KSaiManikanta/gradient_descent

1import streamlit as st2import numpy as np3import plotly.graph_objects as go4import pandas as pd5 6# Title and Description7st.title("Gradient Descent Visualizer with Dynamic Learning Rate 🌟")8st.write(9    """10    Visualize the steps of gradient descent on a user-defined function. 11    Adjust parameters like the starting point and learning rate to see how the algorithm converges.12    Change the learning rate dynamically at any step!13    """14)15st.markdown("---")16 17# Safe evaluation of the function18def safe_eval(func_str, x_val):19    """Evaluate the function safely at a given x value."""20    allowed_names = {"x": x_val, "np": np}  # Allow only x and numpy21    return eval(func_str, {"_builtins_": None}, allowed_names)22 23# Numerical derivative24def derivative(func_str, x_val, h=1e-5):25    """Compute the derivative using the central difference method."""26    return (safe_eval(func_str, x_val + h) - safe_eval(func_str, x_val - h)) / (2 * h)27 28# Tangent line computation29def tangent_line(func_str, x_val, x_range):30    """Compute the tangent line for the function at a given x value."""31    y_val = safe_eval(func_str, x_val)32    slope = derivative(func_str, x_val)33    return slope * (x_range - x_val) + y_val34 35# Reset session state36def reset_state():37    st.session_state.x = st.session_state.starting_point38    st.session_state.iteration = 039    st.session_state.x_vals = [st.session_state.starting_point]40    st.session_state.y_vals = [safe_eval(st.session_state.func_input, st.session_state.starting_point)]41    st.session_state.history = [{42        "Iteration": 0, 43        "Starting Point": st.session_state.starting_point, 44        "Learning Rate": st.session_state.learning_rate,45        "x": st.session_state.x, 46        "f(x)": st.session_state.y_vals[0]47    }]48    st.session_state.learning_rate = initial_learning_rate  # Reset learning rate to initial value49 50# User inputs for the function51st.sidebar.header("Define the Function")52func_input = st.sidebar.text_input(53    "Enter a function of x (e.g., x**2 + x, np.sin(x), etc.):", 54    "x**2 + x", 55    key="func_input", 56    on_change=reset_state57)58 59# Gradient Descent Parameters60st.sidebar.header("Gradient Descent Settings")61 62# Replace slider with number input for Starting Point with high precision63starting_point = st.sidebar.number_input(64    "Starting Point", 65    value=4.0,  # Default value66    step=0.1,   # Step size for increment/decrement67    format="%.10f",  # Allow up to 10 decimal places68    key="starting_point", 69    on_change=reset_state70)71 72# Replace slider with number input for Learning Rate with high precision73initial_learning_rate = st.sidebar.number_input(74    "Initial Learning Rate", 75    value=0.1,  # Default value76    step=0.01,  # Step size for increment/decrement77    min_value=0.0,  # Minimum value78    format="%.10f",  # Allow up to 10 decimal places79    key="initial_learning_rate", 80    on_change=reset_state81)82 83# Dynamically update the learning rate with high precision84new_learning_rate = st.sidebar.number_input(85    "New Learning Rate", 86    value=initial_learning_rate,  # Default value87    step=0.01,  # Step size for increment/decrement88    min_value=0.0,  # Minimum value89    format="%.10f"  # Allow up to 10 decimal places90)91 92# Initialize session state variables93if "x" not in st.session_state:94    st.session_state.x = starting_point95    st.session_state.iteration = 096    st.session_state.x_vals = [starting_point]97    st.session_state.y_vals = [safe_eval(func_input, starting_point)]98    st.session_state.history = [{99        "Iteration": 0, 100        "Starting Point": starting_point, 101        "Learning Rate": initial_learning_rate,102        "x": starting_point, 103        "f(x)": st.session_state.y_vals[0]104    }]105    st.session_state.learning_rate = initial_learning_rate106 107# Update the learning rate dynamically108if st.session_state.learning_rate != new_learning_rate:109    st.session_state.learning_rate = new_learning_rate110    st.sidebar.success(f"Learning rate updated to {new_learning_rate:.2f}")111 112# Perform the next iteration of gradient descent113if st.button("Next Iteration 🚀"):114    try:115        grad = derivative(func_input, st.session_state.x)116        st.session_state.x = st.session_state.x - st.session_state.learning_rate * grad117        st.session_state.iteration += 1118        st.session_state.x_vals.append(st.session_state.x)119        st.session_state.y_vals.append(safe_eval(func_input, st.session_state.x))120 121        # Add the new values to the history122        st.session_state.history.append({123            "Iteration": st.session_state.iteration, 124            "Starting Point": starting_point, 125            "Learning Rate": st.session_state.learning_rate,126            "x": st.session_state.x, 127            "f(x)": st.session_state.y_vals[-1]128        })129    except Exception as e:130        st.error(f"Error: {e}")131 132# Gradient Descent Progress133st.subheader("Progress Overview")134st.write(f"**Iteration:** {st.session_state.iteration}")135st.write(f"**Current x:** {st.session_state.x:.4f}")136st.write(f"**Current f(x):** {st.session_state.y_vals[-1]:.4f}")137st.markdown("---")138 139# Visualization of the function and gradient descent steps140x_plot = np.linspace(-10, 10, 400)141y_plot = [safe_eval(func_input, x) for x in x_plot]142 143fig = go.Figure()144 145# Function curve146fig.add_trace(147    go.Scatter(x=x_plot, y=y_plot, mode="lines", line=dict(color="blue", width=2), name="Function")148)149 150# Gradient descent points151fig.add_trace(152    go.Scatter(153        x=st.session_state.x_vals,154        y=st.session_state.y_vals,155        mode="markers+lines",156        line=dict(color="red", dash="dot"),157        marker=dict(size=8, symbol="circle"),158        name="Gradient Descent Steps"159    )160)161 162# Tangent line at the current point163current_x = st.session_state.x164current_y = safe_eval(func_input, current_x)165tangent_x = np.linspace(current_x - 2, current_x + 2, 100)166tangent_y = tangent_line(func_input, current_x, tangent_x)167 168fig.add_trace(169    go.Scatter(170        x=tangent_x,171        y=tangent_y,172        mode="lines",173        line=dict(color="orange", width=2, dash="dash"),174        name="Tangent Line"175    )176)177 178# Update plot layout179fig.update_layout(180    title="Gradient Descent Visualization with Tangent Lines",181    xaxis_title="x",182    yaxis_title="f(x)",183    template="plotly_white",184    legend=dict(bordercolor="gray", borderwidth=1),185)186 187# Render plot188st.plotly_chart(fig)189# Table of Iterations190st.subheader("Iteration History")191history_df = pd.DataFrame(st.session_state.history)192st.dataframe(history_df, use_container_width=True)