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

#*****************************************************************************80
#
## INTEGRAL_LOG evaluates the test integral with logarithmic singularity.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    05 December 2015
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Output, real VALUE, the integral of the test integrand from 0 to 1.
#
  value = - 0.012771107587415899716

  return value

def integral_log_test ( ):

#*****************************************************************************80
#
## INTEGRAL_LOG_TEST tests INTEGRAL_LOG.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    05 December 2015
#
#  Author:
#
#    John Burkardt
#
  print ( '' )
  print ( 'INTEGRAL_LOG_TEST:' )
  print ( '  INTEGRAL_LOG returns the value of the integral of the log-singular' )
  print ( '  test function over [0,1].' )
  print ( '' )
  value = integral_log ( )
  print ( '  INTEGRAL_LOG = %g' % ( value ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'INTEGRAL_LOG_TEST:' )
  print ( '  Normal end of execution.' )
  return

def integral_power ( ):

#*****************************************************************************80
#
## INTEGRAL_POWER evaluates the test integral with power singularity.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    05 December 2015
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Output, real VALUE, the integral of the test integrand from 0 to 1.
#
  value = 0.079321002746971411182

  return value

def integral_power_test ( ):

#*****************************************************************************80
#
## INTEGRAL_POWER_TEST tests INTEGRAL_POWER.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    05 December 2015
#
#  Author:
#
#    John Burkardt
#
  print ( '' )
  print ( 'INTEGRAL_POWER_TEST:' )
  print ( '  INTEGRAL_POWER returns the value of the integral of the power-singular' )
  print ( '  test function over [0,1].' )
  print ( '' )
  value = integral_power ( )
  print ( '  INTEGRAL_POWER = %g' % ( value ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'INTEGRAL_POWER_TEST:' )
  print ( '  Normal end of execution.' )
  return

def integral_regular ( ):

#*****************************************************************************80
#
## INTEGRAL_REGULAR evaluates the regular test integral.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    05 December 2015
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Output, real VALUE, the integral of the test integrand from 0 to 1.
#
  import numpy as np

  value = ( - np.sin ( 0.3 ) + np.sin ( 200.0 ) + np.sin ( 200.3 ) ) / 200.0

  return value

def integral_regular_test ( ):

#*****************************************************************************80
#
## INTEGRAL_REGULAR_TEST tests INTEGRAL_REGULAR.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    05 December 2015
#
#  Author:
#
#    John Burkardt
#
  print ( '' )
  print ( 'INTEGRAL_REGULAR_TEST:' )
  print ( '  INTEGRAL_REGULAR returns the value of the integral of the regular' )
  print ( '  test function over [0,1].' )
  print ( '' )
  value = integral_regular ( )
  print ( '  INTEGRAL_REGULAR = %g' % ( value ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'INTEGRAL_REGULAR_TEST:' )
  print ( '  Normal end of execution.' )
  return

def integrand_log ( n, x ):

#*****************************************************************************80
#
## INTEGRAND_LOG evaluates the test integrand with logarithmic singularity.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    05 December 2015
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, integer N, the number of evaluation points.
#
#    Input, real X(N), the evaluation points.
#
#    Output, real F(N), the integrand at the evaluation points.
#
  import numpy as np

  f = np.zeros ( n )

  f[0:n] = np.cos ( 200.0 * x[0:n] ) * np.log ( x[0:n] ) \
    + np.cos ( 200.0 * x[0:n] + 0.3 )

  return f

def integrand_log_test ( ):

#*****************************************************************************80
#
## INTEGRAND_LOG_TEST tests INTEGRAND_LOG.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    05 December 2015
#
#  Author:
#
#    John Burkardt
#
  from r8vec_linspace2 import r8vec_linspace2

  print ( '' )
  print ( 'INTEGRAND_LOG_TEST:' )
  print ( '  INTEGRAND_LOG evaluates the log-singular test function.' )

  n = 9
  x = r8vec_linspace2 ( n, 0.0, 1.0 ) 
  f = integrand_log ( n, x )

  print ( '' )
  print ( '                  X             F(X)' )
  print ( '' )
  for i in range ( 0, n ):
    print ( '  %2d  %14.6g  %14.6g' % ( i, x[i], f[i] ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'INTEGRAND_LOG_TEST:' )
  print ( '  Normal end of execution.' )
  return

def integrand_power ( n, x ):

#*****************************************************************************80
#
## INTEGRAND_POWER evaluates the test integrand with power singularity.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    05 December 2015
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, integer N, the number of evaluation points.
#
#    Input, real X(N), the evaluation points.
#
#    Output, real F(N), the integrand at the evaluation points.
#
  import numpy as np

  f = np.zeros ( n )

  f[0:n] = np.cos ( 200.0 * x[0:n] ) * x[0:n] ** ( - 0.5 ) \
    + np.cos ( 200.0 * x[0:n] + 0.3 )

  return f

def integrand_power_test ( ):

#*****************************************************************************80
#
## INTEGRAND_POWER_TEST tests INTEGRAND_POWER.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    05 December 2015
#
#  Author:
#
#    John Burkardt
#
  from r8vec_linspace2 import r8vec_linspace2

  print ( '' )
  print ( 'INTEGRAND_POWER_TEST:' )
  print ( '  INTEGRAND_POWER evaluates the power-singular test function.' )

  n = 9
  x = r8vec_linspace2 ( n, 0.0, 1.0 ) 
  f = integrand_power ( n, x )

  print ( '' )
  print ( '                  X             F(X)' )
  print ( '' )
  for i in range ( 0, n ):
    print ( '  %2d  %14.6g  %14.6g' % ( i, x[i], f[i] ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'INTEGRAND_POWER_TEST:' )
  print ( '  Normal end of execution.' )
  return

def integrand_regular ( n, x ):

#*****************************************************************************80
#
## INTEGRAND_REGULAR evaluates the regular test integrand.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    05 December 2015
#
#  Author:
#
#    John Burkardt
#
#  Parameters:
#
#    Input, integer N, the number of evaluation points.
#
#    Input, real X(N), the evaluation points.
#
#    Output, real F(N), the integrand at the evaluation points.
#
  import numpy as np

  f = np.zeros ( n )

  f[0:n] = np.cos ( 200.0 * x[0:n] ) + np.cos ( 200.0 * x[0:n] + 0.3 )

  return f

def integrand_regular_test ( ):

#*****************************************************************************80
#
## INTEGRAND_REGULAR_TEST tests INTEGRAND_REGULAR.
#
#  Licensing:
#
#    This code is distributed under the GNU LGPL license.
#
#  Modified:
#
#    05 December 2015
#
#  Author:
#
#    John Burkardt
#
  from r8vec_linspace2 import r8vec_linspace2

  print ( '' )
  print ( 'INTEGRAND_REGULAR_TEST:' )
  print ( '  INTEGRAND_REGULAR evaluates the regular test function.' )

  n = 9
  x = r8vec_linspace2 ( n, 0.0, 1.0 ) 
  f = integrand_regular ( n, x )

  print ( '' )
  print ( '                  X             F(X)' )
  print ( '' )
  for i in range ( 0, n ):
    print ( '  %2d  %14.6g  %14.6g' % ( i, x[i], f[i] ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'INTEGRAND_REGULAR_TEST:' )
  print ( '  Normal end of execution.' )
  return

if ( __name__ == '__main__' ):
  from timestamp import timestamp
  timestamp ( ) 
  integral_log_test ( )
  integral_power_test ( )
  integral_regular_test ( )
  integrand_log_test ( )
  integrand_power_test ( )
  integrand_regular_test ( )
  timestamp ( )