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: }