import streamlit as st import numpy as np import plotly.graph_objects as go # Title of the app st.set_page_config(page_title="Interactive Gradient Descent Visualizer", layout="wide") st.markdown("

🌟 Gradient Descent Visualizer

", unsafe_allow_html=True) # Custom CSS for background and button color st.markdown(""" """, unsafe_allow_html=True) # Safe function evaluation def evaluate_function(expression, x_value): """Safely evaluates the mathematical function.""" allowed_names = {"x": x_value, "np": np} # Allow only x and numpy return eval(expression, {"_builtins_": None}, allowed_names) # Compute derivative using finite difference def compute_derivative(expression, x_value, h=1e-5): """Numerically calculates the derivative at a given point.""" return (evaluate_function(expression, x_value + h) - evaluate_function(expression, x_value - h)) / (2 * h) # Tangent line calculation def calculate_tangent(expression, x_value, x_range): """Generates the tangent line for a given point.""" y_value = evaluate_function(expression, x_value) slope = compute_derivative(expression, x_value) return slope * (x_range - x_value) + y_value # Reset state def reset_session_state(): """Resets the session state for a fresh start.""" st.session_state.x_current = st.session_state.initial_point st.session_state.iter_count = 0 st.session_state.history = [ (st.session_state.initial_point, evaluate_function(st.session_state.math_function, st.session_state.initial_point)) ] st.session_state.current_index = 0 # Initialize session state variables if "x_current" not in st.session_state: st.session_state.x_current = 0.0 # Default starting point if "iter_count" not in st.session_state: st.session_state.iter_count = 0 if "history" not in st.session_state: st.session_state.history = [(0.0, evaluate_function("x**2 + x", 0.0))] # Default function example if "current_index" not in st.session_state: st.session_state.current_index = 0 if "learning_rate" not in st.session_state: st.session_state.learning_rate = 0.1 # Create two-column grid layout for the left side (more space for the right graph) left_col, right_col = st.columns([1, 2]) # 1 for left, 2 for right grid proportion # Left side content (Function Input and Gradient Descent Parameters) with left_col: st.markdown("

Input Your Function

", unsafe_allow_html=True) function_input = st.text_input( "Enter Function:`Ex:'x**2`,`np.sin(x)`", "x**2 + x", key="math_function", on_change=reset_session_state ) st.markdown("

Set Parameters

", unsafe_allow_html=True) initial_point = st.number_input( "Initial Value of x", value=4.0, step=0.1, format="%.2f", key="initial_point", on_change=reset_session_state ) st.number_input( "Learning Rate", value=st.session_state.learning_rate, step=0.01, format="%.2f", key="learning_rate" ) # Updates session state directly without reset st.markdown("

Controls

", unsafe_allow_html=True) if st.button("🔄 Run Descent Step", type="primary"): try: gradient = compute_derivative(function_input, st.session_state.x_current) st.session_state.x_current -= st.session_state.learning_rate * gradient st.session_state.iter_count += 1 st.session_state.history.append( (st.session_state.x_current, evaluate_function(function_input, st.session_state.x_current)) ) st.session_state.current_index = st.session_state.iter_count except Exception as e: st.error(f"Error: {str(e)}") if st.button("🔄 Reset"): reset_session_state() # Right side content (Visualization and Iteration Details) with right_col: st.markdown("

Gradient Descent Visualization

", unsafe_allow_html=True) # Display iteration details using buttons col1, col2, col3 = st.columns(3) with col1: if st.button("⬅️ Previous Iteration") and st.session_state.current_index > 0: st.session_state.current_index -= 1 with col2: st.markdown(f"**Iteration:** {st.session_state.current_index}", unsafe_allow_html=True) with col3: if st.button("➡️ Next Iteration") and st.session_state.current_index < st.session_state.iter_count: st.session_state.current_index += 1 try: selected_x, selected_y = st.session_state.history[st.session_state.current_index] st.markdown(f"x Value: {selected_x:.4f}", unsafe_allow_html=True) st.markdown(f"f(x): {selected_y:.4f}", unsafe_allow_html=True) except IndexError: st.warning("No iteration data available. Please run a descent step first.") # Prepare data for visualization x_range = np.linspace(-10, 10, 500) # Define range for x y_range = [evaluate_function(function_input, x) for x in x_range] # Plot function curve with orange color fig = go.Figure() fig.add_trace(go.Scatter( x=x_range, y=y_range, mode='lines', name='Function', line=dict(color='orange') # Curve color set to orange )) # Add current point x_current, y_current = st.session_state.history[st.session_state.current_index] fig.add_trace(go.Scatter( x=[x_current], y=[y_current], mode='markers', name='Current Point', marker=dict(size=10, color='red') )) # Add tangent line tangent_y = calculate_tangent(function_input, x_current, x_range) fig.add_trace(go.Scatter( x=x_range, y=tangent_y, mode='lines', name='Tangent Line', line=dict(dash='dash', color='blue') # Tangent line in blue )) # Layout adjustments fig.update_layout( title="Gradient Descent Progress", xaxis_title="x", yaxis_title="f(x)", template="plotly_white", height=600 ) st.plotly_chart(fig, use_container_width=True)