Actual source code: baijsolvtran4.c
1: #include <../src/mat/impls/baij/seq/baij.h>
2: #include <petsc/private/kernels/blockinvert.h>
4: PetscErrorCode MatSolveTranspose_SeqBAIJ_4_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, s4, x1, x2, x3, x4, *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 = 4 * c[i];
29: t[ii] = b[ic];
30: t[ii + 1] = b[ic + 1];
31: t[ii + 2] = b[ic + 2];
32: t[ii + 3] = b[ic + 3];
33: ii += 4;
34: }
36: /* forward solve the U^T */
37: idx = 0;
38: for (i = 0; i < n; i++) {
39: v = aa + 16 * diag[i];
40: /* multiply by the inverse of the block diagonal */
41: x1 = t[idx];
42: x2 = t[1 + idx];
43: x3 = t[2 + idx];
44: x4 = t[3 + idx];
45: s1 = v[0] * x1 + v[1] * x2 + v[2] * x3 + v[3] * x4;
46: s2 = v[4] * x1 + v[5] * x2 + v[6] * x3 + v[7] * x4;
47: s3 = v[8] * x1 + v[9] * x2 + v[10] * x3 + v[11] * x4;
48: s4 = v[12] * x1 + v[13] * x2 + v[14] * x3 + v[15] * x4;
49: v += 16;
51: vi = aj + diag[i] + 1;
52: nz = ai[i + 1] - diag[i] - 1;
53: while (nz--) {
54: oidx = 4 * (*vi++);
55: t[oidx] -= v[0] * s1 + v[1] * s2 + v[2] * s3 + v[3] * s4;
56: t[oidx + 1] -= v[4] * s1 + v[5] * s2 + v[6] * s3 + v[7] * s4;
57: t[oidx + 2] -= v[8] * s1 + v[9] * s2 + v[10] * s3 + v[11] * s4;
58: t[oidx + 3] -= v[12] * s1 + v[13] * s2 + v[14] * s3 + v[15] * s4;
59: v += 16;
60: }
61: t[idx] = s1;
62: t[1 + idx] = s2;
63: t[2 + idx] = s3;
64: t[3 + idx] = s4;
65: idx += 4;
66: }
67: /* backward solve the L^T */
68: for (i = n - 1; i >= 0; i--) {
69: v = aa + 16 * diag[i] - 16;
70: vi = aj + diag[i] - 1;
71: nz = diag[i] - ai[i];
72: idt = 4 * i;
73: s1 = t[idt];
74: s2 = t[1 + idt];
75: s3 = t[2 + idt];
76: s4 = t[3 + idt];
77: while (nz--) {
78: idx = 4 * (*vi--);
79: t[idx] -= v[0] * s1 + v[1] * s2 + v[2] * s3 + v[3] * s4;
80: t[idx + 1] -= v[4] * s1 + v[5] * s2 + v[6] * s3 + v[7] * s4;
81: t[idx + 2] -= v[8] * s1 + v[9] * s2 + v[10] * s3 + v[11] * s4;
82: t[idx + 3] -= v[12] * s1 + v[13] * s2 + v[14] * s3 + v[15] * s4;
83: v -= 16;
84: }
85: }
87: /* copy t into x according to permutation */
88: ii = 0;
89: for (i = 0; i < n; i++) {
90: ir = 4 * r[i];
91: x[ir] = t[ii];
92: x[ir + 1] = t[ii + 1];
93: x[ir + 2] = t[ii + 2];
94: x[ir + 3] = t[ii + 3];
95: ii += 4;
96: }
98: PetscCall(ISRestoreIndices(isrow, &rout));
99: PetscCall(ISRestoreIndices(iscol, &cout));
100: PetscCall(VecRestoreArrayRead(bb, &b));
101: PetscCall(VecRestoreArray(xx, &x));
102: PetscCall(PetscLogFlops(2.0 * 16 * (a->nz) - 4.0 * A->cmap->n));
103: PetscFunctionReturn(PETSC_SUCCESS);
104: }
106: PetscErrorCode MatSolveTranspose_SeqBAIJ_4(Mat A, Vec bb, Vec xx)
107: {
108: Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data;
109: IS iscol = a->col, isrow = a->row;
110: const PetscInt n = a->mbs, *vi, *ai = a->i, *aj = a->j, *diag = a->diag;
111: const PetscInt *r, *c, *rout, *cout;
112: PetscInt nz, idx, idt, j, i, oidx, ii, ic, ir;
113: const PetscInt bs = A->rmap->bs, bs2 = a->bs2;
114: const MatScalar *aa = a->a, *v;
115: PetscScalar s1, s2, s3, s4, x1, x2, x3, x4, *x, *t;
116: const PetscScalar *b;
118: PetscFunctionBegin;
119: PetscCall(VecGetArrayRead(bb, &b));
120: PetscCall(VecGetArray(xx, &x));
121: t = a->solve_work;
123: PetscCall(ISGetIndices(isrow, &rout));
124: r = rout;
125: PetscCall(ISGetIndices(iscol, &cout));
126: c = cout;
128: /* copy b into temp work space according to permutation */
129: for (i = 0; i < n; i++) {
130: ii = bs * i;
131: ic = bs * c[i];
132: t[ii] = b[ic];
133: t[ii + 1] = b[ic + 1];
134: t[ii + 2] = b[ic + 2];
135: t[ii + 3] = b[ic + 3];
136: }
138: /* forward solve the U^T */
139: idx = 0;
140: for (i = 0; i < n; i++) {
141: v = aa + bs2 * diag[i];
142: /* multiply by the inverse of the block diagonal */
143: x1 = t[idx];
144: x2 = t[1 + idx];
145: x3 = t[2 + idx];
146: x4 = t[3 + idx];
147: s1 = v[0] * x1 + v[1] * x2 + v[2] * x3 + v[3] * x4;
148: s2 = v[4] * x1 + v[5] * x2 + v[6] * x3 + v[7] * x4;
149: s3 = v[8] * x1 + v[9] * x2 + v[10] * x3 + v[11] * x4;
150: s4 = v[12] * x1 + v[13] * x2 + v[14] * x3 + v[15] * x4;
151: v -= bs2;
153: vi = aj + diag[i] - 1;
154: nz = diag[i] - diag[i + 1] - 1;
155: for (j = 0; j > -nz; j--) {
156: oidx = bs * vi[j];
157: t[oidx] -= v[0] * s1 + v[1] * s2 + v[2] * s3 + v[3] * s4;
158: t[oidx + 1] -= v[4] * s1 + v[5] * s2 + v[6] * s3 + v[7] * s4;
159: t[oidx + 2] -= v[8] * s1 + v[9] * s2 + v[10] * s3 + v[11] * s4;
160: t[oidx + 3] -= v[12] * s1 + v[13] * s2 + v[14] * s3 + v[15] * s4;
161: v -= bs2;
162: }
163: t[idx] = s1;
164: t[1 + idx] = s2;
165: t[2 + idx] = s3;
166: t[3 + idx] = s4;
167: idx += bs;
168: }
169: /* backward solve the L^T */
170: for (i = n - 1; i >= 0; i--) {
171: v = aa + bs2 * ai[i];
172: vi = aj + ai[i];
173: nz = ai[i + 1] - ai[i];
174: idt = bs * i;
175: s1 = t[idt];
176: s2 = t[1 + idt];
177: s3 = t[2 + idt];
178: s4 = t[3 + idt];
179: for (j = 0; j < nz; j++) {
180: idx = bs * vi[j];
181: t[idx] -= v[0] * s1 + v[1] * s2 + v[2] * s3 + v[3] * s4;
182: t[idx + 1] -= v[4] * s1 + v[5] * s2 + v[6] * s3 + v[7] * s4;
183: t[idx + 2] -= v[8] * s1 + v[9] * s2 + v[10] * s3 + v[11] * s4;
184: t[idx + 3] -= v[12] * s1 + v[13] * s2 + v[14] * s3 + v[15] * s4;
185: v += bs2;
186: }
187: }
189: /* copy t into x according to permutation */
190: for (i = 0; i < n; i++) {
191: ii = bs * i;
192: ir = bs * r[i];
193: x[ir] = t[ii];
194: x[ir + 1] = t[ii + 1];
195: x[ir + 2] = t[ii + 2];
196: x[ir + 3] = t[ii + 3];
197: }
199: PetscCall(ISRestoreIndices(isrow, &rout));
200: PetscCall(ISRestoreIndices(iscol, &cout));
201: PetscCall(VecRestoreArrayRead(bb, &b));
202: PetscCall(VecRestoreArray(xx, &x));
203: PetscCall(PetscLogFlops(2.0 * bs2 * (a->nz) - bs * A->cmap->n));
204: PetscFunctionReturn(PETSC_SUCCESS);
205: }