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52 lines
1.1 KiB
Python
52 lines
1.1 KiB
Python
"""
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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 = make_points(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 make_points(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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