driftWn2D: Drift of the WN diffusion in 2D
In egarpor/sdetorus: Statistical Tools for Toroidal Diffusions

driftWn2D

R Documentation

Drift of the WN diffusion in 2D

Description

Computes the drift of the WN diffusion in 2D in a vectorized way.

Usage

driftWn2D(x, A, mu, sigma, rho = 0, maxK = 2L, expTrc = 30)

Arguments

`x`	a matrix of dimension `c(n, 2)` containing angles. They all must be in `[\pi,\pi)` so that the truncated wrapping by `maxK` windings is able to capture periodicity.
`A`	drift matrix of size `c(2, 2)`.
`mu`	a vector of length `2` giving the mean.
`sigma`	vector of length `2` containing the square root of the diagonal of `\Sigma`, the diffusion matrix.
`rho`	correlation coefficient of `\Sigma`.
`maxK`	maximum absolute value of the windings considered in the computation of the WN.
`expTrc`	truncation for exponential: `exp(x)` with `x <= -expTrc` is set to zero. Defaults to `30`.

Value

A matrix of size c(n, 2) containing the drift evaluated at x.

Examples

alpha <- 3:1
mu <- c(0, 0)
sigma <- 1:2
rho <- 0.5
Sigma <- diag(sigma^2)
Sigma[1, 2] <- Sigma[2, 1] <- rho * prod(sigma)
A <- alphaToA(alpha = alpha, sigma = sigma, rho = rho)
x <- rbind(c(0, 1), c(1, 0.1), c(pi, pi), c(-pi, -pi), c(pi / 2, 0))
driftWn2D(x = x, A = A, mu = mu, sigma = sigma, rho = rho)
driftWn(x = x, A = A, mu = c(0, 0), Sigma = Sigma)

egarpor/sdetorus documentation built on March 4, 2024, 1:23 a.m.