#! /usr/bin/env python
#
def chebyshev2_set ( n ):

#*****************************************************************************80
#
## CHEBYSHEV2_SET sets a Chebyshev Type 2 quadrature rule.
#
#  Discussion:
#
#    The integral:
#
#      integral ( -1 <= x <= 1 ) f(x) * sqrt ( 1 - x * x ) dx
#
#    The quadrature rule:
#
#      sum ( 1 <= i <= n ) w(i) * f ( x(i) )
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    11 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 ( [ \
               1.570796326794897 ] )

  elif ( n == 2 ):

    x = np.array ( [ \
             -0.5000000000000000, \
              0.5000000000000000 ] )

    w = np.array ( [ \
              0.7853981633974484, \
              0.7853981633974481 ] )
 
  elif ( n == 3 ):

    x = np.array ( [ \
             -0.7071067811865475, \
              0.0, \
              0.7071067811865476 ] )

    w = np.array ( [ \
              0.3926990816987243, \
              0.7853981633974483, \
              0.3926990816987240 ] )

  elif ( n == 4 ):

    x = np.array ( [ \
             -0.8090169943749473, \
             -0.3090169943749473, \
              0.3090169943749475, \
              0.8090169943749475 ] )

    w = np.array ( [ \
              0.2170787134227061, \
              0.5683194499747424, \
              0.5683194499747423, \
              0.2170787134227060 ] )

  elif ( n == 5 ):

    x = np.array ( [ \
             -0.8660254037844387, \
             -0.5000000000000000, \
              0.0, \
              0.5000000000000000, \
              0.8660254037844387 ] )

    w = np.array ( [ \
              0.1308996938995747, \
              0.3926990816987242, \
              0.5235987755982988, \
              0.3926990816987240, \
              0.1308996938995747 ] )

  elif ( n == 6 ):

    x = np.array ( [ \
             -0.9009688679024190, \
             -0.6234898018587335, \
             -0.2225209339563143, \
              0.2225209339563144, \
              0.6234898018587336, \
              0.9009688679024191 ] )

    w = np.array ( [ \
              0.08448869089158863, \
              0.2743330560697779, \
              0.4265764164360819, \
              0.4265764164360819, \
              0.2743330560697778, \
              0.08448869089158857 ] )

  elif ( n == 7 ):

    x = np.array ( [ \
             -0.9238795325112867, \
             -0.7071067811865475, \
             -0.3826834323650897, \
              0.0, \
              0.3826834323650898, \
              0.7071067811865476, \
              0.9238795325112867 ] )

    w = np.array ( [ \
              0.05750944903191316, \
              0.1963495408493621, \
              0.3351896326668110, \
              0.3926990816987241, \
              0.3351896326668110, \
              0.1963495408493620, \
              0.05750944903191313 ] )

  elif ( n == 8 ):

    x = np.array ( [ \
             -0.9396926207859083, \
             -0.7660444431189779, \
             -0.5000000000000000, \
             -0.1736481776669303, \
              0.1736481776669304, \
              0.5000000000000000, \
              0.7660444431189780, \
              0.9396926207859084 ] ) 

    w = np.array ( [ \
              0.04083294770910712, \
              0.1442256007956728, \
              0.2617993877991495, \
              0.3385402270935190, \
              0.3385402270935190, \
              0.2617993877991494, \
              0.1442256007956727, \
              0.04083294770910708 ] )

  elif ( n == 9 ):

    x = np.array ( [ \
             -0.9510565162951535, \
             -0.8090169943749473, \
             -0.5877852522924730, \
             -0.3090169943749473, \
              0.0, \
              0.3090169943749475, \
              0.5877852522924731, \
              0.8090169943749475, \
              0.9510565162951535 ] )

    w = np.array ( [ \
              0.02999954037160818, \
              0.1085393567113530, \
              0.2056199086476263, \
              0.2841597249873712, \
              0.3141592653589793, \
              0.2841597249873711, \
              0.2056199086476263, \
              0.1085393567113530, \
              0.02999954037160816 ] )

  elif ( n == 10 ):

    x = np.array ( [ \
             -0.9594929736144974, \
             -0.8412535328311811, \
             -0.6548607339452850, \
             -0.4154150130018863, \
             -0.1423148382732850, \
              0.1423148382732851, \
              0.4154150130018864, \
              0.6548607339452851, \
              0.8412535328311812, \
              0.9594929736144974 ] )   

    w = np.array ( [ \
              0.02266894250185884, \
              0.08347854093418908, \
              0.1631221774548166, \
              0.2363135602034873, \
              0.2798149423030966, \
              0.2798149423030965, \
              0.2363135602034873, \
              0.1631221774548166, \
              0.08347854093418902, \
              0.02266894250185884 ] )

  else:

    print ( '' )
    print ( 'CHEBYSHEV2_SET - Fatal error!' )
    print ( '  Illegal value of N = %d' % ( n ) )
    print ( '  Legal values are 1 through 10.' )
    exit ( 'CHEBYSHEV2_SET - Fatal error!' )

  return x, w

def chebyshev2_set_test ( ):

#*****************************************************************************80
#
## CHEBYSHEV2_SET_TEST tests CHEBYSHEV2_SET.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license. 
#
#  Modified:
#
#    11 June 2015
#
#  Author:
#
#    John Burkardt
#
  import platform

  print ( '' )
  print ( 'CHEBYSHEV2_SET_TEST' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  CHEBYSHEV2_SET sets' )
  print ( '  a Chebyshev Type 2 quadrature rule over [-1,1]' )
  print ( '' )
  print ( '  Index       X             W' )

  for n in range ( 1, 11 ):

    x, w = chebyshev2_set ( n )

    print ( '' )

    for i in range ( 0, n ):
      print ( '  %2d  %24.16g  %24.16g' % ( i, x[i], w[i] ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'CHEBYSHEV2_SET_TEST:' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( )
  chebyshev2_set_test ( )
  timestamp ( )