lorentzian
Introduced in 0.99
Synopsis

Lorentzian line shape.

y = lorentzian(x,x0,fwhm)
y = lorentzian(x,x0,fwhm,diff)
Description

This function returns a Lorentzian lineshape with centre x0 and full width at half height fwhm over the abscissa values defined in the vector x.

diff determines the derivative to compute. 0 stands for no derivative, 1 is the first one, 2 the second one, -1 indicates the integral with [eqn] as lower limit. If diff is not given, it is set to 0 by default.

For the definition of the Lorentzian function used see lshape.

Examples

To obtain the first derivative of a Lorentzian with centre at 2 and FWHM of 18, use

x = linspace(-300,300,1e3); x0 = 2; w = 18;
y = lorentzian(x,x0,w,1);
plot(x,y);

The Lorentzian absorption shape is normalised, so the double integral of y should give one. However, since its wings extend much beyond the borders of the above defined abscissa x, the value 1 is not reached.

trapz(x,cumtrapz(x,y))
ans =
    0.9621
See also

convspec, gaussian, lshape, voigtian