app.py

import streamlit as st
import numpy as np
import plotly.graph_objs as go
import sympy as sp

# Streamlit Page Configuration
st.set_page_config(page_title="Gradient Descent Visualizer", layout="wide")

# Sidebar Inputs
st.sidebar.header("Gradient Descent Settings")
func_input = st.sidebar.text_input("Enter a function (use 'x'):", "x**2")
learning_rate = st.sidebar.number_input("Learning Rate", min_value=0.001, max_value=1.0, value=0.1, step=0.01)
initial_x = st.sidebar.number_input("Initial X", min_value=-10.0, max_value=10.0, value=5.0, step=0.1)

# Reset Session State When Function Changes
if "previous_func" not in st.session_state or st.session_state.previous_func != func_input:
    st.session_state.current_x = initial_x
    st.session_state.iteration = 0
    st.session_state.path = [(initial_x, 0)]
    st.session_state.previous_func = func_input

# Symbolic Computation
x = sp.symbols('x')
try:
    func = sp.sympify(func_input)
    derivative = sp.diff(func, x)
    func_np = sp.lambdify(x, func, 'numpy')
    derivative_np = sp.lambdify(x, derivative, 'numpy')
except Exception as e:
    st.error(f"Invalid function: {e}")
    st.stop()

# Gradient Descent Step
def step_gradient_descent(current_x, lr):
    grad = derivative_np(current_x)
    next_x = current_x - lr * grad
    return next_x, grad

# Perform Next Iteration
if st.sidebar.button("Next Iteration"):
    next_x, _ = step_gradient_descent(st.session_state.current_x, learning_rate)
    st.session_state.path.append((st.session_state.current_x, func_np(st.session_state.current_x)))
    st.session_state.current_x = next_x
    st.session_state.iteration += 1

# Calculate Actual Minima
critical_points = sp.solve(derivative, x)
actual_minima = [p.evalf() for p in critical_points if derivative_np(p) == 0 and sp.diff(derivative, x).evalf(subs={x: p}) > 0]

# Generate Graph Data
x_vals = np.linspace(-15, 15, 1000)
y_vals = func_np(x_vals)

# Plotly Visualization
fig = go.Figure()

# Function Plot
fig.add_trace(go.Scatter(
    x=x_vals, y=y_vals, mode='lines',
    line=dict(color='blue', width=2),
    hoverinfo='none'
))

# Gradient Descent Path
path = st.session_state.path
x_path, y_path = zip(*[(pt[0], func_np(pt[0])) for pt in path])
fig.add_trace(go.Scatter(
    x=x_path, y=y_path, mode='markers+lines',
    marker=dict(color='red', size=8),
    line=dict(color='red', width=2),
    hoverinfo='none'
))

# Highlight Current Point
fig.add_trace(go.Scatter(
    x=[st.session_state.current_x], y=[func_np(st.session_state.current_x)],
    mode='markers', marker=dict(color='orange', size=12),
    name="Current Point", hoverinfo='none'
))

# Highlight Actual Minima
if actual_minima:
    minima_x = [float(p) for p in actual_minima]
    minima_y = [func_np(p) for p in minima_x]
    fig.add_trace(go.Scatter(
        x=minima_x, y=minima_y,
        mode='markers', marker=dict(color='green', size=14, symbol='star'),
        name="Actual Minima", hoverinfo='text',
        text=[f"x = {x_val:.4f}, f(x) = {y_val:.4f}" for x_val, y_val in zip(minima_x, minima_y)]
    ))

# Add Cross-Axes (X and Y lines)
fig.add_trace(go.Scatter(
    x=[-15, 15], y=[0, 0], mode='lines',
    line=dict(color='black', width=1, dash='dash'),
    hoverinfo='none'
))
fig.add_trace(go.Scatter(
    x=[0, 0], y=[-15, 15], mode='lines',
    line=dict(color='black', width=1, dash='dash'),
    hoverinfo='none'
))

# Layout Configuration
fig.update_layout(
    title="Gradient Descent Visualization",
    xaxis=dict(
        title="X",
        zeroline=True, zerolinewidth=1, zerolinecolor='black',
        tickvals=np.arange(-15, 16, 5),
        range=[-15, 15]
    ),
    yaxis=dict(
        title="f(X)",
        zeroline=True, zerolinewidth=1, zerolinecolor='black',
        tickvals=np.arange(-15, 16, 5),
        range=[-15, 15]
    ),
    showlegend=False,
    hovermode="closest",
    dragmode="pan",  # Corrected line: removed extra space
    autosize=True,
)

# Fullscreen and Export Options
st.markdown("### Gradient Descent Visualization")
st.plotly_chart(fig, use_container_width=True)

# Display Current Point
st.write(f"**Current Point (x):** {st.session_state.current_x:.4f}")

# Display Iteration History below the graph
st.write("### Iteration History:")
for i, (x_val, _) in enumerate(st.session_state.path):
    st.write(f"Iteration {i+1}: x = {x_val:.4f}")