1 #include <../src/mat/impls/baij/seq/baij.h> 2 3 PetscErrorCode MatSolveTranspose_SeqBAIJ_1_NaturalOrdering(Mat A, Vec bb, Vec xx) 4 { 5 Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data; 6 const PetscInt *adiag = a->diag, *ai = a->i, *aj = a->j, *vi; 7 PetscInt i, n = a->mbs, j; 8 PetscInt nz; 9 PetscScalar *x, *tmp, s1; 10 const MatScalar *aa = a->a, *v; 11 const PetscScalar *b; 12 13 PetscFunctionBegin; 14 PetscCall(VecGetArrayRead(bb, &b)); 15 PetscCall(VecGetArray(xx, &x)); 16 tmp = a->solve_work; 17 18 /* copy the b into temp work space according to permutation */ 19 for (i = 0; i < n; i++) tmp[i] = b[i]; 20 21 /* forward solve the U^T */ 22 for (i = 0; i < n; i++) { 23 v = aa + adiag[i + 1] + 1; 24 vi = aj + adiag[i + 1] + 1; 25 nz = adiag[i] - adiag[i + 1] - 1; 26 s1 = tmp[i]; 27 s1 *= v[nz]; /* multiply by inverse of diagonal entry */ 28 for (j = 0; j < nz; j++) tmp[vi[j]] -= s1 * v[j]; 29 tmp[i] = s1; 30 } 31 32 /* backward solve the L^T */ 33 for (i = n - 1; i >= 0; i--) { 34 v = aa + ai[i]; 35 vi = aj + ai[i]; 36 nz = ai[i + 1] - ai[i]; 37 s1 = tmp[i]; 38 for (j = 0; j < nz; j++) tmp[vi[j]] -= s1 * v[j]; 39 } 40 41 /* copy tmp into x according to permutation */ 42 for (i = 0; i < n; i++) x[i] = tmp[i]; 43 44 PetscCall(VecRestoreArrayRead(bb, &b)); 45 PetscCall(VecRestoreArray(xx, &x)); 46 47 PetscCall(PetscLogFlops(2.0 * a->nz - A->cmap->n)); 48 PetscFunctionReturn(PETSC_SUCCESS); 49 } 50 51 PetscErrorCode MatSolveTranspose_SeqBAIJ_1_NaturalOrdering_inplace(Mat A, Vec bb, Vec xx) 52 { 53 Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data; 54 PetscInt i, nz; 55 const PetscInt *diag = a->diag, n = a->mbs, *vi, *ai = a->i, *aj = a->j; 56 const MatScalar *aa = a->a, *v; 57 PetscScalar s1, *x; 58 59 PetscFunctionBegin; 60 PetscCall(VecCopy(bb, xx)); 61 PetscCall(VecGetArray(xx, &x)); 62 63 /* forward solve the U^T */ 64 for (i = 0; i < n; i++) { 65 v = aa + diag[i]; 66 /* multiply by the inverse of the block diagonal */ 67 s1 = (*v++) * x[i]; 68 vi = aj + diag[i] + 1; 69 nz = ai[i + 1] - diag[i] - 1; 70 while (nz--) x[*vi++] -= (*v++) * s1; 71 x[i] = s1; 72 } 73 /* backward solve the L^T */ 74 for (i = n - 1; i >= 0; i--) { 75 v = aa + diag[i] - 1; 76 vi = aj + diag[i] - 1; 77 nz = diag[i] - ai[i]; 78 s1 = x[i]; 79 while (nz--) x[*vi--] -= (*v--) * s1; 80 } 81 PetscCall(VecRestoreArray(xx, &x)); 82 PetscCall(PetscLogFlops(2.0 * (a->nz) - A->cmap->n)); 83 PetscFunctionReturn(PETSC_SUCCESS); 84 } 85