Scaling_Hyp

import numpy as np
import matplotlib.pyplot as plt

def plot_scaling_laws(equations, x_range, labels=None, title='Scaling Laws Visualization'):
    """
    Plots multiple scaling laws over a specified range.

    Parameters:
    - equations: List of functions representing scaling laws.
    - x_range: Tuple (start, end) defining the range of x-values.
    - labels: List of labels for each equation (optional).
    - title: Title of the plot (optional).
    """
    x_values = np.linspace(x_range[0], x_range[1], 500)
    plt.figure(figsize=(10, 6))

    for i, eq in enumerate(equations):
        y_values = eq(x_values)
        label = labels[i] if labels and i < len(labels) else f'Equation {i+1}'
        plt.plot(x_values, y_values, label=label)

    plt.xlabel('X-axis')
    plt.ylabel('Y-axis')
    plt.title(title)
    plt.legend()
    plt.grid(True)
    plt.show()

# Example scaling laws
def power_law(x, a=1, b=0.5):
    """Power law: y = a * x^b"""
    return a * np.power(x, b)

def logarithmic_law(x, a=1, b=1):
    """Logarithmic law: y = a * log(x) + b"""
    return a * np.log(x) + b

def exponential_law(x, a=1, b=0.1):
    """Exponential law: y = a * exp(b * x)"""
    return a * np.exp(b * x)

# Define the range for x-values
x_start = 1
x_end = 100

# List of scaling law functions
scaling_functions = [
    lambda x: power_law(x, a=2, b=0.5),
    lambda x: logarithmic_law(x, a=1, b=2),
    lambda x: exponential_law(x, a=1, b=0.05)
]

# Corresponding labels for the functions
function_labels = [
    'Power Law: y = 2 * x^0.5',
    'Logarithmic Law: y = log(x) + 2',
    'Exponential Law: y = exp(0.05 * x)'
]

# Plot the scaling laws
plot_scaling_laws(scaling_functions, (x_start, x_end), labels=function_labels)