xref: /petsc/src/mat/impls/baij/seq/baijfact13.c (revision eeffb40d691afbdd57a8091619e7ddd44ac5fdca)
1 #define PETSCMAT_DLL
2 
3 /*
4     Factorization code for BAIJ format.
5 */
6 #include "../src/mat/impls/baij/seq/baij.h"
7 #include "../src/mat/blockinvert.h"
8 
9 /*
10       Version for when blocks are 3 by 3
11 */
12 #undef __FUNCT__
13 #define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_3"
14 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_3(Mat C,Mat A,const MatFactorInfo *info)
15 {
16   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
17   IS             isrow = b->row,isicol = b->icol;
18   PetscErrorCode ierr;
19   const PetscInt *r,*ic;
20   PetscInt       i,j,n = a->mbs,*bi = b->i,*bj = b->j;
21   PetscInt       *ajtmpold,*ajtmp,nz,row,*ai=a->i,*aj=a->j;
22   PetscInt       *diag_offset = b->diag,idx,*pj;
23   MatScalar      *pv,*v,*rtmp,*pc,*w,*x;
24   MatScalar      p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
25   MatScalar      p5,p6,p7,p8,p9,x5,x6,x7,x8,x9;
26   MatScalar      *ba = b->a,*aa = a->a;
27   PetscReal      shift = info->shiftinblocks;
28 
29   PetscFunctionBegin;
30   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
31   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
32   ierr = PetscMalloc(9*(n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
33 
34   for (i=0; i<n; i++) {
35     nz    = bi[i+1] - bi[i];
36     ajtmp = bj + bi[i];
37     for  (j=0; j<nz; j++) {
38       x = rtmp + 9*ajtmp[j];
39       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = 0.0;
40     }
41     /* load in initial (unfactored row) */
42     idx      = r[i];
43     nz       = ai[idx+1] - ai[idx];
44     ajtmpold = aj + ai[idx];
45     v        = aa + 9*ai[idx];
46     for (j=0; j<nz; j++) {
47       x    = rtmp + 9*ic[ajtmpold[j]];
48       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
49       x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
50       v    += 9;
51     }
52     row = *ajtmp++;
53     while (row < i) {
54       pc = rtmp + 9*row;
55       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
56       p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
57       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
58           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0) {
59         pv = ba + 9*diag_offset[row];
60         pj = bj + diag_offset[row] + 1;
61         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
62         x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
63         pc[0] = m1 = p1*x1 + p4*x2 + p7*x3;
64         pc[1] = m2 = p2*x1 + p5*x2 + p8*x3;
65         pc[2] = m3 = p3*x1 + p6*x2 + p9*x3;
66 
67         pc[3] = m4 = p1*x4 + p4*x5 + p7*x6;
68         pc[4] = m5 = p2*x4 + p5*x5 + p8*x6;
69         pc[5] = m6 = p3*x4 + p6*x5 + p9*x6;
70 
71         pc[6] = m7 = p1*x7 + p4*x8 + p7*x9;
72         pc[7] = m8 = p2*x7 + p5*x8 + p8*x9;
73         pc[8] = m9 = p3*x7 + p6*x8 + p9*x9;
74         nz = bi[row+1] - diag_offset[row] - 1;
75         pv += 9;
76         for (j=0; j<nz; j++) {
77           x1   = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
78           x5   = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
79           x    = rtmp + 9*pj[j];
80           x[0] -= m1*x1 + m4*x2 + m7*x3;
81           x[1] -= m2*x1 + m5*x2 + m8*x3;
82           x[2] -= m3*x1 + m6*x2 + m9*x3;
83 
84           x[3] -= m1*x4 + m4*x5 + m7*x6;
85           x[4] -= m2*x4 + m5*x5 + m8*x6;
86           x[5] -= m3*x4 + m6*x5 + m9*x6;
87 
88           x[6] -= m1*x7 + m4*x8 + m7*x9;
89           x[7] -= m2*x7 + m5*x8 + m8*x9;
90           x[8] -= m3*x7 + m6*x8 + m9*x9;
91           pv   += 9;
92         }
93         ierr = PetscLogFlops(54.0*nz+36.0);CHKERRQ(ierr);
94       }
95       row = *ajtmp++;
96     }
97     /* finished row so stick it into b->a */
98     pv = ba + 9*bi[i];
99     pj = bj + bi[i];
100     nz = bi[i+1] - bi[i];
101     for (j=0; j<nz; j++) {
102       x     = rtmp + 9*pj[j];
103       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
104       pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
105       pv   += 9;
106     }
107     /* invert diagonal block */
108     w = ba + 9*diag_offset[i];
109     ierr = Kernel_A_gets_inverse_A_3(w,shift);CHKERRQ(ierr);
110   }
111 
112   ierr = PetscFree(rtmp);CHKERRQ(ierr);
113   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
114   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
115   C->ops->solve          = MatSolve_SeqBAIJ_3;
116   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_3;
117   C->assembled = PETSC_TRUE;
118   ierr = PetscLogFlops(1.3333*27*b->mbs);CHKERRQ(ierr); /* from inverting diagonal blocks */
119   PetscFunctionReturn(0);
120 }
121 
122 /* MatLUFactorNumeric_SeqBAIJ_3_newdatastruct -
123      copied from MatLUFactorNumeric_SeqBAIJ_N_newdatastruct() and manually re-implemented
124        Kernel_A_gets_A_times_B()
125        Kernel_A_gets_A_minus_B_times_C()
126        Kernel_A_gets_inverse_A()
127 */
128 #undef __FUNCT__
129 #define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_3_newdatastruct"
130 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_3_newdatastruct(Mat B,Mat A,const MatFactorInfo *info)
131 {
132   Mat            C=B;
133   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ *)C->data;
134   IS             isrow = b->row,isicol = b->icol;
135   PetscErrorCode ierr;
136   const PetscInt *r,*ic,*ics;
137   PetscInt       i,j,k,n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
138   PetscInt       *ajtmp,*bjtmp,nz,nzL,row,*bdiag=b->diag,*pj;
139   MatScalar      *rtmp,*pc,*mwork,*v,*pv,*aa=a->a;
140   PetscInt       bs2 = a->bs2,flg;
141   PetscReal      shift = info->shiftinblocks;
142 
143   PetscFunctionBegin;
144   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
145   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
146 
147   /* generate work space needed by the factorization */
148   ierr = PetscMalloc((bs2*n+bs2+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
149   mwork = rtmp + bs2*n;
150   ierr = PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));CHKERRQ(ierr);
151   ics  = ic;
152 
153   for (i=0; i<n; i++){
154     /* zero rtmp */
155     /* L part */
156     nz    = bi[i+1] - bi[i];
157     bjtmp = bj + bi[i];
158     for  (j=0; j<nz; j++){
159       ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
160     }
161 
162     /* U part */
163     nz = bi[2*n-i+1] - bi[2*n-i];
164     bjtmp = bj + bi[2*n-i];
165     for  (j=0; j<nz; j++){
166       ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
167     }
168 
169     /* load in initial (unfactored row) */
170     nz    = ai[r[i]+1] - ai[r[i]];
171     ajtmp = aj + ai[r[i]];
172     v     = aa + bs2*ai[r[i]];
173     for (j=0; j<nz; j++) {
174       ierr = PetscMemcpy(rtmp+bs2*ic[ajtmp[j]],v+bs2*j,bs2*sizeof(MatScalar));CHKERRQ(ierr);
175     }
176 
177     /* elimination */
178     bjtmp = bj + bi[i];
179     nzL   = bi[i+1] - bi[i];
180     for(k = 0;k < nzL;k++){
181       row = bjtmp[k];
182       pc = rtmp + bs2*row;
183       for (flg=0,j=0; j<bs2; j++) { if (pc[j]!=0.0) { flg = 1; break; }}
184       if (flg) {
185         pv = b->a + bs2*bdiag[row];
186         /* Kernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
187         ierr = Kernel_A_gets_A_times_B_3(pc,pv,mwork);CHKERRQ(ierr);
188 
189         pj = b->j + bi[2*n-row]; /* begining of U(row,:) */
190         pv = b->a + bs2*bi[2*n-row];
191         nz = bi[2*n-row+1] - bi[2*n-row] - 1; /* num of entries inU(row,:), excluding diag */
192         for (j=0; j<nz; j++) {
193           /* Kernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
194           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
195           v    = rtmp + bs2*pj[j];
196           ierr = Kernel_A_gets_A_minus_B_times_C_3(v,pc,pv);CHKERRQ(ierr);
197           pv  += bs2;
198         }
199         ierr = PetscLogFlops(54*nz+45);CHKERRQ(ierr); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
200       }
201     }
202 
203     /* finished row so stick it into b->a */
204     /* L part */
205     pv   = b->a + bs2*bi[i] ;
206     pj   = b->j + bi[i] ;
207     nz   = bi[i+1] - bi[i];
208     for (j=0; j<nz; j++) {
209       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
210     }
211 
212     /* Mark diagonal and invert diagonal for simplier triangular solves */
213     pv   = b->a + bs2*bdiag[i];
214     pj   = b->j + bdiag[i];
215     ierr = PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));CHKERRQ(ierr);
216     /* ierr = Kernel_A_gets_inverse_A(bs,pv,v_pivots,v_work);CHKERRQ(ierr); */
217     ierr = Kernel_A_gets_inverse_A_3(pv,shift);CHKERRQ(ierr);
218 
219     /* U part */
220     pv = b->a + bs2*bi[2*n-i];
221     pj = b->j + bi[2*n-i];
222     nz = bi[2*n-i+1] - bi[2*n-i] - 1;
223     for (j=0; j<nz; j++){
224       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
225     }
226   }
227 
228   ierr = PetscFree(rtmp);CHKERRQ(ierr);
229   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
230   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
231 
232   C->assembled = PETSC_TRUE;
233   ierr = PetscLogFlops(1.3333*bs2*n);CHKERRQ(ierr); /* from inverting diagonal blocks */
234   PetscFunctionReturn(0);
235 }
236 
237 #undef __FUNCT__
238 #define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_3_newdatastruct_v2"
239 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_3_newdatastruct_v2(Mat B,Mat A,const MatFactorInfo *info)
240 {
241   Mat            C=B;
242   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ *)C->data;
243   IS             isrow = b->row,isicol = b->icol;
244   PetscErrorCode ierr;
245   const PetscInt *r,*ic,*ics;
246   PetscInt       i,j,k,n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
247   PetscInt       *ajtmp,*bjtmp,nz,nzL,row,*bdiag=b->diag,*pj;
248   MatScalar      *rtmp,*pc,*mwork,*v,*pv,*aa=a->a;
249   PetscInt       bs2 = a->bs2,flg;
250   PetscReal      shift = info->shiftinblocks;
251 
252   PetscFunctionBegin;
253   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
254   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
255 
256   /* generate work space needed by the factorization */
257   ierr = PetscMalloc((bs2*n+bs2+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
258   mwork = rtmp + bs2*n;
259   ierr = PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));CHKERRQ(ierr);
260   ics  = ic;
261 
262   for (i=0; i<n; i++){
263     /* zero rtmp */
264     /* L part */
265     nz    = bi[i+1] - bi[i];
266     bjtmp = bj + bi[i];
267     for  (j=0; j<nz; j++){
268       ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
269     }
270 
271     /* U part */
272     nz = bdiag[i] - bdiag[i+1];
273     bjtmp = bj + bdiag[i+1]+1;
274     for  (j=0; j<nz; j++){
275       ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
276     }
277 
278     /* load in initial (unfactored row) */
279     nz    = ai[r[i]+1] - ai[r[i]];
280     ajtmp = aj + ai[r[i]];
281     v     = aa + bs2*ai[r[i]];
282     for (j=0; j<nz; j++) {
283       ierr = PetscMemcpy(rtmp+bs2*ic[ajtmp[j]],v+bs2*j,bs2*sizeof(MatScalar));CHKERRQ(ierr);
284     }
285 
286     /* elimination */
287     bjtmp = bj + bi[i];
288     nzL   = bi[i+1] - bi[i];
289     for(k = 0;k < nzL;k++){
290       row = bjtmp[k];
291       pc = rtmp + bs2*row;
292       for (flg=0,j=0; j<bs2; j++) { if (pc[j]!=0.0) { flg = 1; break; }}
293       if (flg) {
294         pv = b->a + bs2*bdiag[row];
295         /* Kernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
296         ierr = Kernel_A_gets_A_times_B_3(pc,pv,mwork);CHKERRQ(ierr);
297 
298    	pj = b->j + bdiag[row+1] + 1; /* beginning of U(row,:) */
299 	pv = b->a + bs2*(bdiag[row+1]+1);
300 	nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:) excluding diag */
301         for (j=0; j<nz; j++) {
302           /* Kernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
303           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
304           v    = rtmp + bs2*pj[j];
305           ierr = Kernel_A_gets_A_minus_B_times_C_3(v,pc,pv);CHKERRQ(ierr);
306           pv  += bs2;
307         }
308         ierr = PetscLogFlops(54*nz+45);CHKERRQ(ierr); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
309       }
310     }
311 
312     /* finished row so stick it into b->a */
313     /* L part */
314     pv   = b->a + bs2*bi[i] ;
315     pj   = b->j + bi[i] ;
316     nz   = bi[i+1] - bi[i];
317     for (j=0; j<nz; j++) {
318       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
319     }
320 
321     /* Mark diagonal and invert diagonal for simplier triangular solves */
322     pv   = b->a + bs2*bdiag[i];
323     pj   = b->j + bdiag[i];
324     ierr = PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));CHKERRQ(ierr);
325     /* ierr = Kernel_A_gets_inverse_A(bs,pv,v_pivots,v_work);CHKERRQ(ierr); */
326     ierr = Kernel_A_gets_inverse_A_3(pv,shift);CHKERRQ(ierr);
327 
328     /* U part */
329     pj = b->j + bdiag[i+1] + 1;
330     pv = b->a + bs2*(bdiag[i+1]+1);
331     nz = bdiag[i] - bdiag[i+1] - 1;
332     for (j=0; j<nz; j++){
333       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
334     }
335   }
336 
337   ierr = PetscFree(rtmp);CHKERRQ(ierr);
338   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
339   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
340 
341   C->assembled = PETSC_TRUE;
342   ierr = PetscLogFlops(1.3333*bs2*n);CHKERRQ(ierr); /* from inverting diagonal blocks */
343   PetscFunctionReturn(0);
344 }
345 
346 #undef __FUNCT__
347 #define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering"
348 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering(Mat C,Mat A,const MatFactorInfo *info)
349 {
350   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
351   PetscErrorCode ierr;
352   PetscInt       i,j,n = a->mbs,*bi = b->i,*bj = b->j;
353   PetscInt       *ajtmpold,*ajtmp,nz,row;
354   PetscInt       *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
355   MatScalar      *pv,*v,*rtmp,*pc,*w,*x;
356   MatScalar      p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
357   MatScalar      p5,p6,p7,p8,p9,x5,x6,x7,x8,x9;
358   MatScalar      *ba = b->a,*aa = a->a;
359   PetscReal      shift = info->shiftinblocks;
360 
361   PetscFunctionBegin;
362   ierr = PetscMalloc(9*(n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
363 
364   for (i=0; i<n; i++) {
365     nz    = bi[i+1] - bi[i];
366     ajtmp = bj + bi[i];
367     for  (j=0; j<nz; j++) {
368       x = rtmp+9*ajtmp[j];
369       x[0]  = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = 0.0;
370     }
371     /* load in initial (unfactored row) */
372     nz       = ai[i+1] - ai[i];
373     ajtmpold = aj + ai[i];
374     v        = aa + 9*ai[i];
375     for (j=0; j<nz; j++) {
376       x    = rtmp+9*ajtmpold[j];
377       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
378       x[4]  = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
379       v    += 9;
380     }
381     row = *ajtmp++;
382     while (row < i) {
383       pc  = rtmp + 9*row;
384       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
385       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
386       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
387           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0) {
388         pv = ba + 9*diag_offset[row];
389         pj = bj + diag_offset[row] + 1;
390         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
391         x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
392         pc[0] = m1 = p1*x1 + p4*x2 + p7*x3;
393         pc[1] = m2 = p2*x1 + p5*x2 + p8*x3;
394         pc[2] = m3 = p3*x1 + p6*x2 + p9*x3;
395 
396         pc[3] = m4 = p1*x4 + p4*x5 + p7*x6;
397         pc[4] = m5 = p2*x4 + p5*x5 + p8*x6;
398         pc[5] = m6 = p3*x4 + p6*x5 + p9*x6;
399 
400         pc[6] = m7 = p1*x7 + p4*x8 + p7*x9;
401         pc[7] = m8 = p2*x7 + p5*x8 + p8*x9;
402         pc[8] = m9 = p3*x7 + p6*x8 + p9*x9;
403 
404         nz = bi[row+1] - diag_offset[row] - 1;
405         pv += 9;
406         for (j=0; j<nz; j++) {
407           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
408           x5   = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
409           x    = rtmp + 9*pj[j];
410           x[0] -= m1*x1 + m4*x2 + m7*x3;
411           x[1] -= m2*x1 + m5*x2 + m8*x3;
412           x[2] -= m3*x1 + m6*x2 + m9*x3;
413 
414           x[3] -= m1*x4 + m4*x5 + m7*x6;
415           x[4] -= m2*x4 + m5*x5 + m8*x6;
416           x[5] -= m3*x4 + m6*x5 + m9*x6;
417 
418           x[6] -= m1*x7 + m4*x8 + m7*x9;
419           x[7] -= m2*x7 + m5*x8 + m8*x9;
420           x[8] -= m3*x7 + m6*x8 + m9*x9;
421           pv   += 9;
422         }
423         ierr = PetscLogFlops(54.0*nz+36.0);CHKERRQ(ierr);
424       }
425       row = *ajtmp++;
426     }
427     /* finished row so stick it into b->a */
428     pv = ba + 9*bi[i];
429     pj = bj + bi[i];
430     nz = bi[i+1] - bi[i];
431     for (j=0; j<nz; j++) {
432       x      = rtmp+9*pj[j];
433       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
434       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
435       pv   += 9;
436     }
437     /* invert diagonal block */
438     w = ba + 9*diag_offset[i];
439     ierr = Kernel_A_gets_inverse_A_3(w,shift);CHKERRQ(ierr);
440   }
441 
442   ierr = PetscFree(rtmp);CHKERRQ(ierr);
443   C->ops->solve          = MatSolve_SeqBAIJ_3_NaturalOrdering;
444   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_3_NaturalOrdering;
445   C->assembled = PETSC_TRUE;
446   ierr = PetscLogFlops(1.3333*27*b->mbs);CHKERRQ(ierr); /* from inverting diagonal blocks */
447   PetscFunctionReturn(0);
448 }
449 
450 /*
451   MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering_newdatastruct -
452     copied from MatLUFactorNumeric_SeqBAIJ_2_NaturalOrdering_newdatastruct()
453 */
454 #undef __FUNCT__
455 #define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering_newdatastruct"
456 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering_newdatastruct(Mat B,Mat A,const MatFactorInfo *info)
457 {
458   Mat            C=B;
459   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ *)C->data;
460   PetscErrorCode ierr;
461   PetscInt       i,j,k,n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
462   PetscInt       *ajtmp,*bjtmp,nz,nzL,row,*bdiag=b->diag,*pj;
463   MatScalar      *rtmp,*pc,*mwork,*v,*pv,*aa=a->a;
464   PetscInt       bs2 = a->bs2,flg;
465   PetscReal      shift = info->shiftinblocks;
466 
467   PetscFunctionBegin;
468   /* generate work space needed by the factorization */
469   ierr = PetscMalloc((bs2*n+bs2+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
470   mwork = rtmp + bs2*n;
471   ierr = PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));CHKERRQ(ierr);
472 
473   for (i=0; i<n; i++){
474     /* zero rtmp */
475     /* L part */
476     nz    = bi[i+1] - bi[i];
477     bjtmp = bj + bi[i];
478     for  (j=0; j<nz; j++){
479       ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
480     }
481 
482     /* U part */
483     nz = bi[2*n-i+1] - bi[2*n-i];
484     bjtmp = bj + bi[2*n-i];
485     for  (j=0; j<nz; j++){
486       ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
487     }
488 
489     /* load in initial (unfactored row) */
490     nz    = ai[i+1] - ai[i];
491     ajtmp = aj + ai[i];
492     v     = aa + bs2*ai[i];
493     for (j=0; j<nz; j++) {
494       ierr = PetscMemcpy(rtmp+bs2*ajtmp[j],v+bs2*j,bs2*sizeof(MatScalar));CHKERRQ(ierr);
495     }
496 
497     /* elimination */
498     bjtmp = bj + bi[i];
499     nzL   = bi[i+1] - bi[i];
500     for(k=0;k<nzL;k++){
501       row = bjtmp[k];
502       pc = rtmp + bs2*row;
503       for (flg=0,j=0; j<bs2; j++) { if (pc[j]!=0.0) { flg = 1; break; }}
504       if (flg) {
505         pv = b->a + bs2*bdiag[row];
506         /* Kernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
507         ierr = Kernel_A_gets_A_times_B_3(pc,pv,mwork);CHKERRQ(ierr);
508 
509         pj = b->j + bi[2*n-row]; /* begining of U(row,:) */
510         pv = b->a + bs2*bi[2*n-row];
511         nz = bi[2*n-row+1] - bi[2*n-row] - 1; /* num of entries inU(row,:), excluding diag */
512         for (j=0; j<nz; j++) {
513           /* Kernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
514           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
515           v    = rtmp + bs2*pj[j];
516           ierr = Kernel_A_gets_A_minus_B_times_C_3(v,pc,pv);CHKERRQ(ierr);
517           pv  += bs2;
518         }
519         ierr = PetscLogFlops(54*nz+45);CHKERRQ(ierr); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
520       }
521     }
522 
523     /* finished row so stick it into b->a */
524     /* L part */
525     pv   = b->a + bs2*bi[i] ;
526     pj   = b->j + bi[i] ;
527     nz   = bi[i+1] - bi[i];
528     for (j=0; j<nz; j++) {
529       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
530     }
531 
532     /* Mark diagonal and invert diagonal for simplier triangular solves */
533     pv   = b->a + bs2*bdiag[i];
534     pj   = b->j + bdiag[i];
535     ierr = PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));CHKERRQ(ierr);
536     /* ierr = Kernel_A_gets_inverse_A(bs,pv,v_pivots,v_work);CHKERRQ(ierr); */
537     ierr = Kernel_A_gets_inverse_A_3(pv,shift);CHKERRQ(ierr);
538 
539     /* U part */
540     pv = b->a + bs2*bi[2*n-i];
541     pj = b->j + bi[2*n-i];
542     nz = bi[2*n-i+1] - bi[2*n-i] - 1;
543     for (j=0; j<nz; j++){
544       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
545     }
546   }
547 
548   ierr = PetscFree(rtmp);CHKERRQ(ierr);
549   C->assembled = PETSC_TRUE;
550   ierr = PetscLogFlops(1.3333*bs2*n);CHKERRQ(ierr); /* from inverting diagonal blocks */
551   PetscFunctionReturn(0);
552 }
553 
554 #undef __FUNCT__
555 #define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering_newdatastruct_v2"
556 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_3_NaturalOrdering_newdatastruct_v2(Mat B,Mat A,const MatFactorInfo *info)
557 {
558   Mat            C=B;
559   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ *)C->data;
560   PetscErrorCode ierr;
561   PetscInt       i,j,k,n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
562   PetscInt       *ajtmp,*bjtmp,nz,nzL,row,*bdiag=b->diag,*pj;
563   MatScalar      *rtmp,*pc,*mwork,*v,*pv,*aa=a->a;
564   PetscInt       bs2 = a->bs2,flg;
565   PetscReal      shift = info->shiftinblocks;
566 
567   PetscFunctionBegin;
568   /* generate work space needed by the factorization */
569   ierr = PetscMalloc((bs2*n+bs2+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
570   mwork = rtmp + bs2*n;
571   ierr = PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));CHKERRQ(ierr);
572 
573   for (i=0; i<n; i++){
574     /* zero rtmp */
575     /* L part */
576     nz    = bi[i+1] - bi[i];
577     bjtmp = bj + bi[i];
578     for  (j=0; j<nz; j++){
579       ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
580     }
581 
582     /* U part */
583     nz = bdiag[i] - bdiag[i+1];
584     bjtmp = bj + bdiag[i+1] + 1;
585     for  (j=0; j<nz; j++){
586       ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
587     }
588 
589     /* load in initial (unfactored row) */
590     nz    = ai[i+1] - ai[i];
591     ajtmp = aj + ai[i];
592     v     = aa + bs2*ai[i];
593     for (j=0; j<nz; j++) {
594       ierr = PetscMemcpy(rtmp+bs2*ajtmp[j],v+bs2*j,bs2*sizeof(MatScalar));CHKERRQ(ierr);
595     }
596 
597     /* elimination */
598     bjtmp = bj + bi[i];
599     nzL   = bi[i+1] - bi[i];
600     for(k=0;k<nzL;k++){
601       row = bjtmp[k];
602       pc = rtmp + bs2*row;
603       for (flg=0,j=0; j<bs2; j++) { if (pc[j]!=0.0) { flg = 1; break; }}
604       if (flg) {
605         pv = b->a + bs2*bdiag[row];
606         /* Kernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
607         ierr = Kernel_A_gets_A_times_B_3(pc,pv,mwork);CHKERRQ(ierr);
608 
609         pj = b->j + bdiag[row+1]+1; /* beginning of U(row,:) */
610 	pv = b->a + bs2*(bdiag[row+1]+1);
611 	nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries in U(row,:) excluding diag */
612         for (j=0; j<nz; j++) {
613           /* Kernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
614           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
615           v    = rtmp + bs2*pj[j];
616           ierr = Kernel_A_gets_A_minus_B_times_C_3(v,pc,pv);CHKERRQ(ierr);
617           pv  += bs2;
618         }
619         ierr = PetscLogFlops(54*nz+45);CHKERRQ(ierr); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
620       }
621     }
622 
623     /* finished row so stick it into b->a */
624     /* L part */
625     pv   = b->a + bs2*bi[i] ;
626     pj   = b->j + bi[i] ;
627     nz   = bi[i+1] - bi[i];
628     for (j=0; j<nz; j++) {
629       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
630     }
631 
632     /* Mark diagonal and invert diagonal for simplier triangular solves */
633     pv   = b->a + bs2*bdiag[i];
634     pj   = b->j + bdiag[i];
635     ierr = PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));CHKERRQ(ierr);
636     /* ierr = Kernel_A_gets_inverse_A(bs,pv,v_pivots,v_work);CHKERRQ(ierr); */
637     ierr = Kernel_A_gets_inverse_A_3(pv,shift);CHKERRQ(ierr);
638 
639     /* U part */
640     pv = b->a + bs2*(bdiag[i+1]+1);
641     pj = b->j + bdiag[i+1]+1;
642     nz = bdiag[i] - bdiag[i+1] - 1;
643     for (j=0; j<nz; j++){
644       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
645     }
646   }
647 
648   ierr = PetscFree(rtmp);CHKERRQ(ierr);
649   C->assembled = PETSC_TRUE;
650   ierr = PetscLogFlops(1.3333*bs2*n);CHKERRQ(ierr); /* from inverting diagonal blocks */
651   PetscFunctionReturn(0);
652 }
653 
654