R/LegNorm.R

In MissMech: Testing Homoscedasticity, Multivariate Normality, and Missing Completely at Random

LegNorm <- function(x)
{
  # This function evaluates Legendre polynomials on [0,1] (note not [-1,1] at
  # a value x, and the polynomial are such that they have norm 1. It only
  # calculates p1,p2,p3, and p4 [Note p0=1, so it is not reurned]
  # x can be a vector or a matrix. 
  # in return, each element of P1, p2, p3, p4 the values of the poly at each
  # component of x
  
 if (!is.matrix(x))
 {
    x <- as.matrix(x)
 }#end if
 x <- 2 * x - 1 # Transforming the legenre's to 0,1, and we will divide by the norm in each case
 p0 <- matrix(1,nrow(x), ncol(x))
 p1 <- x
 p2 <- (3 * x * p1 - p0) / 2
 p3 <- (5 * x * p2 - 2 * p1) / 3
 p4 <- (7 * x * p3 - 3 * p2) / 4
 p1 <- sqrt(3) * p1
 p2 <- sqrt(5) * p2
 p3 <- sqrt(7) * p3
 p4 <- 3 * p4
 list(p1 = p1, p2 = p2, p3 = p3, p4 = p4)
}