spate.sim {spate}

Simulate from the SPDE.

Description

Generates one sample from the Gaussian process specified through the SPDE.

Usage

spate.sim(par,n,T,seed=NULL,StartVal=NULL,nu=1)

Arguments

par

Vector of parameters for the SPDE in the following order: rho_0, sigma^2, zeta, rho_1, gamma, alpha, mu_x, mu_y, tau^2. rho_0 and sigma^2 are the range and marginal variance of the Matern covariance funtion for the innovation term epsilon. zeta is the damping parameter. rho_1, gamma, and alpha parametrize the diffusion matrix with rho_1 being a range parameter, gamma and alpha determining the amount and the direction, respectively, of anisotropy. mu_x and mu_y are the two components of the drift vector. tau^2 denotes the variance of nugget effect or measurment error.

n

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

T

Number of points in time.

seed

Seed for random number generator.

StartVal

A starting value (field) for the SPDE can be defined. This is the spatial field at the initial time that get propagated forward by the SPDE. The starting fields needs to be a stacked vector of lengths n x n (number of spatial points). Use 'as.vector()' to convert a spatial matrix to a vector.

nu

Smoothness parameter of the Matern covariance function for the innovations. By default this equals 1 corresponding to the Whittle covariance function.

Value

A list containing a simulated spatio-temporal field xi with covariance structure as defined through the SPDE, a simulated observation field w obtained by adding a measurement error, and the simulated Fourier coefficients. The last two are returned only on demand.

Author(s)

Fabio Sigrist

Examples

StartVal <- rep(0,100^2)
StartVal[75*100+75] <- 1000
par <- c(rho0=0.05,sigma2=0.7^2,zeta=-log(0.99),rho1=0.06,
         gamma=3,alpha=pi/4,muX=-0.1,muY=-0.1,tau2=0.00001)
spateSim <- spate.sim(par=par,n=100,T=6,StartVal=StartVal,seed=1)
plot(spateSim,mfrow=c(2,3),mar=c(2,2,2,2),indScale=TRUE,
     cex.axis=1.5,cex.main=2)