R: Evaluating and Plotting Functions Over a Grid

Question

I am working with the R programming language. I have the following function :

#function

my_function_b <- function(input_1, input_2, input_3, input_4) {

final_value = sin(input_1) + cos(input_2) + input_3 + input_4
 
}

Question:

• For "my_function_b", I am trying to evaluate "final_value" for different values of "input_1", "input_2", "input_3" and "input_4" . E.g. input_1, input_2, input_3, input_4 from 1 to 100 at increments of 0.1.

• Then, I want to make a 3 Dimensional plot with "input_1", "input_2" and "input_3".

• Next, I want to a fit a 3 Dimensional surface over this plot

• Finally, I want to "color" this 3 Dimensional surface according to the values of "final_input"

What I tried so far:

I figured out how to make a "grid frame" for the second function and then evaluate "final_value" using this "grid frame", e.g.

#create grid and evaluate function
input_1 <- seq(0,100,0.1)
input_2 <- seq(0,100,0.1)
input_3 <- seq(0,100,0.1)
input_4 <- seq(0,100,0.1)

my_grid <- data.frame(input_1, input_2, input_3, input_4)
my_grid$final_value = sin(input_1) + cos(input_2) + input_3 + input_4

But I am not sure if this is the best way to solve this question. This is now creating problems when I try to plot the results, e.g.

#make a 3d plot for two of the inputs and the output, and fit surface over the plot

persp(my_grid$input_1, my_grid$input_2, my_grid$final_value)

Error in persp.default(my_grid$input_1, my_grid$input_2, my_grid$final_value) : 
  invalid 'z' argument

Alternative #2: Does Not Work

library(plotly)

a = my_grid[,c(1,2,5)]
fig <- plot_ly(a = ~as.matrix(a))
fig <- fig %>% add_surface()

Error: Must supply `z` attribute

Alternative #3 : Does Not Work - Creates an Empty Plot

plot_ly() %>% 
    add_trace(data = my_grid,  x=my_grid$input_1, y=my_grid$input_2, z=my_grid$final_value, type="mesh3d" ) 

Problem: Can someone please show me how to do this? Can this be done using the "lattice" or "rsm" libraries? Or can it be done using the ways I suggested?

Thanks

Answer 1

If you want to get your plotly approach going, you need to configure your z as a matrix, i.e. an object with defined row and col dimensions!

Plotly does not require a dataframe. You can safely supply the variables (objects) directly.

library(plotly)

x <- my_grid$input_1
y <- my_grid$input_2
z <- matrix(my_grid$final_value, nrow = length(x), ncol = length(y)) # proper matrix & dimensions

plot_ly(x = x, y = y, z = z) %>% add_surface()

and voila:

amended answer based on question in comment - how to set on colorscale

This is a bit hidden in the documentation. In principle, you can define your own colorscale with endpoints/colours for the gradient you prefer, and ensure it is scaled in accordance with your surface data. Surface data must be again a well-defined matrix, i.e. having nrow/ncol dimensions check this SO post.

Typically, a colorscale is defined for the interval c(0,1). The plotly documentation speaks about a mapping for the lowest (0) and highest (1) values. The 2nd element of colorscale is the definition of the spectrum end-colours! As an alternative, you use one of the accepted colour palettes.
This SO post provides an example:

colorscale = list(c(0, 1), c("tan", "blue"))     

So for the mapping you can use your min and max values.

# --- define coordinate vectors
x = input_1
y = input_2
z = matrix(input_3, nrow = length(x), ncol = length(y)) # z must be well-dimensioned matrix

# --- define a scale for your colour setting
my_colorscale = list(
    c(min(final_value),max(final_value))    # set min/max value, or use c(0,1)
  , c("tan", "blue")                        # define desired grad. colours
)

# --- plot
plot_ly(x = x, y = y, z = z) %>% 
   add_surface(
       surfacecolor = matrix(final_value, nrow = length(x), ncol = length(y))   # your surface data points 
      ,colorscale = my_colorscale)    # scale for your surface