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Re: st: Problem computing eigenvalues, STATA vs. MATA


From   Austin Nichols <austinnichols@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Problem computing eigenvalues, STATA vs. MATA
Date   Sun, 9 Jan 2011 10:42:14 -0500

Zachary Neal <zpneal@gmail.com>:
You are confusing vectors and values there, and not sorting by values
after computing the eigensystem, but note that the only real
difference is that a couple of vectors are negated (any scalar
multiple of an eigenvector is also an eigenvector and the negation has
the same length so they are essentially equivalent) and Mata is using
quad precision to do the computations.

matrix define A = 0,1,1,0,0 \ 1,0,0,1,0 \ 1,0,0,0,1 \ 0,1,0,0,0 \ 0,0,1,0,0
matrix symeigen vectors1 values1 = A
matrix list values1
matrix list vectors1
mata
values2 = 0
vectors2 = 0
symeigensystem(st_matrix("A"),vectors2,values2)
v2=sort((values2\vectors2)',1)'
v2[1,.]
v2[2..6,.]
end

On Sun, Jan 9, 2011 at 8:08 AM, Zachary Neal <zpneal@gmail.com> wrote:
> I am trying to obtain the eigenvalues of a symmetric matrix.  However,
> I get different results depending on whether I use STATA or MATA.  For
> example:
>
> matrix define A = 0,1,1,0,0 \ 1,0,0,1,0 \ 1,0,0,0,1 \ 0,1,0,0,0 \ 0,0,1,0,0
> matrix symeigen eigenvalues1 eigenvectors1 = A
> matrix list eigenvalues1
>
> mata: A = 0,1,1,0,0 \ 1,0,0,1,0 \ 1,0,0,0,1 \ 0,1,0,0,0 \ 0,0,1,0,0
> mata: eigenvalues2 = 0
> mata: eigenvectors2 = 0
> mata: symeigensystem(A,eigenvalues2,eigenvectors2)
> mata: eigenvalues2
>
> In this case, eigenvalues1 does not equal eigenvalues2.  I believe the
> results yielded by STATA (i.e. eigenvalues1) are what I'm looking for.
>
> Why do these two sets of commands yield different results?  What
> commands are necessary in MATA to yield the same eigenvalues that are
> given by STATA?
>
> Thank you
> Zachary Neal

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