Lapack integration still buggy for complex eigenvalues

[geoeo]

In the notes of nalgebra v. 31 and lapack v.22 it states improved behavior when dealing with the computation of eigenvalue problem.
While I can confirm this for nalgebra, the lapack variant still crashes.

This works: action_matrix.complex_eigenvalues()
This crashes: nalgebra_lapack::Eigen::complex_eigenvalues(action_matrix)

The lapack integration works since I use it use compute SVD etc.

The error is

 ** On entry to DGEEV  parameter number  1 had an illegal value
The application panicked (crashed).
Message:  Lapack error.
Location: /home/marc/.cargo/registry/src/github.com-1ecc6299db9ec823/nalgebra-lapack-0.22.0/src/eigen.rs:272

Tested on Ubuntu 20.04 (WSL)

[geoeo]

The parameters passed in the unsafe block are invalid.
Looking at the source once call is e.g.

        let lwork = T::xgeev_work_size(
            b'T',
            b'T',
            n as i32,
            m.as_mut_slice(),
            lda,
            wr.as_mut_slice(),
            wi.as_mut_slice(),
            &mut placeholder1,
            n as i32,
            &mut placeholder2,
            n as i32,
            &mut info,
        );

        lapack_panic!(info);

        let mut work = vec![T::zero(); lwork as usize];

        T::xgeev(
            b'T',
            b'T',
            n as i32,
            m.as_mut_slice(),
            lda,
            wr.as_mut_slice(),
            wi.as_mut_slice(),
            &mut placeholder1,
            1 as i32,
            &mut placeholder2,
            1 as i32,
            &mut work,
            lwork,
            &mut info,
        );
        lapack_panic!(info); 

According to the docs http://www.netlib.org/lapack/explore-html/d9/d8e/group__double_g_eeigen_ga66e19253344358f5dee1e60502b9e96f.html the only valid chars are 'N' or 'V'.
When I change it to e.g. 'V' I get

 ** On entry to DGEEV  parameter number  9 had an illegal value
The application panicked (crashed).
Message:  Lapack error.
Location: /home/marc/Rust/nalgebra/nalgebra-lapack/src/eigen.rs:292

A different error in the second call! Progress!

[geoeo]

It seem all the work is already done expect the complex part is discarded in the normal eigenvalue() call.
I changed the complex eigenvalue method signature to

    pub fn complex_eigenvalues(mut m: OMatrix<T, D, D>, left_eigenvectors: bool, eigenvectors: bool) 
        -> (OVector<Complex<T>, D>,  Option<OMatrix<Complex<T>, D, D>>,  Option<OMatrix<Complex<T>, D, D>>)

But apparently the check macro doesnt like that

macro_rules! lapack_check(
    ($info: expr) => (
        // TODO: return a richer error.
        if $info != 0 {
            return None;
        }
        // if $info < 0 {
        //     return Err(Error::from(ErrorKind::LapackIllegalArgument(-$info)));
        // } else if $info > 0 {
        //     return Err(Error::from(ErrorKind::LapackFailure($info)));
        // }
    );
);

Any suggestions @Andlon ?

[geoeo]

The accuracy of this method does not seem to be very high when compared to matlab/octave This is not really true.

[Andlon]

@geoeo: did you mean to close this? It looks like you've discovered an important deficiency in nalgebra-lapack here.

I'm otherwise unfortunately not familiar with the codebase of nalgebra-lapack and I'm sorry to say that I don't have the bandwidth to dig into it at the moment. Hopefully someone else is able to step up, however.

[geoeo]

@Andlon I made a PR. maybe its better to discuss this there. #1106

[Andlon]

I've reopened this because the linked PR (#1106) does not directly address this issue.