Dirac Mixture Approximation Library (C++)

Overview

This repository provides a high-performance C++ implementation for Dirac mixture reduction and Gaussian-to-Dirac approximation.

The library focuses on efficient, optimization-based approximation of probability distributions using Localized Cumulative Distribution (LCD) distances and gradient-based minimization.

The implementation is designed for:

• High-dimensional problems
• Performance-critical applications
• Modular integration into estimation pipelines
• Threaded and non-threaded execution

Dirac-to-Dirac Reduction

Reduces a high-resolution Dirac mixture to a compact representation.

Implementations:

• dirac_to_dirac_approx_short
• dirac_to_dirac_approx_short_thread
• dirac_to_dirac_approx_short_function

All implementations follow the dirac_to_dirac_approx_i<T> interface, except:

• dirac_to_dirac_approx_short_function, which follows dirac_to_dirac_approx_function_i<T>.

Supported input formats:

• Raw pointers
• GSL vectors
• GSL matrices

Gaussian-to-Dirac Approximation

Approximates a multivariate Gaussian distribution by a Dirac mixture.

Implementations:

• gm_to_dirac_short
• gm_to_dirac_short_standard_normal_deviation

All implementations follow the gm_to_dirac_approx_i<T> interface.

Design Highlights

• Template-based numeric precision (float, double)
• Unified interface design for interchangeable implementations
• GSL-based minimization backend
• Analytical gradients
• Threaded performance variants
• Configurable optimization via ApproximateOptions

The library is structured to separate interfaces, algorithmic implementations, and optimization backends, enabling clean extension and experimentation.