IntegrationLib.py
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	#!/usr/bin/env python3
	# -- coding: utf-8 --
	"""
	Created on Thu Jan 30

	@author: Simone Deparis
	"""

	import numpy as np

	# This function just provides the midpoint quadrature rule.
	def Midpoint( a, b, N, f ) :
	# [a,b] : inteval
	# N : number of subintervals
	# f : fonction to integrate using the midpoint rule

	# size of the subintervals
	H = (b - a) / N

	# quadrature nodes
	x = np.linspace(a+H/2, b-H/2, N)

	# approximate integral
	return H * np.sum( f(x) );


	# This function just provides the midpoint quadrature rule.
	def Trapezoidal( a, b, N, f ) :
	# [a,b] : inteval
	# N : number of subintervals
	# f : fonction to integrate using the trapezoidal rule

	# size of the subintervals
	H = (b - a) / N

	# quadrature nodes
	x = np.linspace(a, b, N+1)

	# approximate integral
	return H/2 * ( f(a) + f(b) ) + H * sum( f(x[1:N]) );

	# This function just provides the Simpson quadrature rule.
	def Simpson( a, b, N, f ) :
	# [a,b] : inteval
	# N : number of subintervals
	# f : fonction to integrate using the trapezoidal rule

	# size of the subintervals
	H = (b - a) / N
	# points defining intervals
	x = np.linspace(a, b, N+1)

	# left quadrature nodes
	xl = x[0:-1]
	# right quadrature nodes
	xr = x[1:]
	# middle quadrature nodes
	xm = (xl+xr)/2

	# approximate integral
	return H/6 * sum( f(xl) + 4*f(xm) + f(xr) );