ValueError: need at least one array to concatenate

[Haoxiang-Lin]

Hi,

I got this error message whenever the values of Eemin and Eemax
of naima.models.Synchrotron is too close (encountered in some
extreme parameter choices in GRB study). An example code to
reproduce this error is as below:

from naima.models import ExponentialCutoffBrokenPowerLaw, Synchrotron
import astropy.units as u
from astropy.constants import c, m_e

mec2 = (m_e * c**2).to(u.MeV)
Eemin = (1e6 * mec2).to(u.eV)
Eebrk = (1.005e6 * mec2).to(u.eV)
Eemax = (1.01e6 * mec2).to(u.eV)

electrons = ExponentialCutoffBrokenPowerLaw(
    amplitude=1 * 1/u.eV,
    e_0=Eemin,
    e_break=Eebrk,
    alpha_1=2,
    alpha_2=3,
    e_cutoff=Eemax,
    beta=2,
)

SYN = Synchrotron(
    electrons,
    B=0.1 * u.G,
    Eemax=Eemax,
    Eemin=Eemin,
    nEed=100,
)

SYN.flux(1*u.keV, distance=0 * u.cm)

I believe it arises from the zero length of the Lorentz factor sequence
in the source code:

log10gmin = np.log10(self.Eemin / mec2).value
log10gmax = np.log10(self.Eemax / mec2).value
return np.logspace(
            log10gmin, log10gmax, int(self.nEed * (log10gmax - log10gmin))
        )

For example, if Eemax = 1.01*Eemin, and by default nEed = 100, then
self.nEed * (log10gmax - log10gmin) = 100*log10(1.01) = 0.432, and
int(0.432) = 0, which creates the error.

While increasing nEed solves the problem, I wonder if it is better to
avoid this by restricting the length of sequence to be at least 2, e.g.

log10gmin = np.log10(self.Eemin / mec2).value
log10gmax = np.log10(self.Eemax / mec2).value
return np.logspace(
            log10gmin, log10gmax, max(2, int(self.nEed * (log10gmax - log10gmin)))
        )