How to plot graph of functions of two variables in a function in R

Question

I made this derivative script and I wanted to plot the graph of the result of the derivative along with the function. But I am not able to make the graph in the multivariate case f(x,y), the result of the derivative is taken as a value and not as a function. See the example below:

DD7<-function(x,r,contador=1){

dy<- substitute(x)
if(contador<1) {

stop("Grau de derivada menor que 1")
}
if(contador==1) {

der<-D(dy,c(r))

print(der)
x<- y <- seq(-3,3,length=50)
z<- outer(x,y,der)
persp(x,y,z)
}
else {
der2<- DD(D(dy,r),r,contador-1)
print(der2)
x2<- y2 <- seq(-3,3,length=50)
z2<- outer(x,y,der2)
persp(x,y,z2)

}
}

DD7(x*y^2,"y",1)

Error in get(as.character(FUN), mode = "function", envir = envir) : 
object 'der' of mode 'function' was not found

Answer 1

As I said in my comments, outer 's third argument needs to be a function. If you use eval(der) , you may infer (correctly) that it is evaluating the expression ( y^2 in this example) based on the objects found in the calling environment (the function's environment, to be specific). Since x and y are both found, then eval(der) uses those variables, and returns a vector of the appropriate length.

The purpose of outer is to do an outer-join of the values, expanding into length(x)*length(y) combinations. If you look at the function as it is called by outer , its first argument is length(x)*length(y) elements long, all from the original x ; the second argument is also that length, from the original y . The order of the values are such that all values from x are paired with all values of y .

Given this what we need to do is have eval(der) operate in that environment.

DD7 <- function(x, r, contador=1) {
  # ...
  z2 <- outer(x, y, function(x, y) eval(der))
  persp(x, y, z2)
  # ...
}

DD7(x*y^2, "y", 1)
# x * (2 * y)

In that example, it might be confusing which x and y are referenced when; it's straight-forward: inside the anon-function passed to outer , we also name them the same names so that the eval uated der will find the relevant expanded values.