xref: /petsc/src/mat/impls/baij/seq/baijfact9.c (revision eeffb40d691afbdd57a8091619e7ddd44ac5fdca)
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"
15 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5(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;
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;
31   PetscReal       shift = info->shiftinblocks;
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,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;
199   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5;
200   C->assembled = PETSC_TRUE;
201   ierr = PetscLogFlops(1.3333*125*b->mbs);CHKERRQ(ierr); /* from inverting diagonal blocks */
202   PetscFunctionReturn(0);
203 }
204 
205 /* MatLUFactorNumeric_SeqBAIJ_5_newdatastruct -
206      copied from MatLUFactorNumeric_SeqBAIJ_N_newdatastruct() 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 #undef __FUNCT__
212 #define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_5_newdatastruct"
213 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5_newdatastruct(Mat B,Mat A,const MatFactorInfo *info)
214 {
215   Mat            C=B;
216   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ *)C->data;
217   IS             isrow = b->row,isicol = b->icol;
218   PetscErrorCode ierr;
219   const PetscInt *r,*ic,*ics;
220   PetscInt       i,j,k,n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
221   PetscInt       *ajtmp,*bjtmp,nz,nzL,row,*bdiag=b->diag,*pj;
222   MatScalar      *rtmp,*pc,*mwork,*v,*pv,*aa=a->a;
223   PetscInt       bs2 = a->bs2,flg;
224   PetscReal      shift = info->shiftinblocks;
225 
226   PetscFunctionBegin;
227   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
228   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
229 
230   /* generate work space needed by the factorization */
231   ierr = PetscMalloc((bs2*n+bs2+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
232   mwork = rtmp + bs2*n;
233   ierr = PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));CHKERRQ(ierr);
234   ics  = ic;
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       ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
243     }
244 
245     /* U part */
246     nz = bi[2*n-i+1] - bi[2*n-i];
247     bjtmp = bj + bi[2*n-i];
248     for  (j=0; j<nz; j++){
249       ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
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       ierr = PetscMemcpy(rtmp+bs2*ic[ajtmp[j]],v+bs2*j,bs2*sizeof(MatScalar));CHKERRQ(ierr);
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++) { if (pc[j]!=0.0) { flg = 1; break; }}
267       if (flg) {
268         pv = b->a + bs2*bdiag[row];
269         /* Kernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
270         ierr = Kernel_A_gets_A_times_B_5(pc,pv,mwork);CHKERRQ(ierr);
271 
272         pj = b->j + bi[2*n-row]; /* begining of U(row,:) */
273         pv = b->a + bs2*bi[2*n-row];
274         nz = bi[2*n-row+1] - bi[2*n-row] - 1; /* num of entries inU(row,:), excluding diag */
275         for (j=0; j<nz; j++) {
276           /* Kernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
277           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
278           v    = rtmp + bs2*pj[j];
279           ierr = Kernel_A_gets_A_minus_B_times_C_5(v,pc,pv);CHKERRQ(ierr);
280           pv  += bs2;
281         }
282         ierr = PetscLogFlops(250*nz+225);CHKERRQ(ierr); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
283       }
284     }
285 
286     /* finished row so stick it into b->a */
287     /* L part */
288     pv   = b->a + bs2*bi[i] ;
289     pj   = b->j + bi[i] ;
290     nz   = bi[i+1] - bi[i];
291     for (j=0; j<nz; j++) {
292       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
293     }
294 
295     /* Mark diagonal and invert diagonal for simplier triangular solves */
296     pv   = b->a + bs2*bdiag[i];
297     pj   = b->j + bdiag[i];
298     ierr = PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));CHKERRQ(ierr);
299     /* ierr = Kernel_A_gets_inverse_A(bs,pv,v_pivots,v_work);CHKERRQ(ierr); */
300     ierr = Kernel_A_gets_inverse_A_5(pv,shift);CHKERRQ(ierr);
301 
302     /* U part */
303     pv = b->a + bs2*bi[2*n-i];
304     pj = b->j + bi[2*n-i];
305     nz = bi[2*n-i+1] - bi[2*n-i] - 1;
306     for (j=0; j<nz; j++){
307       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
308     }
309   }
310 
311   ierr = PetscFree(rtmp);CHKERRQ(ierr);
312   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
313   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
314 
315   C->assembled = PETSC_TRUE;
316   ierr = PetscLogFlops(1.3333*bs2*n);CHKERRQ(ierr); /* from inverting diagonal blocks */
317   PetscFunctionReturn(0);
318 }
319 
320 #undef __FUNCT__
321 #define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_5_newdatastruct_v2"
322 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5_newdatastruct_v2(Mat B,Mat A,const MatFactorInfo *info)
323 {
324   Mat            C=B;
325   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ *)C->data;
326   IS             isrow = b->row,isicol = b->icol;
327   PetscErrorCode ierr;
328   const PetscInt *r,*ic,*ics;
329   PetscInt       i,j,k,n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
330   PetscInt       *ajtmp,*bjtmp,nz,nzL,row,*bdiag=b->diag,*pj;
331   MatScalar      *rtmp,*pc,*mwork,*v,*pv,*aa=a->a;
332   PetscInt       bs2 = a->bs2,flg;
333   PetscReal      shift = info->shiftinblocks;
334 
335   PetscFunctionBegin;
336   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
337   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
338 
339   /* generate work space needed by the factorization */
340   ierr = PetscMalloc((bs2*n+bs2+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
341   mwork = rtmp + bs2*n;
342   ierr = PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));CHKERRQ(ierr);
343   ics  = ic;
344 
345   for (i=0; i<n; i++){
346     /* zero rtmp */
347     /* L part */
348     nz    = bi[i+1] - bi[i];
349     bjtmp = bj + bi[i];
350     for  (j=0; j<nz; j++){
351       ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
352     }
353 
354     /* U part */
355     nz = bdiag[i] - bdiag[i+1];
356     bjtmp = bj + bdiag[i+1]+1;
357     for  (j=0; j<nz; j++){
358       ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
359     }
360 
361     /* load in initial (unfactored row) */
362     nz    = ai[r[i]+1] - ai[r[i]];
363     ajtmp = aj + ai[r[i]];
364     v     = aa + bs2*ai[r[i]];
365     for (j=0; j<nz; j++) {
366       ierr = PetscMemcpy(rtmp+bs2*ic[ajtmp[j]],v+bs2*j,bs2*sizeof(MatScalar));CHKERRQ(ierr);
367     }
368 
369     /* elimination */
370     bjtmp = bj + bi[i];
371     nzL   = bi[i+1] - bi[i];
372     for(k=0;k < nzL;k++) {
373       row = bjtmp[k];
374       pc = rtmp + bs2*row;
375       for (flg=0,j=0; j<bs2; j++) { if (pc[j]!=0.0) { flg = 1; break; }}
376       if (flg) {
377         pv = b->a + bs2*bdiag[row];
378         /* Kernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
379         ierr = Kernel_A_gets_A_times_B_5(pc,pv,mwork);CHKERRQ(ierr);
380 
381         pj = b->j + bdiag[row+1]+1; /* begining of U(row,:) */
382         pv = b->a + bs2*(bdiag[row+1]+1);
383         nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries inU(row,:), excluding diag */
384         for (j=0; j<nz; j++) {
385           /* Kernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
386           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
387           v    = rtmp + bs2*pj[j];
388           ierr = Kernel_A_gets_A_minus_B_times_C_5(v,pc,pv);CHKERRQ(ierr);
389           pv  += bs2;
390         }
391         ierr = PetscLogFlops(250*nz+225);CHKERRQ(ierr); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
392       }
393     }
394 
395     /* finished row so stick it into b->a */
396     /* L part */
397     pv   = b->a + bs2*bi[i] ;
398     pj   = b->j + bi[i] ;
399     nz   = bi[i+1] - bi[i];
400     for (j=0; j<nz; j++) {
401       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
402     }
403 
404     /* Mark diagonal and invert diagonal for simplier triangular solves */
405     pv   = b->a + bs2*bdiag[i];
406     pj   = b->j + bdiag[i];
407     ierr = PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));CHKERRQ(ierr);
408     /* ierr = Kernel_A_gets_inverse_A(bs,pv,v_pivots,v_work);CHKERRQ(ierr); */
409     ierr = Kernel_A_gets_inverse_A_5(pv,shift);CHKERRQ(ierr);
410 
411     /* U part */
412     pv = b->a + bs2*(bdiag[i+1]+1);
413     pj = b->j + bdiag[i+1]+1;
414     nz = bdiag[i] - bdiag[i+1] - 1;
415     for (j=0; j<nz; j++){
416       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
417     }
418   }
419 
420   ierr = PetscFree(rtmp);CHKERRQ(ierr);
421   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
422   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
423 
424   C->assembled = PETSC_TRUE;
425   ierr = PetscLogFlops(1.3333*bs2*n);CHKERRQ(ierr); /* from inverting diagonal blocks */
426   PetscFunctionReturn(0);
427 }
428 
429 /*
430       Version for when blocks are 5 by 5 Using natural ordering
431 */
432 #undef __FUNCT__
433 #define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_5_NaturalOrdering"
434 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5_NaturalOrdering(Mat C,Mat A,const MatFactorInfo *info)
435 {
436   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ *)C->data;
437   PetscErrorCode ierr;
438   PetscInt       i,j,n = a->mbs,*bi = b->i,*bj = b->j;
439   PetscInt       *ajtmpold,*ajtmp,nz,row;
440   PetscInt       *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
441   MatScalar      *pv,*v,*rtmp,*pc,*w,*x;
442   MatScalar      x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15;
443   MatScalar      x16,x17,x18,x19,x20,x21,x22,x23,x24,x25;
444   MatScalar      p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15;
445   MatScalar      p16,p17,p18,p19,p20,p21,p22,p23,p24,p25;
446   MatScalar      m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12,m13,m14,m15;
447   MatScalar      m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
448   MatScalar      *ba = b->a,*aa = a->a;
449   PetscReal      shift = info->shiftinblocks;
450 
451   PetscFunctionBegin;
452   ierr = PetscMalloc(25*(n+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
453   for (i=0; i<n; i++) {
454     nz    = bi[i+1] - bi[i];
455     ajtmp = bj + bi[i];
456     for  (j=0; j<nz; j++) {
457       x = rtmp+25*ajtmp[j];
458       x[0]  = x[1]  = x[2]  = x[3]  = x[4]  = x[5]  = x[6] = x[7] = x[8] = x[9] = 0.0;
459       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = 0.0;
460       x[16] = x[17] = x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = 0.0;
461     }
462     /* load in initial (unfactored row) */
463     nz       = ai[i+1] - ai[i];
464     ajtmpold = aj + ai[i];
465     v        = aa + 25*ai[i];
466     for (j=0; j<nz; j++) {
467       x    = rtmp+25*ajtmpold[j];
468       x[0]  = v[0];  x[1]  = v[1];  x[2]  = v[2];  x[3]  = v[3];
469       x[4]  = v[4];  x[5]  = v[5];  x[6]  = v[6];  x[7]  = v[7];  x[8]  = v[8];
470       x[9]  = v[9];  x[10] = v[10]; x[11] = v[11]; x[12] = v[12]; x[13] = v[13];
471       x[14] = v[14]; x[15] = v[15]; x[16] = v[16]; x[17] = v[17]; x[18] = v[18];
472       x[19] = v[19]; x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23];
473       x[24] = v[24];
474       v    += 25;
475     }
476     row = *ajtmp++;
477     while (row < i) {
478       pc  = rtmp + 25*row;
479       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
480       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];  p9  = pc[8];
481       p10 = pc[9];  p11 = pc[10]; p12 = pc[11]; p13 = pc[12]; p14 = pc[13];
482       p15 = pc[14]; p16 = pc[15]; p17 = pc[16]; p18 = pc[17];
483       p19 = pc[18]; p20 = pc[19]; p21 = pc[20]; p22 = pc[21]; p23 = pc[22];
484       p24 = pc[23]; p25 = pc[24];
485       if (p1 != 0.0 || p2 != 0.0 || p3 != 0.0 || p4 != 0.0 || p5 != 0.0 ||
486           p6 != 0.0 || p7 != 0.0 || p8 != 0.0 || p9 != 0.0 || p10 != 0.0 ||
487           p11 != 0.0 || p12 != 0.0 || p13 != 0.0 || p14 != 0.0 || p15 != 0.0
488           || p16 != 0.0 || p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0
489           || p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 || p25 != 0.0) {
490         pv = ba + 25*diag_offset[row];
491         pj = bj + diag_offset[row] + 1;
492         x1  = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
493         x5  = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];  x9  = pv[8];
494         x10 = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12]; x14 = pv[13];
495         x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17]; x19 = pv[18];
496         x20 = pv[19]; x21 = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
497         x25 = pv[24];
498         pc[0] = m1 = p1*x1 + p6*x2  + p11*x3 + p16*x4 + p21*x5;
499         pc[1] = m2 = p2*x1 + p7*x2  + p12*x3 + p17*x4 + p22*x5;
500         pc[2] = m3 = p3*x1 + p8*x2  + p13*x3 + p18*x4 + p23*x5;
501         pc[3] = m4 = p4*x1 + p9*x2  + p14*x3 + p19*x4 + p24*x5;
502         pc[4] = m5 = p5*x1 + p10*x2 + p15*x3 + p20*x4 + p25*x5;
503 
504         pc[5]  = m6  = p1*x6 + p6*x7  + p11*x8 + p16*x9 + p21*x10;
505         pc[6]  = m7  = p2*x6 + p7*x7  + p12*x8 + p17*x9 + p22*x10;
506         pc[7]  = m8  = p3*x6 + p8*x7  + p13*x8 + p18*x9 + p23*x10;
507         pc[8]  = m9  = p4*x6 + p9*x7  + p14*x8 + p19*x9 + p24*x10;
508         pc[9]  = m10 = p5*x6 + p10*x7 + p15*x8 + p20*x9 + p25*x10;
509 
510         pc[10] = m11 = p1*x11 + p6*x12  + p11*x13 + p16*x14 + p21*x15;
511         pc[11] = m12 = p2*x11 + p7*x12  + p12*x13 + p17*x14 + p22*x15;
512         pc[12] = m13 = p3*x11 + p8*x12  + p13*x13 + p18*x14 + p23*x15;
513         pc[13] = m14 = p4*x11 + p9*x12  + p14*x13 + p19*x14 + p24*x15;
514         pc[14] = m15 = p5*x11 + p10*x12 + p15*x13 + p20*x14 + p25*x15;
515 
516         pc[15] = m16 = p1*x16 + p6*x17  + p11*x18 + p16*x19 + p21*x20;
517         pc[16] = m17 = p2*x16 + p7*x17  + p12*x18 + p17*x19 + p22*x20;
518         pc[17] = m18 = p3*x16 + p8*x17  + p13*x18 + p18*x19 + p23*x20;
519         pc[18] = m19 = p4*x16 + p9*x17  + p14*x18 + p19*x19 + p24*x20;
520         pc[19] = m20 = p5*x16 + p10*x17 + p15*x18 + p20*x19 + p25*x20;
521 
522         pc[20] = m21 = p1*x21 + p6*x22  + p11*x23 + p16*x24 + p21*x25;
523         pc[21] = m22 = p2*x21 + p7*x22  + p12*x23 + p17*x24 + p22*x25;
524         pc[22] = m23 = p3*x21 + p8*x22  + p13*x23 + p18*x24 + p23*x25;
525         pc[23] = m24 = p4*x21 + p9*x22  + p14*x23 + p19*x24 + p24*x25;
526         pc[24] = m25 = p5*x21 + p10*x22 + p15*x23 + p20*x24 + p25*x25;
527 
528         nz = bi[row+1] - diag_offset[row] - 1;
529         pv += 25;
530         for (j=0; j<nz; j++) {
531           x1   = pv[0];  x2  = pv[1];   x3 = pv[2];  x4  = pv[3];
532           x5   = pv[4];  x6  = pv[5];   x7 = pv[6];  x8  = pv[7]; x9 = pv[8];
533           x10  = pv[9];  x11 = pv[10]; x12 = pv[11]; x13 = pv[12];
534           x14  = pv[13]; x15 = pv[14]; x16 = pv[15]; x17 = pv[16]; x18 = pv[17];
535           x19 = pv[18];  x20 = pv[19]; x21 = pv[20]; x22 = pv[21]; x23 = pv[22];
536           x24 = pv[23];  x25 = pv[24];
537           x    = rtmp + 25*pj[j];
538           x[0] -= m1*x1 + m6*x2   + m11*x3  + m16*x4 + m21*x5;
539           x[1] -= m2*x1 + m7*x2   + m12*x3  + m17*x4 + m22*x5;
540           x[2] -= m3*x1 + m8*x2   + m13*x3  + m18*x4 + m23*x5;
541           x[3] -= m4*x1 + m9*x2   + m14*x3  + m19*x4 + m24*x5;
542           x[4] -= m5*x1 + m10*x2  + m15*x3  + m20*x4 + m25*x5;
543 
544           x[5] -= m1*x6 + m6*x7   + m11*x8  + m16*x9 + m21*x10;
545           x[6] -= m2*x6 + m7*x7   + m12*x8  + m17*x9 + m22*x10;
546           x[7] -= m3*x6 + m8*x7   + m13*x8  + m18*x9 + m23*x10;
547           x[8] -= m4*x6 + m9*x7   + m14*x8  + m19*x9 + m24*x10;
548           x[9] -= m5*x6 + m10*x7  + m15*x8  + m20*x9 + m25*x10;
549 
550           x[10] -= m1*x11 + m6*x12  + m11*x13 + m16*x14 + m21*x15;
551           x[11] -= m2*x11 + m7*x12  + m12*x13 + m17*x14 + m22*x15;
552           x[12] -= m3*x11 + m8*x12  + m13*x13 + m18*x14 + m23*x15;
553           x[13] -= m4*x11 + m9*x12  + m14*x13 + m19*x14 + m24*x15;
554           x[14] -= m5*x11 + m10*x12 + m15*x13 + m20*x14 + m25*x15;
555 
556           x[15] -= m1*x16 + m6*x17  + m11*x18 + m16*x19 + m21*x20;
557           x[16] -= m2*x16 + m7*x17  + m12*x18 + m17*x19 + m22*x20;
558           x[17] -= m3*x16 + m8*x17  + m13*x18 + m18*x19 + m23*x20;
559           x[18] -= m4*x16 + m9*x17  + m14*x18 + m19*x19 + m24*x20;
560           x[19] -= m5*x16 + m10*x17 + m15*x18 + m20*x19 + m25*x20;
561 
562           x[20] -= m1*x21 + m6*x22  + m11*x23 + m16*x24 + m21*x25;
563           x[21] -= m2*x21 + m7*x22  + m12*x23 + m17*x24 + m22*x25;
564           x[22] -= m3*x21 + m8*x22  + m13*x23 + m18*x24 + m23*x25;
565           x[23] -= m4*x21 + m9*x22  + m14*x23 + m19*x24 + m24*x25;
566           x[24] -= m5*x21 + m10*x22 + m15*x23 + m20*x24 + m25*x25;
567           pv   += 25;
568         }
569         ierr = PetscLogFlops(250.0*nz+225.0);CHKERRQ(ierr);
570       }
571       row = *ajtmp++;
572     }
573     /* finished row so stick it into b->a */
574     pv = ba + 25*bi[i];
575     pj = bj + bi[i];
576     nz = bi[i+1] - bi[i];
577     for (j=0; j<nz; j++) {
578       x      = rtmp+25*pj[j];
579       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
580       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7]; pv[8] = x[8];
581       pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11]; pv[12] = x[12];
582       pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15]; pv[16] = x[16]; pv[17] = x[17];
583       pv[18] = x[18]; pv[19] = x[19]; pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22];
584       pv[23] = x[23]; pv[24] = x[24];
585       pv   += 25;
586     }
587     /* invert diagonal block */
588     w = ba + 25*diag_offset[i];
589     ierr = Kernel_A_gets_inverse_A_5(w,shift);CHKERRQ(ierr);
590   }
591 
592   ierr = PetscFree(rtmp);CHKERRQ(ierr);
593   C->ops->solve          = MatSolve_SeqBAIJ_5_NaturalOrdering;
594   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_5_NaturalOrdering;
595   C->assembled = PETSC_TRUE;
596   ierr = PetscLogFlops(1.3333*125*b->mbs);CHKERRQ(ierr); /* from inverting diagonal blocks */
597   PetscFunctionReturn(0);
598 }
599 
600 #undef __FUNCT__
601 #define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_5_NaturalOrdering_newdatastruct"
602 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5_NaturalOrdering_newdatastruct(Mat B,Mat A,const MatFactorInfo *info)
603 {
604   Mat            C=B;
605   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ *)C->data;
606   PetscErrorCode ierr;
607   PetscInt       i,j,k,n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
608   PetscInt       *ajtmp,*bjtmp,nz,nzL,row,*bdiag=b->diag,*pj;
609   MatScalar      *rtmp,*pc,*mwork,*v,*pv,*aa=a->a;
610   PetscInt       bs2 = a->bs2,flg;
611   PetscReal      shift = info->shiftinblocks;
612 
613   PetscFunctionBegin;
614   /* generate work space needed by the factorization */
615   ierr = PetscMalloc((bs2*n+bs2+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
616   mwork = rtmp + bs2*n;
617   ierr = PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));CHKERRQ(ierr);
618 
619   for (i=0; i<n; i++){
620     /* zero rtmp */
621     /* L part */
622     nz    = bi[i+1] - bi[i];
623     bjtmp = bj + bi[i];
624     for  (j=0; j<nz; j++){
625       ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
626     }
627 
628     /* U part */
629     nz = bi[2*n-i+1] - bi[2*n-i];
630     bjtmp = bj + bi[2*n-i];
631     for  (j=0; j<nz; j++){
632       ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
633     }
634 
635     /* load in initial (unfactored row) */
636     nz    = ai[i+1] - ai[i];
637     ajtmp = aj + ai[i];
638     v     = aa + bs2*ai[i];
639     for (j=0; j<nz; j++) {
640       ierr = PetscMemcpy(rtmp+bs2*ajtmp[j],v+bs2*j,bs2*sizeof(MatScalar));CHKERRQ(ierr);
641     }
642 
643     /* elimination */
644     bjtmp = bj + bi[i];
645     nzL   = bi[i+1] - bi[i];
646     for(k=0;k < nzL;k++) {
647       row = bjtmp[k];
648       pc = rtmp + bs2*row;
649       for (flg=0,j=0; j<bs2; j++) { if (pc[j]!=0.0) { flg = 1; break; }}
650       if (flg) {
651         pv = b->a + bs2*bdiag[row];
652         /* Kernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
653         ierr = Kernel_A_gets_A_times_B_5(pc,pv,mwork);CHKERRQ(ierr);
654 
655         pj = b->j + bi[2*n-row]; /* begining of U(row,:) */
656         pv = b->a + bs2*bi[2*n-row];
657         nz = bi[2*n-row+1] - bi[2*n-row] - 1; /* num of entries inU(row,:), excluding diag */
658         for (j=0; j<nz; j++) {
659           /* Kernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
660           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
661           v    = rtmp + bs2*pj[j];
662           ierr = Kernel_A_gets_A_minus_B_times_C_5(v,pc,pv);CHKERRQ(ierr);
663           pv  += bs2;
664         }
665         ierr = PetscLogFlops(250*nz+225);CHKERRQ(ierr); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
666       }
667     }
668 
669     /* finished row so stick it into b->a */
670     /* L part */
671     pv   = b->a + bs2*bi[i] ;
672     pj   = b->j + bi[i] ;
673     nz   = bi[i+1] - bi[i];
674     for (j=0; j<nz; j++) {
675       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
676     }
677 
678     /* Mark diagonal and invert diagonal for simplier triangular solves */
679     pv   = b->a + bs2*bdiag[i];
680     pj   = b->j + bdiag[i];
681     ierr = PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));CHKERRQ(ierr);
682     /* ierr = Kernel_A_gets_inverse_A(bs,pv,v_pivots,v_work);CHKERRQ(ierr); */
683     ierr = Kernel_A_gets_inverse_A_5(pv,shift);CHKERRQ(ierr);
684 
685     /* U part */
686     pv = b->a + bs2*bi[2*n-i];
687     pj = b->j + bi[2*n-i];
688     nz = bi[2*n-i+1] - bi[2*n-i] - 1;
689     for (j=0; j<nz; j++){
690       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
691     }
692   }
693 
694   ierr = PetscFree(rtmp);CHKERRQ(ierr);
695   C->assembled = PETSC_TRUE;
696   ierr = PetscLogFlops(1.3333*bs2*n);CHKERRQ(ierr); /* from inverting diagonal blocks */
697   PetscFunctionReturn(0);
698 }
699 
700 #undef __FUNCT__
701 #define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_5_NaturalOrdering_newdatastruct_v2"
702 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_5_NaturalOrdering_newdatastruct_v2(Mat B,Mat A,const MatFactorInfo *info)
703 {
704   Mat            C=B;
705   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ *)C->data;
706   PetscErrorCode ierr;
707   PetscInt       i,j,k,n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
708   PetscInt       *ajtmp,*bjtmp,nz,nzL,row,*bdiag=b->diag,*pj;
709   MatScalar      *rtmp,*pc,*mwork,*v,*pv,*aa=a->a;
710   PetscInt       bs2 = a->bs2,flg;
711   PetscReal      shift = info->shiftinblocks;
712 
713   PetscFunctionBegin;
714   /* generate work space needed by the factorization */
715   ierr = PetscMalloc((bs2*n+bs2+1)*sizeof(MatScalar),&rtmp);CHKERRQ(ierr);
716   mwork = rtmp + bs2*n;
717   ierr = PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));CHKERRQ(ierr);
718 
719   for (i=0; i<n; i++){
720     /* zero rtmp */
721     /* L part */
722     nz    = bi[i+1] - bi[i];
723     bjtmp = bj + bi[i];
724     for  (j=0; j<nz; j++){
725       ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
726     }
727 
728     /* U part */
729     nz = bdiag[i] - bdiag[i+1];
730     bjtmp = bj + bdiag[i+1]+1;
731     for  (j=0; j<nz; j++){
732       ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
733     }
734 
735     /* load in initial (unfactored row) */
736     nz    = ai[i+1] - ai[i];
737     ajtmp = aj + ai[i];
738     v     = aa + bs2*ai[i];
739     for (j=0; j<nz; j++) {
740       ierr = PetscMemcpy(rtmp+bs2*ajtmp[j],v+bs2*j,bs2*sizeof(MatScalar));CHKERRQ(ierr);
741     }
742 
743     /* elimination */
744     bjtmp = bj + bi[i];
745     nzL   = bi[i+1] - bi[i];
746     for(k=0;k < nzL;k++) {
747       row = bjtmp[k];
748       pc = rtmp + bs2*row;
749       for (flg=0,j=0; j<bs2; j++) { if (pc[j]!=0.0) { flg = 1; break; }}
750       if (flg) {
751         pv = b->a + bs2*bdiag[row];
752         /* Kernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
753         ierr = Kernel_A_gets_A_times_B_5(pc,pv,mwork);CHKERRQ(ierr);
754 
755         pj = b->j + bdiag[row+1]+1; /* begining of U(row,:) */
756         pv = b->a + bs2*(bdiag[row+1]+1);
757         nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries inU(row,:), excluding diag */
758         for (j=0; j<nz; j++) {
759           /* Kernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
760           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
761           v    = rtmp + bs2*pj[j];
762           ierr = Kernel_A_gets_A_minus_B_times_C_5(v,pc,pv);CHKERRQ(ierr);
763           pv  += bs2;
764         }
765         ierr = PetscLogFlops(250*nz+225);CHKERRQ(ierr); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
766       }
767     }
768 
769     /* finished row so stick it into b->a */
770     /* L part */
771     pv   = b->a + bs2*bi[i] ;
772     pj   = b->j + bi[i] ;
773     nz   = bi[i+1] - bi[i];
774     for (j=0; j<nz; j++) {
775       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
776     }
777 
778     /* Mark diagonal and invert diagonal for simplier triangular solves */
779     pv   = b->a + bs2*bdiag[i];
780     pj   = b->j + bdiag[i];
781     ierr = PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));CHKERRQ(ierr);
782     /* ierr = Kernel_A_gets_inverse_A(bs,pv,v_pivots,v_work);CHKERRQ(ierr); */
783     ierr = Kernel_A_gets_inverse_A_5(pv,shift);CHKERRQ(ierr);
784 
785     /* U part */
786     pv = b->a + bs2*(bdiag[i+1]+1);
787     pj = b->j + bdiag[i+1]+1;
788     nz = bdiag[i] - bdiag[i+1] - 1;
789     for (j=0; j<nz; j++){
790       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
791     }
792   }
793 
794   ierr = PetscFree(rtmp);CHKERRQ(ierr);
795   C->assembled = PETSC_TRUE;
796   ierr = PetscLogFlops(1.3333*bs2*n);CHKERRQ(ierr); /* from inverting diagonal blocks */
797   PetscFunctionReturn(0);
798 }
799