Hyper-spherical Coordinates Implementation

Question

Does anyone know of a well-tested, reliable implementation of hyper-spherical coordinates, converting Cartesian vectors to spherical angles? I'd prefer python but I can translate it if necessary.

In other words, essentially the opposite of this question.

Before you tell me it's trivial to implement, here is my implementation (for 5 dimensional space):

def theta(x):
   n = 5
   x = np.array(x)
   toFill = np.array([0.0, 0.0, 0.0, 0.0])
   r_array = np.sqrt( np.array( [ sum( [xj**2 for xj in x[i+1:]] ) for i in range(0,n-1) ] ) )
   for k in range(0,n-2): 
      toFill[k] = np.arctan2( r_array[k] , x[k] ) 
   toFill[n-2] = 2 * np.arctan2( x[n-1] , ( x[n-2] + np.sqrt(x[n-1]**2 + x[n-2]**2) ) ) 
   return toFill

Note that I only care about the angles, not the radius. The implementation is essentially from here.

It seems to work, but I'm getting some odd results in some simulations (which I think may be due to this method, though I haven't found the problem directly yet). If you can see some boundary condition issues here, please let me know.

Answer 1

You can use hyperspherical python package.

import numpy as np
from hyperspherical import cartesian2spherical, spherical2cartesian

# Convert Cartesian to spherical
cartesian_points = np.array([[1, 1, 1], [0, 1, 0], [1, 0, 0]])
spherical_points = cartesian2spherical(cartesian_points)