EIKernel

EIKernel is a modular computational kernel designed for eigenvalue and kernel-based computations in numerical linear algebra. It provides an abstraction layer for matrix-free operations and supports a range of iterative solvers, enabling efficient handling of large-scale problems. The design emphasizes flexibility, performance portability across hardware backends, and interoperability with existing scientific computing ecosystems.

The architecture centers on a kernel abstraction that specializes in matrix-vector products and kernel evaluations. Backends expose CPU, GPU, and distributed execution paths, while a plugin system allows kernel types such as polynomial, radial basis function, and sigmoid kernels, as well as customization of preconditioners and normalization strategies. Lazy evaluation and result caching optimize repeated computations.

Core features include iterative solvers for large sparse or dense matrices (Lanczos, Arnoldi), spectral decomposition routines, and utilities for constructing kernel matrices from data. It offers bindings for Python and C++, support for automatic differentiation in optimization workflows, and integration with common linear algebra libraries.

Common applications span spectral clustering, kernel principal component analysis, model order reduction, quantum chemistry simulations, and graph analytics. EIKernel is designed to be data- and hardware-aware, enabling scalable experiments on multi-core CPUs and accelerators.

The project is community-driven and open-source, with ongoing development and documentation. It aims to provide a standardized, portable infrastructure for eigenvalue and kernel computations across research and industry.