I have a function of several variables H(x,y,z,w)=2xy+3zw-x^2+W^3. I need to draw the contour plot of the function H with respect to x and y when z=3 and w=5. Any help on drawing this contour plot using R would be greatly appreciated. Thank you!

### >Solution :

You can create a sequence of x and y and compute the function:

```
library(ggplot2)
#Create the function
H <- function(x, y, z = 3, w = 5) 2*x*y + 3*z*w - x^2 + w^3
#Sequence of x and y
s <- seq(-100, 100, length.out = 100)
#Grid
g <- expand.grid(x = s, y = s)
#Compute for each value of x and y the function H
g$value <- with(g, H(x, y))
#Plot
ggplot(g) +
aes(x = x, y = y, z = value) +
geom_contour()
#With some customization
library(geomtextpath)
ggplot(g) +
aes(x = x, y = y, z = value) +
geom_contour_filled(show.legend = FALSE) +
geom_textcontour(size = 2) +
theme_bw()
```