1 #include <../src/mat/impls/baij/seq/baij.h>
2
MatSolveTranspose_SeqBAIJ_6_NaturalOrdering_inplace(Mat A,Vec bb,Vec xx)3 PetscErrorCode MatSolveTranspose_SeqBAIJ_6_NaturalOrdering_inplace(Mat A, Vec bb, Vec xx)
4 {
5 Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data;
6 const PetscInt *diag = a->diag, n = a->mbs, *vi, *ai = a->i, *aj = a->j;
7 PetscInt i, nz, idx, idt, oidx;
8 const MatScalar *aa = a->a, *v;
9 PetscScalar s1, s2, s3, s4, s5, s6, x1, x2, x3, x4, x5, x6, *x;
10
11 PetscFunctionBegin;
12 PetscCall(VecCopy(bb, xx));
13 PetscCall(VecGetArray(xx, &x));
14
15 /* forward solve the U^T */
16 idx = 0;
17 for (i = 0; i < n; i++) {
18 v = aa + 36 * diag[i];
19 /* multiply by the inverse of the block diagonal */
20 x1 = x[idx];
21 x2 = x[1 + idx];
22 x3 = x[2 + idx];
23 x4 = x[3 + idx];
24 x5 = x[4 + idx];
25 x6 = x[5 + idx];
26 s1 = v[0] * x1 + v[1] * x2 + v[2] * x3 + v[3] * x4 + v[4] * x5 + v[5] * x6;
27 s2 = v[6] * x1 + v[7] * x2 + v[8] * x3 + v[9] * x4 + v[10] * x5 + v[11] * x6;
28 s3 = v[12] * x1 + v[13] * x2 + v[14] * x3 + v[15] * x4 + v[16] * x5 + v[17] * x6;
29 s4 = v[18] * x1 + v[19] * x2 + v[20] * x3 + v[21] * x4 + v[22] * x5 + v[23] * x6;
30 s5 = v[24] * x1 + v[25] * x2 + v[26] * x3 + v[27] * x4 + v[28] * x5 + v[29] * x6;
31 s6 = v[30] * x1 + v[31] * x2 + v[32] * x3 + v[33] * x4 + v[34] * x5 + v[35] * x6;
32 v += 36;
33
34 vi = aj + diag[i] + 1;
35 nz = ai[i + 1] - diag[i] - 1;
36 while (nz--) {
37 oidx = 6 * (*vi++);
38 x[oidx] -= v[0] * s1 + v[1] * s2 + v[2] * s3 + v[3] * s4 + v[4] * s5 + v[5] * s6;
39 x[oidx + 1] -= v[6] * s1 + v[7] * s2 + v[8] * s3 + v[9] * s4 + v[10] * s5 + v[11] * s6;
40 x[oidx + 2] -= v[12] * s1 + v[13] * s2 + v[14] * s3 + v[15] * s4 + v[16] * s5 + v[17] * s6;
41 x[oidx + 3] -= v[18] * s1 + v[19] * s2 + v[20] * s3 + v[21] * s4 + v[22] * s5 + v[23] * s6;
42 x[oidx + 4] -= v[24] * s1 + v[25] * s2 + v[26] * s3 + v[27] * s4 + v[28] * s5 + v[29] * s6;
43 x[oidx + 5] -= v[30] * s1 + v[31] * s2 + v[32] * s3 + v[33] * s4 + v[34] * s5 + v[35] * s6;
44 v += 36;
45 }
46 x[idx] = s1;
47 x[1 + idx] = s2;
48 x[2 + idx] = s3;
49 x[3 + idx] = s4;
50 x[4 + idx] = s5;
51 x[5 + idx] = s6;
52 idx += 6;
53 }
54 /* backward solve the L^T */
55 for (i = n - 1; i >= 0; i--) {
56 v = aa + 36 * diag[i] - 36;
57 vi = aj + diag[i] - 1;
58 nz = diag[i] - ai[i];
59 idt = 6 * i;
60 s1 = x[idt];
61 s2 = x[1 + idt];
62 s3 = x[2 + idt];
63 s4 = x[3 + idt];
64 s5 = x[4 + idt];
65 s6 = x[5 + idt];
66 while (nz--) {
67 idx = 6 * (*vi--);
68 x[idx] -= v[0] * s1 + v[1] * s2 + v[2] * s3 + v[3] * s4 + v[4] * s5 + v[5] * s6;
69 x[idx + 1] -= v[6] * s1 + v[7] * s2 + v[8] * s3 + v[9] * s4 + v[10] * s5 + v[11] * s6;
70 x[idx + 2] -= v[12] * s1 + v[13] * s2 + v[14] * s3 + v[15] * s4 + v[16] * s5 + v[17] * s6;
71 x[idx + 3] -= v[18] * s1 + v[19] * s2 + v[20] * s3 + v[21] * s4 + v[22] * s5 + v[23] * s6;
72 x[idx + 4] -= v[24] * s1 + v[25] * s2 + v[26] * s3 + v[27] * s4 + v[28] * s5 + v[29] * s6;
73 x[idx + 5] -= v[30] * s1 + v[31] * s2 + v[32] * s3 + v[33] * s4 + v[34] * s5 + v[35] * s6;
74 v -= 36;
75 }
76 }
77 PetscCall(VecRestoreArray(xx, &x));
78 PetscCall(PetscLogFlops(2.0 * 36 * (a->nz) - 6.0 * A->cmap->n));
79 PetscFunctionReturn(PETSC_SUCCESS);
80 }
81
MatSolveTranspose_SeqBAIJ_6_NaturalOrdering(Mat A,Vec bb,Vec xx)82 PetscErrorCode MatSolveTranspose_SeqBAIJ_6_NaturalOrdering(Mat A, Vec bb, Vec xx)
83 {
84 Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data;
85 const PetscInt n = a->mbs, *vi, *ai = a->i, *aj = a->j, *diag = a->diag;
86 PetscInt nz, idx, idt, j, i, oidx;
87 const PetscInt bs = A->rmap->bs, bs2 = a->bs2;
88 const MatScalar *aa = a->a, *v;
89 PetscScalar s1, s2, s3, s4, s5, s6, x1, x2, x3, x4, x5, x6, *x;
90
91 PetscFunctionBegin;
92 PetscCall(VecCopy(bb, xx));
93 PetscCall(VecGetArray(xx, &x));
94
95 /* forward solve the U^T */
96 idx = 0;
97 for (i = 0; i < n; i++) {
98 v = aa + bs2 * diag[i];
99 /* multiply by the inverse of the block diagonal */
100 x1 = x[idx];
101 x2 = x[1 + idx];
102 x3 = x[2 + idx];
103 x4 = x[3 + idx];
104 x5 = x[4 + idx];
105 x6 = x[5 + idx];
106 s1 = v[0] * x1 + v[1] * x2 + v[2] * x3 + v[3] * x4 + v[4] * x5 + v[5] * x6;
107 s2 = v[6] * x1 + v[7] * x2 + v[8] * x3 + v[9] * x4 + v[10] * x5 + v[11] * x6;
108 s3 = v[12] * x1 + v[13] * x2 + v[14] * x3 + v[15] * x4 + v[16] * x5 + v[17] * x6;
109 s4 = v[18] * x1 + v[19] * x2 + v[20] * x3 + v[21] * x4 + v[22] * x5 + v[23] * x6;
110 s5 = v[24] * x1 + v[25] * x2 + v[26] * x3 + v[27] * x4 + v[28] * x5 + v[29] * x6;
111 s6 = v[30] * x1 + v[31] * x2 + v[32] * x3 + v[33] * x4 + v[34] * x5 + v[35] * x6;
112 v -= bs2;
113
114 vi = aj + diag[i] - 1;
115 nz = diag[i] - diag[i + 1] - 1;
116 for (j = 0; j > -nz; j--) {
117 oidx = bs * vi[j];
118 x[oidx] -= v[0] * s1 + v[1] * s2 + v[2] * s3 + v[3] * s4 + v[4] * s5 + v[5] * s6;
119 x[oidx + 1] -= v[6] * s1 + v[7] * s2 + v[8] * s3 + v[9] * s4 + v[10] * s5 + v[11] * s6;
120 x[oidx + 2] -= v[12] * s1 + v[13] * s2 + v[14] * s3 + v[15] * s4 + v[16] * s5 + v[17] * s6;
121 x[oidx + 3] -= v[18] * s1 + v[19] * s2 + v[20] * s3 + v[21] * s4 + v[22] * s5 + v[23] * s6;
122 x[oidx + 4] -= v[24] * s1 + v[25] * s2 + v[26] * s3 + v[27] * s4 + v[28] * s5 + v[29] * s6;
123 x[oidx + 5] -= v[30] * s1 + v[31] * s2 + v[32] * s3 + v[33] * s4 + v[34] * s5 + v[35] * s6;
124 v -= bs2;
125 }
126 x[idx] = s1;
127 x[1 + idx] = s2;
128 x[2 + idx] = s3;
129 x[3 + idx] = s4;
130 x[4 + idx] = s5;
131 x[5 + idx] = s6;
132 idx += bs;
133 }
134 /* backward solve the L^T */
135 for (i = n - 1; i >= 0; i--) {
136 v = aa + bs2 * ai[i];
137 vi = aj + ai[i];
138 nz = ai[i + 1] - ai[i];
139 idt = bs * i;
140 s1 = x[idt];
141 s2 = x[1 + idt];
142 s3 = x[2 + idt];
143 s4 = x[3 + idt];
144 s5 = x[4 + idt];
145 s6 = x[5 + idt];
146 for (j = 0; j < nz; j++) {
147 idx = bs * vi[j];
148 x[idx] -= v[0] * s1 + v[1] * s2 + v[2] * s3 + v[3] * s4 + v[4] * s5 + v[5] * s6;
149 x[idx + 1] -= v[6] * s1 + v[7] * s2 + v[8] * s3 + v[9] * s4 + v[10] * s5 + v[11] * s6;
150 x[idx + 2] -= v[12] * s1 + v[13] * s2 + v[14] * s3 + v[15] * s4 + v[16] * s5 + v[17] * s6;
151 x[idx + 3] -= v[18] * s1 + v[19] * s2 + v[20] * s3 + v[21] * s4 + v[22] * s5 + v[23] * s6;
152 x[idx + 4] -= v[24] * s1 + v[25] * s2 + v[26] * s3 + v[27] * s4 + v[28] * s5 + v[29] * s6;
153 x[idx + 5] -= v[30] * s1 + v[31] * s2 + v[32] * s3 + v[33] * s4 + v[34] * s5 + v[35] * s6;
154 v += bs2;
155 }
156 }
157 PetscCall(VecRestoreArray(xx, &x));
158 PetscCall(PetscLogFlops(2.0 * bs2 * (a->nz) - bs * A->cmap->n));
159 PetscFunctionReturn(PETSC_SUCCESS);
160 }
161