ajout du projet existant

R/fft.density.R

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+# 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)
+}
+
+
+