xref: /petsc/src/mat/impls/baij/seq/baijfact2.c (revision b06ca6b09b3ae4e8a93ed49db16f4412dd6db9d8)
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_6"
1567 PetscErrorCode MatSolve_SeqBAIJ_6(Mat A,Vec bb,Vec xx)
1568 {
1569   Mat_SeqBAIJ       *a=(Mat_SeqBAIJ *)A->data;
1570   IS                iscol=a->col,isrow=a->row;
1571   PetscErrorCode    ierr;
1572   const PetscInt    *r,*c,*rout,*cout;
1573   PetscInt          *diag = a->diag,i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc;
1574   const MatScalar   *aa=a->a,*v;
1575   PetscScalar       *x,s1,s2,s3,s4,s5,s6,x1,x2,x3,x4,x5,x6,*t;
1576   const PetscScalar *b;
1577   PetscFunctionBegin;
1578   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1579   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1580   t  = a->solve_work;
1581 
1582   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1583   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1584 
1585   /* forward solve the lower triangular */
1586   idx    = 6*(*r++);
1587   t[0] = b[idx];   t[1] = b[1+idx];
1588   t[2] = b[2+idx]; t[3] = b[3+idx];
1589   t[4] = b[4+idx]; t[5] = b[5+idx];
1590   for (i=1; i<n; i++) {
1591     v     = aa + 36*ai[i];
1592     vi    = aj + ai[i];
1593     nz    = diag[i] - ai[i];
1594     idx   = 6*(*r++);
1595     s1  = b[idx];s2 = b[1+idx];s3 = b[2+idx];s4 = b[3+idx];
1596     s5  = b[4+idx]; s6 = b[5+idx];
1597     while (nz--) {
1598       idx   = 6*(*vi++);
1599       x1    = t[idx];   x2 = t[1+idx]; x3 = t[2+idx];
1600       x4    = t[3+idx]; x5 = t[4+idx]; x6 = t[5+idx];
1601       s1 -= v[0]*x1 + v[6]*x2  + v[12]*x3 + v[18]*x4 + v[24]*x5 + v[30]*x6;
1602       s2 -= v[1]*x1 + v[7]*x2  + v[13]*x3 + v[19]*x4 + v[25]*x5 + v[31]*x6;
1603       s3 -= v[2]*x1 + v[8]*x2  + v[14]*x3 + v[20]*x4 + v[26]*x5 + v[32]*x6;
1604       s4 -= v[3]*x1 + v[9]*x2  + v[15]*x3 + v[21]*x4 + v[27]*x5 + v[33]*x6;
1605       s5 -= v[4]*x1 + v[10]*x2 + v[16]*x3 + v[22]*x4 + v[28]*x5 + v[34]*x6;
1606       s6 -= v[5]*x1 + v[11]*x2 + v[17]*x3 + v[23]*x4 + v[29]*x5 + v[35]*x6;
1607       v += 36;
1608     }
1609     idx = 6*i;
1610     t[idx]   = s1;t[1+idx] = s2;
1611     t[2+idx] = s3;t[3+idx] = s4;
1612     t[4+idx] = s5;t[5+idx] = s6;
1613   }
1614   /* backward solve the upper triangular */
1615   for (i=n-1; i>=0; i--){
1616     v    = aa + 36*diag[i] + 36;
1617     vi   = aj + diag[i] + 1;
1618     nz   = ai[i+1] - diag[i] - 1;
1619     idt  = 6*i;
1620     s1 = t[idt];  s2 = t[1+idt];
1621     s3 = t[2+idt];s4 = t[3+idt];
1622     s5 = t[4+idt];s6 = t[5+idt];
1623     while (nz--) {
1624       idx   = 6*(*vi++);
1625       x1    = t[idx];   x2 = t[1+idx];
1626       x3    = t[2+idx]; x4 = t[3+idx];
1627       x5    = t[4+idx]; x6 = t[5+idx];
1628       s1 -= v[0]*x1 + v[6]*x2  + v[12]*x3 + v[18]*x4 + v[24]*x5 + v[30]*x6;
1629       s2 -= v[1]*x1 + v[7]*x2  + v[13]*x3 + v[19]*x4 + v[25]*x5 + v[31]*x6;
1630       s3 -= v[2]*x1 + v[8]*x2  + v[14]*x3 + v[20]*x4 + v[26]*x5 + v[32]*x6;
1631       s4 -= v[3]*x1 + v[9]*x2  + v[15]*x3 + v[21]*x4 + v[27]*x5 + v[33]*x6;
1632       s5 -= v[4]*x1 + v[10]*x2 + v[16]*x3 + v[22]*x4 + v[28]*x5 + v[34]*x6;
1633       s6 -= v[5]*x1 + v[11]*x2 + v[17]*x3 + v[23]*x4 + v[29]*x5 + v[35]*x6;
1634       v += 36;
1635     }
1636     idc = 6*(*c--);
1637     v   = aa + 36*diag[i];
1638     x[idc]   = t[idt]   = v[0]*s1+v[6]*s2+v[12]*s3+
1639                                  v[18]*s4+v[24]*s5+v[30]*s6;
1640     x[1+idc] = t[1+idt] = v[1]*s1+v[7]*s2+v[13]*s3+
1641                                  v[19]*s4+v[25]*s5+v[31]*s6;
1642     x[2+idc] = t[2+idt] = v[2]*s1+v[8]*s2+v[14]*s3+
1643                                  v[20]*s4+v[26]*s5+v[32]*s6;
1644     x[3+idc] = t[3+idt] = v[3]*s1+v[9]*s2+v[15]*s3+
1645                                  v[21]*s4+v[27]*s5+v[33]*s6;
1646     x[4+idc] = t[4+idt] = v[4]*s1+v[10]*s2+v[16]*s3+
1647                                  v[22]*s4+v[28]*s5+v[34]*s6;
1648     x[5+idc] = t[5+idt] = v[5]*s1+v[11]*s2+v[17]*s3+
1649                                  v[23]*s4+v[29]*s5+v[35]*s6;
1650   }
1651 
1652   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1653   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1654   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1655   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1656   ierr = PetscLogFlops(2.0*36*(a->nz) - 6.0*A->cmap->n);CHKERRQ(ierr);
1657   PetscFunctionReturn(0);
1658 }
1659 
1660 #undef __FUNCT__
1661 #define __FUNCT__ "MatSolve_SeqBAIJ_6_newdatastruct"
1662 PetscErrorCode MatSolve_SeqBAIJ_6_newdatastruct(Mat A,Vec bb,Vec xx)
1663 {
1664   Mat_SeqBAIJ       *a=(Mat_SeqBAIJ *)A->data;
1665   IS                iscol=a->col,isrow=a->row;
1666   PetscErrorCode    ierr;
1667   const PetscInt    *r,*c,*rout,*cout;
1668   PetscInt          i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,k,m;
1669   const MatScalar   *aa=a->a,*v;
1670   PetscScalar       *x,s1,s2,s3,s4,s5,s6,x1,x2,x3,x4,x5,x6,*t;
1671   const PetscScalar *b;
1672   PetscFunctionBegin;
1673   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1674   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1675   t  = a->solve_work;
1676 
1677   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1678   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
1679 
1680   /* forward solve the lower triangular */
1681   idx    = 6*r[0];
1682   t[0] = b[idx];   t[1] = b[1+idx];
1683   t[2] = b[2+idx]; t[3] = b[3+idx];
1684   t[4] = b[4+idx]; t[5] = b[5+idx];
1685   for (i=1; i<n; i++) {
1686     v     = aa + 36*ai[i];
1687     vi    = aj + ai[i];
1688     nz    = ai[i+1] - ai[i];
1689     idx   = 6*r[i];
1690     s1  = b[idx];s2 = b[1+idx];s3 = b[2+idx];s4 = b[3+idx];
1691     s5  = b[4+idx]; s6 = b[5+idx];
1692     for(m=0;m<nz;m++){
1693       idx   = 6*vi[m];
1694       x1    = t[idx];   x2 = t[1+idx]; x3 = t[2+idx];
1695       x4    = t[3+idx]; x5 = t[4+idx]; x6 = t[5+idx];
1696       s1 -= v[0]*x1 + v[6]*x2  + v[12]*x3 + v[18]*x4 + v[24]*x5 + v[30]*x6;
1697       s2 -= v[1]*x1 + v[7]*x2  + v[13]*x3 + v[19]*x4 + v[25]*x5 + v[31]*x6;
1698       s3 -= v[2]*x1 + v[8]*x2  + v[14]*x3 + v[20]*x4 + v[26]*x5 + v[32]*x6;
1699       s4 -= v[3]*x1 + v[9]*x2  + v[15]*x3 + v[21]*x4 + v[27]*x5 + v[33]*x6;
1700       s5 -= v[4]*x1 + v[10]*x2 + v[16]*x3 + v[22]*x4 + v[28]*x5 + v[34]*x6;
1701       s6 -= v[5]*x1 + v[11]*x2 + v[17]*x3 + v[23]*x4 + v[29]*x5 + v[35]*x6;
1702       v += 36;
1703     }
1704     idx = 6*i;
1705     t[idx]   = s1;t[1+idx] = s2;
1706     t[2+idx] = s3;t[3+idx] = s4;
1707     t[4+idx] = s5;t[5+idx] = s6;
1708   }
1709   /* backward solve the upper triangular */
1710   for (i=n-1; i>=0; i--){
1711     k    = 2*n-i;
1712     v    = aa + 36*ai[k];
1713     vi   = aj + ai[k];
1714     nz   = ai[k+1] - ai[k] - 1;
1715     idt  = 6*i;
1716     s1 = t[idt];  s2 = t[1+idt];
1717     s3 = t[2+idt];s4 = t[3+idt];
1718     s5 = t[4+idt];s6 = t[5+idt];
1719     for(m=0;m<nz;m++){
1720       idx   = 6*vi[m];
1721       x1    = t[idx];   x2 = t[1+idx];
1722       x3    = t[2+idx]; x4 = t[3+idx];
1723       x5    = t[4+idx]; x6 = t[5+idx];
1724       s1 -= v[0]*x1 + v[6]*x2  + v[12]*x3 + v[18]*x4 + v[24]*x5 + v[30]*x6;
1725       s2 -= v[1]*x1 + v[7]*x2  + v[13]*x3 + v[19]*x4 + v[25]*x5 + v[31]*x6;
1726       s3 -= v[2]*x1 + v[8]*x2  + v[14]*x3 + v[20]*x4 + v[26]*x5 + v[32]*x6;
1727       s4 -= v[3]*x1 + v[9]*x2  + v[15]*x3 + v[21]*x4 + v[27]*x5 + v[33]*x6;
1728       s5 -= v[4]*x1 + v[10]*x2 + v[16]*x3 + v[22]*x4 + v[28]*x5 + v[34]*x6;
1729       s6 -= v[5]*x1 + v[11]*x2 + v[17]*x3 + v[23]*x4 + v[29]*x5 + v[35]*x6;
1730       v += 36;
1731     }
1732     idc = 6*c[i];
1733     x[idc]   = t[idt]   = v[0]*s1+v[6]*s2+v[12]*s3+
1734                                  v[18]*s4+v[24]*s5+v[30]*s6;
1735     x[1+idc] = t[1+idt] = v[1]*s1+v[7]*s2+v[13]*s3+
1736                                  v[19]*s4+v[25]*s5+v[31]*s6;
1737     x[2+idc] = t[2+idt] = v[2]*s1+v[8]*s2+v[14]*s3+
1738                                  v[20]*s4+v[26]*s5+v[32]*s6;
1739     x[3+idc] = t[3+idt] = v[3]*s1+v[9]*s2+v[15]*s3+
1740                                  v[21]*s4+v[27]*s5+v[33]*s6;
1741     x[4+idc] = t[4+idt] = v[4]*s1+v[10]*s2+v[16]*s3+
1742                                  v[22]*s4+v[28]*s5+v[34]*s6;
1743     x[5+idc] = t[5+idt] = v[5]*s1+v[11]*s2+v[17]*s3+
1744                                  v[23]*s4+v[29]*s5+v[35]*s6;
1745   }
1746 
1747   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
1748   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
1749   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1750   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1751   ierr = PetscLogFlops(2.0*36*(a->nz) - 6.0*A->cmap->n);CHKERRQ(ierr);
1752   PetscFunctionReturn(0);
1753 }
1754 
1755 
1756 #undef __FUNCT__
1757 #define __FUNCT__ "MatSolve_SeqBAIJ_6_NaturalOrdering"
1758 PetscErrorCode MatSolve_SeqBAIJ_6_NaturalOrdering(Mat A,Vec bb,Vec xx)
1759 {
1760   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ *)A->data;
1761   PetscInt          i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt;
1762   PetscErrorCode    ierr;
1763   PetscInt          *diag = a->diag,jdx;
1764   const MatScalar   *aa=a->a,*v;
1765   PetscScalar       *x,s1,s2,s3,s4,s5,s6,x1,x2,x3,x4,x5,x6;
1766   const PetscScalar *b;
1767 
1768   PetscFunctionBegin;
1769   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1770   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1771   /* forward solve the lower triangular */
1772   idx    = 0;
1773   x[0] = b[idx];   x[1] = b[1+idx]; x[2] = b[2+idx];
1774   x[3] = b[3+idx]; x[4] = b[4+idx]; x[5] = b[5+idx];
1775   for (i=1; i<n; i++) {
1776     v     =  aa + 36*ai[i];
1777     vi    =  aj + ai[i];
1778     nz    =  diag[i] - ai[i];
1779     idx   =  6*i;
1780     s1  =  b[idx];   s2 = b[1+idx]; s3 = b[2+idx];
1781     s4  =  b[3+idx]; s5 = b[4+idx]; s6 = b[5+idx];
1782     while (nz--) {
1783       jdx   = 6*(*vi++);
1784       x1    = x[jdx];   x2 = x[1+jdx]; x3 = x[2+jdx];
1785       x4    = x[3+jdx]; x5 = x[4+jdx]; x6 = x[5+jdx];
1786       s1 -= v[0]*x1 + v[6]*x2  + v[12]*x3 + v[18]*x4 + v[24]*x5 + v[30]*x6;
1787       s2 -= v[1]*x1 + v[7]*x2  + v[13]*x3 + v[19]*x4 + v[25]*x5 + v[31]*x6;
1788       s3 -= v[2]*x1 + v[8]*x2  + v[14]*x3 + v[20]*x4 + v[26]*x5 + v[32]*x6;
1789       s4 -= v[3]*x1 + v[9]*x2  + v[15]*x3 + v[21]*x4 + v[27]*x5 + v[33]*x6;
1790       s5 -= v[4]*x1 + v[10]*x2 + v[16]*x3 + v[22]*x4 + v[28]*x5 + v[34]*x6;
1791       s6 -= v[5]*x1 + v[11]*x2 + v[17]*x3 + v[23]*x4 + v[29]*x5 + v[35]*x6;
1792       v += 36;
1793      }
1794     x[idx]   = s1;
1795     x[1+idx] = s2;
1796     x[2+idx] = s3;
1797     x[3+idx] = s4;
1798     x[4+idx] = s5;
1799     x[5+idx] = s6;
1800   }
1801   /* backward solve the upper triangular */
1802   for (i=n-1; i>=0; i--){
1803     v    = aa + 36*diag[i] + 36;
1804     vi   = aj + diag[i] + 1;
1805     nz   = ai[i+1] - diag[i] - 1;
1806     idt  = 6*i;
1807     s1 = x[idt];   s2 = x[1+idt];
1808     s3 = x[2+idt]; s4 = x[3+idt];
1809     s5 = x[4+idt]; s6 = x[5+idt];
1810     while (nz--) {
1811       idx   = 6*(*vi++);
1812       x1    = x[idx];   x2 = x[1+idx]; x3 = x[2+idx];
1813       x4    = x[3+idx]; x5 = x[4+idx]; x6 = x[5+idx];
1814       s1 -= v[0]*x1 + v[6]*x2  + v[12]*x3 + v[18]*x4 + v[24]*x5 + v[30]*x6;
1815       s2 -= v[1]*x1 + v[7]*x2  + v[13]*x3 + v[19]*x4 + v[25]*x5 + v[31]*x6;
1816       s3 -= v[2]*x1 + v[8]*x2  + v[14]*x3 + v[20]*x4 + v[26]*x5 + v[32]*x6;
1817       s4 -= v[3]*x1 + v[9]*x2  + v[15]*x3 + v[21]*x4 + v[27]*x5 + v[33]*x6;
1818       s5 -= v[4]*x1 + v[10]*x2 + v[16]*x3 + v[22]*x4 + v[28]*x5 + v[34]*x6;
1819       s6 -= v[5]*x1 + v[11]*x2 + v[17]*x3 + v[23]*x4 + v[29]*x5 + v[35]*x6;
1820       v += 36;
1821     }
1822     v        = aa + 36*diag[i];
1823     x[idt]   = v[0]*s1 + v[6]*s2  + v[12]*s3 + v[18]*s4 + v[24]*s5 + v[30]*s6;
1824     x[1+idt] = v[1]*s1 + v[7]*s2  + v[13]*s3 + v[19]*s4 + v[25]*s5 + v[31]*s6;
1825     x[2+idt] = v[2]*s1 + v[8]*s2  + v[14]*s3 + v[20]*s4 + v[26]*s5 + v[32]*s6;
1826     x[3+idt] = v[3]*s1 + v[9]*s2  + v[15]*s3 + v[21]*s4 + v[27]*s5 + v[33]*s6;
1827     x[4+idt] = v[4]*s1 + v[10]*s2 + v[16]*s3 + v[22]*s4 + v[28]*s5 + v[34]*s6;
1828     x[5+idt] = v[5]*s1 + v[11]*s2 + v[17]*s3 + v[23]*s4 + v[29]*s5 + v[35]*s6;
1829   }
1830 
1831   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1832   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1833   ierr = PetscLogFlops(2.0*36*(a->nz) - 6.0*A->cmap->n);CHKERRQ(ierr);
1834   PetscFunctionReturn(0);
1835 }
1836 
1837 #undef __FUNCT__
1838 #define __FUNCT__ "MatSolve_SeqBAIJ_6_NaturalOrdering_newdatastruct"
1839 PetscErrorCode MatSolve_SeqBAIJ_6_NaturalOrdering_newdatastruct(Mat A,Vec bb,Vec xx)
1840 {
1841     Mat_SeqBAIJ       *a = (Mat_SeqBAIJ *)A->data;
1842     PetscInt          i,k,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz;
1843     PetscErrorCode    ierr;
1844     PetscInt          idx,jdx,idt;
1845     PetscInt          bs = A->rmap->bs,bs2 = a->bs2;
1846     const MatScalar   *aa=a->a,*v;
1847     PetscScalar       *x;
1848     const PetscScalar *b;
1849     PetscScalar        s1,s2,s3,s4,s5,s6,x1,x2,x3,x4,x5,x6;
1850 
1851     PetscFunctionBegin;
1852     ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1853     ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1854     /* forward solve the lower triangular */
1855     idx    = 0;
1856     x[0] = b[idx]; x[1] = b[1+idx];x[2] = b[2+idx];x[3] = b[3+idx];
1857     x[4] = b[4+idx];x[5] = b[5+idx];
1858     for (i=1; i<n; i++) {
1859        v    = aa + bs2*ai[i];
1860        vi   = aj + ai[i];
1861        nz   = ai[i+1] - ai[i];
1862       idx   = bs*i;
1863        s1   = b[idx];s2 = b[1+idx];s3 = b[2+idx];s4 = b[3+idx];
1864        s5   = b[4+idx];s6 = b[5+idx];
1865        for(k=0;k<nz;k++){
1866           jdx   = bs*vi[k];
1867           x1    = x[jdx];x2 = x[1+jdx]; x3 =x[2+jdx];x4 =x[3+jdx];
1868 	  x5    = x[4+jdx]; x6 = x[5+jdx];
1869           s1   -= v[0]*x1 + v[6]*x2 + v[12]*x3 + v[18]*x4  + v[24]*x5 + v[30]*x6;
1870           s2   -= v[1]*x1 + v[7]*x2 + v[13]*x3 + v[19]*x4  + v[25]*x5 + v[31]*x6;;
1871           s3   -= v[2]*x1 + v[8]*x2 + v[14]*x3 + v[20]*x4  + v[26]*x5 + v[32]*x6;
1872 	  s4   -= v[3]*x1 + v[9]*x2 + v[15]*x3 + v[21]*x4  + v[27]*x5 + v[33]*x6;
1873           s5   -= v[4]*x1 + v[10]*x2 + v[16]*x3 + v[22]*x4  + v[28]*x5 + v[34]*x6;
1874 	  s6   -= v[5]*x1 + v[11]*x2 + v[17]*x3 + v[23]*x4  + v[29]*x5 + v[35]*x6;
1875           v   +=  bs2;
1876         }
1877 
1878        x[idx]   = s1;
1879        x[1+idx] = s2;
1880        x[2+idx] = s3;
1881        x[3+idx] = s4;
1882        x[4+idx] = s5;
1883        x[5+idx] = s6;
1884     }
1885 
1886    /* backward solve the upper triangular */
1887   for (i=n-1; i>=0; i--){
1888      v   = aa + bs2*ai[2*n-i];
1889      vi  = aj + ai[2*n-i];
1890      nz  = ai[2*n-i +1] - ai[2*n-i]-1;
1891      idt = bs*i;
1892      s1 = x[idt];  s2 = x[1+idt];s3 = x[2+idt];s4 = x[3+idt];
1893      s5 = x[4+idt];s6 = x[5+idt];
1894      for(k=0;k<nz;k++){
1895       idx   = bs*vi[k];
1896        x1    = x[idx];   x2 = x[1+idx]; x3 = x[2+idx];x4 = x[3+idx];
1897        x5    = x[4+idx];x6 = x[5+idx];
1898        s1   -= v[0]*x1 + v[6]*x2 + v[12]*x3 + v[18]*x4  + v[24]*x5 + v[30]*x6;
1899        s2   -= v[1]*x1 + v[7]*x2 + v[13]*x3 + v[19]*x4  + v[25]*x5 + v[31]*x6;;
1900        s3   -= v[2]*x1 + v[8]*x2 + v[14]*x3 + v[20]*x4  + v[26]*x5 + v[32]*x6;
1901        s4   -= v[3]*x1 + v[9]*x2 + v[15]*x3 + v[21]*x4  + v[27]*x5 + v[33]*x6;
1902        s5   -= v[4]*x1 + v[10]*x2 + v[16]*x3 + v[22]*x4  + v[28]*x5 + v[34]*x6;
1903        s6   -= v[5]*x1 + v[11]*x2 + v[17]*x3 + v[23]*x4  + v[29]*x5 + v[35]*x6;
1904         v   +=  bs2;
1905     }
1906     /* x = inv_diagonal*x */
1907    x[idt]   = v[0]*s1 + v[6]*s2 + v[12]*s3 + v[18]*s4 + v[24]*s5 + v[30]*s6;
1908    x[1+idt] = v[1]*s1 + v[7]*s2 + v[13]*s3 + v[19]*s4 + v[25]*s5 + v[31]*s6;
1909    x[2+idt] = v[2]*s1 + v[8]*s2 + v[14]*s3 + v[20]*s4 + v[26]*s5 + v[32]*s6;
1910    x[3+idt] = v[3]*s1 + v[9]*s2 + v[15]*s3 + v[21]*s4 + v[27]*s5 + v[33]*s6;
1911    x[4+idt] = v[4]*s1 + v[10]*s2 + v[16]*s3 + v[22]*s4 + v[28]*s5 + v[34]*s6;
1912    x[5+idt] = v[5]*s1 + v[11]*s2 + v[17]*s3 + v[23]*s4 + v[29]*s5 + v[35]*s6;
1913   }
1914 
1915   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1916   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
1917   ierr = PetscLogFlops(2.0*bs2*(a->nz) - bs*A->cmap->n);CHKERRQ(ierr);
1918   PetscFunctionReturn(0);
1919 }
1920 
1921 #undef __FUNCT__
1922 #define __FUNCT__ "MatSolve_SeqBAIJ_5"
1923 PetscErrorCode MatSolve_SeqBAIJ_5(Mat A,Vec bb,Vec xx)
1924 {
1925   Mat_SeqBAIJ       *a=(Mat_SeqBAIJ *)A->data;
1926   IS                iscol=a->col,isrow=a->row;
1927   PetscErrorCode    ierr;
1928   const PetscInt    *r,*c,*rout,*cout,*diag = a->diag;
1929   PetscInt          i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc;
1930   const MatScalar   *aa=a->a,*v;
1931   PetscScalar       *x,s1,s2,s3,s4,s5,x1,x2,x3,x4,x5,*t;
1932   const PetscScalar *b;
1933 
1934   PetscFunctionBegin;
1935   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
1936   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
1937   t  = a->solve_work;
1938 
1939   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
1940   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
1941 
1942   /* forward solve the lower triangular */
1943   idx    = 5*(*r++);
1944   t[0] = b[idx];   t[1] = b[1+idx];
1945   t[2] = b[2+idx]; t[3] = b[3+idx]; t[4] = b[4+idx];
1946   for (i=1; i<n; i++) {
1947     v     = aa + 25*ai[i];
1948     vi    = aj + ai[i];
1949     nz    = diag[i] - ai[i];
1950     idx   = 5*(*r++);
1951     s1  = b[idx];s2 = b[1+idx];s3 = b[2+idx];s4 = b[3+idx];
1952     s5  = b[4+idx];
1953     while (nz--) {
1954       idx   = 5*(*vi++);
1955       x1    = t[idx];  x2 = t[1+idx];x3 = t[2+idx];
1956       x4    = t[3+idx];x5 = t[4+idx];
1957       s1 -= v[0]*x1 + v[5]*x2 + v[10]*x3 + v[15]*x4 + v[20]*x5;
1958       s2 -= v[1]*x1 + v[6]*x2 + v[11]*x3 + v[16]*x4 + v[21]*x5;
1959       s3 -= v[2]*x1 + v[7]*x2 + v[12]*x3 + v[17]*x4 + v[22]*x5;
1960       s4 -= v[3]*x1 + v[8]*x2 + v[13]*x3 + v[18]*x4 + v[23]*x5;
1961       s5 -= v[4]*x1 + v[9]*x2 + v[14]*x3 + v[19]*x4 + v[24]*x5;
1962       v += 25;
1963     }
1964     idx = 5*i;
1965     t[idx]   = s1;t[1+idx] = s2;
1966     t[2+idx] = s3;t[3+idx] = s4; t[4+idx] = s5;
1967   }
1968   /* backward solve the upper triangular */
1969   for (i=n-1; i>=0; i--){
1970     v    = aa + 25*diag[i] + 25;
1971     vi   = aj + diag[i] + 1;
1972     nz   = ai[i+1] - diag[i] - 1;
1973     idt  = 5*i;
1974     s1 = t[idt];  s2 = t[1+idt];
1975     s3 = t[2+idt];s4 = t[3+idt]; s5 = t[4+idt];
1976     while (nz--) {
1977       idx   = 5*(*vi++);
1978       x1    = t[idx];   x2 = t[1+idx];
1979       x3    = t[2+idx]; x4 = t[3+idx]; x5 = t[4+idx];
1980       s1 -= v[0]*x1 + v[5]*x2 + v[10]*x3 + v[15]*x4 + v[20]*x5;
1981       s2 -= v[1]*x1 + v[6]*x2 + v[11]*x3 + v[16]*x4 + v[21]*x5;
1982       s3 -= v[2]*x1 + v[7]*x2 + v[12]*x3 + v[17]*x4 + v[22]*x5;
1983       s4 -= v[3]*x1 + v[8]*x2 + v[13]*x3 + v[18]*x4 + v[23]*x5;
1984       s5 -= v[4]*x1 + v[9]*x2 + v[14]*x3 + v[19]*x4 + v[24]*x5;
1985       v += 25;
1986     }
1987     idc = 5*(*c--);
1988     v   = aa + 25*diag[i];
1989     x[idc]   = t[idt]   = v[0]*s1+v[5]*s2+v[10]*s3+
1990                                  v[15]*s4+v[20]*s5;
1991     x[1+idc] = t[1+idt] = v[1]*s1+v[6]*s2+v[11]*s3+
1992                                  v[16]*s4+v[21]*s5;
1993     x[2+idc] = t[2+idt] = v[2]*s1+v[7]*s2+v[12]*s3+
1994                                  v[17]*s4+v[22]*s5;
1995     x[3+idc] = t[3+idt] = v[3]*s1+v[8]*s2+v[13]*s3+
1996                                  v[18]*s4+v[23]*s5;
1997     x[4+idc] = t[4+idt] = v[4]*s1+v[9]*s2+v[14]*s3+
1998                                  v[19]*s4+v[24]*s5;
1999   }
2000 
2001   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
2002   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
2003   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2004   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
2005   ierr = PetscLogFlops(2.0*25*(a->nz) - 5.0*A->cmap->n);CHKERRQ(ierr);
2006   PetscFunctionReturn(0);
2007 }
2008 
2009 #undef __FUNCT__
2010 #define __FUNCT__ "MatSolve_SeqBAIJ_5_newdatastruct"
2011 PetscErrorCode MatSolve_SeqBAIJ_5_newdatastruct(Mat A,Vec bb,Vec xx)
2012 {
2013   Mat_SeqBAIJ       *a=(Mat_SeqBAIJ *)A->data;
2014   IS                iscol=a->col,isrow=a->row;
2015   PetscErrorCode    ierr;
2016   const PetscInt    *r,*c,*rout,*cout;
2017   PetscInt          i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,k,m;
2018   const MatScalar   *aa=a->a,*v;
2019   PetscScalar       *x,s1,s2,s3,s4,s5,x1,x2,x3,x4,x5,*t;
2020   const PetscScalar *b;
2021 
2022   PetscFunctionBegin;
2023   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2024   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
2025   t  = a->solve_work;
2026 
2027   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
2028   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
2029 
2030   /* forward solve the lower triangular */
2031   idx    = 5*r[0];
2032   t[0] = b[idx];   t[1] = b[1+idx];
2033   t[2] = b[2+idx]; t[3] = b[3+idx]; t[4] = b[4+idx];
2034   for (i=1; i<n; i++) {
2035     v     = aa + 25*ai[i];
2036     vi    = aj + ai[i];
2037     nz    = ai[i+1] - ai[i];
2038     idx   = 5*r[i];
2039     s1  = b[idx];s2 = b[1+idx];s3 = b[2+idx];s4 = b[3+idx];
2040     s5  = b[4+idx];
2041     for(m=0;m<nz;m++){
2042       idx   = 5*vi[m];
2043       x1    = t[idx];  x2 = t[1+idx];x3 = t[2+idx];
2044       x4    = t[3+idx];x5 = t[4+idx];
2045       s1 -= v[0]*x1 + v[5]*x2 + v[10]*x3 + v[15]*x4 + v[20]*x5;
2046       s2 -= v[1]*x1 + v[6]*x2 + v[11]*x3 + v[16]*x4 + v[21]*x5;
2047       s3 -= v[2]*x1 + v[7]*x2 + v[12]*x3 + v[17]*x4 + v[22]*x5;
2048       s4 -= v[3]*x1 + v[8]*x2 + v[13]*x3 + v[18]*x4 + v[23]*x5;
2049       s5 -= v[4]*x1 + v[9]*x2 + v[14]*x3 + v[19]*x4 + v[24]*x5;
2050       v += 25;
2051     }
2052     idx = 5*i;
2053     t[idx]   = s1;t[1+idx] = s2;
2054     t[2+idx] = s3;t[3+idx] = s4; t[4+idx] = s5;
2055   }
2056   /* backward solve the upper triangular */
2057   for (i=n-1; i>=0; i--){
2058     k    = 2*n-i;
2059     v    = aa + 25*ai[k];
2060     vi   = aj + ai[k];
2061     nz   = ai[k+1] - ai[k] - 1;
2062     idt  = 5*i;
2063     s1 = t[idt];  s2 = t[1+idt];
2064     s3 = t[2+idt];s4 = t[3+idt]; s5 = t[4+idt];
2065     for(m=0;m<nz;m++){
2066       idx   = 5*vi[m];
2067       x1    = t[idx];   x2 = t[1+idx];
2068       x3    = t[2+idx]; x4 = t[3+idx]; x5 = t[4+idx];
2069       s1 -= v[0]*x1 + v[5]*x2 + v[10]*x3 + v[15]*x4 + v[20]*x5;
2070       s2 -= v[1]*x1 + v[6]*x2 + v[11]*x3 + v[16]*x4 + v[21]*x5;
2071       s3 -= v[2]*x1 + v[7]*x2 + v[12]*x3 + v[17]*x4 + v[22]*x5;
2072       s4 -= v[3]*x1 + v[8]*x2 + v[13]*x3 + v[18]*x4 + v[23]*x5;
2073       s5 -= v[4]*x1 + v[9]*x2 + v[14]*x3 + v[19]*x4 + v[24]*x5;
2074       v += 25;
2075     }
2076     idc = 5*c[i];
2077     x[idc]   = t[idt]   = v[0]*s1+v[5]*s2+v[10]*s3+
2078                                  v[15]*s4+v[20]*s5;
2079     x[1+idc] = t[1+idt] = v[1]*s1+v[6]*s2+v[11]*s3+
2080                                  v[16]*s4+v[21]*s5;
2081     x[2+idc] = t[2+idt] = v[2]*s1+v[7]*s2+v[12]*s3+
2082                                  v[17]*s4+v[22]*s5;
2083     x[3+idc] = t[3+idt] = v[3]*s1+v[8]*s2+v[13]*s3+
2084                                  v[18]*s4+v[23]*s5;
2085     x[4+idc] = t[4+idt] = v[4]*s1+v[9]*s2+v[14]*s3+
2086                                  v[19]*s4+v[24]*s5;
2087   }
2088 
2089   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
2090   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
2091   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2092   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
2093   ierr = PetscLogFlops(2.0*25*(a->nz) - 5.0*A->cmap->n);CHKERRQ(ierr);
2094   PetscFunctionReturn(0);
2095 }
2096 #undef __FUNCT__
2097 #define __FUNCT__ "MatSolve_SeqBAIJ_5_NaturalOrdering"
2098 PetscErrorCode MatSolve_SeqBAIJ_5_NaturalOrdering(Mat A,Vec bb,Vec xx)
2099 {
2100   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ *)A->data;
2101   PetscInt          i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt;
2102   PetscErrorCode    ierr;
2103   PetscInt          *diag = a->diag,jdx;
2104   const MatScalar   *aa=a->a,*v;
2105   PetscScalar       *x,s1,s2,s3,s4,s5,x1,x2,x3,x4,x5;
2106   const PetscScalar *b;
2107 
2108   PetscFunctionBegin;
2109   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2110   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
2111   /* forward solve the lower triangular */
2112   idx    = 0;
2113   x[0] = b[idx]; x[1] = b[1+idx]; x[2] = b[2+idx]; x[3] = b[3+idx];x[4] = b[4+idx];
2114   for (i=1; i<n; i++) {
2115     v     =  aa + 25*ai[i];
2116     vi    =  aj + ai[i];
2117     nz    =  diag[i] - ai[i];
2118     idx   =  5*i;
2119     s1  =  b[idx];s2 = b[1+idx];s3 = b[2+idx];s4 = b[3+idx];s5 = b[4+idx];
2120     while (nz--) {
2121       jdx   = 5*(*vi++);
2122       x1    = x[jdx];x2 = x[1+jdx];x3 = x[2+jdx];x4 = x[3+jdx];x5 = x[4+jdx];
2123       s1 -= v[0]*x1 + v[5]*x2 + v[10]*x3  + v[15]*x4 + v[20]*x5;
2124       s2 -= v[1]*x1 + v[6]*x2 + v[11]*x3  + v[16]*x4 + v[21]*x5;
2125       s3 -= v[2]*x1 + v[7]*x2 + v[12]*x3  + v[17]*x4 + v[22]*x5;
2126       s4 -= v[3]*x1 + v[8]*x2 + v[13]*x3  + v[18]*x4 + v[23]*x5;
2127       s5 -= v[4]*x1 + v[9]*x2 + v[14]*x3  + v[19]*x4 + v[24]*x5;
2128       v    += 25;
2129     }
2130     x[idx]   = s1;
2131     x[1+idx] = s2;
2132     x[2+idx] = s3;
2133     x[3+idx] = s4;
2134     x[4+idx] = s5;
2135   }
2136   /* backward solve the upper triangular */
2137   for (i=n-1; i>=0; i--){
2138     v    = aa + 25*diag[i] + 25;
2139     vi   = aj + diag[i] + 1;
2140     nz   = ai[i+1] - diag[i] - 1;
2141     idt  = 5*i;
2142     s1 = x[idt];  s2 = x[1+idt];
2143     s3 = x[2+idt];s4 = x[3+idt]; s5 = x[4+idt];
2144     while (nz--) {
2145       idx   = 5*(*vi++);
2146       x1    = x[idx];   x2 = x[1+idx];x3    = x[2+idx]; x4 = x[3+idx]; x5 = x[4+idx];
2147       s1 -= v[0]*x1 + v[5]*x2 + v[10]*x3  + v[15]*x4 + v[20]*x5;
2148       s2 -= v[1]*x1 + v[6]*x2 + v[11]*x3  + v[16]*x4 + v[21]*x5;
2149       s3 -= v[2]*x1 + v[7]*x2 + v[12]*x3  + v[17]*x4 + v[22]*x5;
2150       s4 -= v[3]*x1 + v[8]*x2 + v[13]*x3  + v[18]*x4 + v[23]*x5;
2151       s5 -= v[4]*x1 + v[9]*x2 + v[14]*x3  + v[19]*x4 + v[24]*x5;
2152       v    += 25;
2153     }
2154     v        = aa + 25*diag[i];
2155     x[idt]   = v[0]*s1 + v[5]*s2 + v[10]*s3  + v[15]*s4 + v[20]*s5;
2156     x[1+idt] = v[1]*s1 + v[6]*s2 + v[11]*s3  + v[16]*s4 + v[21]*s5;
2157     x[2+idt] = v[2]*s1 + v[7]*s2 + v[12]*s3  + v[17]*s4 + v[22]*s5;
2158     x[3+idt] = v[3]*s1 + v[8]*s2 + v[13]*s3  + v[18]*s4 + v[23]*s5;
2159     x[4+idt] = v[4]*s1 + v[9]*s2 + v[14]*s3  + v[19]*s4 + v[24]*s5;
2160   }
2161 
2162   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2163   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
2164   ierr = PetscLogFlops(2.0*25*(a->nz) - 5.0*A->cmap->n);CHKERRQ(ierr);
2165   PetscFunctionReturn(0);
2166 }
2167 
2168 #undef __FUNCT__
2169 #define __FUNCT__ "MatSolve_SeqBAIJ_5_NaturalOrdering_newdatastruct"
2170 PetscErrorCode MatSolve_SeqBAIJ_5_NaturalOrdering_newdatastruct(Mat A,Vec bb,Vec xx)
2171 {
2172   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ *)A->data;
2173   PetscInt          i,k,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt;
2174   PetscErrorCode    ierr;
2175   PetscInt          jdx;
2176   const MatScalar   *aa=a->a,*v;
2177   PetscScalar       *x,s1,s2,s3,s4,s5,x1,x2,x3,x4,x5;
2178   const PetscScalar *b;
2179 
2180   PetscFunctionBegin;
2181   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2182   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
2183   /* forward solve the lower triangular */
2184   idx    = 0;
2185   x[0] = b[idx]; x[1] = b[1+idx]; x[2] = b[2+idx]; x[3] = b[3+idx];x[4] = b[4+idx];
2186   for (i=1; i<n; i++) {
2187     v   = aa + 25*ai[i];
2188     vi  = aj + ai[i];
2189     nz  = ai[i+1] - ai[i];
2190     idx = 5*i;
2191     s1  = b[idx];s2 = b[1+idx];s3 = b[2+idx];s4 = b[3+idx];s5 = b[4+idx];
2192     for(k=0;k<nz;k++) {
2193       jdx   = 5*vi[k];
2194       x1    = x[jdx];x2 = x[1+jdx];x3 = x[2+jdx];x4 = x[3+jdx];x5 = x[4+jdx];
2195       s1 -= v[0]*x1 + v[5]*x2 + v[10]*x3  + v[15]*x4 + v[20]*x5;
2196       s2 -= v[1]*x1 + v[6]*x2 + v[11]*x3  + v[16]*x4 + v[21]*x5;
2197       s3 -= v[2]*x1 + v[7]*x2 + v[12]*x3  + v[17]*x4 + v[22]*x5;
2198       s4 -= v[3]*x1 + v[8]*x2 + v[13]*x3  + v[18]*x4 + v[23]*x5;
2199       s5 -= v[4]*x1 + v[9]*x2 + v[14]*x3  + v[19]*x4 + v[24]*x5;
2200       v    += 25;
2201     }
2202     x[idx]   = s1;
2203     x[1+idx] = s2;
2204     x[2+idx] = s3;
2205     x[3+idx] = s4;
2206     x[4+idx] = s5;
2207   }
2208 
2209   /* backward solve the upper triangular */
2210   for (i=n-1; i>=0; i--){
2211     v   = aa + 25*ai[2*n-i];
2212     vi  = aj + ai[2*n-i];
2213     nz  = ai[2*n-i +1] - ai[2*n-i]-1;
2214     idt = 5*i;
2215     s1 = x[idt];  s2 = x[1+idt];
2216     s3 = x[2+idt];s4 = x[3+idt]; s5 = x[4+idt];
2217     for(k=0;k<nz;k++){
2218       idx   = 5*vi[k];
2219       x1    = x[idx];   x2 = x[1+idx];x3    = x[2+idx]; x4 = x[3+idx]; x5 = x[4+idx];
2220       s1 -= v[0]*x1 + v[5]*x2 + v[10]*x3  + v[15]*x4 + v[20]*x5;
2221       s2 -= v[1]*x1 + v[6]*x2 + v[11]*x3  + v[16]*x4 + v[21]*x5;
2222       s3 -= v[2]*x1 + v[7]*x2 + v[12]*x3  + v[17]*x4 + v[22]*x5;
2223       s4 -= v[3]*x1 + v[8]*x2 + v[13]*x3  + v[18]*x4 + v[23]*x5;
2224       s5 -= v[4]*x1 + v[9]*x2 + v[14]*x3  + v[19]*x4 + v[24]*x5;
2225       v    += 25;
2226     }
2227     /* x = inv_diagonal*x */
2228     x[idt]   = v[0]*s1 + v[5]*s2 + v[10]*s3  + v[15]*s4 + v[20]*s5;
2229     x[1+idt] = v[1]*s1 + v[6]*s2 + v[11]*s3  + v[16]*s4 + v[21]*s5;
2230     x[2+idt] = v[2]*s1 + v[7]*s2 + v[12]*s3  + v[17]*s4 + v[22]*s5;
2231     x[3+idt] = v[3]*s1 + v[8]*s2 + v[13]*s3  + v[18]*s4 + v[23]*s5;
2232     x[4+idt] = v[4]*s1 + v[9]*s2 + v[14]*s3  + v[19]*s4 + v[24]*s5;
2233   }
2234 
2235   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2236   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
2237   ierr = PetscLogFlops(2.0*25*(a->nz) - 5.0*A->cmap->n);CHKERRQ(ierr);
2238   PetscFunctionReturn(0);
2239 }
2240 
2241 #undef __FUNCT__
2242 #define __FUNCT__ "MatSolve_SeqBAIJ_4"
2243 PetscErrorCode MatSolve_SeqBAIJ_4(Mat A,Vec bb,Vec xx)
2244 {
2245   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ *)A->data;
2246   IS                iscol=a->col,isrow=a->row;
2247   PetscErrorCode    ierr;
2248   PetscInt          i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc;
2249   const PetscInt    *r,*c,*diag = a->diag,*rout,*cout;
2250   const MatScalar   *aa=a->a,*v;
2251   PetscScalar       *x,s1,s2,s3,s4,x1,x2,x3,x4,*t;
2252   const PetscScalar *b;
2253 
2254   PetscFunctionBegin;
2255   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2256   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
2257   t  = a->solve_work;
2258 
2259   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
2260   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
2261 
2262   /* forward solve the lower triangular */
2263   idx    = 4*(*r++);
2264   t[0] = b[idx];   t[1] = b[1+idx];
2265   t[2] = b[2+idx]; t[3] = b[3+idx];
2266   for (i=1; i<n; i++) {
2267     v     = aa + 16*ai[i];
2268     vi    = aj + ai[i];
2269     nz    = diag[i] - ai[i];
2270     idx   = 4*(*r++);
2271     s1  = b[idx];s2 = b[1+idx];s3 = b[2+idx];s4 = b[3+idx];
2272     while (nz--) {
2273       idx   = 4*(*vi++);
2274       x1    = t[idx];x2 = t[1+idx];x3 = t[2+idx];x4 = t[3+idx];
2275       s1 -= v[0]*x1 + v[4]*x2 + v[8]*x3  + v[12]*x4;
2276       s2 -= v[1]*x1 + v[5]*x2 + v[9]*x3  + v[13]*x4;
2277       s3 -= v[2]*x1 + v[6]*x2 + v[10]*x3 + v[14]*x4;
2278       s4 -= v[3]*x1 + v[7]*x2 + v[11]*x3 + v[15]*x4;
2279       v    += 16;
2280     }
2281     idx        = 4*i;
2282     t[idx]   = s1;t[1+idx] = s2;
2283     t[2+idx] = s3;t[3+idx] = s4;
2284   }
2285   /* backward solve the upper triangular */
2286   for (i=n-1; i>=0; i--){
2287     v    = aa + 16*diag[i] + 16;
2288     vi   = aj + diag[i] + 1;
2289     nz   = ai[i+1] - diag[i] - 1;
2290     idt  = 4*i;
2291     s1 = t[idt];  s2 = t[1+idt];
2292     s3 = t[2+idt];s4 = t[3+idt];
2293     while (nz--) {
2294       idx   = 4*(*vi++);
2295       x1    = t[idx];   x2 = t[1+idx];
2296       x3    = t[2+idx]; x4 = t[3+idx];
2297       s1 -= v[0]*x1 + v[4]*x2 + v[8]*x3   + v[12]*x4;
2298       s2 -= v[1]*x1 + v[5]*x2 + v[9]*x3   + v[13]*x4;
2299       s3 -= v[2]*x1 + v[6]*x2 + v[10]*x3  + v[14]*x4;
2300       s4 -= v[3]*x1 + v[7]*x2 + v[11]*x3  + v[15]*x4;
2301       v += 16;
2302     }
2303     idc      = 4*(*c--);
2304     v        = aa + 16*diag[i];
2305     x[idc]   = t[idt]   = v[0]*s1+v[4]*s2+v[8]*s3+v[12]*s4;
2306     x[1+idc] = t[1+idt] = v[1]*s1+v[5]*s2+v[9]*s3+v[13]*s4;
2307     x[2+idc] = t[2+idt] = v[2]*s1+v[6]*s2+v[10]*s3+v[14]*s4;
2308     x[3+idc] = t[3+idt] = v[3]*s1+v[7]*s2+v[11]*s3+v[15]*s4;
2309   }
2310 
2311   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
2312   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
2313   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2314   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
2315   ierr = PetscLogFlops(2.0*16*(a->nz) - 4.0*A->cmap->n);CHKERRQ(ierr);
2316   PetscFunctionReturn(0);
2317 }
2318 
2319 #undef __FUNCT__
2320 #define __FUNCT__ "MatSolve_SeqBAIJ_4_newdatastruct"
2321 PetscErrorCode MatSolve_SeqBAIJ_4_newdatastruct(Mat A,Vec bb,Vec xx)
2322 {
2323   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ *)A->data;
2324   IS                iscol=a->col,isrow=a->row;
2325   PetscErrorCode    ierr;
2326   PetscInt          i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,k,m;
2327   const PetscInt    *r,*c,*rout,*cout;
2328   const MatScalar   *aa=a->a,*v;
2329   PetscScalar       *x,s1,s2,s3,s4,x1,x2,x3,x4,*t;
2330   const PetscScalar *b;
2331 
2332   PetscFunctionBegin;
2333   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2334   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
2335   t  = a->solve_work;
2336 
2337   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
2338   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
2339 
2340   /* forward solve the lower triangular */
2341   idx    = 4*r[0];
2342   t[0] = b[idx];   t[1] = b[1+idx];
2343   t[2] = b[2+idx]; t[3] = b[3+idx];
2344   for (i=1; i<n; i++) {
2345     v     = aa + 16*ai[i];
2346     vi    = aj + ai[i];
2347     nz    = ai[i+1] - ai[i];
2348     idx   = 4*r[i];
2349     s1  = b[idx];s2 = b[1+idx];s3 = b[2+idx];s4 = b[3+idx];
2350     for(m=0;m<nz;m++){
2351       idx   = 4*vi[m];
2352       x1    = t[idx];x2 = t[1+idx];x3 = t[2+idx];x4 = t[3+idx];
2353       s1 -= v[0]*x1 + v[4]*x2 + v[8]*x3  + v[12]*x4;
2354       s2 -= v[1]*x1 + v[5]*x2 + v[9]*x3  + v[13]*x4;
2355       s3 -= v[2]*x1 + v[6]*x2 + v[10]*x3 + v[14]*x4;
2356       s4 -= v[3]*x1 + v[7]*x2 + v[11]*x3 + v[15]*x4;
2357       v    += 16;
2358     }
2359     idx        = 4*i;
2360     t[idx]   = s1;t[1+idx] = s2;
2361     t[2+idx] = s3;t[3+idx] = s4;
2362   }
2363   /* backward solve the upper triangular */
2364   for (i=n-1; i>=0; i--){
2365     k    = 2*n-i;
2366     v    = aa + 16*ai[k];
2367     vi   = aj + ai[k];
2368     nz   = ai[k+1] - ai[k] - 1;
2369     idt  = 4*i;
2370     s1 = t[idt];  s2 = t[1+idt];
2371     s3 = t[2+idt];s4 = t[3+idt];
2372     for(m=0;m<nz;m++){
2373       idx   = 4*vi[m];
2374       x1    = t[idx];   x2 = t[1+idx];
2375       x3    = t[2+idx]; x4 = t[3+idx];
2376       s1 -= v[0]*x1 + v[4]*x2 + v[8]*x3   + v[12]*x4;
2377       s2 -= v[1]*x1 + v[5]*x2 + v[9]*x3   + v[13]*x4;
2378       s3 -= v[2]*x1 + v[6]*x2 + v[10]*x3  + v[14]*x4;
2379       s4 -= v[3]*x1 + v[7]*x2 + v[11]*x3  + v[15]*x4;
2380       v += 16;
2381     }
2382     idc      = 4*c[i];
2383     x[idc]   = t[idt]   = v[0]*s1+v[4]*s2+v[8]*s3+v[12]*s4;
2384     x[1+idc] = t[1+idt] = v[1]*s1+v[5]*s2+v[9]*s3+v[13]*s4;
2385     x[2+idc] = t[2+idt] = v[2]*s1+v[6]*s2+v[10]*s3+v[14]*s4;
2386     x[3+idc] = t[3+idt] = v[3]*s1+v[7]*s2+v[11]*s3+v[15]*s4;
2387   }
2388 
2389   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
2390   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
2391   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2392   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
2393   ierr = PetscLogFlops(2.0*16*(a->nz) - 4.0*A->cmap->n);CHKERRQ(ierr);
2394   PetscFunctionReturn(0);
2395 }
2396 
2397 #undef __FUNCT__
2398 #define __FUNCT__ "MatSolve_SeqBAIJ_4_Demotion"
2399 PetscErrorCode MatSolve_SeqBAIJ_4_Demotion(Mat A,Vec bb,Vec xx)
2400 {
2401   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ *)A->data;
2402   IS                iscol=a->col,isrow=a->row;
2403   PetscErrorCode    ierr;
2404   PetscInt          i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc;
2405   const PetscInt    *r,*c,*diag = a->diag,*rout,*cout;
2406   const MatScalar   *aa=a->a,*v;
2407   MatScalar         s1,s2,s3,s4,x1,x2,x3,x4,*t;
2408   PetscScalar       *x;
2409   const PetscScalar *b;
2410 
2411   PetscFunctionBegin;
2412   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2413   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
2414   t  = (MatScalar *)a->solve_work;
2415 
2416   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
2417   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
2418 
2419   /* forward solve the lower triangular */
2420   idx    = 4*(*r++);
2421   t[0] = (MatScalar)b[idx];
2422   t[1] = (MatScalar)b[1+idx];
2423   t[2] = (MatScalar)b[2+idx];
2424   t[3] = (MatScalar)b[3+idx];
2425   for (i=1; i<n; i++) {
2426     v     = aa + 16*ai[i];
2427     vi    = aj + ai[i];
2428     nz    = diag[i] - ai[i];
2429     idx   = 4*(*r++);
2430     s1 = (MatScalar)b[idx];
2431     s2 = (MatScalar)b[1+idx];
2432     s3 = (MatScalar)b[2+idx];
2433     s4 = (MatScalar)b[3+idx];
2434     while (nz--) {
2435       idx   = 4*(*vi++);
2436       x1  = t[idx];
2437       x2  = t[1+idx];
2438       x3  = t[2+idx];
2439       x4  = t[3+idx];
2440       s1 -= v[0]*x1 + v[4]*x2 + v[8]*x3  + v[12]*x4;
2441       s2 -= v[1]*x1 + v[5]*x2 + v[9]*x3  + v[13]*x4;
2442       s3 -= v[2]*x1 + v[6]*x2 + v[10]*x3 + v[14]*x4;
2443       s4 -= v[3]*x1 + v[7]*x2 + v[11]*x3 + v[15]*x4;
2444       v    += 16;
2445     }
2446     idx        = 4*i;
2447     t[idx]   = s1;
2448     t[1+idx] = s2;
2449     t[2+idx] = s3;
2450     t[3+idx] = s4;
2451   }
2452   /* backward solve the upper triangular */
2453   for (i=n-1; i>=0; i--){
2454     v    = aa + 16*diag[i] + 16;
2455     vi   = aj + diag[i] + 1;
2456     nz   = ai[i+1] - diag[i] - 1;
2457     idt  = 4*i;
2458     s1 = t[idt];
2459     s2 = t[1+idt];
2460     s3 = t[2+idt];
2461     s4 = t[3+idt];
2462     while (nz--) {
2463       idx   = 4*(*vi++);
2464       x1  = t[idx];
2465       x2  = t[1+idx];
2466       x3  = t[2+idx];
2467       x4  = t[3+idx];
2468       s1 -= v[0]*x1 + v[4]*x2 + v[8]*x3   + v[12]*x4;
2469       s2 -= v[1]*x1 + v[5]*x2 + v[9]*x3   + v[13]*x4;
2470       s3 -= v[2]*x1 + v[6]*x2 + v[10]*x3  + v[14]*x4;
2471       s4 -= v[3]*x1 + v[7]*x2 + v[11]*x3  + v[15]*x4;
2472       v += 16;
2473     }
2474     idc      = 4*(*c--);
2475     v        = aa + 16*diag[i];
2476     t[idt]   = v[0]*s1+v[4]*s2+v[8]*s3+v[12]*s4;
2477     t[1+idt] = v[1]*s1+v[5]*s2+v[9]*s3+v[13]*s4;
2478     t[2+idt] = v[2]*s1+v[6]*s2+v[10]*s3+v[14]*s4;
2479     t[3+idt] = v[3]*s1+v[7]*s2+v[11]*s3+v[15]*s4;
2480     x[idc]   = (PetscScalar)t[idt];
2481     x[1+idc] = (PetscScalar)t[1+idt];
2482     x[2+idc] = (PetscScalar)t[2+idt];
2483     x[3+idc] = (PetscScalar)t[3+idt];
2484  }
2485 
2486   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
2487   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
2488   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2489   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
2490   ierr = PetscLogFlops(2.0*16*(a->nz) - 4.0*A->cmap->n);CHKERRQ(ierr);
2491   PetscFunctionReturn(0);
2492 }
2493 
2494 #if defined (PETSC_HAVE_SSE)
2495 
2496 #include PETSC_HAVE_SSE
2497 
2498 #undef __FUNCT__
2499 #define __FUNCT__ "MatSolve_SeqBAIJ_4_SSE_Demotion"
2500 PetscErrorCode MatSolve_SeqBAIJ_4_SSE_Demotion(Mat A,Vec bb,Vec xx)
2501 {
2502   /*
2503      Note: This code uses demotion of double
2504      to float when performing the mixed-mode computation.
2505      This may not be numerically reasonable for all applications.
2506   */
2507   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ *)A->data;
2508   IS             iscol=a->col,isrow=a->row;
2509   PetscErrorCode ierr;
2510   PetscInt       i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,ai16;
2511   const PetscInt *r,*c,*diag = a->diag,*rout,*cout;
2512   MatScalar      *aa=a->a,*v;
2513   PetscScalar    *x,*b,*t;
2514 
2515   /* Make space in temp stack for 16 Byte Aligned arrays */
2516   float           ssealignedspace[11],*tmps,*tmpx;
2517   unsigned long   offset;
2518 
2519   PetscFunctionBegin;
2520   SSE_SCOPE_BEGIN;
2521 
2522     offset = (unsigned long)ssealignedspace % 16;
2523     if (offset) offset = (16 - offset)/4;
2524     tmps = &ssealignedspace[offset];
2525     tmpx = &ssealignedspace[offset+4];
2526     PREFETCH_NTA(aa+16*ai[1]);
2527 
2528     ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
2529     ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
2530     t  = a->solve_work;
2531 
2532     ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
2533     ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
2534 
2535     /* forward solve the lower triangular */
2536     idx  = 4*(*r++);
2537     t[0] = b[idx];   t[1] = b[1+idx];
2538     t[2] = b[2+idx]; t[3] = b[3+idx];
2539     v    =  aa + 16*ai[1];
2540 
2541     for (i=1; i<n;) {
2542       PREFETCH_NTA(&v[8]);
2543       vi   =  aj      + ai[i];
2544       nz   =  diag[i] - ai[i];
2545       idx  =  4*(*r++);
2546 
2547       /* Demote sum from double to float */
2548       CONVERT_DOUBLE4_FLOAT4(tmps,&b[idx]);
2549       LOAD_PS(tmps,XMM7);
2550 
2551       while (nz--) {
2552         PREFETCH_NTA(&v[16]);
2553         idx = 4*(*vi++);
2554 
2555         /* Demote solution (so far) from double to float */
2556         CONVERT_DOUBLE4_FLOAT4(tmpx,&x[idx]);
2557 
2558         /* 4x4 Matrix-Vector product with negative accumulation: */
2559         SSE_INLINE_BEGIN_2(tmpx,v)
2560           SSE_LOAD_PS(SSE_ARG_1,FLOAT_0,XMM6)
2561 
2562           /* First Column */
2563           SSE_COPY_PS(XMM0,XMM6)
2564           SSE_SHUFFLE(XMM0,XMM0,0x00)
2565           SSE_MULT_PS_M(XMM0,SSE_ARG_2,FLOAT_0)
2566           SSE_SUB_PS(XMM7,XMM0)
2567 
2568           /* Second Column */
2569           SSE_COPY_PS(XMM1,XMM6)
2570           SSE_SHUFFLE(XMM1,XMM1,0x55)
2571           SSE_MULT_PS_M(XMM1,SSE_ARG_2,FLOAT_4)
2572           SSE_SUB_PS(XMM7,XMM1)
2573 
2574           SSE_PREFETCH_NTA(SSE_ARG_2,FLOAT_24)
2575 
2576           /* Third Column */
2577           SSE_COPY_PS(XMM2,XMM6)
2578           SSE_SHUFFLE(XMM2,XMM2,0xAA)
2579           SSE_MULT_PS_M(XMM2,SSE_ARG_2,FLOAT_8)
2580           SSE_SUB_PS(XMM7,XMM2)
2581 
2582           /* Fourth Column */
2583           SSE_COPY_PS(XMM3,XMM6)
2584           SSE_SHUFFLE(XMM3,XMM3,0xFF)
2585           SSE_MULT_PS_M(XMM3,SSE_ARG_2,FLOAT_12)
2586           SSE_SUB_PS(XMM7,XMM3)
2587         SSE_INLINE_END_2
2588 
2589         v  += 16;
2590       }
2591       idx = 4*i;
2592       v   = aa + 16*ai[++i];
2593       PREFETCH_NTA(v);
2594       STORE_PS(tmps,XMM7);
2595 
2596       /* Promote result from float to double */
2597       CONVERT_FLOAT4_DOUBLE4(&t[idx],tmps);
2598     }
2599     /* backward solve the upper triangular */
2600     idt  = 4*(n-1);
2601     ai16 = 16*diag[n-1];
2602     v    = aa + ai16 + 16;
2603     for (i=n-1; i>=0;){
2604       PREFETCH_NTA(&v[8]);
2605       vi = aj + diag[i] + 1;
2606       nz = ai[i+1] - diag[i] - 1;
2607 
2608       /* Demote accumulator from double to float */
2609       CONVERT_DOUBLE4_FLOAT4(tmps,&t[idt]);
2610       LOAD_PS(tmps,XMM7);
2611 
2612       while (nz--) {
2613         PREFETCH_NTA(&v[16]);
2614         idx = 4*(*vi++);
2615 
2616         /* Demote solution (so far) from double to float */
2617         CONVERT_DOUBLE4_FLOAT4(tmpx,&t[idx]);
2618 
2619         /* 4x4 Matrix-Vector Product with negative accumulation: */
2620         SSE_INLINE_BEGIN_2(tmpx,v)
2621           SSE_LOAD_PS(SSE_ARG_1,FLOAT_0,XMM6)
2622 
2623           /* First Column */
2624           SSE_COPY_PS(XMM0,XMM6)
2625           SSE_SHUFFLE(XMM0,XMM0,0x00)
2626           SSE_MULT_PS_M(XMM0,SSE_ARG_2,FLOAT_0)
2627           SSE_SUB_PS(XMM7,XMM0)
2628 
2629           /* Second Column */
2630           SSE_COPY_PS(XMM1,XMM6)
2631           SSE_SHUFFLE(XMM1,XMM1,0x55)
2632           SSE_MULT_PS_M(XMM1,SSE_ARG_2,FLOAT_4)
2633           SSE_SUB_PS(XMM7,XMM1)
2634 
2635           SSE_PREFETCH_NTA(SSE_ARG_2,FLOAT_24)
2636 
2637           /* Third Column */
2638           SSE_COPY_PS(XMM2,XMM6)
2639           SSE_SHUFFLE(XMM2,XMM2,0xAA)
2640           SSE_MULT_PS_M(XMM2,SSE_ARG_2,FLOAT_8)
2641           SSE_SUB_PS(XMM7,XMM2)
2642 
2643           /* Fourth Column */
2644           SSE_COPY_PS(XMM3,XMM6)
2645           SSE_SHUFFLE(XMM3,XMM3,0xFF)
2646           SSE_MULT_PS_M(XMM3,SSE_ARG_2,FLOAT_12)
2647           SSE_SUB_PS(XMM7,XMM3)
2648         SSE_INLINE_END_2
2649         v  += 16;
2650       }
2651       v    = aa + ai16;
2652       ai16 = 16*diag[--i];
2653       PREFETCH_NTA(aa+ai16+16);
2654       /*
2655          Scale the result by the diagonal 4x4 block,
2656          which was inverted as part of the factorization
2657       */
2658       SSE_INLINE_BEGIN_3(v,tmps,aa+ai16)
2659         /* First Column */
2660         SSE_COPY_PS(XMM0,XMM7)
2661         SSE_SHUFFLE(XMM0,XMM0,0x00)
2662         SSE_MULT_PS_M(XMM0,SSE_ARG_1,FLOAT_0)
2663 
2664         /* Second Column */
2665         SSE_COPY_PS(XMM1,XMM7)
2666         SSE_SHUFFLE(XMM1,XMM1,0x55)
2667         SSE_MULT_PS_M(XMM1,SSE_ARG_1,FLOAT_4)
2668         SSE_ADD_PS(XMM0,XMM1)
2669 
2670         SSE_PREFETCH_NTA(SSE_ARG_3,FLOAT_24)
2671 
2672         /* Third Column */
2673         SSE_COPY_PS(XMM2,XMM7)
2674         SSE_SHUFFLE(XMM2,XMM2,0xAA)
2675         SSE_MULT_PS_M(XMM2,SSE_ARG_1,FLOAT_8)
2676         SSE_ADD_PS(XMM0,XMM2)
2677 
2678         /* Fourth Column */
2679         SSE_COPY_PS(XMM3,XMM7)
2680         SSE_SHUFFLE(XMM3,XMM3,0xFF)
2681         SSE_MULT_PS_M(XMM3,SSE_ARG_1,FLOAT_12)
2682         SSE_ADD_PS(XMM0,XMM3)
2683 
2684         SSE_STORE_PS(SSE_ARG_2,FLOAT_0,XMM0)
2685       SSE_INLINE_END_3
2686 
2687       /* Promote solution from float to double */
2688       CONVERT_FLOAT4_DOUBLE4(&t[idt],tmps);
2689 
2690       /* Apply reordering to t and stream into x.    */
2691       /* This way, x doesn't pollute the cache.      */
2692       /* Be careful with size: 2 doubles = 4 floats! */
2693       idc  = 4*(*c--);
2694       SSE_INLINE_BEGIN_2((float *)&t[idt],(float *)&x[idc])
2695         /*  x[idc]   = t[idt];   x[1+idc] = t[1+idc]; */
2696         SSE_LOAD_PS(SSE_ARG_1,FLOAT_0,XMM0)
2697         SSE_STREAM_PS(SSE_ARG_2,FLOAT_0,XMM0)
2698         /*  x[idc+2] = t[idt+2]; x[3+idc] = t[3+idc]; */
2699         SSE_LOAD_PS(SSE_ARG_1,FLOAT_4,XMM1)
2700         SSE_STREAM_PS(SSE_ARG_2,FLOAT_4,XMM1)
2701       SSE_INLINE_END_2
2702       v    = aa + ai16 + 16;
2703       idt -= 4;
2704     }
2705 
2706     ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
2707     ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
2708     ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
2709     ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
2710     ierr = PetscLogFlops(2.0*16*(a->nz) - 4.0*A->cmap->n);CHKERRQ(ierr);
2711   SSE_SCOPE_END;
2712   PetscFunctionReturn(0);
2713 }
2714 
2715 #endif
2716 
2717 
2718 /*
2719       Special case where the matrix was ILU(0) factored in the natural
2720    ordering. This eliminates the need for the column and row permutation.
2721 */
2722 #undef __FUNCT__
2723 #define __FUNCT__ "MatSolve_SeqBAIJ_4_NaturalOrdering"
2724 PetscErrorCode MatSolve_SeqBAIJ_4_NaturalOrdering(Mat A,Vec bb,Vec xx)
2725 {
2726   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ *)A->data;
2727   PetscInt          n=a->mbs;
2728   const PetscInt    *ai=a->i,*aj=a->j;
2729   PetscErrorCode    ierr;
2730   const PetscInt    *diag = a->diag;
2731   const MatScalar   *aa=a->a;
2732   PetscScalar       *x;
2733   const PetscScalar *b;
2734 
2735   PetscFunctionBegin;
2736   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2737   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
2738 
2739 #if defined(PETSC_USE_FORTRAN_KERNEL_SOLVEBAIJBLAS)
2740   {
2741     static PetscScalar w[2000]; /* very BAD need to fix */
2742     fortransolvebaij4blas_(&n,x,ai,aj,diag,aa,b,w);
2743   }
2744 #elif defined(PETSC_USE_FORTRAN_KERNEL_SOLVEBAIJ)
2745   {
2746     static PetscScalar w[2000]; /* very BAD need to fix */
2747     fortransolvebaij4_(&n,x,ai,aj,diag,aa,b,w);
2748   }
2749 #elif defined(PETSC_USE_FORTRAN_KERNEL_SOLVEBAIJUNROLL)
2750   fortransolvebaij4unroll_(&n,x,ai,aj,diag,aa,b);
2751 #else
2752   {
2753     PetscScalar     s1,s2,s3,s4,x1,x2,x3,x4;
2754     const MatScalar *v;
2755     PetscInt        jdx,idt,idx,nz,i,ai16;
2756     const PetscInt  *vi;
2757 
2758   /* forward solve the lower triangular */
2759   idx    = 0;
2760   x[0]   = b[0]; x[1] = b[1]; x[2] = b[2]; x[3] = b[3];
2761   for (i=1; i<n; i++) {
2762     v     =  aa      + 16*ai[i];
2763     vi    =  aj      + ai[i];
2764     nz    =  diag[i] - ai[i];
2765     idx   +=  4;
2766     s1  =  b[idx];s2 = b[1+idx];s3 = b[2+idx];s4 = b[3+idx];
2767     while (nz--) {
2768       jdx   = 4*(*vi++);
2769       x1    = x[jdx];x2 = x[1+jdx];x3 = x[2+jdx];x4 = x[3+jdx];
2770       s1 -= v[0]*x1 + v[4]*x2 + v[8]*x3  + v[12]*x4;
2771       s2 -= v[1]*x1 + v[5]*x2 + v[9]*x3  + v[13]*x4;
2772       s3 -= v[2]*x1 + v[6]*x2 + v[10]*x3 + v[14]*x4;
2773       s4 -= v[3]*x1 + v[7]*x2 + v[11]*x3 + v[15]*x4;
2774       v    += 16;
2775     }
2776     x[idx]   = s1;
2777     x[1+idx] = s2;
2778     x[2+idx] = s3;
2779     x[3+idx] = s4;
2780   }
2781   /* backward solve the upper triangular */
2782   idt = 4*(n-1);
2783   for (i=n-1; i>=0; i--){
2784     ai16 = 16*diag[i];
2785     v    = aa + ai16 + 16;
2786     vi   = aj + diag[i] + 1;
2787     nz   = ai[i+1] - diag[i] - 1;
2788     s1 = x[idt];  s2 = x[1+idt];
2789     s3 = x[2+idt];s4 = x[3+idt];
2790     while (nz--) {
2791       idx   = 4*(*vi++);
2792       x1    = x[idx];   x2 = x[1+idx];x3    = x[2+idx]; x4 = x[3+idx];
2793       s1 -= v[0]*x1 + v[4]*x2 + v[8]*x3   + v[12]*x4;
2794       s2 -= v[1]*x1 + v[5]*x2 + v[9]*x3   + v[13]*x4;
2795       s3 -= v[2]*x1 + v[6]*x2 + v[10]*x3  + v[14]*x4;
2796       s4 -= v[3]*x1 + v[7]*x2 + v[11]*x3  + v[15]*x4;
2797       v    += 16;
2798     }
2799     v        = aa + ai16;
2800     x[idt]   = v[0]*s1 + v[4]*s2 + v[8]*s3  + v[12]*s4;
2801     x[1+idt] = v[1]*s1 + v[5]*s2 + v[9]*s3  + v[13]*s4;
2802     x[2+idt] = v[2]*s1 + v[6]*s2 + v[10]*s3 + v[14]*s4;
2803     x[3+idt] = v[3]*s1 + v[7]*s2 + v[11]*s3 + v[15]*s4;
2804     idt -= 4;
2805   }
2806   }
2807 #endif
2808 
2809   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2810   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
2811   ierr = PetscLogFlops(2.0*16*(a->nz) - 4.0*A->cmap->n);CHKERRQ(ierr);
2812   PetscFunctionReturn(0);
2813 }
2814 
2815 #undef __FUNCT__
2816 #define __FUNCT__ "MatSolve_SeqBAIJ_4_NaturalOrdering_newdatastruct"
2817 PetscErrorCode MatSolve_SeqBAIJ_4_NaturalOrdering_newdatastruct(Mat A,Vec bb,Vec xx)
2818 {
2819     Mat_SeqBAIJ       *a = (Mat_SeqBAIJ *)A->data;
2820     PetscInt          i,k,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz;
2821     PetscErrorCode    ierr;
2822     PetscInt          idx,jdx,idt;
2823     PetscInt          bs = A->rmap->bs,bs2 = a->bs2;
2824     const MatScalar   *aa=a->a,*v;
2825     PetscScalar       *x;
2826     const PetscScalar *b;
2827     PetscScalar        s1,s2,s3,s4,x1,x2,x3,x4;
2828 
2829     PetscFunctionBegin;
2830     ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2831     ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
2832     /* forward solve the lower triangular */
2833     idx    = 0;
2834     x[0] = b[idx]; x[1] = b[1+idx];x[2] = b[2+idx];x[3] = b[3+idx];
2835     for (i=1; i<n; i++) {
2836        v    = aa + bs2*ai[i];
2837        vi   = aj + ai[i];
2838        nz   = ai[i+1] - ai[i];
2839       idx   = bs*i;
2840        s1   = b[idx];s2 = b[1+idx];s3 = b[2+idx];s4 = b[3+idx];
2841       for(k=0;k<nz;k++) {
2842           jdx   = bs*vi[k];
2843           x1    = x[jdx];x2 = x[1+jdx]; x3 =x[2+jdx];x4 =x[3+jdx];
2844           s1   -= v[0]*x1 + v[4]*x2 + v[8]*x3 + v[12]*x4;
2845           s2   -= v[1]*x1 + v[5]*x2 + v[9]*x3 + v[13]*x4;
2846           s3   -= v[2]*x1 + v[6]*x2 + v[10]*x3 + v[14]*x4;
2847 	  s4   -= v[3]*x1 + v[7]*x2 + v[11]*x3 + v[15]*x4;
2848 
2849           v   +=  bs2;
2850         }
2851 
2852        x[idx]   = s1;
2853        x[1+idx] = s2;
2854        x[2+idx] = s3;
2855        x[3+idx] = s4;
2856     }
2857 
2858    /* backward solve the upper triangular */
2859   for (i=n-1; i>=0; i--){
2860      v   = aa + bs2*ai[2*n-i];
2861      vi  = aj + ai[2*n-i];
2862      nz  = ai[2*n-i +1] - ai[2*n-i]-1;
2863      idt = bs*i;
2864      s1 = x[idt];  s2 = x[1+idt];s3 = x[2+idt];s4 = x[3+idt];
2865 
2866     for(k=0;k<nz;k++){
2867       idx   = bs*vi[k];
2868        x1    = x[idx];   x2 = x[1+idx]; x3 = x[2+idx];x4 = x[3+idx];
2869        s1   -= v[0]*x1 + v[4]*x2 + v[8]*x3 + v[12]*x4;
2870        s2   -= v[1]*x1 + v[5]*x2 + v[9]*x3 + v[13]*x4;
2871        s3   -= v[2]*x1 + v[6]*x2 + v[10]*x3 + v[14]*x4;
2872        s4   -= v[3]*x1 + v[7]*x2 + v[11]*x3 + v[15]*x4;
2873 
2874         v   +=  bs2;
2875     }
2876     /* x = inv_diagonal*x */
2877    x[idt]   = v[0]*s1 + v[4]*s2 + v[8]*s3 + v[12]*s4;
2878    x[1+idt] = v[1]*s1 + v[5]*s2 + v[9]*s3 + v[13]*s4;;
2879    x[2+idt] = v[2]*s1 + v[6]*s2 + v[10]*s3 + v[14]*s4;
2880    x[3+idt] = v[3]*s1 + v[7]*s2 + v[11]*s3 + v[15]*s4;
2881 
2882   }
2883 
2884   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
2885   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
2886   ierr = PetscLogFlops(2.0*bs2*(a->nz) - bs*A->cmap->n);CHKERRQ(ierr);
2887   PetscFunctionReturn(0);
2888 }
2889 
2890 
2891 
2892 #undef __FUNCT__
2893 #define __FUNCT__ "MatSolve_SeqBAIJ_4_NaturalOrdering_Demotion"
2894 PetscErrorCode MatSolve_SeqBAIJ_4_NaturalOrdering_Demotion(Mat A,Vec bb,Vec xx)
2895 {
2896   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ *)A->data;
2897   PetscInt       n=a->mbs,*ai=a->i,*aj=a->j;
2898   PetscErrorCode ierr;
2899   PetscInt       *diag = a->diag;
2900   MatScalar      *aa=a->a;
2901   PetscScalar    *x,*b;
2902 
2903   PetscFunctionBegin;
2904   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
2905   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
2906 
2907   {
2908     MatScalar  s1,s2,s3,s4,x1,x2,x3,x4;
2909     MatScalar  *v,*t=(MatScalar *)x;
2910     PetscInt   jdx,idt,idx,nz,*vi,i,ai16;
2911 
2912     /* forward solve the lower triangular */
2913     idx  = 0;
2914     t[0] = (MatScalar)b[0];
2915     t[1] = (MatScalar)b[1];
2916     t[2] = (MatScalar)b[2];
2917     t[3] = (MatScalar)b[3];
2918     for (i=1; i<n; i++) {
2919       v     =  aa      + 16*ai[i];
2920       vi    =  aj      + ai[i];
2921       nz    =  diag[i] - ai[i];
2922       idx   +=  4;
2923       s1 = (MatScalar)b[idx];
2924       s2 = (MatScalar)b[1+idx];
2925       s3 = (MatScalar)b[2+idx];
2926       s4 = (MatScalar)b[3+idx];
2927       while (nz--) {
2928         jdx = 4*(*vi++);
2929         x1  = t[jdx];
2930         x2  = t[1+jdx];
2931         x3  = t[2+jdx];
2932         x4  = t[3+jdx];
2933         s1 -= v[0]*x1 + v[4]*x2 + v[8]*x3  + v[12]*x4;
2934         s2 -= v[1]*x1 + v[5]*x2 + v[9]*x3  + v[13]*x4;
2935         s3 -= v[2]*x1 + v[6]*x2 + v[10]*x3 + v[14]*x4;
2936         s4 -= v[3]*x1 + v[7]*x2 + v[11]*x3 + v[15]*x4;
2937         v    += 16;
2938       }
2939       t[idx]   = s1;
2940       t[1+idx] = s2;
2941       t[2+idx] = s3;
2942       t[3+idx] = s4;
2943     }
2944     /* backward solve the upper triangular */
2945     idt = 4*(n-1);
2946     for (i=n-1; i>=0; i--){
2947       ai16 = 16*diag[i];
2948       v    = aa + ai16 + 16;
2949       vi   = aj + diag[i] + 1;
2950       nz   = ai[i+1] - diag[i] - 1;
2951       s1   = t[idt];
2952       s2   = t[1+idt];
2953       s3   = t[2+idt];
2954       s4   = t[3+idt];
2955       while (nz--) {
2956         idx = 4*(*vi++);
2957         x1  = (MatScalar)x[idx];
2958         x2  = (MatScalar)x[1+idx];
2959         x3  = (MatScalar)x[2+idx];
2960         x4  = (MatScalar)x[3+idx];
2961         s1 -= v[0]*x1 + v[4]*x2 + v[8]*x3  + v[12]*x4;
2962         s2 -= v[1]*x1 + v[5]*x2 + v[9]*x3  + v[13]*x4;
2963         s3 -= v[2]*x1 + v[6]*x2 + v[10]*x3 + v[14]*x4;
2964         s4 -= v[3]*x1 + v[7]*x2 + v[11]*x3 + v[15]*x4;
2965         v    += 16;
2966       }
2967       v        = aa + ai16;
2968       x[idt]   = (PetscScalar)(v[0]*s1 + v[4]*s2 + v[8]*s3  + v[12]*s4);
2969       x[1+idt] = (PetscScalar)(v[1]*s1 + v[5]*s2 + v[9]*s3  + v[13]*s4);
2970       x[2+idt] = (PetscScalar)(v[2]*s1 + v[6]*s2 + v[10]*s3 + v[14]*s4);
2971       x[3+idt] = (PetscScalar)(v[3]*s1 + v[7]*s2 + v[11]*s3 + v[15]*s4);
2972       idt -= 4;
2973     }
2974   }
2975 
2976   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
2977   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
2978   ierr = PetscLogFlops(2.0*16*(a->nz) - 4.0*A->cmap->n);CHKERRQ(ierr);
2979   PetscFunctionReturn(0);
2980 }
2981 
2982 #if defined (PETSC_HAVE_SSE)
2983 
2984 #include PETSC_HAVE_SSE
2985 #undef __FUNCT__
2986 #define __FUNCT__ "MatSolve_SeqBAIJ_4_NaturalOrdering_SSE_Demotion_usj"
2987 PetscErrorCode MatSolve_SeqBAIJ_4_NaturalOrdering_SSE_Demotion_usj(Mat A,Vec bb,Vec xx)
2988 {
2989   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ *)A->data;
2990   unsigned short *aj=(unsigned short *)a->j;
2991   PetscErrorCode ierr;
2992   int            *ai=a->i,n=a->mbs,*diag = a->diag;
2993   MatScalar      *aa=a->a;
2994   PetscScalar    *x,*b;
2995 
2996   PetscFunctionBegin;
2997   SSE_SCOPE_BEGIN;
2998   /*
2999      Note: This code currently uses demotion of double
3000      to float when performing the mixed-mode computation.
3001      This may not be numerically reasonable for all applications.
3002   */
3003   PREFETCH_NTA(aa+16*ai[1]);
3004 
3005   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
3006   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
3007   {
3008     /* x will first be computed in single precision then promoted inplace to double */
3009     MatScalar      *v,*t=(MatScalar *)x;
3010     int            nz,i,idt,ai16;
3011     unsigned int   jdx,idx;
3012     unsigned short *vi;
3013     /* Forward solve the lower triangular factor. */
3014 
3015     /* First block is the identity. */
3016     idx  = 0;
3017     CONVERT_DOUBLE4_FLOAT4(t,b);
3018     v    =  aa + 16*((unsigned int)ai[1]);
3019 
3020     for (i=1; i<n;) {
3021       PREFETCH_NTA(&v[8]);
3022       vi   =  aj      + ai[i];
3023       nz   =  diag[i] - ai[i];
3024       idx +=  4;
3025 
3026       /* Demote RHS from double to float. */
3027       CONVERT_DOUBLE4_FLOAT4(&t[idx],&b[idx]);
3028       LOAD_PS(&t[idx],XMM7);
3029 
3030       while (nz--) {
3031         PREFETCH_NTA(&v[16]);
3032         jdx = 4*((unsigned int)(*vi++));
3033 
3034         /* 4x4 Matrix-Vector product with negative accumulation: */
3035         SSE_INLINE_BEGIN_2(&t[jdx],v)
3036           SSE_LOAD_PS(SSE_ARG_1,FLOAT_0,XMM6)
3037 
3038           /* First Column */
3039           SSE_COPY_PS(XMM0,XMM6)
3040           SSE_SHUFFLE(XMM0,XMM0,0x00)
3041           SSE_MULT_PS_M(XMM0,SSE_ARG_2,FLOAT_0)
3042           SSE_SUB_PS(XMM7,XMM0)
3043 
3044           /* Second Column */
3045           SSE_COPY_PS(XMM1,XMM6)
3046           SSE_SHUFFLE(XMM1,XMM1,0x55)
3047           SSE_MULT_PS_M(XMM1,SSE_ARG_2,FLOAT_4)
3048           SSE_SUB_PS(XMM7,XMM1)
3049 
3050           SSE_PREFETCH_NTA(SSE_ARG_2,FLOAT_24)
3051 
3052           /* Third Column */
3053           SSE_COPY_PS(XMM2,XMM6)
3054           SSE_SHUFFLE(XMM2,XMM2,0xAA)
3055           SSE_MULT_PS_M(XMM2,SSE_ARG_2,FLOAT_8)
3056           SSE_SUB_PS(XMM7,XMM2)
3057 
3058           /* Fourth Column */
3059           SSE_COPY_PS(XMM3,XMM6)
3060           SSE_SHUFFLE(XMM3,XMM3,0xFF)
3061           SSE_MULT_PS_M(XMM3,SSE_ARG_2,FLOAT_12)
3062           SSE_SUB_PS(XMM7,XMM3)
3063         SSE_INLINE_END_2
3064 
3065         v  += 16;
3066       }
3067       v    =  aa + 16*ai[++i];
3068       PREFETCH_NTA(v);
3069       STORE_PS(&t[idx],XMM7);
3070     }
3071 
3072     /* Backward solve the upper triangular factor.*/
3073 
3074     idt  = 4*(n-1);
3075     ai16 = 16*diag[n-1];
3076     v    = aa + ai16 + 16;
3077     for (i=n-1; i>=0;){
3078       PREFETCH_NTA(&v[8]);
3079       vi = aj + diag[i] + 1;
3080       nz = ai[i+1] - diag[i] - 1;
3081 
3082       LOAD_PS(&t[idt],XMM7);
3083 
3084       while (nz--) {
3085         PREFETCH_NTA(&v[16]);
3086         idx = 4*((unsigned int)(*vi++));
3087 
3088         /* 4x4 Matrix-Vector Product with negative accumulation: */
3089         SSE_INLINE_BEGIN_2(&t[idx],v)
3090           SSE_LOAD_PS(SSE_ARG_1,FLOAT_0,XMM6)
3091 
3092           /* First Column */
3093           SSE_COPY_PS(XMM0,XMM6)
3094           SSE_SHUFFLE(XMM0,XMM0,0x00)
3095           SSE_MULT_PS_M(XMM0,SSE_ARG_2,FLOAT_0)
3096           SSE_SUB_PS(XMM7,XMM0)
3097 
3098           /* Second Column */
3099           SSE_COPY_PS(XMM1,XMM6)
3100           SSE_SHUFFLE(XMM1,XMM1,0x55)
3101           SSE_MULT_PS_M(XMM1,SSE_ARG_2,FLOAT_4)
3102           SSE_SUB_PS(XMM7,XMM1)
3103 
3104           SSE_PREFETCH_NTA(SSE_ARG_2,FLOAT_24)
3105 
3106           /* Third Column */
3107           SSE_COPY_PS(XMM2,XMM6)
3108           SSE_SHUFFLE(XMM2,XMM2,0xAA)
3109           SSE_MULT_PS_M(XMM2,SSE_ARG_2,FLOAT_8)
3110           SSE_SUB_PS(XMM7,XMM2)
3111 
3112           /* Fourth Column */
3113           SSE_COPY_PS(XMM3,XMM6)
3114           SSE_SHUFFLE(XMM3,XMM3,0xFF)
3115           SSE_MULT_PS_M(XMM3,SSE_ARG_2,FLOAT_12)
3116           SSE_SUB_PS(XMM7,XMM3)
3117         SSE_INLINE_END_2
3118         v  += 16;
3119       }
3120       v    = aa + ai16;
3121       ai16 = 16*diag[--i];
3122       PREFETCH_NTA(aa+ai16+16);
3123       /*
3124          Scale the result by the diagonal 4x4 block,
3125          which was inverted as part of the factorization
3126       */
3127       SSE_INLINE_BEGIN_3(v,&t[idt],aa+ai16)
3128         /* First Column */
3129         SSE_COPY_PS(XMM0,XMM7)
3130         SSE_SHUFFLE(XMM0,XMM0,0x00)
3131         SSE_MULT_PS_M(XMM0,SSE_ARG_1,FLOAT_0)
3132 
3133         /* Second Column */
3134         SSE_COPY_PS(XMM1,XMM7)
3135         SSE_SHUFFLE(XMM1,XMM1,0x55)
3136         SSE_MULT_PS_M(XMM1,SSE_ARG_1,FLOAT_4)
3137         SSE_ADD_PS(XMM0,XMM1)
3138 
3139         SSE_PREFETCH_NTA(SSE_ARG_3,FLOAT_24)
3140 
3141         /* Third Column */
3142         SSE_COPY_PS(XMM2,XMM7)
3143         SSE_SHUFFLE(XMM2,XMM2,0xAA)
3144         SSE_MULT_PS_M(XMM2,SSE_ARG_1,FLOAT_8)
3145         SSE_ADD_PS(XMM0,XMM2)
3146 
3147         /* Fourth Column */
3148         SSE_COPY_PS(XMM3,XMM7)
3149         SSE_SHUFFLE(XMM3,XMM3,0xFF)
3150         SSE_MULT_PS_M(XMM3,SSE_ARG_1,FLOAT_12)
3151         SSE_ADD_PS(XMM0,XMM3)
3152 
3153         SSE_STORE_PS(SSE_ARG_2,FLOAT_0,XMM0)
3154       SSE_INLINE_END_3
3155 
3156       v    = aa + ai16 + 16;
3157       idt -= 4;
3158     }
3159 
3160     /* Convert t from single precision back to double precision (inplace)*/
3161     idt = 4*(n-1);
3162     for (i=n-1;i>=0;i--) {
3163       /*     CONVERT_FLOAT4_DOUBLE4(&x[idt],&t[idt]); */
3164       /* Unfortunately, CONVERT_ will count from 0 to 3 which doesn't work here. */
3165       PetscScalar *xtemp=&x[idt];
3166       MatScalar   *ttemp=&t[idt];
3167       xtemp[3] = (PetscScalar)ttemp[3];
3168       xtemp[2] = (PetscScalar)ttemp[2];
3169       xtemp[1] = (PetscScalar)ttemp[1];
3170       xtemp[0] = (PetscScalar)ttemp[0];
3171       idt -= 4;
3172     }
3173 
3174   } /* End of artificial scope. */
3175   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
3176   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
3177   ierr = PetscLogFlops(2.0*16*(a->nz) - 4.0*A->cmap->n);CHKERRQ(ierr);
3178   SSE_SCOPE_END;
3179   PetscFunctionReturn(0);
3180 }
3181 
3182 #undef __FUNCT__
3183 #define __FUNCT__ "MatSolve_SeqBAIJ_4_NaturalOrdering_SSE_Demotion"
3184 PetscErrorCode MatSolve_SeqBAIJ_4_NaturalOrdering_SSE_Demotion(Mat A,Vec bb,Vec xx)
3185 {
3186   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ *)A->data;
3187   int            *aj=a->j;
3188   PetscErrorCode ierr;
3189   int            *ai=a->i,n=a->mbs,*diag = a->diag;
3190   MatScalar      *aa=a->a;
3191   PetscScalar    *x,*b;
3192 
3193   PetscFunctionBegin;
3194   SSE_SCOPE_BEGIN;
3195   /*
3196      Note: This code currently uses demotion of double
3197      to float when performing the mixed-mode computation.
3198      This may not be numerically reasonable for all applications.
3199   */
3200   PREFETCH_NTA(aa+16*ai[1]);
3201 
3202   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
3203   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
3204   {
3205     /* x will first be computed in single precision then promoted inplace to double */
3206     MatScalar *v,*t=(MatScalar *)x;
3207     int       nz,i,idt,ai16;
3208     int       jdx,idx;
3209     int       *vi;
3210     /* Forward solve the lower triangular factor. */
3211 
3212     /* First block is the identity. */
3213     idx  = 0;
3214     CONVERT_DOUBLE4_FLOAT4(t,b);
3215     v    =  aa + 16*ai[1];
3216 
3217     for (i=1; i<n;) {
3218       PREFETCH_NTA(&v[8]);
3219       vi   =  aj      + ai[i];
3220       nz   =  diag[i] - ai[i];
3221       idx +=  4;
3222 
3223       /* Demote RHS from double to float. */
3224       CONVERT_DOUBLE4_FLOAT4(&t[idx],&b[idx]);
3225       LOAD_PS(&t[idx],XMM7);
3226 
3227       while (nz--) {
3228         PREFETCH_NTA(&v[16]);
3229         jdx = 4*(*vi++);
3230 /*          jdx = *vi++; */
3231 
3232         /* 4x4 Matrix-Vector product with negative accumulation: */
3233         SSE_INLINE_BEGIN_2(&t[jdx],v)
3234           SSE_LOAD_PS(SSE_ARG_1,FLOAT_0,XMM6)
3235 
3236           /* First Column */
3237           SSE_COPY_PS(XMM0,XMM6)
3238           SSE_SHUFFLE(XMM0,XMM0,0x00)
3239           SSE_MULT_PS_M(XMM0,SSE_ARG_2,FLOAT_0)
3240           SSE_SUB_PS(XMM7,XMM0)
3241 
3242           /* Second Column */
3243           SSE_COPY_PS(XMM1,XMM6)
3244           SSE_SHUFFLE(XMM1,XMM1,0x55)
3245           SSE_MULT_PS_M(XMM1,SSE_ARG_2,FLOAT_4)
3246           SSE_SUB_PS(XMM7,XMM1)
3247 
3248           SSE_PREFETCH_NTA(SSE_ARG_2,FLOAT_24)
3249 
3250           /* Third Column */
3251           SSE_COPY_PS(XMM2,XMM6)
3252           SSE_SHUFFLE(XMM2,XMM2,0xAA)
3253           SSE_MULT_PS_M(XMM2,SSE_ARG_2,FLOAT_8)
3254           SSE_SUB_PS(XMM7,XMM2)
3255 
3256           /* Fourth Column */
3257           SSE_COPY_PS(XMM3,XMM6)
3258           SSE_SHUFFLE(XMM3,XMM3,0xFF)
3259           SSE_MULT_PS_M(XMM3,SSE_ARG_2,FLOAT_12)
3260           SSE_SUB_PS(XMM7,XMM3)
3261         SSE_INLINE_END_2
3262 
3263         v  += 16;
3264       }
3265       v    =  aa + 16*ai[++i];
3266       PREFETCH_NTA(v);
3267       STORE_PS(&t[idx],XMM7);
3268     }
3269 
3270     /* Backward solve the upper triangular factor.*/
3271 
3272     idt  = 4*(n-1);
3273     ai16 = 16*diag[n-1];
3274     v    = aa + ai16 + 16;
3275     for (i=n-1; i>=0;){
3276       PREFETCH_NTA(&v[8]);
3277       vi = aj + diag[i] + 1;
3278       nz = ai[i+1] - diag[i] - 1;
3279 
3280       LOAD_PS(&t[idt],XMM7);
3281 
3282       while (nz--) {
3283         PREFETCH_NTA(&v[16]);
3284         idx = 4*(*vi++);
3285 /*          idx = *vi++; */
3286 
3287         /* 4x4 Matrix-Vector Product with negative accumulation: */
3288         SSE_INLINE_BEGIN_2(&t[idx],v)
3289           SSE_LOAD_PS(SSE_ARG_1,FLOAT_0,XMM6)
3290 
3291           /* First Column */
3292           SSE_COPY_PS(XMM0,XMM6)
3293           SSE_SHUFFLE(XMM0,XMM0,0x00)
3294           SSE_MULT_PS_M(XMM0,SSE_ARG_2,FLOAT_0)
3295           SSE_SUB_PS(XMM7,XMM0)
3296 
3297           /* Second Column */
3298           SSE_COPY_PS(XMM1,XMM6)
3299           SSE_SHUFFLE(XMM1,XMM1,0x55)
3300           SSE_MULT_PS_M(XMM1,SSE_ARG_2,FLOAT_4)
3301           SSE_SUB_PS(XMM7,XMM1)
3302 
3303           SSE_PREFETCH_NTA(SSE_ARG_2,FLOAT_24)
3304 
3305           /* Third Column */
3306           SSE_COPY_PS(XMM2,XMM6)
3307           SSE_SHUFFLE(XMM2,XMM2,0xAA)
3308           SSE_MULT_PS_M(XMM2,SSE_ARG_2,FLOAT_8)
3309           SSE_SUB_PS(XMM7,XMM2)
3310 
3311           /* Fourth Column */
3312           SSE_COPY_PS(XMM3,XMM6)
3313           SSE_SHUFFLE(XMM3,XMM3,0xFF)
3314           SSE_MULT_PS_M(XMM3,SSE_ARG_2,FLOAT_12)
3315           SSE_SUB_PS(XMM7,XMM3)
3316         SSE_INLINE_END_2
3317         v  += 16;
3318       }
3319       v    = aa + ai16;
3320       ai16 = 16*diag[--i];
3321       PREFETCH_NTA(aa+ai16+16);
3322       /*
3323          Scale the result by the diagonal 4x4 block,
3324          which was inverted as part of the factorization
3325       */
3326       SSE_INLINE_BEGIN_3(v,&t[idt],aa+ai16)
3327         /* First Column */
3328         SSE_COPY_PS(XMM0,XMM7)
3329         SSE_SHUFFLE(XMM0,XMM0,0x00)
3330         SSE_MULT_PS_M(XMM0,SSE_ARG_1,FLOAT_0)
3331 
3332         /* Second Column */
3333         SSE_COPY_PS(XMM1,XMM7)
3334         SSE_SHUFFLE(XMM1,XMM1,0x55)
3335         SSE_MULT_PS_M(XMM1,SSE_ARG_1,FLOAT_4)
3336         SSE_ADD_PS(XMM0,XMM1)
3337 
3338         SSE_PREFETCH_NTA(SSE_ARG_3,FLOAT_24)
3339 
3340         /* Third Column */
3341         SSE_COPY_PS(XMM2,XMM7)
3342         SSE_SHUFFLE(XMM2,XMM2,0xAA)
3343         SSE_MULT_PS_M(XMM2,SSE_ARG_1,FLOAT_8)
3344         SSE_ADD_PS(XMM0,XMM2)
3345 
3346         /* Fourth Column */
3347         SSE_COPY_PS(XMM3,XMM7)
3348         SSE_SHUFFLE(XMM3,XMM3,0xFF)
3349         SSE_MULT_PS_M(XMM3,SSE_ARG_1,FLOAT_12)
3350         SSE_ADD_PS(XMM0,XMM3)
3351 
3352         SSE_STORE_PS(SSE_ARG_2,FLOAT_0,XMM0)
3353       SSE_INLINE_END_3
3354 
3355       v    = aa + ai16 + 16;
3356       idt -= 4;
3357     }
3358 
3359     /* Convert t from single precision back to double precision (inplace)*/
3360     idt = 4*(n-1);
3361     for (i=n-1;i>=0;i--) {
3362       /*     CONVERT_FLOAT4_DOUBLE4(&x[idt],&t[idt]); */
3363       /* Unfortunately, CONVERT_ will count from 0 to 3 which doesn't work here. */
3364       PetscScalar *xtemp=&x[idt];
3365       MatScalar   *ttemp=&t[idt];
3366       xtemp[3] = (PetscScalar)ttemp[3];
3367       xtemp[2] = (PetscScalar)ttemp[2];
3368       xtemp[1] = (PetscScalar)ttemp[1];
3369       xtemp[0] = (PetscScalar)ttemp[0];
3370       idt -= 4;
3371     }
3372 
3373   } /* End of artificial scope. */
3374   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
3375   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
3376   ierr = PetscLogFlops(2.0*16*(a->nz) - 4.0*A->cmap->n);CHKERRQ(ierr);
3377   SSE_SCOPE_END;
3378   PetscFunctionReturn(0);
3379 }
3380 
3381 #endif
3382 
3383 #undef __FUNCT__
3384 #define __FUNCT__ "MatSolve_SeqBAIJ_3"
3385 PetscErrorCode MatSolve_SeqBAIJ_3(Mat A,Vec bb,Vec xx)
3386 {
3387   Mat_SeqBAIJ       *a=(Mat_SeqBAIJ *)A->data;
3388   IS                iscol=a->col,isrow=a->row;
3389   PetscErrorCode    ierr;
3390   PetscInt          i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc;
3391   const PetscInt    *r,*c,*diag = a->diag,*rout,*cout;
3392   const MatScalar   *aa=a->a,*v;
3393   PetscScalar       *x,s1,s2,s3,x1,x2,x3,*t;
3394   const PetscScalar *b;
3395 
3396   PetscFunctionBegin;
3397   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3398   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
3399   t  = a->solve_work;
3400 
3401   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
3402   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
3403 
3404   /* forward solve the lower triangular */
3405   idx    = 3*(*r++);
3406   t[0] = b[idx]; t[1] = b[1+idx]; t[2] = b[2+idx];
3407   for (i=1; i<n; i++) {
3408     v     = aa + 9*ai[i];
3409     vi    = aj + ai[i];
3410     nz    = diag[i] - ai[i];
3411     idx   = 3*(*r++);
3412     s1  = b[idx]; s2 = b[1+idx]; s3 = b[2+idx];
3413     while (nz--) {
3414       idx   = 3*(*vi++);
3415       x1    = t[idx]; x2 = t[1+idx]; x3 = t[2+idx];
3416       s1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
3417       s2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
3418       s3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
3419       v += 9;
3420     }
3421     idx = 3*i;
3422     t[idx] = s1; t[1+idx] = s2; t[2+idx] = s3;
3423   }
3424   /* backward solve the upper triangular */
3425   for (i=n-1; i>=0; i--){
3426     v    = aa + 9*diag[i] + 9;
3427     vi   = aj + diag[i] + 1;
3428     nz   = ai[i+1] - diag[i] - 1;
3429     idt  = 3*i;
3430     s1 = t[idt]; s2 = t[1+idt]; s3 = t[2+idt];
3431     while (nz--) {
3432       idx   = 3*(*vi++);
3433       x1    = t[idx]; x2 = t[1+idx]; x3 = t[2+idx];
3434       s1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
3435       s2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
3436       s3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
3437       v += 9;
3438     }
3439     idc = 3*(*c--);
3440     v   = aa + 9*diag[i];
3441     x[idc]   = t[idt]   = v[0]*s1 + v[3]*s2 + v[6]*s3;
3442     x[1+idc] = t[1+idt] = v[1]*s1 + v[4]*s2 + v[7]*s3;
3443     x[2+idc] = t[2+idt] = v[2]*s1 + v[5]*s2 + v[8]*s3;
3444   }
3445   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
3446   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
3447   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3448   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
3449   ierr = PetscLogFlops(2.0*9*(a->nz) - 3.0*A->cmap->n);CHKERRQ(ierr);
3450   PetscFunctionReturn(0);
3451 }
3452 
3453 #undef __FUNCT__
3454 #define __FUNCT__ "MatSolve_SeqBAIJ_3_newdatastruct"
3455 PetscErrorCode MatSolve_SeqBAIJ_3_newdatastruct(Mat A,Vec bb,Vec xx)
3456 {
3457   Mat_SeqBAIJ       *a=(Mat_SeqBAIJ *)A->data;
3458   IS                iscol=a->col,isrow=a->row;
3459   PetscErrorCode    ierr;
3460   PetscInt          i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc,k,m;
3461   const PetscInt    *r,*c,*rout,*cout;
3462   const MatScalar   *aa=a->a,*v;
3463   PetscScalar       *x,s1,s2,s3,x1,x2,x3,*t;
3464   const PetscScalar *b;
3465 
3466   PetscFunctionBegin;
3467   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3468   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
3469   t  = a->solve_work;
3470 
3471   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
3472   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
3473 
3474   /* forward solve the lower triangular */
3475   idx    = 3*r[0];
3476   t[0] = b[idx]; t[1] = b[1+idx]; t[2] = b[2+idx];
3477   for (i=1; i<n; i++) {
3478     v     = aa + 9*ai[i];
3479     vi    = aj + ai[i];
3480     nz    = ai[i+1] - ai[i];
3481     idx   = 3*r[i];
3482     s1  = b[idx]; s2 = b[1+idx]; s3 = b[2+idx];
3483     for(m=0;m<nz;m++){
3484       idx   = 3*vi[m];
3485       x1    = t[idx]; x2 = t[1+idx]; x3 = t[2+idx];
3486       s1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
3487       s2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
3488       s3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
3489       v += 9;
3490     }
3491     idx = 3*i;
3492     t[idx] = s1; t[1+idx] = s2; t[2+idx] = s3;
3493   }
3494   /* backward solve the upper triangular */
3495   for (i=n-1; i>=0; i--){
3496     k    = 2*n-i;
3497     v    = aa + 9*ai[k];
3498     vi   = aj + ai[k];
3499     nz   = ai[k +1] - ai[k] - 1;
3500     idt  = 3*i;
3501     s1 = t[idt]; s2 = t[1+idt]; s3 = t[2+idt];
3502     for(m=0;m<nz;m++){
3503       idx   = 3*vi[m];
3504       x1    = t[idx]; x2 = t[1+idx]; x3 = t[2+idx];
3505       s1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
3506       s2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
3507       s3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
3508       v += 9;
3509     }
3510     idc = 3*c[i];
3511     x[idc]   = t[idt]   = v[0]*s1 + v[3]*s2 + v[6]*s3;
3512     x[1+idc] = t[1+idt] = v[1]*s1 + v[4]*s2 + v[7]*s3;
3513     x[2+idc] = t[2+idt] = v[2]*s1 + v[5]*s2 + v[8]*s3;
3514   }
3515   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
3516   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
3517   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3518   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
3519   ierr = PetscLogFlops(2.0*9*(a->nz) - 3.0*A->cmap->n);CHKERRQ(ierr);
3520   PetscFunctionReturn(0);
3521 }
3522 
3523 /*
3524       Special case where the matrix was ILU(0) factored in the natural
3525    ordering. This eliminates the need for the column and row permutation.
3526 */
3527 #undef __FUNCT__
3528 #define __FUNCT__ "MatSolve_SeqBAIJ_3_NaturalOrdering"
3529 PetscErrorCode MatSolve_SeqBAIJ_3_NaturalOrdering(Mat A,Vec bb,Vec xx)
3530 {
3531   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ *)A->data;
3532   PetscInt          n=a->mbs,*ai=a->i,*aj=a->j;
3533   PetscErrorCode    ierr;
3534   PetscInt          *diag = a->diag;
3535   const MatScalar   *aa=a->a,*v;
3536   PetscScalar       *x,s1,s2,s3,x1,x2,x3;
3537   const PetscScalar *b;
3538   PetscInt          jdx,idt,idx,nz,*vi,i;
3539 
3540   PetscFunctionBegin;
3541   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3542   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
3543 
3544   /* forward solve the lower triangular */
3545   idx    = 0;
3546   x[0]   = b[0]; x[1] = b[1]; x[2] = b[2];
3547   for (i=1; i<n; i++) {
3548     v     =  aa      + 9*ai[i];
3549     vi    =  aj      + ai[i];
3550     nz    =  diag[i] - ai[i];
3551     idx   +=  3;
3552     s1  =  b[idx];s2 = b[1+idx];s3 = b[2+idx];
3553     while (nz--) {
3554       jdx   = 3*(*vi++);
3555       x1    = x[jdx];x2 = x[1+jdx];x3 = x[2+jdx];
3556       s1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
3557       s2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
3558       s3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
3559       v    += 9;
3560     }
3561     x[idx]   = s1;
3562     x[1+idx] = s2;
3563     x[2+idx] = s3;
3564   }
3565   /* backward solve the upper triangular */
3566   for (i=n-1; i>=0; i--){
3567     v    = aa + 9*diag[i] + 9;
3568     vi   = aj + diag[i] + 1;
3569     nz   = ai[i+1] - diag[i] - 1;
3570     idt  = 3*i;
3571     s1 = x[idt];  s2 = x[1+idt];
3572     s3 = x[2+idt];
3573     while (nz--) {
3574       idx   = 3*(*vi++);
3575       x1    = x[idx];   x2 = x[1+idx];x3    = x[2+idx];
3576       s1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
3577       s2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
3578       s3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
3579       v    += 9;
3580     }
3581     v        = aa +  9*diag[i];
3582     x[idt]   = v[0]*s1 + v[3]*s2 + v[6]*s3;
3583     x[1+idt] = v[1]*s1 + v[4]*s2 + v[7]*s3;
3584     x[2+idt] = v[2]*s1 + v[5]*s2 + v[8]*s3;
3585   }
3586 
3587   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3588   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
3589   ierr = PetscLogFlops(2.0*9*(a->nz) - 3.0*A->cmap->n);CHKERRQ(ierr);
3590   PetscFunctionReturn(0);
3591 }
3592 
3593 #undef __FUNCT__
3594 #define __FUNCT__ "MatSolve_SeqBAIJ_3_NaturalOrdering_newdatastruct"
3595 PetscErrorCode MatSolve_SeqBAIJ_3_NaturalOrdering_newdatastruct(Mat A,Vec bb,Vec xx)
3596 {
3597     Mat_SeqBAIJ       *a = (Mat_SeqBAIJ *)A->data;
3598     PetscInt          i,k,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz;
3599     PetscErrorCode    ierr;
3600     PetscInt          idx,jdx,idt;
3601     PetscInt          bs = A->rmap->bs,bs2 = a->bs2;
3602     const MatScalar   *aa=a->a,*v;
3603     PetscScalar       *x;
3604     const PetscScalar *b;
3605     PetscScalar        s1,s2,s3,x1,x2,x3;
3606 
3607     PetscFunctionBegin;
3608     ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3609     ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
3610     /* forward solve the lower triangular */
3611     idx    = 0;
3612     x[0] = b[idx]; x[1] = b[1+idx];x[2] = b[2+idx];
3613     for (i=1; i<n; i++) {
3614        v    = aa + bs2*ai[i];
3615        vi   = aj + ai[i];
3616        nz   = ai[i+1] - ai[i];
3617       idx   = bs*i;
3618        s1   = b[idx];s2 = b[1+idx];s3 = b[2+idx];
3619       for(k=0;k<nz;k++){
3620          jdx   = bs*vi[k];
3621           x1    = x[jdx];x2 = x[1+jdx]; x3 =x[2+jdx];
3622           s1   -= v[0]*x1 + v[3]*x2 + v[6]*x3;
3623           s2   -= v[1]*x1 + v[4]*x2 + v[7]*x3;
3624           s3   -= v[2]*x1 + v[5]*x2 + v[8]*x3;
3625 
3626           v   +=  bs2;
3627         }
3628 
3629        x[idx]   = s1;
3630        x[1+idx] = s2;
3631        x[2+idx] = s3;
3632     }
3633 
3634    /* backward solve the upper triangular */
3635   for (i=n-1; i>=0; i--){
3636      v   = aa + bs2*ai[2*n-i];
3637      vi  = aj + ai[2*n-i];
3638      nz  = ai[2*n-i +1] - ai[2*n-i]-1;
3639      idt = bs*i;
3640      s1 = x[idt];  s2 = x[1+idt];s3 = x[2+idt];
3641 
3642      for(k=0;k<nz;k++){
3643        idx   = bs*vi[k];
3644        x1    = x[idx];   x2 = x[1+idx]; x3 = x[2+idx];
3645        s1 -= v[0]*x1 + v[3]*x2 + v[6]*x3;
3646        s2 -= v[1]*x1 + v[4]*x2 + v[7]*x3;
3647        s3 -= v[2]*x1 + v[5]*x2 + v[8]*x3;
3648 
3649         v   +=  bs2;
3650     }
3651     /* x = inv_diagonal*x */
3652    x[idt]   = v[0]*s1 + v[3]*s2 + v[6]*s3;
3653    x[1+idt] = v[1]*s1 + v[4]*s2 + v[7]*s3;
3654    x[2+idt] = v[2]*s1 + v[5]*s2 + v[8]*s3;
3655 
3656   }
3657 
3658   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3659   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
3660   ierr = PetscLogFlops(2.0*bs2*(a->nz) - bs*A->cmap->n);CHKERRQ(ierr);
3661   PetscFunctionReturn(0);
3662 }
3663 
3664 #undef __FUNCT__
3665 #define __FUNCT__ "MatSolve_SeqBAIJ_2"
3666 PetscErrorCode MatSolve_SeqBAIJ_2(Mat A,Vec bb,Vec xx)
3667 {
3668   Mat_SeqBAIJ       *a=(Mat_SeqBAIJ *)A->data;
3669   IS                iscol=a->col,isrow=a->row;
3670   PetscErrorCode    ierr;
3671   PetscInt          i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt,idc;
3672   const PetscInt    *r,*c,*diag = a->diag,*rout,*cout;
3673   const MatScalar   *aa=a->a,*v;
3674   PetscScalar       *x,s1,s2,x1,x2,*t;
3675   const PetscScalar *b;
3676 
3677   PetscFunctionBegin;
3678   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3679   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
3680   t  = a->solve_work;
3681 
3682   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
3683   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
3684 
3685   /* forward solve the lower triangular */
3686   idx    = 2*(*r++);
3687   t[0] = b[idx]; t[1] = b[1+idx];
3688   for (i=1; i<n; i++) {
3689     v     = aa + 4*ai[i];
3690     vi    = aj + ai[i];
3691     nz    = diag[i] - ai[i];
3692     idx   = 2*(*r++);
3693     s1  = b[idx]; s2 = b[1+idx];
3694     while (nz--) {
3695       idx   = 2*(*vi++);
3696       x1    = t[idx]; x2 = t[1+idx];
3697       s1 -= v[0]*x1 + v[2]*x2;
3698       s2 -= v[1]*x1 + v[3]*x2;
3699       v += 4;
3700     }
3701     idx = 2*i;
3702     t[idx] = s1; t[1+idx] = s2;
3703   }
3704   /* backward solve the upper triangular */
3705   for (i=n-1; i>=0; i--){
3706     v    = aa + 4*diag[i] + 4;
3707     vi   = aj + diag[i] + 1;
3708     nz   = ai[i+1] - diag[i] - 1;
3709     idt  = 2*i;
3710     s1 = t[idt]; s2 = t[1+idt];
3711     while (nz--) {
3712       idx   = 2*(*vi++);
3713       x1    = t[idx]; x2 = t[1+idx];
3714       s1 -= v[0]*x1 + v[2]*x2;
3715       s2 -= v[1]*x1 + v[3]*x2;
3716       v += 4;
3717     }
3718     idc = 2*(*c--);
3719     v   = aa + 4*diag[i];
3720     x[idc]   = t[idt]   = v[0]*s1 + v[2]*s2;
3721     x[1+idc] = t[1+idt] = v[1]*s1 + v[3]*s2;
3722   }
3723   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
3724   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
3725   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3726   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
3727   ierr = PetscLogFlops(2.0*4*(a->nz) - 2.0*A->cmap->n);CHKERRQ(ierr);
3728   PetscFunctionReturn(0);
3729 }
3730 
3731 #undef __FUNCT__
3732 #define __FUNCT__ "MatSolve_SeqBAIJ_2_newdatastruct"
3733 PetscErrorCode MatSolve_SeqBAIJ_2_newdatastruct(Mat A,Vec bb,Vec xx)
3734 {
3735   Mat_SeqBAIJ       *a=(Mat_SeqBAIJ *)A->data;
3736   IS                iscol=a->col,isrow=a->row;
3737   PetscErrorCode    ierr;
3738   PetscInt          i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,jdx,idt,idc,k,m;
3739   const PetscInt    *r,*c,*rout,*cout;
3740   const MatScalar   *aa=a->a,*v;
3741   PetscScalar       *x,s1,s2,x1,x2,*t;
3742   const PetscScalar *b;
3743 
3744   PetscFunctionBegin;
3745   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3746   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
3747   t  = a->solve_work;
3748 
3749   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
3750   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout;
3751 
3752   /* forward solve the lower triangular */
3753   idx    = 2*r[0];
3754   t[0] = b[idx]; t[1] = b[1+idx];
3755   for (i=1; i<n; i++) {
3756     v     = aa + 4*ai[i];
3757     vi    = aj + ai[i];
3758     nz    = ai[i+1] - ai[i];
3759     idx   = 2*r[i];
3760     s1  = b[idx]; s2 = b[1+idx];
3761     for(m=0;m<nz;m++){
3762       jdx   = 2*vi[m];
3763       x1    = t[jdx]; x2 = t[1+jdx];
3764       s1 -= v[0]*x1 + v[2]*x2;
3765       s2 -= v[1]*x1 + v[3]*x2;
3766       v += 4;
3767     }
3768     idx = 2*i;
3769     t[idx] = s1; t[1+idx] = s2;
3770   }
3771   /* backward solve the upper triangular */
3772   for (i=n-1; i>=0; i--){
3773     k = 2*n-i;
3774     v    = aa + 4*ai[k];
3775     vi   = aj + ai[k];
3776     nz   = ai[k +1] - ai[k] - 1;
3777     idt  = 2*i;
3778     s1 = t[idt]; s2 = t[1+idt];
3779     for(m=0;m<nz;m++){
3780       idx   = 2*vi[m];
3781       x1    = t[idx]; x2 = t[1+idx];
3782       s1 -= v[0]*x1 + v[2]*x2;
3783       s2 -= v[1]*x1 + v[3]*x2;
3784       v += 4;
3785     }
3786     idc = 2*c[i];
3787     x[idc]   = t[idt]   = v[0]*s1 + v[2]*s2;
3788     x[1+idc] = t[1+idt] = v[1]*s1 + v[3]*s2;
3789   }
3790   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
3791   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
3792   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3793   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
3794   ierr = PetscLogFlops(2.0*4*(a->nz) - 2.0*A->cmap->n);CHKERRQ(ierr);
3795   PetscFunctionReturn(0);
3796 }
3797 
3798 
3799 /*
3800       Special case where the matrix was ILU(0) factored in the natural
3801    ordering. This eliminates the need for the column and row permutation.
3802 */
3803 #undef __FUNCT__
3804 #define __FUNCT__ "MatSolve_SeqBAIJ_2_NaturalOrdering"
3805 PetscErrorCode MatSolve_SeqBAIJ_2_NaturalOrdering(Mat A,Vec bb,Vec xx)
3806 {
3807   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ *)A->data;
3808   PetscInt          n=a->mbs,*ai=a->i,*aj=a->j;
3809   PetscErrorCode    ierr;
3810   PetscInt          *diag = a->diag;
3811   const MatScalar   *aa=a->a,*v;
3812   PetscScalar       *x,s1,s2,x1,x2;
3813   const PetscScalar *b;
3814   PetscInt          jdx,idt,idx,nz,*vi,i;
3815 
3816   PetscFunctionBegin;
3817   ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3818   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
3819 
3820   /* forward solve the lower triangular */
3821   idx    = 0;
3822   x[0]   = b[0]; x[1] = b[1];
3823   for (i=1; i<n; i++) {
3824     v     =  aa      + 4*ai[i];
3825     vi    =  aj      + ai[i];
3826     nz    =  diag[i] - ai[i];
3827     idx   +=  2;
3828     s1  =  b[idx];s2 = b[1+idx];
3829     while (nz--) {
3830       jdx   = 2*(*vi++);
3831       x1    = x[jdx];x2 = x[1+jdx];
3832       s1 -= v[0]*x1 + v[2]*x2;
3833       s2 -= v[1]*x1 + v[3]*x2;
3834       v    += 4;
3835     }
3836     x[idx]   = s1;
3837     x[1+idx] = s2;
3838   }
3839   /* backward solve the upper triangular */
3840   for (i=n-1; i>=0; i--){
3841     v    = aa + 4*diag[i] + 4;
3842     vi   = aj + diag[i] + 1;
3843     nz   = ai[i+1] - diag[i] - 1;
3844     idt  = 2*i;
3845     s1 = x[idt];  s2 = x[1+idt];
3846     while (nz--) {
3847       idx   = 2*(*vi++);
3848       x1    = x[idx];   x2 = x[1+idx];
3849       s1 -= v[0]*x1 + v[2]*x2;
3850       s2 -= v[1]*x1 + v[3]*x2;
3851       v    += 4;
3852     }
3853     v        = aa +  4*diag[i];
3854     x[idt]   = v[0]*s1 + v[2]*s2;
3855     x[1+idt] = v[1]*s1 + v[3]*s2;
3856   }
3857 
3858   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3859   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
3860   ierr = PetscLogFlops(2.0*4*(a->nz) - 2.0*A->cmap->n);CHKERRQ(ierr);
3861   PetscFunctionReturn(0);
3862 }
3863 
3864 #undef __FUNCT__
3865 #define __FUNCT__ "MatSolve_SeqBAIJ_2_NaturalOrdering_newdatastruct"
3866 PetscErrorCode MatSolve_SeqBAIJ_2_NaturalOrdering_newdatastruct(Mat A,Vec bb,Vec xx)
3867 {
3868     Mat_SeqBAIJ       *a = (Mat_SeqBAIJ *)A->data;
3869     PetscInt          i,k,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz,idx,idt;
3870     PetscErrorCode    ierr;
3871     PetscInt          jdx;
3872     const MatScalar   *aa=a->a,*v;
3873     PetscScalar       *x,s1,s2,x1,x2;
3874     const PetscScalar *b;
3875 
3876     PetscFunctionBegin;
3877     ierr = VecGetArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3878     ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
3879     /* forward solve the lower triangular */
3880     idx    = 0;
3881     x[0] = b[idx]; x[1] = b[1+idx];
3882     for (i=1; i<n; i++) {
3883         v   = aa + 4*ai[i];
3884        vi   = aj + ai[i];
3885        nz   = ai[i+1] - ai[i];
3886        idx  = 2*i;
3887        s1   = b[idx];s2 = b[1+idx];
3888       for(k=0;k<nz;k++){
3889          jdx   = 2*vi[k];
3890           x1    = x[jdx];x2 = x[1+jdx];
3891           s1   -= v[0]*x1 + v[2]*x2;
3892           s2   -= v[1]*x1 + v[3]*x2;
3893            v   +=  4;
3894         }
3895        x[idx]   = s1;
3896        x[1+idx] = s2;
3897     }
3898 
3899    /* backward solve the upper triangular */
3900   for (i=n-1; i>=0; i--){
3901      v   = aa + 4*ai[2*n-i];
3902      vi  = aj + ai[2*n-i];
3903      nz  = ai[2*n-i +1] - ai[2*n-i]-1;
3904      idt = 2*i;
3905      s1 = x[idt];  s2 = x[1+idt];
3906      for(k=0;k<nz;k++){
3907       idx   = 2*vi[k];
3908        x1    = x[idx];   x2 = x[1+idx];
3909        s1 -= v[0]*x1 + v[2]*x2;
3910        s2 -= v[1]*x1 + v[3]*x2;
3911          v    += 4;
3912     }
3913     /* x = inv_diagonal*x */
3914    x[idt]   = v[0]*s1 + v[2]*s2;
3915    x[1+idt] = v[1]*s1 + v[3]*s2;
3916   }
3917 
3918   ierr = VecRestoreArray(bb,(PetscScalar**)&b);CHKERRQ(ierr);
3919   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
3920   ierr = PetscLogFlops(2.0*4*(a->nz) - 2.0*A->cmap->n);CHKERRQ(ierr);
3921   PetscFunctionReturn(0);
3922 }
3923 
3924 #undef __FUNCT__
3925 #define __FUNCT__ "MatSolve_SeqBAIJ_1"
3926 PetscErrorCode MatSolve_SeqBAIJ_1(Mat A,Vec bb,Vec xx)
3927 {
3928   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ *)A->data;
3929   IS             iscol=a->col,isrow=a->row;
3930   PetscErrorCode ierr;
3931   PetscInt       i,n=a->mbs,*vi,*ai=a->i,*aj=a->j,nz;
3932   const PetscInt *r,*c,*diag = a->diag,*rout,*cout;
3933   MatScalar      *aa=a->a,*v;
3934   PetscScalar    *x,*b,s1,*t;
3935 
3936   PetscFunctionBegin;
3937   if (!n) PetscFunctionReturn(0);
3938 
3939   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
3940   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
3941   t  = a->solve_work;
3942 
3943   ierr = ISGetIndices(isrow,&rout);CHKERRQ(ierr); r = rout;
3944   ierr = ISGetIndices(iscol,&cout);CHKERRQ(ierr); c = cout + (n-1);
3945 
3946   /* forward solve the lower triangular */
3947   t[0] = b[*r++];
3948   for (i=1; i<n; i++) {
3949     v     = aa + ai[i];
3950     vi    = aj + ai[i];
3951     nz    = diag[i] - ai[i];
3952     s1  = b[*r++];
3953     while (nz--) {
3954       s1 -= (*v++)*t[*vi++];
3955     }
3956     t[i] = s1;
3957   }
3958   /* backward solve the upper triangular */
3959   for (i=n-1; i>=0; i--){
3960     v    = aa + diag[i] + 1;
3961     vi   = aj + diag[i] + 1;
3962     nz   = ai[i+1] - diag[i] - 1;
3963     s1 = t[i];
3964     while (nz--) {
3965       s1 -= (*v++)*t[*vi++];
3966     }
3967     x[*c--] = t[i] = aa[diag[i]]*s1;
3968   }
3969 
3970   ierr = ISRestoreIndices(isrow,&rout);CHKERRQ(ierr);
3971   ierr = ISRestoreIndices(iscol,&cout);CHKERRQ(ierr);
3972   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
3973   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
3974   ierr = PetscLogFlops(2.0*1*(a->nz) - A->cmap->n);CHKERRQ(ierr);
3975   PetscFunctionReturn(0);
3976 }
3977 /*
3978       Special case where the matrix was ILU(0) factored in the natural
3979    ordering. This eliminates the need for the column and row permutation.
3980 */
3981 #undef __FUNCT__
3982 #define __FUNCT__ "MatSolve_SeqBAIJ_1_NaturalOrdering"
3983 PetscErrorCode MatSolve_SeqBAIJ_1_NaturalOrdering(Mat A,Vec bb,Vec xx)
3984 {
3985   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ *)A->data;
3986   PetscInt       n=a->mbs,*ai=a->i,*aj=a->j;
3987   PetscErrorCode ierr;
3988   PetscInt       *diag = a->diag;
3989   MatScalar      *aa=a->a;
3990   PetscScalar    *x,*b;
3991   PetscScalar    s1,x1;
3992   MatScalar      *v;
3993   PetscInt       jdx,idt,idx,nz,*vi,i;
3994 
3995   PetscFunctionBegin;
3996   ierr = VecGetArray(bb,&b);CHKERRQ(ierr);
3997   ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
3998 
3999   /* forward solve the lower triangular */
4000   idx    = 0;
4001   x[0]   = b[0];
4002   for (i=1; i<n; i++) {
4003     v     =  aa      + ai[i];
4004     vi    =  aj      + ai[i];
4005     nz    =  diag[i] - ai[i];
4006     idx   +=  1;
4007     s1  =  b[idx];
4008     while (nz--) {
4009       jdx   = *vi++;
4010       x1    = x[jdx];
4011       s1 -= v[0]*x1;
4012       v    += 1;
4013     }
4014     x[idx]   = s1;
4015   }
4016   /* backward solve the upper triangular */
4017   for (i=n-1; i>=0; i--){
4018     v    = aa + diag[i] + 1;
4019     vi   = aj + diag[i] + 1;
4020     nz   = ai[i+1] - diag[i] - 1;
4021     idt  = i;
4022     s1 = x[idt];
4023     while (nz--) {
4024       idx   = *vi++;
4025       x1    = x[idx];
4026       s1 -= v[0]*x1;
4027       v    += 1;
4028     }
4029     v        = aa +  diag[i];
4030     x[idt]   = v[0]*s1;
4031   }
4032   ierr = VecRestoreArray(bb,&b);CHKERRQ(ierr);
4033   ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
4034   ierr = PetscLogFlops(2.0*(a->nz) - A->cmap->n);CHKERRQ(ierr);
4035   PetscFunctionReturn(0);
4036 }
4037 
4038 /* ----------------------------------------------------------------*/
4039 EXTERN PetscErrorCode MatDuplicateNoCreate_SeqBAIJ(Mat,Mat,MatDuplicateOption,PetscTruth);
4040 EXTERN PetscErrorCode MatSeqBAIJSetNumericFactorization(Mat,PetscTruth);
4041 
4042 extern PetscErrorCode MatSolve_SeqBAIJ_N_NaturalOrdering_newdatastruct(Mat,Vec,Vec);
4043 extern PetscErrorCode MatSolve_SeqBAIJ_N_newdatastruct(Mat,Vec,Vec);
4044 
4045 #undef __FUNCT__
4046 #define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_N_newdatastruct"
4047 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_N_newdatastruct(Mat B,Mat A,const MatFactorInfo *info)
4048 {
4049   Mat            C=B;
4050   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ *)C->data;
4051   IS             isrow = b->row,isicol = b->icol;
4052   PetscErrorCode ierr;
4053   const PetscInt *r,*ic,*ics;
4054   PetscInt       i,j,k,n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
4055   PetscInt       *ajtmp,*bjtmp,nz,nzL,row,*bdiag=b->diag,*pj;
4056   MatScalar      *rtmp,*pc,*mwork,*v,*pv,*aa=a->a;
4057   PetscInt       bs=A->rmap->bs,bs2 = a->bs2,*v_pivots,flg;
4058   MatScalar      *v_work;
4059 
4060   PetscFunctionBegin;
4061   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
4062   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
4063   ierr = PetscMalloc((bs2*n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
4064   ierr = PetscMemzero(rtmp,(bs2*n+1)*sizeof(MatScalar));CHKERRQ(ierr);
4065   ics  = ic;
4066 
4067   /* generate work space needed by dense LU factorization */
4068   ierr     = PetscMalloc(bs*sizeof(PetscInt) + (bs+bs2)*sizeof(MatScalar),&v_work);CHKERRQ(ierr);
4069   mwork    = v_work + bs;
4070   v_pivots = (PetscInt*)(mwork + bs2);
4071 
4072   for (i=0; i<n; i++){
4073     /* zero rtmp */
4074     /* L part */
4075     nz    = bi[i+1] - bi[i];
4076     bjtmp = bj + bi[i];
4077     for  (j=0; j<nz; j++){
4078       ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
4079     }
4080 
4081     /* U part */
4082     nz = bi[2*n-i+1] - bi[2*n-i];
4083     bjtmp = bj + bi[2*n-i];
4084     for  (j=0; j<nz; j++){
4085       ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
4086     }
4087 
4088     /* load in initial (unfactored row) */
4089     nz    = ai[r[i]+1] - ai[r[i]];
4090     ajtmp = aj + ai[r[i]];
4091     v     = aa + bs2*ai[r[i]];
4092     for (j=0; j<nz; j++) {
4093       ierr = PetscMemcpy(rtmp+bs2*ic[ajtmp[j]],v+bs2*j,bs2*sizeof(MatScalar));CHKERRQ(ierr);
4094     }
4095 
4096     /* elimination */
4097     bjtmp = bj + bi[i];
4098     nzL   = bi[i+1] - bi[i];
4099     for(k=0;k < nzL;k++) {
4100       row = bjtmp[k];
4101       pc = rtmp + bs2*row;
4102       for (flg=0,j=0; j<bs2; j++) { if (pc[j]!=0.0) { flg = 1; break; }}
4103       if (flg) {
4104         pv         = b->a + bs2*bdiag[row];
4105         Kernel_A_gets_A_times_B(bs,pc,pv,mwork); /* *pc = *pc * (*pv); */
4106         pj         = b->j + bi[2*n-row]; /* begining of U(row,:) */
4107         pv         = b->a + bs2*bi[2*n-row];
4108         nz         = bi[2*n-row+1] - bi[2*n-row] - 1; /* num of entries inU(row,:), excluding diag */
4109         for (j=0; j<nz; j++) {
4110           Kernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j);
4111         }
4112         ierr = PetscLogFlops(2*bs2*bs*(nz+1)-bs2);CHKERRQ(ierr); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
4113       }
4114     }
4115 
4116     /* finished row so stick it into b->a */
4117     /* L part */
4118     pv   = b->a + bs2*bi[i] ;
4119     pj   = b->j + bi[i] ;
4120     nz   = bi[i+1] - bi[i];
4121     for (j=0; j<nz; j++) {
4122       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
4123     }
4124 
4125     /* Mark diagonal and invert diagonal for simplier triangular solves */
4126     pv  = b->a + bs2*bdiag[i];
4127     pj  = b->j + bdiag[i];
4128     /* if (*pj != i)SETERRQ2(PETSC_ERR_SUP,"row %d != *pj %d",i,*pj); */
4129     ierr = PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));CHKERRQ(ierr);
4130     ierr = Kernel_A_gets_inverse_A(bs,pv,v_pivots,v_work);CHKERRQ(ierr);
4131 
4132     /* U part */
4133     pv = b->a + bs2*bi[2*n-i];
4134     pj = b->j + bi[2*n-i];
4135     nz = bi[2*n-i+1] - bi[2*n-i] - 1;
4136     for (j=0; j<nz; j++){
4137       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
4138     }
4139   }
4140 
4141   ierr = PetscFree(rtmp);CHKERRQ(ierr);
4142   ierr = PetscFree(v_work);CHKERRQ(ierr);
4143   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
4144   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
4145 
4146   C->assembled = PETSC_TRUE;
4147   ierr = PetscLogFlops(1.3333*bs*bs2*b->mbs);CHKERRQ(ierr); /* from inverting diagonal blocks */
4148   PetscFunctionReturn(0);
4149 }
4150 
4151 /*
4152    ilu(0) with natural ordering under new data structure.
4153    See MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct() for detailed description
4154    because this code is almost identical to MatILUFactorSymbolic_SeqAIJ_ilu0_newdatastruct().
4155 */
4156 #undef __FUNCT__
4157 #define __FUNCT__ "MatILUFactorSymbolic_SeqBAIJ_ilu0_newdatastruct"
4158 PetscErrorCode MatILUFactorSymbolic_SeqBAIJ_ilu0_newdatastruct(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
4159 {
4160 
4161   Mat_SeqBAIJ        *a = (Mat_SeqBAIJ*)A->data,*b;
4162   PetscErrorCode     ierr;
4163   PetscInt           n=a->mbs,*ai=a->i,*aj,*adiag=a->diag,bs2 = a->bs2;
4164   PetscInt           i,j,nz,*bi,*bj,*bdiag;
4165 
4166   PetscFunctionBegin;
4167   /* printf("MatILUFactorSymbolic_SeqBAIJ_ilu0_newdatastruct...\n"); */
4168   ierr = MatDuplicateNoCreate_SeqBAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_FALSE);CHKERRQ(ierr);
4169   b    = (Mat_SeqBAIJ*)(fact)->data;
4170 
4171   /* allocate matrix arrays for new data structure */
4172   ierr = PetscMalloc3(bs2*ai[n]+1,PetscScalar,&b->a,ai[n]+1,PetscInt,&b->j,2*n+2,PetscInt,&b->i);CHKERRQ(ierr);
4173   ierr = PetscLogObjectMemory(fact,ai[n]*(bs2*sizeof(PetscScalar)+sizeof(PetscInt))+(2*n+2)*sizeof(PetscInt));CHKERRQ(ierr);
4174   b->singlemalloc = PETSC_TRUE;
4175   if (!b->diag){
4176     ierr = PetscMalloc((n+1)*sizeof(PetscInt),&b->diag);CHKERRQ(ierr);
4177   }
4178   bdiag = b->diag;
4179 
4180   if (n > 0) {
4181     ierr = PetscMemzero(b->a,bs2*ai[n]*sizeof(MatScalar));CHKERRQ(ierr);
4182   }
4183 
4184   /* set bi and bj with new data structure */
4185   bi = b->i;
4186   bj = b->j;
4187 
4188   /* L part */
4189   bi[0] = 0;
4190   for (i=0; i<n; i++){
4191     nz = adiag[i] - ai[i];
4192     bi[i+1] = bi[i] + nz;
4193     aj = a->j + ai[i];
4194     for (j=0; j<nz; j++){
4195       *bj = aj[j]; bj++;
4196     }
4197   }
4198 
4199   /* U part */
4200   bi[n+1] = bi[n];
4201   for (i=n-1; i>=0; i--){
4202     nz = ai[i+1] - adiag[i] - 1;
4203     bi[2*n-i+1] = bi[2*n-i] + nz + 1;
4204     aj = a->j + adiag[i] + 1;
4205     for (j=0; j<nz; j++){
4206       *bj = aj[j]; bj++;
4207     }
4208     /* diag[i] */
4209     *bj = i; bj++;
4210     bdiag[i] = bi[2*n-i+1]-1;
4211   }
4212   PetscFunctionReturn(0);
4213 }
4214 
4215 #undef __FUNCT__
4216 #define __FUNCT__ "MatILUFactorSymbolic_SeqBAIJ_newdatastruct"
4217 PetscErrorCode MatILUFactorSymbolic_SeqBAIJ_newdatastruct(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
4218 {
4219   Mat_SeqBAIJ        *a = (Mat_SeqBAIJ*)A->data,*b;
4220   IS                 isicol;
4221   PetscErrorCode     ierr;
4222   const PetscInt     *r,*ic;
4223   PetscInt           n=a->mbs,*ai=a->i,*aj=a->j,d;
4224   PetscInt           *bi,*cols,nnz,*cols_lvl;
4225   PetscInt           *bdiag,prow,fm,nzbd,reallocs=0,dcount=0;
4226   PetscInt           i,levels,diagonal_fill;
4227   PetscTruth         col_identity,row_identity,both_identity;
4228   PetscReal          f;
4229   PetscInt           nlnk,*lnk,*lnk_lvl=PETSC_NULL;
4230   PetscBT            lnkbt;
4231   PetscInt           nzi,*bj,**bj_ptr,**bjlvl_ptr;
4232   PetscFreeSpaceList free_space=PETSC_NULL,current_space=PETSC_NULL;
4233   PetscFreeSpaceList free_space_lvl=PETSC_NULL,current_space_lvl=PETSC_NULL;
4234   PetscTruth         missing;
4235   PetscInt           bs=A->rmap->bs,bs2=a->bs2;
4236 
4237   PetscFunctionBegin;
4238   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);
4239   ierr = MatMissingDiagonal(A,&missing,&d);CHKERRQ(ierr);
4240   if (missing) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix is missing diagonal entry %D",d);
4241 
4242   f             = info->fill;
4243   levels        = (PetscInt)info->levels;
4244   diagonal_fill = (PetscInt)info->diagonal_fill;
4245   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
4246 
4247   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
4248   ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr);
4249   both_identity = (PetscTruth) (row_identity && col_identity);
4250 
4251   if (!levels && both_identity) {
4252     /* special case: ilu(0) with natural ordering */
4253     ierr = MatILUFactorSymbolic_SeqBAIJ_ilu0_newdatastruct(fact,A,isrow,iscol,info);CHKERRQ(ierr);
4254     (fact)->ops->lufactornumeric = MatLUFactorNumeric_SeqBAIJ_N_newdatastruct;
4255     /* set MatSolve routines */
4256     switch (bs){
4257     case 2:
4258       fact->ops->solve = MatSolve_SeqBAIJ_2_NaturalOrdering_newdatastruct;
4259       break;
4260     case 3:
4261       fact->ops->solve = MatSolve_SeqBAIJ_3_NaturalOrdering_newdatastruct;
4262       break;
4263     case 4:
4264       fact->ops->solve = MatSolve_SeqBAIJ_4_NaturalOrdering_newdatastruct;
4265       break;
4266     case 5:
4267       fact->ops->solve = MatSolve_SeqBAIJ_5_NaturalOrdering_newdatastruct;
4268       break;
4269     case 6:
4270       fact->ops->solve = MatSolve_SeqBAIJ_6_NaturalOrdering_newdatastruct;
4271       break;
4272     case 7:
4273       fact->ops->solve = MatSolve_SeqBAIJ_7_NaturalOrdering_newdatastruct;
4274       break;
4275     default:
4276       fact->ops->solve = MatSolve_SeqBAIJ_N_NaturalOrdering_newdatastruct;
4277       break;
4278     }
4279 
4280     fact->factor = MAT_FACTOR_ILU;
4281     (fact)->info.factor_mallocs    = 0;
4282     (fact)->info.fill_ratio_given  = info->fill;
4283     (fact)->info.fill_ratio_needed = 1.0;
4284     b                = (Mat_SeqBAIJ*)(fact)->data;
4285     b->row           = isrow;
4286     b->col           = iscol;
4287     b->icol          = isicol;
4288     ierr             = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
4289     ierr             = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
4290     b->pivotinblocks = (info->pivotinblocks) ? PETSC_TRUE : PETSC_FALSE;
4291     ierr = PetscMalloc((n+1)*bs*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
4292     PetscFunctionReturn(0);
4293   }
4294 
4295   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
4296   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
4297 
4298   /* get new row pointers */
4299   ierr = PetscMalloc((2*n+2)*sizeof(PetscInt),&bi);CHKERRQ(ierr);
4300   bi[0] = 0;
4301   /* bdiag is location of diagonal in factor */
4302   ierr = PetscMalloc((n+1)*sizeof(PetscInt),&bdiag);CHKERRQ(ierr);
4303   bdiag[0]  = 0;
4304 
4305   ierr = PetscMalloc((2*n+1)*sizeof(PetscInt**),&bj_ptr);CHKERRQ(ierr);
4306   bjlvl_ptr = (PetscInt**)(bj_ptr + n);
4307 
4308   /* create a linked list for storing column indices of the active row */
4309   nlnk = n + 1;
4310   ierr = PetscIncompleteLLCreate(n,n,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
4311 
4312   /* initial FreeSpace size is f*(ai[n]+1) */
4313   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space);CHKERRQ(ierr);
4314   current_space = free_space;
4315   ierr = PetscFreeSpaceGet((PetscInt)(f*(ai[n]+1)),&free_space_lvl);CHKERRQ(ierr);
4316   current_space_lvl = free_space_lvl;
4317 
4318   for (i=0; i<n; i++) {
4319     nzi = 0;
4320     /* copy current row into linked list */
4321     nnz  = ai[r[i]+1] - ai[r[i]];
4322     if (!nnz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[i],i);
4323     cols = aj + ai[r[i]];
4324     lnk[i] = -1; /* marker to indicate if diagonal exists */
4325     ierr = PetscIncompleteLLInit(nnz,cols,n,ic,nlnk,lnk,lnk_lvl,lnkbt);CHKERRQ(ierr);
4326     nzi += nlnk;
4327 
4328     /* make sure diagonal entry is included */
4329     if (diagonal_fill && lnk[i] == -1) {
4330       fm = n;
4331       while (lnk[fm] < i) fm = lnk[fm];
4332       lnk[i]     = lnk[fm]; /* insert diagonal into linked list */
4333       lnk[fm]    = i;
4334       lnk_lvl[i] = 0;
4335       nzi++; dcount++;
4336     }
4337 
4338     /* add pivot rows into the active row */
4339     nzbd = 0;
4340     prow = lnk[n];
4341     while (prow < i) {
4342       nnz      = bdiag[prow];
4343       cols     = bj_ptr[prow] + nnz + 1;
4344       cols_lvl = bjlvl_ptr[prow] + nnz + 1;
4345       nnz      = bi[prow+1] - bi[prow] - nnz - 1;
4346       ierr = PetscILULLAddSorted(nnz,cols,levels,cols_lvl,prow,nlnk,lnk,lnk_lvl,lnkbt,prow);CHKERRQ(ierr);
4347       nzi += nlnk;
4348       prow = lnk[prow];
4349       nzbd++;
4350     }
4351     bdiag[i] = nzbd;
4352     bi[i+1]  = bi[i] + nzi;
4353 
4354     /* if free space is not available, make more free space */
4355     if (current_space->local_remaining<nzi) {
4356       nnz = 2*nzi*(n - i); /* estimated and max additional space needed */
4357       ierr = PetscFreeSpaceGet(nnz,&current_space);CHKERRQ(ierr);
4358       ierr = PetscFreeSpaceGet(nnz,&current_space_lvl);CHKERRQ(ierr);
4359       reallocs++;
4360     }
4361 
4362     /* copy data into free_space and free_space_lvl, then initialize lnk */
4363     ierr = PetscIncompleteLLClean(n,n,nzi,lnk,lnk_lvl,current_space->array,current_space_lvl->array,lnkbt);CHKERRQ(ierr);
4364     bj_ptr[i]    = current_space->array;
4365     bjlvl_ptr[i] = current_space_lvl->array;
4366 
4367     /* make sure the active row i has diagonal entry */
4368     if (*(bj_ptr[i]+bdiag[i]) != i) {
4369       SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\
4370     try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",i);
4371     }
4372 
4373     current_space->array           += nzi;
4374     current_space->local_used      += nzi;
4375     current_space->local_remaining -= nzi;
4376     current_space_lvl->array           += nzi;
4377     current_space_lvl->local_used      += nzi;
4378     current_space_lvl->local_remaining -= nzi;
4379   }
4380 
4381   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
4382   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
4383 
4384   /* destroy list of free space and other temporary arrays */
4385   ierr = PetscMalloc((bi[n]+1)*sizeof(PetscInt),&bj);CHKERRQ(ierr);
4386 
4387   /* copy free_space into bj and free free_space; set bi, bj, bdiag in new datastructure; */
4388   ierr = PetscFreeSpaceContiguous_LU(&free_space,bj,n,bi,bdiag);CHKERRQ(ierr);
4389 
4390   ierr = PetscIncompleteLLDestroy(lnk,lnkbt);CHKERRQ(ierr);
4391   ierr = PetscFreeSpaceDestroy(free_space_lvl);CHKERRQ(ierr);
4392   ierr = PetscFree(bj_ptr);CHKERRQ(ierr);
4393 
4394 #if defined(PETSC_USE_INFO)
4395   {
4396     PetscReal af = ((PetscReal)bi[n])/((PetscReal)ai[n]);
4397     ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocs,f,af);CHKERRQ(ierr);
4398     ierr = PetscInfo1(A,"Run with -[sub_]pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
4399     ierr = PetscInfo1(A,"PCFactorSetFill([sub]pc,%G);\n",af);CHKERRQ(ierr);
4400     ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr);
4401     if (diagonal_fill) {
4402       ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals",dcount);CHKERRQ(ierr);
4403     }
4404   }
4405 #endif
4406 
4407   /* put together the new matrix */
4408   ierr = MatSeqBAIJSetPreallocation_SeqBAIJ(fact,bs,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
4409   ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr);
4410   b = (Mat_SeqBAIJ*)(fact)->data;
4411   b->free_a       = PETSC_TRUE;
4412   b->free_ij      = PETSC_TRUE;
4413   b->singlemalloc = PETSC_FALSE;
4414   ierr = PetscMalloc( (bs2*bi[2*n+1] )*sizeof(MatScalar),&b->a);CHKERRQ(ierr);
4415   b->j          = bj;
4416   b->i          = bi;
4417   b->diag       = bdiag;
4418   b->free_diag  = PETSC_TRUE;
4419   b->ilen       = 0;
4420   b->imax       = 0;
4421   b->row        = isrow;
4422   b->col        = iscol;
4423   ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
4424   ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
4425   b->icol       = isicol;
4426   ierr = PetscMalloc((bs*n+bs)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
4427   /* In b structure:  Free imax, ilen, old a, old j.
4428      Allocate bdiag, solve_work, new a, new j */
4429   ierr = PetscLogObjectMemory(fact,bi[2*n+1] * (sizeof(PetscInt)+bs2*sizeof(PetscScalar)));CHKERRQ(ierr);
4430   b->maxnz = b->nz = bi[2*n+1] ;
4431   (fact)->info.factor_mallocs    = reallocs;
4432   (fact)->info.fill_ratio_given  = f;
4433   (fact)->info.fill_ratio_needed = ((PetscReal)bi[2*n+1])/((PetscReal)ai[n]);
4434   (fact)->ops->lufactornumeric   = MatLUFactorNumeric_SeqBAIJ_N_newdatastruct;
4435   /* set MatSolve routines */
4436   if (both_identity){
4437     switch (bs){
4438     case 2:
4439       fact->ops->solve = MatSolve_SeqBAIJ_2_NaturalOrdering_newdatastruct;
4440       break;
4441     case 3:
4442       fact->ops->solve = MatSolve_SeqBAIJ_3_NaturalOrdering_newdatastruct;
4443       break;
4444     case 4:
4445       fact->ops->solve = MatSolve_SeqBAIJ_4_NaturalOrdering_newdatastruct;
4446       break;
4447     case 5:
4448       fact->ops->solve = MatSolve_SeqBAIJ_5_NaturalOrdering_newdatastruct;
4449       break;
4450     case 6:
4451       fact->ops->solve = MatSolve_SeqBAIJ_6_NaturalOrdering_newdatastruct;
4452       break;
4453     case 7:
4454       fact->ops->solve = MatSolve_SeqBAIJ_7_NaturalOrdering_newdatastruct;
4455       break;
4456     default:
4457       fact->ops->solve = MatSolve_SeqBAIJ_N_NaturalOrdering_newdatastruct;
4458       break;
4459     }
4460   } else {
4461     switch (bs){
4462     case 2:
4463       fact->ops->solve = MatSolve_SeqBAIJ_2_newdatastruct;
4464       break;
4465     case 3:
4466       fact->ops->solve = MatSolve_SeqBAIJ_3_newdatastruct;
4467       break;
4468     case 4:
4469       fact->ops->solve = MatSolve_SeqBAIJ_4_newdatastruct;
4470       break;
4471     case 5:
4472       fact->ops->solve = MatSolve_SeqBAIJ_5_newdatastruct;
4473       break;
4474     case 6:
4475       fact->ops->solve = MatSolve_SeqBAIJ_6_newdatastruct;
4476       break;
4477     case 7:
4478       fact->ops->solve = MatSolve_SeqBAIJ_7_newdatastruct;
4479       break;
4480     default:
4481       fact->ops->solve = MatSolve_SeqBAIJ_N_newdatastruct;
4482       break;
4483     }
4484   }
4485   PetscFunctionReturn(0);
4486 }
4487 
4488 /*
4489      This code is virtually identical to MatILUFactorSymbolic_SeqAIJ
4490    except that the data structure of Mat_SeqAIJ is slightly different.
4491    Not a good example of code reuse.
4492 */
4493 #undef __FUNCT__
4494 #define __FUNCT__ "MatILUFactorSymbolic_SeqBAIJ"
4495 PetscErrorCode MatILUFactorSymbolic_SeqBAIJ(Mat fact,Mat A,IS isrow,IS iscol,const MatFactorInfo *info)
4496 {
4497   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ*)A->data,*b;
4498   IS             isicol;
4499   PetscErrorCode ierr;
4500   const PetscInt *r,*ic,*ai = a->i,*aj = a->j,*xi;
4501   PetscInt       prow,n = a->mbs,*ainew,*ajnew,jmax,*fill,nz,*im,*ajfill,*flev,*xitmp;
4502   PetscInt       *dloc,idx,row,m,fm,nzf,nzi,reallocate = 0,dcount = 0;
4503   PetscInt       incrlev,nnz,i,bs = A->rmap->bs,bs2 = a->bs2,levels,diagonal_fill,dd;
4504   PetscTruth     col_identity,row_identity,both_identity,flg;
4505   PetscReal      f;
4506   PetscTruth     newdatastruct=PETSC_FALSE;
4507 
4508   PetscFunctionBegin;
4509   ierr = PetscOptionsGetTruth(PETSC_NULL,"-ilu_new",&newdatastruct,PETSC_NULL);CHKERRQ(ierr);
4510   if (newdatastruct){
4511     ierr = MatILUFactorSymbolic_SeqBAIJ_newdatastruct(fact,A,isrow,iscol,info);CHKERRQ(ierr);
4512     PetscFunctionReturn(0);
4513   }
4514 
4515   ierr = MatMissingDiagonal_SeqBAIJ(A,&flg,&dd);CHKERRQ(ierr);
4516   if (flg) SETERRQ1(PETSC_ERR_ARG_WRONGSTATE,"Matrix A is missing diagonal entry in row %D",dd);
4517 
4518   f             = info->fill;
4519   levels        = (PetscInt)info->levels;
4520   diagonal_fill = (PetscInt)info->diagonal_fill;
4521   ierr = ISInvertPermutation(iscol,PETSC_DECIDE,&isicol);CHKERRQ(ierr);
4522 
4523   ierr = ISIdentity(isrow,&row_identity);CHKERRQ(ierr);
4524   ierr = ISIdentity(iscol,&col_identity);CHKERRQ(ierr);
4525   both_identity = (PetscTruth) (row_identity && col_identity);
4526 
4527   if (!levels && both_identity) {  /* special case copy the nonzero structure */
4528     ierr = MatDuplicateNoCreate_SeqBAIJ(fact,A,MAT_DO_NOT_COPY_VALUES,PETSC_TRUE);CHKERRQ(ierr);
4529     ierr = MatSeqBAIJSetNumericFactorization(fact,both_identity);CHKERRQ(ierr);
4530 
4531     fact->factor = MAT_FACTOR_ILU;
4532     b            = (Mat_SeqBAIJ*)(fact)->data;
4533     b->row       = isrow;
4534     b->col       = iscol;
4535     ierr         = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
4536     ierr         = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
4537     b->icol      = isicol;
4538     b->pivotinblocks = (info->pivotinblocks) ? PETSC_TRUE : PETSC_FALSE;
4539     ierr         = PetscMalloc((n+1)*bs*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
4540     PetscFunctionReturn(0);
4541   }
4542 
4543   /* general case perform the symbolic factorization */
4544     ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
4545     ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
4546 
4547     /* get new row pointers */
4548     ierr = PetscMalloc((n+1)*sizeof(PetscInt),&ainew);CHKERRQ(ierr);
4549     ainew[0] = 0;
4550     /* don't know how many column pointers are needed so estimate */
4551     jmax = (PetscInt)(f*ai[n] + 1);
4552     ierr = PetscMalloc((jmax)*sizeof(PetscInt),&ajnew);CHKERRQ(ierr);
4553     /* ajfill is level of fill for each fill entry */
4554     ierr = PetscMalloc((jmax)*sizeof(PetscInt),&ajfill);CHKERRQ(ierr);
4555     /* fill is a linked list of nonzeros in active row */
4556     ierr = PetscMalloc((n+1)*sizeof(PetscInt),&fill);CHKERRQ(ierr);
4557     /* im is level for each filled value */
4558     ierr = PetscMalloc((n+1)*sizeof(PetscInt),&im);CHKERRQ(ierr);
4559     /* dloc is location of diagonal in factor */
4560     ierr = PetscMalloc((n+1)*sizeof(PetscInt),&dloc);CHKERRQ(ierr);
4561     dloc[0]  = 0;
4562     for (prow=0; prow<n; prow++) {
4563 
4564       /* copy prow into linked list */
4565       nzf        = nz  = ai[r[prow]+1] - ai[r[prow]];
4566       if (!nz) SETERRQ2(PETSC_ERR_MAT_LU_ZRPVT,"Empty row in matrix: row in original ordering %D in permuted ordering %D",r[prow],prow);
4567       xi         = aj + ai[r[prow]];
4568       fill[n]    = n;
4569       fill[prow] = -1; /* marker for diagonal entry */
4570       while (nz--) {
4571 	fm  = n;
4572 	idx = ic[*xi++];
4573 	do {
4574 	  m  = fm;
4575 	  fm = fill[m];
4576 	} while (fm < idx);
4577 	fill[m]   = idx;
4578 	fill[idx] = fm;
4579 	im[idx]   = 0;
4580       }
4581 
4582       /* make sure diagonal entry is included */
4583       if (diagonal_fill && fill[prow] == -1) {
4584 	fm = n;
4585 	while (fill[fm] < prow) fm = fill[fm];
4586 	fill[prow] = fill[fm];  /* insert diagonal into linked list */
4587 	fill[fm]   = prow;
4588 	im[prow]   = 0;
4589 	nzf++;
4590 	dcount++;
4591       }
4592 
4593       nzi = 0;
4594       row = fill[n];
4595       while (row < prow) {
4596 	incrlev = im[row] + 1;
4597 	nz      = dloc[row];
4598 	xi      = ajnew  + ainew[row] + nz + 1;
4599 	flev    = ajfill + ainew[row] + nz + 1;
4600 	nnz     = ainew[row+1] - ainew[row] - nz - 1;
4601 	fm      = row;
4602 	while (nnz-- > 0) {
4603 	  idx = *xi++;
4604 	  if (*flev + incrlev > levels) {
4605 	    flev++;
4606 	    continue;
4607 	  }
4608 	  do {
4609 	    m  = fm;
4610 	    fm = fill[m];
4611 	  } while (fm < idx);
4612 	  if (fm != idx) {
4613 	    im[idx]   = *flev + incrlev;
4614 	    fill[m]   = idx;
4615 	    fill[idx] = fm;
4616 	    fm        = idx;
4617 	    nzf++;
4618 	  } else {
4619 	    if (im[idx] > *flev + incrlev) im[idx] = *flev+incrlev;
4620 	  }
4621 	  flev++;
4622 	}
4623 	row = fill[row];
4624 	nzi++;
4625       }
4626       /* copy new filled row into permanent storage */
4627       ainew[prow+1] = ainew[prow] + nzf;
4628       if (ainew[prow+1] > jmax) {
4629 
4630 	/* estimate how much additional space we will need */
4631 	/* use the strategy suggested by David Hysom <hysom@perch-t.icase.edu> */
4632 	/* just double the memory each time */
4633 	PetscInt maxadd = jmax;
4634 	/* maxadd = (int)(((f*ai[n]+1)*(n-prow+5))/n); */
4635 	if (maxadd < nzf) maxadd = (n-prow)*(nzf+1);
4636 	jmax += maxadd;
4637 
4638 	/* allocate a longer ajnew and ajfill */
4639 	ierr = PetscMalloc(jmax*sizeof(PetscInt),&xitmp);CHKERRQ(ierr);
4640 	ierr = PetscMemcpy(xitmp,ajnew,ainew[prow]*sizeof(PetscInt));CHKERRQ(ierr);
4641 	ierr = PetscFree(ajnew);CHKERRQ(ierr);
4642 	ajnew = xitmp;
4643 	ierr = PetscMalloc(jmax*sizeof(PetscInt),&xitmp);CHKERRQ(ierr);
4644 	ierr = PetscMemcpy(xitmp,ajfill,ainew[prow]*sizeof(PetscInt));CHKERRQ(ierr);
4645 	ierr = PetscFree(ajfill);CHKERRQ(ierr);
4646 	ajfill = xitmp;
4647 	reallocate++; /* count how many reallocations are needed */
4648       }
4649       xitmp       = ajnew + ainew[prow];
4650       flev        = ajfill + ainew[prow];
4651       dloc[prow]  = nzi;
4652       fm          = fill[n];
4653       while (nzf--) {
4654 	*xitmp++ = fm;
4655 	*flev++ = im[fm];
4656 	fm      = fill[fm];
4657       }
4658       /* make sure row has diagonal entry */
4659       if (ajnew[ainew[prow]+dloc[prow]] != prow) {
4660 	SETERRQ1(PETSC_ERR_MAT_LU_ZRPVT,"Row %D has missing diagonal in factored matrix\n\
4661     try running with -pc_factor_nonzeros_along_diagonal or -pc_factor_diagonal_fill",prow);
4662       }
4663     }
4664     ierr = PetscFree(ajfill);CHKERRQ(ierr);
4665     ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
4666     ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
4667     ierr = PetscFree(fill);CHKERRQ(ierr);
4668     ierr = PetscFree(im);CHKERRQ(ierr);
4669 
4670 #if defined(PETSC_USE_INFO)
4671     {
4672       PetscReal af = ((PetscReal)ainew[n])/((PetscReal)ai[n]);
4673       ierr = PetscInfo3(A,"Reallocs %D Fill ratio:given %G needed %G\n",reallocate,f,af);CHKERRQ(ierr);
4674       ierr = PetscInfo1(A,"Run with -pc_factor_fill %G or use \n",af);CHKERRQ(ierr);
4675       ierr = PetscInfo1(A,"PCFactorSetFill(pc,%G);\n",af);CHKERRQ(ierr);
4676       ierr = PetscInfo(A,"for best performance.\n");CHKERRQ(ierr);
4677       if (diagonal_fill) {
4678 	ierr = PetscInfo1(A,"Detected and replaced %D missing diagonals\n",dcount);CHKERRQ(ierr);
4679       }
4680     }
4681 #endif
4682 
4683     /* put together the new matrix */
4684     ierr = MatSeqBAIJSetPreallocation_SeqBAIJ(fact,bs,MAT_SKIP_ALLOCATION,PETSC_NULL);CHKERRQ(ierr);
4685     ierr = PetscLogObjectParent(fact,isicol);CHKERRQ(ierr);
4686     b    = (Mat_SeqBAIJ*)(fact)->data;
4687     b->free_a       = PETSC_TRUE;
4688     b->free_ij      = PETSC_TRUE;
4689     b->singlemalloc = PETSC_FALSE;
4690     ierr = PetscMalloc(bs2*ainew[n]*sizeof(MatScalar),&b->a);CHKERRQ(ierr);
4691     b->j          = ajnew;
4692     b->i          = ainew;
4693     for (i=0; i<n; i++) dloc[i] += ainew[i];
4694     b->diag       = dloc;
4695     b->free_diag  = PETSC_TRUE;
4696     b->ilen       = 0;
4697     b->imax       = 0;
4698     b->row        = isrow;
4699     b->col        = iscol;
4700     b->pivotinblocks = (info->pivotinblocks) ? PETSC_TRUE : PETSC_FALSE;
4701     ierr          = PetscObjectReference((PetscObject)isrow);CHKERRQ(ierr);
4702     ierr          = PetscObjectReference((PetscObject)iscol);CHKERRQ(ierr);
4703     b->icol       = isicol;
4704     ierr = PetscMalloc((bs*n+bs)*sizeof(PetscScalar),&b->solve_work);CHKERRQ(ierr);
4705     /* In b structure:  Free imax, ilen, old a, old j.
4706        Allocate dloc, solve_work, new a, new j */
4707     ierr = PetscLogObjectMemory(fact,(ainew[n]-n)*(sizeof(PetscInt))+bs2*ainew[n]*sizeof(PetscScalar));CHKERRQ(ierr);
4708     b->maxnz          = b->nz = ainew[n];
4709 
4710     (fact)->info.factor_mallocs    = reallocate;
4711     (fact)->info.fill_ratio_given  = f;
4712     (fact)->info.fill_ratio_needed = ((PetscReal)ainew[n])/((PetscReal)ai[prow]);
4713 
4714   ierr = MatSeqBAIJSetNumericFactorization(fact,both_identity);CHKERRQ(ierr);
4715   PetscFunctionReturn(0);
4716 }
4717 
4718 #undef __FUNCT__
4719 #define __FUNCT__ "MatSetUnfactored_SeqBAIJ_4_NaturalOrdering_SSE"
4720 PetscErrorCode MatSetUnfactored_SeqBAIJ_4_NaturalOrdering_SSE(Mat A)
4721 {
4722   /* Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data; */
4723   /* int i,*AJ=a->j,nz=a->nz; */
4724   PetscFunctionBegin;
4725   /* Undo Column scaling */
4726 /*    while (nz--) { */
4727 /*      AJ[i] = AJ[i]/4; */
4728 /*    } */
4729   /* This should really invoke a push/pop logic, but we don't have that yet. */
4730   A->ops->setunfactored = PETSC_NULL;
4731   PetscFunctionReturn(0);
4732 }
4733 
4734 #undef __FUNCT__
4735 #define __FUNCT__ "MatSetUnfactored_SeqBAIJ_4_NaturalOrdering_SSE_usj"
4736 PetscErrorCode MatSetUnfactored_SeqBAIJ_4_NaturalOrdering_SSE_usj(Mat A)
4737 {
4738   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ *)A->data;
4739   PetscInt       *AJ=a->j,nz=a->nz;
4740   unsigned short *aj=(unsigned short *)AJ;
4741   PetscFunctionBegin;
4742   /* Is this really necessary? */
4743   while (nz--) {
4744     AJ[nz] = (int)((unsigned int)aj[nz]); /* First extend, then convert to signed. */
4745   }
4746   A->ops->setunfactored = PETSC_NULL;
4747   PetscFunctionReturn(0);
4748 }
4749 
4750 
4751