xref: /petsc/src/mat/impls/baij/seq/baijsolvtrannat3.c (revision 58d68138c660dfb4e9f5b03334792cd4f2ffd7cc)
1 #include <../src/mat/impls/baij/seq/baij.h>
2 
3 PetscErrorCode MatSolveTranspose_SeqBAIJ_3_NaturalOrdering_inplace(Mat A, Vec bb, Vec xx) {
4   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *)A->data;
5   const PetscInt   n = a->mbs, *vi, *ai = a->i, *aj = a->j, *diag = a->diag;
6   PetscInt         i, nz, idx, idt, oidx;
7   const MatScalar *aa = a->a, *v;
8   PetscScalar      s1, s2, s3, x1, x2, x3, *x;
9 
10   PetscFunctionBegin;
11   PetscCall(VecCopy(bb, xx));
12   PetscCall(VecGetArray(xx, &x));
13 
14   /* forward solve the U^T */
15   idx = 0;
16   for (i = 0; i < n; i++) {
17     v  = aa + 9 * diag[i];
18     /* multiply by the inverse of the block diagonal */
19     x1 = x[idx];
20     x2 = x[1 + idx];
21     x3 = x[2 + idx];
22     s1 = v[0] * x1 + v[1] * x2 + v[2] * x3;
23     s2 = v[3] * x1 + v[4] * x2 + v[5] * x3;
24     s3 = v[6] * x1 + v[7] * x2 + v[8] * x3;
25     v += 9;
26 
27     vi = aj + diag[i] + 1;
28     nz = ai[i + 1] - diag[i] - 1;
29     while (nz--) {
30       oidx = 3 * (*vi++);
31       x[oidx] -= v[0] * s1 + v[1] * s2 + v[2] * s3;
32       x[oidx + 1] -= v[3] * s1 + v[4] * s2 + v[5] * s3;
33       x[oidx + 2] -= v[6] * s1 + v[7] * s2 + v[8] * s3;
34       v += 9;
35     }
36     x[idx]     = s1;
37     x[1 + idx] = s2;
38     x[2 + idx] = s3;
39     idx += 3;
40   }
41   /* backward solve the L^T */
42   for (i = n - 1; i >= 0; i--) {
43     v   = aa + 9 * diag[i] - 9;
44     vi  = aj + diag[i] - 1;
45     nz  = diag[i] - ai[i];
46     idt = 3 * i;
47     s1  = x[idt];
48     s2  = x[1 + idt];
49     s3  = x[2 + idt];
50     while (nz--) {
51       idx = 3 * (*vi--);
52       x[idx] -= v[0] * s1 + v[1] * s2 + v[2] * s3;
53       x[idx + 1] -= v[3] * s1 + v[4] * s2 + v[5] * s3;
54       x[idx + 2] -= v[6] * s1 + v[7] * s2 + v[8] * s3;
55       v -= 9;
56     }
57   }
58   PetscCall(VecRestoreArray(xx, &x));
59   PetscCall(PetscLogFlops(2.0 * 9.0 * (a->nz) - 3.0 * A->cmap->n));
60   PetscFunctionReturn(0);
61 }
62 
63 PetscErrorCode MatSolveTranspose_SeqBAIJ_3_NaturalOrdering(Mat A, Vec bb, Vec xx) {
64   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *)A->data;
65   const PetscInt   n = a->mbs, *vi, *ai = a->i, *aj = a->j, *diag = a->diag;
66   PetscInt         nz, idx, idt, j, i, oidx;
67   const PetscInt   bs = A->rmap->bs, bs2 = a->bs2;
68   const MatScalar *aa = a->a, *v;
69   PetscScalar      s1, s2, s3, x1, x2, x3, *x;
70 
71   PetscFunctionBegin;
72   PetscCall(VecCopy(bb, xx));
73   PetscCall(VecGetArray(xx, &x));
74 
75   /* forward solve the U^T */
76   idx = 0;
77   for (i = 0; i < n; i++) {
78     v  = aa + bs2 * diag[i];
79     /* multiply by the inverse of the block diagonal */
80     x1 = x[idx];
81     x2 = x[1 + idx];
82     x3 = x[2 + idx];
83     s1 = v[0] * x1 + v[1] * x2 + v[2] * x3;
84     s2 = v[3] * x1 + v[4] * x2 + v[5] * x3;
85     s3 = v[6] * x1 + v[7] * x2 + v[8] * x3;
86     v -= bs2;
87 
88     vi = aj + diag[i] - 1;
89     nz = diag[i] - diag[i + 1] - 1;
90     for (j = 0; j > -nz; j--) {
91       oidx = bs * vi[j];
92       x[oidx] -= v[0] * s1 + v[1] * s2 + v[2] * s3;
93       x[oidx + 1] -= v[3] * s1 + v[4] * s2 + v[5] * s3;
94       x[oidx + 2] -= v[6] * s1 + v[7] * s2 + v[8] * s3;
95       v -= bs2;
96     }
97     x[idx]     = s1;
98     x[1 + idx] = s2;
99     x[2 + idx] = s3;
100     idx += bs;
101   }
102   /* backward solve the L^T */
103   for (i = n - 1; i >= 0; i--) {
104     v   = aa + bs2 * ai[i];
105     vi  = aj + ai[i];
106     nz  = ai[i + 1] - ai[i];
107     idt = bs * i;
108     s1  = x[idt];
109     s2  = x[1 + idt];
110     s3  = x[2 + idt];
111     for (j = 0; j < nz; j++) {
112       idx = bs * vi[j];
113       x[idx] -= v[0] * s1 + v[1] * s2 + v[2] * s3;
114       x[idx + 1] -= v[3] * s1 + v[4] * s2 + v[5] * s3;
115       x[idx + 2] -= v[6] * s1 + v[7] * s2 + v[8] * s3;
116       v += bs2;
117     }
118   }
119   PetscCall(VecRestoreArray(xx, &x));
120   PetscCall(PetscLogFlops(2.0 * bs2 * (a->nz) - bs * A->cmap->n));
121   PetscFunctionReturn(0);
122 }
123