pseudo-voigt.jl

### A Pluto.jl notebook ###
# v0.19.19

using Plots
using SpecialFunctions

x = range(start = -3, stop = 3, step = 0.01)

function Gaussian(x, fwhm)
    #g1 = 2.0 * √(log(2)/π)
    #g2 = 4.0 * log(2)
    #return @. (g1 / fwhm) * exp((-g2 * x^2) / (fwhm^2)) 
    σ = fwhm / (2√(2log(2)))
    return @. 1 / √(2π) / σ * exp(-x^2 / 2σ^2)
end

function Lorentzian(x, fwhm)
    #l1 = 2/π
    #l2 = 4.0
    #return @. (l1 / fwhm) / ((1 + l2 * x^2) / fwhm^2 ) 
    γ = fwhm / 2
    return @. (γ / pi) / (x^2 + γ^2)
end

function pseudo_Voigt(x, fwhm, n)
    return n * Lorentzian(x, fwhm) + (1 - n) * Gaussian(x, fwhm)
end

function Voigt(x, fwhm_L, fwhm_G)
    γ = fwhm_L / 2
    σ = fwhm_G / (2√(2log(2)))
    z = @. -im * (x + im * γ) / (√2 * σ)
    return @. real(erfcx(z)) / (√(2pi) * σ)
end


y1 = Lorentzian(x, 1)
y2 = Gaussian(x, 1)
y3 = pseudo_Voigt(x, 1, 0.5)
y4 = Voigt(x, 0.45, 0.72)

p = plot(x, [y1 y2 y3 y4], label = ["Lorentzian" "Gaussian" "Pseudo Voigt" "Voigt"])
#p = plot(x,[y1 y2 y3], label=["Lorentzian" "Gaussian" "Pseudo Voigt"])
title!("peak functions")
xlabel!(raw"x")
ylabel!(raw"y")

#display(p)

#savefig(plot,"file.png")