CODEWITHSUNDEEP
r4d
carnecol88
carnecol88

Reputation: 43

Plotting function with 3 parameters (4d) in R

I want to see how three variables x, y, and z respond to a function f using R.

I've searched for R solutions (e.g. rgl using 4d plots) but none seem to allow the input of a function as the fourth variable while allowing manipulation of x, y, and z across their full range of values.

# First I create three variables that each have a domain 0 to 4
x 
y 
z 

# Then I create a function from those three variables
f <- sqrt(x^2 + y^2 + z^2)

EDIT: I originally stated that I wanted x, y, and z to be seq(0, 4, 0.01) but in fact I only want them to range from 0 to 4, and do so independently of other variables. In other words, I want to plot the function across a range of values letting x move independently of y and z and so forth, rather than plotting a 3-D line. The result should be a 3-D surface.

I want to: a) see how the function f responds to all possible combinations of x, y, and z across a range of x, y, and z values 0 to 4, and b) find what maxima/minima exist especially when holding one variable constant.

Upvotes: 0

Views: 826

Answers (1)

Chelmy88
Chelmy88

Reputation: 1116

This is rather a mathematical questions. Unfortunately, our computer screens are not really made fro 4D, neither our brains. So what you ask wont be possible as if. Indeed, you want to show a dense set of data (a cube between 0 and 4), and we can not display what is "inside" the cube.

To come back to R, you can always display a slice of it, for example fixing z and plot sqrt(x^2 + y^2 + z^2) for x and y. Here you have two examples:

# Points where the function should be evaluated
x <- seq(0, 4, 0.01)
y <- seq(0, 4, 0.01)
z <- seq(0, 4, 0.01)

# Compute the distance from origin
distance <- function(x,y,z) {
  sqrt(x^2 + y^2 + z^2)
}

# Matrix to store the results
slice=matrix(0, nrow=length(x),ncol=length(y))
# Fill the matrix with a slice at z=3
i=1
for (y_val in y)
{
  slice[,i]=distance(x,y_val,3)
  i=i+1
}

# PLot with plot3D library
require(plot3D)
persp3D(z = slice, theta = 100,phi=50)

# PLot with raster library
library(raster)
plot(raster(slice,xmn=min(x), xmx=max(x), ymn=min(y), ymx=max(y)))

If you change your z values, you will not really change the shape (just making it "flatter" for bigger z). Note that the function being symmetric in x, y and z, the same plots are produced if you keep xor y constant.

For your last question about the maximum, you can re-use the slice matrix and do:

max_ind=which(slice==max(slice),arr.ind = TRUE)
x[max_ind[,1]]
y[max_ind[,2]]

(see Get the row and column name of the minimum element of a matrix)

But again with math we can see from your equation that the maximum will always be obtained by maxing x, y and z. Indeed, the function simply measure the distance from the origin.

Upvotes: 1

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