#! /usr/bin/env python
#
def chebyshev1_set ( n ):

#*****************************************************************************80
#
## CHEBYSHEV1_SET sets a Chebyshev Type 1 quadrature rule.
#
#  Discussion:
#
#    The integral:
#
#      integral  (-1 <= x <= 1 ) f(x) / sqrt  (1 - x * x ) dx
#
#    The quadrature rule:
#
#      sum  (1 <= i <= n )  (i) * f  ( (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 ( [ \
            3.141592653589793 ] )

  elif ( n == 2 ):

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

    w = np.array ( [ \
               1.570796326794897, \
               1.570796326794897 ] )

  elif ( n == 3 ):

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

    w = np.array ( [ \
               1.047197551196598, \
               1.047197551196598, \
               1.047197551196598 ] )

  elif ( n == 4 ):

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

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

  elif ( n == 5 ):

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

    w = np.array ( [ \
              0.6283185307179586, \
              0.6283185307179586, \
              0.6283185307179586, \
              0.6283185307179586, \
              0.6283185307179586 ] )

  elif ( n == 6 ):

    x = np.array ( [ \
             -0.9659258262890682, \
             -0.7071067811865475, \
             -0.2588190451025206, \
              0.2588190451025207, \
              0.7071067811865476, \
              0.9659258262890683 ] )

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

  elif ( n == 7 ):

    x = np.array ( [ \
             -0.9749279121818237, \
             -0.7818314824680295, \
             -0.4338837391175581, \
              0.0, \
              0.4338837391175582, \
              0.7818314824680298, \
              0.9749279121818236  ] )
   
    w = np.array ( [ \
              0.4487989505128276, \
              0.4487989505128276, \
              0.4487989505128276, \
              0.4487989505128276, \
              0.4487989505128276, \
              0.4487989505128276, \
              0.4487989505128276 ] )

  elif ( n == 8 ):

    x = np.array ( [ \
             -0.9807852804032304, \
             -0.8314696123025453, \
             -0.5555702330196020, \
             -0.1950903220161282, \
              0.1950903220161283, \
              0.5555702330196023, \
              0.8314696123025452, \
              0.9807852804032304 ] )

    w = np.array ( [ \
              0.3926990816987241, \
              0.3926990816987241, \
              0.3926990816987241, \
              0.3926990816987241, \
              0.3926990816987241, \
              0.3926990816987241, \
              0.3926990816987241, \
              0.3926990816987241 ] )

  elif ( n == 9 ):

    x = np.array ( [ \
             -0.9848077530122080, \
             -0.8660254037844385, \
             -0.6427876096865394, \
             -0.3420201433256688, \
              0.0, \
              0.3420201433256688, \
              0.6427876096865394, \
              0.8660254037844387, \
              0.9848077530122080 ] )

    w = np.array ( [ \
              0.3490658503988659, \
              0.3490658503988659, \
              0.3490658503988659, \
              0.3490658503988659, \
              0.3490658503988659, \
              0.3490658503988659, \
              0.3490658503988659, \
              0.3490658503988659, \
              0.3490658503988659 ] )

  elif ( n == 10 ):

    x = np.array ( [ \
             -0.9876883405951377, \
             -0.8910065241883678, \
             -0.7071067811865475, \
             -0.4539904997395467, \
             -0.1564344650402306, \
              0.1564344650402309, \
              0.4539904997395468, \
              0.7071067811865476, \
              0.8910065241883679, \
              0.9876883405951378 ] )

    w = np.array ( [ \
              0.3141592653589793, \
              0.3141592653589793, \
              0.3141592653589793, \
              0.3141592653589793, \
              0.3141592653589793, \
              0.3141592653589793, \
              0.3141592653589793, \
              0.3141592653589793, \
              0.3141592653589793, \
              0.3141592653589793 ] )

  else:

    print ( '' )
    print ( 'CHEBYSHEV1_SET - Fatal error!' )
    print ( '  Illegal value of N = %d' %  ( n ) )
    print ( '  Legal values are 1 through 10.' )
    exit ( 'CHEBYSHEV1_SET - Fatal error!' )

  return x, w

def chebyshev1_set_test ( ):

#*****************************************************************************80
#
## CHEBYSHEV1_SET_TEST tests CHEBYSHEV1_SET.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license. 
#
#  Modified:
#
#    11 June 2015
#
#  Author:
#
#    John Burkardt
#
  import platform

  print ( '' )
  print ( 'CHEBYSHEV1_SET_TEST' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  CHEBYSHEV1_SET sets' )
  print ( '  a Chebyshev Type 1 quadrature rule over [-1,1]' )

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

  for n in range ( 1, 11 ):

    x, w = chebyshev1_set ( n )

    print ( '' )

    for i in range ( 0, n ):
      print ( '  %2d  %24.16g  %24.16g' % ( i, x[i], w[i] ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'CHEBYSHEV1_SET_TEST:' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( )
  chebyshev1_set_test ( )
  timestamp ( )