xref: /petsc/src/mat/impls/baij/seq/baijfact7.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 6 by 6
11 */
12 #undef __FUNCT__
13 #define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_6_inplace"
14 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_6_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 *ajtmpold,*ajtmp,*diag_offset = b->diag,*r,*ic,*bi = b->i,*bj = b->j,*ai=a->i,*aj=a->j,*pj;
20   PetscInt       nz,row,i,j,n = a->mbs,idx;
21   MatScalar      *pv,*v,*rtmp,*pc,*w,*x;
22   MatScalar      p1,p2,p3,p4,m1,m2,m3,m4,m5,m6,m7,m8,m9,x1,x2,x3,x4;
23   MatScalar      p5,p6,p7,p8,p9,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15,x16;
24   MatScalar      x17,x18,x19,x20,x21,x22,x23,x24,x25,p10,p11,p12,p13,p14;
25   MatScalar      p15,p16,p17,p18,p19,p20,p21,p22,p23,p24,p25,m10,m11,m12;
26   MatScalar      m13,m14,m15,m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
27   MatScalar      p26,p27,p28,p29,p30,p31,p32,p33,p34,p35,p36;
28   MatScalar      x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36;
29   MatScalar      m26,m27,m28,m29,m30,m31,m32,m33,m34,m35,m36;
30   MatScalar      *ba   = b->a,*aa = a->a;
31   PetscReal      shift = info->shiftamount;
32   PetscBool      allowzeropivot,zeropivotdetected;
33 
34   PetscFunctionBegin;
35   allowzeropivot = PetscNot(A->erroriffailure);
36   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
37   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
38   ierr = PetscMalloc1(36*(n+1),&rtmp);CHKERRQ(ierr);
39 
40   for (i=0; i<n; i++) {
41     nz    = bi[i+1] - bi[i];
42     ajtmp = bj + bi[i];
43     for  (j=0; j<nz; j++) {
44       x     = rtmp+36*ajtmp[j];
45       x[0]  = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
46       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
47       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = x[25] = 0.0;
48       x[26] = x[27] = x[28] = x[29] = x[30] = x[31] = x[32] = x[33] = 0.0;
49       x[34] = x[35] = 0.0;
50     }
51     /* load in initial (unfactored row) */
52     idx      = r[i];
53     nz       = ai[idx+1] - ai[idx];
54     ajtmpold = aj + ai[idx];
55     v        = aa + 36*ai[idx];
56     for (j=0; j<nz; j++) {
57       x     = rtmp+36*ic[ajtmpold[j]];
58       x[0]  =  v[0];  x[1] =  v[1];  x[2] =  v[2];  x[3] =  v[3];
59       x[4]  =  v[4];  x[5] =  v[5];  x[6] =  v[6];  x[7] =  v[7];
60       x[8]  =  v[8];  x[9] =  v[9];  x[10] = v[10]; x[11] = v[11];
61       x[12] = v[12]; x[13] = v[13]; x[14] = v[14]; x[15] = v[15];
62       x[16] = v[16]; x[17] = v[17]; x[18] = v[18]; x[19] = v[19];
63       x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23];
64       x[24] = v[24]; x[25] = v[25]; x[26] = v[26]; x[27] = v[27];
65       x[28] = v[28]; x[29] = v[29]; x[30] = v[30]; x[31] = v[31];
66       x[32] = v[32]; x[33] = v[33]; x[34] = v[34]; x[35] = v[35];
67       v    += 36;
68     }
69     row = *ajtmp++;
70     while (row < i) {
71       pc  =  rtmp + 36*row;
72       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
73       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];
74       p9  = pc[8];  p10 = pc[9];  p11 = pc[10]; p12 = pc[11];
75       p13 = pc[12]; p14 = pc[13]; p15 = pc[14]; p16 = pc[15];
76       p17 = pc[16]; p18 = pc[17]; p19 = pc[18]; p20 = pc[19];
77       p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
78       p25 = pc[24]; p26 = pc[25]; p27 = pc[26]; p28 = pc[27];
79       p29 = pc[28]; p30 = pc[29]; p31 = pc[30]; p32 = pc[31];
80       p33 = pc[32]; p34 = pc[33]; p35 = pc[34]; p36 = pc[35];
81       if (p1  != 0.0 || p2  != 0.0 || p3  != 0.0 || p4  != 0.0 ||
82           p5  != 0.0 || p6  != 0.0 || p7  != 0.0 || p8  != 0.0 ||
83           p9  != 0.0 || p10 != 0.0 || p11 != 0.0 || p12 != 0.0 ||
84           p13 != 0.0 || p14 != 0.0 || p15 != 0.0 || p16 != 0.0 ||
85           p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 ||
86           p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 ||
87           p25 != 0.0 || p26 != 0.0 || p27 != 0.0 || p28 != 0.0 ||
88           p29 != 0.0 || p30 != 0.0 || p31 != 0.0 || p32 != 0.0 ||
89           p33 != 0.0 || p34 != 0.0 || p35 != 0.0 || p36 != 0.0) {
90         pv    = ba + 36*diag_offset[row];
91         pj    = bj + diag_offset[row] + 1;
92         x1    = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
93         x5    = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
94         x9    = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
95         x13   = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
96         x17   = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
97         x21   = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
98         x25   = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
99         x29   = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
100         x33   = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
101         pc[0] = m1  = p1*x1  + p7*x2   + p13*x3  + p19*x4  + p25*x5  + p31*x6;
102         pc[1] = m2  = p2*x1  + p8*x2   + p14*x3  + p20*x4  + p26*x5  + p32*x6;
103         pc[2] = m3  = p3*x1  + p9*x2   + p15*x3  + p21*x4  + p27*x5  + p33*x6;
104         pc[3] = m4  = p4*x1  + p10*x2  + p16*x3  + p22*x4  + p28*x5  + p34*x6;
105         pc[4] = m5  = p5*x1  + p11*x2  + p17*x3  + p23*x4  + p29*x5  + p35*x6;
106         pc[5] = m6  = p6*x1  + p12*x2  + p18*x3  + p24*x4  + p30*x5  + p36*x6;
107 
108         pc[6]  = m7  = p1*x7  + p7*x8   + p13*x9  + p19*x10 + p25*x11 + p31*x12;
109         pc[7]  = m8  = p2*x7  + p8*x8   + p14*x9  + p20*x10 + p26*x11 + p32*x12;
110         pc[8]  = m9  = p3*x7  + p9*x8   + p15*x9  + p21*x10 + p27*x11 + p33*x12;
111         pc[9]  = m10 = p4*x7  + p10*x8  + p16*x9  + p22*x10 + p28*x11 + p34*x12;
112         pc[10] = m11 = p5*x7  + p11*x8  + p17*x9  + p23*x10 + p29*x11 + p35*x12;
113         pc[11] = m12 = p6*x7  + p12*x8  + p18*x9  + p24*x10 + p30*x11 + p36*x12;
114 
115         pc[12] = m13 = p1*x13 + p7*x14  + p13*x15 + p19*x16 + p25*x17 + p31*x18;
116         pc[13] = m14 = p2*x13 + p8*x14  + p14*x15 + p20*x16 + p26*x17 + p32*x18;
117         pc[14] = m15 = p3*x13 + p9*x14  + p15*x15 + p21*x16 + p27*x17 + p33*x18;
118         pc[15] = m16 = p4*x13 + p10*x14 + p16*x15 + p22*x16 + p28*x17 + p34*x18;
119         pc[16] = m17 = p5*x13 + p11*x14 + p17*x15 + p23*x16 + p29*x17 + p35*x18;
120         pc[17] = m18 = p6*x13 + p12*x14 + p18*x15 + p24*x16 + p30*x17 + p36*x18;
121 
122         pc[18] = m19 = p1*x19 + p7*x20  + p13*x21 + p19*x22 + p25*x23 + p31*x24;
123         pc[19] = m20 = p2*x19 + p8*x20  + p14*x21 + p20*x22 + p26*x23 + p32*x24;
124         pc[20] = m21 = p3*x19 + p9*x20  + p15*x21 + p21*x22 + p27*x23 + p33*x24;
125         pc[21] = m22 = p4*x19 + p10*x20 + p16*x21 + p22*x22 + p28*x23 + p34*x24;
126         pc[22] = m23 = p5*x19 + p11*x20 + p17*x21 + p23*x22 + p29*x23 + p35*x24;
127         pc[23] = m24 = p6*x19 + p12*x20 + p18*x21 + p24*x22 + p30*x23 + p36*x24;
128 
129         pc[24] = m25 = p1*x25 + p7*x26  + p13*x27 + p19*x28 + p25*x29 + p31*x30;
130         pc[25] = m26 = p2*x25 + p8*x26  + p14*x27 + p20*x28 + p26*x29 + p32*x30;
131         pc[26] = m27 = p3*x25 + p9*x26  + p15*x27 + p21*x28 + p27*x29 + p33*x30;
132         pc[27] = m28 = p4*x25 + p10*x26 + p16*x27 + p22*x28 + p28*x29 + p34*x30;
133         pc[28] = m29 = p5*x25 + p11*x26 + p17*x27 + p23*x28 + p29*x29 + p35*x30;
134         pc[29] = m30 = p6*x25 + p12*x26 + p18*x27 + p24*x28 + p30*x29 + p36*x30;
135 
136         pc[30] = m31 = p1*x31 + p7*x32  + p13*x33 + p19*x34 + p25*x35 + p31*x36;
137         pc[31] = m32 = p2*x31 + p8*x32  + p14*x33 + p20*x34 + p26*x35 + p32*x36;
138         pc[32] = m33 = p3*x31 + p9*x32  + p15*x33 + p21*x34 + p27*x35 + p33*x36;
139         pc[33] = m34 = p4*x31 + p10*x32 + p16*x33 + p22*x34 + p28*x35 + p34*x36;
140         pc[34] = m35 = p5*x31 + p11*x32 + p17*x33 + p23*x34 + p29*x35 + p35*x36;
141         pc[35] = m36 = p6*x31 + p12*x32 + p18*x33 + p24*x34 + p30*x35 + p36*x36;
142 
143         nz  = bi[row+1] - diag_offset[row] - 1;
144         pv += 36;
145         for (j=0; j<nz; j++) {
146           x1    = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
147           x5    = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
148           x9    = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
149           x13   = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
150           x17   = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
151           x21   = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
152           x25   = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
153           x29   = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
154           x33   = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
155           x     = rtmp + 36*pj[j];
156           x[0] -= m1*x1  + m7*x2   + m13*x3  + m19*x4  + m25*x5  + m31*x6;
157           x[1] -= m2*x1  + m8*x2   + m14*x3  + m20*x4  + m26*x5  + m32*x6;
158           x[2] -= m3*x1  + m9*x2   + m15*x3  + m21*x4  + m27*x5  + m33*x6;
159           x[3] -= m4*x1  + m10*x2  + m16*x3  + m22*x4  + m28*x5  + m34*x6;
160           x[4] -= m5*x1  + m11*x2  + m17*x3  + m23*x4  + m29*x5  + m35*x6;
161           x[5] -= m6*x1  + m12*x2  + m18*x3  + m24*x4  + m30*x5  + m36*x6;
162 
163           x[6]  -= m1*x7  + m7*x8   + m13*x9  + m19*x10 + m25*x11 + m31*x12;
164           x[7]  -= m2*x7  + m8*x8   + m14*x9  + m20*x10 + m26*x11 + m32*x12;
165           x[8]  -= m3*x7  + m9*x8   + m15*x9  + m21*x10 + m27*x11 + m33*x12;
166           x[9]  -= m4*x7  + m10*x8  + m16*x9  + m22*x10 + m28*x11 + m34*x12;
167           x[10] -= m5*x7  + m11*x8  + m17*x9  + m23*x10 + m29*x11 + m35*x12;
168           x[11] -= m6*x7  + m12*x8  + m18*x9  + m24*x10 + m30*x11 + m36*x12;
169 
170           x[12] -= m1*x13 + m7*x14  + m13*x15 + m19*x16 + m25*x17 + m31*x18;
171           x[13] -= m2*x13 + m8*x14  + m14*x15 + m20*x16 + m26*x17 + m32*x18;
172           x[14] -= m3*x13 + m9*x14  + m15*x15 + m21*x16 + m27*x17 + m33*x18;
173           x[15] -= m4*x13 + m10*x14 + m16*x15 + m22*x16 + m28*x17 + m34*x18;
174           x[16] -= m5*x13 + m11*x14 + m17*x15 + m23*x16 + m29*x17 + m35*x18;
175           x[17] -= m6*x13 + m12*x14 + m18*x15 + m24*x16 + m30*x17 + m36*x18;
176 
177           x[18] -= m1*x19 + m7*x20  + m13*x21 + m19*x22 + m25*x23 + m31*x24;
178           x[19] -= m2*x19 + m8*x20  + m14*x21 + m20*x22 + m26*x23 + m32*x24;
179           x[20] -= m3*x19 + m9*x20  + m15*x21 + m21*x22 + m27*x23 + m33*x24;
180           x[21] -= m4*x19 + m10*x20 + m16*x21 + m22*x22 + m28*x23 + m34*x24;
181           x[22] -= m5*x19 + m11*x20 + m17*x21 + m23*x22 + m29*x23 + m35*x24;
182           x[23] -= m6*x19 + m12*x20 + m18*x21 + m24*x22 + m30*x23 + m36*x24;
183 
184           x[24] -= m1*x25 + m7*x26  + m13*x27 + m19*x28 + m25*x29 + m31*x30;
185           x[25] -= m2*x25 + m8*x26  + m14*x27 + m20*x28 + m26*x29 + m32*x30;
186           x[26] -= m3*x25 + m9*x26  + m15*x27 + m21*x28 + m27*x29 + m33*x30;
187           x[27] -= m4*x25 + m10*x26 + m16*x27 + m22*x28 + m28*x29 + m34*x30;
188           x[28] -= m5*x25 + m11*x26 + m17*x27 + m23*x28 + m29*x29 + m35*x30;
189           x[29] -= m6*x25 + m12*x26 + m18*x27 + m24*x28 + m30*x29 + m36*x30;
190 
191           x[30] -= m1*x31 + m7*x32  + m13*x33 + m19*x34 + m25*x35 + m31*x36;
192           x[31] -= m2*x31 + m8*x32  + m14*x33 + m20*x34 + m26*x35 + m32*x36;
193           x[32] -= m3*x31 + m9*x32  + m15*x33 + m21*x34 + m27*x35 + m33*x36;
194           x[33] -= m4*x31 + m10*x32 + m16*x33 + m22*x34 + m28*x35 + m34*x36;
195           x[34] -= m5*x31 + m11*x32 + m17*x33 + m23*x34 + m29*x35 + m35*x36;
196           x[35] -= m6*x31 + m12*x32 + m18*x33 + m24*x34 + m30*x35 + m36*x36;
197 
198           pv += 36;
199         }
200         ierr = PetscLogFlops(432.0*nz+396.0);CHKERRQ(ierr);
201       }
202       row = *ajtmp++;
203     }
204     /* finished row so stick it into b->a */
205     pv = ba + 36*bi[i];
206     pj = bj + bi[i];
207     nz = bi[i+1] - bi[i];
208     for (j=0; j<nz; j++) {
209       x      = rtmp+36*pj[j];
210       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
211       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7];
212       pv[8]  = x[8];  pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11];
213       pv[12] = x[12]; pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
214       pv[16] = x[16]; pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19];
215       pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23];
216       pv[24] = x[24]; pv[25] = x[25]; pv[26] = x[26]; pv[27] = x[27];
217       pv[28] = x[28]; pv[29] = x[29]; pv[30] = x[30]; pv[31] = x[31];
218       pv[32] = x[32]; pv[33] = x[33]; pv[34] = x[34]; pv[35] = x[35];
219       pv    += 36;
220     }
221     /* invert diagonal block */
222     w    = ba + 36*diag_offset[i];
223     ierr = PetscKernel_A_gets_inverse_A_6(w,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
224     if (zeropivotdetected) C->errortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
225   }
226 
227   ierr = PetscFree(rtmp);CHKERRQ(ierr);
228   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
229   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
230 
231   C->ops->solve          = MatSolve_SeqBAIJ_6_inplace;
232   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_6_inplace;
233   C->assembled           = PETSC_TRUE;
234 
235   ierr = PetscLogFlops(1.333333333333*6*6*6*b->mbs);CHKERRQ(ierr); /* from inverting diagonal blocks */
236   PetscFunctionReturn(0);
237 }
238 
239 #undef __FUNCT__
240 #define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_6"
241 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_6(Mat B,Mat A,const MatFactorInfo *info)
242 {
243   Mat            C     = B;
244   Mat_SeqBAIJ    *a    = (Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ*)C->data;
245   IS             isrow = b->row,isicol = b->icol;
246   PetscErrorCode ierr;
247   const PetscInt *r,*ic;
248   PetscInt       i,j,k,nz,nzL,row;
249   const PetscInt n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
250   const PetscInt *ajtmp,*bjtmp,*bdiag=b->diag,*pj,bs2=a->bs2;
251   MatScalar      *rtmp,*pc,*mwork,*v,*pv,*aa=a->a;
252   PetscInt       flg;
253   PetscReal      shift = info->shiftamount;
254   PetscBool      allowzeropivot,zeropivotdetected;
255 
256   PetscFunctionBegin;
257   allowzeropivot = PetscNot(A->erroriffailure);
258   ierr = ISGetIndices(isrow,&r);CHKERRQ(ierr);
259   ierr = ISGetIndices(isicol,&ic);CHKERRQ(ierr);
260 
261   /* generate work space needed by the factorization */
262   ierr = PetscMalloc2(bs2*n,&rtmp,bs2,&mwork);CHKERRQ(ierr);
263   ierr = PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));CHKERRQ(ierr);
264 
265   for (i=0; i<n; i++) {
266     /* zero rtmp */
267     /* L part */
268     nz    = bi[i+1] - bi[i];
269     bjtmp = bj + bi[i];
270     for  (j=0; j<nz; j++) {
271       ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
272     }
273 
274     /* U part */
275     nz    = bdiag[i] - bdiag[i+1];
276     bjtmp = bj + bdiag[i+1]+1;
277     for  (j=0; j<nz; j++) {
278       ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
279     }
280 
281     /* load in initial (unfactored row) */
282     nz    = ai[r[i]+1] - ai[r[i]];
283     ajtmp = aj + ai[r[i]];
284     v     = aa + bs2*ai[r[i]];
285     for (j=0; j<nz; j++) {
286       ierr = PetscMemcpy(rtmp+bs2*ic[ajtmp[j]],v+bs2*j,bs2*sizeof(MatScalar));CHKERRQ(ierr);
287     }
288 
289     /* elimination */
290     bjtmp = bj + bi[i];
291     nzL   = bi[i+1] - bi[i];
292     for (k=0; k < nzL; k++) {
293       row = bjtmp[k];
294       pc  = rtmp + bs2*row;
295       for (flg=0,j=0; j<bs2; j++) {
296         if (pc[j]!=0.0) {
297           flg = 1;
298           break;
299         }
300       }
301       if (flg) {
302         pv = b->a + bs2*bdiag[row];
303         /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
304         ierr = PetscKernel_A_gets_A_times_B_6(pc,pv,mwork);CHKERRQ(ierr);
305 
306         pj = b->j + bdiag[row+1]+1; /* begining of U(row,:) */
307         pv = b->a + bs2*(bdiag[row+1]+1);
308         nz = bdiag[row] - bdiag[row+1] -  1; /* num of entries inU(row,:), excluding diag */
309         for (j=0; j<nz; j++) {
310           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
311           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
312           v    = rtmp + bs2*pj[j];
313           ierr = PetscKernel_A_gets_A_minus_B_times_C_6(v,pc,pv);CHKERRQ(ierr);
314           pv  += bs2;
315         }
316         ierr = PetscLogFlops(432*nz+396);CHKERRQ(ierr); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
317       }
318     }
319 
320     /* finished row so stick it into b->a */
321     /* L part */
322     pv = b->a + bs2*bi[i];
323     pj = b->j + bi[i];
324     nz = bi[i+1] - bi[i];
325     for (j=0; j<nz; j++) {
326       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
327     }
328 
329     /* Mark diagonal and invert diagonal for simplier triangular solves */
330     pv   = b->a + bs2*bdiag[i];
331     pj   = b->j + bdiag[i];
332     ierr = PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));CHKERRQ(ierr);
333     ierr = PetscKernel_A_gets_inverse_A_6(pv,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
334     if (zeropivotdetected) C->errortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
335 
336     /* U part */
337     pv = b->a + bs2*(bdiag[i+1]+1);
338     pj = b->j + bdiag[i+1]+1;
339     nz = bdiag[i] - bdiag[i+1] - 1;
340     for (j=0; j<nz; j++) {
341       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
342     }
343   }
344 
345   ierr = PetscFree2(rtmp,mwork);CHKERRQ(ierr);
346   ierr = ISRestoreIndices(isicol,&ic);CHKERRQ(ierr);
347   ierr = ISRestoreIndices(isrow,&r);CHKERRQ(ierr);
348 
349   C->ops->solve          = MatSolve_SeqBAIJ_6;
350   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_6;
351   C->assembled           = PETSC_TRUE;
352 
353   ierr = PetscLogFlops(1.333333333333*6*6*6*n);CHKERRQ(ierr); /* from inverting diagonal blocks */
354   PetscFunctionReturn(0);
355 }
356 
357 #undef __FUNCT__
358 #define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_6_NaturalOrdering_inplace"
359 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_6_NaturalOrdering_inplace(Mat C,Mat A,const MatFactorInfo *info)
360 {
361   Mat_SeqBAIJ    *a = (Mat_SeqBAIJ*)A->data,*b = (Mat_SeqBAIJ*)C->data;
362   PetscErrorCode ierr;
363   PetscInt       i,j,n = a->mbs,*bi = b->i,*bj = b->j;
364   PetscInt       *ajtmpold,*ajtmp,nz,row;
365   PetscInt       *diag_offset = b->diag,*ai=a->i,*aj=a->j,*pj;
366   MatScalar      *pv,*v,*rtmp,*pc,*w,*x;
367   MatScalar      x1,x2,x3,x4,x5,x6,x7,x8,x9,x10,x11,x12,x13,x14,x15;
368   MatScalar      x16,x17,x18,x19,x20,x21,x22,x23,x24,x25;
369   MatScalar      p1,p2,p3,p4,p5,p6,p7,p8,p9,p10,p11,p12,p13,p14,p15;
370   MatScalar      p16,p17,p18,p19,p20,p21,p22,p23,p24,p25;
371   MatScalar      m1,m2,m3,m4,m5,m6,m7,m8,m9,m10,m11,m12,m13,m14,m15;
372   MatScalar      m16,m17,m18,m19,m20,m21,m22,m23,m24,m25;
373   MatScalar      p26,p27,p28,p29,p30,p31,p32,p33,p34,p35,p36;
374   MatScalar      x26,x27,x28,x29,x30,x31,x32,x33,x34,x35,x36;
375   MatScalar      m26,m27,m28,m29,m30,m31,m32,m33,m34,m35,m36;
376   MatScalar      *ba   = b->a,*aa = a->a;
377   PetscReal      shift = info->shiftamount;
378   PetscBool      allowzeropivot,zeropivotdetected;
379 
380   PetscFunctionBegin;
381   allowzeropivot = PetscNot(A->erroriffailure);
382   ierr = PetscMalloc1(36*(n+1),&rtmp);CHKERRQ(ierr);
383   for (i=0; i<n; i++) {
384     nz    = bi[i+1] - bi[i];
385     ajtmp = bj + bi[i];
386     for  (j=0; j<nz; j++) {
387       x     = rtmp+36*ajtmp[j];
388       x[0]  = x[1] = x[2] = x[3] = x[4] = x[5] = x[6] = x[7] = x[8] = x[9] = 0.0;
389       x[10] = x[11] = x[12] = x[13] = x[14] = x[15] = x[16] = x[17] = 0.0;
390       x[18] = x[19] = x[20] = x[21] = x[22] = x[23] = x[24] = x[25] = 0.0;
391       x[26] = x[27] = x[28] = x[29] = x[30] = x[31] = x[32] = x[33] = 0.0;
392       x[34] = x[35] = 0.0;
393     }
394     /* load in initial (unfactored row) */
395     nz       = ai[i+1] - ai[i];
396     ajtmpold = aj + ai[i];
397     v        = aa + 36*ai[i];
398     for (j=0; j<nz; j++) {
399       x     = rtmp+36*ajtmpold[j];
400       x[0]  =  v[0];  x[1] =  v[1];  x[2] =  v[2];  x[3] =  v[3];
401       x[4]  =  v[4];  x[5] =  v[5];  x[6] =  v[6];  x[7] =  v[7];
402       x[8]  =  v[8];  x[9] =  v[9];  x[10] = v[10]; x[11] = v[11];
403       x[12] = v[12]; x[13] = v[13]; x[14] = v[14]; x[15] = v[15];
404       x[16] = v[16]; x[17] = v[17]; x[18] = v[18]; x[19] = v[19];
405       x[20] = v[20]; x[21] = v[21]; x[22] = v[22]; x[23] = v[23];
406       x[24] = v[24]; x[25] = v[25]; x[26] = v[26]; x[27] = v[27];
407       x[28] = v[28]; x[29] = v[29]; x[30] = v[30]; x[31] = v[31];
408       x[32] = v[32]; x[33] = v[33]; x[34] = v[34]; x[35] = v[35];
409       v    += 36;
410     }
411     row = *ajtmp++;
412     while (row < i) {
413       pc  = rtmp + 36*row;
414       p1  = pc[0];  p2  = pc[1];  p3  = pc[2];  p4  = pc[3];
415       p5  = pc[4];  p6  = pc[5];  p7  = pc[6];  p8  = pc[7];
416       p9  = pc[8];  p10 = pc[9];  p11 = pc[10]; p12 = pc[11];
417       p13 = pc[12]; p14 = pc[13]; p15 = pc[14]; p16 = pc[15];
418       p17 = pc[16]; p18 = pc[17]; p19 = pc[18]; p20 = pc[19];
419       p21 = pc[20]; p22 = pc[21]; p23 = pc[22]; p24 = pc[23];
420       p25 = pc[24]; p26 = pc[25]; p27 = pc[26]; p28 = pc[27];
421       p29 = pc[28]; p30 = pc[29]; p31 = pc[30]; p32 = pc[31];
422       p33 = pc[32]; p34 = pc[33]; p35 = pc[34]; p36 = pc[35];
423       if (p1  != 0.0 || p2  != 0.0 || p3  != 0.0 || p4  != 0.0 ||
424           p5  != 0.0 || p6  != 0.0 || p7  != 0.0 || p8  != 0.0 ||
425           p9  != 0.0 || p10 != 0.0 || p11 != 0.0 || p12 != 0.0 ||
426           p13 != 0.0 || p14 != 0.0 || p15 != 0.0 || p16 != 0.0 ||
427           p17 != 0.0 || p18 != 0.0 || p19 != 0.0 || p20 != 0.0 ||
428           p21 != 0.0 || p22 != 0.0 || p23 != 0.0 || p24 != 0.0 ||
429           p25 != 0.0 || p26 != 0.0 || p27 != 0.0 || p28 != 0.0 ||
430           p29 != 0.0 || p30 != 0.0 || p31 != 0.0 || p32 != 0.0 ||
431           p33 != 0.0 || p34 != 0.0 || p35 != 0.0 || p36 != 0.0) {
432         pv    = ba + 36*diag_offset[row];
433         pj    = bj + diag_offset[row] + 1;
434         x1    = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
435         x5    = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
436         x9    = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
437         x13   = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
438         x17   = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
439         x21   = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
440         x25   = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
441         x29   = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
442         x33   = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
443         pc[0] = m1  = p1*x1  + p7*x2   + p13*x3  + p19*x4  + p25*x5  + p31*x6;
444         pc[1] = m2  = p2*x1  + p8*x2   + p14*x3  + p20*x4  + p26*x5  + p32*x6;
445         pc[2] = m3  = p3*x1  + p9*x2   + p15*x3  + p21*x4  + p27*x5  + p33*x6;
446         pc[3] = m4  = p4*x1  + p10*x2  + p16*x3  + p22*x4  + p28*x5  + p34*x6;
447         pc[4] = m5  = p5*x1  + p11*x2  + p17*x3  + p23*x4  + p29*x5  + p35*x6;
448         pc[5] = m6  = p6*x1  + p12*x2  + p18*x3  + p24*x4  + p30*x5  + p36*x6;
449 
450         pc[6]  = m7  = p1*x7  + p7*x8   + p13*x9  + p19*x10 + p25*x11 + p31*x12;
451         pc[7]  = m8  = p2*x7  + p8*x8   + p14*x9  + p20*x10 + p26*x11 + p32*x12;
452         pc[8]  = m9  = p3*x7  + p9*x8   + p15*x9  + p21*x10 + p27*x11 + p33*x12;
453         pc[9]  = m10 = p4*x7  + p10*x8  + p16*x9  + p22*x10 + p28*x11 + p34*x12;
454         pc[10] = m11 = p5*x7  + p11*x8  + p17*x9  + p23*x10 + p29*x11 + p35*x12;
455         pc[11] = m12 = p6*x7  + p12*x8  + p18*x9  + p24*x10 + p30*x11 + p36*x12;
456 
457         pc[12] = m13 = p1*x13 + p7*x14  + p13*x15 + p19*x16 + p25*x17 + p31*x18;
458         pc[13] = m14 = p2*x13 + p8*x14  + p14*x15 + p20*x16 + p26*x17 + p32*x18;
459         pc[14] = m15 = p3*x13 + p9*x14  + p15*x15 + p21*x16 + p27*x17 + p33*x18;
460         pc[15] = m16 = p4*x13 + p10*x14 + p16*x15 + p22*x16 + p28*x17 + p34*x18;
461         pc[16] = m17 = p5*x13 + p11*x14 + p17*x15 + p23*x16 + p29*x17 + p35*x18;
462         pc[17] = m18 = p6*x13 + p12*x14 + p18*x15 + p24*x16 + p30*x17 + p36*x18;
463 
464         pc[18] = m19 = p1*x19 + p7*x20  + p13*x21 + p19*x22 + p25*x23 + p31*x24;
465         pc[19] = m20 = p2*x19 + p8*x20  + p14*x21 + p20*x22 + p26*x23 + p32*x24;
466         pc[20] = m21 = p3*x19 + p9*x20  + p15*x21 + p21*x22 + p27*x23 + p33*x24;
467         pc[21] = m22 = p4*x19 + p10*x20 + p16*x21 + p22*x22 + p28*x23 + p34*x24;
468         pc[22] = m23 = p5*x19 + p11*x20 + p17*x21 + p23*x22 + p29*x23 + p35*x24;
469         pc[23] = m24 = p6*x19 + p12*x20 + p18*x21 + p24*x22 + p30*x23 + p36*x24;
470 
471         pc[24] = m25 = p1*x25 + p7*x26  + p13*x27 + p19*x28 + p25*x29 + p31*x30;
472         pc[25] = m26 = p2*x25 + p8*x26  + p14*x27 + p20*x28 + p26*x29 + p32*x30;
473         pc[26] = m27 = p3*x25 + p9*x26  + p15*x27 + p21*x28 + p27*x29 + p33*x30;
474         pc[27] = m28 = p4*x25 + p10*x26 + p16*x27 + p22*x28 + p28*x29 + p34*x30;
475         pc[28] = m29 = p5*x25 + p11*x26 + p17*x27 + p23*x28 + p29*x29 + p35*x30;
476         pc[29] = m30 = p6*x25 + p12*x26 + p18*x27 + p24*x28 + p30*x29 + p36*x30;
477 
478         pc[30] = m31 = p1*x31 + p7*x32  + p13*x33 + p19*x34 + p25*x35 + p31*x36;
479         pc[31] = m32 = p2*x31 + p8*x32  + p14*x33 + p20*x34 + p26*x35 + p32*x36;
480         pc[32] = m33 = p3*x31 + p9*x32  + p15*x33 + p21*x34 + p27*x35 + p33*x36;
481         pc[33] = m34 = p4*x31 + p10*x32 + p16*x33 + p22*x34 + p28*x35 + p34*x36;
482         pc[34] = m35 = p5*x31 + p11*x32 + p17*x33 + p23*x34 + p29*x35 + p35*x36;
483         pc[35] = m36 = p6*x31 + p12*x32 + p18*x33 + p24*x34 + p30*x35 + p36*x36;
484 
485         nz  = bi[row+1] - diag_offset[row] - 1;
486         pv += 36;
487         for (j=0; j<nz; j++) {
488           x1    = pv[0];  x2  = pv[1];  x3  = pv[2];  x4  = pv[3];
489           x5    = pv[4];  x6  = pv[5];  x7  = pv[6];  x8  = pv[7];
490           x9    = pv[8];  x10 = pv[9];  x11 = pv[10]; x12 = pv[11];
491           x13   = pv[12]; x14 = pv[13]; x15 = pv[14]; x16 = pv[15];
492           x17   = pv[16]; x18 = pv[17]; x19 = pv[18]; x20 = pv[19];
493           x21   = pv[20]; x22 = pv[21]; x23 = pv[22]; x24 = pv[23];
494           x25   = pv[24]; x26 = pv[25]; x27 = pv[26]; x28 = pv[27];
495           x29   = pv[28]; x30 = pv[29]; x31 = pv[30]; x32 = pv[31];
496           x33   = pv[32]; x34 = pv[33]; x35 = pv[34]; x36 = pv[35];
497           x     = rtmp + 36*pj[j];
498           x[0] -= m1*x1  + m7*x2   + m13*x3  + m19*x4  + m25*x5  + m31*x6;
499           x[1] -= m2*x1  + m8*x2   + m14*x3  + m20*x4  + m26*x5  + m32*x6;
500           x[2] -= m3*x1  + m9*x2   + m15*x3  + m21*x4  + m27*x5  + m33*x6;
501           x[3] -= m4*x1  + m10*x2  + m16*x3  + m22*x4  + m28*x5  + m34*x6;
502           x[4] -= m5*x1  + m11*x2  + m17*x3  + m23*x4  + m29*x5  + m35*x6;
503           x[5] -= m6*x1  + m12*x2  + m18*x3  + m24*x4  + m30*x5  + m36*x6;
504 
505           x[6]  -= m1*x7  + m7*x8   + m13*x9  + m19*x10 + m25*x11 + m31*x12;
506           x[7]  -= m2*x7  + m8*x8   + m14*x9  + m20*x10 + m26*x11 + m32*x12;
507           x[8]  -= m3*x7  + m9*x8   + m15*x9  + m21*x10 + m27*x11 + m33*x12;
508           x[9]  -= m4*x7  + m10*x8  + m16*x9  + m22*x10 + m28*x11 + m34*x12;
509           x[10] -= m5*x7  + m11*x8  + m17*x9  + m23*x10 + m29*x11 + m35*x12;
510           x[11] -= m6*x7  + m12*x8  + m18*x9  + m24*x10 + m30*x11 + m36*x12;
511 
512           x[12] -= m1*x13 + m7*x14  + m13*x15 + m19*x16 + m25*x17 + m31*x18;
513           x[13] -= m2*x13 + m8*x14  + m14*x15 + m20*x16 + m26*x17 + m32*x18;
514           x[14] -= m3*x13 + m9*x14  + m15*x15 + m21*x16 + m27*x17 + m33*x18;
515           x[15] -= m4*x13 + m10*x14 + m16*x15 + m22*x16 + m28*x17 + m34*x18;
516           x[16] -= m5*x13 + m11*x14 + m17*x15 + m23*x16 + m29*x17 + m35*x18;
517           x[17] -= m6*x13 + m12*x14 + m18*x15 + m24*x16 + m30*x17 + m36*x18;
518 
519           x[18] -= m1*x19 + m7*x20  + m13*x21 + m19*x22 + m25*x23 + m31*x24;
520           x[19] -= m2*x19 + m8*x20  + m14*x21 + m20*x22 + m26*x23 + m32*x24;
521           x[20] -= m3*x19 + m9*x20  + m15*x21 + m21*x22 + m27*x23 + m33*x24;
522           x[21] -= m4*x19 + m10*x20 + m16*x21 + m22*x22 + m28*x23 + m34*x24;
523           x[22] -= m5*x19 + m11*x20 + m17*x21 + m23*x22 + m29*x23 + m35*x24;
524           x[23] -= m6*x19 + m12*x20 + m18*x21 + m24*x22 + m30*x23 + m36*x24;
525 
526           x[24] -= m1*x25 + m7*x26  + m13*x27 + m19*x28 + m25*x29 + m31*x30;
527           x[25] -= m2*x25 + m8*x26  + m14*x27 + m20*x28 + m26*x29 + m32*x30;
528           x[26] -= m3*x25 + m9*x26  + m15*x27 + m21*x28 + m27*x29 + m33*x30;
529           x[27] -= m4*x25 + m10*x26 + m16*x27 + m22*x28 + m28*x29 + m34*x30;
530           x[28] -= m5*x25 + m11*x26 + m17*x27 + m23*x28 + m29*x29 + m35*x30;
531           x[29] -= m6*x25 + m12*x26 + m18*x27 + m24*x28 + m30*x29 + m36*x30;
532 
533           x[30] -= m1*x31 + m7*x32  + m13*x33 + m19*x34 + m25*x35 + m31*x36;
534           x[31] -= m2*x31 + m8*x32  + m14*x33 + m20*x34 + m26*x35 + m32*x36;
535           x[32] -= m3*x31 + m9*x32  + m15*x33 + m21*x34 + m27*x35 + m33*x36;
536           x[33] -= m4*x31 + m10*x32 + m16*x33 + m22*x34 + m28*x35 + m34*x36;
537           x[34] -= m5*x31 + m11*x32 + m17*x33 + m23*x34 + m29*x35 + m35*x36;
538           x[35] -= m6*x31 + m12*x32 + m18*x33 + m24*x34 + m30*x35 + m36*x36;
539 
540           pv += 36;
541         }
542         ierr = PetscLogFlops(432.0*nz+396.0);CHKERRQ(ierr);
543       }
544       row = *ajtmp++;
545     }
546     /* finished row so stick it into b->a */
547     pv = ba + 36*bi[i];
548     pj = bj + bi[i];
549     nz = bi[i+1] - bi[i];
550     for (j=0; j<nz; j++) {
551       x      = rtmp+36*pj[j];
552       pv[0]  = x[0];  pv[1]  = x[1];  pv[2]  = x[2];  pv[3]  = x[3];
553       pv[4]  = x[4];  pv[5]  = x[5];  pv[6]  = x[6];  pv[7]  = x[7];
554       pv[8]  = x[8];  pv[9]  = x[9];  pv[10] = x[10]; pv[11] = x[11];
555       pv[12] = x[12]; pv[13] = x[13]; pv[14] = x[14]; pv[15] = x[15];
556       pv[16] = x[16]; pv[17] = x[17]; pv[18] = x[18]; pv[19] = x[19];
557       pv[20] = x[20]; pv[21] = x[21]; pv[22] = x[22]; pv[23] = x[23];
558       pv[24] = x[24]; pv[25] = x[25]; pv[26] = x[26]; pv[27] = x[27];
559       pv[28] = x[28]; pv[29] = x[29]; pv[30] = x[30]; pv[31] = x[31];
560       pv[32] = x[32]; pv[33] = x[33]; pv[34] = x[34]; pv[35] = x[35];
561       pv    += 36;
562     }
563     /* invert diagonal block */
564     w    = ba + 36*diag_offset[i];
565     ierr = PetscKernel_A_gets_inverse_A_6(w,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
566     if (zeropivotdetected) C->errortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
567   }
568 
569   ierr = PetscFree(rtmp);CHKERRQ(ierr);
570 
571   C->ops->solve          = MatSolve_SeqBAIJ_6_NaturalOrdering_inplace;
572   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_6_NaturalOrdering_inplace;
573   C->assembled           = PETSC_TRUE;
574 
575   ierr = PetscLogFlops(1.333333333333*6*6*6*b->mbs);CHKERRQ(ierr); /* from inverting diagonal blocks */
576   PetscFunctionReturn(0);
577 }
578 
579 #undef __FUNCT__
580 #define __FUNCT__ "MatLUFactorNumeric_SeqBAIJ_6_NaturalOrdering"
581 PetscErrorCode MatLUFactorNumeric_SeqBAIJ_6_NaturalOrdering(Mat B,Mat A,const MatFactorInfo *info)
582 {
583   Mat            C =B;
584   Mat_SeqBAIJ    *a=(Mat_SeqBAIJ*)A->data,*b=(Mat_SeqBAIJ*)C->data;
585   PetscErrorCode ierr;
586   PetscInt       i,j,k,nz,nzL,row;
587   const PetscInt n=a->mbs,*ai=a->i,*aj=a->j,*bi=b->i,*bj=b->j;
588   const PetscInt *ajtmp,*bjtmp,*bdiag=b->diag,*pj,bs2=a->bs2;
589   MatScalar      *rtmp,*pc,*mwork,*v,*pv,*aa=a->a;
590   PetscInt       flg;
591   PetscReal      shift = info->shiftamount;
592   PetscBool      allowzeropivot,zeropivotdetected;
593 
594   PetscFunctionBegin;
595   allowzeropivot = PetscNot(A->erroriffailure);
596 
597   /* generate work space needed by the factorization */
598   ierr = PetscMalloc2(bs2*n,&rtmp,bs2,&mwork);CHKERRQ(ierr);
599   ierr = PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));CHKERRQ(ierr);
600 
601   for (i=0; i<n; i++) {
602     /* zero rtmp */
603     /* L part */
604     nz    = bi[i+1] - bi[i];
605     bjtmp = bj + bi[i];
606     for  (j=0; j<nz; j++) {
607       ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
608     }
609 
610     /* U part */
611     nz    = bdiag[i] - bdiag[i+1];
612     bjtmp = bj + bdiag[i+1]+1;
613     for  (j=0; j<nz; j++) {
614       ierr = PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
615     }
616 
617     /* load in initial (unfactored row) */
618     nz    = ai[i+1] - ai[i];
619     ajtmp = aj + ai[i];
620     v     = aa + bs2*ai[i];
621     for (j=0; j<nz; j++) {
622       ierr = PetscMemcpy(rtmp+bs2*ajtmp[j],v+bs2*j,bs2*sizeof(MatScalar));CHKERRQ(ierr);
623     }
624 
625     /* elimination */
626     bjtmp = bj + bi[i];
627     nzL   = bi[i+1] - bi[i];
628     for (k=0; k < nzL; k++) {
629       row = bjtmp[k];
630       pc  = rtmp + bs2*row;
631       for (flg=0,j=0; j<bs2; j++) {
632         if (pc[j]!=0.0) {
633           flg = 1;
634           break;
635         }
636       }
637       if (flg) {
638         pv = b->a + bs2*bdiag[row];
639         /* PetscKernel_A_gets_A_times_B(bs,pc,pv,mwork); *pc = *pc * (*pv); */
640         ierr = PetscKernel_A_gets_A_times_B_6(pc,pv,mwork);CHKERRQ(ierr);
641 
642         pj = b->j + bdiag[row+1]+1; /* begining of U(row,:) */
643         pv = b->a + bs2*(bdiag[row+1]+1);
644         nz = bdiag[row] - bdiag[row+1] - 1; /* num of entries inU(row,:), excluding diag */
645         for (j=0; j<nz; j++) {
646           /* PetscKernel_A_gets_A_minus_B_times_C(bs,rtmp+bs2*pj[j],pc,pv+bs2*j); */
647           /* rtmp+bs2*pj[j] = rtmp+bs2*pj[j] - (*pc)*(pv+bs2*j) */
648           v    = rtmp + bs2*pj[j];
649           ierr = PetscKernel_A_gets_A_minus_B_times_C_6(v,pc,pv);CHKERRQ(ierr);
650           pv  += bs2;
651         }
652         ierr = PetscLogFlops(432*nz+396);CHKERRQ(ierr); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
653       }
654     }
655 
656     /* finished row so stick it into b->a */
657     /* L part */
658     pv = b->a + bs2*bi[i];
659     pj = b->j + bi[i];
660     nz = bi[i+1] - bi[i];
661     for (j=0; j<nz; j++) {
662       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
663     }
664 
665     /* Mark diagonal and invert diagonal for simplier triangular solves */
666     pv   = b->a + bs2*bdiag[i];
667     pj   = b->j + bdiag[i];
668     ierr = PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));CHKERRQ(ierr);
669     ierr = PetscKernel_A_gets_inverse_A_6(pv,shift,allowzeropivot,&zeropivotdetected);CHKERRQ(ierr);
670     if (zeropivotdetected) C->errortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
671 
672     /* U part */
673     pv = b->a + bs2*(bdiag[i+1]+1);
674     pj = b->j + bdiag[i+1]+1;
675     nz = bdiag[i] - bdiag[i+1] - 1;
676     for (j=0; j<nz; j++) {
677       ierr = PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));CHKERRQ(ierr);
678     }
679   }
680   ierr = PetscFree2(rtmp,mwork);CHKERRQ(ierr);
681 
682   C->ops->solve          = MatSolve_SeqBAIJ_6_NaturalOrdering;
683   C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_6_NaturalOrdering;
684   C->assembled           = PETSC_TRUE;
685 
686   ierr = PetscLogFlops(1.333333333333*6*6*6*n);CHKERRQ(ierr); /* from inverting diagonal blocks */
687   PetscFunctionReturn(0);
688 }
689