Actual source code: baijfact7.c
petsc-3.7.3 2016-08-01
2: /*
3: Factorization code for BAIJ format.
4: */
5: #include <../src/mat/impls/baij/seq/baij.h>
6: #include <petsc/private/kernels/blockinvert.h>
8: /* ------------------------------------------------------------*/
9: /*
10: Version for when blocks are 6 by 6
11: */
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;
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;
35: allowzeropivot = PetscNot(A->erroriffailure);
36: ISGetIndices(isrow,&r);
37: ISGetIndices(isicol,&ic);
38: PetscMalloc1(36*(n+1),&rtmp);
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;
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;
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;
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;
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;
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;
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;
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;
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;
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;
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;
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;
198: pv += 36;
199: }
200: PetscLogFlops(432.0*nz+396.0);
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: PetscKernel_A_gets_inverse_A_6(w,shift,allowzeropivot,&zeropivotdetected);
224: if (zeropivotdetected) C->errortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
225: }
227: PetscFree(rtmp);
228: ISRestoreIndices(isicol,&ic);
229: ISRestoreIndices(isrow,&r);
231: C->ops->solve = MatSolve_SeqBAIJ_6_inplace;
232: C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_6_inplace;
233: C->assembled = PETSC_TRUE;
235: PetscLogFlops(1.333333333333*6*6*6*b->mbs); /* from inverting diagonal blocks */
236: return(0);
237: }
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;
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;
257: allowzeropivot = PetscNot(A->erroriffailure);
258: ISGetIndices(isrow,&r);
259: ISGetIndices(isicol,&ic);
261: /* generate work space needed by the factorization */
262: PetscMalloc2(bs2*n,&rtmp,bs2,&mwork);
263: PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));
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: PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
272: }
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: PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
279: }
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: PetscMemcpy(rtmp+bs2*ic[ajtmp[j]],v+bs2*j,bs2*sizeof(MatScalar));
287: }
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: PetscKernel_A_gets_A_times_B_6(pc,pv,mwork);
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: PetscKernel_A_gets_A_minus_B_times_C_6(v,pc,pv);
314: pv += bs2;
315: }
316: PetscLogFlops(432*nz+396); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
317: }
318: }
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: PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
327: }
329: /* Mark diagonal and invert diagonal for simplier triangular solves */
330: pv = b->a + bs2*bdiag[i];
331: pj = b->j + bdiag[i];
332: PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));
333: PetscKernel_A_gets_inverse_A_6(pv,shift,allowzeropivot,&zeropivotdetected);
334: if (zeropivotdetected) C->errortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
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: PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
342: }
343: }
345: PetscFree2(rtmp,mwork);
346: ISRestoreIndices(isicol,&ic);
347: ISRestoreIndices(isrow,&r);
349: C->ops->solve = MatSolve_SeqBAIJ_6;
350: C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_6;
351: C->assembled = PETSC_TRUE;
353: PetscLogFlops(1.333333333333*6*6*6*n); /* from inverting diagonal blocks */
354: return(0);
355: }
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;
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;
381: allowzeropivot = PetscNot(A->erroriffailure);
382: PetscMalloc1(36*(n+1),&rtmp);
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;
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;
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;
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;
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;
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;
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;
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;
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;
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;
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;
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;
540: pv += 36;
541: }
542: PetscLogFlops(432.0*nz+396.0);
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: PetscKernel_A_gets_inverse_A_6(w,shift,allowzeropivot,&zeropivotdetected);
566: if (zeropivotdetected) C->errortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
567: }
569: PetscFree(rtmp);
571: C->ops->solve = MatSolve_SeqBAIJ_6_NaturalOrdering_inplace;
572: C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_6_NaturalOrdering_inplace;
573: C->assembled = PETSC_TRUE;
575: PetscLogFlops(1.333333333333*6*6*6*b->mbs); /* from inverting diagonal blocks */
576: return(0);
577: }
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;
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;
595: allowzeropivot = PetscNot(A->erroriffailure);
597: /* generate work space needed by the factorization */
598: PetscMalloc2(bs2*n,&rtmp,bs2,&mwork);
599: PetscMemzero(rtmp,bs2*n*sizeof(MatScalar));
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: PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
608: }
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: PetscMemzero(rtmp+bs2*bjtmp[j],bs2*sizeof(MatScalar));
615: }
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: PetscMemcpy(rtmp+bs2*ajtmp[j],v+bs2*j,bs2*sizeof(MatScalar));
623: }
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: PetscKernel_A_gets_A_times_B_6(pc,pv,mwork);
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: PetscKernel_A_gets_A_minus_B_times_C_6(v,pc,pv);
650: pv += bs2;
651: }
652: PetscLogFlops(432*nz+396); /* flops = 2*bs^3*nz + 2*bs^3 - bs2) */
653: }
654: }
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: PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
663: }
665: /* Mark diagonal and invert diagonal for simplier triangular solves */
666: pv = b->a + bs2*bdiag[i];
667: pj = b->j + bdiag[i];
668: PetscMemcpy(pv,rtmp+bs2*pj[0],bs2*sizeof(MatScalar));
669: PetscKernel_A_gets_inverse_A_6(pv,shift,allowzeropivot,&zeropivotdetected);
670: if (zeropivotdetected) C->errortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
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: PetscMemcpy(pv+bs2*j,rtmp+bs2*pj[j],bs2*sizeof(MatScalar));
678: }
679: }
680: PetscFree2(rtmp,mwork);
682: C->ops->solve = MatSolve_SeqBAIJ_6_NaturalOrdering;
683: C->ops->solvetranspose = MatSolveTranspose_SeqBAIJ_6_NaturalOrdering;
684: C->assembled = PETSC_TRUE;
686: PetscLogFlops(1.333333333333*6*6*6*n); /* from inverting diagonal blocks */
687: return(0);
688: }