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import numpy as np
def angle(a, b):
"""# Get Angle Between Row Vectors"""
from numpy import arctan2, pi
theta_a = arctan2(a[:, 1], a[:, 0])
theta_b = arctan2(b[:, 1], b[:, 0])
d_theta = theta_b - theta_a
assert (-pi <= d_theta) and (d_theta <= pi), "Theta difference outside of [-π,π]"
return d_theta
def normalize(column):
"""# Normalize Column Vector"""
from numpy.linalg import norm
return column / norm(column, axis=0)
def winding(xy_grid, trajectory_start, trajectory_end):
"""# Get Winding Number on Grid"""
from numpy import zeros, cross, clip, arcsin
trajectories = trajectory_end - trajectory_start
winding = zeros((xy_grid.shape[0]))
for idx, trajectory in enumerate(trajectories):
r = xy_grid - trajectory_start[idx]
cross = cross(normalize(trajectory), normalize(r))
cross = clip(cross, -1, 1)
theta = arcsin(cross)
winding += theta
return winding
def vorticity(xy_grid, trajectory_start, trajectory_end):
"""# Get Vorticity Number on Grid"""
from numpy import zeros, cross
trajectories = trajectory_end - trajectory_start
vorticity = zeros((xy_grid.shape[0]))
for idx, trajectory in enumerate(trajectories):
r = xy_grid - trajectory_start[idx]
vorticity += cross(normalize(trajectory), normalize(r))
return vorticity
def data_range(data):
"""# Get the range of values for each row"""
from numpy import min, max
return min(data, axis=0), max(data, axis=0)
np.normalize = normalize
np.range = data_range
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