# hyperspy._components.lorentzian module

class hyperspy._components.lorentzian.Lorentzian(A=1.0, gamma=1.0, centre=0.0, module='numexpr', **kwargs)

Bases: Expression

Cauchy-Lorentz distribution (a.k.a. Lorentzian function) component.

$f(x)=\frac{A}{\pi}\left[\frac{\gamma}{\left(x-x_{0}\right)^{2} +\gamma^{2}}\right]$

Variable

Parameter

$$A$$

A

$$\gamma$$

gamma

$$x_0$$

centre

Parameters:
• A (float) – Area parameter, where $$A/(\gamma\pi)$$ is the maximum (height) of peak.

• gamma (float) – Scale parameter corresponding to the half-width-at-half-maximum of the peak, which corresponds to the interquartile spread.

• centre (float) – Location of the peak maximum.

• **kwargs – Extra keyword arguments are passed to the Expression component.

For convenience the fwhm and height attributes can be used to get and set the full-with-half-maximum and height of the distribution, respectively.

estimate_parameters(signal, x1, x2, only_current=False)

Estimate the Lorentzian by calculating the median (centre) and half the interquartile range (gamma).

Note that an insufficient range will affect the accuracy of this method.

Parameters:
• signal (Signal1D instance) –

• x1 (float) – Defines the left limit of the spectral range to use for the estimation.

• x2 (float) – Defines the right limit of the spectral range to use for the estimation.

• only_current (bool) – If False estimates the parameters for the full dataset.

Return type:

bool

Notes

>>> g = hs.model.components1D.Lorentzian()