`priors`¶

`banded_angles`(\*models)
`cartesian2polar`(ratios)	ratios : np.ndarray (k, n):
`difference_operator`(order, nobs)	Get a finite difference operator matrix of size nobs.
`polar2cartesian`(angles[, radius, …])	Convert a set of angles of a sphere defined in n-dimensional space to cartesian coordinates.
`sample_spherical_polar`(ndimensions[, …])
`sample_uniform_hypersphere`(ndimensions[, …])	S2 has a solution: http://mathworld.wolfram.com/SpherePointPicking.html
`sample_uniform_sphere`([nsamples])	S2 has a solution: http://mathworld.wolfram.com/SpherePointPicking.html
`show_spherical_angles`([theta1, theta2, …])	Draw a vector on the unit sphere defined by the angles theta1 (inclination on last axis, x_3, x_3->x1) and theta2 (asymuth x_1->x_2 plane).
`simple_polar2cartesian`(angle[, radius])	Given some polar coordinates, return the cartesian coordinates.
`simple_sphere_angle`(x, y, z)
`simple_sphere_coord`([radius, theta1, theta2])
`spherical_coordinates_n2`([offset, nsamples, …])
`spherical_coordinates_n3`([offset, nsamples, …])
`standard_sphere_coord`(angle[, radius])	standard physics way theta1: inclination (angle between z and x/y theta2: asymuth (angle on x-y plane)
`test_spherical_coords`()

banded_angles¶

tikreg.priors.banded_angles(*models)¶

cartesian2polar¶

tikreg.priors.cartesian2polar(ratios)¶

ratios : np.ndarray (k, n):: k coordinates in n dimensional space

Returns:	angles : np.ndarray (k, n-1) Poolar angles defining the ratios [x_1, …, x_n] phi_i is angle

difference_operator¶

tikreg.priors.difference_operator(order, nobs)¶

Get a finite difference operator matrix of size nobs.

Parameters:	order : int The order of the derivative (e.g. 2nd derivative) nobs : int The size of the output matrix
Returns:	mat : (nobs,`nobs`) np.ndarray

polar2cartesian¶

tikreg.priors.polar2cartesian(angles, radius=1.0, physics_convention=False)¶

Convert a set of angles of a sphere defined in n-dimensional space to cartesian coordinates.

Parameters:	angles : np.ndarray (n-1, k) The k angles in n dimensional space to convert from polar to cartesian coordinates. raw : bool Use hypersphere standard form. This differs from the standard 3-dimensional sphere in axis orientation.
Returns:	coords : np.ndarray (n, k) All the x_i coordinates corresponding to the k angles

Notes

theta_1 is angle away from x_{n} (inclination towards x_{n-1}) in [0,pi] theta_2 is angle away from x_{n-1} (inclination towards x_{n-2}) in [0,pi] …etc theta_{n-1} is the angle between x_1 and x_2 (asymuth) in [0,2pi]

https://en.wikipedia.org/wiki/N-sphere#Spherical_coordinates

sample_spherical_polar¶

tikreg.priors.sample_spherical_polar(ndimensions, offset=1, nsamples=10, max_angle=90.0, spacing=<function linspace at 0x7f65ad9021b8>)¶

sample_uniform_hypersphere¶

tikreg.priors.sample_uniform_hypersphere(ndimensions, nsamples=10)¶

S2 has a solution: http://mathworld.wolfram.com/SpherePointPicking.html

S3 has a solution: http://mathworld.wolfram.com/HyperspherePointPicking.html

No general solution for higher dimensions

sample_uniform_sphere¶

tikreg.priors.sample_uniform_sphere(nsamples=10)¶: S2 has a solution: http://mathworld.wolfram.com/SpherePointPicking.html

show_spherical_angles¶

tikreg.priors.show_spherical_angles(theta1=30.0, theta2=60.0, physics_convention=False)¶: Draw a vector on the unit sphere defined by the angles theta1 (inclination on last axis, x_3, x_3->x1) and theta2 (asymuth x_1->x_2 plane).

simple_polar2cartesian¶

tikreg.priors.simple_polar2cartesian(angle, radius=1.0)¶

Given some polar coordinates, return the cartesian coordinates.

Parameters:	angle : vector (p,) The angles should be given in radians radius: float-like The n-sphere radius
Returns:	coords : vector, (p+1,) The cartesian coordinate of the points (x_n,…,x_1)

simple_sphere_angle¶

tikreg.priors.simple_sphere_angle(x, y, z)¶

simple_sphere_coord¶

tikreg.priors.simple_sphere_coord(radius=1.0, theta1=45.0, theta2=45.0)¶

spherical_coordinates_n2¶

tikreg.priors.spherical_coordinates_n2(offset=0, nsamples=10, spacing=<function linspace at 0x7f65ad9021b8>)¶

spherical_coordinates_n3¶

tikreg.priors.spherical_coordinates_n3(offset=0, nsamples=10, spacing=<function linspace at 0x7f65ad9021b8>)¶

standard_sphere_coord¶

tikreg.priors.standard_sphere_coord(angle, radius=1.0)¶: standard physics way theta1: inclination (angle between z and x/y theta2: asymuth (angle on x-y plane)

test_spherical_coords¶

tikreg.priors.test_spherical_coords()¶

priors¶