program main !*****************************************************************************80 ! !! MAIN is the main program for MATRIX_EXPONENTIAL_TEST. ! ! Discussion: ! ! MATRIX_EXPONENTIAL_TEST tests the MATRIX_EXPONENTIAL library. ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 26 November 2011 ! ! Author: ! ! John Burkardt ! implicit none call timestamp ( ) write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'MATRIX_EXPONENTIAL_TEST:' write ( *, '(a)' ) ' FORTRAN90 version' write ( *, '(a)' ) ' Test the MATRIX_EXPONENTIAL library.' write ( *, '(a)' ) ' The C8LIB and R8LIB libraries are needed.' write ( *, '(a)' ) ' This test needs the TEST_MATRIX_EXPONENTIAL library.' call matrix_exponential_test01 ( ) call matrix_exponential_test02 ( ) ! ! Terminate. ! write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'MATRIX_EXPONENTIAL_TEST:' write ( *, '(a)' ) ' Normal end of execution.' write ( *, '(a)' ) ' ' call timestamp ( ) stop 0 end subroutine matrix_exponential_test01 ( ) !*****************************************************************************80 ! !! MATRIX_EXPONENTIAL_TEST01 compares matrix exponential algorithms. ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 28 November 2011 ! ! Author: ! ! John Burkardt ! implicit none real ( kind = 8 ), allocatable :: a(:,:) real ( kind = 8 ), allocatable :: a_exp(:,:) integer ( kind = 4 ) n integer ( kind = 4 ) test integer ( kind = 4 ) test_num write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'MATRIX_EXPONENTIAL_TEST01:' write ( *, '(a)' ) ' EXPM is MATLAB''s matrix exponential function.' write ( *, '(a)' ) ' R8MAT_EXPM1 is based on EXPM;' write ( *, '(a)' ) ' R8MAT_EXPM2 uses a Taylor series approach;' write ( *, '(a)' ) ' R8MAT_EXPM3 relies on an eigenvalue calculation.' call r8mat_exp_test_num ( test_num ) do test = 1, test_num write ( *, '(a)' ) ' ' write ( *, '(a,i4)' ) ' Test #', test call r8mat_exp_story ( test ) call r8mat_exp_n ( test, n ) write ( *, '(a,i4)' ) ' Matrix order N = ', n allocate ( a(1:n,1:n) ) call r8mat_exp_a ( test, n, a ) call r8mat_print ( n, n, a, ' Matrix:' ) allocate ( a_exp(1:n,1:n) ) call r8mat_expm1 ( n, a, a_exp ) call r8mat_print ( n, n, a_exp, ' EXPM1(A):' ) call r8mat_expm2 ( n, a, a_exp ) call r8mat_print ( n, n, a_exp, ' EXPM2(A):' ) ! call r8mat_expm3 ( n, a, a_exp ) ! call r8mat_print ( n, n, a_exp, ' EXPM3(A):' ) call r8mat_exp_expa ( test, n, a_exp ) call r8mat_print ( n, n, a_exp, ' Exact Exponential:' ) deallocate ( a ) deallocate ( a_exp ) end do return end subroutine matrix_exponential_test02 ( ) !*****************************************************************************80 ! !! MATRIX_EXPONENTIAL_TEST02 compares matrix exponential algorithms. ! ! Licensing: ! ! This code is distributed under the GNU LGPL license. ! ! Modified: ! ! 02 March 2013 ! ! Author: ! ! John Burkardt ! implicit none complex ( kind = 8 ), allocatable :: a(:,:) complex ( kind = 8 ), allocatable :: a_exp(:,:) integer ( kind = 4 ) n integer ( kind = 4 ) test integer ( kind = 4 ) test_num write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'MATRIX_EXPONENTIAL_TEST02:' write ( *, '(a)' ) ' EXPM is MATLAB''s matrix exponential function.' write ( *, '(a)' ) ' R8MAT_EXPM1 is based on EXPM;' write ( *, '(a)' ) ' R8MAT_EXPM2 uses a Taylor series approach;' write ( *, '(a)' ) ' R8MAT_EXPM3 relies on an eigenvalue calculation.' call c8mat_exp_test_num ( test_num ) do test = 1, test_num write ( *, '(a)' ) ' ' write ( *, '(a,i4)' ) ' Test #', test call c8mat_exp_story ( test ) call c8mat_exp_n ( test, n ) write ( *, '(a,i4)' ) ' Matrix order N = ', n allocate ( a(1:n,1:n) ) call c8mat_exp_a ( test, n, a ) call c8mat_print ( n, n, a, ' Matrix:' ) allocate ( a_exp(1:n,1:n) ) call c8mat_expm1 ( n, a, a_exp ) call c8mat_print ( n, n, a_exp, ' EXPM1(A):' ) ! call c8mat_expm2 ( n, a, a_exp ) ! call c8mat_print ( n, n, a_exp, ' EXPM2(A):' ) ! call c8mat_expm3 ( n, a, a_exp ) ! call c8mat_print ( n, n, a_exp, ' EXPM3(A):' ) call c8mat_exp_expa ( test, n, a_exp ) call c8mat_print ( n, n, a_exp, ' Exact Exponential:' ) deallocate ( a ) deallocate ( a_exp ) end do return end