The built-in PDF interpolator

MadSpace carries its own interpolator for parton distributions in the LHAPDF grid format, so it does not need the LHAPDF library at runtime. This example reads a grid file directly and evaluates it at a few points, using NNPDF40_lo_as_01180, the default PDF set MadGraph7 uses.

Locating the grid file

lhapdf is only used here to find where a PDF set is installed. The interpolation itself, below, is done entirely by MadSpace:

import os
import numpy as np
import lhapdf
import madspace as ms

PDF_SET = "NNPDF40_lo_as_01180"
pdf_dir = os.path.join(lhapdf.paths()[0], PDF_SET)

Loading the grid

PdfGrid reads the set’s .dat member file. Its initialize_globals method uploads the grid to a Context, which every compute-graph function that reads it needs done once beforehand:

ctx = ms.default_context()
grid = ms.PdfGrid(os.path.join(pdf_dir, f"{PDF_SET}_0000.dat"))
grid.initialize_globals(ctx)

Evaluating the PDF

PartonDensity interpolates the grid at a batch of (x, Q) points, for the requested flavours, returning \(x f(x, Q)\):

pids = [-5, -4, -3, -2, -1, 21, 1, 2, 3, 4, 5]
pdf = ms.PartonDensity(grid, pids)

x = np.array([0.01, 0.1, 0.5])
q = np.array([100.0, 100.0, 100.0])
xfx = pdf(x, q)
gluon_index = pids.index(21)
print("x f_g(x, Q=100 GeV):", xfx[:, gluon_index])

The gluon density falls steeply towards larger \(x\):

x f_g(x, Q=100 GeV): [7.92869630e+00 7.67957430e-01 4.62209124e-03]

The running coupling

AlphaSGrid and RunningCoupling are the same pattern, for \(\alpha_s\):

alphas_grid = ms.AlphaSGrid(os.path.join(pdf_dir, f"{PDF_SET}.info"))
alphas_grid.initialize_globals(ctx)
alpha_s = ms.RunningCoupling(alphas_grid)
print(f"alpha_s(M_Z): {alpha_s(np.array([91.188]))[0]:.5f}")

alpha_s(M_Z): 0.11800

This matches the set’s name: NNPDF40_lo_as_01180 is fit with \(\alpha_s(M_Z) = 0.118\).