# Source code for geomstats.visualization.hyperbolic

```"""Visualization for Geometric Statistics."""
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D  # NOQA

import geomstats.backend as gs
from geomstats.geometry.hyperboloid import Hyperboloid
from geomstats.geometry.poincare_half_space import PoincareHalfSpace

H2 = Hyperboloid(dim=2)
POINCARE_HALF_PLANE = PoincareHalfSpace(dim=2)

AX_SCALE = 1.2

[docs]
class KleinDisk:
def __init__(self, points=None):
self.center = gs.array([0.0, 0.0])
self.points = []
if points is not None:

[docs]
@staticmethod
def set_ax(ax=None):
"""Set axis."""
if ax is None:
ax = plt.subplot()
ax_s = AX_SCALE
plt.setp(ax, xlim=(-ax_s, ax_s), ylim=(-ax_s, ax_s), xlabel="X", ylabel="Y")
return ax

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if not gs.all(H2.belongs(points)):
raise ValueError("Points do not belong to the hyperbolic space.")
points = self.convert_to_klein_coordinates(points)
if not isinstance(points, list):
points = list(points)
self.points.extend(points)

[docs]
@staticmethod
def convert_to_klein_coordinates(points):
poincare_coords = points[:, 1:] / (1 + points[:, :1])
poincare_angle = gs.arctan2(poincare_coords[:, 1], poincare_coords[:, 0])

klein_angle = poincare_angle

coords_0 = gs.expand_dims(klein_radius * gs.cos(klein_angle), axis=1)
coords_1 = gs.expand_dims(klein_radius * gs.sin(klein_angle), axis=1)
klein_coords = gs.concatenate([coords_0, coords_1], axis=1)
return klein_coords

[docs]
def draw(self, ax, **kwargs):
circle = plt.Circle((0, 0), radius=1.0, color="black", fill=False)
points_x = [gs.to_numpy(point[0]) for point in self.points]
points_y = [gs.to_numpy(point[1]) for point in self.points]
ax.scatter(points_x, points_y, **kwargs)

[docs]
def plot(self, points, ax=None, **point_draw_kwargs):
ax = self.set_ax(ax=ax)
self.points = []
self.draw(ax, **point_draw_kwargs)

[docs]
class PoincareDisk:
def __init__(self, points=None, coords_type="extrinsic"):
self.center = gs.array([0.0, 0.0])
self.points = []
self.coords_type = coords_type
if points is not None:

[docs]
@staticmethod
def set_ax(ax=None):
"""Set axis."""
if ax is None:
ax = plt.subplot()
ax_s = AX_SCALE
plt.setp(
ax,
xlim=(-ax_s, ax_s),
ylim=(-ax_s, ax_s),
xlabel="X",
ylabel="Y",
)
return ax

[docs]
if self.coords_type == "extrinsic":
if not gs.all(H2.belongs(points)):
raise ValueError("Points do not belong to the hyperbolic space.")
points = self.convert_to_poincare_coordinates(points)

if not isinstance(points, list):
points = list(points)

if gs.all([len(point) == 2 for point in self.points]):
self.points.extend(points)
else:
raise ValueError("Points do not have dimension 2.")

[docs]
@staticmethod
def convert_to_poincare_coordinates(points):
poincare_coords = points[:, 1:] / (1 + points[:, :1])
return poincare_coords

[docs]
def draw(self, ax, **kwargs):
circle = plt.Circle((0, 0), radius=1.0, color="black", fill=False)
if len(self.points) > 0:
if gs.all([len(point) == 2 for point in self.points]):
points_x = gs.stack([point[0] for point in self.points], axis=0)
points_y = gs.stack([point[1] for point in self.points], axis=0)
ax.scatter(points_x, points_y, **kwargs)
else:
raise ValueError("Points do not have dimension 2.")

[docs]
def plot(self, points, ax=None, coords_type=None, **point_draw_kwargs):
if coords_type is None:
coords_type = "extrinsic"
poincare_disk = PoincareDisk(coords_type=coords_type)
ax = poincare_disk.set_ax(ax=ax)
self.points = []
poincare_disk.draw(ax, **point_draw_kwargs)
plt.axis("off")

[docs]
class PoincareHalfPlane:
"""Class used to plot points in the Poincare Half Plane."""

def __init__(self, points=None, coords_type="half-space"):
self.points = []
self.coords_type = coords_type
if points is not None:

[docs]
if self.coords_type == "extrinsic":
if not gs.all(H2.belongs(points)):
raise ValueError(
"Points do not belong to the hyperbolic space "
"(extrinsic coordinates)"
)
points = self.convert_to_half_plane_coordinates(points)
elif self.coords_type == "half-space":
if not gs.all(POINCARE_HALF_PLANE.belongs(points)):
raise ValueError(
"Points do not belong to the hyperbolic space "
"(Poincare half plane coordinates)."
)
if not isinstance(points, list):
points = list(points)
self.points.extend(points)

[docs]
def set_ax(self, ax=None):
"""Set axis."""
if ax is None:
ax = plt.subplot()

plt.setp(ax, xlabel="X", ylabel="Y")
return ax

[docs]
@staticmethod
def convert_to_half_plane_coordinates(points):
disk_coords = points[:, 1:] / (1 + points[:, :1])
disk_x = disk_coords[:, 0]
disk_y = disk_coords[:, 1]

denominator = disk_x**2 + (1 - disk_y) ** 2
coords_0 = gs.expand_dims(2 * disk_x / denominator, axis=1)
coords_1 = gs.expand_dims((1 - disk_x**2 - disk_y**2) / denominator, axis=1)

half_plane_coords = gs.concatenate([coords_0, coords_1], axis=1)
return half_plane_coords

[docs]
def draw(self, ax, **kwargs):
points_x = [gs.to_numpy(point[0]) for point in self.points]
points_y = [gs.to_numpy(point[1]) for point in self.points]
ax.scatter(points_x, points_y, **kwargs)

[docs]
def plot(self, points, ax=None, coords_type=None, **point_draw_kwargs):
if coords_type is None:
coords_type = "half-space"
poincare_half_plane = PoincareHalfPlane(coords_type=coords_type)
ax = poincare_half_plane.set_ax(ax=ax)
self.points = []