BivMatFun

BivMatFun is a Julia package to evaluate bivariate-matrix functions. To install the package into your Julia environment you may run:

import Pkg;
Pkg.add(url = "https://github.com/numpi/BivMatFun.git")

or, alternatively, enter the pkg mode by typing ], and then running:

pkg> add https://github.com/numpi/BivMatFun.git

The function fun2m can be used to evaluate a bivariate matrix function as follows:

using BivMatFun;
X = fun2m(f, A, B, C)

where f(x,y,i,j) computes the (i,j)-th derivative of the desired function. Unless the method based on Taylor expansions is specifically chosen by setting the optional parameter method = BivMatFun.Taylor, the (i,j) parameters can be ignored, as they will always be equal to (0,0)·

Tests

You may run all the tests, which repeat the experiments included in [1]. In order to do that, run the following commands (as above, in pkg mode, which can be enabled by typing ]):

pkg> activate .
pkg> test

Please note that the tests run the solver several times for getting accurate timings, and use reference solutions precomputed using high precision arithmetic. If you wish, these can be regenerated using the script test/construct_test_cases.jl. The latter operation is computationally demanding, so it may require several minutes to an hour to complete.

References

• S. Massei, L. Robol, Recursive Block Diagonalization for evaluating bivariate functions of matrices, in preparation, 2021.