MCARtest (version 1.2.1)

computeR: A function computing the incompatibility index for sequences of correlation matrices

Description

A function solving a SDP problem to compute the incompatibility index \(R()\) for a sequence of correlation matrices, as defined in BB2024;textualMCARtest. Writes the SDP problem in standard primal form, and uses csdp to solve this.

Usage

computeR(patterns = list(), SigmaS = list())

Value

The value of \(R()\), in the interval \([0,1]\).

The optimal \(X_\mathbb{S}\) for the primal problem.

The sequence of matrices \(X_\mathbb{S}^{0}\) as defined in BB2024;textualMCARtest.

The optimal \(\Sigma\) for the dual problem.

The sequence of correlation matrices \(\Sigma_\mathbb{S}\) in input.

Arguments

patterns

A vector with all the patterns in \(\mathbb{S}\)

SigmaS

The sequence of correlation matrices \(\Sigma_\mathbb{S}\)

References

BB2024MCARtest

Examples

d = 3

SigmaS=list() #Random 2x2 correlation matrices (necessarily consistent)
for(j in 1:d){
x=runif(2,min=-1,max=1); y=runif(2,min=-1,max=1)
SigmaS[[j]]=cov2cor(x%*%t(x) + y%*%t(y))
}

result = computeR(list(c(1,2),c(2,3), c(1,3)), SigmaS = SigmaS)
result$R