matrices-expm is a collection of MATLAB functions that generate the selected matrices for testing the matrix exponential. All matrices are square and have a fixed size, ranging from 2-by-2 to 20-by-20. Most of the matrices are taken from the matrix exponential literature.
The matrices are used in
X. Liu. Mixed-precision Paterson–Stockmeyer method for evaluating polynomials of matrices, preprint, https://arxiv.org/abs/2312.17396.
The 42 selective test matrices (see the .m files for the full reference) are as follows.
alhi09r1 - 2-by-2 matrix used in \cite{alhi09}.
alhi09r2 - 2-by-2 matrix used in \cite{alhi09}.
alhi09r3 - 2-by-2 matrix used in \cite{alhi09}.
alhi09r4 - 4-by-4 matrix used in \cite{alhi09}.
dahi03 - 4-by-4 matrix from \cite[Ex.~3]{dahi03}.
dipa00 - 8-by-8 matrix from \cite[Ex.~3.10]{dipa00}.
edst04 - 20-by-20, the logarithm of Cholesky factor of Pascal matrix from \cite{edst04}.
eigt7 - 7-by-7 matrix from EIGTOOL1.
fahi19r1 - 4-by-4 matrix from \cite{fahi19}.
fahi19r2 - 3-by-3 matrix from \cite{fahi19}.
fahi19r3 - 2-by-2 matrix from \cite{fahi19}.
fahi19r4 - 10-by-10 matrix from \cite{fahi19}.
fasi7 - 7-by-7, Massimiliano Fasi's idea from \cite[p. 81]{kags77a}.
jemc05r1 - 3-by-3 matrix from \cite[(52)]{jemc05}.
jemc05r2 - 6-by-6 matrix from \cite[(55)]{jemc05}.
kase99 - 10-by-10 matrix from \cite[Table 1]{kase99}.
kela89r1 - 4-by-4 matrix from \cite[p.~206]{kela89}.
kela89r2 - 2-by-2 matrix from \cite[Ex.5]{kela89}.
kela98r1 - 2-by-2 matrix from \cite[Ex.~2]{kela98}.
kela98r2 - 5-by-5 matrix from \cite[p.~655]{kela98}.
kela98r3 - 2-by-2 matrix from \cite[Ex.~3]{kela98}.
kuda10 - 20-by-20 matrix from \cite{kuda10}.
lara17r1 - 2-by-2 matrix from \cite[Benchmark #1]{lara17}, \cite[Problem 1]{zhao17}.
lara17r2 - 3-by-3 matrix from \cite[Benchmark #2]{lara17}, \cite[Problem 2]{zhao17}.
lara17r3 - 3-by-3 matrix from \cite[Benchmark #3]{lara17}, \cite[Problem 3]{zhao17}.
lara17r4 - 4-by-4 matrix from \cite[Benchmark #4]{lara17}, \cite[Problem 4]{zhao17}.
lara17r5 - 12-by-12 matrix from \cite[Benchmark #5]{lara17}, \cite[Problem 5]{zhao17}.
lara17r6 - 8-by-8 matrix from \cite[Benchmark #6]{lara17}, \cite[Problem 6]{zhao17}.
mopa03r1 - 4-by-4 matrix from \cite{mopa03}.
mopa03r2 - 3-by-3 matrix from \cite{mopa03}.
naha95 - 3-by-3 matrix from \cite[p. 370]{naha95}.
nies19 - 2-by-2 matrix from Jitse Niesen, used in \cite{fahi19}.
pang85r1 - 6-by-6 matrix from \cite[p.~7, Ex I]{pang85}.
pang85r2 - 20-by-20 matrix from \cite[p.~9, Ex II]{pang85}.
pang85r3 - 20-by-20 matrix from \cite[p.~10, Ex III]{pang85}.
ross8 - 8-by-8 classic symmetric eigenvalue test problem, scaled.
trem05 - 3-by-3 matrix from \cite[(14.17), p. 141]{trem05}.
tsin13 - 13-by-13 matrix, strictly upper triangular part of the Schur matrix of the involutory matrix generated by MATLAB gallery.
ward77r1 - 3-by-3 matrix from Test 1 of \cite{ward77}.
ward77r2 - 3-by-3 matrix from Test 2 of \cite{ward77}.
ward77r3 - 3-by-3 matrix from Test 3 of \cite{ward77}.
ward77r4 - 10-by-10 matrix from Test 4 of \cite{ward77}.
Other M-files: am_properties.m: lists properties of the matrices and is intended for use when this collection is integrated
as a group in the Anymatrix collection.
This collection is ready to include as a group in the Anymatrix for which the name expm should be used.
MATLAB 2020b or newer is required for the use of Anymatrix.
Any forms of contributions are welcomed; feel free to pull request or contact the developer for suggestions.
See license.txt for licensing information.