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