SpectralShapeSkewedGaussian

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

Bases: SpectralShapeGaussian

A skewed Gaussian spectral shape

Method generated by attrs for class SpectralShapeSkewedGaussian.

Attributes Summary

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

Methods Summary

`calculate`	Calculate the skewed Gaussian shape for `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: ParameterType | None

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

Calculate the skewed Gaussian shape for axis.

The following equation is used for the calculation:

$f(x, x_0, A, \Delta, b) = \left\{ \begin{array}{ll} 0 & \mbox{if } \theta \leq 0 \\ A \exp \left({- \dfrac{\log{\left(2 \right)} \log{\left(\theta(x, x_0, \Delta, b) \right)}^{2}}{b^{2}}}\right) & \mbox{if } \theta > 0 \end{array} \right.$

With:

$\theta(x, x_0, \Delta, b) = \frac{2 b \left(x - x_{0}\right) + \Delta}{\Delta}$

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

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

Where $\Delta$ represents the full width at half maximum (FWHM), see calculate_gaussian().

Note that in the limit of skewness parameter $b$ equal to zero $f(x, x_0, A, \Delta, b)$ simplifies to a normal gaussian (since $\lim_{b \to 0} \frac{\ln(1+bx)}{b}=x$ ), see the definition in SpectralShapeGaussian.calculate().