xref: /petsc/src/mat/impls/baij/seq/baijsolvnat7.c (revision 58d68138c660dfb4e9f5b03334792cd4f2ffd7cc)
1 #include <../src/mat/impls/baij/seq/baij.h>
2 #include <petsc/private/kernels/blockinvert.h>
3 
4 PetscErrorCode MatSolve_SeqBAIJ_7_NaturalOrdering_inplace(Mat A, Vec bb, Vec xx) {
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, jdx;
8   const MatScalar   *aa = a->a, *v;
9   PetscScalar       *x, s1, s2, s3, s4, s5, s6, s7, x1, x2, x3, x4, x5, x6, x7;
10   const PetscScalar *b;
11 
12   PetscFunctionBegin;
13   PetscCall(VecGetArrayRead(bb, &b));
14   PetscCall(VecGetArray(xx, &x));
15   /* forward solve the lower triangular */
16   idx  = 0;
17   x[0] = b[idx];
18   x[1] = b[1 + idx];
19   x[2] = b[2 + idx];
20   x[3] = b[3 + idx];
21   x[4] = b[4 + idx];
22   x[5] = b[5 + idx];
23   x[6] = b[6 + idx];
24   for (i = 1; i < n; i++) {
25     v   = aa + 49 * ai[i];
26     vi  = aj + ai[i];
27     nz  = diag[i] - ai[i];
28     idx = 7 * i;
29     s1  = b[idx];
30     s2  = b[1 + idx];
31     s3  = b[2 + idx];
32     s4  = b[3 + idx];
33     s5  = b[4 + idx];
34     s6  = b[5 + idx];
35     s7  = b[6 + idx];
36     while (nz--) {
37       jdx = 7 * (*vi++);
38       x1  = x[jdx];
39       x2  = x[1 + jdx];
40       x3  = x[2 + jdx];
41       x4  = x[3 + jdx];
42       x5  = x[4 + jdx];
43       x6  = x[5 + jdx];
44       x7  = x[6 + jdx];
45       s1 -= v[0] * x1 + v[7] * x2 + v[14] * x3 + v[21] * x4 + v[28] * x5 + v[35] * x6 + v[42] * x7;
46       s2 -= v[1] * x1 + v[8] * x2 + v[15] * x3 + v[22] * x4 + v[29] * x5 + v[36] * x6 + v[43] * x7;
47       s3 -= v[2] * x1 + v[9] * x2 + v[16] * x3 + v[23] * x4 + v[30] * x5 + v[37] * x6 + v[44] * x7;
48       s4 -= v[3] * x1 + v[10] * x2 + v[17] * x3 + v[24] * x4 + v[31] * x5 + v[38] * x6 + v[45] * x7;
49       s5 -= v[4] * x1 + v[11] * x2 + v[18] * x3 + v[25] * x4 + v[32] * x5 + v[39] * x6 + v[46] * x7;
50       s6 -= v[5] * x1 + v[12] * x2 + v[19] * x3 + v[26] * x4 + v[33] * x5 + v[40] * x6 + v[47] * x7;
51       s7 -= v[6] * x1 + v[13] * x2 + v[20] * x3 + v[27] * x4 + v[34] * x5 + v[41] * x6 + v[48] * x7;
52       v += 49;
53     }
54     x[idx]     = s1;
55     x[1 + idx] = s2;
56     x[2 + idx] = s3;
57     x[3 + idx] = s4;
58     x[4 + idx] = s5;
59     x[5 + idx] = s6;
60     x[6 + idx] = s7;
61   }
62   /* backward solve the upper triangular */
63   for (i = n - 1; i >= 0; i--) {
64     v   = aa + 49 * diag[i] + 49;
65     vi  = aj + diag[i] + 1;
66     nz  = ai[i + 1] - diag[i] - 1;
67     idt = 7 * i;
68     s1  = x[idt];
69     s2  = x[1 + idt];
70     s3  = x[2 + idt];
71     s4  = x[3 + idt];
72     s5  = x[4 + idt];
73     s6  = x[5 + idt];
74     s7  = x[6 + idt];
75     while (nz--) {
76       idx = 7 * (*vi++);
77       x1  = x[idx];
78       x2  = x[1 + idx];
79       x3  = x[2 + idx];
80       x4  = x[3 + idx];
81       x5  = x[4 + idx];
82       x6  = x[5 + idx];
83       x7  = x[6 + idx];
84       s1 -= v[0] * x1 + v[7] * x2 + v[14] * x3 + v[21] * x4 + v[28] * x5 + v[35] * x6 + v[42] * x7;
85       s2 -= v[1] * x1 + v[8] * x2 + v[15] * x3 + v[22] * x4 + v[29] * x5 + v[36] * x6 + v[43] * x7;
86       s3 -= v[2] * x1 + v[9] * x2 + v[16] * x3 + v[23] * x4 + v[30] * x5 + v[37] * x6 + v[44] * x7;
87       s4 -= v[3] * x1 + v[10] * x2 + v[17] * x3 + v[24] * x4 + v[31] * x5 + v[38] * x6 + v[45] * x7;
88       s5 -= v[4] * x1 + v[11] * x2 + v[18] * x3 + v[25] * x4 + v[32] * x5 + v[39] * x6 + v[46] * x7;
89       s6 -= v[5] * x1 + v[12] * x2 + v[19] * x3 + v[26] * x4 + v[33] * x5 + v[40] * x6 + v[47] * x7;
90       s7 -= v[6] * x1 + v[13] * x2 + v[20] * x3 + v[27] * x4 + v[34] * x5 + v[41] * x6 + v[48] * x7;
91       v += 49;
92     }
93     v          = aa + 49 * diag[i];
94     x[idt]     = v[0] * s1 + v[7] * s2 + v[14] * s3 + v[21] * s4 + v[28] * s5 + v[35] * s6 + v[42] * s7;
95     x[1 + idt] = v[1] * s1 + v[8] * s2 + v[15] * s3 + v[22] * s4 + v[29] * s5 + v[36] * s6 + v[43] * s7;
96     x[2 + idt] = v[2] * s1 + v[9] * s2 + v[16] * s3 + v[23] * s4 + v[30] * s5 + v[37] * s6 + v[44] * s7;
97     x[3 + idt] = v[3] * s1 + v[10] * s2 + v[17] * s3 + v[24] * s4 + v[31] * s5 + v[38] * s6 + v[45] * s7;
98     x[4 + idt] = v[4] * s1 + v[11] * s2 + v[18] * s3 + v[25] * s4 + v[32] * s5 + v[39] * s6 + v[46] * s7;
99     x[5 + idt] = v[5] * s1 + v[12] * s2 + v[19] * s3 + v[26] * s4 + v[33] * s5 + v[40] * s6 + v[47] * s7;
100     x[6 + idt] = v[6] * s1 + v[13] * s2 + v[20] * s3 + v[27] * s4 + v[34] * s5 + v[41] * s6 + v[48] * s7;
101   }
102 
103   PetscCall(VecRestoreArrayRead(bb, &b));
104   PetscCall(VecRestoreArray(xx, &x));
105   PetscCall(PetscLogFlops(2.0 * 36 * (a->nz) - 6.0 * A->cmap->n));
106   PetscFunctionReturn(0);
107 }
108 
109 PetscErrorCode MatSolve_SeqBAIJ_7_NaturalOrdering(Mat A, Vec bb, Vec xx) {
110   Mat_SeqBAIJ       *a = (Mat_SeqBAIJ *)A->data;
111   const PetscInt     n = a->mbs, *vi, *ai = a->i, *aj = a->j, *adiag = a->diag;
112   PetscInt           i, k, nz, idx, jdx, idt;
113   const PetscInt     bs = A->rmap->bs, bs2 = a->bs2;
114   const MatScalar   *aa = a->a, *v;
115   PetscScalar       *x;
116   const PetscScalar *b;
117   PetscScalar        s1, s2, s3, s4, s5, s6, s7, x1, x2, x3, x4, x5, x6, x7;
118 
119   PetscFunctionBegin;
120   PetscCall(VecGetArrayRead(bb, &b));
121   PetscCall(VecGetArray(xx, &x));
122   /* forward solve the lower triangular */
123   idx  = 0;
124   x[0] = b[idx];
125   x[1] = b[1 + idx];
126   x[2] = b[2 + idx];
127   x[3] = b[3 + idx];
128   x[4] = b[4 + idx];
129   x[5] = b[5 + idx];
130   x[6] = b[6 + idx];
131   for (i = 1; i < n; i++) {
132     v   = aa + bs2 * ai[i];
133     vi  = aj + ai[i];
134     nz  = ai[i + 1] - ai[i];
135     idx = bs * i;
136     s1  = b[idx];
137     s2  = b[1 + idx];
138     s3  = b[2 + idx];
139     s4  = b[3 + idx];
140     s5  = b[4 + idx];
141     s6  = b[5 + idx];
142     s7  = b[6 + idx];
143     for (k = 0; k < nz; k++) {
144       jdx = bs * vi[k];
145       x1  = x[jdx];
146       x2  = x[1 + jdx];
147       x3  = x[2 + jdx];
148       x4  = x[3 + jdx];
149       x5  = x[4 + jdx];
150       x6  = x[5 + jdx];
151       x7  = x[6 + jdx];
152       s1 -= v[0] * x1 + v[7] * x2 + v[14] * x3 + v[21] * x4 + v[28] * x5 + v[35] * x6 + v[42] * x7;
153       s2 -= v[1] * x1 + v[8] * x2 + v[15] * x3 + v[22] * x4 + v[29] * x5 + v[36] * x6 + v[43] * x7;
154       s3 -= v[2] * x1 + v[9] * x2 + v[16] * x3 + v[23] * x4 + v[30] * x5 + v[37] * x6 + v[44] * x7;
155       s4 -= v[3] * x1 + v[10] * x2 + v[17] * x3 + v[24] * x4 + v[31] * x5 + v[38] * x6 + v[45] * x7;
156       s5 -= v[4] * x1 + v[11] * x2 + v[18] * x3 + v[25] * x4 + v[32] * x5 + v[39] * x6 + v[46] * x7;
157       s6 -= v[5] * x1 + v[12] * x2 + v[19] * x3 + v[26] * x4 + v[33] * x5 + v[40] * x6 + v[47] * x7;
158       s7 -= v[6] * x1 + v[13] * x2 + v[20] * x3 + v[27] * x4 + v[34] * x5 + v[41] * x6 + v[48] * x7;
159       v += bs2;
160     }
161 
162     x[idx]     = s1;
163     x[1 + idx] = s2;
164     x[2 + idx] = s3;
165     x[3 + idx] = s4;
166     x[4 + idx] = s5;
167     x[5 + idx] = s6;
168     x[6 + idx] = s7;
169   }
170 
171   /* backward solve the upper triangular */
172   for (i = n - 1; i >= 0; i--) {
173     v   = aa + bs2 * (adiag[i + 1] + 1);
174     vi  = aj + adiag[i + 1] + 1;
175     nz  = adiag[i] - adiag[i + 1] - 1;
176     idt = bs * i;
177     s1  = x[idt];
178     s2  = x[1 + idt];
179     s3  = x[2 + idt];
180     s4  = x[3 + idt];
181     s5  = x[4 + idt];
182     s6  = x[5 + idt];
183     s7  = x[6 + idt];
184     for (k = 0; k < nz; k++) {
185       idx = bs * vi[k];
186       x1  = x[idx];
187       x2  = x[1 + idx];
188       x3  = x[2 + idx];
189       x4  = x[3 + idx];
190       x5  = x[4 + idx];
191       x6  = x[5 + idx];
192       x7  = x[6 + idx];
193       s1 -= v[0] * x1 + v[7] * x2 + v[14] * x3 + v[21] * x4 + v[28] * x5 + v[35] * x6 + v[42] * x7;
194       s2 -= v[1] * x1 + v[8] * x2 + v[15] * x3 + v[22] * x4 + v[29] * x5 + v[36] * x6 + v[43] * x7;
195       s3 -= v[2] * x1 + v[9] * x2 + v[16] * x3 + v[23] * x4 + v[30] * x5 + v[37] * x6 + v[44] * x7;
196       s4 -= v[3] * x1 + v[10] * x2 + v[17] * x3 + v[24] * x4 + v[31] * x5 + v[38] * x6 + v[45] * x7;
197       s5 -= v[4] * x1 + v[11] * x2 + v[18] * x3 + v[25] * x4 + v[32] * x5 + v[39] * x6 + v[46] * x7;
198       s6 -= v[5] * x1 + v[12] * x2 + v[19] * x3 + v[26] * x4 + v[33] * x5 + v[40] * x6 + v[47] * x7;
199       s7 -= v[6] * x1 + v[13] * x2 + v[20] * x3 + v[27] * x4 + v[34] * x5 + v[41] * x6 + v[48] * x7;
200       v += bs2;
201     }
202     /* x = inv_diagonal*x */
203     x[idt]     = v[0] * s1 + v[7] * s2 + v[14] * s3 + v[21] * s4 + v[28] * s5 + v[35] * s6 + v[42] * s7;
204     x[1 + idt] = v[1] * s1 + v[8] * s2 + v[15] * s3 + v[22] * s4 + v[29] * s5 + v[36] * s6 + v[43] * s7;
205     x[2 + idt] = v[2] * s1 + v[9] * s2 + v[16] * s3 + v[23] * s4 + v[30] * s5 + v[37] * s6 + v[44] * s7;
206     x[3 + idt] = v[3] * s1 + v[10] * s2 + v[17] * s3 + v[24] * s4 + v[31] * s5 + v[38] * s6 + v[45] * s7;
207     x[4 + idt] = v[4] * s1 + v[11] * s2 + v[18] * s3 + v[25] * s4 + v[32] * s5 + v[39] * s6 + v[46] * s7;
208     x[5 + idt] = v[5] * s1 + v[12] * s2 + v[19] * s3 + v[26] * s4 + v[33] * s5 + v[40] * s6 + v[47] * s7;
209     x[6 + idt] = v[6] * s1 + v[13] * s2 + v[20] * s3 + v[27] * s4 + v[34] * s5 + v[41] * s6 + v[48] * s7;
210   }
211 
212   PetscCall(VecRestoreArrayRead(bb, &b));
213   PetscCall(VecRestoreArray(xx, &x));
214   PetscCall(PetscLogFlops(2.0 * bs2 * (a->nz) - bs * A->cmap->n));
215   PetscFunctionReturn(0);
216 }
217