1 #include <../src/mat/impls/baij/seq/baij.h>
2 #include <petsc/private/kernels/blockinvert.h>
3
MatSolveTranspose_SeqBAIJ_5_inplace(Mat A,Vec bb,Vec xx)4 PetscErrorCode MatSolveTranspose_SeqBAIJ_5_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, x1, x2, x3, x4, x5, *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 = 5 * 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 ii += 5;
35 }
36
37 /* forward solve the U^T */
38 idx = 0;
39 for (i = 0; i < n; i++) {
40 v = aa + 25 * diag[i];
41 /* multiply by the inverse of the block diagonal */
42 x1 = t[idx];
43 x2 = t[1 + idx];
44 x3 = t[2 + idx];
45 x4 = t[3 + idx];
46 x5 = t[4 + idx];
47 s1 = v[0] * x1 + v[1] * x2 + v[2] * x3 + v[3] * x4 + v[4] * x5;
48 s2 = v[5] * x1 + v[6] * x2 + v[7] * x3 + v[8] * x4 + v[9] * x5;
49 s3 = v[10] * x1 + v[11] * x2 + v[12] * x3 + v[13] * x4 + v[14] * x5;
50 s4 = v[15] * x1 + v[16] * x2 + v[17] * x3 + v[18] * x4 + v[19] * x5;
51 s5 = v[20] * x1 + v[21] * x2 + v[22] * x3 + v[23] * x4 + v[24] * x5;
52 v += 25;
53
54 vi = aj + diag[i] + 1;
55 nz = ai[i + 1] - diag[i] - 1;
56 while (nz--) {
57 oidx = 5 * (*vi++);
58 t[oidx] -= v[0] * s1 + v[1] * s2 + v[2] * s3 + v[3] * s4 + v[4] * s5;
59 t[oidx + 1] -= v[5] * s1 + v[6] * s2 + v[7] * s3 + v[8] * s4 + v[9] * s5;
60 t[oidx + 2] -= v[10] * s1 + v[11] * s2 + v[12] * s3 + v[13] * s4 + v[14] * s5;
61 t[oidx + 3] -= v[15] * s1 + v[16] * s2 + v[17] * s3 + v[18] * s4 + v[19] * s5;
62 t[oidx + 4] -= v[20] * s1 + v[21] * s2 + v[22] * s3 + v[23] * s4 + v[24] * s5;
63 v += 25;
64 }
65 t[idx] = s1;
66 t[1 + idx] = s2;
67 t[2 + idx] = s3;
68 t[3 + idx] = s4;
69 t[4 + idx] = s5;
70 idx += 5;
71 }
72 /* backward solve the L^T */
73 for (i = n - 1; i >= 0; i--) {
74 v = aa + 25 * diag[i] - 25;
75 vi = aj + diag[i] - 1;
76 nz = diag[i] - ai[i];
77 idt = 5 * i;
78 s1 = t[idt];
79 s2 = t[1 + idt];
80 s3 = t[2 + idt];
81 s4 = t[3 + idt];
82 s5 = t[4 + idt];
83 while (nz--) {
84 idx = 5 * (*vi--);
85 t[idx] -= v[0] * s1 + v[1] * s2 + v[2] * s3 + v[3] * s4 + v[4] * s5;
86 t[idx + 1] -= v[5] * s1 + v[6] * s2 + v[7] * s3 + v[8] * s4 + v[9] * s5;
87 t[idx + 2] -= v[10] * s1 + v[11] * s2 + v[12] * s3 + v[13] * s4 + v[14] * s5;
88 t[idx + 3] -= v[15] * s1 + v[16] * s2 + v[17] * s3 + v[18] * s4 + v[19] * s5;
89 t[idx + 4] -= v[20] * s1 + v[21] * s2 + v[22] * s3 + v[23] * s4 + v[24] * s5;
90 v -= 25;
91 }
92 }
93
94 /* copy t into x according to permutation */
95 ii = 0;
96 for (i = 0; i < n; i++) {
97 ir = 5 * r[i];
98 x[ir] = t[ii];
99 x[ir + 1] = t[ii + 1];
100 x[ir + 2] = t[ii + 2];
101 x[ir + 3] = t[ii + 3];
102 x[ir + 4] = t[ii + 4];
103 ii += 5;
104 }
105
106 PetscCall(ISRestoreIndices(isrow, &rout));
107 PetscCall(ISRestoreIndices(iscol, &cout));
108 PetscCall(VecRestoreArrayRead(bb, &b));
109 PetscCall(VecRestoreArray(xx, &x));
110 PetscCall(PetscLogFlops(2.0 * 25 * (a->nz) - 5.0 * A->cmap->n));
111 PetscFunctionReturn(PETSC_SUCCESS);
112 }
113
MatSolveTranspose_SeqBAIJ_5(Mat A,Vec bb,Vec xx)114 PetscErrorCode MatSolveTranspose_SeqBAIJ_5(Mat A, Vec bb, Vec xx)
115 {
116 Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data;
117 IS iscol = a->col, isrow = a->row;
118 const PetscInt n = a->mbs, *vi, *ai = a->i, *aj = a->j, *diag = a->diag;
119 const PetscInt *r, *c, *rout, *cout;
120 PetscInt nz, idx, idt, j, i, oidx, ii, ic, ir;
121 const PetscInt bs = A->rmap->bs, bs2 = a->bs2;
122 const MatScalar *aa = a->a, *v;
123 PetscScalar s1, s2, s3, s4, s5, x1, x2, x3, x4, x5, *x, *t;
124 const PetscScalar *b;
125
126 PetscFunctionBegin;
127 PetscCall(VecGetArrayRead(bb, &b));
128 PetscCall(VecGetArray(xx, &x));
129 t = a->solve_work;
130
131 PetscCall(ISGetIndices(isrow, &rout));
132 r = rout;
133 PetscCall(ISGetIndices(iscol, &cout));
134 c = cout;
135
136 /* copy b into temp work space according to permutation */
137 for (i = 0; i < n; i++) {
138 ii = bs * i;
139 ic = bs * c[i];
140 t[ii] = b[ic];
141 t[ii + 1] = b[ic + 1];
142 t[ii + 2] = b[ic + 2];
143 t[ii + 3] = b[ic + 3];
144 t[ii + 4] = b[ic + 4];
145 }
146
147 /* forward solve the U^T */
148 idx = 0;
149 for (i = 0; i < n; i++) {
150 v = aa + bs2 * diag[i];
151 /* multiply by the inverse of the block diagonal */
152 x1 = t[idx];
153 x2 = t[1 + idx];
154 x3 = t[2 + idx];
155 x4 = t[3 + idx];
156 x5 = t[4 + idx];
157 s1 = v[0] * x1 + v[1] * x2 + v[2] * x3 + v[3] * x4 + v[4] * x5;
158 s2 = v[5] * x1 + v[6] * x2 + v[7] * x3 + v[8] * x4 + v[9] * x5;
159 s3 = v[10] * x1 + v[11] * x2 + v[12] * x3 + v[13] * x4 + v[14] * x5;
160 s4 = v[15] * x1 + v[16] * x2 + v[17] * x3 + v[18] * x4 + v[19] * x5;
161 s5 = v[20] * x1 + v[21] * x2 + v[22] * x3 + v[23] * x4 + v[24] * x5;
162 v -= bs2;
163
164 vi = aj + diag[i] - 1;
165 nz = diag[i] - diag[i + 1] - 1;
166 for (j = 0; j > -nz; j--) {
167 oidx = bs * vi[j];
168 t[oidx] -= v[0] * s1 + v[1] * s2 + v[2] * s3 + v[3] * s4 + v[4] * s5;
169 t[oidx + 1] -= v[5] * s1 + v[6] * s2 + v[7] * s3 + v[8] * s4 + v[9] * s5;
170 t[oidx + 2] -= v[10] * s1 + v[11] * s2 + v[12] * s3 + v[13] * s4 + v[14] * s5;
171 t[oidx + 3] -= v[15] * s1 + v[16] * s2 + v[17] * s3 + v[18] * s4 + v[19] * s5;
172 t[oidx + 4] -= v[20] * s1 + v[21] * s2 + v[22] * s3 + v[23] * s4 + v[24] * s5;
173 v -= bs2;
174 }
175 t[idx] = s1;
176 t[1 + idx] = s2;
177 t[2 + idx] = s3;
178 t[3 + idx] = s4;
179 t[4 + idx] = s5;
180 idx += bs;
181 }
182 /* backward solve the L^T */
183 for (i = n - 1; i >= 0; i--) {
184 v = aa + bs2 * ai[i];
185 vi = aj + ai[i];
186 nz = ai[i + 1] - ai[i];
187 idt = bs * i;
188 s1 = t[idt];
189 s2 = t[1 + idt];
190 s3 = t[2 + idt];
191 s4 = t[3 + idt];
192 s5 = t[4 + idt];
193 for (j = 0; j < nz; j++) {
194 idx = bs * vi[j];
195 t[idx] -= v[0] * s1 + v[1] * s2 + v[2] * s3 + v[3] * s4 + v[4] * s5;
196 t[idx + 1] -= v[5] * s1 + v[6] * s2 + v[7] * s3 + v[8] * s4 + v[9] * s5;
197 t[idx + 2] -= v[10] * s1 + v[11] * s2 + v[12] * s3 + v[13] * s4 + v[14] * s5;
198 t[idx + 3] -= v[15] * s1 + v[16] * s2 + v[17] * s3 + v[18] * s4 + v[19] * s5;
199 t[idx + 4] -= v[20] * s1 + v[21] * s2 + v[22] * s3 + v[23] * s4 + v[24] * s5;
200 v += bs2;
201 }
202 }
203
204 /* copy t into x according to permutation */
205 for (i = 0; i < n; i++) {
206 ii = bs * i;
207 ir = bs * r[i];
208 x[ir] = t[ii];
209 x[ir + 1] = t[ii + 1];
210 x[ir + 2] = t[ii + 2];
211 x[ir + 3] = t[ii + 3];
212 x[ir + 4] = t[ii + 4];
213 }
214
215 PetscCall(ISRestoreIndices(isrow, &rout));
216 PetscCall(ISRestoreIndices(iscol, &cout));
217 PetscCall(VecRestoreArrayRead(bb, &b));
218 PetscCall(VecRestoreArray(xx, &x));
219 PetscCall(PetscLogFlops(2.0 * bs2 * (a->nz) - bs * A->cmap->n));
220 PetscFunctionReturn(PETSC_SUCCESS);
221 }
222