[R] Numerical stability of eigenvalue and hessian matrix in R

[Thierry Onkelinx]

Have a look at FAQ 7.31

ir. Thierry Onkelinx
Instituut voor natuur- en bosonderzoek / Research Institute for Nature and
Forest
team Biometrie & Kwaliteitszorg / team Biometrics & Quality Assurance
Kliniekstraat 25
1070 Anderlecht
Belgium

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than asking him to perform a post-mortem examination: he may be able to say
what the experiment died of. ~ Sir Ronald Aylmer Fisher
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~ John Tukey

2015-02-18 17:44 GMT+01:00 C W <tmrsg11 op gmail.com>:

> Hi Ben and JS,
>
> Thanks for the reply.
>
> I tried using: hessian(func = h_x, x, method = "complex"), it gives zero,
> that's good.
>
> # R code
>
> > hess.h <- hessian(func = h_x, x, method = "complex")
>
> > mat <- h_x(x)*hess.h - grad(h_x, x) %o% grad(h_x, x)
>
> > mat
>
>         [,1]    [,2]     [,3]    [,4]
>
> [1,] 2060602       0        0       0
>
> [2,]       0 2060602        0       0
>
> [3,]       0       0 -4039596 -816080
>
> [4,]       0       0  -816080 4039596
>
>
> But later I do,
>
> > eigen(mat)
>
> $values
>
> [1] -4121204  4121204  2060602  2060602
>
> $vectors
>
>             [,1]        [,2] [,3] [,4]
>
> [1,]  0.00000000  0.00000000    1    0
>
> [2,]  0.00000000  0.00000000    0    1
>
> [3,] -0.99503719  0.09950372    0    0
>
> [4,] -0.09950372 -0.99503719    0    0
>
>
> And here is the problem,
>
> > eigen(mat)$values[2] == 4121204
>
> [1] FALSE
>
> > eigen(mat)$values[2] - 4121204
>
> [1] -5.494803e-08
>
> Why doesn't the second value equal to 412104?  How do I overcome that?
>
> Thanks,
>
> Mike
>
> On Wed, Feb 18, 2015 at 9:13 AM, JS Huang <js.huang op protective.com> wrote:
>
> > Hi,
> >
> >   Since all entries in your hessian matrix and grad vector are integers,
> I
> > suggest you execute the following for mat assignment.
> >
> > > mat <- round(h_x(x),digits=0)*round(hess.h,digits=0) - round(grad(h_x,
> > > x),digits=0) %o% round(grad(h_x, x),digits=0)
> > > mat
> >          [,1]     [,2]     [,3]     [,4]
> > [1,]        0        0        0 -4080400
> > [2,]        0  7920000        0 -1600000
> > [3,]        0        0 12160400        0
> > [4,] -4080400 -1600000        0 -7920000
> >
> >
> >
> > --
> > View this message in context:
> >
> http://r.789695.n4.nabble.com/Numerical-stability-of-eigenvalue-and-hessian-matrix-in-R-tp4703443p4703456.html
> > Sent from the R help mailing list archive at Nabble.com.
> >
> > ______________________________________________
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>
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