Port GeneralizedKSineSkewedWrappedCauchyDistribution (GSSC) from libDirectional

[Copilot]

Summary

Ports the Generalized K Sine-Skewed Wrapped Cauchy Distribution (GSSC) from libDirectional to PyRecEst.

Changes

pyrecest/distributions/circle/sine_skewed_distributions.py

• Added cos, cosh, sinh to the backend imports
• Added GeneralizedKSineSkewedWrappedCauchyDistribution — the Generalized K Sine-Skewed Wrapped Cauchy distribution, analogous to the existing GeneralizedKSineSkewedVonMisesDistribution but using the Wrapped Cauchy as the base distribution

The PDF is:

f(x) = wc(x; μ, γ) · (1 + λ·sin(k·(x−μ)))^m / Z

where wc is the wrapped Cauchy density and Z is the closed-form normalization constant derived from the wrapped Cauchy trigonometric moments E[cos(n(x−μ))] = exp(−nkγ). Supports m = 1, 2, 3, 4 with:

• m=1: Z = 1
• m=2: Z = 1 + λ²/2·(1 − e^{−2kγ})
• m=3: Z = 1 + 3λ²/2·(1 − e^{−2kγ})
• m=4: Z = 1 + 3λ²·(1 − e^{−2kγ}) + λ⁴/8·(3 − 4e^{−2kγ} + e^{−4kγ})

Note: The pdf uses the WC formula directly rather than calling the existing WrappedCauchyDistribution.pdf, which has a known centering bug for non-zero mu (it computes WC centered at 2μ rather than μ).

pyrecest/distributions/__init__.py

• Added GeneralizedKSineSkewedWrappedCauchyDistribution to both the import and __all__

pyrecest/tests/distributions/test_sine_skewed_distributions.py

• Moved import numpy.testing as npt to the top of the file
• Added TestGeneralizedKSineSkewedWrappedCauchyDistribution test class covering:
  • test_initialization — valid params work, invalid lambda_, m, and gamma raise AssertionError
  • test_pdf_m1_normalizes — m=1 integrates to 1
  • test_pdf_m2_normalizes — m=2 integrates to 1
  • test_pdf_m3_normalizes — m=3 integrates to 1
  • test_pdf_m4_normalizes — m=4 integrates to 1
  • test_pdf_nonnegative — PDF values are ≥ 0 for all m
  • test_shift — shift() updates mu correctly

Reference

Bekker, A., Nakhaei Rad, N., Arashi, M., Ley, C. (2020). Generalized Skew-Symmetric Circular and Toroidal Distributions, Florence Nightingale Directional Statistics volume, Springer.

[github-actions]

❌MegaLinter analysis: Error

Descriptor	Linter	Files	Fixed	Errors	Warnings	Elapsed time
✅ COPYPASTE	jscpd	yes		no	no	8.14s
✅ JSON	prettier	2	0	0	0	0.42s
✅ JSON	v8r	2		0	0	2.82s
✅ MARKDOWN	markdownlint	1	0	0	0	0.66s
✅ MARKDOWN	markdown-table-formatter	1	0	0	0	0.25s
✅ PYTHON	bandit	262		0	0	3.32s
✅ PYTHON	black	262	2	0	0	4.95s
✅ PYTHON	flake8	262		0	0	1.88s
✅ PYTHON	isort	262	2	0	0	0.51s
✅ PYTHON	mypy	262		0	0	4.19s
❌ PYTHON	pylint	262		4	0	75.7s
✅ PYTHON	ruff	262	2	0	0	0.05s
✅ REPOSITORY	checkov	yes		no	no	21.71s
✅ REPOSITORY	gitleaks	yes		no	no	4.19s
✅ REPOSITORY	git_diff	yes		no	no	0.04s
✅ REPOSITORY	secretlint	yes		no	no	6.41s
✅ REPOSITORY	syft	yes		no	no	3.02s
✅ REPOSITORY	trivy-sbom	yes		no	no	1.7s
✅ REPOSITORY	trufflehog	yes		no	no	17.71s
✅ YAML	prettier	4	0	0	0	0.47s
✅ YAML	v8r	4		0	0	5.16s
✅ YAML	yamllint	4		0	0	0.41s

Detailed Issues

❌ PYTHON / pylint - 4 errors

************* Module pyrecest.tests.distributions.test_sine_skewed_distributions
pyrecest/tests/distributions/test_sine_skewed_distributions.py:139:8: E1101: Module 'pyrecest' has no 'backend' member (no-member)
pyrecest/tests/distributions/test_sine_skewed_distributions.py:152:8: E1101: Module 'pyrecest' has no 'backend' member (no-member)
pyrecest/tests/distributions/test_sine_skewed_distributions.py:165:8: E1101: Module 'pyrecest' has no 'backend' member (no-member)
pyrecest/tests/distributions/test_sine_skewed_distributions.py:178:8: E1101: Module 'pyrecest' has no 'backend' member (no-member)

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[github-actions]

Test Results

   12 files  ± 0     12 suites  ±0   3h 18m 21s ⏱️ + 1m 18s
  623 tests + 7    623 ✅ + 7      0 💤 ± 0  0 ❌ ±0 
7 688 runs  +84  6 376 ✅ +52  1 312 💤 +32  0 ❌ ±0 

Results for commit 9ba24a2. ± Comparison against base commit 4bdfab5.

♻️ This comment has been updated with latest results.

[FlorianPfaff]

@copilot Can use the "skipif" decorator to skip the tests that are not supporrted for other backends? There are similar cases in the code base that you can use as reference.

FAILED pyrecest/tests/distributions/test_sine_skewed_distributions.py::TestGeneralizedKSineSkewedWrappedCauchyDistribution::test_pdf_m1_normalizes - AssertionError: Only supported for numpy backend
FAILED pyrecest/tests/distributions/test_sine_skewed_distributions.py::TestGeneralizedKSineSkewedWrappedCauchyDistribution::test_pdf_m2_normalizes - AssertionError: Only supported for numpy backend
FAILED pyrecest/tests/distributions/test_sine_skewed_distributions.py::TestGeneralizedKSineSkewedWrappedCauchyDistribution::test_pdf_m3_normalizes - AssertionError: Only supported for numpy backend
FAILED pyrecest/tests/distributions/test_sine_skewed_distributions.py::TestGeneralizedKSineSkewedWrappedCauchyDistribution::test_pdf_m4_normalizes - AssertionError: Only supported for numpy backend

[Copilot]

@copilot Can use the "skipif" decorator to skip the tests that are not supporrted for other backends? There are similar cases in the code base that you can use as reference.

FAILED pyrecest/tests/d...

Done in commit 7a752fa. Added import pyrecest.backend to the test file and decorated all four normalization tests (test_pdf_m1_normalizes through test_pdf_m4_normalizes) with @unittest.skipIf(pyrecest.backend.__backend_name__ in ("pytorch", "jax"), reason="Not supported on this backend"), following the same pattern used in e.g. test_toroidal_wrapped_normal_distribution.py.