cyjax.random.projective_overlap#

cyjax.random.projective_overlap(key, count, dim, this_patch, other_patch, patch_size)#

Sample points lying in overlap region of two affine patches.

The overlap region is defined such that the coordinate values do not exceed patch_size in either patch, i.e. \(z^i \leq \mathrm{patch\_size}\). The points are sampled such that the distribution is invariant under cyjax.change_chart().

Parameters:

  • key (Union[PRNGKeyArray, Array]) – PRNG random key.

  • count (int) – Number of random points to generate.

  • dim (int) – Dimension of complex projective space.

  • this_patch (int) – Patch to sample affine coordinates in.

  • other_patch (int) – Generate points in overlap region with this patch.

Returns:

Shape \(\mathrm{count} \times \mathrm{dim}\) array of affine coordinates which lie in the overlap region.