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# Copyright (c) 2016 Weitian LI <liweitianux@live.com>
# MIT license
"""
Custom utilities of random number generations.
"""
import numpy as np
def spherical_uniform(n=1):
"""Uniformly pick random points on the surface of a unit sphere.
The algorithm is described in [SpherePointPicking]_.
Parameters
----------
n : int
Number of points to be randomly picked
Returns
-------
theta : float, or 1D `~numpy.ndarray`
The polar angles, θ ∈ [0, π]. (unit: rad)
If ``n > 1``, then returns a 1D array containing all the generated
coordinates. (unit: rad)
phi : float, or 1D `~numpy.ndarray`
The azimuthal angles, φ ∈ [0, 2π).
NOTE
----
Physicists usually adopt the (radial, polar, azimuthal) order with
the (r, θ, φ) notation for the spherical coordinates convention, which
is adopted here and by ``healpy``.
However, this convention is *different* to the convention generally
used by mathematicians.
The following relation can be used to convert the generated (theta, phi)
to the Galactic longitude and latitude convention:
glon = np.rad2deg(phi)
glat = 90.0 - np.rad2deg(theta)
References
----------
.. [SpherePointPicking]
Wolfram MathWorld - Sphere Point Picking
http://mathworld.wolfram.com/SpherePointPicking.html
.. [SphericalCoordinates]
Wolfram MathWorld - Spherical Coordinates
http://mathworld.wolfram.com/SphericalCoordinates.html
"""
u = np.random.uniform(size=n)
v = np.random.uniform(size=n)
phi = 2*np.pi * u
theta = np.arccos(2*v - 1)
return (theta, phi)
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