#! /usr/bin/env python3
#
def quad_serial ( ):

#*****************************************************************************80
#
## quad_serial() estimates an integral using a quadrature rule.
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    25 October 2011
#
#  Author:
#
#    John Burkardt
#
  import platform
  import time

  a =  0.0
  b = 10.0
  n = 10000000
  exact = 0.49936338107645674464

  print ( '' )
  print ( 'quad_serial:' )
  print ( '  Python version: %s' % ( platform.python_version ( ) ) )
  print ( '  Estimate the integral of f(x) from A to B.' )
  print ( '  f(x) = 50 / ( pi * ( 2500 * x * x + 1 ) ).' )
  print ( '' )
  print ( '  A        = %g' % ( a ) )
  print ( '  B        = %g' % ( b ) )
  print ( '  N        = %d' % ( n ) )
  print ( '  Exact    = %g' % ( exact ) )

  wtime = time.time ( )

  total = 0.0

  for i in range ( n ):
    x = ( float ( n - i - 1 ) * a + float ( i ) * b ) / float ( n - 1 )
    total = total + f ( x )

  wtime = time.time ( ) - wtime

  total = ( b - a ) * total / float ( n )
  error = abs ( total - exact )
 
  print ( '' )
  print ( '  Estimate = %g' % ( total ) )
  print ( '  Error    = %g' % ( error ) )
  print ( '  Time     = %g' % ( wtime ) )
#
#  Terminate.
#
  print ( '' )
  print ( 'quad_serial:' )
  print ( '  Normal end of execution.' )
  return

def f ( x ):

#*****************************************************************************80
#
## f() evaluates the function.
#
#  Licensing:
#
#    This code is distributed under the MIT license.
#
#  Modified:
#
#    26 October 2012
#
#  Author:
#
#    John Burkardt
#
#  Input:
#
#    real X, the evaluation point.
#
#  Output:
#
#    real VALUE, the function value at X.
#
  import numpy as np

  value = 50.0 / ( np.pi * ( 2500.0 * x * x + 1.0 ) )

  return value

def timestamp ( ):

#*****************************************************************************80
#
## timestamp() prints the date as a timestamp.
#
#  Licensing:
#
#    This code is distributed under the MIT license. 
#
#  Modified:
#
#    06 April 2013
#
#  Author:
#
#    John Burkardt
#
  import time

  t = time.time ( )
  print ( time.ctime ( t ) )

  return None

if ( __name__ == '__main__' ):
  timestamp ( )
  quad_serial ( )
  timestamp ( )