program main

!*****************************************************************************80
!
!! sde_test() tests sde().
!
!  Licensing:
!
!    This code is distributed under the MIT license.
!
!  Modified:
!
!    21 September 2012
!
!  Author:
!
!    John Burkardt
!
  implicit none

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

  call timestamp ( )
  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) 'sde_test():'
  write ( *, '(a)' ) '  Fortran90 version'
  write ( *, '(a)' ) '  Test sde().'

  call test01 ( )
  call test02 ( )
  call test03 ( )
  call test04 ( )
  call test05 ( )
  call test06 ( )
  call test07 ( )
  call test08 ( )
  call test09 ( )
  call test10 ( )
  call test11 ( )
!
!  Terminate.
!
  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) 'SDE_TEST'
  write ( *, '(a)' ) '  Normal end of execution.'
  write ( *, '(a)' ) ' '
  call timestamp ( )

  stop 0
end
subroutine test01 ( )

!*****************************************************************************80
!
!! TEST01 tests BPATH.
!
!  Licensing:
!
!    This code is distributed under the MIT license.
!
!  Modified:
!
!    14 September 2012
!
!  Author:
!
!    John Burkardt
!
  implicit none

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

  integer, parameter :: n = 500

  real ( kind = rk ) w(0:n)

  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) 'TEST01:'
  write ( *, '(a)' ) '  BPATH generates a sample Brownian motion path'

  call bpath ( n, w )

  call bpath_gnuplot ( n, w )

  return
end
subroutine test02 ( )

!*****************************************************************************80
!
!! TEST02 tests BPATH_AVERAGE.
!
!  Licensing:
!
!    This code is distributed under the MIT license.
!
!  Modified:
!
!    14 September 2012
!
!  Author:
!
!    John Burkardt
!
  implicit none

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

  integer, parameter :: m = 1000
  integer, parameter :: n = 500

  real ( kind = rk ) error
  real ( kind = rk ), allocatable :: u(:,:)
  real ( kind = rk ) umean(0:n)

  allocate ( u(1:m,0:n) )

  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) 'TEST02:'
  write ( *, '(a)' ) '  BPATH_AVERAGE generates many Brownian paths'
  write ( *, '(a)' ) '  and averages them.'

  call bpath_average ( m, n, u, umean, error )

  call bpath_average_gnuplot ( m, n, u, umean )

  deallocate ( u )

  return
end
subroutine test03 ( )

!*****************************************************************************80
!
!! TEST03 tests CHAIN.
!
!  Licensing:
!
!    This code is distributed under the MIT license.
!
!  Modified:
!
!    15 September 2012
!
!  Author:
!
!    John Burkardt
!
  implicit none

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

  integer, parameter :: n = 200

  real ( kind = rk ) diff
  real ( kind = rk ) vem(0:n)
  real ( kind = rk ) xem(0:n)

  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) 'TEST03:'
  write ( *, '(a)' ) '  CHAIN solves a stochastic differential equation for'
  write ( *, '(a)' ) '  a function of a stochastic variable X.'
  write ( *, '(a)' ) '  We can solve for X(t), and then evaluate V(X(t)).'
  write ( *, '(a)' ) '  Or, we can apply the stochastic chain rule to derive an'
  write ( *, '(a)' ) '  an SDE for V, and solve that.'

  call chain ( n, xem, vem, diff )

  write ( *, '(a)' ) ' '
  write ( *, '(a,g14.6)' ) '  Maximum | Sqrt(X) - V | = ', diff

  call chain_gnuplot ( n, xem, vem )

  return
end
subroutine test04 ( )

!*****************************************************************************80
!
!! TEST04 tests EM.
!
!  Licensing:
!
!    This code is distributed under the MIT license.
!
!  Modified:
!
!    15 September 2012
!
!  Author:
!
!    John Burkardt
!
  implicit none

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

  integer, parameter :: n = 256

  real ( kind = rk ) diff
  real ( kind = rk ) t(0:n)
  real ( kind = rk ) t2(0:n/4)
  real ( kind = rk ) xtrue(0:n)
  real ( kind = rk ) xem(0:n/4)

  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) 'TEST04:'
  write ( *, '(a)' ) '  EM solves a stochastic differential equation'
  write ( *, '(a)' ) '  using the Euler-Maruyama method.'

  call em ( n, t, xtrue, t2, xem, diff )

  write ( *, '(a)' ) ' '
  write ( *, '(a,g14.6)' ) '  | Exact X(T) - EM X(T) | = ', diff

  call em_gnuplot ( n, t, xtrue, t2, xem )

  return
end
subroutine test05 ( )

!*****************************************************************************80
!
!! TEST05 tests EMSTRONG.
!
!  Licensing:
!
!    This code is distributed under the MIT license.
!
!  Modified:
!
!    16 September 2012
!
!  Author:
!
!    John Burkardt
!
  implicit none

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

  integer, parameter :: m = 100
  integer, parameter :: n = 512
  integer, parameter :: p_max = 6

  real ( kind = rk ) dtvals(p_max)
  real ( kind = rk ) xerr(p_max)

  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) 'TEST05:'
  write ( *, '(a)' ) '  EMSTRONG investigates the strong convergence'
  write ( *, '(a)' ) '  of the Euler-Maruyama method.'

  call emstrong ( m, n, p_max, dtvals, xerr )

  call emstrong_gnuplot ( p_max, dtvals, xerr )

  return
end
subroutine test06 ( )

!*****************************************************************************80
!
!! TEST06 tests EMWEAK.
!
!  Licensing:
!
!    This code is distributed under the MIT license.
!
!  Modified:
!
!    17 September 2012
!
!  Author:
!
!    John Burkardt
!
  implicit none

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

  integer, parameter :: m = 50000
  integer, parameter :: p_max = 5

  real ( kind = rk ) dtvals(p_max)
  integer method
  real ( kind = rk ) xerr(p_max)

  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) 'TEST06:'
  write ( *, '(a)' ) '  EMWEAK investigates the weak convergence'
  write ( *, '(a)' ) '  of the Euler-Maruyama method.'

  method = 0

  call emweak ( method, m, p_max, dtvals, xerr )

  call emweak_gnuplot ( p_max, dtvals, xerr, method )

  method = 1

  call emweak ( method, m, p_max, dtvals, xerr )

  call emweak_gnuplot ( p_max, dtvals, xerr, method )

  return
end
subroutine test07 ( )

!*****************************************************************************80
!
!! TEST07 tests MILSTRONG.
!
!  Licensing:
!
!    This code is distributed under the MIT license.
!
!  Modified:
!
!    18 September 2012
!
!  Author:
!
!    John Burkardt
!
  implicit none

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

  integer, parameter :: p_max = 4

  real ( kind = rk ) dtvals(p_max)
  real ( kind = rk ) xerr(p_max)

  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) 'TEST07:'
  write ( *, '(a)' ) '  MILSTRONG investigates the strong convergence'
  write ( *, '(a)' ) '  of the Milstein method.'

  call milstrong ( p_max, dtvals, xerr )

  call milstrong_gnuplot ( p_max, dtvals, xerr )

  return
end
subroutine test08 ( )

!*****************************************************************************80
!
!! TEST08 tests STAB_ASYMPTOTIC.
!
!  Licensing:
!
!    This code is distributed under the MIT license.
!
!  Modified:
!
!    18 September 2012
!
!  Author:
!
!    John Burkardt
!
  implicit none

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

  integer, parameter :: n = 1000
  integer, parameter :: p_max = 3

  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) 'TEST08:'
  write ( *, '(a)' ) '  STAB_ASYMPTOTIC investigates the asymptotic'
  write ( *, '(a)' ) '  stability of the Euler-Maruyama method.'
  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) '  For technical reasons, the plotting is done'
  write ( *, '(a)' ) '  in the same routine as the computations.'

  call stab_asymptotic ( n, p_max )

  return
end
subroutine test09 ( )

!*****************************************************************************80
!
!! TEST09 tests STAB_MEANSQUARE.
!
!  Licensing:
!
!    This code is distributed under the MIT license.
!
!  Modified:
!
!    26 September 2012
!
!  Author:
!
!    John Burkardt
!
  implicit none

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

  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) 'TEST09:'
  write ( *, '(a)' ) '  STAB_MEANSQUARE investigates the mean square'
  write ( *, '(a)' ) '  stability of the Euler-Maruyama method.'
  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) '  For technical reasons, the plotting is done'
  write ( *, '(a)' ) '  in the same routine as the computations.'

  call stab_meansquare ( )

  return
end
subroutine test10 ( )

!*****************************************************************************80
!
!! TEST10 tests STOCHASTIC_INTEGRAL_ITO.
!
!  Licensing:
!
!    This code is distributed under the MIT license.
!
!  Modified:
!
!    21 September 2012
!
!  Author:
!
!    John Burkardt
!
  implicit none

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

  real ( kind = rk ) error
  real ( kind = rk ) estimate
  real ( kind = rk ) exact
  integer i
  integer n

  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) 'TEST10:'
  write ( *, '(a)' ) '  Estimate the Ito integral of W(t) dW over [0,1].'
  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) &
    '                                                 Abs          Rel'
  write ( *, '(a)' ) &
    '         N        Exact        Estimate          Error        Error'
  write ( *, '(a)' ) ' '

  n = 100

  do i = 1, 7

    call stochastic_integral_ito ( n, estimate, exact, error )

    write ( *, '(2x,i8,2x,g16.8,2x,g16.8,2x,g10.2,2x,g10.2)' ) &
      n, exact, estimate, error, error / exact

    n = n * 4

  end do

  return
end
subroutine test11 ( )

!*****************************************************************************80
!
!! TEST11 tests STOCHASTIC_INTEGRAL_STRAT.
!
!  Licensing:
!
!    This code is distributed under the MIT license.
!
!  Modified:
!
!    21 September 2012
!
!  Author:
!
!    John Burkardt
!
  implicit none

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

  real ( kind = rk ) error
  real ( kind = rk ) estimate
  real ( kind = rk ) exact
  integer i
  integer n

  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) 'TEST11:'
  write ( *, '(a)' ) &
    '  Estimate the Stratonovich integral of W(t) dW over [0,1].'
  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) &
    '                                                 Abs          Rel'
  write ( *, '(a)' ) &
    '         N        Exact        Estimate          Error        Error'
  write ( *, '(a)' ) ' '

  n = 100

  do i = 1, 7

    call stochastic_integral_strat ( n, estimate, exact, error )

    write ( *, '(2x,i8,2x,g16.8,2x,g16.8,2x,g10.2,2x,g10.2)' ) &
      n, exact, estimate, error, error / exact

    n = n * 4

  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