propagate.spectral {spate}

Function that propagates a state (spectral coefficients).

Description

Function that propagates the vector 'alphat'. This is equivalent to multiplying 'alphat' with the propagator matrix G. It is a lot faster though, due to the block-diagonal structure of G. This is a wrapper function of a C function.

Usage

propagate.spectral(alphat,spateFT=NULL,n=NULL,Gvec=NULL,par=NULL)

Arguments

alphat

A vector of spectral coefficients.

spateFT

A 'spateFT' obtained from 'spate.init'. Either this or 'n' needs to be given.

n

Number of points on each axis. n x n is the total number of spatial points. Either this or 'spateFT' needs to be given.

Gvec

The propagator matrix G in vector format obtained from 'get.propagator.vec'. If 'Gvec' is not given, it is constructed based on 'par'.

par

Parameters for the SPDE in the following order: rho_0, sigma^2, zeta, rho_1, gamma, alpha, mu_x, mu_y, tau^2. If 'Gvec' is not given, 'par' needs to be given.

Value

A vector of propagated coefficients G*alphat.

Author(s)

Fabio Sigrist

Examples

n <- 50
spec <- matern.spec(wave=spate.init(n=n,T=1)$wave,n=n,rho0=0.05,sigma2=1,norm=TRUE)
alphat <- sqrt(spec)*rnorm(n*n)
##Propagate initial state
wave <- wave.numbers(n)
Gvec <- get.propagator.vec(wave=wave$wave,indCos=wave$indCos,zeta=0.1,rho1=0.02,gamma=2,
                  alpha=pi/4,muX=0.2,muY=0.2,dt=1,ns=4)
alphat1 <- propagate.spectral(alphat,n=n,Gvec=Gvec)

opar <- par(no.readonly = TRUE)
par(mfrow=c(1,2))
image(1:n,1:n,matrix(real.fft(alphat,n=n,inv=FALSE),nrow=n),main="Whittle
field",xlab="",ylab="",col=cols())
image(1:n,1:n,matrix(real.fft(alphat1,n=n,inv=FALSE),nrow=n),main="Propagated
field",xlab="",ylab="",col=cols())
par(opar) # Reset par() settings