Create app.py

app.py

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+import streamlit as st
+import numpy as np
+import matplotlib.pyplot as plt
+import re
+import math
+
+# Initialize session state for storing history and iteration count
+if "history" not in st.session_state:
+    st.session_state.history = []
+if "iteration" not in st.session_state:
+    st.session_state.iteration = 0
+
+# Function for gradient calculation
+def gradient(func, x):
+    return (func(x + 1e-5) - func(x)) / 1e-5  # Numerical derivative approximation
+
+# Sidebar for user input
+st.sidebar.title("Gradient Descent Visualizer")
+
+# Function input
+function_str = st.sidebar.text_input("Enter the function (in terms of x):", "x**2 + 2*x + 1")
+start_point = st.sidebar.number_input("Enter the starting point:", value=0.0)
+learning_rate = st.sidebar.number_input("Enter the learning rate:", value=0.1, step=0.01)
+
+# Replace common symbols with Python-friendly syntax
+function_str = re.sub(r'\^', '**', function_str)
+function_str = re.sub(r'([0-9])([a-zA-Z])', r'\1*\2', function_str)  # 2x -> 2*x
+function_str = re.sub(r'([a-zA-Z])([0-9])', r'\1*\2', function_str)  # x2 -> x*2
+
+# Setup button to initialize history
+if st.sidebar.button("Set Up"):
+    st.session_state.history = [start_point]
+    st.session_state.iteration = 0
+
+# Button to perform the next iteration
+if st.sidebar.button("Next Iteration"):
+    if st.session_state.history:
+        try:
+            # Convert string function to Python function, supporting more functions
+            def func(x):
+                return eval(function_str, {"x": x, "sin": np.sin, "cos": np.cos, "tan": np.tan, "log": np.log, "exp": np.exp, "sqrt": np.sqrt, "pi": np.pi, "e": np.e})
+            
+            # Calculate the gradient and the next point
+            current_x = st.session_state.history[-1]
+            grad = gradient(func, current_x)
+            next_x = current_x - learning_rate * grad
+
+            # Append next point to history
+            st.session_state.history.append(next_x)
+            st.session_state.iteration += 1
+
+            # Plot the function and the gradient descent path
+            x_vals = np.linspace(min(st.session_state.history) - 2, max(st.session_state.history) + 2, 100)
+            y_vals = func(x_vals)
+
+            plt.figure(figsize=(10, 6))
+            plt.plot(x_vals, y_vals, label=f'{function_str}')
+            plt.scatter(st.session_state.history, [func(x) for x in st.session_state.history], color='red', s=50)
+            plt.plot(st.session_state.history, [func(x) for x in st.session_state.history], linestyle='--', color='gray')
+
+            # Plot the slope (tangent line) at the current point
+            tangent_x_vals = np.linspace(current_x - 2, current_x + 2, 10)
+            tangent_y_vals = func(current_x) + grad * (tangent_x_vals - current_x)
+            plt.plot(tangent_x_vals, tangent_y_vals, color='orange', label=f"Slope at x={current_x:.2f}")
+
+            plt.xlabel("x")
+            plt.ylabel("f(x)")
+            plt.title(f"Iteration {st.session_state.iteration}")
+            plt.legend()
+            st.pyplot(plt)
+
+        except Exception as e:
+            st.sidebar.error(f"Error in function: {e}")
+    else:
+        st.sidebar.error("Please click 'Set Up' first to initialize the starting point.")
+
+# Display current point and iteration
+if st.session_state.history:
+    st.sidebar.write(f"**Current Point:** {st.session_state.history[-1]:.4f}")
+    st.sidebar.write(f"**Iteration:** {st.session_state.iteration}")