Using Eigen for Matrix Operations in Quantitative Finance
Summary
The article explains why production quantitative software should generally rely on a maintained numerical library instead of a custom matrix implementation. It introduces Eigen as a C++ option, describing its runtime-sized matrices, dense and sparse structures, storage choices, community testing, and expression templates, which can combine arithmetic into fewer passes over data.
Examples demonstrate matrix and vector construction, addition and subtraction, scalar arithmetic, transposition, matrix products, dot and cross products, and reductions such as sums and traces. The article also cautions that in-place transpose assignment can produce unexpected behavior and points to a dedicated in-place operation. It briefly surveys decompositions, eigenvalue calculations, and geometric transforms, with applications such as correlated asset paths and finite-difference pricing. The material is introductory: it presents API examples and qualitative benefits, but does not benchmark performance or compare Eigen systematically with other libraries.
Key ideas
- A maintained matrix library can reduce the development, testing, and optimization burden of custom numerical code.
- Eigen supports fixed-size and runtime-sized matrices, dense and sparse storage, and common linear algebra operations.
- Expression templates can let the compiler combine arithmetic expressions into a single pass over vector data.
- In-place transposition should use the library’s dedicated operation to avoid unintended results.
- The article identifies decompositions and eigenvalue tools as building blocks for quantitative finance applications.
Tags
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.