Stable, efficient, and modular computational tools for solving large and dense eigenvalue and linear problems are critically important in all areas of quantum chemistry. Direct solution methods based on element-wise operations are virtually useless for the extremely large, dense or irregularly sparse coefficient matrices frequently encountered in electronic structure calculations; even explicit computation and storage of the coefficient matrices is often prohibitive. Many codes include custom matrix-free implementations of Krylov subspace algorithms for some types of large and dense linear problems. However, these implementations tend to be narrowly tailored to specific environments and deeply buried in — often proprietary — other code. I present 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 application programming interface (API) design and modular structure, which enables integration with specialized matrix–vector evaluation “engines”. The flexible API  of libkrylov features pluggable preconditioning, orthonormalization, and convergence control options. Diagonal (conjugate gradient, CG), Davidson, and Jacobi–Davidson preconditioners are available, along with orthonormal (conventional) and nonorthonormal schemes. The library is implemented in portable Fortran 2003 and takes advantage of the runtime polymorphism capabilities afforded by this standard. It can also be interfaced from C/C++ code bases through a simple funtion-based API.

Libkrylov, a modular open-source software library for extremely large on-the-fly matrix computations

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