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# -*- coding: utf-8 -*-
import numpy as np
import matplotlib
class Interval:
def __init__(self, birth, death = None):
if death is not None and death < birth:
raise ValueError("Death must be at least birth.")
self.birth = birth
self.death = death
def is_finite(self):
return self.death is not None
def __str__(self):
if self.is_finite():
return "(%s, %s)" %(str(self.birth), str(self.death))
else:
return "(%s, ∞)" %(str(self.birth))
def __repr__(self):
if self.is_finite():
return "Interval(%s, %s)" %(repr(self.birth), repr(self.death))
else:
return "Interval(%s)" %(repr(self.birth))
def size(self):
if self.is_finite():
return self.death - self.birth
else:
return float("inf")
def finitize(barcode, max_scale):
ret = []
for bar in barcode:
if bar.is_finite():
ret.append(bar)
else:
ret.append(Interval(bar.birth, max_scale))
return ret
def betti_curve(barcode, min_scale, max_scale):
xs = []
for interval in barcode:
xs.append((interval.birth, 1))
if interval.is_finite():
xs.append((interval.death, -1))
if not xs:
return np.zeros((2,1))
xs.sort()
scales = [min_scale]
bettis = [0]
for (t, delta) in xs:
if scales[-1] == t:
bettis[-1] += delta
else:
scales.append(t)
bettis.append(bettis[-1] + delta)
if scales[-1] < max_scale:
scales.append(max_scale)
bettis.append(bettis[-1])
return (np.array(scales), np.array(bettis, dtype=int))
def plot(ax, barcode, min_scale, max_scale, color = "black", finite_marker = ".", infinite_marker = "^", alpha = 1.0):
finites = []
infinites = []
for interval in barcode:
if interval.is_finite():
finites.append((interval.birth, interval.death))
else:
infinites.append((interval.birth, max_scale))
finites = np.array(finites)
infinites = np.array(infinites)
if finites.shape[0] > 0:
ax.plot(finites[:, 0], finites[:, 1], color = color, marker = finite_marker, linestyle = "None", alpha = alpha, zorder=10)
if infinites.shape[0] > 0:
ax.plot(infinites[:, 0], infinites[:, 1], color = color, marker = infinite_marker, linestyle = "None", alpha = alpha, zorder=10)
below_diag_patch = ax.add_patch(
matplotlib.patches.Polygon([[min_scale, min_scale],
[max_scale, min_scale],
[max_scale, max_scale]],
closed = True, fill = True, color = "lightgray"))
min_scale_line = ax.add_line(matplotlib.lines.Line2D([min_scale, min_scale],
[min_scale, max_scale],
color = "black", linewidth=0.5))
max_scale_line = ax.add_line(matplotlib.lines.Line2D([min_scale, max_scale],
[max_scale, max_scale],
color = "black", linewidth=0.5))
def callback(cax):
(xmin, xmax) = cax.get_xlim()
(ymin, ymax) = cax.get_ylim()
low = min(xmin, ymin)
high = max(xmax, ymax)
below_diag_patch.set_xy([[low, low],
[high, low],
[high, high]])
ax.callbacks.connect('xlim_changed', callback)
ax.callbacks.connect('ylim_changed', callback)
ax.set_xlim(min_scale, max_scale)
ax.set_ylim(min_scale, max_scale)
ax.set_xlabel("Birth")
ax.set_ylabel("Death")
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