numerics

numerics is a C++20 library of numerical methods. It covers dense, banded and sparse linear algebra, Krylov solvers, eigenvalues and the SVD, ODE integrators, PDE operators, spectral transforms, quadrature, root finding, graphs and sampling. The arithmetic lives in num::kernel, a set of allocation-free loops over raw pointers with no dependencies. BLAS, LAPACK, OpenMP, CUDA, FFTW and SuiteSparse are used when they are present.

I started numerics to pull the code from my research and my numerical methods courses (fluid simulation, stochastic modeling, graph algorithms, linear algebra) into one library. I maintain it myself, and it keeps growing alongside my research, so use it with appropriate caution!!

Every feature is explained by a complete program in examples/, with the output it prints. The documentation indexes them by feature and has a reference page for every container, concept and kernel.

Setup

include(FetchContent)
FetchContent_Declare(numerics
    GIT_REPOSITORY https://github.com/AdityaDendukuri/numerics.git
    GIT_TAG v1.0.0)
FetchContent_MakeAvailable(numerics)
target_link_libraries(my_program PRIVATE numerics::numerics)

numerics::core has no external dependency, and numerics::kernel is num::kernel alone.

cmake --preset dev && cmake --build --preset dev && ctest --preset dev

Standout features from my PhD research

Feature	Example
Refactoring after a local change, with Woodbury-corrected LU while few states differ and block LU that keeps every block before the first change	16_factor_reuse.cpp
Solving with A + PQT from a factorization of A	17_woodbury_low_rank_update.cpp
diag(A-1) of a sparse M-matrix from a block of random probes	19_probed_inverse_diagonal.cpp
Shifted systems (sI - A)x = b at many shifts from one Hessenberg reduction, and Talbot inversion	03_resolvent_and_expv.cpp, 13_talbot_spectral_validation.cpp

License

MIT. See LICENSE and THIRD_PARTY_LICENSES.md.