test_matrix_exponential
test_matrix_exponential,
a MATLAB 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.
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
a Python version.
Related Data and Programs:
matrix_exponential,
a MATLAB code which
demonstrates some simple approaches to the problem of computing the
exponential of a matrix.
r8lib,
a MATLAB code which
contains many utility routines using double precision real (R8) arithmetic.
test_mat,
a MATLAB code which
defines test matrices.
test_matrix_exponential_test
Reference:

Alan Laub,
Review of "Linear System Theory" by Joao Hespanha,
SIAM Review,
Volume 52, Number 4, December 2010, page 779781.

Cleve Moler, Charles VanLoan,
Nineteen Dubious Ways to Compute the Exponential of a Matrix,
SIAM Review,
Volume 20, Number 4, October 1978, pages 801836.

Cleve Moler, Charles VanLoan,
Nineteen Dubious Ways to Compute the Exponential of a Matrix,
TwentyFive Years Later,
SIAM Review,
Volume 45, Number 1, March 2003, pages 349.

Cleve Moler,
Cleve's Corner: A Balancing Act for the Matrix Exponential,
July 23rd, 2012.

Roger Sidje,
EXPOKIT: Software Package for Computing Matrix Exponentials,
ACM Transactions on Mathematical Software,
Volume 24, Number 1, 1998, pages 130156.

Robert Ward,
Numerical computation of the matrix exponential with accuracy estimate,
SIAM Journal on Numerical Analysis,
Volume 14, Number 4, September 1977, pages 600610.
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;
Last modified on 29 March 2019.