#! /usr/bin/env python
#
def chi_square_noncentral_cdf_values ( n_data ):

#*****************************************************************************80
#
## CHI_SQUARE_NONCENTRAL_CDF_VALUES returns values of the noncentral chi CDF.
#
#  Discussion:
#
#    In Mathematica, the function can be evaluated by:
#
#      Needs["Statistics`ContinuousDistributions`"]
#      dist = NoncentralChiSquareDistribution [ df, lambda ]
#      CDF [ dist, x ]
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    24 January 2015
#
#  Author:
#
#    John Burkardt
#
#  Reference:
#
#    Stephen Wolfram,
#    The Mathematica Book,
#    Fourth Edition,
#    Wolfram Media / Cambridge University Press, 1999.
#
#  Parameters:
#
#    Input/output, integer N_DATA.  The user sets N_DATA to 0 before the
#    first call.  On each call, the routine increments N_DATA by 1, and
#    returns the corresponding data; when there is no more data, the
#    output value of N_DATA will be 0 again.
#
#    Output, integer DF, the number of degrees of freedom.
#
#    Output, real LAMBDA, the noncentrality parameter.
#
#    Output, real X, the argument of the function.
#
#    Output, real F, the noncentral chi CDF.
#
  import numpy as np

  n_max = 28

  df_vec = np.array ( ( \
      1,   2,   3, \
      1,   2,   3, \
      1,   2,   3, \
      1,   2,   3, \
     60,  80, 100, \
      1,   2,   3, \
     10,  10,  10, \
     10,  10,  10, \
     10,  10,  10, \
      8 ) )

  f_vec = np.array ( ( \
     0.8399444269398261E+00, \
     0.6959060300435139E+00, \
     0.5350879697078847E+00, \
     0.7647841496310313E+00, \
     0.6206436532195436E+00, \
     0.4691667375373180E+00, \
     0.3070884345937569E+00, \
     0.2203818092990903E+00, \
     0.1500251895581519E+00, \
     0.3071163194335791E-02, \
     0.1763982670131894E-02, \
     0.9816792594625022E-03, \
     0.1651753140866208E-01, \
     0.2023419573950451E-03, \
     0.4984476352854074E-06, \
     0.1513252400654827E-01, \
     0.2090414910614367E-02, \
     0.2465021206048452E-03, \
     0.2636835050342939E-01, \
     0.1857983220079215E-01, \
     0.1305736595486640E-01, \
     0.5838039534819351E-01, \
     0.4249784402463712E-01, \
     0.3082137716021596E-01, \
     0.1057878223400849E+00, \
     0.7940842984598509E-01, \
     0.5932010895599639E-01, \
     0.2110395656918684E+00 ) )

  lam_vec = np.array ( ( \
       0.5E+00, \
       0.5E+00, \
       0.5E+00, \
       1.0E+00, \
       1.0E+00, \
       1.0E+00, \
       5.0E+00, \
       5.0E+00, \
       5.0E+00, \
      20.0E+00, \
      20.0E+00, \
      20.0E+00, \
      30.0E+00, \
      30.0E+00, \
      30.0E+00, \
       5.0E+00, \
       5.0E+00, \
       5.0E+00, \
       2.0E+00, \
       3.0E+00, \
       4.0E+00, \
       2.0E+00, \
       3.0E+00, \
       4.0E+00, \
       2.0E+00, \
       3.0E+00, \
       4.0E+00, \
       0.5E+00 ) )

  x_vec = np.array ( ( \
      3.000E+00, \
      3.000E+00, \
      3.000E+00, \
      3.000E+00, \
      3.000E+00, \
      3.000E+00, \
      3.000E+00, \
      3.000E+00, \
      3.000E+00, \
      3.000E+00, \
      3.000E+00, \
      3.000E+00, \
     60.000E+00, \
     60.000E+00, \
     60.000E+00, \
      0.050E+00, \
      0.050E+00, \
      0.050E+00, \
      4.000E+00, \
      4.000E+00, \
      4.000E+00, \
      5.000E+00, \
      5.000E+00, \
      5.000E+00, \
      6.000E+00, \
      6.000E+00, \
      6.000E+00, \
      5.000E+00 ))

  if ( n_data < 0 ):
    n_data = 0

  if ( n_max <= n_data ):
    n_data = 0
    df = 0
    lam = 0.0
    x = 0.0
    f = 0.0
  else:
    df = df_vec[n_data]
    lam = lam_vec[n_data]
    x = x_vec[n_data]
    f = f_vec[n_data]
    n_data = n_data + 1

  return n_data, df, lam, x, f

def chi_square_noncentral_cdf_values_test ( ):

#*****************************************************************************80
#
## CHI_SQUARE_NONCENTRAL_CDF_VALUES_TEST tests CHI_SQUARE_NONCENTRAL_CDF_VALUES.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    23 January 2015
#
#  Author:
#
#    John Burkardt
#
  import platform

  print ( '' )
  print ( 'CHI_SQUARE_NONCENTRAL_CDF_VALUES_TEST:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  CHI_SQUARE_NONCENTRAL_CDF_VALUES: values of the noncentral Chi Square CDF.' )
  print ( '' )
  print ( '      DF      LAM      X        CHI_SQUARE_NONCENTRAL_CDF' )
  print ( '' )

  n_data = 0

  while ( True ):

    n_data, df, lam, x, f = chi_square_noncentral_cdf_values ( n_data )

    if ( n_data == 0 ):
      break

    print ( '  %12d  %12f  %12f  %24.16g' % ( df, lam, x, f ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'CHI_SQUARE_NONCENTRAL_CDF_VALUES_TEST:' )
  print ( '  Normal end of execution.' )
  return

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


37ce452a9c7ee6805557115e7e17b94e4f32ea3a
<mask token>

<mask token>


def chi_square_noncentral_cdf_values_test():
    import platform
    print('')
    print('CHI_SQUARE_NONCENTRAL_CDF_VALUES_TEST:')
    print('  Python version: %s' % platform.python_version())
    print(
        '  CHI_SQUARE_NONCENTRAL_CDF_VALUES: values of the noncentral Chi Square CDF.'
        )
    print('')
    print('      DF      LAM      X        CHI_SQUARE_NONCENTRAL_CDF')
    print('')
    n_data = 0
    while True:
        n_data, df, lam, x, f = chi_square_noncentral_cdf_values(n_data)
        if n_data == 0:
            break
        print('  %12d  %12f  %12f  %24.16g' % (df, lam, x, f))
    print('')
    print('CHI_SQUARE_NONCENTRAL_CDF_VALUES_TEST:')
    print('  Normal end of execution.')
    return


<mask token>

def chi_square_noncentral_cdf_values(n_data):
    import numpy as np
    n_max = 28
    df_vec = np.array((1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 60, 80, 100, 1, 
        2, 3, 10, 10, 10, 10, 10, 10, 10, 10, 10, 8))
    f_vec = np.array((0.8399444269398261, 0.6959060300435139, 
        0.5350879697078847, 0.7647841496310313, 0.6206436532195436, 
        0.469166737537318, 0.3070884345937569, 0.2203818092990903, 
        0.1500251895581519, 0.003071163194335791, 0.001763982670131894, 
        0.000981679259462502, 0.01651753140866208, 0.0002023419573950451, 
        4.984476352854074e-07, 0.01513252400654827, 0.002090414910614367, 
        0.0002465021206048452, 0.02636835050342939, 0.01857983220079215, 
        0.0130573659548664, 0.05838039534819351, 0.04249784402463712, 
        0.03082137716021596, 0.1057878223400849, 0.07940842984598509, 
        0.05932010895599639, 0.2110395656918684))
    lam_vec = np.array((0.5, 0.5, 0.5, 1.0, 1.0, 1.0, 5.0, 5.0, 5.0, 20.0, 
        20.0, 20.0, 30.0, 30.0, 30.0, 5.0, 5.0, 5.0, 2.0, 3.0, 4.0, 2.0, 
        3.0, 4.0, 2.0, 3.0, 4.0, 0.5))
    x_vec = np.array((3.0, 3.0, 3.0, 3.0, 3.0, 3.0, 3.0, 3.0, 3.0, 3.0, 3.0,
        3.0, 60.0, 60.0, 60.0, 0.05, 0.05, 0.05, 4.0, 4.0, 4.0, 5.0, 5.0, 
        5.0, 6.0, 6.0, 6.0, 5.0))
    if n_data < 0:
        n_data = 0
    if n_max <= n_data:
        n_data = 0
        df = 0
        lam = 0.0
        x = 0.0
        f = 0.0
    else:
        df = df_vec[n_data]
        lam = lam_vec[n_data]
        x = x_vec[n_data]
        f = f_vec[n_data]
        n_data = n_data + 1
    return n_data, df, lam, x, f


def chi_square_noncentral_cdf_values_test():
    import platform
    print('')
    print('CHI_SQUARE_NONCENTRAL_CDF_VALUES_TEST:')
    print('  Python version: %s' % platform.python_version())
    print(
        '  CHI_SQUARE_NONCENTRAL_CDF_VALUES: values of the noncentral Chi Square CDF.'
        )
    print('')
    print('      DF      LAM      X        CHI_SQUARE_NONCENTRAL_CDF')
    print('')
    n_data = 0
    while True:
        n_data, df, lam, x, f = chi_square_noncentral_cdf_values(n_data)
        if n_data == 0:
            break
        print('  %12d  %12f  %12f  %24.16g' % (df, lam, x, f))
    print('')
    print('CHI_SQUARE_NONCENTRAL_CDF_VALUES_TEST:')
    print('  Normal end of execution.')
    return


<mask token>

def chi_square_noncentral_cdf_values(n_data):
    import numpy as np
    n_max = 28
    df_vec = np.array((1, 2, 3, 1, 2, 3, 1, 2, 3, 1, 2, 3, 60, 80, 100, 1, 
        2, 3, 10, 10, 10, 10, 10, 10, 10, 10, 10, 8))
    f_vec = np.array((0.8399444269398261, 0.6959060300435139, 
        0.5350879697078847, 0.7647841496310313, 0.6206436532195436, 
        0.469166737537318, 0.3070884345937569, 0.2203818092990903, 
        0.1500251895581519, 0.003071163194335791, 0.001763982670131894, 
        0.000981679259462502, 0.01651753140866208, 0.0002023419573950451, 
        4.984476352854074e-07, 0.01513252400654827, 0.002090414910614367, 
        0.0002465021206048452, 0.02636835050342939, 0.01857983220079215, 
        0.0130573659548664, 0.05838039534819351, 0.04249784402463712, 
        0.03082137716021596, 0.1057878223400849, 0.07940842984598509, 
        0.05932010895599639, 0.2110395656918684))
    lam_vec = np.array((0.5, 0.5, 0.5, 1.0, 1.0, 1.0, 5.0, 5.0, 5.0, 20.0, 
        20.0, 20.0, 30.0, 30.0, 30.0, 5.0, 5.0, 5.0, 2.0, 3.0, 4.0, 2.0, 
        3.0, 4.0, 2.0, 3.0, 4.0, 0.5))
    x_vec = np.array((3.0, 3.0, 3.0, 3.0, 3.0, 3.0, 3.0, 3.0, 3.0, 3.0, 3.0,
        3.0, 60.0, 60.0, 60.0, 0.05, 0.05, 0.05, 4.0, 4.0, 4.0, 5.0, 5.0, 
        5.0, 6.0, 6.0, 6.0, 5.0))
    if n_data < 0:
        n_data = 0
    if n_max <= n_data:
        n_data = 0
        df = 0
        lam = 0.0
        x = 0.0
        f = 0.0
    else:
        df = df_vec[n_data]
        lam = lam_vec[n_data]
        x = x_vec[n_data]
        f = f_vec[n_data]
        n_data = n_data + 1
    return n_data, df, lam, x, f


def chi_square_noncentral_cdf_values_test():
    import platform
    print('')
    print('CHI_SQUARE_NONCENTRAL_CDF_VALUES_TEST:')
    print('  Python version: %s' % platform.python_version())
    print(
        '  CHI_SQUARE_NONCENTRAL_CDF_VALUES: values of the noncentral Chi Square CDF.'
        )
    print('')
    print('      DF      LAM      X        CHI_SQUARE_NONCENTRAL_CDF')
    print('')
    n_data = 0
    while True:
        n_data, df, lam, x, f = chi_square_noncentral_cdf_values(n_data)
        if n_data == 0:
            break
        print('  %12d  %12f  %12f  %24.16g' % (df, lam, x, f))
    print('')
    print('CHI_SQUARE_NONCENTRAL_CDF_VALUES_TEST:')
    print('  Normal end of execution.')
    return


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

#! /usr/bin/env python
#
def chi_square_noncentral_cdf_values ( n_data ):

#*****************************************************************************80
#
## CHI_SQUARE_NONCENTRAL_CDF_VALUES returns values of the noncentral chi CDF.
#
#  Discussion:
#
#    In Mathematica, the function can be evaluated by:
#
#      Needs["Statistics`ContinuousDistributions`"]
#      dist = NoncentralChiSquareDistribution [ df, lambda ]
#      CDF [ dist, x ]
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    24 January 2015
#
#  Author:
#
#    John Burkardt
#
#  Reference:
#
#    Stephen Wolfram,
#    The Mathematica Book,
#    Fourth Edition,
#    Wolfram Media / Cambridge University Press, 1999.
#
#  Parameters:
#
#    Input/output, integer N_DATA.  The user sets N_DATA to 0 before the
#    first call.  On each call, the routine increments N_DATA by 1, and
#    returns the corresponding data; when there is no more data, the
#    output value of N_DATA will be 0 again.
#
#    Output, integer DF, the number of degrees of freedom.
#
#    Output, real LAMBDA, the noncentrality parameter.
#
#    Output, real X, the argument of the function.
#
#    Output, real F, the noncentral chi CDF.
#
  import numpy as np

  n_max = 28

  df_vec = np.array ( ( \
      1,   2,   3, \
      1,   2,   3, \
      1,   2,   3, \
      1,   2,   3, \
     60,  80, 100, \
      1,   2,   3, \
     10,  10,  10, \
     10,  10,  10, \
     10,  10,  10, \
      8 ) )

  f_vec = np.array ( ( \
     0.8399444269398261E+00, \
     0.6959060300435139E+00, \
     0.5350879697078847E+00, \
     0.7647841496310313E+00, \
     0.6206436532195436E+00, \
     0.4691667375373180E+00, \
     0.3070884345937569E+00, \
     0.2203818092990903E+00, \
     0.1500251895581519E+00, \
     0.3071163194335791E-02, \
     0.1763982670131894E-02, \
     0.9816792594625022E-03, \
     0.1651753140866208E-01, \
     0.2023419573950451E-03, \
     0.4984476352854074E-06, \
     0.1513252400654827E-01, \
     0.2090414910614367E-02, \
     0.2465021206048452E-03, \
     0.2636835050342939E-01, \
     0.1857983220079215E-01, \
     0.1305736595486640E-01, \
     0.5838039534819351E-01, \
     0.4249784402463712E-01, \
     0.3082137716021596E-01, \
     0.1057878223400849E+00, \
     0.7940842984598509E-01, \
     0.5932010895599639E-01, \
     0.2110395656918684E+00 ) )

  lam_vec = np.array ( ( \
       0.5E+00, \
       0.5E+00, \
       0.5E+00, \
       1.0E+00, \
       1.0E+00, \
       1.0E+00, \
       5.0E+00, \
       5.0E+00, \
       5.0E+00, \
      20.0E+00, \
      20.0E+00, \
      20.0E+00, \
      30.0E+00, \
      30.0E+00, \
      30.0E+00, \
       5.0E+00, \
       5.0E+00, \
       5.0E+00, \
       2.0E+00, \
       3.0E+00, \
       4.0E+00, \
       2.0E+00, \
       3.0E+00, \
       4.0E+00, \
       2.0E+00, \
       3.0E+00, \
       4.0E+00, \
       0.5E+00 ) )

  x_vec = np.array ( ( \
      3.000E+00, \
      3.000E+00, \
      3.000E+00, \
      3.000E+00, \
      3.000E+00, \
      3.000E+00, \
      3.000E+00, \
      3.000E+00, \
      3.000E+00, \
      3.000E+00, \
      3.000E+00, \
      3.000E+00, \
     60.000E+00, \
     60.000E+00, \
     60.000E+00, \
      0.050E+00, \
      0.050E+00, \
      0.050E+00, \
      4.000E+00, \
      4.000E+00, \
      4.000E+00, \
      5.000E+00, \
      5.000E+00, \
      5.000E+00, \
      6.000E+00, \
      6.000E+00, \
      6.000E+00, \
      5.000E+00 ))

  if ( n_data < 0 ):
    n_data = 0

  if ( n_max <= n_data ):
    n_data = 0
    df = 0
    lam = 0.0
    x = 0.0
    f = 0.0
  else:
    df = df_vec[n_data]
    lam = lam_vec[n_data]
    x = x_vec[n_data]
    f = f_vec[n_data]
    n_data = n_data + 1

  return n_data, df, lam, x, f

def chi_square_noncentral_cdf_values_test ( ):

#*****************************************************************************80
#
## CHI_SQUARE_NONCENTRAL_CDF_VALUES_TEST tests CHI_SQUARE_NONCENTRAL_CDF_VALUES.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    23 January 2015
#
#  Author:
#
#    John Burkardt
#
  import platform

  print ( '' )
  print ( 'CHI_SQUARE_NONCENTRAL_CDF_VALUES_TEST:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  CHI_SQUARE_NONCENTRAL_CDF_VALUES: values of the noncentral Chi Square CDF.' )
  print ( '' )
  print ( '      DF      LAM      X        CHI_SQUARE_NONCENTRAL_CDF' )
  print ( '' )

  n_data = 0

  while ( True ):

    n_data, df, lam, x, f = chi_square_noncentral_cdf_values ( n_data )

    if ( n_data == 0 ):
      break

    print ( '  %12d  %12f  %12f  %24.16g' % ( df, lam, x, f ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'CHI_SQUARE_NONCENTRAL_CDF_VALUES_TEST:' )
  print ( '  Normal end of execution.' )
  return

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

