Type conversion issue in generalized_eigenvalue_decomposition()

[ldelebec]

🐛 Bug

Function dsp.beamforming.generalized_eigenvalue_decomposition() returns complex eigen values whereas _generalized_eigenvalue_decomposition() returns real eigen values (along with complex eigen vectors) when passing complex tensor as input.

To Reproduce

import torch
from asteroid.dsp.beamforming import (
    generalized_eigenvalue_decomposition,
    compute_scm,
    _generalized_eigenvalue_decomposition,
)

shape = (2, 2, 3, 4)

a = torch.randn(shape, dtype=torch.complex64)
b = torch.randn(shape, dtype=torch.complex64)

scm_a = compute_scm(a).permute(0, 3, 1, 2)  # bmmf -> bfmm
scm_b = compute_scm(b).permute(0, 3, 1, 2)

e_values, e_vectors = generalized_eigenvalue_decomposition(scm_a, scm_b)

print("e_values type: ", e_values.dtype)
print("e_vectors type: ", e_vectors.dtype)

e_values, e_vectors = _generalized_eigenvalue_decomposition(scm_a, scm_b)

print("e_values type: ", e_values.dtype)
print("e_vectors type: ", e_vectors.dtype)

Outputs

e_values type:  torch.complex64
e_vectors type:  torch.complex64
e_values type:  torch.float32
e_vectors type:  torch.complex64

Expected behavior

generalized_eigenvalue_decomposition() should return real eigen values with dtype = torch.float32.

Solutions

1. Add another type mapping that handles complex to real type conversion:

        return {
            torch.complex32: torch.float16,
            torch.complex64: torch.float32,
            torch.complex128: torch.float64
        }

2. An other solution is to drop out conversion type for generalized_eigenvalue_decomposition().

[mpariente]

Thanks for the bug report.

How about replacing

    return e_val.to(input_dtype), e_vec.to(input_dtype)

with

    return e_val.to(input_dtype).real, e_vec.to(input_dtype)

with a comment about the realness of the eigenvalues?

Do you feel like to submit a PR with that?

[ldelebec]

Nice, this allows to preserve precision from complex to real.
Ok I will do a PR.

[mpariente]

Fixed in #519