spheres.stars.star_utils.antipodal

spheres.stars.star_utils.antipodal(to_invert, from_cartesian=False, from_spherical=False)

If given an extended complex coordinate, takes the point to its antipode on the sphere via the map:

\[z \rightarrow -\frac{z}{|z|^2} = - \frac{1}{z^{*}}\]

If \(z=\infty\), \(z \rightarrow 0\) and if \(z=0\), \(z \rightarrow \infty\).

If given a spin state or polynomial coefficients, inverts the whole sphere. This could be done by inverting the individual roots, or directly on the state/polynomial by reversing the components, complex conjugating, and multiplying every other component by \(-1\).

If from_cartesian=True or from_spherical=True, the argument is interpreted as a single coordinate in terms of those coordinate systems and the flipped coordinate is returned in the same.

Parameters

to_invert (complex/inf or qt.Qobj or np.ndarray) – Extended complex coordinate, cartesian coordinate, spherical coordinate, or spin state/polynomial to invert.

Returns

inverted – Inverted extended complex coordinate, cartesian coordinate, spherical coordinate or spin state/polynomial.

Return type

complex/inf or qt.Qobj or np.ndarray