Actual source code: baijsolvtran5.c

  1: #include <../src/mat/impls/baij/seq/baij.h>
  2: #include <petsc/private/kernels/blockinvert.h>

  4: PetscErrorCode MatSolveTranspose_SeqBAIJ_5_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, x1, x2, x3, x4, x5, *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        = 5 * 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:     ii += 5;
 34:   }

 36:   /* forward solve the U^T */
 37:   idx = 0;
 38:   for (i = 0; i < n; i++) {
 39:     v = aa + 25 * 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:     x5 = t[4 + idx];
 46:     s1 = v[0] * x1 + v[1] * x2 + v[2] * x3 + v[3] * x4 + v[4] * x5;
 47:     s2 = v[5] * x1 + v[6] * x2 + v[7] * x3 + v[8] * x4 + v[9] * x5;
 48:     s3 = v[10] * x1 + v[11] * x2 + v[12] * x3 + v[13] * x4 + v[14] * x5;
 49:     s4 = v[15] * x1 + v[16] * x2 + v[17] * x3 + v[18] * x4 + v[19] * x5;
 50:     s5 = v[20] * x1 + v[21] * x2 + v[22] * x3 + v[23] * x4 + v[24] * x5;
 51:     v += 25;

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

 93:   /* copy t into x according to permutation */
 94:   ii = 0;
 95:   for (i = 0; i < n; i++) {
 96:     ir        = 5 * r[i];
 97:     x[ir]     = t[ii];
 98:     x[ir + 1] = t[ii + 1];
 99:     x[ir + 2] = t[ii + 2];
100:     x[ir + 3] = t[ii + 3];
101:     x[ir + 4] = t[ii + 4];
102:     ii += 5;
103:   }

105:   ISRestoreIndices(isrow, &rout);
106:   ISRestoreIndices(iscol, &cout);
107:   VecRestoreArrayRead(bb, &b);
108:   VecRestoreArray(xx, &x);
109:   PetscLogFlops(2.0 * 25 * (a->nz) - 5.0 * A->cmap->n);
110:   return 0;
111: }

113: PetscErrorCode MatSolveTranspose_SeqBAIJ_5(Mat A, Vec bb, Vec xx)
114: {
115:   Mat_SeqBAIJ       *a     = (Mat_SeqBAIJ *)A->data;
116:   IS                 iscol = a->col, isrow = a->row;
117:   const PetscInt     n = a->mbs, *vi, *ai = a->i, *aj = a->j, *diag = a->diag;
118:   const PetscInt    *r, *c, *rout, *cout;
119:   PetscInt           nz, idx, idt, j, i, oidx, ii, ic, ir;
120:   const PetscInt     bs = A->rmap->bs, bs2 = a->bs2;
121:   const MatScalar   *aa = a->a, *v;
122:   PetscScalar        s1, s2, s3, s4, s5, x1, x2, x3, x4, x5, *x, *t;
123:   const PetscScalar *b;

125:   VecGetArrayRead(bb, &b);
126:   VecGetArray(xx, &x);
127:   t = a->solve_work;

129:   ISGetIndices(isrow, &rout);
130:   r = rout;
131:   ISGetIndices(iscol, &cout);
132:   c = cout;

134:   /* copy b into temp work space according to permutation */
135:   for (i = 0; i < n; i++) {
136:     ii        = bs * i;
137:     ic        = bs * c[i];
138:     t[ii]     = b[ic];
139:     t[ii + 1] = b[ic + 1];
140:     t[ii + 2] = b[ic + 2];
141:     t[ii + 3] = b[ic + 3];
142:     t[ii + 4] = b[ic + 4];
143:   }

145:   /* forward solve the U^T */
146:   idx = 0;
147:   for (i = 0; i < n; i++) {
148:     v = aa + bs2 * diag[i];
149:     /* multiply by the inverse of the block diagonal */
150:     x1 = t[idx];
151:     x2 = t[1 + idx];
152:     x3 = t[2 + idx];
153:     x4 = t[3 + idx];
154:     x5 = t[4 + idx];
155:     s1 = v[0] * x1 + v[1] * x2 + v[2] * x3 + v[3] * x4 + v[4] * x5;
156:     s2 = v[5] * x1 + v[6] * x2 + v[7] * x3 + v[8] * x4 + v[9] * x5;
157:     s3 = v[10] * x1 + v[11] * x2 + v[12] * x3 + v[13] * x4 + v[14] * x5;
158:     s4 = v[15] * x1 + v[16] * x2 + v[17] * x3 + v[18] * x4 + v[19] * x5;
159:     s5 = v[20] * x1 + v[21] * x2 + v[22] * x3 + v[23] * x4 + v[24] * x5;
160:     v -= bs2;

162:     vi = aj + diag[i] - 1;
163:     nz = diag[i] - diag[i + 1] - 1;
164:     for (j = 0; j > -nz; j--) {
165:       oidx = bs * vi[j];
166:       t[oidx] -= v[0] * s1 + v[1] * s2 + v[2] * s3 + v[3] * s4 + v[4] * s5;
167:       t[oidx + 1] -= v[5] * s1 + v[6] * s2 + v[7] * s3 + v[8] * s4 + v[9] * s5;
168:       t[oidx + 2] -= v[10] * s1 + v[11] * s2 + v[12] * s3 + v[13] * s4 + v[14] * s5;
169:       t[oidx + 3] -= v[15] * s1 + v[16] * s2 + v[17] * s3 + v[18] * s4 + v[19] * s5;
170:       t[oidx + 4] -= v[20] * s1 + v[21] * s2 + v[22] * s3 + v[23] * s4 + v[24] * s5;
171:       v -= bs2;
172:     }
173:     t[idx]     = s1;
174:     t[1 + idx] = s2;
175:     t[2 + idx] = s3;
176:     t[3 + idx] = s4;
177:     t[4 + idx] = s5;
178:     idx += bs;
179:   }
180:   /* backward solve the L^T */
181:   for (i = n - 1; i >= 0; i--) {
182:     v   = aa + bs2 * ai[i];
183:     vi  = aj + ai[i];
184:     nz  = ai[i + 1] - ai[i];
185:     idt = bs * i;
186:     s1  = t[idt];
187:     s2  = t[1 + idt];
188:     s3  = t[2 + idt];
189:     s4  = t[3 + idt];
190:     s5  = t[4 + idt];
191:     for (j = 0; j < nz; j++) {
192:       idx = bs * vi[j];
193:       t[idx] -= v[0] * s1 + v[1] * s2 + v[2] * s3 + v[3] * s4 + v[4] * s5;
194:       t[idx + 1] -= v[5] * s1 + v[6] * s2 + v[7] * s3 + v[8] * s4 + v[9] * s5;
195:       t[idx + 2] -= v[10] * s1 + v[11] * s2 + v[12] * s3 + v[13] * s4 + v[14] * s5;
196:       t[idx + 3] -= v[15] * s1 + v[16] * s2 + v[17] * s3 + v[18] * s4 + v[19] * s5;
197:       t[idx + 4] -= v[20] * s1 + v[21] * s2 + v[22] * s3 + v[23] * s4 + v[24] * s5;
198:       v += bs2;
199:     }
200:   }

202:   /* copy t into x according to permutation */
203:   for (i = 0; i < n; i++) {
204:     ii        = bs * i;
205:     ir        = bs * r[i];
206:     x[ir]     = t[ii];
207:     x[ir + 1] = t[ii + 1];
208:     x[ir + 2] = t[ii + 2];
209:     x[ir + 3] = t[ii + 3];
210:     x[ir + 4] = t[ii + 4];
211:   }

213:   ISRestoreIndices(isrow, &rout);
214:   ISRestoreIndices(iscol, &cout);
215:   VecRestoreArrayRead(bb, &b);
216:   VecRestoreArray(xx, &x);
217:   PetscLogFlops(2.0 * bs2 * (a->nz) - bs * A->cmap->n);
218:   return 0;
219: }