pylal.sphericalutils

Module sphericalutils

Utilities to perform operations on (polar, azimuthal) vectors.

Author: Nickolas Fotopoulos <nvf@gravity.phys.uwm.edu>

Functions

rotate_euler(sph_coords, alpha, beta, gamma)
Take an Nx2 array of N (theta, phi) vectors on the unit sphere (that is, (polar, azimuthal) angles in radians) and apply rotations through the Euler angles alpha, beta, and gamma in radians, using the ZXZ convention.

source code

new_z_to_euler(new_z)
From the new Z axis expressed in (polar, azimuthal) angles of the initial coordinate system, return the (alpha, beta) Euler angles that rotate the old Z axis (0, 0) to the new Z axis.

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rotate_about_axis(x, axis, ang)
Return the result of rotating x about axis by ang (in radians).

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_abs_diff(c)
For some angular difference c = |a - b| in radians, find the magnitude of the difference, taking into account the wrap-around at 2*pi.

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_haversine(angle)

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_archaversine(h)
Compute the inverse of the _haversine function, using clip as protection for the antipodes.

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angle_between_points(a, b)
Find the angle in radians between a and b, each expressed in (polar, azimuthal) angles in radians.

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fisher_rvs(mu, kappa, size=1)
Return a random (polar, azimuthal) angle drawn from the Fisher distribution.

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fisher_pdf(theta, kappa)
Return the PDF of theta, the opening angle of X with respect to mu where X is Fisher-distributed about mu.

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fisher_cdf(theta, kappa)

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Function Details

[hide private]

rotate_about_axis(x, axis, ang)

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Return the result of rotating x about axis by ang (in radians). axis must be a unit vector.

angle_between_points(a, b)

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Find the angle in radians between a and b, each expressed in (polar, azimuthal) angles in radians. If a and b are Nx2 arrays of vectors, then return the N pairwise angles between them.

This formula is the law of _haversines, which is derivable from the spherical law of cosines, but is more numerically stable about a == b. This technique is slightly unstable for antipodal a and b.

fisher_rvs(mu, kappa, size=1)

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Return a random (polar, azimuthal) angle drawn from the Fisher
distribution. Assume that the concentration parameter (kappa) is large
so that we can use a Rayleigh distribution about the north pole and
rotate it to be centered at the (polar, azimuthal) coordinate mu.

Assume kappa = 1 / sigma**2

References:
  * http://en.wikipedia.org/wiki/Von_Mises-Fisher_distribution
  * http://arxiv.org/pdf/0902.0737v1 (states the Rayleigh limit)

fisher_pdf(theta, kappa)

source code

Return the PDF of theta, the opening angle of X with respect to mu where X is Fisher-distributed about mu. See fisher_rvs for the definition of mu.