#! /usr/bin/env python
#
def pn_polynomial_value ( m, n, x ):

#*****************************************************************************80
#
## PN_POLYNOMIAL_VALUE evaluates the normalized Legendre polynomials Pn(n,x).
#
#  Discussion:
#
#    The normalized Legendre polynomials are orthonormal under the inner product 
#    defined as integration from -1 to 1:
#
#      Integral ( -1 <= x <= +1 ) Pn(i,x) * Pn(j,x) dx = delta(i,j)
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license. 
#
#  Modified:
#
#    17 March 2016
#
#  Author:
#
#    John Burkardt
#
#  Reference:
#
#    Milton Abramowitz, Irene Stegun,
#    Handbook of Mathematical Functions,
#    National Bureau of Standards, 1964,
#    ISBN: 0-486-61272-4,
#    LC: QA47.A34.
#
#    Daniel Zwillinger, editor,
#    CRC Standard Mathematical Tables and Formulae,
#    30th Edition,
#    CRC Press, 1996.
#
#  Parameters:
#
#    Input, integer M, the number of evaluation points.
#
#    Input, integer N, the highest order polynomial to evaluate.
#    Note that polynomials 0 through N will be evaluated.
#
#    Input, real X(M,1), the evaluation points.
#
#    Output, real V(M,1:N+1), the values of the Legendre polynomials 
#    of order 0 through N,
#
  import numpy as np
  from p_polynomial_value import p_polynomial_value

  v = p_polynomial_value ( m, n, x );

  for j in range ( 0, n + 1 ):
    norm = np.sqrt ( 2.0 / ( 2 * j + 1 ) )
    for i in range ( 0, m ):
      v[i,j] = v[i,j] / norm
 
  return v

def pn_polynomial_value_test ( ):

#*****************************************************************************80
#
## PN_POLYNOMIAL_VALUE_TEST tests PN_POLYNOMIAL_VALUE.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    17 March 2012
#
#  Author:
#
#    John Burkardt
#
  import numpy as np
  import platform
  from pn_polynomial_values import pn_polynomial_values

  m = 1
  xvec = np.zeros ( 1 )

  print ( '' )
  print ( 'PN_POLYNOMIAL_VALUE_TEST:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  PN_POLYNOMIAL_VALUE evaluates the normalized Legendre polynomial Pn(n,x).' )
  print ( '' )
  print ( '                        Tabulated                 Computed' )
  print ( '     N        X          Pn(N,X)                   Pn(N,X)                     Error' )
  print ( '' )

  n_data = 0

  while ( True ):

    n_data, n, x, fx1 = pn_polynomial_values ( n_data )

    if ( n_data == 0 ):
      break

    xvec[0] = x
    v = pn_polynomial_value ( m, n, xvec )
    fx2 = v[0,n]

    e = fx1 - fx2

    print ( '  %4d  %12g  %24.16g  %24.16g  %8g' % ( n, x, fx1, fx2, e ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'PN_POLYNOMIAL_VALUE_TEST' )
  print ( '  Normal end of execution.' )
  return

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