FunctionFitting/test/数据集生成.py

import numpy as np
import matplotlib.pyplot as plt

def generate_dataset(func_type, coeff, n_samples=100, noise_level=0.0):
    """
    Generate a dataset based on a mathematical function.

    Parameters:
    func_type (str): Type of function ('linear', 'quadratic', 'cubic', 'quartic', 'exponential', 'logarithmic').
    coeff (list): Coefficients of the function.
    n_samples (int): Number of samples to generate.
    noise_level (float): Standard deviation of Gaussian noise added to the data.

    Returns:
    np.ndarray: Generated dataset.
    """
    # Generate x values
    x_values = np.linspace(-1000, 1000, n_samples)

    # Define the functions
    functions = {
        'linear': lambda x: coeff[0] + coeff[1] * x,
        'quadratic': lambda x: coeff[0] + coeff[1] * x + coeff[2] * x**2,
        'cubic': lambda x: coeff[0] + coeff[1] * x + coeff[2] * x**2 + coeff[3] * x**3,
        'quartic': lambda x: coeff[0] + coeff[1] * x + coeff[2] * x**2 + coeff[3] * x**3 + coeff[4] * x**4,
        'exponential': lambda x: coeff[0] * np.exp(coeff[1] * x),
        'logarithmic': lambda x: coeff[0] + coeff[1] * np.log(np.abs(x) + 1)  # Avoid log(0)
    }

    # Generate y values based on the selected function
    y_values = functions[func_type](x_values)

    # Add noise
    noise = np.random.normal(0, noise_level, n_samples)
    y_values_noisy = y_values + noise

    # Combine x and y values
    dataset = np.vstack((x_values, y_values_noisy)).T

    return dataset


def plot_dataset(dataset, func_type, coeff):
    """
    Plot the generated dataset.

    Parameters:
    dataset (np.ndarray): Generated dataset.
    func_type (str): Type of function used to generate the dataset.
    coeff (list): Coefficients of the function.
    """
    x_values = dataset[:, 0]
    y_values = dataset[:, 1]

    # Plotting the dataset
    plt.figure(figsize=(10, 6))
    plt.scatter(x_values, y_values, color='blue', label='Generated Data')

    # Plot the original function without noise for comparison
    if func_type == 'linear':
        y_original = coeff[0] + coeff[1] * x_values
    elif func_type == 'quadratic':
        y_original = coeff[0] + coeff[1] * x_values + coeff[2] * x_values**2
    elif func_type == 'cubic':
        y_original = coeff[0] + coeff[1] * x_values + coeff[2] * x_values**2 + coeff[3] * x_values**3
    elif func_type == 'quartic':
        y_original = coeff[0] + coeff[1] * x_values + coeff[2] * x_values**2 + coeff[3] * x_values**3 + coeff[4] * x_values**4
    elif func_type == 'exponential':
        y_original = coeff[0] * np.exp(coeff[1] * x_values)
    elif func_type == 'logarithmic':
        y_original = coeff[0] + coeff[1] * np.log(np.abs(x_values) + 1)

    plt.plot(x_values, y_original, color='red', label='Original Function')

    plt.title(f'{func_type.capitalize()} Function Dataset Visualization')
    plt.xlabel('X Values')
    plt.ylabel('Y Values')
    plt.legend()
    plt.grid(True)
    plt.show()

def generate_dataset2(func_type, coeff, x_range=(-1000, 1000), n_samples=100, noise_level=0.0):
    """
    Generate a dataset based on a mathematical function with a specified x range.

    Parameters:
    func_type (str): Type of function ('linear', 'quadratic', 'cubic', 'quartic', 'exponential', 'logarithmic').
    coeff (list): Coefficients of the function.
    x_range (tuple): The range of x values (min, max).
    n_samples (int): Number of samples to generate.
    noise_level (float): Standard deviation of Gaussian noise added to the data.

    Returns:
    np.ndarray: Generated dataset.
    """
    # Generate x values within the specified range
    x_values = np.linspace(x_range[0], x_range[1], n_samples)

    # Define the functions
    functions = {
        'linear': lambda x: coeff[0] + coeff[1] * x,
        'quadratic': lambda x: coeff[0] + coeff[1] * x + coeff[2] * x**2,
        'cubic': lambda x: coeff[0] + coeff[1] * x + coeff[2] * x**2 + coeff[3] * x**3,
        'quartic': lambda x: coeff[0] + coeff[1] * x + coeff[2] * x**2 + coeff[3] * x**3 + coeff[4] * x**4,
        'exponential': lambda x: coeff[0] * np.exp(coeff[1] * x),
        'logarithmic': lambda x: coeff[0] + coeff[1] * np.log(np.abs(x) + 1)  # Avoid log(0)
    }

    # Generate y values based on the selected function
    y_values = functions[func_type](x_values)

    # Clip y values to stay within the specified range
    y_values = np.clip(y_values, x_range[0], x_range[1])

    # Add noise
    noise = np.random.normal(0, noise_level, n_samples)
    y_values_noisy = y_values + noise

    # Clip noisy y values to stay within the specified range
    y_values_noisy = np.clip(y_values_noisy, x_range[0], x_range[1])

    # Combine x and y values
    dataset = np.vstack((x_values, y_values_noisy)).T

    return dataset

# Example usage
dataset = generate_dataset('quadratic', [1, 2, 3], n_samples=10, noise_level=10)
print(dataset)

# Visualize the dataset
dataset = generate_dataset('quadratic', [1, 2, 3], n_samples=10, noise_level=10)
plot_dataset(dataset, 'quadratic', [1, 2, 3])