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:   VecGetArrayRead(bb, &b);
 16:   VecGetArray(xx, &x);
 17:   t = a->solve_work;

 19:   ISGetIndices(isrow, &rout);
 20:   r = rout;
 21:   ISGetIndices(iscol, &cout);
 22:   c = cout;

 24:   /* copy the b into temp work space according to permutation */
 25:   ii = 0;
 26:   for (i = 0; i < n; i++) {
 27:     ic        = 6 * c[i];
 28:     t[ii]     = b[ic];
 29:     t[ii + 1] = b[ic + 1];
 30:     t[ii + 2] = b[ic + 2];
 31:     t[ii + 3] = b[ic + 3];
 32:     t[ii + 4] = b[ic + 4];
 33:     t[ii + 5] = b[ic + 5];
 34:     ii += 6;
 35:   }

 37:   /* forward solve the U^T */
 38:   idx = 0;
 39:   for (i = 0; i < n; i++) {
 40:     v = aa + 36 * diag[i];
 41:     /* multiply by the inverse of the block diagonal */
 42:     x1 = t[idx];
 43:     x2 = t[1 + idx];
 44:     x3 = t[2 + idx];
 45:     x4 = t[3 + idx];
 46:     x5 = t[4 + idx];
 47:     x6 = t[5 + idx];
 48:     s1 = v[0] * x1 + v[1] * x2 + v[2] * x3 + v[3] * x4 + v[4] * x5 + v[5] * x6;
 49:     s2 = v[6] * x1 + v[7] * x2 + v[8] * x3 + v[9] * x4 + v[10] * x5 + v[11] * x6;
 50:     s3 = v[12] * x1 + v[13] * x2 + v[14] * x3 + v[15] * x4 + v[16] * x5 + v[17] * x6;
 51:     s4 = v[18] * x1 + v[19] * x2 + v[20] * x3 + v[21] * x4 + v[22] * x5 + v[23] * x6;
 52:     s5 = v[24] * x1 + v[25] * x2 + v[26] * x3 + v[27] * x4 + v[28] * x5 + v[29] * x6;
 53:     s6 = v[30] * x1 + v[31] * x2 + v[32] * x3 + v[33] * x4 + v[34] * x5 + v[35] * x6;
 54:     v += 36;

 56:     vi = aj + diag[i] + 1;
 57:     nz = ai[i + 1] - diag[i] - 1;
 58:     while (nz--) {
 59:       oidx = 6 * (*vi++);
 60:       t[oidx] -= v[0] * s1 + v[1] * s2 + v[2] * s3 + v[3] * s4 + v[4] * s5 + v[5] * s6;
 61:       t[oidx + 1] -= v[6] * s1 + v[7] * s2 + v[8] * s3 + v[9] * s4 + v[10] * s5 + v[11] * s6;
 62:       t[oidx + 2] -= v[12] * s1 + v[13] * s2 + v[14] * s3 + v[15] * s4 + v[16] * s5 + v[17] * s6;
 63:       t[oidx + 3] -= v[18] * s1 + v[19] * s2 + v[20] * s3 + v[21] * s4 + v[22] * s5 + v[23] * s6;
 64:       t[oidx + 4] -= v[24] * s1 + v[25] * s2 + v[26] * s3 + v[27] * s4 + v[28] * s5 + v[29] * s6;
 65:       t[oidx + 5] -= v[30] * s1 + v[31] * s2 + v[32] * s3 + v[33] * s4 + v[34] * s5 + v[35] * s6;
 66:       v += 36;
 67:     }
 68:     t[idx]     = s1;
 69:     t[1 + idx] = s2;
 70:     t[2 + idx] = s3;
 71:     t[3 + idx] = s4;
 72:     t[4 + idx] = s5;
 73:     t[5 + idx] = s6;
 74:     idx += 6;
 75:   }
 76:   /* backward solve the L^T */
 77:   for (i = n - 1; i >= 0; i--) {
 78:     v   = aa + 36 * diag[i] - 36;
 79:     vi  = aj + diag[i] - 1;
 80:     nz  = diag[i] - ai[i];
 81:     idt = 6 * i;
 82:     s1  = t[idt];
 83:     s2  = t[1 + idt];
 84:     s3  = t[2 + idt];
 85:     s4  = t[3 + idt];
 86:     s5  = t[4 + idt];
 87:     s6  = t[5 + idt];
 88:     while (nz--) {
 89:       idx = 6 * (*vi--);
 90:       t[idx] -= v[0] * s1 + v[1] * s2 + v[2] * s3 + v[3] * s4 + v[4] * s5 + v[5] * s6;
 91:       t[idx + 1] -= v[6] * s1 + v[7] * s2 + v[8] * s3 + v[9] * s4 + v[10] * s5 + v[11] * s6;
 92:       t[idx + 2] -= v[12] * s1 + v[13] * s2 + v[14] * s3 + v[15] * s4 + v[16] * s5 + v[17] * s6;
 93:       t[idx + 3] -= v[18] * s1 + v[19] * s2 + v[20] * s3 + v[21] * s4 + v[22] * s5 + v[23] * s6;
 94:       t[idx + 4] -= v[24] * s1 + v[25] * s2 + v[26] * s3 + v[27] * s4 + v[28] * s5 + v[29] * s6;
 95:       t[idx + 5] -= v[30] * s1 + v[31] * s2 + v[32] * s3 + v[33] * s4 + v[34] * s5 + v[35] * s6;
 96:       v -= 36;
 97:     }
 98:   }

100:   /* copy t into x according to permutation */
101:   ii = 0;
102:   for (i = 0; i < n; i++) {
103:     ir        = 6 * r[i];
104:     x[ir]     = t[ii];
105:     x[ir + 1] = t[ii + 1];
106:     x[ir + 2] = t[ii + 2];
107:     x[ir + 3] = t[ii + 3];
108:     x[ir + 4] = t[ii + 4];
109:     x[ir + 5] = t[ii + 5];
110:     ii += 6;
111:   }

113:   ISRestoreIndices(isrow, &rout);
114:   ISRestoreIndices(iscol, &cout);
115:   VecRestoreArrayRead(bb, &b);
116:   VecRestoreArray(xx, &x);
117:   PetscLogFlops(2.0 * 36 * (a->nz) - 6.0 * A->cmap->n);
118:   return 0;
119: }

121: PetscErrorCode MatSolveTranspose_SeqBAIJ_6(Mat A, Vec bb, Vec xx)
122: {
123:   Mat_SeqBAIJ       *a     = (Mat_SeqBAIJ *)A->data;
124:   IS                 iscol = a->col, isrow = a->row;
125:   const PetscInt     n = a->mbs, *vi, *ai = a->i, *aj = a->j, *diag = a->diag;
126:   const PetscInt    *r, *c, *rout, *cout;
127:   PetscInt           nz, idx, idt, j, i, oidx, ii, ic, ir;
128:   const PetscInt     bs = A->rmap->bs, bs2 = a->bs2;
129:   const MatScalar   *aa = a->a, *v;
130:   PetscScalar        s1, s2, s3, s4, s5, s6, x1, x2, x3, x4, x5, x6, *x, *t;
131:   const PetscScalar *b;

133:   VecGetArrayRead(bb, &b);
134:   VecGetArray(xx, &x);
135:   t = a->solve_work;

137:   ISGetIndices(isrow, &rout);
138:   r = rout;
139:   ISGetIndices(iscol, &cout);
140:   c = cout;

142:   /* copy b into temp work space according to permutation */
143:   for (i = 0; i < n; i++) {
144:     ii        = bs * i;
145:     ic        = bs * c[i];
146:     t[ii]     = b[ic];
147:     t[ii + 1] = b[ic + 1];
148:     t[ii + 2] = b[ic + 2];
149:     t[ii + 3] = b[ic + 3];
150:     t[ii + 4] = b[ic + 4];
151:     t[ii + 5] = b[ic + 5];
152:   }

154:   /* forward solve the U^T */
155:   idx = 0;
156:   for (i = 0; i < n; i++) {
157:     v = aa + bs2 * diag[i];
158:     /* multiply by the inverse of the block diagonal */
159:     x1 = t[idx];
160:     x2 = t[1 + idx];
161:     x3 = t[2 + idx];
162:     x4 = t[3 + idx];
163:     x5 = t[4 + idx];
164:     x6 = t[5 + idx];
165:     s1 = v[0] * x1 + v[1] * x2 + v[2] * x3 + v[3] * x4 + v[4] * x5 + v[5] * x6;
166:     s2 = v[6] * x1 + v[7] * x2 + v[8] * x3 + v[9] * x4 + v[10] * x5 + v[11] * x6;
167:     s3 = v[12] * x1 + v[13] * x2 + v[14] * x3 + v[15] * x4 + v[16] * x5 + v[17] * x6;
168:     s4 = v[18] * x1 + v[19] * x2 + v[20] * x3 + v[21] * x4 + v[22] * x5 + v[23] * x6;
169:     s5 = v[24] * x1 + v[25] * x2 + v[26] * x3 + v[27] * x4 + v[28] * x5 + v[29] * x6;
170:     s6 = v[30] * x1 + v[31] * x2 + v[32] * x3 + v[33] * x4 + v[34] * x5 + v[35] * x6;
171:     v -= bs2;

173:     vi = aj + diag[i] - 1;
174:     nz = diag[i] - diag[i + 1] - 1;
175:     for (j = 0; j > -nz; j--) {
176:       oidx = bs * vi[j];
177:       t[oidx] -= v[0] * s1 + v[1] * s2 + v[2] * s3 + v[3] * s4 + v[4] * s5 + v[5] * s6;
178:       t[oidx + 1] -= v[6] * s1 + v[7] * s2 + v[8] * s3 + v[9] * s4 + v[10] * s5 + v[11] * s6;
179:       t[oidx + 2] -= v[12] * s1 + v[13] * s2 + v[14] * s3 + v[15] * s4 + v[16] * s5 + v[17] * s6;
180:       t[oidx + 3] -= v[18] * s1 + v[19] * s2 + v[20] * s3 + v[21] * s4 + v[22] * s5 + v[23] * s6;
181:       t[oidx + 4] -= v[24] * s1 + v[25] * s2 + v[26] * s3 + v[27] * s4 + v[28] * s5 + v[29] * s6;
182:       t[oidx + 5] -= v[30] * s1 + v[31] * s2 + v[32] * s3 + v[33] * s4 + v[34] * s5 + v[35] * s6;
183:       v -= bs2;
184:     }
185:     t[idx]     = s1;
186:     t[1 + idx] = s2;
187:     t[2 + idx] = s3;
188:     t[3 + idx] = s4;
189:     t[4 + idx] = s5;
190:     t[5 + idx] = s6;
191:     idx += bs;
192:   }
193:   /* backward solve the L^T */
194:   for (i = n - 1; i >= 0; i--) {
195:     v   = aa + bs2 * ai[i];
196:     vi  = aj + ai[i];
197:     nz  = ai[i + 1] - ai[i];
198:     idt = bs * i;
199:     s1  = t[idt];
200:     s2  = t[1 + idt];
201:     s3  = t[2 + idt];
202:     s4  = t[3 + idt];
203:     s5  = t[4 + idt];
204:     s6  = t[5 + idt];
205:     for (j = 0; j < nz; j++) {
206:       idx = bs * vi[j];
207:       t[idx] -= v[0] * s1 + v[1] * s2 + v[2] * s3 + v[3] * s4 + v[4] * s5 + v[5] * s6;
208:       t[idx + 1] -= v[6] * s1 + v[7] * s2 + v[8] * s3 + v[9] * s4 + v[10] * s5 + v[11] * s6;
209:       t[idx + 2] -= v[12] * s1 + v[13] * s2 + v[14] * s3 + v[15] * s4 + v[16] * s5 + v[17] * s6;
210:       t[idx + 3] -= v[18] * s1 + v[19] * s2 + v[20] * s3 + v[21] * s4 + v[22] * s5 + v[23] * s6;
211:       t[idx + 4] -= v[24] * s1 + v[25] * s2 + v[26] * s3 + v[27] * s4 + v[28] * s5 + v[29] * s6;
212:       t[idx + 5] -= v[30] * s1 + v[31] * s2 + v[32] * s3 + v[33] * s4 + v[34] * s5 + v[35] * s6;
213:       v += bs2;
214:     }
215:   }

217:   /* copy t into x according to permutation */
218:   for (i = 0; i < n; i++) {
219:     ii        = bs * i;
220:     ir        = bs * r[i];
221:     x[ir]     = t[ii];
222:     x[ir + 1] = t[ii + 1];
223:     x[ir + 2] = t[ii + 2];
224:     x[ir + 3] = t[ii + 3];
225:     x[ir + 4] = t[ii + 4];
226:     x[ir + 5] = t[ii + 5];
227:   }

229:   ISRestoreIndices(isrow, &rout);
230:   ISRestoreIndices(iscol, &cout);
231:   VecRestoreArrayRead(bb, &b);
232:   VecRestoreArray(xx, &x);
233:   PetscLogFlops(2.0 * bs2 * (a->nz) - bs * A->cmap->n);
234:   return 0;
235: }