get.propagator.vec: 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)

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.

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.

Author

Fabio Sigrist

Examples

Run this code

##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)