arguments sigma1 and sigma2 renamed to Sigma1 and Sigma2

R/kldggd.R

-kldggd <- function(sigma1, beta1, sigma2, beta2, eps = 1e-06) {
+kldggd <- function(Sigma1, beta1, Sigma2, beta2, eps = 1e-06) {
   #' Kullback-Leibler Divergence between Centered Multivariate generalized Gaussian Distributions
   #'
   #' Computes the Kullback- Leibler divergence between two random variables distributed
@@ -6,10 +6,10 @@ kldggd <- function(sigma1, beta1, sigma2, beta2, eps = 1e-06) {
   #'
   #' @aliases kldggd
   #'
-  #' @usage kldggd(sigma1, beta1, sigma2, beta2, eps = 1e-06)
-  #' @param sigma1 symmetric, positive-definite matrix. The dispersion matrix of the first distribution.
+  #' @usage kldggd(Sigma1, beta1, Sigma2, beta2, eps = 1e-06)
+  #' @param Sigma1 symmetric, positive-definite matrix. The dispersion matrix of the first distribution.
   #' @param beta1 positive real number. The shape parameter of the first distribution.
-  #' @param sigma2 symmetric, positive-definite matrix. The dispersion matrix of the second distribution.
+  #' @param Sigma2 symmetric, positive-definite matrix. The dispersion matrix of the second distribution.
   #' @param beta2 positive real number. The shape parameter of the second distribution.
   #' @param eps numeric. Precision for the computation of the Lauricella function
   #' (see \code{\link{lauricella}}). Default: 1e-06.
@@ -63,35 +63,35 @@ kldggd <- function(sigma1, beta1, sigma2, beta2, eps = 1e-06) {
   #'
   #' @export
   
-  # sigma1 and sigma2 must be matrices
-  if (is.numeric(sigma1) & !is.matrix(sigma1))
-    sigma1 <- as.matrix(sigma1)
-  if (is.numeric(sigma2) & !is.matrix(sigma2))
-    sigma2 <- as.matrix(sigma2)
+  # Sigma1 and Sigma2 must be matrices
+  if (is.numeric(Sigma1) & !is.matrix(Sigma1))
+    Sigma1 <- as.matrix(Sigma1)
+  if (is.numeric(Sigma2) & !is.matrix(Sigma2))
+    Sigma2 <- as.matrix(Sigma2)
   
   # Number of variables
-  p <- nrow(sigma1)
+  p <- nrow(Sigma1)
   
   # if (p == 1)
-  #   stop("kldggd computes the KL divergence between multivariate probability distributions.\nsigma1 and sigma2 must be square matrices with p > 1 rows.")
+  #   stop("kldggd computes the KL divergence between multivariate probability distributions.\nSigma1 and Sigma2 must be square matrices with p > 1 rows.")
   
-  # sigma1 and sigma2 must be square matrices with the same size
-  if (ncol(sigma1) != p | nrow(sigma2) != p | ncol(sigma2) != p)
-    stop("sigma1 et sigma2 doivent must be square matrices with rank p.")
+  # Sigma1 and Sigma2 must be square matrices with the same size
+  if (ncol(Sigma1) != p | nrow(Sigma2) != p | ncol(Sigma2) != p)
+    stop("Sigma1 et Sigma2 doivent must be square matrices with rank p.")
   
-  # IS sigma1 symmetric, positive-definite?
-  if (!isSymmetric(sigma1))
-    stop("sigma1 must be a symmetric, positive-definite matrix.")
-  lambda1 <- eigen(sigma1, only.values = TRUE)$values
+  # IS Sigma1 symmetric, positive-definite?
+  if (!isSymmetric(Sigma1))
+    stop("Sigma1 must be a symmetric, positive-definite matrix.")
+  lambda1 <- eigen(Sigma1, only.values = TRUE)$values
   if (any(lambda1 < .Machine$double.eps))
-    stop("sigma1 must be a symmetric, positive-definite matrix.")
+    stop("Sigma1 must be a symmetric, positive-definite matrix.")
   
-  # IS sigma2 symmetric, positive-definite?
-  if (!isSymmetric(sigma2))
-    stop("sigma2 must be a symmetric, positive-definite matrix.")
-  lambda2 <- eigen(sigma2, only.values = TRUE)$values
+  # IS Sigma2 symmetric, positive-definite?
+  if (!isSymmetric(Sigma2))
+    stop("Sigma2 must be a symmetric, positive-definite matrix.")
+  lambda2 <- eigen(Sigma2, only.values = TRUE)$values
   if (any(lambda2 < .Machine$double.eps))
-    stop("sigma2 must be a symmetric, positive-definite matrix.")
+    stop("Sigma2 must be a symmetric, positive-definite matrix.")
   
   if (beta1 < .Machine$double.eps)
     stop("beta1 must be non-negative.")
@@ -101,14 +101,14 @@ kldggd <- function(sigma1, beta1, sigma2, beta2, eps = 1e-06) {
   pb1 <- p/(2*beta1)
   pb2 <- p/(2*beta2)
   
-  # Eigenvalues of sigma1 %*% inv(sigma2)
-  lambda <- sort(eigen(sigma1 %*% solve(sigma2), only.values = TRUE)$values, decreasing = FALSE)
+  # Eigenvalues of Sigma1 %*% inv(Sigma2)
+  lambda <- sort(eigen(Sigma1 %*% solve(Sigma2), only.values = TRUE)$values, decreasing = FALSE)
   
   if (p > 1) {
     lauric <- lauricella(a = -beta2, b = rep(0.5, p-1), g = p/2, x = 1 - lambda[(p-1):1]/lambda[p],
                          eps = eps)
     result <- as.numeric(
-      log( (beta1*gamma(pb2)/sqrt(det(sigma1))) / (beta2*gamma(pb1)/sqrt(det(sigma2))) ) +
+      log( (beta1*gamma(pb2)/sqrt(det(Sigma1))) / (beta2*gamma(pb1)/sqrt(det(Sigma2))) ) +
         p/2 * (1/beta2 - 1/beta1) * log(2) - pb1 +
         2^(beta2/beta1 - 1) * gamma(beta2/beta1 + pb1) / gamma(pb1) * lambda[p]^beta2 * lauric
     )
@@ -116,9 +116,9 @@ kldggd <- function(sigma1, beta1, sigma2, beta2, eps = 1e-06) {
     attr(result, "epsilon") <- attr(lauric, "epsilon")
   } else {
     result <- as.numeric(
-      log( (beta1*gamma(pb2)/sqrt(sigma1)) / (beta2*gamma(pb1)/sqrt(sigma2)) ) +
+      log( (beta1*gamma(pb2)/sqrt(Sigma1)) / (beta2*gamma(pb1)/sqrt(Sigma2)) ) +
         1/2 * (1/beta2 - 1/beta1) * log(2) - pb1 +
-        2^(beta2/beta1 - 1) * gamma(beta2/beta1 + pb1) / gamma(pb1) * (sigma1/sigma2)^beta2
+        2^(beta2/beta1 - 1) * gamma(beta2/beta1 + pb1) / gamma(pb1) * (Sigma1/Sigma2)^beta2
     )
     attr(result, "k") <- NULL
     attr(result, "epsilon") <- 0

man/kldggd.Rd

@@ -4,14 +4,14 @@
 \alias{kldggd}
 \title{Kullback-Leibler Divergence between Centered Multivariate generalized Gaussian Distributions}
 \usage{
-kldggd(sigma1, beta1, sigma2, beta2, eps = 1e-06)
+kldggd(Sigma1, beta1, Sigma2, beta2, eps = 1e-06)
 }
 \arguments{
-\item{sigma1}{symmetric, positive-definite matrix. The dispersion matrix of the first distribution.}
+\item{Sigma1}{symmetric, positive-definite matrix. The dispersion matrix of the first distribution.}
 
 \item{beta1}{positive real number. The shape parameter of the first distribution.}
 
-\item{sigma2}{symmetric, positive-definite matrix. The dispersion matrix of the second distribution.}
+\item{Sigma2}{symmetric, positive-definite matrix. The dispersion matrix of the second distribution.}
 
 \item{beta2}{positive real number. The shape parameter of the second distribution.}