spatial.py 8.35 KB
 Martin Bauer committed Jan 11, 2019 1 ``````from typing import Tuple `````` Martin Bauer committed Sep 20, 2018 2 ``````import sympy as sp `````` Martin Bauer committed Mar 28, 2019 3 ``````from pystencils.astnodes import LoopOverCoordinate `````` Martin Bauer committed Jan 11, 2019 4 ``````from pystencils.cache import memorycache `````` Martin Bauer committed Mar 28, 2019 5 ``````from pystencils import Field `````` Martin Bauer committed Sep 20, 2018 6 ``````from pystencils.fd import Diff `````` Martin Bauer committed Mar 28, 2019 7 ``````from pystencils.transformations import generic_visit `````` Martin Bauer committed Sep 20, 2018 8 ``````from .derivative import diff_args `````` Martin Bauer committed Jan 11, 2019 9 ``````from .derivation import FiniteDifferenceStencilDerivation `````` Martin Bauer committed Sep 20, 2018 10 11 12 13 `````` def fd_stencils_standard(indices, dx, fa): order = len(indices) `````` Martin Bauer committed Apr 28, 2019 14 `````` assert all(i >= 0 for i in indices), "Can only discretize objects with (integer) subscripts" `````` Martin Bauer committed Sep 20, 2018 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 `````` if order == 1: idx = indices[0] return (fa.neighbor(idx, 1) - fa.neighbor(idx, -1)) / (2 * dx) elif order == 2: if indices[0] == indices[1]: return (-2 * fa + fa.neighbor(indices[0], -1) + fa.neighbor(indices[0], +1)) / (dx ** 2) else: offsets = [(1, 1), [-1, 1], [1, -1], [-1, -1]] return sum(o1 * o2 * fa.neighbor(indices[0], o1).neighbor(indices[1], o2) for o1, o2 in offsets) / (4 * dx ** 2) raise NotImplementedError("Supports only derivatives up to order 2") def fd_stencils_isotropic(indices, dx, fa): dim = fa.field.spatial_dimensions if dim == 1: return fd_stencils_standard(indices, dx, fa) elif dim == 2: order = len(indices) if order == 1: idx = indices[0] assert 0 <= idx < 2 other_idx = 1 if indices[0] == 0 else 0 weights = {-1: sp.Rational(1, 12) / dx, 0: sp.Rational(1, 3) / dx, 1: sp.Rational(1, 12) / dx} upper_terms = sum(fa.neighbor(idx, +1).neighbor(other_idx, off) * w for off, w in weights.items()) lower_terms = sum(fa.neighbor(idx, -1).neighbor(other_idx, off) * w for off, w in weights.items()) return upper_terms - lower_terms elif order == 2: if indices[0] == indices[1]: idx = indices[0] other_idx = 1 if idx == 0 else 0 diagonals = sp.Rational(1, 12) * sum(fa.neighbor(0, i).neighbor(1, j) for i in (-1, 1) for j in (-1, 1)) div_direction = sp.Rational(5, 6) * sum(fa.neighbor(idx, i) for i in (-1, 1)) other_direction = - sp.Rational(1, 6) * sum(fa.neighbor(other_idx, i) for i in (-1, 1)) center = - sp.Rational(5, 3) * fa return (diagonals + div_direction + other_direction + center) / (dx ** 2) else: return fd_stencils_standard(indices, dx, fa) raise NotImplementedError("Supports only derivatives up to order 2 for 1D and 2D setups") `````` Martin Bauer committed Jan 11, 2019 59 60 61 62 63 64 65 66 67 68 69 70 71 ``````def fd_stencils_forth_order_isotropic(indices, dx, fa): order = len(indices) if order != 1: raise NotImplementedError("Forth order finite difference discretization is " "currently only supported for first derivatives") dim = indices[0] if dim not in (0, 1): raise NotImplementedError("Forth order finite difference discretization is only implemented for 2D") stencils = forth_order_2d_derivation() return stencils[dim].apply(fa) / dx `````` Martin Bauer committed Dec 03, 2018 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 ``````def fd_stencils_isotropic_high_density_code(indices, dx, fa): dim = fa.field.spatial_dimensions if dim == 1: return fd_stencils_standard(indices, dx, fa) elif dim == 2: order = len(indices) if order == 1: idx = indices[0] assert 0 <= idx < 2 other_idx = 1 if indices[0] == 0 else 0 weights = {-1: sp.Rational(1, 12) / dx, 0: sp.Rational(1, 3) / dx, 1: sp.Rational(1, 12) / dx} upper_terms = sum(fa.neighbor(idx, +1).neighbor(other_idx, off) * w for off, w in weights.items()) lower_terms = sum(fa.neighbor(idx, -1).neighbor(other_idx, off) * w for off, w in weights.items()) return upper_terms - lower_terms elif order == 2: if indices[0] == indices[1]: idx = indices[0] diagonals = sp.Rational(1, 8) * sum(fa.neighbor(0, i).neighbor(1, j) for i in (-1, 1) for j in (-1, 1)) div_direction = sp.Rational(1, 2) * sum(fa.neighbor(idx, i) for i in (-1, 1)) center = - sp.Rational(3, 2) * fa return (diagonals + div_direction + center) / (dx ** 2) else: return fd_stencils_standard(indices, dx, fa) raise NotImplementedError("Supports only derivatives up to order 2 for 1D and 2D setups") `````` Martin Bauer committed Sep 20, 2018 101 102 103 104 105 106 ``````def discretize_spatial(expr, dx, stencil=fd_stencils_standard): if isinstance(stencil, str): if stencil == 'standard': stencil = fd_stencils_standard elif stencil == 'isotropic': stencil = fd_stencils_isotropic `````` Martin Bauer committed Dec 05, 2018 107 108 `````` elif stencil == 'isotropic_hd': stencil = fd_stencils_isotropic_high_density_code `````` Martin Bauer committed Sep 20, 2018 109 110 111 `````` else: raise ValueError("Unknown stencil. Supported 'standard' and 'isotropic'") `````` Martin Bauer committed Mar 28, 2019 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 `````` def visitor(e): if isinstance(e, Diff): arg, *indices = diff_args(e) if not isinstance(arg, Field.Access): raise ValueError("Only derivatives with field or field accesses as arguments can be discretized") return stencil(indices, dx, arg) else: new_args = [discretize_spatial(a, dx, stencil) for a in e.args] return e.func(*new_args) if new_args else e return generic_visit(expr, visitor) def discretize_spatial_staggered(expr, dx, stencil=fd_stencils_standard): def staggered_visitor(e, coordinate, sign): if isinstance(e, Diff): arg, *indices = diff_args(e) if len(indices) != 1: raise ValueError("Function supports only up to second derivatives") if not isinstance(arg, Field.Access): raise ValueError("Argument of inner derivative has to be field access") target = indices[0] if target == coordinate: assert sign in (-1, 1) return (arg.neighbor(coordinate, sign) - arg) / dx * sign else: return (stencil(indices, dx, arg.neighbor(coordinate, sign)) + stencil(indices, dx, arg)) / 2 elif isinstance(e, Field.Access): return (e.neighbor(coordinate, sign) + e) / 2 elif isinstance(e, sp.Symbol): loop_idx = LoopOverCoordinate.is_loop_counter_symbol(e) return e + sign / 2 if loop_idx == coordinate else e else: new_args = [staggered_visitor(a, coordinate, sign) for a in e.args] return e.func(*new_args) if new_args else e def visitor(e): if isinstance(e, Diff): arg, *indices = diff_args(e) if isinstance(arg, Field.Access): return stencil(indices, dx, arg) else: if not len(indices) == 1: raise ValueError("This term is not support by the staggered discretization strategy") target = indices[0] return (staggered_visitor(arg, target, 1) - staggered_visitor(arg, target, -1)) / dx else: new_args = [visitor(a) for a in e.args] return e.func(*new_args) if new_args else e `````` Martin Bauer committed Jan 11, 2019 162 `````` `````` Martin Bauer committed Mar 28, 2019 163 `````` return generic_visit(expr, visitor) `````` Martin Bauer committed Jan 11, 2019 164 `````` `````` Martin Bauer committed Mar 28, 2019 165 `````` `````` Martin Bauer committed Jan 11, 2019 166 167 ``````# -------------------------------------- special stencils -------------------------------------------------------------- `````` Martin Bauer committed Mar 28, 2019 168 `````` `````` Martin Bauer committed Jan 11, 2019 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 ``````@memorycache(maxsize=1) def forth_order_2d_derivation() -> Tuple[FiniteDifferenceStencilDerivation.Result, ...]: # Symmetry, isotropy and 4th order conditions are not enough to fully specify the stencil # one weight has to be specifically set to a somewhat arbitrary value second_neighbor_weight = sp.Rational(1, 10) second_neighbor_stencil = [(i, j) for i in (-2, -1, 0, 1, 2) for j in (-2, -1, 0, 1, 2) ] x_diff = FiniteDifferenceStencilDerivation((0,), second_neighbor_stencil) x_diff.set_weight((2, 0), second_neighbor_weight) x_diff.assume_symmetric(0, anti_symmetric=True) x_diff.assume_symmetric(1) x_diff_stencil = x_diff.get_stencil(isotropic=True) y_diff = FiniteDifferenceStencilDerivation((1,), second_neighbor_stencil) y_diff.set_weight((0, 2), second_neighbor_weight) y_diff.assume_symmetric(1, anti_symmetric=True) y_diff.assume_symmetric(0) y_diff_stencil = y_diff.get_stencil(isotropic=True) return x_diff_stencil, y_diff_stencil``````