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# This file is part of the Gudhi Library - https://gudhi.inria.fr/ - which is released under MIT.
# See file LICENSE or go to https://gudhi.inria.fr/licensing/ for full license details.
# Author(s): Hind Montassif
#
# Copyright (C) 2021 Inria
#
# Modification(s):
# - YYYY/MM Author: Description of the modification
import numpy as np
from ._points import ctorus
from ._points import sphere
def _generate_random_points_on_torus(n_samples, dim):
# Generate random angles of size n_samples*dim
alpha = 2*np.pi*np.random.rand(n_samples*dim)
# Based on angles, construct points of size n_samples*dim on a circle and reshape the result in a n_samples*2*dim array
array_points = np.column_stack([np.cos(alpha), np.sin(alpha)]).reshape(-1, 2*dim)
return array_points
def _generate_grid_points_on_torus(n_samples, dim):
# Generate points on a dim-torus as a grid
n_samples_grid = int((n_samples+.5)**(1./dim)) # add .5 to avoid rounding down with numerical approximations
alpha = np.linspace(0, 2*np.pi, n_samples_grid, endpoint=False)
array_points = np.column_stack([np.cos(alpha), np.sin(alpha)])
array_points_idx = np.empty([n_samples_grid]*dim + [dim], dtype=int)
for i, x in enumerate(np.ix_(*([np.arange(n_samples_grid)]*dim))):
array_points_idx[...,i] = x
return array_points[array_points_idx].reshape(-1, 2*dim)
def torus(n_samples, dim, sample='random'):
"""
Generate points on a flat dim-torus in R^2dim either randomly or on a grid
:param n_samples: The number of points to be generated.
:param dim: The dimension of the torus on which points would be generated in R^2*dim.
:param sample: The sample type of the generated points. Can be 'random' or 'grid'.
:returns: numpy array containing the generated points on a torus.
The shape of returned numpy array is:
If sample is 'random': (n_samples, 2*dim).
If sample is 'grid': (⌊n_samples**(1./dim)⌋**dim, 2*dim), where shape[0] is rounded down to the closest perfect 'dim'th power.
"""
if sample == 'random':
# Generate points randomly
return _generate_random_points_on_torus(n_samples, dim)
elif sample == 'grid':
# Generate points on a grid
return _generate_grid_points_on_torus(n_samples, dim)
else:
raise ValueError("Sample type '{}' is not supported".format(sample))
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