#! /usr/bin/env python
#
def ttt_product_integral ( i, j, k ):

#*****************************************************************************80
#
## TTT_PRODUCT_INTEGRAL: integral (-1<=x<=1) T(i,x)*T(j,x)*T(k,x)/sqrt(1-x^2) dx
#
#  Discussion:
#
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    14 July 2015
#
#  Author:
#
#    John Burkardt
#
#  Reference:
#
#    John Mason, David Handscomb,
#    Chebyshev Polynomials,
#    CRC Press, 2002,
#    ISBN: 0-8493-035509,
#    LC: QA404.5.M37.
#
#  Parameters:
#
#    Input, integer I, J, K, the polynomial indices.
#    0 <= I, J.
#
#    Output, real VALUE, the integral.
#
  from tt_product_integral import tt_product_integral

  if ( i < 0 ):
    value = 0.0
    return value

  if ( j < 0 ):
    value = 0.0
    return value

  if ( k < 0 ):
    value = 0.0
    return value

  value = 0.5 * ( \
      tt_product_integral (       i + j,   k ) + \
    + tt_product_integral ( abs ( i - j ), k ) )

  return value

def ttt_product_integral_test ( ):

#*****************************************************************************80
#
## TTT_PRODUCT_INTEGRAL_TEST tests TTT_PRODUCT_INTEGRAL.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    14 July 2015
#
#  Author:
#
#    John Burkardt
#
  import platform
  from i4_uniform_ab import i4_uniform_ab
  from t_polynomial_value import t_polynomial_value
  from t_quadrature_rule import t_quadrature_rule

  test_num = 20

  print ( '' )
  print ( 'TTT_PRODUCT_INTEGRAL_TEST:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  TTT_PRODUCT_INTEGRAL computes the triple integral' )
  print ( '  Tijk = integral ( -1 <= x <= 1 ) T(i,x) T(j,x) T(k,x) / sqrt ( 1-x^2) dx' )
  print ( '' )
  print ( '   I   J   K     Tijk           Tijk' )
  print ( '                 computed       exact' )
  print ( '' )

  n = 15
  x, w = t_quadrature_rule ( n )

  seed = 123456789

  for test in range ( 0, test_num ):
    i, seed = i4_uniform_ab ( 2, 6, seed )
    j, seed = i4_uniform_ab ( 1, 3, seed )
    k, seed = i4_uniform_ab ( 0, 4, seed )
    fx1 = ttt_product_integral ( i, j, k )
    fx2 = 0.0
    for l in range ( 0, n ):
      ti = t_polynomial_value ( i, x[l] )
      tj = t_polynomial_value ( j, x[l] )
      tk = t_polynomial_value ( k, x[l] )
      fx2 = fx2 + w[l] * ti * tj * tk

    print ( '  %2d  %2d  %2d  %14.6g  %14.6g' % ( i, j, k, fx1, fx2 ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'TTT_PRODUCT_INTEGRAL_TEST:' )
  print ( '  Normal end of execution.' )
  return

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