Plots Directory

This directory contains Python scripts for generating interactive Plotly visualizations for the Jekyll blog.

Files

• interactive_plot.py - Main script for orthogonal projection visualization
• README.md - This file

Available Plots

Orthogonal Projection Visualization (interactive_plot.py)

Creates two interactive visualizations:

1. 3D Orthogonal Projection - Shows a 2D subspace in 3D space with:
   • Subspace S (light blue plane) spanned by basis functions φ₀(x) = 1 and φ₁(x)
   • Vector y (green arrow) representing target values
   • Orthogonal projection ŷ = Proj_S(y) (orange arrow)
   • Residual vector (purple arrow) orthogonal to the subspace
2. 2D Vector Decomposition - Shows vector decomposition in 2D space

Usage

Direct Execution

# From the plots directory
python interactive_plot.py

Using the Helper Script

# From the utils directory
python generate_plot.py interactive_plot.py

Output

The script generates:

• orthogonal_projection_3d.html - 3D interactive visualization
• orthogonal_projection_2d.html - 2D interactive visualization

These files are automatically moved to ../assets/plots/ when using the helper script.

Creating New Plots

1. Create a new Python script in this directory
2. Use Plotly to create interactive visualizations
3. Generate HTML output using fig.write_html("filename.html")
4. Use the helper script to move files to the assets directory

Example Template

import plotly.graph_objects as go
import numpy as np

def create_my_plot():
    fig = go.Figure()
    # Add your plot elements here
    return fig

if __name__ == "__main__":
    fig = create_my_plot()
    fig.write_html("my_plot.html")

Dependencies

• plotly - For interactive visualizations
• numpy - For numerical computations