1 #include <../src/mat/impls/baij/seq/baij.h>
2 #include <petsc/private/kernels/blockinvert.h>
3
MatSolveTranspose_SeqBAIJ_3_inplace(Mat A,Vec bb,Vec xx)4 PetscErrorCode MatSolveTranspose_SeqBAIJ_3_inplace(Mat A, Vec bb, Vec xx)
5 {
6 Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data;
7 IS iscol = a->col, isrow = a->row;
8 const PetscInt *r, *c, *rout, *cout;
9 const PetscInt *diag = a->diag, n = a->mbs, *vi, *ai = a->i, *aj = a->j;
10 PetscInt i, nz, idx, idt, ii, ic, ir, oidx;
11 const MatScalar *aa = a->a, *v;
12 PetscScalar s1, s2, s3, x1, x2, x3, *x, *t;
13 const PetscScalar *b;
14
15 PetscFunctionBegin;
16 PetscCall(VecGetArrayRead(bb, &b));
17 PetscCall(VecGetArray(xx, &x));
18 t = a->solve_work;
19
20 PetscCall(ISGetIndices(isrow, &rout));
21 r = rout;
22 PetscCall(ISGetIndices(iscol, &cout));
23 c = cout;
24
25 /* copy the b into temp work space according to permutation */
26 ii = 0;
27 for (i = 0; i < n; i++) {
28 ic = 3 * c[i];
29 t[ii] = b[ic];
30 t[ii + 1] = b[ic + 1];
31 t[ii + 2] = b[ic + 2];
32 ii += 3;
33 }
34
35 /* forward solve the U^T */
36 idx = 0;
37 for (i = 0; i < n; i++) {
38 v = aa + 9 * diag[i];
39 /* multiply by the inverse of the block diagonal */
40 x1 = t[idx];
41 x2 = t[1 + idx];
42 x3 = t[2 + idx];
43 s1 = v[0] * x1 + v[1] * x2 + v[2] * x3;
44 s2 = v[3] * x1 + v[4] * x2 + v[5] * x3;
45 s3 = v[6] * x1 + v[7] * x2 + v[8] * x3;
46 v += 9;
47
48 vi = aj + diag[i] + 1;
49 nz = ai[i + 1] - diag[i] - 1;
50 while (nz--) {
51 oidx = 3 * (*vi++);
52 t[oidx] -= v[0] * s1 + v[1] * s2 + v[2] * s3;
53 t[oidx + 1] -= v[3] * s1 + v[4] * s2 + v[5] * s3;
54 t[oidx + 2] -= v[6] * s1 + v[7] * s2 + v[8] * s3;
55 v += 9;
56 }
57 t[idx] = s1;
58 t[1 + idx] = s2;
59 t[2 + idx] = s3;
60 idx += 3;
61 }
62 /* backward solve the L^T */
63 for (i = n - 1; i >= 0; i--) {
64 v = aa + 9 * diag[i] - 9;
65 vi = aj + diag[i] - 1;
66 nz = diag[i] - ai[i];
67 idt = 3 * i;
68 s1 = t[idt];
69 s2 = t[1 + idt];
70 s3 = t[2 + idt];
71 while (nz--) {
72 idx = 3 * (*vi--);
73 t[idx] -= v[0] * s1 + v[1] * s2 + v[2] * s3;
74 t[idx + 1] -= v[3] * s1 + v[4] * s2 + v[5] * s3;
75 t[idx + 2] -= v[6] * s1 + v[7] * s2 + v[8] * s3;
76 v -= 9;
77 }
78 }
79
80 /* copy t into x according to permutation */
81 ii = 0;
82 for (i = 0; i < n; i++) {
83 ir = 3 * r[i];
84 x[ir] = t[ii];
85 x[ir + 1] = t[ii + 1];
86 x[ir + 2] = t[ii + 2];
87 ii += 3;
88 }
89
90 PetscCall(ISRestoreIndices(isrow, &rout));
91 PetscCall(ISRestoreIndices(iscol, &cout));
92 PetscCall(VecRestoreArrayRead(bb, &b));
93 PetscCall(VecRestoreArray(xx, &x));
94 PetscCall(PetscLogFlops(2.0 * 9 * (a->nz) - 3.0 * A->cmap->n));
95 PetscFunctionReturn(PETSC_SUCCESS);
96 }
97
MatSolveTranspose_SeqBAIJ_3(Mat A,Vec bb,Vec xx)98 PetscErrorCode MatSolveTranspose_SeqBAIJ_3(Mat A, Vec bb, Vec xx)
99 {
100 Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data;
101 IS iscol = a->col, isrow = a->row;
102 const PetscInt n = a->mbs, *vi, *ai = a->i, *aj = a->j, *diag = a->diag;
103 const PetscInt *r, *c, *rout, *cout;
104 PetscInt nz, idx, idt, j, i, oidx, ii, ic, ir;
105 const PetscInt bs = A->rmap->bs, bs2 = a->bs2;
106 const MatScalar *aa = a->a, *v;
107 PetscScalar s1, s2, s3, x1, x2, x3, *x, *t;
108 const PetscScalar *b;
109
110 PetscFunctionBegin;
111 PetscCall(VecGetArrayRead(bb, &b));
112 PetscCall(VecGetArray(xx, &x));
113 t = a->solve_work;
114
115 PetscCall(ISGetIndices(isrow, &rout));
116 r = rout;
117 PetscCall(ISGetIndices(iscol, &cout));
118 c = cout;
119
120 /* copy b into temp work space according to permutation */
121 for (i = 0; i < n; i++) {
122 ii = bs * i;
123 ic = bs * c[i];
124 t[ii] = b[ic];
125 t[ii + 1] = b[ic + 1];
126 t[ii + 2] = b[ic + 2];
127 }
128
129 /* forward solve the U^T */
130 idx = 0;
131 for (i = 0; i < n; i++) {
132 v = aa + bs2 * diag[i];
133 /* multiply by the inverse of the block diagonal */
134 x1 = t[idx];
135 x2 = t[1 + idx];
136 x3 = t[2 + idx];
137 s1 = v[0] * x1 + v[1] * x2 + v[2] * x3;
138 s2 = v[3] * x1 + v[4] * x2 + v[5] * x3;
139 s3 = v[6] * x1 + v[7] * x2 + v[8] * x3;
140 v -= bs2;
141
142 vi = aj + diag[i] - 1;
143 nz = diag[i] - diag[i + 1] - 1;
144 for (j = 0; j > -nz; j--) {
145 oidx = bs * vi[j];
146 t[oidx] -= v[0] * s1 + v[1] * s2 + v[2] * s3;
147 t[oidx + 1] -= v[3] * s1 + v[4] * s2 + v[5] * s3;
148 t[oidx + 2] -= v[6] * s1 + v[7] * s2 + v[8] * s3;
149 v -= bs2;
150 }
151 t[idx] = s1;
152 t[1 + idx] = s2;
153 t[2 + idx] = s3;
154 idx += bs;
155 }
156 /* backward solve the L^T */
157 for (i = n - 1; i >= 0; i--) {
158 v = aa + bs2 * ai[i];
159 vi = aj + ai[i];
160 nz = ai[i + 1] - ai[i];
161 idt = bs * i;
162 s1 = t[idt];
163 s2 = t[1 + idt];
164 s3 = t[2 + idt];
165 for (j = 0; j < nz; j++) {
166 idx = bs * vi[j];
167 t[idx] -= v[0] * s1 + v[1] * s2 + v[2] * s3;
168 t[idx + 1] -= v[3] * s1 + v[4] * s2 + v[5] * s3;
169 t[idx + 2] -= v[6] * s1 + v[7] * s2 + v[8] * s3;
170 v += bs2;
171 }
172 }
173
174 /* copy t into x according to permutation */
175 for (i = 0; i < n; i++) {
176 ii = bs * i;
177 ir = bs * r[i];
178 x[ir] = t[ii];
179 x[ir + 1] = t[ii + 1];
180 x[ir + 2] = t[ii + 2];
181 }
182
183 PetscCall(ISRestoreIndices(isrow, &rout));
184 PetscCall(ISRestoreIndices(iscol, &cout));
185 PetscCall(VecRestoreArrayRead(bb, &b));
186 PetscCall(VecRestoreArray(xx, &x));
187 PetscCall(PetscLogFlops(2.0 * bs2 * (a->nz) - bs * A->cmap->n));
188 PetscFunctionReturn(PETSC_SUCCESS);
189 }
190