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

## Description

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

## Usage

 `1` ```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 [π,π) 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 Σ, the diffusion matrix. `rho` correlation coefficient of Σ. `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

 ``` 1 2 3 4 5 6 7 8 9 10``` ```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) ```

sdetorus documentation built on Aug. 19, 2021, 9:06 a.m.