"""
pdfplots.py
Plots of quantities that are mostly functions of the PDFs only.
"""
import abc
import copy
import functools
import logging
import numbers
from types import SimpleNamespace
import warnings
from matplotlib import cm
from matplotlib import colors as mcolors
import numpy as np
from reportengine.checks import make_argcheck
from reportengine.figure import figure, figuregen
from reportengine.floatformatting import format_number
from validphys import plotutils
from validphys.checks import (
check_have_two_pdfs,
check_mixband_as_replicas,
check_pdf_normalize_to,
check_pdfs_noband,
check_scale,
)
from validphys.core import MCStats
from validphys.gridvalues import LUMI_CHANNELS
from validphys.utils import scale_from_grid
log = logging.getLogger(__name__)
[docs]class FlavourState(SimpleNamespace):
"""This is the namespace for the pats specific for each flavour"""
pass
[docs]class PDFPlotter(metaclass=abc.ABCMeta):
"""Stateful object breaks plotting grids by favour, as a function of x and
for fixed Q.
This class has a lot of state, but it should all be defined at
initialization time. Things that change e.g. per flavour should be passed
explicitly as arguments.
"""
def __init__(self, pdfs, xplotting_grids, xscale, normalize_to, ymin, ymax):
self.pdfs = pdfs
self._xplotting_grids = xplotting_grids
self._xscale = xscale
self.normalize_to = normalize_to
self.xplotting_grids = self.normalize()
self.ymin = ymin
self.ymax = ymax
[docs] def setup_flavour(self, flstate):
pass
[docs] def normalize(self):
normalize_to = self.normalize_to
if normalize_to is not None:
normalize_pdf = self.normalize_pdf
normalize_grid = self._xplotting_grids[normalize_to]
normvals = normalize_grid.grid_values.central_value()
# Handle division by zero more quietly
def fp_error(tp, flag):
log.warning(
"Invalid values found computing "
f"normalization to {normalize_pdf}: "
f"Floating point error ({tp})."
)
# Show warning only once
np.seterr(all='ignore')
newgrids = []
with np.errstate(all='call'):
np.seterrcall(fp_error)
for pdf, grid in zip(self.pdfs, self._xplotting_grids):
newvalues = pdf.stats_class(grid.grid_values.data / normvals)
newgrids.append(grid.copy_grid(grid_values=newvalues))
return newgrids
return self._xplotting_grids
@property
def normalize_pdf(self):
if self.normalize_to is None:
raise AttributeError("Need to set a normalize_to index.")
return self.pdfs[self.normalize_to]
[docs] def get_ylabel(self, parton_name):
if self.normalize_to is not None:
return f"Ratio to {self.normalize_pdf.label}"
base_str = f"x{parton_name}(x)"
# Ask the xplotting grid if it has something to add:
final_str = self.firstgrid.process_label(base_str)
# Wrap it in latex
return f"${final_str}$"
[docs] def get_title(self, parton_name):
return f"${parton_name}$ at {self.Q} GeV"
@property
def xscale(self):
if self._xscale is None:
return scale_from_grid(self.firstgrid)
return self._xscale
@property
def Q(self):
return self.firstgrid.Q
@property
def firstgrid(self):
if self.xplotting_grids:
return self.xplotting_grids[0]
raise AttributeError("Need at least one xgrid")
[docs] @abc.abstractmethod
def draw(self, pdf, grid, flstate):
"""Plot the desired function of the grid and return the array to be
used for autoscaling"""
pass
[docs] def legend(self, flstate):
return flstate.ax.legend()
def __iter__(self):
yield from self()
def __call__(self):
if not self.xplotting_grids:
return
basis = self.firstgrid.basis
for flindex, fl in enumerate(self.firstgrid.flavours):
fig, ax = plotutils.subplots()
parton_name = basis.elementlabel(fl)
flstate = FlavourState(flindex=flindex, fl=fl, fig=fig, ax=ax, parton_name=parton_name)
self.setup_flavour(flstate)
ax.set_title(self.get_title(parton_name))
all_vals = []
for pdf, grid in zip(self.pdfs, self.xplotting_grids):
limits = self.draw(pdf, grid, flstate)
if limits is not None:
all_vals.append(np.atleast_2d(limits))
# Note these two lines do not conmute!
ax.set_xscale(self.xscale)
plotutils.frame_center(ax, self.firstgrid.xgrid, np.concatenate(all_vals))
if self.ymin is not None:
ax.set_ylim(ymin=self.ymin)
if self.ymax is not None:
ax.set_ylim(ymax=self.ymax)
ax.set_xlabel('$x$')
ax.set_xlim(self.firstgrid.xgrid[0])
ax.set_ylabel(self.get_ylabel(parton_name))
ax.set_axisbelow(True)
self.legend(flstate)
yield fig, parton_name
@functools.lru_cache()
def _warn_pdf_not_montecarlo(pdf):
et = pdf.error_type
if et != 'replicas':
log.warning(
f"Plotting members of a non-Monte Carlo PDF set: {pdf.name} with error type '{et}'."
)
# Cant't add the lru_cache here because pdfs is not hashable at the moment
@make_argcheck
def _warn_any_pdf_not_montecarlo(pdfs):
for pdf in pdfs:
_warn_pdf_not_montecarlo(pdf)
[docs]class ReplicaPDFPlotter(PDFPlotter):
[docs] def draw(self, pdf, grid, flstate):
ax = flstate.ax
color = ax._get_lines.get_next_color()
flavour_grid = grid.select_flavour(flstate.flindex)
stats = flavour_grid.grid_values
gv = stats.data
ax.plot(grid.xgrid, gv.T, alpha=0.2, linewidth=0.5, color=color, zorder=1)
ax.plot(grid.xgrid, stats.central_value(), color=color, linewidth=2, label=pdf.label)
return gv
[docs]@figuregen
@check_pdf_normalize_to
@check_scale('xscale', allow_none=True)
@_warn_any_pdf_not_montecarlo
def plot_pdfreplicas(
pdfs,
xplotting_grids,
xscale: (str, type(None)) = None,
normalize_to: (int, str, type(None)) = None,
ymin=None,
ymax=None,
):
"""Plot the replicas of the specified PDFs. Otherise it works the same as
plot_pdfs.
- xscale sets the scale of the plot. E.g. 'linear' or 'log'. Default is
deduced from the xplotting_grid, which in turn is 'log' by default.
- normalize_to should be, a pdf id or an index of the pdf (starting from one).
"""
yield from ReplicaPDFPlotter(
pdfs=pdfs,
xplotting_grids=xplotting_grids,
xscale=xscale,
normalize_to=normalize_to,
ymin=ymin,
ymax=ymax,
)
[docs]class UncertaintyPDFPlotter(PDFPlotter):
[docs] def get_ylabel(self, parton_name):
if self.normalize_to is not None:
return r"$\sigma($%s$)$" % super().get_ylabel(parton_name)
return r"$\sigma$"
[docs] def draw(self, pdf, grid, flstate):
ax = flstate.ax
flindex = flstate.flindex
stats = grid.select_flavour(flindex).grid_values
res = stats.std_error()
ax.plot(grid.xgrid, res, label=pdf.label)
return res
def __call__(self):
# Fixup y limit to not be below zero
for fig, parton_name in super().__call__():
ax = fig.get_axes()[0]
ymin, _ = ax.get_ylim()
ax.set_ylim(max(0, ymin), None)
yield fig, parton_name
[docs]@figuregen
@check_pdf_normalize_to
@check_scale('xscale', allow_none=True)
def plot_pdf_uncertainties(
pdfs,
xplotting_grids,
xscale: (str, type(None)) = None,
normalize_to: (int, str, type(None)) = None,
ymin=None,
ymax=None,
):
"""Plot the PDF standard deviations as a function of x.
If normalize_to is set, the ratio to that
PDF's central value is plotted. Otherwise it is the absolute values."""
yield from UncertaintyPDFPlotter(pdfs, xplotting_grids, xscale, normalize_to, ymin, ymax)
[docs]class PullPDFPlotter(metaclass=abc.ABCMeta):
"""Auxiliary class which groups multiple pulls in one plot.
pdfs_list is a list of dictionaries, each containing the two PDFs to be used
for the pull.
pull_grids_list is the list of the pull computed for the PDF pairs described
by pdfs_list.
"""
def __init__(self, pdfs_list, pull_grids_list, xscale, normalize_to, ymin, ymax):
self.pdfs_list = pdfs_list
self.pull_grids_list = pull_grids_list
self._xscale = xscale
self.normalize_to = normalize_to
self.ymin = ymin
self.ymax = ymax
self.firstgrid = pull_grids_list[0][0]
[docs] def legend(self, flstate):
return flstate.ax.legend()
[docs] def get_ylabel(self):
return "Pull"
@property
def Q(self):
return self.firstgrid.Q
@property
def xscale(self):
if self._xscale is None:
return scale_from_grid(self.firstgrid)
return self._xscale
[docs] def get_title(self, flstate):
return '$%s$' % flstate.parton_name + f', Q={self.Q : .1f} GeV'
[docs] def draw(self, pdfs, grid, flstate):
ax = flstate.ax
flindex = flstate.flindex
color = ax._get_lines.get_next_color()
# The grid for the pull is (1, flavours, points)
# take only the flavour we are interested in
gv = grid.select_flavour(flindex).grid_values.data.squeeze()
ax.plot(grid.xgrid, gv, color=color, label=f'{pdfs[0].label}-{pdfs[1].label}')
return gv
[docs] def plot_call(self):
basis = self.firstgrid.basis
for flindex, fl in enumerate(self.firstgrid.flavours):
fig, ax = plotutils.subplots()
parton_name = basis.elementlabel(fl)
flstate = FlavourState(flindex=flindex, fl=fl, fig=fig, ax=ax, parton_name=parton_name)
ax.set_title(self.get_title(flstate))
all_vals = []
for pdf, grids in zip(self.pdfs_list, self.pull_grids_list):
limits = self.draw([pdf['pdfs'][0], pdf['pdfs'][1]], grids[1], flstate)
if limits is not None:
all_vals.append(np.atleast_2d(limits))
# Note these two lines do not conmute!
ax.set_xscale(self.xscale)
plotutils.frame_center(ax, self.firstgrid.xgrid, np.concatenate(all_vals))
if self.ymin is not None:
ax.set_ylim(ymin=self.ymin)
if self.ymax is not None:
ax.set_ylim(ymax=self.ymax)
ax.set_xlabel('$x$')
ax.set_xlim(self.firstgrid.xgrid[0])
ax.set_ylabel(self.get_ylabel())
ax.set_axisbelow(True)
self.legend(flstate)
yield fig, parton_name
def __call__(self):
for fig, parton_name in self.plot_call():
ax = fig.get_axes()[0]
ymin, _ = ax.get_ylim()
ax.set_ylim(max(0, ymin), None)
yield fig, parton_name
[docs]@figuregen
@check_scale('xscale', allow_none=True)
def plot_pdf_pulls(
pdfs_list,
pull_grids_list,
xscale: (str, type(None)) = None,
normalize_to: (int, str, type(None)) = None,
ymin=None,
ymax=None,
):
"""Plot the PDF standard deviations as a function of x.
If normalize_to is set, the ratio to that
PDF's central value is plotted. Otherwise it is the absolute values."""
yield from PullPDFPlotter(pdfs_list, pull_grids_list, xscale, normalize_to, ymin, ymax)()
[docs]class AllFlavoursPlotter(PDFPlotter):
"""Auxiliary class which groups multiple PDF flavours in one plot."""
[docs] def setup_flavour(self, flstate):
flstate.handles = self.handles
flstate.labels = self.doesnothing
flstate.hatchit = self.hatchit
def __call__(self):
if not self.xplotting_grids:
return
self.handles = []
self.doesnothing = []
self.labels = []
self.hatchit = plotutils.hatch_iter()
basis = self.firstgrid.basis
fig, ax = plotutils.subplots()
ax.set_xlabel('$x$')
ax.set_ylabel(self.get_ylabel(None))
ax.set_xscale(self.xscale)
ax.set_title(self.get_title(None))
all_vals = []
for flindex, fl in enumerate(self.firstgrid.flavours):
parton_name = basis.elementlabel(fl)
self.labels.append(f'${parton_name}$')
flstate = FlavourState(flindex=flindex, fl=fl, fig=fig, ax=ax, parton_name=parton_name)
self.setup_flavour(flstate)
for pdf, grid in zip(self.pdfs, self.xplotting_grids):
limits = self.draw(pdf, grid, flstate)
if limits is not None:
all_vals.append(np.atleast_2d(limits))
# It can happen that we don't get anything to concatenate
# e.g. because we are comparing to the base PDF several times.
if all_vals:
plotutils.frame_center(ax, self.firstgrid.xgrid, np.concatenate(all_vals))
if self.ymin is not None:
ax.set_ylim(ymin=self.ymin)
if self.ymax is not None:
ax.set_ylim(ymax=self.ymax)
ax.set_axisbelow(True)
ax.set_xlim(self.firstgrid.xgrid[0])
flstate.labels = self.labels
self.legend(flstate)
return fig
[docs] def get_ylabel(self, parton_name):
return ''
[docs]class DistancePDFPlotter(PDFPlotter):
"""Auxiliary class which draws the distance plots."""
[docs] def normalize(self):
return self._xplotting_grids
[docs] def get_ylabel(self, parton_name):
return "Distance from {}".format(self.normalize_pdf.label)
[docs] def draw(self, pdf, grid, flstate):
if pdf == self.normalize_pdf:
return None
ax = flstate.ax
flindex = flstate.flindex
color = ax._get_lines.get_next_color()
# The grid for the distance is (1, flavours, points)
# take only the flavour we are interested in
gv = grid.select_flavour(flindex).grid_values.data.squeeze()
ax.plot(grid.xgrid, gv, color=color, label='$%s$' % flstate.parton_name)
return gv
[docs] def get_title(self, parton_name):
return f'{self.pdfs[(1+self.normalize_to)%2]} Q={self.Q : .1f} GeV'
[docs]class VarDistancePDFPlotter(DistancePDFPlotter):
"""Auxiliary class which draws the variance distance plots"""
[docs] def get_ylabel(self, parton_name):
return "Variance distance from {}".format(self.normalize_pdf.label)
[docs] def get_title(self, parton_name):
return f'{self.pdfs[(1+self.normalize_to)%2]} Q={self.Q : .1f} GeV'
[docs]class FlavoursDistancePlotter(DistancePDFPlotter, AllFlavoursPlotter):
pass
[docs]class FlavoursVarDistancePlotter(VarDistancePDFPlotter, AllFlavoursPlotter):
pass
[docs]@figure
@check_pdf_normalize_to
@check_have_two_pdfs
@check_scale('xscale', allow_none=True)
def plot_pdfdistances(
pdfs,
distance_grids,
*,
xscale: (str, type(None)) = None,
normalize_to: (int, str),
ymin=None,
ymax=None,
):
"""Plots the distances between different PDF sets and a reference PDF set
for all flavours. Distances are normalized such that a value of order 10
is unlikely to be explained by purely statistical fluctuations
"""
return FlavoursDistancePlotter(pdfs, distance_grids, xscale, normalize_to, ymin, ymax)()
[docs]@figure
@check_pdf_normalize_to
@check_have_two_pdfs
@check_scale('xscale', allow_none=True)
def plot_pdfvardistances(
pdfs,
variance_distance_grids,
*,
xscale: (str, type(None)) = None,
normalize_to: (int, str),
ymin=None,
ymax=None,
):
"""Plots the distances between different PDF sets and a reference PDF set
for all flavours. Distances are normalized such that a value of order 10
is unlikely to be explained by purely statistical fluctuations
"""
return FlavoursVarDistancePlotter(
pdfs, variance_distance_grids, xscale, normalize_to, ymin, ymax
)()
[docs]class BandPDFPlotter(PDFPlotter):
def __init__(
self, *args, pdfs_noband=None, show_mc_errors=True, legend_stat_labels=True, **kwargs
):
if pdfs_noband is None:
pdfs_noband = []
self.pdfs_noband = pdfs_noband
self.show_mc_errors = show_mc_errors
self.legend_stat_labels = legend_stat_labels
super().__init__(*args, **kwargs)
[docs] def setup_flavour(self, flstate):
flstate.handles = []
flstate.labels = []
flstate.hatchit = plotutils.hatch_iter()
[docs] def draw(self, pdf, grid, flstate):
ax = flstate.ax
hatchit = flstate.hatchit
labels = flstate.labels
handles = flstate.handles
# Take only the flavours we are interested in
stats = grid.select_flavour(flstate.flindex).grid_values
cv = stats.central_value()
xgrid = grid.xgrid
# Ignore spurious normalization warnings
with warnings.catch_warnings():
warnings.simplefilter('ignore', RuntimeWarning)
err68down, err68up = stats.errorbar68()
# http://stackoverflow.com/questions/5195466/matplotlib-does-not-display-hatching-when-rendering-to-pdf
hatch = next(hatchit)
color = ax._get_lines.get_next_color()
(cvline,) = ax.plot(xgrid, cv, color=color)
if pdf in self.pdfs_noband:
labels.append(pdf.label)
handles.append(cvline)
return [cv, cv]
alpha = 0.5
ax.fill_between(xgrid, err68up, err68down, color=color, alpha=alpha, zorder=1)
ax.fill_between(
xgrid,
err68up,
err68down,
facecolor='None',
alpha=alpha,
edgecolor=color,
hatch=hatch,
zorder=1,
)
if isinstance(stats, MCStats) and self.show_mc_errors:
errorstdup, errorstddown = stats.errorbarstd()
ax.plot(xgrid, errorstdup, linestyle='--', color=color)
ax.plot(xgrid, errorstddown, linestyle='--', color=color)
label = (
rf"{pdf.label} ($68\%$ c.l.+$1\sigma$)" if self.legend_stat_labels else pdf.label
)
outer = True
else:
outer = False
label = rf"{pdf.label} ($68\%$ c.l.)" if self.legend_stat_labels else pdf.label
handle = plotutils.HandlerSpec(color=color, alpha=alpha, hatch=hatch, outer=outer)
handles.append(handle)
labels.append(label)
return [err68down, err68up]
[docs] def legend(self, flstate):
return flstate.ax.legend(
flstate.handles,
flstate.labels,
handler_map={plotutils.HandlerSpec: plotutils.ComposedHandler()},
)
[docs]class BandPDFPlotterBC(BandPDFPlotter):
def __init__(self, *args, unpolarized_bcs, boundary_xplotting_grids, **kwargs):
self.unpolarized_bcs = unpolarized_bcs
self.boundary_xplotting_grids = boundary_xplotting_grids
super().__init__(*args, **kwargs)
[docs] def draw(self, pdf, grid, flstate):
xgrid = grid.xgrid
ax = flstate.ax
labels = flstate.labels
handles = flstate.handles
if pdf.name == self.pdfs[0].name: # Make sure to plot only for 1st pdfs
# Check if BC PDFs are the same and if so do not plot them twice
if len(set(i.name for i in self.unpolarized_bcs)) == 1:
plotting_bcs = [self.boundary_xplotting_grids[0]]
else:
plotting_bcs = self.boundary_xplotting_grids
for idx, xplot_repr in enumerate(plotting_bcs):
unpol_stats = xplot_repr.select_flavour(flstate.flindex).grid_values
unpol_cv = unpol_stats.central_value()
unpol_std = unpol_stats.std_error()
(cvline,) = ax.plot(xgrid, unpol_cv + unpol_std, color=f"C{idx + 2}")
ax.plot(xgrid, -(unpol_cv + unpol_std), color=f"C{idx + 2}")
handles.append(cvline)
labels.append(self.unpolarized_bcs[idx].label)
return super().draw(pdf, grid, flstate)
[docs]@figuregen
@check_pdf_normalize_to
@check_pdfs_noband
@check_scale("xscale", allow_none=True)
def plot_pdfs(
pdfs,
xplotting_grids,
xscale: (str, type(None)) = None,
normalize_to: (int, str, type(None)) = None,
ymin=None,
ymax=None,
pdfs_noband: (list, type(None)) = None,
show_mc_errors: bool = True,
legend_stat_labels: bool = True,
):
"""Plot the central value and the uncertainty of a list of pdfs as a
function of x for a given value of Q. If normalize_to is given, plot the
ratios to the corresponding PDF. Otherwise, plot absolute values.
See the help for ``xplotting_grid`` for information on how to set basis,
flavours and x ranges. Yields one figure per PDF flavour.
normalize_to: Either the name of one of the PDFs or its corresponding
index in the list, starting from one, or None to plot absolute values.
xscale: One of the matplotlib allowed scales. If undefined, it will be
set based on the scale in xgrid, which should be used instead.
pdfs_noband: A list of PDFs to plot without error bands, i.e. only the
central values of these PDFs will be plotted. The list can be formed of
strings, corresponding to PDF IDs, integers (starting from one),
corresponding to the index of the PDF in the list of PDFs, or a mixture
of both.
show_mc_errors (bool): Plot 1σ bands in addition to 68% errors for Monte Carlo
PDF.
legend_stat_labels (bool): Show detailed information on what kind of confidence
interval is being plotted in the legend labels.
"""
yield from BandPDFPlotter(
pdfs,
xplotting_grids,
xscale,
normalize_to,
ymin,
ymax,
pdfs_noband=pdfs_noband,
show_mc_errors=show_mc_errors,
legend_stat_labels=legend_stat_labels,
)
[docs]@figuregen
@check_pdf_normalize_to
@check_pdfs_noband
@check_scale("xscale", allow_none=True)
def plot_polarized_boundaries(
pdfs,
xplotting_grids,
unpolarized_bcs,
boundary_xplotting_grids,
xscale: (str, type(None)) = None,
normalize_to: (int, str, type(None)) = None,
ymin=None,
ymax=None,
pdfs_noband: (list, type(None)) = None,
show_mc_errors: bool = True,
legend_stat_labels: bool = True,
):
"""Possess the exact same functionalities as `plot_pdfs` but for a list
of Polarized PDF sets. In addition, it plots the unpolarized PDF set used
as a Boundary Condition.
"""
yield from BandPDFPlotterBC(
pdfs,
xplotting_grids,
xscale,
normalize_to,
ymin,
ymax,
unpolarized_bcs=unpolarized_bcs,
boundary_xplotting_grids=boundary_xplotting_grids,
pdfs_noband=pdfs_noband,
show_mc_errors=show_mc_errors,
legend_stat_labels=legend_stat_labels,
)
[docs]@figuregen
@check_pdf_normalize_to
@check_mixband_as_replicas
@check_pdfs_noband
@check_scale("xscale", allow_none=True)
def plot_pdfs_mixed(
pdfs,
xplotting_grids,
xscale: (str, type(None)) = None,
normalize_to: (int, str, type(None)) = None,
ymin=None,
ymax=None,
pdfs_noband: (list, type(None)) = None,
show_mc_errors: bool = True,
legend_stat_labels: bool = True,
mixband_as_replicas: (list, type(None)) = None,
):
"""This function is similar to plot_pdfs, except instead of only plotting
the central value and the uncertainty of the PDFs, those PDFs indicated by
mixband_as_replicas will be plotted as replicas without the central value.
Inputs are the same as plot_pdfs, with the exeption of mixband_as_replicas,
which only exists here.
mixband_as_replicas: A list of PDFs to plot as replicas, i.e. the
central values and replicas of these PDFs will be plotted. The list can be
formed of strings, corresponding to PDF IDs, integers (starting from one),
corresponding to the index of the PDF in the list of PDFs, or a mixture
of both.
"""
yield from MixBandPDFPlotter(
pdfs,
xplotting_grids,
xscale,
normalize_to,
ymin,
ymax,
pdfs_noband=pdfs_noband,
show_mc_errors=show_mc_errors,
legend_stat_labels=legend_stat_labels,
mixband_as_replicas=mixband_as_replicas,
)
[docs]@figuregen
@check_pdf_normalize_to
@check_pdfs_noband
@check_scale("xscale", allow_none=True)
def plot_pdfs_kinetic_energy(
pdfs,
kinetic_xplotting_grids,
xscale: (str, type(None)) = None,
normalize_to: (int, str, type(None)) = None,
ymin=None,
ymax=None,
pdfs_noband: (list, type(None)) = None,
show_mc_errors: bool = True,
legend_stat_labels: bool = True,
):
"""Band plotting of the "kinetic energy" of the PDF as a function of x for a given value of Q.
The input of this function is similar to those of ``plot_pdfs``.
"""
return plot_pdfs(
pdfs,
kinetic_xplotting_grids,
xscale=xscale,
normalize_to=normalize_to,
ymin=ymin,
ymax=ymax,
pdfs_noband=pdfs_noband,
show_mc_errors=show_mc_errors,
legend_stat_labels=legend_stat_labels,
)
[docs]@figuregen
@check_pdf_normalize_to
@check_scale('xscale', allow_none=True)
@_warn_any_pdf_not_montecarlo
def plot_pdfreplicas_kinetic_energy(
pdfs,
kinetic_xplotting_grids,
xscale: (str, type(None)) = None,
normalize_to: (int, str, type(None)) = None,
ymin=None,
ymax=None,
):
"""Plot the kinetic energy of the replicas of the specified PDFs.
Otherise it works the same as ``plot_pdfs_kinetic_energy``.
"""
return plot_pdfreplicas(
pdfs,
kinetic_xplotting_grids,
xscale=xscale,
normalize_to=normalize_to,
ymin=ymin,
ymax=ymax,
)
[docs]@figuregen
@check_pdf_normalize_to
@check_pdfs_noband
@check_mixband_as_replicas
@check_scale("xscale", allow_none=True)
def plot_pdfs_mixed_kinetic_energy(
pdfs,
kinetic_xplotting_grids,
xscale: (str, type(None)) = None,
normalize_to: (int, str, type(None)) = None,
ymin=None,
ymax=None,
pdfs_noband: (list, type(None)) = None,
show_mc_errors: bool = True,
legend_stat_labels: bool = True,
mixband_as_replicas: (list, type(None)) = None,
):
"""Mixed band and replica plotting of the "kinetic energy" of the PDF as a
function of x for a given value of Q.
"""
return plot_pdfs_mixed(
pdfs,
kinetic_xplotting_grids,
xscale=xscale,
normalize_to=normalize_to,
ymin=ymin,
ymax=ymax,
pdfs_noband=pdfs_noband,
show_mc_errors=show_mc_errors,
legend_stat_labels=legend_stat_labels,
mixband_as_replicas=mixband_as_replicas,
)
[docs]class FlavoursPlotter(AllFlavoursPlotter, BandPDFPlotter):
[docs] def get_title(self, parton_name):
return f'{self.pdfs[0]} Q={self.Q : .1f} GeV'
[docs]@figure
@check_scale('xscale', allow_none=True)
def plot_flavours(
pdf,
xplotting_grid,
xscale: (str, type(None)) = None,
normalize_to: (int, str, type(None)) = None,
ymin=None,
ymax=None,
):
"""Plot the absolute central value and the uncertainty of all the flavours
of a pdf as a function of x for a given value of Q.
xscale: One of the matplotlib allowed scales. If undefined, it will be
set based on the scale in xgrid, which should be used instead.
"""
return FlavoursPlotter(
[pdf], [xplotting_grid], xscale, normalize_to=None, ymin=ymin, ymax=ymax
)()
[docs]@figure
@check_pdf_normalize_to
@check_pdfs_noband
def plot_lumi1d(
pdfs,
pdfs_lumis,
lumi_channel,
sqrts: numbers.Real,
y_cut: (numbers.Real, type(None)) = None,
normalize_to=None,
show_mc_errors: bool = True,
ymin: (numbers.Real, type(None)) = None,
ymax: (numbers.Real, type(None)) = None,
pdfs_noband=None,
scale="log",
legend_stat_labels: bool = True,
):
"""Plot PDF luminosities at a given center of mass energy.
sqrts is the center of mass energy (GeV).
This action plots the luminosity (as computed by `lumigrid1d`) as a
function of invariant mass for all PDFs for a single lumi channel.
``normalize_to`` works as for `plot_pdfs` and allows to plot a ratio to the
central value of some of the PDFs. `ymin` and `ymax` can be used to set
exact bounds for the scale. `y_cut` can be used to specify a rapidity cut
over the integration range. `show_mc_errors` controls whether the 1σ error
bands are shown in addition to the 68% confidence intervals for Monte Carlo
PDFs. A list `pdfs_noband` can be passed to supress the error bands for
certain PDFs and plot the central values only. `legend_stat_labels` controls
whether to show detailed information on what kind of confidence interval
is being plotted in the legend labels.
"""
fig, ax = plotutils.subplots()
if normalize_to is not None:
norm = pdfs_lumis[normalize_to].grid_values.central_value()
ylabel = f"Ratio to {pdfs[normalize_to]}"
else:
norm = 1
ylabel = r"$\mathcal{L} (GeV^{-2})$"
hatchit = plotutils.hatch_iter()
pcycler = plotutils.color_iter()
handles = []
labels = []
for pdf, lumigrid1d in zip(pdfs, pdfs_lumis):
mx = lumigrid1d.m
gv = lumigrid1d.grid_values
cv = gv.central_value()
err68down, err68up = gv.errorbar68()
errstddown, errstdup = gv.errorbarstd()
color = next(pcycler)
hatch = next(hatchit)
alpha = 0.5
(central_line,) = ax.plot(mx, cv / norm, color=color)
if pdfs_noband and pdf in pdfs_noband:
handles.append(central_line)
labels.append(pdf.label)
continue
ax.fill_between(mx, err68down / norm, err68up / norm, color=color, alpha=alpha, zorder=1)
ax.fill_between(
mx,
err68down / norm,
err68up / norm,
facecolor="None",
alpha=alpha,
edgecolor=color,
hatch=hatch,
zorder=1,
)
if isinstance(gv, MCStats) and show_mc_errors:
ax.plot(mx, errstddown / norm, linestyle="--", color=color)
ax.plot(mx, errstdup / norm, linestyle="--", color=color)
label_add = r"($68\%$ c.l.+$1\sigma$)" if legend_stat_labels else ""
outer = True
else:
label_add = r"($68\%$ c.l.)" if legend_stat_labels else ""
outer = False
handle = plotutils.HandlerSpec(color=color, alpha=alpha, hatch=hatch, outer=outer)
handles.append(handle)
labels.append(f"{pdf.label} {label_add}")
ax.legend(handles, labels, handler_map={plotutils.HandlerSpec: plotutils.ComposedHandler()})
ax.set_ylabel(ylabel)
ax.set_xlabel("$m_{X}$ (GeV)")
ax.set_xlim(mx[0], mx[-1])
ax.set_ylim(ymin, ymax)
ax.set_xscale(scale)
ax.grid(False)
if y_cut == None:
ax.set_title(
f"${LUMI_CHANNELS[lumi_channel]}$ luminosity\n"
f"$\\sqrt{{s}}={format_number(sqrts/1000)}$ TeV"
)
else:
ax.set_title(
f"${LUMI_CHANNELS[lumi_channel]}$ luminosity\n"
f"$\\sqrt{{s}}={format_number(sqrts/1000)}$ TeV "
f"$\\|y\\|<{format_number(y_cut)}$"
)
return fig
[docs]@figure
@check_pdf_normalize_to
def plot_lumi1d_uncertainties(
pdfs,
pdfs_lumis,
lumi_channel,
sqrts: numbers.Real,
y_cut: (numbers.Real, type(None)) = None,
normalize_to=None,
ymin: (numbers.Real, type(None)) = None,
ymax: (numbers.Real, type(None)) = None,
scale="log",
):
"""Plot PDF luminosity uncertainties at a given center of mass energy.
sqrts is the center of mass energy (GeV).
If `normalize_to` is set, the values are normalized to the central value of
the corresponding PDFs. `y_cut` can be used to specify a rapidity cut
over the integration range.
"""
fig, ax = plotutils.subplots()
if normalize_to is not None:
norm = pdfs_lumis[normalize_to].grid_values.central_value()
ylabel = f"Ratio to {pdfs[normalize_to]}"
else:
norm = None
ylabel = r"$\sigma\left(\mathcal{L} (GeV^{-2})\right)$"
for pdf, lumigrid1d, color in zip(pdfs, pdfs_lumis, plotutils.color_iter()):
mx = lumigrid1d.m
gv = lumigrid1d.grid_values
err = gv.std_error()
if norm is not None:
err /= norm
ax.plot(mx, err, color=color, label=pdf.label)
ax.legend()
ax.set_ylabel(ylabel)
ax.set_xlabel("$m_{X}$ (GeV)")
ax.set_xlim(mx[0], mx[-1])
ax.set_xscale(scale)
ax.grid(False)
if y_cut is None:
ax.set_title(
f"${LUMI_CHANNELS[lumi_channel]}$ luminosity uncertainty\n"
f"$\\sqrt{{s}}={format_number(sqrts/1000)}$ TeV"
)
else:
ax.set_title(
f"${LUMI_CHANNELS[lumi_channel]}$ luminosity uncertainty\n"
f"$\\sqrt{{s}}={format_number(sqrts/1000)}$ TeV "
f"$\\|y|<{format_number(y_cut)}$"
)
ax.set_ylim(ymin, ymax)
current_ymin, _ = ax.get_ylim()
ax.set_ylim(max(0, current_ymin), None)
return fig
[docs]@figure
@check_pdf_normalize_to
def plot_lumi1d_replicas(
pdfs,
pdfs_lumis,
lumi_channel,
sqrts: numbers.Real,
y_cut: (numbers.Real, type(None)) = None,
normalize_to=None,
ymin: (numbers.Real, type(None)) = None,
ymax: (numbers.Real, type(None)) = None,
scale="log",
):
"""This function is similar to `plot_lumi1d`, but instead of plotting
the standard deviation and 68% c.i. it plots the luminosities for
individual replicas.
Plot PDF replica luminosities at a given center of mass energy.
sqrts is the center of mass energy (GeV).
This action plots the luminosity (as computed by `lumigrid1d`) as a
function of invariant mass for all PDFs for a single lumi channel.
``normalize_to`` works as for `plot_pdfs` and allows to plot a ratio to the
central value of some of the PDFs. `ymin` and `ymax` can be used to set
exact bounds for the scale. `y_cut` can be used to specify a rapidity cut
over the integration range. `show_mc_errors` controls whether the 1σ error
bands are shown in addition to the 68% confidence intervals for Monte Carlo
PDFs.
"""
fig, ax = plotutils.subplots()
if normalize_to is not None:
norm = pdfs_lumis[normalize_to].grid_values.central_value()
ylabel = f"Ratio to {pdfs[normalize_to]}"
else:
norm = 1
ylabel = r"$\mathcal{L} (GeV^{-2})$"
pcycler = plotutils.color_iter()
lines = []
labels = []
for pdf, lumigrid1d in zip(pdfs, pdfs_lumis):
mx = lumigrid1d.m
gv = lumigrid1d.grid_values
cv = gv.central_value()
replicas = gv.data
color = next(pcycler)
ax.plot(mx, (replicas / norm).T, alpha=0.2, linewidth=0.5, color=color, zorder=1)
(line,) = ax.plot(mx, cv / norm, color=color, linewidth=2)
lines.append(line)
labels.append(pdf.label)
ax.set_ylabel(ylabel)
ax.set_xlabel("$m_{X}$ (GeV)")
ax.set_xlim(mx[0], mx[-1])
ax.set_ylim(ymin, ymax)
ax.set_xscale(scale)
ax.legend(lines, labels)
ax.grid(False)
if y_cut is None:
ax.set_title(
f"${LUMI_CHANNELS[lumi_channel]}$ luminosity\n"
f"$\\sqrt{{s}}={format_number(sqrts/1000)}$ TeV"
)
else:
ax.set_title(
f"${LUMI_CHANNELS[lumi_channel]}$ luminosity\n"
f"$\\sqrt{{s}}={format_number(sqrts/1000)}$ TeV "
f"$\\|y|<{format_number(y_cut)}$"
)
return fig
# TODO: Move these to utils somewhere? Find better implementations?
def _reflect_matrl(mat, odd=False):
"""Reflect a matrix with positive values in the first axis to have the
same balues for the nwgative axis. The first value is not reflected.
If ``odd`` is set, the negative part will be multiplied by -1.
"""
mat = np.asarray(mat)
res = np.empty(shape=(mat.shape[0] * 2 - 1, *mat.shape[1:]), dtype=mat.dtype)
neglen = mat.shape[0] - 1
fact = -1 if odd else 1
res[:neglen, ...] = fact * mat[:0:-1, ...]
res[neglen:, ...] = mat
return res
def _reflect_matud(mat, odd=False):
"""Reflect a matrix with positive values in the second axis to have the
same balues for the nwgative axis. The first value is not reflected.
If ``odd`` is set, the negative part will be multiplied by -1.
"""
mat = np.asarray(mat)
res = np.empty(shape=(mat.shape[0], mat.shape[1] * 2 - 1, *mat.shape[2:]), dtype=mat.dtype)
neglen = mat.shape[1] - 1
fact = -1 if odd else 1
res[:, :neglen, ...] = fact * mat[:, :0:-1, ...]
res[:, neglen:, ...] = mat
return res
[docs]@figure
def plot_lumi2d(pdf, lumi_channel, lumigrid2d, sqrts, display_negative: bool = True):
"""Plot the absolute luminosity on a grid of invariant mass and
rapidity for a given center of mass energy `sqrts`.
The color scale is logarithmic.
If `display_negative` is True, mark the negative values.
The luminosity is calculated for positive rapidity, and reflected for
negative rapidity for display purposes.
"""
cmap = copy.copy(cm.viridis_r)
cmap.set_bad("white", alpha=0)
fig, ax = plotutils.subplots()
gv = lumigrid2d.grid_values
mat = gv.central_value()
fig, ax = plotutils.subplots()
mat = _reflect_matud(mat)
y = _reflect_matrl(lumigrid2d.y, odd=True)
masked_weights = np.ma.masked_invalid(mat, copy=False)
# TODO: SymLogNorm is really the right thing to do here, but I can't be
# bothered to make it work. Mostly the ticks around zero are completely
# broken and looks like it takes a lot of fidlling wirh the mpl internals
# to fix it.
with np.errstate(invalid='ignore'):
positive_mask = masked_weights > 0
linlim = np.nanpercentile(masked_weights[positive_mask], 90) / 1e5
# norm = mcolors.SymLogNorm(linlim, vmin=None)
norm = mcolors.LogNorm(vmin=linlim)
with np.errstate(invalid='ignore'):
masked_weights[masked_weights < linlim] = linlim
mesh = ax.pcolormesh(
y,
lumigrid2d.m,
masked_weights,
cmap=cmap,
shading='gouraud',
linewidth=0,
edgecolor='None',
rasterized=True,
norm=norm,
)
# Annoying code because mpl does the defaults horribly
# loc = mticker.SymmetricalLogLocator(base=10, linthresh=linlim,)
# loc.numticks = 5
# fig.colorbar(mesh, ticks=loc)
if display_negative:
cmap_neg = mcolors.ListedColormap(['red', (0, 0, 0, 0)])
neg_norm = mcolors.BoundaryNorm([0, 0.5, 1], 2)
ax.pcolormesh(
y,
lumigrid2d.m,
positive_mask,
cmap=cmap_neg,
shading='gouraud',
linewidth=0,
edgecolor='None',
rasterized=True,
norm=neg_norm,
)
fig.colorbar(mesh, extend='min', label="Differential luminosity ($GeV^{-1}$)")
ax.set_ylabel('$m_{X}$ (GeV)')
ax.set_xlabel('y')
ax.set_yscale('log')
ax.grid(False)
ax.set_title(
("$%s$ luminosity\n%s - $\\sqrt{s}=%.1f$ GeV")
% (LUMI_CHANNELS[lumi_channel], pdf.label, sqrts)
)
return fig
[docs]@figure
def plot_lumi2d_uncertainty(pdf, lumi_channel, lumigrid2d, sqrts: numbers.Real):
"""
Plot 2D luminosity unciertainty plot at a given center of mass energy.
Porting code from https://github.com/scarrazza/lumi2d.
The luminosity is calculated for positive rapidity, and reflected for
negative rapidity for display purposes.
"""
norm = mcolors.LogNorm(vmin=1, vmax=50)
cmap = copy.copy(cm.viridis_r)
cmap.set_bad("white", alpha=0)
grid = lumigrid2d
channel = lumi_channel
gv = grid.grid_values
mat = gv.std_error() / np.abs(gv.central_value()) * 100
fig, ax = plotutils.subplots()
mat = _reflect_matud(mat)
y = _reflect_matrl(grid.y, odd=True)
masked_weights = np.ma.masked_invalid(mat, copy=False)
mesh = ax.pcolormesh(
y,
grid.m,
masked_weights,
norm=norm,
cmap=cmap,
shading='gouraud',
linewidth=0,
edgecolor='None',
rasterized=True,
)
# some extra options
extup = np.nanmax(masked_weights) > 50
extdown = np.nanmin(masked_weights) < 1
# TODO: Wrap this somewhere
if extup:
if extdown:
extend = 'both'
else:
extend = 'max'
elif extdown:
extend = 'min'
else:
extend = None
fig.colorbar(
mesh,
label="Relative uncertainty (%)",
ticks=[1, 5, 10, 25, 50],
format='%.0f',
extend=extend,
)
ax.set_yscale('log')
ax.set_title(
("Relative uncertainty for $%s$-luminosity\n%s - $\\sqrt{s}=%.1f$ GeV")
% (LUMI_CHANNELS[channel], pdf.label, sqrts)
)
ax.set_ylabel('$m_{X}$ (GeV)')
ax.set_xlabel('y')
ax.grid(False)
return fig
[docs]class MixBandPDFPlotter(BandPDFPlotter):
"""Special wrapper class to plot, in the same figure, PDF bands and PDF replicas
depending on the type of PDF.
Practical use: plot together the PDF central values with the NNPDF bands
"""
def __init__(self, *args, mixband_as_replicas, **kwargs):
self.mixband_as_replicas = mixband_as_replicas
super().__init__(*args, **kwargs)
[docs] def draw(self, pdf, grid, flstate):
if pdf in self.mixband_as_replicas:
labels = flstate.labels
handles = flstate.handles
ax = flstate.ax
color = ax._get_lines.get_next_color()
stats = grid.select_flavour(flstate.flindex).grid_values
gv = stats.data
ax.plot(grid.xgrid, gv.T, alpha=0.2, linewidth=0.5, color=color, zorder=1)
cv_line = ax.plot(grid.xgrid[0:1], stats.central_value()[0:1], color=color, linewidth=2)
handle = cv_line[0]
labels.append(pdf.label)
handles.append(handle)
return gv
return super().draw(pdf, grid, flstate)