Support domain inclusion in chained TrueMeasure transformations

[Laasya-73]

Summary

This PR generalizes compatibility checking for chained TrueMeasure transformations.

Previously, consecutive transformations were considered compatible only when the range of the preceding transformation exactly matched the domain of the next:

$$ [ R_{j-1} = D_j ] $$

This is more restrictive than necessary. The updated rule accepts the chain whenever the preceding range is contained within the next domain:

$$ [ R_{j-1} \subseteq D_j ] $$

This allows valid chained transformations with strict domain inclusion while continuing to reject genuinely incompatible ranges.

Changes

• Add _range_in_domain() to AbstractTrueMeasure.
• Replace exact domain/range equality checking with coordinate-wise containment.
• Preserve NumPy broadcasting between (1, 2) and (d, 2) domain/range representations.
• Support finite and unbounded interval bounds.
• Update compatibility error messages to reflect containment semantics.
• Add tests covering:
  • exact equality;
  • strict inclusion;
  • unbounded domains;
  • multidimensional inclusion;
  • broadcasting;
  • malformed/non-broadcastable bounds;
  • actual out-of-domain failures.
• Add demos/true_measure_domain_inclusion.ipynb demonstrating:
  • the previous and updated compatibility behavior;
  • valid 1D and multidimensional TrueMeasure chains;
  • rejection of incompatible chains;
  • the distinction between domain compatibility, deterministic transport, and importance sampling;
  • the Gaussian/Logistic QMC example and the relationship between the importance-sampling likelihood ratio and the corresponding transport Jacobian.

Scope

This change is intentionally limited to domains/ranges represented as one-dimensional intervals or multidimensional axis-aligned boxes.

It does not introduce arbitrary measure-transport semantics, disconnected support representations, or changes to the existing importance-sampling implementation.

Notes

This PR replaces #602 after moving the feature branch into the QMCSoftware repository.

[codecov]

Codecov Report

✅ All modified and coverable lines are covered by tests.
✅ Project coverage is 88.71%. Comparing base (dc3d923) to head (c25697b).

Additional details and impacted files

@@             Coverage Diff             @@
##           develop     #609      +/-   ##
===========================================
+ Coverage    88.65%   88.71%   +0.05%     
===========================================
  Files          104      104              
  Lines         8508     8530      +22     
===========================================
+ Hits          7543     7567      +24     
+ Misses         965      963       -2     

Flag	Coverage Δ
alltests	88.71% <100.00%> (+0.05%)	⬆️

Flags with carried forward coverage won't be shown. Click here to find out more.

Files with missing lines	Coverage Δ
qmcpy/true_measure/abstract_true_measure.py	94.65% <100.00%> (+2.91%)	⬆️

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.

[Copilot]

Pull request overview

Generalizes chained TrueMeasure compatibility from exact range/domain equality to interval containment.

Changes:

• Adds broadcast-aware range containment checks and revised errors.
• Adds unit tests for valid and invalid chains.
• Adds a detailed demonstration notebook.

Reviewed changes

Copilot reviewed 2 out of 3 changed files in this pull request and generated 2 comments.

File	Description
qmcpy/true_measure/abstract_true_measure.py	Implements containment-based compatibility.
test/test_true_measures.py	Tests containment and chaining behavior.
demos/true_measure_domain_inclusion.ipynb	Demonstrates the new semantics and mathematical context.

---

💡 Add a code-review agent skill or configure MCP servers for context-aware, tailored reviews. Learn more in the docs.

[fjhickernell]

@Laasya-73 you should add some examples in the demo notebook of integration with the chained measures.

[Laasya-73]

@Laasya-73 you should add some examples in the demo notebook of integration with the chained measures.

Sure, I will add and update the PR.

[sou-cheng-choi]

@Laasya-73

1. Could you add the notebook to mkdocs.yml? Thank you.
2. Validate input to _range_in_domain:

>>> AbstractTrueMeasure._range_in_domain(np.empty((0, 2)),[[0, 1]]) 
True
>>> AbstractTrueMeasure._range_in_domain([["a", "z"]], [["a", "z"]])
True

3. In the notebook, from qmcpy import DigitalNetB2, Kumaraswamy, Uniform from qmcpy.true_measure.abstract_true_measure import AbstractTrueMeasure can be simplified to from qmcpy import AbstractTrueMeasure, DigitalNetB2, Kumaraswamy, Uniform

4. In a command line window, you could run "make format" to beautify the files. Give it a try and see if it helps.

5. For the notebook sub-section title, "### One compatibility visual", do you want to make it "D."? Sections 3 and 5 have sub-section labels. Would you like to make them consistent?