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A library for computing samplings in arbitrary dimensions

Project description

A Collection of Space-filling Sampling Designs for Arbitrary Dimensions. The API is structured such that the top level packages represent the shape of the domain you are interested in:

  • ball - The n-dimensional solid unit ball

  • directional - The space of unit length directions in n-dimensional space. You can also consider this a sampling of the boundary of the n-dimensional unit ball.

  • hypercube - The n-dimensional solid unit hypercube \(x \\in [0,1]^n\).

  • subspace - Sampling a n-1-dimensional subspace orthogonal to a unit vector or sampling the Grassmanian Atlas of projections from a dimension n to a lower dimension m.

  • shape - a collection of (n-1)-manifold and non-manifold shapes embedded in an n dimensional space. For now these must all be sampled using a uniform distribution.

Within each module is a list of ways to fill the space of the samples. Note, that not all of the methods listed below are applicable to the modules listed above. They include:

  • Uniform - a random, uniform distribution of points (available for ball, directional, hypercube, subspace, and shape)

  • Normal - a Gaussian distribution of points (available for hypercube)

  • Multimodal - a mixture of Gaussian distributions of points (available for hypercube)

  • CVT - an approximate centroidal Voronoi tessellation of the points constrained to the given space (available for hypercube and directional)

  • LHS - a Latin hypercube sampling design of points constrained to the space (available for hypercube)

Including:
  • Uniform sampling of a n-dimensional ball

  • Uniform sampling of the directions on an n-dimensional sphere

  • Sampling the Grassmannian Atlas

  • An approximate Centroidal Voronoi Tessellation using a Probabilistic Lloyd’s Algorithm

  • An approximate Constrained Centroidal Voronoi Tessellation on an n-sphere

The python CVT code is adapted from a C++ implementation provided by Carlos Correa. The Grassmannian sampler is adapted from code from Shusen Liu.

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