Port SE2PWDDistribution from libDirectional as SE2DiracDistribution

[Copilot]

Ports the MATLAB SE2PWDDistribution from libDirectional to Python as SE2DiracDistribution — a particle distribution on SE(2) = S¹ × ℝ².

New class: SE2DiracDistribution

Inherits from HypercylindricalDiracDistribution (bound_dim=1) and AbstractSE2Distribution.

• mean_4d() — weighted mean of [cos θ, sin θ, x, y]; delegates to hybrid_moment()
• covariance_4d() — 4×4 second-moment matrix Σ wᵢ sᵢ sᵢᵀ where sᵢ = [cos θᵢ, sin θᵢ, xᵢ, yᵢ]
• mean() — delegates to hybrid_mean() for interface consistency with other manifold distributions
• from_distribution(dist, n_particles) — factory accepting any AbstractHypercylindricalDistribution with bound_dim=1, lin_dim=2 (faithful to the MATLAB signature)

from pyrecest.distributions import SE2DiracDistribution, PartiallyWrappedNormalDistribution
import numpy as np

pwn = PartiallyWrappedNormalDistribution(
    np.array([1.0, 2.0, 3.0]),
    np.diag([0.5, 1.0, 1.0]),
    bound_dim=1,
)
dist = SE2DiracDistribution.from_distribution(pwn, n_particles=1000)
print(dist.mean_4d())       # [E[cos θ], E[sin θ], E[x], E[y]]
print(dist.covariance_4d()) # 4×4 second-moment matrix

Other changes

• distributions/__init__.py — exports SE2DiracDistribution

[github-actions]

✅MegaLinter analysis: Success

Descriptor	Linter	Files	Fixed	Errors	Warnings	Elapsed time
✅ COPYPASTE	jscpd	yes		no	no	7.34s
✅ JSON	prettier	2	0	0	0	0.41s
✅ JSON	v8r	2		0	0	2.34s
✅ MARKDOWN	markdownlint	1	0	0	0	0.63s
✅ MARKDOWN	markdown-table-formatter	1	0	0	0	0.21s
✅ PYTHON	bandit	252		0	0	2.89s
✅ PYTHON	black	252	2	0	0	3.89s
✅ PYTHON	flake8	252		0	0	1.58s
✅ PYTHON	isort	252	2	0	0	0.48s
✅ PYTHON	mypy	252		0	0	3.7s
✅ PYTHON	pylint	252		0	0	72.42s
✅ PYTHON	ruff	252	2	0	0	0.04s
✅ REPOSITORY	checkov	yes		no	no	23.79s
✅ REPOSITORY	gitleaks	yes		no	no	3.97s
✅ REPOSITORY	git_diff	yes		no	no	0.04s
✅ REPOSITORY	secretlint	yes		no	no	6.77s
✅ REPOSITORY	syft	yes		no	no	4.02s
✅ REPOSITORY	trivy-sbom	yes		no	no	1.75s
✅ REPOSITORY	trufflehog	yes		no	no	18.7s
✅ YAML	prettier	4	0	0	0	0.44s
✅ YAML	v8r	4		0	0	4.81s
✅ YAML	yamllint	4		0	0	0.39s

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[github-actions]

Test Results

    8 files   -     4      8 suites   - 4   1h 31m 4s ⏱️ - 1h 40m 55s
  629 tests +   83    629 ✅ + 83    0 💤 ±  0  0 ❌ ±0 
5 224 runs   - 1 540  4 932 ✅  - 656  292 💤  - 884  0 ❌ ±0 

Results for commit 60a69dd. ± Comparison against base commit deb475e.

♻️ This comment has been updated with latest results.

[FlorianPfaff]

@copilot can you increase the tolerance to 1e-7 to prevent failure?
FAILED pyrecest/tests/distributions/test_se2_dirac_distribution.py::TestSE2DiracDistribution::test_covariance_4d_symmetric - AssertionError:
Not equal to tolerance rtol=1e-07, atol=1e-12

Mismatched elements: 4 / 16 (25%)
Mismatch at indices:
[0, 2]: 0.07270358502864838 (ACTUAL), 0.07270359992980957 (DESIRED)
[1, 2]: 0.4852354824542999 (ACTUAL), 0.48523542284965515 (DESIRED)
[2, 0]: 0.07270359992980957 (ACTUAL), 0.07270358502864838 (DESIRED)
[2, 1]: 0.48523542284965515 (ACTUAL), 0.4852354824542999 (DESIRED)
Max absolute difference among violations: 5.9604645e-08
Max relative difference among violations: 2.0495773e-07
ACTUAL: array([[ 5.777081e-01, -1.312899e-01, 7.270359e-02, 6.615561e+00],
[-1.312899e-01, 4.222919e-01, 4.852355e-01, -9.556433e+00],
[ 7.270360e-02, 4.852354e-01, 3.437500e+00, 2.708333e+01],...
DESIRED: array([[ 5.777081e-01, -1.312899e-01, 7.270360e-02, 6.615561e+00],
[-1.312899e-01, 4.222919e-01, 4.852354e-01, -9.556433e+00],
[ 7.270359e-02, 4.852355e-01, 3.437500e+00, 2.708333e+01],...
FAILED pyrecest/tests/test_euclidean_sampler.py::TestGaussianSampler::test_samples_follow_gaussian_distribution - AssertionError: np.float64(0.008930226739329363) not greater than 0.05
= 2 failed, 327 passed, 230 skipped, 43 warnings, 5 subtests passed in 1297.38s (0:21:37) =

[Copilot]

@copilot can you increase the tolerance to 1e-7 to prevent failure?
FAILED pyrecest/tests/distributions/test_se2_dirac_distribution.py::TestSE2DiracDistribution::test_covariance_4d_symmetric - Assert...

Done — increased atol from 1e-12 to 1e-7 in test_covariance_4d_symmetric in commit abee2a4.

[FlorianPfaff]

@copilot Fix this linter error
update_init_helper.py:1:0: R0801: Similar lines in 2 files
==pyrecest.tests.distributions.test_hypercylindrical_dirac_distribution:[34:43]
==pyrecest.tests.distributions.test_se2_dirac_distribution:[17:26]
self.d = array(
[
[1.0, 2.0, 3.0, 4.0, 5.0, 6.0],
[2.0, 4.0, 0.0, 0.5, 1.0, 1.0],
[0.0, 10.0, 20.0, 30.0, 40.0, 50.0],
]
).T
self.w = array([1.0, 2.0, 3.0, 1.0, 2.0, 3.0])
self.w = self.w / sum(self.w) (duplicate-code)

[Copilot]

@copilot Fix this linter error
update_init_helper.py:1:0: R0801: Similar lines in 2 files
==pyrecest.tests.distributions.test_hypercylindrical_dirac_distribution:[34:43]
...

Fixed in commit 60a69dd by adding duplicate-code to the pylint disable comment in the SE2 test file, which suppresses the R0801 warning for the shared setUp data.