Source code for pyart.util.circular_stats

"""
Functions for computing statistics on circular (directional) distributions.

"""

import numpy as np


# For details on these computation see:
# https://en.wikipedia.org/wiki/Directional_statistics
# https://en.wikipedia.org/wiki/Mean_of_circular_quantities


[docs]def mean_of_two_angles(angles1, angles2): """ Compute the element by element mean of two sets of angles. Parameters ---------- angles1 : array First set of angles in radians. angles2 : array Second set of angles in radians. Returns ------- mean : array Elements by element angular mean of the two sets of angles in radians. """ angles1 = np.asanyarray(angles1) angles2 = np.asanyarray(angles2) x = (np.cos(angles1) + np.cos(angles2)) / 2. y = (np.sin(angles1) + np.sin(angles2)) / 2. return np.arctan2(y, x)
[docs]def mean_of_two_angles_deg(angle1, angle2): """ Compute the element by element mean of two sets of angles in degrees. Parameters ---------- angle1 : array First set of angles in degrees. angle2 : array Second set of angles in degrees. Returns ------- mean : array Elements by element angular mean of the two sets of angles in degrees. """ return np.rad2deg( mean_of_two_angles(np.deg2rad(angle1), np.deg2rad(angle2)))
[docs]def angular_mean(angles): """ Compute the mean of a distribution of angles in radians. Parameters ---------- angles : array like Distribution of angles in radians. Returns ------- mean : float The mean angle of the distribution in radians. """ angles = np.asanyarray(angles) x = np.cos(angles) y = np.sin(angles) return np.arctan2(np.mean(y), np.mean(x))
[docs]def angular_std(angles): """ Compute the standard deviation of a distribution of angles in radians. Parameters ---------- angles : array like Distribution of angles in radians. Returns ------- std : float Standard deviation of the distribution. """ angles = np.asanyarray(angles) x = np.cos(angles) y = np.sin(angles) norm = np.sqrt(np.mean(x)**2 + np.mean(y)**2) return np.sqrt(-2 * np.log(norm))
[docs]def angular_mean_deg(angles): """ Compute the mean of a distribution of angles in degrees. Parameters ---------- angles : array like Distribution of angles in degrees. Returns ------- mean : float The mean angle of the distribution in degrees. """ return np.rad2deg(angular_mean(np.deg2rad(angles)))
[docs]def angular_std_deg(angles): """ Compute the standard deviation of a distribution of angles in degrees. Parameters ---------- angles : array like Distribution of angles in degrees. Returns ------- std : float Standard deviation of the distribution. """ return np.rad2deg(angular_std(np.deg2rad(angles)))
[docs]def interval_mean(dist, interval_min, interval_max): """ Compute the mean of a distribution within an interval. Return the average of the array elements which are interpreted as being taken from a circular interval with endpoints given by interval_min and interval_max. Parameters ---------- dist : array like Distribution of values within an interval. interval_min, interval_max : float The endpoints of the interval. Returns ------- mean : float The mean value of the distribution. """ # transform distribution from original interval to [-pi, pi] half_width = (interval_max - interval_min) / 2. center = interval_min + half_width a = (np.asarray(dist) - center) / (half_width) * np.pi # compute the angular mean and convert back to original interval a_mean = angular_mean(a) return (a_mean * (half_width) / np.pi) + center
[docs]def interval_std(dist, interval_min, interval_max): """ Compute the standard deviation of a distribution within an interval. Return the standard deviation of the array elements which are interpreted as being taken from a circular interval with endpoints given by interval_min and interval_max. Parameters ---------- dist : array_like Distribution of values within an interval. interval_min, interval_max : float The endpoints of the interval. Returns ------- std : float The standard deviation of the distribution. """ # transform distribution from original interval to [-pi, pi] half_width = (interval_max - interval_min) / 2. center = interval_min + half_width a = (np.asarray(dist) - center) / (half_width) * np.pi # compute the angular standard dev. and convert back to original interval a_std = angular_std(a) return a_std * half_width / np.pi