calculate

SpectralShapeGaussian.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 $\sigma = \Delta/(2\sqrt{2\ln(2)})=\Delta/2.35482$

Parameters:: axis (np.ndarray) – The axis to calculate the shape for.
Returns:: An array representing a Gaussian shape.
Return type:: np.ndarray