R/nearPD.R

In pvermees/IsoplotR: Statistical Toolbox for Radiometric Geochronology

## Code lifted from the Matrix package
## Copyright (C) 2007-2019 Martin Maechler
## Computes the nearest correlation matrix to an approximate
## correlation matrix, i.e. not positive semidefinite.
nearPD <- function(x, corr = FALSE, keepDiag = FALSE,
                   do2eigen = TRUE, doSym = FALSE, doDykstra = TRUE,
                   only.values = FALSE, eig.tol = 1e-6,
                   conv.tol = 1e-7, posd.tol = 1e-8,
                   maxit = 100L, conv.norm.type = "I",
                   trace = FALSE){
    n <- ncol(x)
    if(keepDiag) diagX0 <- diag(x)
    if(doDykstra) {
        D_S <- x; D_S[] <- 0
    }
    X <- x
    iter <- 0L ; converged <- FALSE; conv <- Inf
    while (iter < maxit && !converged) {
        Y <- X
        if(doDykstra)
            R <- Y - D_S
        ## project onto PSD matrices  X_k  =  P_S (R_k)
        e <- eigen(if(doDykstra) R else Y, symmetric = TRUE)
        ##
        Q <- e$vectors
        d <- e$values ## D <- diag(d)
        ## create mask from relative positive eigenvalues
        p <- d > eig.tol*d[1]
	if(!any(p)) stop("Matrix seems negative semi-definite")
        ## use p mask to only compute 'positive' part
        Q <- Q[,p, drop = FALSE]
        ## X <- Q %*% D[p,p,drop = FALSE] %*% t(Q)  --- more efficiently :
        X <- tcrossprod(Q * rep(d[p], each=nrow(Q)), Q)
        if(doDykstra)
            ## update Dykstra's correction D_S = \Delta S_k
            D_S <- X - R
        ## project onto symmetric and possibly 'given diag' matrices:
        if(doSym)
            X <- (X + t(X))/2
	if(corr)
	    diag(X) <- 1
	else if(keepDiag)
	    diag(X) <- diagX0

        conv <- norm(Y-X, conv.norm.type) / norm(Y, conv.norm.type)
        iter <- iter + 1L
	if (trace)
	    cat(sprintf("iter %3d : #{p}=%d, ||Y-X|| / ||Y||= %11g\n",
			iter, sum(p), conv))
        converged <- (conv <= conv.tol)
    }
    if(!converged)
	warning(gettextf("'nearPD()' did not converge in %d iterations",
			 iter), domain = NA)
    ## force symmetry is *NEVER* needed, we have symmetric X here!
    ## X <- (X + t(X))/2
    if(do2eigen || only.values) { ## begin from posdefify(sfsmisc)
        e <- eigen(X, symmetric = TRUE)
        d <- e$values
        Eps <- posd.tol * abs(d[1])
        if (d[n] < Eps) {
            d[d < Eps] <- Eps
            if(!only.values) {
                Q <- e$vectors
                o.diag <- diag(X)
                X <- Q %*% (d * t(Q))
                D <- sqrt(pmax(Eps, o.diag)/diag(X))
                X[] <- D * X * rep(D, each = n)
            }
        }
        if(only.values) return(d)
        ## unneeded(?!): X <- (X + t(X))/2
	if(corr)
	    diag(X) <- 1
	else if(keepDiag)
	    diag(X) <- diagX0
    } ## end from posdefify(sfsmisc)
    dimnames(X) <- dimnames(x)
    X
}