solarwindpy.fitfunctions.exponentials

Fit functions for exponential models.

Classes in this module implement exponential decay and related forms using the FitFunction API. They provide reasonable starting parameters and formatted LaTeX output for visualization.

Classes

`Exponential`(xobs, yobs, **kwargs)	Assuming that you don't want special formatting, call order is:
`ExponentialCDF`(xobs, yobs, **kwargs)	Assuming that you don't want special formatting, call order is:
`ExponentialPlusC`(xobs, yobs, **kwargs)	Assuming that you don't want special formatting, call order is:

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

Bases: FitFunction

Assuming that you don’t want special formatting, call order is:

fit_function = FitFunction(function, TeX_string) fit_function.make_fit()

Instances are callable. If the fit fails, calling the instance will return an array of NaNs the same shape as the x-values.

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

Fit A * exp(-c x) to the data.

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 fitting procedure uses scipy.optimize.least_squares with robust loss functions (Huber by default) to handle outliers. The initial parameter guess is provided by the p0 property, which must be implemented by subclasses.

All subclasses inherit this documentation automatically through the docstring-inheritance metaclass.

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 [c, A] for the fit.

property TeX_function: Function written in LaTeX.

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

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

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.

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

Bases: FitFunction

Assuming that you don’t want special formatting, call order is:

fit_function = FitFunction(function, TeX_string) fit_function.make_fit()

Instances are callable. If the fit fails, calling the instance will return an array of NaNs the same shape as the x-values.

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

Fit A * exp(-c x) + d to the data.

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 fitting procedure uses scipy.optimize.least_squares with robust loss functions (Huber by default) to handle outliers. The initial parameter guess is provided by the p0 property, which must be implemented by subclasses.

All subclasses inherit this documentation automatically through the docstring-inheritance metaclass.

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 [c, A, d] for the fit.

property TeX_function: Function written in LaTeX.

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

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

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.

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

Bases: FitFunction

Assuming that you don’t want special formatting, call order is:

fit_function = FitFunction(function, TeX_string) fit_function.make_fit()

Instances are callable. If the fit fails, calling the instance will return an array of NaNs the same shape as the x-values.

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

Fit an exponential cumulative distribution function.

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 fitting procedure uses scipy.optimize.least_squares with robust loss functions (Huber by default) to handle outliers. The initial parameter guess is provided by the p0 property, which must be implemented by subclasses.

All subclasses inherit this documentation automatically through the docstring-inheritance metaclass.

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 y0: Amplitude of the CDF.

set_y0(new)[source]

property p0: Return initial guess [c] for the fit.

property TeX_function: Function written in LaTeX.

set_TeX_info(**kwargs)[source]

Include A value in the TeX annotation.

Parameters:: **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

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

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.