[Numpy-discussion] finding eigenvectors etc

[Warren Focke]

Yes.

Your first eigenvalue is effectively 0, the values you see are just noise. 
Different implementations produce different noise.

As for the signs ot the eigenvector components, which direction is + or - X is 
arbitrary.  Different implementations follow different conventions as to which 
is which.  Sometimes it's just an accident.

Nothing-to-see-here-move-along-ly,
w

On Wed, 20 Feb 2008, Matthieu Brucher wrote:

> Hi,
>
> The results are OK, they are very close. Your matrix is almost singular, is
> badly conditionned, ... But the results are very close is you check them in
> a relative way. 3.84433376e-03 or -6.835301757686207E-4 is the same compared
> to 2.76980401e+13
>
> Matthieu
>
> 2008/2/20, devnew at gmail.com <devnew at gmail.com>:
>>
>> hi
>> i was calculating eigenvalues and eigenvectors for a covariancematrix
>> using numpy
>>
>> adjfaces=matrix(adjarr)
>> faces_trans=adjfaces.transpose()
>> covarmat=adjfaces*faces_trans
>> evalues,evect=eigh(covarmat)
>>
>> for a sample covarmat like
>> [[  1.69365981e+13 , -5.44960784e+12,  -9.00346400e+12 , -2.48352625e
>> +12]
>> [ -5.44960784e+12,   5.08860660e+12,  -8.67539205e+11  , 1.22854045e
>> +12]
>> [ -9.00346400e+12,  -8.67539205e+11,   1.78184943e+13  ,-7.94749110e
>> +12]
>> [ -2.48352625e+12 ,  1.22854045e+12,  -7.94749110e+12 ,  9.20247690e
>> +12]]
>>
>> i get these
>> evalues
>> [  3.84433376e-03,  4.17099934e+12 , 1.71771364e+13 ,  2.76980401e+13]
>>
>> evect
>> [[ 0.5        -0.04330262  0.60041892 -0.62259297]
>> [ 0.5        -0.78034307 -0.35933516  0.10928372]
>> [ 0.5         0.25371931  0.3700265   0.74074753]
>> [ 0.5         0.56992638 -0.61111026 -0.22743827]]
>>
>> what bothers me is that for the same covarmat i get a different set of
>> eigenvectors and eigenvalues when i use java library Jama's methods
>> Matrix faceM = new Matrix(faces, nrfaces,length);
>> Matrix faceM_transpose = faceM.transpose();
>> Matrix covarM = faceM.times(faceM_transpose);
>> EigenvalueDecomposition E = covarM.eig();
>> double[] eigValue = diag(E.getD().getArray());
>> double[][] eigVector = E.getV().getArray();
>>
>> here the eigValue=
>> [-6.835301757686207E-4, 4.170999335736721E12, 1.7177136443134865E13,
>> 2.7698040117669414E13]
>>
>> and eigVector
>> [
>> [0.5, -0.04330262221379265, 0.6004189175979487, 0.6225929700052174],
>> [0.5, -0.7803430730840767, -0.3593351608695496, -0.10928371540423852],
>> [0.49999999999999994, 0.2537193127299541, 0.370026504572483,
>> -0.7407475253159538],
>> [0.49999999999999994, 0.5699263825679145, -0.6111102613008821,
>> 0.22743827071497524]
>> ]
>>
>> I am quite confused bythis difference in results ..the first element
>> in eigValue is different and also the signs in last column of
>> eigVectors are diff..can someone tell me why this happens?
>> thanks
>> dn
>>
>>
>>
>>
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>>
>
>
>
> -- 
> French PhD student
> Website : http://matthieu-brucher.developpez.com/
> Blogs : http://matt.eifelle.com and http://blog.developpez.com/?blog=92
> LinkedIn : http://www.linkedin.com/in/matthieubrucher
>