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| -rw-r--r-- | fg21sim/utils/random.py | 51 |
1 files changed, 51 insertions, 0 deletions
diff --git a/fg21sim/utils/random.py b/fg21sim/utils/random.py new file mode 100644 index 0000000..f652f6d --- /dev/null +++ b/fg21sim/utils/random.py @@ -0,0 +1,51 @@ +# 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, φ ∈ [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, θ ∈ [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. + + 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) |