topic I tried LAPACKE_dgeev. It in Intel® Integrated Performance Primitives

left and right eigenvector

steffenroeber — Fri, 21 Feb 2014 08:30:53 GMT

Hi,

I'M trying to use the ippmEigenValuesVectorsLeft_m_64f and ippmEigenValuesVectorsRight_m_64f functions.

I think there is a bug (or I missunderstand) the defintion:

A*z=λ*z for the right eigenvectors z,

z^H*A=λ*z^H for the left eigenvectors z,

My example:

A(2x2) = 2, -2, 1, 5

ippmEigenValuesVectorsLeft_m_64f gives λ1=3, λ2=4

and eigenvectors(2x2) = -0,89, 0.71, 0.44, -0.71

ippmEigenValuesVectorsRight_m_64f gives λ1=3, λ2=4

and eigenvectors(2x2) = -0,71, -0.44, -0.71, -0.89

The test of the definition fails. It seems that the result of ippmEigenValuesVectorsLeft_m_64f are the right eigenvectors. The result of ippmEigenValuesVectorsRight_m_64f I does not match do any defintion.

Example:

z1 = -0.89, 0.44

A*z1=-2.69, 1.34 and 3*z1=-2.69, 1.34 -> defintion of right eigenvectors but result of left eigenvectors

yes, at the first glance it

Gennady_F_Intel — Fri, 21 Feb 2014 14:07:32 GMT

yes, at the first glance it looks like a bug. I would recommend you to try mkl's implementation of EigenSolvers. MKL's implementation much more stable (I mean eignesolvers only in that case ) and optimize for medium and big problems.

I tried LAPACKE_dgeev. It

steffenroeber — Mon, 24 Feb 2014 08:44:10 GMT

I tried LAPACKE_dgeev. It works mostly. But for example.A(2,2) = 1,2, -2, 5. gives two (same) eigenvalues 3,3., but only one eigenvector. Is this the correct behaviour?

Hi Steffen.

Andrey_B_Intel — Mon, 24 Feb 2014 13:40:49 GMT

Hi Steffen.

I've checked your issue with matlab. You are absolutely right, there is error in IPP func.

>> A=[2 -2 ;1 5]

A =

2 -2
1 5

>> [V D] = eig(A)

V =

-0.8944 0.7071
0.4472 -0.7071

D =

3 0
0 4

>> [VL D] = eig(A')

VL =

-0.7071 -0.4472
-0.7071 -0.8944

D =

3 0
0 4

It looks like that IPP left and right vectors are just swapped. This issue wil be fixed in next release.