[Numpy-discussion] linalg.eigh orders eigenvalues/eigenvectors differently than linalg.eig

[Zachary Pincus]

Hello all,

It seems that the 'eigh' routine from numpy.linalg does not follow  
the same convention as numpy.linalg.eig in terms of the order of the  
returned eigenvalues. (And thus eigenvectors as well...)

Specifically, eig returns eigenvalues in order from largest to  
smallest, while eigh returns them from smallest to largest.

Example:
 >>> a = numpy.array([[21, 28, 35],[28, 38, 48],[35, 48, 61]])
 >>> numpy.linalg.eigh(a)
(array([ -1.02825542e-14,   7.04131679e-01,   1.19295868e+02]),
array([[ 0.40824829, -0.81314396, -0.41488581],
        [-0.81649658, -0.12200588, -0.56431188],
        [ 0.40824829,  0.56913221, -0.71373795]]))

 >>> numpy.linalg.eig(a)
(array([  1.19295868e+02,   7.04131679e-01,   4.62814557e-15]),
array([[-0.41488581, -0.81314396,  0.40824829],
        [-0.56431188, -0.12200588, -0.81649658],
        [-0.71373795,  0.56913221,  0.40824829]]))

Is this a bug? If it is, though, fixing it now might break code that  
depends on this 'wrong' order. (This is also present in  
scipy.linalg.) If not a bug, or not-fixable-now, then at least some  
documentation as to the convention regarding ordering of eigenvalues  
is probably worthwhile...

Any thoughts?

Zach