get.propagator.vec: Propagator matrix G in vector form.

In spate: Spatio-Temporal Modeling of Large Data Using a Spectral SPDE Approach

Propagator matrix G in vector form.

Description

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

Usage

get.propagator.vec(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

A list with three elements 'G11C', 'G11', and 'G12'. The first element contains a vector of length 'ns' which corresponds to the diagonal propagator of the cosin-only terms. The second element contains the remaining diagonal entries of G, i.e., the diagonal entries of the propagator for the cosine / sine pairs. Note that for each pair, only one value is taken since the diagonal elements for both the cosin and sine terms are equal. The third element is a vector with the off-diagonal terms of the propagator for the cosine / sine pairs.

Author(s)

Fabio Sigrist

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)
diag(G)[1:4]
diag(G[wave$indCos,wave$indCos])
diag(G[wave$indCos,wave$indCos+1])
get.propagator.vec(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)

spate documentation built on Oct. 3, 2023, 5:09 p.m.