test_matrix_exponential

test_matrix_exponential, an Octave 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!

test_matrix_exponential 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 MIT 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

jordan_matrix_random, an Octave code which returns a random matrix in Jordan canonical form.

matrix_exponential, an Octave code which demonstrates some simple approaches to the problem of computing the exponential of a matrix.

r8lib, an Octave code which contains many utility routines using double precision real (R8) arithmetic.

test_matrix, an Octave code which defines test matrices for which the condition number, determinant, eigenvalues, eigenvectors, inverse, null vectors, P*L*U factorization or linear system solution are known. Examples include the Fibonacci, Hilbert, Redheffer, Vandermonde, Wathen and Wilkinson 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:

• c8mat_exp_a.m, returns a complex test matrix.
• c8mat_exp_expa.m, returns the exact exponential of the complex test matrix.
• c8mat_exp_n.m, returns the order of a complex test matrix.
• c8mat_exp_story.m, prints a "story" for each complex test case.
• c8mat_exp_test_num.m, returns the number of complex test matrices.
• c8mat_print.m, prints a C8MAT;
• c8mat_print_some.m, prints some of a C8MAT;
• r8mat_exp_a.m, returns a real test matrix.
• r8mat_exp_expa.m, returns the exact exponential of the real test matrix.
• r8mat_exp_n.m, returns the order of a real test matrix.
• r8mat_exp_story.m, prints a "story" for each real test case.
• r8mat_exp_test_num.m, returns the number of real test matrices.
• r8mat_print.m, prints an R8MAT;
• r8mat_print_some.m, prints some of an R8MAT;