simulate.covAll: Simulation of a 'covAll' Object
In kergp: Gaussian Process Laboratory

Description Usage Arguments Value Note See Also Examples

Simulation of a covAll object.

## S4 method for signature 'covAll'
simulate(object, nsim = 1, seed = NULL,
         X, mu = NULL, method = "mvrnorm", checkNames = TRUE,
         ...)

`object`	A covariance kernel object.
`nsim`	Number of simulated paths.
`seed`	Not used yet.
`X`	A matrix with the needed inputs as its columns.
`mu`	Optional vector with length `nrow(X)` giving the expectation μ(x) of the Gaussian Process at the simulation locations x.
`method`	Character used to choose the simulation method. For now the only possible value is `"mvrnorm"` corresponding to the function with this name in the MASS package.
`checkNames`	Logical. It `TRUE` the colnames of `X` and the input names of `object` as given by `inputNames(object)` must be identical sets.
`...`	Other arguments for methods.

A numeric matrix with nrow(X) rows and nsim columns. Each column is the vector of the simulated path at the simulation locations.

The simulation is unconditional.

The mvrnorm function.

## -- as in example(kergp) define an argumentwise invariant kernel --

kernFun <- function(x1, x2, par) {
  h <- (abs(x1) - abs(x2)) / par[1]
  S <- sum(h^2)
  d2 <- exp(-S)
  K <- par[2] * d2
  d1 <- 2 * K * S / par[1]   
  attr(K, "gradient") <- c(theta = d1,  sigma2 = d2)
  return(K)
}

covSymGauss <- covMan(kernel = kernFun,
                      hasGrad = TRUE,
                      label = "argumentwise invariant",
                      d = 2,
                      parNames = c("theta", "sigma2"),
                      par = c(theta = 0.5, sigma2 = 2))

## -- simulate a path from the corresponding GP --

nGrid <- 24; n <- nGrid^2; d <- 2
xGrid <- seq(from = -1, to = 1, length.out = nGrid)
Xgrid <- expand.grid(x1 = xGrid, x2 = xGrid)

ySim <- simulate(covSymGauss, X = Xgrid)
contour(x = xGrid, y = xGrid,
        z = matrix(ySim, nrow = nGrid, ncol = nGrid), 
        nlevels = 15)