Hi everyone,

I want to convert an R function into VBA for calculating the eigenvectors and eigenvalues of a matrix using the "Power Method". The function is:


PowerMethod <- function(x, tolerance) {
    my.mat <- var(x[,-1], na.method="available")
    matSize <- dim(my.mat)[1]
    eigenVec <- matrix(NA, nrow=matSize, ncol=matSize)
    eigenVal <- rep(NA, matSize)
    for(j in 1:matSize) {
        x <- rep(1, matSize)
        yk <- x + tolerance + 1
         while(all(x-yk<tolerance)) {
            yk <- my.mat%*%x
            beta <- yk[abs(yk)==max(abs(yk))]
            x <- (1/beta)*yk
        }
        eigenVec[,j] <- (1/sqrt(sum(x^2)))*x
        eigenVal[j] <- beta
        my.mat <- my.mat - eigenVal[j]*eigenVec[,j]%*%t(eigenVec[,j])
    }
    list(eigenVec, eigenVal)
}

I want to input a matrix from the excel spreadsheet along with a tolerance level (i.e. two inputs).

The function then calculates the covariance matrix, call this M (m x m), of the input data. You then make an initial guess of the eigenvector, let's say this is a vector of 1's (m x 1) (call this x), you multiply the two together to get

y=Mx

You then calculate beta which is the element of y with the largest modulus. And, recalculate x as

x=(1/beta)y

and then calculate new y, y=Mx

This is done iteratively until the difference between the old x and new x is less than the tolerance level.

The normalised x, i.e. (1/sqrt(sum(x^2)))*x , call this v, is the first prinicipal component and the last value of beta is the associated eigenvalue.

A new M is calculated as Mnew = M-beta*v*transpose(v)

And, the whole procedure is repeated for Mnew to get the second prinicipal component and associated eigenvalue. The is done m times.

I want to output all the eigenvectors (prinicipal components) and eigenvalues to some location in the spreadsheet.


I would be extremely grateful if someone could assist me in converting this function to VBA.

Thanks in advance.
Eric



      
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