For Aukosh

gistfile1.py

from numpy import array,sin,cos,cov
import numpy.random as random

def obs_to_xyz(obs):
    D,th,phi,vr,vth,vphi = tuple(obs)
    sth,cth = sin(th),cos(th)
    sphi,cphi = sin(phi),cos(phi)
    return [D*sth*cphi,
            D*sth*sphi,
            D*cth,
            vr*sth*cphi + vth*cth*cphi - vphi*sphi,
            vr*sth*sphi + vth*cth*sphi + vphi*cphi,
            vr*cth - vth*sth]

N = 10000
random.seed()
obs = 10.0+random.randn(6*N).reshape((N,6))
print cov(obs)
xyz = []
for o in obs:
    xyz.append(obs_to_xyz(o))
xyz = array(xyz)
print cov(xyz)