How to apply this code in n-dimension using R? - r

Question

Under R I developed this script:
Sphere_1 = function (x1,x2) return(x1^2+x2^2) #sphere function / objective function
Initial_search_domain_function <- function(N,p,MIN_t_x,MAX_t_x,MIN_t_y,MAX_t_y , Objfun=custom_fun ) {
x1 <- runif(N, min = MIN_t_x, max = MAX_t_x) # Create x vector (same as in Example 1 & 2)
y1 <- runif(N, min = MIN_t_y, max = MAX_t_y) # Create y vector (same as in Example 2)
m <- outer(x1, y1, Objfun) #matrix of minimum objective values
print("matrix of objective function")
#print(m)
p_minimum_value <- sort(m)[1:p] # search p minimum values of the objective function 'Objfun' within m
X_Y_indices=which(relist(m %in% p_minimum_value, m), arr.ind = TRUE) # retrieve their corresponding row/cloumn at m
#print(X_Y_indices)
print("list of respective positions")
v1=x1[X_Y_indices[,1]] # retrieve their corresponding x-coordinate from x1 list
v2=y1[X_Y_indices[,2]] # retrieve their corresponding y-coordinate from y1 list
respective_positions=rbind(v1,v2) # store those coordinate in a matrix
respective_positions=rbind(respective_positions, `fun(x, y)` = apply(respective_positions, 2, function(x) Objfun(x[1], x[2])))
# compute the objective function for each row
rownames(respective_positions)=c("x:","y:","obj-val")
print(respective_positions)
return(respective_positions)
}
Example of output:
Initial_search_domain_function(40,5,-4.5,4.5,-4.5,4.5, Sphere_1 ) ;
[1] "matrix of objective function"
[1] "list of respective positions"
[,1] [,2] [,3] [,4] [,5]
x: 0.2904639 0.29046393 0.29046393 -0.40499210 0.29046393
y: 0.2894644 0.07744045 0.05273694 0.05273694 0.11452047
obj-val 0.1681589 0.09036632 0.08715048 0.16679979 0.09748423
I'm wanting a way such that the code not only work for a two-variables function f(x,y) , but also for n-dimensions function.
For example if n=3 I could get something like:
[1] "list of respective positions"
[,1] [,2] [,3] [,4] [,5]
x: 0.2904639 0.29046393 0.29046393 -0.40499210 0.29046393
y: 0.2894644 0.07744045 0.05273694 0.05273694 0.11452047
z: 0.2904639 0.27046393 0.50046393 -0.90499210 0.129046393
obj-val 0.1681589 0.09036632 0.08715048 0.16679979 0.09748423
with n-dimensional function like:
Sphere = function (x) return(sum(x^2)) #sphere function / objective function
The main problem is that I don't know how to compute Cartesian products for n-sets with their respective objective function values f (X) where X is n-dimensional.

Answer 1

Here is an p-dimensional function. Note that this is just an exact replica of your code, only made to work for p-dimensions. Notice that I gave it a seed argument in order for one to make comparisons:
Sphere_1_pdim = function (x) return(sum(x^2))
Initial_search_domain_function_pdim <- function(N, p, MIN, MAX, Objfun, seed = NULL) {
stopifnot(length(MIN) == length(MAX),length(N) == 1,length(p) == 1)
dims <- numeric(length(MIN)) + N
set.seed(seed)
X <- Map(runif,N,MIN,MAX)
names(X) <- paste0("X",seq_along(X),":")
m <- array(apply(expand.grid(X),1,Objfun), dims)
p_minimum_value <- sort(m)[1:p]
indices <-which(array(m %in% p_minimum_value, dim(m)), arr.ind = TRUE)
t(cbind(mapply("[",X,data.frame(indices)),"obj-val:" = m[indices]))
}
Initial_search_domain_function_pdim(40, 5, c(-4.5,-4.5,-4.5), c(4.5,4.5,4.5), Sphere_1_pdim, 0)
[,1] [,2] [,3] [,4] [,5]
X1: -0.02070682 -0.02070682 -0.05812824 -0.02070682 -0.05812824
X2: -0.20142340 0.16770837 0.16770837 -0.19309277 -0.19309277
X3: -0.19693769 -0.19693769 -0.19693769 -0.19693769 -0.19693769
obj-val: 0.07978461 0.06733932 0.07028944 0.07649804 0.07944816
Your code output:
Initial_search_domain_function(40,5, -4.5, 4.5, -4.5, 4.5, Sphere_1, 0)
[,1] [,2] [,3] [,4] [,5]
x: -0.02070682 -0.02070682 -0.05812824 -0.02070682 -0.05812824
y: -0.20142340 0.16770837 0.16770837 -0.19309277 -0.19309277
obj-val 0.04100016 0.02855487 0.03150499 0.03771359 0.04066371