Update app.py

app.py

@@ -2,6 +2,16 @@ 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")
@@ -29,8 +39,8 @@ def calculate_tangent(expression, x_value, x_range):
 def reset_session_state():
     st.session_state.x_current = st.session_state.initial_point
     st.session_state.iter_count = 0
-    st.session_state.x_points = [st.session_state.initial_point]
-    st.session_state.y_points = [evaluate_function(st.session_state.math_function, st.session_state.initial_point)]
+    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
 
 # 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
@@ -59,19 +69,14 @@ with left_col:
 # Right side content (Gradient Descent Updates and Progress)
 with right_col:
     st.header("Gradient Descent Updates")
-    if "x_current" not in st.session_state:
-        st.session_state.x_current = initial_point
-        st.session_state.iter_count = 0
-        st.session_state.x_points = [initial_point]
-        st.session_state.y_points = [evaluate_function(function_input, initial_point)]
-
     if st.button("🔄 Run Descent Step", type="primary"):
         try:
             gradient = compute_derivative(function_input, st.session_state.x_current)
             st.session_state.x_current -= learning_rate * gradient
             st.session_state.iter_count += 1
-            st.session_state.x_points.append(st.session_state.x_current)
-            st.session_state.y_points.append(evaluate_function(function_input, st.session_state.x_current))
+            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.current_index = st.session_state.iter_count
         except Exception as e:
             st.error(f"Error: {str(e)}")
 
@@ -105,10 +110,11 @@ with right_col:
     )
     
     # Add gradient descent points
+    x_points, y_points = zip(*st.session_state.history)
     plot.add_trace(
         go.Scatter(
-            x=st.session_state.x_points,
-            y=st.session_state.y_points,
+            x=x_points,
+            y=y_points,
             mode="markers",
             marker=dict(color="red", size=10, symbol="diamond"),
             name="Descent Steps",