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Compute d2#83

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jtgasparik wants to merge 6 commits intoARM-DOE:mainfrom
jtgasparik:compute_d2
Open

Compute d2#83
jtgasparik wants to merge 6 commits intoARM-DOE:mainfrom
jtgasparik:compute_d2

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Function to compute the statistical distance ($d^2$) for an associated value of $\tau$. This PR contains:

  1. Added helper functions for the NDM module which consolidates the overlapping computations between the $\tau$ and $d^2$ functions.
  2. Function to compute the $d^2$ value used to determine the best $\tau$ value in the non-evaporative region.
  3. Tests to compare the calculated $\tau$ value based on the best $d^2$ value and compare to true values from purely scattering particles.
  4. One test to compare the best $\tau$ value for an absorbing particle and compare to the true value from the purely scattering particle (this is an approximate way to test because $\tau$ values should not vary significantly within a single population). Testing tolerance slightly higher to accommodate the evaporative particle.
  5. Added an optional flag to the plot_normalized_derivative function to plot the scattering signal on the same plot as the normalized derivative for comparison purposes.

@jtgasparik jtgasparik requested a review from rcjackson April 16, 2026 19:21
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