Spherical to cartesian and vice versa

gistfile1.py

def s2c(s):
    """
    Converts vector from spherical to cartesian coordinates
    using physics convention (radius, polar/zenith, azimuth)

        r : radiu [0, inf]
        pol : polar [0, pi]
        azi : azimuth [0, 2pi]

    """

    r, pol, azi = np.hsplit(s, 3)
    
    x = r * np.sin(pol) * np.cos(azi)
    y = r * np.sin(pol) * np.sin(azi)
    z = r * np.cos(pol)

    return np.hstack((x,y,z))

def c2s(c):
    """
    Converts vector from cartesian to spherical coordinates
    using physics convention (radius, polar/zenith, azimuth)
    """
    x, y, z = np.hsplit(c, 3)

    r = np.sqrt(x**2 + y**2 + z**2)
    # should we make a workaround when r close to zero?
    pol = np.arccos(z/r)
    # np.arctan2 returns a number in [-pi,pi]. Shift to [0,2pi]
    azi = np.fmod(np.arctan2(y, x) + 2*np.pi, 2*np.pi) 

    return np.hstack((r, pol, azi))