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simonsobs / fgspectra

Foreground SED and power spectrum library for building cross frequency power spectrum models
BSD 3-Clause "New" or "Revised" License
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General cross spectrum function #15

Closed mabitbol closed 5 years ago

mabitbol commented 5 years ago

We'd like to have a function that takes the SED of X and Y and produces an SED of (X1Y2 + X2Y1) for the CorrelatedFactorizedCrossSpectrum class. But we need to be careful that things aren't going to be double counted (e.g. is there an issue when nu1=nu2?).

mabitbol commented 5 years ago

We don't want to have to write a cross spectrum SED for each potential correlated foreground signal that is factorizable is what I'm trying to get at. Instead we want to have a function that will do CrossSED(X,Y) for you. (I am thinking specifically about the frequency.tSZxCIB function in add_models_back_in branch. It's fine for now though glad it is working!)

dpole commented 5 years ago

I'm not clear about why you need that. FactorizedCorrelatedComponent is already supposed to compute it automatically. As said in another issue, we probably need more information about how this class works and what exactly the output contains.

mabitbol commented 5 years ago

I was thinking that we don't want to write a frequency.XxY function for every possible combination of correlated SEDs (e.g. all the potential galactic signals and any other extra-galactic correlations). If there not so many of these then it is ok to hand write them for now. Or maybe I am not understanding the usage of FactorizedCorrelatedComponent?

dpole commented 5 years ago

Ok, I propose that I push a commit containing the correlated CIB/tSZ, I open a PR and we discuss it there more concretely there (or in a call?)

mabitbol commented 5 years ago

Sounds good.

On 18 Apr 2019, at 17:24, Davide Poletti notifications@github.com<mailto:notifications@github.com> wrote:

Ok, I propose that I push a commit containing the correlated CIB/tSZ, I open a PR and we discuss it there more concretely there (or in a call?)

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dpole commented 5 years ago

19 addresses this point and (too many) others.

Reporting here a relevant offline discussion, while we create better documentation

image (Eq 12 only accounts for the correlated power)

let’s say, in a matrix A whose first column is SZ and the second is CIB A C A^t is the result of CorrelatedFactorizedCrossSpectrum where C is the component-component covariance matrix if C is a 2x2 matrix made of only ones you get A C A^t = f f^t + mu mu^t + f mu^t + mu f^t The last two terms are your Eq 12