Peaklorentzian

Purpose

Outputs a Lorentzian function, Jacobian, and Hessian for a given set of input parameters and axis.

Synopsis

[y,y1,y2] = peaklorentzian(x,ax)

Description

Given a 3-element vector of parameters (x) and a vector of independent variables e.g. a wavelength or frequency axis (ax), PEAKLORENTZIAN outputs a Lorentzian peak (y). If more than one output is requested, it also outputs the Jacobian (y1) and Hessian (y2). Derivatives are with respect to the parameters and are evaluated at (x). This function is called by PEAKFUNCTION.

Inputs

• x = 3 element vector with parameters

• x(1) = coefficient ,

• x(2) = mean , and

• x(3) = spread .

• ax = vector of independent variables e.g. a wavelength or frequency axis with elements , .

Outputs

• y = vector with the Lorentzian function, .

• y1 = matrix of the Jacobian of evaluated at (x).

• y2 = matrix of the Hessian of evaluated at (x).

Algorithm

The function is

y = x(1)*1./(1 + ((p-x(2))/x(3)).^2 ); %1xN.

Examples

%Make a single known peak

ax = 0:0.1:100;

y = peaklorentzian([2 51 8],ax);

plot(ax,y)

See Also

peakfunction, peakgaussian, peakpvoigt1, peakpvoigt2, peakstruct