Create app.py

app.py

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+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}")