rk803/gradient_app

1import streamlit as st2import numpy as np3import plotly.graph_objects as go4 5# Title of the app6st.title("Gradient Descent Visualizer with Tangent Lines")7st.markdown(8    """9    This app visualizes the **Gradient Descent Algorithm**. 10    Use the sidebar to define your function, starting point, and learning rate. 11    Click "Next Iteration" to see the algorithm in action.12    """13)14 15# Safe function evaluation16def safe_eval(func_str, x_val):17    """Safely evaluates the function at a given x value."""18    try:19        allowed_names = {"x": x_val, "np": np}  # Only allow x and numpy20        return eval(func_str, {"__builtins__": None}, allowed_names)21    except Exception as e:22        st.error(f"Error in function evaluation: {e}")23        raise24 25# Function derivative using finite difference method26def derivative(func_str, x_val, h=1e-5):27    """Numerically compute the derivative of the function at x using finite differences."""28    try:29        return (safe_eval(func_str, x_val + h) - safe_eval(func_str, x_val - h)) / (2 * h)30    except Exception as e:31        st.error(f"Error in derivative computation: {e}")32        raise33 34# Tangent Line Equation35def tangent_line(func_str, x_val, x_range):36    """Compute the tangent line at a given x value."""37    y_val = safe_eval(func_str, x_val)38    slope = derivative(func_str, x_val)39    return slope * (x_range - x_val) + y_val40 41# Initialize session state variables42def initialize_state(func_str, starting_point):43    """Initialize or reset session state variables."""44    try:45        st.session_state.x = starting_point46        st.session_state.iteration = 047        st.session_state.x_vals = [starting_point]48        st.session_state.y_vals = [safe_eval(func_str, starting_point)]49    except Exception as e:50        st.error(f"Initialization error: {e}")51        raise52 53# Sidebar: Function input54st.sidebar.header("Gradient Descent Settings")55func_input = st.sidebar.text_input(56    "Function (use 'x' as the variable):",57    value="x**2 + x",58    key="func_input"59)60 61# Sidebar: Starting point and learning rate62starting_point = st.sidebar.number_input(63    "Starting Point:",64    value=4.0,65    step=0.1,66    format="%.2f",67    key="starting_point"68)69learning_rate = st.sidebar.number_input(70    "Learning Rate:",71    value=0.1,72    step=0.00001,73    format="%.5f",74    key="learning_rate"75)76 77# Reset button78if st.sidebar.button("Reset Gradient Descent"):79    initialize_state(func_input, starting_point)80 81# Initialize session state on first load82if "x" not in st.session_state:83    initialize_state(func_input, starting_point)84 85# Sidebar: Perform next iteration86if st.sidebar.button("Next Iteration"):87    try:88        grad = derivative(func_input, st.session_state.x)89        st.session_state.x -= learning_rate * grad90        st.session_state.iteration += 191        st.session_state.x_vals.append(st.session_state.x)92        st.session_state.y_vals.append(safe_eval(func_input, st.session_state.x))93    except Exception as e:94        st.error(f"Error during iteration: {e}")95 96# Sidebar: Display gradient descent progress97st.sidebar.subheader("Progress")98st.sidebar.write(f"Iteration: {st.session_state.iteration}")99st.sidebar.write(f"Current x: {st.session_state.x:.4f}")100st.sidebar.write(f"Current f(x): {st.session_state.y_vals[-1]:.4f}")101progress = st.sidebar.progress(st.session_state.iteration % 100 / 100)102 103# Main area: Plot function, points, and tangent line104try:105    x_plot = np.linspace(-10, 10, 400)106    y_plot = [safe_eval(func_input, x) for x in x_plot]107 108    fig = go.Figure()109 110    # Function curve111    fig.add_trace(go.Scatter(x=x_plot, y=y_plot, mode="lines", name="Function"))112 113    # Gradient descent points114    fig.add_trace(go.Scatter(115        x=st.session_state.x_vals,116        y=st.session_state.y_vals,117        mode="markers",118        marker=dict(color="red", size=8),119        name="Gradient Descent Points"120    ))121 122    # Tangent line123    current_x = st.session_state.x124    tangent_x = np.linspace(current_x - 2, current_x + 2, 100)125    tangent_y = tangent_line(func_input, current_x, tangent_x)126 127    fig.add_trace(go.Scatter(128        x=tangent_x,129        y=tangent_y,130        mode="lines",131        line=dict(color="orange", width=3),132        name="Tangent Line"133    ))134 135    # Update layout136    fig.update_layout(137        xaxis_title="x",138        yaxis_title="f(x)",139        title="Gradient Descent Visualization",140        template="plotly_white"141    )142 143    st.plotly_chart(fig)144 145except Exception as e:146    st.error(f"Error during plotting: {e}")147