Sporadic HotRegion.RayError for certain parameter vectors about xpsi

[thjsal]

Looks like I was wrong and the sporadic error reported above seems to actually originate from X-PSI producing NaNs for high emission angles, for which the emission angle is very close to 90 degrees. For those situations are apparently checked if sin_alpha==1 , but that does not thus capture e.g. sin_alpha= 0.9999999999999989 , which is also problematically close to 1.0, and produces NaNs in the further calculation.
Here is the line causing the problem (giving NaN for the w_R parameter):

xpsi/xpsi/cellmesh/rays.pyx

Line 223 in 29ead0d

w_R = sqrt(1.0 - r_c_over_r_s * r_s_over_R)

This can be fixed either by modifying the sin_alpha check (to avoid also small deviations from sin_alpha=1) or by setting (after those lines):

if gsl_isnan(w_R):
            w_R = 0.0  

After doing this fix (the latter way), the calculation is not anymore sporadically terminated (or neglected if doing sampling). After this fix, the likelihood changes in my test case (for the first parameter vector reported above) from -37043.99135451222 to -37043.99135647802.

[thjsal]

If commenting the error handling raising this error in Likelihood.py, the code instead crashes and raises randomly this error
RayError: Fatal numerical problem during ray integration.
It seems to originate from GSL library functions used for integration in rays.pyx. There lines with status = gsl_integration_qag(...) can return some times Failed as their status and some times not, given the same input (but need to still re-check that). So it looks likely a problem with GSL to me.

[thjsal]

The randomness of the warning apparently comes from this line

xpsi/xpsi/cellmesh/rays.pyx

Line 401 in 29ead0d

rayParams[4*T] <= deflection[i,j - 1])):

where the termination condition depends on the deflection angle calculated for the previous grid point. And when having NaNs, that previous grid point has not been properly set but it includes some random values from the memory.