# Voigt: The Voigt function, corresponding to the convolution of a... In RcppFaddeeva: 'Rcpp' Bindings for the 'Faddeeva' Package

 Voigt R Documentation

## The Voigt function, corresponding to the convolution of a lorentzian and a gaussian distribution

### Description

Voigt distribution

Lorentzian distribution

Gaussian distribution

### Usage

```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 `...` passed to Faddeeva_w

### Value

numeric or complex vector

### Functions

• `Voigt`: Voigt lineshape function

• `Lorentz`: Lorentzian lineshape function

• `Gauss`: Gaussian lineshape function

baptiste Auguie

### Examples

```## should integrate to 1 in all cases
integrate(Lorentz, -Inf, Inf, x0=200, gamma=100)
integrate(Gauss, -Inf, Inf, x0=200, sigma=50)
integrate(Voigt, -Inf, Inf, x0=200, sigma=50, gamma=100)

## 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)
```

RcppFaddeeva documentation built on May 30, 2022, 5:07 p.m.