solarwindpy.fitfunctions.gaussians.GaussianNormalized

class GaussianNormalized(xobs, yobs, **kwargs)[source]

Bases: FitFunction

Normalized Gaussian distribution where integral equals n.

Fits data to the form: (n / (sqrt(2*pi) * sigma)) * exp(-0.5 * ((x - mu) / sigma)^2)

__init__(xobs, yobs, **kwargs)[source]

Initialize normalized Gaussian fit.

Parameters:

  • xobs (array-like) – Observed x values (independent variable). Shape must match yobs.

  • yobs (array-like) – Observed y values (dependent variable). Shape must match xobs.

  • **kwargs – The description is missing.

Notes

The normalization parameter n represents the total area under the Gaussian curve, useful for fitting probability distributions or particle count distributions.

Examples

>>> import numpy as np
>>> from solarwindpy.fitfunctions import Gaussian
>>> x = np.linspace(-5, 5, 100)
>>> y = 3 * np.exp(-0.5 * x**2) + np.random.normal(0, 0.1, 100)
>>> fit = Gaussian(x, y, xmin=-3, xmax=3)
>>> fit.make_fit()
>>> print(f"Fitted mu: {fit.popt['mu']:.3f}")

See also

make_fit

Execute the fitting procedure

popt

Access optimized parameters

rsq

Calculate coefficient of determination

property function

Get the function that`curve_fit` fits.

The function is set at instantiation. It doesn’t make sense to change it unless you redefine the entire FitFunction, so there is no new kwarg.

property p0

Return initial guesses [mu, sigma, n] for the fit.

property TeX_function

Function written in LaTeX.

make_fit(*args, **kwargs)[source]

Fit the function with the independent xobs and dependent yobs.

Uses least_squares and returns the OptimizeResult object, but treats weights as in curve_fit.

Parameters:

  • *args – The description is missing.

  • **kwargs – The description is missing.

property TeX_info
property argnames

The names of the actual function arguments pulled by getfullargspec.

build_TeX_info()
build_plotter()
property chisq_dof

Chisq per degree of freedom \(\chi^2_\nu\).

If None, not calculated by make_fit_old. If np.nan, fit failed.

property combined_popt_psigma

Return optimized parameters and uncertainties as a DataFrame.

Returns:

DataFrame with columns ‘popt’ and ‘psigma’, indexed by parameter names. Relative uncertainty can be computed as: df[‘psigma’] / df[‘popt’]

Return type:

pd.DataFrame

property dof

Degrees of freedom in the fit.

property fit_bounds

Bounds used when running the fit.

property fit_result
property initial_guess_info
property logger
property nobs

The total number of observations used in the fit.

property observations
property pcov

Returns a copy so that the matrix isn’t accidentally edited.

property plotter
property popt

Optimized fit parameters.

property psigma
residuals(pct=False, use_all=False)

Calculate fit residuals.

Parameters:

  • pct (bool, default=False) – If True, return percentage residuals.

  • use_all (bool, default=False) – If True, calculate residuals for all input data including points excluded by constraints (xmin, xmax, etc.) passed during initialization. If False (default), calculate only for points used in fit.

Returns:

Residuals as observed - fitted.

Return type:

numpy.ndarray

Examples

>>> # Create FitFunction with constraints
>>> ff = Gaussian(x, y, xmin=3, xmax=7)
>>> ff.make_fit()
>>>
>>> # Residuals for fitted region only
>>> r_fit = ff.residuals()
>>>
>>> # Residuals for all original data
>>> r_all = ff.residuals(use_all=True)
>>>
>>> # Percentage residuals
>>> r_pct = ff.residuals(pct=True)

Notes

Addresses TODO: “calculate with all values…including those excluded by set_extrema” (though set_extrema doesn’t exist - constraints are passed in __init__).

property rsq

Coefficient of determination.

Source: <en.wikipedia.org/wiki/Coefficient_of_determination#Definitions>

set_fit_obs(xobs_raw, yobs_raw, weights_raw, xmin=None, xmax=None, xoutside=None, ymin=None, ymax=None, youtside=None, wmin=None, wmax=None, logx=False, logy=False)

Set the observed values we’ll actually use in the fit.

By applying limits to xobs_raw and yobs_raw and checking for finite values.

All boundaries are inclusive <= or >=.

If logy, then make selection of wmin and wmax based on \(w/(y \ln(10))\).

Parameters:

  • xobs_raw – The description is missing.

  • yobs_raw – The description is missing.

  • weights_raw – The description is missing.

  • xmin – The description is missing.

  • xmax – The description is missing.

  • xoutside – The description is missing.

  • ymin – The description is missing.

  • ymax – The description is missing.

  • youtside – The description is missing.

  • wmin – The description is missing.

  • wmax – The description is missing.

  • logx – The description is missing.

  • logy – The description is missing.

property sufficient_data

Ensure that we can fit the data before doing any computations.