solarwindpy.fitfunctions.gaussians.GaussianLn

class GaussianLn(xobs, yobs, **kwargs)[source]

Bases: FitFunction

Log-normal distribution for skewed data fitting.

Fits a Gaussian in logarithmic space where \(\ln(x)\) follows a normal distribution.

References

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

Initialize log-normal 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

xobs must be positive for log transformation. This distribution is commonly used for particle size distributions and velocity distributions in solar wind where values are positively skewed.

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 [ln(mu), ln(sigma), ln(A)].

property TeX_function

Function written in LaTeX.

property normal_parameters

Calculate the normal parameters from log-normal parameters.

\[\mu = \exp[m + (s^2)/2] \sigma = \sqrt{\exp[s^2 + 2m] (\exp[s^2] - 1)}\]
property TeX_report_normal_parameters

Report normal parameters, not log-normal parameters in the TeX info.

set_TeX_report_normal_parameters(new)[source]
property TeX_popt

Create a dictionary with (k, v) pairs corresponding to parameter values.

(self.argnames, :math:`p_{\mathrm{opt}} \pm \sigma_p`) with the appropriate uncertainty.

See set_TeX_trans_argnames to translate the argnames for TeX.

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

Convenience to extract all versions of the optimized parameters.

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
make_fit(return_exception=False, **kwargs)

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:

  • return_exception (bool) – If True, return exceptions from fitting routine, instead of raising. This is useful when looping through many fits and wanting to identify failed fits after the fact.

  • **kwargs – The description is missing.

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
property psigma_relative
residuals(pct=False)

Calculate the fit residuals.

If pct, normalize by fit yvalues.

Parameters:

pct – The description is missing.

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.