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


From   Zachary Neal <zpneal@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: Problem computing eigenvalues, STATA vs. MATA
Date   Sun, 9 Jan 2011 17:30:09 -0500

This doesn't seem to help.  Running the code suggested below by Austin
Nichols, the values in the first eigenvector using matrix symeigen
are:

.5773502692
.5
.5
.2886751346
.2886751346

However, the values in the first eigenvector using
symeigensystem(st_matrix("A"),vectors2,values2) are:

.5773502692
-.5
-.5
.2886751346
.2886751346

I'm not clear why the 2nd and 3rd values here are not positive, as
they are in the results produced by matrix symeigen.

Best
Zachary

On Sun, Jan 9, 2011 at 10:42 AM, Austin Nichols <austinnichols@gmail.com> wrote:
> 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
>
> *
> *   For searches and help try:
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>



-- 
Zachary Neal, PhD
Department of Sociology
Michigan State University
zpneal@msu.edu
http://www.msu.edu/~zpneal

*
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