test_matrix_exponential

test_matrix_exponential, a FORTRAN77 code which contains some simple tests for software that computes 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, that is

exp(A) = sum ( 0 <= i < oo ) A^i / i!
Even for this simple case, and for a matrix of small order, it can be quite difficult to compute the matrix exponential accurately.

The code needs the C8LIB and R8LIB libraries.

Licensing:

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

Languages:

test_matrix_exponential is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

Related Data and Programs:

test_matrix_exponential_test

expokit, a FORTRAN77 library which solves various forms of the matrix exponential problem, by Roger Sidje.

matrix_exponential, a FORTRAN77 library which demonstrates some simple approaches to the problem of computing the exponential of a matrix.

R8LIB, a FORTRAN77 library which contains many utility routines using double precision real (R8) arithmetic.

TEST_MAT, a FORTRAN77 library which defines test matrices.

Reference:

  1. Alan Laub,
    Review of "Linear System Theory" by Joao Hespanha,
    SIAM Review,
    Volume 52, Number 4, December 2010, page 779-781.
  2. 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.
  3. 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.
  4. Cleve Moler,
    Cleve's Corner: A Balancing Act for the Matrix Exponential,
    July 23rd, 2012.
  5. Roger Sidje,
    EXPOKIT: Software Package for Computing Matrix Exponentials,
    ACM Transactions on Mathematical Software,
    Volume 24, Number 1, 1998, pages 130-156.
  6. 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:

Last modified on 24 October 2023.