# This file is part of the Gudhi Library - https://gudhi.inria.fr/ - which is released under MIT.
# See file LICENSE or go to https://gudhi.inria.fr/licensing/ for full license details.
# Author(s): Vincent Rouvreau, Bertrand Michel
#
# Copyright (C) 2016 Inria
#
# Modification(s):
# - 2020/02 Theo Lacombe: Added more options for improved rendering and more flexibility.
# - YYYY/MM Author: Description of the modification
from os import path
from math import isfinite
import numpy as np
from gudhi.reader_utils import read_persistence_intervals_in_dimension
from gudhi.reader_utils import read_persistence_intervals_grouped_by_dimension
__author__ = "Vincent Rouvreau, Bertrand Michel, Theo Lacombe"
__copyright__ = "Copyright (C) 2016 Inria"
__license__ = "MIT"
def __min_birth_max_death(persistence, band=0.0):
"""This function returns (min_birth, max_death) from the persistence.
:param persistence: The persistence to plot.
:type persistence: list of tuples(dimension, tuple(birth, death)).
:param band: band
:type band: float.
:returns: (float, float) -- (min_birth, max_death).
"""
# Look for minimum birth date and maximum death date for plot optimisation
max_death = 0
min_birth = persistence[0][1][0]
for interval in reversed(persistence):
if float(interval[1][1]) != float("inf"):
if float(interval[1][1]) > max_death:
max_death = float(interval[1][1])
if float(interval[1][0]) > max_death:
max_death = float(interval[1][0])
if float(interval[1][0]) < min_birth:
min_birth = float(interval[1][0])
if band > 0.0:
max_death += band
return (min_birth, max_death)
def _array_handler(a):
'''
:param a: if array, assumes it is a (n x 2) np.array and return a
persistence-compatible list (padding with 0), so that the
plot can be performed seamlessly.
'''
if isinstance(a[0][1], np.float64) or isinstance(a[0][1], float):
return [[0, x] for x in a]
else:
return a
[docs]def plot_persistence_barcode(
persistence=[],
persistence_file="",
alpha=0.6,
max_intervals=1000,
max_barcodes=1000,
inf_delta=0.1,
legend=False,
colormap=None,
axes=None,
fontsize=16,
):
"""This function plots the persistence bar code from persistence values list
, a np.array of shape (N x 2) (representing a diagram
in a single homology dimension),
or from a `persistence diagram <fileformats.html#persistence-diagram>`_ file.
:param persistence: Persistence intervals values list. Can be grouped by dimension or not.
:type persistence: an array of (dimension, array of (birth, death)) or an array of (birth, death).
:param persistence_file: A `persistence diagram <fileformats.html#persistence-diagram>`_ file style name
(reset persistence if both are set).
:type persistence_file: string
:param alpha: barcode transparency value (0.0 transparent through 1.0
opaque - default is 0.6).
:type alpha: float.
:param max_intervals: maximal number of intervals to display.
Selected intervals are those with the longest life time. Set it
to 0 to see all. Default value is 1000.
:type max_intervals: int.
:param inf_delta: Infinity is placed at :code:`((max_death - min_birth) x
inf_delta)` above :code:`max_death` value. A reasonable value is
between 0.05 and 0.5 - default is 0.1.
:type inf_delta: float.
:param legend: Display the dimension color legend (default is False).
:type legend: boolean.
:param colormap: A matplotlib-like qualitative colormaps. Default is None
which means :code:`matplotlib.cm.Set1.colors`.
:type colormap: tuple of colors (3-tuple of float between 0. and 1.).
:param axes: A matplotlib-like subplot axes. If None, the plot is drawn on
a new set of axes.
:type axes: `matplotlib.axes.Axes`
:param fontsize: Fontsize to use in axis.
:type fontsize: int
:returns: (`matplotlib.axes.Axes`): The axes on which the plot was drawn.
"""
try:
import matplotlib.pyplot as plt
import matplotlib.patches as mpatches
from matplotlib import rc
plt.rc('text', usetex=True)
plt.rc('font', family='serif')
if persistence_file != "":
if path.isfile(persistence_file):
# Reset persistence
persistence = []
diag = read_persistence_intervals_grouped_by_dimension(
persistence_file=persistence_file
)
for key in diag.keys():
for persistence_interval in diag[key]:
persistence.append((key, persistence_interval))
else:
print("file " + persistence_file + " not found.")
return None
persistence = _array_handler(persistence)
if max_barcodes != 1000:
print("Deprecated parameter. It has been replaced by max_intervals")
max_intervals = max_barcodes
if max_intervals > 0 and max_intervals < len(persistence):
# Sort by life time, then takes only the max_intervals elements
persistence = sorted(
persistence,
key=lambda life_time: life_time[1][1] - life_time[1][0],
reverse=True,
)[:max_intervals]
if colormap == None:
colormap = plt.cm.Set1.colors
if axes == None:
fig, axes = plt.subplots(1, 1)
persistence = sorted(persistence, key=lambda birth: birth[1][0])
(min_birth, max_death) = __min_birth_max_death(persistence)
ind = 0
delta = (max_death - min_birth) * inf_delta
# Replace infinity values with max_death + delta for bar code to be more
# readable
infinity = max_death + delta
axis_start = min_birth - delta
# Draw horizontal bars in loop
for interval in reversed(persistence):
if float(interval[1][1]) != float("inf"):
# Finite death case
axes.barh(
ind,
(interval[1][1] - interval[1][0]),
height=0.8,
left=interval[1][0],
alpha=alpha,
color=colormap[interval[0]],
linewidth=0,
)
else:
# Infinite death case for diagram to be nicer
axes.barh(
ind,
(infinity - interval[1][0]),
height=0.8,
left=interval[1][0],
alpha=alpha,
color=colormap[interval[0]],
linewidth=0,
)
ind = ind + 1
if legend:
dimensions = list(set(item[0] for item in persistence))
axes.legend(
handles=[
mpatches.Patch(color=colormap[dim], label=str(dim))
for dim in dimensions
],
loc="lower right",
)
axes.set_title("Persistence barcode", fontsize=fontsize)
# Ends plot on infinity value and starts a little bit before min_birth
axes.axis([axis_start, infinity, 0, ind])
return axes
except ImportError:
print("This function is not available, you may be missing matplotlib.")
[docs]def plot_persistence_diagram(
persistence=[],
persistence_file="",
alpha=0.6,
band=0.0,
max_intervals=1000,
max_plots=1000,
inf_delta=0.1,
legend=False,
colormap=None,
axes=None,
fontsize=16,
greyblock=True
):
"""This function plots the persistence diagram from persistence values
list, a np.array of shape (N x 2) representing a diagram in a single
homology dimension, or from a `persistence diagram <fileformats.html#persistence-diagram>`_ file`.
:param persistence: Persistence intervals values list. Can be grouped by dimension or not.
:type persistence: an array of (dimension, array of (birth, death)) or an array of (birth, death).
:param persistence_file: A `persistence diagram <fileformats.html#persistence-diagram>`_ file style name
(reset persistence if both are set).
:type persistence_file: string
:param alpha: plot transparency value (0.0 transparent through 1.0
opaque - default is 0.6).
:type alpha: float.
:param band: band (not displayed if :math:`\leq` 0. - default is 0.)
:type band: float.
:param max_intervals: maximal number of intervals to display.
Selected intervals are those with the longest life time. Set it
to 0 to see all. Default value is 1000.
:type max_intervals: int.
:param inf_delta: Infinity is placed at :code:`((max_death - min_birth) x
inf_delta)` above :code:`max_death` value. A reasonable value is
between 0.05 and 0.5 - default is 0.1.
:type inf_delta: float.
:param legend: Display the dimension color legend (default is False).
:type legend: boolean.
:param colormap: A matplotlib-like qualitative colormaps. Default is None
which means :code:`matplotlib.cm.Set1.colors`.
:type colormap: tuple of colors (3-tuple of float between 0. and 1.).
:param axes: A matplotlib-like subplot axes. If None, the plot is drawn on
a new set of axes.
:type axes: `matplotlib.axes.Axes`
:param fontsize: Fontsize to use in axis.
:type fontsize: int
:param greyblock: if we want to plot a grey patch on the lower half plane for nicer rendering. Default True.
:type greyblock: boolean
:returns: (`matplotlib.axes.Axes`): The axes on which the plot was drawn.
"""
try:
import matplotlib.pyplot as plt
import matplotlib.patches as mpatches
from matplotlib import rc
plt.rc('text', usetex=True)
plt.rc('font', family='serif')
if persistence_file != "":
if path.isfile(persistence_file):
# Reset persistence
persistence = []
diag = read_persistence_intervals_grouped_by_dimension(
persistence_file=persistence_file
)
for key in diag.keys():
for persistence_interval in diag[key]:
persistence.append((key, persistence_interval))
else:
print("file " + persistence_file + " not found.")
return None
persistence = _array_handler(persistence)
if max_plots != 1000:
print("Deprecated parameter. It has been replaced by max_intervals")
max_intervals = max_plots
if max_intervals > 0 and max_intervals < len(persistence):
# Sort by life time, then takes only the max_intervals elements
persistence = sorted(
persistence,
key=lambda life_time: life_time[1][1] - life_time[1][0],
reverse=True,
)[:max_intervals]
if colormap == None:
colormap = plt.cm.Set1.colors
if axes == None:
fig, axes = plt.subplots(1, 1)
(min_birth, max_death) = __min_birth_max_death(persistence, band)
delta = (max_death - min_birth) * inf_delta
# Replace infinity values with max_death + delta for diagram to be more
# readable
infinity = max_death + delta
axis_end = max_death + delta / 2
axis_start = min_birth - delta
# bootstrap band
if band > 0.0:
x = np.linspace(axis_start, infinity, 1000)
axes.fill_between(x, x, x + band, alpha=alpha, facecolor="red")
# lower diag patch
if greyblock:
axes.add_patch(mpatches.Polygon([[axis_start, axis_start], [axis_end, axis_start], [axis_end, axis_end]], fill=True, color='lightgrey'))
# Draw points in loop
pts_at_infty = False # Records presence of pts at infty
for interval in reversed(persistence):
if float(interval[1][1]) != float("inf"):
# Finite death case
axes.scatter(
interval[1][0],
interval[1][1],
alpha=alpha,
color=colormap[interval[0]],
)
else:
pts_at_infty = True
# Infinite death case for diagram to be nicer
axes.scatter(
interval[1][0], infinity, alpha=alpha, color=colormap[interval[0]]
)
if pts_at_infty:
# infinity line and text
axes.plot([axis_start, axis_end], [axis_start, axis_end], linewidth=1.0, color="k")
axes.plot([axis_start, axis_end], [infinity, infinity], linewidth=1.0, color="k", alpha=alpha)
# Infinity label
yt = axes.get_yticks()
yt = yt[np.where(yt < axis_end)] # to avoid ploting ticklabel higher than infinity
yt = np.append(yt, infinity)
ytl = ["%.3f" % e for e in yt] # to avoid float precision error
ytl[-1] = r'$+\infty$'
axes.set_yticks(yt)
axes.set_yticklabels(ytl)
if legend:
dimensions = list(set(item[0] for item in persistence))
axes.legend(
handles=[
mpatches.Patch(color=colormap[dim], label=str(dim))
for dim in dimensions
]
)
axes.set_xlabel("Birth", fontsize=fontsize)
axes.set_ylabel("Death", fontsize=fontsize)
axes.set_title("Persistence diagram", fontsize=fontsize)
# Ends plot on infinity value and starts a little bit before min_birth
axes.axis([axis_start, axis_end, axis_start, infinity + delta/2])
return axes
except ImportError:
print("This function is not available, you may be missing matplotlib.")
[docs]def plot_persistence_density(
persistence=[],
persistence_file="",
nbins=300,
bw_method=None,
max_intervals=1000,
dimension=None,
cmap=None,
legend=False,
axes=None,
fontsize=16,
greyblock=False
):
"""This function plots the persistence density from persistence
values list, np.array of shape (N x 2) representing a diagram
in a single homology dimension,
or from a `persistence diagram <fileformats.html#persistence-diagram>`_ file.
Be aware that this function does not distinguish the dimension, it is
up to you to select the required one. This function also does not handle
degenerate data set (scipy correlation matrix inversion can fail).
:Requires: `SciPy <installation.html#scipy>`_
:param persistence: Persistence intervals values list.
Can be grouped by dimension or not.
:type persistence: an array of (dimension, array of (birth, death))
or an array of (birth, death).
:param persistence_file: A `persistence diagram <fileformats.html#persistence-diagram>`_
file style name (reset persistence if both are set).
:type persistence_file: string
:param nbins: Evaluate a gaussian kde on a regular grid of nbins x
nbins over data extents (default is 300)
:type nbins: int.
:param bw_method: The method used to calculate the estimator
bandwidth. This can be 'scott', 'silverman', a scalar constant
or a callable. If a scalar, this will be used directly as
kde.factor. If a callable, it should take a gaussian_kde
instance as only parameter and return a scalar. If None
(default), 'scott' is used. See
`scipy.stats.gaussian_kde documentation
<http://scipy.github.io/devdocs/generated/scipy.stats.gaussian_kde.html>`_
for more details.
:type bw_method: str, scalar or callable, optional.
:param max_intervals: maximal number of points used in the density
estimation.
Selected intervals are those with the longest life time. Set it
to 0 to see all. Default value is 1000.
:type max_intervals: int.
:param dimension: the dimension to be selected in the intervals
(default is None to mix all dimensions).
:type dimension: int.
:param cmap: A matplotlib colormap (default is
matplotlib.pyplot.cm.hot_r).
:type cmap: cf. matplotlib colormap.
:param legend: Display the color bar values (default is False).
:type legend: boolean.
:param axes: A matplotlib-like subplot axes. If None, the plot is drawn on
a new set of axes.
:type axes: `matplotlib.axes.Axes`
:param fontsize: Fontsize to use in axis.
:type fontsize: int
:param greyblock: if we want to plot a grey patch on the lower half plane
for nicer rendering. Default False.
:type greyblock: boolean
:returns: (`matplotlib.axes.Axes`): The axes on which the plot was drawn.
"""
try:
import matplotlib.pyplot as plt
import matplotlib.patches as mpatches
from scipy.stats import kde
from matplotlib import rc
plt.rc('text', usetex=True)
plt.rc('font', family='serif')
if persistence_file != "":
if dimension is None:
# All dimension case
dimension = -1
if path.isfile(persistence_file):
persistence_dim = read_persistence_intervals_in_dimension(
persistence_file=persistence_file, only_this_dim=dimension
)
else:
print("file " + persistence_file + " not found.")
return None
if len(persistence) > 0:
persistence = _array_handler(persistence)
persistence_dim = np.array(
[
(dim_interval[1][0], dim_interval[1][1])
for dim_interval in persistence
if (dim_interval[0] == dimension) or (dimension is None)
]
)
persistence_dim = persistence_dim[np.isfinite(persistence_dim[:, 1])]
if max_intervals > 0 and max_intervals < len(persistence_dim):
# Sort by life time, then takes only the max_intervals elements
persistence_dim = np.array(
sorted(
persistence_dim,
key=lambda life_time: life_time[1] - life_time[0],
reverse=True,
)[:max_intervals]
)
# Set as numpy array birth and death (remove undefined values - inf and NaN)
birth = persistence_dim[:, 0]
death = persistence_dim[:, 1]
# default cmap value cannot be done at argument definition level as matplotlib is not yet defined.
if cmap is None:
cmap = plt.cm.hot_r
if axes == None:
fig, axes = plt.subplots(1, 1)
# line display of equation : birth = death
x = np.linspace(death.min(), birth.max(), 1000)
axes.plot(x, x, color="k", linewidth=1.0)
# Evaluate a gaussian kde on a regular grid of nbins x nbins over data extents
k = kde.gaussian_kde([birth, death], bw_method=bw_method)
xi, yi = np.mgrid[
birth.min() : birth.max() : nbins * 1j,
death.min() : death.max() : nbins * 1j,
]
zi = k(np.vstack([xi.flatten(), yi.flatten()]))
# Make the plot
img = axes.pcolormesh(xi, yi, zi.reshape(xi.shape), cmap=cmap)
if greyblock:
axes.add_patch(mpatches.Polygon([[birth.min(), birth.min()], [death.max(), birth.min()], [death.max(), death.max()]], fill=True, color='lightgrey'))
if legend:
plt.colorbar(img, ax=axes)
axes.set_xlabel("Birth", fontsize=fontsize)
axes.set_ylabel("Death", fontsize=fontsize)
axes.set_title("Persistence density", fontsize=fontsize)
return axes
except ImportError:
print(
"This function is not available, you may be missing matplotlib and/or scipy."
)