autoarray.inversion.mesh.mesh.Delaunay#

class Delaunay[source]#

Bases: AbstractMesh

A Delaunay mesh composed of irregular triangular pixels used to reconstruct a source on an unstructured grid.

The mesh consists of pixels vertices in the source plane, which are connected via a Delaunay triangulation to form triangular elements. Each vertex represents a linear parameter in the inversion.

Source-plane coordinates are interpolated onto this mesh using barycentric interpolation within the enclosing triangle. For each coordinate, the three vertices of the containing Delaunay triangle are identified and weighted according to their barycentric distances, providing a smooth, piecewise-linear reconstruction.

JAX & gradient support (2026-07-26, FD-certified): the likelihood runs under jax.jit and is differentiable — the host-called qhull pure_callback returns only integer connectivity tables (frozen under differentiation via stop_gradient; their true derivative is zero between re-wiring events), while point location, barycentric weights, dual areas and split points are computed in-graph from the traced vertices, so jax.grad returns the exact almost-everywhere derivative.

In what sense “autodifferentiable”? The same sense as a ReLU network: the likelihood is piecewise-smooth — perfectly smooth within each triangulation topology, with measure-zero jump discontinuities at the triangle-flip (re-wiring) boundaries, where the barycentric interpolant jumps and has no gradient. A sampler almost surely never lands on a seam, and on either side autodiff returns the exact gradient of the branch the evaluation point is on (FD comparisons show the seams, autodiff does not — individual finite-difference steps can straddle a flip). This contrasts the adaptive rectangular (kernel-CDF) meshes, which are C-infinity by construction with no seams at all. DelaunayNN is the local, linearly precise alternative when continuity through Delaunay flips is required: its Sibson natural-neighbour weights approach the same value from either triangulation.

Caveat for batched samplers: the callback is vmap_method="sequential" (one host qhull call per vmap lane) — the KNearestNeighbor / KNNBarycentric subclasses avoid the callback entirely and remain the batched-throughput option.

Methods

`interpolator_from`	Mapper objects describe the mappings between pixels in the masked 2D data and the pixels in a mesh, in both the data and source frames.
`relocated_grid_from`	Relocates all coordinates of the input source_plane_data_grid that are outside of a border (which is defined by a grid of (y,x) coordinates) to the edge of this border.
`relocated_mesh_grid_from`	Relocates all coordinates of the input source_plane_mesh_grid that are outside of a border (which is defined by a grid of (y,x) coordinates) to the edge of this border.

Attributes

`interpolator_cls`
`skip_areas`	Whether to skip barycentric area calculations and split point computations during Delaunay triangulation.
`supports_split_regularization`	Whether this mesh supports "split" regularization schemes (e.g. `ConstantSplit`, `AdaptSplit`, `AdaptSplitZeroth`).
`zeroed_pixels`	Return the positive mesh-local pixel indices to zero for a Delaunay mesh.

property zeroed_pixels#

Return the positive mesh-local pixel indices to zero for a Delaunay mesh.

For Delaunay meshes, self.zeroed_pixels is interpreted as a count of pixels to be zeroed at the end of the pixel block. For example:

self.pixels = 780, self.zeroed_pixels = 30

returns indices 750..779.

Returns:: 1D array of positive pixel indices to zero.
Return type:: np.ndarray

property skip_areas#: Whether to skip barycentric area calculations and split point computations during Delaunay triangulation. When True, the Delaunay interface returns only the minimal set of outputs (points, simplices, mappings) without computing split_points or splitted_mappings. This optimization is useful for regularization schemes like Matérn kernels that don’t require area-based calculations. Default is False.

property interpolator_cls#

interpolator_from(source_plane_data_grid, source_plane_mesh_grid, border_relocator=None, adapt_data=None, xp=<module 'numpy' from '/home/docs/checkouts/readthedocs.org/user_builds/pyautogalaxy/envs/latest/lib/python3.12/site-packages/numpy/__init__.py'>)[source]#

Mapper objects describe the mappings between pixels in the masked 2D data and the pixels in a mesh, in both the data and source frames.

This function returns a MapperDelaunay as follows:

Before this routine is called, a sparse grid of (y,x) coordinates are computed from the 2D masked data, the image_plane_mesh_grid, which acts as the Delaunay triangle vertexes of the mesh and mapper.
Before this routine is called, operations are performed on this image_plane_mesh_grid that transform it from a 2D grid which overlaps with the 2D mask of the data in the data frame to an irregular grid in the source frame, the source_plane_mesh_grid.
If the border relocator is input, the border of the input source_plane_data_grid is used to relocate all of the grid’s (y,x) coordinates beyond the border to the edge of the border.
If the border relocatiro is input, the border of the input source_plane_data_grid is used to relocate all of the transformed source_plane_mesh_grid’s (y,x) coordinates beyond the border to the edge of the border.
Use the transformed source_plane_mesh_grid’s (y,x) coordinates as the Vertex of the Delaunay mesh.

Parameters:

border_relocator (Optional[BorderRelocator]) – The border relocator, which relocates coordinates outside the border of the source-plane data grid to its edge.
source_plane_data_grid (Grid2D) – A 2D grid of (y,x) coordinates associated with the unmasked 2D data after it has been transformed to the source reference frame.
source_plane_mesh_grid (Grid2DIrregular) – The vertex of every Delaunay triangle pixel in the source frame, which are initially derived by computing a sparse set of (y,x) coordinates computed from the unmasked data in the data frame and applying a transformation to this.
image_plane_mesh_grid – The sparse set of (y,x) coordinates computed from the unmasked data in the data frame. This has a transformation applied to it to create the source_plane_mesh_grid.
adapt_data (ndarray) – Not used for a rectangular mesh.