Update app.py

app.py

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+# Import required libraries
+import numpy as np
+import matplotlib.pyplot as plt
+import streamlit as st
+import sympy as sp
+
+# Functions and their derivatives
+def square(x): 
+    return x**2
+
+def derivative_square(x):
+    return 2*x
+
+def cube(x): 
+    return x**3
+
+def derivative_cube(x):
+    return 3 * x**2
+
+def sin(x):
+    return np.sin(x)
+
+def derivative_sin(x):
+    return np.cos(x)
+    
+def inverse(x):
+    return 1/x
+
+def derivative_inverse(x):
+    return - (1 / x **2)
+
+def poly(x):
+    return x + 2 * (x**2) + (0.4) * x**3
+
+def derivative_poly(x):
+    return 1 + 4 * x + 1.2 * x**2
+
+# Function to calculate the derivative
+def calculate_derivative(func_str):
+    x = sp.symbols('x')
+    try:
+        # Parse the function string into a sympy expression
+        func = sp.sympify(func_str)
+        # Calculate the derivative
+        derivative = sp.diff(func, x)
+        return func, derivative
+    except sp.SympifyError:
+        return None, None
+
+# Title
+st.title('Gradient Descent Visualizer')
+st.sidebar.title("It's your turn..")
+
+# User input
+function = st.sidebar.selectbox('Pre Defined Functions', ['Square', 'Cube', 'Polynomial', 'sin', '1/x', 'None'])
+starting_point = st.sidebar.number_input('Starting Point', value=5, step=1)
+learning_rate = st.sidebar.number_input('Learning Rate', value=0.1, step=0.01)
+
+# Define the selected function and its derivative
+if function == 'Square':
+    func = square
+    derivative_func = derivative_square
+elif function == 'Cube':
+    func = cube
+    derivative_func = derivative_cube
+elif function == 'Polynomial':
+    func = poly
+    derivative_func = derivative_poly
+elif function == 'sin':
+    func = sin
+    derivative_func = derivative_sin
+elif function == '1/x':
+    func = inverse
+    derivative_func = derivative_inverse
+elif function == 'None':
+    user_func = st.text_input("Enter a function: ")
+    func, derivative = calculate_derivative(user_func)
+
+# Check if the starting point has changed
+if 'last_starting_point' not in st.session_state or st.session_state.last_starting_point != starting_point:
+    st.session_state.path = [starting_point]
+    st.session_state.iteration = 0  
+    st.session_state.last_starting_point = starting_point  
+
+# Perform one iteration of gradient descent
+if st.sidebar.button('Next Iteration'):
+    current_point = st.session_state.path[-1]
+    new_point = current_point - learning_rate * derivative_func(current_point)
+    st.session_state.path.append(new_point)
+    st.session_state.iteration += 1 
+
+# Create an array of values for plotting
+x_values = np.linspace(-10, 10, 500)
+y_values = func(x_values)
+
+# Dynamic scaling based on the function's range
+y_min, y_max = np.min(y_values), np.max(y_values)
+y_padding = (y_max - y_min) * 0.1
+
+# Plot the function and the path of points
+plt.figure(figsize=(8, 6))
+plt.plot(x_values, y_values, label=function, color='blue')
+plt.scatter(st.session_state.path, [func(x) for x in st.session_state.path], color='red', zorder=5)
+
+# Calculate and plot the tangent line
+current_point = st.session_state.path[-1]
+slope = derivative_func(current_point)
+y_tangent = slope * (x_values - current_point) + func(current_point)
+plt.plot(x_values, y_tangent, '--', color='red')
+
+# Set plot limits dynamically
+plt.xlim([-10, 10])
+plt.ylim([y_min - y_padding, y_max + y_padding])
+
+# Display the iteration number
+plt.title(f'Iteration: {st.session_state.iteration}')
+
+# Labels and legend
+plt.xlabel('x')
+plt.ylabel('y')
+plt.legend()
+plt.grid(True)
+
+# Display the plot
+st.pyplot(plt)