Adds an spherical basis that is an exact deprojection of an exponential surface density

[The9Cat]

Summary

Adds an spherical basis that is an exact deprojection of an exponential surface density. Specifically, using the Abel inversion, the exponential surface density
$$\qquad\Sigma(R)=\Sigma_0 e^{-R/a}$$
for $R>0$ deprojects to
$$\qquad\rho(r)=\frac{\Sigma_0}{\pi a} K_0\left(\frac{r}{a}\right).$$

Implementation

The exact deprojected spherical basis is the default in this branch and has the ascii tag ExpDeproj. The previous default was Exponential. The cumulative mass needed by SLGridSph is analytic but only in terms of modified Bessel and Struve functions. The latter is not available in the stdlib. The cumulative mass is computed using brute-force quadrature instead.

Note

I would recommend renaming ExpDeproj to Exponential and delete the older, original implementation. I've left both for testing.

[Copilot]

Pull request overview

Adds a new spherical “exponential deprojection” density model (based on the Abel inversion / modified Bessel (K_0)) and wires it into the cylindrical EOF basis generation as the new default option, with an additional configurable scale-length bias factor and a small test driver.

Changes:

• Introduces ExpDeproj profile implementation (density + tabulated enclosed-mass) and exposes it as a selectable EmpCylSL model (ExpSphere).
• Switches the default spherical model for EmpCylSL EOF generation to the new deprojected exponential-sphere option and updates cache validation to include the model label.
• Adds a bias configuration parameter to rescale the effective disk scale length used for basis construction; adds a testED executable.

Reviewed changes

Copilot reviewed 11 out of 11 changed files in this pull request and generated 7 comments.

Show a summary per file

File	Description
utils/Test/testED.cc	Adds a small executable to numerically re-project the deprojected density and compare against an exponential surface density.
utils/Test/CMakeLists.txt	Builds the new testED utility.
src/Cylinder.cc	Adds bias config support and applies it to the scale length passed into the cylindrical basis constructor.
src/Cylinder.H	Documents and stores the new bias parameter.
include/ExpDeproj.H	Declares the new ExpDeproj profile helper.
include/EmpCylSL.H	Adds ExpSphere to EmpModel and stores a precomputed ExpDeproj instance.
exputil/ExpDeproj.cc	Implements ExpDeproj density and tabulated/interpolated enclosed mass.
exputil/EmpCylSL.cc	Makes ExpSphere the default model, routes densR/massR to ExpDeproj, adds debug output, and tightens HDF5 cache validation via model.
exputil/CMakeLists.txt	Compiles ExpDeproj.cc into exputil.
expui/BiorthBasis.cc	Adds bias, changes default mtype, and expands mtype parsing to include the new model.
expui/BiorthBasis.H	Stores the new bias parameter in the cylindrical basis configuration.

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[Copilot]

@The9Cat I've opened a new pull request, #201, to work on those changes. Once the pull request is ready, I'll request review from you.

[Copilot]

@The9Cat I've opened a new pull request, #202, to work on those changes. Once the pull request is ready, I'll request review from you.

[Copilot]

@The9Cat I've opened a new pull request, #203, to work on those changes. Once the pull request is ready, I'll request review from you.