#! /usr/bin/env python
#
def tu_product ( i, j, x ):

#*****************************************************************************80
#
## TU_PRODUCT: evaluate T(i,x)*U(j,x)
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    16 July 2015
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, integer I, J, the indices.
#
#    Input, real X, the argument.
#
#    Output, real VALUE, the value.
#
  from u_polynomial_value import u_polynomial_value
  from uu_product import uu_product

  if ( i < 0 ):
    value = 0.0
  elif ( j < 0 ):
    value = 0.0
  elif ( i == 0 ):
    value = u_polynomial_value ( j, x )
  else:
    value = 0.5 * ( uu_product ( i, j, x ) - uu_product ( i - 2, j, x ) )

  return value

def tu_product_test ( ):

#*****************************************************************************80
#
## TU_PRODUCT_TEST tests TU_PRODUCT.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license. 
#
#  Modified:
#
#    16 July 2015
#
#  Author:
#
#    John Burkardt
#
  import platform
  from i4_uniform_ab import i4_uniform_ab
  from r8_uniform_ab import r8_uniform_ab
  from t_polynomial_value import t_polynomial_value
  from u_polynomial_value import u_polynomial_value

  print ( '' )
  print ( 'TU_PRODUCT_TEST:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  TU_PRODUCT(I,J;X) = T(I,X) * U(J,X)' )

  r8_lo = -1.0
  r8_hi = +1.0
  seed = 123456789

  print ( '' )
  print ( '   I   J      X               TI              UJ              TI*UJ       TU_PRODUCT' )
  print ( '' )
  for test in range ( 0, 10 ):
    x, seed = r8_uniform_ab ( r8_lo, r8_hi, seed )
    i, seed = i4_uniform_ab ( 0, 6, seed )
    ti = t_polynomial_value ( i, x )
    j, seed = i4_uniform_ab ( -1, 4, seed )
    uj = u_polynomial_value ( j, x )
    tiuj = tu_product ( i, j, x )
    print ( '  %2d  %2d  %14.6g  %14.6g  %14.6g  %14.6g  %14.6g'\
      % ( i, j, x, ti, uj, ti * uj, tiuj ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'TU_PRODUCT_TEST:' )
  print ( '  Normal end of execution.' )
  return

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