Commit 296de5db by Martin Bauer

### Merge branch 'fvm' into 'master'

```finite difference stencil derivation for staggered positions

See merge request pycodegen/pystencils!99```
parents 47aee5fa d002888a
 import warnings import warnings from collections import defaultdict from collections import defaultdict import itertools import numpy as np import numpy as np import sympy as sp import sympy as sp from pystencils.field import Field from pystencils.field import Field from pystencils.stencil import direction_string_to_offset from pystencils.sympyextensions import multidimensional_sum, prod from pystencils.sympyextensions import multidimensional_sum, prod from pystencils.utils import LinearEquationSystem, fully_contains from pystencils.utils import LinearEquationSystem, fully_contains ... @@ -228,3 +230,120 @@ class FiniteDifferenceStencilDerivation: ... @@ -228,3 +230,120 @@ class FiniteDifferenceStencilDerivation: def __repr__(self): def __repr__(self): return "Finite difference stencil of accuracy {}, isotropic error: {}".format(self.accuracy, return "Finite difference stencil of accuracy {}, isotropic error: {}".format(self.accuracy, self.is_isotropic) self.is_isotropic) class FiniteDifferenceStaggeredStencilDerivation: """Derives a finite difference stencil for application at a staggered position Args: neighbor: the neighbor direction string or vector at whose staggered position to calculate the derivative dim: how many dimensions (2 or 3) derivative: a tuple of directions over which to perform derivatives """ def __init__(self, neighbor, dim, derivative=tuple()): if type(neighbor) is str: neighbor = direction_string_to_offset(neighbor) if dim == 2: assert neighbor[dim:] == 0 assert derivative is tuple() or max(derivative) < dim neighbor = sp.Matrix(neighbor[:dim]) pos = neighbor / 2 def unitvec(i): """return the `i`-th unit vector in three dimensions""" a = np.zeros(dim, dtype=int) a[i] = 1 return a def flipped(a, i): """return `a` with its `i`-th element's sign flipped""" a = a.copy() a[i] *= -1 return a # determine the points to use, coordinates are relative to position points = [] if np.linalg.norm(neighbor, 1) == 1: main_points = [neighbor / 2, neighbor / -2] elif np.linalg.norm(neighbor, 1) == 2: nonzero_indices = [i for i, v in enumerate(neighbor) if v != 0 and i < dim] main_points = [neighbor / 2, neighbor / -2, flipped(neighbor / 2, nonzero_indices[0]), flipped(neighbor / -2, nonzero_indices[0])] else: main_points = [neighbor.multiply_elementwise(sp.Matrix(c) / 2) for c in itertools.product([-1, 1], repeat=3)] points += main_points zero_indices = [i for i, v in enumerate(neighbor) if v == 0 and i < dim] for i in zero_indices: points += [point + sp.Matrix(unitvec(i)) for point in main_points] points += [point - sp.Matrix(unitvec(i)) for point in main_points] points_tuple = tuple([tuple(p) for p in points]) self._stencil = points_tuple # determine the stencil weights if len(derivative) == 0: weights = None else: derivation = FiniteDifferenceStencilDerivation(derivative, points_tuple).get_stencil() if not derivation.accuracy: raise Exception('the requested derivative cannot be performed with the available neighbors') weights = derivation.weights # if the weights are underdefined, we can choose the free symbols to find the sparsest stencil free_weights = set(itertools.chain(*[w.free_symbols for w in weights])) if len(free_weights) > 0: zero_counts = defaultdict(list) for values in itertools.product([-1, -sp.Rational(1, 2), 0, 1, sp.Rational(1, 2)], repeat=len(free_weights)): subs = {free_weight: value for free_weight, value in zip(free_weights, values)} weights = [w.subs(subs) for w in derivation.weights] if not all(a == 0 for a in weights): zero_count = sum([1 for w in weights if w == 0]) zero_counts[zero_count].append(weights) best = zero_counts[max(zero_counts.keys())] if len(best) > 1: # if there are multiple, pick the one that contains a nonzero center weight center = [tuple(p + pos) for p in points].index((0, 0, 0)) best = [b for b in best if b[center] != 0] if len(best) > 1: raise NotImplementedError("more than one suitable set of weights found, don't know how to proceed") weights = best[0] assert weights points_tuple = tuple([tuple(p + pos) for p in points]) self._points = points_tuple self._weights = weights @property def points(self): """return the points of the stencil""" return self._points @property def stencil(self): """return the points of the stencil relative to the staggered position specified by neighbor""" return self._stencil @property def weights(self): """return the weights of the stencil""" assert self._weights is not None return self._weights def visualize(self): if self._weights is None: ws = None else: ws = np.array([w for w in self.weights if w != 0], dtype=float) pts = np.array([p for i, p in enumerate(self.points) if self.weights[i] != 0], dtype=int) from pystencils.stencil import plot plot(pts, data=ws) def apply(self, field): if field.index_dimensions == 0: return sum([field.__getitem__(point) * weight for point, weight in zip(self.points, self.weights)]) else: total = field.neighbor_vector(self.points[0]) * self.weights[0] for point, weight in zip(self.points[1:], self.weights[1:]): total += field.neighbor_vector(point) * weight return total
 ... @@ -441,6 +441,22 @@ class Field(AbstractField): ... @@ -441,6 +441,22 @@ class Field(AbstractField): center = tuple([0] * self.spatial_dimensions) center = tuple([0] * self.spatial_dimensions) return Field.Access(self, center) return Field.Access(self, center) def neighbor_vector(self, offset): """Like neighbor, but returns the entire vector/tensor stored at offset.""" if self.spatial_dimensions == 2 and len(offset) == 3: assert offset[2] == 0 offset = offset[:2] if self.index_dimensions == 0: return sp.Matrix([self.__getitem__(offset)]) elif self.index_dimensions == 1: return sp.Matrix([self.__getitem__(offset)(i) for i in range(self.index_shape[0])]) elif self.index_dimensions == 2: return sp.Matrix([[self.__getitem__(offset)(i, k) for k in range(self.index_shape[1])] for i in range(self.index_shape[0])]) else: raise NotImplementedError("neighbor_vector is not implemented for more than 2 index dimensions") def __getitem__(self, offset): def __getitem__(self, offset): if type(offset) is np.ndarray: if type(offset) is np.ndarray: offset = tuple(offset) offset = tuple(offset) ... ...
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