xref: /petsc/src/mat/impls/baij/seq/baijsolvtran4.c (revision 58d68138c660dfb4e9f5b03334792cd4f2ffd7cc)
1 #include <../src/mat/impls/baij/seq/baij.h>
2 #include <petsc/private/kernels/blockinvert.h>
3 
4 PetscErrorCode MatSolveTranspose_SeqBAIJ_4_inplace(Mat A, Vec bb, Vec xx) {
5   Mat_SeqBAIJ       *a     = (Mat_SeqBAIJ *)A->data;
6   IS                 iscol = a->col, isrow = a->row;
7   const PetscInt    *r, *c, *rout, *cout;
8   const PetscInt    *diag = a->diag, n = a->mbs, *vi, *ai = a->i, *aj = a->j;
9   PetscInt           i, nz, idx, idt, ii, ic, ir, oidx;
10   const MatScalar   *aa = a->a, *v;
11   PetscScalar        s1, s2, s3, s4, x1, x2, x3, x4, *x, *t;
12   const PetscScalar *b;
13 
14   PetscFunctionBegin;
15   PetscCall(VecGetArrayRead(bb, &b));
16   PetscCall(VecGetArray(xx, &x));
17   t = a->solve_work;
18 
19   PetscCall(ISGetIndices(isrow, &rout));
20   r = rout;
21   PetscCall(ISGetIndices(iscol, &cout));
22   c = cout;
23 
24   /* copy the b into temp work space according to permutation */
25   ii = 0;
26   for (i = 0; i < n; i++) {
27     ic        = 4 * c[i];
28     t[ii]     = b[ic];
29     t[ii + 1] = b[ic + 1];
30     t[ii + 2] = b[ic + 2];
31     t[ii + 3] = b[ic + 3];
32     ii += 4;
33   }
34 
35   /* forward solve the U^T */
36   idx = 0;
37   for (i = 0; i < n; i++) {
38     v  = aa + 16 * 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     x4 = t[3 + idx];
44     s1 = v[0] * x1 + v[1] * x2 + v[2] * x3 + v[3] * x4;
45     s2 = v[4] * x1 + v[5] * x2 + v[6] * x3 + v[7] * x4;
46     s3 = v[8] * x1 + v[9] * x2 + v[10] * x3 + v[11] * x4;
47     s4 = v[12] * x1 + v[13] * x2 + v[14] * x3 + v[15] * x4;
48     v += 16;
49 
50     vi = aj + diag[i] + 1;
51     nz = ai[i + 1] - diag[i] - 1;
52     while (nz--) {
53       oidx = 4 * (*vi++);
54       t[oidx] -= v[0] * s1 + v[1] * s2 + v[2] * s3 + v[3] * s4;
55       t[oidx + 1] -= v[4] * s1 + v[5] * s2 + v[6] * s3 + v[7] * s4;
56       t[oidx + 2] -= v[8] * s1 + v[9] * s2 + v[10] * s3 + v[11] * s4;
57       t[oidx + 3] -= v[12] * s1 + v[13] * s2 + v[14] * s3 + v[15] * s4;
58       v += 16;
59     }
60     t[idx]     = s1;
61     t[1 + idx] = s2;
62     t[2 + idx] = s3;
63     t[3 + idx] = s4;
64     idx += 4;
65   }
66   /* backward solve the L^T */
67   for (i = n - 1; i >= 0; i--) {
68     v   = aa + 16 * diag[i] - 16;
69     vi  = aj + diag[i] - 1;
70     nz  = diag[i] - ai[i];
71     idt = 4 * i;
72     s1  = t[idt];
73     s2  = t[1 + idt];
74     s3  = t[2 + idt];
75     s4  = t[3 + idt];
76     while (nz--) {
77       idx = 4 * (*vi--);
78       t[idx] -= v[0] * s1 + v[1] * s2 + v[2] * s3 + v[3] * s4;
79       t[idx + 1] -= v[4] * s1 + v[5] * s2 + v[6] * s3 + v[7] * s4;
80       t[idx + 2] -= v[8] * s1 + v[9] * s2 + v[10] * s3 + v[11] * s4;
81       t[idx + 3] -= v[12] * s1 + v[13] * s2 + v[14] * s3 + v[15] * s4;
82       v -= 16;
83     }
84   }
85 
86   /* copy t into x according to permutation */
87   ii = 0;
88   for (i = 0; i < n; i++) {
89     ir        = 4 * r[i];
90     x[ir]     = t[ii];
91     x[ir + 1] = t[ii + 1];
92     x[ir + 2] = t[ii + 2];
93     x[ir + 3] = t[ii + 3];
94     ii += 4;
95   }
96 
97   PetscCall(ISRestoreIndices(isrow, &rout));
98   PetscCall(ISRestoreIndices(iscol, &cout));
99   PetscCall(VecRestoreArrayRead(bb, &b));
100   PetscCall(VecRestoreArray(xx, &x));
101   PetscCall(PetscLogFlops(2.0 * 16 * (a->nz) - 4.0 * A->cmap->n));
102   PetscFunctionReturn(0);
103 }
104 
105 PetscErrorCode MatSolveTranspose_SeqBAIJ_4(Mat A, Vec bb, Vec xx) {
106   Mat_SeqBAIJ       *a     = (Mat_SeqBAIJ *)A->data;
107   IS                 iscol = a->col, isrow = a->row;
108   const PetscInt     n = a->mbs, *vi, *ai = a->i, *aj = a->j, *diag = a->diag;
109   const PetscInt    *r, *c, *rout, *cout;
110   PetscInt           nz, idx, idt, j, i, oidx, ii, ic, ir;
111   const PetscInt     bs = A->rmap->bs, bs2 = a->bs2;
112   const MatScalar   *aa = a->a, *v;
113   PetscScalar        s1, s2, s3, s4, x1, x2, x3, x4, *x, *t;
114   const PetscScalar *b;
115 
116   PetscFunctionBegin;
117   PetscCall(VecGetArrayRead(bb, &b));
118   PetscCall(VecGetArray(xx, &x));
119   t = a->solve_work;
120 
121   PetscCall(ISGetIndices(isrow, &rout));
122   r = rout;
123   PetscCall(ISGetIndices(iscol, &cout));
124   c = cout;
125 
126   /* copy b into temp work space according to permutation */
127   for (i = 0; i < n; i++) {
128     ii        = bs * i;
129     ic        = bs * c[i];
130     t[ii]     = b[ic];
131     t[ii + 1] = b[ic + 1];
132     t[ii + 2] = b[ic + 2];
133     t[ii + 3] = b[ic + 3];
134   }
135 
136   /* forward solve the U^T */
137   idx = 0;
138   for (i = 0; i < n; i++) {
139     v  = aa + bs2 * diag[i];
140     /* multiply by the inverse of the block diagonal */
141     x1 = t[idx];
142     x2 = t[1 + idx];
143     x3 = t[2 + idx];
144     x4 = t[3 + idx];
145     s1 = v[0] * x1 + v[1] * x2 + v[2] * x3 + v[3] * x4;
146     s2 = v[4] * x1 + v[5] * x2 + v[6] * x3 + v[7] * x4;
147     s3 = v[8] * x1 + v[9] * x2 + v[10] * x3 + v[11] * x4;
148     s4 = v[12] * x1 + v[13] * x2 + v[14] * x3 + v[15] * x4;
149     v -= bs2;
150 
151     vi = aj + diag[i] - 1;
152     nz = diag[i] - diag[i + 1] - 1;
153     for (j = 0; j > -nz; j--) {
154       oidx = bs * vi[j];
155       t[oidx] -= v[0] * s1 + v[1] * s2 + v[2] * s3 + v[3] * s4;
156       t[oidx + 1] -= v[4] * s1 + v[5] * s2 + v[6] * s3 + v[7] * s4;
157       t[oidx + 2] -= v[8] * s1 + v[9] * s2 + v[10] * s3 + v[11] * s4;
158       t[oidx + 3] -= v[12] * s1 + v[13] * s2 + v[14] * s3 + v[15] * s4;
159       v -= bs2;
160     }
161     t[idx]     = s1;
162     t[1 + idx] = s2;
163     t[2 + idx] = s3;
164     t[3 + idx] = s4;
165     idx += bs;
166   }
167   /* backward solve the L^T */
168   for (i = n - 1; i >= 0; i--) {
169     v   = aa + bs2 * ai[i];
170     vi  = aj + ai[i];
171     nz  = ai[i + 1] - ai[i];
172     idt = bs * i;
173     s1  = t[idt];
174     s2  = t[1 + idt];
175     s3  = t[2 + idt];
176     s4  = t[3 + idt];
177     for (j = 0; j < nz; j++) {
178       idx = bs * vi[j];
179       t[idx] -= v[0] * s1 + v[1] * s2 + v[2] * s3 + v[3] * s4;
180       t[idx + 1] -= v[4] * s1 + v[5] * s2 + v[6] * s3 + v[7] * s4;
181       t[idx + 2] -= v[8] * s1 + v[9] * s2 + v[10] * s3 + v[11] * s4;
182       t[idx + 3] -= v[12] * s1 + v[13] * s2 + v[14] * s3 + v[15] * s4;
183       v += bs2;
184     }
185   }
186 
187   /* copy t into x according to permutation */
188   for (i = 0; i < n; i++) {
189     ii        = bs * i;
190     ir        = bs * r[i];
191     x[ir]     = t[ii];
192     x[ir + 1] = t[ii + 1];
193     x[ir + 2] = t[ii + 2];
194     x[ir + 3] = t[ii + 3];
195   }
196 
197   PetscCall(ISRestoreIndices(isrow, &rout));
198   PetscCall(ISRestoreIndices(iscol, &cout));
199   PetscCall(VecRestoreArrayRead(bb, &b));
200   PetscCall(VecRestoreArray(xx, &x));
201   PetscCall(PetscLogFlops(2.0 * bs2 * (a->nz) - bs * A->cmap->n));
202   PetscFunctionReturn(0);
203 }
204