Feat/plateaux for t0 extraction

[jkuhl-uni]

Hi,
this is a pitch for an additional plot that can be generated during the extraction of the flowed energy density.
With a new kwarg, "plot_Ysl", the functions also produce a plot of the plateaus used to extract t0/w0, which (at the moment) looks as follows:

This is useful to check whether the plateau region the user gives by means of xmin in the function calls can indeed be justified by the data, which is of course crucial for a reliable extraction of t0. This is something that Patrick suggested to me during our analyses and I thought it might be worth sharing with others, as the implementation is a bit tedious when using the currently available pyerrors read routines.

Please let me know what you think. I am aware that the plot has limitations in terms of customizability, see particularly ll. 93,94, which hardcodes how many plateaus are shown. Altering this would also mean to alter the signature of _extract_flowed_energy_density which is why I refrained from it for the time being.

[s-kuberski]

Hi,

I think that this can be a useful feature, especially since the details of the computation are currently hidden inside of our functions to compute t0 and w0.

I agree that it seems to be difficult to pass on specified values of the flow time to show, when t0 is not yet known. Of course, the user could supply it, but this might also be a bit much. With the current version, a lot of work from the computation of t0 is repeated in your new function in order to be able to plot the data around the value of t0. Also, I guess that the data points in a close region around some fixed flow time are basically 100% correlated.

Would it be an option to just show the plateau for 5 values of the flow time that are equally spaced in the space of available flow times? This would then give details for all possible choices of flow observables, not only t0 with the standard choice of 0.3. In this case, it is possible that the data has to be shifted by some offset.

A bit orthogonal to this, I was thinking about Ysl in your new version of the code. In your implemementation, it is only needed if the plot is to be performed but contains a lot of data. I would suggest to only fill Ysl in this case. Otherwise, the memory overhead can be sizable in the case of long chains with multiple replica, even in the case where one does not want to plot.