Port ComplexAngularCentralGaussianDistribution from libDirectional MATLAB

[Copilot]

Summary

Ports ComplexAngularCentralGaussian.m from libDirectional to Python as ComplexAngularCentralGaussianDistribution.

Changes

New file: pyrecest/distributions/hypersphere_subset/complex_angular_central_gaussian_distribution.py

Implements the Complex Angular Central Gaussian distribution on the complex unit hypersphere C^d (equivalently S^{2d-1} in R^{2d}), parameterized by a Hermitian positive definite matrix C of shape (d, d).

• __init__(C): validates C is Hermitian (using allclose), stores parameter matrix and dimension
• pdf(za): evaluates gamma(d)/(2·π^d) · |z^H C^{-1} z|^{-d} / det(C) for each row of za (shape n×d complex). Uses exp(gammaln(d) - log(2) - d·log(π)) for numerical stability
• sample(n): generates samples via lower Cholesky factorization (C = L L^H), draws from CN(0, C), then normalizes to the complex unit sphere
• fit(Z, n_iterations=100) (static): fits the distribution to observed unit vectors using estimate_parameter_matrix
• estimate_parameter_matrix(Z, n_iterations=100) (static): fixed-point EM-style iterations: C ← (1/N) Σ_k weights_k z_k z_k^H where weights_k = (d-1) / |z_k^H C^{-1} z_k|

Updated: pyrecets/distributions/__init__.py

Added import and __all__ entry for ComplexAngularCentralGaussianDistribution.

New test file: pyrecets/tests/distributions/test_complex_angular_central_gaussian_distribution.py

10 tests covering:

• Constructor validation (accepts Hermitian, rejects non-Hermitian)
• PDF correctness: for C=I, pdf is uniform (γ(d)/(2π^d)) on the complex unit sphere (tested for d=2 and d=3)
• PDF positivity and consistency between batch and single-vector evaluation
• Sampling: correct shape and unit norms
• Parameter estimation: fitted C approximately recovers identity when data is uniform
• fit() returns correct type and dimension

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✅MegaLinter analysis: Success

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✅ PYTHON	pylint	288		0	0	83.3s
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✅ REPOSITORY	gitleaks	yes		no	no	4.26s
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✅ REPOSITORY	secretlint	yes		no	no	6.62s
✅ REPOSITORY	syft	yes		no	no	3.06s
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Test Results

   12 files     12 suites   4h 41m 14s ⏱️
  745 tests   745 ✅     0 💤 0 ❌
9 224 runs  7 720 ✅ 1 504 💤 0 ❌

Results for commit 31dd8aa.