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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 :math:`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)
*

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

Project details


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