Actual source code: baijsolvtran7.c
1: #include <../src/mat/impls/baij/seq/baij.h>
2: #include <petsc/private/kernels/blockinvert.h>
4: PetscErrorCode MatSolveTranspose_SeqBAIJ_7_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, s7, x1, x2, x3, x4, x5, x6, x7, *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 = 7 * 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: t[ii + 6] = b[ic + 6];
36: ii += 7;
37: }
39: /* forward solve the U^T */
40: idx = 0;
41: for (i = 0; i < n; i++) {
42: v = aa + 49 * diag[i];
43: /* multiply by the inverse of the block diagonal */
44: x1 = t[idx];
45: x2 = t[1 + idx];
46: x3 = t[2 + idx];
47: x4 = t[3 + idx];
48: x5 = t[4 + idx];
49: x6 = t[5 + idx];
50: x7 = t[6 + idx];
51: s1 = v[0] * x1 + v[1] * x2 + v[2] * x3 + v[3] * x4 + v[4] * x5 + v[5] * x6 + v[6] * x7;
52: s2 = v[7] * x1 + v[8] * x2 + v[9] * x3 + v[10] * x4 + v[11] * x5 + v[12] * x6 + v[13] * x7;
53: s3 = v[14] * x1 + v[15] * x2 + v[16] * x3 + v[17] * x4 + v[18] * x5 + v[19] * x6 + v[20] * x7;
54: s4 = v[21] * x1 + v[22] * x2 + v[23] * x3 + v[24] * x4 + v[25] * x5 + v[26] * x6 + v[27] * x7;
55: s5 = v[28] * x1 + v[29] * x2 + v[30] * x3 + v[31] * x4 + v[32] * x5 + v[33] * x6 + v[34] * x7;
56: s6 = v[35] * x1 + v[36] * x2 + v[37] * x3 + v[38] * x4 + v[39] * x5 + v[40] * x6 + v[41] * x7;
57: s7 = v[42] * x1 + v[43] * x2 + v[44] * x3 + v[45] * x4 + v[46] * x5 + v[47] * x6 + v[48] * x7;
58: v += 49;
60: vi = aj + diag[i] + 1;
61: nz = ai[i + 1] - diag[i] - 1;
62: while (nz--) {
63: oidx = 7 * (*vi++);
64: t[oidx] -= v[0] * s1 + v[1] * s2 + v[2] * s3 + v[3] * s4 + v[4] * s5 + v[5] * s6 + v[6] * s7;
65: t[oidx + 1] -= v[7] * s1 + v[8] * s2 + v[9] * s3 + v[10] * s4 + v[11] * s5 + v[12] * s6 + v[13] * s7;
66: t[oidx + 2] -= v[14] * s1 + v[15] * s2 + v[16] * s3 + v[17] * s4 + v[18] * s5 + v[19] * s6 + v[20] * s7;
67: t[oidx + 3] -= v[21] * s1 + v[22] * s2 + v[23] * s3 + v[24] * s4 + v[25] * s5 + v[26] * s6 + v[27] * s7;
68: t[oidx + 4] -= v[28] * s1 + v[29] * s2 + v[30] * s3 + v[31] * s4 + v[32] * s5 + v[33] * s6 + v[34] * s7;
69: t[oidx + 5] -= v[35] * s1 + v[36] * s2 + v[37] * s3 + v[38] * s4 + v[39] * s5 + v[40] * s6 + v[41] * s7;
70: t[oidx + 6] -= v[42] * s1 + v[43] * s2 + v[44] * s3 + v[45] * s4 + v[46] * s5 + v[47] * s6 + v[48] * s7;
71: v += 49;
72: }
73: t[idx] = s1;
74: t[1 + idx] = s2;
75: t[2 + idx] = s3;
76: t[3 + idx] = s4;
77: t[4 + idx] = s5;
78: t[5 + idx] = s6;
79: t[6 + idx] = s7;
80: idx += 7;
81: }
82: /* backward solve the L^T */
83: for (i = n - 1; i >= 0; i--) {
84: v = aa + 49 * diag[i] - 49;
85: vi = aj + diag[i] - 1;
86: nz = diag[i] - ai[i];
87: idt = 7 * i;
88: s1 = t[idt];
89: s2 = t[1 + idt];
90: s3 = t[2 + idt];
91: s4 = t[3 + idt];
92: s5 = t[4 + idt];
93: s6 = t[5 + idt];
94: s7 = t[6 + idt];
95: while (nz--) {
96: idx = 7 * (*vi--);
97: t[idx] -= v[0] * s1 + v[1] * s2 + v[2] * s3 + v[3] * s4 + v[4] * s5 + v[5] * s6 + v[6] * s7;
98: t[idx + 1] -= v[7] * s1 + v[8] * s2 + v[9] * s3 + v[10] * s4 + v[11] * s5 + v[12] * s6 + v[13] * s7;
99: t[idx + 2] -= v[14] * s1 + v[15] * s2 + v[16] * s3 + v[17] * s4 + v[18] * s5 + v[19] * s6 + v[20] * s7;
100: t[idx + 3] -= v[21] * s1 + v[22] * s2 + v[23] * s3 + v[24] * s4 + v[25] * s5 + v[26] * s6 + v[27] * s7;
101: t[idx + 4] -= v[28] * s1 + v[29] * s2 + v[30] * s3 + v[31] * s4 + v[32] * s5 + v[33] * s6 + v[34] * s7;
102: t[idx + 5] -= v[35] * s1 + v[36] * s2 + v[37] * s3 + v[38] * s4 + v[39] * s5 + v[40] * s6 + v[41] * s7;
103: t[idx + 6] -= v[42] * s1 + v[43] * s2 + v[44] * s3 + v[45] * s4 + v[46] * s5 + v[47] * s6 + v[48] * s7;
104: v -= 49;
105: }
106: }
108: /* copy t into x according to permutation */
109: ii = 0;
110: for (i = 0; i < n; i++) {
111: ir = 7 * r[i];
112: x[ir] = t[ii];
113: x[ir + 1] = t[ii + 1];
114: x[ir + 2] = t[ii + 2];
115: x[ir + 3] = t[ii + 3];
116: x[ir + 4] = t[ii + 4];
117: x[ir + 5] = t[ii + 5];
118: x[ir + 6] = t[ii + 6];
119: ii += 7;
120: }
122: PetscCall(ISRestoreIndices(isrow, &rout));
123: PetscCall(ISRestoreIndices(iscol, &cout));
124: PetscCall(VecRestoreArrayRead(bb, &b));
125: PetscCall(VecRestoreArray(xx, &x));
126: PetscCall(PetscLogFlops(2.0 * 49 * (a->nz) - 7.0 * A->cmap->n));
127: PetscFunctionReturn(PETSC_SUCCESS);
128: }
129: PetscErrorCode MatSolveTranspose_SeqBAIJ_7(Mat A, Vec bb, Vec xx)
130: {
131: Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data;
132: IS iscol = a->col, isrow = a->row;
133: const PetscInt n = a->mbs, *vi, *ai = a->i, *aj = a->j, *diag = a->diag;
134: const PetscInt *r, *c, *rout, *cout;
135: PetscInt nz, idx, idt, j, i, oidx, ii, ic, ir;
136: const PetscInt bs = A->rmap->bs, bs2 = a->bs2;
137: const MatScalar *aa = a->a, *v;
138: PetscScalar s1, s2, s3, s4, s5, s6, s7, x1, x2, x3, x4, x5, x6, x7, *x, *t;
139: const PetscScalar *b;
141: PetscFunctionBegin;
142: PetscCall(VecGetArrayRead(bb, &b));
143: PetscCall(VecGetArray(xx, &x));
144: t = a->solve_work;
146: PetscCall(ISGetIndices(isrow, &rout));
147: r = rout;
148: PetscCall(ISGetIndices(iscol, &cout));
149: c = cout;
151: /* copy b into temp work space according to permutation */
152: for (i = 0; i < n; i++) {
153: ii = bs * i;
154: ic = bs * c[i];
155: t[ii] = b[ic];
156: t[ii + 1] = b[ic + 1];
157: t[ii + 2] = b[ic + 2];
158: t[ii + 3] = b[ic + 3];
159: t[ii + 4] = b[ic + 4];
160: t[ii + 5] = b[ic + 5];
161: t[ii + 6] = b[ic + 6];
162: }
164: /* forward solve the U^T */
165: idx = 0;
166: for (i = 0; i < n; i++) {
167: v = aa + bs2 * diag[i];
168: /* multiply by the inverse of the block diagonal */
169: x1 = t[idx];
170: x2 = t[1 + idx];
171: x3 = t[2 + idx];
172: x4 = t[3 + idx];
173: x5 = t[4 + idx];
174: x6 = t[5 + idx];
175: x7 = t[6 + idx];
176: s1 = v[0] * x1 + v[1] * x2 + v[2] * x3 + v[3] * x4 + v[4] * x5 + v[5] * x6 + v[6] * x7;
177: s2 = v[7] * x1 + v[8] * x2 + v[9] * x3 + v[10] * x4 + v[11] * x5 + v[12] * x6 + v[13] * x7;
178: s3 = v[14] * x1 + v[15] * x2 + v[16] * x3 + v[17] * x4 + v[18] * x5 + v[19] * x6 + v[20] * x7;
179: s4 = v[21] * x1 + v[22] * x2 + v[23] * x3 + v[24] * x4 + v[25] * x5 + v[26] * x6 + v[27] * x7;
180: s5 = v[28] * x1 + v[29] * x2 + v[30] * x3 + v[31] * x4 + v[32] * x5 + v[33] * x6 + v[34] * x7;
181: s6 = v[35] * x1 + v[36] * x2 + v[37] * x3 + v[38] * x4 + v[39] * x5 + v[40] * x6 + v[41] * x7;
182: s7 = v[42] * x1 + v[43] * x2 + v[44] * x3 + v[45] * x4 + v[46] * x5 + v[47] * x6 + v[48] * x7;
183: v -= bs2;
185: vi = aj + diag[i] - 1;
186: nz = diag[i] - diag[i + 1] - 1;
187: for (j = 0; j > -nz; j--) {
188: oidx = bs * vi[j];
189: t[oidx] -= v[0] * s1 + v[1] * s2 + v[2] * s3 + v[3] * s4 + v[4] * s5 + v[5] * s6 + v[6] * s7;
190: t[oidx + 1] -= v[7] * s1 + v[8] * s2 + v[9] * s3 + v[10] * s4 + v[11] * s5 + v[12] * s6 + v[13] * s7;
191: t[oidx + 2] -= v[14] * s1 + v[15] * s2 + v[16] * s3 + v[17] * s4 + v[18] * s5 + v[19] * s6 + v[20] * s7;
192: t[oidx + 3] -= v[21] * s1 + v[22] * s2 + v[23] * s3 + v[24] * s4 + v[25] * s5 + v[26] * s6 + v[27] * s7;
193: t[oidx + 4] -= v[28] * s1 + v[29] * s2 + v[30] * s3 + v[31] * s4 + v[32] * s5 + v[33] * s6 + v[34] * s7;
194: t[oidx + 5] -= v[35] * s1 + v[36] * s2 + v[37] * s3 + v[38] * s4 + v[39] * s5 + v[40] * s6 + v[41] * s7;
195: t[oidx + 6] -= v[42] * s1 + v[43] * s2 + v[44] * s3 + v[45] * s4 + v[46] * s5 + v[47] * s6 + v[48] * s7;
196: v -= bs2;
197: }
198: t[idx] = s1;
199: t[1 + idx] = s2;
200: t[2 + idx] = s3;
201: t[3 + idx] = s4;
202: t[4 + idx] = s5;
203: t[5 + idx] = s6;
204: t[6 + idx] = s7;
205: idx += bs;
206: }
207: /* backward solve the L^T */
208: for (i = n - 1; i >= 0; i--) {
209: v = aa + bs2 * ai[i];
210: vi = aj + ai[i];
211: nz = ai[i + 1] - ai[i];
212: idt = bs * i;
213: s1 = t[idt];
214: s2 = t[1 + idt];
215: s3 = t[2 + idt];
216: s4 = t[3 + idt];
217: s5 = t[4 + idt];
218: s6 = t[5 + idt];
219: s7 = t[6 + idt];
220: for (j = 0; j < nz; j++) {
221: idx = bs * vi[j];
222: t[idx] -= v[0] * s1 + v[1] * s2 + v[2] * s3 + v[3] * s4 + v[4] * s5 + v[5] * s6 + v[6] * s7;
223: t[idx + 1] -= v[7] * s1 + v[8] * s2 + v[9] * s3 + v[10] * s4 + v[11] * s5 + v[12] * s6 + v[13] * s7;
224: t[idx + 2] -= v[14] * s1 + v[15] * s2 + v[16] * s3 + v[17] * s4 + v[18] * s5 + v[19] * s6 + v[20] * s7;
225: t[idx + 3] -= v[21] * s1 + v[22] * s2 + v[23] * s3 + v[24] * s4 + v[25] * s5 + v[26] * s6 + v[27] * s7;
226: t[idx + 4] -= v[28] * s1 + v[29] * s2 + v[30] * s3 + v[31] * s4 + v[32] * s5 + v[33] * s6 + v[34] * s7;
227: t[idx + 5] -= v[35] * s1 + v[36] * s2 + v[37] * s3 + v[38] * s4 + v[39] * s5 + v[40] * s6 + v[41] * s7;
228: t[idx + 6] -= v[42] * s1 + v[43] * s2 + v[44] * s3 + v[45] * s4 + v[46] * s5 + v[47] * s6 + v[48] * s7;
229: v += bs2;
230: }
231: }
233: /* copy t into x according to permutation */
234: for (i = 0; i < n; i++) {
235: ii = bs * i;
236: ir = bs * r[i];
237: x[ir] = t[ii];
238: x[ir + 1] = t[ii + 1];
239: x[ir + 2] = t[ii + 2];
240: x[ir + 3] = t[ii + 3];
241: x[ir + 4] = t[ii + 4];
242: x[ir + 5] = t[ii + 5];
243: x[ir + 6] = t[ii + 6];
244: }
246: PetscCall(ISRestoreIndices(isrow, &rout));
247: PetscCall(ISRestoreIndices(iscol, &cout));
248: PetscCall(VecRestoreArrayRead(bb, &b));
249: PetscCall(VecRestoreArray(xx, &x));
250: PetscCall(PetscLogFlops(2.0 * bs2 * (a->nz) - bs * A->cmap->n));
251: PetscFunctionReturn(PETSC_SUCCESS);
252: }