TheAlgorithms-Python

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"""
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Approximates the area under the curve using the trapezoidal rule
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"""
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from __future__ import annotations
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from collections.abc import Callable
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def trapezoidal_area(
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    fnc: Callable[[float], float],
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    x_start: float,
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    x_end: float,
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    steps: int = 100,
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) -> float:
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    """
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    Treats curve as a collection of linear lines and sums the area of the
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    trapezium shape they form
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    :param fnc: a function which defines a curve
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    :param x_start: left end point to indicate the start of line segment
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    :param x_end: right end point to indicate end of line segment
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    :param steps: an accuracy gauge; more steps increases the accuracy
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    :return: a float representing the length of the curve
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    >>> def f(x):
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    ...    return 5
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    >>> f"{trapezoidal_area(f, 12.0, 14.0, 1000):.3f}"
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    '10.000'
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    >>> def f(x):
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    ...    return 9*x**2
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    >>> f"{trapezoidal_area(f, -4.0, 0, 10000):.4f}"
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    '192.0000'
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    >>> f"{trapezoidal_area(f, -4.0, 4.0, 10000):.4f}"
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    '384.0000'
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    """
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    x1 = x_start
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    fx1 = fnc(x_start)
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    area = 0.0
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    for _ in range(steps):
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        # Approximates small segments of curve as linear and solve
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        # for trapezoidal area
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        x2 = (x_end - x_start) / steps + x1
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        fx2 = fnc(x2)
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        area += abs(fx2 + fx1) * (x2 - x1) / 2
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        # Increment step
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        x1 = x2
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        fx1 = fx2
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    return area
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if __name__ == "__main__":
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    def f(x):
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        return x**3 + x**2
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    print("f(x) = x^3 + x^2")
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    print("The area between the curve, x = -5, x = 5 and the x axis is:")
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    i = 10
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    while i <= 100000:
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        print(f"with {i} steps: {trapezoidal_area(f, -5, 5, i)}")
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        i *= 10
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