#! /usr/bin/env python
#
def hermite_1_set ( n ):

#*****************************************************************************80
#
## HERMITE_1_SET sets abscissas and weights for Hermite quadrature.
#
#  Discussion:
#
#    This routine is for the case with unit density:
#      integral ( -oo < x < +oo ) f(x) dx
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    19 June 2015
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, integer N, the order.
#    N must be between 1 and 10.
#
#    Output, real X(N), the abscissas.
#
#    Output, real W(N), the weights.
#
  import numpy as np
  from sys import exit

  if ( n == 1 ):

    x = np.array ( [ \
           0.0 ] )

    w = np.array ( [ \
           1.7724538509055161 ] )

  elif ( n == 2 ):

    x = np.array ( [ \
           - 0.707106781186547524400844362105, \
             0.707106781186547524400844362105 ] )

    w = np.array ( [ \
           1.4611411826611391, \
           1.4611411826611391 ] )

  elif ( n == 3 ):

    x = np.array ( [ \
           - 1.22474487139158904909864203735, \
             0.0, \
             1.22474487139158904909864203735 ] )

    w = np.array ( [ \
           1.3239311752136438, \
           1.1816359006036774, \
           1.3239311752136438 ] )

  elif ( n == 4 ):

    x = np.array ( [ \
           - 1.65068012388578455588334111112, \
           - 0.524647623275290317884060253835, \
             0.524647623275290317884060253835, \
             1.65068012388578455588334111112 ] )

    w = np.array ( [ \
           1.2402258176958150, \
           1.0599644828949693, \
           1.0599644828949693, \
           1.2402258176958150 ] )

  elif ( n == 5 ):

    x = np.array ( [ \
           - 2.02018287045608563292872408814, \
           - 0.958572464613818507112770593893, \
             0.0, \
             0.958572464613818507112770593893, \
             2.02018287045608563292872408814 ] )

    w = np.array ( [ \
           1.1814886255359869, \
           0.98658099675142830, \
           0.94530872048294190, \
           0.98658099675142830, \
           1.1814886255359869 ] )

  elif ( n == 6 ):

    x = np.array ( [ \
           - 2.35060497367449222283392198706, \
           - 1.33584907401369694971489528297, \
           - 0.436077411927616508679215948251, \
             0.436077411927616508679215948251, \
             1.33584907401369694971489528297, \
             2.35060497367449222283392198706 ] )

    w = np.array ( [ \
           1.1369083326745253, \
           0.93558055763118075, \
           0.87640133443623058, \
           0.87640133443623058, \
           0.93558055763118075, \
           1.1369083326745253 ] )

  elif ( n == 7 ):

    x = np.array ( [ \
           - 2.65196135683523349244708200652, \
           - 1.67355162876747144503180139830, \
           - 0.816287882858964663038710959027, \
             0.0, \
             0.816287882858964663038710959027, \
             1.67355162876747144503180139830, \
             2.65196135683523349244708200652 ] )

    w = np.array ( [ \
           1.1013307296103216, \
           0.89718460022518409, \
           0.82868730328363926, \
           0.81026461755680734, \
           0.82868730328363926, \
           0.89718460022518409, \
           1.1013307296103216 ] )

  elif ( n == 8 ):

    x = np.array ( [ \
           - 2.93063742025724401922350270524, \
           - 1.98165675669584292585463063977, \
           - 1.15719371244678019472076577906, \
           - 0.381186990207322116854718885584, \
             0.381186990207322116854718885584, \
             1.15719371244678019472076577906, \
             1.98165675669584292585463063977, \
             2.93063742025724401922350270524 ] )

    w = np.array ( [ \
           1.0719301442479805, \
           0.86675260656338138, \
           0.79289004838640131, \
           0.76454412865172916, \
           0.76454412865172916, \
           0.79289004838640131, \
           0.86675260656338138, \
           1.0719301442479805 ] )

  elif ( n == 9 ):

    x = np.array ( [ \
           - 3.19099320178152760723004779538, \
           - 2.26658058453184311180209693284, \
           - 1.46855328921666793166701573925, \
           - 0.723551018752837573322639864579, \
             0.0, \
             0.723551018752837573322639864579, \
             1.46855328921666793166701573925, \
             2.26658058453184311180209693284, \
             3.19099320178152760723004779538 ] )

    w = np.array ( [ \
           1.0470035809766838, \
           0.84175270147867043, \
           0.76460812509455023, \
           0.73030245274509220, \
           0.72023521560605097, \
           0.73030245274509220, \
           0.76460812509455023, \
           0.84175270147867043, \
           1.0470035809766838 ] )

  elif ( n == 10 ):

    x = np.array ( [ \
            - 3.43615911883773760332672549432, \
            - 2.53273167423278979640896079775, \
            - 1.75668364929988177345140122011, \
            - 1.03661082978951365417749191676, \
            - 0.342901327223704608789165025557, \
              0.342901327223704608789165025557, \
              1.03661082978951365417749191676, \
              1.75668364929988177345140122011, \
              2.53273167423278979640896079775, \
              3.43615911883773760332672549432 ] )

    w = np.array ( [ \
           1.0254516913657352, \
           0.82066612640481640, \
           0.74144193194356511, \
           0.70329632310490608, \
           0.68708185395127341, \
           0.68708185395127341, \
           0.70329632310490608, \
           0.74144193194356511, \
           0.82066612640481640, \
            1.0254516913657352 ] )
    
  else:

    print ( '' )
    print ( 'HERMITE_1_SET - Fatal error!' )
    print ( '  Illegal value of N = %d' % ( n ) )
    print ( '  Legal values are 1 to 10.' )
    exit ( 'HERMITE_1_SET - Fatal error!' )

  return x, w

def hermite_1_set_test ( ):

#*****************************************************************************80
#
## HERMITE_1_SET_TEST tests HERMITE_1_SET.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license. 
#
#  Modified:
#
#    19 June 2015
#
#  Author:
#
#    John Burkardt
#
  import platform

  print ( '' )
  print ( 'HERMITE_1_SET_TEST' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  HERMITE_1_SET sets a unit density Hermite quadrature rule.' )
  print ( '  The interval is (-oo,+oo).' )
  print ( '  The density is 1.0.' )

  print ( '' )
  print ( '  Index       X             W' )
  print ( '' )

  for n in range ( 1, 11 ):

    x, w = hermite_1_set ( n )

    print ( '' )

    for i in range ( 0, n ):
      print ( '  %2d  %24.16g  %24.16g' % ( i, x[i], w[i] ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'HERMITE_1_SET_TEST:' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( )
  hermite_1_set_test ( )
  timestamp ( )