scippneutron.peaks.FitResult#

class scippneutron.peaks.FitResult(*, aic, assessment, background, message, p_value, peak, popt, red_chisq, window)[source]#

Optimized parameters and fit statistics for a single peak.

__init__(*, aic, assessment, background, message, p_value, peak, popt, red_chisq, window)#

Methods

`__init__`(*, aic, assessment, background, ...)
`better_than`(other)	Return True if this result is better than another.
`eval_model`(x)	Evaluate the model with optimized parameters.
`eval_peak`(x)	Evaluate the peak model with optimized parameters.
`for_failure`(*[, assessment, message])	Create a `FitResult` for a failed fit.
`for_too_narrow_window`(*, peak, background, ...)	Create a `FitResult` for a fit where the window is too narrow.
`report`()	Format an overview of the fit result.

Attributes

`aic`	Akaike Information Criterion.
`assessment`	Indicates whether the fit was successful or how if failed.
`background`	Model for the background.
`message`	Short message describing the fit assessment.
`p_value`	Probability of the given chi-squared or higher.
`peak`	Model for the peak.
`popt`	Optimized parameters.
`red_chisq`	Reduced chi-squared for the model and optimized parameters.
`window`	Fit window for this peak.
`success`	Return whether the fit was successful.

Akaike Information Criterion.

A relative estimate of fit quality. Defined as

\[\mathsf{AIC} = 2k - 2\ln(L)\]

Where \(k\) is the number of parameters and \(L\) the likelihood if the model with the optimized parameters.

assessment: FitAssessment#: Indicates whether the fit was successful or how if failed.

better_than(other)[source]#

Return True if this result is better than another.

Uses aic to compare the results.

eval_model(x)[source]#

Evaluate the model with optimized parameters.

Parameters:: x (Variable) – Independent variable.
Returns:: Variable – The model evaluated at x with optimized parameters.

eval_peak(x)[source]#

Evaluate the peak model with optimized parameters.

Parameters:: x (Variable) – Independent variable.
Returns:: Variable – The peak model evaluated at x with optimized parameters.

classmethod for_failure(*, assessment=None, peak, background, window, message=None)[source]#

Create a FitResult for a failed fit.

classmethod for_too_narrow_window(*, peak, background, window)[source]#

Create a FitResult for a fit where the window is too narrow.

Probability of the given chi-squared or higher.

The \(p\)-value is the probability to get the same \(\chi^2\) or higher when repeating the fit. It is defined as

\[p = 1 - F(\chi^2;\,\nu)\]

where \(F(\chi^2;\,\nu)\) is the cumulative distribution function of the \(\chi^2\)–distribution with \(\nu\) degrees of freedom.

Reduced chi-squared for the model and optimized parameters.

\[\chi^2_{\nu} = \frac1{\nu} \sum_{i=0}^n\, \frac{(y_i - f(x_i))^2}{\sigma_i^2}\]

where \(\nu\) is the number of degrees of freedom.

Format an overview of the fit result.