subroutine get_unit ( iunit ) !*****************************************************************************80 ! !! get_unit() returns a free FORTRAN unit number. ! ! Discussion: ! ! A "free" FORTRAN unit number is a value between 1 and 99 which ! is not currently associated with an I/O device. A free FORTRAN unit ! number is needed in order to open a file with the OPEN command. ! ! If IUNIT = 0, then no free FORTRAN unit could be found, although ! all 99 units were checked (except for units 5, 6 and 9, which ! are commonly reserved for console I/O). ! ! Otherwise, IUNIT is a value between 1 and 99, representing a ! free FORTRAN unit. Note that GET_UNIT assumes that units 5 and 6 ! are special, and will never return those values. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 26 October 2008 ! ! Author: ! ! John Burkardt ! ! Output: ! ! integer IUNIT, the free unit number. ! implicit none integer i integer ios integer iunit logical lopen iunit = 0 do i = 1, 99 if ( i /= 5 .and. i /= 6 .and. i /= 9 ) then inquire ( unit = i, opened = lopen, iostat = ios ) if ( ios == 0 ) then if ( .not. lopen ) then iunit = i return end if end if end if end do return end subroutine midpoint_explicit ( dydt, tspan, y0, n, m, t, y ) !*****************************************************************************80 ! !! midpoint_explicit() uses the explicit midpoint method to solve an ODE. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 06 April 2021 ! ! Author: ! ! John Burkardt ! ! Input: ! ! external dydt: a subroutine that evaluates the right ! hand side of the ODE. ! ! real ( kind = rk ) tspan(2): contains the initial and final times. ! ! real ( kind = rk ) y0(m): a column vector containing the initial condition. ! ! integer n: the number of steps to take. ! ! integer m: the number of variables. ! ! Output: ! ! real ( kind = rk ) t(n+1), y(n+1,m): the times and solution values. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer m integer n real ( kind = rk ) dt external dydt real ( kind = rk ) f(m) integer i real ( kind = rk ) t(n+1) real ( kind = rk ) tm real ( kind = rk ) tspan(2) real ( kind = rk ) y(n+1,m) real ( kind = rk ) y0(m) real ( kind = rk ) ym(m) dt = ( tspan(2) - tspan(1) ) / n t(1) = tspan(1) y(1,1:m) = y0(1:m) do i = 1, n call dydt ( t(i), y(i,1:m), f ) tm = t(i) + 0.5D+00 * dt ym(1:m) = y(i,1:m) + 0.5D+00 * dt * f(1:m) call dydt ( tm, ym, f ) t(i+1) = t(i) + dt y(i+1,1:m) = y(i,1:m) + dt * f(1:m) end do return end subroutine r8_fake_use ( x ) !*****************************************************************************80 ! !! r8_fake_use() pretends to use a variable. ! ! Discussion: ! ! Some compilers will issue a warning if a variable is unused. ! Sometimes there's a good reason to include a variable in a program, ! but not to use it. Calling this function with that variable as ! the argument will shut the compiler up. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 21 April 2020 ! ! Author: ! ! John Burkardt ! ! Input: ! ! real ( kind = rk ) X, the variable to be "used". ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) real ( kind = rk ) x if ( x /= x ) then write ( *, '(a)' ) ' r8_fake_use: variable is NAN.' end if return end subroutine r8vec_linspace ( n, a, b, x ) !*****************************************************************************80 ! !! r8vec_linspace() creates a vector of linearly spaced values. ! ! Discussion: ! ! An R8VEC is a vector of R8's. ! ! 4 points evenly spaced between 0 and 12 will yield 0, 4, 8, 12. ! ! In other words, the interval is divided into N-1 even subintervals, ! and the endpoints of intervals are used as the points. ! ! Licensing: ! ! This code is distributed under the MIT license. ! ! Modified: ! ! 14 March 2011 ! ! Author: ! ! John Burkardt ! ! Input: ! ! integer N, the number of entries in the vector. ! ! real ( kind = rk ) A, B, the first and last entries. ! ! Output: ! ! real ( kind = rk ) X(N), a vector of linearly spaced data. ! implicit none integer, parameter :: rk = kind ( 1.0D+00 ) integer n real ( kind = rk ) a real ( kind = rk ) b integer i real ( kind = rk ) x(n) if ( n == 1 ) then x(1) = ( a + b ) / 2.0D+00 else do i = 1, n x(i) = ( real ( n - i, kind = rk ) * a & + real ( i - 1, kind = rk ) * b ) & / real ( n - 1, kind = rk ) end do end if 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 ! implicit none 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 ( *, '(i2.2,1x,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