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