Port ToroidalVMRivestDistribution from libDirectional

[Copilot]

Ports the bivariate von Mises distribution (Rivest 1988 variant) from the MATLAB libDirectional library into PyRecEst.

New distribution: ToroidalVMRivestDistribution

Models dependent unit vectors on the torus via two correlation parameters alpha and beta (corresponding to A = diag([alpha, beta])):

from pyrecest.distributions import ToroidalVMRivestDistribution
import numpy as np

dist = ToroidalVMRivestDistribution(
    mu=np.array([1.0, 2.0]),
    kappa=np.array([0.7, 1.4]),
    alpha=np.array(0.5),
    beta=np.array(0.3),
)
dist.pdf(np.array([1.5, 2.5]))          # evaluate density
dist.trigonometric_moment(1)            # analytical first moment
dist.circular_correlation_jammalamadaka()  # analytical correlation
dist.shift(np.array([0.5, 1.0]))        # returns shifted copy

Changes

• hypertorus/toroidal_vm_rivest_distribution.py — new class extending AbstractToroidalDistribution with:
  • norm_const: double series over modified Bessel functions (truncated at ±10 terms)
  • pdf: vectorized evaluation supporting batched inputs
  • trigonometric_moment: closed-form for n=1; falls back to numerical otherwise
  • circular_correlation_jammalamadaka: analytical override of the base class numerical fallback
  • shift: returns a new instance with shifted mu
• distributions/__init__.py — exports ToroidalVMRivestDistribution
• tests/distributions/test_toroidal_vm_rivest_distribution.py — 15 tests covering normalization, pdf correctness, analytical vs. numerical moments, shift, correlation, and the zero-correlation special case (reduces to independent von Mises product)

[github-actions]

✅MegaLinter analysis: Success

Descriptor	Linter	Files	Fixed	Errors	Warnings	Elapsed time
✅ COPYPASTE	jscpd	yes		no	no	7.43s
✅ JSON	prettier	2	0	0	0	0.48s
✅ JSON	v8r	2		0	0	2.34s
✅ MARKDOWN	markdownlint	1	0	0	0	0.65s
✅ MARKDOWN	markdown-table-formatter	1	0	0	0	0.2s
✅ PYTHON	bandit	252		0	0	3.09s
✅ PYTHON	black	252	2	0	0	4.47s
✅ PYTHON	flake8	252		0	0	1.76s
✅ PYTHON	isort	252	2	0	0	0.48s
✅ PYTHON	mypy	252		0	0	3.98s
✅ PYTHON	pylint	252		0	0	70.32s
✅ PYTHON	ruff	252	2	0	0	0.04s
✅ REPOSITORY	checkov	yes		no	no	23.33s
✅ REPOSITORY	gitleaks	yes		no	no	4.47s
✅ REPOSITORY	git_diff	yes		no	no	0.02s
✅ REPOSITORY	secretlint	yes		no	no	6.32s
✅ REPOSITORY	syft	yes		no	no	3.1s
✅ REPOSITORY	trivy-sbom	yes		no	no	1.82s
✅ REPOSITORY	trufflehog	yes		no	no	15.63s
✅ YAML	prettier	4	0	0	0	0.49s
✅ YAML	v8r	4		0	0	5.01s
✅ YAML	yamllint	4		0	0	0.43s

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[github-actions]

Test Results

   12 files  ±  0     12 suites  ±0   3h 16m 35s ⏱️ + 4m 36s
  561 tests + 15    561 ✅ + 15      0 💤 ± 0  0 ❌ ±0 
6 944 runs  +180  5 744 ✅ +156  1 200 💤 +24  0 ❌ ±0 

Results for commit 60b71f7. ± Comparison against base commit deb475e.

[FlorianPfaff]

@copilot Can you fix the megalinter errors?

[Copilot]

@copilot Can you fix the megalinter errors?

Fixed in 8b974d1. Three issues were addressed:

• flake8/ruff E741: renamed loop variable l → ell (ambiguous name) in norm_const, trigonometric_moment, and the correlation helper
• pylint R0914: extracted a _correlation_series_sums() helper method from circular_correlation_jammalamadaka to reduce local variable count from 17 to within the 15-variable limit
• pylint W0237: renamed shift_angles → shift_by to match the base class parameter name