ApproxManifoldProducts.jl

Introduction

Approximate the product between infinite functional objects on a manifold -- i.e. belief products. ApproxManifoldProducts (AMP) is intended for use with the Caesar.jl framework. AMP is intended for development and testing of various kernel embedding methods for approximating functional products.

See Caesar documentation for more details.

Installation

For Julia 0.7 and above press ']' in the Julia REPL:

pkg> add ApproxManifoldProducts

Current Supported (Mixed) Manifolds

NOTE Current work on v0.3.x is transitioning to JuliaManifolds for some of the Manifold abstractions. This package AMP then adds non-parametric probabilistic computations on those and user manifolds.

The following on-manifold function approximations:

• Euclidean (2DOF),
• S1/Circular (1DOF), or SO(2) equivalent.
• SE(2)
• S2 (not implemented yet)

Work in progress on so-called 'subgroup' mixed-manifolds, where DOFs are bunched together for particular manifolds:

• SO(3) / Quaternion,
• Plucker coordinates (SP(3)) for rigid transforms,
• SE(3) for rigid transforms.

Implementation of multivariate methodology requires code to consider "double loops" that iterate over sub-groups, and then within each sub-group as required. The supported list above can be implemented with "single loop" over all DOFs.

Any suggestions or issues welcome.