Actual source code: baijsolvtran3.c

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

  4: PetscErrorCode MatSolveTranspose_SeqBAIJ_3_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, x1, x2, x3, *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        = 3 * c[i];
 28:     t[ii]     = b[ic];
 29:     t[ii + 1] = b[ic + 1];
 30:     t[ii + 2] = b[ic + 2];
 31:     ii += 3;
 32:   }

 34:   /* forward solve the U^T */
 35:   idx = 0;
 36:   for (i = 0; i < n; i++) {
 37:     v = aa + 9 * diag[i];
 38:     /* multiply by the inverse of the block diagonal */
 39:     x1 = t[idx];
 40:     x2 = t[1 + idx];
 41:     x3 = t[2 + idx];
 42:     s1 = v[0] * x1 + v[1] * x2 + v[2] * x3;
 43:     s2 = v[3] * x1 + v[4] * x2 + v[5] * x3;
 44:     s3 = v[6] * x1 + v[7] * x2 + v[8] * x3;
 45:     v += 9;

 47:     vi = aj + diag[i] + 1;
 48:     nz = ai[i + 1] - diag[i] - 1;
 49:     while (nz--) {
 50:       oidx = 3 * (*vi++);
 51:       t[oidx] -= v[0] * s1 + v[1] * s2 + v[2] * s3;
 52:       t[oidx + 1] -= v[3] * s1 + v[4] * s2 + v[5] * s3;
 53:       t[oidx + 2] -= v[6] * s1 + v[7] * s2 + v[8] * s3;
 54:       v += 9;
 55:     }
 56:     t[idx]     = s1;
 57:     t[1 + idx] = s2;
 58:     t[2 + idx] = s3;
 59:     idx += 3;
 60:   }
 61:   /* backward solve the L^T */
 62:   for (i = n - 1; i >= 0; i--) {
 63:     v   = aa + 9 * diag[i] - 9;
 64:     vi  = aj + diag[i] - 1;
 65:     nz  = diag[i] - ai[i];
 66:     idt = 3 * i;
 67:     s1  = t[idt];
 68:     s2  = t[1 + idt];
 69:     s3  = t[2 + idt];
 70:     while (nz--) {
 71:       idx = 3 * (*vi--);
 72:       t[idx] -= v[0] * s1 + v[1] * s2 + v[2] * s3;
 73:       t[idx + 1] -= v[3] * s1 + v[4] * s2 + v[5] * s3;
 74:       t[idx + 2] -= v[6] * s1 + v[7] * s2 + v[8] * s3;
 75:       v -= 9;
 76:     }
 77:   }

 79:   /* copy t into x according to permutation */
 80:   ii = 0;
 81:   for (i = 0; i < n; i++) {
 82:     ir        = 3 * r[i];
 83:     x[ir]     = t[ii];
 84:     x[ir + 1] = t[ii + 1];
 85:     x[ir + 2] = t[ii + 2];
 86:     ii += 3;
 87:   }

 89:   ISRestoreIndices(isrow, &rout);
 90:   ISRestoreIndices(iscol, &cout);
 91:   VecRestoreArrayRead(bb, &b);
 92:   VecRestoreArray(xx, &x);
 93:   PetscLogFlops(2.0 * 9 * (a->nz) - 3.0 * A->cmap->n);
 94:   return 0;
 95: }

 97: PetscErrorCode MatSolveTranspose_SeqBAIJ_3(Mat A, Vec bb, Vec xx)
 98: {
 99:   Mat_SeqBAIJ       *a     = (Mat_SeqBAIJ *)A->data;
100:   IS                 iscol = a->col, isrow = a->row;
101:   const PetscInt     n = a->mbs, *vi, *ai = a->i, *aj = a->j, *diag = a->diag;
102:   const PetscInt    *r, *c, *rout, *cout;
103:   PetscInt           nz, idx, idt, j, i, oidx, ii, ic, ir;
104:   const PetscInt     bs = A->rmap->bs, bs2 = a->bs2;
105:   const MatScalar   *aa = a->a, *v;
106:   PetscScalar        s1, s2, s3, x1, x2, x3, *x, *t;
107:   const PetscScalar *b;

109:   VecGetArrayRead(bb, &b);
110:   VecGetArray(xx, &x);
111:   t = a->solve_work;

113:   ISGetIndices(isrow, &rout);
114:   r = rout;
115:   ISGetIndices(iscol, &cout);
116:   c = cout;

118:   /* copy b into temp work space according to permutation */
119:   for (i = 0; i < n; i++) {
120:     ii        = bs * i;
121:     ic        = bs * c[i];
122:     t[ii]     = b[ic];
123:     t[ii + 1] = b[ic + 1];
124:     t[ii + 2] = b[ic + 2];
125:   }

127:   /* forward solve the U^T */
128:   idx = 0;
129:   for (i = 0; i < n; i++) {
130:     v = aa + bs2 * diag[i];
131:     /* multiply by the inverse of the block diagonal */
132:     x1 = t[idx];
133:     x2 = t[1 + idx];
134:     x3 = t[2 + idx];
135:     s1 = v[0] * x1 + v[1] * x2 + v[2] * x3;
136:     s2 = v[3] * x1 + v[4] * x2 + v[5] * x3;
137:     s3 = v[6] * x1 + v[7] * x2 + v[8] * x3;
138:     v -= bs2;

140:     vi = aj + diag[i] - 1;
141:     nz = diag[i] - diag[i + 1] - 1;
142:     for (j = 0; j > -nz; j--) {
143:       oidx = bs * vi[j];
144:       t[oidx] -= v[0] * s1 + v[1] * s2 + v[2] * s3;
145:       t[oidx + 1] -= v[3] * s1 + v[4] * s2 + v[5] * s3;
146:       t[oidx + 2] -= v[6] * s1 + v[7] * s2 + v[8] * s3;
147:       v -= bs2;
148:     }
149:     t[idx]     = s1;
150:     t[1 + idx] = s2;
151:     t[2 + idx] = s3;
152:     idx += bs;
153:   }
154:   /* backward solve the L^T */
155:   for (i = n - 1; i >= 0; i--) {
156:     v   = aa + bs2 * ai[i];
157:     vi  = aj + ai[i];
158:     nz  = ai[i + 1] - ai[i];
159:     idt = bs * i;
160:     s1  = t[idt];
161:     s2  = t[1 + idt];
162:     s3  = t[2 + idt];
163:     for (j = 0; j < nz; j++) {
164:       idx = bs * vi[j];
165:       t[idx] -= v[0] * s1 + v[1] * s2 + v[2] * s3;
166:       t[idx + 1] -= v[3] * s1 + v[4] * s2 + v[5] * s3;
167:       t[idx + 2] -= v[6] * s1 + v[7] * s2 + v[8] * s3;
168:       v += bs2;
169:     }
170:   }

172:   /* copy t into x according to permutation */
173:   for (i = 0; i < n; i++) {
174:     ii        = bs * i;
175:     ir        = bs * r[i];
176:     x[ir]     = t[ii];
177:     x[ir + 1] = t[ii + 1];
178:     x[ir + 2] = t[ii + 2];
179:   }

181:   ISRestoreIndices(isrow, &rout);
182:   ISRestoreIndices(iscol, &cout);
183:   VecRestoreArrayRead(bb, &b);
184:   VecRestoreArray(xx, &x);
185:   PetscLogFlops(2.0 * bs2 * (a->nz) - bs * A->cmap->n);
186:   return 0;
187: }