#! /usr/bin/env python
#
def nc_compute_weights ( n, x_min, x_max, x ):

#*****************************************************************************80
#
## NC_COMPUTE_WEIGHTS computes weights for a Newton-Cotes quadrature rule.
#
#  Discussion:
#
#    For the interval [X_MIN,X_MAX], the Newton-Cotes quadrature rule 
#    estimates
#
#      Integral ( X_MIN <= X <= X_MAX ) F(X) dX
#
#    using N abscissas X and weights W:
#
#      Sum ( 1 <= I <= N ) W(I) * F ( X(I) ).
#
#    For the CLOSED rule, the equally spaced abscissas include A and B.
#    For the OPEN rule, the equally spaced abscissas do not include A and B.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    20 April 2010
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, integer N, the order.
#
#    Input, real X_MIN, X_MAX, the endpoints of the interval.
#
#    Input, real X(N), the abscissas.
#
#    Output, real W(N), the weights.
#
  import numpy as np

  d = np.zeros ( n )
  w = np.zeros ( n )

  for i in range ( 1, n + 1 ):
#
#  Compute the Lagrange basis polynomial which is 1 at X(I),
#  and zero at the other nodes.
#
    d = np.zeros ( n )
    d[i-1] = 1.0

    for j in range ( 2, n + 1 ):
      for k in range ( j, n + 1 ):
        d[n+j-k-1] = ( d[n+j-k-1-1] - d[n+j-k-1] ) / ( x[n+1-k-1] - x[n+j-k-1] )

    for j in range ( 1, n ):
      for k in range ( 1, n - j + 1 ):
        d[n-k-1] = d[n-k-1] - x[n-k-j] * d[n-k]
#
#  Evaluate the antiderivative of the polynomial at the endpoints.
#
    yvala = d[n-1] / float ( n )
    for j in range ( n - 1, 0, -1 ):
      yvala = yvala * x_min + d[j-1] / float ( j )
    yvala = yvala * x_min

    yvalb = d[n-1] / float ( n )
    for j in range ( n - 1, 0, -1 ):
      yvalb = yvalb * x_max + d[j-1] / float ( j )
    yvalb = yvalb * x_max

    w[i-1] = yvalb - yvala

  return w

def nc_compute_weights_test ( ):

#*****************************************************************************80
#
#% NC_COMPUTE_WEIGHTS_TEST tests NC_COMPUTE_WEIGHTS.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license. 
#
#  Modified:
#
#    20 June 2015
#
#  Author:
#
#    John Burkardt
#
  import numpy as np
  import platform
  from r8vec_linspace import r8vec_linspace

  print ( '' )
  print ( 'NC_COMPUTE_WEIGHTS_TEST' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  NC_COMPUTE_WEIGHTS computes weights for' )
  print ( '  a Newton-Cotes quadrature rule' )
  print ( '' )
  print ( '  Index       X             W' )

  x_min = 0.0
  x_max = 1.0

  for n in range ( 1, 11 ):

    x = r8vec_linspace ( n, x_min, x_max )

    w = nc_compute_weights ( n, x_min, x_max, x )

    print ( '' )

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

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