xref: /petsc/src/mat/impls/baij/seq/baijfact9.c (revision 2b8d69ca7ea5fe9190df62c1dce3bbd66fce84dd)
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   PetscBool       allowzeropivot,zeropivotdetected;
32 
33   PetscFunctionBegin;
34   allowzeropivot = PetscNot(A->erroriffailure);
35   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
36   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
37   ierr = PetscMalloc1(25*(n+1),&rtmp);CHKERRQ(ierr);
38 
39 #define PETSC_USE_MEMZERO 1
40 #define PETSC_USE_MEMCPY 1
41 
42   for (i=0; i<n; i++) {
43     nz    = bi[i+1] - bi[i];
44     ajtmp = bj + bi[i];
45     for  (j=0; j<nz; j++) {
46 #if defined(PETSC_USE_MEMZERO)
47       ierr = PetscMemzero(rtmp+25*ajtmp[j],25*sizeof(PetscScalar));CHKERRQ(ierr);
48 #else
49       x     = rtmp+25*ajtmp[j];
50       x[0]  = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
51       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
52       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0;
53 #endif
54     }
55     /* load in initial (unfactored row) */
56     idx      = r[i];
57     nz       = ai[idx+1] - ai[idx];
58     ajtmpold = aj + ai[idx];
59     v        = aa + 25*ai[idx];
60     for (j=0; j<nz; j++) {
61 #if defined(PETSC_USE_MEMCPY)
62       ierr = PetscMemcpy(rtmp+25*ic[ajtmpold[j]],v,25*sizeof(PetscScalar));CHKERRQ(ierr);
63 #else
64       x     = rtmp+25*ic[ajtmpold[j]];
65       x[0]  = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
66       x[4]  = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
67       x[9]  = v[9]; x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
68       x[14] = v[14]; x[15] = v[15]; x[16] = v[16]; x[17] = v[17];
69       x[18] = v[18]; x[19] = v[19]; x[20] = v[20]; x[21] = v[21];
70       x[22] = v[22]; x[23] = v[23]; x[24] = v[24];
71 #endif
72       v += 25;
73     }
74     row = *ajtmp++;
75     while (row < i) {
76       pc  = rtmp + 25*row;
77       p1  = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
78       p5  = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
79       p10 = pc[9]; p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
80       p15 = pc[14]; p16 = pc[15]; p17 = pc[16]; p18 = pc[17]; p19 = pc[18];
81       p20 = pc[19]; p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
82       p25 = pc[24];
83       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
84           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
85           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
86           || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 ||
87           p20 != 0.0 || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 ||
88           p24 != 0.0 || p25 != 0.0) {
89         pv    = ba + 25*diag_offset[row];
90         pj    = bj + diag_offset[row] + 1;
91         x1    = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
92         x5    = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
93         x10   = pv[9]; x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
94         x15   = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17];
95         x19   = pv[18]; x20 = pv[19]; x21 = pv[20]; x22 = pv[21];
96         x23   = pv[22]; x24 = pv[23]; x25 = pv[24];
97         pc[0] = m1 = p1*x1 + p6*x2  + p11*x3 + p16*x4 + p21*x5;
98         pc[1] = m2 = p2*x1 + p7*x2  + p12*x3 + p17*x4 + p22*x5;
99         pc[2] = m3 = p3*x1 + p8*x2  + p13*x3 + p18*x4 + p23*x5;
100         pc[3] = m4 = p4*x1 + p9*x2  + p14*x3 + p19*x4 + p24*x5;
101         pc[4] = m5 = p5*x1 + p10*x2 + p15*x3 + p20*x4 + p25*x5;
102 
103         pc[5] = m6 = p1*x6 + p6*x7  + p11*x8 + p16*x9 + p21*x10;
104         pc[6] = m7 = p2*x6 + p7*x7  + p12*x8 + p17*x9 + p22*x10;
105         pc[7] = m8 = p3*x6 + p8*x7  + p13*x8 + p18*x9 + p23*x10;
106         pc[8] = m9 = p4*x6 + p9*x7  + p14*x8 + p19*x9 + p24*x10;
107         pc[9] = m10 = p5*x6 + p10*x7 + p15*x8 + p20*x9 + p25*x10;
108 
109         pc[10] = m11 = p1*x11 + p6*x12  + p11*x13 + p16*x14 + p21*x15;
110         pc[11] = m12 = p2*x11 + p7*x12  + p12*x13 + p17*x14 + p22*x15;
111         pc[12] = m13 = p3*x11 + p8*x12  + p13*x13 + p18*x14 + p23*x15;
112         pc[13] = m14 = p4*x11 + p9*x12  + p14*x13 + p19*x14 + p24*x15;
113         pc[14] = m15 = p5*x11 + p10*x12 + p15*x13 + p20*x14 + p25*x15;
114 
115         pc[15] = m16 = p1*x16 + p6*x17  + p11*x18 + p16*x19 + p21*x20;
116         pc[16] = m17 = p2*x16 + p7*x17  + p12*x18 + p17*x19 + p22*x20;
117         pc[17] = m18 = p3*x16 + p8*x17  + p13*x18 + p18*x19 + p23*x20;
118         pc[18] = m19 = p4*x16 + p9*x17  + p14*x18 + p19*x19 + p24*x20;
119         pc[19] = m20 = p5*x16 + p10*x17 + p15*x18 + p20*x19 + p25*x20;
120 
121         pc[20] = m21 = p1*x21 + p6*x22  + p11*x23 + p16*x24 + p21*x25;
122         pc[21] = m22 = p2*x21 + p7*x22  + p12*x23 + p17*x24 + p22*x25;
123         pc[22] = m23 = p3*x21 + p8*x22  + p13*x23 + p18*x24 + p23*x25;
124         pc[23] = m24 = p4*x21 + p9*x22  + p14*x23 + p19*x24 + p24*x25;
125         pc[24] = m25 = p5*x21 + p10*x22 + p15*x23 + p20*x24 + p25*x25;
126 
127         nz  = bi[row+1] - diag_offset[row] - 1;
128         pv += 25;
129         for (j=0; j<nz; j++) {
130           x1    = pv[0];  x2 = pv[1];   x3  = pv[2];  x4  = pv[3];
131           x5    = pv[4];  x6 = pv[5];   x7  = pv[6];  x8  = pv[7]; x9 = pv[8];
132           x10   = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
133           x14   = pv[13]; x15 = pv[14]; x16 = pv[15]; x17 = pv[16];
134           x18   = pv[17]; x19 = pv[18]; x20 = pv[19]; x21 = pv[20];
135           x22   = pv[21]; x23 = pv[22]; x24 = pv[23]; x25 = pv[24];
136           x     = rtmp + 25*pj[j];
137           x[0] -= m1*x1 + m6*x2  + m11*x3 + m16*x4 + m21*x5;
138           x[1] -= m2*x1 + m7*x2  + m12*x3 + m17*x4 + m22*x5;
139           x[2] -= m3*x1 + m8*x2  + m13*x3 + m18*x4 + m23*x5;
140           x[3] -= m4*x1 + m9*x2  + m14*x3 + m19*x4 + m24*x5;
141           x[4] -= m5*x1 + m10*x2 + m15*x3 + m20*x4 + m25*x5;
142 
143           x[5] -= m1*x6 + m6*x7  + m11*x8 + m16*x9 + m21*x10;
144           x[6] -= m2*x6 + m7*x7  + m12*x8 + m17*x9 + m22*x10;
145           x[7] -= m3*x6 + m8*x7  + m13*x8 + m18*x9 + m23*x10;
146           x[8] -= m4*x6 + m9*x7  + m14*x8 + m19*x9 + m24*x10;
147           x[9] -= m5*x6 + m10*x7 + m15*x8 + m20*x9 + m25*x10;
148 
149           x[10] -= m1*x11 + m6*x12  + m11*x13 + m16*x14 + m21*x15;
150           x[11] -= m2*x11 + m7*x12  + m12*x13 + m17*x14 + m22*x15;
151           x[12] -= m3*x11 + m8*x12  + m13*x13 + m18*x14 + m23*x15;
152           x[13] -= m4*x11 + m9*x12  + m14*x13 + m19*x14 + m24*x15;
153           x[14] -= m5*x11 + m10*x12 + m15*x13 + m20*x14 + m25*x15;
154 
155           x[15] -= m1*x16 + m6*x17  + m11*x18 + m16*x19 + m21*x20;
156           x[16] -= m2*x16 + m7*x17  + m12*x18 + m17*x19 + m22*x20;
157           x[17] -= m3*x16 + m8*x17  + m13*x18 + m18*x19 + m23*x20;
158           x[18] -= m4*x16 + m9*x17  + m14*x18 + m19*x19 + m24*x20;
159           x[19] -= m5*x16 + m10*x17 + m15*x18 + m20*x19 + m25*x20;
160 
161           x[20] -= m1*x21 + m6*x22  + m11*x23 + m16*x24 + m21*x25;
162           x[21] -= m2*x21 + m7*x22  + m12*x23 + m17*x24 + m22*x25;
163           x[22] -= m3*x21 + m8*x22  + m13*x23 + m18*x24 + m23*x25;
164           x[23] -= m4*x21 + m9*x22  + m14*x23 + m19*x24 + m24*x25;
165           x[24] -= m5*x21 + m10*x22 + m15*x23 + m20*x24 + m25*x25;
166 
167           pv += 25;
168         }
169         ierr = PetscLogFlops(250.0*nz+225.0);CHKERRQ(ierr);
170       }
171       row = *ajtmp++;
172     }
173     /* finished row so stick it into b->a */
174     pv = ba + 25*bi[i];
175     pj = bj + bi[i];
176     nz = bi[i+1] - bi[i];
177     for (j=0; j<nz; j++) {
178 #if defined(PETSC_USE_MEMCPY)
179       ierr = PetscMemcpy(pv,rtmp+25*pj[j],25*sizeof(PetscScalar));CHKERRQ(ierr);
180 #else
181       x      = rtmp+25*pj[j];
182       pv[0]  = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
183       pv[4]  = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
184       pv[9]  = x[9]; pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
185       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; pv[16] = x[16];
186       pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19]; pv[20] = x[20];
187       pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23]; pv[24] = x[24];
188 #endif
189       pv += 25;
190     }
191     /* invert diagonal block */
192     w    = ba + 25*diag_offset[i];
193     ierr = PetscKernel_A_gets_inverse_A_5(w,ipvt,work,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
194     if (zeropivotdetected) C->errortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
195   }
196 
197   ierr = PetscFree(rtmp);CHKERRQ(ierr);
198   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
199   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
200 
201   C->ops->solve          = MatSolve_SeqBAIJ_5_inplace;
202   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5_inplace;
203   C->assembled           = PETSC_TRUE;
204 
205   ierr = PetscLogFlops(1.333333333333*5*5*5*b->mbs);CHKERRQ(ierr); /* from inverting diagonal blocks */
206   PetscFunctionReturn(0);
207 }
208 
209 /* MatLUFactorNumeric_SeqBAIJ_5 -
210      copied from MatLUFactorNumeric_SeqBAIJ_N_inplace() and manually re-implemented
211        PetscKernel_A_gets_A_times_B()
212        PetscKernel_A_gets_A_minus_B_times_C()
213        PetscKernel_A_gets_inverse_A()
214 */
215 
216 #undef __FUNCT__
217 #define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_5"
218 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5(Mat B,Mat A,const MatFactorInfo *info)
219 {
220   Mat            C     =B;
221   Mat_SeqBAIJ    *a    =(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ*)C->data;
222   IS             isrow = b->row,isicol = b->icol;
223   PetscErrorCode ierr;
224   const PetscInt *r,*ic;
225   PetscInt       i,j,k,nz,nzL,row;
226   const PetscInt n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
227   const PetscInt *ajtmp,*bjtmp,*bdiag=b->diag,*pj,bs2=a->bs2;
228   MatScalar      *rtmp,*pc,*mwork,*v,*pv,*aa=a->a,work[25];
229   PetscInt       flg,ipvt[5];
230   PetscReal      shift = info->shiftamount;
231   PetscBool      allowzeropivot,zeropivotdetected;
232 
233   PetscFunctionBegin;
234   allowzeropivot = PetscNot(A->erroriffailure);
235   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
236   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
237 
238   /* generate work space needed by the factorization */
239   ierr = PetscMalloc2(bs2*n,&rtmp,bs2,&mwork);CHKERRQ(ierr);
240   ierr = PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));CHKERRQ(ierr);
241 
242   for (i=0; i<n; i++) {
243     /* zero rtmp */
244     /* L part */
245     nz    = bi[i+1] - bi[i];
246     bjtmp = bj + bi[i];
247     for  (j=0; j<nz; j++) {
248       ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
249     }
250 
251     /* U part */
252     nz    = bdiag[i] - bdiag[i+1];
253     bjtmp = bj + bdiag[i+1]+1;
254     for  (j=0; j<nz; j++) {
255       ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
256     }
257 
258     /* load in initial (unfactored row) */
259     nz    = ai[r[i]+1] - ai[r[i]];
260     ajtmp = aj + ai[r[i]];
261     v     = aa + bs2*ai[r[i]];
262     for (j=0; j<nz; j++) {
263       ierr = PetscMemcpy(rtmp+bs2*ic[ajtmp[j]],v+bs2*j,bs2*sizeof(MatScalar));CHKERRQ(ierr);
264     }
265 
266     /* elimination */
267     bjtmp = bj + bi[i];
268     nzL   = bi[i+1] - bi[i];
269     for (k=0; k < nzL; k++) {
270       row = bjtmp[k];
271       pc  = rtmp + bs2*row;
272       for (flg=0,j=0; j<bs2; j++) {
273         if (pc[j]!=0.0) {
274           flg = 1;
275           break;
276         }
277       }
278       if (flg) {
279         pv = b->a + bs2*bdiag[row];
280         /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
281         ierr = PetscKernel_A_gets_A_times_B_5(pc,pv,mwork);CHKERRQ(ierr);
282 
283         pj = b->j + bdiag[row+1]+1; /* begining of U(row,:) */
284         pv = b->a + bs2*(bdiag[row+1]+1);
285         nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries inU(row,:), excluding diag */
286         for (j=0; j<nz; j++) {
287           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
288           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
289           v    = rtmp + bs2*pj[j];
290           ierr = PetscKernel_A_gets_A_minus_B_times_C_5(v,pc,pv);CHKERRQ(ierr);
291           pv  += bs2;
292         }
293         ierr = PetscLogFlops(250*nz+225);CHKERRQ(ierr); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
294       }
295     }
296 
297     /* finished row so stick it into b->a */
298     /* L part */
299     pv = b->a + bs2*bi[i];
300     pj = b->j + bi[i];
301     nz = bi[i+1] - bi[i];
302     for (j=0; j<nz; j++) {
303       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
304     }
305 
306     /* Mark diagonal and invert diagonal for simplier triangular solves */
307     pv   = b->a + bs2*bdiag[i];
308     pj   = b->j + bdiag[i];
309     ierr = PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));CHKERRQ(ierr);
310     ierr = PetscKernel_A_gets_inverse_A_5(pv,ipvt,work,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
311     if (zeropivotdetected) C->errortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
312 
313     /* U part */
314     pv = b->a + bs2*(bdiag[i+1]+1);
315     pj = b->j + bdiag[i+1]+1;
316     nz = bdiag[i] - bdiag[i+1] - 1;
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 
322   ierr = PetscFree2(rtmp,mwork);CHKERRQ(ierr);
323   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
324   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
325 
326   C->ops->solve          = MatSolve_SeqBAIJ_5;
327   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5;
328   C->assembled           = PETSC_TRUE;
329 
330   ierr = PetscLogFlops(1.333333333333*5*5*5*n);CHKERRQ(ierr); /* from inverting diagonal blocks */
331   PetscFunctionReturn(0);
332 }
333 
334 /*
335       Version for when blocks are 5 by 5 Using natural ordering
336 */
337 #undef __FUNCT__
338 #define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_5_NaturalOrdering_inplace"
339 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5_NaturalOrdering_inplace(Mat C,Mat A,const MatFactorInfo *info)
340 {
341   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ*)C->data;
342   PetscErrorCode ierr;
343   PetscInt       i,j,n = a->mbs,*bi = b->i,*bj = b->j,ipvt[5];
344   PetscInt       *ajtmpold,*ajtmp,nz,row;
345   PetscInt       *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
346   MatScalar      *pv,*v,*rtmp,*pc,*w,*x;
347   MatScalar      x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15;
348   MatScalar      x16,x17,x18,x19,x20,x21,x22,x23,x24,x25;
349   MatScalar      p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15;
350   MatScalar      p16,p17,p18,p19,p20,p21,p22,p23,p24,p25;
351   MatScalar      m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12,m13,m14,m15;
352   MatScalar      m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
353   MatScalar      *ba   = b->a,*aa = a->a,work[25];
354   PetscReal      shift = info->shiftamount;
355   PetscBool      allowzeropivot,zeropivotdetected;
356 
357   PetscFunctionBegin;
358   allowzeropivot = PetscNot(A->erroriffailure);
359   ierr = PetscMalloc1(25*(n+1),&rtmp);CHKERRQ(ierr);
360   for (i=0; i<n; i++) {
361     nz    = bi[i+1] - bi[i];
362     ajtmp = bj + bi[i];
363     for  (j=0; j<nz; j++) {
364       x     = rtmp+25*ajtmp[j];
365       x[0]  = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = x[9] = 0.0;
366       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
367       x[16] = x[17] = x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0;
368     }
369     /* load in initial (unfactored row) */
370     nz       = ai[i+1] - ai[i];
371     ajtmpold = aj + ai[i];
372     v        = aa + 25*ai[i];
373     for (j=0; j<nz; j++) {
374       x     = rtmp+25*ajtmpold[j];
375       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
376       x[4]  = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
377       x[9]  = v[9];  x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
378       x[14] = v[14]; x[15] = v[15]; x[16] = v[16]; x[17] = v[17]; x[18] = v[18];
379       x[19] = v[19]; x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23];
380       x[24] = v[24];
381       v    += 25;
382     }
383     row = *ajtmp++;
384     while (row < i) {
385       pc  = rtmp + 25*row;
386       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
387       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
388       p10 = pc[9];  p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
389       p15 = pc[14]; p16 = pc[15]; p17 = pc[16]; p18 = pc[17];
390       p19 = pc[18]; p20 = pc[19]; p21 = pc[20]; p22 = pc[21]; p23 = pc[22];
391       p24 = pc[23]; p25 = pc[24];
392       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
393           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
394           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
395           || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0
396           || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 || p25 != 0.0) {
397         pv    = ba + 25*diag_offset[row];
398         pj    = bj + diag_offset[row] + 1;
399         x1    = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
400         x5    = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
401         x10   = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
402         x15   = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17]; x19 = pv[18];
403         x20   = pv[19]; x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
404         x25   = pv[24];
405         pc[0] = m1 = p1*x1 + p6*x2  + p11*x3 + p16*x4 + p21*x5;
406         pc[1] = m2 = p2*x1 + p7*x2  + p12*x3 + p17*x4 + p22*x5;
407         pc[2] = m3 = p3*x1 + p8*x2  + p13*x3 + p18*x4 + p23*x5;
408         pc[3] = m4 = p4*x1 + p9*x2  + p14*x3 + p19*x4 + p24*x5;
409         pc[4] = m5 = p5*x1 + p10*x2 + p15*x3 + p20*x4 + p25*x5;
410 
411         pc[5] = m6  = p1*x6 + p6*x7  + p11*x8 + p16*x9 + p21*x10;
412         pc[6] = m7  = p2*x6 + p7*x7  + p12*x8 + p17*x9 + p22*x10;
413         pc[7] = m8  = p3*x6 + p8*x7  + p13*x8 + p18*x9 + p23*x10;
414         pc[8] = m9  = p4*x6 + p9*x7  + p14*x8 + p19*x9 + p24*x10;
415         pc[9] = m10 = p5*x6 + p10*x7 + p15*x8 + p20*x9 + p25*x10;
416 
417         pc[10] = m11 = p1*x11 + p6*x12  + p11*x13 + p16*x14 + p21*x15;
418         pc[11] = m12 = p2*x11 + p7*x12  + p12*x13 + p17*x14 + p22*x15;
419         pc[12] = m13 = p3*x11 + p8*x12  + p13*x13 + p18*x14 + p23*x15;
420         pc[13] = m14 = p4*x11 + p9*x12  + p14*x13 + p19*x14 + p24*x15;
421         pc[14] = m15 = p5*x11 + p10*x12 + p15*x13 + p20*x14 + p25*x15;
422 
423         pc[15] = m16 = p1*x16 + p6*x17  + p11*x18 + p16*x19 + p21*x20;
424         pc[16] = m17 = p2*x16 + p7*x17  + p12*x18 + p17*x19 + p22*x20;
425         pc[17] = m18 = p3*x16 + p8*x17  + p13*x18 + p18*x19 + p23*x20;
426         pc[18] = m19 = p4*x16 + p9*x17  + p14*x18 + p19*x19 + p24*x20;
427         pc[19] = m20 = p5*x16 + p10*x17 + p15*x18 + p20*x19 + p25*x20;
428 
429         pc[20] = m21 = p1*x21 + p6*x22  + p11*x23 + p16*x24 + p21*x25;
430         pc[21] = m22 = p2*x21 + p7*x22  + p12*x23 + p17*x24 + p22*x25;
431         pc[22] = m23 = p3*x21 + p8*x22  + p13*x23 + p18*x24 + p23*x25;
432         pc[23] = m24 = p4*x21 + p9*x22  + p14*x23 + p19*x24 + p24*x25;
433         pc[24] = m25 = p5*x21 + p10*x22 + p15*x23 + p20*x24 + p25*x25;
434 
435         nz  = bi[row+1] - diag_offset[row] - 1;
436         pv += 25;
437         for (j=0; j<nz; j++) {
438           x1    = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
439           x5    = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
440           x10   = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
441           x14   = pv[13]; x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17];
442           x19   = pv[18];  x20 = pv[19]; x21 = pv[20]; x22 = pv[21]; x23 = pv[22];
443           x24   = pv[23];  x25 = pv[24];
444           x     = rtmp + 25*pj[j];
445           x[0] -= m1*x1 + m6*x2   + m11*x3  + m16*x4 + m21*x5;
446           x[1] -= m2*x1 + m7*x2   + m12*x3  + m17*x4 + m22*x5;
447           x[2] -= m3*x1 + m8*x2   + m13*x3  + m18*x4 + m23*x5;
448           x[3] -= m4*x1 + m9*x2   + m14*x3  + m19*x4 + m24*x5;
449           x[4] -= m5*x1 + m10*x2  + m15*x3  + m20*x4 + m25*x5;
450 
451           x[5] -= m1*x6 + m6*x7   + m11*x8  + m16*x9 + m21*x10;
452           x[6] -= m2*x6 + m7*x7   + m12*x8  + m17*x9 + m22*x10;
453           x[7] -= m3*x6 + m8*x7   + m13*x8  + m18*x9 + m23*x10;
454           x[8] -= m4*x6 + m9*x7   + m14*x8  + m19*x9 + m24*x10;
455           x[9] -= m5*x6 + m10*x7  + m15*x8  + m20*x9 + m25*x10;
456 
457           x[10] -= m1*x11 + m6*x12  + m11*x13 + m16*x14 + m21*x15;
458           x[11] -= m2*x11 + m7*x12  + m12*x13 + m17*x14 + m22*x15;
459           x[12] -= m3*x11 + m8*x12  + m13*x13 + m18*x14 + m23*x15;
460           x[13] -= m4*x11 + m9*x12  + m14*x13 + m19*x14 + m24*x15;
461           x[14] -= m5*x11 + m10*x12 + m15*x13 + m20*x14 + m25*x15;
462 
463           x[15] -= m1*x16 + m6*x17  + m11*x18 + m16*x19 + m21*x20;
464           x[16] -= m2*x16 + m7*x17  + m12*x18 + m17*x19 + m22*x20;
465           x[17] -= m3*x16 + m8*x17  + m13*x18 + m18*x19 + m23*x20;
466           x[18] -= m4*x16 + m9*x17  + m14*x18 + m19*x19 + m24*x20;
467           x[19] -= m5*x16 + m10*x17 + m15*x18 + m20*x19 + m25*x20;
468 
469           x[20] -= m1*x21 + m6*x22  + m11*x23 + m16*x24 + m21*x25;
470           x[21] -= m2*x21 + m7*x22  + m12*x23 + m17*x24 + m22*x25;
471           x[22] -= m3*x21 + m8*x22  + m13*x23 + m18*x24 + m23*x25;
472           x[23] -= m4*x21 + m9*x22  + m14*x23 + m19*x24 + m24*x25;
473           x[24] -= m5*x21 + m10*x22 + m15*x23 + m20*x24 + m25*x25;
474           pv    += 25;
475         }
476         ierr = PetscLogFlops(250.0*nz+225.0);CHKERRQ(ierr);
477       }
478       row = *ajtmp++;
479     }
480     /* finished row so stick it into b->a */
481     pv = ba + 25*bi[i];
482     pj = bj + bi[i];
483     nz = bi[i+1] - bi[i];
484     for (j=0; j<nz; j++) {
485       x      = rtmp+25*pj[j];
486       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
487       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
488       pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
489       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; pv[16] = x[16]; pv[17] = x[17];
490       pv[18] = x[18]; pv[19] = x[19]; pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22];
491       pv[23] = x[23]; pv[24] = x[24];
492       pv    += 25;
493     }
494     /* invert diagonal block */
495     w    = ba + 25*diag_offset[i];
496     ierr = PetscKernel_A_gets_inverse_A_5(w,ipvt,work,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
497     if (zeropivotdetected) C->errortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
498   }
499 
500   ierr = PetscFree(rtmp);CHKERRQ(ierr);
501 
502   C->ops->solve          = MatSolve_SeqBAIJ_5_NaturalOrdering_inplace;
503   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5_NaturalOrdering_inplace;
504   C->assembled           = PETSC_TRUE;
505 
506   ierr = PetscLogFlops(1.333333333333*5*5*5*b->mbs);CHKERRQ(ierr); /* from inverting diagonal blocks */
507   PetscFunctionReturn(0);
508 }
509 
510 #undef __FUNCT__
511 #define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_5_NaturalOrdering"
512 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5_NaturalOrdering(Mat B,Mat A,const MatFactorInfo *info)
513 {
514   Mat            C =B;
515   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ*)C->data;
516   PetscErrorCode ierr;
517   PetscInt       i,j,k,nz,nzL,row;
518   const PetscInt n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
519   const PetscInt *ajtmp,*bjtmp,*bdiag=b->diag,*pj,bs2=a->bs2;
520   MatScalar      *rtmp,*pc,*mwork,*v,*vv,*pv,*aa=a->a,work[25];
521   PetscInt       flg,ipvt[5];
522   PetscReal      shift = info->shiftamount;
523   PetscBool      allowzeropivot,zeropivotdetected;
524 
525   PetscFunctionBegin;
526   allowzeropivot = PetscNot(A->erroriffailure);
527 
528   /* generate work space needed by the factorization */
529   ierr = PetscMalloc2(bs2*n,&rtmp,bs2,&mwork);CHKERRQ(ierr);
530   ierr = PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));CHKERRQ(ierr);
531 
532   for (i=0; i<n; i++) {
533     /* zero rtmp */
534     /* L part */
535     nz    = bi[i+1] - bi[i];
536     bjtmp = bj + bi[i];
537     for  (j=0; j<nz; j++) {
538       ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
539     }
540 
541     /* U part */
542     nz    = bdiag[i] - bdiag[i+1];
543     bjtmp = bj + bdiag[i+1]+1;
544     for  (j=0; j<nz; j++) {
545       ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
546     }
547 
548     /* load in initial (unfactored row) */
549     nz    = ai[i+1] - ai[i];
550     ajtmp = aj + ai[i];
551     v     = aa + bs2*ai[i];
552     for (j=0; j<nz; j++) {
553       ierr = PetscMemcpy(rtmp+bs2*ajtmp[j],v+bs2*j,bs2*sizeof(MatScalar));CHKERRQ(ierr);
554     }
555 
556     /* elimination */
557     bjtmp = bj + bi[i];
558     nzL   = bi[i+1] - bi[i];
559     for (k=0; k < nzL; k++) {
560       row = bjtmp[k];
561       pc  = rtmp + bs2*row;
562       for (flg=0,j=0; j<bs2; j++) {
563         if (pc[j]!=0.0) {
564           flg = 1;
565           break;
566         }
567       }
568       if (flg) {
569         pv = b->a + bs2*bdiag[row];
570         /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
571         ierr = PetscKernel_A_gets_A_times_B_5(pc,pv,mwork);CHKERRQ(ierr);
572 
573         pj = b->j + bdiag[row+1]+1; /* begining of U(row,:) */
574         pv = b->a + bs2*(bdiag[row+1]+1);
575         nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries inU(row,:), excluding diag */
576         for (j=0; j<nz; j++) {
577           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
578           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
579           vv   = rtmp + bs2*pj[j];
580           ierr = PetscKernel_A_gets_A_minus_B_times_C_5(vv,pc,pv);CHKERRQ(ierr);
581           pv  += bs2;
582         }
583         ierr = PetscLogFlops(250*nz+225);CHKERRQ(ierr); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
584       }
585     }
586 
587     /* finished row so stick it into b->a */
588     /* L part */
589     pv = b->a + bs2*bi[i];
590     pj = b->j + bi[i];
591     nz = bi[i+1] - bi[i];
592     for (j=0; j<nz; j++) {
593       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
594     }
595 
596     /* Mark diagonal and invert diagonal for simplier triangular solves */
597     pv   = b->a + bs2*bdiag[i];
598     pj   = b->j + bdiag[i];
599     ierr = PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));CHKERRQ(ierr);
600     ierr = PetscKernel_A_gets_inverse_A_5(pv,ipvt,work,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
601     if (zeropivotdetected) C->errortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
602 
603     /* U part */
604     pv = b->a + bs2*(bdiag[i+1]+1);
605     pj = b->j + bdiag[i+1]+1;
606     nz = bdiag[i] - bdiag[i+1] - 1;
607     for (j=0; j<nz; j++) {
608       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
609     }
610   }
611   ierr = PetscFree2(rtmp,mwork);CHKERRQ(ierr);
612 
613   C->ops->solve          = MatSolve_SeqBAIJ_5_NaturalOrdering;
614   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5_NaturalOrdering;
615   C->assembled           = PETSC_TRUE;
616 
617   ierr = PetscLogFlops(1.333333333333*5*5*5*n);CHKERRQ(ierr); /* from inverting diagonal blocks */
618   PetscFunctionReturn(0);
619 }
620