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897f1d0fb4
* Improved Formatting and Style I improved formatting and style to make PyLama happier. Linters used: - mccabe - pep257 - pydocstyle - pep8 - pycodestyle - pyflakes - pylint - isort * Create volume.py This script calculates the volumes of various shapes. * Delete lucasSeries.py * Revert "Delete lucasSeries.py" This reverts commit 64c19f7a6c8b74e15bed07f0f0337598a001ceb4. * Update lucasSeries.py
50 lines
1.1 KiB
Python
50 lines
1.1 KiB
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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from __future__ import print_function
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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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