Implementation of FB8, a generalization of the Kent (1982) and Bingham-Mardia (1978) distributions on a sphere
pip install fb8
import numpy as np from matplotlib import pyplot as plt from matplotlib import cm from mpl_toolkits.mplot3d import Axes3D from sphere.distribution import fb8 def grid(npts): return [_.flatten() for _ in np.meshgrid(np.linspace(0, np.pi, npts), np.linspace(0,2*np.pi, npts))] def plot_fb8(fb8, npts): """ Plot fb8 on 3D sphere """ xs = fb8.spherical_coordinates_to_nu(*grid(npts)) pdfs = fb8.pdf(xs) z,x,y = xs.T #!!! Note the ordering for xs here is used consistently throughout. Follows Kent's 1982 paper. fig = plt.figure(figsize=plt.figaspect(1.)) ax = fig.add_subplot(111, projection='3d') ax.plot_surface(x.reshape(npts, npts), y.reshape(npts, npts), z.reshape(npts, npts), alpha=0.5, rstride=1, cstride=1, facecolors=cm.plasma(pdfs.reshape(npts, npts)/pdfs.max())) ax.set_axis_off() plt.tight_layout(-5) plt.show() plot_fb8(fb8(np.pi/16,-np.pi/3,0,10,10,-1,0.5,0.3), 200)
Implements calculation of the density and fitting (using maximum likelihood estimate) of the FB8 distribution on a sphere, which is a generalization of the FB6, FB5 (Kent), and FB4 (Bingham-Mardia) distributions described below.
Implements the FB6 distribution that is first introduced in Rivest (1984).
Implements calculation of the density and fitting (using maximum likelihood estimate) of the Kent distribution based on Kent (1982). A unittest is performed if distribution.py is called from the command line.
Implements the Bingham-Mardia distribution whose mode is a small-circle on the sphere based on Bingham, Mardia (1978).
Also calculates directional, percentile levels which can be used to indicate the N% highest-posterior-density regions in the sky.
Kent, Hussein, Jah, Directional distributions in tracking of space debris
Terdik, Jammalamadaka, Wainwright, Simulation and visualization of spherical distributions
Mardia, Jupp, Directional statistics
scipy.special.hyp2f1 is used and may exhibit inaccuracies for large parameters. See github issues.
This project was originally developed for the FB5 (Kent) distribution here.
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