[Numpy-discussion] finding eigenvectors etc
Warren Focke
focke@slac.stanford....
Wed Feb 20 01:24:01 CST 2008
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@gmail.com <devnew@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
>
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