spate (version 1.5)

real.fft.TS: Fast calculation of the two-dimensional real Fourier transform of a space-time field. For each time point, the spatial field is transformed.

Description

This function calculates the two-dimensional real Fourier transform of a space-time field. This is a wrapper function for a C function which uses the complex FFT function from the 'fftw3' library. In contrast to using T times the function 'real.FFT', R needs to communicate with C only once and not T times which saves computational time.

Usage

real.fft.TS(w,n,T,inv=TRUE,indFFT=NULL)

Arguments

w

Spatio-temporal field in a stacked vector of length T x N. Stacking is done first over space and then time. E.g., the first N=n^2 entries contain the spatial field at time t=1. Note that the spatial field itself is stacked as well, i.e., each spatial field is in a vector of length N=n^2.

n

Number of grid points on each axis. n x n is the total number of spatial points.

T

Number of time points.

inv

Indicates whether the inverse Fourier transform should be calculated or not.

indFFT

A list of containing vectors of natural numbers representing indices used to transform between the real and the complex Fourier transform.

Value

A vector of length T x N containing the (inverse) Fourier transform of 'w'.

Examples

n <- 100
T <- 4
spec <- matern.spec(wave=spate.init(n=n,T=1)$wave,n=n,rho0=0.05,sigma2=1,norm=TRUE)
specsim <- matrix(0,nrow=T,ncol=n*n)
for(t in 1:T) specsim[t,] <- rnorm(n*n)*sqrt(spec)
maternsim <- vect.to.TSmat(real.fft.TS(TSmat.to.vect(specsim),n=n,T=T,inv=FALSE),T=T)
par(mfrow=c(2,2))
for(t in 1:T) image(1:n,1:n,matrix(maternsim[t,],nrow=n),
                    main="Sample from Matern field",xlab="",ylab="")