Voigt distribution

Lorentzian distribution

Gaussian distribution

Voigt(x, x0, sigma, gamma, real = TRUE, ...)

Lorentz(x, x0, gamma)

Gauss(x, x0, sigma)

## Arguments

x
numeric vector
x0
scalar, peak position
sigma
parameter of the gaussian
gamma
parameter of the lorentzian
real
logical, return only the real part of the complex Faddeeva
...

## Value

numeric or complex vector

## Functions

• Voigt: Voigt lineshape function

• Lorentz: Lorentzian lineshape function

• Gauss: Gaussian lineshape function

## Examples

## should integrate to 1 in all cases
integrate(Lorentz, -Inf, Inf, x0=200, gamma=100)#> 1 with absolute error < 1.2e-06integrate(Gauss, -Inf, Inf, x0=200, sigma=50)#> 1 with absolute error < 6.4e-06integrate(Voigt, -Inf, Inf, x0=200, sigma=50, gamma=100)#> 1 with absolute error < 7.6e-09
## visual comparison
x <- seq(-1000, 1000)
x0 <- 200
l <- Lorentz(x, x0, 30)
g <- Gauss(x, x0, 100)
N <- length(x)
c <- convolve(Gauss(x, 0, 100),
rev(Lorentz(x, x0, 30)), type="o")[seq(N/2, length=N)]
v <- Voigt(x, x0, 100, 30)
matplot(x, cbind(v, l, g, c), t="l", lty=c(1,2,2,1), xlab="x", ylab="")legend("topleft", legend = c("Voigt", "Lorentz", "Gauss", "Convolution"), bty="n",
lty=c(1,2,2,1), col=1:4)