#!/usr/bin/env python3
"""
Day {{DAY_N}}: {{TOPIC_NAME}}
The Math Skeleton - Pure numpy/torch operations, no high-level APIs

Expected functions:
- def {{function_name}}():  # Your implementation here
"""

import numpy as np
import torch
import matplotlib.pyplot as plt
from typing import Tuple

# Configure visualization
plt.style.use('seaborn-v0_8-darkgrid')


def {{function_name}}({{parameters}}):
    """
    {{brief_description}}

    Parameters:
        {{param1}}: {{param1_type}} - {{param1_desc}}
        {{param2}}: {{param2_type}} - {{param2_desc}}

    Returns:
        {{return_type}}: {{return_desc}}
    """
    # TODO: Implement the mathematical operation
    # Your math translation here...

    # Example: numpy implementation
    return result


def plot_concept():
    """
    Visualize the concept with matplotlib.
    Include this in your solution.

    Typical visualizations:
    - Loss contours
    - Activation functions
    - Geometric interpretations
    """
    fig, ax = plt.subplots(figsize=(10, 6))

    # TODO: Add your visualization logic here

    ax.set_xlabel('{{x_label}}')
    ax.set_ylabel('{{y_label}}')
    ax.set_title('{{visualization_title}}')
    ax.legend()
    plt.tight_layout()
    plt.show()


if __name__ == "__main__":
    # Manual testing
    print(f"Testing Day {{DAY_N}}: {{TOPIC_NAME}}")

    # Test the core function
    result = {{function_name}}()
    print(f"Result: {result}")

    # Run the visualizer
    plot_concept()