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What is coupling coefficients? #61
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Hi @YutoMinami I'm slightly confused by the notation you're using. Let's see if this clarifies things:
Does this make sense? |
Hi @damonge With such expression, I'd like to compute the covariance between power spectrum cl_A1A2 cl_A1A2.
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Hmmmh, that's surprising. Also, note that if you just want power spectra and covariances for two spin-2 fields, you don't really need to generate any spin-0 fields at all (e.g. you could just pass |
Yes. I checked again whether the same mask is passed to the different field and it is. Therefore I wondered what coefficients are intended to be calculated in the function.
Thanks. |
Hi @damonge I'm sorry I checked and re-run my program and found there is an incorrect explanation. This means even for the calculation of variance of cross correlation, the same field is needed as an input. I reproduced the small variance problem as the following: So, my question should be "How can I calculate correct variance from different realization?" |
Hi @YutoMinami I'm still suprised that the resulting covariance depends on the fields you pass to |
I'll close this for now, but feel free to reopen |
Hi @damonge |
What does the function "compute_coupling_coefficients" actually compute in astro-ph/0307515 and/or arXiv/1609.09730?
I have this question because the covariance and sample variance with 100 samples are different.
For the sample variance, I prepared 100 Gaussian fluctuated maps and calculated pseudo-C_\ell with two different maps, e.g. mapN x mapN+1, using NaMaster.
For the covariance with NaMaster, I followed the example in https://namaster.readthedocs.io/en/latest/sample_covariance.html.
The difference is that I prepared two fields,
f0_1,f2_1, f0_2, f2_2, because I wanted to calculate correlation between two different maps.
I modified "cw.compute_coupling_coefficients(f0, f0, f0, f0)" to "cw.compute_coupling_coefficients(f0_1 f0_2, f0_1, f0_2)".
And, "w22.compute_coupling_matrix(f2, f2, b)" to "w22.compute_coupling_matrix(f2_1, f2_2, b)".
These show difference from sample variance.
However, when I revert the calculation of coupling coefficients like "cw.compute_coupling_coefficients(f0_1 f0_2, f0_1, f0_2)" to "cw.compute_coupling_coefficients(f0, f0, f0, f0)", the covariance agreed to sample variance.
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