program main

c*********************************************************************72
c
cc zero_itp_test() tests zero_itp().
c
c  Licensing:
c
c    This code is distributed under the MIT license. 
c
c  Modified:
c
c    03 March 2024
c
c  Author:
c
c    John Burkardt
c
      implicit none

      double precision a
      double precision b
      double precision epsi
      double precision f_01
      external f_01
      double precision f_02
      external f_02
      double precision f_03
      external f_03
      double precision f_04
      external f_04
      double precision f_05
      external f_05
      double precision f_06
      external f_06
      double precision k1
      double precision k2
      integer n0
      character * ( 80 ) title
      logical verbose

      write ( *, '(a)' ) ' '
      call timestamp ( )
      write ( *, '(a)' ) 'zero_itp_test():'
      write ( *, '(a)' ) '  Fortran77 version.'
      write ( *, '(a)' ) '  Test zero_itp(), which seeks a root of'
      write ( *, '(a)' ) '  a function f(x) in an interval [A,B].'

      a = 1.0D+00
      b = 2.0D+00
      epsi = sqrt ( epsilon ( 1.0D+00 ) )
      k1 = 1.0D+00 / ( b - a ) / 5.0D+00
      k2 = 2.0D+00
      n0 = 1
      verbose = .false.
      title = 'f_01(x) = sin ( x ) - x / 2'
      call zero_itp_example ( f_01, a, b, epsi, k1, k2, n0, verbose, 
     &  title )

      a = 0.0D+00
      b = 1.0D+00
      epsi = sqrt ( epsilon ( 1.0D+00 ) )
      k1 = 1.0D+00 / ( b - a ) / 5.0D+00
      k2 = 2.0D+00
      n0 = 1
      verbose = .false.
      title = 'f_02(x) = 2 * x - exp ( - x )'
      call zero_itp_example ( f_02, a, b, epsi, k1, k2, n0, verbose, 
     &  title )

      a = -1.0D+00
      b =  0.5D+00
      epsi = sqrt ( epsilon ( 1.0D+00 ) )
      k1 = 1.0D+00 / ( b - a ) / 5.0D+00
      k2 = 2.0D+00
      n0 = 1
      verbose = .false.
      title = 'f_03(x) = x * exp ( - x )'
      call zero_itp_example ( f_03, a, b, epsi, k1, k2, n0, verbose, 
     &  title )

      a =  0.0001D+00
      b =  20.0D+00
      epsi = sqrt ( epsilon ( 1.0D+00 ) )
      k1 = 1.0D+00 / ( b - a ) / 5.0D+00
      k2 = 2.0D+00
      n0 = 1
      verbose = .false.
      title = 'f_04(x) = exp ( x ) - 1 / ( 100 * x * x )'
      call zero_itp_example ( f_04, a, b, epsi, k1, k2, n0, verbose, 
     &  title )

      a = -5.0D+00
      b =  2.0D+00
      epsi = sqrt ( epsilon ( 1.0D+00 ) )
      k1 = 1.0D+00 / ( b - a ) / 5.0D+00
      k2 = 2.0D+00
      n0 = 1
      verbose = .false.
      title = 'f_05(x) = (x+3) * (x-1) * (x-1)'
      call zero_itp_example ( f_05, a, b, epsi, k1, k2, n0, verbose, 
     &  title )

      a = 1.0D+00
      b =  2.0D+00
      epsi = 0.0005D+00
      k1 = 1.0D+00 / ( b - a ) / 5.0D+00
      k2 = 2.0D+00
      n0 = 1
      verbose = .false.
      title = 'f_06(x) = x^3 - x - 2'
      call zero_itp_example ( f_06, a, b, epsi, k1, k2, n0, verbose, 
     &  title )
c
c  Terminate.
c
      write ( *, '(a)' ) ' '
      write ( *, '(a)' ) 'zero_itp_test():'
      write ( *, '(a)' ) '  Normal end of execution.'
      write ( *, '(a)' ) ' '
      call timestamp ( )

      stop 0
      end
      subroutine zero_itp_example ( f, a, b, epsi, k1, k2, n0, 
     &  verbose, title )

c*********************************************************************72
c
cc zero_itp_example() tests zero_itp() on one test function.
c
c  Licensing:
c
c    This code is distributed under the MIT license. 
c
c  Modified:
c
c    03 March 2024
c
c  Author:
c
c    John Burkardt
c
c  Input:
c
c    external double precision F, the name of a user-supplied
c    function, of the form "FUNCTION F ( X )", which evaluates the
c    function whose zero is being sought.
c
c    double precision A, B, the endpoints of the change of sign interval.
c
c    double precision epsi: error tolerance between exact and computed roots.
c
c    double precision k1: a parameter, with suggested value 0.2 / ( b - a ).
c
c    double precision k2: a parameter, typically set to 2.
c
c    integer n0: a parameter that can be set to 0 for difficult problems,
c    but is usually set to 1, to take more advantage of the secant method.
c
c    logical verbose: if true, requests additional output from zero_itp().
c
c    character ( len = * ) TITLE, a title for the problem.
c
      implicit none

      double precision a
      double precision b
      integer calls
      double precision epsi
      double precision f
      external f
      double precision fa
      double precision fb
      double precision fz
      double precision k1
      double precision k2
      integer n0
      character * ( *  ) title
      logical verbose
      double precision z
  
      call zero_itp ( f, a, b, epsi, k1, k2, n0, verbose, z, fz, calls )

      fa = f ( a )
      fb = f ( b )

      write ( *, '(a)' ) ' '
      write ( *, '(2x,a)' ) trim ( title )
      write ( *, '(a)' ) ' '
      write ( *, '(a)' ) '      A                 Z             B'
      write ( *, '(a)' ) '    F(A)              F(Z)          F(B)'
      write ( *, '(a)' ) ' '
      write ( *, '(2x,f14.8,2x,f14.8,2x,f14.8)' ) a,  z,  b
      write ( *, '(2x,g14.6,2x,g14.6,2x,g14.6)' ) fa, fz, fb
      write ( *, '(a,i8)' ) '  Number of calls to F = ', calls
      write ( *, '(a,g14.6)' ) '  Tolerance epsi = ', epsi 
      write ( *, '(a,g14.6,a,g14.6,a,i4)' ) 
     &  '  Parameters k1 =', k1, ', k2 = ', k2, ', n0 = ', n0

      return
      end
      function f_01 ( x )

c*********************************************************************72
c
cc f_01() evaluates sin ( x ) - x / 2.
c
c  Licensing:
c
c    This code is distributed under the MIT license. 
c
c  Modified:
c
c    07 March 1999
c
c  Author:
c
c    John Burkardt
c
c  Input:
c
c    double precision X, the evaluation point.
c
c  Output:
c
c    double precision F_01, the value of the function at X.
c
      implicit none

      double precision f_01
      double precision x

      f_01 = sin ( x ) - 0.5D+00 * x

      return
      end
      function f_02 ( x )

c*********************************************************************72
c
cc f_02() evaluates 2*x-exp(-x).
c
c  Licensing:
c
c    This code is distributed under the MIT license. 
c
c  Modified:
c
c    07 March 1999
c
c  Author:
c
c    John Burkardt
c
c  Input:
c
c    double precision X, the evaluation point.
c
c  Output:
c
c    double precision F_02, the value of the function at X.
c
      implicit none

      double precision f_02
      double precision x

      f_02 = 2.0D+00 * x - exp ( - x )

      return
      end
      function f_03 ( x )

c*********************************************************************72
c
cc f_03() evaluates x*exp(-x).
c
c  Modified:
c
c    07 March 1999
c
c  Author:
c
c    John Burkardt
c
c  Input:
c
c    double precision X, the evaluation point.
c
c  Output:
c
c    double precision F_03, the value of the function at X.
c
      implicit none

      double precision f_03
      double precision x

      f_03 = x * exp ( - x )

      return
      end
      function f_04 ( x )

c*********************************************************************72
c
cc f_04() evaluates exp(x) - 1 / (100*x*x).
c
c  Licensing:
c
c    This code is distributed under the MIT license. 
c
c  Modified:
c
c    07 March 1999
c
c  Author:
c
c    John Burkardt
c
c  Input:
c
c    double precision X, the evaluation point.
c
c  Output:
c
c    double precision F_04, the value of the function at X.
c
      implicit none

      double precision f_04
      double precision x

      f_04 = exp ( x ) - 1.0D+00 / 100.0D+00 / x / x

      return
      end
      function f_05 ( x )

c*********************************************************************72
c
cc f_05() evaluates (x+3)*(x-1)*(x-1).
c
c  Licensing:
c
c    This code is distributed under the MIT license. 
c
c  Modified:
c
c    07 March 1999
c
c  Author:
c
c    John Burkardt
c
c  Input:
c
c    double precision X, the evaluation point.
c
c  Output:
c
c    double precision F_05, the value of the function at X.
c
      implicit none

      double precision f_05
      double precision x

      f_05 = ( x + 3.0D+00 ) * ( x - 1.0D+00 ) * ( x - 1.0D+00 )

      return
      end
      function f_06 ( x )

c*********************************************************************72
c
cc f_06() evaluates x^3 - x - 2.
c
c  Licensing:
c
c    This code is distributed under the MIT license. 
c
c  Modified:
c
c    03 March 2024
c
c  Author:
c
c    John Burkardt
c
c  Input:
c
c    double precision X, the evaluation point.
c
c  Output:
c
c    double precision F_06, the value of the function at X.
c
      implicit none

      double precision f_06
      double precision x

      f_06 = x ** 3 - x - 2.0D+00

      return
      end
      subroutine timestamp ( )

c*********************************************************************72
c
cc timestamp() prints the YMDHMS date as a timestamp.
c
c  Licensing:
c
c    This code is distributed under the MIT license.
c
c  Modified:
c
c    12 June 2014
c
c  Author:
c
c    John Burkardt
c
      implicit none

      character * ( 8 ) ampm
      integer d
      character * ( 8 ) date
      integer h
      integer m
      integer mm
      character * ( 9 ) month(12)
      integer n
      integer s
      character * ( 10 ) time
      integer y

      save month

      data month /
     &  'January  ', 'February ', 'March    ', 'April    ', 
     &  'May      ', 'June     ', 'July     ', 'August   ', 
     &  'September', 'October  ', 'November ', 'December ' /

      call date_and_time ( date, time )

      read ( date, '(i4,i2,i2)' ) y, m, d
      read ( time, '(i2,i2,i2,1x,i3)' ) h, n, s, mm

      if ( h .lt. 12 ) then
        ampm = 'AM'
      else if ( h .eq. 12 ) then
        if ( n .eq. 0 .and. s .eq. 0 ) then
          ampm = 'Noon'
        else
          ampm = 'PM'
        end if
      else
        h = h - 12
        if ( h .lt. 12 ) then
          ampm = 'PM'
        else if ( h .eq. 12 ) then
          if ( n .eq. 0 .and. s .eq. 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