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)