Add flag for the derivative of thePDF
Created by: scarlehoff
This PR adds the derivative flag to validphys which can be used to get derivatives of the xplotting_grids (so it will be used automatically by any PDF plotting routine).
Example: https://vp.nnpdf.science/Tj8jTeWhSki5ObB17nV1BQ==/#pdf-bands-2
Merge request reports
Activity
requested review from @enocera
Created by: scarlehoff
That was yet a different thing, right?
And again, not super clear, they want the derivative of the PDF so basically a plot of d(xf(x))/dx ? or xd(f(x))/dx or d(xf(x))/dlogx?
(that I will just do a simple plot using lhapdf though, unless it turns out to be super important)
Created by: ldd69
Hi Juan
What was in my mail is clear:
|df/dx|^2 as a function of x
You can add simply df/dx, so that the other quantities can easily be derived using the chain rule.
Cheers, L.
On 23 Sep 2022, at 12:23, Juan M. Cruz-Martinez @.***@.***>> wrote:
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That was yet a different thing, right?
And again, not super clear, they want the derivative of the PDF so basically a plot of d(xf(x))/dx ? or xd(f(x))/dx or d(xf(x))/dlogx?
(that I will just do a simple plot using lhapdf though, unless it turns out to be super important)
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Created by: ldd69
Hi Juan
The previous email is pasted below.
The thing I would like to see is the derivative of the quantity that multiplies the FK tables in our parametrisation.
So for DIS:
F_I = FK_{Ij} f_j
Where F_I is the observable. Can you remind me what our convention is?
In any case we know that: d\dx (xf(x)) = f(x) + x df/dx
Cheers, L.
Previous email:
Hello
What we need is
|df/dx|^2 as a function of x (plot in log scale in x would be better) for each PDF.
Cheers, L.
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Hi @ldd69https://github.com/ldd69, could you resend that email? I've recently changed e-mails and I cannot find it now so maybe it slipped between the cracks. Thanks.
In any case, when you say f do you mean f(x) or xf(x) (we are always plotting xf(x))?
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Created by: scarlehoff
I've done the derivative for
f_j = xf(x), the result is:(log scale in both x and y)
For representation purposes I've also done d/dlog(x) so that I could use a linear scale in y:
Not sure which is better. In any case, I'm a bit worried that the results are not very different between CT and NNPDF (below the gluon with a log scale as well for comparison)
I'll do it using vp so that people can audit the code to make sure I didn't made any mistakes. And to facilitate as well plotting the 1-sigma bands for NNPDF instead of raw replicas.
For completeness, the output of the arclength using an xgrid
with respect to using the normal one:
The arclength one I will remove (since as @RoyStegeman said above, it would be inconsistent) and I will add instead the possibility of plotting the derivative with vp as @ldd69 requested then we can play with it as we see fit.
Created by: RoyStegeman
The arclength one I will remove (since as @RoyStegeman said above, it would be inconsistent)
Not inconsistent per se I think; we're just not calculating the arclength of the PDFs themselves (according to its common definition), but rather of an object that combines the PDFs with a logarithmic scaling of
x. It is still an arclength-like feature of the PDF so perhaps it's useful(?)In particular the first plot is a bit spoiled by numerical issues, but could it be that the second derivative of the NNPDF replicas are pretty much flat, while that of the CT pdfs is not? On the other hand, after the bump between x=1e-5 and 1e-4, also the CT central value seems to have a rather constant second derivative.
Created by: scarlehoff
I've added a
derivative: boolflag which gets read byxplotting_gridso any derived (heh) quantity will receive actually the derivative of the PDF (for instance the PDF plots).Example report with the df / dlogx for NNPDF and CT with band plots and replica plots: https://vp.nnpdf.science/jM9wSap9RlyRDRkgbr4Ezg==/
I'm using
np.gradientwith the plotting x-grid of the PDF and letting vp deal with the rest. I've opted for d/dlog(x) since it worked best with vp (otherwise I would have to deal with the y-scale, maybe differently per-flavour).Things to-do: the y-axis label needs to depend not only on the PDF flavour but has to allow for some extra information. I'll see how to do that without too much hacking, but it is relatively minor point.
Created by: scarlehoff
Taking further derivatives is simply a question of changing the flag from a
boolto anint:* https://vp.nnpdf.science/hrCzYH0cRJG2N0mT16Xo4w== but let's first make sure that I didn't make any mistakes in the first one :P(the changes to vp are actually very minimal at this point so it should be easy on whoever wants to review it!)
*in this report I also removed the central value for ct from the replicas which is misleading, but this needs atm a bit of ugly patching
Created by: Zaharid
@enocera @scarlehoff how does np.gradient compare with the thing in here !1581 (merged)?
@enocera @scarlehoff how does np.gradient compare with the thing in here #1581 (comment)?
@Zaharid That's an interesting question - I guess that your suggestion would be: if np.gradient does the same thing as in !1581 (merged), why not using np.gradient also in #1581?
Created by: Zaharid
I think I'd prefer a separate provider for the derivative grid (and subsequent stuff). For one if you set
derivative: Trueall the labels in all the plots (minus the one being looked at here) become wrong. That smells like it would be handled better by separate code paths.We do something similar for the distances.