torch_topological.data

Module for various data operations and data set creation strategies.

torch_topological.data.sample_from_annulus(n, r, R, seed=None)

Sample points from a 2D annulus.

This function samples N points from an annulus with inner radius r and outer radius R.

Parameters:

• n (int) – Number of points to sample

• r (float) – Inner radius of annulus

• R (float) – Outer radius of annulus

• seed (int, instance of np.random.Generator, or None) – Seed for the random number generator, or an instance of such a generator. If set to None, the default random number generator will be used.

Returns:

Tensor containing sampled coordinates.

Return type:

torch.tensor of shape (n, 2)

torch_topological.data.sample_from_disk(n=100, r=0.9, R=1.0, seed=None)

Sample points from disk.

Parameters:

• n (int) – Number of points to sample.

• r (float) – Minimum radius, i.e. the radius of the inner circle of a perfect sampling.

• R (float) – Maximum radius, i.e. the radius of the outer circle of a perfect sampling.

• seed (int, instance of np.random.Generator, or None) – Seed for the random number generator, or an instance of such a generator. If set to None, the default random number generator will be used.

Returns:

Tensor containing the sampled coordinates.

Return type:

torch.tensor of shape (n, 2)

torch_topological.data.sample_from_sphere(n=100, d=2, r=1, noise=None, ambient=None, seed=None)

Sample n data points from a d-sphere in d + 1 dimensions.

Parameters:

• n (int) – Number of data points in shape.

• d (int) – Dimension of the sphere.

• r (float) – Radius of sphere.

• noise (float or None) – Optional noise factor. If set, data coordinates will be perturbed by a standard normal distribution, scaled by noise.

• ambient (int or None) – Embed the sphere into a space with ambient dimension equal to ambient. The sphere is randomly rotated into this high-dimensional space.

• seed (int, instance of np.random.Generator, or None) – Seed for the random number generator, or an instance of such a generator. If set to None, the default random number generator will be used.

Returns:

Tensor of sampled coordinates. If ambient is set, array will be of shape (n, ambient). Else, array will be of shape (n, d + 1).

Return type:

torch.tensor

Notes

This function was originally authored by Nathaniel Saul as part of the tadasets package. [tadasets]

References

[tadasets]

https://github.com/scikit-tda/tadasets

torch_topological.data.sample_from_torus(n, d=3, r=1.0, R=2.0, seed=None)

Sample points uniformly from torus and embed it in d dimensions.

Parameters:

• n (int) – Number of points to sample

• d (int) – Number of dimensions.

• r (float) – Radius of the ‘tube’ of the torus.

• R (float) – Radius of the torus, i.e. the distance from the centre of the ‘tube’ to the centre of the torus.

• seed (int, instance of np.random.Generator, or None) – Seed for the random number generator, or an instance of such a generator. If set to None, the default random number generator will be used.

Returns:

Tensor of sampled coordinates.

Return type:

torch.tensor of shape (n, d)

torch_topological.data.sample_from_unit_cube(n, d=3, seed=None)

Sample points uniformly from unit cube in d dimensions.

Parameters:

• n (int) – Number of points to sample

• d (int) – Number of dimensions.

• seed (int, instance of np.random.Generator, or None) – Seed for the random number generator, or an instance of such a generator. If set to None, the default random number generator will be used.

Returns:

Tensor containing the sampled coordinates.

Return type:

torch.tensor of shape (n, d)