34 lines
1.7 KiB
R
34 lines
1.7 KiB
R
# Get density from characteristic function
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#
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# Author: François Pelletier
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###############################################################################
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#' Get density from characteristic function
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#'
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#' @param char.fun Vectorized characteristic function
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#' @param n Amount of discretization points
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#' @param min Lower bound for density function
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#' @param max Upper bound for density function
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#' @return A data.frame object containing
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#' @return transform.grid: transform variate grid
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#' @return char.fun.t: characteristic function evaluated at t
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#' @return density.grid: density function grid
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#' @return density.value: density function evaluated at point x
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#' @author François Pelletier
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fft.density <- function(char.fun,n,min,max,...)
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{
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index <- 0:(n-1) # Index
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density.step <- (max-min)/n # Step for density function
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density.grid <- min + index * density.step # Grid for density function
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transform.step <- 2*pi / ( n * density.step) # Step for transform variate
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lbound.char.fun <- -n/2 * transform.step # Evaluate characteristic function on range [c,d]
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ubound.char.fun <- n/2 * transform.step # Range centered at 0
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transform.grid <- lbound.char.fun + index * transform.step # Grid for transform variate
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char.fun.t <- char.fun(transform.grid,...) # Evaluate characteristifc function
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tilted.char.fun.t <- exp( -1i * index * transform.step * min ) * char.fun.t # Tilt characteristic function
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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
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data.frame(transform.grid,char.fun.t,density.grid,density.value)
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}
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