TEST_MATRIX_EXPONENTIAL\
Matrix Exponential Tests {#test_matrix_exponential-matrix-exponential-tests align=”center”}
==========================
TEST_MATRIX_EXPONENTIAL is a C++ 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!
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: {#licensing align=”center”}
The computer code and data files described and made available on this
web page are distributed under the GNU LGPL
license.
Languages: {#languages align=”center”}
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.
EXPOKIT, a FORTRAN77 library which
solves various forms of the matrix exponential problem, by Roger Sidje.
MATRIX_EXPONENTIAL,
a C++ library which demonstrates some simple approaches to the problem
of computing the exponential of a matrix.
R8LIB, a C++ library which contains
many utility routines using double precision real (R8) arithmetic.
TEST_MAT, a C++ library which
defines test matrices.
Reference: {#reference align=”center”}
- 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.
- 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 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: {#source-code align=”center”}
Examples and Tests: {#examples-and-tests align=”center”}
List of Routines: {#list-of-routines align=”center”}
- C8MAT_EXP_A returns the matrix for a given complex test.
- C8MAT_EXP_EXPA returns the “exact” exponential matrix for a
given complex test.
- C8MAT_EXP_N returns the matrix order for a given complex test.
- C8MAT_EXP_STORY prints explanatory text for each complex
problem.
- C8MAT_EXP_TEST_NUM returns the number of complex tests.
- R8MAT_EXP_A returns the matrix for a given real test.
- R8MAT_EXP_EXPA returns the “exact” exponential matrix for a
given real test.
- R8MAT_EXP_N returns the matrix order for a given real test.
- R8MAT_EXP_STORY prints explanatory text for each real problem.
- R8MAT_EXP_TEST_NUM returns the number of real tests.
You can go up one level to the C++ source codes.
Last modified on 05 March 2013.