[R] positive semi-definite matrix

Martin Maechler maechler at stat.math.ethz.ch
Fri Jul 21 17:00:41 CEST 2006

>>>>> "Duncan" == Duncan Murdoch <murdoch at stats.uwo.ca>
>>>>>     on Fri, 21 Jul 2006 09:44:42 -0400 writes:

    Duncan> On 7/21/2006 8:59 AM, roger bos wrote:
    >> I have a covariance matrix that is not positive semi-definite matrix and I
    >> need it to be via some sort of adjustment.  Is there any R routine or
    >> package to help me do this?

    Duncan> I think you need to be more specific about what have and what you want, 
    Duncan> but if the matrix is symmetric and nearly positive semi-definite (but 
    Duncan> not exactly because of rounding error), you might try something like

    Duncan> fixit <- function(A) {
    Duncan> eig <- eigen(A, symmetric = TRUE)
    Duncan> eig$values <- pmax(0, eig$values)
    Duncan> return(eig$vectors %*% diag(eig$values) %*% t(eig$vectors))
    Duncan> }

    Duncan> Rounding error means this is not guaranteed to be positive 
    Duncan> semi-definite, but it will be very close.

A slightly more general and stable version of the above
is available via  sfsmisc::posdefify(.) :


Martin Maechler, ETH Zurich

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