samply 0.1.2

A Python library for generating space-filling sample sets of low to moderate dimensional data from domains including:

• Euclidean space

• Grassmannian atlas

• Surface of an n-Sphere

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)

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

pip install samply

git clone https://github.com/maljovec/samply.git
cd samply
python setup.py [build|develop|install]

import samply

direction_samples = samply.directional.uniform(10000, 2)
ball_samples = samply.ball.uniform(10000, 2)
scvt_samples = samply.directional.cvt(10000, 2)
cvt_samples = samply.hypercube.cvt(10000, 2)

projection_samples = samply.subspace.grassmannian(10000, 3, 2)

python setup.py test