gram2edm {edmcr}

Linear Matrix Operator

Description

gram2edm Inverse Operator of edm2gram

Usage

gram2edm(B)

Arguments

B

A centered, positive semi-definite matrix.

Details

The edm2gram function performs the following transformation:

edm2gram(D_{n}^{-}) = B_{n}^{+}

where D_{n}^{-} is the space of symmetric, hollow matrices, negative definite on the space spanned by x'e = 0 and B_{n}^{+} is the space of centered positive definite matrices.

The gram2edm function performs the inverse operation, taking a matrix in B_{n}^{+} and transforming it to a matrix in D_{n}^{-}.

gram2edm(B_{n}^{+}) = D_{n}^{-}

Therfore, gram2edm on B_{n}^{+} is the inverse operator of edm2gram on D_{n}^{-}.

Value

D A matrix in D_{n}^{-}. If the input matrix B is a gram matrix, D is a Euclidean Distance Matrix.

See Also

edm2gram

Examples

 
X <- cbind(runif(100,0,1),runif(100,0,1))
G <- X %*% t(X)
gram2edm(G)