + v[24]*x5;
508       v  += 25;
509     }
510     idc    = 5*(*c--);
511     v      = aa + 25*diag[i];
512     x[idc] = t[idt]   = v[0]*s1+v[5]*s2+v[10]*s3+
513                         v[15]*s4+v[20]*s5;
514     x[1+idc] = t[1+idt] = v[1]*s1+v[6]*s2+v[11]*s3+
515                           v[16]*s4+v[21]*s5;
516     x[2+idc] = t[2+idt] = v[2]*s1+v[7]*s2+v[12]*s3+
517                           v[17]*s4+v[22]*s5;
518     x[3+idc] = t[3+idt] = v[3]*s1+v[8]*s2+v[13]*s3+
519                           v[18]*s4+v[23]*s5;
520     x[4+idc] = t[4+idt] = v[4]*s1+v[9]*s2+v[14]*s3+
521                           v[19]*s4+v[24]*s5;
522   }
523 
524   PetscCall(ISRestoreIndices(isrow,&rout));
525   PetscCall(ISRestoreIndices(iscol,&cout));
526   PetscCall(VecRestoreArrayRead(bb,&b));
527   PetscCall(VecRestoreArray(xx,&x));
528   PetscCall(PetscLogFlops(2.0*25*(a->nz) - 5.0*A->cmap->n));
529   PetscFunctionReturn(0);
530 }
531 
532 PetscErrorCode MatSolve_SeqBAIJ_5(Mat A,Vec bb,Vec xx)
533 {
534   Mat_SeqBAIJ       *a   =(Mat_SeqBAIJ*)A->data;
535   IS                iscol=a->col,isrow=a->row;
536   const PetscInt    *r,*c,*rout,*cout;
537   const PetscInt    n=a->mbs,*vi,*ai=a->i,*aj=a->j,*adiag=a->diag;
538   PetscInt          i,nz,idx,idt,idc,m;
539   const MatScalar   *aa=a->a,*v;
540   PetscScalar       *x,s1,s2,s3,s4,s5,x1,x2,x3,x4,x5,*t;
541   const PetscScalar *b;
542 
543   PetscFunctionBegin;
544   PetscCall(VecGetArrayRead(bb,&b));
545   PetscCall(VecGetArray(xx,&x));
546   t    = a->solve_work;
547 
548   PetscCall(ISGetIndices(isrow,&rout)); r = rout;
549   PetscCall(ISGetIndices(iscol,&cout)); c = cout;
550 
551   /* forward solve the lower triangular */
552   idx  = 5*r[0];
553   t[0] = b[idx];   t[1] = b[1+idx];
554   t[2] = b[2+idx]; t[3] = b[3+idx]; t[4] = b[4+idx];
555   for (i=1; i<n; i++) {
556     v   = aa + 25*ai[i];
557     vi  = aj + ai[i];
558     nz  = ai[i+1] - ai[i];
559     idx = 5*r[i];
560     s1  = b[idx];s2 = b[1+idx];s3 = b[2+idx];s4 = b[3+idx];
561     s5  = b[4+idx];
562     for (m=0; m<nz; m++) {
563       idx = 5*vi[m];
564       x1  = t[idx];  x2 = t[1+idx];x3 = t[2+idx];
565       x4  = t[3+idx];x5 = t[4+idx];
566       s1 -= v[0]*x1 + v[5]*x2 + v[10]*x3 + v[15]*x4 + v[20]*x5;
567       s2 -= v[1]*x1 + v[6]*x2 + v[11]*x3 + v[16]*x4 + v[21]*x5;
568       s3 -= v[2]*x1 + v[7]*x2 + v[12]*x3 + v[17]*x4 + v[22]*x5;
569       s4 -= v[3]*x1 + v[8]*x2 + v[13]*x3 + v[18]*x4 + v[23]*x5;
570       s5 -= v[4]*x1 + v[9]*x2 + v[14]*x3 + v[19]*x4 + v[24]*x5;
571       v  += 25;
572     }
573     idx      = 5*i;
574     t[idx]   = s1;t[1+idx] = s2;
575     t[2+idx] = s3;t[3+idx] = s4; t[4+idx] = s5;
576   }
577   /* backward solve the upper triangular */
578   for (i=n-1; i>=0; i--) {
579     v   = aa + 25*(adiag[i+1]+1);
580     vi  = aj + adiag[i+1]+1;
581     nz  = adiag[i] - adiag[i+1] - 1;
582     idt = 5*i;
583     s1  = t[idt];  s2 = t[1+idt];
584     s3  = t[2+idt];s4 = t[3+idt]; s5 = t[4+idt];
585     for (m=0; m<nz; m++) {
586       idx = 5*vi[m];
587       x1  = t[idx];   x2 = t[1+idx];
588       x3  = t[2+idx]; x4 = t[3+idx]; x5 = t[4+idx];
589       s1 -= v[0]*x1 + v[5]*x2 + v[10]*x3 + v[15]*x4 + v[20]*x5;
590       s2 -= v[1]*x1 + v[6]*x2 + v[11]*x3 + v[16]*x4 + v[21]*x5;
591       s3 -= v[2]*x1 + v[7]*x2 + v[12]*x3 + v[17]*x4 + v[22]*x5;
592       s4 -= v[3]*x1 + v[8]*x2 + v[13]*x3 + v[18]*x4 + v[23]*x5;
593       s5 -= v[4]*x1 + v[9]*x2 + v[14]*x3 + v[19]*x4 + v[24]*x5;
594       v  += 25;
595     }
596     idc    = 5*c[i];
597     x[idc] = t[idt]   = v[0]*s1+v[5]*s2+v[10]*s3+
598                         v[15]*s4+v[20]*s5;
599     x[1+idc] = t[1+idt] = v[1]*s1+v[6]*s2+v[11]*s3+
600                           v[16]*s4+v[21]*s5;
601     x[2+idc] = t[2+idt] = v[2]*s1+v[7]*s2+v[12]*s3+
602                           v[17]*s4+v[22]*s5;
603     x[3+idc] = t[3+idt] = v[3]*s1+v[8]*s2+v[13]*s3+
604                           v[18]*s4+v[23]*s5;
605     x[4+idc] = t[4+idt] = v[4]*s1+v[9]*s2+v[14]*s3+
606                           v[19]*s4+v[24]*s5;
607   }
608 
609   PetscCall(ISRestoreIndices(isrow,&rout));
610   PetscCall(ISRestoreIndices(iscol,&cout));
611   PetscCall(VecRestoreArrayRead(bb,&b));
612   PetscCall(VecRestoreArray(xx,&x));
613   PetscCall(PetscLogFlops(2.0*25*(a->nz) - 5.0*A->cmap->n));
614   PetscFunctionReturn(0);
615 }
616 
617 PetscErrorCode MatSolve_SeqBAIJ_4_inplace(Mat A,Vec bb,Vec xx)
618 {
619   Mat_SeqBAIJ       *a   = (Mat_SeqBAIJ*)A->data;
620   IS                iscol=a->col,isrow=a->row;
621   const PetscInt    n=a->mbs,*vi,*ai=a->i,*aj=a->j;
622   PetscInt          i,nz,idx,idt,idc;
623   const PetscInt    *r,*c,*diag = a->diag,*rout,*cout;
624   const MatScalar   *aa=a->a,*v;
625   PetscScalar       *x,s1,s2,s3,s4,x1,x2,x3,x4,*t;
626   const PetscScalar *b;
627 
628   PetscFunctionBegin;
629   PetscCall(VecGetArrayRead(bb,&b));
630   PetscCall(VecGetArray(xx,&x));
631   t    = a->solve_work;
632 
633   PetscCall(ISGetIndices(isrow,&rout)); r = rout;
634   PetscCall(ISGetIndices(iscol,&cout)); c = cout + (n-1);
635 
636   /* forward solve the lower triangular */
637   idx  = 4*(*r++);
638   t[0] = b[idx];   t[1] = b[1+idx];
639   t[2] = b[2+idx]; t[3] = b[3+idx];
640   for (i=1; i<n; i++) {
641     v   = aa + 16*ai[i];
642     vi  = aj + ai[i];
643     nz  = diag[i] - ai[i];
644     idx = 4*(*r++);
645     s1  = b[idx];s2 = b[1+idx];s3 = b[2+idx];s4 = b[3+idx];
646     while (nz--) {
647       idx = 4*(*vi++);
648       x1  = t[idx];x2 = t[1+idx];x3 = t[2+idx];x4 = t[3+idx];
649       s1 -= v[0]*x1 + v[4]*x2 + v[8]*x3  + v[12]*x4;
650       s2 -= v[1]*x1 + v[5]*x2 + v[9]*x3  + v[13]*x4;
651       s3 -= v[2]*x1 + v[6]*x2 + v[10]*x3 + v[14]*x4;
652       s4 -= v[3]*x1 + v[7]*x2 + v[11]*x3 + v[15]*x4;
653       v  += 16;
654     }
655     idx      = 4*i;
656     t[idx]   = s1;t[1+idx] = s2;
657     t[2+idx] = s3;t[3+idx] = s4;
658   }
659   /* backward solve the upper triangular */
660   for (i=n-1; i>=0; i--) {
661     v   = aa + 16*diag[i] + 16;
662     vi  = aj + diag[i] + 1;
663     nz  = ai[i+1] - diag[i] - 1;
664     idt = 4*i;
665     s1  = t[idt];  s2 = t[1+idt];
666     s3  = t[2+idt];s4 = t[3+idt];
667     while (nz--) {
668       idx = 4*(*vi++);
669       x1  = t[idx];   x2 = t[1+idx];
670       x3  = t[2+idx]; x4 = t[3+idx];
671       s1 -= v[0]*x1 + v[4]*x2 + v[8]*x3   + v[12]*x4;
672       s2 -= v[1]*x1 + v[5]*x2 + v[9]*x3   + v[13]*x4;
673       s3 -= v[2]*x1 + v[6]*x2 + v[10]*x3  + v[14]*x4;
674       s4 -= v[3]*x1 + v[7]*x2 + v[11]*x3  + v[15]*x4;
675       v  += 16;
676     }
677     idc      = 4*(*c--);
678     v        = aa + 16*diag[i];
679     x[idc]   = t[idt]   = v[0]*s1+v[4]*s2+v[8]*s3+v[12]*s4;
680     x[1+idc] = t[1+idt] = v[1]*s1+v[5]*s2+v[9]*s3+v[13]*s4;
681     x[2+idc] = t[2+idt] = v[2]*s1+v[6]*s2+v[10]*s3+v[14]*s4;
682     x[3+idc] = t[3+idt] = v[3]*s1+v[7]*s2+v[11]*s3+v[15]*s4;
683   }
684 
685   PetscCall(ISRestoreIndices(isrow,&rout));
686   PetscCall(ISRestoreIndices(iscol,&cout));
687   PetscCall(VecRestoreArrayRead(bb,&b));
688   PetscCall(VecRestoreArray(xx,&x));
689   PetscCall(PetscLogFlops(2.0*16*(a->nz) - 4.0*A->cmap->n));
690   PetscFunctionReturn(0);
691 }
692 
693 PetscErrorCode MatSolve_SeqBAIJ_4(Mat A,Vec bb,Vec xx)
694 {
695   Mat_SeqBAIJ       *a   = (Mat_SeqBAIJ*)A->data;
696   IS                iscol=a->col,isrow=a->row;
697   const PetscInt    n=a->mbs,*vi,*ai=a->i,*aj=a->j,*adiag=a->diag;
698   PetscInt          i,nz,idx,idt,idc,m;
699   const PetscInt    *r,*c,*rout,*cout;
700   const MatScalar   *aa=a->a,*v;
701   PetscScalar       *x,s1,s2,s3,s4,x1,x2,x3,x4,*t;
702   const PetscScalar *b;
703 
704   PetscFunctionBegin;
705   PetscCall(VecGetArrayRead(bb,&b));
706   PetscCall(VecGetArray(xx,&x));
707   t    = a->solve_work;
708 
709   PetscCall(ISGetIndices(isrow,&rout)); r = rout;
710   PetscCall(ISGetIndices(iscol,&cout)); c = cout;
711 
712   /* forward solve the lower triangular */
713   idx  = 4*r[0];
714   t[0] = b[idx];   t[1] = b[1+idx];
715   t[2] = b[2+idx]; t[3] = b[3+idx];
716   for (i=1; i<n; i++) {
717     v   = aa + 16*ai[i];
718     vi  = aj + ai[i];
719     nz  = ai[i+1] - ai[i];
720     idx = 4*r[i];
721     s1  = b[idx];s2 = b[1+idx];s3 = b[2+idx];s4 = b[3+idx];
722     for (m=0; m<nz; m++) {
723       idx = 4*vi[m];
724       x1  = t[idx];x2 = t[1+idx];x3 = t[2+idx];x4 = t[3+idx];
725       s1 -= v[0]*x1 + v[4]*x2 + v[8]*x3  + v[12]*x4;
726       s2 -= v[1]*x1 + v[5]*x2 + v[9]*x3  + v[13]*x4;
727       s3 -= v[2]*x1 + v[6]*x2 + v[10]*x3 + v[14]*x4;
728       s4 -= v[3]*x1 + v[7]*x2 + v[11]*x3 + v[15]*x4;
729       v  += 16;
730     }
731     idx      = 4*i;
732     t[idx]   = s1;t[1+idx] = s2;
733     t[2+idx] = s3;t[3+idx] = s4;
734   }
735   /* backward solve the upper triangular */
736   for (i=n-1; i>=0; i--) {
737     v   = aa + 16*(adiag[i+1]+1);
738     vi  = aj + adiag[i+1]+1;
739     nz  = adiag[i] - adiag[i+1] - 1;
740     idt = 4*i;
741     s1  = t[idt];  s2 = t[1+idt];
742     s3  = t[2+idt];s4 = t[3+idt];
743     for (m=0; m<nz; m++) {
744       idx = 4*vi[m];
745       x1  = t[idx];   x2 = t[1+idx];
746       x3  = t[2+idx]; x4 = t[3+idx];
747       s1 -= v[0]*x1 + v[4]*x2 + v[8]*x3   + v[12]*x4;
748       s2 -= v[1]*x1 + v[5]*x2 + v[9]*x3   + v[13]*x4;
749       s3 -= v[2]*x1 + v[6]*x2 + v[10]*x3  + v[14]*x4;
750       s4 -= v[3]*x1 + v[7]*x2 + v[11]*x3  + v[15]*x4;
751       v  += 16;
752     }
753     idc      = 4*c[i];
754     x[idc]   = t[idt]   = v[0]*s1+v[4]*s2+v[8]*s3+v[12]*s4;
755     x[1+idc] = t[1+idt] = v[1]*s1+v[5]*s2+v[9]*s3+v[13]*s4;
756     x[2+idc] = t[2+idt] = v[2]*s1+v[6]*s2+v[10]*s3+v[14]*s4;
757     x[3+idc] = t[3+idt] = v[3]*s1+v[7]*s2+v[11]*s3+v[15]*s4;
758   }
759 
760   PetscCall(ISRestoreIndices(isrow,&rout));
761   PetscCall(ISRestoreIndices(iscol,&cout));
762   PetscCall(VecRestoreArrayRead(bb,&b));
763   PetscCall(VecRestoreArray(xx,&x));
764   PetscCall(PetscLogFlops(2.0*16*(a->nz) - 4.0*A->cmap->n));
765   PetscFunctionReturn(0);
766 }
767 
768 PetscErrorCode MatSolve_SeqBAIJ_4_Demotion(Mat A,Vec bb,Vec xx)
769 {
770   Mat_SeqBAIJ       *a   = (Mat_SeqBAIJ*)A->data;
771   IS                iscol=a->col,isrow=a->row;
772   const PetscInt    n=a->mbs,*vi,*ai=a->i,*aj=a->j;
773   PetscInt          i,nz,idx,idt,idc;
774   const PetscInt    *r,*c,*diag = a->diag,*rout,*cout;
775   const MatScalar   *aa=a->a,*v;
776   MatScalar         s1,s2,s3,s4,x1,x2,x3,x4,*t;
777   PetscScalar       *x;
778   const PetscScalar *b;
779 
780   PetscFunctionBegin;
781   PetscCall(VecGetArrayRead(bb,&b));
782   PetscCall(VecGetArray(xx,&x));
783   t    = (MatScalar*)a->solve_work;
784 
785   PetscCall(ISGetIndices(isrow,&rout)); r = rout;
786   PetscCall(ISGetIndices(iscol,&cout)); c = cout + (n-1);
787 
788   /* forward solve the lower triangular */
789   idx  = 4*(*r++);
790   t[0] = (MatScalar)b[idx];
791   t[1] = (MatScalar)b[1+idx];
792   t[2] = (MatScalar)b[2+idx];
793   t[3] = (MatScalar)b[3+idx];
794   for (i=1; i<n; i++) {
795     v   = aa + 16*ai[i];
796     vi  = aj + ai[i];
797     nz  = diag[i] - ai[i];
798     idx = 4*(*r++);
799     s1  = (MatScalar)b[idx];
800     s2  = (MatScalar)b[1+idx];
801     s3  = (MatScalar)b[2+idx];
802     s4  = (MatScalar)b[3+idx];
803     while (nz--) {
804       idx = 4*(*vi++);
805       x1  = t[idx];
806       x2  = t[1+idx];
807       x3  = t[2+idx];
808       x4  = t[3+idx];
809       s1 -= v[0]*x1 + v[4]*x2 + v[8]*x3  + v[12]*x4;
810       s2 -= v[1]*x1 + v[5]*x2 + v[9]*x3  + v[13]*x4;
811       s3 -= v[2]*x1 + v[6]*x2 + v[10]*x3 + v[14]*x4;
812       s4 -= v[3]*x1 + v[7]*x2 + v[11]*x3 + v[15]*x4;
813       v  += 16;
814     }
815     idx      = 4*i;
816     t[idx]   = s1;
817     t[1+idx] = s2;
818     t[2+idx] = s3;
819     t[3+idx] = s4;
820   }
821   /* backward solve the upper triangular */
822   for (i=n-1; i>=0; i--) {
823     v   = aa + 16*diag[i] + 16;
824     vi  = aj + diag[i] + 1;
825     nz  = ai[i+1] - diag[i] - 1;
826     idt = 4*i;
827     s1  = t[idt];
828     s2  = t[1+idt];
829     s3  = t[2+idt];
830     s4  = t[3+idt];
831     while (nz--) {
832       idx = 4*(*vi++);
833       x1  = t[idx];
834       x2  = t[1+idx];
835       x3  = t[2+idx];
836       x4  = t[3+idx];
837       s1 -= v[0]*x1 + v[4]*x2 + v[8]*x3   + v[12]*x4;
838       s2 -= v[1]*x1 + v[5]*x2 + v[9]*x3   + v[13]*x4;
839       s3 -= v[2]*x1 + v[6]*x2 + v[10]*x3  + v[14]*x4;
840       s4 -= v[3]*x1 + v[7]*x2 + v[11]*x3  + v[15]*x4;
841       v  += 16;
842     }
843     idc      = 4*(*c--);
844     v        = aa + 16*diag[i];
845     t[idt]   = v[0]*s1+v[4]*s2+v[8]*s3+v[12]*s4;
846     t[1+idt] = v[1]*s1+v[5]*s2+v[9]*s3+v[13]*s4;
847     t[2+idt] = v[2]*s1+v[6]*s2+v[10]*s3+v[14]*s4;
848     t[3+idt] = v[3]*s1+v[7]*s2+v[11]*s3+v[15]*s4;
849     x[idc]   = (PetscScalar)t[idt];
850     x[1+idc] = (PetscScalar)t[1+idt];
851     x[2+idc] = (PetscScalar)t[2+idt];
852     x[3+idc] = (PetscScalar)t[3+idt];
853   }
854 
855   PetscCall(ISRestoreIndices(isrow,&rout));
856   PetscCall(ISRestoreIndices(iscol,&cout));
857   PetscCall(VecRestoreArrayRead(bb,&b));
858   PetscCall(VecRestoreArray(xx,&x));
859   PetscCall(PetscLogFlops(2.0*16*(a->nz) - 4.0*A->cmap->n));
860   PetscFunctionReturn(0);
861 }
862 
863 #if defined(PETSC_HAVE_SSE)
864 
865 #include PETSC_HAVE_SSE
866 
867 PetscErrorCode MatSolve_SeqBAIJ_4_SSE_Demotion(Mat A,Vec bb,Vec xx)
868 {
869   /*
870      Note: This code uses demotion of double
871      to float when performing the mixed-mode computation.
872      This may not be numerically reasonable for all applications.
873   */
874   Mat_SeqBAIJ    *a   = (Mat_SeqBAIJ*)A->data;
875   IS             iscol=a->col,isrow=a->row;
876   PetscInt       i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,ai16;
877   const PetscInt *r,*c,*diag = a->diag,*rout,*cout;
878   MatScalar      *aa=a->a,*v;
879   PetscScalar    *x,*b,*t;
880 
881   /* Make space in temp stack for 16 Byte Aligned arrays */
882   float         ssealignedspace[11],*tmps,*tmpx;
883   unsigned long offset;
884 
885   PetscFunctionBegin;
886   SSE_SCOPE_BEGIN;
887 
888   offset = (unsigned long)ssealignedspace % 16;
889   if (offset) offset = (16 - offset)/4;
890   tmps = &ssealignedspace[offset];
891   tmpx = &ssealignedspace[offset+4];
892   PREFETCH_NTA(aa+16*ai[1]);
893 
894   PetscCall(VecGetArray(bb,&b));
895   PetscCall(VecGetArray(xx,&x));
896   t    = a->solve_work;
897 
898   PetscCall(ISGetIndices(isrow,&rout)); r = rout;
899   PetscCall(ISGetIndices(iscol,&cout)); c = cout + (n-1);
900 
901   /* forward solve the lower triangular */
902   idx  = 4*(*r++);
903   t[0] = b[idx];   t[1] = b[1+idx];
904   t[2] = b[2+idx]; t[3] = b[3+idx];
905   v    =  aa + 16*ai[1];
906 
907   for (i=1; i<n;) {
908     PREFETCH_NTA(&v[8]);
909     vi  =  aj      + ai[i];
910     nz  =  diag[i] - ai[i];
911     idx =  4*(*r++);
912 
913     /* Demote sum from double to float */
914     CONVERT_DOUBLE4_FLOAT4(tmps,&b[idx]);
915     LOAD_PS(tmps,XMM7);
916 
917     while (nz--) {
918       PREFETCH_NTA(&v[16]);
919       idx = 4*(*vi++);
920 
921       /* Demote solution (so far) from double to float */
922       CONVERT_DOUBLE4_FLOAT4(tmpx,&x[idx]);
923 
924       /* 4x4 Matrix-Vector product with negative accumulation: */
925       SSE_INLINE_BEGIN_2(tmpx,v)
926       SSE_LOAD_PS(SSE_ARG_1,FLOAT_0,XMM6)
927 
928       /* First Column */
929       SSE_COPY_PS(XMM0,XMM6)
930       SSE_SHUFFLE(XMM0,XMM0,0x00)
931       SSE_MULT_PS_M(XMM0,SSE_ARG_2,FLOAT_0)
932       SSE_SUB_PS(XMM7,XMM0)
933 
934       /* Second Column */
935       SSE_COPY_PS(XMM1,XMM6)
936       SSE_SHUFFLE(XMM1,XMM1,0x55)
937       SSE_MULT_PS_M(XMM1,SSE_ARG_2,FLOAT_4)
938       SSE_SUB_PS(XMM7,XMM1)
939 
940       SSE_PREFETCH_NTA(SSE_ARG_2,FLOAT_24)
941 
942       /* Third Column */
943       SSE_COPY_PS(XMM2,XMM6)
944       SSE_SHUFFLE(XMM2,XMM2,0xAA)
945       SSE_MULT_PS_M(XMM2,SSE_ARG_2,FLOAT_8)
946       SSE_SUB_PS(XMM7,XMM2)
947 
948       /* Fourth Column */
949       SSE_COPY_PS(XMM3,XMM6)
950       SSE_SHUFFLE(XMM3,XMM3,0xFF)
951       SSE_MULT_PS_M(XMM3,SSE_ARG_2,FLOAT_12)
952       SSE_SUB_PS(XMM7,XMM3)
953       SSE_INLINE_END_2
954 
955       v += 16;
956     }
957     idx = 4*i;
958     v   = aa + 16*ai[++i];
959     PREFETCH_NTA(v);
960     STORE_PS(tmps,XMM7);
961 
962     /* Promote result from float to double */
963     CONVERT_FLOAT4_DOUBLE4(&t[idx],tmps);
964   }
965   /* backward solve the upper triangular */
966   idt  = 4*(n-1);
967   ai16 = 16*diag[n-1];
968   v    = aa + ai16 + 16;
969   for (i=n-1; i>=0;) {
970     PREFETCH_NTA(&v[8]);
971     vi = aj + diag[i] + 1;
972     nz = ai[i+1] - diag[i] - 1;
973 
974     /* Demote accumulator from double to float */
975     CONVERT_DOUBLE4_FLOAT4(tmps,&t[idt]);
976     LOAD_PS(tmps,XMM7);
977 
978     while (nz--) {
979       PREFETCH_NTA(&v[16]);
980       idx = 4*(*vi++);
981 
982       /* Demote solution (so far) from double to float */
983       CONVERT_DOUBLE4_FLOAT4(tmpx,&t[idx]);
984 
985       /* 4x4 Matrix-Vector Product with negative accumulation: */
986       SSE_INLINE_BEGIN_2(tmpx,v)
987       SSE_LOAD_PS(SSE_ARG_1,FLOAT_0,XMM6)
988 
989       /* First Column */
990       SSE_COPY_PS(XMM0,XMM6)
991       SSE_SHUFFLE(XMM0,XMM0,0x00)
992       SSE_MULT_PS_M(XMM0,SSE_ARG_2,FLOAT_0)
993       SSE_SUB_PS(XMM7,XMM0)
994 
995       /* Second Column */
996       SSE_COPY_PS(XMM1,XMM6)
997       SSE_SHUFFLE(XMM1,XMM1,0x55)
998       SSE_MULT_PS_M(XMM1,SSE_ARG_2,FLOAT_4)
999       SSE_SUB_PS(XMM7,XMM1)
1000 
1001       SSE_PREFETCH_NTA(SSE_ARG_2,FLOAT_24)
1002 
1003       /* Third Column */
1004       SSE_COPY_PS(XMM2,XMM6)
1005       SSE_SHUFFLE(XMM2,XMM2,0xAA)
1006       SSE_MULT_PS_M(XMM2,SSE_ARG_2,FLOAT_8)
1007       SSE_SUB_PS(XMM7,XMM2)
1008 
1009       /* Fourth Column */
1010       SSE_COPY_PS(XMM3,XMM6)
1011       SSE_SHUFFLE(XMM3,XMM3,0xFF)
1012       SSE_MULT_PS_M(XMM3,SSE_ARG_2,FLOAT_12)
1013       SSE_SUB_PS(XMM7,XMM3)
1014       SSE_INLINE_END_2
1015       v += 16;
1016     }
1017     v    = aa + ai16;
1018     ai16 = 16*diag[--i];
1019     PREFETCH_NTA(aa+ai16+16);
1020     /*
1021        Scale the result by the diagonal 4x4 block,
1022        which was inverted as part of the factorization
1023     */
1024     SSE_INLINE_BEGIN_3(v,tmps,aa+ai16)
1025     /* First Column */
1026     SSE_COPY_PS(XMM0,XMM7)
1027     SSE_SHUFFLE(XMM0,XMM0,0x00)
1028     SSE_MULT_PS_M(XMM0,SSE_ARG_1,FLOAT_0)
1029 
1030     /* Second Column */
1031     SSE_COPY_PS(XMM1,XMM7)
1032     SSE_SHUFFLE(XMM1,XMM1,0x55)
1033     SSE_MULT_PS_M(XMM1,SSE_ARG_1,FLOAT_4)
1034     SSE_ADD_PS(XMM0,XMM1)
1035 
1036     SSE_PREFETCH_NTA(SSE_ARG_3,FLOAT_24)
1037 
1038     /* Third Column */
1039     SSE_COPY_PS(XMM2,XMM7)
1040     SSE_SHUFFLE(XMM2,XMM2,0xAA)
1041     SSE_MULT_PS_M(XMM2,SSE_ARG_1,FLOAT_8)
1042     SSE_ADD_PS(XMM0,XMM2)
1043 
1044     /* Fourth Column */
1045     SSE_COPY_PS(XMM3,XMM7)
1046     SSE_SHUFFLE(XMM3,XMM3,0xFF)
1047     SSE_MULT_PS_M(XMM3,SSE_ARG_1,FLOAT_12)
1048     SSE_ADD_PS(XMM0,XMM3)
1049 
1050     SSE_STORE_PS(SSE_ARG_2,FLOAT_0,XMM0)
1051     SSE_INLINE_END_3
1052 
1053     /* Promote solution from float to double */
1054     CONVERT_FLOAT4_DOUBLE4(&t[idt],tmps);
1055 
1056     /* Apply reordering to t and stream into x.    */
1057     /* This way, x doesn't pollute the cache.      */
1058     /* Be careful with size: 2 doubles = 4 floats! */
1059     idc = 4*(*c--);
1060     SSE_INLINE_BEGIN_2((float*)&t[idt],(float*)&x[idc])
1061     /*  x[idc]   = t[idt];   x[1+idc] = t[1+idc]; */
1062     SSE_LOAD_PS(SSE_ARG_1,FLOAT_0,XMM0)
1063     SSE_STREAM_PS(SSE_ARG_2,FLOAT_0,XMM0)
1064     /*  x[idc+2] = t[idt+2]; x[3+idc] = t[3+idc]; */
1065     SSE_LOAD_PS(SSE_ARG_1,FLOAT_4,XMM1)
1066     SSE_STREAM_PS(SSE_ARG_2,FLOAT_4,XMM1)
1067     SSE_INLINE_END_2
1068     v    = aa + ai16 + 16;
1069     idt -= 4;
1070   }
1071 
1072   PetscCall(ISRestoreIndices(isrow,&rout));
1073   PetscCall(ISRestoreIndices(iscol,&cout));
1074   PetscCall(VecRestoreArray(bb,&b));
1075   PetscCall(VecRestoreArray(xx,&x));
1076   PetscCall(PetscLogFlops(2.0*16*(a->nz) - 4.0*A->cmap->n));
1077   SSE_SCOPE_END;
1078   PetscFunctionReturn(0);
1079 }
1080 
1081 #endif
1082 
1083 PetscErrorCode MatSolve_SeqBAIJ_3_inplace(Mat A,Vec bb,Vec xx)
1084 {
1085   Mat_SeqBAIJ       *a   =(Mat_SeqBAIJ*)A->data;
1086   IS                iscol=a->col,isrow=a->row;
1087   const PetscInt    n=a->mbs,*vi,*ai=a->i,*aj=a->j;
1088   PetscInt          i,nz,idx,idt,idc;
1089   const PetscInt    *r,*c,*diag = a->diag,*rout,*cout;
1090   const MatScalar   *aa=a->a,*v;
1091   PetscScalar       *x,s1,s2,s3,x1,x2,x3,*t;
1092   const PetscScalar *b;
1093 
1094   PetscFunctionBegin;
1095   PetscCall(VecGetArrayRead(bb,&b));
1096   PetscCall(VecGetArray(xx,&x));
1097   t    = a->solve_work;
1098 
1099   PetscCall(ISGetIndices(isrow,&rout)); r = rout;
1100   PetscCall(ISGetIndices(iscol,&cout)); c = cout + (n-1);
1101 
1102   /* forward solve the lower triangular */
1103   idx  = 3*(*r++);
1104   t[0] = b[idx]; t[1] = b[1+idx]; t[2] = b[2+idx];
1105   for (i=1; i<n; i++) {
1106     v   = aa + 9*ai[i];
1107     vi  = aj + ai[i];
1108     nz  = diag[i] - ai[i];
1109     idx = 3*(*r++);
1110     s1  = b[idx]; s2 = b[1+idx]; s3 = b[2+idx];
1111     while (nz--) {
1112       idx = 3*(*vi++);
1113       x1  = t[idx]; x2 = t[1+idx]; x3 = t[2+idx];
1114       s1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
1115       s2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
1116       s3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
1117       v  += 9;
1118     }
1119     idx    = 3*i;
1120     t[idx] = s1; t[1+idx] = s2; t[2+idx] = s3;
1121   }
1122   /* backward solve the upper triangular */
1123   for (i=n-1; i>=0; i--) {
1124     v   = aa + 9*diag[i] + 9;
1125     vi  = aj + diag[i] + 1;
1126     nz  = ai[i+1] - diag[i] - 1;
1127     idt = 3*i;
1128     s1  = t[idt]; s2 = t[1+idt]; s3 = t[2+idt];
1129     while (nz--) {
1130       idx = 3*(*vi++);
1131       x1  = t[idx]; x2 = t[1+idx]; x3 = t[2+idx];
1132       s1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
1133       s2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
1134       s3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
1135       v  += 9;
1136     }
1137     idc      = 3*(*c--);
1138     v        = aa + 9*diag[i];
1139     x[idc]   = t[idt]   = v[0]*s1 + v[3]*s2 + v[6]*s3;
1140     x[1+idc] = t[1+idt] = v[1]*s1 + v[4]*s2 + v[7]*s3;
1141     x[2+idc] = t[2+idt] = v[2]*s1 + v[5]*s2 + v[8]*s3;
1142   }
1143   PetscCall(ISRestoreIndices(isrow,&rout));
1144   PetscCall(ISRestoreIndices(iscol,&cout));
1145   PetscCall(VecRestoreArrayRead(bb,&b));
1146   PetscCall(VecRestoreArray(xx,&x));
1147   PetscCall(PetscLogFlops(2.0*9*(a->nz) - 3.0*A->cmap->n));
1148   PetscFunctionReturn(0);
1149 }
1150 
1151 PetscErrorCode MatSolve_SeqBAIJ_3(Mat A,Vec bb,Vec xx)
1152 {
1153   Mat_SeqBAIJ       *a   =(Mat_SeqBAIJ*)A->data;
1154   IS                iscol=a->col,isrow=a->row;
1155   const PetscInt    n=a->mbs,*vi,*ai=a->i,*aj=a->j,*adiag=a->diag;
1156   PetscInt          i,nz,idx,idt,idc,m;
1157   const PetscInt    *r,*c,*rout,*cout;
1158   const MatScalar   *aa=a->a,*v;
1159   PetscScalar       *x,s1,s2,s3,x1,x2,x3,*t;
1160   const PetscScalar *b;
1161 
1162   PetscFunctionBegin;
1163   PetscCall(VecGetArrayRead(bb,&b));
1164   PetscCall(VecGetArray(xx,&x));
1165   t    = a->solve_work;
1166 
1167   PetscCall(ISGetIndices(isrow,&rout)); r = rout;
1168   PetscCall(ISGetIndices(iscol,&cout)); c = cout;
1169 
1170   /* forward solve the lower triangular */
1171   idx  = 3*r[0];
1172   t[0] = b[idx]; t[1] = b[1+idx]; t[2] = b[2+idx];
1173   for (i=1; i<n; i++) {
1174     v   = aa + 9*ai[i];
1175     vi  = aj + ai[i];
1176     nz  = ai[i+1] - ai[i];
1177     idx = 3*r[i];
1178     s1  = b[idx]; s2 = b[1+idx]; s3 = b[2+idx];
1179     for (m=0; m<nz; m++) {
1180       idx = 3*vi[m];
1181       x1  = t[idx]; x2 = t[1+idx]; x3 = t[2+idx];
1182       s1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
1183       s2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
1184       s3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
1185       v  += 9;
1186     }
1187     idx    = 3*i;
1188     t[idx] = s1; t[1+idx] = s2; t[2+idx] = s3;
1189   }
1190   /* backward solve the upper triangular */
1191   for (i=n-1; i>=0; i--) {
1192     v   = aa + 9*(adiag[i+1]+1);
1193     vi  = aj + adiag[i+1]+1;
1194     nz  = adiag[i] - adiag[i+1] - 1;
1195     idt = 3*i;
1196     s1  = t[idt]; s2 = t[1+idt]; s3 = t[2+idt];
1197     for (m=0; m<nz; m++) {
1198       idx = 3*vi[m];
1199       x1  = t[idx]; x2 = t[1+idx]; x3 = t[2+idx];
1200       s1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
1201       s2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
1202       s3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
1203       v  += 9;
1204     }
1205     idc      = 3*c[i];
1206     x[idc]   = t[idt]   = v[0]*s1 + v[3]*s2 + v[6]*s3;
1207     x[1+idc] = t[1+idt] = v[1]*s1 + v[4]*s2 + v[7]*s3;
1208     x[2+idc] = t[2+idt] = v[2]*s1 + v[5]*s2 + v[8]*s3;
1209   }
1210   PetscCall(ISRestoreIndices(isrow,&rout));
1211   PetscCall(ISRestoreIndices(iscol,&cout));
1212   PetscCall(VecRestoreArrayRead(bb,&b));
1213   PetscCall(VecRestoreArray(xx,&x));
1214   PetscCall(PetscLogFlops(2.0*9*(a->nz) - 3.0*A->cmap->n));
1215   PetscFunctionReturn(0);
1216 }
1217 
1218 PetscErrorCode MatSolve_SeqBAIJ_2_inplace(Mat A,Vec bb,Vec xx)
1219 {
1220   Mat_SeqBAIJ       *a   =(Mat_SeqBAIJ*)A->data;
1221   IS                iscol=a->col,isrow=a->row;
1222   const PetscInt    n=a->mbs,*vi,*ai=a->i,*aj=a->j;
1223   PetscInt          i,nz,idx,idt,idc;
1224   const PetscInt    *r,*c,*diag = a->diag,*rout,*cout;
1225   const MatScalar   *aa=a->a,*v;
1226   PetscScalar       *x,s1,s2,x1,x2,*t;
1227   const PetscScalar *b;
1228 
1229   PetscFunctionBegin;
1230   PetscCall(VecGetArrayRead(bb,&b));
1231   PetscCall(VecGetArray(xx,&x));
1232   t    = a->solve_work;
1233 
1234   PetscCall(ISGetIndices(isrow,&rout)); r = rout;
1235   PetscCall(ISGetIndices(iscol,&cout)); c = cout + (n-1);
1236 
1237   /* forward solve the lower triangular */
1238   idx  = 2*(*r++);
1239   t[0] = b[idx]; t[1] = b[1+idx];
1240   for (i=1; i<n; i++) {
1241     v   = aa + 4*ai[i];
1242     vi  = aj + ai[i];
1243     nz  = diag[i] - ai[i];
1244     idx = 2*(*r++);
1245     s1  = b[idx]; s2 = b[1+idx];
1246     while (nz--) {
1247       idx = 2*(*vi++);
1248       x1  = t[idx]; x2 = t[1+idx];
1249       s1 -= v[0]*x1 + v[2]*x2;
1250       s2 -= v[1]*x1 + v[3]*x2;
1251       v  += 4;
1252     }
1253     idx    = 2*i;
1254     t[idx] = s1; t[1+idx] = s2;
1255   }
1256   /* backward solve the upper triangular */
1257   for (i=n-1; i>=0; i--) {
1258     v   = aa + 4*diag[i] + 4;
1259     vi  = aj + diag[i] + 1;
1260     nz  = ai[i+1] - diag[i] - 1;
1261     idt = 2*i;
1262     s1  = t[idt]; s2 = t[1+idt];
1263     while (nz--) {
1264       idx = 2*(*vi++);
1265       x1  = t[idx]; x2 = t[1+idx];
1266       s1 -= v[0]*x1 + v[2]*x2;
1267       s2 -= v[1]*x1 + v[3]*x2;
1268       v  += 4;
1269     }
1270     idc      = 2*(*c--);
1271     v        = aa + 4*diag[i];
1272     x[idc]   = t[idt]   = v[0]*s1 + v[2]*s2;
1273     x[1+idc] = t[1+idt] = v[1]*s1 + v[3]*s2;
1274   }
1275   PetscCall(ISRestoreIndices(isrow,&rout));
1276   PetscCall(ISRestoreIndices(iscol,&cout));
1277   PetscCall(VecRestoreArrayRead(bb,&b));
1278   PetscCall(VecRestoreArray(xx,&x));
1279   PetscCall(PetscLogFlops(2.0*4*(a->nz) - 2.0*A->cmap->n));
1280   PetscFunctionReturn(0);
1281 }
1282 
1283 PetscErrorCode MatSolve_SeqBAIJ_2(Mat A,Vec bb,Vec xx)
1284 {
1285   Mat_SeqBAIJ       *a   =(Mat_SeqBAIJ*)A->data;
1286   IS                iscol=a->col,isrow=a->row;
1287   const PetscInt    n=a->mbs,*vi,*ai=a->i,*aj=a->j,*adiag=a->diag;
1288   PetscInt          i,nz,idx,jdx,idt,idc,m;
1289   const PetscInt    *r,*c,*rout,*cout;
1290   const MatScalar   *aa=a->a,*v;
1291   PetscScalar       *x,s1,s2,x1,x2,*t;
1292   const PetscScalar *b;
1293 
1294   PetscFunctionBegin;
1295   PetscCall(VecGetArrayRead(bb,&b));
1296   PetscCall(VecGetArray(xx,&x));
1297   t    = a->solve_work;
1298 
1299   PetscCall(ISGetIndices(isrow,&rout)); r = rout;
1300   PetscCall(ISGetIndices(iscol,&cout)); c = cout;
1301 
1302   /* forward solve the lower triangular */
1303   idx  = 2*r[0];
1304   t[0] = b[idx]; t[1] = b[1+idx];
1305   for (i=1; i<n; i++) {
1306     v   = aa + 4*ai[i];
1307     vi  = aj + ai[i];
1308     nz  = ai[i+1] - ai[i];
1309     idx = 2*r[i];
1310     s1  = b[idx]; s2 = b[1+idx];
1311     for (m=0; m<nz; m++) {
1312       jdx = 2*vi[m];
1313       x1  = t[jdx]; x2 = t[1+jdx];
1314       s1 -= v[0]*x1 + v[2]*x2;
1315       s2 -= v[1]*x1 + v[3]*x2;
1316       v  += 4;
1317     }
1318     idx    = 2*i;
1319     t[idx] = s1; t[1+idx] = s2;
1320   }
1321   /* backward solve the upper triangular */
1322   for (i=n-1; i>=0; i--) {
1323     v   = aa + 4*(adiag[i+1]+1);
1324     vi  = aj + adiag[i+1]+1;
1325     nz  = adiag[i] - adiag[i+1] - 1;
1326     idt = 2*i;
1327     s1  = t[idt]; s2 = t[1+idt];
1328     for (m=0; m<nz; m++) {
1329       idx = 2*vi[m];
1330       x1  = t[idx]; x2 = t[1+idx];
1331       s1 -= v[0]*x1 + v[2]*x2;
1332       s2 -= v[1]*x1 + v[3]*x2;
1333       v  += 4;
1334     }
1335     idc      = 2*c[i];
1336     x[idc]   = t[idt]   = v[0]*s1 + v[2]*s2;
1337     x[1+idc] = t[1+idt] = v[1]*s1 + v[3]*s2;
1338   }
1339   PetscCall(ISRestoreIndices(isrow,&rout));
1340   PetscCall(ISRestoreIndices(iscol,&cout));
1341   PetscCall(VecRestoreArrayRead(bb,&b));
1342   PetscCall(VecRestoreArray(xx,&x));
1343   PetscCall(PetscLogFlops(2.0*4*(a->nz) - 2.0*A->cmap->n));
1344   PetscFunctionReturn(0);
1345 }
1346 
1347 PetscErrorCode MatSolve_SeqBAIJ_1_inplace(Mat A,Vec bb,Vec xx)
1348 {
1349   Mat_SeqBAIJ       *a   =(Mat_SeqBAIJ*)A->data;
1350   IS                iscol=a->col,isrow=a->row;
1351   const PetscInt    n=a->mbs,*vi,*ai=a->i,*aj=a->j;
1352   PetscInt          i,nz;
1353   const PetscInt    *r,*c,*diag = a->diag,*rout,*cout;
1354   const MatScalar   *aa=a->a,*v;
1355   PetscScalar       *x,s1,*t;
1356   const PetscScalar *b;
1357 
1358   PetscFunctionBegin;
1359   if (!n) PetscFunctionReturn(0);
1360 
1361   PetscCall(VecGetArrayRead(bb,&b));
1362   PetscCall(VecGetArray(xx,&x));
1363   t    = a->solve_work;
1364 
1365   PetscCall(ISGetIndices(isrow,&rout)); r = rout;
1366   PetscCall(ISGetIndices(iscol,&cout)); c = cout + (n-1);
1367 
1368   /* forward solve the lower triangular */
1369   t[0] = b[*r++];
1370   for (i=1; i<n; i++) {
1371     v  = aa + ai[i];
1372     vi = aj + ai[i];
1373     nz = diag[i] - ai[i];
1374     s1 = b[*r++];
1375     while (nz--) {
1376       s1 -= (*v++)*t[*vi++];
1377     }
1378     t[i] = s1;
1379   }
1380   /* backward solve the upper triangular */
1381   for (i=n-1; i>=0; i--) {
1382     v  = aa + diag[i] + 1;
1383     vi = aj + diag[i] + 1;
1384     nz = ai[i+1] - diag[i] - 1;
1385     s1 = t[i];
1386     while (nz--) {
1387       s1 -= (*v++)*t[*vi++];
1388     }
1389     x[*c--] = t[i] = aa[diag[i]]*s1;
1390   }
1391 
1392   PetscCall(ISRestoreIndices(isrow,&rout));
1393   PetscCall(ISRestoreIndices(iscol,&cout));
1394   PetscCall(VecRestoreArrayRead(bb,&b));
1395   PetscCall(VecRestoreArray(xx,&x));
1396   PetscCall(PetscLogFlops(2.0*1*(a->nz) - A->cmap->n));
1397   PetscFunctionReturn(0);
1398 }
1399 
1400 PetscErrorCode MatSolve_SeqBAIJ_1(Mat A,Vec bb,Vec xx)
1401 {
1402   Mat_SeqBAIJ       *a    = (Mat_SeqBAIJ*)A->data;
1403   IS                iscol = a->col,isrow = a->row;
1404   PetscInt          i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,*adiag = a->diag,nz;
1405   const PetscInt    *rout,*cout,*r,*c;
1406   PetscScalar       *x,*tmp,sum;
1407   const PetscScalar *b;
1408   const MatScalar   *aa = a->a,*v;
1409 
1410   PetscFunctionBegin;
1411   if (!n) PetscFunctionReturn(0);
1412 
1413   PetscCall(VecGetArrayRead(bb,&b));
1414   PetscCall(VecGetArray(xx,&x));
1415   tmp  = a->solve_work;
1416 
1417   PetscCall(ISGetIndices(isrow,&rout)); r = rout;
1418   PetscCall(ISGetIndices(iscol,&cout)); c = cout;
1419 
1420   /* forward solve the lower triangular */
1421   tmp[0] = b[r[0]];
1422   v      = aa;
1423   vi     = aj;
1424   for (i=1; i<n; i++) {
1425     nz  = ai[i+1] - ai[i];
1426     sum = b[r[i]];
1427     PetscSparseDenseMinusDot(sum,tmp,v,vi,nz);
1428     tmp[i] = sum;
1429     v     += nz; vi += nz;
1430   }
1431 
1432   /* backward solve the upper triangular */
1433   for (i=n-1; i>=0; i--) {
1434     v   = aa + adiag[i+1]+1;
1435     vi  = aj + adiag[i+1]+1;
1436     nz  = adiag[i]-adiag[i+1]-1;
1437     sum = tmp[i];
1438     PetscSparseDenseMinusDot(sum,tmp,v,vi,nz);
1439     x[c[i]] = tmp[i] = sum*v[nz]; /* v[nz] = aa[adiag[i]] */
1440   }
1441 
1442   PetscCall(ISRestoreIndices(isrow,&rout));
1443   PetscCall(ISRestoreIndices(iscol,&cout));
1444   PetscCall(VecRestoreArrayRead(bb,&b));
1445   PetscCall(VecRestoreArray(xx,&x));
1446   PetscCall(PetscLogFlops(2.0*a->nz - A->cmap->n));
1447   PetscFunctionReturn(0);
1448 }
1449