"""Matplotlib trajectories and interactive Plotly geometry plots."""
import numpy as np
from .style import prettify, set_style
from .training import coefficients, training_history
[docs]
def embedding(points, *, ax=None, color="black", linewidth=0.6):
"""Plot a three-coordinate trajectory and return its Matplotlib axes."""
import matplotlib.pyplot as plt
points = np.asarray(points)
if points.ndim != 2 or points.shape[1] != 3:
raise ValueError("Expected shape (N, 3)")
if ax is None:
ax = plt.figure().add_subplot(111, projection="3d")
ax.plot(*points.T, color=color, lw=linewidth)
ax.set(xlabel="x(t)", ylabel="x(t-tau)", zlabel="x(t-2tau)")
return ax
[docs]
def torus(points, fit, *, opacity=0.15):
"""Return a rotatable Plotly point cloud and fitted ring/torus surface."""
import plotly.graph_objects as go
points = np.asarray(points)
theta = np.linspace(0, 2 * np.pi, 64)
if fit.kind == "ring":
radial = np.linspace(0, 1, 24)
phi, weight = np.meshgrid(theta, radial)
outer1, outer2 = fit.major_radii
inner1, inner2 = fit.inner_radii
u = (inner1 + weight * (outer1 - inner1)) * np.cos(phi)
v = (inner2 + weight * (outer2 - inner2)) * np.sin(phi)
surface = (
fit.center[:, None, None]
+ fit.u_axis[:, None, None] * u
+ fit.v_axis[:, None, None] * v
)
else:
phi, angle = np.meshgrid(theta, theta)
r1, r2 = fit.major_radii
denom = np.sqrt((r2 * np.cos(phi)) ** 2 + (r1 * np.sin(phi)) ** 2) + 1e-12
outward = (
r2 * np.cos(phi)[None, :, :] * fit.u_axis[:, None, None]
+ r1 * np.sin(phi)[None, :, :] * fit.v_axis[:, None, None]
) / denom
surface = (
fit.center[:, None, None]
+ r1 * np.cos(phi) * fit.u_axis[:, None, None]
+ r2 * np.sin(phi) * fit.v_axis[:, None, None]
+ fit.tube_radius * np.cos(angle) * outward
+ fit.tube_radius * np.sin(angle) * fit.normal[:, None, None]
)
fig = go.Figure(
[
go.Surface(
x=surface[0],
y=surface[1],
z=surface[2],
opacity=opacity,
colorscale=[[0, "gray"], [1, "gray"]],
showscale=False,
),
go.Scatter3d(
x=points[:, 0],
y=points[:, 1],
z=points[:, 2],
mode="lines",
line=dict(color="black", width=2),
name="Signal",
),
]
)
fig.update_layout(
scene=dict(
aspectmode="data",
xaxis_title="x(t)",
yaxis_title="x(t-tau)",
zaxis_title="x(t-2tau)",
)
)
return fig
