def test_circumsphere():
from numpy import allclose
from numpy.random import normal, uniform
from adaptive.learner.triangulation import circumsphere, fast_norm
def generate_random_sphere_points(dim, radius=0):
"""https://math.stackexchange.com/a/1585996"""
vec = [None] * (dim + 1)
center = uniform(-100, 100, dim)
radius = uniform(1.0, 100.0) if radius == 0 else radius
for i in range(dim + 1):
points = normal(0, size=dim)
x = fast_norm(points)
points = points / x * radius
vec[i] = tuple(points + center)
return radius, center, vec
for dim in range(2, 10):
radius, center, points = generate_random_sphere_points(dim)
circ_center, circ_radius = circumsphere(points)
err_msg = ""
if not allclose(circ_center, center):
err_msg += f"Calculated center ({circ_center}) differs from true center ({center})\n"
if not allclose(radius, circ_radius):
err_msg += (
f"Calculated radius {circ_radius} differs from true radius {radius}\n"
)
if err_msg:
raise AssertionError(err_msg)
def choose_point_in_simplex(simplex, transform=None):
"""Choose a new point in inside a simplex.
Pick the center of the simplex if the shape is nice (that is, the
circumcenter lies within the simplex). Otherwise take the middle of the
longest edge.
Parameters
----------
simplex : numpy array
The coordinates of a triangle with shape (N+1, N).
transform : N*N matrix
The multiplication to apply to the simplex before choosing
the new point.
Returns
-------
point : numpy array of length N
The coordinates of the suggested new point.
"""
if transform is not None:
simplex = np.dot(simplex, transform)
# choose center if and only if the shape of the simplex is nice,
# otherwise: the center the longest edge
center, _radius = circumsphere(simplex)
if point_in_simplex(center, simplex):
point = np.average(simplex, axis=0)
else:
distances = scipy.spatial.distance.pdist(simplex)
distance_matrix = scipy.spatial.distance.squareform(distances)
i, j = np.unravel_index(np.argmax(distance_matrix),
distance_matrix.shape)
point = (simplex[i, :] + simplex[j, :]) / 2
if transform is not None:
point = np.linalg.solve(transform, point) # undo the transform
return point
