diff --git a/.project b/.project new file mode 100644 index 0000000..dace9a3 --- /dev/null +++ b/.project @@ -0,0 +1,19 @@ + + + FourierStuff + + + + + + de.walware.statet.r.builders.RSupport + + + + + + de.walware.statet.base.StatetNature + de.walware.statet.r.RNature + de.walware.statet.r.RPkgNature + + diff --git a/.settings/de.walware.r.core.prefs b/.settings/de.walware.r.core.prefs new file mode 100644 index 0000000..b677fbb --- /dev/null +++ b/.settings/de.walware.r.core.prefs @@ -0,0 +1,2 @@ +RProjectBuild/Package.name=FourierStuff +eclipse.preferences.version=1 diff --git a/DESCRIPTION b/DESCRIPTION new file mode 100644 index 0000000..53e7d72 --- /dev/null +++ b/DESCRIPTION @@ -0,0 +1,9 @@ +Package: FourierStuff +Title: Some probability stuff around Fourier transforms +Version: 0.1 +Date: 2014-01-06 +Author: Francois Pelletier +Maintainer: Francois Pelletier +Description: This is a package gathering different functions to work with the + characteristic function and Fourier transforms +License: LGPL-3 diff --git a/NAMESPACE b/NAMESPACE new file mode 100644 index 0000000..e69de29 diff --git a/R/fft.density.R b/R/fft.density.R new file mode 100644 index 0000000..ca4e257 --- /dev/null +++ b/R/fft.density.R @@ -0,0 +1,34 @@ +# Get density from characteristic function +# +# Author: François Pelletier +############################################################################### + +#' Get density from characteristic function +#' +#' @param char.fun Vectorized characteristic function +#' @param n Amount of discretization points +#' @param min Lower bound for density function +#' @param max Upper bound for density function +#' @return A data.frame object containing +#' @return transform.grid: transform variate grid +#' @return char.fun.t: characteristic function evaluated at t +#' @return density.grid: density function grid +#' @return density.value: density function evaluated at point x +#' @author François Pelletier +fft.density <- function(char.fun,n,min,max,...) +{ + index <- 0:(n-1) # Index + density.step <- (max-min)/n # Step for density function + density.grid <- min + index * density.step # Grid for density function + transform.step <- 2*pi / ( n * density.step) # Step for transform variate + lbound.char.fun <- -n/2 * transform.step # Evaluate characteristic function on range [c,d] + ubound.char.fun <- n/2 * transform.step # Range centered at 0 + transform.grid <- lbound.char.fun + index * transform.step # Grid for transform variate + char.fun.t <- char.fun(transform.grid,...) # Evaluate characteristifc function + tilted.char.fun.t <- exp( -1i * index * transform.step * min ) * char.fun.t # Tilt characteristic function + density.value <- Re(transform.step / (2*pi) * exp( - 1i * lbound.char.fun * density.grid ) * fft(tilted.char.fun.t)) #Use FFT to get density value, then untilt and normalize + data.frame(transform.grid,char.fun.t,density.grid,density.value) +} + + + diff --git a/man/fft.density.Rd b/man/fft.density.Rd new file mode 100644 index 0000000..f83c013 --- /dev/null +++ b/man/fft.density.Rd @@ -0,0 +1,33 @@ +\name{fft.density} +\alias{fft.density} +\title{Get density from characteristic function} +\usage{ +fft.density(char.fun, n, min, max, ...) +} +\arguments{ + \item{char.fun}{Vectorized characteristic function} + + \item{n}{Amount of discretization points} + + \item{min}{Lower bound for density function} + + \item{max}{Upper bound for density function} +} +\value{ +A data.frame object containing + +transform.grid: transform variate grid + +char.fun.t: characteristic function evaluated at t + +density.grid: density function grid + +density.value: density function evaluated at point x +} +\description{ +Get density from characteristic function +} +\author{ +François Pelletier +} +