user1819274 - 1 year ago 88
R Question

# Optimizing all values in a matrix

I'm trying to write code to efficiently solve for all values in a matrix based on an optimization. I'm trying to find the value of x that minimizes the equation:

``````(x - (1 / ((1 / x) - sqrt(1 / x))))^2
``````

I wrote some code that accomplishes this task, but it isn't pretty (nor is it fast).

``````mSS <- function(x)
{
#Sum of squares for X and the transformation
(x - (1 / ((1 / test_mat[rows, cols]) - sqrt(1 / x))))^2
}

n = 151
m = 50000
test_mat  = matrix(rnorm(n * m, mean = 0, sd = 1), n, m)
trans_mat = matrix(data = NA, n, m)

#Go through each row/col position in array, find value that minimizes mSS function
for (cols in 1:ncol(test_mat)) {
for (rows in 1:nrow(test_mat)) {
trans_mat[rows, cols] = optimize(mSS, c(0, 3))\$minimum
}
}
``````

I'm mentally stuck trying to figure out the best approach for making this go faster. I was thinking maybe using apply with some custom functions might be the route, but I'm having difficulty figuring out a workable solution. Any pointers in the right direction would be appreciated.

``````mSS<-function(x, a)