SpectralShapeGaussian

class glotaran.builtin.megacomplexes.spectral.shape.SpectralShapeGaussian(*, label: str, type: str = 'gaussian', amplitude: Parameter | str | None = None, location: Parameter | str, width: Parameter | str)[source]

Bases: SpectralShape

A Gaussian spectral shape

Method generated by attrs for class SpectralShapeGaussian.

Attributes Summary

`type`
`amplitude`
`location`
`width`
`label`

Methods Summary

`calculate`	Calculate a normal Gaussian shape for a given `axis`.
`get_item_type`	Get the type string.
`get_item_type_class`	Get the type for a type string.
`get_item_types`	Get all type strings.

Methods Documentation

amplitude: Parameter | str | None

calculate(axis: ndarray) → ndarray[source]

Calculate a normal Gaussian shape for a given axis.

The following equation is used for the calculation:

$f(x, A, x_0, \Delta) = A \exp \left({- \frac{ \log{\left(2 \right) \left(2(x - x_{0})\right)^{2} }}{\Delta^{2}}}\right)$

The parameters of the equation represent the following attributes of the shape:

$x$ : axis
$A$ : amplitude
$x_0$ : location
$\Delta$ : width

In this formalism, $\Delta$ represents the full width at half maximum (FWHM). Compared to the more common definition $\exp \left(- (x-\mu )^{2}/(2\sigma^{2})\right)$ we have $\sigma = \Delta/(2\sqrt{2\ln(2)})=\Delta/2.35482$