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51 lines
1.0 KiB
Python
51 lines
1.0 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 approach of suming 'Equally Spaced Abscissas'
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method 1:
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"extended trapezoidal rule"
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"""
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def method_1(boundary, steps):
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# "extended trapezoidal rule"
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# int(f) = dx/2 * (f1 + 2f2 + ... + 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 / 2.0) * f(a)
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for i in x_i:
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# print(i)
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y += h * f(i)
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y += (h / 2.0) * 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_1(boundary, steps)
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print(f"y = {y}")
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if __name__ == "__main__":
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main()
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