Port ComplexBinghamDistribution from libDirectional MATLAB

[Copilot]

Summary

Ports the ComplexBinghamDistribution from MATLAB/libDirectional to Python.

The distribution is defined on the complex unit sphere S^{2d-1} = {z ∈ C^d : ‖z‖ = 1} with pdf p(z) ∝ exp(z^H B z), where B is a d×d Hermitian parameter matrix.

Reference: Kent, J. T. (1994). "The Complex Bingham Distribution and Shape Analysis." Journal of the Royal Statistical Society. Series B, 285-299.

Changes

• New file pyrecets/distributions/hypersphere_subset/complex_bingham_distribution.py:
  • __init__: validates Hermitian B, computes and stores log_norm_const
  • pdf(z): evaluates p(z) = exp(log_norm_const + Re(z^H B z)), supports single or batch complex unit vectors
  • sample(n): Kent, Constable & Er (2004) rejection sampling via truncated-exponential inversions
  • log_norm(B): static method; computes −log C(B) using the Kent (1994) partial-fraction analytical formula after eigenvalue shift; near-equal eigenvalues are perturbed (mirrors MATLAB makeSureEigenvaluesAreNotTooClose)
  • fit(Z): classmethod; MLE via eigendecomposition of sample scatter matrix + least-squares optimization (finite-difference gradient)
  • cauchy_schwarz_divergence(cB1, cB2): static method; non-negative, symmetric divergence matching MATLAB convention
• New file pyrecets/tests/distributions/test_complex_bingham_distribution.py: 17 tests covering all methods (all passing)
• Updated pyrecets/distributions/__init__.py: adds ComplexBinghamDistribution import and __all__ entry

[github-actions]

❌MegaLinter analysis: Error

Descriptor	Linter	Files	Fixed	Errors	Warnings	Elapsed time
✅ COPYPASTE	jscpd	yes		no	no	8.4s
✅ JSON	prettier	2	0	0	0	0.48s
✅ JSON	v8r	2		0	0	2.71s
✅ MARKDOWN	markdownlint	1	0	0	0	0.64s
✅ MARKDOWN	markdown-table-formatter	1	0	0	0	0.27s
✅ PYTHON	bandit	288		0	0	3.74s
✅ PYTHON	black	288	9	0	0	5.72s
❌ PYTHON	flake8	288		1	0	2.08s
✅ PYTHON	isort	288	12	0	0	0.55s
✅ PYTHON	mypy	288		0	0	4.16s
❌ PYTHON	pylint	288		1	0	85.09s
✅ PYTHON	ruff	288	12	0	0	0.05s
✅ REPOSITORY	checkov	yes		no	no	21.92s
✅ REPOSITORY	gitleaks	yes		no	no	4.61s
✅ REPOSITORY	git_diff	yes		no	no	0.04s
✅ REPOSITORY	secretlint	yes		no	no	6.64s
✅ REPOSITORY	syft	yes		no	no	3.54s
✅ REPOSITORY	trivy-sbom	yes		no	no	1.72s
✅ REPOSITORY	trufflehog	yes		no	no	17.93s
✅ YAML	prettier	4	0	0	0	0.49s
✅ YAML	v8r	4		0	0	6.11s
✅ YAML	yamllint	4		0	0	0.46s

Detailed Issues

❌ PYTHON / flake8 - 1 error

pyrecest/distributions/hypersphere_subset/complex_bingham_distribution.py:14:1: F401 'pyrecest.backend.maximum' imported but unused

❌ PYTHON / pylint - 1 error

************* Module pyrecest.distributions.hypersphere_subset.complex_bingham_distribution
pyrecest/distributions/hypersphere_subset/complex_bingham_distribution.py:13:0: W0611: Unused maximum imported from pyrecest.backend (unused-import)

------------------------------------
Your code has been rated at 10.00/10

See detailed reports in MegaLinter artifacts

Your project could benefit from a custom flavor, which would allow you to run only the linters you need, and thus improve runtime performances. (Skip this info by defining FLAVOR_SUGGESTIONS: false)

• Documentation: Custom Flavors
• Command: npx mega-linter-runner@9.4.0 --custom-flavor-setup --custom-flavor-linters PYTHON_PYLINT,PYTHON_BLACK,PYTHON_FLAKE8,PYTHON_ISORT,PYTHON_BANDIT,PYTHON_MYPY,PYTHON_RUFF,COPYPASTE_JSCPD,JSON_V8R,JSON_PRETTIER,MARKDOWN_MARKDOWNLINT,MARKDOWN_MARKDOWN_TABLE_FORMATTER,REPOSITORY_CHECKOV,REPOSITORY_GIT_DIFF,REPOSITORY_GITLEAKS,REPOSITORY_SECRETLINT,REPOSITORY_SYFT,REPOSITORY_TRIVY_SBOM,REPOSITORY_TRUFFLEHOG,YAML_PRETTIER,YAML_YAMLLINT,YAML_V8R

Show us your support by starring ⭐ the repository

[github-actions]

Test Results

    4 files      4 suites   42m 16s ⏱️
  752 tests   752 ✅ 0 💤 0 ❌
3 184 runs  3 184 ✅ 0 💤 0 ❌

Results for commit a5f140d.

♻️ This comment has been updated with latest results.

[FlorianPfaff]

@copilot eliminate the use of numpy function calls and use pyrecest.backend instead

[Copilot]

@copilot eliminate the use of numpy function calls and use pyrecest.backend instead

Done in commit a5f140d. All numpy calls in the implementation have been replaced with pyrecest.backend equivalents:

• Removed import numpy as np and from scipy.linalg import eigh
• Added imports from pyrecest.backend: abs, all, allclose, arange, argsort, array, asarray, complex128, concatenate, conj, cumsum, diff, diag, einsum, empty, exp, linalg, linspace, log, max, maximum, minimum, pi, prod, random, real, sign, sort, sqrt, sum, zeros
• Uses linalg.eigh / linalg.eigvalsh from backend instead of scipy
• Uses random.uniform(size=(n,)) for sampling
• Uses concatenate instead of np.append

The test file was updated similarly (using random.seed, random.normal, linalg.norm, ones, etc. from backend; numpy.testing kept only for assertion helpers). JAX skip decorators added for sampling tests. All 17 tests pass.