1 #include <../src/mat/impls/baij/seq/baij.h> 2 3 PetscErrorCode MatSolveTranspose_SeqBAIJ_3_NaturalOrdering_inplace(Mat A, Vec bb, Vec xx) 4 { 5 Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data; 6 const PetscInt n = a->mbs, *vi, *ai = a->i, *aj = a->j, *diag = a->diag; 7 PetscInt i, nz, idx, idt, oidx; 8 const MatScalar *aa = a->a, *v; 9 PetscScalar s1, s2, s3, x1, x2, x3, *x; 10 11 PetscFunctionBegin; 12 PetscCall(VecCopy(bb, xx)); 13 PetscCall(VecGetArray(xx, &x)); 14 15 /* forward solve the U^T */ 16 idx = 0; 17 for (i = 0; i < n; i++) { 18 v = aa + 9 * diag[i]; 19 /* multiply by the inverse of the block diagonal */ 20 x1 = x[idx]; 21 x2 = x[1 + idx]; 22 x3 = x[2 + idx]; 23 s1 = v[0] * x1 + v[1] * x2 + v[2] * x3; 24 s2 = v[3] * x1 + v[4] * x2 + v[5] * x3; 25 s3 = v[6] * x1 + v[7] * x2 + v[8] * x3; 26 v += 9; 27 28 vi = aj + diag[i] + 1; 29 nz = ai[i + 1] - diag[i] - 1; 30 while (nz--) { 31 oidx = 3 * (*vi++); 32 x[oidx] -= v[0] * s1 + v[1] * s2 + v[2] * s3; 33 x[oidx + 1] -= v[3] * s1 + v[4] * s2 + v[5] * s3; 34 x[oidx + 2] -= v[6] * s1 + v[7] * s2 + v[8] * s3; 35 v += 9; 36 } 37 x[idx] = s1; 38 x[1 + idx] = s2; 39 x[2 + idx] = s3; 40 idx += 3; 41 } 42 /* backward solve the L^T */ 43 for (i = n - 1; i >= 0; i--) { 44 v = aa + 9 * diag[i] - 9; 45 vi = aj + diag[i] - 1; 46 nz = diag[i] - ai[i]; 47 idt = 3 * i; 48 s1 = x[idt]; 49 s2 = x[1 + idt]; 50 s3 = x[2 + idt]; 51 while (nz--) { 52 idx = 3 * (*vi--); 53 x[idx] -= v[0] * s1 + v[1] * s2 + v[2] * s3; 54 x[idx + 1] -= v[3] * s1 + v[4] * s2 + v[5] * s3; 55 x[idx + 2] -= v[6] * s1 + v[7] * s2 + v[8] * s3; 56 v -= 9; 57 } 58 } 59 PetscCall(VecRestoreArray(xx, &x)); 60 PetscCall(PetscLogFlops(2.0 * 9.0 * (a->nz) - 3.0 * A->cmap->n)); 61 PetscFunctionReturn(PETSC_SUCCESS); 62 } 63 64 PetscErrorCode MatSolveTranspose_SeqBAIJ_3_NaturalOrdering(Mat A, Vec bb, Vec xx) 65 { 66 Mat_SeqBAIJ *a = (Mat_SeqBAIJ *)A->data; 67 const PetscInt n = a->mbs, *vi, *ai = a->i, *aj = a->j, *diag = a->diag; 68 PetscInt nz, idx, idt, j, i, oidx; 69 const PetscInt bs = A->rmap->bs, bs2 = a->bs2; 70 const MatScalar *aa = a->a, *v; 71 PetscScalar s1, s2, s3, x1, x2, x3, *x; 72 73 PetscFunctionBegin; 74 PetscCall(VecCopy(bb, xx)); 75 PetscCall(VecGetArray(xx, &x)); 76 77 /* forward solve the U^T */ 78 idx = 0; 79 for (i = 0; i < n; i++) { 80 v = aa + bs2 * diag[i]; 81 /* multiply by the inverse of the block diagonal */ 82 x1 = x[idx]; 83 x2 = x[1 + idx]; 84 x3 = x[2 + idx]; 85 s1 = v[0] * x1 + v[1] * x2 + v[2] * x3; 86 s2 = v[3] * x1 + v[4] * x2 + v[5] * x3; 87 s3 = v[6] * x1 + v[7] * x2 + v[8] * x3; 88 v -= bs2; 89 90 vi = aj + diag[i] - 1; 91 nz = diag[i] - diag[i + 1] - 1; 92 for (j = 0; j > -nz; j--) { 93 oidx = bs * vi[j]; 94 x[oidx] -= v[0] * s1 + v[1] * s2 + v[2] * s3; 95 x[oidx + 1] -= v[3] * s1 + v[4] * s2 + v[5] * s3; 96 x[oidx + 2] -= v[6] * s1 + v[7] * s2 + v[8] * s3; 97 v -= bs2; 98 } 99 x[idx] = s1; 100 x[1 + idx] = s2; 101 x[2 + idx] = s3; 102 idx += bs; 103 } 104 /* backward solve the L^T */ 105 for (i = n - 1; i >= 0; i--) { 106 v = aa + bs2 * ai[i]; 107 vi = aj + ai[i]; 108 nz = ai[i + 1] - ai[i]; 109 idt = bs * i; 110 s1 = x[idt]; 111 s2 = x[1 + idt]; 112 s3 = x[2 + idt]; 113 for (j = 0; j < nz; j++) { 114 idx = bs * vi[j]; 115 x[idx] -= v[0] * s1 + v[1] * s2 + v[2] * s3; 116 x[idx + 1] -= v[3] * s1 + v[4] * s2 + v[5] * s3; 117 x[idx + 2] -= v[6] * s1 + v[7] * s2 + v[8] * s3; 118 v += bs2; 119 } 120 } 121 PetscCall(VecRestoreArray(xx, &x)); 122 PetscCall(PetscLogFlops(2.0 * bs2 * (a->nz) - bs * A->cmap->n)); 123 PetscFunctionReturn(PETSC_SUCCESS); 124 } 125