How to assign the Orthogonal Polynomials to functions?-CodePudding

Im trying to plot Laguerre's orthogonal polynomials for class assignment. I thought to create 10 functions, each function assigned to a specific polynomial by the index i.


for (i in 1:10){
  opl[i] <- function(x) {opl[3]}
}

and then use curve() to plot it. But it's not working. the laguerre.polynomials() function gives you the polynomials as a list and I think that the problem is that my loop can't extract items from a list by the index and assign it to the function.

Any ideas on how to do it?

CodePudding user response：

You could convert the polynomials into functions using as.function, e.g. by

library(orthopolynom)
library(ggplot2)

opl <- laguerre.polynomials(10)

opl_functions <- lapply(opl, as.function)

# x interval
x <- seq(-1, 1, 0.05)

# plot the first two polynomials
ggplot(data.frame(x), aes(x = x, y = y))        # basic graphical object
    geom_line(aes(y = opl_functions[[1]](x)), colour = "red")    # first layer
    geom_line(aes(y = opl_functions[[2]](x)), colour = "blue") # second layer

# and so on ...

The i-th element of opl_functions is then the i-th polynomial, depending on x. This can then be used in order to plot the polynomials.