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}

Different parameterizations of f encompass a wide variety of spectral quantities, including the matrix inverse A^{-1}, the matrix exponential \mathrm{exp}(A), the matrix logarithm \mathrm{log}(A), etc.

Similarly, trace or diagonal estimators may be used to approximate the numerical rank, the log-determinant, the Schatten norms, the eigencount, the Estrada index, the Heat Kernel Signature, etc.

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

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