import streamlit as st import numpy as np import plotly.graph_objects as go # Page Configurations st.set_page_config(page_title="Gradient Descent Visualization", layout="wide") st.markdown("

⚡ Gradient Descent Visualization ⚡

", unsafe_allow_html=True) # Custom CSS for Background and Buttons st.markdown(""" """, unsafe_allow_html=True) # Safe Function Evaluation def evaluate_function(expression, x_value): allowed_names = {"x": x_value, "np": np} # Allow only x and numpy return eval(expression, {"_builtins_": None}, allowed_names) # Compute Derivative def compute_derivative(expression, x_value, h=1e-5): 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): y_value = evaluate_function(expression, x_value) slope = compute_derivative(expression, x_value) return slope * (x_range - x_value) + y_value # Reset Session State def reset_session_state(): 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 if "x_current" not in st.session_state: st.session_state.x_current = 0.0 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))] 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 # Layout left_col, right_col = st.columns([1, 2]) # Left Column: Inputs with left_col: st.markdown("### 📝 Define Your Equation") function_input = st.text_input( "Input Equation (e.g., `x**2`, `np.sin(x)`):", "x**2 + x", key="math_function", on_change=reset_session_state ) st.markdown("### 🔧 Configure Settings") initial_point = st.number_input( "Starting Value of x:", value=4.0, step=0.1, format="%.2f", key="initial_point", on_change=reset_session_state ) st.number_input( "Step Size (Learning Rate):", value=st.session_state.learning_rate, step=0.01, format="%.2f", key="learning_rate" ) st.markdown("### đŸ•šī¸ Actions") col1, col2 = st.columns(2) with col1: if st.button("🌀 Compute Next Step"): 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)}") with col2: if st.button("🔃 Restart"): reset_session_state() # Right Column: Visualization with right_col: st.markdown("### 📈 Gradient Descent Steps") # Navigation Buttons col1, col2, col3 = st.columns(3) with col1: if st.button("âŦ…ī¸ Previous Step") and st.session_state.current_index > 0: st.session_state.current_index -= 1 with col2: st.markdown(f"

Step Count: {st.session_state.current_index}

", unsafe_allow_html=True) with col3: if st.button("âžĄī¸ Next Step") 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"📍 **Current x:** `{selected_x:.4f}`") st.markdown(f"📈 **f(x) at Current Step:** `{selected_y:.4f}`") except IndexError: st.warning("No data to display. Perform a computation first.") # Visualization x_range = np.linspace(-10, 10, 500) y_range = [evaluate_function(function_input, x) for x in x_range] fig = go.Figure() fig.add_trace(go.Scatter(x=x_range, y=y_range, mode='lines', name='Equation', line=dict(color='#FFD700'))) # Get current position from history 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 Position', marker=dict(size=12, color='#FF4500'))) # Calculate and plot the updated tangent line at the current position 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=dict(dash='dash', color='#00FFFF'))) fig.update_layout( title="Gradient Descent Progress", xaxis_title="x", yaxis_title="f(x)", template="plotly_dark", height=500, width=900, margin=dict(l=20, r=20, t=50, b=20), ) st.plotly_chart(fig, use_container_width=True)