consteig: Compile-Time Eigenvalue and Eigenvector Solver
consteig is a header-only C++ compile-time eigenvalue and eigenvector solver that relies solely on a C++17 compatible compiler (no stdlib dependency or .cpp files). I started this project six years ago and only recently returned to finish it. Although technically this is a "personal project", I intend for it to be used by other C++ programmers (or math enthusiasts) and consider it "production-quality", thus a formal post is warranted.
Eigenvalues and eigenvectors are crucial concepts in linear algebra. Eigenvectors are vectors whose directions remain unchanged when linear transformations are applied. Eigenvalues are the factors by which an eigenvector is stretched or shrunk. They are useful in many engineering problems. In certain cases, the matrix from which you want to compute eigenvalues/vectors remains constant, effectively making the eigenvalues/vectors constants. This includes state space matrices for LTI systems, roots of a polynomial, structural dynamics, and some graph/network problems.
In a C++ program, if you need these eigenvalues/eigenvectors, the typical approaches are (1) calculate them at runtime using libraries like Eigen or (2) compute them in MATLAB/Python and hard-code them into your program. My project pushes all that math to compile-time using the compiler itself. This means you can define static matrices at compile time and save the eigenvalues/vectors as constants in memory, without consuming any runtime cycles or independently tracking/calculating them with another tool.
For example, you can do something like:
// 3rd order butterworth with 100Hz cut-off and 1kHz sample rate
static constexpr constfilt::Butterworth<double, 3> b(100.0, 1000.0);
//Call at 1kHz at run-time
b(new_sample);This way, you never need to use Python or MATLAB to figure out what those coefficients are. Additionally, I have another less-polished/less-tested/less-complete compile-time library called constfilt that does exactly that. consteig is available on GitHub and in vcpkg; I'm also working on Conan.
Blogger's Review: The implementation of consteig showcases the immense potential of compile-time computation in C++. By transferring complex linear algebra operations to the compile phase, it not only boosts runtime efficiency but also reduces external dependencies, expanding the applicability of C++ in scientific computing. It will be interesting to see how it performs in practical engineering applications, especially in real-time systems.