Actual source code: baijsolvtrannat4.c
1: #include <../src/mat/impls/baij/seq/baij.h>
3: PetscErrorCode MatSolveTranspose_SeqBAIJ_4_NaturalOrdering_inplace(Mat A, Vec bb, Vec xx)
4: {
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, oidx;
8: const MatScalar *aa = a->a, *v;
9: PetscScalar s1, s2, s3, s4, x1, x2, x3, x4, *x;
11: PetscFunctionBegin;
12: PetscCall(VecCopy(bb, xx));
13: PetscCall(VecGetArray(xx, &x));
15: /* forward solve the U^T */
16: idx = 0;
17: for (i = 0; i < n; i++) {
18: v = aa + 16 * diag[i];
19: /* multiply by the inverse of the block diagonal */
20: x1 = x[idx];
21: x2 = x[1 + idx];
22: x3 = x[2 + idx];
23: x4 = x[3 + idx];
24: s1 = v[0] * x1 + v[1] * x2 + v[2] * x3 + v[3] * x4;
25: s2 = v[4] * x1 + v[5] * x2 + v[6] * x3 + v[7] * x4;
26: s3 = v[8] * x1 + v[9] * x2 + v[10] * x3 + v[11] * x4;
27: s4 = v[12] * x1 + v[13] * x2 + v[14] * x3 + v[15] * x4;
28: v += 16;
30: vi = aj + diag[i] + 1;
31: nz = ai[i + 1] - diag[i] - 1;
32: while (nz--) {
33: oidx = 4 * (*vi++);
34: x[oidx] -= v[0] * s1 + v[1] * s2 + v[2] * s3 + v[3] * s4;
35: x[oidx + 1] -= v[4] * s1 + v[5] * s2 + v[6] * s3 + v[7] * s4;
36: x[oidx + 2] -= v[8] * s1 + v[9] * s2 + v[10] * s3 + v[11] * s4;
37: x[oidx + 3] -= v[12] * s1 + v[13] * s2 + v[14] * s3 + v[15] * s4;
38: v += 16;
39: }
40: x[idx] = s1;
41: x[1 + idx] = s2;
42: x[2 + idx] = s3;
43: x[3 + idx] = s4;
44: idx += 4;
45: }
46: /* backward solve the L^T */
47: for (i = n - 1; i >= 0; i--) {
48: v = aa + 16 * diag[i] - 16;
49: vi = aj + diag[i] - 1;
50: nz = diag[i] - ai[i];
51: idt = 4 * i;
52: s1 = x[idt];
53: s2 = x[1 + idt];
54: s3 = x[2 + idt];
55: s4 = x[3 + idt];
56: while (nz--) {
57: idx = 4 * (*vi--);
58: x[idx] -= v[0] * s1 + v[1] * s2 + v[2] * s3 + v[3] * s4;
59: x[idx + 1] -= v[4] * s1 + v[5] * s2 + v[6] * s3 + v[7] * s4;
60: x[idx + 2] -= v[8] * s1 + v[9] * s2 + v[10] * s3 + v[11] * s4;
61: x[idx + 3] -= v[12] * s1 + v[13] * s2 + v[14] * s3 + v[15] * s4;
62: v -= 16;
63: }
64: }
65: PetscCall(VecRestoreArray(xx, &x));
66: PetscCall(PetscLogFlops(2.0 * 16 * (a->nz) - 4.0 * A->cmap->n));
67: PetscFunctionReturn(PETSC_SUCCESS);
68: }
70: PetscErrorCode MatSolveTranspose_SeqBAIJ_4_NaturalOrdering(Mat A, Vec bb, Vec xx)
71: {
72: Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data;
73: const PetscInt n = a->mbs, *vi, *ai = a->i, *aj = a->j, *diag = a->diag;
74: PetscInt nz, idx, idt, j, i, oidx;
75: const PetscInt bs = A->rmap->bs, bs2 = a->bs2;
76: const MatScalar *aa = a->a, *v;
77: PetscScalar s1, s2, s3, s4, x1, x2, x3, x4, *x;
79: PetscFunctionBegin;
80: PetscCall(VecCopy(bb, xx));
81: PetscCall(VecGetArray(xx, &x));
83: /* forward solve the U^T */
84: idx = 0;
85: for (i = 0; i < n; i++) {
86: v = aa + bs2 * diag[i];
87: /* multiply by the inverse of the block diagonal */
88: x1 = x[idx];
89: x2 = x[1 + idx];
90: x3 = x[2 + idx];
91: x4 = x[3 + idx];
92: s1 = v[0] * x1 + v[1] * x2 + v[2] * x3 + v[3] * x4;
93: s2 = v[4] * x1 + v[5] * x2 + v[6] * x3 + v[7] * x4;
94: s3 = v[8] * x1 + v[9] * x2 + v[10] * x3 + v[11] * x4;
95: s4 = v[12] * x1 + v[13] * x2 + v[14] * x3 + v[15] * x4;
96: v -= bs2;
98: vi = aj + diag[i] - 1;
99: nz = diag[i] - diag[i + 1] - 1;
100: for (j = 0; j > -nz; j--) {
101: oidx = bs * vi[j];
102: x[oidx] -= v[0] * s1 + v[1] * s2 + v[2] * s3 + v[3] * s4;
103: x[oidx + 1] -= v[4] * s1 + v[5] * s2 + v[6] * s3 + v[7] * s4;
104: x[oidx + 2] -= v[8] * s1 + v[9] * s2 + v[10] * s3 + v[11] * s4;
105: x[oidx + 3] -= v[12] * s1 + v[13] * s2 + v[14] * s3 + v[15] * s4;
106: v -= bs2;
107: }
108: x[idx] = s1;
109: x[1 + idx] = s2;
110: x[2 + idx] = s3;
111: x[3 + idx] = s4;
112: idx += bs;
113: }
114: /* backward solve the L^T */
115: for (i = n - 1; i >= 0; i--) {
116: v = aa + bs2 * ai[i];
117: vi = aj + ai[i];
118: nz = ai[i + 1] - ai[i];
119: idt = bs * i;
120: s1 = x[idt];
121: s2 = x[1 + idt];
122: s3 = x[2 + idt];
123: s4 = x[3 + idt];
124: for (j = 0; j < nz; j++) {
125: idx = bs * vi[j];
126: x[idx] -= v[0] * s1 + v[1] * s2 + v[2] * s3 + v[3] * s4;
127: x[idx + 1] -= v[4] * s1 + v[5] * s2 + v[6] * s3 + v[7] * s4;
128: x[idx + 2] -= v[8] * s1 + v[9] * s2 + v[10] * s3 + v[11] * s4;
129: x[idx + 3] -= v[12] * s1 + v[13] * s2 + v[14] * s3 + v[15] * s4;
130: v += bs2;
131: }
132: }
133: PetscCall(VecRestoreArray(xx, &x));
134: PetscCall(PetscLogFlops(2.0 * bs2 * (a->nz) - bs * A->cmap->n));
135: PetscFunctionReturn(PETSC_SUCCESS);
136: }