1 #include <../src/mat/impls/baij/seq/baij.h>
2
MatSolveTranspose_SeqBAIJ_7_NaturalOrdering_inplace(Mat A,Vec bb,Vec xx)3 PetscErrorCode MatSolveTranspose_SeqBAIJ_7_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, s7, x1, x2, x3, x4, x5, x6, x7, *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 + 49 * 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 x7 = x[6 + idx];
27 s1 = v[0] * x1 + v[1] * x2 + v[2] * x3 + v[3] * x4 + v[4] * x5 + v[5] * x6 + v[6] * x7;
28 s2 = v[7] * x1 + v[8] * x2 + v[9] * x3 + v[10] * x4 + v[11] * x5 + v[12] * x6 + v[13] * x7;
29 s3 = v[14] * x1 + v[15] * x2 + v[16] * x3 + v[17] * x4 + v[18] * x5 + v[19] * x6 + v[20] * x7;
30 s4 = v[21] * x1 + v[22] * x2 + v[23] * x3 + v[24] * x4 + v[25] * x5 + v[26] * x6 + v[27] * x7;
31 s5 = v[28] * x1 + v[29] * x2 + v[30] * x3 + v[31] * x4 + v[32] * x5 + v[33] * x6 + v[34] * x7;
32 s6 = v[35] * x1 + v[36] * x2 + v[37] * x3 + v[38] * x4 + v[39] * x5 + v[40] * x6 + v[41] * x7;
33 s7 = v[42] * x1 + v[43] * x2 + v[44] * x3 + v[45] * x4 + v[46] * x5 + v[47] * x6 + v[48] * x7;
34 v += 49;
35
36 vi = aj + diag[i] + 1;
37 nz = ai[i + 1] - diag[i] - 1;
38 while (nz--) {
39 oidx = 7 * (*vi++);
40 x[oidx] -= v[0] * s1 + v[1] * s2 + v[2] * s3 + v[3] * s4 + v[4] * s5 + v[5] * s6 + v[6] * s7;
41 x[oidx + 1] -= v[7] * s1 + v[8] * s2 + v[9] * s3 + v[10] * s4 + v[11] * s5 + v[12] * s6 + v[13] * s7;
42 x[oidx + 2] -= v[14] * s1 + v[15] * s2 + v[16] * s3 + v[17] * s4 + v[18] * s5 + v[19] * s6 + v[20] * s7;
43 x[oidx + 3] -= v[21] * s1 + v[22] * s2 + v[23] * s3 + v[24] * s4 + v[25] * s5 + v[26] * s6 + v[27] * s7;
44 x[oidx + 4] -= v[28] * s1 + v[29] * s2 + v[30] * s3 + v[31] * s4 + v[32] * s5 + v[33] * s6 + v[34] * s7;
45 x[oidx + 5] -= v[35] * s1 + v[36] * s2 + v[37] * s3 + v[38] * s4 + v[39] * s5 + v[40] * s6 + v[41] * s7;
46 x[oidx + 6] -= v[42] * s1 + v[43] * s2 + v[44] * s3 + v[45] * s4 + v[46] * s5 + v[47] * s6 + v[48] * s7;
47 v += 49;
48 }
49 x[idx] = s1;
50 x[1 + idx] = s2;
51 x[2 + idx] = s3;
52 x[3 + idx] = s4;
53 x[4 + idx] = s5;
54 x[5 + idx] = s6;
55 x[6 + idx] = s7;
56 idx += 7;
57 }
58 /* backward solve the L^T */
59 for (i = n - 1; i >= 0; i--) {
60 v = aa + 49 * diag[i] - 49;
61 vi = aj + diag[i] - 1;
62 nz = diag[i] - ai[i];
63 idt = 7 * i;
64 s1 = x[idt];
65 s2 = x[1 + idt];
66 s3 = x[2 + idt];
67 s4 = x[3 + idt];
68 s5 = x[4 + idt];
69 s6 = x[5 + idt];
70 s7 = x[6 + idt];
71 while (nz--) {
72 idx = 7 * (*vi--);
73 x[idx] -= v[0] * s1 + v[1] * s2 + v[2] * s3 + v[3] * s4 + v[4] * s5 + v[5] * s6 + v[6] * s7;
74 x[idx + 1] -= v[7] * s1 + v[8] * s2 + v[9] * s3 + v[10] * s4 + v[11] * s5 + v[12] * s6 + v[13] * s7;
75 x[idx + 2] -= v[14] * s1 + v[15] * s2 + v[16] * s3 + v[17] * s4 + v[18] * s5 + v[19] * s6 + v[20] * s7;
76 x[idx + 3] -= v[21] * s1 + v[22] * s2 + v[23] * s3 + v[24] * s4 + v[25] * s5 + v[26] * s6 + v[27] * s7;
77 x[idx + 4] -= v[28] * s1 + v[29] * s2 + v[30] * s3 + v[31] * s4 + v[32] * s5 + v[33] * s6 + v[34] * s7;
78 x[idx + 5] -= v[35] * s1 + v[36] * s2 + v[37] * s3 + v[38] * s4 + v[39] * s5 + v[40] * s6 + v[41] * s7;
79 x[idx + 6] -= v[42] * s1 + v[43] * s2 + v[44] * s3 + v[45] * s4 + v[46] * s5 + v[47] * s6 + v[48] * s7;
80 v -= 49;
81 }
82 }
83 PetscCall(VecRestoreArray(xx, &x));
84 PetscCall(PetscLogFlops(2.0 * 49 * (a->nz) - 7.0 * A->cmap->n));
85 PetscFunctionReturn(PETSC_SUCCESS);
86 }
MatSolveTranspose_SeqBAIJ_7_NaturalOrdering(Mat A,Vec bb,Vec xx)87 PetscErrorCode MatSolveTranspose_SeqBAIJ_7_NaturalOrdering(Mat A, Vec bb, Vec xx)
88 {
89 Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data;
90 const PetscInt n = a->mbs, *vi, *ai = a->i, *aj = a->j, *diag = a->diag;
91 PetscInt nz, idx, idt, j, i, oidx;
92 const PetscInt bs = A->rmap->bs, bs2 = a->bs2;
93 const MatScalar *aa = a->a, *v;
94 PetscScalar s1, s2, s3, s4, s5, s6, s7, x1, x2, x3, x4, x5, x6, x7, *x;
95
96 PetscFunctionBegin;
97 PetscCall(VecCopy(bb, xx));
98 PetscCall(VecGetArray(xx, &x));
99
100 /* forward solve the U^T */
101 idx = 0;
102 for (i = 0; i < n; i++) {
103 v = aa + bs2 * diag[i];
104 /* multiply by the inverse of the block diagonal */
105 x1 = x[idx];
106 x2 = x[1 + idx];
107 x3 = x[2 + idx];
108 x4 = x[3 + idx];
109 x5 = x[4 + idx];
110 x6 = x[5 + idx];
111 x7 = x[6 + idx];
112 s1 = v[0] * x1 + v[1] * x2 + v[2] * x3 + v[3] * x4 + v[4] * x5 + v[5] * x6 + v[6] * x7;
113 s2 = v[7] * x1 + v[8] * x2 + v[9] * x3 + v[10] * x4 + v[11] * x5 + v[12] * x6 + v[13] * x7;
114 s3 = v[14] * x1 + v[15] * x2 + v[16] * x3 + v[17] * x4 + v[18] * x5 + v[19] * x6 + v[20] * x7;
115 s4 = v[21] * x1 + v[22] * x2 + v[23] * x3 + v[24] * x4 + v[25] * x5 + v[26] * x6 + v[27] * x7;
116 s5 = v[28] * x1 + v[29] * x2 + v[30] * x3 + v[31] * x4 + v[32] * x5 + v[33] * x6 + v[34] * x7;
117 s6 = v[35] * x1 + v[36] * x2 + v[37] * x3 + v[38] * x4 + v[39] * x5 + v[40] * x6 + v[41] * x7;
118 s7 = v[42] * x1 + v[43] * x2 + v[44] * x3 + v[45] * x4 + v[46] * x5 + v[47] * x6 + v[48] * x7;
119 v -= bs2;
120 vi = aj + diag[i] - 1;
121 nz = diag[i] - diag[i + 1] - 1;
122 for (j = 0; j > -nz; j--) {
123 oidx = bs * vi[j];
124 x[oidx] -= v[0] * s1 + v[1] * s2 + v[2] * s3 + v[3] * s4 + v[4] * s5 + v[5] * s6 + v[6] * s7;
125 x[oidx + 1] -= v[7] * s1 + v[8] * s2 + v[9] * s3 + v[10] * s4 + v[11] * s5 + v[12] * s6 + v[13] * s7;
126 x[oidx + 2] -= v[14] * s1 + v[15] * s2 + v[16] * s3 + v[17] * s4 + v[18] * s5 + v[19] * s6 + v[20] * s7;
127 x[oidx + 3] -= v[21] * s1 + v[22] * s2 + v[23] * s3 + v[24] * s4 + v[25] * s5 + v[26] * s6 + v[27] * s7;
128 x[oidx + 4] -= v[28] * s1 + v[29] * s2 + v[30] * s3 + v[31] * s4 + v[32] * s5 + v[33] * s6 + v[34] * s7;
129 x[oidx + 5] -= v[35] * s1 + v[36] * s2 + v[37] * s3 + v[38] * s4 + v[39] * s5 + v[40] * s6 + v[41] * s7;
130 x[oidx + 6] -= v[42] * s1 + v[43] * s2 + v[44] * s3 + v[45] * s4 + v[46] * s5 + v[47] * s6 + v[48] * s7;
131 v -= bs2;
132 }
133 x[idx] = s1;
134 x[1 + idx] = s2;
135 x[2 + idx] = s3;
136 x[3 + idx] = s4;
137 x[4 + idx] = s5;
138 x[5 + idx] = s6;
139 x[6 + idx] = s7;
140 idx += bs;
141 }
142 /* backward solve the L^T */
143 for (i = n - 1; i >= 0; i--) {
144 v = aa + bs2 * ai[i];
145 vi = aj + ai[i];
146 nz = ai[i + 1] - ai[i];
147 idt = bs * i;
148 s1 = x[idt];
149 s2 = x[1 + idt];
150 s3 = x[2 + idt];
151 s4 = x[3 + idt];
152 s5 = x[4 + idt];
153 s6 = x[5 + idt];
154 s7 = x[6 + idt];
155 for (j = 0; j < nz; j++) {
156 idx = bs * vi[j];
157 x[idx] -= v[0] * s1 + v[1] * s2 + v[2] * s3 + v[3] * s4 + v[4] * s5 + v[5] * s6 + v[6] * s7;
158 x[idx + 1] -= v[7] * s1 + v[8] * s2 + v[9] * s3 + v[10] * s4 + v[11] * s5 + v[12] * s6 + v[13] * s7;
159 x[idx + 2] -= v[14] * s1 + v[15] * s2 + v[16] * s3 + v[17] * s4 + v[18] * s5 + v[19] * s6 + v[20] * s7;
160 x[idx + 3] -= v[21] * s1 + v[22] * s2 + v[23] * s3 + v[24] * s4 + v[25] * s5 + v[26] * s6 + v[27] * s7;
161 x[idx + 4] -= v[28] * s1 + v[29] * s2 + v[30] * s3 + v[31] * s4 + v[32] * s5 + v[33] * s6 + v[34] * s7;
162 x[idx + 5] -= v[35] * s1 + v[36] * s2 + v[37] * s3 + v[38] * s4 + v[39] * s5 + v[40] * s6 + v[41] * s7;
163 x[idx + 6] -= v[42] * s1 + v[43] * s2 + v[44] * s3 + v[45] * s4 + v[46] * s5 + v[47] * s6 + v[48] * s7;
164 v += bs2;
165 }
166 }
167 PetscCall(VecRestoreArray(xx, &x));
168 PetscCall(PetscLogFlops(2.0 * bs2 * (a->nz) - bs * A->cmap->n));
169 PetscFunctionReturn(PETSC_SUCCESS);
170 }
171