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""" This module provides functions to generate non-dominated points for testing purposes """
import math
import random
def get_non_dominated_points(n_points, n_dim=3, mode='spherical'):
""" Returns a list of non-dominated points:
- n_points: number of points
- n_dim: number of dimensions
- mode: 'spherical' or 'linear' """
if n_dim == 2:
if mode == 'spherical':
return spherical_front_2d(1, n_points, normalized=False)
elif mode == 'linear':
return linear_front_2d(1, n_points, normalized=False)
if n_dim == 3:
if mode == 'spherical':
return spherical_front_3d(1, n_points, normalized=False)
elif mode == 'linear':
return linear_front_3d(1, n_points, normalized=False)
elif n_dim == 4:
if mode == 'spherical':
return spherical_front_4d(1, n_points, normalized=False)
elif mode == 'linear':
return linear_front_4d(1, n_points, normalized=False)
else:
raise ValueError("Invalid number of dimensions")
def get_random_points(n_points, n_dim):
""" Returns a list of random points between 0 and 1, with n_points and n_dim dimensions """
return [[random.random() for _ in range(n_dim)] for _ in range(n_points)]
def get_stacked_points(n_points, points_definitions):
""" Returns a list of points with n_points and n_dim dimensions,
where point from i-th dimension is defined by points_definitions[i]:
- 'random' for random value between 0 and 1
- int for a fixed value """
points = []
for i in range(n_points):
points.append([])
for p_def in points_definitions:
if p_def == 'random':
points[-1].append(random.random())
elif isinstance(p_def, int):
points[-1].append(p_def)
else:
raise ValueError("Invalid point definition")
return points
def permute_points(points, permutation):
""" takes a list of points (n x dim) and a permutation (dim)
and returns the points with the permutation applied """
return [[point[permutation[i]] for i in range(len(permutation))] for point in points]
def spherical_front_2d(distance, num_points, normalized):
""" Returns a list of non-dominated points on the 2D spherical front """
vectors = []
if normalized:
v1 = [0, distance]
v2 = [distance, 0]
vectors = [v1, v2]
while len(vectors) < num_points:
phi = random.random() * math.pi / 2
vectors.append([distance * math.cos(phi), distance * math.sin(phi)])
return vectors
def linear_front_2d(distance, num_points, normalized=True):
""" Returns a list of non-dominated points on the 2D linear front """
vectors = []
if normalized:
v1 = [1, 1 - distance]
v2 = [1 - distance, 1]
vectors = [v1, v2]
while len(vectors) < num_points:
x = random.random()
vectors.append([x, 1 - x])
return vectors
def spherical_front_3d(distance, num_points, normalized=True):
""" Returns a list of non-dominated points on the 3D spherical front """
vectors = []
if normalized:
v1 = [0, 0, distance]
v2 = [0, distance, 0]
v3 = [distance, 0, 0]
vectors = [v1, v2, v3]
while len(vectors) < num_points:
x, y, z = 1, 1, 1
while (math.sqrt(x * x + y * y + z * z) > 1) or (x < 0.5 and y < 0.5 and z < 0.5):
x = next_gaussian_double()
y = next_gaussian_double()
z = next_gaussian_double()
r1 = math.sqrt(x * x + y * y + z * z)
alpha = math.acos(z / r1)
beta = math.atan2(y, x)
vect = [distance * math.sin(alpha) * math.cos(beta),
distance * math.sin(alpha) * math.sin(beta),
distance * math.cos(alpha)]
vectors.append(vect)
return vectors
def linear_front_3d(distance, num_points, normalized):
""" Returns a list of non-dominated points on the 3D linear front """
vectors = []
if normalized:
v1 = [1, 1, 1 - distance]
v2 = [1, 1 - distance, 1]
v3 = [1 - distance, 1, 1]
vectors = [v1, v2, v3]
while len(vectors) < num_points:
array = [0.0]
for _ in range(2):
array.append(distance * random.random())
array.append(distance)
array.sort()
x = 1 - (array[1] - array[0])
y = 1 - (array[2] - array[1])
z = 1 - (array[3] - array[2])
vectors.append([x, y, z])
return vectors
def linear_front_4d(distance, num_points, normalized):
""" Returns a list of non-dominated points on the 4D linear front """
vectors = []
if normalized:
v1 = [0, 0, 0, distance]
v2 = [0, 0, distance, 0]
v3 = [0, distance, 0, 0]
v4 = [distance, 0, 0, 0]
vectors = [v1, v2, v3, v4]
while len(vectors) < num_points:
array = [0.0] + [distance * random.random() for _ in range(3)] + [distance]
array.sort()
x = array[1] - array[0]
y = array[2] - array[1]
z = array[3] - array[2]
w = array[4] - array[3]
v = [x, y, z, w]
vectors.append(v)
return vectors
def spherical_front_4d(distance, num_points, normalized):
""" Returns a list of non-dominated points on the 4D spherical front """
vectors = []
if normalized:
v1 = [0, 0, 0, distance]
v2 = [0, 0, distance, 0]
v3 = [0, distance, 0, 0]
v4 = [distance, 0, 0, 0]
vectors = [v1, v2, v3, v4]
while len(vectors) < num_points:
x, y, z, w = 1, 1, 1, 1
while (math.sqrt(x * x + y * y + z * z + w * w) > 1) or (x < 0.5 and y < 0.5 and z < 0.5 and w < 0.5):
x = next_gaussian_double()
y = next_gaussian_double()
z = next_gaussian_double()
w = next_gaussian_double()
alpha = math.atan(math.sqrt(y * y + z * z + w * w) / x)
beta = math.atan(math.sqrt(z * z + w * w) / y)
gamma = 2 * math.atan(z / (math.sqrt(z * z + w * w) + w))
v = [
distance * math.cos(alpha),
distance * math.sin(alpha) * math.cos(beta),
distance * math.sin(alpha) * math.sin(beta) * math.cos(gamma),
distance * math.sin(alpha) * math.sin(beta) * math.sin(gamma)
]
vectors.append(v)
return vectors
def next_gaussian_double():
factor = 2.0
while True:
result = random.gauss(0, 1)
if result < -factor:
continue
if result > factor:
continue
if result >= 0:
result = result / (2 * factor)
else:
result = (2 * factor + result) / (2 * factor)
return result
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