PubNumAnalysisIpynb/IntegrationLib.py
b1a83d7cb001Modifications-for-2025

IntegrationLib.py
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			import numpy as np

			# This function 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 provides the trapezoidal 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 Simpson 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) );