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.
• Fixed a bug in Cylindrical parameter parsing: the dmodel key was read as a bool rather than a string.
• 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.
• I added a Python functor for the disk profile used in the spherical deprojection; this adds more generality for non-traditional surface density profiles.
• A standalone test driver named testEmp that uses the same algorithm as EmpCylSL is included in utils/Test. I also provided two basic sanity checks on Abel transforms for verification and debugging. These could be removed.

Notes and comments

• Trying to make an exponential profile with an inner cutoff (doughnut) with a an exponential deprojection results in ringing features in the doughnut hole
• A more gradual surface density with no cusp for the deprojection, such as a Toomre surface density, helps reduce the wiggle features a bit. Only a bit because the inner roll over needs to be very shallow for positive density.
• One can not use a basis with a sharp inner cut because this yields negative density in the deprojection.
• It is additionally helpful, although not strictly necessary, to roll over the inner density for the basis construction more slowly than the target density to keep the Abel deprojected density positive.

Examples

• First 8 basis functions for m=0 for a exponential disk with h/a=0.1, a=1 and a $(1+\tanh([R-0.005]/0.001)$ inner hole. The target basis is the deprojected disk with $\Sigma=(1+R^2)^{-3/2}$ with the inner rollover $(1+\tanh([R-0.005]/0.02)$, the smallest width that gives positive deprojected density. The inner edge of the model is obvious in these images.

- First 8 basis functions as above but for a deprojected exponential basis with no hole. It is not too terrible and the orthogonality remains excellent, but there is more noise inside the cutoff for this one.

[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

---

💡 Add Copilot custom instructions for smarter, more guided reviews. Learn how to get started.

You can also share your feedback on Copilot code review. Take the survey.

[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.

---

💡 Add Copilot custom instructions for smarter, more guided reviews. Learn how to get started.

You can also share your feedback on Copilot code review. Take the survey.

[Copilot]

Pull request overview

This PR enhances cylindrical-basis deprojection support by adding a Toomre disk option and improving the numerical Abel inversion implementation, along with new test/verification utilities under utils/Test.

Changes:

• Add a Toomre disk model for cylindrical deprojection to provide a less-cuspy alternative to exponential.
• Introduce selectable Abel inversion variants (derivative/subtraction/IBP) and change the default to the internal-derivative form.
• Add standalone test programs and supporting spline/deprojection utilities for verification.

Reviewed changes

Copilot reviewed 15 out of 15 changed files in this pull request and generated 12 comments.

Show a summary per file

File	Description
expui/BiorthBasis.cc	Adds dmodel string handling and deprojection-model selection (mn/exponential/toomre/python) + pyproj config.
expui/BiorthBasis.H	Extends Cylindrical config/state with pyproj, adds DeprojType, and converts DiskType to enum class.
exputil/EmpCylSL.cc	Updates Abel inversion implementation and routes through a new abel_type selection.
include/EmpCylSL.H	Adds AbelType enum + abel_type member to control deprojection inversion method.
include/DiskModels.H	Adds a Toomre disk model usable for deprojection conditioning.
utils/Test/CMakeLists.txt	Builds new test executables (testDeproj, testEmpDeproj, testEmp) and links Python embed for testEmp.
utils/Test/testDeproject.cc	New CLI tool to validate Deprojector against analytic profiles.
utils/Test/testEmpDeproj.cc	New CLI tool comparing EmpDeproj vs Deprojector across profiles/Abel variants.
utils/Test/testEmp.cc	New CLI tool driving EmpDeproj, optionally via embedded Python-provided functions.
utils/Test/EmpDeproj.cc	Implements a test-local EmpDeproj (EmpCylSL-like) deprojection routine with selectable Abel variants.
utils/Test/EmpDeproj.H	Declares the test-local EmpDeproj class API.
utils/Test/Deprojector.cc	Implements an independent Abel deprojector with improved inner-radius systematics.
utils/Test/Deprojector.H	Declares the Deprojector API and data-driven/analytic constructors.
utils/Test/CubicSpline.cc	Adds a minimal natural cubic spline implementation used by Deprojector.
utils/Test/CubicSpline.H	Declares the minimal spline interface used by Deprojector.

---

💡 Add Copilot custom instructions for smarter, more guided reviews. Learn how to get started.

You can also share your feedback on Copilot code review. Take the survey.

[The9Cat]

@copilot You suggested changing M_PI to constexpr double pi = std::acos(-1.0);. However, all clang builds are now failing because std::acos is not available as a constexpr. Please fix this, since it was your idea.

[Copilot]

@The9Cat I've opened a new pull request, #209, to work on those changes. Once the pull request is ready, I'll request review from you.

[Copilot]

Pull request overview

This PR enhances cylindrical basis deprojection support by adding a Toomre disk option and improving/expanding the numerical Abel inversion approach used during deprojection and verification, along with several new standalone test drivers under utils/Test.

Changes:

• Add a Toomre disk model for smoother, less-cuspy cylindrical deprojection.
• Introduce selectable Abel inversion variants (derivative/subtraction/IBP) in EmpCylSL deprojection logic (defaulting to derivative).
• Add standalone C++ test/verification utilities for deprojection and Abel transform behavior, including optional Python-supplied surface-density functions.

Reviewed changes

Copilot reviewed 15 out of 15 changed files in this pull request and generated 5 comments.

Show a summary per file

File	Description
utils/Test/testEmpDeproj.cc	New CLI test comparing EmpDeproj vs Deprojector for multiple analytic profiles.
utils/Test/testEmp.cc	New CLI test driver supporting Python-embedded callable for Σ(R) or Σ(R,z).
utils/Test/testDeproject.cc	New independent Deprojector test driver for analytic profiles.
utils/Test/EmpDeproj.cc	Adds an empirical deprojection helper implementation with multiple Abel variants (test utility).
utils/Test/EmpDeproj.H	Declares the EmpDeproj test utility API and AbelType enum.
utils/Test/Deprojector.cc	Adds an independent deprojection implementation and improved near-origin handling (test utility).
utils/Test/Deprojector.H	Declares Deprojector test utility API (analytic- and sampled-data constructors).
utils/Test/CubicSpline.cc	New natural cubic spline implementation used by Deprojector (test utility).
utils/Test/CubicSpline.H	Declares the spline implementation (test utility).
utils/Test/CMakeLists.txt	Wires new test executables (testDeproj, testEmpDeproj, testEmp) into the utils/Test build.
include/EmpCylSL.H	Adds internal AbelType and abel_type state for deprojection.
include/DiskModels.H	Adds Toomre disk model for deprojection inputs.
exputil/EmpCylSL.cc	Updates Abel inversion integral logic to support multiple numerical variants.
expui/BiorthBasis.cc	Adds dmodel mapping/selection for deprojection model types, plus pyproj support.
expui/BiorthBasis.H	Adds deprojection model typing (DeprojType), pyproj, and modernizes DiskType to enum class.

---

💡 Add Copilot custom instructions for smarter, more guided reviews. Learn how to get started.

You can also share your feedback on Copilot code review. Take the survey.