1 #include <../src/mat/impls/baij/seq/baij.h>
2 #include <petsc/private/kernels/blockinvert.h>
3
4 /*
5 Special case where the matrix was ILU(0) factored in the natural
6 ordering. This eliminates the need for the column and row permutation.
7 */
MatSolve_SeqBAIJ_4_NaturalOrdering_inplace(Mat A,Vec bb,Vec xx)8 PetscErrorCode MatSolve_SeqBAIJ_4_NaturalOrdering_inplace(Mat A, Vec bb, Vec xx)
9 {
10 Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data;
11 PetscInt n = a->mbs;
12 const PetscInt *ai = a->i, *aj = a->j;
13 const PetscInt *diag = a->diag;
14 const MatScalar *aa = a->a;
15 PetscScalar *x;
16 const PetscScalar *b;
17
18 PetscFunctionBegin;
19 PetscCall(VecGetArrayRead(bb, &b));
20 PetscCall(VecGetArray(xx, &x));
21
22 #if defined(PETSC_USE_FORTRAN_KERNEL_SOLVEBAIJ)
23 {
24 static PetscScalar w[2000]; /* very BAD need to fix */
25 fortransolvebaij4_(&n, x, ai, aj, diag, aa, b, w);
26 }
27 #elif defined(PETSC_USE_FORTRAN_KERNEL_SOLVEBAIJUNROLL)
28 fortransolvebaij4unroll_(&n, x, ai, aj, diag, aa, b);
29 #else
30 {
31 PetscScalar s1, s2, s3, s4, x1, x2, x3, x4;
32 const MatScalar *v;
33 PetscInt jdx, idt, idx, nz, i, ai16;
34 const PetscInt *vi;
35
36 /* forward solve the lower triangular */
37 idx = 0;
38 x[0] = b[0];
39 x[1] = b[1];
40 x[2] = b[2];
41 x[3] = b[3];
42 for (i = 1; i < n; i++) {
43 v = aa + 16 * ai[i];
44 vi = aj + ai[i];
45 nz = diag[i] - ai[i];
46 idx += 4;
47 s1 = b[idx];
48 s2 = b[1 + idx];
49 s3 = b[2 + idx];
50 s4 = b[3 + idx];
51 while (nz--) {
52 jdx = 4 * (*vi++);
53 x1 = x[jdx];
54 x2 = x[1 + jdx];
55 x3 = x[2 + jdx];
56 x4 = x[3 + jdx];
57 s1 -= v[0] * x1 + v[4] * x2 + v[8] * x3 + v[12] * x4;
58 s2 -= v[1] * x1 + v[5] * x2 + v[9] * x3 + v[13] * x4;
59 s3 -= v[2] * x1 + v[6] * x2 + v[10] * x3 + v[14] * x4;
60 s4 -= v[3] * x1 + v[7] * x2 + v[11] * x3 + v[15] * x4;
61 v += 16;
62 }
63 x[idx] = s1;
64 x[1 + idx] = s2;
65 x[2 + idx] = s3;
66 x[3 + idx] = s4;
67 }
68 /* backward solve the upper triangular */
69 idt = 4 * (n - 1);
70 for (i = n - 1; i >= 0; i--) {
71 ai16 = 16 * diag[i];
72 v = aa + ai16 + 16;
73 vi = aj + diag[i] + 1;
74 nz = ai[i + 1] - diag[i] - 1;
75 s1 = x[idt];
76 s2 = x[1 + idt];
77 s3 = x[2 + idt];
78 s4 = x[3 + idt];
79 while (nz--) {
80 idx = 4 * (*vi++);
81 x1 = x[idx];
82 x2 = x[1 + idx];
83 x3 = x[2 + idx];
84 x4 = x[3 + idx];
85 s1 -= v[0] * x1 + v[4] * x2 + v[8] * x3 + v[12] * x4;
86 s2 -= v[1] * x1 + v[5] * x2 + v[9] * x3 + v[13] * x4;
87 s3 -= v[2] * x1 + v[6] * x2 + v[10] * x3 + v[14] * x4;
88 s4 -= v[3] * x1 + v[7] * x2 + v[11] * x3 + v[15] * x4;
89 v += 16;
90 }
91 v = aa + ai16;
92 x[idt] = v[0] * s1 + v[4] * s2 + v[8] * s3 + v[12] * s4;
93 x[1 + idt] = v[1] * s1 + v[5] * s2 + v[9] * s3 + v[13] * s4;
94 x[2 + idt] = v[2] * s1 + v[6] * s2 + v[10] * s3 + v[14] * s4;
95 x[3 + idt] = v[3] * s1 + v[7] * s2 + v[11] * s3 + v[15] * s4;
96 idt -= 4;
97 }
98 }
99 #endif
100
101 PetscCall(VecRestoreArrayRead(bb, &b));
102 PetscCall(VecRestoreArray(xx, &x));
103 PetscCall(PetscLogFlops(2.0 * 16 * (a->nz) - 4.0 * A->cmap->n));
104 PetscFunctionReturn(PETSC_SUCCESS);
105 }
106
MatSolve_SeqBAIJ_4_NaturalOrdering(Mat A,Vec bb,Vec xx)107 PetscErrorCode MatSolve_SeqBAIJ_4_NaturalOrdering(Mat A, Vec bb, Vec xx)
108 {
109 Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data;
110 const PetscInt n = a->mbs, *vi, *ai = a->i, *aj = a->j, *adiag = a->diag;
111 PetscInt i, k, nz, idx, jdx, idt;
112 const PetscInt bs = A->rmap->bs, bs2 = a->bs2;
113 const MatScalar *aa = a->a, *v;
114 PetscScalar *x;
115 const PetscScalar *b;
116 PetscScalar s1, s2, s3, s4, x1, x2, x3, x4;
117
118 PetscFunctionBegin;
119 PetscCall(VecGetArrayRead(bb, &b));
120 PetscCall(VecGetArray(xx, &x));
121 /* forward solve the lower triangular */
122 idx = 0;
123 x[0] = b[idx];
124 x[1] = b[1 + idx];
125 x[2] = b[2 + idx];
126 x[3] = b[3 + idx];
127 for (i = 1; i < n; i++) {
128 v = aa + bs2 * ai[i];
129 vi = aj + ai[i];
130 nz = ai[i + 1] - ai[i];
131 idx = bs * i;
132 s1 = b[idx];
133 s2 = b[1 + idx];
134 s3 = b[2 + idx];
135 s4 = b[3 + idx];
136 for (k = 0; k < nz; k++) {
137 jdx = bs * vi[k];
138 x1 = x[jdx];
139 x2 = x[1 + jdx];
140 x3 = x[2 + jdx];
141 x4 = x[3 + jdx];
142 s1 -= v[0] * x1 + v[4] * x2 + v[8] * x3 + v[12] * x4;
143 s2 -= v[1] * x1 + v[5] * x2 + v[9] * x3 + v[13] * x4;
144 s3 -= v[2] * x1 + v[6] * x2 + v[10] * x3 + v[14] * x4;
145 s4 -= v[3] * x1 + v[7] * x2 + v[11] * x3 + v[15] * x4;
146
147 v += bs2;
148 }
149
150 x[idx] = s1;
151 x[1 + idx] = s2;
152 x[2 + idx] = s3;
153 x[3 + idx] = s4;
154 }
155
156 /* backward solve the upper triangular */
157 for (i = n - 1; i >= 0; i--) {
158 v = aa + bs2 * (adiag[i + 1] + 1);
159 vi = aj + adiag[i + 1] + 1;
160 nz = adiag[i] - adiag[i + 1] - 1;
161 idt = bs * i;
162 s1 = x[idt];
163 s2 = x[1 + idt];
164 s3 = x[2 + idt];
165 s4 = x[3 + idt];
166
167 for (k = 0; k < nz; k++) {
168 idx = bs * vi[k];
169 x1 = x[idx];
170 x2 = x[1 + idx];
171 x3 = x[2 + idx];
172 x4 = x[3 + idx];
173 s1 -= v[0] * x1 + v[4] * x2 + v[8] * x3 + v[12] * x4;
174 s2 -= v[1] * x1 + v[5] * x2 + v[9] * x3 + v[13] * x4;
175 s3 -= v[2] * x1 + v[6] * x2 + v[10] * x3 + v[14] * x4;
176 s4 -= v[3] * x1 + v[7] * x2 + v[11] * x3 + v[15] * x4;
177
178 v += bs2;
179 }
180 /* x = inv_diagonal*x */
181 x[idt] = v[0] * s1 + v[4] * s2 + v[8] * s3 + v[12] * s4;
182 x[1 + idt] = v[1] * s1 + v[5] * s2 + v[9] * s3 + v[13] * s4;
183 x[2 + idt] = v[2] * s1 + v[6] * s2 + v[10] * s3 + v[14] * s4;
184 x[3 + idt] = v[3] * s1 + v[7] * s2 + v[11] * s3 + v[15] * s4;
185 }
186
187 PetscCall(VecRestoreArrayRead(bb, &b));
188 PetscCall(VecRestoreArray(xx, &x));
189 PetscCall(PetscLogFlops(2.0 * bs2 * (a->nz) - bs * A->cmap->n));
190 PetscFunctionReturn(PETSC_SUCCESS);
191 }
192