"""
mc2hessian.py
This module containts the functionality to compute reduced set using the `mc2hessian` algorithm
(See section 2.1 of of `1602.00005 <https://arxiv.org/pdf/1602.00005.pdf#subsection.2.1>`_).
"""
import logging
import numbers
import pathlib
import shutil
import numpy as np
from reportengine.checks import check, check_positive, make_argcheck
from validphys import lhaindex
from validphys.checks import check_pdf_is_montecarlo
from validphys.lhio import hessian_from_lincomb
from validphys.pdfgrids import xplotting_grid
log = logging.getLogger(__name__)
[docs]def gridname(pdf, Neig, mc2hname: (str, type(None)) = None):
"""If no custom `mc2hname' is specified, the name of the Hessian PDF is automatically generated."""
if mc2hname is None:
grid_name = f"{pdf.name}_hessian_{Neig}"
else:
grid_name = mc2hname
return grid_name
@make_argcheck
def _check_xminmax(xmin, xminlin, xmax):
check(0 < xmin < xminlin < xmax <= 1, "Expecting 0 < xmin < xminlin < xmax <= 1")
[docs]@_check_xminmax
@check_positive("nplog")
@check_positive("nplin")
def mc2hessian_xgrid(
xmin: float = 1e-5,
xminlin: float = 1e-1,
xmax: numbers.Real = 1,
nplog: int = 50,
nplin: int = 50,
):
"""Provides the points in x to sample the PDF. `logspace` and `linspace`
will be called with the respsctive parameters.
Generates a grid with ``nplog`` logarithmically spaced points between
``xmin`` and ``xminlin`` followed by ``nplin`` linearly spaced points
between ``xminlin`` and ``xmax``
"""
return np.append(
np.geomspace(xmin, xminlin, num=nplog, endpoint=False),
np.linspace(xminlin, xmax, num=nplin, endpoint=False),
)
[docs]@check_pdf_is_montecarlo
def mc2hessian(
pdf, Q, Neig: int, mc2hessian_xgrid, output_path, gridname, installgrid: bool = False
):
"""Produces a Hessian PDF by transfroming a Monte Carlo PDF set.
Parameters
-----------
pdf : validphys.core.PDF
An existng validphys PDF object which will be converted into a Hessian PDF set
Q : float
Energy scale at which the Monte Carlo PDF is sampled
Neig : int
Number of basis eigenvectors in the Hessian PDF set
mc2hessian_xgrid : numpy.ndarray
The points in x at which to sample the Monte Carlo PDF set
output path : pathlib.PosixPath
The validphys output path where the PDF will be written
gridname : str
Name of the Hessian PDF set
installgrid : bool, optional, default=``False``
Whether to copyt the Hessian grid to the LHAPDF path
"""
result_path = _create_mc2hessian(
pdf, Q=Q, xgrid=mc2hessian_xgrid, Neig=Neig, output_path=output_path, name=gridname
)
if installgrid:
lhafolder = pathlib.Path(lhaindex.get_lha_datapath())
dest = lhafolder / gridname
if lhaindex.isinstalled(gridname):
log.warning(
"Target directory for new PDF, %s, already exists. " "Removing contents.",
dest,
)
if dest.is_dir():
shutil.rmtree(str(dest))
else:
dest.unlink()
shutil.copytree(result_path, dest)
log.info("Hessian PDF set installed at %s", dest)
def _create_mc2hessian(pdf, Q, xgrid, Neig, output_path, name=None):
X = _get_X(pdf, Q, xgrid, reshape=True)
vec = _compress_X(X, Neig)
norm = _pdf_normalization(pdf)
return hessian_from_lincomb(pdf, vec / norm, folder=output_path, set_name=name)
def _get_X(pdf, Q, xgrid, reshape=False):
pdf_grid = xplotting_grid(pdf, Q, xgrid=xgrid)
pdf_grid_values = pdf_grid.grid_values
replicas = pdf_grid_values.error_members()
mean = pdf_grid_values.central_value()
Xt = replicas - mean
if reshape:
Xt = Xt.reshape(Xt.shape[0], Xt.shape[1] * Xt.shape[2])
return Xt.T
def _compress_X(X, neig):
_U, _S, V = np.linalg.svd(X, full_matrices=False)
vec = V[:neig, :].T
return vec
def _pdf_normalization(pdf):
"""Extract the quantity by which we have to divide the eigenvectors to
get the correct errors, depending on the `error_type` of `pdf`."""
nrep = len(pdf) - 1
if pdf.error_type == "replicas":
norm = np.sqrt(nrep - 1)
elif pdf.error_type in ("hessian", "symmhessian"):
norm = 1
else:
raise NotImplementedError(
"This PDF error type is not supported." "PDF error: %s" % pdf.error_type
)
return norm