program main

!*****************************************************************************80
!
!! log_normal_test() tests log_normal().
!
!  Licensing:
!
!    This code is distributed under the MIT license.
!
!  Modified:
!
!    24 March 2016
!
!  Author:
!
!    John Burkardt
!
  implicit none

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

  call timestamp ( )
  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) 'log_normal_test():'
  write ( *, '(a)' ) '  Fortran90 version:'
  write ( *, '(a)' ) '  Test log_normal().'

  call log_normal_cdf_test ( )
  call log_normal_sample_test ( )
!
!  Terminate.
!
  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) 'log_normal_test():'
  write ( *, '(a)' ) '  Normal end of execution.'
  write ( *, '(a)' ) ' '
  call timestamp ( )

  stop 0
end
subroutine log_normal_cdf_test ( )

!*****************************************************************************80
!
!! LOG_NORMAL_CDF_TEST tests LOG_NORMAL_CDF, LOG_NORMAL_CDF_INV, LOG_NORMAL_PDF.
!
!  Licensing:
!
!    This code is distributed under the MIT license.
!
!  Modified:
!
!    27 February 2007
!
!  Author:
!
!    John Burkardt
!
  implicit none

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

  real ( kind = rk ) cdf
  integer i
  logical log_normal_check
  real ( kind = rk ) mu
  real ( kind = rk ) pdf
  real ( kind = rk ) sigma
  real ( kind = rk ) x
  real ( kind = rk ) x2

  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) 'LOG_NORMAL_CDF_TEST'
  write ( *, '(a)' ) '  LOG_NORMAL_CDF evaluates the Log Normal CDF;'
  write ( *, '(a)' ) '  LOG_NORMAL_CDF_INV inverts the Log Normal CDF.'
  write ( *, '(a)' ) '  LOG_NORMAL_PDF evaluates the Log Normal PDF;'

  mu = 10.0D+00
  sigma = 2.25D+00

  write ( *, '(a)' ) ' '
  write ( *, '(a,g14.6)' ) '  PDF parameter MU =    ', mu
  write ( *, '(a,g14.6)' ) '  PDF parameter SIGMA = ', sigma

  if ( .not. log_normal_check ( mu, sigma ) ) then
    write ( *, '(a)' ) ' '
    write ( *, '(a)' ) 'LOG_NORMAL_CDF_TEST - Fatal error!'
    write ( *, '(a)' ) '  The parameters are not legal.'
    return
  end if

  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) '       X            PDF           CDF            CDF_INV'
  write ( *, '(a)' ) ' '

  do i = 1, 10

    call log_normal_sample ( mu, sigma, x )

    call log_normal_pdf ( x, mu, sigma, pdf )

    call log_normal_cdf ( x, mu, sigma, cdf )

    call log_normal_cdf_inv ( cdf, mu, sigma, x2 )

    write ( *, '(2x,4g14.6)' ) x, pdf, cdf, x2

  end do

  return
end
subroutine log_normal_sample_test ( )

!*****************************************************************************80
!
!! LOG_NORMAL_SAMPLE_TEST tests LOG_NORMAL_MEAN, LOG_NORMAL_SAMPLE, LOG_NORMAL_VARIANCE.
!
!  Licensing:
!
!    This code is distributed under the MIT license.
!
!  Modified:
!
!    24 March 2016
!
!  Author:
!
!    John Burkardt
!
  implicit none

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

  integer, parameter :: sample_num = 1000

  integer i
  logical log_normal_check
  real ( kind = rk ) mean
  real ( kind = rk ) mu
  real ( kind = rk ) sigma
  real ( kind = rk ) variance
  real ( kind = rk ) x(sample_num)
  real ( kind = rk ) xmax
  real ( kind = rk ) xmin

  write ( *, '(a)' ) ' '
  write ( *, '(a)' ) 'LOG_NORMAL_SAMPLE_TEST'
  write ( *, '(a)' ) '  LOG_NORMAL_MEAN computes the Log Normal mean;'
  write ( *, '(a)' ) '  LOG_NORMAL_SAMPLE samples the Log Normal distribution;'
  write ( *, '(a)' ) '  LOG_NORMAL_VARIANCE computes the Log Normal variance.'

  mu = 1.0D+00
  sigma = 2.0D+00

  write ( *, '(a)' ) ' '
  write ( *, '(a,g14.6)' ) '  PDF parameter MU =    ', mu
  write ( *, '(a,g14.6)' ) '  PDF parameter SIGMA = ', sigma

  if ( .not. log_normal_check ( mu, sigma ) ) then
    write ( *, '(a)' ) ' '
    write ( *, '(a)' ) 'LOG_NORMAL_SAMPLE_TEST - Fatal error!'
    write ( *, '(a)' ) '  The parameters are not legal.'
    return
  end if

  call log_normal_mean ( mu, sigma, mean )
  call log_normal_variance ( mu, sigma, variance )

  write ( *, '(a,g14.6)' ) '  PDF mean =                    ', mean
  write ( *, '(a,g14.6)' ) '  PDF variance =                ', variance

  do i = 1, sample_num
    call log_normal_sample ( mu, sigma, x(i) )
  end do

  call r8vec_mean ( sample_num, x, mean )
  call r8vec_variance ( sample_num, x, variance )
  call r8vec_max ( sample_num, x, xmax )
  call r8vec_min ( sample_num, x, xmin )

  write ( *, '(a)' ) ' '
  write ( *, '(a,i8)'    ) '  Sample size =     ', sample_num
  write ( *, '(a,g14.6)' ) '  Sample mean =     ', mean
  write ( *, '(a,g14.6)' ) '  Sample variance = ', variance
  write ( *, '(a,g14.6)' ) '  Sample maximum =  ', xmax
  write ( *, '(a,g14.6)' ) '  Sample minimum =  ', xmin

  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