Voigt model fit

Fits data to a Voigt profile. Voigt models are commonly used to fit XPS spectra.
[estimates, model] = voigtfit(x, y, initGuess, peakBounds) fits the x and y data to one or more Voigt profile models, returning the Voigt profile parameters in the vector estimates and the fit function handle, model. The Voigt model fit is initialized with the parameters in initGuess. The background is fit to a 2nd order polynomial which is fit to all data except for a user-defined region contained within the upper and lower bounds given in peakBounds (see below).
[estimates, model] = voigtfit(x, y, initGuess, peakBounds, bkgdFitOrder) fits the background to a polynomial of order bkgdFitOrder.
Inputs:
xdata - A column vector containing x data.
ydata - A column vector containing y data.

initGuess - A row vector containing initial guesses for the nonlinear fit parameters. There are 3 parameters for each peak: peak center value, gamma, and sigma. For multiple peaks, use the format [peak_1, gamma_1, sigma_1, peak_2, gamma_2, sigma_2, ...]. For more info on Voigt profile parameters, see https://en.wikipedia.org/wiki/Voigt_profile.

peakBounds - A 1x2 vector of the form [LB, UB]. The user must select upper and lower bounds for the region containing the peak(s). The background is fit to a polynomial by excluding this data.

bkgdOrder - Optional input. The order of the polynomial used for the background fit. The default value is 2.

Outputs:

estimates - A row vector containing the final estimates for nonlinear parameters. The elements are organized identically to the initGuess input parameter.

model - A handle to the model function.

This code uses Steven G. Johnsons's Faddeeva package, which needs to be in the search path. It can be found at http://www.mathworks.com/matlabcentral/fileexchange/38787-faddeeva-package--complex-error-functions.