xref: /petsc/src/mat/impls/baij/seq/baijfact2.c (revision 0c4413a7bab1432485e668e274eb71cdbea65977)
1 #define PETSCMAT_DLL
2 
3 
4 /*
5     Factorization code for BAIJ format.
6 */
7 
8 #include "../src/mat/impls/baij/seq/baij.h"
9 #include "../src/mat/blockinvert.h"
10 #include "petscbt.h"
11 #include "../src/mat/utils/freespace.h"
12 
13 #undef __FUNCT__
14 #define __FUNCT__ "MatSolveTranspose_SeqBAIJ_1_NaturalOrdering"
15 PetscErrorCode MatSolveTranspose_SeqBAIJ_1_NaturalOrdering(Mat A,Vec bb,Vec xx)
16 {
17   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ *)A->data;
18   PetscErrorCode ierr;
19   PetscInt       i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz;
20   PetscInt       *diag = a->diag;
21   MatScalar      *aa=a->a,*v;
22   PetscScalar    s1,*x,*b;
23 
24   PetscFunctionBegin;
25   ierr = VecCopy(bb,xx);CHKERRQ(ierr);
26   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
27   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
28 
29   /* forward solve the U^T */
30   for (i=0; i<n; i++) {
31 
32     v     = aa + diag[i];
33     /* multiply by the inverse of the block diagonal */
34     s1    = (*v++)*x[i];
35     vi    = aj + diag[i] + 1;
36     nz    = ai[i+1] - diag[i] - 1;
37     while (nz--) {
38       x[*vi++]  -= (*v++)*s1;
39     }
40     x[i]   = s1;
41   }
42   /* backward solve the L^T */
43   for (i=n-1; i>=0; i--){
44     v    = aa + diag[i] - 1;
45     vi   = aj + diag[i] - 1;
46     nz   = diag[i] - ai[i];
47     s1   = x[i];
48     while (nz--) {
49       x[*vi--]   -=  (*v--)*s1;
50     }
51   }
52   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
53   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
54   ierr = PetscLogFlops(2.0*(a->nz) - A->cmap->n);CHKERRQ(ierr);
55   PetscFunctionReturn(0);
56 }
57 
58 #undef __FUNCT__
59 #define __FUNCT__ "MatSolveTranspose_SeqBAIJ_2_NaturalOrdering"
60 PetscErrorCode MatSolveTranspose_SeqBAIJ_2_NaturalOrdering(Mat A,Vec bb,Vec xx)
61 {
62   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ *)A->data;
63   PetscErrorCode ierr;
64   PetscInt       i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt;
65   PetscInt       *diag = a->diag,oidx;
66   MatScalar      *aa=a->a,*v;
67   PetscScalar    s1,s2,x1,x2;
68   PetscScalar    *x,*b;
69 
70   PetscFunctionBegin;
71   ierr = VecCopy(bb,xx);CHKERRQ(ierr);
72   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
73   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
74 
75   /* forward solve the U^T */
76   idx = 0;
77   for (i=0; i<n; i++) {
78 
79     v     = aa + 4*diag[i];
80     /* multiply by the inverse of the block diagonal */
81     x1 = x[idx];   x2 = x[1+idx];
82     s1 = v[0]*x1  +  v[1]*x2;
83     s2 = v[2]*x1  +  v[3]*x2;
84     v += 4;
85 
86     vi    = aj + diag[i] + 1;
87     nz    = ai[i+1] - diag[i] - 1;
88     while (nz--) {
89       oidx = 2*(*vi++);
90       x[oidx]   -= v[0]*s1  +  v[1]*s2;
91       x[oidx+1] -= v[2]*s1  +  v[3]*s2;
92       v  += 4;
93     }
94     x[idx]   = s1;x[1+idx] = s2;
95     idx += 2;
96   }
97   /* backward solve the L^T */
98   for (i=n-1; i>=0; i--){
99     v    = aa + 4*diag[i] - 4;
100     vi   = aj + diag[i] - 1;
101     nz   = diag[i] - ai[i];
102     idt  = 2*i;
103     s1   = x[idt];  s2 = x[1+idt];
104     while (nz--) {
105       idx   = 2*(*vi--);
106       x[idx]   -=  v[0]*s1 +  v[1]*s2;
107       x[idx+1] -=  v[2]*s1 +  v[3]*s2;
108       v -= 4;
109     }
110   }
111   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
112   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
113   ierr = PetscLogFlops(2.0*4.0*(a->nz) - 2.0*A->cmap->n);CHKERRQ(ierr);
114   PetscFunctionReturn(0);
115 }
116 
117 #undef __FUNCT__
118 #define __FUNCT__ "MatSolveTranspose_SeqBAIJ_3_NaturalOrdering"
119 PetscErrorCode MatSolveTranspose_SeqBAIJ_3_NaturalOrdering(Mat A,Vec bb,Vec xx)
120 {
121   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ *)A->data;
122   PetscErrorCode ierr;
123   PetscInt       i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt;
124   PetscInt       *diag = a->diag,oidx;
125   MatScalar      *aa=a->a,*v;
126   PetscScalar    s1,s2,s3,x1,x2,x3;
127   PetscScalar    *x,*b;
128 
129   PetscFunctionBegin;
130   ierr = VecCopy(bb,xx);CHKERRQ(ierr);
131   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
132   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
133 
134   /* forward solve the U^T */
135   idx = 0;
136   for (i=0; i<n; i++) {
137 
138     v     = aa + 9*diag[i];
139     /* multiply by the inverse of the block diagonal */
140     x1 = x[idx];   x2 = x[1+idx]; x3    = x[2+idx];
141     s1 = v[0]*x1  +  v[1]*x2 +  v[2]*x3;
142     s2 = v[3]*x1  +  v[4]*x2 +  v[5]*x3;
143     s3 = v[6]*x1  +  v[7]*x2 + v[8]*x3;
144     v += 9;
145 
146     vi    = aj + diag[i] + 1;
147     nz    = ai[i+1] - diag[i] - 1;
148     while (nz--) {
149       oidx = 3*(*vi++);
150       x[oidx]   -= v[0]*s1  +  v[1]*s2 +  v[2]*s3;
151       x[oidx+1] -= v[3]*s1  +  v[4]*s2 +  v[5]*s3;
152       x[oidx+2] -= v[6]*s1 + v[7]*s2 + v[8]*s3;
153       v  += 9;
154     }
155     x[idx]   = s1;x[1+idx] = s2; x[2+idx] = s3;
156     idx += 3;
157   }
158   /* backward solve the L^T */
159   for (i=n-1; i>=0; i--){
160     v    = aa + 9*diag[i] - 9;
161     vi   = aj + diag[i] - 1;
162     nz   = diag[i] - ai[i];
163     idt  = 3*i;
164     s1 = x[idt];  s2 = x[1+idt]; s3 = x[2+idt];
165     while (nz--) {
166       idx   = 3*(*vi--);
167       x[idx]   -=  v[0]*s1 +  v[1]*s2 +  v[2]*s3;
168       x[idx+1] -=  v[3]*s1 +  v[4]*s2 +  v[5]*s3;
169       x[idx+2] -= v[6]*s1 + v[7]*s2 + v[8]*s3;
170       v -= 9;
171     }
172   }
173   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
174   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
175   ierr = PetscLogFlops(2.0*9.0*(a->nz) - 3.0*A->cmap->n);CHKERRQ(ierr);
176   PetscFunctionReturn(0);
177 }
178 
179 #undef __FUNCT__
180 #define __FUNCT__ "MatSolveTranspose_SeqBAIJ_4_NaturalOrdering"
181 PetscErrorCode MatSolveTranspose_SeqBAIJ_4_NaturalOrdering(Mat A,Vec bb,Vec xx)
182 {
183   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ *)A->data;
184   PetscErrorCode ierr;
185   PetscInt       i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt;
186   PetscInt       *diag = a->diag,oidx;
187   MatScalar      *aa=a->a,*v;
188   PetscScalar    s1,s2,s3,s4,x1,x2,x3,x4;
189   PetscScalar    *x,*b;
190 
191   PetscFunctionBegin;
192   ierr = VecCopy(bb,xx);CHKERRQ(ierr);
193   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
194   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
195 
196   /* forward solve the U^T */
197   idx = 0;
198   for (i=0; i<n; i++) {
199 
200     v     = aa + 16*diag[i];
201     /* multiply by the inverse of the block diagonal */
202     x1    = x[idx];   x2 = x[1+idx]; x3    = x[2+idx]; x4 = x[3+idx];
203     s1 = v[0]*x1  +  v[1]*x2 +  v[2]*x3 +  v[3]*x4;
204     s2 = v[4]*x1  +  v[5]*x2 +  v[6]*x3 +  v[7]*x4;
205     s3 = v[8]*x1  +  v[9]*x2 + v[10]*x3 + v[11]*x4;
206     s4 = v[12]*x1 + v[13]*x2 + v[14]*x3 + v[15]*x4;
207     v += 16;
208 
209     vi    = aj + diag[i] + 1;
210     nz    = ai[i+1] - diag[i] - 1;
211     while (nz--) {
212       oidx = 4*(*vi++);
213       x[oidx]   -= v[0]*s1  +  v[1]*s2 +  v[2]*s3 +  v[3]*s4;
214       x[oidx+1] -= v[4]*s1  +  v[5]*s2 +  v[6]*s3 +  v[7]*s4;
215       x[oidx+2] -= v[8]*s1 + v[9]*s2 + v[10]*s3 + v[11]*s4;
216       x[oidx+3] -= v[12]*s1 + v[13]*s2 + v[14]*s3 + v[15]*s4;
217       v  += 16;
218     }
219     x[idx]   = s1;x[1+idx] = s2; x[2+idx] = s3;x[3+idx] = s4;
220     idx += 4;
221   }
222   /* backward solve the L^T */
223   for (i=n-1; i>=0; i--){
224     v    = aa + 16*diag[i] - 16;
225     vi   = aj + diag[i] - 1;
226     nz   = diag[i] - ai[i];
227     idt  = 4*i;
228     s1 = x[idt];  s2 = x[1+idt]; s3 = x[2+idt];s4 = x[3+idt];
229     while (nz--) {
230       idx   = 4*(*vi--);
231       x[idx]   -=  v[0]*s1 +  v[1]*s2 +  v[2]*s3 +  v[3]*s4;
232       x[idx+1] -=  v[4]*s1 +  v[5]*s2 +  v[6]*s3 +  v[7]*s4;
233       x[idx+2] -= v[8]*s1 + v[9]*s2 + v[10]*s3 + v[11]*s4;
234       x[idx+3] -= v[12]*s1 + v[13]*s2 + v[14]*s3 + v[15]*s4;
235       v -= 16;
236     }
237   }
238   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
239   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
240   ierr = PetscLogFlops(2.0*16*(a->nz) - 4.0*A->cmap->n);CHKERRQ(ierr);
241   PetscFunctionReturn(0);
242 }
243 
244 #undef __FUNCT__
245 #define __FUNCT__ "MatSolveTranspose_SeqBAIJ_5_NaturalOrdering"
246 PetscErrorCode MatSolveTranspose_SeqBAIJ_5_NaturalOrdering(Mat A,Vec bb,Vec xx)
247 {
248   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ *)A->data;
249   PetscErrorCode ierr;
250   PetscInt       i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt;
251   PetscInt       *diag = a->diag,oidx;
252   MatScalar      *aa=a->a,*v;
253   PetscScalar    s1,s2,s3,s4,s5,x1,x2,x3,x4,x5;
254   PetscScalar    *x,*b;
255 
256   PetscFunctionBegin;
257   ierr = VecCopy(bb,xx);CHKERRQ(ierr);
258   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
259   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
260 
261   /* forward solve the U^T */
262   idx = 0;
263   for (i=0; i<n; i++) {
264 
265     v     = aa + 25*diag[i];
266     /* multiply by the inverse of the block diagonal */
267     x1    = x[idx];   x2 = x[1+idx]; x3    = x[2+idx]; x4 = x[3+idx]; x5 = x[4+idx];
268     s1 = v[0]*x1  +  v[1]*x2 +  v[2]*x3 +  v[3]*x4 +  v[4]*x5;
269     s2 = v[5]*x1  +  v[6]*x2 +  v[7]*x3 +  v[8]*x4 +  v[9]*x5;
270     s3 = v[10]*x1 + v[11]*x2 + v[12]*x3 + v[13]*x4 + v[14]*x5;
271     s4 = v[15]*x1 + v[16]*x2 + v[17]*x3 + v[18]*x4 + v[19]*x5;
272     s5 = v[20]*x1 + v[21]*x2 + v[22]*x3 + v[23]*x4 + v[24]*x5;
273     v += 25;
274 
275     vi    = aj + diag[i] + 1;
276     nz    = ai[i+1] - diag[i] - 1;
277     while (nz--) {
278       oidx = 5*(*vi++);
279       x[oidx]   -= v[0]*s1  +  v[1]*s2 +  v[2]*s3 +  v[3]*s4 +  v[4]*s5;
280       x[oidx+1] -= v[5]*s1  +  v[6]*s2 +  v[7]*s3 +  v[8]*s4 +  v[9]*s5;
281       x[oidx+2] -= v[10]*s1 + v[11]*s2 + v[12]*s3 + v[13]*s4 + v[14]*s5;
282       x[oidx+3] -= v[15]*s1 + v[16]*s2 + v[17]*s3 + v[18]*s4 + v[19]*s5;
283       x[oidx+4] -= v[20]*s1 + v[21]*s2 + v[22]*s3 + v[23]*s4 + v[24]*s5;
284       v  += 25;
285     }
286     x[idx]   = s1;x[1+idx] = s2; x[2+idx] = s3;x[3+idx] = s4; x[4+idx] = s5;
287     idx += 5;
288   }
289   /* backward solve the L^T */
290   for (i=n-1; i>=0; i--){
291     v    = aa + 25*diag[i] - 25;
292     vi   = aj + diag[i] - 1;
293     nz   = diag[i] - ai[i];
294     idt  = 5*i;
295     s1 = x[idt];  s2 = x[1+idt]; s3 = x[2+idt];s4 = x[3+idt]; s5 = x[4+idt];
296     while (nz--) {
297       idx   = 5*(*vi--);
298       x[idx]   -=  v[0]*s1 +  v[1]*s2 +  v[2]*s3 +  v[3]*s4 +  v[4]*s5;
299       x[idx+1] -=  v[5]*s1 +  v[6]*s2 +  v[7]*s3 +  v[8]*s4 +  v[9]*s5;
300       x[idx+2] -= v[10]*s1 + v[11]*s2 + v[12]*s3 + v[13]*s4 + v[14]*s5;
301       x[idx+3] -= v[15]*s1 + v[16]*s2 + v[17]*s3 + v[18]*s4 + v[19]*s5;
302       x[idx+4] -= v[20]*s1 + v[21]*s2 + v[22]*s3 + v[23]*s4 + v[24]*s5;
303       v -= 25;
304     }
305   }
306   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
307   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
308   ierr = PetscLogFlops(2.0*25*(a->nz) - 5.0*A->cmap->n);CHKERRQ(ierr);
309   PetscFunctionReturn(0);
310 }
311 
312 #undef __FUNCT__
313 #define __FUNCT__ "MatSolveTranspose_SeqBAIJ_6_NaturalOrdering"
314 PetscErrorCode MatSolveTranspose_SeqBAIJ_6_NaturalOrdering(Mat A,Vec bb,Vec xx)
315 {
316   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ *)A->data;
317   PetscErrorCode ierr;
318   PetscInt       i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt;
319   PetscInt       *diag = a->diag,oidx;
320   MatScalar      *aa=a->a,*v;
321   PetscScalar    s1,s2,s3,s4,s5,s6,x1,x2,x3,x4,x5,x6;
322   PetscScalar    *x,*b;
323 
324   PetscFunctionBegin;
325   ierr = VecCopy(bb,xx);CHKERRQ(ierr);
326   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
327   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
328 
329   /* forward solve the U^T */
330   idx = 0;
331   for (i=0; i<n; i++) {
332 
333     v     = aa + 36*diag[i];
334     /* multiply by the inverse of the block diagonal */
335     x1    = x[idx];   x2 = x[1+idx]; x3    = x[2+idx]; x4 = x[3+idx]; x5 = x[4+idx];
336     x6    = x[5+idx];
337     s1 = v[0]*x1  +  v[1]*x2 +  v[2]*x3 +  v[3]*x4 +  v[4]*x5 +  v[5]*x6;
338     s2 = v[6]*x1  +  v[7]*x2 +  v[8]*x3 +  v[9]*x4 + v[10]*x5 + v[11]*x6;
339     s3 = v[12]*x1 + v[13]*x2 + v[14]*x3 + v[15]*x4 + v[16]*x5 + v[17]*x6;
340     s4 = v[18]*x1 + v[19]*x2 + v[20]*x3 + v[21]*x4 + v[22]*x5 + v[23]*x6;
341     s5 = v[24]*x1 + v[25]*x2 + v[26]*x3 + v[27]*x4 + v[28]*x5 + v[29]*x6;
342     s6 = v[30]*x1 + v[31]*x2 + v[32]*x3 + v[33]*x4 + v[34]*x5 + v[35]*x6;
343     v += 36;
344 
345     vi    = aj + diag[i] + 1;
346     nz    = ai[i+1] - diag[i] - 1;
347     while (nz--) {
348       oidx = 6*(*vi++);
349       x[oidx]   -= v[0]*s1  +  v[1]*s2 +  v[2]*s3 +  v[3]*s4 +  v[4]*s5 +  v[5]*s6;
350       x[oidx+1] -= v[6]*s1  +  v[7]*s2 +  v[8]*s3 +  v[9]*s4 + v[10]*s5 + v[11]*s6;
351       x[oidx+2] -= v[12]*s1 + v[13]*s2 + v[14]*s3 + v[15]*s4 + v[16]*s5 + v[17]*s6;
352       x[oidx+3] -= v[18]*s1 + v[19]*s2 + v[20]*s3 + v[21]*s4 + v[22]*s5 + v[23]*s6;
353       x[oidx+4] -= v[24]*s1 + v[25]*s2 + v[26]*s3 + v[27]*s4 + v[28]*s5 + v[29]*s6;
354       x[oidx+5] -= v[30]*s1 + v[31]*s2 + v[32]*s3 + v[33]*s4 + v[34]*s5 + v[35]*s6;
355       v  += 36;
356     }
357     x[idx]   = s1;x[1+idx] = s2; x[2+idx] = s3;x[3+idx] = s4; x[4+idx] = s5;
358     x[5+idx] = s6;
359     idx += 6;
360   }
361   /* backward solve the L^T */
362   for (i=n-1; i>=0; i--){
363     v    = aa + 36*diag[i] - 36;
364     vi   = aj + diag[i] - 1;
365     nz   = diag[i] - ai[i];
366     idt  = 6*i;
367     s1 = x[idt];  s2 = x[1+idt]; s3 = x[2+idt];s4 = x[3+idt]; s5 = x[4+idt];
368     s6 = x[5+idt];
369     while (nz--) {
370       idx   = 6*(*vi--);
371       x[idx]   -=  v[0]*s1 +  v[1]*s2 +  v[2]*s3 +  v[3]*s4 +  v[4]*s5 +  v[5]*s6;
372       x[idx+1] -=  v[6]*s1 +  v[7]*s2 +  v[8]*s3 +  v[9]*s4 + v[10]*s5 + v[11]*s6;
373       x[idx+2] -= v[12]*s1 + v[13]*s2 + v[14]*s3 + v[15]*s4 + v[16]*s5 + v[17]*s6;
374       x[idx+3] -= v[18]*s1 + v[19]*s2 + v[20]*s3 + v[21]*s4 + v[22]*s5 + v[23]*s6;
375       x[idx+4] -= v[24]*s1 + v[25]*s2 + v[26]*s3 + v[27]*s4 + v[28]*s5 + v[29]*s6;
376       x[idx+5] -= v[30]*s1 + v[31]*s2 + v[32]*s3 + v[33]*s4 + v[34]*s5 + v[35]*s6;
377       v -= 36;
378     }
379   }
380   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
381   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
382   ierr = PetscLogFlops(2.0*36*(a->nz) - 6.0*A->cmap->n);CHKERRQ(ierr);
383   PetscFunctionReturn(0);
384 }
385 
386 #undef __FUNCT__
387 #define __FUNCT__ "MatSolveTranspose_SeqBAIJ_7_NaturalOrdering"
388 PetscErrorCode MatSolveTranspose_SeqBAIJ_7_NaturalOrdering(Mat A,Vec bb,Vec xx)
389 {
390   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ *)A->data;
391   PetscErrorCode ierr;
392   PetscInt       i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt;
393   PetscInt       *diag = a->diag,oidx;
394   MatScalar      *aa=a->a,*v;
395   PetscScalar    s1,s2,s3,s4,s5,s6,s7,x1,x2,x3,x4,x5,x6,x7;
396   PetscScalar    *x,*b;
397 
398   PetscFunctionBegin;
399   ierr = VecCopy(bb,xx);CHKERRQ(ierr);
400   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
401   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
402 
403   /* forward solve the U^T */
404   idx = 0;
405   for (i=0; i<n; i++) {
406 
407     v     = aa + 49*diag[i];
408     /* multiply by the inverse of the block diagonal */
409     x1    = x[idx];   x2 = x[1+idx]; x3    = x[2+idx]; x4 = x[3+idx]; x5 = x[4+idx];
410     x6    = x[5+idx]; x7 = x[6+idx];
411     s1 = v[0]*x1  +  v[1]*x2 +  v[2]*x3 +  v[3]*x4 +  v[4]*x5 +  v[5]*x6 +  v[6]*x7;
412     s2 = v[7]*x1  +  v[8]*x2 +  v[9]*x3 + v[10]*x4 + v[11]*x5 + v[12]*x6 + v[13]*x7;
413     s3 = v[14]*x1 + v[15]*x2 + v[16]*x3 + v[17]*x4 + v[18]*x5 + v[19]*x6 + v[20]*x7;
414     s4 = v[21]*x1 + v[22]*x2 + v[23]*x3 + v[24]*x4 + v[25]*x5 + v[26]*x6 + v[27]*x7;
415     s5 = v[28]*x1 + v[29]*x2 + v[30]*x3 + v[31]*x4 + v[32]*x5 + v[33]*x6 + v[34]*x7;
416     s6 = v[35]*x1 + v[36]*x2 + v[37]*x3 + v[38]*x4 + v[39]*x5 + v[40]*x6 + v[41]*x7;
417     s7 = v[42]*x1 + v[43]*x2 + v[44]*x3 + v[45]*x4 + v[46]*x5 + v[47]*x6 + v[48]*x7;
418     v += 49;
419 
420     vi    = aj + diag[i] + 1;
421     nz    = ai[i+1] - diag[i] - 1;
422     while (nz--) {
423       oidx = 7*(*vi++);
424       x[oidx]   -= v[0]*s1  +  v[1]*s2 +  v[2]*s3 +  v[3]*s4 +  v[4]*s5 +  v[5]*s6 +  v[6]*s7;
425       x[oidx+1] -= v[7]*s1  +  v[8]*s2 +  v[9]*s3 + v[10]*s4 + v[11]*s5 + v[12]*s6 + v[13]*s7;
426       x[oidx+2] -= v[14]*s1 + v[15]*s2 + v[16]*s3 + v[17]*s4 + v[18]*s5 + v[19]*s6 + v[20]*s7;
427       x[oidx+3] -= v[21]*s1 + v[22]*s2 + v[23]*s3 + v[24]*s4 + v[25]*s5 + v[26]*s6 + v[27]*s7;
428       x[oidx+4] -= v[28]*s1 + v[29]*s2 + v[30]*s3 + v[31]*s4 + v[32]*s5 + v[33]*s6 + v[34]*s7;
429       x[oidx+5] -= v[35]*s1 + v[36]*s2 + v[37]*s3 + v[38]*s4 + v[39]*s5 + v[40]*s6 + v[41]*s7;
430       x[oidx+6] -= v[42]*s1 + v[43]*s2 + v[44]*s3 + v[45]*s4 + v[46]*s5 + v[47]*s6 + v[48]*s7;
431       v  += 49;
432     }
433     x[idx]   = s1;x[1+idx] = s2; x[2+idx] = s3;x[3+idx] = s4; x[4+idx] = s5;
434     x[5+idx] = s6;x[6+idx] = s7;
435     idx += 7;
436   }
437   /* backward solve the L^T */
438   for (i=n-1; i>=0; i--){
439     v    = aa + 49*diag[i] - 49;
440     vi   = aj + diag[i] - 1;
441     nz   = diag[i] - ai[i];
442     idt  = 7*i;
443     s1 = x[idt];  s2 = x[1+idt]; s3 = x[2+idt];s4 = x[3+idt]; s5 = x[4+idt];
444     s6 = x[5+idt];s7 = x[6+idt];
445     while (nz--) {
446       idx   = 7*(*vi--);
447       x[idx]   -=  v[0]*s1 +  v[1]*s2 +  v[2]*s3 +  v[3]*s4 +  v[4]*s5 +  v[5]*s6 +  v[6]*s7;
448       x[idx+1] -=  v[7]*s1 +  v[8]*s2 +  v[9]*s3 + v[10]*s4 + v[11]*s5 + v[12]*s6 + v[13]*s7;
449       x[idx+2] -= v[14]*s1 + v[15]*s2 + v[16]*s3 + v[17]*s4 + v[18]*s5 + v[19]*s6 + v[20]*s7;
450       x[idx+3] -= v[21]*s1 + v[22]*s2 + v[23]*s3 + v[24]*s4 + v[25]*s5 + v[26]*s6 + v[27]*s7;
451       x[idx+4] -= v[28]*s1 + v[29]*s2 + v[30]*s3 + v[31]*s4 + v[32]*s5 + v[33]*s6 + v[34]*s7;
452       x[idx+5] -= v[35]*s1 + v[36]*s2 + v[37]*s3 + v[38]*s4 + v[39]*s5 + v[40]*s6 + v[41]*s7;
453       x[idx+6] -= v[42]*s1 + v[43]*s2 + v[44]*s3 + v[45]*s4 + v[46]*s5 + v[47]*s6 + v[48]*s7;
454       v -= 49;
455     }
456   }
457   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
458   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
459   ierr = PetscLogFlops(2.0*49*(a->nz) - 7.0*A->cmap->n);CHKERRQ(ierr);
460   PetscFunctionReturn(0);
461 }
462 
463 /*---------------------------------------------------------------------------------------------*/
464 #undef __FUNCT__
465 #define __FUNCT__ "MatSolveTranspose_SeqBAIJ_1"
466 PetscErrorCode MatSolveTranspose_SeqBAIJ_1(Mat A,Vec bb,Vec xx)
467 {
468   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ *)A->data;
469   IS             iscol=a->col,isrow=a->row;
470   PetscErrorCode ierr;
471   const PetscInt *r,*c,*rout,*cout;
472   PetscInt       i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz;
473   PetscInt       *diag = a->diag;
474   MatScalar      *aa=a->a,*v;
475   PetscScalar    s1,*x,*b,*t;
476 
477   PetscFunctionBegin;
478   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
479   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
480   t  = a->solve_work;
481 
482   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
483   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
484 
485   /* copy the b into temp work space according to permutation */
486   for (i=0; i<n; i++) {
487     t[i] = b[c[i]];
488   }
489 
490   /* forward solve the U^T */
491   for (i=0; i<n; i++) {
492 
493     v     = aa + diag[i];
494     /* multiply by the inverse of the block diagonal */
495     s1    = (*v++)*t[i];
496     vi    = aj + diag[i] + 1;
497     nz    = ai[i+1] - diag[i] - 1;
498     while (nz--) {
499       t[*vi++]  -= (*v++)*s1;
500     }
501     t[i]   = s1;
502   }
503   /* backward solve the L^T */
504   for (i=n-1; i>=0; i--){
505     v    = aa + diag[i] - 1;
506     vi   = aj + diag[i] - 1;
507     nz   = diag[i] - ai[i];
508     s1   = t[i];
509     while (nz--) {
510       t[*vi--]   -=  (*v--)*s1;
511     }
512   }
513 
514   /* copy t into x according to permutation */
515   for (i=0; i<n; i++) {
516     x[r[i]]   = t[i];
517   }
518 
519   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
520   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
521   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
522   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
523   ierr = PetscLogFlops(2.0*(a->nz) - A->cmap->n);CHKERRQ(ierr);
524   PetscFunctionReturn(0);
525 }
526 
527 #undef __FUNCT__
528 #define __FUNCT__ "MatSolveTranspose_SeqBAIJ_2"
529 PetscErrorCode MatSolveTranspose_SeqBAIJ_2(Mat A,Vec bb,Vec xx)
530 {
531   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ *)A->data;
532   IS             iscol=a->col,isrow=a->row;
533   PetscErrorCode ierr;
534   const PetscInt *r,*c,*rout,*cout;
535   PetscInt       i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt;
536   PetscInt       *diag = a->diag,ii,ic,ir,oidx;
537   MatScalar      *aa=a->a,*v;
538   PetscScalar    s1,s2,x1,x2;
539   PetscScalar    *x,*b,*t;
540 
541   PetscFunctionBegin;
542   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
543   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
544   t  = a->solve_work;
545 
546   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
547   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
548 
549   /* copy the b into temp work space according to permutation */
550   ii = 0;
551   for (i=0; i<n; i++) {
552     ic      = 2*c[i];
553     t[ii]   = b[ic];
554     t[ii+1] = b[ic+1];
555     ii += 2;
556   }
557 
558   /* forward solve the U^T */
559   idx = 0;
560   for (i=0; i<n; i++) {
561 
562     v     = aa + 4*diag[i];
563     /* multiply by the inverse of the block diagonal */
564     x1    = t[idx];   x2 = t[1+idx];
565     s1 = v[0]*x1  +  v[1]*x2;
566     s2 = v[2]*x1  +  v[3]*x2;
567     v += 4;
568 
569     vi    = aj + diag[i] + 1;
570     nz    = ai[i+1] - diag[i] - 1;
571     while (nz--) {
572       oidx = 2*(*vi++);
573       t[oidx]   -= v[0]*s1  +  v[1]*s2;
574       t[oidx+1] -= v[2]*s1  +  v[3]*s2;
575       v  += 4;
576     }
577     t[idx]   = s1;t[1+idx] = s2;
578     idx += 2;
579   }
580   /* backward solve the L^T */
581   for (i=n-1; i>=0; i--){
582     v    = aa + 4*diag[i] - 4;
583     vi   = aj + diag[i] - 1;
584     nz   = diag[i] - ai[i];
585     idt  = 2*i;
586     s1 = t[idt];  s2 = t[1+idt];
587     while (nz--) {
588       idx   = 2*(*vi--);
589       t[idx]   -=  v[0]*s1 +  v[1]*s2;
590       t[idx+1] -=  v[2]*s1 +  v[3]*s2;
591       v -= 4;
592     }
593   }
594 
595   /* copy t into x according to permutation */
596   ii = 0;
597   for (i=0; i<n; i++) {
598     ir      = 2*r[i];
599     x[ir]   = t[ii];
600     x[ir+1] = t[ii+1];
601     ii += 2;
602   }
603 
604   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
605   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
606   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
607   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
608   ierr = PetscLogFlops(2.0*4*(a->nz) - 2.0*A->cmap->n);CHKERRQ(ierr);
609   PetscFunctionReturn(0);
610 }
611 
612 #undef __FUNCT__
613 #define __FUNCT__ "MatSolveTranspose_SeqBAIJ_3"
614 PetscErrorCode MatSolveTranspose_SeqBAIJ_3(Mat A,Vec bb,Vec xx)
615 {
616   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ *)A->data;
617   IS             iscol=a->col,isrow=a->row;
618   PetscErrorCode ierr;
619   const PetscInt *r,*c,*rout,*cout;
620   PetscInt       i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt;
621   PetscInt       *diag = a->diag,ii,ic,ir,oidx;
622   MatScalar      *aa=a->a,*v;
623   PetscScalar    s1,s2,s3,x1,x2,x3;
624   PetscScalar    *x,*b,*t;
625 
626   PetscFunctionBegin;
627   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
628   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
629   t  = a->solve_work;
630 
631   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
632   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
633 
634   /* copy the b into temp work space according to permutation */
635   ii = 0;
636   for (i=0; i<n; i++) {
637     ic      = 3*c[i];
638     t[ii]   = b[ic];
639     t[ii+1] = b[ic+1];
640     t[ii+2] = b[ic+2];
641     ii += 3;
642   }
643 
644   /* forward solve the U^T */
645   idx = 0;
646   for (i=0; i<n; i++) {
647 
648     v     = aa + 9*diag[i];
649     /* multiply by the inverse of the block diagonal */
650     x1    = t[idx];   x2 = t[1+idx]; x3    = t[2+idx];
651     s1 = v[0]*x1  +  v[1]*x2 +  v[2]*x3;
652     s2 = v[3]*x1  +  v[4]*x2 +  v[5]*x3;
653     s3 = v[6]*x1  +  v[7]*x2 + v[8]*x3;
654     v += 9;
655 
656     vi    = aj + diag[i] + 1;
657     nz    = ai[i+1] - diag[i] - 1;
658     while (nz--) {
659       oidx = 3*(*vi++);
660       t[oidx]   -= v[0]*s1  +  v[1]*s2 +  v[2]*s3;
661       t[oidx+1] -= v[3]*s1  +  v[4]*s2 +  v[5]*s3;
662       t[oidx+2] -= v[6]*s1 + v[7]*s2 + v[8]*s3;
663       v  += 9;
664     }
665     t[idx]   = s1;t[1+idx] = s2; t[2+idx] = s3;
666     idx += 3;
667   }
668   /* backward solve the L^T */
669   for (i=n-1; i>=0; i--){
670     v    = aa + 9*diag[i] - 9;
671     vi   = aj + diag[i] - 1;
672     nz   = diag[i] - ai[i];
673     idt  = 3*i;
674     s1 = t[idt];  s2 = t[1+idt]; s3 = t[2+idt];
675     while (nz--) {
676       idx   = 3*(*vi--);
677       t[idx]   -=  v[0]*s1 +  v[1]*s2 +  v[2]*s3;
678       t[idx+1] -=  v[3]*s1 +  v[4]*s2 +  v[5]*s3;
679       t[idx+2] -= v[6]*s1 + v[7]*s2 + v[8]*s3;
680       v -= 9;
681     }
682   }
683 
684   /* copy t into x according to permutation */
685   ii = 0;
686   for (i=0; i<n; i++) {
687     ir      = 3*r[i];
688     x[ir]   = t[ii];
689     x[ir+1] = t[ii+1];
690     x[ir+2] = t[ii+2];
691     ii += 3;
692   }
693 
694   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
695   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
696   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
697   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
698   ierr = PetscLogFlops(2.0*9*(a->nz) - 3.0*A->cmap->n);CHKERRQ(ierr);
699   PetscFunctionReturn(0);
700 }
701 
702 #undef __FUNCT__
703 #define __FUNCT__ "MatSolveTranspose_SeqBAIJ_4"
704 PetscErrorCode MatSolveTranspose_SeqBAIJ_4(Mat A,Vec bb,Vec xx)
705 {
706   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ *)A->data;
707   IS             iscol=a->col,isrow=a->row;
708   PetscErrorCode ierr;
709   const PetscInt *r,*c,*rout,*cout;
710   PetscInt       i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt;
711   PetscInt       *diag = a->diag,ii,ic,ir,oidx;
712   MatScalar      *aa=a->a,*v;
713   PetscScalar    s1,s2,s3,s4,x1,x2,x3,x4;
714   PetscScalar    *x,*b,*t;
715 
716   PetscFunctionBegin;
717   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
718   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
719   t  = a->solve_work;
720 
721   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
722   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
723 
724   /* copy the b into temp work space according to permutation */
725   ii = 0;
726   for (i=0; i<n; i++) {
727     ic      = 4*c[i];
728     t[ii]   = b[ic];
729     t[ii+1] = b[ic+1];
730     t[ii+2] = b[ic+2];
731     t[ii+3] = b[ic+3];
732     ii += 4;
733   }
734 
735   /* forward solve the U^T */
736   idx = 0;
737   for (i=0; i<n; i++) {
738 
739     v     = aa + 16*diag[i];
740     /* multiply by the inverse of the block diagonal */
741     x1    = t[idx];   x2 = t[1+idx]; x3    = t[2+idx]; x4 = t[3+idx];
742     s1 = v[0]*x1  +  v[1]*x2 +  v[2]*x3 +  v[3]*x4;
743     s2 = v[4]*x1  +  v[5]*x2 +  v[6]*x3 +  v[7]*x4;
744     s3 = v[8]*x1  +  v[9]*x2 + v[10]*x3 + v[11]*x4;
745     s4 = v[12]*x1 + v[13]*x2 + v[14]*x3 + v[15]*x4;
746     v += 16;
747 
748     vi    = aj + diag[i] + 1;
749     nz    = ai[i+1] - diag[i] - 1;
750     while (nz--) {
751       oidx = 4*(*vi++);
752       t[oidx]   -= v[0]*s1  +  v[1]*s2 +  v[2]*s3 +  v[3]*s4;
753       t[oidx+1] -= v[4]*s1  +  v[5]*s2 +  v[6]*s3 +  v[7]*s4;
754       t[oidx+2] -= v[8]*s1 + v[9]*s2 + v[10]*s3 + v[11]*s4;
755       t[oidx+3] -= v[12]*s1 + v[13]*s2 + v[14]*s3 + v[15]*s4;
756       v  += 16;
757     }
758     t[idx]   = s1;t[1+idx] = s2; t[2+idx] = s3;t[3+idx] = s4;
759     idx += 4;
760   }
761   /* backward solve the L^T */
762   for (i=n-1; i>=0; i--){
763     v    = aa + 16*diag[i] - 16;
764     vi   = aj + diag[i] - 1;
765     nz   = diag[i] - ai[i];
766     idt  = 4*i;
767     s1 = t[idt];  s2 = t[1+idt]; s3 = t[2+idt];s4 = t[3+idt];
768     while (nz--) {
769       idx   = 4*(*vi--);
770       t[idx]   -=  v[0]*s1 +  v[1]*s2 +  v[2]*s3 +  v[3]*s4;
771       t[idx+1] -=  v[4]*s1 +  v[5]*s2 +  v[6]*s3 +  v[7]*s4;
772       t[idx+2] -= v[8]*s1 + v[9]*s2 + v[10]*s3 + v[11]*s4;
773       t[idx+3] -= v[12]*s1 + v[13]*s2 + v[14]*s3 + v[15]*s4;
774       v -= 16;
775     }
776   }
777 
778   /* copy t into x according to permutation */
779   ii = 0;
780   for (i=0; i<n; i++) {
781     ir      = 4*r[i];
782     x[ir]   = t[ii];
783     x[ir+1] = t[ii+1];
784     x[ir+2] = t[ii+2];
785     x[ir+3] = t[ii+3];
786     ii += 4;
787   }
788 
789   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
790   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
791   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
792   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
793   ierr = PetscLogFlops(2.0*16*(a->nz) - 4.0*A->cmap->n);CHKERRQ(ierr);
794   PetscFunctionReturn(0);
795 }
796 
797 #undef __FUNCT__
798 #define __FUNCT__ "MatSolveTranspose_SeqBAIJ_5"
799 PetscErrorCode MatSolveTranspose_SeqBAIJ_5(Mat A,Vec bb,Vec xx)
800 {
801   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ *)A->data;
802   IS             iscol=a->col,isrow=a->row;
803   PetscErrorCode ierr;
804   const PetscInt *r,*c,*rout,*cout;
805   PetscInt       i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt;
806   PetscInt       *diag = a->diag,ii,ic,ir,oidx;
807   MatScalar      *aa=a->a,*v;
808   PetscScalar    s1,s2,s3,s4,s5,x1,x2,x3,x4,x5;
809   PetscScalar    *x,*b,*t;
810 
811   PetscFunctionBegin;
812   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
813   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
814   t  = a->solve_work;
815 
816   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
817   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
818 
819   /* copy the b into temp work space according to permutation */
820   ii = 0;
821   for (i=0; i<n; i++) {
822     ic      = 5*c[i];
823     t[ii]   = b[ic];
824     t[ii+1] = b[ic+1];
825     t[ii+2] = b[ic+2];
826     t[ii+3] = b[ic+3];
827     t[ii+4] = b[ic+4];
828     ii += 5;
829   }
830 
831   /* forward solve the U^T */
832   idx = 0;
833   for (i=0; i<n; i++) {
834 
835     v     = aa + 25*diag[i];
836     /* multiply by the inverse of the block diagonal */
837     x1    = t[idx];   x2 = t[1+idx]; x3    = t[2+idx]; x4 = t[3+idx]; x5 = t[4+idx];
838     s1 = v[0]*x1  +  v[1]*x2 +  v[2]*x3 +  v[3]*x4 +  v[4]*x5;
839     s2 = v[5]*x1  +  v[6]*x2 +  v[7]*x3 +  v[8]*x4 +  v[9]*x5;
840     s3 = v[10]*x1 + v[11]*x2 + v[12]*x3 + v[13]*x4 + v[14]*x5;
841     s4 = v[15]*x1 + v[16]*x2 + v[17]*x3 + v[18]*x4 + v[19]*x5;
842     s5 = v[20]*x1 + v[21]*x2 + v[22]*x3 + v[23]*x4 + v[24]*x5;
843     v += 25;
844 
845     vi    = aj + diag[i] + 1;
846     nz    = ai[i+1] - diag[i] - 1;
847     while (nz--) {
848       oidx = 5*(*vi++);
849       t[oidx]   -= v[0]*s1  +  v[1]*s2 +  v[2]*s3 +  v[3]*s4 +  v[4]*s5;
850       t[oidx+1] -= v[5]*s1  +  v[6]*s2 +  v[7]*s3 +  v[8]*s4 +  v[9]*s5;
851       t[oidx+2] -= v[10]*s1 + v[11]*s2 + v[12]*s3 + v[13]*s4 + v[14]*s5;
852       t[oidx+3] -= v[15]*s1 + v[16]*s2 + v[17]*s3 + v[18]*s4 + v[19]*s5;
853       t[oidx+4] -= v[20]*s1 + v[21]*s2 + v[22]*s3 + v[23]*s4 + v[24]*s5;
854       v  += 25;
855     }
856     t[idx]   = s1;t[1+idx] = s2; t[2+idx] = s3;t[3+idx] = s4; t[4+idx] = s5;
857     idx += 5;
858   }
859   /* backward solve the L^T */
860   for (i=n-1; i>=0; i--){
861     v    = aa + 25*diag[i] - 25;
862     vi   = aj + diag[i] - 1;
863     nz   = diag[i] - ai[i];
864     idt  = 5*i;
865     s1 = t[idt];  s2 = t[1+idt]; s3 = t[2+idt];s4 = t[3+idt]; s5 = t[4+idt];
866     while (nz--) {
867       idx   = 5*(*vi--);
868       t[idx]   -=  v[0]*s1 +  v[1]*s2 +  v[2]*s3 +  v[3]*s4 +  v[4]*s5;
869       t[idx+1] -=  v[5]*s1 +  v[6]*s2 +  v[7]*s3 +  v[8]*s4 +  v[9]*s5;
870       t[idx+2] -= v[10]*s1 + v[11]*s2 + v[12]*s3 + v[13]*s4 + v[14]*s5;
871       t[idx+3] -= v[15]*s1 + v[16]*s2 + v[17]*s3 + v[18]*s4 + v[19]*s5;
872       t[idx+4] -= v[20]*s1 + v[21]*s2 + v[22]*s3 + v[23]*s4 + v[24]*s5;
873       v -= 25;
874     }
875   }
876 
877   /* copy t into x according to permutation */
878   ii = 0;
879   for (i=0; i<n; i++) {
880     ir      = 5*r[i];
881     x[ir]   = t[ii];
882     x[ir+1] = t[ii+1];
883     x[ir+2] = t[ii+2];
884     x[ir+3] = t[ii+3];
885     x[ir+4] = t[ii+4];
886     ii += 5;
887   }
888 
889   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
890   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
891   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
892   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
893   ierr = PetscLogFlops(2.0*25*(a->nz) - 5.0*A->cmap->n);CHKERRQ(ierr);
894   PetscFunctionReturn(0);
895 }
896 
897 #undef __FUNCT__
898 #define __FUNCT__ "MatSolveTranspose_SeqBAIJ_6"
899 PetscErrorCode MatSolveTranspose_SeqBAIJ_6(Mat A,Vec bb,Vec xx)
900 {
901   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ *)A->data;
902   IS             iscol=a->col,isrow=a->row;
903   PetscErrorCode ierr;
904   const PetscInt *r,*c,*rout,*cout;
905   PetscInt       i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt;
906   PetscInt       *diag = a->diag,ii,ic,ir,oidx;
907   MatScalar      *aa=a->a,*v;
908   PetscScalar    s1,s2,s3,s4,s5,s6,x1,x2,x3,x4,x5,x6;
909   PetscScalar    *x,*b,*t;
910 
911   PetscFunctionBegin;
912   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
913   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
914   t  = a->solve_work;
915 
916   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
917   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
918 
919   /* copy the b into temp work space according to permutation */
920   ii = 0;
921   for (i=0; i<n; i++) {
922     ic      = 6*c[i];
923     t[ii]   = b[ic];
924     t[ii+1] = b[ic+1];
925     t[ii+2] = b[ic+2];
926     t[ii+3] = b[ic+3];
927     t[ii+4] = b[ic+4];
928     t[ii+5] = b[ic+5];
929     ii += 6;
930   }
931 
932   /* forward solve the U^T */
933   idx = 0;
934   for (i=0; i<n; i++) {
935 
936     v     = aa + 36*diag[i];
937     /* multiply by the inverse of the block diagonal */
938     x1    = t[idx];   x2 = t[1+idx]; x3    = t[2+idx]; x4 = t[3+idx]; x5 = t[4+idx];
939     x6    = t[5+idx];
940     s1 = v[0]*x1  +  v[1]*x2 +  v[2]*x3 +  v[3]*x4 +  v[4]*x5 +  v[5]*x6;
941     s2 = v[6]*x1  +  v[7]*x2 +  v[8]*x3 +  v[9]*x4 + v[10]*x5 + v[11]*x6;
942     s3 = v[12]*x1 + v[13]*x2 + v[14]*x3 + v[15]*x4 + v[16]*x5 + v[17]*x6;
943     s4 = v[18]*x1 + v[19]*x2 + v[20]*x3 + v[21]*x4 + v[22]*x5 + v[23]*x6;
944     s5 = v[24]*x1 + v[25]*x2 + v[26]*x3 + v[27]*x4 + v[28]*x5 + v[29]*x6;
945     s6 = v[30]*x1 + v[31]*x2 + v[32]*x3 + v[33]*x4 + v[34]*x5 + v[35]*x6;
946     v += 36;
947 
948     vi    = aj + diag[i] + 1;
949     nz    = ai[i+1] - diag[i] - 1;
950     while (nz--) {
951       oidx = 6*(*vi++);
952       t[oidx]   -= v[0]*s1  +  v[1]*s2 +  v[2]*s3 +  v[3]*s4 +  v[4]*s5 +  v[5]*s6;
953       t[oidx+1] -= v[6]*s1  +  v[7]*s2 +  v[8]*s3 +  v[9]*s4 + v[10]*s5 + v[11]*s6;
954       t[oidx+2] -= v[12]*s1 + v[13]*s2 + v[14]*s3 + v[15]*s4 + v[16]*s5 + v[17]*s6;
955       t[oidx+3] -= v[18]*s1 + v[19]*s2 + v[20]*s3 + v[21]*s4 + v[22]*s5 + v[23]*s6;
956       t[oidx+4] -= v[24]*s1 + v[25]*s2 + v[26]*s3 + v[27]*s4 + v[28]*s5 + v[29]*s6;
957       t[oidx+5] -= v[30]*s1 + v[31]*s2 + v[32]*s3 + v[33]*s4 + v[34]*s5 + v[35]*s6;
958       v  += 36;
959     }
960     t[idx]   = s1;t[1+idx] = s2; t[2+idx] = s3;t[3+idx] = s4; t[4+idx] = s5;
961     t[5+idx] = s6;
962     idx += 6;
963   }
964   /* backward solve the L^T */
965   for (i=n-1; i>=0; i--){
966     v    = aa + 36*diag[i] - 36;
967     vi   = aj + diag[i] - 1;
968     nz   = diag[i] - ai[i];
969     idt  = 6*i;
970     s1 = t[idt];  s2 = t[1+idt]; s3 = t[2+idt];s4 = t[3+idt]; s5 = t[4+idt];
971     s6 = t[5+idt];
972     while (nz--) {
973       idx   = 6*(*vi--);
974       t[idx]   -=  v[0]*s1 +  v[1]*s2 +  v[2]*s3 +  v[3]*s4 +  v[4]*s5 +  v[5]*s6;
975       t[idx+1] -=  v[6]*s1 +  v[7]*s2 +  v[8]*s3 +  v[9]*s4 + v[10]*s5 + v[11]*s6;
976       t[idx+2] -= v[12]*s1 + v[13]*s2 + v[14]*s3 + v[15]*s4 + v[16]*s5 + v[17]*s6;
977       t[idx+3] -= v[18]*s1 + v[19]*s2 + v[20]*s3 + v[21]*s4 + v[22]*s5 + v[23]*s6;
978       t[idx+4] -= v[24]*s1 + v[25]*s2 + v[26]*s3 + v[27]*s4 + v[28]*s5 + v[29]*s6;
979       t[idx+5] -= v[30]*s1 + v[31]*s2 + v[32]*s3 + v[33]*s4 + v[34]*s5 + v[35]*s6;
980       v -= 36;
981     }
982   }
983 
984   /* copy t into x according to permutation */
985   ii = 0;
986   for (i=0; i<n; i++) {
987     ir      = 6*r[i];
988     x[ir]   = t[ii];
989     x[ir+1] = t[ii+1];
990     x[ir+2] = t[ii+2];
991     x[ir+3] = t[ii+3];
992     x[ir+4] = t[ii+4];
993     x[ir+5] = t[ii+5];
994     ii += 6;
995   }
996 
997   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
998   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
999   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
1000   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1001   ierr = PetscLogFlops(2.0*36*(a->nz) - 6.0*A->cmap->n);CHKERRQ(ierr);
1002   PetscFunctionReturn(0);
1003 }
1004 
1005 #undef __FUNCT__
1006 #define __FUNCT__ "MatSolveTranspose_SeqBAIJ_7"
1007 PetscErrorCode MatSolveTranspose_SeqBAIJ_7(Mat A,Vec bb,Vec xx)
1008 {
1009   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ *)A->data;
1010   IS             iscol=a->col,isrow=a->row;
1011   PetscErrorCode ierr;
1012   const PetscInt *r,*c,*rout,*cout;
1013   PetscInt       i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt;
1014   PetscInt       *diag = a->diag,ii,ic,ir,oidx;
1015   MatScalar      *aa=a->a,*v;
1016   PetscScalar    s1,s2,s3,s4,s5,s6,s7,x1,x2,x3,x4,x5,x6,x7;
1017   PetscScalar    *x,*b,*t;
1018 
1019   PetscFunctionBegin;
1020   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
1021   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1022   t  = a->solve_work;
1023 
1024   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1025   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1026 
1027   /* copy the b into temp work space according to permutation */
1028   ii = 0;
1029   for (i=0; i<n; i++) {
1030     ic      = 7*c[i];
1031     t[ii]   = b[ic];
1032     t[ii+1] = b[ic+1];
1033     t[ii+2] = b[ic+2];
1034     t[ii+3] = b[ic+3];
1035     t[ii+4] = b[ic+4];
1036     t[ii+5] = b[ic+5];
1037     t[ii+6] = b[ic+6];
1038     ii += 7;
1039   }
1040 
1041   /* forward solve the U^T */
1042   idx = 0;
1043   for (i=0; i<n; i++) {
1044 
1045     v     = aa + 49*diag[i];
1046     /* multiply by the inverse of the block diagonal */
1047     x1    = t[idx];   x2 = t[1+idx]; x3    = t[2+idx]; x4 = t[3+idx]; x5 = t[4+idx];
1048     x6    = t[5+idx]; x7 = t[6+idx];
1049     s1 = v[0]*x1  +  v[1]*x2 +  v[2]*x3 +  v[3]*x4 +  v[4]*x5 +  v[5]*x6 +  v[6]*x7;
1050     s2 = v[7]*x1  +  v[8]*x2 +  v[9]*x3 + v[10]*x4 + v[11]*x5 + v[12]*x6 + v[13]*x7;
1051     s3 = v[14]*x1 + v[15]*x2 + v[16]*x3 + v[17]*x4 + v[18]*x5 + v[19]*x6 + v[20]*x7;
1052     s4 = v[21]*x1 + v[22]*x2 + v[23]*x3 + v[24]*x4 + v[25]*x5 + v[26]*x6 + v[27]*x7;
1053     s5 = v[28]*x1 + v[29]*x2 + v[30]*x3 + v[31]*x4 + v[32]*x5 + v[33]*x6 + v[34]*x7;
1054     s6 = v[35]*x1 + v[36]*x2 + v[37]*x3 + v[38]*x4 + v[39]*x5 + v[40]*x6 + v[41]*x7;
1055     s7 = v[42]*x1 + v[43]*x2 + v[44]*x3 + v[45]*x4 + v[46]*x5 + v[47]*x6 + v[48]*x7;
1056     v += 49;
1057 
1058     vi    = aj + diag[i] + 1;
1059     nz    = ai[i+1] - diag[i] - 1;
1060     while (nz--) {
1061       oidx = 7*(*vi++);
1062       t[oidx]   -= v[0]*s1  +  v[1]*s2 +  v[2]*s3 +  v[3]*s4 +  v[4]*s5 +  v[5]*s6 +  v[6]*s7;
1063       t[oidx+1] -= v[7]*s1  +  v[8]*s2 +  v[9]*s3 + v[10]*s4 + v[11]*s5 + v[12]*s6 + v[13]*s7;
1064       t[oidx+2] -= v[14]*s1 + v[15]*s2 + v[16]*s3 + v[17]*s4 + v[18]*s5 + v[19]*s6 + v[20]*s7;
1065       t[oidx+3] -= v[21]*s1 + v[22]*s2 + v[23]*s3 + v[24]*s4 + v[25]*s5 + v[26]*s6 + v[27]*s7;
1066       t[oidx+4] -= v[28]*s1 + v[29]*s2 + v[30]*s3 + v[31]*s4 + v[32]*s5 + v[33]*s6 + v[34]*s7;
1067       t[oidx+5] -= v[35]*s1 + v[36]*s2 + v[37]*s3 + v[38]*s4 + v[39]*s5 + v[40]*s6 + v[41]*s7;
1068       t[oidx+6] -= v[42]*s1 + v[43]*s2 + v[44]*s3 + v[45]*s4 + v[46]*s5 + v[47]*s6 + v[48]*s7;
1069       v  += 49;
1070     }
1071     t[idx]   = s1;t[1+idx] = s2; t[2+idx] = s3;t[3+idx] = s4; t[4+idx] = s5;
1072     t[5+idx] = s6;t[6+idx] = s7;
1073     idx += 7;
1074   }
1075   /* backward solve the L^T */
1076   for (i=n-1; i>=0; i--){
1077     v    = aa + 49*diag[i] - 49;
1078     vi   = aj + diag[i] - 1;
1079     nz   = diag[i] - ai[i];
1080     idt  = 7*i;
1081     s1 = t[idt];  s2 = t[1+idt]; s3 = t[2+idt];s4 = t[3+idt]; s5 = t[4+idt];
1082     s6 = t[5+idt];s7 = t[6+idt];
1083     while (nz--) {
1084       idx   = 7*(*vi--);
1085       t[idx]   -=  v[0]*s1 +  v[1]*s2 +  v[2]*s3 +  v[3]*s4 +  v[4]*s5 +  v[5]*s6 +  v[6]*s7;
1086       t[idx+1] -=  v[7]*s1 +  v[8]*s2 +  v[9]*s3 + v[10]*s4 + v[11]*s5 + v[12]*s6 + v[13]*s7;
1087       t[idx+2] -= v[14]*s1 + v[15]*s2 + v[16]*s3 + v[17]*s4 + v[18]*s5 + v[19]*s6 + v[20]*s7;
1088       t[idx+3] -= v[21]*s1 + v[22]*s2 + v[23]*s3 + v[24]*s4 + v[25]*s5 + v[26]*s6 + v[27]*s7;
1089       t[idx+4] -= v[28]*s1 + v[29]*s2 + v[30]*s3 + v[31]*s4 + v[32]*s5 + v[33]*s6 + v[34]*s7;
1090       t[idx+5] -= v[35]*s1 + v[36]*s2 + v[37]*s3 + v[38]*s4 + v[39]*s5 + v[40]*s6 + v[41]*s7;
1091       t[idx+6] -= v[42]*s1 + v[43]*s2 + v[44]*s3 + v[45]*s4 + v[46]*s5 + v[47]*s6 + v[48]*s7;
1092       v -= 49;
1093     }
1094   }
1095 
1096   /* copy t into x according to permutation */
1097   ii = 0;
1098   for (i=0; i<n; i++) {
1099     ir      = 7*r[i];
1100     x[ir]   = t[ii];
1101     x[ir+1] = t[ii+1];
1102     x[ir+2] = t[ii+2];
1103     x[ir+3] = t[ii+3];
1104     x[ir+4] = t[ii+4];
1105     x[ir+5] = t[ii+5];
1106     x[ir+6] = t[ii+6];
1107     ii += 7;
1108   }
1109 
1110   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1111   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1112   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
1113   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1114   ierr = PetscLogFlops(2.0*49*(a->nz) - 7.0*A->cmap->n);CHKERRQ(ierr);
1115   PetscFunctionReturn(0);
1116 }
1117 
1118 /* ----------------------------------------------------------- */
1119 #undef __FUNCT__
1120 #define __FUNCT__ "MatSolve_SeqBAIJ_N"
1121 PetscErrorCode MatSolve_SeqBAIJ_N(Mat A,Vec bb,Vec xx)
1122 {
1123   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ *)A->data;
1124   IS             iscol=a->col,isrow=a->row;
1125   PetscErrorCode ierr;
1126   const PetscInt *r,*c,*rout,*cout,*ai=a->i,*aj=a->j,*vi;
1127   PetscInt       i,n=a->mbs;
1128   PetscInt       nz,bs=A->rmap->bs,bs2=a->bs2;
1129   MatScalar      *aa=a->a,*v;
1130   PetscScalar    *x,*b,*s,*t,*ls;
1131 
1132   PetscFunctionBegin;
1133   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
1134   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1135   t  = a->solve_work;
1136 
1137   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1138   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1139 
1140   /* forward solve the lower triangular */
1141   ierr = PetscMemcpy(t,b+bs*(*r++),bs*sizeof(PetscScalar));CHKERRQ(ierr);
1142   for (i=1; i<n; i++) {
1143     v   = aa + bs2*ai[i];
1144     vi  = aj + ai[i];
1145     nz  = a->diag[i] - ai[i];
1146     s = t + bs*i;
1147     ierr = PetscMemcpy(s,b+bs*(*r++),bs*sizeof(PetscScalar));CHKERRQ(ierr);
1148     while (nz--) {
1149       Kernel_v_gets_v_minus_A_times_w(bs,s,v,t+bs*(*vi++));
1150       v += bs2;
1151     }
1152   }
1153   /* backward solve the upper triangular */
1154   ls = a->solve_work + A->cmap->n;
1155   for (i=n-1; i>=0; i--){
1156     v   = aa + bs2*(a->diag[i] + 1);
1157     vi  = aj + a->diag[i] + 1;
1158     nz  = ai[i+1] - a->diag[i] - 1;
1159     ierr = PetscMemcpy(ls,t+i*bs,bs*sizeof(PetscScalar));CHKERRQ(ierr);
1160     while (nz--) {
1161       Kernel_v_gets_v_minus_A_times_w(bs,ls,v,t+bs*(*vi++));
1162       v += bs2;
1163     }
1164     Kernel_w_gets_A_times_v(bs,ls,aa+bs2*a->diag[i],t+i*bs);
1165     ierr = PetscMemcpy(x + bs*(*c--),t+i*bs,bs*sizeof(PetscScalar));CHKERRQ(ierr);
1166   }
1167 
1168   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1169   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1170   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
1171   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1172   ierr = PetscLogFlops(2.0*(a->bs2)*(a->nz) - A->rmap->bs*A->cmap->n);CHKERRQ(ierr);
1173   PetscFunctionReturn(0);
1174 }
1175 
1176 #undef __FUNCT__
1177 #define __FUNCT__ "MatSolve_SeqBAIJ_7"
1178 PetscErrorCode MatSolve_SeqBAIJ_7(Mat A,Vec bb,Vec xx)
1179 {
1180   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ *)A->data;
1181   IS             iscol=a->col,isrow=a->row;
1182   PetscErrorCode ierr;
1183   const PetscInt *r,*c,*ai=a->i,*aj=a->j,*rout,*cout,*diag = a->diag,*vi;
1184   PetscInt       i,n=a->mbs,nz,idx,idt,idc;
1185   MatScalar      *aa=a->a,*v;
1186   PetscScalar    s1,s2,s3,s4,s5,s6,s7,x1,x2,x3,x4,x5,x6,x7;
1187   PetscScalar    *x,*b,*t;
1188 
1189   PetscFunctionBegin;
1190   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
1191   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1192   t  = a->solve_work;
1193 
1194   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1195   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1196 
1197   /* forward solve the lower triangular */
1198   idx    = 7*(*r++);
1199   t[0] = b[idx];   t[1] = b[1+idx];
1200   t[2] = b[2+idx]; t[3] = b[3+idx]; t[4] = b[4+idx];
1201   t[5] = b[5+idx]; t[6] = b[6+idx];
1202 
1203   for (i=1; i<n; i++) {
1204     v     = aa + 49*ai[i];
1205     vi    = aj + ai[i];
1206     nz    = diag[i] - ai[i];
1207     idx   = 7*(*r++);
1208     s1  = b[idx];s2 = b[1+idx];s3 = b[2+idx];s4 = b[3+idx];
1209     s5  = b[4+idx];s6 = b[5+idx];s7 = b[6+idx];
1210     while (nz--) {
1211       idx   = 7*(*vi++);
1212       x1    = t[idx];  x2 = t[1+idx];x3 = t[2+idx];
1213       x4    = t[3+idx];x5 = t[4+idx];
1214       x6    = t[5+idx];x7 = t[6+idx];
1215       s1 -= v[0]*x1 + v[7]*x2  + v[14]*x3 + v[21]*x4 + v[28]*x5 + v[35]*x6 + v[42]*x7;
1216       s2 -= v[1]*x1 + v[8]*x2  + v[15]*x3 + v[22]*x4 + v[29]*x5 + v[36]*x6 + v[43]*x7;
1217       s3 -= v[2]*x1 + v[9]*x2  + v[16]*x3 + v[23]*x4 + v[30]*x5 + v[37]*x6 + v[44]*x7;
1218       s4 -= v[3]*x1 + v[10]*x2 + v[17]*x3 + v[24]*x4 + v[31]*x5 + v[38]*x6 + v[45]*x7;
1219       s5 -= v[4]*x1 + v[11]*x2 + v[18]*x3 + v[25]*x4 + v[32]*x5 + v[39]*x6 + v[46]*x7;
1220       s6 -= v[5]*x1 + v[12]*x2 + v[19]*x3 + v[26]*x4 + v[33]*x5 + v[40]*x6 + v[47]*x7;
1221       s7 -= v[6]*x1 + v[13]*x2 + v[20]*x3 + v[27]*x4 + v[34]*x5 + v[41]*x6 + v[48]*x7;
1222       v += 49;
1223     }
1224     idx = 7*i;
1225     t[idx]   = s1;t[1+idx] = s2;
1226     t[2+idx] = s3;t[3+idx] = s4; t[4+idx] = s5;
1227     t[5+idx] = s6;t[6+idx] = s7;
1228   }
1229   /* backward solve the upper triangular */
1230   for (i=n-1; i>=0; i--){
1231     v    = aa + 49*diag[i] + 49;
1232     vi   = aj + diag[i] + 1;
1233     nz   = ai[i+1] - diag[i] - 1;
1234     idt  = 7*i;
1235     s1 = t[idt];  s2 = t[1+idt];
1236     s3 = t[2+idt];s4 = t[3+idt]; s5 = t[4+idt];
1237     s6 = t[5+idt];s7 = t[6+idt];
1238     while (nz--) {
1239       idx   = 7*(*vi++);
1240       x1    = t[idx];   x2 = t[1+idx];
1241       x3    = t[2+idx]; x4 = t[3+idx]; x5 = t[4+idx];
1242       x6    = t[5+idx]; x7 = t[6+idx];
1243       s1 -= v[0]*x1 + v[7]*x2  + v[14]*x3 + v[21]*x4 + v[28]*x5 + v[35]*x6 + v[42]*x7;
1244       s2 -= v[1]*x1 + v[8]*x2  + v[15]*x3 + v[22]*x4 + v[29]*x5 + v[36]*x6 + v[43]*x7;
1245       s3 -= v[2]*x1 + v[9]*x2  + v[16]*x3 + v[23]*x4 + v[30]*x5 + v[37]*x6 + v[44]*x7;
1246       s4 -= v[3]*x1 + v[10]*x2 + v[17]*x3 + v[24]*x4 + v[31]*x5 + v[38]*x6 + v[45]*x7;
1247       s5 -= v[4]*x1 + v[11]*x2 + v[18]*x3 + v[25]*x4 + v[32]*x5 + v[39]*x6 + v[46]*x7;
1248       s6 -= v[5]*x1 + v[12]*x2 + v[19]*x3 + v[26]*x4 + v[33]*x5 + v[40]*x6 + v[47]*x7;
1249       s7 -= v[6]*x1 + v[13]*x2 + v[20]*x3 + v[27]*x4 + v[34]*x5 + v[41]*x6 + v[48]*x7;
1250       v += 49;
1251     }
1252     idc = 7*(*c--);
1253     v   = aa + 49*diag[i];
1254     x[idc]   = t[idt]   = v[0]*s1+v[7]*s2+v[14]*s3+
1255                                  v[21]*s4+v[28]*s5+v[35]*s6+v[42]*s7;
1256     x[1+idc] = t[1+idt] = v[1]*s1+v[8]*s2+v[15]*s3+
1257                                  v[22]*s4+v[29]*s5+v[36]*s6+v[43]*s7;
1258     x[2+idc] = t[2+idt] = v[2]*s1+v[9]*s2+v[16]*s3+
1259                                  v[23]*s4+v[30]*s5+v[37]*s6+v[44]*s7;
1260     x[3+idc] = t[3+idt] = v[3]*s1+v[10]*s2+v[17]*s3+
1261                                  v[24]*s4+v[31]*s5+v[38]*s6+v[45]*s7;
1262     x[4+idc] = t[4+idt] = v[4]*s1+v[11]*s2+v[18]*s3+
1263                                  v[25]*s4+v[32]*s5+v[39]*s6+v[46]*s7;
1264     x[5+idc] = t[5+idt] = v[5]*s1+v[12]*s2+v[19]*s3+
1265                                  v[26]*s4+v[33]*s5+v[40]*s6+v[47]*s7;
1266     x[6+idc] = t[6+idt] = v[6]*s1+v[13]*s2+v[20]*s3+
1267                                  v[27]*s4+v[34]*s5+v[41]*s6+v[48]*s7;
1268   }
1269 
1270   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1271   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1272   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
1273   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1274   ierr = PetscLogFlops(2.0*49*(a->nz) - 7.0*A->cmap->n);CHKERRQ(ierr);
1275   PetscFunctionReturn(0);
1276 }
1277 
1278 #undef __FUNCT__
1279 #define __FUNCT__ "MatSolve_SeqBAIJ_7_newdatastruct"
1280 PetscErrorCode MatSolve_SeqBAIJ_7_newdatastruct(Mat A,Vec bb,Vec xx)
1281 {
1282   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ *)A->data;
1283   IS             iscol=a->col,isrow=a->row;
1284   PetscErrorCode ierr;
1285   const PetscInt *r,*c,*ai=a->i,*aj=a->j,*rout,*cout,*vi;
1286   PetscInt       i,n=a->mbs,nz,idx,idt,idc,k,m;
1287   MatScalar      *aa=a->a,*v;
1288   PetscScalar    s1,s2,s3,s4,s5,s6,s7,x1,x2,x3,x4,x5,x6,x7;
1289   PetscScalar    *x,*b,*t;
1290 
1291   PetscFunctionBegin;
1292   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
1293   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1294   t  = a->solve_work;
1295 
1296   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1297   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1298 
1299   /* forward solve the lower triangular */
1300   idx    = 7*r[0];
1301   t[0] = b[idx];   t[1] = b[1+idx];
1302   t[2] = b[2+idx]; t[3] = b[3+idx]; t[4] = b[4+idx];
1303   t[5] = b[5+idx]; t[6] = b[6+idx];
1304 
1305   for (i=1; i<n; i++) {
1306     v     = aa + 49*ai[i];
1307     vi    = aj + ai[i];
1308     nz    = ai[i+1] - ai[i];
1309     idx   = 7*r[i];
1310     s1  = b[idx];s2 = b[1+idx];s3 = b[2+idx];s4 = b[3+idx];
1311     s5  = b[4+idx];s6 = b[5+idx];s7 = b[6+idx];
1312     for(m=0;m<nz;m++){
1313       idx   = 7*vi[m];
1314       x1    = t[idx];  x2 = t[1+idx];x3 = t[2+idx];
1315       x4    = t[3+idx];x5 = t[4+idx];
1316       x6    = t[5+idx];x7 = t[6+idx];
1317       s1 -= v[0]*x1 + v[7]*x2  + v[14]*x3 + v[21]*x4 + v[28]*x5 + v[35]*x6 + v[42]*x7;
1318       s2 -= v[1]*x1 + v[8]*x2  + v[15]*x3 + v[22]*x4 + v[29]*x5 + v[36]*x6 + v[43]*x7;
1319       s3 -= v[2]*x1 + v[9]*x2  + v[16]*x3 + v[23]*x4 + v[30]*x5 + v[37]*x6 + v[44]*x7;
1320       s4 -= v[3]*x1 + v[10]*x2 + v[17]*x3 + v[24]*x4 + v[31]*x5 + v[38]*x6 + v[45]*x7;
1321       s5 -= v[4]*x1 + v[11]*x2 + v[18]*x3 + v[25]*x4 + v[32]*x5 + v[39]*x6 + v[46]*x7;
1322       s6 -= v[5]*x1 + v[12]*x2 + v[19]*x3 + v[26]*x4 + v[33]*x5 + v[40]*x6 + v[47]*x7;
1323       s7 -= v[6]*x1 + v[13]*x2 + v[20]*x3 + v[27]*x4 + v[34]*x5 + v[41]*x6 + v[48]*x7;
1324       v += 49;
1325     }
1326     idx = 7*i;
1327     t[idx]   = s1;t[1+idx] = s2;
1328     t[2+idx] = s3;t[3+idx] = s4; t[4+idx] = s5;
1329     t[5+idx] = s6;t[6+idx] = s7;
1330   }
1331   /* backward solve the upper triangular */
1332   for (i=n-1; i>=0; i--){
1333     k    = 2*n-i;
1334     v    = aa + 49*ai[k];
1335     vi   = aj + ai[k];
1336     nz   = ai[k+1] - ai[k] - 1;
1337     idt  = 7*i;
1338     s1 = t[idt];  s2 = t[1+idt];
1339     s3 = t[2+idt];s4 = t[3+idt]; s5 = t[4+idt];
1340     s6 = t[5+idt];s7 = t[6+idt];
1341     for(m=0;m<nz;m++){
1342       idx   = 7*vi[m];
1343       x1    = t[idx];   x2 = t[1+idx];
1344       x3    = t[2+idx]; x4 = t[3+idx]; x5 = t[4+idx];
1345       x6    = t[5+idx]; x7 = t[6+idx];
1346       s1 -= v[0]*x1 + v[7]*x2  + v[14]*x3 + v[21]*x4 + v[28]*x5 + v[35]*x6 + v[42]*x7;
1347       s2 -= v[1]*x1 + v[8]*x2  + v[15]*x3 + v[22]*x4 + v[29]*x5 + v[36]*x6 + v[43]*x7;
1348       s3 -= v[2]*x1 + v[9]*x2  + v[16]*x3 + v[23]*x4 + v[30]*x5 + v[37]*x6 + v[44]*x7;
1349       s4 -= v[3]*x1 + v[10]*x2 + v[17]*x3 + v[24]*x4 + v[31]*x5 + v[38]*x6 + v[45]*x7;
1350       s5 -= v[4]*x1 + v[11]*x2 + v[18]*x3 + v[25]*x4 + v[32]*x5 + v[39]*x6 + v[46]*x7;
1351       s6 -= v[5]*x1 + v[12]*x2 + v[19]*x3 + v[26]*x4 + v[33]*x5 + v[40]*x6 + v[47]*x7;
1352       s7 -= v[6]*x1 + v[13]*x2 + v[20]*x3 + v[27]*x4 + v[34]*x5 + v[41]*x6 + v[48]*x7;
1353       v += 49;
1354     }
1355     idc = 7*c[i];
1356     x[idc]   = t[idt]   = v[0]*s1+v[7]*s2+v[14]*s3+
1357                                  v[21]*s4+v[28]*s5+v[35]*s6+v[42]*s7;
1358     x[1+idc] = t[1+idt] = v[1]*s1+v[8]*s2+v[15]*s3+
1359                                  v[22]*s4+v[29]*s5+v[36]*s6+v[43]*s7;
1360     x[2+idc] = t[2+idt] = v[2]*s1+v[9]*s2+v[16]*s3+
1361                                  v[23]*s4+v[30]*s5+v[37]*s6+v[44]*s7;
1362     x[3+idc] = t[3+idt] = v[3]*s1+v[10]*s2+v[17]*s3+
1363                                  v[24]*s4+v[31]*s5+v[38]*s6+v[45]*s7;
1364     x[4+idc] = t[4+idt] = v[4]*s1+v[11]*s2+v[18]*s3+
1365                                  v[25]*s4+v[32]*s5+v[39]*s6+v[46]*s7;
1366     x[5+idc] = t[5+idt] = v[5]*s1+v[12]*s2+v[19]*s3+
1367                                  v[26]*s4+v[33]*s5+v[40]*s6+v[47]*s7;
1368     x[6+idc] = t[6+idt] = v[6]*s1+v[13]*s2+v[20]*s3+
1369                                  v[27]*s4+v[34]*s5+v[41]*s6+v[48]*s7;
1370   }
1371 
1372   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1373   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1374   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
1375   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1376   ierr = PetscLogFlops(2.0*49*(a->nz) - 7.0*A->cmap->n);CHKERRQ(ierr);
1377   PetscFunctionReturn(0);
1378 }
1379 
1380 #undef __FUNCT__
1381 #define __FUNCT__ "MatSolve_SeqBAIJ_7_NaturalOrdering"
1382 PetscErrorCode MatSolve_SeqBAIJ_7_NaturalOrdering(Mat A,Vec bb,Vec xx)
1383 {
1384   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ *)A->data;
1385   PetscInt          i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt;
1386   PetscErrorCode    ierr;
1387   PetscInt          *diag = a->diag,jdx;
1388   const MatScalar   *aa=a->a,*v;
1389   PetscScalar       *x,s1,s2,s3,s4,s5,s6,s7,x1,x2,x3,x4,x5,x6,x7;
1390   const PetscScalar *b;
1391 
1392   PetscFunctionBegin;
1393   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1394   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1395   /* forward solve the lower triangular */
1396   idx    = 0;
1397   x[0] = b[idx];   x[1] = b[1+idx]; x[2] = b[2+idx];
1398   x[3] = b[3+idx]; x[4] = b[4+idx]; x[5] = b[5+idx];
1399   x[6] = b[6+idx];
1400   for (i=1; i<n; i++) {
1401     v     =  aa + 49*ai[i];
1402     vi    =  aj + ai[i];
1403     nz    =  diag[i] - ai[i];
1404     idx   =  7*i;
1405     s1  =  b[idx];   s2 = b[1+idx]; s3 = b[2+idx];
1406     s4  =  b[3+idx]; s5 = b[4+idx]; s6 = b[5+idx];
1407     s7  =  b[6+idx];
1408     while (nz--) {
1409       jdx   = 7*(*vi++);
1410       x1    = x[jdx];   x2 = x[1+jdx]; x3 = x[2+jdx];
1411       x4    = x[3+jdx]; x5 = x[4+jdx]; x6 = x[5+jdx];
1412       x7    = x[6+jdx];
1413       s1 -= v[0]*x1 + v[7]*x2  + v[14]*x3 + v[21]*x4 + v[28]*x5 + v[35]*x6 + v[42]*x7;
1414       s2 -= v[1]*x1 + v[8]*x2  + v[15]*x3 + v[22]*x4 + v[29]*x5 + v[36]*x6 + v[43]*x7;
1415       s3 -= v[2]*x1 + v[9]*x2  + v[16]*x3 + v[23]*x4 + v[30]*x5 + v[37]*x6 + v[44]*x7;
1416       s4 -= v[3]*x1 + v[10]*x2 + v[17]*x3 + v[24]*x4 + v[31]*x5 + v[38]*x6 + v[45]*x7;
1417       s5 -= v[4]*x1 + v[11]*x2 + v[18]*x3 + v[25]*x4 + v[32]*x5 + v[39]*x6 + v[46]*x7;
1418       s6 -= v[5]*x1 + v[12]*x2 + v[19]*x3 + v[26]*x4 + v[33]*x5 + v[40]*x6 + v[47]*x7;
1419       s7 -= v[6]*x1 + v[13]*x2 + v[20]*x3 + v[27]*x4 + v[34]*x5 + v[41]*x6 + v[48]*x7;
1420       v += 49;
1421      }
1422     x[idx]   = s1;
1423     x[1+idx] = s2;
1424     x[2+idx] = s3;
1425     x[3+idx] = s4;
1426     x[4+idx] = s5;
1427     x[5+idx] = s6;
1428     x[6+idx] = s7;
1429   }
1430   /* backward solve the upper triangular */
1431   for (i=n-1; i>=0; i--){
1432     v    = aa + 49*diag[i] + 49;
1433     vi   = aj + diag[i] + 1;
1434     nz   = ai[i+1] - diag[i] - 1;
1435     idt  = 7*i;
1436     s1 = x[idt];   s2 = x[1+idt];
1437     s3 = x[2+idt]; s4 = x[3+idt];
1438     s5 = x[4+idt]; s6 = x[5+idt];
1439     s7 = x[6+idt];
1440     while (nz--) {
1441       idx   = 7*(*vi++);
1442       x1    = x[idx];   x2 = x[1+idx]; x3 = x[2+idx];
1443       x4    = x[3+idx]; x5 = x[4+idx]; x6 = x[5+idx];
1444       x7    = x[6+idx];
1445       s1 -= v[0]*x1 + v[7]*x2  + v[14]*x3 + v[21]*x4 + v[28]*x5 + v[35]*x6 + v[42]*x7;
1446       s2 -= v[1]*x1 + v[8]*x2  + v[15]*x3 + v[22]*x4 + v[29]*x5 + v[36]*x6 + v[43]*x7;
1447       s3 -= v[2]*x1 + v[9]*x2  + v[16]*x3 + v[23]*x4 + v[30]*x5 + v[37]*x6 + v[44]*x7;
1448       s4 -= v[3]*x1 + v[10]*x2 + v[17]*x3 + v[24]*x4 + v[31]*x5 + v[38]*x6 + v[45]*x7;
1449       s5 -= v[4]*x1 + v[11]*x2 + v[18]*x3 + v[25]*x4 + v[32]*x5 + v[39]*x6 + v[46]*x7;
1450       s6 -= v[5]*x1 + v[12]*x2 + v[19]*x3 + v[26]*x4 + v[33]*x5 + v[40]*x6 + v[47]*x7;
1451       s7 -= v[6]*x1 + v[13]*x2 + v[20]*x3 + v[27]*x4 + v[34]*x5 + v[41]*x6 + v[48]*x7;
1452       v += 49;
1453     }
1454     v        = aa + 49*diag[i];
1455     x[idt]   = v[0]*s1 + v[7]*s2  + v[14]*s3 + v[21]*s4
1456                          + v[28]*s5 + v[35]*s6 + v[42]*s7;
1457     x[1+idt] = v[1]*s1 + v[8]*s2  + v[15]*s3 + v[22]*s4
1458                          + v[29]*s5 + v[36]*s6 + v[43]*s7;
1459     x[2+idt] = v[2]*s1 + v[9]*s2  + v[16]*s3 + v[23]*s4
1460                          + v[30]*s5 + v[37]*s6 + v[44]*s7;
1461     x[3+idt] = v[3]*s1 + v[10]*s2  + v[17]*s3 + v[24]*s4
1462                          + v[31]*s5 + v[38]*s6 + v[45]*s7;
1463     x[4+idt] = v[4]*s1 + v[11]*s2  + v[18]*s3 + v[25]*s4
1464                          + v[32]*s5 + v[39]*s6 + v[46]*s7;
1465     x[5+idt] = v[5]*s1 + v[12]*s2  + v[19]*s3 + v[26]*s4
1466                          + v[33]*s5 + v[40]*s6 + v[47]*s7;
1467     x[6+idt] = v[6]*s1 + v[13]*s2  + v[20]*s3 + v[27]*s4
1468                          + v[34]*s5 + v[41]*s6 + v[48]*s7;
1469   }
1470 
1471   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1472   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1473   ierr = PetscLogFlops(2.0*36*(a->nz) - 6.0*A->cmap->n);CHKERRQ(ierr);
1474   PetscFunctionReturn(0);
1475 }
1476 
1477 #undef __FUNCT__
1478 #define __FUNCT__ "MatSolve_SeqBAIJ_7_NaturalOrdering_newdatastruct"
1479 PetscErrorCode MatSolve_SeqBAIJ_7_NaturalOrdering_newdatastruct(Mat A,Vec bb,Vec xx)
1480 {
1481     Mat_SeqBAIJ       *a = (Mat_SeqBAIJ *)A->data;
1482     PetscInt          i,k,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz;
1483     PetscErrorCode    ierr;
1484     PetscInt          idx,jdx,idt;
1485     PetscInt          bs = A->rmap->bs,bs2 = a->bs2;
1486     const MatScalar   *aa=a->a,*v;
1487     PetscScalar       *x;
1488     const PetscScalar *b;
1489     PetscScalar        s1,s2,s3,s4,s5,s6,s7,x1,x2,x3,x4,x5,x6,x7;
1490 
1491     PetscFunctionBegin;
1492     ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1493     ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1494     /* forward solve the lower triangular */
1495     idx    = 0;
1496     x[0] = b[idx]; x[1] = b[1+idx];x[2] = b[2+idx];x[3] = b[3+idx];
1497     x[4] = b[4+idx];x[5] = b[5+idx];x[6] = b[6+idx];
1498     for (i=1; i<n; i++) {
1499        v    = aa + bs2*ai[i];
1500        vi   = aj + ai[i];
1501        nz   = ai[i+1] - ai[i];
1502       idx   = bs*i;
1503        s1   = b[idx];s2 = b[1+idx];s3 = b[2+idx];s4 = b[3+idx];
1504        s5   = b[4+idx];s6 = b[5+idx];s7 = b[6+idx];
1505        for(k=0;k<nz;k++) {
1506           jdx   = bs*vi[k];
1507           x1    = x[jdx];x2 = x[1+jdx]; x3 =x[2+jdx];x4 =x[3+jdx];
1508 	  x5    = x[4+jdx]; x6 = x[5+jdx];x7 = x[6+jdx];
1509           s1   -= v[0]*x1 + v[7]*x2 + v[14]*x3 + v[21]*x4  + v[28]*x5 + v[35]*x6 + v[42]*x7;
1510           s2   -= v[1]*x1 + v[8]*x2 + v[15]*x3 + v[22]*x4  + v[29]*x5 + v[36]*x6 + v[43]*x7;
1511           s3   -= v[2]*x1 + v[9]*x2 + v[16]*x3 + v[23]*x4  + v[30]*x5 + v[37]*x6 + v[44]*x7;
1512 	  s4   -= v[3]*x1 + v[10]*x2 + v[17]*x3 + v[24]*x4  + v[31]*x5 + v[38]*x6 + v[45]*x7;
1513           s5   -= v[4]*x1 + v[11]*x2 + v[18]*x3 + v[25]*x4  + v[32]*x5 + v[39]*x6 + v[46]*x7;
1514 	  s6   -= v[5]*x1 + v[12]*x2 + v[19]*x3 + v[26]*x4  + v[33]*x5 + v[40]*x6 + v[47]*x7;
1515 	  s7   -= v[6]*x1 + v[13]*x2 + v[20]*x3 + v[27]*x4  + v[34]*x5 + v[41]*x6 + v[48]*x7;
1516           v   +=  bs2;
1517         }
1518 
1519        x[idx]   = s1;
1520        x[1+idx] = s2;
1521        x[2+idx] = s3;
1522        x[3+idx] = s4;
1523        x[4+idx] = s5;
1524        x[5+idx] = s6;
1525        x[6+idx] = s7;
1526     }
1527 
1528    /* backward solve the upper triangular */
1529   for (i=n-1; i>=0; i--){
1530      v   = aa + bs2*ai[2*n-i];
1531      vi  = aj + ai[2*n-i];
1532      nz  = ai[2*n-i +1] - ai[2*n-i]-1;
1533      idt = bs*i;
1534      s1 = x[idt];  s2 = x[1+idt];s3 = x[2+idt];s4 = x[3+idt];
1535      s5 = x[4+idt];s6 = x[5+idt];s7 = x[6+idt];
1536     for(k=0;k<nz;k++) {
1537       idx   = bs*vi[k];
1538        x1    = x[idx];   x2 = x[1+idx]; x3 = x[2+idx];x4 = x[3+idx];
1539        x5    = x[4+idx];x6 = x[5+idx];x7 = x[6+idx];
1540        s1   -= v[0]*x1 + v[7]*x2 + v[14]*x3 + v[21]*x4  + v[28]*x5 + v[35]*x6 + v[42]*x7;
1541        s2   -= v[1]*x1 + v[8]*x2 + v[15]*x3 + v[22]*x4  + v[29]*x5 + v[36]*x6 + v[43]*x7;
1542        s3   -= v[2]*x1 + v[9]*x2 + v[16]*x3 + v[23]*x4  + v[30]*x5 + v[37]*x6 + v[44]*x7;
1543        s4   -= v[3]*x1 + v[10]*x2 + v[17]*x3 + v[24]*x4  + v[31]*x5 + v[38]*x6 + v[45]*x7;
1544        s5   -= v[4]*x1 + v[11]*x2 + v[18]*x3 + v[25]*x4  + v[32]*x5 + v[39]*x6 + v[46]*x7;
1545        s6   -= v[5]*x1 + v[12]*x2 + v[19]*x3 + v[26]*x4  + v[33]*x5 + v[40]*x6 + v[47]*x7;
1546        s7   -= v[6]*x1 + v[13]*x2 + v[20]*x3 + v[27]*x4  + v[34]*x5 + v[41]*x6 + v[48]*x7;
1547         v   +=  bs2;
1548     }
1549     /* x = inv_diagonal*x */
1550     x[idt]   = v[0]*s1 + v[7]*s2 + v[14]*s3 + v[21]*s4  + v[28]*s5 + v[35]*s6 + v[42]*s7;
1551     x[1+idt] = v[1]*s1 + v[8]*s2 + v[15]*s3 + v[22]*s4  + v[29]*s5 + v[36]*s6 + v[43]*s7;
1552     x[2+idt] = v[2]*s1 + v[9]*s2 + v[16]*s3 + v[23]*s4  + v[30]*s5 + v[37]*s6 + v[44]*s7;
1553     x[3+idt] = v[3]*s1 + v[10]*s2 + v[17]*s3 + v[24]*s4  + v[31]*s5 + v[38]*s6 + v[45]*s7;
1554     x[4+idt] = v[4]*s1 + v[11]*s2 + v[18]*s3 + v[25]*s4  + v[32]*s5 + v[39]*s6 + v[46]*s7;
1555     x[5+idt] = v[5]*s1 + v[12]*s2 + v[19]*s3 + v[26]*s4  + v[33]*s5 + v[40]*s6 + v[47]*s7;
1556     x[6+idt] = v[6]*s1 + v[13]*s2 + v[20]*s3 + v[27]*s4  + v[34]*s5 + v[41]*s6 + v[48]*s7;
1557   }
1558 
1559   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1560   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1561   ierr = PetscLogFlops(2.0*bs2*(a->nz) - bs*A->cmap->n);CHKERRQ(ierr);
1562   PetscFunctionReturn(0);
1563 }
1564 
1565 #undef __FUNCT__
1566 #define __FUNCT__ "MatSolve_SeqBAIJ_7_NaturalOrdering_newdatastruct_v2"
1567 PetscErrorCode MatSolve_SeqBAIJ_7_NaturalOrdering_newdatastruct_v2(Mat A,Vec bb,Vec xx)
1568 {
1569     Mat_SeqBAIJ       *a = (Mat_SeqBAIJ *)A->data;
1570     PetscInt          i,k,n=a->mbs,*vi,*ai=a->i,*aj=a->j,*adiag=a->diag,nz;
1571     PetscErrorCode    ierr;
1572     PetscInt          idx,jdx,idt;
1573     PetscInt          bs = A->rmap->bs,bs2 = a->bs2;
1574     const MatScalar   *aa=a->a,*v;
1575     PetscScalar       *x;
1576     const PetscScalar *b;
1577     PetscScalar        s1,s2,s3,s4,s5,s6,s7,x1,x2,x3,x4,x5,x6,x7;
1578 
1579     PetscFunctionBegin;
1580     ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1581     ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1582     /* forward solve the lower triangular */
1583     idx    = 0;
1584     x[0] = b[idx]; x[1] = b[1+idx];x[2] = b[2+idx];x[3] = b[3+idx];
1585     x[4] = b[4+idx];x[5] = b[5+idx];x[6] = b[6+idx];
1586     for (i=1; i<n; i++) {
1587        v    = aa + bs2*ai[i];
1588        vi   = aj + ai[i];
1589        nz   = ai[i+1] - ai[i];
1590       idx   = bs*i;
1591        s1   = b[idx];s2 = b[1+idx];s3 = b[2+idx];s4 = b[3+idx];
1592        s5   = b[4+idx];s6 = b[5+idx];s7 = b[6+idx];
1593        for(k=0;k<nz;k++) {
1594           jdx   = bs*vi[k];
1595           x1    = x[jdx];x2 = x[1+jdx]; x3 =x[2+jdx];x4 =x[3+jdx];
1596 	  x5    = x[4+jdx]; x6 = x[5+jdx];x7 = x[6+jdx];
1597           s1   -= v[0]*x1 + v[7]*x2 + v[14]*x3 + v[21]*x4  + v[28]*x5 + v[35]*x6 + v[42]*x7;
1598           s2   -= v[1]*x1 + v[8]*x2 + v[15]*x3 + v[22]*x4  + v[29]*x5 + v[36]*x6 + v[43]*x7;
1599           s3   -= v[2]*x1 + v[9]*x2 + v[16]*x3 + v[23]*x4  + v[30]*x5 + v[37]*x6 + v[44]*x7;
1600 	  s4   -= v[3]*x1 + v[10]*x2 + v[17]*x3 + v[24]*x4  + v[31]*x5 + v[38]*x6 + v[45]*x7;
1601           s5   -= v[4]*x1 + v[11]*x2 + v[18]*x3 + v[25]*x4  + v[32]*x5 + v[39]*x6 + v[46]*x7;
1602 	  s6   -= v[5]*x1 + v[12]*x2 + v[19]*x3 + v[26]*x4  + v[33]*x5 + v[40]*x6 + v[47]*x7;
1603 	  s7   -= v[6]*x1 + v[13]*x2 + v[20]*x3 + v[27]*x4  + v[34]*x5 + v[41]*x6 + v[48]*x7;
1604           v   +=  bs2;
1605         }
1606 
1607        x[idx]   = s1;
1608        x[1+idx] = s2;
1609        x[2+idx] = s3;
1610        x[3+idx] = s4;
1611        x[4+idx] = s5;
1612        x[5+idx] = s6;
1613        x[6+idx] = s7;
1614     }
1615 
1616    /* backward solve the upper triangular */
1617   for (i=n-1; i>=0; i--){
1618     v   = aa + bs2*(adiag[i+1]+1);
1619      vi  = aj + adiag[i+1]+1;
1620      nz  = adiag[i] - adiag[i+1]-1;
1621      idt = bs*i;
1622      s1 = x[idt];  s2 = x[1+idt];s3 = x[2+idt];s4 = x[3+idt];
1623      s5 = x[4+idt];s6 = x[5+idt];s7 = x[6+idt];
1624     for(k=0;k<nz;k++) {
1625       idx   = bs*vi[k];
1626        x1    = x[idx];   x2 = x[1+idx]; x3 = x[2+idx];x4 = x[3+idx];
1627        x5    = x[4+idx];x6 = x[5+idx];x7 = x[6+idx];
1628        s1   -= v[0]*x1 + v[7]*x2 + v[14]*x3 + v[21]*x4  + v[28]*x5 + v[35]*x6 + v[42]*x7;
1629        s2   -= v[1]*x1 + v[8]*x2 + v[15]*x3 + v[22]*x4  + v[29]*x5 + v[36]*x6 + v[43]*x7;
1630        s3   -= v[2]*x1 + v[9]*x2 + v[16]*x3 + v[23]*x4  + v[30]*x5 + v[37]*x6 + v[44]*x7;
1631        s4   -= v[3]*x1 + v[10]*x2 + v[17]*x3 + v[24]*x4  + v[31]*x5 + v[38]*x6 + v[45]*x7;
1632        s5   -= v[4]*x1 + v[11]*x2 + v[18]*x3 + v[25]*x4  + v[32]*x5 + v[39]*x6 + v[46]*x7;
1633        s6   -= v[5]*x1 + v[12]*x2 + v[19]*x3 + v[26]*x4  + v[33]*x5 + v[40]*x6 + v[47]*x7;
1634        s7   -= v[6]*x1 + v[13]*x2 + v[20]*x3 + v[27]*x4  + v[34]*x5 + v[41]*x6 + v[48]*x7;
1635         v   +=  bs2;
1636     }
1637     /* x = inv_diagonal*x */
1638     x[idt]   = v[0]*s1 + v[7]*s2 + v[14]*s3 + v[21]*s4  + v[28]*s5 + v[35]*s6 + v[42]*s7;
1639     x[1+idt] = v[1]*s1 + v[8]*s2 + v[15]*s3 + v[22]*s4  + v[29]*s5 + v[36]*s6 + v[43]*s7;
1640     x[2+idt] = v[2]*s1 + v[9]*s2 + v[16]*s3 + v[23]*s4  + v[30]*s5 + v[37]*s6 + v[44]*s7;
1641     x[3+idt] = v[3]*s1 + v[10]*s2 + v[17]*s3 + v[24]*s4  + v[31]*s5 + v[38]*s6 + v[45]*s7;
1642     x[4+idt] = v[4]*s1 + v[11]*s2 + v[18]*s3 + v[25]*s4  + v[32]*s5 + v[39]*s6 + v[46]*s7;
1643     x[5+idt] = v[5]*s1 + v[12]*s2 + v[19]*s3 + v[26]*s4  + v[33]*s5 + v[40]*s6 + v[47]*s7;
1644     x[6+idt] = v[6]*s1 + v[13]*s2 + v[20]*s3 + v[27]*s4  + v[34]*s5 + v[41]*s6 + v[48]*s7;
1645   }
1646 
1647   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1648   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1649   ierr = PetscLogFlops(2.0*bs2*(a->nz) - bs*A->cmap->n);CHKERRQ(ierr);
1650   PetscFunctionReturn(0);
1651 }
1652 
1653 #undef __FUNCT__
1654 #define __FUNCT__ "MatSolve_SeqBAIJ_6"
1655 PetscErrorCode MatSolve_SeqBAIJ_6(Mat A,Vec bb,Vec xx)
1656 {
1657   Mat_SeqBAIJ       *a=(Mat_SeqBAIJ *)A->data;
1658   IS                iscol=a->col,isrow=a->row;
1659   PetscErrorCode    ierr;
1660   const PetscInt    *r,*c,*rout,*cout;
1661   PetscInt          *diag = a->diag,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc;
1662   const MatScalar   *aa=a->a,*v;
1663   PetscScalar       *x,s1,s2,s3,s4,s5,s6,x1,x2,x3,x4,x5,x6,*t;
1664   const PetscScalar *b;
1665   PetscFunctionBegin;
1666   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1667   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1668   t  = a->solve_work;
1669 
1670   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1671   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1672 
1673   /* forward solve the lower triangular */
1674   idx    = 6*(*r++);
1675   t[0] = b[idx];   t[1] = b[1+idx];
1676   t[2] = b[2+idx]; t[3] = b[3+idx];
1677   t[4] = b[4+idx]; t[5] = b[5+idx];
1678   for (i=1; i<n; i++) {
1679     v     = aa + 36*ai[i];
1680     vi    = aj + ai[i];
1681     nz    = diag[i] - ai[i];
1682     idx   = 6*(*r++);
1683     s1  = b[idx];s2 = b[1+idx];s3 = b[2+idx];s4 = b[3+idx];
1684     s5  = b[4+idx]; s6 = b[5+idx];
1685     while (nz--) {
1686       idx   = 6*(*vi++);
1687       x1    = t[idx];   x2 = t[1+idx]; x3 = t[2+idx];
1688       x4    = t[3+idx]; x5 = t[4+idx]; x6 = t[5+idx];
1689       s1 -= v[0]*x1 + v[6]*x2  + v[12]*x3 + v[18]*x4 + v[24]*x5 + v[30]*x6;
1690       s2 -= v[1]*x1 + v[7]*x2  + v[13]*x3 + v[19]*x4 + v[25]*x5 + v[31]*x6;
1691       s3 -= v[2]*x1 + v[8]*x2  + v[14]*x3 + v[20]*x4 + v[26]*x5 + v[32]*x6;
1692       s4 -= v[3]*x1 + v[9]*x2  + v[15]*x3 + v[21]*x4 + v[27]*x5 + v[33]*x6;
1693       s5 -= v[4]*x1 + v[10]*x2 + v[16]*x3 + v[22]*x4 + v[28]*x5 + v[34]*x6;
1694       s6 -= v[5]*x1 + v[11]*x2 + v[17]*x3 + v[23]*x4 + v[29]*x5 + v[35]*x6;
1695       v += 36;
1696     }
1697     idx = 6*i;
1698     t[idx]   = s1;t[1+idx] = s2;
1699     t[2+idx] = s3;t[3+idx] = s4;
1700     t[4+idx] = s5;t[5+idx] = s6;
1701   }
1702   /* backward solve the upper triangular */
1703   for (i=n-1; i>=0; i--){
1704     v    = aa + 36*diag[i] + 36;
1705     vi   = aj + diag[i] + 1;
1706     nz   = ai[i+1] - diag[i] - 1;
1707     idt  = 6*i;
1708     s1 = t[idt];  s2 = t[1+idt];
1709     s3 = t[2+idt];s4 = t[3+idt];
1710     s5 = t[4+idt];s6 = t[5+idt];
1711     while (nz--) {
1712       idx   = 6*(*vi++);
1713       x1    = t[idx];   x2 = t[1+idx];
1714       x3    = t[2+idx]; x4 = t[3+idx];
1715       x5    = t[4+idx]; x6 = t[5+idx];
1716       s1 -= v[0]*x1 + v[6]*x2  + v[12]*x3 + v[18]*x4 + v[24]*x5 + v[30]*x6;
1717       s2 -= v[1]*x1 + v[7]*x2  + v[13]*x3 + v[19]*x4 + v[25]*x5 + v[31]*x6;
1718       s3 -= v[2]*x1 + v[8]*x2  + v[14]*x3 + v[20]*x4 + v[26]*x5 + v[32]*x6;
1719       s4 -= v[3]*x1 + v[9]*x2  + v[15]*x3 + v[21]*x4 + v[27]*x5 + v[33]*x6;
1720       s5 -= v[4]*x1 + v[10]*x2 + v[16]*x3 + v[22]*x4 + v[28]*x5 + v[34]*x6;
1721       s6 -= v[5]*x1 + v[11]*x2 + v[17]*x3 + v[23]*x4 + v[29]*x5 + v[35]*x6;
1722       v += 36;
1723     }
1724     idc = 6*(*c--);
1725     v   = aa + 36*diag[i];
1726     x[idc]   = t[idt]   = v[0]*s1+v[6]*s2+v[12]*s3+
1727                                  v[18]*s4+v[24]*s5+v[30]*s6;
1728     x[1+idc] = t[1+idt] = v[1]*s1+v[7]*s2+v[13]*s3+
1729                                  v[19]*s4+v[25]*s5+v[31]*s6;
1730     x[2+idc] = t[2+idt] = v[2]*s1+v[8]*s2+v[14]*s3+
1731                                  v[20]*s4+v[26]*s5+v[32]*s6;
1732     x[3+idc] = t[3+idt] = v[3]*s1+v[9]*s2+v[15]*s3+
1733                                  v[21]*s4+v[27]*s5+v[33]*s6;
1734     x[4+idc] = t[4+idt] = v[4]*s1+v[10]*s2+v[16]*s3+
1735                                  v[22]*s4+v[28]*s5+v[34]*s6;
1736     x[5+idc] = t[5+idt] = v[5]*s1+v[11]*s2+v[17]*s3+
1737                                  v[23]*s4+v[29]*s5+v[35]*s6;
1738   }
1739 
1740   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1741   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1742   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1743   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1744   ierr = PetscLogFlops(2.0*36*(a->nz) - 6.0*A->cmap->n);CHKERRQ(ierr);
1745   PetscFunctionReturn(0);
1746 }
1747 
1748 #undef __FUNCT__
1749 #define __FUNCT__ "MatSolve_SeqBAIJ_6_newdatastruct"
1750 PetscErrorCode MatSolve_SeqBAIJ_6_newdatastruct(Mat A,Vec bb,Vec xx)
1751 {
1752   Mat_SeqBAIJ       *a=(Mat_SeqBAIJ *)A->data;
1753   IS                iscol=a->col,isrow=a->row;
1754   PetscErrorCode    ierr;
1755   const PetscInt    *r,*c,*rout,*cout;
1756   PetscInt          i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,k,m;
1757   const MatScalar   *aa=a->a,*v;
1758   PetscScalar       *x,s1,s2,s3,s4,s5,s6,x1,x2,x3,x4,x5,x6,*t;
1759   const PetscScalar *b;
1760   PetscFunctionBegin;
1761   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1762   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1763   t  = a->solve_work;
1764 
1765   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1766   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1767 
1768   /* forward solve the lower triangular */
1769   idx    = 6*r[0];
1770   t[0] = b[idx];   t[1] = b[1+idx];
1771   t[2] = b[2+idx]; t[3] = b[3+idx];
1772   t[4] = b[4+idx]; t[5] = b[5+idx];
1773   for (i=1; i<n; i++) {
1774     v     = aa + 36*ai[i];
1775     vi    = aj + ai[i];
1776     nz    = ai[i+1] - ai[i];
1777     idx   = 6*r[i];
1778     s1  = b[idx];s2 = b[1+idx];s3 = b[2+idx];s4 = b[3+idx];
1779     s5  = b[4+idx]; s6 = b[5+idx];
1780     for(m=0;m<nz;m++){
1781       idx   = 6*vi[m];
1782       x1    = t[idx];   x2 = t[1+idx]; x3 = t[2+idx];
1783       x4    = t[3+idx]; x5 = t[4+idx]; x6 = t[5+idx];
1784       s1 -= v[0]*x1 + v[6]*x2  + v[12]*x3 + v[18]*x4 + v[24]*x5 + v[30]*x6;
1785       s2 -= v[1]*x1 + v[7]*x2  + v[13]*x3 + v[19]*x4 + v[25]*x5 + v[31]*x6;
1786       s3 -= v[2]*x1 + v[8]*x2  + v[14]*x3 + v[20]*x4 + v[26]*x5 + v[32]*x6;
1787       s4 -= v[3]*x1 + v[9]*x2  + v[15]*x3 + v[21]*x4 + v[27]*x5 + v[33]*x6;
1788       s5 -= v[4]*x1 + v[10]*x2 + v[16]*x3 + v[22]*x4 + v[28]*x5 + v[34]*x6;
1789       s6 -= v[5]*x1 + v[11]*x2 + v[17]*x3 + v[23]*x4 + v[29]*x5 + v[35]*x6;
1790       v += 36;
1791     }
1792     idx = 6*i;
1793     t[idx]   = s1;t[1+idx] = s2;
1794     t[2+idx] = s3;t[3+idx] = s4;
1795     t[4+idx] = s5;t[5+idx] = s6;
1796   }
1797   /* backward solve the upper triangular */
1798   for (i=n-1; i>=0; i--){
1799     k    = 2*n-i;
1800     v    = aa + 36*ai[k];
1801     vi   = aj + ai[k];
1802     nz   = ai[k+1] - ai[k] - 1;
1803     idt  = 6*i;
1804     s1 = t[idt];  s2 = t[1+idt];
1805     s3 = t[2+idt];s4 = t[3+idt];
1806     s5 = t[4+idt];s6 = t[5+idt];
1807     for(m=0;m<nz;m++){
1808       idx   = 6*vi[m];
1809       x1    = t[idx];   x2 = t[1+idx];
1810       x3    = t[2+idx]; x4 = t[3+idx];
1811       x5    = t[4+idx]; x6 = t[5+idx];
1812       s1 -= v[0]*x1 + v[6]*x2  + v[12]*x3 + v[18]*x4 + v[24]*x5 + v[30]*x6;
1813       s2 -= v[1]*x1 + v[7]*x2  + v[13]*x3 + v[19]*x4 + v[25]*x5 + v[31]*x6;
1814       s3 -= v[2]*x1 + v[8]*x2  + v[14]*x3 + v[20]*x4 + v[26]*x5 + v[32]*x6;
1815       s4 -= v[3]*x1 + v[9]*x2  + v[15]*x3 + v[21]*x4 + v[27]*x5 + v[33]*x6;
1816       s5 -= v[4]*x1 + v[10]*x2 + v[16]*x3 + v[22]*x4 + v[28]*x5 + v[34]*x6;
1817       s6 -= v[5]*x1 + v[11]*x2 + v[17]*x3 + v[23]*x4 + v[29]*x5 + v[35]*x6;
1818       v += 36;
1819     }
1820     idc = 6*c[i];
1821     x[idc]   = t[idt]   = v[0]*s1+v[6]*s2+v[12]*s3+
1822                                  v[18]*s4+v[24]*s5+v[30]*s6;
1823     x[1+idc] = t[1+idt] = v[1]*s1+v[7]*s2+v[13]*s3+
1824                                  v[19]*s4+v[25]*s5+v[31]*s6;
1825     x[2+idc] = t[2+idt] = v[2]*s1+v[8]*s2+v[14]*s3+
1826                                  v[20]*s4+v[26]*s5+v[32]*s6;
1827     x[3+idc] = t[3+idt] = v[3]*s1+v[9]*s2+v[15]*s3+
1828                                  v[21]*s4+v[27]*s5+v[33]*s6;
1829     x[4+idc] = t[4+idt] = v[4]*s1+v[10]*s2+v[16]*s3+
1830                                  v[22]*s4+v[28]*s5+v[34]*s6;
1831     x[5+idc] = t[5+idt] = v[5]*s1+v[11]*s2+v[17]*s3+
1832                                  v[23]*s4+v[29]*s5+v[35]*s6;
1833   }
1834 
1835   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1836   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1837   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1838   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1839   ierr = PetscLogFlops(2.0*36*(a->nz) - 6.0*A->cmap->n);CHKERRQ(ierr);
1840   PetscFunctionReturn(0);
1841 }
1842 
1843 
1844 #undef __FUNCT__
1845 #define __FUNCT__ "MatSolve_SeqBAIJ_6_NaturalOrdering"
1846 PetscErrorCode MatSolve_SeqBAIJ_6_NaturalOrdering(Mat A,Vec bb,Vec xx)
1847 {
1848   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ *)A->data;
1849   PetscInt          i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt;
1850   PetscErrorCode    ierr;
1851   PetscInt          *diag = a->diag,jdx;
1852   const MatScalar   *aa=a->a,*v;
1853   PetscScalar       *x,s1,s2,s3,s4,s5,s6,x1,x2,x3,x4,x5,x6;
1854   const PetscScalar *b;
1855 
1856   PetscFunctionBegin;
1857   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1858   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1859   /* forward solve the lower triangular */
1860   idx    = 0;
1861   x[0] = b[idx];   x[1] = b[1+idx]; x[2] = b[2+idx];
1862   x[3] = b[3+idx]; x[4] = b[4+idx]; x[5] = b[5+idx];
1863   for (i=1; i<n; i++) {
1864     v     =  aa + 36*ai[i];
1865     vi    =  aj + ai[i];
1866     nz    =  diag[i] - ai[i];
1867     idx   =  6*i;
1868     s1  =  b[idx];   s2 = b[1+idx]; s3 = b[2+idx];
1869     s4  =  b[3+idx]; s5 = b[4+idx]; s6 = b[5+idx];
1870     while (nz--) {
1871       jdx   = 6*(*vi++);
1872       x1    = x[jdx];   x2 = x[1+jdx]; x3 = x[2+jdx];
1873       x4    = x[3+jdx]; x5 = x[4+jdx]; x6 = x[5+jdx];
1874       s1 -= v[0]*x1 + v[6]*x2  + v[12]*x3 + v[18]*x4 + v[24]*x5 + v[30]*x6;
1875       s2 -= v[1]*x1 + v[7]*x2  + v[13]*x3 + v[19]*x4 + v[25]*x5 + v[31]*x6;
1876       s3 -= v[2]*x1 + v[8]*x2  + v[14]*x3 + v[20]*x4 + v[26]*x5 + v[32]*x6;
1877       s4 -= v[3]*x1 + v[9]*x2  + v[15]*x3 + v[21]*x4 + v[27]*x5 + v[33]*x6;
1878       s5 -= v[4]*x1 + v[10]*x2 + v[16]*x3 + v[22]*x4 + v[28]*x5 + v[34]*x6;
1879       s6 -= v[5]*x1 + v[11]*x2 + v[17]*x3 + v[23]*x4 + v[29]*x5 + v[35]*x6;
1880       v += 36;
1881      }
1882     x[idx]   = s1;
1883     x[1+idx] = s2;
1884     x[2+idx] = s3;
1885     x[3+idx] = s4;
1886     x[4+idx] = s5;
1887     x[5+idx] = s6;
1888   }
1889   /* backward solve the upper triangular */
1890   for (i=n-1; i>=0; i--){
1891     v    = aa + 36*diag[i] + 36;
1892     vi   = aj + diag[i] + 1;
1893     nz   = ai[i+1] - diag[i] - 1;
1894     idt  = 6*i;
1895     s1 = x[idt];   s2 = x[1+idt];
1896     s3 = x[2+idt]; s4 = x[3+idt];
1897     s5 = x[4+idt]; s6 = x[5+idt];
1898     while (nz--) {
1899       idx   = 6*(*vi++);
1900       x1    = x[idx];   x2 = x[1+idx]; x3 = x[2+idx];
1901       x4    = x[3+idx]; x5 = x[4+idx]; x6 = x[5+idx];
1902       s1 -= v[0]*x1 + v[6]*x2  + v[12]*x3 + v[18]*x4 + v[24]*x5 + v[30]*x6;
1903       s2 -= v[1]*x1 + v[7]*x2  + v[13]*x3 + v[19]*x4 + v[25]*x5 + v[31]*x6;
1904       s3 -= v[2]*x1 + v[8]*x2  + v[14]*x3 + v[20]*x4 + v[26]*x5 + v[32]*x6;
1905       s4 -= v[3]*x1 + v[9]*x2  + v[15]*x3 + v[21]*x4 + v[27]*x5 + v[33]*x6;
1906       s5 -= v[4]*x1 + v[10]*x2 + v[16]*x3 + v[22]*x4 + v[28]*x5 + v[34]*x6;
1907       s6 -= v[5]*x1 + v[11]*x2 + v[17]*x3 + v[23]*x4 + v[29]*x5 + v[35]*x6;
1908       v += 36;
1909     }
1910     v        = aa + 36*diag[i];
1911     x[idt]   = v[0]*s1 + v[6]*s2  + v[12]*s3 + v[18]*s4 + v[24]*s5 + v[30]*s6;
1912     x[1+idt] = v[1]*s1 + v[7]*s2  + v[13]*s3 + v[19]*s4 + v[25]*s5 + v[31]*s6;
1913     x[2+idt] = v[2]*s1 + v[8]*s2  + v[14]*s3 + v[20]*s4 + v[26]*s5 + v[32]*s6;
1914     x[3+idt] = v[3]*s1 + v[9]*s2  + v[15]*s3 + v[21]*s4 + v[27]*s5 + v[33]*s6;
1915     x[4+idt] = v[4]*s1 + v[10]*s2 + v[16]*s3 + v[22]*s4 + v[28]*s5 + v[34]*s6;
1916     x[5+idt] = v[5]*s1 + v[11]*s2 + v[17]*s3 + v[23]*s4 + v[29]*s5 + v[35]*s6;
1917   }
1918 
1919   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1920   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1921   ierr = PetscLogFlops(2.0*36*(a->nz) - 6.0*A->cmap->n);CHKERRQ(ierr);
1922   PetscFunctionReturn(0);
1923 }
1924 
1925 #undef __FUNCT__
1926 #define __FUNCT__ "MatSolve_SeqBAIJ_6_NaturalOrdering_newdatastruct"
1927 PetscErrorCode MatSolve_SeqBAIJ_6_NaturalOrdering_newdatastruct(Mat A,Vec bb,Vec xx)
1928 {
1929     Mat_SeqBAIJ       *a = (Mat_SeqBAIJ *)A->data;
1930     PetscInt          i,k,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz;
1931     PetscErrorCode    ierr;
1932     PetscInt          idx,jdx,idt;
1933     PetscInt          bs = A->rmap->bs,bs2 = a->bs2;
1934     const MatScalar   *aa=a->a,*v;
1935     PetscScalar       *x;
1936     const PetscScalar *b;
1937     PetscScalar        s1,s2,s3,s4,s5,s6,x1,x2,x3,x4,x5,x6;
1938 
1939     PetscFunctionBegin;
1940     ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1941     ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1942     /* forward solve the lower triangular */
1943     idx    = 0;
1944     x[0] = b[idx]; x[1] = b[1+idx];x[2] = b[2+idx];x[3] = b[3+idx];
1945     x[4] = b[4+idx];x[5] = b[5+idx];
1946     for (i=1; i<n; i++) {
1947        v    = aa + bs2*ai[i];
1948        vi   = aj + ai[i];
1949        nz   = ai[i+1] - ai[i];
1950       idx   = bs*i;
1951        s1   = b[idx];s2 = b[1+idx];s3 = b[2+idx];s4 = b[3+idx];
1952        s5   = b[4+idx];s6 = b[5+idx];
1953        for(k=0;k<nz;k++){
1954           jdx   = bs*vi[k];
1955           x1    = x[jdx];x2 = x[1+jdx]; x3 =x[2+jdx];x4 =x[3+jdx];
1956 	  x5    = x[4+jdx]; x6 = x[5+jdx];
1957           s1   -= v[0]*x1 + v[6]*x2 + v[12]*x3 + v[18]*x4  + v[24]*x5 + v[30]*x6;
1958           s2   -= v[1]*x1 + v[7]*x2 + v[13]*x3 + v[19]*x4  + v[25]*x5 + v[31]*x6;;
1959           s3   -= v[2]*x1 + v[8]*x2 + v[14]*x3 + v[20]*x4  + v[26]*x5 + v[32]*x6;
1960 	  s4   -= v[3]*x1 + v[9]*x2 + v[15]*x3 + v[21]*x4  + v[27]*x5 + v[33]*x6;
1961           s5   -= v[4]*x1 + v[10]*x2 + v[16]*x3 + v[22]*x4  + v[28]*x5 + v[34]*x6;
1962 	  s6   -= v[5]*x1 + v[11]*x2 + v[17]*x3 + v[23]*x4  + v[29]*x5 + v[35]*x6;
1963           v   +=  bs2;
1964         }
1965 
1966        x[idx]   = s1;
1967        x[1+idx] = s2;
1968        x[2+idx] = s3;
1969        x[3+idx] = s4;
1970        x[4+idx] = s5;
1971        x[5+idx] = s6;
1972     }
1973 
1974    /* backward solve the upper triangular */
1975   for (i=n-1; i>=0; i--){
1976      v   = aa + bs2*ai[2*n-i];
1977      vi  = aj + ai[2*n-i];
1978      nz  = ai[2*n-i +1] - ai[2*n-i]-1;
1979      idt = bs*i;
1980      s1 = x[idt];  s2 = x[1+idt];s3 = x[2+idt];s4 = x[3+idt];
1981      s5 = x[4+idt];s6 = x[5+idt];
1982      for(k=0;k<nz;k++){
1983       idx   = bs*vi[k];
1984        x1    = x[idx];   x2 = x[1+idx]; x3 = x[2+idx];x4 = x[3+idx];
1985        x5    = x[4+idx];x6 = x[5+idx];
1986        s1   -= v[0]*x1 + v[6]*x2 + v[12]*x3 + v[18]*x4  + v[24]*x5 + v[30]*x6;
1987        s2   -= v[1]*x1 + v[7]*x2 + v[13]*x3 + v[19]*x4  + v[25]*x5 + v[31]*x6;;
1988        s3   -= v[2]*x1 + v[8]*x2 + v[14]*x3 + v[20]*x4  + v[26]*x5 + v[32]*x6;
1989        s4   -= v[3]*x1 + v[9]*x2 + v[15]*x3 + v[21]*x4  + v[27]*x5 + v[33]*x6;
1990        s5   -= v[4]*x1 + v[10]*x2 + v[16]*x3 + v[22]*x4  + v[28]*x5 + v[34]*x6;
1991        s6   -= v[5]*x1 + v[11]*x2 + v[17]*x3 + v[23]*x4  + v[29]*x5 + v[35]*x6;
1992         v   +=  bs2;
1993     }
1994     /* x = inv_diagonal*x */
1995    x[idt]   = v[0]*s1 + v[6]*s2 + v[12]*s3 + v[18]*s4 + v[24]*s5 + v[30]*s6;
1996    x[1+idt] = v[1]*s1 + v[7]*s2 + v[13]*s3 + v[19]*s4 + v[25]*s5 + v[31]*s6;
1997    x[2+idt] = v[2]*s1 + v[8]*s2 + v[14]*s3 + v[20]*s4 + v[26]*s5 + v[32]*s6;
1998    x[3+idt] = v[3]*s1 + v[9]*s2 + v[15]*s3 + v[21]*s4 + v[27]*s5 + v[33]*s6;
1999    x[4+idt] = v[4]*s1 + v[10]*s2 + v[16]*s3 + v[22]*s4 + v[28]*s5 + v[34]*s6;
2000    x[5+idt] = v[5]*s1 + v[11]*s2 + v[17]*s3 + v[23]*s4 + v[29]*s5 + v[35]*s6;
2001   }
2002 
2003   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2004   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
2005   ierr = PetscLogFlops(2.0*bs2*(a->nz) - bs*A->cmap->n);CHKERRQ(ierr);
2006   PetscFunctionReturn(0);
2007 }
2008 
2009 #undef __FUNCT__
2010 #define __FUNCT__ "MatSolve_SeqBAIJ_6_NaturalOrdering_newdatastruct_v2"
2011 PetscErrorCode MatSolve_SeqBAIJ_6_NaturalOrdering_newdatastruct_v2(Mat A,Vec bb,Vec xx)
2012 {
2013     Mat_SeqBAIJ       *a = (Mat_SeqBAIJ *)A->data;
2014     PetscInt          i,k,n=a->mbs,*vi,*ai=a->i,*aj=a->j,*adiag=a->diag,nz;
2015     PetscErrorCode    ierr;
2016     PetscInt          idx,jdx,idt;
2017     PetscInt          bs = A->rmap->bs,bs2 = a->bs2;
2018     const MatScalar   *aa=a->a,*v;
2019     PetscScalar       *x;
2020     const PetscScalar *b;
2021     PetscScalar        s1,s2,s3,s4,s5,s6,x1,x2,x3,x4,x5,x6;
2022 
2023     PetscFunctionBegin;
2024     ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2025     ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
2026     /* forward solve the lower triangular */
2027     idx    = 0;
2028     x[0] = b[idx]; x[1] = b[1+idx];x[2] = b[2+idx];x[3] = b[3+idx];
2029     x[4] = b[4+idx];x[5] = b[5+idx];
2030     for (i=1; i<n; i++) {
2031        v    = aa + bs2*ai[i];
2032        vi   = aj + ai[i];
2033        nz   = ai[i+1] - ai[i];
2034       idx   = bs*i;
2035        s1   = b[idx];s2 = b[1+idx];s3 = b[2+idx];s4 = b[3+idx];
2036        s5   = b[4+idx];s6 = b[5+idx];
2037        for(k=0;k<nz;k++){
2038           jdx   = bs*vi[k];
2039           x1    = x[jdx];x2 = x[1+jdx]; x3 =x[2+jdx];x4 =x[3+jdx];
2040 	  x5    = x[4+jdx]; x6 = x[5+jdx];
2041           s1   -= v[0]*x1 + v[6]*x2 + v[12]*x3 + v[18]*x4  + v[24]*x5 + v[30]*x6;
2042           s2   -= v[1]*x1 + v[7]*x2 + v[13]*x3 + v[19]*x4  + v[25]*x5 + v[31]*x6;;
2043           s3   -= v[2]*x1 + v[8]*x2 + v[14]*x3 + v[20]*x4  + v[26]*x5 + v[32]*x6;
2044 	  s4   -= v[3]*x1 + v[9]*x2 + v[15]*x3 + v[21]*x4  + v[27]*x5 + v[33]*x6;
2045           s5   -= v[4]*x1 + v[10]*x2 + v[16]*x3 + v[22]*x4  + v[28]*x5 + v[34]*x6;
2046 	  s6   -= v[5]*x1 + v[11]*x2 + v[17]*x3 + v[23]*x4  + v[29]*x5 + v[35]*x6;
2047           v   +=  bs2;
2048         }
2049 
2050        x[idx]   = s1;
2051        x[1+idx] = s2;
2052        x[2+idx] = s3;
2053        x[3+idx] = s4;
2054        x[4+idx] = s5;
2055        x[5+idx] = s6;
2056     }
2057 
2058    /* backward solve the upper triangular */
2059   for (i=n-1; i>=0; i--){
2060     v   = aa + bs2*(adiag[i+1]+1);
2061      vi  = aj + adiag[i+1]+1;
2062      nz  = adiag[i] - adiag[i+1]-1;
2063      idt = bs*i;
2064      s1 = x[idt];  s2 = x[1+idt];s3 = x[2+idt];s4 = x[3+idt];
2065      s5 = x[4+idt];s6 = x[5+idt];
2066      for(k=0;k<nz;k++){
2067       idx   = bs*vi[k];
2068        x1    = x[idx];   x2 = x[1+idx]; x3 = x[2+idx];x4 = x[3+idx];
2069        x5    = x[4+idx];x6 = x[5+idx];
2070        s1   -= v[0]*x1 + v[6]*x2 + v[12]*x3 + v[18]*x4  + v[24]*x5 + v[30]*x6;
2071        s2   -= v[1]*x1 + v[7]*x2 + v[13]*x3 + v[19]*x4  + v[25]*x5 + v[31]*x6;;
2072        s3   -= v[2]*x1 + v[8]*x2 + v[14]*x3 + v[20]*x4  + v[26]*x5 + v[32]*x6;
2073        s4   -= v[3]*x1 + v[9]*x2 + v[15]*x3 + v[21]*x4  + v[27]*x5 + v[33]*x6;
2074        s5   -= v[4]*x1 + v[10]*x2 + v[16]*x3 + v[22]*x4  + v[28]*x5 + v[34]*x6;
2075        s6   -= v[5]*x1 + v[11]*x2 + v[17]*x3 + v[23]*x4  + v[29]*x5 + v[35]*x6;
2076         v   +=  bs2;
2077     }
2078     /* x = inv_diagonal*x */
2079    x[idt]   = v[0]*s1 + v[6]*s2 + v[12]*s3 + v[18]*s4 + v[24]*s5 + v[30]*s6;
2080    x[1+idt] = v[1]*s1 + v[7]*s2 + v[13]*s3 + v[19]*s4 + v[25]*s5 + v[31]*s6;
2081    x[2+idt] = v[2]*s1 + v[8]*s2 + v[14]*s3 + v[20]*s4 + v[26]*s5 + v[32]*s6;
2082    x[3+idt] = v[3]*s1 + v[9]*s2 + v[15]*s3 + v[21]*s4 + v[27]*s5 + v[33]*s6;
2083    x[4+idt] = v[4]*s1 + v[10]*s2 + v[16]*s3 + v[22]*s4 + v[28]*s5 + v[34]*s6;
2084    x[5+idt] = v[5]*s1 + v[11]*s2 + v[17]*s3 + v[23]*s4 + v[29]*s5 + v[35]*s6;
2085   }
2086 
2087   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2088   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
2089   ierr = PetscLogFlops(2.0*bs2*(a->nz) - bs*A->cmap->n);CHKERRQ(ierr);
2090   PetscFunctionReturn(0);
2091 }
2092 
2093 #undef __FUNCT__
2094 #define __FUNCT__ "MatSolve_SeqBAIJ_5"
2095 PetscErrorCode MatSolve_SeqBAIJ_5(Mat A,Vec bb,Vec xx)
2096 {
2097   Mat_SeqBAIJ       *a=(Mat_SeqBAIJ *)A->data;
2098   IS                iscol=a->col,isrow=a->row;
2099   PetscErrorCode    ierr;
2100   const PetscInt    *r,*c,*rout,*cout,*diag = a->diag;
2101   PetscInt          i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc;
2102   const MatScalar   *aa=a->a,*v;
2103   PetscScalar       *x,s1,s2,s3,s4,s5,x1,x2,x3,x4,x5,*t;
2104   const PetscScalar *b;
2105 
2106   PetscFunctionBegin;
2107   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2108   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
2109   t  = a->solve_work;
2110 
2111   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
2112   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
2113 
2114   /* forward solve the lower triangular */
2115   idx    = 5*(*r++);
2116   t[0] = b[idx];   t[1] = b[1+idx];
2117   t[2] = b[2+idx]; t[3] = b[3+idx]; t[4] = b[4+idx];
2118   for (i=1; i<n; i++) {
2119     v     = aa + 25*ai[i];
2120     vi    = aj + ai[i];
2121     nz    = diag[i] - ai[i];
2122     idx   = 5*(*r++);
2123     s1  = b[idx];s2 = b[1+idx];s3 = b[2+idx];s4 = b[3+idx];
2124     s5  = b[4+idx];
2125     while (nz--) {
2126       idx   = 5*(*vi++);
2127       x1    = t[idx];  x2 = t[1+idx];x3 = t[2+idx];
2128       x4    = t[3+idx];x5 = t[4+idx];
2129       s1 -= v[0]*x1 + v[5]*x2 + v[10]*x3 + v[15]*x4 + v[20]*x5;
2130       s2 -= v[1]*x1 + v[6]*x2 + v[11]*x3 + v[16]*x4 + v[21]*x5;
2131       s3 -= v[2]*x1 + v[7]*x2 + v[12]*x3 + v[17]*x4 + v[22]*x5;
2132       s4 -= v[3]*x1 + v[8]*x2 + v[13]*x3 + v[18]*x4 + v[23]*x5;
2133       s5 -= v[4]*x1 + v[9]*x2 + v[14]*x3 + v[19]*x4 + v[24]*x5;
2134       v += 25;
2135     }
2136     idx = 5*i;
2137     t[idx]   = s1;t[1+idx] = s2;
2138     t[2+idx] = s3;t[3+idx] = s4; t[4+idx] = s5;
2139   }
2140   /* backward solve the upper triangular */
2141   for (i=n-1; i>=0; i--){
2142     v    = aa + 25*diag[i] + 25;
2143     vi   = aj + diag[i] + 1;
2144     nz   = ai[i+1] - diag[i] - 1;
2145     idt  = 5*i;
2146     s1 = t[idt];  s2 = t[1+idt];
2147     s3 = t[2+idt];s4 = t[3+idt]; s5 = t[4+idt];
2148     while (nz--) {
2149       idx   = 5*(*vi++);
2150       x1    = t[idx];   x2 = t[1+idx];
2151       x3    = t[2+idx]; x4 = t[3+idx]; x5 = t[4+idx];
2152       s1 -= v[0]*x1 + v[5]*x2 + v[10]*x3 + v[15]*x4 + v[20]*x5;
2153       s2 -= v[1]*x1 + v[6]*x2 + v[11]*x3 + v[16]*x4 + v[21]*x5;
2154       s3 -= v[2]*x1 + v[7]*x2 + v[12]*x3 + v[17]*x4 + v[22]*x5;
2155       s4 -= v[3]*x1 + v[8]*x2 + v[13]*x3 + v[18]*x4 + v[23]*x5;
2156       s5 -= v[4]*x1 + v[9]*x2 + v[14]*x3 + v[19]*x4 + v[24]*x5;
2157       v += 25;
2158     }
2159     idc = 5*(*c--);
2160     v   = aa + 25*diag[i];
2161     x[idc]   = t[idt]   = v[0]*s1+v[5]*s2+v[10]*s3+
2162                                  v[15]*s4+v[20]*s5;
2163     x[1+idc] = t[1+idt] = v[1]*s1+v[6]*s2+v[11]*s3+
2164                                  v[16]*s4+v[21]*s5;
2165     x[2+idc] = t[2+idt] = v[2]*s1+v[7]*s2+v[12]*s3+
2166                                  v[17]*s4+v[22]*s5;
2167     x[3+idc] = t[3+idt] = v[3]*s1+v[8]*s2+v[13]*s3+
2168                                  v[18]*s4+v[23]*s5;
2169     x[4+idc] = t[4+idt] = v[4]*s1+v[9]*s2+v[14]*s3+
2170                                  v[19]*s4+v[24]*s5;
2171   }
2172 
2173   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
2174   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
2175   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2176   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
2177   ierr = PetscLogFlops(2.0*25*(a->nz) - 5.0*A->cmap->n);CHKERRQ(ierr);
2178   PetscFunctionReturn(0);
2179 }
2180 
2181 #undef __FUNCT__
2182 #define __FUNCT__ "MatSolve_SeqBAIJ_5_newdatastruct"
2183 PetscErrorCode MatSolve_SeqBAIJ_5_newdatastruct(Mat A,Vec bb,Vec xx)
2184 {
2185   Mat_SeqBAIJ       *a=(Mat_SeqBAIJ *)A->data;
2186   IS                iscol=a->col,isrow=a->row;
2187   PetscErrorCode    ierr;
2188   const PetscInt    *r,*c,*rout,*cout;
2189   PetscInt          i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,k,m;
2190   const MatScalar   *aa=a->a,*v;
2191   PetscScalar       *x,s1,s2,s3,s4,s5,x1,x2,x3,x4,x5,*t;
2192   const PetscScalar *b;
2193 
2194   PetscFunctionBegin;
2195   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2196   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
2197   t  = a->solve_work;
2198 
2199   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
2200   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
2201 
2202   /* forward solve the lower triangular */
2203   idx    = 5*r[0];
2204   t[0] = b[idx];   t[1] = b[1+idx];
2205   t[2] = b[2+idx]; t[3] = b[3+idx]; t[4] = b[4+idx];
2206   for (i=1; i<n; i++) {
2207     v     = aa + 25*ai[i];
2208     vi    = aj + ai[i];
2209     nz    = ai[i+1] - ai[i];
2210     idx   = 5*r[i];
2211     s1  = b[idx];s2 = b[1+idx];s3 = b[2+idx];s4 = b[3+idx];
2212     s5  = b[4+idx];
2213     for(m=0;m<nz;m++){
2214       idx   = 5*vi[m];
2215       x1    = t[idx];  x2 = t[1+idx];x3 = t[2+idx];
2216       x4    = t[3+idx];x5 = t[4+idx];
2217       s1 -= v[0]*x1 + v[5]*x2 + v[10]*x3 + v[15]*x4 + v[20]*x5;
2218       s2 -= v[1]*x1 + v[6]*x2 + v[11]*x3 + v[16]*x4 + v[21]*x5;
2219       s3 -= v[2]*x1 + v[7]*x2 + v[12]*x3 + v[17]*x4 + v[22]*x5;
2220       s4 -= v[3]*x1 + v[8]*x2 + v[13]*x3 + v[18]*x4 + v[23]*x5;
2221       s5 -= v[4]*x1 + v[9]*x2 + v[14]*x3 + v[19]*x4 + v[24]*x5;
2222       v += 25;
2223     }
2224     idx = 5*i;
2225     t[idx]   = s1;t[1+idx] = s2;
2226     t[2+idx] = s3;t[3+idx] = s4; t[4+idx] = s5;
2227   }
2228   /* backward solve the upper triangular */
2229   for (i=n-1; i>=0; i--){
2230     k    = 2*n-i;
2231     v    = aa + 25*ai[k];
2232     vi   = aj + ai[k];
2233     nz   = ai[k+1] - ai[k] - 1;
2234     idt  = 5*i;
2235     s1 = t[idt];  s2 = t[1+idt];
2236     s3 = t[2+idt];s4 = t[3+idt]; s5 = t[4+idt];
2237     for(m=0;m<nz;m++){
2238       idx   = 5*vi[m];
2239       x1    = t[idx];   x2 = t[1+idx];
2240       x3    = t[2+idx]; x4 = t[3+idx]; x5 = t[4+idx];
2241       s1 -= v[0]*x1 + v[5]*x2 + v[10]*x3 + v[15]*x4 + v[20]*x5;
2242       s2 -= v[1]*x1 + v[6]*x2 + v[11]*x3 + v[16]*x4 + v[21]*x5;
2243       s3 -= v[2]*x1 + v[7]*x2 + v[12]*x3 + v[17]*x4 + v[22]*x5;
2244       s4 -= v[3]*x1 + v[8]*x2 + v[13]*x3 + v[18]*x4 + v[23]*x5;
2245       s5 -= v[4]*x1 + v[9]*x2 + v[14]*x3 + v[19]*x4 + v[24]*x5;
2246       v += 25;
2247     }
2248     idc = 5*c[i];
2249     x[idc]   = t[idt]   = v[0]*s1+v[5]*s2+v[10]*s3+
2250                                  v[15]*s4+v[20]*s5;
2251     x[1+idc] = t[1+idt] = v[1]*s1+v[6]*s2+v[11]*s3+
2252                                  v[16]*s4+v[21]*s5;
2253     x[2+idc] = t[2+idt] = v[2]*s1+v[7]*s2+v[12]*s3+
2254                                  v[17]*s4+v[22]*s5;
2255     x[3+idc] = t[3+idt] = v[3]*s1+v[8]*s2+v[13]*s3+
2256                                  v[18]*s4+v[23]*s5;
2257     x[4+idc] = t[4+idt] = v[4]*s1+v[9]*s2+v[14]*s3+
2258                                  v[19]*s4+v[24]*s5;
2259   }
2260 
2261   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
2262   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
2263   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2264   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
2265   ierr = PetscLogFlops(2.0*25*(a->nz) - 5.0*A->cmap->n);CHKERRQ(ierr);
2266   PetscFunctionReturn(0);
2267 }
2268 #undef __FUNCT__
2269 #define __FUNCT__ "MatSolve_SeqBAIJ_5_NaturalOrdering"
2270 PetscErrorCode MatSolve_SeqBAIJ_5_NaturalOrdering(Mat A,Vec bb,Vec xx)
2271 {
2272   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ *)A->data;
2273   PetscInt          i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt;
2274   PetscErrorCode    ierr;
2275   PetscInt          *diag = a->diag,jdx;
2276   const MatScalar   *aa=a->a,*v;
2277   PetscScalar       *x,s1,s2,s3,s4,s5,x1,x2,x3,x4,x5;
2278   const PetscScalar *b;
2279 
2280   PetscFunctionBegin;
2281   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2282   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
2283   /* forward solve the lower triangular */
2284   idx    = 0;
2285   x[0] = b[idx]; x[1] = b[1+idx]; x[2] = b[2+idx]; x[3] = b[3+idx];x[4] = b[4+idx];
2286   for (i=1; i<n; i++) {
2287     v     =  aa + 25*ai[i];
2288     vi    =  aj + ai[i];
2289     nz    =  diag[i] - ai[i];
2290     idx   =  5*i;
2291     s1  =  b[idx];s2 = b[1+idx];s3 = b[2+idx];s4 = b[3+idx];s5 = b[4+idx];
2292     while (nz--) {
2293       jdx   = 5*(*vi++);
2294       x1    = x[jdx];x2 = x[1+jdx];x3 = x[2+jdx];x4 = x[3+jdx];x5 = x[4+jdx];
2295       s1 -= v[0]*x1 + v[5]*x2 + v[10]*x3  + v[15]*x4 + v[20]*x5;
2296       s2 -= v[1]*x1 + v[6]*x2 + v[11]*x3  + v[16]*x4 + v[21]*x5;
2297       s3 -= v[2]*x1 + v[7]*x2 + v[12]*x3  + v[17]*x4 + v[22]*x5;
2298       s4 -= v[3]*x1 + v[8]*x2 + v[13]*x3  + v[18]*x4 + v[23]*x5;
2299       s5 -= v[4]*x1 + v[9]*x2 + v[14]*x3  + v[19]*x4 + v[24]*x5;
2300       v    += 25;
2301     }
2302     x[idx]   = s1;
2303     x[1+idx] = s2;
2304     x[2+idx] = s3;
2305     x[3+idx] = s4;
2306     x[4+idx] = s5;
2307   }
2308   /* backward solve the upper triangular */
2309   for (i=n-1; i>=0; i--){
2310     v    = aa + 25*diag[i] + 25;
2311     vi   = aj + diag[i] + 1;
2312     nz   = ai[i+1] - diag[i] - 1;
2313     idt  = 5*i;
2314     s1 = x[idt];  s2 = x[1+idt];
2315     s3 = x[2+idt];s4 = x[3+idt]; s5 = x[4+idt];
2316     while (nz--) {
2317       idx   = 5*(*vi++);
2318       x1    = x[idx];   x2 = x[1+idx];x3    = x[2+idx]; x4 = x[3+idx]; x5 = x[4+idx];
2319       s1 -= v[0]*x1 + v[5]*x2 + v[10]*x3  + v[15]*x4 + v[20]*x5;
2320       s2 -= v[1]*x1 + v[6]*x2 + v[11]*x3  + v[16]*x4 + v[21]*x5;
2321       s3 -= v[2]*x1 + v[7]*x2 + v[12]*x3  + v[17]*x4 + v[22]*x5;
2322       s4 -= v[3]*x1 + v[8]*x2 + v[13]*x3  + v[18]*x4 + v[23]*x5;
2323       s5 -= v[4]*x1 + v[9]*x2 + v[14]*x3  + v[19]*x4 + v[24]*x5;
2324       v    += 25;
2325     }
2326     v        = aa + 25*diag[i];
2327     x[idt]   = v[0]*s1 + v[5]*s2 + v[10]*s3  + v[15]*s4 + v[20]*s5;
2328     x[1+idt] = v[1]*s1 + v[6]*s2 + v[11]*s3  + v[16]*s4 + v[21]*s5;
2329     x[2+idt] = v[2]*s1 + v[7]*s2 + v[12]*s3  + v[17]*s4 + v[22]*s5;
2330     x[3+idt] = v[3]*s1 + v[8]*s2 + v[13]*s3  + v[18]*s4 + v[23]*s5;
2331     x[4+idt] = v[4]*s1 + v[9]*s2 + v[14]*s3  + v[19]*s4 + v[24]*s5;
2332   }
2333 
2334   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2335   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
2336   ierr = PetscLogFlops(2.0*25*(a->nz) - 5.0*A->cmap->n);CHKERRQ(ierr);
2337   PetscFunctionReturn(0);
2338 }
2339 
2340 #undef __FUNCT__
2341 #define __FUNCT__ "MatSolve_SeqBAIJ_5_NaturalOrdering_newdatastruct"
2342 PetscErrorCode MatSolve_SeqBAIJ_5_NaturalOrdering_newdatastruct(Mat A,Vec bb,Vec xx)
2343 {
2344   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ *)A->data;
2345   PetscInt          i,k,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt;
2346   PetscErrorCode    ierr;
2347   PetscInt          jdx;
2348   const MatScalar   *aa=a->a,*v;
2349   PetscScalar       *x,s1,s2,s3,s4,s5,x1,x2,x3,x4,x5;
2350   const PetscScalar *b;
2351 
2352   PetscFunctionBegin;
2353   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2354   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
2355   /* forward solve the lower triangular */
2356   idx    = 0;
2357   x[0] = b[idx]; x[1] = b[1+idx]; x[2] = b[2+idx]; x[3] = b[3+idx];x[4] = b[4+idx];
2358   for (i=1; i<n; i++) {
2359     v   = aa + 25*ai[i];
2360     vi  = aj + ai[i];
2361     nz  = ai[i+1] - ai[i];
2362     idx = 5*i;
2363     s1  = b[idx];s2 = b[1+idx];s3 = b[2+idx];s4 = b[3+idx];s5 = b[4+idx];
2364     for(k=0;k<nz;k++) {
2365       jdx   = 5*vi[k];
2366       x1    = x[jdx];x2 = x[1+jdx];x3 = x[2+jdx];x4 = x[3+jdx];x5 = x[4+jdx];
2367       s1 -= v[0]*x1 + v[5]*x2 + v[10]*x3  + v[15]*x4 + v[20]*x5;
2368       s2 -= v[1]*x1 + v[6]*x2 + v[11]*x3  + v[16]*x4 + v[21]*x5;
2369       s3 -= v[2]*x1 + v[7]*x2 + v[12]*x3  + v[17]*x4 + v[22]*x5;
2370       s4 -= v[3]*x1 + v[8]*x2 + v[13]*x3  + v[18]*x4 + v[23]*x5;
2371       s5 -= v[4]*x1 + v[9]*x2 + v[14]*x3  + v[19]*x4 + v[24]*x5;
2372       v    += 25;
2373     }
2374     x[idx]   = s1;
2375     x[1+idx] = s2;
2376     x[2+idx] = s3;
2377     x[3+idx] = s4;
2378     x[4+idx] = s5;
2379   }
2380 
2381   /* backward solve the upper triangular */
2382   for (i=n-1; i>=0; i--){
2383     v   = aa + 25*ai[2*n-i];
2384     vi  = aj + ai[2*n-i];
2385     nz  = ai[2*n-i +1] - ai[2*n-i]-1;
2386     idt = 5*i;
2387     s1 = x[idt];  s2 = x[1+idt];
2388     s3 = x[2+idt];s4 = x[3+idt]; s5 = x[4+idt];
2389     for(k=0;k<nz;k++){
2390       idx   = 5*vi[k];
2391       x1    = x[idx];   x2 = x[1+idx];x3    = x[2+idx]; x4 = x[3+idx]; x5 = x[4+idx];
2392       s1 -= v[0]*x1 + v[5]*x2 + v[10]*x3  + v[15]*x4 + v[20]*x5;
2393       s2 -= v[1]*x1 + v[6]*x2 + v[11]*x3  + v[16]*x4 + v[21]*x5;
2394       s3 -= v[2]*x1 + v[7]*x2 + v[12]*x3  + v[17]*x4 + v[22]*x5;
2395       s4 -= v[3]*x1 + v[8]*x2 + v[13]*x3  + v[18]*x4 + v[23]*x5;
2396       s5 -= v[4]*x1 + v[9]*x2 + v[14]*x3  + v[19]*x4 + v[24]*x5;
2397       v    += 25;
2398     }
2399     /* x = inv_diagonal*x */
2400     x[idt]   = v[0]*s1 + v[5]*s2 + v[10]*s3  + v[15]*s4 + v[20]*s5;
2401     x[1+idt] = v[1]*s1 + v[6]*s2 + v[11]*s3  + v[16]*s4 + v[21]*s5;
2402     x[2+idt] = v[2]*s1 + v[7]*s2 + v[12]*s3  + v[17]*s4 + v[22]*s5;
2403     x[3+idt] = v[3]*s1 + v[8]*s2 + v[13]*s3  + v[18]*s4 + v[23]*s5;
2404     x[4+idt] = v[4]*s1 + v[9]*s2 + v[14]*s3  + v[19]*s4 + v[24]*s5;
2405   }
2406 
2407   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2408   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
2409   ierr = PetscLogFlops(2.0*25*(a->nz) - 5.0*A->cmap->n);CHKERRQ(ierr);
2410   PetscFunctionReturn(0);
2411 }
2412 
2413 #undef __FUNCT__
2414 #define __FUNCT__ "MatSolve_SeqBAIJ_5_NaturalOrdering_newdatastruct_v2"
2415 PetscErrorCode MatSolve_SeqBAIJ_5_NaturalOrdering_newdatastruct_v2(Mat A,Vec bb,Vec xx)
2416 {
2417   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ *)A->data;
2418   PetscInt          i,k,n=a->mbs,*vi,*ai=a->i,*aj=a->j,*adiag=a->diag,nz,idx,idt;
2419   PetscErrorCode    ierr;
2420   PetscInt          jdx;
2421   const MatScalar   *aa=a->a,*v;
2422   PetscScalar       *x,s1,s2,s3,s4,s5,x1,x2,x3,x4,x5;
2423   const PetscScalar *b;
2424 
2425   PetscFunctionBegin;
2426   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2427   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
2428   /* forward solve the lower triangular */
2429   idx    = 0;
2430   x[0] = b[idx]; x[1] = b[1+idx]; x[2] = b[2+idx]; x[3] = b[3+idx];x[4] = b[4+idx];
2431   for (i=1; i<n; i++) {
2432     v   = aa + 25*ai[i];
2433     vi  = aj + ai[i];
2434     nz  = ai[i+1] - ai[i];
2435     idx = 5*i;
2436     s1  = b[idx];s2 = b[1+idx];s3 = b[2+idx];s4 = b[3+idx];s5 = b[4+idx];
2437     for(k=0;k<nz;k++) {
2438       jdx   = 5*vi[k];
2439       x1    = x[jdx];x2 = x[1+jdx];x3 = x[2+jdx];x4 = x[3+jdx];x5 = x[4+jdx];
2440       s1 -= v[0]*x1 + v[5]*x2 + v[10]*x3  + v[15]*x4 + v[20]*x5;
2441       s2 -= v[1]*x1 + v[6]*x2 + v[11]*x3  + v[16]*x4 + v[21]*x5;
2442       s3 -= v[2]*x1 + v[7]*x2 + v[12]*x3  + v[17]*x4 + v[22]*x5;
2443       s4 -= v[3]*x1 + v[8]*x2 + v[13]*x3  + v[18]*x4 + v[23]*x5;
2444       s5 -= v[4]*x1 + v[9]*x2 + v[14]*x3  + v[19]*x4 + v[24]*x5;
2445       v    += 25;
2446     }
2447     x[idx]   = s1;
2448     x[1+idx] = s2;
2449     x[2+idx] = s3;
2450     x[3+idx] = s4;
2451     x[4+idx] = s5;
2452   }
2453 
2454   /* backward solve the upper triangular */
2455   for (i=n-1; i>=0; i--){
2456     v   = aa + 25*(adiag[i+1]+1);
2457     vi  = aj + adiag[i+1]+1;
2458     nz  = adiag[i] - adiag[i+1]-1;
2459     idt = 5*i;
2460     s1 = x[idt];  s2 = x[1+idt];
2461     s3 = x[2+idt];s4 = x[3+idt]; s5 = x[4+idt];
2462     for(k=0;k<nz;k++){
2463       idx   = 5*vi[k];
2464       x1    = x[idx];   x2 = x[1+idx];x3    = x[2+idx]; x4 = x[3+idx]; x5 = x[4+idx];
2465       s1 -= v[0]*x1 + v[5]*x2 + v[10]*x3  + v[15]*x4 + v[20]*x5;
2466       s2 -= v[1]*x1 + v[6]*x2 + v[11]*x3  + v[16]*x4 + v[21]*x5;
2467       s3 -= v[2]*x1 + v[7]*x2 + v[12]*x3  + v[17]*x4 + v[22]*x5;
2468       s4 -= v[3]*x1 + v[8]*x2 + v[13]*x3  + v[18]*x4 + v[23]*x5;
2469       s5 -= v[4]*x1 + v[9]*x2 + v[14]*x3  + v[19]*x4 + v[24]*x5;
2470       v    += 25;
2471     }
2472     /* x = inv_diagonal*x */
2473     x[idt]   = v[0]*s1 + v[5]*s2 + v[10]*s3  + v[15]*s4 + v[20]*s5;
2474     x[1+idt] = v[1]*s1 + v[6]*s2 + v[11]*s3  + v[16]*s4 + v[21]*s5;
2475     x[2+idt] = v[2]*s1 + v[7]*s2 + v[12]*s3  + v[17]*s4 + v[22]*s5;
2476     x[3+idt] = v[3]*s1 + v[8]*s2 + v[13]*s3  + v[18]*s4 + v[23]*s5;
2477     x[4+idt] = v[4]*s1 + v[9]*s2 + v[14]*s3  + v[19]*s4 + v[24]*s5;
2478   }
2479 
2480   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2481   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
2482   ierr = PetscLogFlops(2.0*25*(a->nz) - 5.0*A->cmap->n);CHKERRQ(ierr);
2483   PetscFunctionReturn(0);
2484 }
2485 
2486 #undef __FUNCT__
2487 #define __FUNCT__ "MatSolve_SeqBAIJ_4"
2488 PetscErrorCode MatSolve_SeqBAIJ_4(Mat A,Vec bb,Vec xx)
2489 {
2490   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ *)A->data;
2491   IS                iscol=a->col,isrow=a->row;
2492   PetscErrorCode    ierr;
2493   PetscInt          i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc;
2494   const PetscInt    *r,*c,*diag = a->diag,*rout,*cout;
2495   const MatScalar   *aa=a->a,*v;
2496   PetscScalar       *x,s1,s2,s3,s4,x1,x2,x3,x4,*t;
2497   const PetscScalar *b;
2498 
2499   PetscFunctionBegin;
2500   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2501   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
2502   t  = a->solve_work;
2503 
2504   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
2505   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
2506 
2507   /* forward solve the lower triangular */
2508   idx    = 4*(*r++);
2509   t[0] = b[idx];   t[1] = b[1+idx];
2510   t[2] = b[2+idx]; t[3] = b[3+idx];
2511   for (i=1; i<n; i++) {
2512     v     = aa + 16*ai[i];
2513     vi    = aj + ai[i];
2514     nz    = diag[i] - ai[i];
2515     idx   = 4*(*r++);
2516     s1  = b[idx];s2 = b[1+idx];s3 = b[2+idx];s4 = b[3+idx];
2517     while (nz--) {
2518       idx   = 4*(*vi++);
2519       x1    = t[idx];x2 = t[1+idx];x3 = t[2+idx];x4 = t[3+idx];
2520       s1 -= v[0]*x1 + v[4]*x2 + v[8]*x3  + v[12]*x4;
2521       s2 -= v[1]*x1 + v[5]*x2 + v[9]*x3  + v[13]*x4;
2522       s3 -= v[2]*x1 + v[6]*x2 + v[10]*x3 + v[14]*x4;
2523       s4 -= v[3]*x1 + v[7]*x2 + v[11]*x3 + v[15]*x4;
2524       v    += 16;
2525     }
2526     idx        = 4*i;
2527     t[idx]   = s1;t[1+idx] = s2;
2528     t[2+idx] = s3;t[3+idx] = s4;
2529   }
2530   /* backward solve the upper triangular */
2531   for (i=n-1; i>=0; i--){
2532     v    = aa + 16*diag[i] + 16;
2533     vi   = aj + diag[i] + 1;
2534     nz   = ai[i+1] - diag[i] - 1;
2535     idt  = 4*i;
2536     s1 = t[idt];  s2 = t[1+idt];
2537     s3 = t[2+idt];s4 = t[3+idt];
2538     while (nz--) {
2539       idx   = 4*(*vi++);
2540       x1    = t[idx];   x2 = t[1+idx];
2541       x3    = t[2+idx]; x4 = t[3+idx];
2542       s1 -= v[0]*x1 + v[4]*x2 + v[8]*x3   + v[12]*x4;
2543       s2 -= v[1]*x1 + v[5]*x2 + v[9]*x3   + v[13]*x4;
2544       s3 -= v[2]*x1 + v[6]*x2 + v[10]*x3  + v[14]*x4;
2545       s4 -= v[3]*x1 + v[7]*x2 + v[11]*x3  + v[15]*x4;
2546       v += 16;
2547     }
2548     idc      = 4*(*c--);
2549     v        = aa + 16*diag[i];
2550     x[idc]   = t[idt]   = v[0]*s1+v[4]*s2+v[8]*s3+v[12]*s4;
2551     x[1+idc] = t[1+idt] = v[1]*s1+v[5]*s2+v[9]*s3+v[13]*s4;
2552     x[2+idc] = t[2+idt] = v[2]*s1+v[6]*s2+v[10]*s3+v[14]*s4;
2553     x[3+idc] = t[3+idt] = v[3]*s1+v[7]*s2+v[11]*s3+v[15]*s4;
2554   }
2555 
2556   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
2557   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
2558   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2559   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
2560   ierr = PetscLogFlops(2.0*16*(a->nz) - 4.0*A->cmap->n);CHKERRQ(ierr);
2561   PetscFunctionReturn(0);
2562 }
2563 
2564 #undef __FUNCT__
2565 #define __FUNCT__ "MatSolve_SeqBAIJ_4_newdatastruct"
2566 PetscErrorCode MatSolve_SeqBAIJ_4_newdatastruct(Mat A,Vec bb,Vec xx)
2567 {
2568   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ *)A->data;
2569   IS                iscol=a->col,isrow=a->row;
2570   PetscErrorCode    ierr;
2571   PetscInt          i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,k,m;
2572   const PetscInt    *r,*c,*rout,*cout;
2573   const MatScalar   *aa=a->a,*v;
2574   PetscScalar       *x,s1,s2,s3,s4,x1,x2,x3,x4,*t;
2575   const PetscScalar *b;
2576 
2577   PetscFunctionBegin;
2578   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2579   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
2580   t  = a->solve_work;
2581 
2582   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
2583   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
2584 
2585   /* forward solve the lower triangular */
2586   idx    = 4*r[0];
2587   t[0] = b[idx];   t[1] = b[1+idx];
2588   t[2] = b[2+idx]; t[3] = b[3+idx];
2589   for (i=1; i<n; i++) {
2590     v     = aa + 16*ai[i];
2591     vi    = aj + ai[i];
2592     nz    = ai[i+1] - ai[i];
2593     idx   = 4*r[i];
2594     s1  = b[idx];s2 = b[1+idx];s3 = b[2+idx];s4 = b[3+idx];
2595     for(m=0;m<nz;m++){
2596       idx   = 4*vi[m];
2597       x1    = t[idx];x2 = t[1+idx];x3 = t[2+idx];x4 = t[3+idx];
2598       s1 -= v[0]*x1 + v[4]*x2 + v[8]*x3  + v[12]*x4;
2599       s2 -= v[1]*x1 + v[5]*x2 + v[9]*x3  + v[13]*x4;
2600       s3 -= v[2]*x1 + v[6]*x2 + v[10]*x3 + v[14]*x4;
2601       s4 -= v[3]*x1 + v[7]*x2 + v[11]*x3 + v[15]*x4;
2602       v    += 16;
2603     }
2604     idx        = 4*i;
2605     t[idx]   = s1;t[1+idx] = s2;
2606     t[2+idx] = s3;t[3+idx] = s4;
2607   }
2608   /* backward solve the upper triangular */
2609   for (i=n-1; i>=0; i--){
2610     k    = 2*n-i;
2611     v    = aa + 16*ai[k];
2612     vi   = aj + ai[k];
2613     nz   = ai[k+1] - ai[k] - 1;
2614     idt  = 4*i;
2615     s1 = t[idt];  s2 = t[1+idt];
2616     s3 = t[2+idt];s4 = t[3+idt];
2617     for(m=0;m<nz;m++){
2618       idx   = 4*vi[m];
2619       x1    = t[idx];   x2 = t[1+idx];
2620       x3    = t[2+idx]; x4 = t[3+idx];
2621       s1 -= v[0]*x1 + v[4]*x2 + v[8]*x3   + v[12]*x4;
2622       s2 -= v[1]*x1 + v[5]*x2 + v[9]*x3   + v[13]*x4;
2623       s3 -= v[2]*x1 + v[6]*x2 + v[10]*x3  + v[14]*x4;
2624       s4 -= v[3]*x1 + v[7]*x2 + v[11]*x3  + v[15]*x4;
2625       v += 16;
2626     }
2627     idc      = 4*c[i];
2628     x[idc]   = t[idt]   = v[0]*s1+v[4]*s2+v[8]*s3+v[12]*s4;
2629     x[1+idc] = t[1+idt] = v[1]*s1+v[5]*s2+v[9]*s3+v[13]*s4;
2630     x[2+idc] = t[2+idt] = v[2]*s1+v[6]*s2+v[10]*s3+v[14]*s4;
2631     x[3+idc] = t[3+idt] = v[3]*s1+v[7]*s2+v[11]*s3+v[15]*s4;
2632   }
2633 
2634   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
2635   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
2636   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2637   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
2638   ierr = PetscLogFlops(2.0*16*(a->nz) - 4.0*A->cmap->n);CHKERRQ(ierr);
2639   PetscFunctionReturn(0);
2640 }
2641 
2642 #undef __FUNCT__
2643 #define __FUNCT__ "MatSolve_SeqBAIJ_4_Demotion"
2644 PetscErrorCode MatSolve_SeqBAIJ_4_Demotion(Mat A,Vec bb,Vec xx)
2645 {
2646   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ *)A->data;
2647   IS                iscol=a->col,isrow=a->row;
2648   PetscErrorCode    ierr;
2649   PetscInt          i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc;
2650   const PetscInt    *r,*c,*diag = a->diag,*rout,*cout;
2651   const MatScalar   *aa=a->a,*v;
2652   MatScalar         s1,s2,s3,s4,x1,x2,x3,x4,*t;
2653   PetscScalar       *x;
2654   const PetscScalar *b;
2655 
2656   PetscFunctionBegin;
2657   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2658   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
2659   t  = (MatScalar *)a->solve_work;
2660 
2661   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
2662   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
2663 
2664   /* forward solve the lower triangular */
2665   idx    = 4*(*r++);
2666   t[0] = (MatScalar)b[idx];
2667   t[1] = (MatScalar)b[1+idx];
2668   t[2] = (MatScalar)b[2+idx];
2669   t[3] = (MatScalar)b[3+idx];
2670   for (i=1; i<n; i++) {
2671     v     = aa + 16*ai[i];
2672     vi    = aj + ai[i];
2673     nz    = diag[i] - ai[i];
2674     idx   = 4*(*r++);
2675     s1 = (MatScalar)b[idx];
2676     s2 = (MatScalar)b[1+idx];
2677     s3 = (MatScalar)b[2+idx];
2678     s4 = (MatScalar)b[3+idx];
2679     while (nz--) {
2680       idx   = 4*(*vi++);
2681       x1  = t[idx];
2682       x2  = t[1+idx];
2683       x3  = t[2+idx];
2684       x4  = t[3+idx];
2685       s1 -= v[0]*x1 + v[4]*x2 + v[8]*x3  + v[12]*x4;
2686       s2 -= v[1]*x1 + v[5]*x2 + v[9]*x3  + v[13]*x4;
2687       s3 -= v[2]*x1 + v[6]*x2 + v[10]*x3 + v[14]*x4;
2688       s4 -= v[3]*x1 + v[7]*x2 + v[11]*x3 + v[15]*x4;
2689       v    += 16;
2690     }
2691     idx        = 4*i;
2692     t[idx]   = s1;
2693     t[1+idx] = s2;
2694     t[2+idx] = s3;
2695     t[3+idx] = s4;
2696   }
2697   /* backward solve the upper triangular */
2698   for (i=n-1; i>=0; i--){
2699     v    = aa + 16*diag[i] + 16;
2700     vi   = aj + diag[i] + 1;
2701     nz   = ai[i+1] - diag[i] - 1;
2702     idt  = 4*i;
2703     s1 = t[idt];
2704     s2 = t[1+idt];
2705     s3 = t[2+idt];
2706     s4 = t[3+idt];
2707     while (nz--) {
2708       idx   = 4*(*vi++);
2709       x1  = t[idx];
2710       x2  = t[1+idx];
2711       x3  = t[2+idx];
2712       x4  = t[3+idx];
2713       s1 -= v[0]*x1 + v[4]*x2 + v[8]*x3   + v[12]*x4;
2714       s2 -= v[1]*x1 + v[5]*x2 + v[9]*x3   + v[13]*x4;
2715       s3 -= v[2]*x1 + v[6]*x2 + v[10]*x3  + v[14]*x4;
2716       s4 -= v[3]*x1 + v[7]*x2 + v[11]*x3  + v[15]*x4;
2717       v += 16;
2718     }
2719     idc      = 4*(*c--);
2720     v        = aa + 16*diag[i];
2721     t[idt]   = v[0]*s1+v[4]*s2+v[8]*s3+v[12]*s4;
2722     t[1+idt] = v[1]*s1+v[5]*s2+v[9]*s3+v[13]*s4;
2723     t[2+idt] = v[2]*s1+v[6]*s2+v[10]*s3+v[14]*s4;
2724     t[3+idt] = v[3]*s1+v[7]*s2+v[11]*s3+v[15]*s4;
2725     x[idc]   = (PetscScalar)t[idt];
2726     x[1+idc] = (PetscScalar)t[1+idt];
2727     x[2+idc] = (PetscScalar)t[2+idt];
2728     x[3+idc] = (PetscScalar)t[3+idt];
2729  }
2730 
2731   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
2732   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
2733   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2734   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
2735   ierr = PetscLogFlops(2.0*16*(a->nz) - 4.0*A->cmap->n);CHKERRQ(ierr);
2736   PetscFunctionReturn(0);
2737 }
2738 
2739 #if defined (PETSC_HAVE_SSE)
2740 
2741 #include PETSC_HAVE_SSE
2742 
2743 #undef __FUNCT__
2744 #define __FUNCT__ "MatSolve_SeqBAIJ_4_SSE_Demotion"
2745 PetscErrorCode MatSolve_SeqBAIJ_4_SSE_Demotion(Mat A,Vec bb,Vec xx)
2746 {
2747   /*
2748      Note: This code uses demotion of double
2749      to float when performing the mixed-mode computation.
2750      This may not be numerically reasonable for all applications.
2751   */
2752   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ *)A->data;
2753   IS             iscol=a->col,isrow=a->row;
2754   PetscErrorCode ierr;
2755   PetscInt       i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,ai16;
2756   const PetscInt *r,*c,*diag = a->diag,*rout,*cout;
2757   MatScalar      *aa=a->a,*v;
2758   PetscScalar    *x,*b,*t;
2759 
2760   /* Make space in temp stack for 16 Byte Aligned arrays */
2761   float           ssealignedspace[11],*tmps,*tmpx;
2762   unsigned long   offset;
2763 
2764   PetscFunctionBegin;
2765   SSE_SCOPE_BEGIN;
2766 
2767     offset = (unsigned long)ssealignedspace % 16;
2768     if (offset) offset = (16 - offset)/4;
2769     tmps = &ssealignedspace[offset];
2770     tmpx = &ssealignedspace[offset+4];
2771     PREFETCH_NTA(aa+16*ai[1]);
2772 
2773     ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
2774     ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
2775     t  = a->solve_work;
2776 
2777     ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
2778     ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
2779 
2780     /* forward solve the lower triangular */
2781     idx  = 4*(*r++);
2782     t[0] = b[idx];   t[1] = b[1+idx];
2783     t[2] = b[2+idx]; t[3] = b[3+idx];
2784     v    =  aa + 16*ai[1];
2785 
2786     for (i=1; i<n;) {
2787       PREFETCH_NTA(&v[8]);
2788       vi   =  aj      + ai[i];
2789       nz   =  diag[i] - ai[i];
2790       idx  =  4*(*r++);
2791 
2792       /* Demote sum from double to float */
2793       CONVERT_DOUBLE4_FLOAT4(tmps,&b[idx]);
2794       LOAD_PS(tmps,XMM7);
2795 
2796       while (nz--) {
2797         PREFETCH_NTA(&v[16]);
2798         idx = 4*(*vi++);
2799 
2800         /* Demote solution (so far) from double to float */
2801         CONVERT_DOUBLE4_FLOAT4(tmpx,&x[idx]);
2802 
2803         /* 4x4 Matrix-Vector product with negative accumulation: */
2804         SSE_INLINE_BEGIN_2(tmpx,v)
2805           SSE_LOAD_PS(SSE_ARG_1,FLOAT_0,XMM6)
2806 
2807           /* First Column */
2808           SSE_COPY_PS(XMM0,XMM6)
2809           SSE_SHUFFLE(XMM0,XMM0,0x00)
2810           SSE_MULT_PS_M(XMM0,SSE_ARG_2,FLOAT_0)
2811           SSE_SUB_PS(XMM7,XMM0)
2812 
2813           /* Second Column */
2814           SSE_COPY_PS(XMM1,XMM6)
2815           SSE_SHUFFLE(XMM1,XMM1,0x55)
2816           SSE_MULT_PS_M(XMM1,SSE_ARG_2,FLOAT_4)
2817           SSE_SUB_PS(XMM7,XMM1)
2818 
2819           SSE_PREFETCH_NTA(SSE_ARG_2,FLOAT_24)
2820 
2821           /* Third Column */
2822           SSE_COPY_PS(XMM2,XMM6)
2823           SSE_SHUFFLE(XMM2,XMM2,0xAA)
2824           SSE_MULT_PS_M(XMM2,SSE_ARG_2,FLOAT_8)
2825           SSE_SUB_PS(XMM7,XMM2)
2826 
2827           /* Fourth Column */
2828           SSE_COPY_PS(XMM3,XMM6)
2829           SSE_SHUFFLE(XMM3,XMM3,0xFF)
2830           SSE_MULT_PS_M(XMM3,SSE_ARG_2,FLOAT_12)
2831           SSE_SUB_PS(XMM7,XMM3)
2832         SSE_INLINE_END_2
2833 
2834         v  += 16;
2835       }
2836       idx = 4*i;
2837       v   = aa + 16*ai[++i];
2838       PREFETCH_NTA(v);
2839       STORE_PS(tmps,XMM7);
2840 
2841       /* Promote result from float to double */
2842       CONVERT_FLOAT4_DOUBLE4(&t[idx],tmps);
2843     }
2844     /* backward solve the upper triangular */
2845     idt  = 4*(n-1);
2846     ai16 = 16*diag[n-1];
2847     v    = aa + ai16 + 16;
2848     for (i=n-1; i>=0;){
2849       PREFETCH_NTA(&v[8]);
2850       vi = aj + diag[i] + 1;
2851       nz = ai[i+1] - diag[i] - 1;
2852 
2853       /* Demote accumulator from double to float */
2854       CONVERT_DOUBLE4_FLOAT4(tmps,&t[idt]);
2855       LOAD_PS(tmps,XMM7);
2856 
2857       while (nz--) {
2858         PREFETCH_NTA(&v[16]);
2859         idx = 4*(*vi++);
2860 
2861         /* Demote solution (so far) from double to float */
2862         CONVERT_DOUBLE4_FLOAT4(tmpx,&t[idx]);
2863 
2864         /* 4x4 Matrix-Vector Product with negative accumulation: */
2865         SSE_INLINE_BEGIN_2(tmpx,v)
2866           SSE_LOAD_PS(SSE_ARG_1,FLOAT_0,XMM6)
2867 
2868           /* First Column */
2869           SSE_COPY_PS(XMM0,XMM6)
2870           SSE_SHUFFLE(XMM0,XMM0,0x00)
2871           SSE_MULT_PS_M(XMM0,SSE_ARG_2,FLOAT_0)
2872           SSE_SUB_PS(XMM7,XMM0)
2873 
2874           /* Second Column */
2875           SSE_COPY_PS(XMM1,XMM6)
2876           SSE_SHUFFLE(XMM1,XMM1,0x55)
2877           SSE_MULT_PS_M(XMM1,SSE_ARG_2,FLOAT_4)
2878           SSE_SUB_PS(XMM7,XMM1)
2879 
2880           SSE_PREFETCH_NTA(SSE_ARG_2,FLOAT_24)
2881 
2882           /* Third Column */
2883           SSE_COPY_PS(XMM2,XMM6)
2884           SSE_SHUFFLE(XMM2,XMM2,0xAA)
2885           SSE_MULT_PS_M(XMM2,SSE_ARG_2,FLOAT_8)
2886           SSE_SUB_PS(XMM7,XMM2)
2887 
2888           /* Fourth Column */
2889           SSE_COPY_PS(XMM3,XMM6)
2890           SSE_SHUFFLE(XMM3,XMM3,0xFF)
2891           SSE_MULT_PS_M(XMM3,SSE_ARG_2,FLOAT_12)
2892           SSE_SUB_PS(XMM7,XMM3)
2893         SSE_INLINE_END_2
2894         v  += 16;
2895       }
2896       v    = aa + ai16;
2897       ai16 = 16*diag[--i];
2898       PREFETCH_NTA(aa+ai16+16);
2899       /*
2900          Scale the result by the diagonal 4x4 block,
2901          which was inverted as part of the factorization
2902       */
2903       SSE_INLINE_BEGIN_3(v,tmps,aa+ai16)
2904         /* First Column */
2905         SSE_COPY_PS(XMM0,XMM7)
2906         SSE_SHUFFLE(XMM0,XMM0,0x00)
2907         SSE_MULT_PS_M(XMM0,SSE_ARG_1,FLOAT_0)
2908 
2909         /* Second Column */
2910         SSE_COPY_PS(XMM1,XMM7)
2911         SSE_SHUFFLE(XMM1,XMM1,0x55)
2912         SSE_MULT_PS_M(XMM1,SSE_ARG_1,FLOAT_4)
2913         SSE_ADD_PS(XMM0,XMM1)
2914 
2915         SSE_PREFETCH_NTA(SSE_ARG_3,FLOAT_24)
2916 
2917         /* Third Column */
2918         SSE_COPY_PS(XMM2,XMM7)
2919         SSE_SHUFFLE(XMM2,XMM2,0xAA)
2920         SSE_MULT_PS_M(XMM2,SSE_ARG_1,FLOAT_8)
2921         SSE_ADD_PS(XMM0,XMM2)
2922 
2923         /* Fourth Column */
2924         SSE_COPY_PS(XMM3,XMM7)
2925         SSE_SHUFFLE(XMM3,XMM3,0xFF)
2926         SSE_MULT_PS_M(XMM3,SSE_ARG_1,FLOAT_12)
2927         SSE_ADD_PS(XMM0,XMM3)
2928 
2929         SSE_STORE_PS(SSE_ARG_2,FLOAT_0,XMM0)
2930       SSE_INLINE_END_3
2931 
2932       /* Promote solution from float to double */
2933       CONVERT_FLOAT4_DOUBLE4(&t[idt],tmps);
2934 
2935       /* Apply reordering to t and stream into x.    */
2936       /* This way, x doesn't pollute the cache.      */
2937       /* Be careful with size: 2 doubles = 4 floats! */
2938       idc  = 4*(*c--);
2939       SSE_INLINE_BEGIN_2((float *)&t[idt],(float *)&x[idc])
2940         /*  x[idc]   = t[idt];   x[1+idc] = t[1+idc]; */
2941         SSE_LOAD_PS(SSE_ARG_1,FLOAT_0,XMM0)
2942         SSE_STREAM_PS(SSE_ARG_2,FLOAT_0,XMM0)
2943         /*  x[idc+2] = t[idt+2]; x[3+idc] = t[3+idc]; */
2944         SSE_LOAD_PS(SSE_ARG_1,FLOAT_4,XMM1)
2945         SSE_STREAM_PS(SSE_ARG_2,FLOAT_4,XMM1)
2946       SSE_INLINE_END_2
2947       v    = aa + ai16 + 16;
2948       idt -= 4;
2949     }
2950 
2951     ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
2952     ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
2953     ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
2954     ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
2955     ierr = PetscLogFlops(2.0*16*(a->nz) - 4.0*A->cmap->n);CHKERRQ(ierr);
2956   SSE_SCOPE_END;
2957   PetscFunctionReturn(0);
2958 }
2959 
2960 #endif
2961 
2962 
2963 /*
2964       Special case where the matrix was ILU(0) factored in the natural
2965    ordering. This eliminates the need for the column and row permutation.
2966 */
2967 #undef __FUNCT__
2968 #define __FUNCT__ "MatSolve_SeqBAIJ_4_NaturalOrdering"
2969 PetscErrorCode MatSolve_SeqBAIJ_4_NaturalOrdering(Mat A,Vec bb,Vec xx)
2970 {
2971   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ *)A->data;
2972   PetscInt          n=a->mbs;
2973   const PetscInt    *ai=a->i,*aj=a->j;
2974   PetscErrorCode    ierr;
2975   const PetscInt    *diag = a->diag;
2976   const MatScalar   *aa=a->a;
2977   PetscScalar       *x;
2978   const PetscScalar *b;
2979 
2980   PetscFunctionBegin;
2981   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2982   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
2983 
2984 #if defined(PETSC_USE_FORTRAN_KERNEL_SOLVEBAIJBLAS)
2985   {
2986     static PetscScalar w[2000]; /* very BAD need to fix */
2987     fortransolvebaij4blas_(&n,x,ai,aj,diag,aa,b,w);
2988   }
2989 #elif defined(PETSC_USE_FORTRAN_KERNEL_SOLVEBAIJ)
2990   {
2991     static PetscScalar w[2000]; /* very BAD need to fix */
2992     fortransolvebaij4_(&n,x,ai,aj,diag,aa,b,w);
2993   }
2994 #elif defined(PETSC_USE_FORTRAN_KERNEL_SOLVEBAIJUNROLL)
2995   fortransolvebaij4unroll_(&n,x,ai,aj,diag,aa,b);
2996 #else
2997   {
2998     PetscScalar     s1,s2,s3,s4,x1,x2,x3,x4;
2999     const MatScalar *v;
3000     PetscInt        jdx,idt,idx,nz,i,ai16;
3001     const PetscInt  *vi;
3002 
3003   /* forward solve the lower triangular */
3004   idx    = 0;
3005   x[0]   = b[0]; x[1] = b[1]; x[2] = b[2]; x[3] = b[3];
3006   for (i=1; i<n; i++) {
3007     v     =  aa      + 16*ai[i];
3008     vi    =  aj      + ai[i];
3009     nz    =  diag[i] - ai[i];
3010     idx   +=  4;
3011     s1  =  b[idx];s2 = b[1+idx];s3 = b[2+idx];s4 = b[3+idx];
3012     while (nz--) {
3013       jdx   = 4*(*vi++);
3014       x1    = x[jdx];x2 = x[1+jdx];x3 = x[2+jdx];x4 = x[3+jdx];
3015       s1 -= v[0]*x1 + v[4]*x2 + v[8]*x3  + v[12]*x4;
3016       s2 -= v[1]*x1 + v[5]*x2 + v[9]*x3  + v[13]*x4;
3017       s3 -= v[2]*x1 + v[6]*x2 + v[10]*x3 + v[14]*x4;
3018       s4 -= v[3]*x1 + v[7]*x2 + v[11]*x3 + v[15]*x4;
3019       v    += 16;
3020     }
3021     x[idx]   = s1;
3022     x[1+idx] = s2;
3023     x[2+idx] = s3;
3024     x[3+idx] = s4;
3025   }
3026   /* backward solve the upper triangular */
3027   idt = 4*(n-1);
3028   for (i=n-1; i>=0; i--){
3029     ai16 = 16*diag[i];
3030     v    = aa + ai16 + 16;
3031     vi   = aj + diag[i] + 1;
3032     nz   = ai[i+1] - diag[i] - 1;
3033     s1 = x[idt];  s2 = x[1+idt];
3034     s3 = x[2+idt];s4 = x[3+idt];
3035     while (nz--) {
3036       idx   = 4*(*vi++);
3037       x1    = x[idx];   x2 = x[1+idx];x3    = x[2+idx]; x4 = x[3+idx];
3038       s1 -= v[0]*x1 + v[4]*x2 + v[8]*x3   + v[12]*x4;
3039       s2 -= v[1]*x1 + v[5]*x2 + v[9]*x3   + v[13]*x4;
3040       s3 -= v[2]*x1 + v[6]*x2 + v[10]*x3  + v[14]*x4;
3041       s4 -= v[3]*x1 + v[7]*x2 + v[11]*x3  + v[15]*x4;
3042       v    += 16;
3043     }
3044     v        = aa + ai16;
3045     x[idt]   = v[0]*s1 + v[4]*s2 + v[8]*s3  + v[12]*s4;
3046     x[1+idt] = v[1]*s1 + v[5]*s2 + v[9]*s3  + v[13]*s4;
3047     x[2+idt] = v[2]*s1 + v[6]*s2 + v[10]*s3 + v[14]*s4;
3048     x[3+idt] = v[3]*s1 + v[7]*s2 + v[11]*s3 + v[15]*s4;
3049     idt -= 4;
3050   }
3051   }
3052 #endif
3053 
3054   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3055   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
3056   ierr = PetscLogFlops(2.0*16*(a->nz) - 4.0*A->cmap->n);CHKERRQ(ierr);
3057   PetscFunctionReturn(0);
3058 }
3059 
3060 #undef __FUNCT__
3061 #define __FUNCT__ "MatSolve_SeqBAIJ_4_NaturalOrdering_newdatastruct"
3062 PetscErrorCode MatSolve_SeqBAIJ_4_NaturalOrdering_newdatastruct(Mat A,Vec bb,Vec xx)
3063 {
3064     Mat_SeqBAIJ       *a = (Mat_SeqBAIJ *)A->data;
3065     PetscInt          i,k,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz;
3066     PetscErrorCode    ierr;
3067     PetscInt          idx,jdx,idt;
3068     PetscInt          bs = A->rmap->bs,bs2 = a->bs2;
3069     const MatScalar   *aa=a->a,*v;
3070     PetscScalar       *x;
3071     const PetscScalar *b;
3072     PetscScalar        s1,s2,s3,s4,x1,x2,x3,x4;
3073 
3074     PetscFunctionBegin;
3075     ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3076     ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
3077     /* forward solve the lower triangular */
3078     idx    = 0;
3079     x[0] = b[idx]; x[1] = b[1+idx];x[2] = b[2+idx];x[3] = b[3+idx];
3080     for (i=1; i<n; i++) {
3081        v    = aa + bs2*ai[i];
3082        vi   = aj + ai[i];
3083        nz   = ai[i+1] - ai[i];
3084       idx   = bs*i;
3085        s1   = b[idx];s2 = b[1+idx];s3 = b[2+idx];s4 = b[3+idx];
3086       for(k=0;k<nz;k++) {
3087           jdx   = bs*vi[k];
3088           x1    = x[jdx];x2 = x[1+jdx]; x3 =x[2+jdx];x4 =x[3+jdx];
3089           s1   -= v[0]*x1 + v[4]*x2 + v[8]*x3 + v[12]*x4;
3090           s2   -= v[1]*x1 + v[5]*x2 + v[9]*x3 + v[13]*x4;
3091           s3   -= v[2]*x1 + v[6]*x2 + v[10]*x3 + v[14]*x4;
3092 	  s4   -= v[3]*x1 + v[7]*x2 + v[11]*x3 + v[15]*x4;
3093 
3094           v   +=  bs2;
3095         }
3096 
3097        x[idx]   = s1;
3098        x[1+idx] = s2;
3099        x[2+idx] = s3;
3100        x[3+idx] = s4;
3101     }
3102 
3103    /* backward solve the upper triangular */
3104   for (i=n-1; i>=0; i--){
3105      v   = aa + bs2*ai[2*n-i];
3106      vi  = aj + ai[2*n-i];
3107      nz  = ai[2*n-i +1] - ai[2*n-i]-1;
3108      idt = bs*i;
3109      s1 = x[idt];  s2 = x[1+idt];s3 = x[2+idt];s4 = x[3+idt];
3110 
3111     for(k=0;k<nz;k++){
3112       idx   = bs*vi[k];
3113        x1    = x[idx];   x2 = x[1+idx]; x3 = x[2+idx];x4 = x[3+idx];
3114        s1   -= v[0]*x1 + v[4]*x2 + v[8]*x3 + v[12]*x4;
3115        s2   -= v[1]*x1 + v[5]*x2 + v[9]*x3 + v[13]*x4;
3116        s3   -= v[2]*x1 + v[6]*x2 + v[10]*x3 + v[14]*x4;
3117        s4   -= v[3]*x1 + v[7]*x2 + v[11]*x3 + v[15]*x4;
3118 
3119         v   +=  bs2;
3120     }
3121     /* x = inv_diagonal*x */
3122    x[idt]   = v[0]*s1 + v[4]*s2 + v[8]*s3 + v[12]*s4;
3123    x[1+idt] = v[1]*s1 + v[5]*s2 + v[9]*s3 + v[13]*s4;;
3124    x[2+idt] = v[2]*s1 + v[6]*s2 + v[10]*s3 + v[14]*s4;
3125    x[3+idt] = v[3]*s1 + v[7]*s2 + v[11]*s3 + v[15]*s4;
3126 
3127   }
3128 
3129   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3130   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
3131   ierr = PetscLogFlops(2.0*bs2*(a->nz) - bs*A->cmap->n);CHKERRQ(ierr);
3132   PetscFunctionReturn(0);
3133 }
3134 
3135 #undef __FUNCT__
3136 #define __FUNCT__ "MatSolve_SeqBAIJ_4_NaturalOrdering_newdatastruct_v2"
3137 PetscErrorCode MatSolve_SeqBAIJ_4_NaturalOrdering_newdatastruct_v2(Mat A,Vec bb,Vec xx)
3138 {
3139     Mat_SeqBAIJ       *a = (Mat_SeqBAIJ *)A->data;
3140     PetscInt          i,k,n=a->mbs,*vi,*ai=a->i,*aj=a->j,*adiag=a->diag,nz;
3141     PetscErrorCode    ierr;
3142     PetscInt          idx,jdx,idt;
3143     PetscInt          bs = A->rmap->bs,bs2 = a->bs2;
3144     const MatScalar   *aa=a->a,*v;
3145     PetscScalar       *x;
3146     const PetscScalar *b;
3147     PetscScalar        s1,s2,s3,s4,x1,x2,x3,x4;
3148 
3149     PetscFunctionBegin;
3150     ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3151     ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
3152     /* forward solve the lower triangular */
3153     idx    = 0;
3154     x[0] = b[idx]; x[1] = b[1+idx];x[2] = b[2+idx];x[3] = b[3+idx];
3155     for (i=1; i<n; i++) {
3156        v    = aa + bs2*ai[i];
3157        vi   = aj + ai[i];
3158        nz   = ai[i+1] - ai[i];
3159       idx   = bs*i;
3160        s1   = b[idx];s2 = b[1+idx];s3 = b[2+idx];s4 = b[3+idx];
3161       for(k=0;k<nz;k++) {
3162           jdx   = bs*vi[k];
3163           x1    = x[jdx];x2 = x[1+jdx]; x3 =x[2+jdx];x4 =x[3+jdx];
3164           s1   -= v[0]*x1 + v[4]*x2 + v[8]*x3 + v[12]*x4;
3165           s2   -= v[1]*x1 + v[5]*x2 + v[9]*x3 + v[13]*x4;
3166           s3   -= v[2]*x1 + v[6]*x2 + v[10]*x3 + v[14]*x4;
3167 	  s4   -= v[3]*x1 + v[7]*x2 + v[11]*x3 + v[15]*x4;
3168 
3169           v   +=  bs2;
3170         }
3171 
3172        x[idx]   = s1;
3173        x[1+idx] = s2;
3174        x[2+idx] = s3;
3175        x[3+idx] = s4;
3176     }
3177 
3178    /* backward solve the upper triangular */
3179   for (i=n-1; i>=0; i--){
3180     v   = aa + bs2*(adiag[i+1]+1);
3181      vi  = aj + adiag[i+1]+1;
3182      nz  = adiag[i] - adiag[i+1]-1;
3183      idt = bs*i;
3184      s1 = x[idt];  s2 = x[1+idt];s3 = x[2+idt];s4 = x[3+idt];
3185 
3186     for(k=0;k<nz;k++){
3187       idx   = bs*vi[k];
3188        x1    = x[idx];   x2 = x[1+idx]; x3 = x[2+idx];x4 = x[3+idx];
3189        s1   -= v[0]*x1 + v[4]*x2 + v[8]*x3 + v[12]*x4;
3190        s2   -= v[1]*x1 + v[5]*x2 + v[9]*x3 + v[13]*x4;
3191        s3   -= v[2]*x1 + v[6]*x2 + v[10]*x3 + v[14]*x4;
3192        s4   -= v[3]*x1 + v[7]*x2 + v[11]*x3 + v[15]*x4;
3193 
3194         v   +=  bs2;
3195     }
3196     /* x = inv_diagonal*x */
3197    x[idt]   = v[0]*s1 + v[4]*s2 + v[8]*s3 + v[12]*s4;
3198    x[1+idt] = v[1]*s1 + v[5]*s2 + v[9]*s3 + v[13]*s4;;
3199    x[2+idt] = v[2]*s1 + v[6]*s2 + v[10]*s3 + v[14]*s4;
3200    x[3+idt] = v[3]*s1 + v[7]*s2 + v[11]*s3 + v[15]*s4;
3201 
3202   }
3203 
3204   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3205   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
3206   ierr = PetscLogFlops(2.0*bs2*(a->nz) - bs*A->cmap->n);CHKERRQ(ierr);
3207   PetscFunctionReturn(0);
3208 }
3209 
3210 #undef __FUNCT__
3211 #define __FUNCT__ "MatSolve_SeqBAIJ_4_NaturalOrdering_Demotion"
3212 PetscErrorCode MatSolve_SeqBAIJ_4_NaturalOrdering_Demotion(Mat A,Vec bb,Vec xx)
3213 {
3214   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ *)A->data;
3215   PetscInt       n=a->mbs,*ai=a->i,*aj=a->j;
3216   PetscErrorCode ierr;
3217   PetscInt       *diag = a->diag;
3218   MatScalar      *aa=a->a;
3219   PetscScalar    *x,*b;
3220 
3221   PetscFunctionBegin;
3222   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
3223   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
3224 
3225   {
3226     MatScalar  s1,s2,s3,s4,x1,x2,x3,x4;
3227     MatScalar  *v,*t=(MatScalar *)x;
3228     PetscInt   jdx,idt,idx,nz,*vi,i,ai16;
3229 
3230     /* forward solve the lower triangular */
3231     idx  = 0;
3232     t[0] = (MatScalar)b[0];
3233     t[1] = (MatScalar)b[1];
3234     t[2] = (MatScalar)b[2];
3235     t[3] = (MatScalar)b[3];
3236     for (i=1; i<n; i++) {
3237       v     =  aa      + 16*ai[i];
3238       vi    =  aj      + ai[i];
3239       nz    =  diag[i] - ai[i];
3240       idx   +=  4;
3241       s1 = (MatScalar)b[idx];
3242       s2 = (MatScalar)b[1+idx];
3243       s3 = (MatScalar)b[2+idx];
3244       s4 = (MatScalar)b[3+idx];
3245       while (nz--) {
3246         jdx = 4*(*vi++);
3247         x1  = t[jdx];
3248         x2  = t[1+jdx];
3249         x3  = t[2+jdx];
3250         x4  = t[3+jdx];
3251         s1 -= v[0]*x1 + v[4]*x2 + v[8]*x3  + v[12]*x4;
3252         s2 -= v[1]*x1 + v[5]*x2 + v[9]*x3  + v[13]*x4;
3253         s3 -= v[2]*x1 + v[6]*x2 + v[10]*x3 + v[14]*x4;
3254         s4 -= v[3]*x1 + v[7]*x2 + v[11]*x3 + v[15]*x4;
3255         v    += 16;
3256       }
3257       t[idx]   = s1;
3258       t[1+idx] = s2;
3259       t[2+idx] = s3;
3260       t[3+idx] = s4;
3261     }
3262     /* backward solve the upper triangular */
3263     idt = 4*(n-1);
3264     for (i=n-1; i>=0; i--){
3265       ai16 = 16*diag[i];
3266       v    = aa + ai16 + 16;
3267       vi   = aj + diag[i] + 1;
3268       nz   = ai[i+1] - diag[i] - 1;
3269       s1   = t[idt];
3270       s2   = t[1+idt];
3271       s3   = t[2+idt];
3272       s4   = t[3+idt];
3273       while (nz--) {
3274         idx = 4*(*vi++);
3275         x1  = (MatScalar)x[idx];
3276         x2  = (MatScalar)x[1+idx];
3277         x3  = (MatScalar)x[2+idx];
3278         x4  = (MatScalar)x[3+idx];
3279         s1 -= v[0]*x1 + v[4]*x2 + v[8]*x3  + v[12]*x4;
3280         s2 -= v[1]*x1 + v[5]*x2 + v[9]*x3  + v[13]*x4;
3281         s3 -= v[2]*x1 + v[6]*x2 + v[10]*x3 + v[14]*x4;
3282         s4 -= v[3]*x1 + v[7]*x2 + v[11]*x3 + v[15]*x4;
3283         v    += 16;
3284       }
3285       v        = aa + ai16;
3286       x[idt]   = (PetscScalar)(v[0]*s1 + v[4]*s2 + v[8]*s3  + v[12]*s4);
3287       x[1+idt] = (PetscScalar)(v[1]*s1 + v[5]*s2 + v[9]*s3  + v[13]*s4);
3288       x[2+idt] = (PetscScalar)(v[2]*s1 + v[6]*s2 + v[10]*s3 + v[14]*s4);
3289       x[3+idt] = (PetscScalar)(v[3]*s1 + v[7]*s2 + v[11]*s3 + v[15]*s4);
3290       idt -= 4;
3291     }
3292   }
3293 
3294   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
3295   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
3296   ierr = PetscLogFlops(2.0*16*(a->nz) - 4.0*A->cmap->n);CHKERRQ(ierr);
3297   PetscFunctionReturn(0);
3298 }
3299 
3300 #if defined (PETSC_HAVE_SSE)
3301 
3302 #include PETSC_HAVE_SSE
3303 #undef __FUNCT__
3304 #define __FUNCT__ "MatSolve_SeqBAIJ_4_NaturalOrdering_SSE_Demotion_usj"
3305 PetscErrorCode MatSolve_SeqBAIJ_4_NaturalOrdering_SSE_Demotion_usj(Mat A,Vec bb,Vec xx)
3306 {
3307   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ *)A->data;
3308   unsigned short *aj=(unsigned short *)a->j;
3309   PetscErrorCode ierr;
3310   int            *ai=a->i,n=a->mbs,*diag = a->diag;
3311   MatScalar      *aa=a->a;
3312   PetscScalar    *x,*b;
3313 
3314   PetscFunctionBegin;
3315   SSE_SCOPE_BEGIN;
3316   /*
3317      Note: This code currently uses demotion of double
3318      to float when performing the mixed-mode computation.
3319      This may not be numerically reasonable for all applications.
3320   */
3321   PREFETCH_NTA(aa+16*ai[1]);
3322 
3323   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
3324   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
3325   {
3326     /* x will first be computed in single precision then promoted inplace to double */
3327     MatScalar      *v,*t=(MatScalar *)x;
3328     int            nz,i,idt,ai16;
3329     unsigned int   jdx,idx;
3330     unsigned short *vi;
3331     /* Forward solve the lower triangular factor. */
3332 
3333     /* First block is the identity. */
3334     idx  = 0;
3335     CONVERT_DOUBLE4_FLOAT4(t,b);
3336     v    =  aa + 16*((unsigned int)ai[1]);
3337 
3338     for (i=1; i<n;) {
3339       PREFETCH_NTA(&v[8]);
3340       vi   =  aj      + ai[i];
3341       nz   =  diag[i] - ai[i];
3342       idx +=  4;
3343 
3344       /* Demote RHS from double to float. */
3345       CONVERT_DOUBLE4_FLOAT4(&t[idx],&b[idx]);
3346       LOAD_PS(&t[idx],XMM7);
3347 
3348       while (nz--) {
3349         PREFETCH_NTA(&v[16]);
3350         jdx = 4*((unsigned int)(*vi++));
3351 
3352         /* 4x4 Matrix-Vector product with negative accumulation: */
3353         SSE_INLINE_BEGIN_2(&t[jdx],v)
3354           SSE_LOAD_PS(SSE_ARG_1,FLOAT_0,XMM6)
3355 
3356           /* First Column */
3357           SSE_COPY_PS(XMM0,XMM6)
3358           SSE_SHUFFLE(XMM0,XMM0,0x00)
3359           SSE_MULT_PS_M(XMM0,SSE_ARG_2,FLOAT_0)
3360           SSE_SUB_PS(XMM7,XMM0)
3361 
3362           /* Second Column */
3363           SSE_COPY_PS(XMM1,XMM6)
3364           SSE_SHUFFLE(XMM1,XMM1,0x55)
3365           SSE_MULT_PS_M(XMM1,SSE_ARG_2,FLOAT_4)
3366           SSE_SUB_PS(XMM7,XMM1)
3367 
3368           SSE_PREFETCH_NTA(SSE_ARG_2,FLOAT_24)
3369 
3370           /* Third Column */
3371           SSE_COPY_PS(XMM2,XMM6)
3372           SSE_SHUFFLE(XMM2,XMM2,0xAA)
3373           SSE_MULT_PS_M(XMM2,SSE_ARG_2,FLOAT_8)
3374           SSE_SUB_PS(XMM7,XMM2)
3375 
3376           /* Fourth Column */
3377           SSE_COPY_PS(XMM3,XMM6)
3378           SSE_SHUFFLE(XMM3,XMM3,0xFF)
3379           SSE_MULT_PS_M(XMM3,SSE_ARG_2,FLOAT_12)
3380           SSE_SUB_PS(XMM7,XMM3)
3381         SSE_INLINE_END_2
3382 
3383         v  += 16;
3384       }
3385       v    =  aa + 16*ai[++i];
3386       PREFETCH_NTA(v);
3387       STORE_PS(&t[idx],XMM7);
3388     }
3389 
3390     /* Backward solve the upper triangular factor.*/
3391 
3392     idt  = 4*(n-1);
3393     ai16 = 16*diag[n-1];
3394     v    = aa + ai16 + 16;
3395     for (i=n-1; i>=0;){
3396       PREFETCH_NTA(&v[8]);
3397       vi = aj + diag[i] + 1;
3398       nz = ai[i+1] - diag[i] - 1;
3399 
3400       LOAD_PS(&t[idt],XMM7);
3401 
3402       while (nz--) {
3403         PREFETCH_NTA(&v[16]);
3404         idx = 4*((unsigned int)(*vi++));
3405 
3406         /* 4x4 Matrix-Vector Product with negative accumulation: */
3407         SSE_INLINE_BEGIN_2(&t[idx],v)
3408           SSE_LOAD_PS(SSE_ARG_1,FLOAT_0,XMM6)
3409 
3410           /* First Column */
3411           SSE_COPY_PS(XMM0,XMM6)
3412           SSE_SHUFFLE(XMM0,XMM0,0x00)
3413           SSE_MULT_PS_M(XMM0,SSE_ARG_2,FLOAT_0)
3414           SSE_SUB_PS(XMM7,XMM0)
3415 
3416           /* Second Column */
3417           SSE_COPY_PS(XMM1,XMM6)
3418           SSE_SHUFFLE(XMM1,XMM1,0x55)
3419           SSE_MULT_PS_M(XMM1,SSE_ARG_2,FLOAT_4)
3420           SSE_SUB_PS(XMM7,XMM1)
3421 
3422           SSE_PREFETCH_NTA(SSE_ARG_2,FLOAT_24)
3423 
3424           /* Third Column */
3425           SSE_COPY_PS(XMM2,XMM6)
3426           SSE_SHUFFLE(XMM2,XMM2,0xAA)
3427           SSE_MULT_PS_M(XMM2,SSE_ARG_2,FLOAT_8)
3428           SSE_SUB_PS(XMM7,XMM2)
3429 
3430           /* Fourth Column */
3431           SSE_COPY_PS(XMM3,XMM6)
3432           SSE_SHUFFLE(XMM3,XMM3,0xFF)
3433           SSE_MULT_PS_M(XMM3,SSE_ARG_2,FLOAT_12)
3434           SSE_SUB_PS(XMM7,XMM3)
3435         SSE_INLINE_END_2
3436         v  += 16;
3437       }
3438       v    = aa + ai16;
3439       ai16 = 16*diag[--i];
3440       PREFETCH_NTA(aa+ai16+16);
3441       /*
3442          Scale the result by the diagonal 4x4 block,
3443          which was inverted as part of the factorization
3444       */
3445       SSE_INLINE_BEGIN_3(v,&t[idt],aa+ai16)
3446         /* First Column */
3447         SSE_COPY_PS(XMM0,XMM7)
3448         SSE_SHUFFLE(XMM0,XMM0,0x00)
3449         SSE_MULT_PS_M(XMM0,SSE_ARG_1,FLOAT_0)
3450 
3451         /* Second Column */
3452         SSE_COPY_PS(XMM1,XMM7)
3453         SSE_SHUFFLE(XMM1,XMM1,0x55)
3454         SSE_MULT_PS_M(XMM1,SSE_ARG_1,FLOAT_4)
3455         SSE_ADD_PS(XMM0,XMM1)
3456 
3457         SSE_PREFETCH_NTA(SSE_ARG_3,FLOAT_24)
3458 
3459         /* Third Column */
3460         SSE_COPY_PS(XMM2,XMM7)
3461         SSE_SHUFFLE(XMM2,XMM2,0xAA)
3462         SSE_MULT_PS_M(XMM2,SSE_ARG_1,FLOAT_8)
3463         SSE_ADD_PS(XMM0,XMM2)
3464 
3465         /* Fourth Column */
3466         SSE_COPY_PS(XMM3,XMM7)
3467         SSE_SHUFFLE(XMM3,XMM3,0xFF)
3468         SSE_MULT_PS_M(XMM3,SSE_ARG_1,FLOAT_12)
3469         SSE_ADD_PS(XMM0,XMM3)
3470 
3471         SSE_STORE_PS(SSE_ARG_2,FLOAT_0,XMM0)
3472       SSE_INLINE_END_3
3473 
3474       v    = aa + ai16 + 16;
3475       idt -= 4;
3476     }
3477 
3478     /* Convert t from single precision back to double precision (inplace)*/
3479     idt = 4*(n-1);
3480     for (i=n-1;i>=0;i--) {
3481       /*     CONVERT_FLOAT4_DOUBLE4(&x[idt],&t[idt]); */
3482       /* Unfortunately, CONVERT_ will count from 0 to 3 which doesn't work here. */
3483       PetscScalar *xtemp=&x[idt];
3484       MatScalar   *ttemp=&t[idt];
3485       xtemp[3] = (PetscScalar)ttemp[3];
3486       xtemp[2] = (PetscScalar)ttemp[2];
3487       xtemp[1] = (PetscScalar)ttemp[1];
3488       xtemp[0] = (PetscScalar)ttemp[0];
3489       idt -= 4;
3490     }
3491 
3492   } /* End of artificial scope. */
3493   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
3494   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
3495   ierr = PetscLogFlops(2.0*16*(a->nz) - 4.0*A->cmap->n);CHKERRQ(ierr);
3496   SSE_SCOPE_END;
3497   PetscFunctionReturn(0);
3498 }
3499 
3500 #undef __FUNCT__
3501 #define __FUNCT__ "MatSolve_SeqBAIJ_4_NaturalOrdering_SSE_Demotion"
3502 PetscErrorCode MatSolve_SeqBAIJ_4_NaturalOrdering_SSE_Demotion(Mat A,Vec bb,Vec xx)
3503 {
3504   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ *)A->data;
3505   int            *aj=a->j;
3506   PetscErrorCode ierr;
3507   int            *ai=a->i,n=a->mbs,*diag = a->diag;
3508   MatScalar      *aa=a->a;
3509   PetscScalar    *x,*b;
3510 
3511   PetscFunctionBegin;
3512   SSE_SCOPE_BEGIN;
3513   /*
3514      Note: This code currently uses demotion of double
3515      to float when performing the mixed-mode computation.
3516      This may not be numerically reasonable for all applications.
3517   */
3518   PREFETCH_NTA(aa+16*ai[1]);
3519 
3520   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
3521   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
3522   {
3523     /* x will first be computed in single precision then promoted inplace to double */
3524     MatScalar *v,*t=(MatScalar *)x;
3525     int       nz,i,idt,ai16;
3526     int       jdx,idx;
3527     int       *vi;
3528     /* Forward solve the lower triangular factor. */
3529 
3530     /* First block is the identity. */
3531     idx  = 0;
3532     CONVERT_DOUBLE4_FLOAT4(t,b);
3533     v    =  aa + 16*ai[1];
3534 
3535     for (i=1; i<n;) {
3536       PREFETCH_NTA(&v[8]);
3537       vi   =  aj      + ai[i];
3538       nz   =  diag[i] - ai[i];
3539       idx +=  4;
3540 
3541       /* Demote RHS from double to float. */
3542       CONVERT_DOUBLE4_FLOAT4(&t[idx],&b[idx]);
3543       LOAD_PS(&t[idx],XMM7);
3544 
3545       while (nz--) {
3546         PREFETCH_NTA(&v[16]);
3547         jdx = 4*(*vi++);
3548 /*          jdx = *vi++; */
3549 
3550         /* 4x4 Matrix-Vector product with negative accumulation: */
3551         SSE_INLINE_BEGIN_2(&t[jdx],v)
3552           SSE_LOAD_PS(SSE_ARG_1,FLOAT_0,XMM6)
3553 
3554           /* First Column */
3555           SSE_COPY_PS(XMM0,XMM6)
3556           SSE_SHUFFLE(XMM0,XMM0,0x00)
3557           SSE_MULT_PS_M(XMM0,SSE_ARG_2,FLOAT_0)
3558           SSE_SUB_PS(XMM7,XMM0)
3559 
3560           /* Second Column */
3561           SSE_COPY_PS(XMM1,XMM6)
3562           SSE_SHUFFLE(XMM1,XMM1,0x55)
3563           SSE_MULT_PS_M(XMM1,SSE_ARG_2,FLOAT_4)
3564           SSE_SUB_PS(XMM7,XMM1)
3565 
3566           SSE_PREFETCH_NTA(SSE_ARG_2,FLOAT_24)
3567 
3568           /* Third Column */
3569           SSE_COPY_PS(XMM2,XMM6)
3570           SSE_SHUFFLE(XMM2,XMM2,0xAA)
3571           SSE_MULT_PS_M(XMM2,SSE_ARG_2,FLOAT_8)
3572           SSE_SUB_PS(XMM7,XMM2)
3573 
3574           /* Fourth Column */
3575           SSE_COPY_PS(XMM3,XMM6)
3576           SSE_SHUFFLE(XMM3,XMM3,0xFF)
3577           SSE_MULT_PS_M(XMM3,SSE_ARG_2,FLOAT_12)
3578           SSE_SUB_PS(XMM7,XMM3)
3579         SSE_INLINE_END_2
3580 
3581         v  += 16;
3582       }
3583       v    =  aa + 16*ai[++i];
3584       PREFETCH_NTA(v);
3585       STORE_PS(&t[idx],XMM7);
3586     }
3587 
3588     /* Backward solve the upper triangular factor.*/
3589 
3590     idt  = 4*(n-1);
3591     ai16 = 16*diag[n-1];
3592     v    = aa + ai16 + 16;
3593     for (i=n-1; i>=0;){
3594       PREFETCH_NTA(&v[8]);
3595       vi = aj + diag[i] + 1;
3596       nz = ai[i+1] - diag[i] - 1;
3597 
3598       LOAD_PS(&t[idt],XMM7);
3599 
3600       while (nz--) {
3601         PREFETCH_NTA(&v[16]);
3602         idx = 4*(*vi++);
3603 /*          idx = *vi++; */
3604 
3605         /* 4x4 Matrix-Vector Product with negative accumulation: */
3606         SSE_INLINE_BEGIN_2(&t[idx],v)
3607           SSE_LOAD_PS(SSE_ARG_1,FLOAT_0,XMM6)
3608 
3609           /* First Column */
3610           SSE_COPY_PS(XMM0,XMM6)
3611           SSE_SHUFFLE(XMM0,XMM0,0x00)
3612           SSE_MULT_PS_M(XMM0,SSE_ARG_2,FLOAT_0)
3613           SSE_SUB_PS(XMM7,XMM0)
3614 
3615           /* Second Column */
3616           SSE_COPY_PS(XMM1,XMM6)
3617           SSE_SHUFFLE(XMM1,XMM1,0x55)
3618           SSE_MULT_PS_M(XMM1,SSE_ARG_2,FLOAT_4)
3619           SSE_SUB_PS(XMM7,XMM1)
3620 
3621           SSE_PREFETCH_NTA(SSE_ARG_2,FLOAT_24)
3622 
3623           /* Third Column */
3624           SSE_COPY_PS(XMM2,XMM6)
3625           SSE_SHUFFLE(XMM2,XMM2,0xAA)
3626           SSE_MULT_PS_M(XMM2,SSE_ARG_2,FLOAT_8)
3627           SSE_SUB_PS(XMM7,XMM2)
3628 
3629           /* Fourth Column */
3630           SSE_COPY_PS(XMM3,XMM6)
3631           SSE_SHUFFLE(XMM3,XMM3,0xFF)
3632           SSE_MULT_PS_M(XMM3,SSE_ARG_2,FLOAT_12)
3633           SSE_SUB_PS(XMM7,XMM3)
3634         SSE_INLINE_END_2
3635         v  += 16;
3636       }
3637       v    = aa + ai16;
3638       ai16 = 16*diag[--i];
3639       PREFETCH_NTA(aa+ai16+16);
3640       /*
3641          Scale the result by the diagonal 4x4 block,
3642          which was inverted as part of the factorization
3643       */
3644       SSE_INLINE_BEGIN_3(v,&t[idt],aa+ai16)
3645         /* First Column */
3646         SSE_COPY_PS(XMM0,XMM7)
3647         SSE_SHUFFLE(XMM0,XMM0,0x00)
3648         SSE_MULT_PS_M(XMM0,SSE_ARG_1,FLOAT_0)
3649 
3650         /* Second Column */
3651         SSE_COPY_PS(XMM1,XMM7)
3652         SSE_SHUFFLE(XMM1,XMM1,0x55)
3653         SSE_MULT_PS_M(XMM1,SSE_ARG_1,FLOAT_4)
3654         SSE_ADD_PS(XMM0,XMM1)
3655 
3656         SSE_PREFETCH_NTA(SSE_ARG_3,FLOAT_24)
3657 
3658         /* Third Column */
3659         SSE_COPY_PS(XMM2,XMM7)
3660         SSE_SHUFFLE(XMM2,XMM2,0xAA)
3661         SSE_MULT_PS_M(XMM2,SSE_ARG_1,FLOAT_8)
3662         SSE_ADD_PS(XMM0,XMM2)
3663 
3664         /* Fourth Column */
3665         SSE_COPY_PS(XMM3,XMM7)
3666         SSE_SHUFFLE(XMM3,XMM3,0xFF)
3667         SSE_MULT_PS_M(XMM3,SSE_ARG_1,FLOAT_12)
3668         SSE_ADD_PS(XMM0,XMM3)
3669 
3670         SSE_STORE_PS(SSE_ARG_2,FLOAT_0,XMM0)
3671       SSE_INLINE_END_3
3672 
3673       v    = aa + ai16 + 16;
3674       idt -= 4;
3675     }
3676 
3677     /* Convert t from single precision back to double precision (inplace)*/
3678     idt = 4*(n-1);
3679     for (i=n-1;i>=0;i--) {
3680       /*     CONVERT_FLOAT4_DOUBLE4(&x[idt],&t[idt]); */
3681       /* Unfortunately, CONVERT_ will count from 0 to 3 which doesn't work here. */
3682       PetscScalar *xtemp=&x[idt];
3683       MatScalar   *ttemp=&t[idt];
3684       xtemp[3] = (PetscScalar)ttemp[3];
3685       xtemp[2] = (PetscScalar)ttemp[2];
3686       xtemp[1] = (PetscScalar)ttemp[1];
3687       xtemp[0] = (PetscScalar)ttemp[0];
3688       idt -= 4;
3689     }
3690 
3691   } /* End of artificial scope. */
3692   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
3693   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
3694   ierr = PetscLogFlops(2.0*16*(a->nz) - 4.0*A->cmap->n);CHKERRQ(ierr);
3695   SSE_SCOPE_END;
3696   PetscFunctionReturn(0);
3697 }
3698 
3699 #endif
3700 
3701 #undef __FUNCT__
3702 #define __FUNCT__ "MatSolve_SeqBAIJ_3"
3703 PetscErrorCode MatSolve_SeqBAIJ_3(Mat A,Vec bb,Vec xx)
3704 {
3705   Mat_SeqBAIJ       *a=(Mat_SeqBAIJ *)A->data;
3706   IS                iscol=a->col,isrow=a->row;
3707   PetscErrorCode    ierr;
3708   PetscInt          i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc;
3709   const PetscInt    *r,*c,*diag = a->diag,*rout,*cout;
3710   const MatScalar   *aa=a->a,*v;
3711   PetscScalar       *x,s1,s2,s3,x1,x2,x3,*t;
3712   const PetscScalar *b;
3713 
3714   PetscFunctionBegin;
3715   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3716   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
3717   t  = a->solve_work;
3718 
3719   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
3720   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
3721 
3722   /* forward solve the lower triangular */
3723   idx    = 3*(*r++);
3724   t[0] = b[idx]; t[1] = b[1+idx]; t[2] = b[2+idx];
3725   for (i=1; i<n; i++) {
3726     v     = aa + 9*ai[i];
3727     vi    = aj + ai[i];
3728     nz    = diag[i] - ai[i];
3729     idx   = 3*(*r++);
3730     s1  = b[idx]; s2 = b[1+idx]; s3 = b[2+idx];
3731     while (nz--) {
3732       idx   = 3*(*vi++);
3733       x1    = t[idx]; x2 = t[1+idx]; x3 = t[2+idx];
3734       s1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
3735       s2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
3736       s3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
3737       v += 9;
3738     }
3739     idx = 3*i;
3740     t[idx] = s1; t[1+idx] = s2; t[2+idx] = s3;
3741   }
3742   /* backward solve the upper triangular */
3743   for (i=n-1; i>=0; i--){
3744     v    = aa + 9*diag[i] + 9;
3745     vi   = aj + diag[i] + 1;
3746     nz   = ai[i+1] - diag[i] - 1;
3747     idt  = 3*i;
3748     s1 = t[idt]; s2 = t[1+idt]; s3 = t[2+idt];
3749     while (nz--) {
3750       idx   = 3*(*vi++);
3751       x1    = t[idx]; x2 = t[1+idx]; x3 = t[2+idx];
3752       s1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
3753       s2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
3754       s3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
3755       v += 9;
3756     }
3757     idc = 3*(*c--);
3758     v   = aa + 9*diag[i];
3759     x[idc]   = t[idt]   = v[0]*s1 + v[3]*s2 + v[6]*s3;
3760     x[1+idc] = t[1+idt] = v[1]*s1 + v[4]*s2 + v[7]*s3;
3761     x[2+idc] = t[2+idt] = v[2]*s1 + v[5]*s2 + v[8]*s3;
3762   }
3763   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
3764   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
3765   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3766   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
3767   ierr = PetscLogFlops(2.0*9*(a->nz) - 3.0*A->cmap->n);CHKERRQ(ierr);
3768   PetscFunctionReturn(0);
3769 }
3770 
3771 #undef __FUNCT__
3772 #define __FUNCT__ "MatSolve_SeqBAIJ_3_newdatastruct"
3773 PetscErrorCode MatSolve_SeqBAIJ_3_newdatastruct(Mat A,Vec bb,Vec xx)
3774 {
3775   Mat_SeqBAIJ       *a=(Mat_SeqBAIJ *)A->data;
3776   IS                iscol=a->col,isrow=a->row;
3777   PetscErrorCode    ierr;
3778   PetscInt          i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,k,m;
3779   const PetscInt    *r,*c,*rout,*cout;
3780   const MatScalar   *aa=a->a,*v;
3781   PetscScalar       *x,s1,s2,s3,x1,x2,x3,*t;
3782   const PetscScalar *b;
3783 
3784   PetscFunctionBegin;
3785   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3786   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
3787   t  = a->solve_work;
3788 
3789   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
3790   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
3791 
3792   /* forward solve the lower triangular */
3793   idx    = 3*r[0];
3794   t[0] = b[idx]; t[1] = b[1+idx]; t[2] = b[2+idx];
3795   for (i=1; i<n; i++) {
3796     v     = aa + 9*ai[i];
3797     vi    = aj + ai[i];
3798     nz    = ai[i+1] - ai[i];
3799     idx   = 3*r[i];
3800     s1  = b[idx]; s2 = b[1+idx]; s3 = b[2+idx];
3801     for(m=0;m<nz;m++){
3802       idx   = 3*vi[m];
3803       x1    = t[idx]; x2 = t[1+idx]; x3 = t[2+idx];
3804       s1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
3805       s2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
3806       s3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
3807       v += 9;
3808     }
3809     idx = 3*i;
3810     t[idx] = s1; t[1+idx] = s2; t[2+idx] = s3;
3811   }
3812   /* backward solve the upper triangular */
3813   for (i=n-1; i>=0; i--){
3814     k    = 2*n-i;
3815     v    = aa + 9*ai[k];
3816     vi   = aj + ai[k];
3817     nz   = ai[k +1] - ai[k] - 1;
3818     idt  = 3*i;
3819     s1 = t[idt]; s2 = t[1+idt]; s3 = t[2+idt];
3820     for(m=0;m<nz;m++){
3821       idx   = 3*vi[m];
3822       x1    = t[idx]; x2 = t[1+idx]; x3 = t[2+idx];
3823       s1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
3824       s2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
3825       s3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
3826       v += 9;
3827     }
3828     idc = 3*c[i];
3829     x[idc]   = t[idt]   = v[0]*s1 + v[3]*s2 + v[6]*s3;
3830     x[1+idc] = t[1+idt] = v[1]*s1 + v[4]*s2 + v[7]*s3;
3831     x[2+idc] = t[2+idt] = v[2]*s1 + v[5]*s2 + v[8]*s3;
3832   }
3833   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
3834   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
3835   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3836   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
3837   ierr = PetscLogFlops(2.0*9*(a->nz) - 3.0*A->cmap->n);CHKERRQ(ierr);
3838   PetscFunctionReturn(0);
3839 }
3840 
3841 #undef __FUNCT__
3842 #define __FUNCT__ "MatSolve_SeqBAIJ_3_newdatastruct_v2"
3843 PetscErrorCode MatSolve_SeqBAIJ_3_newdatastruct_v2(Mat A,Vec bb,Vec xx)
3844 {
3845   Mat_SeqBAIJ       *a=(Mat_SeqBAIJ *)A->data;
3846   IS                iscol=a->col,isrow=a->row;
3847   PetscErrorCode    ierr;
3848   PetscInt          i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,*adiag=a->diag,nz,idx,idt,idc,m;
3849   const PetscInt    *r,*c,*rout,*cout;
3850   const MatScalar   *aa=a->a,*v;
3851   PetscScalar       *x,s1,s2,s3,x1,x2,x3,*t;
3852   const PetscScalar *b;
3853 
3854   PetscFunctionBegin;
3855   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3856   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
3857   t  = a->solve_work;
3858 
3859   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
3860   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
3861 
3862   /* forward solve the lower triangular */
3863   idx    = 3*r[0];
3864   t[0] = b[idx]; t[1] = b[1+idx]; t[2] = b[2+idx];
3865   for (i=1; i<n; i++) {
3866     v     = aa + 9*ai[i];
3867     vi    = aj + ai[i];
3868     nz    = ai[i+1] - ai[i];
3869     idx   = 3*r[i];
3870     s1  = b[idx]; s2 = b[1+idx]; s3 = b[2+idx];
3871     for(m=0;m<nz;m++){
3872       idx   = 3*vi[m];
3873       x1    = t[idx]; x2 = t[1+idx]; x3 = t[2+idx];
3874       s1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
3875       s2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
3876       s3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
3877       v += 9;
3878     }
3879     idx = 3*i;
3880     t[idx] = s1; t[1+idx] = s2; t[2+idx] = s3;
3881   }
3882   /* backward solve the upper triangular */
3883   for (i=n-1; i>=0; i--){
3884     v    = aa + 9*(adiag[i+1]+1);
3885     vi   = aj + adiag[i+1]+1;
3886     nz   = adiag[i] - adiag[i+1] - 1;
3887     idt  = 3*i;
3888     s1 = t[idt]; s2 = t[1+idt]; s3 = t[2+idt];
3889     for(m=0;m<nz;m++){
3890       idx   = 3*vi[m];
3891       x1    = t[idx]; x2 = t[1+idx]; x3 = t[2+idx];
3892       s1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
3893       s2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
3894       s3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
3895       v += 9;
3896     }
3897     idc = 3*c[i];
3898     x[idc]   = t[idt]   = v[0]*s1 + v[3]*s2 + v[6]*s3;
3899     x[1+idc] = t[1+idt] = v[1]*s1 + v[4]*s2 + v[7]*s3;
3900     x[2+idc] = t[2+idt] = v[2]*s1 + v[5]*s2 + v[8]*s3;
3901   }
3902   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
3903   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
3904   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3905   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
3906   ierr = PetscLogFlops(2.0*9*(a->nz) - 3.0*A->cmap->n);CHKERRQ(ierr);
3907   PetscFunctionReturn(0);
3908 }
3909 
3910 /*
3911       Special case where the matrix was ILU(0) factored in the natural
3912    ordering. This eliminates the need for the column and row permutation.
3913 */
3914 #undef __FUNCT__
3915 #define __FUNCT__ "MatSolve_SeqBAIJ_3_NaturalOrdering"
3916 PetscErrorCode MatSolve_SeqBAIJ_3_NaturalOrdering(Mat A,Vec bb,Vec xx)
3917 {
3918   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ *)A->data;
3919   PetscInt          n=a->mbs,*ai=a->i,*aj=a->j;
3920   PetscErrorCode    ierr;
3921   PetscInt          *diag = a->diag;
3922   const MatScalar   *aa=a->a,*v;
3923   PetscScalar       *x,s1,s2,s3,x1,x2,x3;
3924   const PetscScalar *b;
3925   PetscInt          jdx,idt,idx,nz,*vi,i;
3926 
3927   PetscFunctionBegin;
3928   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3929   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
3930 
3931   /* forward solve the lower triangular */
3932   idx    = 0;
3933   x[0]   = b[0]; x[1] = b[1]; x[2] = b[2];
3934   for (i=1; i<n; i++) {
3935     v     =  aa      + 9*ai[i];
3936     vi    =  aj      + ai[i];
3937     nz    =  diag[i] - ai[i];
3938     idx   +=  3;
3939     s1  =  b[idx];s2 = b[1+idx];s3 = b[2+idx];
3940     while (nz--) {
3941       jdx   = 3*(*vi++);
3942       x1    = x[jdx];x2 = x[1+jdx];x3 = x[2+jdx];
3943       s1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
3944       s2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
3945       s3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
3946       v    += 9;
3947     }
3948     x[idx]   = s1;
3949     x[1+idx] = s2;
3950     x[2+idx] = s3;
3951   }
3952   /* backward solve the upper triangular */
3953   for (i=n-1; i>=0; i--){
3954     v    = aa + 9*diag[i] + 9;
3955     vi   = aj + diag[i] + 1;
3956     nz   = ai[i+1] - diag[i] - 1;
3957     idt  = 3*i;
3958     s1 = x[idt];  s2 = x[1+idt];
3959     s3 = x[2+idt];
3960     while (nz--) {
3961       idx   = 3*(*vi++);
3962       x1    = x[idx];   x2 = x[1+idx];x3    = x[2+idx];
3963       s1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
3964       s2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
3965       s3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
3966       v    += 9;
3967     }
3968     v        = aa +  9*diag[i];
3969     x[idt]   = v[0]*s1 + v[3]*s2 + v[6]*s3;
3970     x[1+idt] = v[1]*s1 + v[4]*s2 + v[7]*s3;
3971     x[2+idt] = v[2]*s1 + v[5]*s2 + v[8]*s3;
3972   }
3973 
3974   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3975   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
3976   ierr = PetscLogFlops(2.0*9*(a->nz) - 3.0*A->cmap->n);CHKERRQ(ierr);
3977   PetscFunctionReturn(0);
3978 }
3979 
3980 #undef __FUNCT__
3981 #define __FUNCT__ "MatSolve_SeqBAIJ_3_NaturalOrdering_newdatastruct"
3982 PetscErrorCode MatSolve_SeqBAIJ_3_NaturalOrdering_newdatastruct(Mat A,Vec bb,Vec xx)
3983 {
3984     Mat_SeqBAIJ       *a = (Mat_SeqBAIJ *)A->data;
3985     PetscInt          i,k,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz;
3986     PetscErrorCode    ierr;
3987     PetscInt          idx,jdx,idt;
3988     PetscInt          bs = A->rmap->bs,bs2 = a->bs2;
3989     const MatScalar   *aa=a->a,*v;
3990     PetscScalar       *x;
3991     const PetscScalar *b;
3992     PetscScalar        s1,s2,s3,x1,x2,x3;
3993 
3994     PetscFunctionBegin;
3995     ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3996     ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
3997     /* forward solve the lower triangular */
3998     idx    = 0;
3999     x[0] = b[idx]; x[1] = b[1+idx];x[2] = b[2+idx];
4000     for (i=1; i<n; i++) {
4001        v    = aa + bs2*ai[i];
4002        vi   = aj + ai[i];
4003        nz   = ai[i+1] - ai[i];
4004       idx   = bs*i;
4005        s1   = b[idx];s2 = b[1+idx];s3 = b[2+idx];
4006       for(k=0;k<nz;k++){
4007          jdx   = bs*vi[k];
4008           x1    = x[jdx];x2 = x[1+jdx]; x3 =x[2+jdx];
4009           s1   -= v[0]*x1 + v[3]*x2 + v[6]*x3;
4010           s2   -= v[1]*x1 + v[4]*x2 + v[7]*x3;
4011           s3   -= v[2]*x1 + v[5]*x2 + v[8]*x3;
4012 
4013           v   +=  bs2;
4014         }
4015 
4016        x[idx]   = s1;
4017        x[1+idx] = s2;
4018        x[2+idx] = s3;
4019     }
4020 
4021    /* backward solve the upper triangular */
4022   for (i=n-1; i>=0; i--){
4023      v   = aa + bs2*ai[2*n-i];
4024      vi  = aj + ai[2*n-i];
4025      nz  = ai[2*n-i +1] - ai[2*n-i]-1;
4026      idt = bs*i;
4027      s1 = x[idt];  s2 = x[1+idt];s3 = x[2+idt];
4028 
4029      for(k=0;k<nz;k++){
4030        idx   = bs*vi[k];
4031        x1    = x[idx];   x2 = x[1+idx]; x3 = x[2+idx];
4032        s1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
4033        s2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
4034        s3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
4035 
4036         v   +=  bs2;
4037     }
4038     /* x = inv_diagonal*x */
4039    x[idt]   = v[0]*s1 + v[3]*s2 + v[6]*s3;
4040    x[1+idt] = v[1]*s1 + v[4]*s2 + v[7]*s3;
4041    x[2+idt] = v[2]*s1 + v[5]*s2 + v[8]*s3;
4042 
4043   }
4044 
4045   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
4046   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
4047   ierr = PetscLogFlops(2.0*bs2*(a->nz) - bs*A->cmap->n);CHKERRQ(ierr);
4048   PetscFunctionReturn(0);
4049 }
4050 
4051 #undef __FUNCT__
4052 #define __FUNCT__ "MatSolve_SeqBAIJ_3_NaturalOrdering_newdatastruct_v2"
4053 PetscErrorCode MatSolve_SeqBAIJ_3_NaturalOrdering_newdatastruct_v2(Mat A,Vec bb,Vec xx)
4054 {
4055     Mat_SeqBAIJ       *a = (Mat_SeqBAIJ *)A->data;
4056     PetscInt          i,k,n=a->mbs,*vi,*ai=a->i,*aj=a->j,*adiag=a->diag,nz;
4057     PetscErrorCode    ierr;
4058     PetscInt          idx,jdx,idt;
4059     PetscInt          bs = A->rmap->bs,bs2 = a->bs2;
4060     const MatScalar   *aa=a->a,*v;
4061     PetscScalar       *x;
4062     const PetscScalar *b;
4063     PetscScalar        s1,s2,s3,x1,x2,x3;
4064 
4065     PetscFunctionBegin;
4066     ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
4067     ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
4068     /* forward solve the lower triangular */
4069     idx    = 0;
4070     x[0] = b[idx]; x[1] = b[1+idx];x[2] = b[2+idx];
4071     for (i=1; i<n; i++) {
4072        v    = aa + bs2*ai[i];
4073        vi   = aj + ai[i];
4074        nz   = ai[i+1] - ai[i];
4075       idx   = bs*i;
4076        s1   = b[idx];s2 = b[1+idx];s3 = b[2+idx];
4077       for(k=0;k<nz;k++){
4078          jdx   = bs*vi[k];
4079           x1    = x[jdx];x2 = x[1+jdx]; x3 =x[2+jdx];
4080           s1   -= v[0]*x1 + v[3]*x2 + v[6]*x3;
4081           s2   -= v[1]*x1 + v[4]*x2 + v[7]*x3;
4082           s3   -= v[2]*x1 + v[5]*x2 + v[8]*x3;
4083 
4084           v   +=  bs2;
4085         }
4086 
4087        x[idx]   = s1;
4088        x[1+idx] = s2;
4089        x[2+idx] = s3;
4090     }
4091 
4092    /* backward solve the upper triangular */
4093   for (i=n-1; i>=0; i--){
4094     v   = aa + bs2*(adiag[i+1]+1);
4095      vi  = aj + adiag[i+1]+1;
4096      nz  = adiag[i] - adiag[i+1]-1;
4097      idt = bs*i;
4098      s1 = x[idt];  s2 = x[1+idt];s3 = x[2+idt];
4099 
4100      for(k=0;k<nz;k++){
4101        idx   = bs*vi[k];
4102        x1    = x[idx];   x2 = x[1+idx]; x3 = x[2+idx];
4103        s1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
4104        s2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
4105        s3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
4106 
4107         v   +=  bs2;
4108     }
4109     /* x = inv_diagonal*x */
4110    x[idt]   = v[0]*s1 + v[3]*s2 + v[6]*s3;
4111    x[1+idt] = v[1]*s1 + v[4]*s2 + v[7]*s3;
4112    x[2+idt] = v[2]*s1 + v[5]*s2 + v[8]*s3;
4113 
4114   }
4115 
4116   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
4117   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
4118   ierr = PetscLogFlops(2.0*bs2*(a->nz) - bs*A->cmap->n);CHKERRQ(ierr);
4119   PetscFunctionReturn(0);
4120 }
4121 
4122 #undef __FUNCT__
4123 #define __FUNCT__ "MatSolve_SeqBAIJ_2"
4124 PetscErrorCode MatSolve_SeqBAIJ_2(Mat A,Vec bb,Vec xx)
4125 {
4126   Mat_SeqBAIJ       *a=(Mat_SeqBAIJ *)A->data;
4127   IS                iscol=a->col,isrow=a->row;
4128   PetscErrorCode    ierr;
4129   PetscInt          i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc;
4130   const PetscInt    *r,*c,*diag = a->diag,*rout,*cout;
4131   const MatScalar   *aa=a->a,*v;
4132   PetscScalar       *x,s1,s2,x1,x2,*t;
4133   const PetscScalar *b;
4134 
4135   PetscFunctionBegin;
4136   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
4137   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
4138   t  = a->solve_work;
4139 
4140   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
4141   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
4142 
4143   /* forward solve the lower triangular */
4144   idx    = 2*(*r++);
4145   t[0] = b[idx]; t[1] = b[1+idx];
4146   for (i=1; i<n; i++) {
4147     v     = aa + 4*ai[i];
4148     vi    = aj + ai[i];
4149     nz    = diag[i] - ai[i];
4150     idx   = 2*(*r++);
4151     s1  = b[idx]; s2 = b[1+idx];
4152     while (nz--) {
4153       idx   = 2*(*vi++);
4154       x1    = t[idx]; x2 = t[1+idx];
4155       s1 -= v[0]*x1 + v[2]*x2;
4156       s2 -= v[1]*x1 + v[3]*x2;
4157       v += 4;
4158     }
4159     idx = 2*i;
4160     t[idx] = s1; t[1+idx] = s2;
4161   }
4162   /* backward solve the upper triangular */
4163   for (i=n-1; i>=0; i--){
4164     v    = aa + 4*diag[i] + 4;
4165     vi   = aj + diag[i] + 1;
4166     nz   = ai[i+1] - diag[i] - 1;
4167     idt  = 2*i;
4168     s1 = t[idt]; s2 = t[1+idt];
4169     while (nz--) {
4170       idx   = 2*(*vi++);
4171       x1    = t[idx]; x2 = t[1+idx];
4172       s1 -= v[0]*x1 + v[2]*x2;
4173       s2 -= v[1]*x1 + v[3]*x2;
4174       v += 4;
4175     }
4176     idc = 2*(*c--);
4177     v   = aa + 4*diag[i];
4178     x[idc]   = t[idt]   = v[0]*s1 + v[2]*s2;
4179     x[1+idc] = t[1+idt] = v[1]*s1 + v[3]*s2;
4180   }
4181   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
4182   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
4183   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
4184   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
4185   ierr = PetscLogFlops(2.0*4*(a->nz) - 2.0*A->cmap->n);CHKERRQ(ierr);
4186   PetscFunctionReturn(0);
4187 }
4188 
4189 #undef __FUNCT__
4190 #define __FUNCT__ "MatSolve_SeqBAIJ_2_newdatastruct"
4191 PetscErrorCode MatSolve_SeqBAIJ_2_newdatastruct(Mat A,Vec bb,Vec xx)
4192 {
4193   Mat_SeqBAIJ       *a=(Mat_SeqBAIJ *)A->data;
4194   IS                iscol=a->col,isrow=a->row;
4195   PetscErrorCode    ierr;
4196   PetscInt          i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,jdx,idt,idc,k,m;
4197   const PetscInt    *r,*c,*rout,*cout;
4198   const MatScalar   *aa=a->a,*v;
4199   PetscScalar       *x,s1,s2,x1,x2,*t;
4200   const PetscScalar *b;
4201 
4202   PetscFunctionBegin;
4203   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
4204   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
4205   t  = a->solve_work;
4206 
4207   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
4208   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
4209 
4210   /* forward solve the lower triangular */
4211   idx    = 2*r[0];
4212   t[0] = b[idx]; t[1] = b[1+idx];
4213   for (i=1; i<n; i++) {
4214     v     = aa + 4*ai[i];
4215     vi    = aj + ai[i];
4216     nz    = ai[i+1] - ai[i];
4217     idx   = 2*r[i];
4218     s1  = b[idx]; s2 = b[1+idx];
4219     for(m=0;m<nz;m++){
4220       jdx   = 2*vi[m];
4221       x1    = t[jdx]; x2 = t[1+jdx];
4222       s1 -= v[0]*x1 + v[2]*x2;
4223       s2 -= v[1]*x1 + v[3]*x2;
4224       v += 4;
4225     }
4226     idx = 2*i;
4227     t[idx] = s1; t[1+idx] = s2;
4228   }
4229   /* backward solve the upper triangular */
4230   for (i=n-1; i>=0; i--){
4231     k = 2*n-i;
4232     v    = aa + 4*ai[k];
4233     vi   = aj + ai[k];
4234     nz   = ai[k +1] - ai[k] - 1;
4235     idt  = 2*i;
4236     s1 = t[idt]; s2 = t[1+idt];
4237     for(m=0;m<nz;m++){
4238       idx   = 2*vi[m];
4239       x1    = t[idx]; x2 = t[1+idx];
4240       s1 -= v[0]*x1 + v[2]*x2;
4241       s2 -= v[1]*x1 + v[3]*x2;
4242       v += 4;
4243     }
4244     idc = 2*c[i];
4245     x[idc]   = t[idt]   = v[0]*s1 + v[2]*s2;
4246     x[1+idc] = t[1+idt] = v[1]*s1 + v[3]*s2;
4247   }
4248   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
4249   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
4250   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
4251   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
4252   ierr = PetscLogFlops(2.0*4*(a->nz) - 2.0*A->cmap->n);CHKERRQ(ierr);
4253   PetscFunctionReturn(0);
4254 }
4255 
4256 #undef __FUNCT__
4257 #define __FUNCT__ "MatSolve_SeqBAIJ_2_newdatastruct_v2"
4258 PetscErrorCode MatSolve_SeqBAIJ_2_newdatastruct_v2(Mat A,Vec bb,Vec xx)
4259 {
4260   Mat_SeqBAIJ       *a=(Mat_SeqBAIJ *)A->data;
4261   IS                iscol=a->col,isrow=a->row;
4262   PetscErrorCode    ierr;
4263   PetscInt          i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,*adiag=a->diag,nz,idx,jdx,idt,idc,m;
4264   const PetscInt    *r,*c,*rout,*cout;
4265   const MatScalar   *aa=a->a,*v;
4266   PetscScalar       *x,s1,s2,x1,x2,*t;
4267   const PetscScalar *b;
4268 
4269   PetscFunctionBegin;
4270   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
4271   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
4272   t  = a->solve_work;
4273 
4274   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
4275   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
4276 
4277   /* forward solve the lower triangular */
4278   idx    = 2*r[0];
4279   t[0] = b[idx]; t[1] = b[1+idx];
4280   for (i=1; i<n; i++) {
4281     v     = aa + 4*ai[i];
4282     vi    = aj + ai[i];
4283     nz    = ai[i+1] - ai[i];
4284     idx   = 2*r[i];
4285     s1  = b[idx]; s2 = b[1+idx];
4286     for(m=0;m<nz;m++){
4287       jdx   = 2*vi[m];
4288       x1    = t[jdx]; x2 = t[1+jdx];
4289       s1 -= v[0]*x1 + v[2]*x2;
4290       s2 -= v[1]*x1 + v[3]*x2;
4291       v += 4;
4292     }
4293     idx = 2*i;
4294     t[idx] = s1; t[1+idx] = s2;
4295   }
4296   /* backward solve the upper triangular */
4297   for (i=n-1; i>=0; i--){
4298     v    = aa + 4*(adiag[i+1]+1);
4299     vi   = aj + adiag[i+1]+1;
4300     nz   = adiag[i] - adiag[i+1] - 1;
4301     idt  = 2*i;
4302     s1 = t[idt]; s2 = t[1+idt];
4303     for(m=0;m<nz;m++){
4304       idx   = 2*vi[m];
4305       x1    = t[idx]; x2 = t[1+idx];
4306       s1 -= v[0]*x1 + v[2]*x2;
4307       s2 -= v[1]*x1 + v[3]*x2;
4308       v += 4;
4309     }
4310     idc = 2*c[i];
4311     x[idc]   = t[idt]   = v[0]*s1 + v[2]*s2;
4312     x[1+idc] = t[1+idt] = v[1]*s1 + v[3]*s2;
4313   }
4314   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
4315   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
4316   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
4317   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
4318   ierr = PetscLogFlops(2.0*4*(a->nz) - 2.0*A->cmap->n);CHKERRQ(ierr);
4319   PetscFunctionReturn(0);
4320 }
4321 
4322 /*
4323       Special case where the matrix was ILU(0) factored in the natural
4324    ordering. This eliminates the need for the column and row permutation.
4325 */
4326 #undef __FUNCT__
4327 #define __FUNCT__ "MatSolve_SeqBAIJ_2_NaturalOrdering"
4328 PetscErrorCode MatSolve_SeqBAIJ_2_NaturalOrdering(Mat A,Vec bb,Vec xx)
4329 {
4330   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ *)A->data;
4331   PetscInt          n=a->mbs,*ai=a->i,*aj=a->j;
4332   PetscErrorCode    ierr;
4333   PetscInt          *diag = a->diag;
4334   const MatScalar   *aa=a->a,*v;
4335   PetscScalar       *x,s1,s2,x1,x2;
4336   const PetscScalar *b;
4337   PetscInt          jdx,idt,idx,nz,*vi,i;
4338 
4339   PetscFunctionBegin;
4340   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
4341   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
4342 
4343   /* forward solve the lower triangular */
4344   idx    = 0;
4345   x[0]   = b[0]; x[1] = b[1];
4346   for (i=1; i<n; i++) {
4347     v     =  aa      + 4*ai[i];
4348     vi    =  aj      + ai[i];
4349     nz    =  diag[i] - ai[i];
4350     idx   +=  2;
4351     s1  =  b[idx];s2 = b[1+idx];
4352     while (nz--) {
4353       jdx   = 2*(*vi++);
4354       x1    = x[jdx];x2 = x[1+jdx];
4355       s1 -= v[0]*x1 + v[2]*x2;
4356       s2 -= v[1]*x1 + v[3]*x2;
4357       v    += 4;
4358     }
4359     x[idx]   = s1;
4360     x[1+idx] = s2;
4361   }
4362   /* backward solve the upper triangular */
4363   for (i=n-1; i>=0; i--){
4364     v    = aa + 4*diag[i] + 4;
4365     vi   = aj + diag[i] + 1;
4366     nz   = ai[i+1] - diag[i] - 1;
4367     idt  = 2*i;
4368     s1 = x[idt];  s2 = x[1+idt];
4369     while (nz--) {
4370       idx   = 2*(*vi++);
4371       x1    = x[idx];   x2 = x[1+idx];
4372       s1 -= v[0]*x1 + v[2]*x2;
4373       s2 -= v[1]*x1 + v[3]*x2;
4374       v    += 4;
4375     }
4376     v        = aa +  4*diag[i];
4377     x[idt]   = v[0]*s1 + v[2]*s2;
4378     x[1+idt] = v[1]*s1 + v[3]*s2;
4379   }
4380 
4381   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
4382   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
4383   ierr = PetscLogFlops(2.0*4*(a->nz) - 2.0*A->cmap->n);CHKERRQ(ierr);
4384   PetscFunctionReturn(0);
4385 }
4386 
4387 #undef __FUNCT__
4388 #define __FUNCT__ "MatSolve_SeqBAIJ_2_NaturalOrdering_newdatastruct"
4389 PetscErrorCode MatSolve_SeqBAIJ_2_NaturalOrdering_newdatastruct(Mat A,Vec bb,Vec xx)
4390 {
4391     Mat_SeqBAIJ       *a = (Mat_SeqBAIJ *)A->data;
4392     PetscInt          i,k,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt;
4393     PetscErrorCode    ierr;
4394     PetscInt          jdx;
4395     const MatScalar   *aa=a->a,*v;
4396     PetscScalar       *x,s1,s2,x1,x2;
4397     const PetscScalar *b;
4398 
4399     PetscFunctionBegin;
4400     ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
4401     ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
4402     /* forward solve the lower triangular */
4403     idx    = 0;
4404     x[0] = b[idx]; x[1] = b[1+idx];
4405     for (i=1; i<n; i++) {
4406         v   = aa + 4*ai[i];
4407        vi   = aj + ai[i];
4408        nz   = ai[i+1] - ai[i];
4409        idx  = 2*i;
4410        s1   = b[idx];s2 = b[1+idx];
4411       for(k=0;k<nz;k++){
4412          jdx   = 2*vi[k];
4413           x1    = x[jdx];x2 = x[1+jdx];
4414           s1   -= v[0]*x1 + v[2]*x2;
4415           s2   -= v[1]*x1 + v[3]*x2;
4416            v   +=  4;
4417         }
4418        x[idx]   = s1;
4419        x[1+idx] = s2;
4420     }
4421 
4422    /* backward solve the upper triangular */
4423   for (i=n-1; i>=0; i--){
4424      v   = aa + 4*ai[2*n-i];
4425      vi  = aj + ai[2*n-i];
4426      nz  = ai[2*n-i +1] - ai[2*n-i]-1;
4427      idt = 2*i;
4428      s1 = x[idt];  s2 = x[1+idt];
4429      for(k=0;k<nz;k++){
4430       idx   = 2*vi[k];
4431        x1    = x[idx];   x2 = x[1+idx];
4432        s1 -= v[0]*x1 + v[2]*x2;
4433        s2 -= v[1]*x1 + v[3]*x2;
4434          v    += 4;
4435     }
4436     /* x = inv_diagonal*x */
4437    x[idt]   = v[0]*s1 + v[2]*s2;
4438    x[1+idt] = v[1]*s1 + v[3]*s2;
4439   }
4440 
4441   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
4442   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
4443   ierr = PetscLogFlops(2.0*4*(a->nz) - 2.0*A->cmap->n);CHKERRQ(ierr);
4444   PetscFunctionReturn(0);
4445 }
4446 
4447 #undef __FUNCT__
4448 #define __FUNCT__ "MatSolve_SeqBAIJ_2_NaturalOrdering_newdatastruct_v2"
4449 PetscErrorCode MatSolve_SeqBAIJ_2_NaturalOrdering_newdatastruct_v2(Mat A,Vec bb,Vec xx)
4450 {
4451     Mat_SeqBAIJ       *a = (Mat_SeqBAIJ *)A->data;
4452     PetscInt          i,k,n=a->mbs,*vi,*ai=a->i,*aj=a->j,*adiag=a->diag,nz,idx,idt;
4453     PetscErrorCode    ierr;
4454     PetscInt          jdx;
4455     const MatScalar   *aa=a->a,*v;
4456     PetscScalar       *x,s1,s2,x1,x2;
4457     const PetscScalar *b;
4458 
4459     PetscFunctionBegin;
4460     ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
4461     ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
4462     /* forward solve the lower triangular */
4463     idx    = 0;
4464     x[0] = b[idx]; x[1] = b[1+idx];
4465     for (i=1; i<n; i++) {
4466         v   = aa + 4*ai[i];
4467        vi   = aj + ai[i];
4468        nz   = ai[i+1] - ai[i];
4469        idx  = 2*i;
4470        s1   = b[idx];s2 = b[1+idx];
4471       for(k=0;k<nz;k++){
4472          jdx   = 2*vi[k];
4473           x1    = x[jdx];x2 = x[1+jdx];
4474           s1   -= v[0]*x1 + v[2]*x2;
4475           s2   -= v[1]*x1 + v[3]*x2;
4476            v   +=  4;
4477         }
4478        x[idx]   = s1;
4479        x[1+idx] = s2;
4480     }
4481 
4482    /* backward solve the upper triangular */
4483   for (i=n-1; i>=0; i--){
4484      v   = aa + 4*(adiag[i+1]+1);
4485      vi  = aj + adiag[i+1]+1;
4486      nz  = adiag[i] - adiag[i+1]-1;
4487      idt = 2*i;
4488      s1 = x[idt];  s2 = x[1+idt];
4489      for(k=0;k<nz;k++){
4490       idx   = 2*vi[k];
4491        x1    = x[idx];   x2 = x[1+idx];
4492        s1 -= v[0]*x1 + v[2]*x2;
4493        s2 -= v[1]*x1 + v[3]*x2;
4494          v    += 4;
4495     }
4496     /* x = inv_diagonal*x */
4497    x[idt]   = v[0]*s1 + v[2]*s2;
4498    x[1+idt] = v[1]*s1 + v[3]*s2;
4499   }
4500 
4501   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
4502   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
4503   ierr = PetscLogFlops(2.0*4*(a->nz) - 2.0*A->cmap->n);CHKERRQ(ierr);
4504   PetscFunctionReturn(0);
4505 }
4506 
4507 #undef __FUNCT__
4508 #define __FUNCT__ "MatSolve_SeqBAIJ_1"
4509 PetscErrorCode MatSolve_SeqBAIJ_1(Mat A,Vec bb,Vec xx)
4510 {
4511   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ *)A->data;
4512   IS             iscol=a->col,isrow=a->row;
4513   PetscErrorCode ierr;
4514   PetscInt       i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz;
4515   const PetscInt *r,*c,*diag = a->diag,*rout,*cout;
4516   MatScalar      *aa=a->a,*v;
4517   PetscScalar    *x,*b,s1,*t;
4518 
4519   PetscFunctionBegin;
4520   if (!n) PetscFunctionReturn(0);
4521 
4522   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
4523   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
4524   t  = a->solve_work;
4525 
4526   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
4527   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
4528 
4529   /* forward solve the lower triangular */
4530   t[0] = b[*r++];
4531   for (i=1; i<n; i++) {
4532     v     = aa + ai[i];
4533     vi    = aj + ai[i];
4534     nz    = diag[i] - ai[i];
4535     s1  = b[*r++];
4536     while (nz--) {
4537       s1 -= (*v++)*t[*vi++];
4538     }
4539     t[i] = s1;
4540   }
4541   /* backward solve the upper triangular */
4542   for (i=n-1; i>=0; i--){
4543     v    = aa + diag[i] + 1;
4544     vi   = aj + diag[i] + 1;
4545     nz   = ai[i+1] - diag[i] - 1;
4546     s1 = t[i];
4547     while (nz--) {
4548       s1 -= (*v++)*t[*vi++];
4549     }
4550     x[*c--] = t[i] = aa[diag[i]]*s1;
4551   }
4552 
4553   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
4554   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
4555   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
4556   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
4557   ierr = PetscLogFlops(2.0*1*(a->nz) - A->cmap->n);CHKERRQ(ierr);
4558   PetscFunctionReturn(0);
4559 }
4560 /*
4561       Special case where the matrix was ILU(0) factored in the natural
4562    ordering. This eliminates the need for the column and row permutation.
4563 */
4564 #undef __FUNCT__
4565 #define __FUNCT__ "MatSolve_SeqBAIJ_1_NaturalOrdering"
4566 PetscErrorCode MatSolve_SeqBAIJ_1_NaturalOrdering(Mat A,Vec bb,Vec xx)
4567 {
4568   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ *)A->data;
4569   PetscInt       n=a->mbs,*ai=a->i,*aj=a->j;
4570   PetscErrorCode ierr;
4571   PetscInt       *diag = a->diag;
4572   MatScalar      *aa=a->a;
4573   PetscScalar    *x,*b;
4574   PetscScalar    s1,x1;
4575   MatScalar      *v;
4576   PetscInt       jdx,idt,idx,nz,*vi,i;
4577 
4578   PetscFunctionBegin;
4579   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
4580   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
4581 
4582   /* forward solve the lower triangular */
4583   idx    = 0;
4584   x[0]   = b[0];
4585   for (i=1; i<n; i++) {
4586     v     =  aa      + ai[i];
4587     vi    =  aj      + ai[i];
4588     nz    =  diag[i] - ai[i];
4589     idx   +=  1;
4590     s1  =  b[idx];
4591     while (nz--) {
4592       jdx   = *vi++;
4593       x1    = x[jdx];
4594       s1 -= v[0]*x1;
4595       v    += 1;
4596     }
4597     x[idx]   = s1;
4598   }
4599   /* backward solve the upper triangular */
4600   for (i=n-1; i>=0; i--){
4601     v    = aa + diag[i] + 1;
4602     vi   = aj + diag[i] + 1;
4603     nz   = ai[i+1] - diag[i] - 1;
4604     idt  = i;
4605     s1 = x[idt];
4606     while (nz--) {
4607       idx   = *vi++;
4608       x1    = x[idx];
4609       s1 -= v[0]*x1;
4610       v    += 1;
4611     }
4612     v        = aa +  diag[i];
4613     x[idt]   = v[0]*s1;
4614   }
4615   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
4616   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
4617   ierr = PetscLogFlops(2.0*(a->nz) - A->cmap->n);CHKERRQ(ierr);
4618   PetscFunctionReturn(0);
4619 }
4620 
4621 /* ----------------------------------------------------------------*/
4622 EXTERN PetscErrorCode MatDuplicateNoCreate_SeqBAIJ(Mat,Mat,MatDuplicateOption,PetscTruth);
4623 EXTERN PetscErrorCode MatSeqBAIJSetNumericFactorization(Mat,PetscTruth);
4624 
4625 #undef __FUNCT__
4626 #define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_N_newdatastruct"
4627 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_N_newdatastruct(Mat B,Mat A,const MatFactorInfo *info)
4628 {
4629   Mat            C=B;
4630   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ *)C->data;
4631   IS             isrow = b->row,isicol = b->icol;
4632   PetscErrorCode ierr;
4633   const PetscInt *r,*ic,*ics;
4634   PetscInt       i,j,k,n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
4635   PetscInt       *ajtmp,*bjtmp,nz,nzL,row,*bdiag=b->diag,*pj;
4636   MatScalar      *rtmp,*pc,*mwork,*v,*pv,*aa=a->a;
4637   PetscInt       bs=A->rmap->bs,bs2 = a->bs2,*v_pivots,flg;
4638   MatScalar      *v_work;
4639 
4640   PetscFunctionBegin;
4641   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
4642   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
4643   ierr = PetscMalloc((bs2*n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
4644   ierr = PetscMemzero(rtmp,(bs2*n+1)*sizeof(MatScalar));CHKERRQ(ierr);
4645   ics  = ic;
4646 
4647   /* generate work space needed by dense LU factorization */
4648   ierr     = PetscMalloc(bs*sizeof(PetscInt) + (bs+bs2)*sizeof(MatScalar),&v_work);CHKERRQ(ierr);
4649   mwork    = v_work + bs;
4650   v_pivots = (PetscInt*)(mwork + bs2);
4651 
4652   for (i=0; i<n; i++){
4653     /* zero rtmp */
4654     /* L part */
4655     nz    = bi[i+1] - bi[i];
4656     bjtmp = bj + bi[i];
4657     for  (j=0; j<nz; j++){
4658       ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
4659     }
4660 
4661     /* U part */
4662     nz = bi[2*n-i+1] - bi[2*n-i];
4663     bjtmp = bj + bi[2*n-i];
4664     for  (j=0; j<nz; j++){
4665       ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
4666     }
4667 
4668     /* load in initial (unfactored row) */
4669     nz    = ai[r[i]+1] - ai[r[i]];
4670     ajtmp = aj + ai[r[i]];
4671     v     = aa + bs2*ai[r[i]];
4672     for (j=0; j<nz; j++) {
4673       ierr = PetscMemcpy(rtmp+bs2*ic[ajtmp[j]],v+bs2*j,bs2*sizeof(MatScalar));CHKERRQ(ierr);
4674     }
4675 
4676     /* elimination */
4677     bjtmp = bj + bi[i];
4678     nzL   = bi[i+1] - bi[i];
4679     for(k=0;k < nzL;k++) {
4680       row = bjtmp[k];
4681       pc = rtmp + bs2*row;
4682       for (flg=0,j=0; j<bs2; j++) { if (pc[j]!=0.0) { flg = 1; break; }}
4683       if (flg) {
4684         pv         = b->a + bs2*bdiag[row];
4685         Kernel_A_gets_A_times_B(bs,pc,pv,mwork); /* *pc = *pc * (*pv); */
4686         pj         = b->j + bi[2*n-row]; /* begining of U(row,:) */
4687         pv         = b->a + bs2*bi[2*n-row];
4688         nz         = bi[2*n-row+1] - bi[2*n-row] - 1; /* num of entries inU(row,:), excluding diag */
4689         for (j=0; j<nz; j++) {
4690           Kernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j);
4691         }
4692         ierr = PetscLogFlops(2*bs2*bs*(nz+1)-bs2);CHKERRQ(ierr); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
4693       }
4694     }
4695 
4696     /* finished row so stick it into b->a */
4697     /* L part */
4698     pv   = b->a + bs2*bi[i] ;
4699     pj   = b->j + bi[i] ;
4700     nz   = bi[i+1] - bi[i];
4701     for (j=0; j<nz; j++) {
4702       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
4703     }
4704 
4705     /* Mark diagonal and invert diagonal for simplier triangular solves */
4706     pv  = b->a + bs2*bdiag[i];
4707     pj  = b->j + bdiag[i];
4708     /* if (*pj != i)SETERRQ2(PETSC_ERR_SUP,"row %d != *pj %d",i,*pj); */
4709     ierr = PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));CHKERRQ(ierr);
4710     ierr = Kernel_A_gets_inverse_A(bs,pv,v_pivots,v_work);CHKERRQ(ierr);
4711 
4712     /* U part */
4713     pv = b->a + bs2*bi[2*n-i];
4714     pj = b->j + bi[2*n-i];
4715     nz = bi[2*n-i+1] - bi[2*n-i] - 1;
4716     for (j=0; j<nz; j++){
4717       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
4718     }
4719   }
4720 
4721   ierr = PetscFree(rtmp);CHKERRQ(ierr);
4722   ierr = PetscFree(v_work);CHKERRQ(ierr);
4723   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
4724   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
4725 
4726   C->assembled = PETSC_TRUE;
4727   ierr = PetscLogFlops(1.3333*bs*bs2*b->mbs);CHKERRQ(ierr); /* from inverting diagonal blocks */
4728   PetscFunctionReturn(0);
4729 }
4730 
4731 #undef __FUNCT__
4732 #define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_N_newdatastruct_v2"
4733 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_N_newdatastruct_v2(Mat B,Mat A,const MatFactorInfo *info)
4734 {
4735   Mat            C=B;
4736   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ *)C->data;
4737   IS             isrow = b->row,isicol = b->icol;
4738   PetscErrorCode ierr;
4739   const PetscInt *r,*ic,*ics;
4740   PetscInt       i,j,k,n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
4741   PetscInt       *ajtmp,*bjtmp,nz,nzL,row,*bdiag=b->diag,*pj;
4742   MatScalar      *rtmp,*pc,*mwork,*v,*pv,*aa=a->a;
4743   PetscInt       bs=A->rmap->bs,bs2 = a->bs2,*v_pivots,flg;
4744   MatScalar      *v_work;
4745 
4746   PetscFunctionBegin;
4747   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
4748   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
4749   ierr = PetscMalloc((bs2*n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
4750   ierr = PetscMemzero(rtmp,(bs2*n+1)*sizeof(MatScalar));CHKERRQ(ierr);
4751   ics  = ic;
4752 
4753   /* generate work space needed by dense LU factorization */
4754   ierr     = PetscMalloc(bs*sizeof(PetscInt) + (bs+bs2)*sizeof(MatScalar),&v_work);CHKERRQ(ierr);
4755   mwork    = v_work + bs;
4756   v_pivots = (PetscInt*)(mwork + bs2);
4757 
4758   for (i=0; i<n; i++){
4759     /* zero rtmp */
4760     /* L part */
4761     nz    = bi[i+1] - bi[i];
4762     bjtmp = bj + bi[i];
4763     for  (j=0; j<nz; j++){
4764       ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
4765     }
4766 
4767     /* U part */
4768     nz = bdiag[i] - bdiag[i+1];
4769     bjtmp = bj + bdiag[i+1]+1;
4770     for  (j=0; j<nz; j++){
4771       ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
4772     }
4773 
4774     /* load in initial (unfactored row) */
4775     nz    = ai[r[i]+1] - ai[r[i]];
4776     ajtmp = aj + ai[r[i]];
4777     v     = aa + bs2*ai[r[i]];
4778     for (j=0; j<nz; j++) {
4779       ierr = PetscMemcpy(rtmp+bs2*ic[ajtmp[j]],v+bs2*j,bs2*sizeof(MatScalar));CHKERRQ(ierr);
4780     }
4781 
4782     /* elimination */
4783     bjtmp = bj + bi[i];
4784     nzL   = bi[i+1] - bi[i];
4785     for(k=0;k < nzL;k++) {
4786       row = bjtmp[k];
4787       pc = rtmp + bs2*row;
4788       for (flg=0,j=0; j<bs2; j++) { if (pc[j]!=0.0) { flg = 1; break; }}
4789       if (flg) {
4790         pv         = b->a + bs2*bdiag[row];
4791         Kernel_A_gets_A_times_B(bs,pc,pv,mwork); /* *pc = *pc * (*pv); */
4792         pj         = b->j + bdiag[row+1]+1; /* begining of U(row,:) */
4793         pv         = b->a + bs2*(bdiag[row+1]+1);
4794         nz         = bdiag[row] - bdiag[row+1] - 1; /* num of entries inU(row,:), excluding diag */
4795         for (j=0; j<nz; j++) {
4796           Kernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j);
4797         }
4798         ierr = PetscLogFlops(2*bs2*bs*(nz+1)-bs2);CHKERRQ(ierr); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
4799       }
4800     }
4801 
4802     /* finished row so stick it into b->a */
4803     /* L part */
4804     pv   = b->a + bs2*bi[i] ;
4805     pj   = b->j + bi[i] ;
4806     nz   = bi[i+1] - bi[i];
4807     for (j=0; j<nz; j++) {
4808       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
4809     }
4810 
4811     /* Mark diagonal and invert diagonal for simplier triangular solves */
4812     pv  = b->a + bs2*bdiag[i];
4813     pj  = b->j + bdiag[i];
4814     /* if (*pj != i)SETERRQ2(PETSC_ERR_SUP,"row %d != *pj %d",i,*pj); */
4815     ierr = PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));CHKERRQ(ierr);
4816     ierr = Kernel_A_gets_inverse_A(bs,pv,v_pivots,v_work);CHKERRQ(ierr);
4817 
4818     /* U part */
4819     pv = b->a + bs2*(bdiag[i+1]+1);
4820     pj = b->j + bdiag[i+1]+1;
4821     nz = bdiag[i] - bdiag[i+1] - 1;
4822     for (j=0; j<nz; j++){
4823       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
4824     }
4825   }
4826 
4827   ierr = PetscFree(rtmp);CHKERRQ(ierr);
4828   ierr = PetscFree(v_work);CHKERRQ(ierr);
4829   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
4830   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
4831 
4832   C->assembled = PETSC_TRUE;
4833   ierr = PetscLogFlops(1.3333*bs*bs2*b->mbs);CHKERRQ(ierr); /* from inverting diagonal blocks */
4834   PetscFunctionReturn(0);
4835 }
4836 
4837 /*
4838    ilu(0) with natural ordering under new data structure.
4839    See MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct() for detailed description
4840    because this code is almost identical to MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct().
4841 */
4842 #undef __FUNCT__
4843 #define __FUNCT__ "MatILUFactorSymbolic_SeqBAIJ_ilu0_newdatastruct"
4844 PetscErrorCode MatILUFactorSymbolic_SeqBAIJ_ilu0_newdatastruct(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
4845 {
4846 
4847   Mat_SeqBAIJ        *a = (Mat_SeqBAIJ*)A->data,*b;
4848   PetscErrorCode     ierr;
4849   PetscInt           n=a->mbs,*ai=a->i,*aj,*adiag=a->diag,bs2 = a->bs2;
4850   PetscInt           i,j,nz,*bi,*bj,*bdiag;
4851 
4852   PetscFunctionBegin;
4853   /* printf("MatILUFactorSymbolic_SeqBAIJ_ilu0_newdatastruct...\n"); */
4854   ierr = MatDuplicateNoCreate_SeqBAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_FALSE);CHKERRQ(ierr);
4855   b    = (Mat_SeqBAIJ*)(fact)->data;
4856 
4857   /* allocate matrix arrays for new data structure */
4858   ierr = PetscMalloc3(bs2*ai[n]+1,PetscScalar,&b->a,ai[n]+1,PetscInt,&b->j,2*n+2,PetscInt,&b->i);CHKERRQ(ierr);
4859   ierr = PetscLogObjectMemory(fact,ai[n]*(bs2*sizeof(PetscScalar)+sizeof(PetscInt))+(2*n+2)*sizeof(PetscInt));CHKERRQ(ierr);
4860   b->singlemalloc = PETSC_TRUE;
4861   if (!b->diag){
4862     ierr = PetscMalloc((n+1)*sizeof(PetscInt),&b->diag);CHKERRQ(ierr);
4863   }
4864   bdiag = b->diag;
4865 
4866   if (n > 0) {
4867     ierr = PetscMemzero(b->a,bs2*ai[n]*sizeof(MatScalar));CHKERRQ(ierr);
4868   }
4869 
4870   /* set bi and bj with new data structure */
4871   bi = b->i;
4872   bj = b->j;
4873 
4874   /* L part */
4875   bi[0] = 0;
4876   for (i=0; i<n; i++){
4877     nz = adiag[i] - ai[i];
4878     bi[i+1] = bi[i] + nz;
4879     aj = a->j + ai[i];
4880     for (j=0; j<nz; j++){
4881       *bj = aj[j]; bj++;
4882     }
4883   }
4884 
4885   /* U part */
4886   bi[n+1] = bi[n];
4887   for (i=n-1; i>=0; i--){
4888     nz = ai[i+1] - adiag[i] - 1;
4889     bi[2*n-i+1] = bi[2*n-i] + nz + 1;
4890     aj = a->j + adiag[i] + 1;
4891     for (j=0; j<nz; j++){
4892       *bj = aj[j]; bj++;
4893     }
4894     /* diag[i] */
4895     *bj = i; bj++;
4896     bdiag[i] = bi[2*n-i+1]-1;
4897   }
4898   PetscFunctionReturn(0);
4899 }
4900 
4901 #undef __FUNCT__
4902 #define __FUNCT__ "MatILUFactorSymbolic_SeqBAIJ_newdatastruct"
4903 PetscErrorCode MatILUFactorSymbolic_SeqBAIJ_newdatastruct(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
4904 {
4905   Mat_SeqBAIJ        *a = (Mat_SeqBAIJ*)A->data,*b;
4906   IS                 isicol;
4907   PetscErrorCode     ierr;
4908   const PetscInt     *r,*ic;
4909   PetscInt           n=a->mbs,*ai=a->i,*aj=a->j,d;
4910   PetscInt           *bi,*cols,nnz,*cols_lvl;
4911   PetscInt           *bdiag,prow,fm,nzbd,reallocs=0,dcount=0;
4912   PetscInt           i,levels,diagonal_fill;
4913   PetscTruth         col_identity,row_identity,both_identity;
4914   PetscReal          f;
4915   PetscInt           nlnk,*lnk,*lnk_lvl=PETSC_NULL;
4916   PetscBT            lnkbt;
4917   PetscInt           nzi,*bj,**bj_ptr,**bjlvl_ptr;
4918   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
4919   PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL;
4920   PetscTruth         missing;
4921   PetscInt           bs=A->rmap->bs,bs2=a->bs2;
4922 
4923   PetscFunctionBegin;
4924   if (A->rmap->n != A->cmap->n) SETERRQ2(PETSC_ERR_ARG_WRONG,"Must be square matrix, rows %D columns %D",A->rmap->n,A->cmap->n);
4925   ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr);
4926   if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d);
4927 
4928   f             = info->fill;
4929   levels        = (PetscInt)info->levels;
4930   diagonal_fill = (PetscInt)info->diagonal_fill;
4931   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
4932 
4933   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
4934   ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr);
4935   both_identity = (PetscTruth) (row_identity && col_identity);
4936 
4937   if (!levels && both_identity) {
4938     /* special case: ilu(0) with natural ordering */
4939     ierr = MatILUFactorSymbolic_SeqBAIJ_ilu0_newdatastruct(fact,A,isrow,iscol,info);CHKERRQ(ierr);
4940     (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqBAIJ_N_newdatastruct;
4941     /* set MatSolve routines */
4942     switch (bs){
4943     case 2:
4944       fact->ops->solve = MatSolve_SeqBAIJ_2_NaturalOrdering_newdatastruct;
4945       break;
4946     case 3:
4947       fact->ops->solve = MatSolve_SeqBAIJ_3_NaturalOrdering_newdatastruct;
4948       break;
4949     case 4:
4950       fact->ops->solve = MatSolve_SeqBAIJ_4_NaturalOrdering_newdatastruct;
4951       break;
4952     case 5:
4953       fact->ops->solve = MatSolve_SeqBAIJ_5_NaturalOrdering_newdatastruct;
4954       break;
4955     case 6:
4956       fact->ops->solve = MatSolve_SeqBAIJ_6_NaturalOrdering_newdatastruct;
4957       break;
4958     case 7:
4959       fact->ops->solve = MatSolve_SeqBAIJ_7_NaturalOrdering_newdatastruct;
4960       break;
4961     default:
4962       fact->ops->solve = MatSolve_SeqBAIJ_N_NaturalOrdering_newdatastruct;
4963       break;
4964     }
4965 
4966     fact->factor = MAT_FACTOR_ILU;
4967     (fact)->info.factor_mallocs    = 0;
4968     (fact)->info.fill_ratio_given  = info->fill;
4969     (fact)->info.fill_ratio_needed = 1.0;
4970     b                = (Mat_SeqBAIJ*)(fact)->data;
4971     b->row           = isrow;
4972     b->col           = iscol;
4973     b->icol          = isicol;
4974     ierr             = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
4975     ierr             = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
4976     b->pivotinblocks = (info->pivotinblocks) ? PETSC_TRUE : PETSC_FALSE;
4977     ierr = PetscMalloc((n+1)*bs*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
4978     PetscFunctionReturn(0);
4979   }
4980 
4981   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
4982   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
4983 
4984   /* get new row pointers */
4985   ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
4986   bi[0] = 0;
4987   /* bdiag is location of diagonal in factor */
4988   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);
4989   bdiag[0]  = 0;
4990 
4991   ierr = PetscMalloc((2*n+1)*sizeof(PetscInt**),&bj_ptr);CHKERRQ(ierr);
4992   bjlvl_ptr = (PetscInt**)(bj_ptr + n);
4993 
4994   /* create a linked list for storing column indices of the active row */
4995   nlnk = n + 1;
4996   ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
4997 
4998   /* initial FreeSpace size is f*(ai[n]+1) */
4999   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr);
5000   current_space = free_space;
5001   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr);
5002   current_space_lvl = free_space_lvl;
5003 
5004   for (i=0; i<n; i++) {
5005     nzi = 0;
5006     /* copy current row into linked list */
5007     nnz  = ai[r[i]+1] - ai[r[i]];
5008     if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
5009     cols = aj + ai[r[i]];
5010     lnk[i] = -1; /* marker to indicate if diagonal exists */
5011     ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
5012     nzi += nlnk;
5013 
5014     /* make sure diagonal entry is included */
5015     if (diagonal_fill && lnk[i] == -1) {
5016       fm = n;
5017       while (lnk[fm] < i) fm = lnk[fm];
5018       lnk[i]     = lnk[fm]; /* insert diagonal into linked list */
5019       lnk[fm]    = i;
5020       lnk_lvl[i] = 0;
5021       nzi++; dcount++;
5022     }
5023 
5024     /* add pivot rows into the active row */
5025     nzbd = 0;
5026     prow = lnk[n];
5027     while (prow < i) {
5028       nnz      = bdiag[prow];
5029       cols     = bj_ptr[prow] + nnz + 1;
5030       cols_lvl = bjlvl_ptr[prow] + nnz + 1;
5031       nnz      = bi[prow+1] - bi[prow] - nnz - 1;
5032       ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr);
5033       nzi += nlnk;
5034       prow = lnk[prow];
5035       nzbd++;
5036     }
5037     bdiag[i] = nzbd;
5038     bi[i+1]  = bi[i] + nzi;
5039 
5040     /* if free space is not available, make more free space */
5041     if (current_space->local_remaining<nzi) {
5042       nnz = 2*nzi*(n - i); /* estimated and max additional space needed */
5043       ierr = PetscFreeSpaceGet(nnz,&current_space);CHKERRQ(ierr);
5044       ierr = PetscFreeSpaceGet(nnz,&current_space_lvl);CHKERRQ(ierr);
5045       reallocs++;
5046     }
5047 
5048     /* copy data into free_space and free_space_lvl, then initialize lnk */
5049     ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr);
5050     bj_ptr[i]    = current_space->array;
5051     bjlvl_ptr[i] = current_space_lvl->array;
5052 
5053     /* make sure the active row i has diagonal entry */
5054     if (*(bj_ptr[i]+bdiag[i]) != i) {
5055       SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\
5056     try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i);
5057     }
5058 
5059     current_space->array           += nzi;
5060     current_space->local_used      += nzi;
5061     current_space->local_remaining -= nzi;
5062     current_space_lvl->array           += nzi;
5063     current_space_lvl->local_used      += nzi;
5064     current_space_lvl->local_remaining -= nzi;
5065   }
5066 
5067   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
5068   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
5069 
5070   /* destroy list of free space and other temporary arrays */
5071   ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
5072 
5073   /* copy free_space into bj and free free_space; set bi, bj, bdiag in new datastructure; */
5074   ierr = PetscFreeSpaceContiguous_LU(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr);
5075 
5076   ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
5077   ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr);
5078   ierr = PetscFree(bj_ptr);CHKERRQ(ierr);
5079 
5080 #if defined(PETSC_USE_INFO)
5081   {
5082     PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]);
5083     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr);
5084     ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
5085     ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr);
5086     ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr);
5087     if (diagonal_fill) {
5088       ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr);
5089     }
5090   }
5091 #endif
5092 
5093   /* put together the new matrix */
5094   ierr = MatSeqBAIJSetPreallocation_SeqBAIJ(fact,bs,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
5095   ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr);
5096   b = (Mat_SeqBAIJ*)(fact)->data;
5097   b->free_a       = PETSC_TRUE;
5098   b->free_ij      = PETSC_TRUE;
5099   b->singlemalloc = PETSC_FALSE;
5100   ierr = PetscMalloc( (bs2*bi[2*n+1] )*sizeof(MatScalar),&b->a);CHKERRQ(ierr);
5101   b->j          = bj;
5102   b->i          = bi;
5103   b->diag       = bdiag;
5104   b->free_diag  = PETSC_TRUE;
5105   b->ilen       = 0;
5106   b->imax       = 0;
5107   b->row        = isrow;
5108   b->col        = iscol;
5109   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
5110   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
5111   b->icol       = isicol;
5112   ierr = PetscMalloc((bs*n+bs)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
5113   /* In b structure:  Free imax, ilen, old a, old j.
5114      Allocate bdiag, solve_work, new a, new j */
5115   ierr = PetscLogObjectMemory(fact,bi[2*n+1] * (sizeof(PetscInt)+bs2*sizeof(PetscScalar)));CHKERRQ(ierr);
5116   b->maxnz = b->nz = bi[2*n+1] ;
5117   (fact)->info.factor_mallocs    = reallocs;
5118   (fact)->info.fill_ratio_given  = f;
5119   (fact)->info.fill_ratio_needed = ((PetscReal)bi[2*n+1])/((PetscReal)ai[n]);
5120   (fact)->ops->lufactornumeric   = MatLUFactorNumeric_SeqBAIJ_N_newdatastruct;
5121   /* set MatSolve routines */
5122   if (both_identity){
5123     switch (bs){
5124     case 2:
5125       fact->ops->solve = MatSolve_SeqBAIJ_2_NaturalOrdering_newdatastruct;
5126       break;
5127     case 3:
5128       fact->ops->solve = MatSolve_SeqBAIJ_3_NaturalOrdering_newdatastruct;
5129       break;
5130     case 4:
5131       fact->ops->solve = MatSolve_SeqBAIJ_4_NaturalOrdering_newdatastruct;
5132       break;
5133     case 5:
5134       fact->ops->solve = MatSolve_SeqBAIJ_5_NaturalOrdering_newdatastruct;
5135       break;
5136     case 6:
5137       fact->ops->solve = MatSolve_SeqBAIJ_6_NaturalOrdering_newdatastruct;
5138       break;
5139     case 7:
5140       fact->ops->solve = MatSolve_SeqBAIJ_7_NaturalOrdering_newdatastruct;
5141       break;
5142     default:
5143       fact->ops->solve = MatSolve_SeqBAIJ_N_NaturalOrdering_newdatastruct;
5144       break;
5145     }
5146   } else {
5147     switch (bs){
5148     case 2:
5149       fact->ops->solve = MatSolve_SeqBAIJ_2_newdatastruct;
5150       break;
5151     case 3:
5152       fact->ops->solve = MatSolve_SeqBAIJ_3_newdatastruct;
5153       break;
5154     case 4:
5155       fact->ops->solve = MatSolve_SeqBAIJ_4_newdatastruct;
5156       break;
5157     case 5:
5158       fact->ops->solve = MatSolve_SeqBAIJ_5_newdatastruct;
5159       break;
5160     case 6:
5161       fact->ops->solve = MatSolve_SeqBAIJ_6_newdatastruct;
5162       break;
5163     case 7:
5164       fact->ops->solve = MatSolve_SeqBAIJ_7_newdatastruct;
5165       break;
5166     default:
5167       fact->ops->solve = MatSolve_SeqBAIJ_N_newdatastruct;
5168       break;
5169     }
5170   }
5171   PetscFunctionReturn(0);
5172 }
5173 
5174 /*
5175      This code is virtually identical to MatILUFactorSymbolic_SeqAIJ
5176    except that the data structure of Mat_SeqAIJ is slightly different.
5177    Not a good example of code reuse.
5178 */
5179 #undef __FUNCT__
5180 #define __FUNCT__ "MatILUFactorSymbolic_SeqBAIJ"
5181 PetscErrorCode MatILUFactorSymbolic_SeqBAIJ(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
5182 {
5183   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ*)A->data,*b;
5184   IS             isicol;
5185   PetscErrorCode ierr;
5186   const PetscInt *r,*ic,*ai = a->i,*aj = a->j,*xi;
5187   PetscInt       prow,n = a->mbs,*ainew,*ajnew,jmax,*fill,nz,*im,*ajfill,*flev,*xitmp;
5188   PetscInt       *dloc,idx,row,m,fm,nzf,nzi,reallocate = 0,dcount = 0;
5189   PetscInt       incrlev,nnz,i,bs = A->rmap->bs,bs2 = a->bs2,levels,diagonal_fill,dd;
5190   PetscTruth     col_identity,row_identity,both_identity,flg;
5191   PetscReal      f;
5192   PetscTruth     newdatastruct=PETSC_FALSE;
5193 
5194   PetscFunctionBegin;
5195   ierr = PetscOptionsGetTruth(PETSC_NULL,"-ilu_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr);
5196   if (newdatastruct){
5197     ierr = MatILUFactorSymbolic_SeqBAIJ_newdatastruct(fact,A,isrow,iscol,info);CHKERRQ(ierr);
5198     PetscFunctionReturn(0);
5199   }
5200 
5201   ierr = MatMissingDiagonal_SeqBAIJ(A,&flg,&dd);CHKERRQ(ierr);
5202   if (flg) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix A is missing diagonal entry in row %D",dd);
5203 
5204   f             = info->fill;
5205   levels        = (PetscInt)info->levels;
5206   diagonal_fill = (PetscInt)info->diagonal_fill;
5207   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
5208 
5209   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
5210   ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr);
5211   both_identity = (PetscTruth) (row_identity && col_identity);
5212 
5213   if (!levels && both_identity) {  /* special case copy the nonzero structure */
5214     ierr = MatDuplicateNoCreate_SeqBAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_TRUE);CHKERRQ(ierr);
5215     ierr = MatSeqBAIJSetNumericFactorization(fact,both_identity);CHKERRQ(ierr);
5216 
5217     fact->factor = MAT_FACTOR_ILU;
5218     b            = (Mat_SeqBAIJ*)(fact)->data;
5219     b->row       = isrow;
5220     b->col       = iscol;
5221     ierr         = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
5222     ierr         = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
5223     b->icol      = isicol;
5224     b->pivotinblocks = (info->pivotinblocks) ? PETSC_TRUE : PETSC_FALSE;
5225     ierr         = PetscMalloc((n+1)*bs*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
5226     PetscFunctionReturn(0);
5227   }
5228 
5229   /* general case perform the symbolic factorization */
5230     ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
5231     ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
5232 
5233     /* get new row pointers */
5234     ierr = PetscMalloc((n+1)*sizeof(PetscInt),&ainew);CHKERRQ(ierr);
5235     ainew[0] = 0;
5236     /* don't know how many column pointers are needed so estimate */
5237     jmax = (PetscInt)(f*ai[n] + 1);
5238     ierr = PetscMalloc((jmax)*sizeof(PetscInt),&ajnew);CHKERRQ(ierr);
5239     /* ajfill is level of fill for each fill entry */
5240     ierr = PetscMalloc((jmax)*sizeof(PetscInt),&ajfill);CHKERRQ(ierr);
5241     /* fill is a linked list of nonzeros in active row */
5242     ierr = PetscMalloc((n+1)*sizeof(PetscInt),&fill);CHKERRQ(ierr);
5243     /* im is level for each filled value */
5244     ierr = PetscMalloc((n+1)*sizeof(PetscInt),&im);CHKERRQ(ierr);
5245     /* dloc is location of diagonal in factor */
5246     ierr = PetscMalloc((n+1)*sizeof(PetscInt),&dloc);CHKERRQ(ierr);
5247     dloc[0]  = 0;
5248     for (prow=0; prow<n; prow++) {
5249 
5250       /* copy prow into linked list */
5251       nzf        = nz  = ai[r[prow]+1] - ai[r[prow]];
5252       if (!nz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[prow],prow);
5253       xi         = aj + ai[r[prow]];
5254       fill[n]    = n;
5255       fill[prow] = -1; /* marker for diagonal entry */
5256       while (nz--) {
5257 	fm  = n;
5258 	idx = ic[*xi++];
5259 	do {
5260 	  m  = fm;
5261 	  fm = fill[m];
5262 	} while (fm < idx);
5263 	fill[m]   = idx;
5264 	fill[idx] = fm;
5265 	im[idx]   = 0;
5266       }
5267 
5268       /* make sure diagonal entry is included */
5269       if (diagonal_fill && fill[prow] == -1) {
5270 	fm = n;
5271 	while (fill[fm] < prow) fm = fill[fm];
5272 	fill[prow] = fill[fm];  /* insert diagonal into linked list */
5273 	fill[fm]   = prow;
5274 	im[prow]   = 0;
5275 	nzf++;
5276 	dcount++;
5277       }
5278 
5279       nzi = 0;
5280       row = fill[n];
5281       while (row < prow) {
5282 	incrlev = im[row] + 1;
5283 	nz      = dloc[row];
5284 	xi      = ajnew  + ainew[row] + nz + 1;
5285 	flev    = ajfill + ainew[row] + nz + 1;
5286 	nnz     = ainew[row+1] - ainew[row] - nz - 1;
5287 	fm      = row;
5288 	while (nnz-- > 0) {
5289 	  idx = *xi++;
5290 	  if (*flev + incrlev > levels) {
5291 	    flev++;
5292 	    continue;
5293 	  }
5294 	  do {
5295 	    m  = fm;
5296 	    fm = fill[m];
5297 	  } while (fm < idx);
5298 	  if (fm != idx) {
5299 	    im[idx]   = *flev + incrlev;
5300 	    fill[m]   = idx;
5301 	    fill[idx] = fm;
5302 	    fm        = idx;
5303 	    nzf++;
5304 	  } else {
5305 	    if (im[idx] > *flev + incrlev) im[idx] = *flev+incrlev;
5306 	  }
5307 	  flev++;
5308 	}
5309 	row = fill[row];
5310 	nzi++;
5311       }
5312       /* copy new filled row into permanent storage */
5313       ainew[prow+1] = ainew[prow] + nzf;
5314       if (ainew[prow+1] > jmax) {
5315 
5316 	/* estimate how much additional space we will need */
5317 	/* use the strategy suggested by David Hysom <hysom@perch-t.icase.edu> */
5318 	/* just double the memory each time */
5319 	PetscInt maxadd = jmax;
5320 	/* maxadd = (int)(((f*ai[n]+1)*(n-prow+5))/n); */
5321 	if (maxadd < nzf) maxadd = (n-prow)*(nzf+1);
5322 	jmax += maxadd;
5323 
5324 	/* allocate a longer ajnew and ajfill */
5325 	ierr = PetscMalloc(jmax*sizeof(PetscInt),&xitmp);CHKERRQ(ierr);
5326 	ierr = PetscMemcpy(xitmp,ajnew,ainew[prow]*sizeof(PetscInt));CHKERRQ(ierr);
5327 	ierr = PetscFree(ajnew);CHKERRQ(ierr);
5328 	ajnew = xitmp;
5329 	ierr = PetscMalloc(jmax*sizeof(PetscInt),&xitmp);CHKERRQ(ierr);
5330 	ierr = PetscMemcpy(xitmp,ajfill,ainew[prow]*sizeof(PetscInt));CHKERRQ(ierr);
5331 	ierr = PetscFree(ajfill);CHKERRQ(ierr);
5332 	ajfill = xitmp;
5333 	reallocate++; /* count how many reallocations are needed */
5334       }
5335       xitmp       = ajnew + ainew[prow];
5336       flev        = ajfill + ainew[prow];
5337       dloc[prow]  = nzi;
5338       fm          = fill[n];
5339       while (nzf--) {
5340 	*xitmp++ = fm;
5341 	*flev++ = im[fm];
5342 	fm      = fill[fm];
5343       }
5344       /* make sure row has diagonal entry */
5345       if (ajnew[ainew[prow]+dloc[prow]] != prow) {
5346 	SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\
5347     try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",prow);
5348       }
5349     }
5350     ierr = PetscFree(ajfill);CHKERRQ(ierr);
5351     ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
5352     ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
5353     ierr = PetscFree(fill);CHKERRQ(ierr);
5354     ierr = PetscFree(im);CHKERRQ(ierr);
5355 
5356 #if defined(PETSC_USE_INFO)
5357     {
5358       PetscReal af = ((PetscReal)ainew[n])/((PetscReal)ai[n]);
5359       ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocate,f,af);CHKERRQ(ierr);
5360       ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
5361       ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G);\n",af);CHKERRQ(ierr);
5362       ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr);
5363       if (diagonal_fill) {
5364 	ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals\n",dcount);CHKERRQ(ierr);
5365       }
5366     }
5367 #endif
5368 
5369     /* put together the new matrix */
5370     ierr = MatSeqBAIJSetPreallocation_SeqBAIJ(fact,bs,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
5371     ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr);
5372     b    = (Mat_SeqBAIJ*)(fact)->data;
5373     b->free_a       = PETSC_TRUE;
5374     b->free_ij      = PETSC_TRUE;
5375     b->singlemalloc = PETSC_FALSE;
5376     ierr = PetscMalloc(bs2*ainew[n]*sizeof(MatScalar),&b->a);CHKERRQ(ierr);
5377     b->j          = ajnew;
5378     b->i          = ainew;
5379     for (i=0; i<n; i++) dloc[i] += ainew[i];
5380     b->diag       = dloc;
5381     b->free_diag  = PETSC_TRUE;
5382     b->ilen       = 0;
5383     b->imax       = 0;
5384     b->row        = isrow;
5385     b->col        = iscol;
5386     b->pivotinblocks = (info->pivotinblocks) ? PETSC_TRUE : PETSC_FALSE;
5387     ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
5388     ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
5389     b->icol       = isicol;
5390     ierr = PetscMalloc((bs*n+bs)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
5391     /* In b structure:  Free imax, ilen, old a, old j.
5392        Allocate dloc, solve_work, new a, new j */
5393     ierr = PetscLogObjectMemory(fact,(ainew[n]-n)*(sizeof(PetscInt))+bs2*ainew[n]*sizeof(PetscScalar));CHKERRQ(ierr);
5394     b->maxnz          = b->nz = ainew[n];
5395 
5396     (fact)->info.factor_mallocs    = reallocate;
5397     (fact)->info.fill_ratio_given  = f;
5398     (fact)->info.fill_ratio_needed = ((PetscReal)ainew[n])/((PetscReal)ai[prow]);
5399 
5400   ierr = MatSeqBAIJSetNumericFactorization(fact,both_identity);CHKERRQ(ierr);
5401   PetscFunctionReturn(0);
5402 }
5403 
5404 #undef __FUNCT__
5405 #define __FUNCT__ "MatSetUnfactored_SeqBAIJ_4_NaturalOrdering_SSE"
5406 PetscErrorCode MatSetUnfactored_SeqBAIJ_4_NaturalOrdering_SSE(Mat A)
5407 {
5408   /* Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data; */
5409   /* int i,*AJ=a->j,nz=a->nz; */
5410   PetscFunctionBegin;
5411   /* Undo Column scaling */
5412 /*    while (nz--) { */
5413 /*      AJ[i] = AJ[i]/4; */
5414 /*    } */
5415   /* This should really invoke a push/pop logic, but we don't have that yet. */
5416   A->ops->setunfactored = PETSC_NULL;
5417   PetscFunctionReturn(0);
5418 }
5419 
5420 #undef __FUNCT__
5421 #define __FUNCT__ "MatSetUnfactored_SeqBAIJ_4_NaturalOrdering_SSE_usj"
5422 PetscErrorCode MatSetUnfactored_SeqBAIJ_4_NaturalOrdering_SSE_usj(Mat A)
5423 {
5424   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ *)A->data;
5425   PetscInt       *AJ=a->j,nz=a->nz;
5426   unsigned short *aj=(unsigned short *)AJ;
5427   PetscFunctionBegin;
5428   /* Is this really necessary? */
5429   while (nz--) {
5430     AJ[nz] = (int)((unsigned int)aj[nz]); /* First extend, then convert to signed. */
5431   }
5432   A->ops->setunfactored = PETSC_NULL;
5433   PetscFunctionReturn(0);
5434 }
5435 
5436 
5437