1 #include <../src/mat/impls/baij/seq/baij.h>
2 #include <petsc/private/kernels/blockinvert.h>
3
MatSolveTranspose_SeqBAIJ_6_inplace(Mat A,Vec bb,Vec xx)4 PetscErrorCode MatSolveTranspose_SeqBAIJ_6_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, s4, s5, s6, x1, x2, x3, x4, x5, x6, *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 = 6 * c[i];
29 t[ii] = b[ic];
30 t[ii + 1] = b[ic + 1];
31 t[ii + 2] = b[ic + 2];
32 t[ii + 3] = b[ic + 3];
33 t[ii + 4] = b[ic + 4];
34 t[ii + 5] = b[ic + 5];
35 ii += 6;
36 }
37
38 /* forward solve the U^T */
39 idx = 0;
40 for (i = 0; i < n; i++) {
41 v = aa + 36 * diag[i];
42 /* multiply by the inverse of the block diagonal */
43 x1 = t[idx];
44 x2 = t[1 + idx];
45 x3 = t[2 + idx];
46 x4 = t[3 + idx];
47 x5 = t[4 + idx];
48 x6 = t[5 + idx];
49 s1 = v[0] * x1 + v[1] * x2 + v[2] * x3 + v[3] * x4 + v[4] * x5 + v[5] * x6;
50 s2 = v[6] * x1 + v[7] * x2 + v[8] * x3 + v[9] * x4 + v[10] * x5 + v[11] * x6;
51 s3 = v[12] * x1 + v[13] * x2 + v[14] * x3 + v[15] * x4 + v[16] * x5 + v[17] * x6;
52 s4 = v[18] * x1 + v[19] * x2 + v[20] * x3 + v[21] * x4 + v[22] * x5 + v[23] * x6;
53 s5 = v[24] * x1 + v[25] * x2 + v[26] * x3 + v[27] * x4 + v[28] * x5 + v[29] * x6;
54 s6 = v[30] * x1 + v[31] * x2 + v[32] * x3 + v[33] * x4 + v[34] * x5 + v[35] * x6;
55 v += 36;
56
57 vi = aj + diag[i] + 1;
58 nz = ai[i + 1] - diag[i] - 1;
59 while (nz--) {
60 oidx = 6 * (*vi++);
61 t[oidx] -= v[0] * s1 + v[1] * s2 + v[2] * s3 + v[3] * s4 + v[4] * s5 + v[5] * s6;
62 t[oidx + 1] -= v[6] * s1 + v[7] * s2 + v[8] * s3 + v[9] * s4 + v[10] * s5 + v[11] * s6;
63 t[oidx + 2] -= v[12] * s1 + v[13] * s2 + v[14] * s3 + v[15] * s4 + v[16] * s5 + v[17] * s6;
64 t[oidx + 3] -= v[18] * s1 + v[19] * s2 + v[20] * s3 + v[21] * s4 + v[22] * s5 + v[23] * s6;
65 t[oidx + 4] -= v[24] * s1 + v[25] * s2 + v[26] * s3 + v[27] * s4 + v[28] * s5 + v[29] * s6;
66 t[oidx + 5] -= v[30] * s1 + v[31] * s2 + v[32] * s3 + v[33] * s4 + v[34] * s5 + v[35] * s6;
67 v += 36;
68 }
69 t[idx] = s1;
70 t[1 + idx] = s2;
71 t[2 + idx] = s3;
72 t[3 + idx] = s4;
73 t[4 + idx] = s5;
74 t[5 + idx] = s6;
75 idx += 6;
76 }
77 /* backward solve the L^T */
78 for (i = n - 1; i >= 0; i--) {
79 v = aa + 36 * diag[i] - 36;
80 vi = aj + diag[i] - 1;
81 nz = diag[i] - ai[i];
82 idt = 6 * i;
83 s1 = t[idt];
84 s2 = t[1 + idt];
85 s3 = t[2 + idt];
86 s4 = t[3 + idt];
87 s5 = t[4 + idt];
88 s6 = t[5 + idt];
89 while (nz--) {
90 idx = 6 * (*vi--);
91 t[idx] -= v[0] * s1 + v[1] * s2 + v[2] * s3 + v[3] * s4 + v[4] * s5 + v[5] * s6;
92 t[idx + 1] -= v[6] * s1 + v[7] * s2 + v[8] * s3 + v[9] * s4 + v[10] * s5 + v[11] * s6;
93 t[idx + 2] -= v[12] * s1 + v[13] * s2 + v[14] * s3 + v[15] * s4 + v[16] * s5 + v[17] * s6;
94 t[idx + 3] -= v[18] * s1 + v[19] * s2 + v[20] * s3 + v[21] * s4 + v[22] * s5 + v[23] * s6;
95 t[idx + 4] -= v[24] * s1 + v[25] * s2 + v[26] * s3 + v[27] * s4 + v[28] * s5 + v[29] * s6;
96 t[idx + 5] -= v[30] * s1 + v[31] * s2 + v[32] * s3 + v[33] * s4 + v[34] * s5 + v[35] * s6;
97 v -= 36;
98 }
99 }
100
101 /* copy t into x according to permutation */
102 ii = 0;
103 for (i = 0; i < n; i++) {
104 ir = 6 * r[i];
105 x[ir] = t[ii];
106 x[ir + 1] = t[ii + 1];
107 x[ir + 2] = t[ii + 2];
108 x[ir + 3] = t[ii + 3];
109 x[ir + 4] = t[ii + 4];
110 x[ir + 5] = t[ii + 5];
111 ii += 6;
112 }
113
114 PetscCall(ISRestoreIndices(isrow, &rout));
115 PetscCall(ISRestoreIndices(iscol, &cout));
116 PetscCall(VecRestoreArrayRead(bb, &b));
117 PetscCall(VecRestoreArray(xx, &x));
118 PetscCall(PetscLogFlops(2.0 * 36 * (a->nz) - 6.0 * A->cmap->n));
119 PetscFunctionReturn(PETSC_SUCCESS);
120 }
121
MatSolveTranspose_SeqBAIJ_6(Mat A,Vec bb,Vec xx)122 PetscErrorCode MatSolveTranspose_SeqBAIJ_6(Mat A, Vec bb, Vec xx)
123 {
124 Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data;
125 IS iscol = a->col, isrow = a->row;
126 const PetscInt n = a->mbs, *vi, *ai = a->i, *aj = a->j, *diag = a->diag;
127 const PetscInt *r, *c, *rout, *cout;
128 PetscInt nz, idx, idt, j, i, oidx, ii, ic, ir;
129 const PetscInt bs = A->rmap->bs, bs2 = a->bs2;
130 const MatScalar *aa = a->a, *v;
131 PetscScalar s1, s2, s3, s4, s5, s6, x1, x2, x3, x4, x5, x6, *x, *t;
132 const PetscScalar *b;
133
134 PetscFunctionBegin;
135 PetscCall(VecGetArrayRead(bb, &b));
136 PetscCall(VecGetArray(xx, &x));
137 t = a->solve_work;
138
139 PetscCall(ISGetIndices(isrow, &rout));
140 r = rout;
141 PetscCall(ISGetIndices(iscol, &cout));
142 c = cout;
143
144 /* copy b into temp work space according to permutation */
145 for (i = 0; i < n; i++) {
146 ii = bs * i;
147 ic = bs * c[i];
148 t[ii] = b[ic];
149 t[ii + 1] = b[ic + 1];
150 t[ii + 2] = b[ic + 2];
151 t[ii + 3] = b[ic + 3];
152 t[ii + 4] = b[ic + 4];
153 t[ii + 5] = b[ic + 5];
154 }
155
156 /* forward solve the U^T */
157 idx = 0;
158 for (i = 0; i < n; i++) {
159 v = aa + bs2 * diag[i];
160 /* multiply by the inverse of the block diagonal */
161 x1 = t[idx];
162 x2 = t[1 + idx];
163 x3 = t[2 + idx];
164 x4 = t[3 + idx];
165 x5 = t[4 + idx];
166 x6 = t[5 + idx];
167 s1 = v[0] * x1 + v[1] * x2 + v[2] * x3 + v[3] * x4 + v[4] * x5 + v[5] * x6;
168 s2 = v[6] * x1 + v[7] * x2 + v[8] * x3 + v[9] * x4 + v[10] * x5 + v[11] * x6;
169 s3 = v[12] * x1 + v[13] * x2 + v[14] * x3 + v[15] * x4 + v[16] * x5 + v[17] * x6;
170 s4 = v[18] * x1 + v[19] * x2 + v[20] * x3 + v[21] * x4 + v[22] * x5 + v[23] * x6;
171 s5 = v[24] * x1 + v[25] * x2 + v[26] * x3 + v[27] * x4 + v[28] * x5 + v[29] * x6;
172 s6 = v[30] * x1 + v[31] * x2 + v[32] * x3 + v[33] * x4 + v[34] * x5 + v[35] * x6;
173 v -= bs2;
174
175 vi = aj + diag[i] - 1;
176 nz = diag[i] - diag[i + 1] - 1;
177 for (j = 0; j > -nz; j--) {
178 oidx = bs * vi[j];
179 t[oidx] -= v[0] * s1 + v[1] * s2 + v[2] * s3 + v[3] * s4 + v[4] * s5 + v[5] * s6;
180 t[oidx + 1] -= v[6] * s1 + v[7] * s2 + v[8] * s3 + v[9] * s4 + v[10] * s5 + v[11] * s6;
181 t[oidx + 2] -= v[12] * s1 + v[13] * s2 + v[14] * s3 + v[15] * s4 + v[16] * s5 + v[17] * s6;
182 t[oidx + 3] -= v[18] * s1 + v[19] * s2 + v[20] * s3 + v[21] * s4 + v[22] * s5 + v[23] * s6;
183 t[oidx + 4] -= v[24] * s1 + v[25] * s2 + v[26] * s3 + v[27] * s4 + v[28] * s5 + v[29] * s6;
184 t[oidx + 5] -= v[30] * s1 + v[31] * s2 + v[32] * s3 + v[33] * s4 + v[34] * s5 + v[35] * s6;
185 v -= bs2;
186 }
187 t[idx] = s1;
188 t[1 + idx] = s2;
189 t[2 + idx] = s3;
190 t[3 + idx] = s4;
191 t[4 + idx] = s5;
192 t[5 + idx] = s6;
193 idx += bs;
194 }
195 /* backward solve the L^T */
196 for (i = n - 1; i >= 0; i--) {
197 v = aa + bs2 * ai[i];
198 vi = aj + ai[i];
199 nz = ai[i + 1] - ai[i];
200 idt = bs * i;
201 s1 = t[idt];
202 s2 = t[1 + idt];
203 s3 = t[2 + idt];
204 s4 = t[3 + idt];
205 s5 = t[4 + idt];
206 s6 = t[5 + idt];
207 for (j = 0; j < nz; j++) {
208 idx = bs * vi[j];
209 t[idx] -= v[0] * s1 + v[1] * s2 + v[2] * s3 + v[3] * s4 + v[4] * s5 + v[5] * s6;
210 t[idx + 1] -= v[6] * s1 + v[7] * s2 + v[8] * s3 + v[9] * s4 + v[10] * s5 + v[11] * s6;
211 t[idx + 2] -= v[12] * s1 + v[13] * s2 + v[14] * s3 + v[15] * s4 + v[16] * s5 + v[17] * s6;
212 t[idx + 3] -= v[18] * s1 + v[19] * s2 + v[20] * s3 + v[21] * s4 + v[22] * s5 + v[23] * s6;
213 t[idx + 4] -= v[24] * s1 + v[25] * s2 + v[26] * s3 + v[27] * s4 + v[28] * s5 + v[29] * s6;
214 t[idx + 5] -= v[30] * s1 + v[31] * s2 + v[32] * s3 + v[33] * s4 + v[34] * s5 + v[35] * s6;
215 v += bs2;
216 }
217 }
218
219 /* copy t into x according to permutation */
220 for (i = 0; i < n; i++) {
221 ii = bs * i;
222 ir = bs * r[i];
223 x[ir] = t[ii];
224 x[ir + 1] = t[ii + 1];
225 x[ir + 2] = t[ii + 2];
226 x[ir + 3] = t[ii + 3];
227 x[ir + 4] = t[ii + 4];
228 x[ir + 5] = t[ii + 5];
229 }
230
231 PetscCall(ISRestoreIndices(isrow, &rout));
232 PetscCall(ISRestoreIndices(iscol, &cout));
233 PetscCall(VecRestoreArrayRead(bb, &b));
234 PetscCall(VecRestoreArray(xx, &x));
235 PetscCall(PetscLogFlops(2.0 * bs2 * (a->nz) - bs * A->cmap->n));
236 PetscFunctionReturn(PETSC_SUCCESS);
237 }
238