CODEWITHSUNDEEP
rmatrixsummathematical-optimization
mac
mac

Reputation: 25

R - function input and optimization

I usually have trouble inputing functions in R but they are always simple functions that I manage to work it out. However now I have a very complicated problem at hand that requires functions that has unknowns, summation and a matrix. And I am clueless where to begin. (This is not my homework question, just trying to work out something using a different method, hoping it works)

So I want to input a function:
A=∑i=1 N exp ^ [ ∑j=1 M Matrix ij * unknownj ]

and then minimize the function:
B= log A - ∑j=1 M unknown j * C j

so my goal is to find the j unknown parameters that minimizes function B.

But this is very complicated. You do not have to give me an answer directly. You can use another example to answer my question indirectly. Any help/tips/guidance is appreciated.

Upvotes: 0

Views: 905

Answers (1)

Barranka
Barranka

Reputation: 21047

Let's see if we can break the problem into smaller things:

Let's name some variables first:

  • Let Q be an matrix with N rows and M columns
  • Let x be a (column) vector of length M (for a moment, think it's not an "unknown")
  • Let C be a (column) vector of length M

Notice that both A and B will be "scalars" (or, in R parlance, 1x1 vectors).

Hint: In R, you can do matrix multiplication using the %*% operator. See Quick-R: Matrix algebra.

Working on function A

Q %*% x is the product inside the sum which is inside the exponential function, so:

A <- function (Q, x) {
  y <- Q %*% x # This will be a (column) vector of length `N`
  return(sum(exp(y)) # This will be a scalar (more precisely, a 1x1 vector)
}

Not so hard, is it?

Working on function B

B <- function(Q, C, x) {
  y <- sum(x * C) # or, since both x and C are column vectors:
                  # y <- t(x) %*% C
  a <- A(Q, x)
  return(log(a) - y)
}

So, that's how you would input the functions.

As for the optimization, I suggest you take a look to the optimx package; you'll need to supply starting values for vector x.

Upvotes: 2

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