1 #include <../src/mat/impls/baij/seq/baij.h>
2
MatSolveTranspose_SeqBAIJ_3_NaturalOrdering_inplace(Mat A,Vec bb,Vec xx)3 PetscErrorCode MatSolveTranspose_SeqBAIJ_3_NaturalOrdering_inplace(Mat A, Vec bb, Vec xx)
4 {
5 Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data;
6 const PetscInt n = a->mbs, *vi, *ai = a->i, *aj = a->j, *diag = a->diag;
7 PetscInt i, nz, idx, idt, oidx;
8 const MatScalar *aa = a->a, *v;
9 PetscScalar s1, s2, s3, x1, x2, x3, *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 + 9 * 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 s1 = v[0] * x1 + v[1] * x2 + v[2] * x3;
24 s2 = v[3] * x1 + v[4] * x2 + v[5] * x3;
25 s3 = v[6] * x1 + v[7] * x2 + v[8] * x3;
26 v += 9;
27
28 vi = aj + diag[i] + 1;
29 nz = ai[i + 1] - diag[i] - 1;
30 while (nz--) {
31 oidx = 3 * (*vi++);
32 x[oidx] -= v[0] * s1 + v[1] * s2 + v[2] * s3;
33 x[oidx + 1] -= v[3] * s1 + v[4] * s2 + v[5] * s3;
34 x[oidx + 2] -= v[6] * s1 + v[7] * s2 + v[8] * s3;
35 v += 9;
36 }
37 x[idx] = s1;
38 x[1 + idx] = s2;
39 x[2 + idx] = s3;
40 idx += 3;
41 }
42 /* backward solve the L^T */
43 for (i = n - 1; i >= 0; i--) {
44 v = aa + 9 * diag[i] - 9;
45 vi = aj + diag[i] - 1;
46 nz = diag[i] - ai[i];
47 idt = 3 * i;
48 s1 = x[idt];
49 s2 = x[1 + idt];
50 s3 = x[2 + idt];
51 while (nz--) {
52 idx = 3 * (*vi--);
53 x[idx] -= v[0] * s1 + v[1] * s2 + v[2] * s3;
54 x[idx + 1] -= v[3] * s1 + v[4] * s2 + v[5] * s3;
55 x[idx + 2] -= v[6] * s1 + v[7] * s2 + v[8] * s3;
56 v -= 9;
57 }
58 }
59 PetscCall(VecRestoreArray(xx, &x));
60 PetscCall(PetscLogFlops(2.0 * 9.0 * (a->nz) - 3.0 * A->cmap->n));
61 PetscFunctionReturn(PETSC_SUCCESS);
62 }
63
MatSolveTranspose_SeqBAIJ_3_NaturalOrdering(Mat A,Vec bb,Vec xx)64 PetscErrorCode MatSolveTranspose_SeqBAIJ_3_NaturalOrdering(Mat A, Vec bb, Vec xx)
65 {
66 Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data;
67 const PetscInt n = a->mbs, *vi, *ai = a->i, *aj = a->j, *diag = a->diag;
68 PetscInt nz, idx, idt, j, i, oidx;
69 const PetscInt bs = A->rmap->bs, bs2 = a->bs2;
70 const MatScalar *aa = a->a, *v;
71 PetscScalar s1, s2, s3, x1, x2, x3, *x;
72
73 PetscFunctionBegin;
74 PetscCall(VecCopy(bb, xx));
75 PetscCall(VecGetArray(xx, &x));
76
77 /* forward solve the U^T */
78 idx = 0;
79 for (i = 0; i < n; i++) {
80 v = aa + bs2 * diag[i];
81 /* multiply by the inverse of the block diagonal */
82 x1 = x[idx];
83 x2 = x[1 + idx];
84 x3 = x[2 + idx];
85 s1 = v[0] * x1 + v[1] * x2 + v[2] * x3;
86 s2 = v[3] * x1 + v[4] * x2 + v[5] * x3;
87 s3 = v[6] * x1 + v[7] * x2 + v[8] * x3;
88 v -= bs2;
89
90 vi = aj + diag[i] - 1;
91 nz = diag[i] - diag[i + 1] - 1;
92 for (j = 0; j > -nz; j--) {
93 oidx = bs * vi[j];
94 x[oidx] -= v[0] * s1 + v[1] * s2 + v[2] * s3;
95 x[oidx + 1] -= v[3] * s1 + v[4] * s2 + v[5] * s3;
96 x[oidx + 2] -= v[6] * s1 + v[7] * s2 + v[8] * s3;
97 v -= bs2;
98 }
99 x[idx] = s1;
100 x[1 + idx] = s2;
101 x[2 + idx] = s3;
102 idx += bs;
103 }
104 /* backward solve the L^T */
105 for (i = n - 1; i >= 0; i--) {
106 v = aa + bs2 * ai[i];
107 vi = aj + ai[i];
108 nz = ai[i + 1] - ai[i];
109 idt = bs * i;
110 s1 = x[idt];
111 s2 = x[1 + idt];
112 s3 = x[2 + idt];
113 for (j = 0; j < nz; j++) {
114 idx = bs * vi[j];
115 x[idx] -= v[0] * s1 + v[1] * s2 + v[2] * s3;
116 x[idx + 1] -= v[3] * s1 + v[4] * s2 + v[5] * s3;
117 x[idx + 2] -= v[6] * s1 + v[7] * s2 + v[8] * s3;
118 v += bs2;
119 }
120 }
121 PetscCall(VecRestoreArray(xx, &x));
122 PetscCall(PetscLogFlops(2.0 * bs2 * (a->nz) - bs * A->cmap->n));
123 PetscFunctionReturn(PETSC_SUCCESS);
124 }
125