#! /usr/bin/env python
#
def trapezoid_log_test ( ):

#*****************************************************************************80
#
## TRAPEZOID_LOG_TEST tests the trapezoid rule on the log-singular integrand.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    06 December 2015
#
#  Author:
#
#    John Burkardt
#
  import numpy as np
  from test_functions import integral_log
  from test_functions import integrand_log
  from r8vec_uniform_01 import r8vec_uniform_01

  print ( '' )
  print ( 'TRAPEZOID_LOG_TEST' )
  print ( '  Test the trapezoidal rule on the log-singular integrand.' )
  print ( '' )
  print ( '        N        Estimate           Error' )
  print ( '' )
  n = 17
  v2 = integral_log ( )
  for nlog in range ( 5, 13 ):
    n = ( n - 1 ) * 2 + 1
    h = 1.0 / float ( n - 1 )
    x = np.linspace ( 0.0, 1.0, n )
    x[0] = 0.5 * ( x[0] + x[1] )
    f = integrand_log ( n, x )
    v1 = h * ( np.sum ( f ) - 0.5 * ( f[1] + f[n-1] ) )
    print ( '  %7d  %14.6g  %14.6g' % ( n, v1, abs ( v1 - v2 ) ) )
  print ( '' )
  print ( '    Exact: %14.6g' % ( v2 ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'TRAPEZOID_LOG_TEST' )
  print ( '  Normal end of execution.' )
  return

def trapezoid_power_test ( ):

#*****************************************************************************80
#
## TRAPEZOID_POWER_TEST tests the trapezoid rule on the power-singular integrand.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    06 December 2015
#
#  Author:
#
#    John Burkardt
#
  import numpy as np
  from test_functions import integral_power
  from test_functions import integrand_power
  from r8vec_uniform_01 import r8vec_uniform_01

  print ( '' )
  print ( 'TRAPEZOID_POWER_TEST' )
  print ( '  Test the trapezoidal rule on the power-singular integrand.' )
  print ( '' )
  print ( '        N        Estimate           Error' )
  print ( '' )
  n = 17
  v2 = integral_power ( )
  for nlog in range ( 5, 13 ):
    n = ( n - 1 ) * 2 + 1
    h = 1.0 / float ( n - 1 )
    x = np.linspace ( 0.0, 1.0, n )
    x[0] = 0.5 * ( x[0] + x[1] )
    f = integrand_power ( n, x )
    v1 = h * ( np.sum ( f ) - 0.5 * ( f[1] + f[n-1] ) )
    print ( '  %7d  %14.6g  %14.6g' % ( n, v1, abs ( v1 - v2 ) ) )
  print ( '' )
  print ( '    Exact: %14.6g' % ( v2 ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'TRAPEZOID_POWER_TEST' )
  print ( '  Normal end of execution.' )
  return

def trapezoid_regular_test ( ):

#*****************************************************************************80
#
## TRAPEZOID_REGULAR_TEST tests the trapezoid rule on the regular integrand.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    06 December 2015
#
#  Author:
#
#    John Burkardt
#
  import numpy as np
  from test_functions import integral_regular
  from test_functions import integrand_regular
  from r8vec_uniform_01 import r8vec_uniform_01

  print ( '' )
  print ( 'TRAPEZOID_REGULAR_TEST' )
  print ( '  Test the trapezoidal rule on the regular integrand.' )
  print ( '' )
  print ( '        N        Estimate           Error' )
  print ( '' )
  n = 17
  v2 = integral_regular ( )
  for nlog in range ( 5, 13 ):
    n = ( n - 1 ) * 2 + 1
    h = 1.0 / float ( n - 1 )
    x = np.linspace ( 0.0, 1.0, n )
    f = integrand_regular ( n, x )
    v1 = h * ( np.sum ( f ) - 0.5 * ( f[0] + f[n-1] ) )
    print ( '  %7d  %14.6g  %14.6g' % ( n, v1, abs ( v1 - v2 ) ) )
  print ( '' )
  print ( '    Exact: %14.6g' % ( v2 ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'TRAPEZOID_REGULAR_TEST' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( ) 
  trapezoid_log_test ( )
  trapezoid_power_test ( )
  trapezoid_regular_test ( )
  timestamp ( )