R/GaussLegendre.R

In SMR: Externally Studentized Midrange Distribution

#############################################################
# Function to calculate nodes and weights of Gauss-Legendre #
# quadrature, where size is the number of points. It uses the  #
# Golub-Welsh algorithm                                     #
#############################################################
# GaussLegendre <- function(size)
# {
#   size <- as.integer(size)
#   if (size < 0)
#     stop("Must be a non-negative number of nodes!")
#   if (size == 0)
#      return(list(x = numeric(0), w = numeric(0)))
#   i  <- 1:size
#   j   <- 1:(size-1)
#   mu0 <- 2
#   b <- j / (4 * j^2 - 1)^0.5
#   A <- rep(0, size * size)
#   A[(size + 1) * (j - 1) + 2] <- b
#   A[(size + 1) * j] <- b
#   dim(A) <- c(size, size)
#   sd <- eigen(A, symmetric = TRUE)
#   w <- rev(as.vector(sd$vectors[1, ]))
#   w <- mu0 * w^2
#   x <- rev(sd$values)
#   return(list(nodes = x, weights = w))
# }
#