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#' Secular Equation
#'
#' @param a matrix
#' @param b matrix
#'
#' @importFrom stats uniroot
secularEq<-function(a,b) {
n<-dim(a)[1]
eig<-eigen(a)
eva<-eig$values
eve<-eig$vectors
beta<-drop(crossprod(eve, b))
f<-function(mu) {
return(sum((beta/(eva+mu))^2)-1)
}
lmn<-eva [n]
uup<-sqrt(sum(b^2))-lmn
ulw<-abs(beta [n])-lmn
rot<-stats::uniroot(f,lower= ulw,upper= uup)$root
cve<-beta/(eva+rot)
return(drop(eve%*%cve))
}
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