Merge pull request #1 from ltdouthit/Maths/Numerical_Intergration

Maths/numerical intergration

Author: ltdouthit

Maths/SimpsonRule.py

@@ -0,0 +1,47 @@
+
+'''
+Numerical integration or quadrature for a smooth function f with known values at x_i
+
+This method is the classical approch of suming 'Equally Spaced Abscissas' 
+
+method 2: 
+"Simpson Rule"
+
+'''
+
+def method_2(boundary, steps):
+# "Simpson Rule"
+# int(f) = delta_x/2 * (b-a)/3*(f1 + 4f2 + 2f_3 + ... + fn)
+	h = (boundary[1] - boundary[0]) / steps
+	a = boundary[0]
+	b = boundary[1]
+	x_i = makePoints(a,b,h)
+	y = 0.0
+	y += (h/3.0)*f(a)
+	cnt = 2
+	for i in x_i:
+		y += (h/3)*(4-2*(cnt%2))*f(i)	
+		cnt += 1
+	y += (h/3.0)*f(b)
+	return y
+
+def makePoints(a,b,h):
+	x = a + h
+	while x < (b-h):
+		yield x
+		x = x + h
+
+def f(x): #enter your function here
+	y = (x-0)*(x-0)
+	return y
+
+def main():
+	a = 0.0 #Lower bound of integration
+	b = 1.0	#Upper bound of integration
+	steps = 10.0		#define number of steps or resolution
+	boundary = [a, b]	#define boundary of integration
+	y = method_2(boundary, steps)
+	print 'y = {0}'.format(y)
+
+if __name__ == '__main__':
+        main()

Maths/TrapezoidalRule.py

@@ -0,0 +1,45 @@
+'''
+Numerical integration or quadrature for a smooth function f with known values at x_i
+
+This method is the classical approch of suming 'Equally Spaced Abscissas' 
+
+method 1: 
+"extended trapezoidal rule"
+
+'''
+
+def method_1(boundary, steps):
+# "extended trapezoidal rule"
+# int(f) = dx/2 * (f1 + 2f2 + ... + fn)
+	h = (boundary[1] - boundary[0]) / steps
+	a = boundary[0]
+	b = boundary[1]
+	x_i = makePoints(a,b,h)
+	y = 0.0	
+	y += (h/2.0)*f(a)
+	for i in x_i:
+		#print(i)	
+		y += h*f(i)
+	y += (h/2.0)*f(b)	
+	return y	
+
+def makePoints(a,b,h):
+	x = a + h	
+	while x < (b-h):
+		yield x
+		x = x + h
+		
+def f(x): #enter your function here
+	y = (x-0)*(x-0)
+	return y
+
+def main():
+	a = 0.0 #Lower bound of integration
+	b = 1.0	#Upper bound of integration
+	steps = 10.0		#define number of steps or resolution	
+	boundary = [a, b]	#define boundary of integration
+	y = method_1(boundary, steps)
+	print 'y = {0}'.format(y)
+
+if __name__ == '__main__':
+	main()