Physicslab-coda

A Python library for data analysis in physics laboratories, including:

• linear interpolation with uncertainties
• statistical variables
• common statistical tests (χ², t-Student, F-test, etc.)

The goal is to provide ready-to-use tools for students and researchers working with experimental data.

Statistics

Interpolation

Class for linear interpolation with experimental uncertainties.

• linear_function(x, a, b)
  Simple linear function.

• erry_var_errx_null(x, y, erry, verbose=False)
  Linear interpolation with variable error on Y and negligible error on X.

• linear_interpolation(x, y, errx, erry, threshold=30, tries=10, verbose=False)
  Linear interpolation with variable errors on both X and Y.
  Automatically chooses the best approximation depending on error magnitudes.

StatisticalVariables

Class for calculating basic statistical variables.

• r(x, y)
  Computes the sample correlation coefficient.
  Output: r (sample correlation coefficient)

• mean(x)
  Computes the mean of a data set.
  Output: mean (data set mean)

• var(x, sample=True)
  Computes the sample variance of a data set.
  Output: var (data set variance)

• sdev(x, sample=True)
  Computes the sample standard deviation of a data set.
  Output: sdev (data set standard deviation)

• post_var(f, parameters, x, y)
  Computes the posterior variance of a data set.
  Output: pv (data set posterior variance)

• cov(x, y, sample=True)
  Computes the sample covariance of a data set.
  Output: cov (data set covariance)

StatisticalTests

Class for applying common statistical tests.

• chi_sqrd(f, parameters, x, y, erry)
  Compute chi-squared.
  Output: chi2 (chi-squared value), df (degrees of freedom)

• reduced_chi_sqrd(f, parameters, x, y, erry)
  Compute reduced chi-squared.
  Output: reduced_chi2 (reduced chi-squared value), df (degrees of freedom)

• post_error(f, parameters, x, y)
  Compute posterior error.
  Output: pe (posterior error), df (degrees of freedom)

• r_t_student(x, y)
  Compute Student’s t-value for correlation.
  Output: t (t-value), df (degrees of freedom)

• t_student(x, mu)
  Compute Student’s t-value for a sample mean.
  Output: t (t-value), df (degrees of freedom)

• alternative_f_test(f_0, f_a, v_0, v_a, x, y)
  Perform F-test to compare two models.
  Output: f_test (F-test value), df1, df2 (degrees of freedom)

• t_student_comp(x, y)
  Student’s t-test for two samples with different variances.
  Output: t (t-value), df (degrees of freedom)

Installation

git clone https://github.com/yourusername/physics-lab-data-analysis.git
cd physics-lab-data-analysis
pip install -r requirements.txt

Usage Example

import numpy as np
from physicslab-coda import Interpolation, StatisticalVariables, StatisticalTests

# Example data
x = np.array([1, 2, 3, 4])
y = np.array([2.1, 4.2, 5.9, 8.2])
erry = np.array([0.1, 0.2, 0.1, 0.3])
errx = np.array([0.05, 0.05, 0.05, 0.05])

# Linear interpolation
interp = Interpolation()
a, b, s_a, s_b = interp.linear_interpolation(x, y, errx, erry, verbose=True)
print("a =", a, " b =", b, " σa =", s_a, " σb =", s_b)

# Correlation coefficient
stat_vars = StatisticalVariables()
r = stat_vars.r(x, y)
print("r =", r)

# Reduced chi-squared
tests = StatisticalTests()
y_fit = a + b*x
rchi2, df = tests.reduced_chi_sqrd(lambda x: a + b*x, parameters=2, x=x, y=y, erry=erry)
print("Reduced χ² =", rchi2, " with degrees of freedom =", df)

Author

Andrea Codarin