program main

c*********************************************************************72
c
cc runge_test() tests runge().
c
c  Licensing:
c
c    This code is distributed under the MIT license.
c
c  Modified:
c
c    25 May 2024
c
c  Author:
c
c    John Burkardt
c
      call timestamp ( )
      write ( *, '(a)' ) ''
      write ( *, '(a)' ) 'runge_test():'
      write ( *, '(a)' ) '  Fortran77 version'
      write ( *, '(a)' ) '  Test runge.'

      call runge_antideriv_test ( )
      call runge_deriv_test ( )
      call runge_deriv2_test ( )
      call runge_fun_test ( )
      call runge_power_series_test ( )
c
c  Terminate.
c
      write ( *, '(a)' ) ''
      write ( *, '(a)' ) 'runge_test():'
      write ( *, '(a)' ) '  Normal end of execution.'
      write ( *, '(a)' ) ''
      call timestamp ( )

      return
      end
      subroutine runge_antideriv_test ( )

c*********************************************************************72
c
cc runge_antideriv_test() tests runge_antideriv().
c
c  Licensing:
c
c    This code is distributed under the MIT license.
c
c  Modified:
c
c    24 March 2025
c
c  Author:
c
c    John Burkardt
c
      implicit none

      integer, parameter :: n = 51

      double precision a
      double precision b
      character ( len = 255 ) header
      integer i
      double precision runge_antideriv
      double precision x(n)
      double precision y(n)

      write ( *, '(a)' ) ''
      write ( *, '(a)' ) 'runge_antideriv_test():'
      write ( *, '(a)' ) 
     &  '  runge_antideriv() evaluates the antiderivative'
      write ( *, '(a)' ) '  of the runge function.'

      a = -1.0D+00
      b = +1.0D+00
      call r8vec_linspace ( n, a, b, x )
      do i = 1, n
        y(i) = runge_antideriv ( x(i) )
      end do
      header = 'runge_antideriv'
      call gnuplot_fx ( n, x, y, trim ( header ) )

      return
      end
      subroutine runge_deriv_test ( )

c*********************************************************************72
c
cc runge_deriv_test() tests runge_deriv().
c
c  Licensing:
c
c    This code is distributed under the MIT license.
c
c  Modified:
c
c    24 March 2025
c
c  Author:
c
c    John Burkardt
c
      implicit none

      integer, parameter :: n = 51

      double precision a
      double precision b
      character ( len = 255 ) header
      integer i
      double precision runge_deriv
      double precision x(n)
      double precision y(n)

      write ( *, '(a)' ) ''
      write ( *, '(a)' ) 'runge_deriv_test():'
      write ( *, '(a)' ) '  runge_deriv() evaluates the derivative'
      write ( *, '(a)' ) '  of the runge function.'

      a = -1.0D+00
      b = +1.0D+00
      call r8vec_linspace ( n, a, b, x )
      do i = 1, n
        y(i) = runge_deriv ( x(i) )
      end do
      header = 'runge_deriv'
      call gnuplot_fx ( n, x, y, trim ( header ) )

      return
      end
      subroutine runge_deriv2_test ( )

c*********************************************************************72
c
cc runge_deriv2_test() tests runge_deriv2().
c
c  Licensing:
c
c    This code is distributed under the MIT license.
c
c  Modified:
c
c    24 March 2025
c
c  Author:
c
c    John Burkardt
c
      implicit none

      integer, parameter :: n = 51

      double precision a
      double precision b
      character ( len = 255 ) header
      integer i
      double precision runge_deriv2
      double precision x(n)
      double precision y(n)

      write ( *, '(a)' ) ''
      write ( *, '(a)' ) 'runge_deriv2_test():'
      write ( *, '(a)' ) 
     &  '  runge_deriv2() evaluates the second derivative'
      write ( *, '(a)' ) '  of the runge function.'

      a = -1.0D+00
      b = +1.0D+00
      call r8vec_linspace ( n, a, b, x )
      do i = 1, n
        y(i) = runge_deriv2 ( x(i) )
      end do
      header = 'runge_deriv2'
      call gnuplot_fx ( n, x, y, trim ( header ) )

      return
      end
      subroutine runge_fun_test ( )

c*********************************************************************72
c
cc runge_fun_test() tests runge_fun().
c
c  Licensing:
c
c    This code is distributed under the MIT license.
c
c  Modified:
c
c    24 March 2025
c
c  Author:
c
c    John Burkardt
c
      implicit none

      integer, parameter :: n = 51

      double precision a
      double precision b
      character ( len = 255 ) header
      integer i
      double precision runge_fun
      double precision x(n)
      double precision y(n)

      write ( *, '(a)' ) ''
      write ( *, '(a)' ) 'runge_fun_test():'
      write ( *, '(a)' ) '  runge_fun() evaluates the runge function.'

      a = -1.0D+00
      b = +1.0D+00
      call r8vec_linspace ( n, a, b, x )
      do i = 1, n
        y(i) = runge_fun ( x(i) )
      end do
      header = 'runge_fun'
      call gnuplot_fx ( n, x, y, trim ( header ) )

      return
      end
      subroutine runge_power_series_test ( )

c*********************************************************************72
c
cc runge_power_series_test() tests runge_power_series().
c
c  Licensing:
c
c    This code is distributed under the MIT license.
c
c  Modified:
c
c    25 March 2025
c
c  Author:
c
c    John Burkardt
c
      implicit none

      integer, parameter :: n = 51

      double precision a
      double precision b
      character ( len = 255 ) header
      integer i
      integer n2
      double precision runge_fun
      double precision runge_power_series
      double precision x(n)
      double precision y1(n)
      double precision y2(n)

      write ( *, '(a)' ) ''
      write ( *, '(a)' ) 'runge_power_series_test():'
      write ( *, '(a)' ) 
     &  '  runge_power_series() estimates the runge function'
      write ( *, '(a)' ) '  using a power series.'

      a = -0.2D+00
      b = +0.2D+00
      call r8vec_linspace ( n, a, b, x )

      n2 = 8
      do i = 1, n
        y1(i) = runge_fun ( x(i) )
        y2(i) = runge_power_series ( x(i), n2 )
      end do
      header = 'runge_power_series'
      call gnuplot_fxfd ( n, x, y1, y2, trim ( header ) )

      return
      end
      subroutine get_unit ( iunit )

c*********************************************************************72
c
cc get_unit() returns a free FORTRAN unit number.
c
c  Discussion:
c
c    A "free" FORTRAN unit number is a value between 1 and 99 which
c    is not currently associated with an I/O device.  A free FORTRAN unit
c    number is needed in order to open a file with the OPEN command.
c
c    If IUNIT = 0, then no free FORTRAN unit could be found, although
c    all 99 units were checked (except for units 5, 6 and 9, which
c    are commonly reserved for console I/O).
c
c    Otherwise, IUNIT is a value between 1 and 99, representing a
c    free FORTRAN unit.  The code assumes that units 5 and 6
c    are special, and will never return those values.
c
c  Licensing:
c
c    This code is distributed under the MIT license.
c
c  Modified:
c
c    26 October 2008
c
c  Author:
c
c    John Burkardt
c
c  Output:
c
c    integer IUNIT, the free unit number.
c
      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 gnuplot_fx ( n, x, y, header )

c*********************************************************************72
c
cc gnuplot_fx() plots x, f(x) data.
c
c  Discussion:
c
c    Actually, we simply create two files for processing by gnuplot().
c
c  Licensing:
c
c    This code is distributed under the MIT license.
c
c  Modified:
c
c    24 March 2025
c
c  Author:
c
c    John Burkardt
c
      implicit none

      integer n

      character ( len = 255 ) command_filename
      integer command_unit
      character ( len = 255 ) data_filename
      integer data_unit
      character ( len = * ) header
      integer i
      character ( len = 255 ) png_filename
      double precision x(n)
      double precision y(n)
c
c  Create a graphics data file.
c
      data_filename = header // '_data.txt'
      call get_unit ( data_unit )

      open ( unit = data_unit, file = data_filename, 
     &  status = 'replace' )
      do i = 1, n
        write ( data_unit, '(2g14.6)' ) x(i), y(i)
      end do
      close ( unit = data_unit )
      write ( *, '(a)' ) ' '
      write ( *, '(a)' ) '  Created graphics data file "'
     &  // trim ( data_filename ) // '".'

      png_filename = header // '.png'
c
c  Create graphics command file.
c
      call get_unit ( command_unit )
      command_filename = header // '_commands.txt'
      open ( unit = command_unit, file = command_filename, 
     &  status = 'replace' )
      write ( command_unit, '(a)' ) '# ' // trim ( command_filename )
      write ( command_unit, '(a)' ) '#'
      write ( command_unit, '(a)' ) '# Usage:'
      write ( command_unit, '(a)' ) '#  gnuplot < ' 
     &  // trim ( command_filename )
      write ( command_unit, '(a)' ) '#'
      write ( command_unit, '(a)' ) 'set term png'
      write ( command_unit, '(a)' ) 'set output "' 
     &  // trim ( png_filename ) // '"'
      write ( command_unit, '(a)' ) 'set xlabel "<--- X --->"'
      write ( command_unit, '(a)' ) 'set ylabel "<-- Y(X) -->"'
      write ( command_unit, '(a)' ) 'set title "' // header // '"'
      write ( command_unit, '(a)' ) 'set grid'
      write ( command_unit, '(a)' ) 'set style data lines'
      write ( command_unit, '(a)' ) 'plot "' 
     &  // trim ( data_filename ) 
     &  //     '" using 1:2 lw 3 linecolor rgb "blue"'
      close ( unit = command_unit )
      write ( *, '(a)' )     '  Created command file "' 
     &  // trim ( command_filename ) // '".'

      return
      end
      subroutine gnuplot_fxfd ( n, x, y1, y2, header )

c*********************************************************************72
c
cc gnuplot_fxfd() plots x, f(x) curve and x, y data.
c
c  Discussion:
c
c    Actually, we simply create two files for processing by gnuplot().
c
c  Licensing:
c
c    This code is distributed under the MIT license.
c
c  Modified:
c
c    25 March 2025
c
c  Author:
c
c    John Burkardt
c
      implicit none

      integer n

      character ( len = 255 ) command_filename
      integer command_unit
      character ( len = 255 ) data_filename
      integer data_unit
      character ( len = * ) header
      integer i
      character ( len = 255 ) png_filename
      double precision x(n)
      double precision y1(n)
      double precision y2(n)
c
c  Create a graphics data file.
c
      data_filename = header // '_data.txt'
      call get_unit ( data_unit )

      open ( unit = data_unit, file = data_filename, 
     &  status = 'replace' )
      do i = 1, n
        write ( data_unit, '(3g14.6)' ) x(i), y1(i), y2(i)
      end do
      close ( unit = data_unit )
      write ( *, '(a)' ) ' '
      write ( *, '(a)' ) '  Created graphics data file "'
     &  // trim ( data_filename ) // '".'

      png_filename = header // '.png'
c
c  Create graphics command file.
c
      call get_unit ( command_unit )
      command_filename = header // '_commands.txt'
      open ( unit = command_unit, file = command_filename, 
     &  status = 'replace' )
      write ( command_unit, '(a)' ) '# ' // trim ( command_filename )
      write ( command_unit, '(a)' ) '#'
      write ( command_unit, '(a)' ) '# Usage:'
      write ( command_unit, '(a)' ) '#  gnuplot < ' 
     &  // trim ( command_filename )
      write ( command_unit, '(a)' ) '#'
      write ( command_unit, '(a)' ) 'set term png'
      write ( command_unit, '(a)' ) 'set output "' 
     &  // trim ( png_filename ) // '"'
      write ( command_unit, '(a)' ) 'set xlabel "<--- X --->"'
      write ( command_unit, '(a)' ) 'set ylabel "<-- Y(X) -->"'
      write ( command_unit, '(a)' ) 'set title "' // header // '"'
      write ( command_unit, '(a)' ) 'set grid'
      write ( command_unit, '(a)' ) 'set style data lines'

      write ( command_unit, '(a)' ) 
     &  'plot "' // trim ( data_filename ) //
     &  '" using 1:2 lw 3 linecolor rgb "blue",\'
      write ( command_unit, '(a)' ) 
     &  '     "' // trim ( data_filename ) // 
     &  '"  using 1:3 with points pointtype 7 linecolor "red"'
      close ( unit = command_unit )
      write ( *, '(a)' )     '  Created command file "' 
     &  // trim ( command_filename ) // '".'

      return
      end
      subroutine r8vec_linspace ( n, a, b, x )

c*********************************************************************72
c
cc r8vec_linspace() creates a vector of linearly spaced values.
c
c  Discussion:
c
c    An R8VEC is a vector of R8's.
c
c    4 points evenly spaced between 0 and 12 will yield 0, 4, 8, 12.
c
c    In other words, the interval is divided into N-1 even subintervals,
c    and the endpoints of intervals are used as the points.
c
c  Licensing:
c
c    This code is distributed under the MIT license.
c
c  Modified:
c
c    14 March 2011
c
c  Author:
c
c    John Burkardt
c
c  Input:
c
c    integer N, the number of entries in the vector.
c
c    double precision A, B, the first and last entries.
c
c  Output:
c
c    double precision X(N), a vector of linearly spaced data.
c
      implicit none

      integer n

      double precision a
      double precision b
      integer i
      double precision x(n)

      if ( n == 1 ) then

        x(1) = ( a + b ) / 2.0D+00

      else

        do i = 1, n
          x(i) = ( dble ( n - i     ) * a
     &           + dble (     i - 1 ) * b )
     &           / dble ( n     - 1 )
        end do

      end if

      return
      end
      subroutine timestamp ( )

c*********************************************************************72
c
cc timestamp() prints the current YMDHMS date as a time stamp.
c
c  Example:
c
c    31 May 2001   9:45:54.872 AM
c
c  Licensing:
c
c    This code is distributed under the MIT license.
c
c  Modified:
c
c    15 August 2021
c
c  Author:
c
c    John Burkardt
c
      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