pygra.fitting

fitting.py — fit functions for histogram and xy data

pygra.fitting.fit_gaussian(data)[source]

Fit a Gaussian (normal) distribution to data using MLE.

Parameters:

data (numpy.ndarray) – 1-D array of sample values.

Returns:

  • x (numpy.ndarray) – 300 evenly-spaced points spanning [data.min(), data.max()].

  • y (numpy.ndarray) – Gaussian PDF evaluated at each point in x.

  • label (str) – Human-readable label including the fitted μ and σ.

  • params (dict) – {"μ": float, "σ": float} — fitted mean and standard deviation.

pygra.fitting.fit_exponential(data)[source]

Fit an exponential distribution to data with fixed location (loc=0).

Parameters:

data (numpy.ndarray) – 1-D array of non-negative sample values.

Returns:

  • x (numpy.ndarray) – 300 evenly-spaced points spanning [data.min(), data.max()].

  • y (numpy.ndarray) – Exponential PDF evaluated at each point in x.

  • label (str) – Human-readable label including the fitted rate λ.

  • params (dict) – {"λ": float} — fitted rate parameter (1 / scale).

pygra.fitting.fit_maxwell_boltzmann(data)[source]

Fit a Maxwell-Boltzmann distribution to data with fixed location (loc=0).

Parameters:

data (numpy.ndarray) – 1-D array of positive sample values.

Returns:

  • x (numpy.ndarray) – 300 evenly-spaced points spanning [max(data.min(), 0), data.max()].

  • y (numpy.ndarray) – Maxwell-Boltzmann PDF evaluated at each point in x.

  • label (str) – Human-readable label including the fitted scale parameter a.

  • params (dict) – {"a": float} — fitted scale parameter.

pygra.fitting.fit_poisson(data)[source]

Estimate the Poisson parameter μ from data and compute the PMF.

The estimator is the sample mean, which is the MLE for the Poisson distribution.

Parameters:

data (numpy.ndarray) – 1-D array of non-negative integer-valued samples (stored as float).

Returns:

  • x (numpy.ndarray) – Integer x-values from int(data.min()) to int(data.max()) inclusive, cast to float.

  • y (numpy.ndarray) – Poisson PMF values at each integer in x.

  • label (str) – Human-readable label including the estimated μ.

  • params (dict) – {"μ": float} — estimated mean (sample mean of data).

pygra.fitting.fit_gaussian_curve(x, y)[source]

Fit A * exp(-(x - mu)**2 / (2 * sigma**2)) to xy data.

Parameters:

  • x (numpy.ndarray) – 1-D array of x values.

  • y (numpy.ndarray) – 1-D array of y values.

Returns:

  • x_fine (numpy.ndarray) – 300 evenly-spaced points spanning [x.min(), x.max()].

  • y_fine (numpy.ndarray) – Fitted curve evaluated at each point in x_fine.

  • label (str) – Human-readable label including the fitted parameters.

  • params (dict) – {"A": float, "μ": float, "σ": float}.

pygra.fitting.fit_exponential_curve(x, y)[source]

Fit A * exp(-x / tau) + C to xy data.

Parameters:

  • x (numpy.ndarray) – 1-D array of x values.

  • y (numpy.ndarray) – 1-D array of y values.

Returns:

  • x_fine (numpy.ndarray) – 300 evenly-spaced points spanning [x.min(), x.max()].

  • y_fine (numpy.ndarray) – Fitted curve evaluated at each point in x_fine.

  • label (str) – Human-readable label including the fitted parameters.

  • params (dict) – {"A": float, "τ": float, "C": float}.

pygra.fitting.fit_custom(data, formula, param_names)[source]

Fit a user-defined formula to the density histogram of data.

The formula is evaluated in a sandboxed namespace that exposes NumPy ufuncs (e.g. exp, sin, sqrt) and math constants. NumPy ufuncs take priority over their scalar math counterparts so that array formulas work correctly.

Parameters:

  • data (numpy.ndarray) – 1-D array of sample values used to build the histogram.

  • formula (str) – Python expression in terms of x and the names listed in param_names. Example: "a * exp(-b * x)".

  • param_names (list of str) – Names of the free parameters appearing in formula. All initial guesses are set to 1.0.

Returns:

  • x (numpy.ndarray) – 300 evenly-spaced points spanning [data.min(), data.max()].

  • y (numpy.ndarray) – Formula evaluated at x with the optimised parameters.

  • label (str) – Human-readable label listing each fitted parameter value.

  • params (dict) – Mapping of parameter name → fitted float value.

Raises:

  • scipy.optimize.OptimizeWarning – If the covariance of the parameters could not be estimated.

  • RuntimeError – If the least-squares minimisation fails entirely.

Notes

All initial parameter guesses are 1.0. Formulas that require very different starting points may not converge from these defaults.