cyjax.fs_metric#

cyjax.fs_metric(zs, zs_c=None)#

Fubini-Study metric in terms of affine coordinates.

This computes:

\[\frac{1}{1+|z|^2} \mathbb{1} - \frac{1}{(1+|z|^2)^2} \bar{z} z^T\]

Since the FS metric is symmetric, don’t need the patch index as input.

The coordinate array zs can have any shape (at least rank 1). The last dimension of the array is interpreted as the coordinate-index and gives the projective dimension.

Parameters:

  • zs (Union[Array, ndarray, bool_, number]) – Affine coordinates.

  • zs_c (Union[Array, ndarray, bool_, number, None]) – (Optional) Complex conjugate affine coordinates. Can be explicitly passed to facilitate holomorphic gradient computation or to avoid re-computation.

Return type:

Union[Array, ndarray, bool_, number]

Returns:

Matrix representing the value of the Fubini-Study metric and the given point. If the input is an array of coordinates, the output is a matching array of matrices.