computeR.reg | R Documentation |
A function solving a SDP problem to compute the regularised incompatibility index R_z()
for a collection of correlation matrices, as defined in (7) in \insertCiteBB2024;textualMCARtest.
Writes the SDP problem in standard primal form, and uses csdp
to solve this.
computeR.reg(patterns = list(), SigmaS = list(), alpha)
patterns |
A vector with all the patterns in |
SigmaS |
The sequence of correlation matrices |
alpha |
The regularisation parameter, which satisfies alpha = 1/z. |
The value of R_z()
, 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 \insertCiteBB2024;textualMCARtest.
The optimal \Sigma
for the dual problem.
The sequence of correlation matrices \Sigma_\mathbb{S}
in input.
BB2024MCARtest
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))
}
c = 1
for(i in 1:d){
cand = min(eigen(SigmaS[[i]])$values)
if (cand < c){
c = cand
}
}
computeR.reg(list(c(1,2),c(2,3), c(1,3)), SigmaS = SigmaS, alpha = 1/c)$R
computeR.reg(list(c(1,2),c(2,3), c(1,3)), SigmaS = SigmaS, alpha = 2)$R
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