Actual source code: baijsolvtran6.c
1: #include <../src/mat/impls/baij/seq/baij.h>
2: #include <petsc/private/kernels/blockinvert.h>
4: PetscErrorCode MatSolveTranspose_SeqBAIJ_6_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, s5, s6, x1, x2, x3, x4, x5, x6, *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 = 6 * 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: t[ii + 4] = b[ic + 4];
34: t[ii + 5] = b[ic + 5];
35: ii += 6;
36: }
38: /* forward solve the U^T */
39: idx = 0;
40: for (i = 0; i < n; i++) {
41: v = aa + 36 * diag[i];
42: /* multiply by the inverse of the block diagonal */
43: x1 = t[idx];
44: x2 = t[1 + idx];
45: x3 = t[2 + idx];
46: x4 = t[3 + idx];
47: x5 = t[4 + idx];
48: x6 = t[5 + idx];
49: s1 = v[0] * x1 + v[1] * x2 + v[2] * x3 + v[3] * x4 + v[4] * x5 + v[5] * x6;
50: s2 = v[6] * x1 + v[7] * x2 + v[8] * x3 + v[9] * x4 + v[10] * x5 + v[11] * x6;
51: s3 = v[12] * x1 + v[13] * x2 + v[14] * x3 + v[15] * x4 + v[16] * x5 + v[17] * x6;
52: s4 = v[18] * x1 + v[19] * x2 + v[20] * x3 + v[21] * x4 + v[22] * x5 + v[23] * x6;
53: s5 = v[24] * x1 + v[25] * x2 + v[26] * x3 + v[27] * x4 + v[28] * x5 + v[29] * x6;
54: s6 = v[30] * x1 + v[31] * x2 + v[32] * x3 + v[33] * x4 + v[34] * x5 + v[35] * x6;
55: v += 36;
57: vi = aj + diag[i] + 1;
58: nz = ai[i + 1] - diag[i] - 1;
59: while (nz--) {
60: oidx = 6 * (*vi++);
61: t[oidx] -= v[0] * s1 + v[1] * s2 + v[2] * s3 + v[3] * s4 + v[4] * s5 + v[5] * s6;
62: t[oidx + 1] -= v[6] * s1 + v[7] * s2 + v[8] * s3 + v[9] * s4 + v[10] * s5 + v[11] * s6;
63: t[oidx + 2] -= v[12] * s1 + v[13] * s2 + v[14] * s3 + v[15] * s4 + v[16] * s5 + v[17] * s6;
64: t[oidx + 3] -= v[18] * s1 + v[19] * s2 + v[20] * s3 + v[21] * s4 + v[22] * s5 + v[23] * s6;
65: t[oidx + 4] -= v[24] * s1 + v[25] * s2 + v[26] * s3 + v[27] * s4 + v[28] * s5 + v[29] * s6;
66: t[oidx + 5] -= v[30] * s1 + v[31] * s2 + v[32] * s3 + v[33] * s4 + v[34] * s5 + v[35] * s6;
67: v += 36;
68: }
69: t[idx] = s1;
70: t[1 + idx] = s2;
71: t[2 + idx] = s3;
72: t[3 + idx] = s4;
73: t[4 + idx] = s5;
74: t[5 + idx] = s6;
75: idx += 6;
76: }
77: /* backward solve the L^T */
78: for (i = n - 1; i >= 0; i--) {
79: v = aa + 36 * diag[i] - 36;
80: vi = aj + diag[i] - 1;
81: nz = diag[i] - ai[i];
82: idt = 6 * i;
83: s1 = t[idt];
84: s2 = t[1 + idt];
85: s3 = t[2 + idt];
86: s4 = t[3 + idt];
87: s5 = t[4 + idt];
88: s6 = t[5 + idt];
89: while (nz--) {
90: idx = 6 * (*vi--);
91: t[idx] -= v[0] * s1 + v[1] * s2 + v[2] * s3 + v[3] * s4 + v[4] * s5 + v[5] * s6;
92: t[idx + 1] -= v[6] * s1 + v[7] * s2 + v[8] * s3 + v[9] * s4 + v[10] * s5 + v[11] * s6;
93: t[idx + 2] -= v[12] * s1 + v[13] * s2 + v[14] * s3 + v[15] * s4 + v[16] * s5 + v[17] * s6;
94: t[idx + 3] -= v[18] * s1 + v[19] * s2 + v[20] * s3 + v[21] * s4 + v[22] * s5 + v[23] * s6;
95: t[idx + 4] -= v[24] * s1 + v[25] * s2 + v[26] * s3 + v[27] * s4 + v[28] * s5 + v[29] * s6;
96: t[idx + 5] -= v[30] * s1 + v[31] * s2 + v[32] * s3 + v[33] * s4 + v[34] * s5 + v[35] * s6;
97: v -= 36;
98: }
99: }
101: /* copy t into x according to permutation */
102: ii = 0;
103: for (i = 0; i < n; i++) {
104: ir = 6 * r[i];
105: x[ir] = t[ii];
106: x[ir + 1] = t[ii + 1];
107: x[ir + 2] = t[ii + 2];
108: x[ir + 3] = t[ii + 3];
109: x[ir + 4] = t[ii + 4];
110: x[ir + 5] = t[ii + 5];
111: ii += 6;
112: }
114: PetscCall(ISRestoreIndices(isrow, &rout));
115: PetscCall(ISRestoreIndices(iscol, &cout));
116: PetscCall(VecRestoreArrayRead(bb, &b));
117: PetscCall(VecRestoreArray(xx, &x));
118: PetscCall(PetscLogFlops(2.0 * 36 * (a->nz) - 6.0 * A->cmap->n));
119: PetscFunctionReturn(PETSC_SUCCESS);
120: }
122: PetscErrorCode MatSolveTranspose_SeqBAIJ_6(Mat A, Vec bb, Vec xx)
123: {
124: Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data;
125: IS iscol = a->col, isrow = a->row;
126: const PetscInt n = a->mbs, *vi, *ai = a->i, *aj = a->j, *diag = a->diag;
127: const PetscInt *r, *c, *rout, *cout;
128: PetscInt nz, idx, idt, j, i, oidx, ii, ic, ir;
129: const PetscInt bs = A->rmap->bs, bs2 = a->bs2;
130: const MatScalar *aa = a->a, *v;
131: PetscScalar s1, s2, s3, s4, s5, s6, x1, x2, x3, x4, x5, x6, *x, *t;
132: const PetscScalar *b;
134: PetscFunctionBegin;
135: PetscCall(VecGetArrayRead(bb, &b));
136: PetscCall(VecGetArray(xx, &x));
137: t = a->solve_work;
139: PetscCall(ISGetIndices(isrow, &rout));
140: r = rout;
141: PetscCall(ISGetIndices(iscol, &cout));
142: c = cout;
144: /* copy b into temp work space according to permutation */
145: for (i = 0; i < n; i++) {
146: ii = bs * i;
147: ic = bs * c[i];
148: t[ii] = b[ic];
149: t[ii + 1] = b[ic + 1];
150: t[ii + 2] = b[ic + 2];
151: t[ii + 3] = b[ic + 3];
152: t[ii + 4] = b[ic + 4];
153: t[ii + 5] = b[ic + 5];
154: }
156: /* forward solve the U^T */
157: idx = 0;
158: for (i = 0; i < n; i++) {
159: v = aa + bs2 * diag[i];
160: /* multiply by the inverse of the block diagonal */
161: x1 = t[idx];
162: x2 = t[1 + idx];
163: x3 = t[2 + idx];
164: x4 = t[3 + idx];
165: x5 = t[4 + idx];
166: x6 = t[5 + idx];
167: s1 = v[0] * x1 + v[1] * x2 + v[2] * x3 + v[3] * x4 + v[4] * x5 + v[5] * x6;
168: s2 = v[6] * x1 + v[7] * x2 + v[8] * x3 + v[9] * x4 + v[10] * x5 + v[11] * x6;
169: s3 = v[12] * x1 + v[13] * x2 + v[14] * x3 + v[15] * x4 + v[16] * x5 + v[17] * x6;
170: s4 = v[18] * x1 + v[19] * x2 + v[20] * x3 + v[21] * x4 + v[22] * x5 + v[23] * x6;
171: s5 = v[24] * x1 + v[25] * x2 + v[26] * x3 + v[27] * x4 + v[28] * x5 + v[29] * x6;
172: s6 = v[30] * x1 + v[31] * x2 + v[32] * x3 + v[33] * x4 + v[34] * x5 + v[35] * x6;
173: v -= bs2;
175: vi = aj + diag[i] - 1;
176: nz = diag[i] - diag[i + 1] - 1;
177: for (j = 0; j > -nz; j--) {
178: oidx = bs * vi[j];
179: t[oidx] -= v[0] * s1 + v[1] * s2 + v[2] * s3 + v[3] * s4 + v[4] * s5 + v[5] * s6;
180: t[oidx + 1] -= v[6] * s1 + v[7] * s2 + v[8] * s3 + v[9] * s4 + v[10] * s5 + v[11] * s6;
181: t[oidx + 2] -= v[12] * s1 + v[13] * s2 + v[14] * s3 + v[15] * s4 + v[16] * s5 + v[17] * s6;
182: t[oidx + 3] -= v[18] * s1 + v[19] * s2 + v[20] * s3 + v[21] * s4 + v[22] * s5 + v[23] * s6;
183: t[oidx + 4] -= v[24] * s1 + v[25] * s2 + v[26] * s3 + v[27] * s4 + v[28] * s5 + v[29] * s6;
184: t[oidx + 5] -= v[30] * s1 + v[31] * s2 + v[32] * s3 + v[33] * s4 + v[34] * s5 + v[35] * s6;
185: v -= bs2;
186: }
187: t[idx] = s1;
188: t[1 + idx] = s2;
189: t[2 + idx] = s3;
190: t[3 + idx] = s4;
191: t[4 + idx] = s5;
192: t[5 + idx] = s6;
193: idx += bs;
194: }
195: /* backward solve the L^T */
196: for (i = n - 1; i >= 0; i--) {
197: v = aa + bs2 * ai[i];
198: vi = aj + ai[i];
199: nz = ai[i + 1] - ai[i];
200: idt = bs * i;
201: s1 = t[idt];
202: s2 = t[1 + idt];
203: s3 = t[2 + idt];
204: s4 = t[3 + idt];
205: s5 = t[4 + idt];
206: s6 = t[5 + idt];
207: for (j = 0; j < nz; j++) {
208: idx = bs * vi[j];
209: t[idx] -= v[0] * s1 + v[1] * s2 + v[2] * s3 + v[3] * s4 + v[4] * s5 + v[5] * s6;
210: t[idx + 1] -= v[6] * s1 + v[7] * s2 + v[8] * s3 + v[9] * s4 + v[10] * s5 + v[11] * s6;
211: t[idx + 2] -= v[12] * s1 + v[13] * s2 + v[14] * s3 + v[15] * s4 + v[16] * s5 + v[17] * s6;
212: t[idx + 3] -= v[18] * s1 + v[19] * s2 + v[20] * s3 + v[21] * s4 + v[22] * s5 + v[23] * s6;
213: t[idx + 4] -= v[24] * s1 + v[25] * s2 + v[26] * s3 + v[27] * s4 + v[28] * s5 + v[29] * s6;
214: t[idx + 5] -= v[30] * s1 + v[31] * s2 + v[32] * s3 + v[33] * s4 + v[34] * s5 + v[35] * s6;
215: v += bs2;
216: }
217: }
219: /* copy t into x according to permutation */
220: for (i = 0; i < n; i++) {
221: ii = bs * i;
222: ir = bs * r[i];
223: x[ir] = t[ii];
224: x[ir + 1] = t[ii + 1];
225: x[ir + 2] = t[ii + 2];
226: x[ir + 3] = t[ii + 3];
227: x[ir + 4] = t[ii + 4];
228: x[ir + 5] = t[ii + 5];
229: }
231: PetscCall(ISRestoreIndices(isrow, &rout));
232: PetscCall(ISRestoreIndices(iscol, &cout));
233: PetscCall(VecRestoreArrayRead(bb, &b));
234: PetscCall(VecRestoreArray(xx, &x));
235: PetscCall(PetscLogFlops(2.0 * bs2 * (a->nz) - bs * A->cmap->n));
236: PetscFunctionReturn(PETSC_SUCCESS);
237: }