Update app.py

app.py

@@ -3,8 +3,8 @@ import numpy as np
 import plotly.graph_objects as go
 
 # Page Configurations
-st.set_page_config(page_title="Gradient Descent Visualizer", layout="wide")
-st.markdown("<h1 style='text-align: center; color: #FFD700;'>✨ Gradient Descent Visualizer ✨</h1>", unsafe_allow_html=True)
+st.set_page_config(page_title="Optimization Explorer", layout="wide")
+st.markdown("<h1 style='text-align: center; color: #FFD700;'>⚡ Optimization Explorer ⚡</h1>", unsafe_allow_html=True)
 
 # Custom CSS for Background and Buttons
 st.markdown("""
@@ -14,17 +14,17 @@ st.markdown("""
             color: white;  /* White text for contrast */
         }
         .stButton>button {
-            background: linear-gradient(to right, #FF7F50, #FF4500);  /* Coral to orange gradient */
+            background: linear-gradient(to right, #4CAF50, #2E7D32);  /* Green gradient */
             color: white;  /* White text */
             border-radius: 8px;
             padding: 8px 16px;
             font-size: 16px;
         }
         .stButton>button:hover {
-            background: linear-gradient(to right, #FF4500, #FF7F50);  /* Reverse gradient on hover */
+            background: linear-gradient(to right, #2E7D32, #4CAF50);  /* Reverse gradient on hover */
         }
         .stMarkdown h3 {
-            color: #FFD700;  /* Gold color for section titles */
+            color: #03A9F4;  /* Blue color for section titles */
         }
     </style>
 """, unsafe_allow_html=True)
@@ -70,16 +70,16 @@ left_col, right_col = st.columns([1, 2])
 
 # Left Column: Inputs
 with left_col:
-    st.markdown("### 📚 Input Your Function")
+    st.markdown("### 📝 Define Your Equation")
     function_input = st.text_input(
-        "Enter Function (e.g., `x**2`, `np.sin(x)`):", 
+        "Input Equation (e.g., `x**2`, `np.sin(x)`):", 
         "x**2 + x", 
         key="math_function", 
         on_change=reset_session_state
     )
-    st.markdown("### 🔧 Set Parameters")
+    st.markdown("### 🔧 Configure Settings")
     initial_point = st.number_input(
-        "Initial Value of x:", 
+        "Starting Value of x:", 
         value=4.0, 
         step=0.1, 
         format="%.2f", 
@@ -87,17 +87,17 @@ with left_col:
         on_change=reset_session_state
     )
     st.number_input(
-        "Learning Rate:", 
+        "Step Size (Learning Rate):", 
         value=st.session_state.learning_rate, 
         step=0.01, 
         format="%.2f", 
         key="learning_rate"
     )
     
-    st.markdown("### 🎮 Controls")
+    st.markdown("### 🕹️ Actions")
     col1, col2 = st.columns(2)
     with col1:
-        if st.button("🚀 Run Step"):
+        if st.button("🌀 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
@@ -109,44 +109,44 @@ with left_col:
             except Exception as e:
                 st.error(f"Error: {str(e)}")
     with col2:
-        if st.button("🔄 Reset"):
+        if st.button("🔃 Restart"):
             reset_session_state()
 
 # Right Column: Visualization
 with right_col:
-    st.markdown("### 📊 Gradient Descent Visualization")
+    st.markdown("### 📈 Exploration of Optimization Steps")
     
     # Navigation Buttons
     col1, col2, col3 = st.columns(3)
     with col1:
-        if st.button("⬅️ Step Back") and st.session_state.current_index > 0:
+        if st.button("⬅️ Previous Step") and st.session_state.current_index > 0:
             st.session_state.current_index -= 1
     with col2:
-        st.markdown(f"<p style='text-align: center;'>Iteration: <strong>{st.session_state.current_index}</strong></p>", unsafe_allow_html=True)
+        st.markdown(f"<p style='text-align: center;'>Step Count: <strong>{st.session_state.current_index}</strong></p>", unsafe_allow_html=True)
     with col3:
-        if st.button("➡️ Step Forward") and st.session_state.current_index < st.session_state.iter_count:
+        if st.button("➡️ 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"📍 **x Value:** `{selected_x:.4f}`")
-        st.markdown(f"📈 **f(x):** `{selected_y:.4f}`")
+        st.markdown(f"📍 **Current x:** `{selected_x:.4f}`")
+        st.markdown(f"📈 **f(x) at Current Step:** `{selected_y:.4f}`")
     except IndexError:
-        st.warning("No iteration data available. Please run a descent step first.")
+        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='Function', line=dict(color='#FFD700')))
+    fig.add_trace(go.Scatter(x=x_range, y=y_range, mode='lines', name='Equation', line=dict(color='#FFD700')))
     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 Point', marker=dict(size=12, color='#FF4500')))
+    fig.add_trace(go.Scatter(x=[x_current], y=[y_current], mode='markers', name='Current Position', marker=dict(size=12, color='#FF4500')))
     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', line=dict(dash='dash', color='#00FFFF')))
+    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",
+        title="Optimization Process",
         xaxis_title="x",
         yaxis_title="f(x)",
         template="plotly_dark",