#! /usr/bin/env python
#
def truncated_normal_a_moments ( order_max, mu, sigma, a ):

#*****************************************************************************80
#
## TRUNCATED_NORMAL_A_MOMENTS: moments of the truncated Normal distribution.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    09 March 2015
#
#  Author:
#
#    John Burkardt
#
#  Reference:
#
#    Phoebus Dhrymes,
#    Moments of Truncated Normal Distributions,
#    May 2005.
#
#  Parameters:
#
#    Input, integer ORDER_MAX, the maximum order of the moments.
#    0 <= ORDER_MAX.
#
#    Input, real MU, SIGMA, the mean and standard deviation of the
#    parent Normal distribution.
#    0 < S.
#
#    Input, real A, the lower truncation limit.
#
#    Output, real VALUE[ORDER_MAX+1], the moments of the PDF.
#
  import numpy as np

  value = np.zeros ( order_max + 1 )

  for order in range ( 0, order_max + 1 ):
    value[order] =  truncated_normal_a_moment ( order, mu, sigma, a )

  return value

def truncated_normal_a_moment ( order, mu, sigma, a ):

#*****************************************************************************80
#
## TRUNCATED_NORMAL_A_MOMENT: a moment of the truncated Normal distribution.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    09 March 2015
#
#  Author:
#
#    John Burkardt
#
#  Reference:
#
#    Phoebus Dhrymes,
#    Moments of Truncated Normal Distributions,
#    May 2005.
#
#  Parameters:
#
#    Input, integer ORDER, the order of the moment.
#    0 <= ORDER.
#
#    Input, real MU, SIGMA, the mean and standard deviation of the
#    parent Normal distribution.
#    0 < S.
#
#    Input, real A, the lower truncation limit.
#
#    Output, real VALUE, the moment of the PDF.
#
  from r8_mop import r8_mop
  from truncated_normal_b_moment import truncated_normal_b_moment

  value = r8_mop ( order ) \
    * truncated_normal_b_moment ( order, -mu, sigma, -a );

  return value

def truncated_normal_a_moment_test ( ):

#*****************************************************************************80
#
## TRUNCATED_NORMAL_A_MOMENT_TEST tests TRUNCATED_NORMAL_A_MOMENT.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    09 March 2015
#
#  Author:
#
#    John Burkardt
#
  import numpy as np
  import platform

  test_num = 6
  mu_test =    np.array ( [  0.0,  0.0,   0.0,   0.0,  0.0,  -5.0 ] )
  sigma_test = np.array ( [  1.0,  1.0,   1.0,   2.0,  2.0,   1.0 ] )
  a_test =     np.array ( [  0.0, -10.0, 10.0, -10.0, 10.0, -10.0 ] )

  print ( '' )
  print ( 'TRUNCATED_NORMAL_A_MOMENT_TEST' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  TRUNCATED_NORMAL_A_MOMENT evaluates moments' )
  print ( '  of the lower Truncated Normal distribution.' )

  for test in range ( 0, test_num ):

    mu = mu_test[test]
    sigma = sigma_test[test]
    a = a_test[test]
    print ( '' )
    print ( '  Test = %d, Mu = %g, Sigma = %g, A = %g' \
      % ( test, mu, sigma, a ) )
    print ( ' Order  Moment' )
    print ( '\n' )

    for order in range ( 0, 9 ):
      value = truncated_normal_a_moment ( order, mu, sigma, a )
      print ( '  %2d  %12g' % ( order, value ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'TRUNCATED_NORMAL_A_MOMENT_TEST:' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( )
  truncated_normal_a_moment_test ( )
  timestamp ( )