I have a equation system and I want to solve it using numerical methods. I want to get a close solution given a starting seed. Let me explain.
I have a vector of constants ,X, of values:
X <- (c(1,-2,3,4))
and a vector W of weights:
W <- (c(0.25,0.25,0.25,0.25))
I want that the sum of the components of W will be (sum(W)=1), and the sum of the multiplication of X and W element by element will be a given number N (sum(W*X)=N).
Is there a easy way to do this in R? I have it in Excel, using Solver, but I need to automatize it.
Here is your constant and your target value:
x <- c(1, -2, 3, 4)
n <- 10
You need a function to minimize. The first line contains each of your conditions, and the second line provides a measure of how to combine the errors into a single score. You may want to change the second line. For example, you could make one error term be more heavily weighted than the other using sum(c(1, 5) * errs ^ 2).
fn <- function(w)
{
errs <- c(sum(w) - 1, sum(x * w) - n)
sum(errs ^ 2)
}
The simplest thing is to start with all the weights the same value.
init_w <- rep.int(1 / length(x), length(x))
Use optim to optimize.
optim(init_w, fn)
## $par
## [1] 0.1204827 -1.2438883 1.1023338 1.0212406
##
## $value
## [1] 7.807847e-08
##
## $counts
## function gradient
## 111 NA
##
## $convergence
## [1] 0
##
## $message
## NULL
The par element contains your weights.