calculate

SpectralShapeSkewedGaussian.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().

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