Economic Potential Energy (EPE)
Description
The provided code conducts a visual analysis and numerical calculation of Economic Potential Energy (EPE) based on a potential function. Here's a description of the code: Potential Function Definition (potential_function): The code starts by defining a potential function that represents the economic potential energy at different points (x). In this example, the potential function is a simple quadratic function (x^2). Users are encouraged to replace it with their actual potential function, which should capture the economic dynamics they are interested in. Integration Range (a to b): The integration process focuses on a specified range, denoted as [a, b], representing the economic state of interest. These limits can be adjusted based on the specific economic conditions or time period under consideration. Integration Using quad Function: The quad function from the scipy library is employed to numerically integrate the potential function over the defined range (a to b). The result of this integration is stored in the variable result. Display of the Result: The numerical result of the integration, representing the Economic Potential Energy (EPE), is printed to the console. This provides a quantitative measure of the economic potential energy within the specified range. Visualization using matplotlib: The code utilizes the matplotlib library to create a visual representation of the potential function and the integration process. The potential function is plotted over a range of x values. The area under the curve, which corresponds to the integrated energy, is shaded for clarity in the plot. Vertical dashed lines are included to highlight the integration limits (a and b). Adaptation for Specific Use Case: Users are encouraged to replace the example potential function with one that accurately models their economic potential energy concept. The integration range (a to b) should be adjusted based on the specific economic conditions or time period of interest. Plot Title and Labels: The plot is adorned with a title ('Economic Potential Energy (EPE) Visualization') and axis labels ('x' for the horizontal axis and 'Potential Function' for the vertical axis). A legend is included to label the potential function curve and the shaded area. In summary, the code provides a comprehensive analysis of Economic Potential Energy, combining numerical computation and visual representation to offer insights into the economic dynamics within a specified range.
Files
Steps to reproduce
import numpy as np import matplotlib.pyplot as plt from scipy.integrate import quad # Define the potential function def potential_function(x): # You should replace this with your actual potential function return x**2 # Example: x^2 # Define the integration range [a, b] a = 0 b = 5 # Perform the integration using quad function from scipy result, _ = quad(potential_function, a, b) # Display the result print(f'Economic Potential Energy (EPE): {result}') # Plotting the potential function x_values = np.linspace(a, b, 100) y_values = potential_function(x_values) plt.plot(x_values, y_values, label='Potential Function') plt.fill_between(x_values, y_values, alpha=0.2, label='Area under the curve') # Highlight the integration range plt.axvline(x=a, color='r', linestyle='--', label=f'a = {a}') plt.axvline(x=b, color='r', linestyle='--', label=f'b = {b}') plt.title('Economic Potential Energy (EPE) Visualization') plt.xlabel('x') plt.ylabel('Potential Function') plt.legend() plt.show()