Overview¶

Installing a PDF set
Instantiating a PDF
PDF interpolation
Strong coupling interpolation

Installing a PDF set ¶

PDF sets can be installed in two ways

downloading directly the PDF sets, from instance from LHAPDF PDF sets page or NNPDF

exploiting the lhapdf scripts, through the following commands:

lhapdf list
lhapdf install <pdf set>

which downloads and install the sets directly to lhapdf-config --datadir.

Instantiating a PDF ¶

mkPDF wrapper¶

PDFs can be instantiated in a similar manner to LHAPDF by calling the provided mkPDF and mkPDFs functions.

If LHAPDF and the pdfset are installed in the system it is enough to call:

from pdfflow import mkPDF
pdf = mkPDF(f"{pdfset}/0")

And pdfflow will try to obtain the PDF directory from LHAPDF. If, instead, we have manually downloaded the PDF, we need to specify the folder in which the PDF folder can be found, for instance:

from pdfflow import mkPDF
pdf = mkPDF(f"{pdfset}/0", dirname="/usr/share/lhapdf/LHAPDF")

To obtain the central member (0) of the pdfset. It is often necessary to require several members of a set, for instance to compute pdf error. This can be achieved with the mkPDFs function, for instance, to obtain members (0,1,2) we can do:

from pdfflow import mkPDFs
pdf = mkPDFs(pdfset, [0, 1, 2])

Note that both mkPDF and mkPDFs accept the keyword argument dirname.

PDF class¶

The aforementioned functions are all wrappers around the low-level PDF class and provide an instance to the class. The class can also be instantiated directly with:

from pdfflow.pflow import PDF
pdf = PDF(dirname, pdfset, [0]) # obtain a PDF instance for member 0
pdf = PDF(dirname, pdfset, [2, 5]) # obtain a PDF instance for members 2 and 5

Note that in order to instantiate a PDF class it is always necessary to provide the source directory of the PDF sets.

PDF interpolation ¶

The PDF interpolation can be worked out calling the py_xfxQ2 method with python or TensorFlow objects as arguments:

Python interface¶

When using python arguments as the input we provide the py_xfxQ2. This function deals with the conversion of the input into TensorFlow variables.

from pdfflow import mkPDFs

pdf = mkPDFs(pdfset, [0,1,2])
x = [10**i for i in range(-6,-1)]
q2 = [10**(2*i) for i in range(1,6)]
pid = [-1,21,1]

pdf.py_xfxQ2(pid, x, q2)

TensorFlow interface¶

Instead, if the arguments are already tensorflow objects, it is possible to call lower level tf.functions such as xfxQ2:

from pdfflow import mkPDFs, flaot_me, int_me

pdf = mkPDFs(pdfset, [0,1,2])
x = float_me([10**i for i in range(-6,-1)])
q2 = float_me([10**(2*i) for i in range(1,6)])
pid = int_me([-1,21,1])

pdf.xfxQ2(pid, x, q2)

Note

The float_me and int_me functions are wrappers around tf.cast which we provide with the aim of ensuring that integers are cast to 32-bit integers and float to 64-bit floats.

If arguments had been tf.Tensor objects, the preferred way to call the interpolation would have been via the xfxQ2 function. To go through the computation of all the pids in the flavor scheme, use xfxQ2_allpid or the py_xfxQ2_allpid version instead.

Strong coupling interpolation ¶

The strong coupling interpolation requires calling its own methods of the PDF object:

from pdfflow import mkPDFs, float_me

pdf = mkPDFs(pdfset, [0,1,2])
pdf.alphas_trace()

q2 = [10**(2*i) for i in range(1,6)]
pdf.py_alphasQ2(q2)
pdf.alphasQ2(float_me(q2))

Akin to the PDF interpolation discussed above, we provide the user with py_alphasQ2 for the Python interface and alphasQ2 for TensorFlow for the strong coupling interpolation.

In order to mimic the LHAPDF set of functions, we implement also the alphasQ and py_alphasQ PDF methods, by which the user is relieved of squaring the query array elements manually.