Update app.py

app.py

@@ -2,16 +2,6 @@ import streamlit as st
 import numpy as np
 import plotly.graph_objects as go
 
-# Initialize session state variables if not already present
-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 = []  # Store (x, f(x)) for each iteration
-if "current_index" not in st.session_state:
-    st.session_state.current_index = 0
-
 # Title of the app
 st.set_page_config(page_title="Interactive Gradient Descent Visualizer", layout="wide")
 st.title("🌟 Gradient Descent Visualizer")
@@ -42,6 +32,16 @@ def reset_session_state():
     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
+
 # 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
 
@@ -74,8 +74,9 @@ with right_col:
             gradient = compute_derivative(function_input, st.session_state.x_current)
             st.session_state.x_current -= learning_rate * gradient
             st.session_state.iter_count += 1
-            current_y = evaluate_function(function_input, st.session_state.x_current)
-            st.session_state.history.append((st.session_state.x_current, current_y))
+            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)}")
@@ -90,12 +91,15 @@ with right_col:
             st.session_state.current_index += 1
 
     # Display selected iteration details
-    selected_x, selected_y = st.session_state.history[st.session_state.current_index]
-    st.subheader("Iteration Details")
-    st.markdown(f"**Iteration:** {st.session_state.current_index}")
-    st.markdown(f"**x Value:** {selected_x:.4f}")
-    st.markdown(f"**f(x):** {selected_y:.4f}")
-    st.markdown("---")
+    try:
+        selected_x, selected_y = st.session_state.history[st.session_state.current_index]
+        st.subheader("Iteration Details")
+        st.markdown(f"**Iteration:** {st.session_state.current_index}")
+        st.markdown(f"**x Value:** {selected_x:.4f}")
+        st.markdown(f"**f(x):** {selected_y:.4f}")
+        st.markdown("---")
+    except IndexError:
+        st.warning("No iteration data available. Please run a descent step first.")
 
     # Generate plot data
     x_vals = np.linspace(-10, 10, 400)
@@ -110,7 +114,8 @@ with right_col:
     )
     
     # Add gradient descent points
-    x_points, y_points = zip(*st.session_state.history)
+    x_points = [point[0] for point in st.session_state.history]
+    y_points = [point[1] for point in st.session_state.history]
     plot.add_trace(
         go.Scatter(
             x=x_points,