Actual source code: baijsolvtran3.c
1: #include <../src/mat/impls/baij/seq/baij.h>
2: #include <petsc/private/kernels/blockinvert.h>
4: PetscErrorCode MatSolveTranspose_SeqBAIJ_3_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, x1, x2, x3, *x, *t;
13: const PetscScalar *b;
15: PetscFunctionBegin;
16: PetscCall(VecGetArrayRead(bb, &b));
17: PetscCall(VecGetArray(xx, &x));
18: t = a->solve_work;
20: PetscCall(ISGetIndices(isrow, &rout));
21: r = rout;
22: PetscCall(ISGetIndices(iscol, &cout));
23: c = cout;
25: /* copy the b into temp work space according to permutation */
26: ii = 0;
27: for (i = 0; i < n; i++) {
28: ic = 3 * c[i];
29: t[ii] = b[ic];
30: t[ii + 1] = b[ic + 1];
31: t[ii + 2] = b[ic + 2];
32: ii += 3;
33: }
35: /* forward solve the U^T */
36: idx = 0;
37: for (i = 0; i < n; i++) {
38: v = aa + 9 * 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: s1 = v[0] * x1 + v[1] * x2 + v[2] * x3;
44: s2 = v[3] * x1 + v[4] * x2 + v[5] * x3;
45: s3 = v[6] * x1 + v[7] * x2 + v[8] * x3;
46: v += 9;
48: vi = aj + diag[i] + 1;
49: nz = ai[i + 1] - diag[i] - 1;
50: while (nz--) {
51: oidx = 3 * (*vi++);
52: t[oidx] -= v[0] * s1 + v[1] * s2 + v[2] * s3;
53: t[oidx + 1] -= v[3] * s1 + v[4] * s2 + v[5] * s3;
54: t[oidx + 2] -= v[6] * s1 + v[7] * s2 + v[8] * s3;
55: v += 9;
56: }
57: t[idx] = s1;
58: t[1 + idx] = s2;
59: t[2 + idx] = s3;
60: idx += 3;
61: }
62: /* backward solve the L^T */
63: for (i = n - 1; i >= 0; i--) {
64: v = aa + 9 * diag[i] - 9;
65: vi = aj + diag[i] - 1;
66: nz = diag[i] - ai[i];
67: idt = 3 * i;
68: s1 = t[idt];
69: s2 = t[1 + idt];
70: s3 = t[2 + idt];
71: while (nz--) {
72: idx = 3 * (*vi--);
73: t[idx] -= v[0] * s1 + v[1] * s2 + v[2] * s3;
74: t[idx + 1] -= v[3] * s1 + v[4] * s2 + v[5] * s3;
75: t[idx + 2] -= v[6] * s1 + v[7] * s2 + v[8] * s3;
76: v -= 9;
77: }
78: }
80: /* copy t into x according to permutation */
81: ii = 0;
82: for (i = 0; i < n; i++) {
83: ir = 3 * r[i];
84: x[ir] = t[ii];
85: x[ir + 1] = t[ii + 1];
86: x[ir + 2] = t[ii + 2];
87: ii += 3;
88: }
90: PetscCall(ISRestoreIndices(isrow, &rout));
91: PetscCall(ISRestoreIndices(iscol, &cout));
92: PetscCall(VecRestoreArrayRead(bb, &b));
93: PetscCall(VecRestoreArray(xx, &x));
94: PetscCall(PetscLogFlops(2.0 * 9 * (a->nz) - 3.0 * A->cmap->n));
95: PetscFunctionReturn(PETSC_SUCCESS);
96: }
98: PetscErrorCode MatSolveTranspose_SeqBAIJ_3(Mat A, Vec bb, Vec xx)
99: {
100: Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data;
101: IS iscol = a->col, isrow = a->row;
102: const PetscInt n = a->mbs, *vi, *ai = a->i, *aj = a->j, *diag = a->diag;
103: const PetscInt *r, *c, *rout, *cout;
104: PetscInt nz, idx, idt, j, i, oidx, ii, ic, ir;
105: const PetscInt bs = A->rmap->bs, bs2 = a->bs2;
106: const MatScalar *aa = a->a, *v;
107: PetscScalar s1, s2, s3, x1, x2, x3, *x, *t;
108: const PetscScalar *b;
110: PetscFunctionBegin;
111: PetscCall(VecGetArrayRead(bb, &b));
112: PetscCall(VecGetArray(xx, &x));
113: t = a->solve_work;
115: PetscCall(ISGetIndices(isrow, &rout));
116: r = rout;
117: PetscCall(ISGetIndices(iscol, &cout));
118: c = cout;
120: /* copy b into temp work space according to permutation */
121: for (i = 0; i < n; i++) {
122: ii = bs * i;
123: ic = bs * c[i];
124: t[ii] = b[ic];
125: t[ii + 1] = b[ic + 1];
126: t[ii + 2] = b[ic + 2];
127: }
129: /* forward solve the U^T */
130: idx = 0;
131: for (i = 0; i < n; i++) {
132: v = aa + bs2 * diag[i];
133: /* multiply by the inverse of the block diagonal */
134: x1 = t[idx];
135: x2 = t[1 + idx];
136: x3 = t[2 + idx];
137: s1 = v[0] * x1 + v[1] * x2 + v[2] * x3;
138: s2 = v[3] * x1 + v[4] * x2 + v[5] * x3;
139: s3 = v[6] * x1 + v[7] * x2 + v[8] * x3;
140: v -= bs2;
142: vi = aj + diag[i] - 1;
143: nz = diag[i] - diag[i + 1] - 1;
144: for (j = 0; j > -nz; j--) {
145: oidx = bs * vi[j];
146: t[oidx] -= v[0] * s1 + v[1] * s2 + v[2] * s3;
147: t[oidx + 1] -= v[3] * s1 + v[4] * s2 + v[5] * s3;
148: t[oidx + 2] -= v[6] * s1 + v[7] * s2 + v[8] * s3;
149: v -= bs2;
150: }
151: t[idx] = s1;
152: t[1 + idx] = s2;
153: t[2 + idx] = s3;
154: idx += bs;
155: }
156: /* backward solve the L^T */
157: for (i = n - 1; i >= 0; i--) {
158: v = aa + bs2 * ai[i];
159: vi = aj + ai[i];
160: nz = ai[i + 1] - ai[i];
161: idt = bs * i;
162: s1 = t[idt];
163: s2 = t[1 + idt];
164: s3 = t[2 + idt];
165: for (j = 0; j < nz; j++) {
166: idx = bs * vi[j];
167: t[idx] -= v[0] * s1 + v[1] * s2 + v[2] * s3;
168: t[idx + 1] -= v[3] * s1 + v[4] * s2 + v[5] * s3;
169: t[idx + 2] -= v[6] * s1 + v[7] * s2 + v[8] * s3;
170: v += bs2;
171: }
172: }
174: /* copy t into x according to permutation */
175: for (i = 0; i < n; i++) {
176: ii = bs * i;
177: ir = bs * r[i];
178: x[ir] = t[ii];
179: x[ir + 1] = t[ii + 1];
180: x[ir + 2] = t[ii + 2];
181: }
183: PetscCall(ISRestoreIndices(isrow, &rout));
184: PetscCall(ISRestoreIndices(iscol, &cout));
185: PetscCall(VecRestoreArrayRead(bb, &b));
186: PetscCall(VecRestoreArray(xx, &x));
187: PetscCall(PetscLogFlops(2.0 * bs2 * (a->nz) - bs * A->cmap->n));
188: PetscFunctionReturn(PETSC_SUCCESS);
189: }