xref: /petsc/src/mat/impls/baij/seq/baijfact9.c (revision 6abefa4f446b2ea91915da4e25ea0defa83db48e)
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 /*
11       Version for when blocks are 5 by 5
12 */
13 #undef __FUNCT__
14 #define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_5_inplace"
15 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5_inplace(Mat C,Mat A,const MatFactorInfo *info)
16 {
17   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
18   IS              isrow = b->row,isicol = b->icol;
19   PetscErrorCode  ierr;
20   const PetscInt  *r,*ic,*bi = b->i,*bj = b->j,*ajtmpold,*ajtmp;
21   PetscInt        i,j,n = a->mbs,nz,row,idx,ipvt[5];
22   const PetscInt  *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
23   MatScalar       *w,*pv,*rtmp,*x,*pc;
24   const MatScalar *v,*aa = a->a;
25   MatScalar       p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
26   MatScalar       p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
27   MatScalar       x17,x18,x19,x20,x21,x22,x23,x24,x25,p10,p11,p12,p13,p14;
28   MatScalar       p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,m10,m11,m12;
29   MatScalar       m13,m14,m15,m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
30   MatScalar       *ba = b->a,work[25];
31   PetscReal       shift = info->shiftamount;
32 
33   PetscFunctionBegin;
34   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
35   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
36   ierr = PetscMalloc(25*(n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
37 
38 #define PETSC_USE_MEMZERO 1
39 #define PETSC_USE_MEMCPY 1
40 
41   for (i=0; i<n; i++) {
42     nz    = bi[i+1] - bi[i];
43     ajtmp = bj + bi[i];
44     for  (j=0; j<nz; j++) {
45 #if defined(PETSC_USE_MEMZERO)
46       ierr = PetscMemzero(rtmp+25*ajtmp[j],25*sizeof(PetscScalar));CHKERRQ(ierr);
47 #else
48       x = rtmp+25*ajtmp[j];
49       x[0] = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
50       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
51       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0;
52 #endif
53     }
54     /* load in initial (unfactored row) */
55     idx      = r[i];
56     nz       = ai[idx+1] - ai[idx];
57     ajtmpold = aj + ai[idx];
58     v        = aa + 25*ai[idx];
59     for (j=0; j<nz; j++) {
60 #if defined(PETSC_USE_MEMCPY)
61       ierr = PetscMemcpy(rtmp+25*ic[ajtmpold[j]],v,25*sizeof(PetscScalar));CHKERRQ(ierr);
62 #else
63       x    = rtmp+25*ic[ajtmpold[j]];
64       x[0] = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
65       x[4] = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
66       x[9] = v[9]; x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
67       x[14] = v[14]; x[15] = v[15]; x[16] = v[16]; x[17] = v[17];
68       x[18] = v[18]; x[19] = v[19]; x[20] = v[20]; x[21] = v[21];
69       x[22] = v[22]; x[23] = v[23]; x[24] = v[24];
70 #endif
71       v    += 25;
72     }
73     row = *ajtmp++;
74     while (row < i) {
75       pc = rtmp + 25*row;
76       p1 = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
77       p5 = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
78       p10 = pc[9]; p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
79       p15 = pc[14]; p16 = pc[15]; p17 = pc[16]; p18 = pc[17]; p19 = pc[18];
80       p20 = pc[19]; p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
81       p25 = pc[24];
82       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
83           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
84           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
85           || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 ||
86           p20 != 0.0 || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 ||
87           p24 != 0.0 || p25 != 0.0) {
88         pv = ba + 25*diag_offset[row];
89         pj = bj + diag_offset[row] + 1;
90         x1 = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
91         x5 = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
92         x10 = pv[9]; x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
93         x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17];
94         x19 = pv[18]; x20 = pv[19]; x21 = pv[20]; x22 = pv[21];
95         x23 = pv[22]; x24 = pv[23]; x25 = pv[24];
96         pc[0] = m1 = p1*x1 + p6*x2  + p11*x3 + p16*x4 + p21*x5;
97         pc[1] = m2 = p2*x1 + p7*x2  + p12*x3 + p17*x4 + p22*x5;
98         pc[2] = m3 = p3*x1 + p8*x2  + p13*x3 + p18*x4 + p23*x5;
99         pc[3] = m4 = p4*x1 + p9*x2  + p14*x3 + p19*x4 + p24*x5;
100         pc[4] = m5 = p5*x1 + p10*x2 + p15*x3 + p20*x4 + p25*x5;
101 
102         pc[5] = m6 = p1*x6 + p6*x7  + p11*x8 + p16*x9 + p21*x10;
103         pc[6] = m7 = p2*x6 + p7*x7  + p12*x8 + p17*x9 + p22*x10;
104         pc[7] = m8 = p3*x6 + p8*x7  + p13*x8 + p18*x9 + p23*x10;
105         pc[8] = m9 = p4*x6 + p9*x7  + p14*x8 + p19*x9 + p24*x10;
106         pc[9] = m10 = p5*x6 + p10*x7 + p15*x8 + p20*x9 + p25*x10;
107 
108         pc[10] = m11 = p1*x11 + p6*x12  + p11*x13 + p16*x14 + p21*x15;
109         pc[11] = m12 = p2*x11 + p7*x12  + p12*x13 + p17*x14 + p22*x15;
110         pc[12] = m13 = p3*x11 + p8*x12  + p13*x13 + p18*x14 + p23*x15;
111         pc[13] = m14 = p4*x11 + p9*x12  + p14*x13 + p19*x14 + p24*x15;
112         pc[14] = m15 = p5*x11 + p10*x12 + p15*x13 + p20*x14 + p25*x15;
113 
114         pc[15] = m16 = p1*x16 + p6*x17  + p11*x18 + p16*x19 + p21*x20;
115         pc[16] = m17 = p2*x16 + p7*x17  + p12*x18 + p17*x19 + p22*x20;
116         pc[17] = m18 = p3*x16 + p8*x17  + p13*x18 + p18*x19 + p23*x20;
117         pc[18] = m19 = p4*x16 + p9*x17  + p14*x18 + p19*x19 + p24*x20;
118         pc[19] = m20 = p5*x16 + p10*x17 + p15*x18 + p20*x19 + p25*x20;
119 
120         pc[20] = m21 = p1*x21 + p6*x22  + p11*x23 + p16*x24 + p21*x25;
121         pc[21] = m22 = p2*x21 + p7*x22  + p12*x23 + p17*x24 + p22*x25;
122         pc[22] = m23 = p3*x21 + p8*x22  + p13*x23 + p18*x24 + p23*x25;
123         pc[23] = m24 = p4*x21 + p9*x22  + p14*x23 + p19*x24 + p24*x25;
124         pc[24] = m25 = p5*x21 + p10*x22 + p15*x23 + p20*x24 + p25*x25;
125 
126         nz = bi[row+1] - diag_offset[row] - 1;
127         pv += 25;
128         for (j=0; j<nz; j++) {
129           x1   = pv[0];  x2 = pv[1];   x3  = pv[2];  x4  = pv[3];
130           x5   = pv[4];  x6 = pv[5];   x7  = pv[6];  x8  = pv[7]; x9 = pv[8];
131           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
132           x14  = pv[13]; x15 = pv[14]; x16 = pv[15]; x17 = pv[16];
133           x18  = pv[17]; x19 = pv[18]; x20 = pv[19]; x21 = pv[20];
134           x22  = pv[21]; x23 = pv[22]; x24 = pv[23]; x25 = pv[24];
135           x    = rtmp + 25*pj[j];
136           x[0] -= m1*x1 + m6*x2  + m11*x3 + m16*x4 + m21*x5;
137           x[1] -= m2*x1 + m7*x2  + m12*x3 + m17*x4 + m22*x5;
138           x[2] -= m3*x1 + m8*x2  + m13*x3 + m18*x4 + m23*x5;
139           x[3] -= m4*x1 + m9*x2  + m14*x3 + m19*x4 + m24*x5;
140           x[4] -= m5*x1 + m10*x2 + m15*x3 + m20*x4 + m25*x5;
141 
142           x[5] -= m1*x6 + m6*x7  + m11*x8 + m16*x9 + m21*x10;
143           x[6] -= m2*x6 + m7*x7  + m12*x8 + m17*x9 + m22*x10;
144           x[7] -= m3*x6 + m8*x7  + m13*x8 + m18*x9 + m23*x10;
145           x[8] -= m4*x6 + m9*x7  + m14*x8 + m19*x9 + m24*x10;
146           x[9] -= m5*x6 + m10*x7 + m15*x8 + m20*x9 + m25*x10;
147 
148           x[10] -= m1*x11 + m6*x12  + m11*x13 + m16*x14 + m21*x15;
149           x[11] -= m2*x11 + m7*x12  + m12*x13 + m17*x14 + m22*x15;
150           x[12] -= m3*x11 + m8*x12  + m13*x13 + m18*x14 + m23*x15;
151           x[13] -= m4*x11 + m9*x12  + m14*x13 + m19*x14 + m24*x15;
152           x[14] -= m5*x11 + m10*x12 + m15*x13 + m20*x14 + m25*x15;
153 
154           x[15] -= m1*x16 + m6*x17  + m11*x18 + m16*x19 + m21*x20;
155           x[16] -= m2*x16 + m7*x17  + m12*x18 + m17*x19 + m22*x20;
156           x[17] -= m3*x16 + m8*x17  + m13*x18 + m18*x19 + m23*x20;
157           x[18] -= m4*x16 + m9*x17  + m14*x18 + m19*x19 + m24*x20;
158           x[19] -= m5*x16 + m10*x17 + m15*x18 + m20*x19 + m25*x20;
159 
160           x[20] -= m1*x21 + m6*x22  + m11*x23 + m16*x24 + m21*x25;
161           x[21] -= m2*x21 + m7*x22  + m12*x23 + m17*x24 + m22*x25;
162           x[22] -= m3*x21 + m8*x22  + m13*x23 + m18*x24 + m23*x25;
163           x[23] -= m4*x21 + m9*x22  + m14*x23 + m19*x24 + m24*x25;
164           x[24] -= m5*x21 + m10*x22 + m15*x23 + m20*x24 + m25*x25;
165 
166           pv   += 25;
167         }
168         ierr = PetscLogFlops(250.0*nz+225.0);CHKERRQ(ierr);
169       }
170       row = *ajtmp++;
171     }
172     /* finished row so stick it into b->a */
173     pv = ba + 25*bi[i];
174     pj = bj + bi[i];
175     nz = bi[i+1] - bi[i];
176     for (j=0; j<nz; j++) {
177 #if defined(PETSC_USE_MEMCPY)
178       ierr = PetscMemcpy(pv,rtmp+25*pj[j],25*sizeof(PetscScalar));CHKERRQ(ierr);
179 #else
180       x     = rtmp+25*pj[j];
181       pv[0] = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
182       pv[4] = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
183       pv[9] = x[9]; pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
184       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; pv[16] = x[16];
185       pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19]; pv[20] = x[20];
186       pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23]; pv[24] = x[24];
187 #endif
188       pv   += 25;
189     }
190     /* invert diagonal block */
191     w = ba + 25*diag_offset[i];
192     ierr = Kernel_A_gets_inverse_A_5(w,ipvt,work,shift);CHKERRQ(ierr);
193   }
194 
195   ierr = PetscFree(rtmp);CHKERRQ(ierr);
196   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
197   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
198   C->ops->solve          = MatSolve_SeqBAIJ_5_inplace;
199   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5_inplace;
200   C->assembled = PETSC_TRUE;
201   ierr = PetscLogFlops(1.333333333333*5*5*5*b->mbs);CHKERRQ(ierr); /* from inverting diagonal blocks */
202   PetscFunctionReturn(0);
203 }
204 
205 /* MatLUFactorNumeric_SeqBAIJ_5 -
206      copied from MatLUFactorNumeric_SeqBAIJ_N_inplace() and manually re-implemented
207        Kernel_A_gets_A_times_B()
208        Kernel_A_gets_A_minus_B_times_C()
209        Kernel_A_gets_inverse_A()
210 */
211 
212 #undef __FUNCT__
213 #define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_5"
214 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5(Mat B,Mat A,const MatFactorInfo *info)
215 {
216   Mat            C=B;
217   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ *)C->data;
218   IS             isrow = b->row,isicol = b->icol;
219   PetscErrorCode ierr;
220   const PetscInt *r,*ic,*ics;
221   PetscInt       i,j,k,nz,nzL,row;
222   const PetscInt n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
223   const PetscInt *ajtmp,*bjtmp,*bdiag=b->diag,*pj,bs2=a->bs2;
224   MatScalar      *rtmp,*pc,*mwork,*v,*pv,*aa=a->a,work[25];
225   PetscInt       flg,ipvt[5];
226   PetscReal      shift = info->shiftamount;
227 
228   PetscFunctionBegin;
229   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
230   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
231 
232   /* generate work space needed by the factorization */
233   ierr = PetscMalloc2(bs2*n,MatScalar,&rtmp,bs2,MatScalar,&mwork);CHKERRQ(ierr);
234   ierr = PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));CHKERRQ(ierr);
235   ics  = ic;
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++) { if (pc[j]!=0.0) { flg = 1; break; }}
268       if (flg) {
269         pv = b->a + bs2*bdiag[row];
270         /* Kernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
271         ierr = Kernel_A_gets_A_times_B_5(pc,pv,mwork);CHKERRQ(ierr);
272 
273         pj = b->j + bdiag[row+1]+1; /* begining of U(row,:) */
274         pv = b->a + bs2*(bdiag[row+1]+1);
275         nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries inU(row,:), excluding diag */
276         for (j=0; j<nz; j++) {
277           /* Kernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
278           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
279           v    = rtmp + bs2*pj[j];
280           ierr = Kernel_A_gets_A_minus_B_times_C_5(v,pc,pv);CHKERRQ(ierr);
281           pv  += bs2;
282         }
283         ierr = PetscLogFlops(250*nz+225);CHKERRQ(ierr); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
284       }
285     }
286 
287     /* finished row so stick it into b->a */
288     /* L part */
289     pv   = b->a + bs2*bi[i] ;
290     pj   = b->j + bi[i] ;
291     nz   = bi[i+1] - bi[i];
292     for (j=0; j<nz; j++) {
293       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
294     }
295 
296     /* Mark diagonal and invert diagonal for simplier triangular solves */
297     pv   = b->a + bs2*bdiag[i];
298     pj   = b->j + bdiag[i];
299     ierr = PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));CHKERRQ(ierr);
300     /* ierr = Kernel_A_gets_inverse_A(bs,pv,v_pivots,v_work);CHKERRQ(ierr); */
301     ierr = Kernel_A_gets_inverse_A_5(pv,ipvt,work,shift);CHKERRQ(ierr);
302 
303     /* U part */
304     pv = b->a + bs2*(bdiag[i+1]+1);
305     pj = b->j + bdiag[i+1]+1;
306     nz = bdiag[i] - bdiag[i+1] - 1;
307     for (j=0; j<nz; j++){
308       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
309     }
310   }
311 
312   ierr = PetscFree2(rtmp,mwork);CHKERRQ(ierr);
313   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
314   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
315   C->ops->solve          = MatSolve_SeqBAIJ_5;
316   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5;
317   C->assembled = PETSC_TRUE;
318   ierr = PetscLogFlops(1.333333333333*5*5*5*n);CHKERRQ(ierr); /* from inverting diagonal blocks */
319   PetscFunctionReturn(0);
320 }
321 
322 /*
323       Version for when blocks are 5 by 5 Using natural ordering
324 */
325 #undef __FUNCT__
326 #define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_5_NaturalOrdering_inplace"
327 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5_NaturalOrdering_inplace(Mat C,Mat A,const MatFactorInfo *info)
328 {
329   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
330   PetscErrorCode ierr;
331   PetscInt       i,j,n = a->mbs,*bi = b->i,*bj = b->j,ipvt[5];
332   PetscInt       *ajtmpold,*ajtmp,nz,row;
333   PetscInt       *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
334   MatScalar      *pv,*v,*rtmp,*pc,*w,*x;
335   MatScalar      x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15;
336   MatScalar      x16,x17,x18,x19,x20,x21,x22,x23,x24,x25;
337   MatScalar      p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15;
338   MatScalar      p16,p17,p18,p19,p20,p21,p22,p23,p24,p25;
339   MatScalar      m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12,m13,m14,m15;
340   MatScalar      m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
341   MatScalar      *ba = b->a,*aa = a->a,work[25];
342   PetscReal      shift = info->shiftamount;
343 
344   PetscFunctionBegin;
345   ierr = PetscMalloc(25*(n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
346   for (i=0; i<n; i++) {
347     nz    = bi[i+1] - bi[i];
348     ajtmp = bj + bi[i];
349     for  (j=0; j<nz; j++) {
350       x = rtmp+25*ajtmp[j];
351       x[0]  = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = x[9] = 0.0;
352       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
353       x[16] = x[17] = x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0;
354     }
355     /* load in initial (unfactored row) */
356     nz       = ai[i+1] - ai[i];
357     ajtmpold = aj + ai[i];
358     v        = aa + 25*ai[i];
359     for (j=0; j<nz; j++) {
360       x    = rtmp+25*ajtmpold[j];
361       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
362       x[4]  = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
363       x[9]  = v[9];  x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
364       x[14] = v[14]; x[15] = v[15]; x[16] = v[16]; x[17] = v[17]; x[18] = v[18];
365       x[19] = v[19]; x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23];
366       x[24] = v[24];
367       v    += 25;
368     }
369     row = *ajtmp++;
370     while (row < i) {
371       pc  = rtmp + 25*row;
372       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
373       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
374       p10 = pc[9];  p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
375       p15 = pc[14]; p16 = pc[15]; p17 = pc[16]; p18 = pc[17];
376       p19 = pc[18]; p20 = pc[19]; p21 = pc[20]; p22 = pc[21]; p23 = pc[22];
377       p24 = pc[23]; p25 = pc[24];
378       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
379           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
380           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
381           || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0
382           || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 || p25 != 0.0) {
383         pv = ba + 25*diag_offset[row];
384         pj = bj + diag_offset[row] + 1;
385         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
386         x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
387         x10 = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
388         x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17]; x19 = pv[18];
389         x20 = pv[19]; x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
390         x25 = pv[24];
391         pc[0] = m1 = p1*x1 + p6*x2  + p11*x3 + p16*x4 + p21*x5;
392         pc[1] = m2 = p2*x1 + p7*x2  + p12*x3 + p17*x4 + p22*x5;
393         pc[2] = m3 = p3*x1 + p8*x2  + p13*x3 + p18*x4 + p23*x5;
394         pc[3] = m4 = p4*x1 + p9*x2  + p14*x3 + p19*x4 + p24*x5;
395         pc[4] = m5 = p5*x1 + p10*x2 + p15*x3 + p20*x4 + p25*x5;
396 
397         pc[5]  = m6  = p1*x6 + p6*x7  + p11*x8 + p16*x9 + p21*x10;
398         pc[6]  = m7  = p2*x6 + p7*x7  + p12*x8 + p17*x9 + p22*x10;
399         pc[7]  = m8  = p3*x6 + p8*x7  + p13*x8 + p18*x9 + p23*x10;
400         pc[8]  = m9  = p4*x6 + p9*x7  + p14*x8 + p19*x9 + p24*x10;
401         pc[9]  = m10 = p5*x6 + p10*x7 + p15*x8 + p20*x9 + p25*x10;
402 
403         pc[10] = m11 = p1*x11 + p6*x12  + p11*x13 + p16*x14 + p21*x15;
404         pc[11] = m12 = p2*x11 + p7*x12  + p12*x13 + p17*x14 + p22*x15;
405         pc[12] = m13 = p3*x11 + p8*x12  + p13*x13 + p18*x14 + p23*x15;
406         pc[13] = m14 = p4*x11 + p9*x12  + p14*x13 + p19*x14 + p24*x15;
407         pc[14] = m15 = p5*x11 + p10*x12 + p15*x13 + p20*x14 + p25*x15;
408 
409         pc[15] = m16 = p1*x16 + p6*x17  + p11*x18 + p16*x19 + p21*x20;
410         pc[16] = m17 = p2*x16 + p7*x17  + p12*x18 + p17*x19 + p22*x20;
411         pc[17] = m18 = p3*x16 + p8*x17  + p13*x18 + p18*x19 + p23*x20;
412         pc[18] = m19 = p4*x16 + p9*x17  + p14*x18 + p19*x19 + p24*x20;
413         pc[19] = m20 = p5*x16 + p10*x17 + p15*x18 + p20*x19 + p25*x20;
414 
415         pc[20] = m21 = p1*x21 + p6*x22  + p11*x23 + p16*x24 + p21*x25;
416         pc[21] = m22 = p2*x21 + p7*x22  + p12*x23 + p17*x24 + p22*x25;
417         pc[22] = m23 = p3*x21 + p8*x22  + p13*x23 + p18*x24 + p23*x25;
418         pc[23] = m24 = p4*x21 + p9*x22  + p14*x23 + p19*x24 + p24*x25;
419         pc[24] = m25 = p5*x21 + p10*x22 + p15*x23 + p20*x24 + p25*x25;
420 
421         nz = bi[row+1] - diag_offset[row] - 1;
422         pv += 25;
423         for (j=0; j<nz; j++) {
424           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
425           x5   = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
426           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
427           x14  = pv[13]; x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17];
428           x19 = pv[18];  x20 = pv[19]; x21 = pv[20]; x22 = pv[21]; x23 = pv[22];
429           x24 = pv[23];  x25 = pv[24];
430           x    = rtmp + 25*pj[j];
431           x[0] -= m1*x1 + m6*x2   + m11*x3  + m16*x4 + m21*x5;
432           x[1] -= m2*x1 + m7*x2   + m12*x3  + m17*x4 + m22*x5;
433           x[2] -= m3*x1 + m8*x2   + m13*x3  + m18*x4 + m23*x5;
434           x[3] -= m4*x1 + m9*x2   + m14*x3  + m19*x4 + m24*x5;
435           x[4] -= m5*x1 + m10*x2  + m15*x3  + m20*x4 + m25*x5;
436 
437           x[5] -= m1*x6 + m6*x7   + m11*x8  + m16*x9 + m21*x10;
438           x[6] -= m2*x6 + m7*x7   + m12*x8  + m17*x9 + m22*x10;
439           x[7] -= m3*x6 + m8*x7   + m13*x8  + m18*x9 + m23*x10;
440           x[8] -= m4*x6 + m9*x7   + m14*x8  + m19*x9 + m24*x10;
441           x[9] -= m5*x6 + m10*x7  + m15*x8  + m20*x9 + m25*x10;
442 
443           x[10] -= m1*x11 + m6*x12  + m11*x13 + m16*x14 + m21*x15;
444           x[11] -= m2*x11 + m7*x12  + m12*x13 + m17*x14 + m22*x15;
445           x[12] -= m3*x11 + m8*x12  + m13*x13 + m18*x14 + m23*x15;
446           x[13] -= m4*x11 + m9*x12  + m14*x13 + m19*x14 + m24*x15;
447           x[14] -= m5*x11 + m10*x12 + m15*x13 + m20*x14 + m25*x15;
448 
449           x[15] -= m1*x16 + m6*x17  + m11*x18 + m16*x19 + m21*x20;
450           x[16] -= m2*x16 + m7*x17  + m12*x18 + m17*x19 + m22*x20;
451           x[17] -= m3*x16 + m8*x17  + m13*x18 + m18*x19 + m23*x20;
452           x[18] -= m4*x16 + m9*x17  + m14*x18 + m19*x19 + m24*x20;
453           x[19] -= m5*x16 + m10*x17 + m15*x18 + m20*x19 + m25*x20;
454 
455           x[20] -= m1*x21 + m6*x22  + m11*x23 + m16*x24 + m21*x25;
456           x[21] -= m2*x21 + m7*x22  + m12*x23 + m17*x24 + m22*x25;
457           x[22] -= m3*x21 + m8*x22  + m13*x23 + m18*x24 + m23*x25;
458           x[23] -= m4*x21 + m9*x22  + m14*x23 + m19*x24 + m24*x25;
459           x[24] -= m5*x21 + m10*x22 + m15*x23 + m20*x24 + m25*x25;
460           pv   += 25;
461         }
462         ierr = PetscLogFlops(250.0*nz+225.0);CHKERRQ(ierr);
463       }
464       row = *ajtmp++;
465     }
466     /* finished row so stick it into b->a */
467     pv = ba + 25*bi[i];
468     pj = bj + bi[i];
469     nz = bi[i+1] - bi[i];
470     for (j=0; j<nz; j++) {
471       x      = rtmp+25*pj[j];
472       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
473       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
474       pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
475       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; pv[16] = x[16]; pv[17] = x[17];
476       pv[18] = x[18]; pv[19] = x[19]; pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22];
477       pv[23] = x[23]; pv[24] = x[24];
478       pv   += 25;
479     }
480     /* invert diagonal block */
481     w = ba + 25*diag_offset[i];
482     ierr = Kernel_A_gets_inverse_A_5(w,ipvt,work,shift);CHKERRQ(ierr);
483   }
484 
485   ierr = PetscFree(rtmp);CHKERRQ(ierr);
486   C->ops->solve          = MatSolve_SeqBAIJ_5_NaturalOrdering_inplace;
487   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5_NaturalOrdering_inplace;
488   C->assembled = PETSC_TRUE;
489   ierr = PetscLogFlops(1.333333333333*5*5*5*b->mbs);CHKERRQ(ierr); /* from inverting diagonal blocks */
490   PetscFunctionReturn(0);
491 }
492 
493 #undef __FUNCT__
494 #define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_5_NaturalOrdering"
495 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5_NaturalOrdering(Mat B,Mat A,const MatFactorInfo *info)
496 {
497   Mat            C=B;
498   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ *)C->data;
499   PetscErrorCode ierr;
500   PetscInt       i,j,k,nz,nzL,row;
501   const PetscInt n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
502   const PetscInt *ajtmp,*bjtmp,*bdiag=b->diag,*pj,bs2=a->bs2;
503   MatScalar      *rtmp,*pc,*mwork,*v,*vv,*pv,*aa=a->a,work[25];
504   PetscInt       flg,ipvt[5];
505   PetscReal      shift = info->shiftamount;
506 
507   PetscFunctionBegin;
508   /* generate work space needed by the factorization */
509   ierr = PetscMalloc2(bs2*n,MatScalar,&rtmp,bs2,MatScalar,&mwork);CHKERRQ(ierr);
510   ierr = PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));CHKERRQ(ierr);
511 
512   for (i=0; i<n; i++){
513     /* zero rtmp */
514     /* L part */
515     nz    = bi[i+1] - bi[i];
516     bjtmp = bj + bi[i];
517     for  (j=0; j<nz; j++){
518       ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
519     }
520 
521     /* U part */
522     nz = bdiag[i] - bdiag[i+1];
523     bjtmp = bj + bdiag[i+1]+1;
524     for  (j=0; j<nz; j++){
525       ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
526     }
527 
528     /* load in initial (unfactored row) */
529     nz    = ai[i+1] - ai[i];
530     ajtmp = aj + ai[i];
531     v     = aa + bs2*ai[i];
532     for (j=0; j<nz; j++) {
533       ierr = PetscMemcpy(rtmp+bs2*ajtmp[j],v+bs2*j,bs2*sizeof(MatScalar));CHKERRQ(ierr);
534     }
535 
536     /* elimination */
537     bjtmp = bj + bi[i];
538     nzL   = bi[i+1] - bi[i];
539     for(k=0;k < nzL;k++) {
540       row = bjtmp[k];
541       pc = rtmp + bs2*row;
542       for (flg=0,j=0; j<bs2; j++) { if (pc[j]!=0.0) { flg = 1; break; }}
543       if (flg) {
544         pv = b->a + bs2*bdiag[row];
545         /* Kernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
546         ierr = Kernel_A_gets_A_times_B_5(pc,pv,mwork);CHKERRQ(ierr);
547 
548         pj = b->j + bdiag[row+1]+1; /* begining of U(row,:) */
549         pv = b->a + bs2*(bdiag[row+1]+1);
550         nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries inU(row,:), excluding diag */
551         for (j=0; j<nz; j++) {
552           /* Kernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
553           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
554           vv    = rtmp + bs2*pj[j];
555           ierr = Kernel_A_gets_A_minus_B_times_C_5(vv,pc,pv);CHKERRQ(ierr);
556           pv  += bs2;
557         }
558         ierr = PetscLogFlops(250*nz+225);CHKERRQ(ierr); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
559       }
560     }
561 
562     /* finished row so stick it into b->a */
563     /* L part */
564     pv   = b->a + bs2*bi[i] ;
565     pj   = b->j + bi[i] ;
566     nz   = bi[i+1] - bi[i];
567     for (j=0; j<nz; j++) {
568       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
569     }
570 
571     /* Mark diagonal and invert diagonal for simplier triangular solves */
572     pv   = b->a + bs2*bdiag[i];
573     pj   = b->j + bdiag[i];
574     ierr = PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));CHKERRQ(ierr);
575     /* ierr = Kernel_A_gets_inverse_A(bs,pv,v_pivots,v_work);CHKERRQ(ierr); */
576     ierr = Kernel_A_gets_inverse_A_5(pv,ipvt,work,shift);CHKERRQ(ierr);
577 
578     /* U part */
579     pv = b->a + bs2*(bdiag[i+1]+1);
580     pj = b->j + bdiag[i+1]+1;
581     nz = bdiag[i] - bdiag[i+1] - 1;
582     for (j=0; j<nz; j++){
583       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
584     }
585   }
586   ierr = PetscFree2(rtmp,mwork);CHKERRQ(ierr);
587   C->ops->solve          = MatSolve_SeqBAIJ_5_NaturalOrdering;
588   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5_NaturalOrdering;
589   C->assembled = PETSC_TRUE;
590   ierr = PetscLogFlops(1.333333333333*5*5*5*n);CHKERRQ(ierr); /* from inverting diagonal blocks */
591   PetscFunctionReturn(0);
592 }
593