Actual source code: baijsolvtran2.c

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

  4: PetscErrorCode MatSolveTranspose_SeqBAIJ_2_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, x1, x2, *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        = 2 * c[i];
 29:     t[ii]     = b[ic];
 30:     t[ii + 1] = b[ic + 1];
 31:     ii += 2;
 32:   }

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

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

 73:   /* copy t into x according to permutation */
 74:   ii = 0;
 75:   for (i = 0; i < n; i++) {
 76:     ir        = 2 * r[i];
 77:     x[ir]     = t[ii];
 78:     x[ir + 1] = t[ii + 1];
 79:     ii += 2;
 80:   }

 82:   PetscCall(ISRestoreIndices(isrow, &rout));
 83:   PetscCall(ISRestoreIndices(iscol, &cout));
 84:   PetscCall(VecRestoreArrayRead(bb, &b));
 85:   PetscCall(VecRestoreArray(xx, &x));
 86:   PetscCall(PetscLogFlops(2.0 * 4 * (a->nz) - 2.0 * A->cmap->n));
 87:   PetscFunctionReturn(PETSC_SUCCESS);
 88: }

 90: PetscErrorCode MatSolveTranspose_SeqBAIJ_2(Mat A, Vec bb, Vec xx)
 91: {
 92:   Mat_SeqBAIJ       *a     = (Mat_SeqBAIJ *)A->data;
 93:   IS                 iscol = a->col, isrow = a->row;
 94:   const PetscInt     n = a->mbs, *vi, *ai = a->i, *aj = a->j, *diag = a->diag;
 95:   const PetscInt    *r, *c, *rout, *cout;
 96:   PetscInt           nz, idx, idt, j, i, oidx, ii, ic, ir;
 97:   const PetscInt     bs = A->rmap->bs, bs2 = a->bs2;
 98:   const MatScalar   *aa = a->a, *v;
 99:   PetscScalar        s1, s2, x1, x2, *x, *t;
100:   const PetscScalar *b;

102:   PetscFunctionBegin;
103:   PetscCall(VecGetArrayRead(bb, &b));
104:   PetscCall(VecGetArray(xx, &x));
105:   t = a->solve_work;

107:   PetscCall(ISGetIndices(isrow, &rout));
108:   r = rout;
109:   PetscCall(ISGetIndices(iscol, &cout));
110:   c = cout;

112:   /* copy b into temp work space according to permutation */
113:   for (i = 0; i < n; i++) {
114:     ii        = bs * i;
115:     ic        = bs * c[i];
116:     t[ii]     = b[ic];
117:     t[ii + 1] = b[ic + 1];
118:   }

120:   /* forward solve the U^T */
121:   idx = 0;
122:   for (i = 0; i < n; i++) {
123:     v = aa + bs2 * diag[i];
124:     /* multiply by the inverse of the block diagonal */
125:     x1 = t[idx];
126:     x2 = t[1 + idx];
127:     s1 = v[0] * x1 + v[1] * x2;
128:     s2 = v[2] * x1 + v[3] * x2;
129:     v -= bs2;

131:     vi = aj + diag[i] - 1;
132:     nz = diag[i] - diag[i + 1] - 1;
133:     for (j = 0; j > -nz; j--) {
134:       oidx = bs * vi[j];
135:       t[oidx] -= v[0] * s1 + v[1] * s2;
136:       t[oidx + 1] -= v[2] * s1 + v[3] * s2;
137:       v -= bs2;
138:     }
139:     t[idx]     = s1;
140:     t[1 + idx] = s2;
141:     idx += bs;
142:   }
143:   /* backward solve the L^T */
144:   for (i = n - 1; i >= 0; i--) {
145:     v   = aa + bs2 * ai[i];
146:     vi  = aj + ai[i];
147:     nz  = ai[i + 1] - ai[i];
148:     idt = bs * i;
149:     s1  = t[idt];
150:     s2  = t[1 + idt];
151:     for (j = 0; j < nz; j++) {
152:       idx = bs * vi[j];
153:       t[idx] -= v[0] * s1 + v[1] * s2;
154:       t[idx + 1] -= v[2] * s1 + v[3] * s2;
155:       v += bs2;
156:     }
157:   }

159:   /* copy t into x according to permutation */
160:   for (i = 0; i < n; i++) {
161:     ii        = bs * i;
162:     ir        = bs * r[i];
163:     x[ir]     = t[ii];
164:     x[ir + 1] = t[ii + 1];
165:   }

167:   PetscCall(ISRestoreIndices(isrow, &rout));
168:   PetscCall(ISRestoreIndices(iscol, &cout));
169:   PetscCall(VecRestoreArrayRead(bb, &b));
170:   PetscCall(VecRestoreArray(xx, &x));
171:   PetscCall(PetscLogFlops(2.0 * bs2 * (a->nz) - bs * A->cmap->n));
172:   PetscFunctionReturn(PETSC_SUCCESS);
173: }