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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