Quick gist for two numerical methods to compute derivatives, mainly to show the error they generate (vs step size) as a plot

ComplexTaylorSeriesMethod.py

import numpy as np
import cmath
import matplotlib.pyplot as plt


def input_function(x):
    return cmath.log(x)

def input_deravative_function(x):
    return 1/x

def ctse(standard_input, delta_x):
    return (input_function(complex(standard_input, delta_x)).imag)/delta_x

def main():

    standard_input = 5

    print("Start")
    standard_output = input_deravative_function(standard_input)
    print(standard_output)

    x_range = np.logspace(-0.02, -14.4, num=500)
    y_range = []
    for index in range(len(x_range)):
        y_range.append(abs(input_deravative_function(standard_input) - ctse(standard_input, x_range[index])))

    # print(y_range)
    plt.plot(x_range, y_range)
    plt.xscale('log')
    plt.xlabel('Img Step Size')
    plt.ylabel('Error')
    plt.show()

if __name__ == '__main__':
    main()

ForwardFiniteDiff.py

import numpy as np
import math
import matplotlib.pyplot as plt


def input_function(x):
    return math.log(x)

def input_deravative_function(x):
    return 1/x

def forward_difference(standard_input, delta_x):
    return (input_function(standard_input + delta_x) - input_function(standard_input))/ delta_x

def main():

    standard_input = 5

    print("Start")
    standard_output = input_deravative_function(standard_input)
    print(standard_output)

    x_range = np.logspace(-0.02, -14.4, num=500)
    y_range = []
    for index in range(len(x_range)):
        y_range.append(abs(input_deravative_function(standard_input) - forward_difference(standard_input, x_range[index])))

    # print(y_range)
    plt.plot(x_range, y_range)
    plt.xscale('log')
    plt.xlabel('Step Size')
    plt.ylabel('Error')
    plt.show()

if __name__ == '__main__':
    main()