def plt_diagram(diagram, homology_dimensions=None):
"""Plot a single persistence diagram.
Parameters
----------
diagram : ndarray, shape (n_points, 3)
The persistence diagram to plot, where the third dimension along axis 1
contains homology dimensions, and the other two contain (birth, death)
pairs to be used as coordinates in the two-dimensional plot.
homology_dimensions : list of int or None, default: ``None``
Homology dimensions which will appear on the plot. If ``None``, all
homology dimensions which appear in `diagram` will be plotted.
"""
if homology_dimensions is None:
homology_dimensions = np.unique(diagram[:, 2])
maximum_persistence = np.where(np.isinf(diagram), -np.inf, diagram).max()
plt.plot(np.array([-1 * maximum_persistence,
1 * maximum_persistence]),
np.array([-1 * maximum_persistence,
1 * maximum_persistence]),
'bo-')
colors = ['r', 'C2', 'c']
for i, dimension in enumerate(homology_dimensions):
name = "H{}".format(int(dimension))
subdiagram = _subdiagrams(np.asarray([diagram]), [dimension],
remove_dim=True)[0]
diff = (subdiagram[:, 1] != subdiagram[:, 0])
subdiagram = subdiagram[diff]
plt.scatter(subdiagram[:, 0], subdiagram[:, 1], c=colors[i])
plt.show()
def plot_diagram(diagram, homology_dimensions=None):
"""Plot a single persistence diagram.
Parameters
----------
diagram : ndarray, shape (n_points, 3)
The persistence diagram to plot, where the third dimension along axis 1
contains homology dimensions, and the other two contain (birth, death)
pairs to be used as coordinates in the two-dimensional plot.
homology_dimensions : list of int or None, default: ``None``
Homology dimensions which will appear on the plot. If ``None``, all
homology dimensions which appear in `diagram` will be plotted.
"""
if homology_dimensions is None:
homology_dimensions = np.unique(diagram[:, 2])
maximum_persistence = np.where(np.isinf(diagram), -np.inf, diagram).max()
layout = {
"title": "Persistence diagram",
"width": 500,
"height": 500,
"xaxis1": {
"title": "Birth",
"side": "bottom",
"type": "linear",
"range": [0, 1.1 * maximum_persistence],
"ticks": "outside",
"anchor": "y1",
"showline": True,
"zeroline": True,
"showexponent": "all",
"exponentformat": "e",
},
"yaxis1": {
"title": "Death",
"side": "left",
"type": "linear",
"range": [0, 1.1 * maximum_persistence],
"ticks": "outside",
"anchor": "x1",
"showline": True,
"zeroline": True,
"showexponent": "all",
"exponentformat": "e",
},
"plot_bgcolor": "white",
}
fig = gobj.Figure(layout=layout)
fig.update_xaxes(zeroline=True,
linewidth=1,
linecolor="black",
mirror=False)
fig.update_yaxes(zeroline=True,
linewidth=1,
linecolor="black",
mirror=False)
fig.add_trace(
gobj.Scatter(
x=np.array([-100 * maximum_persistence,
100 * maximum_persistence]),
y=np.array([-100 * maximum_persistence,
100 * maximum_persistence]),
mode="lines",
line=dict(dash="dash", width=1, color="black"),
showlegend=False,
hoverinfo="none",
))
for i, dimension in enumerate(homology_dimensions):
name = "H{}".format(int(dimension))
subdiagram = _subdiagrams(np.asarray([diagram]), [dimension],
remove_dim=True)[0]
diff = subdiagram[:, 1] != subdiagram[:, 0]
subdiagram = subdiagram[diff]
fig.add_trace(
gobj.Scatter(x=subdiagram[:, 0],
y=subdiagram[:, 1],
mode="markers",
name=name))
fig.show()
def feature_5(X, dim):
X = _subdiagrams(X, [dim])
return np.max(yi_minus_xi(X), axis=1) / X.shape[1]
def feature_4(X, dim):
X = _subdiagrams(X, [dim])
return np.sum(((np.max(X[:, :, 1], axis=1).reshape((X.shape[0], 1)) - X[:, :, 1]) ** 2) * (yi_minus_xi(X) ** 4),
axis=1) / X.shape[1]
def feature_3(X, dim):
X = _subdiagrams(X, [dim])
return np.sum(((X[:, :, 0] ** 2) * (yi_minus_xi(X) ** 4)), axis=1) / X.shape[1]
def plot_diagram(diagram, homology_dimensions=None):
"""Plots one persistence diagram.
Parameters
----------
homology_dimensions : list of int, default: ``None``
The list of homology dimensions that will appear on the plot. None means that all the homology dimensions
contained in diagram will be plotted.
Input
-----
diagram : ndarray of shape (n_points, 3)
The persistence diagram to plot, where the keys of the dict correspond to homology dimensions and each
entry is the collection of (birth,death) points in R^2 of the corresponding homology dimension.
"""
if homology_dimensions is None:
homology_dimensions = np.unique(diagram[:,2])
maximum_persistence = np.where(np.isinf(diagram),-np.inf,diagram).max()
layout = {
"title": "Persistence diagram",
"width": 500,
"height": 500,
"xaxis1": {
"title": "Birth",
"side": "bottom",
"type": "linear",
"range": [0, 1.1*maximum_persistence],
"ticks": "outside",
"anchor": "y1",
"showline": True,
"zeroline": True,
"showexponent": "all",
"exponentformat" : "e"
},
"yaxis1": {
"title": "Death",
"side": "left",
"type": "linear",
"range": [0, 1.1*maximum_persistence],
"ticks": "outside",
"anchor": "x1",
"showline": True,
"zeroline": True,
"showexponent": "all",
"exponentformat" : "e"
},
"plot_bgcolor": "white"
}
fig = gobj.Figure(layout=layout)
fig.update_xaxes(zeroline=True, linewidth=1, linecolor='black', mirror=False)
fig.update_yaxes(zeroline=True, linewidth=1, linecolor='black', mirror=False)
fig.add_trace(gobj.Scatter(x=np.array([-100*maximum_persistence,100*maximum_persistence]),
y=np.array([-100*maximum_persistence,100*maximum_persistence]), mode='lines',
line=dict(dash='dash',width=1,color='black'), showlegend=False, hoverinfo='none'))
for i, dimension in enumerate(homology_dimensions):
name = 'H'+str(int(dimension))
subdiagram = _subdiagrams(np.asarray([diagram]),[dimension],remove_dim=True)[0]
diff = (subdiagram[:, 1] != subdiagram[:, 0])
subdiagram = subdiagram[diff]
fig.add_trace(gobj.Scatter(x=subdiagram[:,0], y=subdiagram[:,1], mode='markers', name=name))
fig.show()