Commit 296de5db authored by Martin Bauer's avatar Martin Bauer
Browse files

Merge branch 'fvm' into 'master'

finite difference stencil derivation for staggered positions

See merge request pycodegen/pystencils!99
parents 47aee5fa d002888a
import warnings
from collections import defaultdict
import itertools
import numpy as np
import sympy as sp
from pystencils.field import Field
from pystencils.stencil import direction_string_to_offset
from pystencils.sympyextensions import multidimensional_sum, prod
from pystencils.utils import LinearEquationSystem, fully_contains
......@@ -228,3 +230,120 @@ class FiniteDifferenceStencilDerivation:
def __repr__(self):
return "Finite difference stencil of accuracy {}, isotropic error: {}".format(self.accuracy,
class FiniteDifferenceStaggeredStencilDerivation:
"""Derives a finite difference stencil for application at a staggered position
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])]
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
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)],
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])
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
def points(self):
"""return the points of the stencil"""
return self._points
def stencil(self):
"""return the points of the stencil relative to the staggered position specified by neighbor"""
return self._stencil
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
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)])
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):
center = tuple([0] * self.spatial_dimensions)
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])])
raise NotImplementedError("neighbor_vector is not implemented for more than 2 index dimensions")
def __getitem__(self, offset):
if type(offset) is np.ndarray:
offset = tuple(offset)
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