xref: /petsc/src/mat/impls/baij/seq/baijfact9.c (revision bebe2cf65d55febe21a5af8db2bd2e168caaa2e7)
1 
2 /*
3     Factorization code for BAIJ format.
4 */
5 #include <../src/mat/impls/baij/seq/baij.h>
6 #include <petsc/private/kernels/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 = PetscMalloc1(25*(n+1),&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 
198   C->ops->solve          = MatSolve_SeqBAIJ_5_inplace;
199   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5_inplace;
200   C->assembled           = PETSC_TRUE;
201 
202   ierr = PetscLogFlops(1.333333333333*5*5*5*b->mbs);CHKERRQ(ierr); /* from inverting diagonal blocks */
203   PetscFunctionReturn(0);
204 }
205 
206 /* MatLUFactorNumeric_SeqBAIJ_5 -
207      copied from MatLUFactorNumeric_SeqBAIJ_N_inplace() and manually re-implemented
208        PetscKernel_A_gets_A_times_B()
209        PetscKernel_A_gets_A_minus_B_times_C()
210        PetscKernel_A_gets_inverse_A()
211 */
212 
213 #undef __FUNCT__
214 #define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_5"
215 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5(Mat B,Mat A,const MatFactorInfo *info)
216 {
217   Mat            C     =B;
218   Mat_SeqBAIJ    *a    =(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ*)C->data;
219   IS             isrow = b->row,isicol = b->icol;
220   PetscErrorCode ierr;
221   const PetscInt *r,*ic;
222   PetscInt       i,j,k,nz,nzL,row;
223   const PetscInt n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
224   const PetscInt *ajtmp,*bjtmp,*bdiag=b->diag,*pj,bs2=a->bs2;
225   MatScalar      *rtmp,*pc,*mwork,*v,*pv,*aa=a->a,work[25];
226   PetscInt       flg,ipvt[5];
227   PetscReal      shift = info->shiftamount;
228 
229   PetscFunctionBegin;
230   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
231   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
232 
233   /* generate work space needed by the factorization */
234   ierr = PetscMalloc2(bs2*n,&rtmp,bs2,&mwork);CHKERRQ(ierr);
235   ierr = PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));CHKERRQ(ierr);
236 
237   for (i=0; i<n; i++) {
238     /* zero rtmp */
239     /* L part */
240     nz    = bi[i+1] - bi[i];
241     bjtmp = bj + bi[i];
242     for  (j=0; j<nz; j++) {
243       ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
244     }
245 
246     /* U part */
247     nz    = bdiag[i] - bdiag[i+1];
248     bjtmp = bj + bdiag[i+1]+1;
249     for  (j=0; j<nz; j++) {
250       ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
251     }
252 
253     /* load in initial (unfactored row) */
254     nz    = ai[r[i]+1] - ai[r[i]];
255     ajtmp = aj + ai[r[i]];
256     v     = aa + bs2*ai[r[i]];
257     for (j=0; j<nz; j++) {
258       ierr = PetscMemcpy(rtmp+bs2*ic[ajtmp[j]],v+bs2*j,bs2*sizeof(MatScalar));CHKERRQ(ierr);
259     }
260 
261     /* elimination */
262     bjtmp = bj + bi[i];
263     nzL   = bi[i+1] - bi[i];
264     for (k=0; k < nzL; k++) {
265       row = bjtmp[k];
266       pc  = rtmp + bs2*row;
267       for (flg=0,j=0; j<bs2; j++) {
268         if (pc[j]!=0.0) {
269           flg = 1;
270           break;
271         }
272       }
273       if (flg) {
274         pv = b->a + bs2*bdiag[row];
275         /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
276         ierr = PetscKernel_A_gets_A_times_B_5(pc,pv,mwork);CHKERRQ(ierr);
277 
278         pj = b->j + bdiag[row+1]+1; /* begining of U(row,:) */
279         pv = b->a + bs2*(bdiag[row+1]+1);
280         nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries inU(row,:), excluding diag */
281         for (j=0; j<nz; j++) {
282           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
283           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
284           v    = rtmp + bs2*pj[j];
285           ierr = PetscKernel_A_gets_A_minus_B_times_C_5(v,pc,pv);CHKERRQ(ierr);
286           pv  += bs2;
287         }
288         ierr = PetscLogFlops(250*nz+225);CHKERRQ(ierr); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
289       }
290     }
291 
292     /* finished row so stick it into b->a */
293     /* L part */
294     pv = b->a + bs2*bi[i];
295     pj = b->j + bi[i];
296     nz = bi[i+1] - bi[i];
297     for (j=0; j<nz; j++) {
298       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
299     }
300 
301     /* Mark diagonal and invert diagonal for simplier triangular solves */
302     pv   = b->a + bs2*bdiag[i];
303     pj   = b->j + bdiag[i];
304     ierr = PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));CHKERRQ(ierr);
305     /* ierr = PetscKernel_A_gets_inverse_A(bs,pv,v_pivots,v_work);CHKERRQ(ierr); */
306     ierr = PetscKernel_A_gets_inverse_A_5(pv,ipvt,work,shift);CHKERRQ(ierr);
307 
308     /* U part */
309     pv = b->a + bs2*(bdiag[i+1]+1);
310     pj = b->j + bdiag[i+1]+1;
311     nz = bdiag[i] - bdiag[i+1] - 1;
312     for (j=0; j<nz; j++) {
313       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
314     }
315   }
316 
317   ierr = PetscFree2(rtmp,mwork);CHKERRQ(ierr);
318   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
319   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
320 
321   C->ops->solve          = MatSolve_SeqBAIJ_5;
322   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5;
323   C->assembled           = PETSC_TRUE;
324 
325   ierr = PetscLogFlops(1.333333333333*5*5*5*n);CHKERRQ(ierr); /* from inverting diagonal blocks */
326   PetscFunctionReturn(0);
327 }
328 
329 /*
330       Version for when blocks are 5 by 5 Using natural ordering
331 */
332 #undef __FUNCT__
333 #define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_5_NaturalOrdering_inplace"
334 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5_NaturalOrdering_inplace(Mat C,Mat A,const MatFactorInfo *info)
335 {
336   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ*)C->data;
337   PetscErrorCode ierr;
338   PetscInt       i,j,n = a->mbs,*bi = b->i,*bj = b->j,ipvt[5];
339   PetscInt       *ajtmpold,*ajtmp,nz,row;
340   PetscInt       *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
341   MatScalar      *pv,*v,*rtmp,*pc,*w,*x;
342   MatScalar      x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15;
343   MatScalar      x16,x17,x18,x19,x20,x21,x22,x23,x24,x25;
344   MatScalar      p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15;
345   MatScalar      p16,p17,p18,p19,p20,p21,p22,p23,p24,p25;
346   MatScalar      m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12,m13,m14,m15;
347   MatScalar      m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
348   MatScalar      *ba   = b->a,*aa = a->a,work[25];
349   PetscReal      shift = info->shiftamount;
350 
351   PetscFunctionBegin;
352   ierr = PetscMalloc1(25*(n+1),&rtmp);CHKERRQ(ierr);
353   for (i=0; i<n; i++) {
354     nz    = bi[i+1] - bi[i];
355     ajtmp = bj + bi[i];
356     for  (j=0; j<nz; j++) {
357       x     = rtmp+25*ajtmp[j];
358       x[0]  = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = x[9] = 0.0;
359       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
360       x[16] = x[17] = x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0;
361     }
362     /* load in initial (unfactored row) */
363     nz       = ai[i+1] - ai[i];
364     ajtmpold = aj + ai[i];
365     v        = aa + 25*ai[i];
366     for (j=0; j<nz; j++) {
367       x     = rtmp+25*ajtmpold[j];
368       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
369       x[4]  = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
370       x[9]  = v[9];  x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
371       x[14] = v[14]; x[15] = v[15]; x[16] = v[16]; x[17] = v[17]; x[18] = v[18];
372       x[19] = v[19]; x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23];
373       x[24] = v[24];
374       v    += 25;
375     }
376     row = *ajtmp++;
377     while (row < i) {
378       pc  = rtmp + 25*row;
379       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
380       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
381       p10 = pc[9];  p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
382       p15 = pc[14]; p16 = pc[15]; p17 = pc[16]; p18 = pc[17];
383       p19 = pc[18]; p20 = pc[19]; p21 = pc[20]; p22 = pc[21]; p23 = pc[22];
384       p24 = pc[23]; p25 = pc[24];
385       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
386           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
387           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
388           || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0
389           || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 || p25 != 0.0) {
390         pv    = ba + 25*diag_offset[row];
391         pj    = bj + diag_offset[row] + 1;
392         x1    = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
393         x5    = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
394         x10   = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
395         x15   = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17]; x19 = pv[18];
396         x20   = pv[19]; x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
397         x25   = pv[24];
398         pc[0] = m1 = p1*x1 + p6*x2  + p11*x3 + p16*x4 + p21*x5;
399         pc[1] = m2 = p2*x1 + p7*x2  + p12*x3 + p17*x4 + p22*x5;
400         pc[2] = m3 = p3*x1 + p8*x2  + p13*x3 + p18*x4 + p23*x5;
401         pc[3] = m4 = p4*x1 + p9*x2  + p14*x3 + p19*x4 + p24*x5;
402         pc[4] = m5 = p5*x1 + p10*x2 + p15*x3 + p20*x4 + p25*x5;
403 
404         pc[5] = m6  = p1*x6 + p6*x7  + p11*x8 + p16*x9 + p21*x10;
405         pc[6] = m7  = p2*x6 + p7*x7  + p12*x8 + p17*x9 + p22*x10;
406         pc[7] = m8  = p3*x6 + p8*x7  + p13*x8 + p18*x9 + p23*x10;
407         pc[8] = m9  = p4*x6 + p9*x7  + p14*x8 + p19*x9 + p24*x10;
408         pc[9] = m10 = p5*x6 + p10*x7 + p15*x8 + p20*x9 + p25*x10;
409 
410         pc[10] = m11 = p1*x11 + p6*x12  + p11*x13 + p16*x14 + p21*x15;
411         pc[11] = m12 = p2*x11 + p7*x12  + p12*x13 + p17*x14 + p22*x15;
412         pc[12] = m13 = p3*x11 + p8*x12  + p13*x13 + p18*x14 + p23*x15;
413         pc[13] = m14 = p4*x11 + p9*x12  + p14*x13 + p19*x14 + p24*x15;
414         pc[14] = m15 = p5*x11 + p10*x12 + p15*x13 + p20*x14 + p25*x15;
415 
416         pc[15] = m16 = p1*x16 + p6*x17  + p11*x18 + p16*x19 + p21*x20;
417         pc[16] = m17 = p2*x16 + p7*x17  + p12*x18 + p17*x19 + p22*x20;
418         pc[17] = m18 = p3*x16 + p8*x17  + p13*x18 + p18*x19 + p23*x20;
419         pc[18] = m19 = p4*x16 + p9*x17  + p14*x18 + p19*x19 + p24*x20;
420         pc[19] = m20 = p5*x16 + p10*x17 + p15*x18 + p20*x19 + p25*x20;
421 
422         pc[20] = m21 = p1*x21 + p6*x22  + p11*x23 + p16*x24 + p21*x25;
423         pc[21] = m22 = p2*x21 + p7*x22  + p12*x23 + p17*x24 + p22*x25;
424         pc[22] = m23 = p3*x21 + p8*x22  + p13*x23 + p18*x24 + p23*x25;
425         pc[23] = m24 = p4*x21 + p9*x22  + p14*x23 + p19*x24 + p24*x25;
426         pc[24] = m25 = p5*x21 + p10*x22 + p15*x23 + p20*x24 + p25*x25;
427 
428         nz  = bi[row+1] - diag_offset[row] - 1;
429         pv += 25;
430         for (j=0; j<nz; j++) {
431           x1    = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
432           x5    = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
433           x10   = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
434           x14   = pv[13]; x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17];
435           x19   = pv[18];  x20 = pv[19]; x21 = pv[20]; x22 = pv[21]; x23 = pv[22];
436           x24   = pv[23];  x25 = pv[24];
437           x     = rtmp + 25*pj[j];
438           x[0] -= m1*x1 + m6*x2   + m11*x3  + m16*x4 + m21*x5;
439           x[1] -= m2*x1 + m7*x2   + m12*x3  + m17*x4 + m22*x5;
440           x[2] -= m3*x1 + m8*x2   + m13*x3  + m18*x4 + m23*x5;
441           x[3] -= m4*x1 + m9*x2   + m14*x3  + m19*x4 + m24*x5;
442           x[4] -= m5*x1 + m10*x2  + m15*x3  + m20*x4 + m25*x5;
443 
444           x[5] -= m1*x6 + m6*x7   + m11*x8  + m16*x9 + m21*x10;
445           x[6] -= m2*x6 + m7*x7   + m12*x8  + m17*x9 + m22*x10;
446           x[7] -= m3*x6 + m8*x7   + m13*x8  + m18*x9 + m23*x10;
447           x[8] -= m4*x6 + m9*x7   + m14*x8  + m19*x9 + m24*x10;
448           x[9] -= m5*x6 + m10*x7  + m15*x8  + m20*x9 + m25*x10;
449 
450           x[10] -= m1*x11 + m6*x12  + m11*x13 + m16*x14 + m21*x15;
451           x[11] -= m2*x11 + m7*x12  + m12*x13 + m17*x14 + m22*x15;
452           x[12] -= m3*x11 + m8*x12  + m13*x13 + m18*x14 + m23*x15;
453           x[13] -= m4*x11 + m9*x12  + m14*x13 + m19*x14 + m24*x15;
454           x[14] -= m5*x11 + m10*x12 + m15*x13 + m20*x14 + m25*x15;
455 
456           x[15] -= m1*x16 + m6*x17  + m11*x18 + m16*x19 + m21*x20;
457           x[16] -= m2*x16 + m7*x17  + m12*x18 + m17*x19 + m22*x20;
458           x[17] -= m3*x16 + m8*x17  + m13*x18 + m18*x19 + m23*x20;
459           x[18] -= m4*x16 + m9*x17  + m14*x18 + m19*x19 + m24*x20;
460           x[19] -= m5*x16 + m10*x17 + m15*x18 + m20*x19 + m25*x20;
461 
462           x[20] -= m1*x21 + m6*x22  + m11*x23 + m16*x24 + m21*x25;
463           x[21] -= m2*x21 + m7*x22  + m12*x23 + m17*x24 + m22*x25;
464           x[22] -= m3*x21 + m8*x22  + m13*x23 + m18*x24 + m23*x25;
465           x[23] -= m4*x21 + m9*x22  + m14*x23 + m19*x24 + m24*x25;
466           x[24] -= m5*x21 + m10*x22 + m15*x23 + m20*x24 + m25*x25;
467           pv    += 25;
468         }
469         ierr = PetscLogFlops(250.0*nz+225.0);CHKERRQ(ierr);
470       }
471       row = *ajtmp++;
472     }
473     /* finished row so stick it into b->a */
474     pv = ba + 25*bi[i];
475     pj = bj + bi[i];
476     nz = bi[i+1] - bi[i];
477     for (j=0; j<nz; j++) {
478       x      = rtmp+25*pj[j];
479       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
480       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
481       pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
482       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; pv[16] = x[16]; pv[17] = x[17];
483       pv[18] = x[18]; pv[19] = x[19]; pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22];
484       pv[23] = x[23]; pv[24] = x[24];
485       pv    += 25;
486     }
487     /* invert diagonal block */
488     w    = ba + 25*diag_offset[i];
489     ierr = PetscKernel_A_gets_inverse_A_5(w,ipvt,work,shift);CHKERRQ(ierr);
490   }
491 
492   ierr = PetscFree(rtmp);CHKERRQ(ierr);
493 
494   C->ops->solve          = MatSolve_SeqBAIJ_5_NaturalOrdering_inplace;
495   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5_NaturalOrdering_inplace;
496   C->assembled           = PETSC_TRUE;
497 
498   ierr = PetscLogFlops(1.333333333333*5*5*5*b->mbs);CHKERRQ(ierr); /* from inverting diagonal blocks */
499   PetscFunctionReturn(0);
500 }
501 
502 #undef __FUNCT__
503 #define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_5_NaturalOrdering"
504 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5_NaturalOrdering(Mat B,Mat A,const MatFactorInfo *info)
505 {
506   Mat            C =B;
507   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ*)C->data;
508   PetscErrorCode ierr;
509   PetscInt       i,j,k,nz,nzL,row;
510   const PetscInt n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
511   const PetscInt *ajtmp,*bjtmp,*bdiag=b->diag,*pj,bs2=a->bs2;
512   MatScalar      *rtmp,*pc,*mwork,*v,*vv,*pv,*aa=a->a,work[25];
513   PetscInt       flg,ipvt[5];
514   PetscReal      shift = info->shiftamount;
515 
516   PetscFunctionBegin;
517   /* generate work space needed by the factorization */
518   ierr = PetscMalloc2(bs2*n,&rtmp,bs2,&mwork);CHKERRQ(ierr);
519   ierr = PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));CHKERRQ(ierr);
520 
521   for (i=0; i<n; i++) {
522     /* zero rtmp */
523     /* L part */
524     nz    = bi[i+1] - bi[i];
525     bjtmp = bj + bi[i];
526     for  (j=0; j<nz; j++) {
527       ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
528     }
529 
530     /* U part */
531     nz    = bdiag[i] - bdiag[i+1];
532     bjtmp = bj + bdiag[i+1]+1;
533     for  (j=0; j<nz; j++) {
534       ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
535     }
536 
537     /* load in initial (unfactored row) */
538     nz    = ai[i+1] - ai[i];
539     ajtmp = aj + ai[i];
540     v     = aa + bs2*ai[i];
541     for (j=0; j<nz; j++) {
542       ierr = PetscMemcpy(rtmp+bs2*ajtmp[j],v+bs2*j,bs2*sizeof(MatScalar));CHKERRQ(ierr);
543     }
544 
545     /* elimination */
546     bjtmp = bj + bi[i];
547     nzL   = bi[i+1] - bi[i];
548     for (k=0; k < nzL; k++) {
549       row = bjtmp[k];
550       pc  = rtmp + bs2*row;
551       for (flg=0,j=0; j<bs2; j++) {
552         if (pc[j]!=0.0) {
553           flg = 1;
554           break;
555         }
556       }
557       if (flg) {
558         pv = b->a + bs2*bdiag[row];
559         /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
560         ierr = PetscKernel_A_gets_A_times_B_5(pc,pv,mwork);CHKERRQ(ierr);
561 
562         pj = b->j + bdiag[row+1]+1; /* begining of U(row,:) */
563         pv = b->a + bs2*(bdiag[row+1]+1);
564         nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries inU(row,:), excluding diag */
565         for (j=0; j<nz; j++) {
566           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
567           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
568           vv   = rtmp + bs2*pj[j];
569           ierr = PetscKernel_A_gets_A_minus_B_times_C_5(vv,pc,pv);CHKERRQ(ierr);
570           pv  += bs2;
571         }
572         ierr = PetscLogFlops(250*nz+225);CHKERRQ(ierr); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
573       }
574     }
575 
576     /* finished row so stick it into b->a */
577     /* L part */
578     pv = b->a + bs2*bi[i];
579     pj = b->j + bi[i];
580     nz = bi[i+1] - bi[i];
581     for (j=0; j<nz; j++) {
582       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
583     }
584 
585     /* Mark diagonal and invert diagonal for simplier triangular solves */
586     pv   = b->a + bs2*bdiag[i];
587     pj   = b->j + bdiag[i];
588     ierr = PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));CHKERRQ(ierr);
589     /* ierr = PetscKernel_A_gets_inverse_A(bs,pv,v_pivots,v_work);CHKERRQ(ierr); */
590     ierr = PetscKernel_A_gets_inverse_A_5(pv,ipvt,work,shift);CHKERRQ(ierr);
591 
592     /* U part */
593     pv = b->a + bs2*(bdiag[i+1]+1);
594     pj = b->j + bdiag[i+1]+1;
595     nz = bdiag[i] - bdiag[i+1] - 1;
596     for (j=0; j<nz; j++) {
597       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
598     }
599   }
600   ierr = PetscFree2(rtmp,mwork);CHKERRQ(ierr);
601 
602   C->ops->solve          = MatSolve_SeqBAIJ_5_NaturalOrdering;
603   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5_NaturalOrdering;
604   C->assembled           = PETSC_TRUE;
605 
606   ierr = PetscLogFlops(1.333333333333*5*5*5*n);CHKERRQ(ierr); /* from inverting diagonal blocks */
607   PetscFunctionReturn(0);
608 }
609