Add PiecewiseConstantDistribution for circular distributions

[Copilot]

Python port of the MATLAB PWCDistribution: a histogram-style circular distribution that divides [0, 2π) into n equal intervals, each with a constant pdf weight.

New class: PiecewiseConstantDistribution

• __init__(w) — accepts raw weights, auto-normalizes via w / (mean(w) · 2π)
• pdf(xs) — maps each point to its interval index via modular arithmetic
• trigonometric_moment(n) — exact analytical formula: −i/n · Σ wⱼ(e^{inrⱼ} − e^{inlⱼ})
• entropy() — exact: −(2π/n) · Σ wⱼ log wⱼ
• sample(n) — categorical sample over intervals, then uniform within the chosen interval
• left_border / right_border / interval_center — 1-indexed static helpers
• calculate_parameters_numerically(pdf_func, n) — fits weights by integrating any circular pdf over each interval via scipy.integrate.quad

import numpy as np
from pyrecest.distributions import PiecewiseConstantDistribution, WrappedNormalDistribution

w = np.array([1, 2, 3, 4, 5, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1], dtype=float)
p = PiecewiseConstantDistribution(w)
print(p.pdf(np.array([0.0, 4.2, 10.9])))

# Fit from an existing distribution
wn = WrappedNormalDistribution(2.0, 1.3)
w_fit = PiecewiseConstantDistribution.calculate_parameters_numerically(wn.pdf, 50)
p_fit = PiecewiseConstantDistribution(w_fit)

Notes

• Tests use exact analytical references or fine-grid numerical integration rather than scipy.nquad, since nquad is unreliable on piecewise-discontinuous integrands.
• Exported from pyrecest/distributions/__init__.py.

[github-actions]

❌MegaLinter analysis: Error

Descriptor	Linter	Files	Fixed	Errors	Warnings	Elapsed time
✅ COPYPASTE	jscpd	yes		no	no	7.7s
✅ JSON	prettier	2	0	0	0	0.48s
✅ JSON	v8r	2		0	0	2.48s
✅ MARKDOWN	markdownlint	1	0	0	0	0.63s
✅ MARKDOWN	markdown-table-formatter	1	0	0	0	0.21s
✅ PYTHON	bandit	251		0	0	3.15s
✅ PYTHON	black	251	3	0	0	4.58s
❌ PYTHON	flake8	251		1	0	1.76s
✅ PYTHON	isort	251	3	0	0	0.49s
✅ PYTHON	mypy	251		0	0	4.14s
✅ PYTHON	pylint	251		0	0	70.36s
✅ PYTHON	ruff	251	3	0	0	0.04s
✅ REPOSITORY	checkov	yes		no	no	22.17s
✅ REPOSITORY	gitleaks	yes		no	no	4.18s
✅ REPOSITORY	git_diff	yes		no	no	0.02s
✅ REPOSITORY	secretlint	yes		no	no	5.65s
✅ REPOSITORY	syft	yes		no	no	3.08s
✅ REPOSITORY	trivy-sbom	yes		no	no	1.82s
✅ REPOSITORY	trufflehog	yes		no	no	16.2s
✅ YAML	prettier	4	0	0	0	0.46s
✅ YAML	v8r	4		0	0	4.81s
✅ YAML	yamllint	4		0	0	0.43s

Detailed Issues

❌ PYTHON / flake8 - 1 error

pyrecest/distributions/__init__.py:87:1: F401 '.circle.piecewise_constant_distribution.PiecewiseConstantDistribution' imported but unused

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[github-actions]

Test Results

    4 files   -     8      4 suites   - 8   19m 52s ⏱️ - 2h 52m 14s
  605 tests +   34    605 ✅ +   34  0 💤 ±    0  0 ❌ ±0 
2 580 runs   - 4 484  2 580 ✅  - 3 300  0 💤  - 1 184  0 ❌ ±0 

Results for commit a6234b8. ± Comparison against base commit 102af46.

♻️ This comment has been updated with latest results.

[FlorianPfaff]

@copilot Can you fix the linter errors below?

************* Module pyrecest.distributions.circle.piecewise_constant_distribution
pyrecest/distributions/circle/piecewise_constant_distribution.py:2:0: W0622: Redefining built-in 'sum' (redefined-builtin)

---

Your code has been rated at 10.00/10

pyrecest/distributions/init.py:87:1: F401 '.circle.piecewise_constant_distribution.PiecewiseConstantDistribution' imported but unused
pyrecest/distributions/circle/piecewise_constant_distribution.py:72:13: E741 ambiguous variable name 'l'
pyrecest/distributions/circle/piecewise_constant_distribution.py:192:13: E741 ambiguous variable name 'l'

[Copilot]

@copilot Can you fix the linter errors below?

************* Module pyrecest.distributions.circle.piecewise_constant_distribution
...

Fixed in a6234b8:

• W0622 — added redefined-builtin to the pylint disable comment
• F401 — added # noqa: F401 to the re-export line in __init__.py
• E741 (×2) — renamed ambiguous l → left in trigonometric_moment and calculate_parameters_numerically

Also fixed a latent bug in pdf where it was iterating range(len(self.w)) instead of over the input points, which caused IndexError when the input array length differed from the number of weight intervals.