# R/plotmcd.R In mcauchyd: Multivariate Cauchy Distribution; Kullback-Leibler Divergence

#### Documented in plotmcd

```plotmcd <- function(mu, Sigma, xlim = c(mu[1] + c(-10, 10)*Sigma[1, 1]),
ylim = c(mu[2] + c(-10, 10)*Sigma[2, 2]), n = 101,
xvals = NULL, yvals = NULL, xlab = "x", ylab = "y",
zlab = "f(x,y)", col = "gray", tol = 1e-6, ...) {
#' Plot of the Bivariate Cauchy Density
#'
#' Plots the probability density of the multivariate Cauchy distribution with 2 variables
#' with location parameter \code{mu} and scatter matrix \code{Sigma}.
#'
#' @aliases plotmcd
#'
#' @usage plotmcd(mu, Sigma, xlim = c(mu[1] + c(-10, 10)*Sigma[1, 1]),
#'                 ylim = c(mu[2] + c(-10, 10)*Sigma[2, 2]), n = 101,
#'                 xvals = NULL, yvals = NULL, xlab = "x", ylab = "y",
#'                 zlab = "f(x,y)", col = "gray", tol = 1e-6, ...)
#' @param mu length 2 numeric vector.
#' @param Sigma symmetric, positive-definite square matrix of order 2. The scatter matrix.
#' @param xlim,ylim x-and y- limits.
#' @param n A one or two element vector giving the number of steps in the x and y grid, passed to \code{\link{plot3d.function}}.
#' @param xvals,yvals The values at which to evaluate \code{x} and \code{y}. If used, \code{xlim} and/or \code{ylim} are ignored.
#' @param xlab,ylab,zlab The axis labels.
#' @param col The color to use for the plot. See \code{\link{plot3d.function}}.
#' @param tol tolerance (relative to largest variance) for numerical lack of positive-definiteness in Sigma, for the estimation of the density. see \code{\link{dmcd}}.
#' @return Returns invisibly the probability density function.
#'
#' @author Pierre Santagostini, Nizar Bouhlel
#' @references N. Bouhlel, D. Rousseau, A Generic Formula and Some Special Cases for the Kullback–Leibler Divergence between Central Multivariate Cauchy Distributions.
#' Entropy, 24, 838, July 2022.
#' \doi{10.3390/e24060838}
#'
#' @seealso \code{\link{dmcd}}: probability density of a multivariate Cauchy density
#'
#' \code{\link{contourmcd}}: contour plot of a bivariate Cauchy density.
#'
#' \code{\link{plot3d.function}}: plot a function of two variables.
#'
#' @examples
#' mu <- c(1, 4)
#' Sigma <- matrix(c(0.8, 0.2, 0.2, 0.2), nrow = 2)
#' plotmcd(mu, Sigma)
#'
#' @import rgl
#' @importFrom rgl plot3d
#' @export

if (length(mu)!=2 | nrow(Sigma)!=2 | ncol(Sigma)!=2)
stop(paste("plotmcd only allows plotting a Cauchy density with 2 variables.",
"mu must be a length 2 numeric vector and Sigma must be a 2*2 square matrix.",
sep = "\n"))

# Estimation of the density
f <- function(x) dmcd(x, mu = mu, Sigma = Sigma, tol = tol)
ff <- function(x, y) sapply(1:length(x), function(i) as.numeric(f(c(x[i], y[i]))))

if (length(n) == 1)
n <- rep(n, 2)
if (is.null(xvals))
xvals = seq.int(min(xlim), max(xlim), length.out = n[1])
if (is.null(yvals))
yvals = seq.int(min(ylim), max(ylim), length.out = n[2])

# Plot
plot3d(ff, xlim = xlim, ylim = ylim, n = n, xvals = xvals, yvals = yvals,
xlab = xlab, ylab = ylab, zlab = zlab, col = col, ...)

return(invisible(f))
}
```

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mcauchyd documentation built on May 29, 2024, 2:21 a.m.