cov2biu {OGI}

Bi-unit Canonical Form

Description

cov2biu(S) returns the bi-unit canonical form of S.

Usage

cov2biu(S, nu = rep(1, nrow(S)), force = FALSE, detail = FALSE)

Arguments

S

Covariance matrix, especially it is positive semi-definite.

nu

Numeric vector of subjective importance. It determines the importance of each of the variates.

force

Logical: if force=FALSE, S should be strictly positive definite. Default: FALSE.

detail

Logical: if detail=TRUE, it returns the list of the bi-unit form and the weight vectors. Default: FALSE.

Value

Numeric matrix of the bi-unit canonical form DSD of S.

Examples

S = matrix(0, 5, 5)
S[1,1] = 1
for(j in 2:5) S[1,j] = S[j,1] = -0.5
for(i in 2:5){
  for(j in 2:5){
    if(i == j) S[i,j] = 1
    else S[i,j] = 0.5
  }
}
B=cov2biu(S)
B