MATRIX_EXPONENTIAL
Algorithms for the Matrix Exponential

MATRIX_EXPONENTIAL is a Python library which exhibits and compares some algorithms for approximating the matrix exponential function.

Formally, for a square matrix A and scalar t, the matrix exponential exp(A*t) can be defined as the sum:

exp(A*t) = sum ( 0 <= i < oo ) A^i t^i / i!

The simplest form of the matrix exponential problem asks for the value when t = 1. Even for this simple case, and for a matrix of small order, it can be quite difficult to compute the matrix exponential accurately.

Licensing:

The computer code and data files described and made available on this web page are distributed under the GNU LGPL license.

Languages:

MATRIX_EXPONENTIAL is available in a C version and a C++ version and a FORTRAN90 version and a MATLAB version and a Python version.

Related Data and Programs:

TEST_MAT, a Python library which defines test matrices.

TEST_MATRIX_EXPONENTIAL, a Python library which defines a set of test cases for computing the matrix exponential.

Reference:

Alan Laub,
Review of "Linear System Theory" by Joao Hespanha,
SIAM Review,
Volume 52, Number 4, December 2010, page 779-781.
Cleve Moler, Charles VanLoan,
Nineteen Dubious Ways to Compute the Exponential of a Matrix, SIAM Review,
Volume 20, Number 4, October 1978, pages 801-836.
Cleve Moler, Charles VanLoan,
Nineteen Dubious Ways to Compute the Exponential of a Matrix, Twenty-Five Years Later,
SIAM Review,
Volume 45, Number 1, March 2003, pages 3-49.
Roger Sidje,
EXPOKIT: Software Package for Computing Matrix Exponentials,
ACM Transactions on Mathematical Software,
Volume 24, Number 1, 1998, pages 130-156.
Robert Ward,
Numerical computation of the matrix exponential with accuracy estimate,
SIAM Journal on Numerical Analysis,
Volume 14, Number 4, September 1977, pages 600-610.

Source Code:

matrix_exponential.py, the source code.
matrix_exponential.sh, runs the tests.
matrix_exponential.txt, the output file.

You can go up one level to the Python source codes.