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Diagonalization with complex eigenvalues fails

Diagonalization using pyobs.linalg.eigLR fails when the eigenvalues/eigenvectors are complex. For example

mat = np.array([[0.0, -1], [1, 0.0]]) # eigenvalues are +- i
obs = pyobs.observable()
obs.create_from_cov('Ens', mat.flatten(), np.zeros(len(mat.flatten())))
obs = pyobs.reshape(obs, mat.shape)
eigv, legiv, reigv = pyobs.linalg.eigLR(obs)

fails with the error

UFuncTypeError                            Traceback (most recent call last)
Cell In[41], line 1
----> 1 eigv, legiv, reigv = pyobs.linalg.eigLR(obs) 
      2 print(eigv)

File ~/pyenv/lib/python3.11/site-packages/pyobs/tensor/linalg.py:157, in eigLR(x)
    154                 gv[:, n] += tmp[m, n] / (l[n] - l[m]) * w[:, m]
    155     return gv
--> 157 gv = pyobs.gradient(gradv, x.mean)
    159 # d w_n = sum_{m \neq n} (v_m, dA^T w_n) / (l_n - l_m) v_m
    160 def gradw(y):

File ~/pyenv/lib/python3.11/site-packages/pyobs/core/gradient.py:36, in gradient.__init__(self, g, x0, gtype)
     33     self.grad = g
     34     return
---> 36 self.Na = numpy.size(g(x0))
     37 self.Ni = numpy.size(x0)
     38 self.gtype = gtype

File ~/pyenv/lib/python3.11/site-packages/pyobs/tensor/linalg.py:154, in eigLR.<locals>.gradv(y)
    152     for m in range(x.shape[1]):
    153         if n != m:
--> 154             gv[:, n] += tmp[m, n] / (l[n] - l[m]) * w[:, m]
    155 return gv

UFuncTypeError: Cannot cast ufunc 'add' output from dtype('complex128') to dtype('float64') with casting rule 'same_kind'

This can be fixed by e.g. defining gv = numpy.zeros(x.shape, dtype=numpy.complex128) instead, but in the subsequent calls to pyobs.gradient arrays of floats are explicitly used in the __init__ call.

How to work with generic matrix observables, which are bound to have complex eigenvalues?

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