#!/usr/bin/env python
# -*- coding: utf-8 -*-
"""
A set of built-in plotting functions to help visualize ``dynesty`` nested
sampling :class:`~dynesty.results.Results`.
"""
import logging
import warnings
import numpy as np
import matplotlib.pyplot as pl
from matplotlib.ticker import MaxNLocator, NullLocator
from matplotlib.colors import LinearSegmentedColormap, colorConverter
from matplotlib.ticker import ScalarFormatter
from scipy.ndimage import gaussian_filter as norm_kde
from scipy.stats import gaussian_kde
from .utils import resample_equal, unitcheck
from .utils import quantile as _quantile
from .utils import get_random_generator, get_nonbounded
from . import bounding
str_type = str
float_type = float
int_type = int
__all__ = [
"runplot", "traceplot", "cornerpoints", "cornerplot", "boundplot",
"cornerbound", "_hist2d"
]
def _make_subplots(fig, nx, ny, xsize, ysize):
# Setting up default plot layout.
if fig is None:
fig, axes = pl.subplots(nx, ny, figsize=(xsize, ysize))
axes = np.asarray(axes).reshape(nx, ny)
else:
fig, axes = fig
try:
axes = np.asarray(axes).reshape(nx, ny)
except ValueError:
raise ValueError("Provided axes do not match the required shape")
return fig, axes
def rotate_ticks(ax, xy):
if xy == 'x':
labs = ax.get_xticklabels()
else:
labs = ax.get_yticklabels()
for lab in labs:
lab.set_rotation(45)
def plot_thruth(ax,
truths,
truth_color,
truth_kwargs,
vertical=None,
horizontal=None):
"""
Plot the thruth line (horizontal or vertical).
truths can be None or one value or a list
"""
if vertical:
func = ax.axvline
elif horizontal:
func = ax.axhline
else:
raise ValueError('vertical or horizontal option must be specified')
if truths is not None:
try:
curt = iter(truths)
except TypeError:
curt = [truths]
for t in curt:
func(t, color=truth_color, **truth_kwargs)
def check_span(span, samples, weights):
"""
If span is a list of scalars, replace it by the list of bounds.
If the input is list of pairs, it is kept intact
"""
for i, _ in enumerate(span):
try:
iter(span[i])
if len(span[i]) != 2:
raise ValueError('Incorrect span value')
except TypeError:
q = [0.5 - 0.5 * span[i], 0.5 + 0.5 * span[i]]
span[i] = _quantile(samples[i], q, weights=weights)
def runplot(results,
span=None,
logplot=False,
kde=True,
nkde=1000,
color='blue',
plot_kwargs=None,
label_kwargs=None,
lnz_error=True,
lnz_truth=None,
truth_color='red',
truth_kwargs=None,
max_x_ticks=8,
max_y_ticks=3,
use_math_text=True,
mark_final_live=True,
fig=None):
"""
Plot live points, ln(likelihood), ln(weight), and ln(evidence)
as a function of ln(prior volume).
Parameters
----------
results : :class:`~dynesty.results.Results` instance
A :class:`~dynesty.results.Results` instance from a nested
sampling run.
span : iterable with shape (4,), optional
A list where each element is either a length-2 tuple containing
lower and upper bounds *or* a float from `(0., 1.]` giving the
fraction below the maximum. If a fraction is provided,
the bounds are chosen to be equal-tailed. An example would be::
span = [(0., 10.), 0.001, 0.2, (5., 6.)]
Default is `(0., 1.05 * max(data))` for each element.
logplot : bool, optional
Whether to plot the evidence on a log scale. Default is `False`.
kde : bool, optional
Whether to use kernel density estimation to estimate and plot
the PDF of the importance weights as a function of log-volume
(as opposed to the importance weights themselves). Default is
`True`.
nkde : int, optional
The number of grid points used when plotting the kernel density
estimate. Default is `1000`.
color : str or iterable with shape (4,), optional
A `~matplotlib`-style color (either a single color or a different
value for each subplot) used when plotting the lines in each subplot.
Default is `'blue'`.
plot_kwargs : dict, optional
Extra keyword arguments that will be passed to `plot`.
label_kwargs : dict, optional
Extra keyword arguments that will be sent to the
`~matplotlib.axes.Axes.set_xlabel` and
`~matplotlib.axes.Axes.set_ylabel` methods.
lnz_error : bool, optional
Whether to plot the 1, 2, and 3-sigma approximate error bars
derived from the ln(evidence) error approximation over the course
of the run. Default is `True`.
lnz_truth : float, optional
A reference value for the evidence that will be overplotted on the
evidence subplot if provided.
truth_color : str or iterable with shape (ndim,), optional
A `~matplotlib`-style color used when plotting :data:`lnz_truth`.
Default is `'red'`.
truth_kwargs : dict, optional
Extra keyword arguments that will be used for plotting
:data:`lnz_truth`.
max_x_ticks : int, optional
Maximum number of ticks allowed for the x axis. Default is `8`.
max_y_ticks : int, optional
Maximum number of ticks allowed for the y axis. Default is `4`.
use_math_text : bool, optional
Whether the axis tick labels for very large/small exponents should be
displayed as powers of 10 rather than using `e`. Default is `False`.
mark_final_live : bool, optional
Whether to indicate the final addition of recycled live points
(if they were added to the resulting samples) using
a dashed vertical line. Default is `True`.
fig : (`~matplotlib.figure.Figure`, `~matplotlib.axes.Axes`), optional
If provided, overplot the run onto the provided figure.
Otherwise, by default an internal figure is generated.
Returns
-------
runplot : (`~matplotlib.figure.Figure`, `~matplotlib.axes.Axes`)
Output summary plot.
"""
# Initialize values.
if label_kwargs is None:
label_kwargs = {}
if plot_kwargs is None:
plot_kwargs = {}
if truth_kwargs is None:
truth_kwargs = {}
rstate = get_random_generator()
# Set defaults.
plot_kwargs['linewidth'] = plot_kwargs.get('linewidth', 5)
plot_kwargs['alpha'] = plot_kwargs.get('alpha', 0.7)
truth_kwargs['linestyle'] = truth_kwargs.get('linestyle', 'solid')
truth_kwargs['linewidth'] = truth_kwargs.get('linewidth', 3)
# Extract results.
niter = results['niter'] # number of iterations
logvol = results['logvol'] # ln(prior volume)
logl = results['logl'] - max(results['logl']) # ln(normalized likelihood)
logwt = results['logwt'] - results['logz'][-1] # ln(importance weight)
logz = results['logz'] # ln(evidence)
logzerr = results['logzerr'] # error in ln(evidence)
logzerr[~np.isfinite(logzerr)] = 0.
nsamps = len(logwt) # number of samples
# Check whether the run was "static" or "dynamic".
try:
nlive = results['samples_n']
mark_final_live = False
except KeyError:
nlive = np.ones(niter) * results['nlive']
if nsamps - niter == results['nlive']:
nlive_final = np.arange(1, results['nlive'] + 1)[::-1]
nlive = np.append(nlive, nlive_final)
# Check if the final set of live points were added to the results.
if mark_final_live:
if nsamps - niter == results['nlive']:
live_idx = niter
else:
warnings.warn("The number of iterations and samples differ "
"by an amount that isn't the number of final "
"live points. `mark_final_live` has been disabled.")
mark_final_live = False
# Determine plotting bounds for each subplot.
data = [
nlive,
np.exp(logl),
np.exp(logwt), logz if logplot else np.exp(logz)
]
if kde:
# Derive kernel density estimate.
wt_kde = gaussian_kde(resample_equal(-logvol, data[2],
rstate=rstate)) # KDE
logvol_new = np.linspace(logvol[0], logvol[-1], nkde) # resample
data[2] = wt_kde.pdf(-logvol_new) # evaluate KDE PDF
if span is None:
span = [(0., 1.05 * max(d)) for d in data]
no_span = True
else:
no_span = False
span = list(span)
if len(span) != 4:
raise ValueError("More bounds provided in `span` than subplots!")
for i, _ in enumerate(span):
try:
iter(span[i])
if len(span[i]) != 2:
raise ValueError('Incorrect span value')
except TypeError:
span[i] = (max(data[i]) * span[i], max(data[i]))
if lnz_error and no_span:
if logplot:
# Same lower bound as in ultranest:
# https://github.com/JohannesBuchner/UltraNest/blob/master/ultranest/plot.py#L139.
zspan = (logz[-1] - 10.3 * 3. * logzerr[-1],
logz[-1] + 1.3 * 3. * logzerr[-1])
else:
zspan = (0., 1.05 * np.exp(logz[-1] + 3. * logzerr[-1]))
span[3] = zspan
# Setting up default plot layout.
had_fig = fig or False
fig, axes = _make_subplots(fig, 4, 1, 16, 16)
axes = axes.flatten()
xspan = [ax.get_xlim() for ax in axes]
if had_fig:
yspan = [ax.get_ylim() for ax in axes]
else:
yspan = span
# One exception: if the bounds are the plotting default `(0., 1.)`,
# overwrite them.
xspan = [t if t != (0., 1.) else (0., -min(logvol)) for t in xspan]
yspan = [t if t != (0., 1.) else (None, None) for t in yspan]
# Set up bounds for plotting.
for i in range(4):
if xspan[i][0] is None:
xmin = None
else:
xmin = min(0., xspan[i][0])
if xspan[i][1] is None:
xmax = -min(logvol)
else:
xmax = max(-min(logvol), xspan[i][1])
if yspan[i][0] is None:
ymin = None
else:
ymin = min(span[i][0], yspan[i][0])
if yspan[i][1] is None:
ymax = span[i][1]
else:
ymax = max(span[i][1], yspan[i][1])
axes[i].set_xlim([xmin, xmax])
axes[i].set_ylim([ymin, ymax])
# Plotting.
labels = [
'Live Points', 'Likelihood\n(normalized)', 'Importance\nWeight',
'log(Evidence)' if logplot else 'Evidence'
]
if kde:
labels[2] += ' PDF'
for i, d in enumerate(data):
# Establish axes.
ax = axes[i]
# Set color(s)/colormap(s).
if isinstance(color, str_type):
c = color
else:
c = color[i]
# Setup axes.
if max_x_ticks == 0:
ax.xaxis.set_major_locator(NullLocator())
else:
ax.xaxis.set_major_locator(MaxNLocator(max_x_ticks))
if max_y_ticks == 0:
ax.yaxis.set_major_locator(NullLocator())
else:
ax.yaxis.set_major_locator(MaxNLocator(max_y_ticks))
# Label axes.
sf = ScalarFormatter(useMathText=use_math_text)
ax.yaxis.set_major_formatter(sf)
ax.set_xlabel(r"$-\ln X$", **label_kwargs)
ax.set_ylabel(labels[i], **label_kwargs)
# Plot run.
if logplot and i == 3:
ax.plot(-logvol, d, color=c, **plot_kwargs)
yspan = [ax.get_ylim() for _ax in axes]
elif kde and i == 2:
ax.plot(-logvol_new, d, color=c, **plot_kwargs)
else:
ax.plot(-logvol, d, color=c, **plot_kwargs)
if i == 3 and lnz_error:
if logplot:
# Same mask as in ultranest:
# https://github.com/JohannesBuchner/UltraNest/blob/master/ultranest/plot.py#L139
mask = logz >= ax.get_ylim()[0] - 10
for s in range(1, 4):
ax.fill_between(-logvol[mask], (logz + s * logzerr)[mask],
(logz - s * logzerr)[mask],
color=c,
alpha=0.2)
else:
for s in range(1, 4):
ax.fill_between(-logvol,
np.exp(logz + s * logzerr),
np.exp(logz - s * logzerr),
color=c,
alpha=0.2)
# Mark addition of final live points.
if mark_final_live:
ax.axvline(-logvol[live_idx],
color=c,
ls="dashed",
lw=2,
**plot_kwargs)
if i == 0:
ax.axhline(live_idx, color=c, ls="dashed", lw=2, **plot_kwargs)
# Add truth value(s).
if i == 3 and lnz_truth is not None:
if logplot:
ax.axhline(lnz_truth, color=truth_color, **truth_kwargs)
else:
ax.axhline(np.exp(lnz_truth),
color=truth_color,
**truth_kwargs)
return fig, axes
def traceplot(results,
span=None,
quantiles=(0.025, 0.5, 0.975),
smooth=0.02,
thin=1,
dims=None,
post_color='blue',
post_kwargs=None,
kde=True,
nkde=1000,
trace_cmap='plasma',
trace_color=None,
trace_kwargs=None,
connect=False,
connect_highlight=10,
connect_color='red',
connect_kwargs=None,
max_n_ticks=5,
use_math_text=False,
labels=None,
label_kwargs=None,
show_titles=False,
title_quantiles=(0.025, 0.5, 0.975),
title_fmt=".2f",
title_kwargs=None,
truths=None,
truth_color='red',
truth_kwargs=None,
verbose=False,
fig=None):
"""
Plot traces and marginalized posteriors for each parameter.
Parameters
----------
results : :class:`~dynesty.results.Results` instance
A :class:`~dynesty.results.Results` instance from a nested
sampling run. **Compatible with results derived from**
`nestle `_.
span : iterable with shape (ndim,), optional
A list where each element is either a length-2 tuple containing
lower and upper bounds or a float from `(0., 1.]` giving the
fraction of (weighted) samples to include. If a fraction is provided,
the bounds are chosen to be equal-tailed. An example would be::
span = [(0., 10.), 0.95, (5., 6.)]
Default is `0.999999426697` (5-sigma credible interval) for each
parameter.
quantiles : iterable, optional
A list of fractional quantiles to overplot on the 1-D marginalized
posteriors as vertical dashed lines. Default is `[0.025, 0.5, 0.975]`
(the 95%/2-sigma credible interval).
smooth : float or iterable with shape (ndim,), optional
The standard deviation (either a single value or a different value for
each subplot) for the Gaussian kernel used to smooth the 1-D
marginalized posteriors, expressed as a fraction of the span.
Default is `0.02` (2% smoothing). If an integer is provided instead,
this will instead default to a simple (weighted) histogram with
`bins=smooth`.
thin : int, optional
Thin the samples so that only each `thin`-th sample is plotted.
Default is `1` (no thinning).
dims : iterable of shape (ndim,), optional
The subset of dimensions that should be plotted. If not provided,
all dimensions will be shown.
post_color : str or iterable with shape (ndim,), optional
A `~matplotlib`-style color (either a single color or a different
value for each subplot) used when plotting the histograms.
Default is `'blue'`.
post_kwargs : dict, optional
Extra keyword arguments that will be used for plotting the
marginalized 1-D posteriors.
kde : bool, optional
Whether to use kernel density estimation to estimate and plot
the PDF of the importance weights as a function of log-volume
(as opposed to the importance weights themselves). Default is
`True`.
nkde : int, optional
The number of grid points used when plotting the kernel density
estimate. Default is `1000`.
trace_cmap : str or iterable with shape (ndim,), optional
A `~matplotlib`-style colormap (either a single colormap or a
different colormap for each subplot) used when plotting the traces,
where each point is colored according to its weight. Default is
`'plasma'`.
trace_color : str or iterable with shape (ndim,), optional
A `~matplotlib`-style color (either a single color or a
different color for each subplot) used when plotting the traces.
This overrides the `trace_cmap` option by giving all points
the same color. Default is `None` (not used).
trace_kwargs : dict, optional
Extra keyword arguments that will be used for plotting the traces.
connect : bool, optional
Whether to draw lines connecting the paths of unique particles.
Default is `False`.
connect_highlight : int or iterable, optional
If `connect=True`, highlights the paths of a specific set of
particles. If an integer is passed, :data:`connect_highlight`
random particle paths will be highlighted. If an iterable is passed,
then the particle paths corresponding to the provided indices
will be highlighted.
connect_color : str, optional
The color of the highlighted particle paths. Default is `'red'`.
connect_kwargs : dict, optional
Extra keyword arguments used for plotting particle paths.
max_n_ticks : int, optional
Maximum number of ticks allowed. Default is `5`.
use_math_text : bool, optional
Whether the axis tick labels for very large/small exponents should be
displayed as powers of 10 rather than using `e`. Default is `False`.
labels : iterable with shape (ndim,), optional
A list of names for each parameter. If not provided, the default name
used when plotting will follow :math:`x_i` style.
label_kwargs : dict, optional
Extra keyword arguments that will be sent to the
`~matplotlib.axes.Axes.set_xlabel` and
`~matplotlib.axes.Axes.set_ylabel` methods.
show_titles : bool, optional
Whether to display a title above each 1-D marginalized posterior
showing the 0.5 quantile along with the upper/lower bounds associated
with the 0.025 and 0.975 (95%/2-sigma credible interval) quantiles.
Default is `False`.
title_quantiles : iterable, optional
A list of fractional quantiles to use in the title. Default is
`[0.025, 0.5, 0.975]` (median plus 95%/2-sigma credible interval).
title_fmt : str, optional
The format string for the quantiles provided in the title. Default is
`'.2f'`.
title_kwargs : dict, optional
Extra keyword arguments that will be sent to the
`~matplotlib.axes.Axes.set_title` command.
truths : iterable with shape (ndim,), optional
A list of reference values that will be overplotted on the traces and
marginalized 1-D posteriors as solid horizontal/vertical lines.
Individual values can be exempt using `None`. Default is `None`.
truth_color : str or iterable with shape (ndim,), optional
A `~matplotlib`-style color (either a single color or a different
value for each subplot) used when plotting `truths`.
Default is `'red'`.
truth_kwargs : dict, optional
Extra keyword arguments that will be used for plotting the vertical
and horizontal lines with `truths`.
verbose : bool, optional
Whether to print the values of the computed quantiles associated with
each parameter. Default is `False`.
fig : (`~matplotlib.figure.Figure`, `~matplotlib.axes.Axes`), optional
If provided, overplot the traces and marginalized 1-D posteriors
onto the provided figure. Otherwise, by default an
internal figure is generated.
Returns
-------
traceplot : (`~matplotlib.figure.Figure`, `~matplotlib.axes.Axes`)
Output trace plot.
"""
# Initialize values.
if title_kwargs is None:
title_kwargs = {}
if label_kwargs is None:
label_kwargs = {}
if trace_kwargs is None:
trace_kwargs = {}
if connect_kwargs is None:
connect_kwargs = {}
if post_kwargs is None:
post_kwargs = {}
if truth_kwargs is None:
truth_kwargs = {}
# Set defaults.
rstate = get_random_generator()
connect_kwargs['alpha'] = connect_kwargs.get('alpha', 0.7)
post_kwargs['alpha'] = post_kwargs.get('alpha', 0.6)
trace_kwargs['s'] = trace_kwargs.get('s', 3)
trace_kwargs['edgecolor'] = trace_kwargs.get('edgecolor', None)
trace_kwargs['edgecolors'] = trace_kwargs.get('edgecolors', None)
truth_kwargs['linestyle'] = truth_kwargs.get('linestyle', 'solid')
truth_kwargs['linewidth'] = truth_kwargs.get('linewidth', 2)
rstate = get_random_generator()
# Extract weighted samples.
samples = results['samples']
logvol = results['logvol']
weights = results.importance_weights()
if kde:
# Derive kernel density estimate.
wt_kde = gaussian_kde(resample_equal(-logvol, weights,
rstate=rstate)) # KDE
logvol_grid = np.linspace(logvol[0], logvol[-1], nkde) # resample
wt_grid = wt_kde.pdf(-logvol_grid) # evaluate KDE PDF
wts = np.interp(-logvol, -logvol_grid, wt_grid) # interpolate
else:
wts = weights
# Deal with 1D results. A number of extra catches are also here
# in case users are trying to plot other results besides the `Results`
# instance generated by `dynesty`.
samples = np.atleast_1d(samples)
if len(samples.shape) == 1:
samples = np.atleast_2d(samples)
else:
assert len(samples.shape) == 2, "Samples must be 1- or 2-D."
samples = samples.T
assert samples.shape[0] <= samples.shape[1], "There are more " \
"dimensions than samples!"
# Slice samples based on provided `dims`.
if dims is not None:
samples = samples[dims]
ndim, nsamps = samples.shape
# Check weights.
if weights.ndim != 1:
raise ValueError("Weights must be 1-D.")
if nsamps != weights.shape[0]:
raise ValueError("The number of weights and samples disagree!")
# Check ln(volume).
if logvol.ndim != 1:
raise ValueError("Ln(volume)'s must be 1-D.")
if nsamps != logvol.shape[0]:
raise ValueError("The number of ln(volume)'s and samples disagree!")
# Check sample IDs.
if connect:
if 'samples_id' in results.keys():
samples_id = results['samples_id']
uid = np.unique(samples_id)
else:
raise ValueError("Sample IDs are not defined!")
try:
ids = connect_highlight[0]
ids = connect_highlight
except:
ids = rstate.choice(uid, size=connect_highlight, replace=False)
# Determine plotting bounds for marginalized 1-D posteriors.
if span is None:
span = [0.999999426697 for i in range(ndim)]
span = list(span)
if len(span) != ndim:
raise ValueError("Dimension mismatch between samples and span.")
check_span(span, samples, weights)
# Setting up labels.
if labels is None:
labels = [r"$x_{" + str(i + 1) + "}$" for i in range(ndim)]
# Setting up smoothing.
if isinstance(smooth, (int_type, float_type)):
smooth = [smooth for i in range(ndim)]
# Setting up default plot layout.
fig, axes = _make_subplots(fig, ndim, 2, 12, 3 * ndim)
# Plotting.
for i, x in enumerate(samples):
# Plot trace.
# Establish axes.
ax = axes[i, 0]
# Set color(s)/colormap(s).
if trace_color is not None:
if isinstance(trace_color, str_type):
color = trace_color
else:
color = trace_color[i]
else:
color = wts[::thin]
if isinstance(trace_cmap, str_type):
cmap = trace_cmap
else:
cmap = trace_cmap[i]
# Setup axes.
ax.set_xlim([0., -min(logvol)])
ax.set_ylim([min(x), max(x)])
if max_n_ticks == 0:
ax.xaxis.set_major_locator(NullLocator())
ax.yaxis.set_major_locator(NullLocator())
else:
ax.xaxis.set_major_locator(MaxNLocator(max_n_ticks))
ax.yaxis.set_major_locator(MaxNLocator(max_n_ticks))
# Label axes.
sf = ScalarFormatter(useMathText=use_math_text)
ax.yaxis.set_major_formatter(sf)
ax.set_xlabel(r"$-\ln X$", **label_kwargs)
ax.set_ylabel(labels[i], **label_kwargs)
# Generate scatter plot.
ax.scatter(-logvol[::thin],
x[::thin],
c=color,
cmap=cmap,
**trace_kwargs)
if connect:
# Add lines highlighting specific particle paths.
for j in ids:
sel = (samples_id[::thin] == j)
ax.plot(-logvol[::thin][sel],
x[::thin][sel],
color=connect_color,
**connect_kwargs)
# Add truth value(s).
if truths is not None:
plot_thruth(ax,
truths[i],
truth_color,
truth_kwargs,
horizontal=True)
# Plot marginalized 1-D posterior.
ax = axes[i, 1]
# Set color(s).
if isinstance(post_color, str_type):
color = post_color
else:
color = post_color[i]
# Setup axes
ax.set_xlim(span[i])
if max_n_ticks == 0:
ax.xaxis.set_major_locator(NullLocator())
ax.yaxis.set_major_locator(NullLocator())
else:
ax.xaxis.set_major_locator(MaxNLocator(max_n_ticks))
ax.yaxis.set_major_locator(NullLocator())
# Label axes.
sf = ScalarFormatter(useMathText=use_math_text)
ax.xaxis.set_major_formatter(sf)
ax.set_xlabel(labels[i], **label_kwargs)
# Generate distribution.
s = smooth[i]
if isinstance(s, int_type):
# If `s` is an integer, plot a weighted histogram with
# `s` bins within the provided bounds.
n, b, _ = ax.hist(x,
bins=s,
weights=weights,
color=color,
range=np.sort(span[i]),
**post_kwargs)
x0 = np.array(list(zip(b[:-1], b[1:]))).flatten()
y0 = np.array(list(zip(n, n))).flatten()
else:
# If `s` is a float, oversample the data relative to the
# smoothing filter by a factor of 10, then use a Gaussian
# filter to smooth the results.
bins = int(round(10. / s))
n, b = np.histogram(x,
bins=bins,
weights=weights,
range=np.sort(span[i]))
n = norm_kde(n, 10.)
x0 = 0.5 * (b[1:] + b[:-1])
y0 = n
ax.fill_between(x0, y0, color=color, **post_kwargs)
ax.set_ylim([0., max(y0) * 1.05])
# Plot quantiles.
if quantiles is not None and len(quantiles) > 0:
qs = _quantile(x, quantiles, weights=weights)
for q in qs:
ax.axvline(q, lw=2, ls="dashed", color=color)
if verbose:
print("Quantiles:")
print(labels[i], list(zip(quantiles, qs)))
# Add truth value(s).
if truths is not None:
plot_thruth(ax,
truths[i],
truth_color,
truth_kwargs,
vertical=True)
# Set titles.
if show_titles:
title = None
if title_fmt is not None:
ql, qm, qh = _quantile(x, title_quantiles, weights=weights)
q_minus, q_plus = qm - ql, qh - qm
fmt = "{{0:{0}}}".format(title_fmt).format
title = r"${{{0}}}_{{-{1}}}^{{+{2}}}$"
title = title.format(fmt(qm), fmt(q_minus), fmt(q_plus))
title = "{0} = {1}".format(labels[i], title)
ax.set_title(title, **title_kwargs)
return fig, axes
def cornerpoints(results,
dims=None,
thin=1,
span=None,
cmap='plasma',
color=None,
kde=True,
nkde=1000,
plot_kwargs=None,
labels=None,
label_kwargs=None,
truths=None,
truth_color='red',
truth_kwargs=None,
max_n_ticks=5,
use_math_text=False,
fig=None):
"""
Generate a (sub-)corner plot of (weighted) samples.
Parameters
----------
results : :class:`~dynesty.results.Results` instance
A :class:`~dynesty.results.Results` instance from a nested
sampling run. **Compatible with results derived from**
`nestle `_.
dims : iterable of shape (ndim,), optional
The subset of dimensions that should be plotted. If not provided,
all dimensions will be shown.
thin : int, optional
Thin the samples so that only each `thin`-th sample is plotted.
Default is `1` (no thinning).
span : iterable with shape (ndim,), optional
A list where each element is either a length-2 tuple containing
lower and upper bounds or a float from `(0., 1.]` giving the
fraction of (weighted) samples to include. If a fraction is provided,
the bounds are chosen to be equal-tailed. An example would be::
span = [(0., 10.), 0.95, (5., 6.)]
Default is `1.` for all parameters (no bound).
cmap : str, optional
A `~matplotlib`-style colormap used when plotting the points,
where each point is colored according to its weight. Default is
`'plasma'`.
color : str, optional
A `~matplotlib`-style color used when plotting the points.
This overrides the `cmap` option by giving all points
the same color. Default is `None` (not used).
kde : bool, optional
Whether to use kernel density estimation to estimate and plot
the PDF of the importance weights as a function of log-volume
(as opposed to the importance weights themselves). Default is
`True`.
nkde : int, optional
The number of grid points used when plotting the kernel density
estimate. Default is `1000`.
plot_kwargs : dict, optional
Extra keyword arguments that will be used for plotting the points.
labels : iterable with shape (ndim,), optional
A list of names for each parameter. If not provided, the default name
used when plotting will follow :math:`x_i` style.
label_kwargs : dict, optional
Extra keyword arguments that will be sent to the
`~matplotlib.axes.Axes.set_xlabel` and
`~matplotlib.axes.Axes.set_ylabel` methods.
truths : iterable with shape (ndim,), optional
A list of reference values that will be overplotted on the traces and
marginalized 1-D posteriors as solid horizontal/vertical lines.
Individual values can be exempt using `None`. Default is `None`.
truth_color : str or iterable with shape (ndim,), optional
A `~matplotlib`-style color (either a single color or a different
value for each subplot) used when plotting `truths`.
Default is `'red'`.
truth_kwargs : dict, optional
Extra keyword arguments that will be used for plotting the vertical
and horizontal lines with `truths`.
max_n_ticks : int, optional
Maximum number of ticks allowed. Default is `5`.
use_math_text : bool, optional
Whether the axis tick labels for very large/small exponents should be
displayed as powers of 10 rather than using `e`. Default is `False`.
fig : (`~matplotlib.figure.Figure`, `~matplotlib.axes.Axes`), optional
If provided, overplot the points onto the provided figure object.
Otherwise, by default an internal figure is generated.
Returns
-------
cornerpoints : (`~matplotlib.figure.Figure`, `~matplotlib.axes.Axes`)
Output (sub-)corner plot of (weighted) samples.
"""
# Initialize values.
if truth_kwargs is None:
truth_kwargs = {}
if label_kwargs is None:
label_kwargs = {}
if plot_kwargs is None:
plot_kwargs = {}
# Set defaults.
plot_kwargs['s'] = plot_kwargs.get('s', 1)
plot_kwargs['edgecolor'] = plot_kwargs.get('edgecolor', None)
plot_kwargs['edgecolors'] = plot_kwargs.get('edgecolors', None)
truth_kwargs['linestyle'] = truth_kwargs.get('linestyle', 'solid')
truth_kwargs['linewidth'] = truth_kwargs.get('linewidth', 2)
truth_kwargs['alpha'] = truth_kwargs.get('alpha', 0.7)
# Extract weighted samples.
samples = results['samples']
logvol = results['logvol']
weights = results.importance_weights()
if kde:
# Derive kernel density estimate.
wt_kde = gaussian_kde(resample_equal(-logvol, weights)) # KDE
logvol_grid = np.linspace(logvol[0], logvol[-1], nkde) # resample
wt_grid = wt_kde.pdf(-logvol_grid) # evaluate KDE PDF
weights = np.interp(-logvol, -logvol_grid, wt_grid) # interpolate
# Deal with 1D results. A number of extra catches are also here
# in case users are trying to plot other results besides the `Results`
# instance generated by `dynesty`.
samples = np.atleast_1d(samples)
if len(samples.shape) == 1:
samples = np.atleast_2d(samples)
else:
assert len(samples.shape) == 2, "Samples must be 1- or 2-D."
samples = samples.T
assert samples.shape[0] <= samples.shape[1], "There are more " \
"dimensions than samples!"
# Slice samples based on provided `dims`.
if dims is not None:
samples = samples[dims]
ndim, nsamps = samples.shape
# Check weights.
if weights.ndim != 1:
raise ValueError("Weights must be 1-D.")
if nsamps != weights.shape[0]:
raise ValueError("The number of weights and samples disagree!")
if ndim == 1:
raise ValueError("cornerpoints does not make sense for 1-D posterior")
# Determine plotting bounds.
if span is not None:
if len(span) != ndim:
raise ValueError("Dimension mismatch between samples and span.")
check_span(span, samples, weights)
# Set labels
if labels is None:
labels = [r"$x_{" + str(i + 1) + "}$" for i in range(ndim)]
# Set colormap.
if color is None:
color = weights
# Setup axis layout (from `corner.py`).
factor = 2.0 # size of side of one panel
lbdim = 0.5 * factor # size of left/bottom margin
trdim = 0.2 * factor # size of top/right margin
whspace = 0.05 # size of width/height margin
plotdim = factor * (ndim - 1.) + factor * (ndim - 2.) * whspace
dim = lbdim + plotdim + trdim # total size
# Initialize figure.
fig, axes = _make_subplots(fig, ndim - 1, ndim - 1, dim, dim)
# Format figure.
lb = lbdim / dim
tr = (lbdim + plotdim) / dim
fig.subplots_adjust(left=lb,
bottom=lb,
right=tr,
top=tr,
wspace=whspace,
hspace=whspace)
# Plot the 2-D projected samples.
for i, x in enumerate(samples[1:]):
for j, y in enumerate(samples[:-1]):
try:
ax = axes[i, j]
except:
ax = axes
# Setup axes.
if span is not None:
ax.set_xlim(span[j])
ax.set_ylim(span[i])
if j > i:
ax.set_frame_on(False)
ax.set_xticks([])
ax.set_yticks([])
continue
if max_n_ticks == 0:
ax.xaxis.set_major_locator(NullLocator())
ax.yaxis.set_major_locator(NullLocator())
else:
ax.xaxis.set_major_locator(
MaxNLocator(max_n_ticks, prune="lower"))
ax.yaxis.set_major_locator(
MaxNLocator(max_n_ticks, prune="lower"))
# Label axes.
sf = ScalarFormatter(useMathText=use_math_text)
ax.xaxis.set_major_formatter(sf)
ax.yaxis.set_major_formatter(sf)
if i < ndim - 2:
ax.set_xticklabels([])
else:
rotate_ticks(ax, 'x')
ax.set_xlabel(labels[j], **label_kwargs)
ax.xaxis.set_label_coords(0.5, -0.3)
if j > 0:
ax.set_yticklabels([])
else:
rotate_ticks(ax, 'y')
ax.set_ylabel(labels[i + 1], **label_kwargs)
ax.yaxis.set_label_coords(-0.3, 0.5)
# Plot distribution.
in_bounds = np.ones_like(y).astype('bool')
if span is not None and span[i] is not None:
in_bounds *= ((x >= span[i][0]) & (x <= span[i][1]))
if span is not None and span[j] is not None:
in_bounds *= ((y >= span[j][0]) & (y <= span[j][1]))
if isinstance(color, str):
cur_color = color
else:
cur_color = color[in_bounds][::thin]
ax.scatter(y[in_bounds][::thin],
x[in_bounds][::thin],
c=cur_color,
cmap=cmap,
**plot_kwargs)
# Add truth values
if truths is not None:
plot_thruth(ax,
truths[j],
truth_color,
truth_kwargs,
vertical=True)
plot_thruth(ax,
truths[i + 1],
truth_color,
truth_kwargs,
horizontal=True)
return (fig, axes)
def cornerplot(results,
dims=None,
span=None,
quantiles=(0.025, 0.5, 0.975),
color='black',
smooth=0.02,
quantiles_2d=None,
hist_kwargs=None,
hist2d_kwargs=None,
labels=None,
label_kwargs=None,
show_titles=False,
title_quantiles=(0.025, 0.5, 0.975),
title_fmt=".2f",
title_kwargs=None,
truths=None,
truth_color='red',
truth_kwargs=None,
max_n_ticks=5,
top_ticks=False,
use_math_text=False,
verbose=False,
fig=None):
"""
Generate a corner plot of the 1-D and 2-D marginalized posteriors.
Parameters
----------
results : :class:`~dynesty.results.Results` instance
A :class:`~dynesty.results.Results` instance from a nested
sampling run. **Compatible with results derived from**
`nestle `_.
dims : iterable of shape (ndim,), optional
The subset of dimensions that should be plotted. If not provided,
all dimensions will be shown.
span : iterable with shape (ndim,), optional
A list where each element is either a length-2 tuple containing
lower and upper bounds or a float from `(0., 1.]` giving the
fraction of (weighted) samples to include. If a fraction is provided,
the bounds are chosen to be equal-tailed. An example would be::
span = [(0., 10.), 0.95, (5., 6.)]
Default is `0.999999426697` (5-sigma credible interval).
quantiles : iterable, optional
A list of fractional quantiles to overplot on the 1-D marginalized
posteriors as vertical dashed lines. Default is `[0.025, 0.5, 0.975]`
(spanning the 95%/2-sigma credible interval).
color : str or iterable with shape (ndim,), optional
A `~matplotlib`-style color (either a single color or a different
value for each subplot) used when plotting the histograms.
Default is `'black'`.
smooth : float or iterable with shape (ndim,), optional
The standard deviation (either a single value or a different value for
each subplot) for the Gaussian kernel used to smooth the 1-D and 2-D
marginalized posteriors, expressed as a fraction of the span.
Default is `0.02` (2% smoothing). If an integer is provided instead,
this will instead default to a simple (weighted) histogram with
`bins=smooth`.
quantiles_2d : iterable with shape (nquant,), optional
The quantiles used for plotting the smoothed 2-D distributions.
If not provided, these default to 0.5, 1, 1.5, and 2-sigma contours
roughly corresponding to quantiles of `[0.1, 0.4, 0.65, 0.85]`.
hist_kwargs : dict, optional
Extra keyword arguments to send to the 1-D (smoothed) histograms.
hist2d_kwargs : dict, optional
Extra keyword arguments to send to the 2-D (smoothed) histograms.
labels : iterable with shape (ndim,), optional
A list of names for each parameter. If not provided, the default name
used when plotting will follow :math:`x_i` style.
label_kwargs : dict, optional
Extra keyword arguments that will be sent to the
`~matplotlib.axes.Axes.set_xlabel` and
`~matplotlib.axes.Axes.set_ylabel` methods.
show_titles : bool, optional
Whether to display a title above each 1-D marginalized posterior
showing the 0.5 quantile along with the upper/lower bounds associated
with the 0.025 and 0.975 (95%/2-sigma credible interval) quantiles.
Default is `False`.
title_quantiles : iterable, optional
A list of fractional quantiles to use in the title. Default is
`[0.025, 0.5, 0.975]` (median plus 95%/2-sigma credible interval).
title_fmt : str, optional
The format string for the quantiles provided in the title. Default is
`'.2f'`.
title_kwargs : dict, optional
Extra keyword arguments that will be sent to the
`~matplotlib.axes.Axes.set_title` command.
truths : iterable with shape (ndim,), optional
A list of reference values that will be overplotted on the traces and
marginalized 1-D posteriors as solid horizontal/vertical lines.
Individual values can be exempt using `None`. Default is `None`.
truth_color : str or iterable with shape (ndim,), optional
A `~matplotlib`-style color (either a single color or a different
value for each subplot) used when plotting `truths`.
Default is `'red'`.
truth_kwargs : dict, optional
Extra keyword arguments that will be used for plotting the vertical
and horizontal lines with `truths`.
max_n_ticks : int, optional
Maximum number of ticks allowed. Default is `5`.
top_ticks : bool, optional
Whether to label the top (rather than bottom) ticks. Default is
`False`.
use_math_text : bool, optional
Whether the axis tick labels for very large/small exponents should be
displayed as powers of 10 rather than using `e`. Default is `False`.
verbose : bool, optional
Whether to print the values of the computed quantiles associated with
each parameter. Default is `False`.
fig : (`~matplotlib.figure.Figure`, `~matplotlib.axes.Axes`), optional
If provided, overplot the traces and marginalized 1-D posteriors
onto the provided figure. Otherwise, by default an
internal figure is generated.
Returns
-------
cornerplot : (`~matplotlib.figure.Figure`, `~matplotlib.axes.Axes`)
Output corner plot.
"""
# Initialize values.
if quantiles is None:
quantiles = []
if truth_kwargs is None:
truth_kwargs = {}
if label_kwargs is None:
label_kwargs = {}
if title_kwargs is None:
title_kwargs = {}
if hist_kwargs is None:
hist_kwargs = {}
if hist2d_kwargs is None:
hist2d_kwargs = {}
# Set defaults.
hist_kwargs['alpha'] = hist_kwargs.get('alpha', 0.6)
hist2d_kwargs['levels'] = hist2d_kwargs.get('levels', quantiles_2d)
truth_kwargs['linestyle'] = truth_kwargs.get('linestyle', 'solid')
truth_kwargs['linewidth'] = truth_kwargs.get('linewidth', 2)
truth_kwargs['alpha'] = truth_kwargs.get('alpha', 0.7)
# Extract weighted samples.
samples = results['samples']
weights = results.importance_weights()
# Deal with 1D results. A number of extra catches are also here
# in case users are trying to plot other results besides the `Results`
# instance generated by `dynesty`.
samples = np.atleast_1d(samples)
if len(samples.shape) == 1:
samples = np.atleast_2d(samples)
else:
assert len(samples.shape) == 2, "Samples must be 1- or 2-D."
samples = samples.T
assert samples.shape[0] <= samples.shape[1], "There are more " \
"dimensions than samples!"
# Slice samples based on provided `dims`.
if dims is not None:
samples = samples[dims]
ndim, nsamps = samples.shape
# Check weights.
if weights.ndim != 1:
raise ValueError("Weights must be 1-D.")
if nsamps != weights.shape[0]:
raise ValueError("The number of weights and samples disagree!")
# Determine plotting bounds.
if span is None:
span = [0.999999426697 for i in range(ndim)]
span = list(span)
if len(span) != ndim:
raise ValueError("Dimension mismatch between samples and span.")
check_span(span, samples, weights)
# Set labels
if labels is None:
labels = [r"$x_{" + str(i + 1) + "}$" for i in range(ndim)]
# Setting up smoothing.
if isinstance(smooth, (int_type, float_type)):
smooth = [smooth for i in range(ndim)]
# Setup axis layout (from `corner.py`).
factor = 2.0 # size of side of one panel
lbdim = 0.5 * factor # size of left/bottom margin
trdim = 0.2 * factor # size of top/right margin
whspace = 0.05 # size of width/height margin
plotdim = factor * ndim + factor * (ndim - 1.) * whspace # plot size
dim = lbdim + plotdim + trdim # total size
# Initialize figure.
fig, axes = _make_subplots(fig, ndim, ndim, dim, dim)
# Format figure.
lb = lbdim / dim
tr = (lbdim + plotdim) / dim
fig.subplots_adjust(left=lb,
bottom=lb,
right=tr,
top=tr,
wspace=whspace,
hspace=whspace)
# Plotting.
for i, x in enumerate(samples):
ax = axes[i, i]
# Plot the 1-D marginalized posteriors.
# Setup axes
ax.set_xlim(span[i])
if max_n_ticks == 0:
ax.xaxis.set_major_locator(NullLocator())
ax.yaxis.set_major_locator(NullLocator())
else:
ax.xaxis.set_major_locator(MaxNLocator(max_n_ticks, prune="lower"))
ax.yaxis.set_major_locator(NullLocator())
# Label axes.
sf = ScalarFormatter(useMathText=use_math_text)
ax.xaxis.set_major_formatter(sf)
if i < ndim - 1:
if top_ticks:
ax.xaxis.set_ticks_position("top")
rotate_ticks(ax, 'x')
else:
ax.set_xticklabels([])
else:
rotate_ticks(ax, 'x')
ax.set_xlabel(labels[i], **label_kwargs)
ax.xaxis.set_label_coords(0.5, -0.3)
# Generate distribution.
sx = smooth[i]
if isinstance(sx, int_type):
# If `sx` is an integer, plot a weighted histogram with
# `sx` bins within the provided bounds.
n, b, _ = ax.hist(x,
bins=sx,
weights=weights,
color=color,
range=np.sort(span[i]),
**hist_kwargs)
else:
# If `sx` is a float, oversample the data relative to the
# smoothing filter by a factor of 10, then use a Gaussian
# filter to smooth the results.
bins = int(round(10. / sx))
n, b = np.histogram(x,
bins=bins,
weights=weights,
range=np.sort(span[i]))
n = norm_kde(n, 10.)
b0 = 0.5 * (b[1:] + b[:-1])
n, b, _ = ax.hist(b0,
bins=b,
weights=n,
range=np.sort(span[i]),
color=color,
**hist_kwargs)
ax.set_ylim([0., max(n) * 1.05])
# Plot quantiles.
if quantiles is not None and len(quantiles) > 0:
qs = _quantile(x, quantiles, weights=weights)
for q in qs:
ax.axvline(q, lw=2, ls="dashed", color=color)
if verbose:
print("Quantiles:")
print(labels[i], list(zip(quantiles, qs)))
# Add truth value(s).
if truths is not None:
plot_thruth(ax,
truths[i],
truth_color,
truth_kwargs,
vertical=True)
# Set titles.
if show_titles:
title = None
if title_fmt is not None:
ql, qm, qh = _quantile(x, title_quantiles, weights=weights)
q_minus, q_plus = qm - ql, qh - qm
fmt = "{{0:{0}}}".format(title_fmt).format
title = r"${{{0}}}_{{-{1}}}^{{+{2}}}$"
title = title.format(fmt(qm), fmt(q_minus), fmt(q_plus))
title = "{0} = {1}".format(labels[i], title)
ax.set_title(title, **title_kwargs)
for j, y in enumerate(samples):
if np.shape(samples)[0] == 1:
ax = axes
else:
ax = axes[i, j]
# Plot the 2-D marginalized posteriors.
# Setup axes.
if j > i:
ax.set_frame_on(False)
ax.set_xticks([])
ax.set_yticks([])
continue
elif j == i:
continue
if max_n_ticks == 0:
ax.xaxis.set_major_locator(NullLocator())
ax.yaxis.set_major_locator(NullLocator())
else:
ax.xaxis.set_major_locator(
MaxNLocator(max_n_ticks, prune="lower"))
ax.yaxis.set_major_locator(
MaxNLocator(max_n_ticks, prune="lower"))
# Label axes.
sf = ScalarFormatter(useMathText=use_math_text)
ax.xaxis.set_major_formatter(sf)
ax.yaxis.set_major_formatter(sf)
if i < ndim - 1:
ax.set_xticklabels([])
else:
rotate_ticks(ax, 'x')
ax.set_xlabel(labels[j], **label_kwargs)
ax.xaxis.set_label_coords(0.5, -0.3)
if j > 0:
ax.set_yticklabels([])
else:
rotate_ticks(ax, 'y')
ax.set_ylabel(labels[i], **label_kwargs)
ax.yaxis.set_label_coords(-0.3, 0.5)
# Generate distribution.
sy = smooth[j]
check_ix = isinstance(sx, int_type)
check_iy = isinstance(sy, int_type)
if check_ix and check_iy:
fill_contours = False
plot_contours = False
else:
fill_contours = True
plot_contours = True
hist2d_kwargs['fill_contours'] = hist2d_kwargs.get(
'fill_contours', fill_contours)
hist2d_kwargs['plot_contours'] = hist2d_kwargs.get(
'plot_contours', plot_contours)
_hist2d(y,
x,
ax=ax,
span=[span[j], span[i]],
weights=weights,
color=color,
smooth=[sy, sx],
**hist2d_kwargs)
# Add truth values
if truths is not None:
plot_thruth(ax,
truths[j],
truth_color,
truth_kwargs,
vertical=True)
plot_thruth(ax,
truths[i],
truth_color,
truth_kwargs,
horizontal=True)
return (fig, axes)
def boundplot(results,
dims,
it=None,
idx=None,
prior_transform=None,
periodic=None,
reflective=None,
ndraws=5000,
color='gray',
plot_kwargs=None,
labels=None,
label_kwargs=None,
max_n_ticks=5,
use_math_text=False,
show_live=False,
live_color='darkviolet',
live_kwargs=None,
span=None,
fig=None):
"""
Return the bounding distribution used to propose either (1) live points
at a given iteration or (2) a specific dead point during
the course of a run, projected onto the two dimensions specified
by `dims`.
Parameters
----------
results : :class:`~dynesty.results.Results` instance
A :class:`~dynesty.results.Results` instance from a nested
sampling run.
dims : length-2 tuple
The dimensions used to plot the bounding.
it : int, optional
If provided, returns the bounding distribution at the specified
iteration of the nested sampling run. **Note that this option and
`idx` are mutually exclusive.**
idx : int, optional
If provided, returns the bounding distribution used to propose the
dead point at the specified iteration of the nested sampling run.
**Note that this option and `it` are mutually exclusive.**
prior_transform : func, optional
The function transforming samples within the unit cube back to samples
in the native model space. If provided, the transformed bounding
distribution will be plotted in the native model space.
periodic : iterable, optional
A list of indices for parameters with periodic boundary conditions.
These parameters *will not* have their positions constrained to be
within the unit cube, enabling smooth behavior for parameters
that may wrap around the edge. Default is `None` (i.e. no periodic
boundary conditions).
reflective : iterable, optional
A list of indices for parameters with reflective boundary conditions.
These parameters *will not* have their positions constrained to be
within the unit cube, enabling smooth behavior for parameters
that may reflect at the edge. Default is `None` (i.e. no reflective
boundary conditions).
ndraws : int, optional
The number of random samples to draw from the bounding distribution
when plotting. Default is `5000`.
color : str, optional
The color of the points randomly sampled from the bounding
distribution. Default is `'gray'`.
plot_kwargs : dict, optional
Extra keyword arguments used when plotting the bounding draws.
labels : iterable with shape (ndim,), optional
A list of names for each parameter. If not provided, the default name
used when plotting will follow :math:`x_i` style.
label_kwargs : dict, optional
Extra keyword arguments that will be sent to the
`~matplotlib.axes.Axes.set_xlabel` and
`~matplotlib.axes.Axes.set_ylabel` methods.
max_n_ticks : int, optional
Maximum number of ticks allowed. Default is `5`.
use_math_text : bool, optional
Whether the axis tick labels for very large/small exponents should be
displayed as powers of 10 rather than using `e`. Default is `False`.
show_live : bool, optional
Whether the live points at a given iteration (for `it`) or
associated with the bounding (for `idx`) should be highlighted.
Default is `False`. In the dynamic case, only the live points
associated with the batch used to construct the relevant bound
are plotted.
live_color : str, optional
The color of the live points. Default is `'darkviolet'`.
live_kwargs : dict, optional
Extra keyword arguments used when plotting the live points.
span : iterable with shape (2,), optional
A list where each element is a length-2 tuple containing
lower and upper bounds. Default is `None` (no bound).
fig : (`~matplotlib.figure.Figure`, `~matplotlib.axes.Axes`), optional
If provided, overplot the draws onto the provided figure.
Otherwise, by default an internal figure is generated.
Returns
-------
bounding_plot : (`~matplotlib.figure.Figure`, `~matplotlib.axes.Axes`)
Output plot of the bounding distribution.
"""
# Initialize values.
if plot_kwargs is None:
plot_kwargs = {}
if label_kwargs is None:
label_kwargs = {}
if live_kwargs is None:
live_kwargs = {}
# Check that either `idx` or `it` has been specified.
if (it is None and idx is None) or (it is not None and idx is not None):
raise ValueError("You must specify either an iteration or an index!")
# Set defaults.
plot_kwargs['marker'] = plot_kwargs.get('marker', 'o')
plot_kwargs['linestyle'] = plot_kwargs.get('linestyle', 'None')
plot_kwargs['markersize'] = plot_kwargs.get('markersize', 1)
plot_kwargs['alpha'] = plot_kwargs.get('alpha', 0.4)
live_kwargs['marker'] = live_kwargs.get('marker', 'o')
live_kwargs['linestyle'] = live_kwargs.get('linestyle', 'None')
live_kwargs['markersize'] = live_kwargs.get('markersize', 1)
# Extract bounding distributions.
try:
bounds = results['bound']
except KeyError:
raise ValueError("No bounds were saved in the results!")
nsamps = len(results['samples'])
nonbounded = get_nonbounded(bounds[0].n, periodic, reflective)
if it is not None:
if it >= nsamps:
raise ValueError("The iteration requested goes beyond the "
"number of iterations in the run.")
# Extract bound iterations.
try:
bound_iter = np.array(results['bound_iter'])
except KeyError:
raise ValueError("Cannot reconstruct the bound used at the "
"specified iteration since bound "
"iterations were not saved in the results.")
# Find bound at the specified iteration.
if it == 0:
pidx = 0
else:
pidx = bound_iter[it]
else:
if idx >= nsamps:
raise ValueError("The index requested goes beyond the "
"number of samples in the run.")
try:
samples_bound = results['samples_bound']
except KeyError:
raise ValueError("Cannot reconstruct the bound used to "
"compute the specified dead point since "
"sample bound indices were not saved "
"in the results.")
# Grab relevant bound.
pidx = samples_bound[idx]
# Get desired bound.
bound = bounds[pidx]
# Do we want to show the live points at the specified iteration?
# If so, we need to rewind our bound to check.
# (We could also go forward; this is an arbitrary choice.)
if show_live:
try:
# We can only reconstruct the run if the final set of live points
# were added to the results. This is true by default for dynamic
# nested sampling runs but not guaranteeed for standard runs.
nlive = results['nlive']
niter = results['niter']
if nsamps - niter != nlive:
raise ValueError("Cannot reconstruct bound because the "
"final set of live points are not included "
"in the results.")
# Grab our final set of live points (with proper IDs).
samples = results['samples_u']
samples_id = results['samples_id']
ndim = samples.shape[1]
live_u = np.empty((nlive, ndim))
live_u[samples_id[-nlive:]] = samples[-nlive:]
# Find generating bound ID if necessary.
if it is None:
it = results['samples_it'][idx]
# Run our sampling backwards.
for i in range(1, niter - it + 1):
r = -(nlive + i)
uidx = samples_id[r]
live_u[uidx] = samples[r]
except:
# In the dynamic sampling case, we will show the live points used
# during the batch associated with a particular iteration/bound.
batch = results['samples_batch'][it] # select batch
nbatch = results['batch_nlive'][batch] # nlive in the batch
bsel = results['samples_batch'] == batch # select batch
niter_eff = sum(bsel) - nbatch # "effective" iterations in batch
# Grab our final set of live points (with proper IDs).
samples = results['samples_u'][bsel]
samples_id = results['samples_id'][bsel]
samples_id -= min(samples_id) # re-index to start at zero
ndim = samples.shape[1]
live_u = np.empty((nbatch, ndim))
live_u[samples_id[-nbatch:]] = samples[-nbatch:]
# Find generating bound ID if necessary.
if it is None:
it = results['samples_it'][idx]
it_eff = sum(bsel[:it + 1]) # effective iteration in batch
# Run our sampling backwards.
for i in range(1, niter_eff - it_eff + 1):
r = -(nbatch + i)
uidx = samples_id[r]
live_u[uidx] = samples[r]
rstate = get_random_generator()
# Draw samples from the bounding distribution.
if not isinstance(bound, (bounding.RadFriends, bounding.SupFriends)):
# If bound is "fixed", go ahead and draw samples from it.
psamps = bound.samples(ndraws, rstate=rstate)
else:
# If bound is based on the distribution of live points at a
# specific iteration, we need to reconstruct what those were.
if not show_live:
try:
# Only reconstruct the run if we haven't done it already.
nlive = results['nlive']
niter = results['niter']
if nsamps - niter != nlive:
raise ValueError("Cannot reconstruct bound because the "
"final set of live points are not "
"included in the results.")
# Grab our final set of live points (with proper IDs).
samples = results['samples_u']
samples_id = results['samples_id']
ndim = samples.shape[1]
live_u = np.empty((nlive, ndim))
live_u[samples_id[-nlive:]] = samples[-nlive:]
# Run our sampling backwards.
if it is None:
it = results['samples_it'][idx]
for i in range(1, niter - it + 1):
r = -(nlive + i)
uidx = samples_id[r]
live_u[uidx] = samples[r]
except:
raise ValueError("Live point tracking currently not "
"implemented for dynamic sampling results.")
# Draw samples.
psamps = bound.samples(ndraws, live_u, rstate=rstate)
# Projecting samples to input dimensions and possibly
# the native model space.
if prior_transform is None:
x1, x2 = psamps[:, dims].T
if show_live:
l1, l2 = live_u[:, dims].T
else:
# Remove points outside of the unit cube as appropriate.
sel = [unitcheck(point, nonbounded) for point in psamps]
vsamps = np.array(list(map(prior_transform, psamps[sel])))
x1, x2 = vsamps[:, dims].T
if show_live:
lsamps = np.array(list(map(prior_transform, live_u)))
l1, l2 = lsamps[:, dims].T
# Setting up default plot layout.
fig, axes = _make_subplots(fig, 1, 1, 6, 6)
axes = axes[0, 0]
# Plotting.
axes.plot(x1, x2, color=color, zorder=1, **plot_kwargs)
if show_live:
axes.plot(l1, l2, color=live_color, zorder=2, **live_kwargs)
# Setup axes
if span is not None:
axes.set_xlim(span[0])
axes.set_ylim(span[1])
if max_n_ticks == 0:
axes.xaxis.set_major_locator(NullLocator())
axes.yaxis.set_major_locator(NullLocator())
else:
axes.xaxis.set_major_locator(MaxNLocator(max_n_ticks))
axes.yaxis.set_major_locator(MaxNLocator(max_n_ticks))
# Label axes.
sf = ScalarFormatter(useMathText=use_math_text)
axes.xaxis.set_major_formatter(sf)
axes.yaxis.set_major_formatter(sf)
if labels is not None:
axes.set_xlabel(labels[0], **label_kwargs)
axes.set_ylabel(labels[1], **label_kwargs)
else:
axes.set_xlabel(r"$x_{" + str(dims[0] + 1) + "}$", **label_kwargs)
axes.set_ylabel(r"$x_{" + str(dims[1] + 1) + "}$", **label_kwargs)
return fig, axes
def cornerbound(results,
it=None,
idx=None,
dims=None,
prior_transform=None,
periodic=None,
reflective=None,
ndraws=5000,
color='gray',
plot_kwargs=None,
labels=None,
label_kwargs=None,
max_n_ticks=5,
use_math_text=False,
show_live=False,
live_color='darkviolet',
live_kwargs=None,
span=None,
fig=None):
"""
Return the bounding distribution used to propose either (1) live points
at a given iteration or (2) a specific dead point during
the course of a run, projected onto all pairs of dimensions.
Parameters
----------
results : :class:`~dynesty.results.Results` instance
A :class:`~dynesty.results.Results` instance from a nested
sampling run.
it : int, optional
If provided, returns the bounding distribution at the specified
iteration of the nested sampling run. **Note that this option and
`idx` are mutually exclusive.**
idx : int, optional
If provided, returns the bounding distribution used to propose the
dead point at the specified iteration of the nested sampling run.
**Note that this option and `it` are mutually exclusive.**
dims : iterable of shape (ndim,), optional
The subset of dimensions that should be plotted. If not provided,
all dimensions will be shown.
prior_transform : func, optional
The function transforming samples within the unit cube back to samples
in the native model space. If provided, the transformed bounding
distribution will be plotted in the native model space.
periodic : iterable, optional
A list of indices for parameters with periodic boundary conditions.
These parameters *will not* have their positions constrained to be
within the unit cube, enabling smooth behavior for parameters
that may wrap around the edge. Default is `None` (i.e. no periodic
boundary conditions).
reflective : iterable, optional
A list of indices for parameters with reflective boundary conditions.
These parameters *will not* have their positions constrained to be
within the unit cube, enabling smooth behavior for parameters
that may reflect at the edge. Default is `None` (i.e. no reflective
boundary conditions).
ndraws : int, optional
The number of random samples to draw from the bounding distribution
when plotting. Default is `5000`.
color : str, optional
The color of the points randomly sampled from the bounding
distribution. Default is `'gray'`.
plot_kwargs : dict, optional
Extra keyword arguments used when plotting the bounding draws.
labels : iterable with shape (ndim,), optional
A list of names for each parameter. If not provided, the default name
used when plotting will be in :math:`x_i` style.
label_kwargs : dict, optional
Extra keyword arguments that will be sent to the
`~matplotlib.axes.Axes.set_xlabel` and
`~matplotlib.axes.Axes.set_ylabel` methods.
max_n_ticks : int, optional
Maximum number of ticks allowed. Default is `5`.
use_math_text : bool, optional
Whether the axis tick labels for very large/small exponents should be
displayed as powers of 10 rather than using `e`. Default is `False`.
show_live : bool, optional
Whether the live points at a given iteration (for `it`) or
associated with the bounding (for `idx`) should be highlighted.
Default is `False`. In the dynamic case, only the live points
associated with the batch used to construct the relevant bound
are plotted.
live_color : str, optional
The color of the live points. Default is `'darkviolet'`.
live_kwargs : dict, optional
Extra keyword arguments used when plotting the live points.
span : iterable with shape (2,), optional
A list where each element is a length-2 tuple containing
lower and upper bounds. Default is `None` (no bound).
fig : (`~matplotlib.figure.Figure`, `~matplotlib.axes.Axes`), optional
If provided, overplot the draws onto the provided figure.
Otherwise, by default an internal figure is generated.
Returns
-------
cornerbound : (`~matplotlib.figure.Figure`, `~matplotlib.axes.Axes`)
Output corner plot of the bounding distribution.
"""
# Initialize values.
if label_kwargs is None:
label_kwargs = {}
if plot_kwargs is None:
plot_kwargs = {}
if live_kwargs is None:
live_kwargs = {}
# Check that either `idx` or `it` is specified.
if (it is None and idx is None) or (it is not None and idx is not None):
raise ValueError("You must specify either an iteration or an index!")
# Set defaults.
plot_kwargs['marker'] = plot_kwargs.get('marker', 'o')
plot_kwargs['linestyle'] = plot_kwargs.get('linestyle', 'None')
plot_kwargs['markersize'] = plot_kwargs.get('markersize', 1)
plot_kwargs['alpha'] = plot_kwargs.get('alpha', 0.4)
live_kwargs['marker'] = live_kwargs.get('marker', 'o')
live_kwargs['linestyle'] = live_kwargs.get('linestyle', 'None')
live_kwargs['markersize'] = live_kwargs.get('markersize', 1)
# Extract bounding distributions.
try:
bounds = results['bound']
except KeyError:
raise ValueError("No bounds were saved in the results!")
nsamps, ndim = results['samples'].shape
if ndim == 1:
raise ValueError('cornerbound does not work for 1-D posteriors')
nonbounded = get_nonbounded(bounds[0].n, periodic, reflective)
if it is not None:
if it >= nsamps:
raise ValueError("The iteration requested goes beyond the "
"number of iterations in the run.")
# Extract bound iterations.
try:
bound_iter = np.array(results['bound_iter'])
except KeyError:
raise ValueError("Cannot reconstruct the bound used at the "
"specified iteration since bound "
"iterations were not saved in the results.")
# Find bound at the specified iteration.
if it == 0:
pidx = 0
else:
pidx = bound_iter[it]
else:
if idx >= nsamps:
raise ValueError("The index requested goes beyond the "
"number of samples in the run.")
try:
samples_bound = results['samples_bound']
except KeyError:
raise ValueError("Cannot reconstruct the bound used to "
"compute the specified dead point since "
"sample bound indices were not saved "
"in the results.")
# Grab relevant bound.
pidx = samples_bound[idx]
# Get desired bound.
bound = bounds[pidx]
# Do we want to show the live points at the specified iteration?
# If so, we need to rewind our bound to check.
# (We could also go forward; this is an arbitrary choice.)
if show_live:
try:
# We can only reconstruct the run if the final set of live points
# were added to the results. This is true by default for dynamic
# nested sampling runs but not guaranteeed for standard runs.
nlive = results['nlive']
niter = results['niter']
if nsamps - niter != nlive:
raise ValueError("Cannot reconstruct bound because the "
"final set of live points are not included "
"in the results.")
# Grab our final set of live points (with proper IDs).
samples = results['samples_u']
samples_id = results['samples_id']
ndim = samples.shape[1]
live_u = np.empty((nlive, ndim))
live_u[samples_id[-nlive:]] = samples[-nlive:]
# Find generating bound ID if necessary.
if it is None:
it = results['samples_it'][idx]
# Run our sampling backwards.
for i in range(1, niter - it + 1):
r = -(nlive + i)
uidx = samples_id[r]
live_u[uidx] = samples[r]
except:
# In the dynamic sampling case, we will show the live points used
# during the batch associated with a particular iteration/bound.
if it is not None:
batch = results['samples_batch'][it] # select batch
else:
batch = results['samples_batch'][idx]
nbatch = results['batch_nlive'][batch] # nlive in the batch
bsel = results['samples_batch'] == batch # select batch
niter_eff = sum(bsel) - nbatch # "effective" iterations in batch
# Grab our final set of live points (with proper IDs).
samples = results['samples_u'][bsel]
samples_id = results['samples_id'][bsel]
samples_id -= min(samples_id) # re-index to start at zero
ndim = samples.shape[1]
live_u = np.empty((nbatch, ndim))
live_u[samples_id[-nbatch:]] = samples[-nbatch:]
# Find generating bound ID if necessary.
if it is None:
it = results['samples_it'][idx]
it_eff = sum(bsel[:it + 1]) # effective iteration in batch
# Run our sampling backwards.
for i in range(1, niter_eff - it_eff + 1):
r = -(nbatch + i)
uidx = samples_id[r]
live_u[uidx] = samples[r]
rstate = get_random_generator()
# Draw samples from the bounding distribution.
if not isinstance(bound, (bounding.RadFriends, bounding.SupFriends)):
# If bound is "fixed", go ahead and draw samples from it.
psamps = bound.samples(ndraws, rstate=rstate)
else:
# If bound is based on the distribution of live points at a
# specific iteration, we need to reconstruct what those were.
if not show_live:
# Only reconstruct the run if we haven't done it already.
nlive = results['nlive']
niter = results['niter']
if nsamps - niter != nlive:
raise ValueError("Cannot reconstruct bound because the "
"final set of live points are not included "
"in the results.")
# Grab our final set of live points (with proper IDs).
samples = results['samples_u']
samples_id = results['samples_id']
ndim = samples.shape[1]
live_u = np.empty((nlive, ndim))
live_u[samples_id[-nlive:]] = samples[-nlive:]
# Run our sampling backwards.
if it is None:
it = results['samples_it'][idx]
for i in range(1, niter - it + 1):
r = -(nlive + i)
uidx = samples_id[r]
live_u[uidx] = samples[r]
# Draw samples.
psamps = bound.samples(ndraws, live_u, rstate=rstate)
# Projecting samples to input dimensions and possibly
# the native model space.
if prior_transform is None:
psamps = psamps.T
if show_live:
lsamps = live_u.T
else:
# Remove points outside of the unit cube.
sel = [unitcheck(point, nonbounded) for point in psamps]
psamps = np.array(list(map(prior_transform, psamps[sel])))
psamps = psamps.T
if show_live:
lsamps = np.array(list(map(prior_transform, live_u)))
lsamps = lsamps.T
# Subsample dimensions.
if dims is not None:
psamps = psamps[dims]
if show_live:
lsamps = lsamps[dims]
ndim = psamps.shape[0]
# Set labels.
if labels is None:
labels = [r"$x_{" + str(i + 1) + "}$" for i in range(ndim)]
# Setup axis layout (from `corner.py`).
factor = 2.0 # size of side of one panel
lbdim = 0.5 * factor # size of left/bottom margin
trdim = 0.2 * factor # size of top/right margin
whspace = 0.05 # size of width/height margin
plotdim = factor * (ndim - 1.) + factor * (ndim - 2.) * whspace
dim = lbdim + plotdim + trdim # total size
# Initialize figure.
fig, axes = _make_subplots(fig, ndim - 1, ndim - 1, dim, dim)
# Format figure.
lb = lbdim / dim
tr = (lbdim + plotdim) / dim
fig.subplots_adjust(left=lb,
bottom=lb,
right=tr,
top=tr,
wspace=whspace,
hspace=whspace)
# Plot the 2-D projected samples.
for i, x in enumerate(psamps[1:]):
for j, y in enumerate(psamps[:-1]):
ax = axes[i, j]
# Setup axes.
if span is not None:
ax.set_xlim(span[j])
ax.set_ylim(span[i])
if j > i:
ax.set_frame_on(False)
ax.set_xticks([])
ax.set_yticks([])
continue
if max_n_ticks == 0:
ax.xaxis.set_major_locator(NullLocator())
ax.yaxis.set_major_locator(NullLocator())
else:
ax.xaxis.set_major_locator(
MaxNLocator(max_n_ticks, prune="lower"))
ax.yaxis.set_major_locator(
MaxNLocator(max_n_ticks, prune="lower"))
# Label axes.
sf = ScalarFormatter(useMathText=use_math_text)
ax.xaxis.set_major_formatter(sf)
ax.yaxis.set_major_formatter(sf)
if i < ndim - 2:
ax.set_xticklabels([])
else:
rotate_ticks(ax, 'x')
ax.set_xlabel(labels[j], **label_kwargs)
ax.xaxis.set_label_coords(0.5, -0.3)
if j > 0:
ax.set_yticklabels([])
else:
rotate_ticks(ax, 'y')
ax.set_ylabel(labels[i + 1], **label_kwargs)
ax.yaxis.set_label_coords(-0.3, 0.5)
# Plot distribution.
ax.plot(y, x, c=color, **plot_kwargs)
# Add live points.
if show_live:
ax.plot(lsamps[j], lsamps[i + 1], c=live_color, **live_kwargs)
return (fig, axes)
def _hist2d(x,
y,
smooth=0.02,
span=None,
weights=None,
levels=None,
ax=None,
color='gray',
plot_datapoints=False,
plot_density=True,
plot_contours=True,
no_fill_contours=False,
fill_contours=True,
contour_kwargs=None,
contourf_kwargs=None,
data_kwargs=None):
"""
Internal function called by :meth:`cornerplot` used to generate a
a 2-D histogram/contour of samples.
Parameters
----------
x : interable with shape (nsamps,)
Sample positions in the first dimension.
y : iterable with shape (nsamps,)
Sample positions in the second dimension.
span : iterable with shape (ndim,), optional
A list where each element is either a length-2 tuple containing
lower and upper bounds or a float from `(0., 1.]` giving the
fraction of (weighted) samples to include. If a fraction is provided,
the bounds are chosen to be equal-tailed. An example would be::
span = [(0., 10.), 0.95, (5., 6.)]
Default is `0.999999426697` (5-sigma credible interval).
weights : iterable with shape (nsamps,)
Weights associated with the samples. Default is `None` (no weights).
levels : iterable, optional
The contour levels to draw. Default are `[0.5, 1, 1.5, 2]`-sigma.
ax : `~matplotlib.axes.Axes`, optional
An `~matplotlib.axes.axes` instance on which to add the 2-D histogram.
If not provided, a figure will be generated.
color : str, optional
The `~matplotlib`-style color used to draw lines and color cells
and contours. Default is `'gray'`.
plot_datapoints : bool, optional
Whether to plot the individual data points. Default is `False`.
plot_density : bool, optional
Whether to draw the density colormap. Default is `True`.
plot_contours : bool, optional
Whether to draw the contours. Default is `True`.
no_fill_contours : bool, optional
Whether to add absolutely no filling to the contours. This differs
from `fill_contours=False`, which still adds a white fill at the
densest points. Default is `False`.
fill_contours : bool, optional
Whether to fill the contours. Default is `True`.
contour_kwargs : dict
Any additional keyword arguments to pass to the `contour` method.
contourf_kwargs : dict
Any additional keyword arguments to pass to the `contourf` method.
data_kwargs : dict
Any additional keyword arguments to pass to the `plot` method when
adding the individual data points.
"""
if ax is None:
ax = pl.gca()
# Determine plotting bounds.
data = [x, y]
if span is None:
span = [0.999999426697 for i in range(2)]
span = list(span)
if len(span) != 2:
raise ValueError("Dimension mismatch between samples and span.")
check_span(span, data, weights)
# The default "sigma" contour levels.
if levels is None:
levels = 1.0 - np.exp(-0.5 * np.arange(0.5, 2.1, 0.5)**2)
# Color map for the density plot, over-plotted to indicate the
# density of the points near the center.
density_cmap = LinearSegmentedColormap.from_list("density_cmap",
[color, (1, 1, 1, 0)])
# Color map used to hide the points at the high density areas.
white_cmap = LinearSegmentedColormap.from_list("white_cmap", [(1, 1, 1),
(1, 1, 1)],
N=2)
# This "color map" is the list of colors for the contour levels if the
# contours are filled.
rgba_color = colorConverter.to_rgba(color)
n_levels = len(levels)
contour_cmap = [list(rgba_color)] * n_levels + [rgba_color]
for i in range(n_levels):
contour_cmap[i][-1] *= float(i) / (n_levels + 1)
# Initialize smoothing.
if isinstance(smooth, (int_type, float_type)):
smooth = [smooth, smooth]
bins = []
svalues = []
for s in smooth:
if isinstance(s, int_type):
# If `s` is an integer, the weighted histogram has
# `s` bins within the provided bounds.
bins.append(s)
svalues.append(0.)
else:
# If `s` is a float, oversample the data relative to the
# smoothing filter by a factor of 2, then use a Gaussian
# filter to smooth the results.
bins.append(int(round(2. / s)))
svalues.append(2.)
# We'll make the 2D histogram to directly estimate the density.
try:
H, X, Y = np.histogram2d(x.flatten(),
y.flatten(),
bins=bins,
range=list(map(np.sort, span)),
weights=weights)
except ValueError:
raise ValueError("It looks like at least one of your sample columns "
"have no dynamic range.")
# Smooth the results.
if not np.all(svalues == 0.):
H = norm_kde(H, svalues)
# Compute the density levels.
Hflat = H.flatten()
inds = np.argsort(Hflat)[::-1]
Hflat = Hflat[inds]
sm = np.cumsum(Hflat)
sm /= sm[-1]
V = np.empty(len(levels))
for i, v0 in enumerate(levels):
try:
V[i] = Hflat[sm <= v0][-1]
except:
V[i] = Hflat[0]
V.sort()
m = (np.diff(V) == 0)
if np.any(m) and plot_contours:
logging.warning("Too few points to create valid contours.")
if np.all(m):
logging.warning('No points at all in the plotted region')
else:
while np.any(m):
V[np.where(m)[0][0]] *= 1.0 - 1e-4
m = (np.diff(V) == 0)
V.sort()
# Compute the bin centers.
X1, Y1 = 0.5 * (X[1:] + X[:-1]), 0.5 * (Y[1:] + Y[:-1])
# Extend the array for the sake of the contours at the plot edges.
H2 = H.min() + np.zeros((H.shape[0] + 4, H.shape[1] + 4))
H2[2:-2, 2:-2] = H
H2[2:-2, 1] = H[:, 0]
H2[2:-2, -2] = H[:, -1]
H2[1, 2:-2] = H[0]
H2[-2, 2:-2] = H[-1]
H2[1, 1] = H[0, 0]
H2[1, -2] = H[0, -1]
H2[-2, 1] = H[-1, 0]
H2[-2, -2] = H[-1, -1]
X2 = np.concatenate([
X1[0] + np.array([-2, -1]) * np.diff(X1[:2]), X1,
X1[-1] + np.array([1, 2]) * np.diff(X1[-2:])
])
Y2 = np.concatenate([
Y1[0] + np.array([-2, -1]) * np.diff(Y1[:2]), Y1,
Y1[-1] + np.array([1, 2]) * np.diff(Y1[-2:])
])
# Plot the data points.
if plot_datapoints:
if data_kwargs is None:
data_kwargs = {}
data_kwargs["color"] = data_kwargs.get("color", color)
data_kwargs["ms"] = data_kwargs.get("ms", 2.0)
data_kwargs["mec"] = data_kwargs.get("mec", "none")
data_kwargs["alpha"] = data_kwargs.get("alpha", 0.1)
ax.plot(x, y, "o", zorder=-1, rasterized=True, **data_kwargs)
# Plot the base fill to hide the densest data points.
if (plot_contours or plot_density) and not no_fill_contours:
ax.contourf(X2,
Y2,
H2.T, [V.min(), H.max()],
cmap=white_cmap,
antialiased=False)
if plot_contours and fill_contours:
if contourf_kwargs is None:
contourf_kwargs = {}
contourf_kwargs["colors"] = contourf_kwargs.get("colors", contour_cmap)
contourf_kwargs["antialiased"] = contourf_kwargs.get(
"antialiased", False)
ax.contourf(X2, Y2, H2.T,
np.concatenate([[0], V, [H.max() * (1 + 1e-4)]]),
**contourf_kwargs)
# Plot the density map. This can't be plotted at the same time as the
# contour fills.
elif plot_density:
ax.pcolor(X, Y, H.max() - H.T, cmap=density_cmap)
# Plot the contour edge colors.
if plot_contours:
if contour_kwargs is None:
contour_kwargs = {}
contour_kwargs["colors"] = contour_kwargs.get("colors", color)
ax.contour(X2, Y2, H2.T, V, **contour_kwargs)
ax.set_xlim(span[0])
ax.set_ylim(span[1])