xref: /petsc/src/mat/impls/baij/seq/baijfact9.c (revision 503c0ea9b45bcfbcebbb1ea5341243bbc69f0bea)
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 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5_inplace(Mat C,Mat A,const MatFactorInfo *info)
13 {
14   Mat_SeqBAIJ     *a    = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ*)C->data;
15   IS              isrow = b->row,isicol = b->icol;
16   const PetscInt  *r,*ic,*bi = b->i,*bj = b->j,*ajtmpold,*ajtmp;
17   PetscInt        i,j,n = a->mbs,nz,row,idx,ipvt[5];
18   const PetscInt  *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
19   MatScalar       *w,*pv,*rtmp,*x,*pc;
20   const MatScalar *v,*aa = a->a;
21   MatScalar       p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
22   MatScalar       p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
23   MatScalar       x17,x18,x19,x20,x21,x22,x23,x24,x25,p10,p11,p12,p13,p14;
24   MatScalar       p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,m10,m11,m12;
25   MatScalar       m13,m14,m15,m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
26   MatScalar       *ba   = b->a,work[25];
27   PetscReal       shift = info->shiftamount;
28   PetscBool       allowzeropivot,zeropivotdetected;
29 
30   PetscFunctionBegin;
31   allowzeropivot = PetscNot(A->erroriffailure);
32   PetscCall(ISGetIndices(isrow,&r));
33   PetscCall(ISGetIndices(isicol,&ic));
34   PetscCall(PetscMalloc1(25*(n+1),&rtmp));
35 
36 #define PETSC_USE_MEMZERO 1
37 #define PETSC_USE_MEMCPY 1
38 
39   for (i=0; i<n; i++) {
40     nz    = bi[i+1] - bi[i];
41     ajtmp = bj + bi[i];
42     for  (j=0; j<nz; j++) {
43 #if defined(PETSC_USE_MEMZERO)
44       PetscCall(PetscArrayzero(rtmp+25*ajtmp[j],25));
45 #else
46       x     = rtmp+25*ajtmp[j];
47       x[0]  = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
48       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
49       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0;
50 #endif
51     }
52     /* load in initial (unfactored row) */
53     idx      = r[i];
54     nz       = ai[idx+1] - ai[idx];
55     ajtmpold = aj + ai[idx];
56     v        = aa + 25*ai[idx];
57     for (j=0; j<nz; j++) {
58 #if defined(PETSC_USE_MEMCPY)
59       PetscCall(PetscArraycpy(rtmp+25*ic[ajtmpold[j]],v,25));
60 #else
61       x     = rtmp+25*ic[ajtmpold[j]];
62       x[0]  = v[0]; x[1] = v[1]; x[2] = v[2]; x[3] = v[3];
63       x[4]  = v[4]; x[5] = v[5]; x[6] = v[6]; x[7] = v[7]; x[8] = v[8];
64       x[9]  = v[9]; x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
65       x[14] = v[14]; x[15] = v[15]; x[16] = v[16]; x[17] = v[17];
66       x[18] = v[18]; x[19] = v[19]; x[20] = v[20]; x[21] = v[21];
67       x[22] = v[22]; x[23] = v[23]; x[24] = v[24];
68 #endif
69       v += 25;
70     }
71     row = *ajtmp++;
72     while (row < i) {
73       pc  = rtmp + 25*row;
74       p1  = pc[0]; p2 = pc[1]; p3 = pc[2]; p4 = pc[3];
75       p5  = pc[4]; p6 = pc[5]; p7 = pc[6]; p8 = pc[7]; p9 = pc[8];
76       p10 = pc[9]; p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
77       p15 = pc[14]; p16 = pc[15]; p17 = pc[16]; p18 = pc[17]; p19 = pc[18];
78       p20 = pc[19]; p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
79       p25 = pc[24];
80       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
81           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
82           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
83           || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 ||
84           p20 != 0.0 || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 ||
85           p24 != 0.0 || p25 != 0.0) {
86         pv    = ba + 25*diag_offset[row];
87         pj    = bj + diag_offset[row] + 1;
88         x1    = pv[0]; x2 = pv[1]; x3 = pv[2]; x4 = pv[3];
89         x5    = pv[4]; x6 = pv[5]; x7 = pv[6]; x8 = pv[7]; x9 = pv[8];
90         x10   = pv[9]; x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
91         x15   = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17];
92         x19   = pv[18]; x20 = pv[19]; x21 = pv[20]; x22 = pv[21];
93         x23   = pv[22]; x24 = pv[23]; x25 = pv[24];
94         pc[0] = m1 = p1*x1 + p6*x2  + p11*x3 + p16*x4 + p21*x5;
95         pc[1] = m2 = p2*x1 + p7*x2  + p12*x3 + p17*x4 + p22*x5;
96         pc[2] = m3 = p3*x1 + p8*x2  + p13*x3 + p18*x4 + p23*x5;
97         pc[3] = m4 = p4*x1 + p9*x2  + p14*x3 + p19*x4 + p24*x5;
98         pc[4] = m5 = p5*x1 + p10*x2 + p15*x3 + p20*x4 + p25*x5;
99 
100         pc[5] = m6 = p1*x6 + p6*x7  + p11*x8 + p16*x9 + p21*x10;
101         pc[6] = m7 = p2*x6 + p7*x7  + p12*x8 + p17*x9 + p22*x10;
102         pc[7] = m8 = p3*x6 + p8*x7  + p13*x8 + p18*x9 + p23*x10;
103         pc[8] = m9 = p4*x6 + p9*x7  + p14*x8 + p19*x9 + p24*x10;
104         pc[9] = m10 = p5*x6 + p10*x7 + p15*x8 + p20*x9 + p25*x10;
105 
106         pc[10] = m11 = p1*x11 + p6*x12  + p11*x13 + p16*x14 + p21*x15;
107         pc[11] = m12 = p2*x11 + p7*x12  + p12*x13 + p17*x14 + p22*x15;
108         pc[12] = m13 = p3*x11 + p8*x12  + p13*x13 + p18*x14 + p23*x15;
109         pc[13] = m14 = p4*x11 + p9*x12  + p14*x13 + p19*x14 + p24*x15;
110         pc[14] = m15 = p5*x11 + p10*x12 + p15*x13 + p20*x14 + p25*x15;
111 
112         pc[15] = m16 = p1*x16 + p6*x17  + p11*x18 + p16*x19 + p21*x20;
113         pc[16] = m17 = p2*x16 + p7*x17  + p12*x18 + p17*x19 + p22*x20;
114         pc[17] = m18 = p3*x16 + p8*x17  + p13*x18 + p18*x19 + p23*x20;
115         pc[18] = m19 = p4*x16 + p9*x17  + p14*x18 + p19*x19 + p24*x20;
116         pc[19] = m20 = p5*x16 + p10*x17 + p15*x18 + p20*x19 + p25*x20;
117 
118         pc[20] = m21 = p1*x21 + p6*x22  + p11*x23 + p16*x24 + p21*x25;
119         pc[21] = m22 = p2*x21 + p7*x22  + p12*x23 + p17*x24 + p22*x25;
120         pc[22] = m23 = p3*x21 + p8*x22  + p13*x23 + p18*x24 + p23*x25;
121         pc[23] = m24 = p4*x21 + p9*x22  + p14*x23 + p19*x24 + p24*x25;
122         pc[24] = m25 = p5*x21 + p10*x22 + p15*x23 + p20*x24 + p25*x25;
123 
124         nz  = bi[row+1] - diag_offset[row] - 1;
125         pv += 25;
126         for (j=0; j<nz; j++) {
127           x1    = pv[0];  x2 = pv[1];   x3  = pv[2];  x4  = pv[3];
128           x5    = pv[4];  x6 = pv[5];   x7  = pv[6];  x8  = pv[7]; x9 = pv[8];
129           x10   = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
130           x14   = pv[13]; x15 = pv[14]; x16 = pv[15]; x17 = pv[16];
131           x18   = pv[17]; x19 = pv[18]; x20 = pv[19]; x21 = pv[20];
132           x22   = pv[21]; x23 = pv[22]; x24 = pv[23]; x25 = pv[24];
133           x     = rtmp + 25*pj[j];
134           x[0] -= m1*x1 + m6*x2  + m11*x3 + m16*x4 + m21*x5;
135           x[1] -= m2*x1 + m7*x2  + m12*x3 + m17*x4 + m22*x5;
136           x[2] -= m3*x1 + m8*x2  + m13*x3 + m18*x4 + m23*x5;
137           x[3] -= m4*x1 + m9*x2  + m14*x3 + m19*x4 + m24*x5;
138           x[4] -= m5*x1 + m10*x2 + m15*x3 + m20*x4 + m25*x5;
139 
140           x[5] -= m1*x6 + m6*x7  + m11*x8 + m16*x9 + m21*x10;
141           x[6] -= m2*x6 + m7*x7  + m12*x8 + m17*x9 + m22*x10;
142           x[7] -= m3*x6 + m8*x7  + m13*x8 + m18*x9 + m23*x10;
143           x[8] -= m4*x6 + m9*x7  + m14*x8 + m19*x9 + m24*x10;
144           x[9] -= m5*x6 + m10*x7 + m15*x8 + m20*x9 + m25*x10;
145 
146           x[10] -= m1*x11 + m6*x12  + m11*x13 + m16*x14 + m21*x15;
147           x[11] -= m2*x11 + m7*x12  + m12*x13 + m17*x14 + m22*x15;
148           x[12] -= m3*x11 + m8*x12  + m13*x13 + m18*x14 + m23*x15;
149           x[13] -= m4*x11 + m9*x12  + m14*x13 + m19*x14 + m24*x15;
150           x[14] -= m5*x11 + m10*x12 + m15*x13 + m20*x14 + m25*x15;
151 
152           x[15] -= m1*x16 + m6*x17  + m11*x18 + m16*x19 + m21*x20;
153           x[16] -= m2*x16 + m7*x17  + m12*x18 + m17*x19 + m22*x20;
154           x[17] -= m3*x16 + m8*x17  + m13*x18 + m18*x19 + m23*x20;
155           x[18] -= m4*x16 + m9*x17  + m14*x18 + m19*x19 + m24*x20;
156           x[19] -= m5*x16 + m10*x17 + m15*x18 + m20*x19 + m25*x20;
157 
158           x[20] -= m1*x21 + m6*x22  + m11*x23 + m16*x24 + m21*x25;
159           x[21] -= m2*x21 + m7*x22  + m12*x23 + m17*x24 + m22*x25;
160           x[22] -= m3*x21 + m8*x22  + m13*x23 + m18*x24 + m23*x25;
161           x[23] -= m4*x21 + m9*x22  + m14*x23 + m19*x24 + m24*x25;
162           x[24] -= m5*x21 + m10*x22 + m15*x23 + m20*x24 + m25*x25;
163 
164           pv += 25;
165         }
166         PetscCall(PetscLogFlops(250.0*nz+225.0));
167       }
168       row = *ajtmp++;
169     }
170     /* finished row so stick it into b->a */
171     pv = ba + 25*bi[i];
172     pj = bj + bi[i];
173     nz = bi[i+1] - bi[i];
174     for (j=0; j<nz; j++) {
175 #if defined(PETSC_USE_MEMCPY)
176       PetscCall(PetscArraycpy(pv,rtmp+25*pj[j],25));
177 #else
178       x      = rtmp+25*pj[j];
179       pv[0]  = x[0]; pv[1] = x[1]; pv[2] = x[2]; pv[3] = x[3];
180       pv[4]  = x[4]; pv[5] = x[5]; pv[6] = x[6]; pv[7] = x[7]; pv[8] = x[8];
181       pv[9]  = x[9]; pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
182       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; pv[16] = x[16];
183       pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19]; pv[20] = x[20];
184       pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23]; pv[24] = x[24];
185 #endif
186       pv += 25;
187     }
188     /* invert diagonal block */
189     w    = ba + 25*diag_offset[i];
190     PetscCall(PetscKernel_A_gets_inverse_A_5(w,ipvt,work,shift,allowzeropivot,&zeropivotdetected));
191     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
192   }
193 
194   PetscCall(PetscFree(rtmp));
195   PetscCall(ISRestoreIndices(isicol,&ic));
196   PetscCall(ISRestoreIndices(isrow,&r));
197 
198   C->ops->solve          = MatSolve_SeqBAIJ_5_inplace;
199   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5_inplace;
200   C->assembled           = PETSC_TRUE;
201 
202   PetscCall(PetscLogFlops(1.333333333333*5*5*5*b->mbs)); /* 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 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   const PetscInt *r,*ic;
219   PetscInt       i,j,k,nz,nzL,row;
220   const PetscInt n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
221   const PetscInt *ajtmp,*bjtmp,*bdiag=b->diag,*pj,bs2=a->bs2;
222   MatScalar      *rtmp,*pc,*mwork,*v,*pv,*aa=a->a,work[25];
223   PetscInt       flg,ipvt[5];
224   PetscReal      shift = info->shiftamount;
225   PetscBool      allowzeropivot,zeropivotdetected;
226 
227   PetscFunctionBegin;
228   allowzeropivot = PetscNot(A->erroriffailure);
229   PetscCall(ISGetIndices(isrow,&r));
230   PetscCall(ISGetIndices(isicol,&ic));
231 
232   /* generate work space needed by the factorization */
233   PetscCall(PetscMalloc2(bs2*n,&rtmp,bs2,&mwork));
234   PetscCall(PetscArrayzero(rtmp,bs2*n));
235 
236   for (i=0; i<n; i++) {
237     /* zero rtmp */
238     /* L part */
239     nz    = bi[i+1] - bi[i];
240     bjtmp = bj + bi[i];
241     for  (j=0; j<nz; j++) {
242       PetscCall(PetscArrayzero(rtmp+bs2*bjtmp[j],bs2));
243     }
244 
245     /* U part */
246     nz    = bdiag[i] - bdiag[i+1];
247     bjtmp = bj + bdiag[i+1]+1;
248     for  (j=0; j<nz; j++) {
249       PetscCall(PetscArrayzero(rtmp+bs2*bjtmp[j],bs2));
250     }
251 
252     /* load in initial (unfactored row) */
253     nz    = ai[r[i]+1] - ai[r[i]];
254     ajtmp = aj + ai[r[i]];
255     v     = aa + bs2*ai[r[i]];
256     for (j=0; j<nz; j++) {
257       PetscCall(PetscArraycpy(rtmp+bs2*ic[ajtmp[j]],v+bs2*j,bs2));
258     }
259 
260     /* elimination */
261     bjtmp = bj + bi[i];
262     nzL   = bi[i+1] - bi[i];
263     for (k=0; k < nzL; k++) {
264       row = bjtmp[k];
265       pc  = rtmp + bs2*row;
266       for (flg=0,j=0; j<bs2; j++) {
267         if (pc[j]!=0.0) {
268           flg = 1;
269           break;
270         }
271       }
272       if (flg) {
273         pv = b->a + bs2*bdiag[row];
274         /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
275         PetscCall(PetscKernel_A_gets_A_times_B_5(pc,pv,mwork));
276 
277         pj = b->j + bdiag[row+1]+1; /* beginning of U(row,:) */
278         pv = b->a + bs2*(bdiag[row+1]+1);
279         nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries inU(row,:), excluding diag */
280         for (j=0; j<nz; j++) {
281           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
282           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
283           v    = rtmp + bs2*pj[j];
284           PetscCall(PetscKernel_A_gets_A_minus_B_times_C_5(v,pc,pv));
285           pv  += bs2;
286         }
287         PetscCall(PetscLogFlops(250.0*nz+225)); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
288       }
289     }
290 
291     /* finished row so stick it into b->a */
292     /* L part */
293     pv = b->a + bs2*bi[i];
294     pj = b->j + bi[i];
295     nz = bi[i+1] - bi[i];
296     for (j=0; j<nz; j++) {
297       PetscCall(PetscArraycpy(pv+bs2*j,rtmp+bs2*pj[j],bs2));
298     }
299 
300     /* Mark diagonal and invert diagonal for simpler triangular solves */
301     pv   = b->a + bs2*bdiag[i];
302     pj   = b->j + bdiag[i];
303     PetscCall(PetscArraycpy(pv,rtmp+bs2*pj[0],bs2));
304     PetscCall(PetscKernel_A_gets_inverse_A_5(pv,ipvt,work,shift,allowzeropivot,&zeropivotdetected));
305     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
306 
307     /* U part */
308     pv = b->a + bs2*(bdiag[i+1]+1);
309     pj = b->j + bdiag[i+1]+1;
310     nz = bdiag[i] - bdiag[i+1] - 1;
311     for (j=0; j<nz; j++) {
312       PetscCall(PetscArraycpy(pv+bs2*j,rtmp+bs2*pj[j],bs2));
313     }
314   }
315 
316   PetscCall(PetscFree2(rtmp,mwork));
317   PetscCall(ISRestoreIndices(isicol,&ic));
318   PetscCall(ISRestoreIndices(isrow,&r));
319 
320   C->ops->solve          = MatSolve_SeqBAIJ_5;
321   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5;
322   C->assembled           = PETSC_TRUE;
323 
324   PetscCall(PetscLogFlops(1.333333333333*5*5*5*n)); /* from inverting diagonal blocks */
325   PetscFunctionReturn(0);
326 }
327 
328 /*
329       Version for when blocks are 5 by 5 Using natural ordering
330 */
331 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5_NaturalOrdering_inplace(Mat C,Mat A,const MatFactorInfo *info)
332 {
333   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ*)C->data;
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   PetscBool      allowzeropivot,zeropivotdetected;
347 
348   PetscFunctionBegin;
349   allowzeropivot = PetscNot(A->erroriffailure);
350   PetscCall(PetscMalloc1(25*(n+1),&rtmp));
351   for (i=0; i<n; i++) {
352     nz    = bi[i+1] - bi[i];
353     ajtmp = bj + bi[i];
354     for  (j=0; j<nz; j++) {
355       x     = rtmp+25*ajtmp[j];
356       x[0]  = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = x[9] = 0.0;
357       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
358       x[16] = x[17] = x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0;
359     }
360     /* load in initial (unfactored row) */
361     nz       = ai[i+1] - ai[i];
362     ajtmpold = aj + ai[i];
363     v        = aa + 25*ai[i];
364     for (j=0; j<nz; j++) {
365       x     = rtmp+25*ajtmpold[j];
366       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
367       x[4]  = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
368       x[9]  = v[9];  x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
369       x[14] = v[14]; x[15] = v[15]; x[16] = v[16]; x[17] = v[17]; x[18] = v[18];
370       x[19] = v[19]; x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23];
371       x[24] = v[24];
372       v    += 25;
373     }
374     row = *ajtmp++;
375     while (row < i) {
376       pc  = rtmp + 25*row;
377       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
378       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
379       p10 = pc[9];  p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
380       p15 = pc[14]; p16 = pc[15]; p17 = pc[16]; p18 = pc[17];
381       p19 = pc[18]; p20 = pc[19]; p21 = pc[20]; p22 = pc[21]; p23 = pc[22];
382       p24 = pc[23]; p25 = pc[24];
383       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
384           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
385           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
386           || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0
387           || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 || p25 != 0.0) {
388         pv    = ba + 25*diag_offset[row];
389         pj    = bj + diag_offset[row] + 1;
390         x1    = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
391         x5    = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
392         x10   = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
393         x15   = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17]; x19 = pv[18];
394         x20   = pv[19]; x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
395         x25   = pv[24];
396         pc[0] = m1 = p1*x1 + p6*x2  + p11*x3 + p16*x4 + p21*x5;
397         pc[1] = m2 = p2*x1 + p7*x2  + p12*x3 + p17*x4 + p22*x5;
398         pc[2] = m3 = p3*x1 + p8*x2  + p13*x3 + p18*x4 + p23*x5;
399         pc[3] = m4 = p4*x1 + p9*x2  + p14*x3 + p19*x4 + p24*x5;
400         pc[4] = m5 = p5*x1 + p10*x2 + p15*x3 + p20*x4 + p25*x5;
401 
402         pc[5] = m6  = p1*x6 + p6*x7  + p11*x8 + p16*x9 + p21*x10;
403         pc[6] = m7  = p2*x6 + p7*x7  + p12*x8 + p17*x9 + p22*x10;
404         pc[7] = m8  = p3*x6 + p8*x7  + p13*x8 + p18*x9 + p23*x10;
405         pc[8] = m9  = p4*x6 + p9*x7  + p14*x8 + p19*x9 + p24*x10;
406         pc[9] = m10 = p5*x6 + p10*x7 + p15*x8 + p20*x9 + p25*x10;
407 
408         pc[10] = m11 = p1*x11 + p6*x12  + p11*x13 + p16*x14 + p21*x15;
409         pc[11] = m12 = p2*x11 + p7*x12  + p12*x13 + p17*x14 + p22*x15;
410         pc[12] = m13 = p3*x11 + p8*x12  + p13*x13 + p18*x14 + p23*x15;
411         pc[13] = m14 = p4*x11 + p9*x12  + p14*x13 + p19*x14 + p24*x15;
412         pc[14] = m15 = p5*x11 + p10*x12 + p15*x13 + p20*x14 + p25*x15;
413 
414         pc[15] = m16 = p1*x16 + p6*x17  + p11*x18 + p16*x19 + p21*x20;
415         pc[16] = m17 = p2*x16 + p7*x17  + p12*x18 + p17*x19 + p22*x20;
416         pc[17] = m18 = p3*x16 + p8*x17  + p13*x18 + p18*x19 + p23*x20;
417         pc[18] = m19 = p4*x16 + p9*x17  + p14*x18 + p19*x19 + p24*x20;
418         pc[19] = m20 = p5*x16 + p10*x17 + p15*x18 + p20*x19 + p25*x20;
419 
420         pc[20] = m21 = p1*x21 + p6*x22  + p11*x23 + p16*x24 + p21*x25;
421         pc[21] = m22 = p2*x21 + p7*x22  + p12*x23 + p17*x24 + p22*x25;
422         pc[22] = m23 = p3*x21 + p8*x22  + p13*x23 + p18*x24 + p23*x25;
423         pc[23] = m24 = p4*x21 + p9*x22  + p14*x23 + p19*x24 + p24*x25;
424         pc[24] = m25 = p5*x21 + p10*x22 + p15*x23 + p20*x24 + p25*x25;
425 
426         nz  = bi[row+1] - diag_offset[row] - 1;
427         pv += 25;
428         for (j=0; j<nz; j++) {
429           x1    = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
430           x5    = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
431           x10   = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
432           x14   = pv[13]; x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17];
433           x19   = pv[18];  x20 = pv[19]; x21 = pv[20]; x22 = pv[21]; x23 = pv[22];
434           x24   = pv[23];  x25 = pv[24];
435           x     = rtmp + 25*pj[j];
436           x[0] -= m1*x1 + m6*x2   + m11*x3  + m16*x4 + m21*x5;
437           x[1] -= m2*x1 + m7*x2   + m12*x3  + m17*x4 + m22*x5;
438           x[2] -= m3*x1 + m8*x2   + m13*x3  + m18*x4 + m23*x5;
439           x[3] -= m4*x1 + m9*x2   + m14*x3  + m19*x4 + m24*x5;
440           x[4] -= m5*x1 + m10*x2  + m15*x3  + m20*x4 + m25*x5;
441 
442           x[5] -= m1*x6 + m6*x7   + m11*x8  + m16*x9 + m21*x10;
443           x[6] -= m2*x6 + m7*x7   + m12*x8  + m17*x9 + m22*x10;
444           x[7] -= m3*x6 + m8*x7   + m13*x8  + m18*x9 + m23*x10;
445           x[8] -= m4*x6 + m9*x7   + m14*x8  + m19*x9 + m24*x10;
446           x[9] -= m5*x6 + m10*x7  + m15*x8  + m20*x9 + m25*x10;
447 
448           x[10] -= m1*x11 + m6*x12  + m11*x13 + m16*x14 + m21*x15;
449           x[11] -= m2*x11 + m7*x12  + m12*x13 + m17*x14 + m22*x15;
450           x[12] -= m3*x11 + m8*x12  + m13*x13 + m18*x14 + m23*x15;
451           x[13] -= m4*x11 + m9*x12  + m14*x13 + m19*x14 + m24*x15;
452           x[14] -= m5*x11 + m10*x12 + m15*x13 + m20*x14 + m25*x15;
453 
454           x[15] -= m1*x16 + m6*x17  + m11*x18 + m16*x19 + m21*x20;
455           x[16] -= m2*x16 + m7*x17  + m12*x18 + m17*x19 + m22*x20;
456           x[17] -= m3*x16 + m8*x17  + m13*x18 + m18*x19 + m23*x20;
457           x[18] -= m4*x16 + m9*x17  + m14*x18 + m19*x19 + m24*x20;
458           x[19] -= m5*x16 + m10*x17 + m15*x18 + m20*x19 + m25*x20;
459 
460           x[20] -= m1*x21 + m6*x22  + m11*x23 + m16*x24 + m21*x25;
461           x[21] -= m2*x21 + m7*x22  + m12*x23 + m17*x24 + m22*x25;
462           x[22] -= m3*x21 + m8*x22  + m13*x23 + m18*x24 + m23*x25;
463           x[23] -= m4*x21 + m9*x22  + m14*x23 + m19*x24 + m24*x25;
464           x[24] -= m5*x21 + m10*x22 + m15*x23 + m20*x24 + m25*x25;
465           pv    += 25;
466         }
467         PetscCall(PetscLogFlops(250.0*nz+225.0));
468       }
469       row = *ajtmp++;
470     }
471     /* finished row so stick it into b->a */
472     pv = ba + 25*bi[i];
473     pj = bj + bi[i];
474     nz = bi[i+1] - bi[i];
475     for (j=0; j<nz; j++) {
476       x      = rtmp+25*pj[j];
477       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
478       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
479       pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
480       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; pv[16] = x[16]; pv[17] = x[17];
481       pv[18] = x[18]; pv[19] = x[19]; pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22];
482       pv[23] = x[23]; pv[24] = x[24];
483       pv    += 25;
484     }
485     /* invert diagonal block */
486     w    = ba + 25*diag_offset[i];
487     PetscCall(PetscKernel_A_gets_inverse_A_5(w,ipvt,work,shift,allowzeropivot,&zeropivotdetected));
488     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
489   }
490 
491   PetscCall(PetscFree(rtmp));
492 
493   C->ops->solve          = MatSolve_SeqBAIJ_5_NaturalOrdering_inplace;
494   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5_NaturalOrdering_inplace;
495   C->assembled           = PETSC_TRUE;
496 
497   PetscCall(PetscLogFlops(1.333333333333*5*5*5*b->mbs)); /* from inverting diagonal blocks */
498   PetscFunctionReturn(0);
499 }
500 
501 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5_NaturalOrdering(Mat B,Mat A,const MatFactorInfo *info)
502 {
503   Mat            C =B;
504   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ*)C->data;
505   PetscInt       i,j,k,nz,nzL,row;
506   const PetscInt n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
507   const PetscInt *ajtmp,*bjtmp,*bdiag=b->diag,*pj,bs2=a->bs2;
508   MatScalar      *rtmp,*pc,*mwork,*v,*vv,*pv,*aa=a->a,work[25];
509   PetscInt       flg,ipvt[5];
510   PetscReal      shift = info->shiftamount;
511   PetscBool      allowzeropivot,zeropivotdetected;
512 
513   PetscFunctionBegin;
514   allowzeropivot = PetscNot(A->erroriffailure);
515 
516   /* generate work space needed by the factorization */
517   PetscCall(PetscMalloc2(bs2*n,&rtmp,bs2,&mwork));
518   PetscCall(PetscArrayzero(rtmp,bs2*n));
519 
520   for (i=0; i<n; i++) {
521     /* zero rtmp */
522     /* L part */
523     nz    = bi[i+1] - bi[i];
524     bjtmp = bj + bi[i];
525     for  (j=0; j<nz; j++) {
526       PetscCall(PetscArrayzero(rtmp+bs2*bjtmp[j],bs2));
527     }
528 
529     /* U part */
530     nz    = bdiag[i] - bdiag[i+1];
531     bjtmp = bj + bdiag[i+1]+1;
532     for  (j=0; j<nz; j++) {
533       PetscCall(PetscArrayzero(rtmp+bs2*bjtmp[j],bs2));
534     }
535 
536     /* load in initial (unfactored row) */
537     nz    = ai[i+1] - ai[i];
538     ajtmp = aj + ai[i];
539     v     = aa + bs2*ai[i];
540     for (j=0; j<nz; j++) {
541       PetscCall(PetscArraycpy(rtmp+bs2*ajtmp[j],v+bs2*j,bs2));
542     }
543 
544     /* elimination */
545     bjtmp = bj + bi[i];
546     nzL   = bi[i+1] - bi[i];
547     for (k=0; k < nzL; k++) {
548       row = bjtmp[k];
549       pc  = rtmp + bs2*row;
550       for (flg=0,j=0; j<bs2; j++) {
551         if (pc[j]!=0.0) {
552           flg = 1;
553           break;
554         }
555       }
556       if (flg) {
557         pv = b->a + bs2*bdiag[row];
558         /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
559         PetscCall(PetscKernel_A_gets_A_times_B_5(pc,pv,mwork));
560 
561         pj = b->j + bdiag[row+1]+1; /* beginning of U(row,:) */
562         pv = b->a + bs2*(bdiag[row+1]+1);
563         nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries inU(row,:), excluding diag */
564         for (j=0; j<nz; j++) {
565           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
566           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
567           vv   = rtmp + bs2*pj[j];
568           PetscCall(PetscKernel_A_gets_A_minus_B_times_C_5(vv,pc,pv));
569           pv  += bs2;
570         }
571         PetscCall(PetscLogFlops(250.0*nz+225)); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
572       }
573     }
574 
575     /* finished row so stick it into b->a */
576     /* L part */
577     pv = b->a + bs2*bi[i];
578     pj = b->j + bi[i];
579     nz = bi[i+1] - bi[i];
580     for (j=0; j<nz; j++) {
581       PetscCall(PetscArraycpy(pv+bs2*j,rtmp+bs2*pj[j],bs2));
582     }
583 
584     /* Mark diagonal and invert diagonal for simpler triangular solves */
585     pv   = b->a + bs2*bdiag[i];
586     pj   = b->j + bdiag[i];
587     PetscCall(PetscArraycpy(pv,rtmp+bs2*pj[0],bs2));
588     PetscCall(PetscKernel_A_gets_inverse_A_5(pv,ipvt,work,shift,allowzeropivot,&zeropivotdetected));
589     if (zeropivotdetected) C->factorerrortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
590 
591     /* U part */
592     pv = b->a + bs2*(bdiag[i+1]+1);
593     pj = b->j + bdiag[i+1]+1;
594     nz = bdiag[i] - bdiag[i+1] - 1;
595     for (j=0; j<nz; j++) {
596       PetscCall(PetscArraycpy(pv+bs2*j,rtmp+bs2*pj[j],bs2));
597     }
598   }
599   PetscCall(PetscFree2(rtmp,mwork));
600 
601   C->ops->solve          = MatSolve_SeqBAIJ_5_NaturalOrdering;
602   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5_NaturalOrdering;
603   C->assembled           = PETSC_TRUE;
604 
605   PetscCall(PetscLogFlops(1.333333333333*5*5*5*n)); /* from inverting diagonal blocks */
606   PetscFunctionReturn(0);
607 }
608