TheAlgorithms-Python

1
"""
2
Numerical integration or quadrature for a smooth function f with known values at x_i
3

4
This method is the classical approach of suming 'Equally Spaced Abscissas'
5

6
method 1:
7
"extended trapezoidal rule"
8

9
"""
10

11

12
def method_1(boundary, steps):
13
    # "extended trapezoidal rule"
14
    # int(f) = dx/2 * (f1 + 2f2 + ... + fn)
15
    h = (boundary[1] - boundary[0]) / steps
16
    a = boundary[0]
17
    b = boundary[1]
18
    x_i = make_points(a, b, h)
19
    y = 0.0
20
    y += (h / 2.0) * f(a)
21
    for i in x_i:
22
        # print(i)
23
        y += h * f(i)
24
    y += (h / 2.0) * f(b)
25
    return y
26

27

28
def make_points(a, b, h):
29
    x = a + h
30
    while x < (b - h):
31
        yield x
32
        x = x + h
33

34

35
def f(x):  # enter your function here
36
    y = (x - 0) * (x - 0)
37
    return y
38

39

40
def main():
41
    a = 0.0  # Lower bound of integration
42
    b = 1.0  # Upper bound of integration
43
    steps = 10.0  # define number of steps or resolution
44
    boundary = [a, b]  # define boundary of integration
45
    y = method_1(boundary, steps)
46
    print(f"y = {y}")
47

48

49
if __name__ == "__main__":
50
    main()
51