Integrate x-cut/k-cut cosmic shear

[pltaylor16]

We are trying to implement x-cut/k-cut cosmic shear (see e.g. https://arxiv.org/abs/2007.00675) as part of the desc-baryon-challenge. A public version of the code which computes the transformation matrix is available here: https://github.com/pltaylor16/x-cut .

[vitenti]

Hi @pltaylor16, do you need guidance on how to incorporate this transformation on C_ells produced by Firecrown? Or are you already creating a PR with this aim?

[pltaylor16]

Thanks for the reply @vitenti. Looking for a little guidance on the best way to go about doing this.
Ideally this could be merged into the main branch of Firecrown.

To give you a little more background, the transformation assumes a fiducial cosmology which is fixed throughout inference. The transformation is then applied to the theory vector, data vector and covariance in a consistent way. One then can choose a new set of angular scale cuts on the transformed data vectors.

[vitenti]

Hello @pltaylor16 great, I'll turn this issue into a discussion and once we have a good plan we move to an issue or PR.

[vitenti]

Hi @pltaylor16,

I have a few questions about this implementation:

• Is this modification intended for the predicted C^{XY}_ell?
• If so, which XY observables does it apply to?
• Does its applicability depend on any specific parameter?
• Could you clarify the role of the fiducial cosmology? In MCMC analyses, we typically explore both cosmological and analysis-specific parameter spaces. Does this code necessitate a fixed cosmology?

I suspect implementing this might involve adding a new systematic object to modify the TheoryVector computed by TwoPoint. However, clarifying these points will help determine the exact approach.

[pltaylor16]

That's almost exactly right. The length of the cut data vector will have a well defined length once the scale cuts are chosen in either ell or theta. The choice of ell and theta scale cuts will not match what we would have chosen if we did not make the transformation. We also do need to account for the covariance of the transformed shear Cells with the other Cells. For example if we say that under the transformation C_ell^{s0,s0} --> D_ell^{s0,s0} then Cov(C_ell^{s0,s0}, C_ell^{l1, l1}) --> Cov(D_ell^{s0,s0}, C_ell^{l1, l1}).

[vitenti]

OK, since it does not depend on parameters, I assume that the modification is constant during a statistical analysis. If that's the case, we can do the following, we write a function that updates the sacc object (all relevant parts of the covariance and the subvectos of the data vector) and create a systematic object that updates just the subvectors of the theory vector on each iteration. The update on the sacc object can be done by the user previously (and kept saved in a sacc file), or we can include a hook in the likelihood initialization so it can be applied once and before the start of the analysis (if it's not too slow).

About the ells (or theta). Currently they are described in the sacc object, for each bin of XY you have many data points (C^{XY}_ell, ell) for ell in a set I:

• after applying the transformation will the set I change?
• is there a restriction on the initial set I?
• what about window functions?

[pltaylor16]

-The set of l will not change in the analysis.
-There is no restriction in the initial set l, as long as the user is somehow able to specify what this is at the beginning.
-The window function remains unaltered.

[vitenti]

OK, great, I think we have the big picture. Are you available for a hands on meeting with the team so we can try to write a first draft implementation? We meet regularly Tuesdays and Thursdays at 17h GMT, next Tuesdays we are already full, are you available next Thursday? If these dates are not good to you, we can create a whenisgood to schedule a meeting.

[pltaylor16]

Fantastic. I am not available next week, but I am available the week after (Jan 22nd -26th). Thurs would be better, but Tuesday is also possible.

[vitenti]

Hello @pltaylor16. We have just completed a significant pull request where we implemented new dataclasses to represent the two-point statistics extracted from a SACC object. I propose the following approach for integrating your method:

1. After extracting all two-point data from the SACC file, the resulting dataclasses can be passed to a filtering code, likely incorporating your code (or calling as an external lib).
2. This filter will generate new versions of the data with your method applied. This can be saved or used directly.
3. Since the dataclasses also contain the indices relating their data points to the covariance matrix, the update can be applied there as well.

The only additional code required would be a Systematic object to apply the transformation to the theory vector at each step of the statistical analysis.

[pltaylor16]

@vitenti Great. This sounds like it will work well. What do you need from me at this stage?

[vitenti]

Each measured correlation is stored in a dataclass TwoPointCell:

class TwoPointCells:
    XY: TwoPointXY
    ells: npt.NDArray[np.int64]
    Cell: None | TwoPointMeasurement = None

class TwoPointXY:
    x: InferredGalaxyZDist
    y: InferredGalaxyZDist
    x_measurement: Measurement
    y_measurement: Measurement

class InferredGalaxyZDist:
    bin_name: str
    z: np.ndarray
    dndz: np.ndarray
    measurements: set[Measurement]

class TwoPointMeasurement:
    data: npt.NDArray[np.float64]
    indices: npt.NDArray[np.int64]
    covariance_name: str

Inside the attributes x and y you can find the n(z) of each tracer, and in x_measurement the measurement (for x-cut I suppose we want any pair containing a Galaxies.SHEAR_E). The indices contain the indices that relate each measurement at ell with an entry of the covariance matrix. Finally, the pair ells and data contain the measured multipoles and their values.

My idea is to write a filter class/function that will take a set of TwoPointCells and a covariance matrix and produce another set with the modifies ells and data for each TwoPointCells and a new covariance matrix.

My question is:

• Do these classes contain enough information so we can apply you procedure?

Once this is done we need to write a Systematic object to apply the appropriate transformation for the theory vector.

---

If all this makes sense, how should we compute the correct transformations? Is there an external library for that, or should we develop something ourselves in Firecrown?

[pltaylor16]

All you need to compute the transformation for x-cut is: the n(z) and you need to assume a fiducial cosmology to map z to chi. The transformation is then applied to the C_ell or correlation function. The covariance matrix also needs to be transformed.

In this repository: https://github.com/pltaylor16/x-cut in BNT.py there is a class to compute the transformation matrix. As you can see it is very straightforward to compute! Applying the transformation to the data vector and covariance will have to be done in firecrown. What do you need from me to do this? I can point you to the equations, or help write the code?

[vitenti]

We reworked the TwoPointMeasurement and finally got a final version. I'll try write the code for your transformation and open a PR so you can review it.

[pltaylor16]

Great thanks. Let me know if there are issues. One quirk is my code may have a division by zero error if you start at a redshift, z=0. I can't remember if I fixed this.