masspcf.point_process#

masspcf.point_process.sample_poisson(shape, dim=2, rate=1.0, lo=None, hi=None, generator=None, dtype=masspcf.pcloud64)#

Sample a homogeneous spatial Poisson point process.

Each element of the returned tensor is a point cloud of shape \((N_i, \text{dim})\) where \(N_i \sim \text{Poisson}(\lambda V)\) and points are drawn uniformly in the hyperrectangle \([\text{lo}, \text{hi}]\). Here \(V\) is the volume of the region.

Parameters:

  • shape (tuple of int) – Shape of the output tensor.

  • dim (int, optional) – Spatial dimension, by default 2.

  • rate (float, optional) – Intensity \(\lambda\) of the Poisson process, by default 1.0.

  • lo (array_like, optional) – Lower bounds per spatial dimension. Default is zeros.

  • hi (array_like, optional) – Upper bounds per spatial dimension. Default is ones.

  • generator (Generator, optional) – Random number generator. If None, the global generator is used.

  • dtype (type, optional) – pcloud32 or pcloud64, by default pcloud64.

Returns:

Tensor of point clouds with the given shape.

Return type:

PointCloudTensor