import numpy as np
from .base import MovementAnalyzer
[docs]class Analyzer(MovementAnalyzer):
r"""Turn Angle analyzer.
Turn angle refers to the angle formed by two successive steps of an
individual motion.
Hence if :math:`p(t_0) = (x_0, y_0)`, :math:`p(t_1) = (x_1, y_1)` and
:math:`p(t_2) = (x_2, y_2)` are the
positions of an individual at times :math:`t_0, t_0` and :math:`t_2` then
the turn angle at time :math:`t_1` is defined by:
.. math::
d_1 = (x_1 - x_0, y_1 - y_0)
d_2 = (x_2 - x_1, y_2 - y_1)
ta = \arccos\left(\frac{d_1 \cdot d_2}{||d_1|| \cdot ||d_2||}\right)
Here :math:`ta` is turn angle.
"""
name = 'Turn Angle'
[docs] def analyze(self, movement):
"""Extract turn angles from movement data.
Get the turn angles of all individuals in movement data at every time
step. Will result in an array of size [num_individuals, time_steps - 2]
so that::
turn_angle = results[i, k]
Means that the ``i``-th individual had a turn angle of ``turn_angle``
at the ``k``-th time step.
Arguments
---------
movement : :py:obj:`.Movement`
Movement data to analyze
Returns
-------
results : :py:obj:`array`
Array of shape [num_individuals, time_steps - 1] containing the
turn angles of all individuals at every time step.
"""
data = movement.data
times = movement.times
dtimes = (times[1:] - times[:-1])[None, :, None]
directions = (data[:, 1:, :] - data[:, :-1, :]) / dtimes
complex_directions = directions[:, :, 0] + 1j * directions[:, :, 1]
turn_angles = np.angle(
complex_directions[:, 1:] /
complex_directions[:, :-1])
return turn_angles
[docs] def plot(
self,
ax=None,
figsize=(10, 10),
num_individual=0,
bins=20,
width=None,
cmap='Reds',
alpha=0.8,
log=True):
"""Plot distribution of turning angles.
Arguments
---------
ax : :py:obj:`matplotlib.axes.Axes`, optional
Axes object in which to plot.
figsize : tuple or list, optional
Size of figure to create if no axes are provided.
num_individual : int or tuple or list or array, optional
Selection of individuals from which to draw turning angle
information. If num_individual='all', all information will
be plotted.
bins : int, optional
Number of bins to use in histogram of turn angle distribution.
Defaults to 20.
width : float, optional
Width of bars in histogram. If none is given, width will be
maximum possible before overlap.
cmap : str, optional
Colormap to use to assign colors to histogram bars. Defaults
to 'Reds'.
alpha : float, optional
Alpha value of plot. Defaults to 0.8.
"""
import matplotlib.pyplot as plt
from matplotlib.cm import get_cmap
if ax is None:
_, ax = plt.subplots(
figsize=figsize, subplot_kw={"polar": True})
if num_individual == 'all':
tdata = self.results.ravel()
elif isinstance(num_individual, int):
tdata = self.results[num_individual, :]
else:
tdata = self.results[num_individual, :].ravel()
range_ = (-np.pi, np.pi)
histogram, _ = np.histogram(
tdata, bins=bins, range=range_, normed=True)
if width is None:
width = (range_[1] - range_[0]) / bins
theta = np.linspace(range_[0], range_[1], bins, endpoint=False)
bars = ax.bar(theta, histogram, width=width, bottom=0.05)
mins, maxs = histogram.min(), histogram.max()
# Use custom colors and opacity
cmap = get_cmap(cmap)
for value, pbar in zip(histogram, bars):
pbar.set_facecolor(
cmap((value - mins + 0.1) / (0.1 + maxs - mins)))
pbar.set_alpha(alpha)
ticks = np.linspace(0.05, 0.05 + histogram.max(), 4)
ax.set_yticks(ticks)
ax.set_yticklabels(np.round(ticks - 0.05, 2))
ax.set_title('Turn Angle distribution')
return ax
