BiorthBasis::Cylinder deprojection improvements

[The9Cat]

Movitation

Needed a less cuspy option than exponential for attempting to produce a doughnut-shaped basis. So this adds a Toomre model for that purpose.

Improvements

• I noticed that the numerical Abel transform had poor systematics in the inner profile. This is not a bug fix, but it is a noticeable improvement. The original version would not cause failure but could result in weaker EOF convergece.
• I added all three numerical variants as source configuration choices and switched to the internal derivative form by default. I provided some verification and test routines for this in utils/Tests. These methods could be made user selectable but I have not done this in this PR.

[Copilot]

Pull request overview

Adds a Toomre disk option for cylindrical-basis deprojection/conditioning, expands the Abel inversion implementations used during deprojection, and introduces several standalone test/verification executables under utils/Test.

Changes:

• Add a new Toomre disk model and wire a configurable deprojection model selector (dmodel) into Cylindrical basis initialization.
• Update EmpCylSL::create_deprojection to support multiple Abel inversion variants (Derivative/Subtraction/IBP) with derivative as default.
• Add Deprojector/EmpDeproj test utilities and build targets in utils/Test.

Reviewed changes

Copilot reviewed 15 out of 15 changed files in this pull request and generated 16 comments.

Show a summary per file

File	Description
utils/Test/testEmpDeproj.cc	New CLI test comparing EmpDeproj vs Deprojector across profiles/methods
utils/Test/testDeproject.cc	New example program for Deprojector (sampled + analytic construction)
utils/Test/testDeprojPlummer.cc	New simple deprojection verification driver (currently hardwired)
utils/Test/EmpDeproj.cc	New empirical deprojection implementation used by test programs
utils/Test/EmpDeproj.H	Header for EmpDeproj test-class API
utils/Test/Deprojector.cc	New numerical Abel deprojection implementation and grid integration logic
utils/Test/Deprojector.H	Header/API for Deprojector
utils/Test/CubicSpline.cc	New spline helper for sampled-data deprojection path
utils/Test/CubicSpline.H	Header for CubicSpline
utils/Test/CMakeLists.txt	Adds new test executables to the build
include/EmpCylSL.H	Adds AbelType + abel_type member to control deprojection variant
include/DiskModels.H	Adds Toomre disk density model for deprojection conditioning
exputil/EmpCylSL.cc	Switchable Abel inversion variants used in deprojection pipeline
expui/BiorthBasis.cc	Adds dmodel config key + lookup map and uses it when deproject is enabled
expui/BiorthBasis.H	Introduces DeprojType enum + lookup map for deprojection disk models

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[Copilot]

Pull request overview

Adds a Toomre-based option for cylindrical deprojection and refines the numerical Abel inversion machinery, along with several small test/verification executables under utils/Test.

Changes:

• Add a new Toomre disk model for deprojection and wire it into cylindrical basis initialization via a dmodel lookup.
• Introduce multiple Abel inversion variants (derivative/subtraction/IBP) in the EmpCylSL deprojection path (defaulting to derivative).
• Add standalone utils/Test deprojection utilities (Deprojector, EmpDeproj) and test drivers, and hook them into utils/Test/CMakeLists.txt.

Reviewed changes

Copilot reviewed 16 out of 16 changed files in this pull request and generated 12 comments.

Show a summary per file

File	Description
utils/Test/testEmpDeproj.cc	New CLI test comparing EmpDeproj against Deprojector for several analytic profiles.
utils/Test/testEmp.cc	New CLI test for donut-shaped (inner cut) empirical deprojection.
utils/Test/testDeproject.cc	New minimal examples for Deprojector from sampled data vs functor.
utils/Test/testDeprojPlummer.cc	New Plummer/Gaussian/Toomre Deprojector validation driver.
utils/Test/EmpDeproj.cc	Adds an empirical deprojection implementation used by the new test drivers.
utils/Test/EmpDeproj.H	Declares the EmpDeproj helper class and AbelType selection.
utils/Test/Deprojector.cc	Adds a standalone deprojection implementation with tail-matching and improved inner integration handling.
utils/Test/Deprojector.H	Declares the standalone Deprojector API used by tests.
utils/Test/CubicSpline.cc	Adds a basic natural cubic spline for sampled-data deprojection.
utils/Test/CubicSpline.H	Declares the cubic spline used by Deprojector sampled-data ctor.
utils/Test/CMakeLists.txt	Registers the new utils/Test executables in the build.
include/EmpCylSL.H	Adds AbelType state to EmpCylSL for selecting deprojection variant.
include/DiskModels.H	Adds a new Toomre disk density model (used for deprojection conditioning).
exputil/EmpCylSL.cc	Updates EmpCylSL’s Abel inversion integral to support multiple variants.
expui/BiorthBasis.cc	Adds dmodel string parsing + lookup for selecting deprojection model (mn/exponential/toomre/python).
expui/BiorthBasis.H	Adds DeprojType and makes DiskType an enum class for stronger typing.

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