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Martin Bauer authored- removed warnings - added flake8 as CI target
Martin Bauer authored- removed warnings - added flake8 as CI target
stencils.py 11.41 KiB
import sympy as sp
def get_stencil(name, ordering='walberla'):
"""
Stencils are tuples of discrete velocities. They are commonly labeled in the 'DxQy' notation, where d is the
dimension (length of the velocity tuples) and y is number of discrete velocities.
:param name: DxQy notation
:param ordering: the LBM literature does not use a common order of the discrete velocities, therefore here
different common orderings are available. All orderings lead to the same method, it just has
to be used consistently. Here more orderings are available to compare intermediate results with
the literature.
"""
try:
return get_stencil.data[name.upper()][ordering.lower()]
except KeyError:
err_msg = ""
for stencil, ordering_names in get_stencil.data.items():
err_msg += " %s: %s\n" % (stencil, ", ".join(ordering_names.keys()))
raise ValueError("No such stencil available. "
"Available stencils: <stencil_name>( <ordering_names> )\n" + err_msg)
get_stencil.data = {
'D2Q9': {
'walberla': ((0, 0),
(0, 1), (0, -1), (-1, 0), (1, 0),
(-1, 1), (1, 1), (-1, -1), (1, -1),),
'counterclockwise': ((0, 0),
(1, 0), (0, 1), (-1, 0), (0, -1),
(1, 1), (-1, 1), (-1, -1), (1, -1)),
'braunschweig': ((0, 0),
(-1, 1), (-1, 0), (-1, -1), (0, -1),
(1, -1), (1, 0), (1, 1), (0, 1)),
},
'D3Q15': {
'walberla':
((0, 0, 0),
(0, 1, 0), (0, -1, 0), (-1, 0, 0), (1, 0, 0), (0, 0, 1), (0, 0, -1),
(1, 1, 1), (-1, 1, 1), (1, -1, 1), (-1, -1, 1), (1, 1, -1), (-1, 1, -1), (1, -1, -1), (-1, -1, -1)),
'premnath': ((0, 0, 0),
(1, 0, 0), (-1, 0, 0), (0, 1, 0), (0, -1, 0), (0, 0, 1), (0, 0, -1),
(1, 1, 1), (-1, 1, 1), (1, -1, 1), (-1, -1, 1),
(1, 1, -1), (-1, 1, -1), (1, -1, -1), (-1, -1, -1)),
},
'D3Q19': {
'walberla': ((0, 0, 0),
(0, 1, 0), (0, -1, 0), (-1, 0, 0), (1, 0, 0), (0, 0, 1), (0, 0, -1),
(-1, 1, 0), (1, 1, 0), (-1, -1, 0), (1, -1, 0),
(0, 1, 1), (0, -1, 1), (-1, 0, 1), (1, 0, 1),
(0, 1, -1), (0, -1, -1), (-1, 0, -1), (1, 0, -1)),
'braunschweig': ((0, 0, 0),
(1, 0, 0), (-1, 0, 0),
(0, 1, 0), (0, -1, 0),
(0, 0, 1), (0, 0, -1),
(1, 1, 0), (-1, -1, 0),
(1, -1, 0), (-1, 1, 0),
(1, 0, 1), (-1, 0, -1),
(1, 0, -1), (-1, 0, 1),
(0, 1, 1), (0, -1, -1),
(0, 1, -1), (0, -1, 1)),
'premnath': ((0, 0, 0),
(1, 0, 0), (-1, 0, 0), (0, 1, 0), (0, -1, 0), (0, 0, 1), (0, 0, -1),
(1, 1, 0), (-1, 1, 0), (1, -1, 0), (-1, -1, 0),
(1, 0, 1), (-1, 0, 1), (1, 0, -1), (-1, 0, -1),
(0, 1, 1), (0, -1, 1), (0, 1, -1), (0, -1, -1)),
},
'D3Q27': {
'walberla': ((0, 0, 0),
(0, 1, 0), (0, -1, 0), (-1, 0, 0), (1, 0, 0), (0, 0, 1), (0, 0, -1),
(-1, 1, 0), (1, 1, 0), (-1, -1, 0), (1, -1, 0),
(0, 1, 1), (0, -1, 1), (-1, 0, 1), (1, 0, 1),
(0, 1, -1), (0, -1, -1), (-1, 0, -1), (1, 0, -1),
(1, 1, 1), (-1, 1, 1), (1, -1, 1), (-1, -1, 1), (1, 1, -1), (-1, 1, -1), (1, -1, -1),
(-1, -1, -1)),
'premnath': ((0, 0, 0),
(1, 0, 0), (-1, 0, 0), (0, 1, 0), (0, -1, 0), (0, 0, 1), (0, 0, -1),
(1, 1, 0), (-1, 1, 0), (1, -1, 0), (-1, -1, 0),
(1, 0, 1), (-1, 0, 1), (1, 0, -1), (-1, 0, -1),
(0, 1, 1), (0, -1, 1), (0, 1, -1), (0, -1, -1),
(1, 1, 1), (-1, 1, 1), (1, -1, 1), (-1, -1, 1),
(1, 1, -1), (-1, 1, -1), (1, -1, -1), (-1, -1, -1))
}
}
def inverse_direction(direction):
"""Returns inverse i.e. negative of given direction tuple"""
return tuple([-i for i in direction])
def is_valid_stencil(stencil, max_neighborhood=None):
"""
Tests if a nested sequence is a valid stencil i.e. all the inner sequences have the same length.
If max_neighborhood is specified, it is also verified that the stencil does not contain any direction components
with absolute value greater than the maximal neighborhood.
"""
expected_dim = len(stencil[0])
for d in stencil:
if len(d) != expected_dim:
return False
if max_neighborhood is not None:
for d_i in d:
if abs(d_i) > max_neighborhood:
return False
return True
def is_symmetric_stencil(stencil):
"""Tests for every direction d, that -d is also in the stencil"""
for d in stencil:
if inverse_direction(d) not in stencil:
return False
return True
def stencils_have_same_entries(s1, s2):
if len(s1) != len(s2):
return False
return len(set(s1) - set(s2)) == 0
# -------------------------------------- Visualization -----------------------------------------------------------------
def visualize_stencil(stencil, **kwargs):
dim = len(stencil[0])
if dim == 2:
visualize_stencil_2d(stencil, **kwargs)
else:
slicing = False
if 'slice' in kwargs:
slicing = kwargs['slice']
del kwargs['slice']
if slicing:
visualize_stencil_3d_by_slicing(stencil, **kwargs)
else:
visualize_stencil_3d(stencil, **kwargs)
def visualize_stencil_2d(stencil, axes=None, figure=None, data=None, textsize='12', **kwargs):
"""
Creates a matplotlib 2D plot of the stencil
:param stencil: sequence of directions
:param axes: optional matplotlib axes
:param data: data to annotate the directions with, if none given, the indices are used
:param textsize: size of annotation text
"""
from matplotlib.patches import BoxStyle
import matplotlib.pyplot as plt
if axes is None:
if figure is None:
figure = plt.gcf()
axes = figure.gca()
text_box_style = BoxStyle("Round", pad=0.3)
head_length = 0.1
text_offset = 1.25
if data is None:
data = list(range(len(stencil)))
for direction, annotation in zip(stencil, data):
assert len(direction) == 2, "Works only for 2D stencils"
if not(direction[0] == 0 and direction[1] == 0):
axes.arrow(0, 0, direction[0], direction[1], head_width=0.08, head_length=head_length, color='k')
if isinstance(annotation, sp.Basic):
annotation = "$" + sp.latex(annotation) + "$"
else:
annotation = str(annotation)
axes.text(direction[0] * text_offset, direction[1] * text_offset, annotation, verticalalignment='center',
zorder=30, horizontalalignment='center', size=textsize,
bbox=dict(boxstyle=text_box_style, facecolor='#00b6eb', alpha=0.85, linewidth=0))
axes.set_axis_off()
axes.set_aspect('equal')
axes.set_xlim([-text_offset * 1.1, text_offset * 1.1])
axes.set_ylim([-text_offset * 1.1, text_offset * 1.1])
def visualize_stencil_3d_by_slicing(stencil, slice_axis=2, figure=None, data=None, **kwargs):
"""Visualizes a 3D, first-neighborhood stencil by plotting 3 slices along a given axis.
Args:
stencil: stencil as sequence of directions
slice_axis: 0, 1, or 2 indicating the axis to slice through
data: optional data to print as text besides the arrows
"""
import matplotlib.pyplot as plt
for d in stencil:
for element in d:
assert element == -1 or element == 0 or element == 1, "This function can only first neighborhood stencils"
if figure is None:
figure = plt.gcf()
axes = [figure.add_subplot(1, 3, i + 1) for i in range(3)]
splitted_directions = [[], [], []]
splitted_data = [[], [], []]
axes_names = ['x', 'y', 'z']
for i, d in enumerate(stencil):
split_idx = d[slice_axis] + 1
reduced_dir = tuple([element for j, element in enumerate(d) if j != slice_axis])
splitted_directions[split_idx].append(reduced_dir)
splitted_data[split_idx].append(i if data is None else data[i])
for i in range(3):
visualize_stencil_2d(splitted_directions[i], axes=axes[i], data=splitted_data[i], **kwargs)
for i in [-1, 0, 1]:
axes[i + 1].set_title("Cut at %s=%d" % (axes_names[slice_axis], i))
def visualize_stencil_3d(stencil, figure=None, axes=None, data=None, textsize='8'):
"""
Draws 3D stencil into a 3D coordinate system, parameters are similar to :func:`visualize_stencil_2d`
If data is None, no labels are drawn. To draw the labels as in the 2D case, use ``data=list(range(len(stencil)))``
"""
from matplotlib.patches import FancyArrowPatch
from mpl_toolkits.mplot3d import proj3d
import matplotlib.pyplot as plt
from matplotlib.patches import BoxStyle
from itertools import product, combinations
import numpy as np
class Arrow3D(FancyArrowPatch):
def __init__(self, xs, ys, zs, *args, **kwargs):
FancyArrowPatch.__init__(self, (0, 0), (0, 0), *args, **kwargs)
self._verts3d = xs, ys, zs
def draw(self, renderer):
xs3d, ys3d, zs3d = self._verts3d
xs, ys, zs = proj3d.proj_transform(xs3d, ys3d, zs3d, renderer.M)
self.set_positions((xs[0], ys[0]), (xs[1], ys[1]))
FancyArrowPatch.draw(self, renderer)
if axes is None:
if figure is None:
figure = plt.figure()
axes = figure.gca(projection='3d')
axes.set_aspect("equal")
if data is None:
data = [None] * len(stencil)
text_offset = 1.25
text_box_style = BoxStyle("Round", pad=0.3)
# Draw cell (cube)
r = [-1, 1]
for s, e in combinations(np.array(list(product(r, r, r))), 2):
if np.sum(np.abs(s - e)) == r[1] - r[0]:
axes.plot3D(*zip(s, e), color="k", alpha=0.5)
for d, annotation in zip(stencil, data):
assert len(d) == 3, "Works only for 3D stencils"
if not (d[0] == 0 and d[1] == 0 and d[2] == 0):
if d[0] == 0:
color = '#348abd'
elif d[1] == 0:
color = '#fac364'
elif sum([abs(d) for d in d]) == 2:
color = '#95bd50'
else:
color = '#808080'
a = Arrow3D([0, d[0]], [0, d[1]], [0, d[2]], mutation_scale=20, lw=2, arrowstyle="-|>", color=color)
axes.add_artist(a)
if annotation:
if isinstance(annotation, sp.Basic):
annotation = "$" + sp.latex(annotation) + "$"
else:
annotation = str(annotation)
axes.text(d[0] * text_offset, d[1] * text_offset, d[2] * text_offset,
annotation, verticalalignment='center', zorder=30,
size=textsize, bbox=dict(boxstyle=text_box_style, facecolor='#777777', alpha=0.6, linewidth=0))
axes.set_xlim([-text_offset * 1.1, text_offset * 1.1])
axes.set_ylim([-text_offset * 1.1, text_offset * 1.1])
axes.set_zlim([-text_offset * 1.1, text_offset * 1.1])
axes.set_axis_off()