W Tilde Imaging With Interpolation

[Jammy2211]

In issue #180 we discuss how we can extend the mapping_matrix_from() function to include source pixel interpolation.

The more efficient w_tilde formalism for an inversion doe not use the mapping_matrix and directly constructs a matrix for the inversion via the function curvature_matrix_via_w_tilde_curvature_preload_imaging_from in the module https://github.com/Jammy2211/PyAutoArray/blob/master/autoarray/inversion/linear_eqn/linear_eqn_util.py

I need to extend this function to use source pixel interpolation. I am not 100% certain on how to do this yet, however I think it can be built into the function data_slim_to_pixelization_unique_from in the module https://github.com/Jammy2211/PyAutoArray/blob/master/autoarray/inversion/mappers/mapper_util.py

This function determines every unique set of mappings between image sub-pixels in a given image pixel and source pixels. For example, if we have a sub-grid of size 2x2 and 3 sub-pixels in image pixel 0 map to the same source pixel 4, this matrix will add an entry to signify that 3 sub-pixels in image pixel 0 map to source pixel 4.

These unique mappings are encoded in the data_to_pixel_unique array, with the weight associated with these mappings in the array data_weights. Again, in the example above, 3 sub-pixels map to a unique source pixel, meaning that their data weight is 0.25*3 = 0.75.

The data weights are constructed as follows (I've simplified the code):

  for ip_sub in range(ip_sub_start, ip_sub_end):

      pix = pixelization_index_for_sub_slim_index[ip_sub]

      for i in range(pix_size):

          if data_to_pix_unique[ip, i] == pix:

              data_weights[ip, i] += sub_fraction

If we have the interpolations arrays described in #180 this becomes:

  for ip_sub in range(ip_sub_start, ip_sub_end):

      pix_indexes = pixelization_indexes_for_sub_slim_index[ip_sub]

     for pix in pix_indexes:

         pixelization_interpolation_weight = pixelization_interpolation_weights[ip_sub, pix]

          for i in range(pix_size):

              if data_to_pix_unique[ip, i] == pix:

                   data_weights[ip, i] += sub_fraction * pixelization_interpolation_weight

Here's hoping...