xref: /petsc/src/mat/impls/baij/seq/baijsolvtrannat4.c (revision 58d68138c660dfb4e9f5b03334792cd4f2ffd7cc)
1 #include <../src/mat/impls/baij/seq/baij.h>
2 
3 PetscErrorCode MatSolveTranspose_SeqBAIJ_4_NaturalOrdering_inplace(Mat A, Vec bb, Vec xx) {
4   Mat_SeqBAIJ     *a    = (Mat_SeqBAIJ *)A->data;
5   const PetscInt  *diag = a->diag, n = a->mbs, *vi, *ai = a->i, *aj = a->j;
6   PetscInt         i, nz, idx, idt, oidx;
7   const MatScalar *aa = a->a, *v;
8   PetscScalar      s1, s2, s3, s4, x1, x2, x3, x4, *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 + 16 * 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     x4 = x[3 + idx];
23     s1 = v[0] * x1 + v[1] * x2 + v[2] * x3 + v[3] * x4;
24     s2 = v[4] * x1 + v[5] * x2 + v[6] * x3 + v[7] * x4;
25     s3 = v[8] * x1 + v[9] * x2 + v[10] * x3 + v[11] * x4;
26     s4 = v[12] * x1 + v[13] * x2 + v[14] * x3 + v[15] * x4;
27     v += 16;
28 
29     vi = aj + diag[i] + 1;
30     nz = ai[i + 1] - diag[i] - 1;
31     while (nz--) {
32       oidx = 4 * (*vi++);
33       x[oidx] -= v[0] * s1 + v[1] * s2 + v[2] * s3 + v[3] * s4;
34       x[oidx + 1] -= v[4] * s1 + v[5] * s2 + v[6] * s3 + v[7] * s4;
35       x[oidx + 2] -= v[8] * s1 + v[9] * s2 + v[10] * s3 + v[11] * s4;
36       x[oidx + 3] -= v[12] * s1 + v[13] * s2 + v[14] * s3 + v[15] * s4;
37       v += 16;
38     }
39     x[idx]     = s1;
40     x[1 + idx] = s2;
41     x[2 + idx] = s3;
42     x[3 + idx] = s4;
43     idx += 4;
44   }
45   /* backward solve the L^T */
46   for (i = n - 1; i >= 0; i--) {
47     v   = aa + 16 * diag[i] - 16;
48     vi  = aj + diag[i] - 1;
49     nz  = diag[i] - ai[i];
50     idt = 4 * i;
51     s1  = x[idt];
52     s2  = x[1 + idt];
53     s3  = x[2 + idt];
54     s4  = x[3 + idt];
55     while (nz--) {
56       idx = 4 * (*vi--);
57       x[idx] -= v[0] * s1 + v[1] * s2 + v[2] * s3 + v[3] * s4;
58       x[idx + 1] -= v[4] * s1 + v[5] * s2 + v[6] * s3 + v[7] * s4;
59       x[idx + 2] -= v[8] * s1 + v[9] * s2 + v[10] * s3 + v[11] * s4;
60       x[idx + 3] -= v[12] * s1 + v[13] * s2 + v[14] * s3 + v[15] * s4;
61       v -= 16;
62     }
63   }
64   PetscCall(VecRestoreArray(xx, &x));
65   PetscCall(PetscLogFlops(2.0 * 16 * (a->nz) - 4.0 * A->cmap->n));
66   PetscFunctionReturn(0);
67 }
68 
69 PetscErrorCode MatSolveTranspose_SeqBAIJ_4_NaturalOrdering(Mat A, Vec bb, Vec xx) {
70   Mat_SeqBAIJ     *a = (Mat_SeqBAIJ *)A->data;
71   const PetscInt   n = a->mbs, *vi, *ai = a->i, *aj = a->j, *diag = a->diag;
72   PetscInt         nz, idx, idt, j, i, oidx;
73   const PetscInt   bs = A->rmap->bs, bs2 = a->bs2;
74   const MatScalar *aa = a->a, *v;
75   PetscScalar      s1, s2, s3, s4, x1, x2, x3, x4, *x;
76 
77   PetscFunctionBegin;
78   PetscCall(VecCopy(bb, xx));
79   PetscCall(VecGetArray(xx, &x));
80 
81   /* forward solve the U^T */
82   idx = 0;
83   for (i = 0; i < n; i++) {
84     v  = aa + bs2 * diag[i];
85     /* multiply by the inverse of the block diagonal */
86     x1 = x[idx];
87     x2 = x[1 + idx];
88     x3 = x[2 + idx];
89     x4 = x[3 + idx];
90     s1 = v[0] * x1 + v[1] * x2 + v[2] * x3 + v[3] * x4;
91     s2 = v[4] * x1 + v[5] * x2 + v[6] * x3 + v[7] * x4;
92     s3 = v[8] * x1 + v[9] * x2 + v[10] * x3 + v[11] * x4;
93     s4 = v[12] * x1 + v[13] * x2 + v[14] * x3 + v[15] * x4;
94     v -= bs2;
95 
96     vi = aj + diag[i] - 1;
97     nz = diag[i] - diag[i + 1] - 1;
98     for (j = 0; j > -nz; j--) {
99       oidx = bs * vi[j];
100       x[oidx] -= v[0] * s1 + v[1] * s2 + v[2] * s3 + v[3] * s4;
101       x[oidx + 1] -= v[4] * s1 + v[5] * s2 + v[6] * s3 + v[7] * s4;
102       x[oidx + 2] -= v[8] * s1 + v[9] * s2 + v[10] * s3 + v[11] * s4;
103       x[oidx + 3] -= v[12] * s1 + v[13] * s2 + v[14] * s3 + v[15] * s4;
104       v -= bs2;
105     }
106     x[idx]     = s1;
107     x[1 + idx] = s2;
108     x[2 + idx] = s3;
109     x[3 + idx] = s4;
110     idx += bs;
111   }
112   /* backward solve the L^T */
113   for (i = n - 1; i >= 0; i--) {
114     v   = aa + bs2 * ai[i];
115     vi  = aj + ai[i];
116     nz  = ai[i + 1] - ai[i];
117     idt = bs * i;
118     s1  = x[idt];
119     s2  = x[1 + idt];
120     s3  = x[2 + idt];
121     s4  = x[3 + idt];
122     for (j = 0; j < nz; j++) {
123       idx = bs * vi[j];
124       x[idx] -= v[0] * s1 + v[1] * s2 + v[2] * s3 + v[3] * s4;
125       x[idx + 1] -= v[4] * s1 + v[5] * s2 + v[6] * s3 + v[7] * s4;
126       x[idx + 2] -= v[8] * s1 + v[9] * s2 + v[10] * s3 + v[11] * s4;
127       x[idx + 3] -= v[12] * s1 + v[13] * s2 + v[14] * s3 + v[15] * s4;
128       v += bs2;
129     }
130   }
131   PetscCall(VecRestoreArray(xx, &x));
132   PetscCall(PetscLogFlops(2.0 * bs2 * (a->nz) - bs * A->cmap->n));
133   PetscFunctionReturn(0);
134 }
135