import numpy as np
import scipy.spatial.distance as dist
[docs]def take_sample(point_cloud, no_samples, seed=None):
""" Take a subsample from samples using a minmax algorithm.
We start from a random point. Then choose the point further appart. Next,
we take the point that is further appart from the taken points. Continuing
we take all the samples from `point_cloud`.
Parameters
----------
point_cloud : :obj:`Numpy Array`
List of points to take samples from.
np_samples : int
Number of samples that we want to take. It has to be smaller than
the dimension of `point_cloud`.
seed : None or int
Set a random seed.
Returns
-------
:obj:`Numpy Array`
Matrix storing the coordinates of the sampled points.
"""
if seed != None:
np.random.seed(seed)
no_points = len(point_cloud)
no_samples = min(no_points, no_samples)
Dist = dist.squareform(dist.pdist(point_cloud))
k = int(np.random.rand() * no_points) - 1
selection = [k]
point_selection = [point_cloud[k]]
for i in range(no_samples-1):
not_selected = np.setdiff1d(range(no_points), selection)
rest_Dist = np.min(Dist[not_selected][:, selection], axis=1)
k = not_selected[np.argmax(rest_Dist)]
selection.append(k)
point_selection.append(point_cloud[k])
return np.array(point_selection)
[docs]def circle(no_points, radius):
""" Take random points from a circle on the plane. This circle has
centre `(0, 0)`.
Parameters
----------
no_points : int
Number of points wanted.
radius : float
Radius of the circle.
Returns
-------
:obj:`Numpy Array`
Coordinates of sampled points from the circle.
"""
point_cloud = []
step = 2 * np.pi / (no_points)
for n in range(no_points):
point_cloud.append([radius * np.cos(n * step),
radius * np.sin(n * step)])
return np.asarray(point_cloud)
[docs]def random_circle(no_points, radius, epsilon, center=[0, 0], seed=None):
""" Take random points around a circle on the plane.
Parameters
----------
no_points : int
Number of points wanted.
radius : float
Radius of the circle.
epsilon : float
Noise that we want to apply to each sampled point.
centre : `list(float, float)`
Two entries specifying the position of the centre.
seed : None or int
Set a random seed.
Returns
-------
:obj:`Numpy Array`
Coordinates of sampled points from around the circle.
"""
if seed != None:
np.random.seed(seed)
point_cloud = []
for n in range(no_points):
random_angle = np.random.rand() * 2 * np.pi
random_rad = radius * (1 + np.random.rand() * epsilon)
point_cloud.append([center[0] + random_rad * np.cos(random_angle),
center[1] + random_rad * np.sin(random_angle)])
return np.asarray(point_cloud)
[docs]def ball(no_points, radius, dim):
""" Take random points from a ball of a given dimension. This ball has
centre `(0, 0, 0)`.
Parameters
----------
no_points : int
Number of points wanted.
radius : float
Radius of the ball.
dim : int
Dimension of the ball.
Returns
-------
:obj:`Numpy Array`
Coordinates of sampled points from the ball.
"""
point_cloud = []
for n in range(no_points):
valid_point = False
while valid_point is False:
point = []
for d in range(dim):
point.append((np.random.rand() - 0.5) * radius)
v = np.array(point)
if np.linalg.norm(v) < radius:
valid_point = True
point_cloud.append(point)
return np.asarray(point_cloud)
[docs]def random_sphere(no_points, radius, dim):
""" Take random points from a sphere of a given dimension. This sphere has
centre `(0, 0, 0)`.
Parameters
----------
no_points : int
Number of points wanted.
radius : float
Radius of the sphere.
dim : int
Dimension of the sphere.
Returns
-------
:obj:`Numpy Array`
Coordinates of sampled points from the sphere.
"""
point_cloud = []
for n in range(no_points):
point = []
for d in range(dim):
point.append((np.random.rand() - 0.5) * radius)
v = np.array(point)
norm = np.linalg.norm(v)
for d in range(dim):
point[d] = point[d] / norm
point_cloud.append(point)
return np.asarray(point_cloud)
[docs]def random_cube(no_points, dim):
""" Take random points from a unit cube around the origin. This cube can be
of various dimensions.
Parameters
----------
no_points : int
Number of points wanted.
dim : int
Dimension of the cube.
Returns
-------
:obj:`Numpy Array`
Coordinates of sampled points from the cube.
"""
point_cloud = []
for n in range(no_points):
point = []
for d in range(dim):
point.append(np.random.rand() - 0.5)
point_cloud.append(point)
return np.asarray(point_cloud)
[docs]def grid(hdiv, vdiv):
""" Take the nodes from a hdiv x vdiv grid on 2D plane.
Parameters
----------
hdiv : int
Number of rows.
vdiv : int
Number of columns.
Returns
-------
:obj:`Numpy Array`
List of points.
"""
hshift = hdiv / 2. - 0.5
vshift = vdiv / 2. - 0.5
point_cloud = []
for i in range(hdiv):
for j in range(vdiv):
point_cloud.append([i - hshift, j - vshift])
return np.asarray(point_cloud)
[docs]def grid_tridimensional(hdiv, vdiv, ddiv):
""" Take the nodes from a hdiv x vdiv x ddiv grid on 3D space.
Parameters
----------
hdiv : int
Number of rows.
vdiv : int
Number of columns.
ddiv : int
Number of flats.
Returns
-------
:obj:`Numpy Array`
List of points.
"""
hshift = hdiv / 2. - 0.5
vshift = vdiv / 2. - 0.5
dshift = ddiv / 2. - 0.5
point_cloud = []
for i in range(hdiv):
for j in range(vdiv):
for k in range(ddiv):
point_cloud.append([i - hshift, j - vshift, k - dshift])
return np.asarray(point_cloud)
[docs]def torus3D(no_points, min_rad=1, max_rad=3):
""" Take samples from a torus embedded in 3D space.
Parameters
----------
no_points : int
Number of points to be taken.
min_rad : float, default is `1`
Radius of circle on section of the torus.
max_rad : float, default is `3`
Distance from the torus centre to the centre of the section.
Returns
-------
:obj:`Numpy Array`
List of points.
"""
if min_rad > max_rad:
raise ValueError
point_cloud = []
for i in range(no_points):
theta = np.random.rand() * 2 * np.pi
alpha = np.random.rand() * 2 * np.pi
point_cloud.append([
(max_rad + min_rad * np.cos(alpha)) * np.cos(theta),
(max_rad + min_rad * np.cos(alpha)) * np.sin(theta),
min_rad * np.sin(alpha)])
return np.asarray(point_cloud)