alacarte-rectgen 0.1.2

Controllable output-density synthetic axis-aligned hyper-rectangle generator

Alacarte RectGen (alacarte-rectgen)

A controllable output-density synthetic generator for axis-aligned hyper-rectangles (boxes), inspired by the ideas in Benchmarking Spatial Joins À La Carte.

It generates two box sets R and S such that the expected spatial-join output density is close to a user-specified target:

$$ \alpha_{\mathrm{out}} = \frac{|J(R,S)|}{|R| + |S|}, \quad J(R,S) = {(r,s)\in R\times S;|; r\cap s \neq \varnothing}. $$

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Installation

pip install alacarte-rectgen

Import name:

import alacarte_rectgen as ar

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Quickstart (matches the typical usage)

import numpy as np
import alacarte_rectgen as ar

# Parameter settings
N_R, N_S = 500_000, 500_000
TARGET_ALPHA = 10.0

# 1. Generate data and solve parameters
R, S, info = ar.make_rectangles_R_S(
    nR=N_R,
    nS=N_S,
    alpha_out=TARGET_ALPHA,
    d=2,
    universe=None,          # Default is [0, 1)^2
    volume_dist="normal",   # Use normal distribution for volume
    volume_cv=0.25,         # Coefficient of variation for volume
    shape_sigma=0.5,        # Enable aspect ratio variation
    seed=42,
    tune_tol_rel=0.01       # Solving tolerance 1%
)

# 2. Access generation results
print(f"Generated R size: {R.n}, S size: {S.n}")
print(f"Coordinates shape: {R.lower.shape}")

# 3. Audit generation parameters
print("\n--- Generation Audit ---")
print(f"Solved Coverage (C): {info['coverage']:.6e}")
print(f"Target Alpha:        {info['alpha_target']:.4f}")
print(f"Expected Alpha:      {info['alpha_expected_est']:.4f}")
print(f"Intersection Prob:   {info['pair_intersection_prob_est']:.6e}")

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What you get back

R and S are BoxSet objects

They store half-open boxes:

$$ \text{box}i = \prod{k} [\text{lower}{i,k}, \text{upper}{i,k}) $$

Key fields/properties:

• R.lower, R.upper: np.ndarray with shape (n, d)
• R.universe: np.ndarray with shape (d, 2) giving [min, max] per dimension
• R.n, R.d: sizes

info is an audit dictionary

Common keys:

• info["coverage"]: solved coverage $C$
• info["alpha_target"]: requested target $\alpha_{out}$
• info["alpha_expected_est"]: Monte-Carlo estimate of expected $\alpha_{out}$ under the tuned coverage
• info["pair_intersection_prob_est"]: estimated pairwise intersection probability $p$
• info["tune_history"]: list of tried coverages + estimated alphas during tuning
• info["params"]: echo of the main generation parameters

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Parameters you will typically tune

• universe (default None): bounds of shape (d,2). If None, uses [0,1)^d.
• volume_dist: "fixed" | "exponential" | "normal" | "lognormal"
• volume_cv: coefficient of variation for "normal" / "lognormal" volume distributions.
• shape_sigma: 0 gives squares/cubes; larger values increase aspect-ratio variation.
• tune_samples: Monte Carlo sample size used by the coverage solver (bigger = more accurate, slower).
• tune_tol_rel: relative tolerance of the solver, e.g. 0.01 for 1%.
• dtype: output coordinate dtype, default np.float32 to save memory.

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Notes on scale & performance

• By default coordinates are float32 to reduce memory use.
• Tuning uses Monte Carlo over length samples (not over all nR*nS pairs), so it stays practical even for large nR, nS.
• If you care about realized alpha on the concrete generated sets (not only the expectation), use:

alpha_hat, p_hat = ar.estimate_alpha_by_pair_sampling(R, S, num_pairs=2_000_000, seed=0)

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License

MIT (see LICENSE).