primme

Primme, short for PReconditioned Iterative Methods for the Eigenvalue Problem, is a software library for computing a subset of eigenpairs of large sparse matrices. It targets generalized eigenproblems Ax = λBx and standard eigenproblems where B is the identity, with support for real or complex matrices and both Hermitian (symmetric) and non-Hermitian cases. The library emphasizes robustness and performance on high-performance computing platforms by providing a range of iterative solvers and preconditioning options.

A core strength of Primme is its collection of solvers, including Jacobi-Davidson variants, generalized Davidson methods, and the locally optimal block preconditioned conjugate gradient (LOBPCG) method. It is designed to compute either extreme eigenvalues or interior eigenvalues using shift-and-invert or other spectral transformation techniques, making it suitable for targeting specific parts of the spectrum. The package also supports various preconditioning strategies, flexible restart and locking schemes, and can operate with different precision levels (real and complex, single and double).

Primme offers a C API with Fortran wrappers and provides interfaces to MATLAB and Python, facilitating integration into diverse workflows. It is intended for parallel execution on multi-core and multi-processor environments using MPI and OpenMP, enabling scalable performance on large problems. The library is used in fields such as quantum chemistry, materials science, and structural engineering, where computing a small number of eigenpairs of large sparse matrices is essential.

In operation, users typically supply a matrix or a function that performs matrix-vector products, along with the desired number of eigenpairs and convergence criteria. The project continues to be developed to improve robustness, efficiency, and usability in large-scale eigenvalue computations.