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 âĄ
", 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("### đ 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("### đ§ 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("### đšī¸ Actions")
col1, col2 = st.columns(2)
with col1:
if st.button("đ 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("đ Restart"):
reset_session_state()
# Right Column: Visualization
with right_col:
st.markdown("### đ 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("âĄī¸ 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"đ **Current x:** `{selected_x:.4f}`")
st.markdown(f"đ **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)