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Optimize lens magnification Hankel transform #17

Description

@bclevine

Goal

The current implementation of the lens magnification Hankel transform in the _gamma_t_LSS function is slow. We should improve the performance by changing to an FFTLog based Hankel transform, such as the ifht provided by scipy.

Scope

Refactor src/dsf/data_vector/mag_bias.py to use FFTLog instead of direct integration.

This will be a $J_2$ transformation from $C_\ell$ to $\gamma_t$ ; we already have a $j_0$ transformation implemented in src/dsf/utils/converters.py as power_spectrum_to_correlation. We should therefore add another converter in this same style for the $J_2$ transformation which we can call in mag_bias.py. We can also consider moving both of the Hankel transforms into src/dsf/utils/integrators.py, and then adding wrappers in src/dsf/utils/converters.py. But this would probably be a separate issue + PR which we can address later.

Acceptance criteria

  • _gamma_t_LSS is refactored and passes all tests/benchmarks.
  • A new $J_2$ Hankel transform function exists in src/dsf/utils/converters.py.
  • Documentation exists for the new $J_2$ Hankel transform function.

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