#' Compute effective range for Matern correlation to drop to a specified level
#'
#' The effective range for an isotropic spatial correlation function is
#' commonly defined to be the distance beyond which the correlation becomes
#' small, typically below .05. Given range and smoothness parameters for a
#' Matern covariance function, this function numerically searches for this
#' distance. Note that the scale is not important for this calculation.
#'
#' @export
#'
#' @importFrom stats optim
#'
#' @param cor Effective correlation to check for
#' @param range Matern range parameter. Controls the decay of pointwise
#' correlations as a function of distance.
#' @param smoothness Matern smoothness parameter. Controls the number of
#' process derivatives.
#'
#' @examples
#'
#' # effective range for exponential covariance function with range = 1,
#' # which is theoretically known to equal -ln(.05)
#' maternEffectiveRange(cor = .05, range = 1, smoothness = .5)
#'
maternEffectiveRange = function(cor = .05, range = 1, smoothness = .5 ) {
optim(1, function(d) {
abs( cor -
maternArray(d, scale = 1, range = range, smoothness = smoothness) )
})$par
}
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