Data Generator

scripts/aniso_simulated_data_gen_v.py

Generates synthetic transverse velocity data with configurable Lorentz violation parameters. Produces generated_sources.csv at the project root.

Usage

# Standalone
python scripts/aniso_simulated_data_gen_v.py

# Also called automatically by the anisotropic model at startup
python scripts/PyMC_Pytensor_noise_v_main_varsig_aniso.py

Simulation Parameters

Configured as constants at the top of regenerate_data():

Parameter	Default	Description
`delta` (\(\delta\))	`-1`	LV coefficient. Controls the sign/type of Lorentz violation.
`Bº` (\(B_0\))	`0.8`	Scalar LV magnitude.
`B_vec` (\(\vec{B}\))	`[0.5, 0.0, 0.2]`	3-vector LV direction.
`N_SOURCES`	`1000`	Number of synthetic sources to generate.

Physics

`solve_wc`

Solves the quadratic equation for the critical inverse velocity \(w_c\) given a direction vector (either the source emission direction \(\hat{v}\) for Cherenkov braking, or the observer direction \(\hat{n}\)):

\[ a\,w_c^2 + b\,w_c + c = 0 \]

where \(a = \delta B_0^2 - 1\), \(\;b = 2\delta B_0 (\vec{B}\cdot\hat{n})\), \(\;c = \delta(\vec{B}\cdot\hat{n})^2 + 1\).

Returns all positive roots, or None if no positive solution exists. When \(\vec{B} = 0\), reduces to \(w_c = 1/\sqrt{1 - \delta B_0^2}\).

Cherenkov braking

If a source's raw velocity \(v\) exceeds the critical velocity \(1/w_c\) in its emission direction, it is braked down to \(1/w_c\). This simulates vacuum Cherenkov radiation losses.

`w_true`

Computes the true inverse transverse velocity for a source with velocity \(v\) in direction \(\hat{v}\) as observed from direction \(\hat{n}\):

\[ w_{\mathrm{true}} = \frac{1 + (v / v_c(\hat{n}))\,(\hat{n}\cdot\hat{v})}{v\,\sqrt{1 - (\hat{n}\cdot\hat{v})^2}} \]

where \(v_c(\hat{n}) = 1/w_c(\hat{n})\) is the critical velocity in the observer direction.

Measurement noise

Each true velocity is perturbed by Gaussian noise: \(v_{\mathrm{obs}} \sim \mathcal{N}(v_{\mathrm{true}},\, \sigma)\) where \(\sigma \sim |\mathcal{N}(0, 0.1)|\). Negative observed velocities are reflected to ensure \(v_{\mathrm{obs}} > 0\).

Output CSV Format

The file generated_sources.csv has the following structure:

Row 1 (header): simulation parameters

delta, B0, B_x, B_y, B_z

Rows 2+: one row per source

Column	Index	Description
`n_x`	0	x-component of observer direction \(\hat{n}\)
`n_y`	1	y-component of observer direction \(\hat{n}\)
`n_z`	2	z-component of observer direction \(\hat{n}\)
`v_obs`	3	Observed transverse velocity (with noise)
`v_sigma`	4	Measurement uncertainty
`v_true`	5	True transverse velocity (before noise)