Real Frequency Flat Density of states has invalid spectral function

[chuffa]

Hello,

I am using the newest TRIQS version on branch unstable 3.0.0.

I am trying to calculate the spectral function of the Flat hyrbdization and by chance included the omega-value of the step in my omega grid. Then one cant use the propper definition of the spectral function as .
I understand that this is hard to deal with as the real-part of the flat DOS indeed diverges, but I would argue that having a huge number as real part (even if it is wrong) is better than having -inf there. And in any case, the spectral function is well defined and should be accessible also using the general formulae provided above.

Even if this doesnt get fixed I think the bug report is good to have for future reference.

import numpy as np
from triqs.gf import *

inds = list(range(2))
d = GfReFreq(indices = inds, window = (-1.1, 0.9), n_points =  21, name = "up")
for i in inds:
    d[i,i] << Flat(half_bandwidth = 1.)

x = [ w.value for w in d.mesh ]    

spec = 1j/(2*np.pi)*( d- d.conjugate().transpose())
print(x[1])
print(d.data[1,:,:])
print(spec.data[1,:,:])

with the output:

-1.0
[[-inf+0.j   0.+0.j]
 [  0.+0.j -inf+0.j]]
[[nan+nanj  0. +0.j]
 [ 0. +0.j nan+nanj]]