#! /usr/bin/env python
#
def p_polynomial_zeros ( nt ):

#*****************************************************************************80
#
## P_POLYNOMIAL_ZEROS: zeros of Legendre function P(n,x).
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    16 March 2016
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, integer NT, the order of the rule.
#
#    Output, real T(NT), the zeros.
#
  import numpy as np
  from imtqlx import imtqlx

  a = np.zeros ( nt )

  b = np.zeros ( nt )

  for i in range ( 0, nt ):
    ip1 = i + 1
    b[i] = ip1 / np.sqrt ( 4 * ip1 * ip1 - 1 )

  c = np.zeros ( nt )
  c[0] = np.sqrt ( 2.0 )

  t, w = imtqlx ( nt, a, b, c )

  return t

def p_polynomial_zeros_test ( ):

#*****************************************************************************80
#
## P_POLYNOMIAL_ZEROS_TEST tests P_POLYNOMIAL_ZEROS.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    16 March 2016
#
#  Author:
#
#    John Burkardt
#
  import numpy as np
  import platform
  from p_polynomial_value import p_polynomial_value
  from r8vec_print import r8vec_print

  print ( '' )
  print ( 'P_POLYNOMIAL_ZEROS_TEST:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  P_POLYNOMIAL_ZEROS computes the zeros of P(n,x)' )
  print ( '  Check by calling P_POLYNOMIAL_VALUE there.' )

  for degree in range ( 1, 6 ):

    z = p_polynomial_zeros ( degree )
    title = '  Computed zeros for P(%d,x)' % ( degree )
    r8vec_print ( degree, z, title )

    lz = p_polynomial_value ( degree, degree, z )
    title = '  Evaluate P(%d,z)' % ( degree )
    lzvec = np.zeros ( degree )
    for i in range ( 0, degree ):
      lzvec[i] = lz[i,degree]
    r8vec_print ( degree, lzvec, title )
#
#  Terminate.
#
  print ( '' )
  print ( 'P_POLYNOMIAL_ZEROS_TEST' )
  print ( '  Normal end of execution.' )
  return

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