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