[R] Derivative of expm function

Martin Maechler maechler at stat.math.ethz.ch
Thu Apr 24 11:01:00 CEST 2014

>>>>> Wagner Bonat <wbonat at gmail.com>
>>>>>     on Wed, 23 Apr 2014 12:12:17 +0200 writes:

    > Hi all !
    > I am look for some efficient method to compute the derivative of
    > exponential matrix function in R. For example, I have a simple matrix like

    > log.Sigma  <- matrix(c(par1, rho, rho, par2),2,2)

    > require(Matrix)
    > Sigma <- expm(log.Sigma)

    > I want some method to compute the derivatives of Sigma in relation the
    > parameters par1, par2 and rho. Some idea ?

The  'expm' package has slightly newer / more reliable
algorithms for the matrix exponential.

It also contains an  expmFrechet()  function
which computes the Frechet derivative of the matrix exponential.

I'm pretty confident -- but did not start thinking more deeply --
that this should provide the necessary parts to get
partial derivatives like yours as well.

Martin Maechler, ETH Zurich

    > Wagner Hugo Bonat
    > LEG - Laboratório de Estatística e Geoinformação
    > UFPR - Universidade Federal do Paraná

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