CODEWITHSUNDEEP
r
Tou Mou
Tou Mou

Reputation: 1274

How to find the list of n minimum values of an objective function from a matrix?

Suppose that we have the following code :

x1<- runif(40, min = -4.5, max = 4.5)                               # Create x vector 
y1 <- runif(40, min = -4.5, max = 4.5)                                 # Create y vector 

custom_fun <- function(x, y) {        # Create custom function in R ; here i used the beale function 
  z <- (1.5 - x + x*y)^2+(2.25 - x + x*y^2)^2+(2.625 - x + x*y^3)^2
  return(z)
}

m <- outer(x1, y1, custom_fun)

print(m)

My question is how the obtain the list of the n minimum values of the matrix m , i need also to retrieve the correspending positions in the vectors x1 and y1 ( which means the couples from x1 and y1 that allow us to obtain those minimum values of the matrix m ).

For example , if the excecution of the previous code gives :

#m
           [,1]      [,2]      [,3]       [,4]      [,5]       [,6]
[1,]  508.64893 11.245614  7887.387  3.4916340  1.517622  3232.9724
[2,]  727.76775 19.629751 17649.225 46.0714031 63.427516  6708.3153
[3,] 2227.94868  7.948157 39784.638  0.3509784  6.073413 15901.8932
[4,]   56.06329 13.568900   432.400 11.4225081 10.455426   205.5854
[5,] 1723.86138 22.552465 39256.366 67.8455312 99.733390 15069.6231
[6,] 1328.44959 21.510099 30755.388 59.7772840 86.142180 11775.4025

and i'm wanting for example the p minimum values of the matrix , let p=3 then i will retrieve the values :

0.3509784 -1.517622- 3.4916340 ( those values are near the optimum of the beale function ).

Next , i need a way to retrieve the couples (x,y) that allow us to obtain those minimum values ( from the current excecution ! ) :

custom_fun(a1,b1)=0.3509784
custom_fun(a2,b2)=1.517622
custom_fun(a3,b3)=3.4916340

so how could i retrieve (a1,b1) from the current x1 and y1 vectors ??? I will need also to retrieve the couples (a2,b2) and (a3,b3). .

Another example , suppose the current excecution gives the following :

[1] "x4 list :"
[1]  2.0695110  3.7844526 -0.6914949
[1] "y4 list :"
[1] -4.079663  1.771313 -4.206778
[1] "matrix of objective function : denoted m "
          [,1]       [,2]      [,3]
[1,] 20870.387 199.495204 25007.158
[2,] 70719.411 521.366216 84647.031
[3,]  2625.535   1.807467  3115.075

with p=2 ; the values 1.807467 and 521.366216 are good while searching the minimum, but the question is how to get their respective coordinates (x,y) from (x4,y4 ) possibilities.

I wish my question is clear.

Thank you a lot for help !

Upvotes: 0

Views: 36

Answers (1)

Ronak Shah
Ronak Shah

Reputation: 388962

I guess something like this might help :

p <- 3
#Get p minimum value
p_minimum_value <- sort(m)[1:p]
#Get their row and column position
which(relist(m %in% p_minimum_value, m), arr.ind = TRUE)

Upvotes: 1

Related Questions