spate (version 1.5)

get.propagator: Propagator matrix G.

Description

Function for obtaining the spectral propagator matrix G of the vector autoregressive model for the Fourier coefficients.

Usage

get.propagator(wave, indCos, zeta, rho1, gamma, alpha, muX, muY, dt = 1, ns=4)

Arguments

wave

Spatial wavenumbers.

indCos

Vector of integers indicating the position of columns in 'wave' of wavenumbers of cosine terms.

zeta

Damping parameter

rho1

Range parameter of the diffusion term

gamma

Parameter that determines the amount of anisotropy in the diffusion term

alpha

Parameter that determines the direction of anisotropy in the diffusion term

muX

X component of the drift vector.

muY

Y component of the drift vector.

dt

Temporal lag between two time points. By default, this equals 1.

ns

Number of real Fourier functions that have only a cosine and no sine term. 'ns' is maximal 4.

Value

Propagator matrix G.

Examples

##For illustration, four grid points on each axis
n <- 4
wave <- wave.numbers(n)
G <- get.propagator(wave=wave$wave,indCos=wave$indCos,zeta=0.5, rho1=0.1, gamma=2,
           alpha=pi/4, muX=0.2, muY=-0.15,dt=1,ns=4)
round(G,digits=2)
## View(round(G,digits=2))

##An example
n <- 50
spec <- matern.spec(wave=spate.init(n=n,T=1)$wave,n=n,rho0=0.05,sigma2=1,norm=TRUE)
alphat <- sqrt(spec)*rnorm(n*n)
##Propagate initial state
wave <- wave.numbers(n)
G <- get.propagator(wave=wave$wave,indCos=wave$indCos,zeta=0.5, rho1=0.02, gamma=2,
            alpha=pi/4, muX=0.2, muY=0.2,dt=1,ns=4)
alphat1 <- G%*%alphat

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())