Last component of `calc_mcm_spin0and2_pure` always seems to be (practically) zero

[mreineck]

When playing with the routine calc_mcm_spin0and2_pure I noticed something interesting: no matter which power spectra are fed into the function, the fifth output matrix always seems to contain extremely small values. This can be verified with the following script:

import numpy as np

from pspy.mcm_fortran.mcm_fortran import mcm_compute as mcm_fortran

lmax=100
mcm = np.zeros((5, lmax+1, lmax+1))
spec = np.random.normal(size=(4, 2*lmax+1))
mcm_fortran.calc_mcm_spin0and2_pure(spec[0], spec[1], spec[2], spec[3], mcm.T)
for i in range(5):
    print (np.max(np.abs(mcm[i,:,:])))

Is this due to a bug in the function, or is there actually some kind of symmetry in the Wigner 3j symbols which makes this component vanish by construction? If the latter, it might be good to simply skip its calculation, saving some CPU time and memory.

[zatkins2]

I'm afraid I don't really know much about how the "pure" matrices are expected to behave. I also don't think we have used these pure methods yet in PSpipe really (though, we may in the future, if/when we use PSpipe on SAT data). I agree I would be surprised if the matrix is basically 0.

Perhaps @damonge would know for sure if this sounds like a bug?