LAPACK fails calculating eigenvectors

Question

I wrote some code to solve the general eigenvalue problem and now I am comparing my results against LAPACK's DSPGVX function. I just worked with this example.

So I obtained the 4 auto vectors

{
 {-0.0319133, -0.265466, -0.713483,  0.64765},
 {-0.425628,  -0.520961, -0.714215,  0.193227},
 { 0.32702,    0.565845, -0.37129,  -0.659561},
 {-0.682699,  -0.056645,  0.0771025, 0.724409}
}

and auto values

{-2.22545, 1.12704, -0.454756, 0.100076}

both with my code and with Mathematica and results agree.

But in the previous link, auto vectors reported from LAPACK are completely different.

 Eigenvalues
    -0.4548  0.1001
 Selected eigenvectors
          1       2
 1   0.3080  0.4469
 2   0.5329  0.0371
 3  -0.3496 -0.0505
 4  -0.6211 -0.4743

Whom should I trust?

P.S. I also checked that my auto values/autovectors are correct since they yield A*x-lambda*B*x=0, while the values from LAPACK do not.

Answer 1

I don't know why you think that LAPACK is giving incorrect answers, they seem fine to me. Using the four figure decimals that you quote I get residuals (r = A*x - lambda*B*x) such that

norm(r1) = 1.5921e-04, norm(r2) = 6.0842e-05.

Since norm(A) = 1.2994 and norm(B) = 7.9874, these residuals seem very satisfactory.

The eigenvectors produced by DSPGVX are normalized so that

norm(x'*B*x) = 1.