Max.py

# Python function that calculates the local extreme point of curvature (vortex)
# in a specified interval of a unimodal function.
# Simply change the target_function argument to the function
# you'd like to test and set the parameters of max_golden_search.
# ---WORKS ONLY FOR ONE VARIABLE FUNCTIONS----
# ---  IT IS RECOMMENDED TO  USE 'x' AS THE VARIABLE---
"""
# References
https://en.wikipedia.org/wiki/Golden-section_search
https://en.wikipedia.org/wiki/Vertex
"""


from matplotlib import pyplot as plt  # import module to plot the result
import numpy as np


target_function = (
    lambda x: x ** 3 - 6 * x ** 2 + 4 * x + 12
)  # type the function of interest here


def max_golden_search(
    func_to_max, upper: float, lower: float, tol: float = 1e-8
) -> float:

    """
    Function in python that calculates the maximum
    point of function in a specified interval
        :param func_to_max : the function to maximize (target_function)
        :param upper: upper boundary of interval
        :param lower: lower boundary of interval
        :param tol: set an appropriate tolerance value
        :returns maximum of specified interval
    >>> max_golden_search(target_function, -2, 4)
    count = 43
    0.3670068499227286
    >>> max_golden_search(target_function, 'm', 4)
    Traceback (most recent call last):
            ...
    ValueError: give numerical values for upper, lower limits
    """

    if type(upper) is str or type(lower) is str:
        raise ValueError("give numerical values for upper, lower limits")

    inv_gr = (np.sqrt(5) - 1) * 0.5  # ~ 0.618, this is the inverse golden ratio
    d_max = (upper - lower) * inv_gr  # # Sets initial value for d
    q1 = lower + d_max  # Sets initial value for q1
    q2 = upper - d_max  # and q2

    count = 0  # Creates a count variable with initial value zero

    while (
        abs(upper - lower) > tol
    ):  # Sets the tolerance condition. Will stop running once |u -l| < tol

        if func_to_max(q1) > func_to_max(q2):
            lower = q2
        else:
            upper = q1
        d_max = (upper - lower) * inv_gr
        q1 = lower + d_max
        q2 = upper - d_max
        count += 1  # Adds one to the count per iteration

    print("count =", count)  # Prints the count number

    return (q1 + q2) * 0.5  # Returns the midpoint of the
    # final interval as the maximum point in the range


max_point = max_golden_search(target_function, -2, 4)


def plot_point(
    maximum_point: float = max_point,
    x_axis_linspace: np.linspace = np.linspace(-5, 5, 200),
) -> None:
    """
    Plots function and maximum point
    """
    fmt = "bo"  # format string for the color of the point
    plt.plot(x_axis_linspace, target_function(x_axis_linspace))
    plt.plot(maximum_point, target_function(maximum_point), fmt)
    plt.show()


if __name__ == "__main__":

    import doctest

    doctest.testmod()