libkrylov, a Modular Open-Source Software Library for Extremely Large On-the-Fly Matrix Computations

We present the design and implementation of libkrylov, an open-source library for solving matrix-free eigenvalue, linear, and shifted linear equations using Krylov subspace methods. The primary objectives of libkrylov are flexible API design and modular structure, which enables integration with specialized matrix--vector evaluation ``engines''. Libkrylov features pluggable preconditioning, orthonormalization, and tunable convergence control. Diagonal (conjugate gradient, CG), Davidson, and Jacobi--Davidson preconditioners are available, along with orthonormal and nonorthonormal (nKs) schemes. All functionality of libkrylov is exposed via Fortran and C application programming interfaces (APIs). We illustrate the performance of libkrylov for eigenvalue calculations arising in the time-dependent density functional theory (TDDFT) in the Tamm--Dancoff approximation (TDA) and discuss the convergence behavior as a function of preconditioning and orthonormalization methods.