xref: /petsc/src/mat/impls/baij/seq/baijfact9.c (revision 2205254efee3a00a594e5e2a3a70f74dcb40bc03)
1 
2 /*
3     Factorization code for BAIJ format.
4 */
5 #include <../src/mat/impls/baij/seq/baij.h>
6 #include <../src/mat/blockinvert.h>
7 
8 /* ------------------------------------------------------------*/
9 /*
10       Version for when blocks are 5 by 5
11 */
12 #undef __FUNCT__
13 #define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_5_inplace"
14 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5_inplace(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,*bi = b->i,*bj = b->j,*ajtmpold,*ajtmp;
20   PetscInt        i,j,n = a->mbs,nz,row,idx,ipvt[5];
21   const PetscInt  *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
22   MatScalar       *w,*pv,*rtmp,*x,*pc;
23   const MatScalar *v,*aa = a->a;
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,x10,x11,x12,x13,x14,x15,x16;
26   MatScalar       x17,x18,x19,x20,x21,x22,x23,x24,x25,p10,p11,p12,p13,p14;
27   MatScalar       p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,m10,m11,m12;
28   MatScalar       m13,m14,m15,m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
29   MatScalar       *ba = b->a,work[25];
30   PetscReal       shift = info->shiftamount;
31 
32   PetscFunctionBegin;
33   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
34   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
35   ierr = PetscMalloc(25*(n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
36 
37 #define PETSC_USE_MEMZERO 1
38 #define PETSC_USE_MEMCPY 1
39 
40   for (i=0; i<n; i++) {
41     nz    = bi[i+1] - bi[i];
42     ajtmp = bj + bi[i];
43     for  (j=0; j<nz; j++) {
44 #if defined(PETSC_USE_MEMZERO)
45       ierr = PetscMemzero(rtmp+25*ajtmp[j],25*sizeof(PetscScalar));CHKERRQ(ierr);
46 #else
47       x = rtmp+25*ajtmp[j];
48       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
49       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
50       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0;
51 #endif
52     }
53     /* load in initial (unfactored row) */
54     idx      = r[i];
55     nz       = ai[idx+1] - ai[idx];
56     ajtmpold = aj + ai[idx];
57     v        = aa + 25*ai[idx];
58     for (j=0; j<nz; j++) {
59 #if defined(PETSC_USE_MEMCPY)
60       ierr = PetscMemcpy(rtmp+25*ic[ajtmpold[j]],v,25*sizeof(PetscScalar));CHKERRQ(ierr);
61 #else
62       x    = rtmp+25*ic[ajtmpold[j]];
63       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
64       x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
65       x[9] = v[9]; x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
66       x[14] = v[14]; x[15] = v[15]; x[16] = v[16]; x[17] = v[17];
67       x[18] = v[18]; x[19] = v[19]; x[20] = v[20]; x[21] = v[21];
68       x[22] = v[22]; x[23] = v[23]; x[24] = v[24];
69 #endif
70       v    += 25;
71     }
72     row = *ajtmp++;
73     while (row < i) {
74       pc = rtmp + 25*row;
75       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
76       p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
77       p10 = pc[9]; p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
78       p15 = pc[14]; p16 = pc[15]; p17 = pc[16]; p18 = pc[17]; p19 = pc[18];
79       p20 = pc[19]; p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
80       p25 = pc[24];
81       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
82           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
83           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
84           || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 ||
85           p20 != 0.0 || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 ||
86           p24 != 0.0 || p25 != 0.0) {
87         pv = ba + 25*diag_offset[row];
88         pj = bj + diag_offset[row] + 1;
89         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
90         x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
91         x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
92         x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17];
93         x19 = pv[18]; x20 = pv[19]; x21 = pv[20]; x22 = pv[21];
94         x23 = pv[22]; x24 = pv[23]; x25 = pv[24];
95         pc[0] = m1 = p1*x1 + p6*x2  + p11*x3 + p16*x4 + p21*x5;
96         pc[1] = m2 = p2*x1 + p7*x2  + p12*x3 + p17*x4 + p22*x5;
97         pc[2] = m3 = p3*x1 + p8*x2  + p13*x3 + p18*x4 + p23*x5;
98         pc[3] = m4 = p4*x1 + p9*x2  + p14*x3 + p19*x4 + p24*x5;
99         pc[4] = m5 = p5*x1 + p10*x2 + p15*x3 + p20*x4 + p25*x5;
100 
101         pc[5] = m6 = p1*x6 + p6*x7  + p11*x8 + p16*x9 + p21*x10;
102         pc[6] = m7 = p2*x6 + p7*x7  + p12*x8 + p17*x9 + p22*x10;
103         pc[7] = m8 = p3*x6 + p8*x7  + p13*x8 + p18*x9 + p23*x10;
104         pc[8] = m9 = p4*x6 + p9*x7  + p14*x8 + p19*x9 + p24*x10;
105         pc[9] = m10 = p5*x6 + p10*x7 + p15*x8 + p20*x9 + p25*x10;
106 
107         pc[10] = m11 = p1*x11 + p6*x12  + p11*x13 + p16*x14 + p21*x15;
108         pc[11] = m12 = p2*x11 + p7*x12  + p12*x13 + p17*x14 + p22*x15;
109         pc[12] = m13 = p3*x11 + p8*x12  + p13*x13 + p18*x14 + p23*x15;
110         pc[13] = m14 = p4*x11 + p9*x12  + p14*x13 + p19*x14 + p24*x15;
111         pc[14] = m15 = p5*x11 + p10*x12 + p15*x13 + p20*x14 + p25*x15;
112 
113         pc[15] = m16 = p1*x16 + p6*x17  + p11*x18 + p16*x19 + p21*x20;
114         pc[16] = m17 = p2*x16 + p7*x17  + p12*x18 + p17*x19 + p22*x20;
115         pc[17] = m18 = p3*x16 + p8*x17  + p13*x18 + p18*x19 + p23*x20;
116         pc[18] = m19 = p4*x16 + p9*x17  + p14*x18 + p19*x19 + p24*x20;
117         pc[19] = m20 = p5*x16 + p10*x17 + p15*x18 + p20*x19 + p25*x20;
118 
119         pc[20] = m21 = p1*x21 + p6*x22  + p11*x23 + p16*x24 + p21*x25;
120         pc[21] = m22 = p2*x21 + p7*x22  + p12*x23 + p17*x24 + p22*x25;
121         pc[22] = m23 = p3*x21 + p8*x22  + p13*x23 + p18*x24 + p23*x25;
122         pc[23] = m24 = p4*x21 + p9*x22  + p14*x23 + p19*x24 + p24*x25;
123         pc[24] = m25 = p5*x21 + p10*x22 + p15*x23 + p20*x24 + p25*x25;
124 
125         nz = bi[row+1] - diag_offset[row] - 1;
126         pv += 25;
127         for (j=0; j<nz; j++) {
128           x1   = pv[0];  x2 = pv[1];   x3  = pv[2];  x4  = pv[3];
129           x5   = pv[4];  x6 = pv[5];   x7  = pv[6];  x8  = pv[7]; x9 = pv[8];
130           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
131           x14  = pv[13]; x15 = pv[14]; x16 = pv[15]; x17 = pv[16];
132           x18  = pv[17]; x19 = pv[18]; x20 = pv[19]; x21 = pv[20];
133           x22  = pv[21]; x23 = pv[22]; x24 = pv[23]; x25 = pv[24];
134           x    = rtmp + 25*pj[j];
135           x[0] -= m1*x1 + m6*x2  + m11*x3 + m16*x4 + m21*x5;
136           x[1] -= m2*x1 + m7*x2  + m12*x3 + m17*x4 + m22*x5;
137           x[2] -= m3*x1 + m8*x2  + m13*x3 + m18*x4 + m23*x5;
138           x[3] -= m4*x1 + m9*x2  + m14*x3 + m19*x4 + m24*x5;
139           x[4] -= m5*x1 + m10*x2 + m15*x3 + m20*x4 + m25*x5;
140 
141           x[5] -= m1*x6 + m6*x7  + m11*x8 + m16*x9 + m21*x10;
142           x[6] -= m2*x6 + m7*x7  + m12*x8 + m17*x9 + m22*x10;
143           x[7] -= m3*x6 + m8*x7  + m13*x8 + m18*x9 + m23*x10;
144           x[8] -= m4*x6 + m9*x7  + m14*x8 + m19*x9 + m24*x10;
145           x[9] -= m5*x6 + m10*x7 + m15*x8 + m20*x9 + m25*x10;
146 
147           x[10] -= m1*x11 + m6*x12  + m11*x13 + m16*x14 + m21*x15;
148           x[11] -= m2*x11 + m7*x12  + m12*x13 + m17*x14 + m22*x15;
149           x[12] -= m3*x11 + m8*x12  + m13*x13 + m18*x14 + m23*x15;
150           x[13] -= m4*x11 + m9*x12  + m14*x13 + m19*x14 + m24*x15;
151           x[14] -= m5*x11 + m10*x12 + m15*x13 + m20*x14 + m25*x15;
152 
153           x[15] -= m1*x16 + m6*x17  + m11*x18 + m16*x19 + m21*x20;
154           x[16] -= m2*x16 + m7*x17  + m12*x18 + m17*x19 + m22*x20;
155           x[17] -= m3*x16 + m8*x17  + m13*x18 + m18*x19 + m23*x20;
156           x[18] -= m4*x16 + m9*x17  + m14*x18 + m19*x19 + m24*x20;
157           x[19] -= m5*x16 + m10*x17 + m15*x18 + m20*x19 + m25*x20;
158 
159           x[20] -= m1*x21 + m6*x22  + m11*x23 + m16*x24 + m21*x25;
160           x[21] -= m2*x21 + m7*x22  + m12*x23 + m17*x24 + m22*x25;
161           x[22] -= m3*x21 + m8*x22  + m13*x23 + m18*x24 + m23*x25;
162           x[23] -= m4*x21 + m9*x22  + m14*x23 + m19*x24 + m24*x25;
163           x[24] -= m5*x21 + m10*x22 + m15*x23 + m20*x24 + m25*x25;
164 
165           pv   += 25;
166         }
167         ierr = PetscLogFlops(250.0*nz+225.0);CHKERRQ(ierr);
168       }
169       row = *ajtmp++;
170     }
171     /* finished row so stick it into b->a */
172     pv = ba + 25*bi[i];
173     pj = bj + bi[i];
174     nz = bi[i+1] - bi[i];
175     for (j=0; j<nz; j++) {
176 #if defined(PETSC_USE_MEMCPY)
177       ierr = PetscMemcpy(pv,rtmp+25*pj[j],25*sizeof(PetscScalar));CHKERRQ(ierr);
178 #else
179       x     = rtmp+25*pj[j];
180       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
181       pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
182       pv[9] = x[9]; pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
183       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; pv[16] = x[16];
184       pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19]; pv[20] = x[20];
185       pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23]; pv[24] = x[24];
186 #endif
187       pv   += 25;
188     }
189     /* invert diagonal block */
190     w = ba + 25*diag_offset[i];
191     ierr = PetscKernel_A_gets_inverse_A_5(w,ipvt,work,shift);CHKERRQ(ierr);
192   }
193 
194   ierr = PetscFree(rtmp);CHKERRQ(ierr);
195   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
196   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
197   C->ops->solve          = MatSolve_SeqBAIJ_5_inplace;
198   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5_inplace;
199   C->assembled = PETSC_TRUE;
200   ierr = PetscLogFlops(1.333333333333*5*5*5*b->mbs);CHKERRQ(ierr); /* from inverting diagonal blocks */
201   PetscFunctionReturn(0);
202 }
203 
204 /* MatLUFactorNumeric_SeqBAIJ_5 -
205      copied from MatLUFactorNumeric_SeqBAIJ_N_inplace() and manually re-implemented
206        PetscKernel_A_gets_A_times_B()
207        PetscKernel_A_gets_A_minus_B_times_C()
208        PetscKernel_A_gets_inverse_A()
209 */
210 
211 #undef __FUNCT__
212 #define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_5"
213 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5(Mat B,Mat A,const MatFactorInfo *info)
214 {
215   Mat            C=B;
216   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ *)C->data;
217   IS             isrow = b->row,isicol = b->icol;
218   PetscErrorCode ierr;
219   const PetscInt *r,*ic;
220   PetscInt       i,j,k,nz,nzL,row;
221   const PetscInt n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
222   const PetscInt *ajtmp,*bjtmp,*bdiag=b->diag,*pj,bs2=a->bs2;
223   MatScalar      *rtmp,*pc,*mwork,*v,*pv,*aa=a->a,work[25];
224   PetscInt       flg,ipvt[5];
225   PetscReal      shift = info->shiftamount;
226 
227   PetscFunctionBegin;
228   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
229   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
230 
231   /* generate work space needed by the factorization */
232   ierr = PetscMalloc2(bs2*n,MatScalar,&rtmp,bs2,MatScalar,&mwork);CHKERRQ(ierr);
233   ierr = PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));CHKERRQ(ierr);
234 
235   for (i=0; i<n; i++) {
236     /* zero rtmp */
237     /* L part */
238     nz    = bi[i+1] - bi[i];
239     bjtmp = bj + bi[i];
240     for  (j=0; j<nz; j++) {
241       ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
242     }
243 
244     /* U part */
245     nz = bdiag[i] - bdiag[i+1];
246     bjtmp = bj + bdiag[i+1]+1;
247     for  (j=0; j<nz; j++) {
248       ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
249     }
250 
251     /* load in initial (unfactored row) */
252     nz    = ai[r[i]+1] - ai[r[i]];
253     ajtmp = aj + ai[r[i]];
254     v     = aa + bs2*ai[r[i]];
255     for (j=0; j<nz; j++) {
256       ierr = PetscMemcpy(rtmp+bs2*ic[ajtmp[j]],v+bs2*j,bs2*sizeof(MatScalar));CHKERRQ(ierr);
257     }
258 
259     /* elimination */
260     bjtmp = bj + bi[i];
261     nzL   = bi[i+1] - bi[i];
262     for (k=0;k < nzL;k++) {
263       row = bjtmp[k];
264       pc = rtmp + bs2*row;
265       for (flg=0,j=0; j<bs2; j++) {
266         if (pc[j]!=0.0) {
267           flg = 1;
268           break;
269         }
270       }
271       if (flg) {
272         pv = b->a + bs2*bdiag[row];
273         /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
274         ierr = PetscKernel_A_gets_A_times_B_5(pc,pv,mwork);CHKERRQ(ierr);
275 
276         pj = b->j + bdiag[row+1]+1; /* begining of U(row,:) */
277         pv = b->a + bs2*(bdiag[row+1]+1);
278         nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries inU(row,:), excluding diag */
279         for (j=0; j<nz; j++) {
280           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
281           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
282           v    = rtmp + bs2*pj[j];
283           ierr = PetscKernel_A_gets_A_minus_B_times_C_5(v,pc,pv);CHKERRQ(ierr);
284           pv  += bs2;
285         }
286         ierr = PetscLogFlops(250*nz+225);CHKERRQ(ierr); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
287       }
288     }
289 
290     /* finished row so stick it into b->a */
291     /* L part */
292     pv   = b->a + bs2*bi[i] ;
293     pj   = b->j + bi[i] ;
294     nz   = bi[i+1] - bi[i];
295     for (j=0; j<nz; j++) {
296       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
297     }
298 
299     /* Mark diagonal and invert diagonal for simplier triangular solves */
300     pv   = b->a + bs2*bdiag[i];
301     pj   = b->j + bdiag[i];
302     ierr = PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));CHKERRQ(ierr);
303     /* ierr = PetscKernel_A_gets_inverse_A(bs,pv,v_pivots,v_work);CHKERRQ(ierr); */
304     ierr = PetscKernel_A_gets_inverse_A_5(pv,ipvt,work,shift);CHKERRQ(ierr);
305 
306     /* U part */
307     pv = b->a + bs2*(bdiag[i+1]+1);
308     pj = b->j + bdiag[i+1]+1;
309     nz = bdiag[i] - bdiag[i+1] - 1;
310     for (j=0; j<nz; j++) {
311       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
312     }
313   }
314 
315   ierr = PetscFree2(rtmp,mwork);CHKERRQ(ierr);
316   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
317   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
318   C->ops->solve          = MatSolve_SeqBAIJ_5;
319   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5;
320   C->assembled = PETSC_TRUE;
321   ierr = PetscLogFlops(1.333333333333*5*5*5*n);CHKERRQ(ierr); /* from inverting diagonal blocks */
322   PetscFunctionReturn(0);
323 }
324 
325 /*
326       Version for when blocks are 5 by 5 Using natural ordering
327 */
328 #undef __FUNCT__
329 #define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_5_NaturalOrdering_inplace"
330 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5_NaturalOrdering_inplace(Mat C,Mat A,const MatFactorInfo *info)
331 {
332   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
333   PetscErrorCode ierr;
334   PetscInt       i,j,n = a->mbs,*bi = b->i,*bj = b->j,ipvt[5];
335   PetscInt       *ajtmpold,*ajtmp,nz,row;
336   PetscInt       *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
337   MatScalar      *pv,*v,*rtmp,*pc,*w,*x;
338   MatScalar      x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15;
339   MatScalar      x16,x17,x18,x19,x20,x21,x22,x23,x24,x25;
340   MatScalar      p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15;
341   MatScalar      p16,p17,p18,p19,p20,p21,p22,p23,p24,p25;
342   MatScalar      m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12,m13,m14,m15;
343   MatScalar      m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
344   MatScalar      *ba = b->a,*aa = a->a,work[25];
345   PetscReal      shift = info->shiftamount;
346 
347   PetscFunctionBegin;
348   ierr = PetscMalloc(25*(n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
349   for (i=0; i<n; i++) {
350     nz    = bi[i+1] - bi[i];
351     ajtmp = bj + bi[i];
352     for  (j=0; j<nz; j++) {
353       x = rtmp+25*ajtmp[j];
354       x[0]  = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = x[9] = 0.0;
355       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
356       x[16] = x[17] = x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0;
357     }
358     /* load in initial (unfactored row) */
359     nz       = ai[i+1] - ai[i];
360     ajtmpold = aj + ai[i];
361     v        = aa + 25*ai[i];
362     for (j=0; j<nz; j++) {
363       x    = rtmp+25*ajtmpold[j];
364       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
365       x[4]  = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
366       x[9]  = v[9];  x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
367       x[14] = v[14]; x[15] = v[15]; x[16] = v[16]; x[17] = v[17]; x[18] = v[18];
368       x[19] = v[19]; x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23];
369       x[24] = v[24];
370       v    += 25;
371     }
372     row = *ajtmp++;
373     while (row < i) {
374       pc  = rtmp + 25*row;
375       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
376       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
377       p10 = pc[9];  p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
378       p15 = pc[14]; p16 = pc[15]; p17 = pc[16]; p18 = pc[17];
379       p19 = pc[18]; p20 = pc[19]; p21 = pc[20]; p22 = pc[21]; p23 = pc[22];
380       p24 = pc[23]; p25 = pc[24];
381       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
382           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
383           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
384           || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0
385           || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 || p25 != 0.0) {
386         pv = ba + 25*diag_offset[row];
387         pj = bj + diag_offset[row] + 1;
388         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
389         x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
390         x10 = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
391         x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17]; x19 = pv[18];
392         x20 = pv[19]; x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
393         x25 = pv[24];
394         pc[0] = m1 = p1*x1 + p6*x2  + p11*x3 + p16*x4 + p21*x5;
395         pc[1] = m2 = p2*x1 + p7*x2  + p12*x3 + p17*x4 + p22*x5;
396         pc[2] = m3 = p3*x1 + p8*x2  + p13*x3 + p18*x4 + p23*x5;
397         pc[3] = m4 = p4*x1 + p9*x2  + p14*x3 + p19*x4 + p24*x5;
398         pc[4] = m5 = p5*x1 + p10*x2 + p15*x3 + p20*x4 + p25*x5;
399 
400         pc[5]  = m6  = p1*x6 + p6*x7  + p11*x8 + p16*x9 + p21*x10;
401         pc[6]  = m7  = p2*x6 + p7*x7  + p12*x8 + p17*x9 + p22*x10;
402         pc[7]  = m8  = p3*x6 + p8*x7  + p13*x8 + p18*x9 + p23*x10;
403         pc[8]  = m9  = p4*x6 + p9*x7  + p14*x8 + p19*x9 + p24*x10;
404         pc[9]  = m10 = p5*x6 + p10*x7 + p15*x8 + p20*x9 + p25*x10;
405 
406         pc[10] = m11 = p1*x11 + p6*x12  + p11*x13 + p16*x14 + p21*x15;
407         pc[11] = m12 = p2*x11 + p7*x12  + p12*x13 + p17*x14 + p22*x15;
408         pc[12] = m13 = p3*x11 + p8*x12  + p13*x13 + p18*x14 + p23*x15;
409         pc[13] = m14 = p4*x11 + p9*x12  + p14*x13 + p19*x14 + p24*x15;
410         pc[14] = m15 = p5*x11 + p10*x12 + p15*x13 + p20*x14 + p25*x15;
411 
412         pc[15] = m16 = p1*x16 + p6*x17  + p11*x18 + p16*x19 + p21*x20;
413         pc[16] = m17 = p2*x16 + p7*x17  + p12*x18 + p17*x19 + p22*x20;
414         pc[17] = m18 = p3*x16 + p8*x17  + p13*x18 + p18*x19 + p23*x20;
415         pc[18] = m19 = p4*x16 + p9*x17  + p14*x18 + p19*x19 + p24*x20;
416         pc[19] = m20 = p5*x16 + p10*x17 + p15*x18 + p20*x19 + p25*x20;
417 
418         pc[20] = m21 = p1*x21 + p6*x22  + p11*x23 + p16*x24 + p21*x25;
419         pc[21] = m22 = p2*x21 + p7*x22  + p12*x23 + p17*x24 + p22*x25;
420         pc[22] = m23 = p3*x21 + p8*x22  + p13*x23 + p18*x24 + p23*x25;
421         pc[23] = m24 = p4*x21 + p9*x22  + p14*x23 + p19*x24 + p24*x25;
422         pc[24] = m25 = p5*x21 + p10*x22 + p15*x23 + p20*x24 + p25*x25;
423 
424         nz = bi[row+1] - diag_offset[row] - 1;
425         pv += 25;
426         for (j=0; j<nz; j++) {
427           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
428           x5   = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
429           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
430           x14  = pv[13]; x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17];
431           x19 = pv[18];  x20 = pv[19]; x21 = pv[20]; x22 = pv[21]; x23 = pv[22];
432           x24 = pv[23];  x25 = pv[24];
433           x    = rtmp + 25*pj[j];
434           x[0] -= m1*x1 + m6*x2   + m11*x3  + m16*x4 + m21*x5;
435           x[1] -= m2*x1 + m7*x2   + m12*x3  + m17*x4 + m22*x5;
436           x[2] -= m3*x1 + m8*x2   + m13*x3  + m18*x4 + m23*x5;
437           x[3] -= m4*x1 + m9*x2   + m14*x3  + m19*x4 + m24*x5;
438           x[4] -= m5*x1 + m10*x2  + m15*x3  + m20*x4 + m25*x5;
439 
440           x[5] -= m1*x6 + m6*x7   + m11*x8  + m16*x9 + m21*x10;
441           x[6] -= m2*x6 + m7*x7   + m12*x8  + m17*x9 + m22*x10;
442           x[7] -= m3*x6 + m8*x7   + m13*x8  + m18*x9 + m23*x10;
443           x[8] -= m4*x6 + m9*x7   + m14*x8  + m19*x9 + m24*x10;
444           x[9] -= m5*x6 + m10*x7  + m15*x8  + m20*x9 + m25*x10;
445 
446           x[10] -= m1*x11 + m6*x12  + m11*x13 + m16*x14 + m21*x15;
447           x[11] -= m2*x11 + m7*x12  + m12*x13 + m17*x14 + m22*x15;
448           x[12] -= m3*x11 + m8*x12  + m13*x13 + m18*x14 + m23*x15;
449           x[13] -= m4*x11 + m9*x12  + m14*x13 + m19*x14 + m24*x15;
450           x[14] -= m5*x11 + m10*x12 + m15*x13 + m20*x14 + m25*x15;
451 
452           x[15] -= m1*x16 + m6*x17  + m11*x18 + m16*x19 + m21*x20;
453           x[16] -= m2*x16 + m7*x17  + m12*x18 + m17*x19 + m22*x20;
454           x[17] -= m3*x16 + m8*x17  + m13*x18 + m18*x19 + m23*x20;
455           x[18] -= m4*x16 + m9*x17  + m14*x18 + m19*x19 + m24*x20;
456           x[19] -= m5*x16 + m10*x17 + m15*x18 + m20*x19 + m25*x20;
457 
458           x[20] -= m1*x21 + m6*x22  + m11*x23 + m16*x24 + m21*x25;
459           x[21] -= m2*x21 + m7*x22  + m12*x23 + m17*x24 + m22*x25;
460           x[22] -= m3*x21 + m8*x22  + m13*x23 + m18*x24 + m23*x25;
461           x[23] -= m4*x21 + m9*x22  + m14*x23 + m19*x24 + m24*x25;
462           x[24] -= m5*x21 + m10*x22 + m15*x23 + m20*x24 + m25*x25;
463           pv   += 25;
464         }
465         ierr = PetscLogFlops(250.0*nz+225.0);CHKERRQ(ierr);
466       }
467       row = *ajtmp++;
468     }
469     /* finished row so stick it into b->a */
470     pv = ba + 25*bi[i];
471     pj = bj + bi[i];
472     nz = bi[i+1] - bi[i];
473     for (j=0; j<nz; j++) {
474       x      = rtmp+25*pj[j];
475       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
476       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
477       pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
478       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; pv[16] = x[16]; pv[17] = x[17];
479       pv[18] = x[18]; pv[19] = x[19]; pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22];
480       pv[23] = x[23]; pv[24] = x[24];
481       pv   += 25;
482     }
483     /* invert diagonal block */
484     w = ba + 25*diag_offset[i];
485     ierr = PetscKernel_A_gets_inverse_A_5(w,ipvt,work,shift);CHKERRQ(ierr);
486   }
487 
488   ierr = PetscFree(rtmp);CHKERRQ(ierr);
489   C->ops->solve          = MatSolve_SeqBAIJ_5_NaturalOrdering_inplace;
490   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5_NaturalOrdering_inplace;
491   C->assembled = PETSC_TRUE;
492   ierr = PetscLogFlops(1.333333333333*5*5*5*b->mbs);CHKERRQ(ierr); /* from inverting diagonal blocks */
493   PetscFunctionReturn(0);
494 }
495 
496 #undef __FUNCT__
497 #define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_5_NaturalOrdering"
498 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5_NaturalOrdering(Mat B,Mat A,const MatFactorInfo *info)
499 {
500   Mat            C=B;
501   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ *)C->data;
502   PetscErrorCode ierr;
503   PetscInt       i,j,k,nz,nzL,row;
504   const PetscInt n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
505   const PetscInt *ajtmp,*bjtmp,*bdiag=b->diag,*pj,bs2=a->bs2;
506   MatScalar      *rtmp,*pc,*mwork,*v,*vv,*pv,*aa=a->a,work[25];
507   PetscInt       flg,ipvt[5];
508   PetscReal      shift = info->shiftamount;
509 
510   PetscFunctionBegin;
511   /* generate work space needed by the factorization */
512   ierr = PetscMalloc2(bs2*n,MatScalar,&rtmp,bs2,MatScalar,&mwork);CHKERRQ(ierr);
513   ierr = PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));CHKERRQ(ierr);
514 
515   for (i=0; i<n; i++) {
516     /* zero rtmp */
517     /* L part */
518     nz    = bi[i+1] - bi[i];
519     bjtmp = bj + bi[i];
520     for  (j=0; j<nz; j++) {
521       ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
522     }
523 
524     /* U part */
525     nz = bdiag[i] - bdiag[i+1];
526     bjtmp = bj + bdiag[i+1]+1;
527     for  (j=0; j<nz; j++) {
528       ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
529     }
530 
531     /* load in initial (unfactored row) */
532     nz    = ai[i+1] - ai[i];
533     ajtmp = aj + ai[i];
534     v     = aa + bs2*ai[i];
535     for (j=0; j<nz; j++) {
536       ierr = PetscMemcpy(rtmp+bs2*ajtmp[j],v+bs2*j,bs2*sizeof(MatScalar));CHKERRQ(ierr);
537     }
538 
539     /* elimination */
540     bjtmp = bj + bi[i];
541     nzL   = bi[i+1] - bi[i];
542     for (k=0;k < nzL;k++) {
543       row = bjtmp[k];
544       pc = rtmp + bs2*row;
545       for (flg=0,j=0; j<bs2; j++) {
546         if (pc[j]!=0.0) {
547           flg = 1;
548           break;
549         }
550       }
551       if (flg) {
552         pv = b->a + bs2*bdiag[row];
553         /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
554         ierr = PetscKernel_A_gets_A_times_B_5(pc,pv,mwork);CHKERRQ(ierr);
555 
556         pj = b->j + bdiag[row+1]+1; /* begining of U(row,:) */
557         pv = b->a + bs2*(bdiag[row+1]+1);
558         nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries inU(row,:), excluding diag */
559         for (j=0; j<nz; j++) {
560           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
561           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
562           vv    = rtmp + bs2*pj[j];
563           ierr = PetscKernel_A_gets_A_minus_B_times_C_5(vv,pc,pv);CHKERRQ(ierr);
564           pv  += bs2;
565         }
566         ierr = PetscLogFlops(250*nz+225);CHKERRQ(ierr); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
567       }
568     }
569 
570     /* finished row so stick it into b->a */
571     /* L part */
572     pv   = b->a + bs2*bi[i] ;
573     pj   = b->j + bi[i] ;
574     nz   = bi[i+1] - bi[i];
575     for (j=0; j<nz; j++) {
576       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
577     }
578 
579     /* Mark diagonal and invert diagonal for simplier triangular solves */
580     pv   = b->a + bs2*bdiag[i];
581     pj   = b->j + bdiag[i];
582     ierr = PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));CHKERRQ(ierr);
583     /* ierr = PetscKernel_A_gets_inverse_A(bs,pv,v_pivots,v_work);CHKERRQ(ierr); */
584     ierr = PetscKernel_A_gets_inverse_A_5(pv,ipvt,work,shift);CHKERRQ(ierr);
585 
586     /* U part */
587     pv = b->a + bs2*(bdiag[i+1]+1);
588     pj = b->j + bdiag[i+1]+1;
589     nz = bdiag[i] - bdiag[i+1] - 1;
590     for (j=0; j<nz; j++) {
591       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
592     }
593   }
594   ierr = PetscFree2(rtmp,mwork);CHKERRQ(ierr);
595   C->ops->solve          = MatSolve_SeqBAIJ_5_NaturalOrdering;
596   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5_NaturalOrdering;
597   C->assembled = PETSC_TRUE;
598   ierr = PetscLogFlops(1.333333333333*5*5*5*n);CHKERRQ(ierr); /* from inverting diagonal blocks */
599   PetscFunctionReturn(0);
600 }
601