program main !*****************************************************************************80 ! !! fem1d_pack_test() tests fem1d_pack(). ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 19 March 2011 ! ! Author: ! ! John Burkardt ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) call timestamp ( ) write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'fem1d_pack_test():' write ( *, '(a)' ) ' FORTRAN90 version' write ( *, '(a)' ) ' Test fem1d_pack().' call test01 ( ) call test02 ( ) ! ! Terminate. ! write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'fem1d_pack_test():' write ( *, '(a)' ) ' Normal end of execution.' write ( *, '(a)' ) ' ' call timestamp ( ) stop 0 end subroutine test01 ( ) !*****************************************************************************80 ! !! TEST01 verifies LOCAL_BASIS_1D. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 18 March 2011 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! None ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer, parameter :: node_num = 4 integer i integer j real ( kind = rk ) node_x(node_num) real ( kind = rk ) phi(node_num) real ( kind = rk ) phi_matrix(node_num,node_num) real ( kind = rk ) r8_uniform_ab real ( kind = rk ) x write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'TEST01:' write ( *, '(a)' ) ' LOCAL_BASIS_1D evaluates the local basis functions' write ( *, '(a)' ) ' for a 1D element.' write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' Test that the basis functions, evaluated at the nodes,' write ( *, '(a)' ) ' form the identity matrix.' write ( *, '(a)' ) ' ' write ( *, '(a,i8)' ) ' Number of nodes = ', node_num node_x(1:node_num) = (/ 1.0D+00, 2.0D+00, 4.0D+00, 4.5D+00 /); write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' Node coordinates:' write ( *, '(a)' ) ' ' do j = 1, node_num write ( *, '(2x,i8,2x,f7.3,2x,f7.3)' ) j, node_x(j) end do do j = 1, node_num x = node_x(j) call local_basis_1d ( node_num, node_x, x, phi_matrix(1,j) ) end do write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' A(I,J) = PHI(I) at node (J):' write ( *, '(a)' ) ' ' do i = 1, node_num write ( *, '(2x,10f7.3)' ) phi_matrix(i,1:node_num) end do write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' The PHI functions should sum to 1 at random X values:' write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' X Sum ( PHI(:)(X) )' write ( *, '(a)' ) ' ' do j = 1, 5 x = r8_uniform_ab ( 1.0D+00, 4.5D+00 ) call local_basis_1d ( node_num, node_x, x, phi ) write ( *, '(2x,g14.6,2x,g14.6)' ) x, sum ( phi(1:node_num) ) end do return end subroutine test02 ( ) !*****************************************************************************80 ! !! TEST02 verifies LOCAL_BASIS_PRIME_1D. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 19 March 2011 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! None ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer, parameter :: node_num = 4 real ( kind = rk ) dphidx(node_num) real ( kind = rk ) dphidx_matrix(node_num,node_num) integer i integer j real ( kind = rk ) node_x(node_num) real ( kind = rk ) r8_uniform_ab real ( kind = rk ) x write ( *, '(a)' ) ' ' write ( *, '(a)' ) 'TEST02:' write ( *, '(a)' ) ' LOCAL_BASIS_PRIME_1D evaluates the local basis function' write ( *, '(a)' ) ' derivatives for a 1D element.' write ( *, '(a)' ) ' ' write ( *, '(a,i8)' ) ' Number of nodes = ', node_num node_x(1:node_num) = (/ 1.0D+00, 2.0D+00, 4.0D+00, 4.5D+00 /); write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' Node coordinates:' write ( *, '(a)' ) ' ' do j = 1, node_num write ( *, '(2x,i8,2x,f7.3,2x,f7.3)' ) j, node_x(j) end do do j = 1, node_num x = node_x(j) call local_basis_prime_1d ( node_num, node_x, x, dphidx_matrix(1,j) ) end do write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' A(I,J) = dPHIdx(I) at node(J):' write ( *, '(a)' ) ' The diagonal should be 0.' write ( *, '(a)' ) ' Columns should sum to 0.' write ( *, '(a)' ) ' ' do i = 1, node_num write ( *, '(2x,10f7.3)' ) dphidx_matrix(i,1:node_num) end do write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' The dPHIdx functions should sum to 0 at random X values:' write ( *, '(a)' ) ' ' write ( *, '(a)' ) ' X Sum ( dPHIdx(:)(X) )' write ( *, '(a)' ) ' ' do j = 1, 5 x = r8_uniform_ab ( 1.0D+00, 4.5D+00 ) call local_basis_prime_1d ( node_num, node_x, x, dphidx ) write ( *, '(2x,g14.6,2x,g14.6)' ) x, sum ( dphidx(1:node_num) ) end do return end subroutine timestamp ( ) !*****************************************************************************80 ! !! timestamp() prints the current YMDHMS date as a time stamp. ! ! Example: ! ! 31 May 2001 9:45:54.872 AM ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 18 May 2013 ! ! Author: ! ! John Burkardt ! ! Parameters: ! ! None ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) character ( len = 8 ) ampm integer d integer h integer m integer mm character ( len = 9 ), parameter, dimension(12) :: month = (/ & 'January ', 'February ', 'March ', 'April ', & 'May ', 'June ', 'July ', 'August ', & 'September', 'October ', 'November ', 'December ' /) integer n integer s integer values(8) integer y call date_and_time ( values = values ) y = values(1) m = values(2) d = values(3) h = values(5) n = values(6) s = values(7) mm = values(8) if ( h < 12 ) then ampm = 'AM' else if ( h == 12 ) then if ( n == 0 .and. s == 0 ) then ampm = 'Noon' else ampm = 'PM' end if else h = h - 12 if ( h < 12 ) then ampm = 'PM' else if ( h == 12 ) then if ( n == 0 .and. s == 0 ) then ampm = 'Midnight' else ampm = 'AM' end if end if end if write ( *, '(i2,1x,a,1x,i4,2x,i2,a1,i2.2,a1,i2.2,a1,i3.3,1x,a)' ) & d, trim ( month(m) ), y, h, ':', n, ':', s, '.', mm, trim ( ampm ) return end