Package overview

primate, short for Probabilistic Implicit Matrix Trace Estimator, is a Python package that provides estimators of quantities from matrices, linear operators, and matrix functions:

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

This definition is quite general in that different parameterizations of f produce a variety of spectral quantities, including the matrix inverse A^{-1}, the matrix exponential \mathrm{exp}(A), the matrix logarithm \mathrm{log}(A), and so on.

Composing these with trace and diagonal estimators yields approximations for the numerical rank, the log-determinant, the Schatten norms, the eigencount, the Estrada index, the Heat Kernel Signature, and so on.

Notable features of primate include:

Efficient methods for trace, diagonal, and matrix function approximation
Support for arbitrary matrix types, e.g. NumPy arrays, sparse matrices, or LinearOperator’s
Support for arbitrary matrix functions, i.e. Callable’s (Python) and invocable’s¹ (C++)
Matrix-free interface to the Lanczos and Golub-Welsch methods
Various composable stopping criteria for easy and adaptive convergence checking

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

Footnotes

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