KernelyzeBase is a library, written in Fortran and with bindings to OCaml and C, that computes low-rank approximations of two-variable functions (”kernels”).

K(x,y) ~ f1(x) g1(y) + f2(x) g2(y) + . . . + fn(x) gn(y)

For many practically useful two-variable functions (”sign-regular kernels”), KernelyzeBase can compute new approximations which numerically achieve the smallest possible worst-case error among all rank-n approximations.

The worst-case error of these new approximations is much smaller than that of existing approximations such as truncated Taylor series or truncated singular function series (though KernelyzeBase also computes these more-familiar approximations, and weighting can help singular function series perform better).

The approximation computed in KernelyzeBase only applies to the single kernel case.

KernelyzeBase is available under a GNU Affero General Public License version 3 on GitHub. AVAILABLE HERE


KernelyzePro increases the functionality of KernelyzeBase by computing approximations for the products of multiple kernels and providing a thread-safe store of approximations (suitable for use in a multithreaded application). KernelyzePro can be used as a library, but it is available as a stand-alone application or as an excel add-in. Academic licenses are available at a reduced fee.