California State University, Fullerton - CPSC 481 - Empirical gradient and gradient descent

empirical_gradient.py

#!/usr/bin/env python


def derivative(f, h=1e-5):
    def df(x):
        return (f(x + h) - f(x)) / h

    return df


if __name__ == "__main__":
    f = lambda x: x * x
    df = derivative(f)
    ddf = derivative(df)

    print("x\tf(x)\tf'(x)\tf''(x)")
    print("-\t----\t-----\t------")
    for i in range(0, 10):
        print(f"{i}\t{f(i)}\t{round(df(i))}\t{round(ddf(i))}")

gradient_descent.py

#!/usr/bin/env python

import random

from empirical_gradient import derivative


def gradient_descent(f, location, delta=1e-2, tolerance=1e-5):
    df = derivative(f)

    while abs(df(location)) > tolerance:
        gradient = df(location)
        location -= delta * gradient

    return location


f = lambda x: (x - 1) ** 2 + 2

start = random.uniform(-10, 10)
print(f"Descending from x = {start}...")

min = gradient_descent(f, start)
y = f(min)
print(f"The minimum value of f(x) is f({round(min)}) = {round(y)}")