Port ToroidalVMMatrixDistribution (bivariate von Mises, matrix version) from libDirectional

[Copilot]

Ports the ToroidalVMMatrixDistribution class from MATLAB/libDirectional to Python, implementing the bivariate von Mises distribution with a 2×2 correlation matrix A (Mardia 1975; Kurz & Hanebeck MFI 2015).

New distribution: ToroidalVMMatrixDistribution

Parameters: mu (2,), kappa (2,), A (2×2)

PDF:

f(x) = C · exp(κ₁cos(x₁−μ₁) + κ₂cos(x₂−μ₂)
             + cos(x₁−μ₁)·A₀₀·cos(x₂−μ₂) + cos(x₁−μ₁)·A₀₁·sin(x₂−μ₂)
             + sin(x₁−μ₁)·A₁₀·cos(x₂−μ₂) + sin(x₁−μ₁)·A₁₁·sin(x₂−μ₂))

• Normalization: Taylor series (≤8 terms) when κ ≤ 1.5 and max|A| ≤ 1; falls back to numerical dblquad for higher concentrations
• multiply(other): Exact closed-form product via matrix rotation formula (combines mu/kappa as in the 1D von Mises case, transforms A via a 4×4 rotation matrix)
• marginalize_to_1d(dimension): Analytic marginal using the identity ∫exp(α·cos θ + β·sin θ)dθ = 2π·I₀(√(α²+β²)), correct for both dimension=0 and dimension=1
• shift(angles): Returns copy with mu shifted mod 2π

mu = array([1.0, 2.0])
kappa = array([0.7, 1.4])
A = array([[0.5, 0.1], [-0.1, 0.3]])
dist = ToroidalVMMatrixDistribution(mu, kappa, A)

dist2 = dist.multiply(dist)           # exact product
marginal = dist.marginalize_to_1d(0)  # CustomCircularDistribution

[github-actions]

✅MegaLinter analysis: Success

Descriptor	Linter	Files	Fixed	Errors	Warnings	Elapsed time
✅ COPYPASTE	jscpd	yes		no	no	7.32s
✅ JSON	prettier	2	0	0	0	0.8s
✅ JSON	v8r	2		0	0	3.08s
✅ MARKDOWN	markdownlint	1	0	0	0	0.66s
✅ MARKDOWN	markdown-table-formatter	1	0	0	0	0.2s
✅ PYTHON	bandit	252		0	0	3.11s
✅ PYTHON	black	252	1	0	0	4.65s
✅ PYTHON	flake8	252		0	0	1.78s
✅ PYTHON	isort	252	1	0	0	0.48s
✅ PYTHON	mypy	252		0	0	4.02s
✅ PYTHON	pylint	252		0	0	71.11s
✅ PYTHON	ruff	252	1	0	0	0.04s
✅ REPOSITORY	checkov	yes		no	no	22.89s
✅ REPOSITORY	gitleaks	yes		no	no	4.01s
✅ REPOSITORY	git_diff	yes		no	no	0.02s
✅ REPOSITORY	secretlint	yes		no	no	5.54s
✅ REPOSITORY	syft	yes		no	no	3.27s
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✅ REPOSITORY	trufflehog	yes		no	no	16.29s
✅ YAML	prettier	4	0	0	0	0.45s
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[github-actions]

Test Results

   12 files     12 suites   3h 20m 51s ⏱️
  597 tests   597 ✅     0 💤 0 ❌
7 376 runs  6 128 ✅ 1 248 💤 0 ❌

Results for commit 94c91a3.

♻️ This comment has been updated with latest results.

[FlorianPfaff]

@copilot My pyrecest.backend can be numpy, pytorch, or Jax (all unified under a numpy-like interface). Please use this and never import anything from numpy.

[Copilot]

@copilot My pyrecest.backend can be numpy, pytorch, or Jax (all unified under a numpy-like interface). Please use this and never import anything from numpy.

Done in commit 7768c8c. Both toroidal_vm_matrix_distribution.py and its test file now use pyrecest.backend exclusively — import numpy as np has been removed and all numpy calls (np.cos, np.sin, np.arctan2, np.sqrt, np.max, np.abs, np.linalg.solve, np.pi, np.array) are replaced with the corresponding pyrecest.backend imports (cos, sin, arctan2, sqrt, max, abs, linalg.solve, pi, array). The test file retains numpy.testing as npt only for assertion utilities, consistent with other test files in the repo.

[FlorianPfaff]

@copilot Can you investigate and fix those two test failures?
=========================== short test summary info ============================
FAILED pyrecest/tests/distributions/test_toroidal_vm_matrix_distribution.py::TestToroidalVMMatrixDistribution::test_marginalize_to_1d_dim0 - TypeError: only 0-dimensional arrays can be converted to Python scalars
FAILED pyrecest/tests/distributions/test_toroidal_vm_matrix_distribution.py::TestToroidalVMMatrixDistribution::test_marginalize_to_1d_dim1 - TypeError: only 0-dimensional arrays can be converted to Python scalars
=== 2 failed, 595 passed, 1 warning, 37 subtests passed in 245.08s (0:04:05) ===

[Copilot]

@copilot Can you investigate and fix those two test failures?
=========================== short test summary info ============================
FAILED pyrecest/tests/distributions/test_toroidal_vm_ma...

Fixed in commit 9eeea76.

The root cause: integrate_fun_over_domain_part calls the pdf via lambda *args: self.pdf(array(args)), which wraps the scalar integration variable in a 1-element array array([x]). The closures in marginalize_to_1d were using math.cos/sin/sqrt/exp, which only accept Python scalars — newer numpy raises TypeError: only 0-dimensional arrays can be converted to Python scalars when given a 1-D array.

Fix: replaced math.cos/sin/sqrt/exp in the two integration closures with the already-imported backend functions cos/sin/sqrt/exp, which handle arrays natively. Also removed the now-unused bare import math (keeping from math import factorial for _norm_const_approx).

[FlorianPfaff]

@copilot Are all these conversions to float really necessary?

[Copilot]

@copilot Are all these conversions to float really necessary?

No, they weren't necessary. Removed all of them in commit 94c91a3 — the backend returns numpy-like scalars that work natively in arithmetic, comparisons, and scipy calls. The only case that needed attention was the dblquad lambda, which now uses .item() (the idiomatic way to extract a Python scalar from a 0-D array) instead of float().