TEST_MATRIX_EXPONENTIAL
Matrix Exponential TESTS

TEST_MATRIX_EXPONENTIAL is a MATLAB library 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!

TEST_MATRIX_EXPONENTIAL needs the R8LIB library.

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 FORTRAN77 version and a FORTRAN90 version and a MATLAB version.

Related Data and Programs:

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

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

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

TEST_MAT, a MATLAB 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:

• mexp_a.m, returns a test matrix.
• mexp_expa.m, returns the exact exponential of the test matrix.
• mexp_n.m, returns the order of a test matrix.
• mexp_story.m, prints a "story" for each test case.
• mexp_test_num.m, returns the number of test matrices.

Examples and Tests:

• test_matrix_exponential_test.m, calls all the tests;
• test_matrix_exponential_test01.m, compares several algorithms on the test matrices.
• test_matrix_exponential_test_output.txt, output from the tests;

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