Package overview

primate, short for Probabalistic Implicit Matrix Trace Estimator, is a Python package that provides estimators of quantities derived from matrix functions; that is, matrices parameterized by functions:

f(A) \triangleq U f(\Lambda) U^{\intercal}, \quad \quad f : [a,b] \to \mathbb{R}

Estimator approximations are obtained via the Lanczos¹ and stochastic Lanczos quadrature² methods, which are well-suited for sparse or structured operators supporting fast v \mapsto Av actions.

Notable features of primate include:

• Efficient methods for trace, quadrature, and matrix function approximation
• Various distribution / engine choices for random vector generation (the stochastic part!)
• Support for arbitrary matrix functions, i.e. Callable’s (Python) and invocable’s³ (C++)
• Support for arbitrary LinearOperator’s, e.g. those in SciPy or Pylops
• Matrix-free interface to the Lanczos, Golub-Welsch, and Gram Schmidt methods

primate was partially inspired by the imate package—for a comparison of the two, see here.

Footnotes

1. Musco, Cameron, Christopher Musco, and Aaron Sidford. (2018) “Stability of the Lanczos method for matrix function approximation.”

2. Ubaru, S., Chen, J., & Saad, Y. (2017). Fast estimation of tr(f(A)) via stochastic Lanczos quadrature.

3. This includes std::function’s, C-style function pointers, functors, and lambda expressions.