program main

!*****************************************************************************80
!
!! ornstein_uhlenbeck_test() tests ornstein_uhlenbeck().
!
!  Licensing:
!
!    This code is distributed under the MIT license.
!
!  Modified:
!
!    18 January 2013
!
!  Author:
!
!    John Burkardt
!
  implicit none

  call timestamp ( )
  write ( *, '(a)') ' '
  write ( *, '(a)' ) 'ornstein_uhlenbeck_test():'
  write ( *, '(a)' ) '  FORTRAN90 version.'
  write ( *, '(a)' ) '  Test ornstein_uhlenbeck().'

  call ou_euler_test ( )
  call ou_euler_maruyama_test ( )
!
!  Terminate.
!
  write ( *, '(a)' ) ''
  write ( *, '(a)' ) 'ornstein_uhlenbeck_test():'
  write ( *, '(a)' ) '  Normal end of execution.'
  write ( *, '(a)' ) ''
  call timestamp ( )

  stop 0
end
subroutine ou_euler_test ( )

!*****************************************************************************80
!
!! ou_euler_test() tests ou_euler().
!
!  Licensing:
!
!    This code is distributed under the MIT license.
!
!  Modified:
!
!    18 January 2013
!
!  Author:
!
!    John Burkardt
!
  implicit none

  integer, parameter :: rk = kind ( 1.0D+00 )

  real ( kind = rk ) mu
  integer n
  real ( kind = rk ) sigma
  real ( kind = rk ) theta
  real ( kind = rk ) tmax
  real ( kind = rk ) x0

  write ( *, '(a)' ) ''
  write ( *, '(a)' ) 'OU_EULER_TEST():'
  write ( *, '(a)' ) '  Estimate a solution to the Ornstein-Uhlenbeck equation'
  write ( *, '(a)' ) '  using the Euler method for stochastic differential equations.'
  write ( *, '(a)' ) ''

  theta = 2.0D+00
  write ( *, '(a,g14.6)' ) '  Using decay rate THETA = ', theta
  mu = 1.0D+00
  write ( *, '(a,g14.6)' ) '  Using mean MU = ', mu
  sigma = 0.15D+00
  write ( *, '(a,g14.6)' ) '  Using variance SIGMA = ', sigma
  x0 = 2.0D+00
  write ( *, '(a,g14.6)' ) '  Using initial value X0 = ', x0
  tmax = 3.0D+00
  write ( *, '(a,g14.6)' ) '  Using final time TMAX = ', tmax
  n = 10000
  write ( *, '(a,i8)' ) '  Using number of timesteps N = ', n

  call ou_euler ( theta, mu, sigma, x0, tmax, n )

  return
end
subroutine ou_euler_maruyama_test ( )

!*****************************************************************************80
!
!! OU_EULER_MARUYAMA_TEST() tests OU_EULER_MARUYAMA().
!
!  Licensing:
!
!    This code is distributed under the MIT license.
!
!  Modified:
!
!    21 January 2013
!
!  Author:
!
!    John Burkardt
!
  implicit none

  integer, parameter :: rk = kind ( 1.0D+00 )

  real ( kind = rk ) mu
  integer n
  integer r
  real ( kind = rk ) sigma
  real ( kind = rk ) theta
  real ( kind = rk ) tmax
  real ( kind = rk ) x0

  write ( *, '(a)' ) ''
  write ( *, '(a)' ) 'OU_EULER_MARUYAMA_TEST():'
  write ( *, '(a)' ) '  Estimate a solution to the Ornstein-Uhlenbeck equation'
  write ( *, '(a)' ) '  using the Euler-Maruyama method for stochastic '
  write ( *, '(a)' ) '  differential equations.'
  write ( *, '(a)' ) ''

  theta = 2.0D+00
  write ( *, '(a,g14.6)' ) '  Using decay rate THETA = ', theta
  mu = 1.0D+00
  write ( *, '(a,g14.6)' ) '  Using mean MU = ', mu
  sigma = 0.15D+00
  write ( *, '(a,g14.6)' ) '  Using variance SIGMA = ', sigma
  x0 = 2.0D+00
  write ( *, '(a,g14.6)' ) '  Using initial value X0 = ', x0
  tmax = 3.0D+00
  write ( *, '(a,g14.6)' ) '  Using final time TMAX = ', tmax
  n = 10000
  write ( *, '(a,i6)' ) '  Using number of large timesteps N = ', n
  r = 16
  write ( *, '(a,i6)' ) '  Using number small time steps per one large time step R = ', r

  call ou_euler_maruyama ( theta, mu, sigma, x0, tmax, n, r )

  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 ( *, '(i2,1x,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