Create app.py

app.py

@@ -0,0 +1,119 @@
+import numpy as np
+import matplotlib.pyplot as plt
+import streamlit as st
+import sympy as sp
+
+st.set_page_config(page_title="Gradient Descent Visualizer", layout="wide", page_icon="📉")
+st.markdown(
+    """
+    <style>
+    .css-18e3th9 { padding-top: 1rem; padding-bottom: 1rem; }
+    .stButton>button { border-radius: 8px; font-weight: bold; }
+    .stNumberInput>div>div>input { border-radius: 8px; }
+    .stTextInput>div>div>input { border-radius: 8px; }
+    .st-sidebar { background-color: #f9f9f9; border-right: 2px solid #eee; }
+    h1, h2, h3 { color: #4a4e69; font-family: 'Arial'; }
+    </style>
+    """,
+    unsafe_allow_html=True,
+)
+
+def parse_function(user_input):
+    x = sp.symbols('x')
+    try:
+        func_expr = sp.sympify(user_input)
+        func = sp.lambdify(x, func_expr, 'numpy')
+        gradient_expr = sp.diff(func_expr, x)
+        gradient = sp.lambdify(x, gradient_expr, 'numpy')
+        return func, gradient, str(gradient_expr)
+    except Exception as e:
+        st.error(f"Invalid function input: {e}")
+        return None, None, None
+
+def gradient_descent_step(x, learning_rate, func, gradient):
+    grad = gradient(x)
+    x_new = x - learning_rate * grad
+    loss_new = func(x_new)
+    return x_new, loss_new, grad
+
+st.title("📉 Interactive Gradient Descent Visualizer")
+with st.sidebar:
+    st.header("🔧 Parameters")
+    user_function = st.text_input("Enter a Function (e.g., 2*x**2 + 3*x)", value="x**2")
+    start_point = st.number_input("Starting Point", value=5.0, step=0.00001, format="%.5f")
+    learning_rate = st.number_input("Learning Rate", value=0.1, step=0.00001, format="%.5f")
+
+    def setup_gradient_descent():
+        st.session_state.iteration = 0
+        st.session_state.final_minimum = False
+        st.session_state.x_values = [start_point]
+        st.session_state.loss_values = [func(start_point)]
+        st.session_state.gradients = []
+
+    st.button("🚀 Setup", on_click=setup_gradient_descent)
+
+func, gradient, gradient_str = parse_function(user_function)
+
+if func and gradient:
+    if 'iteration' not in st.session_state:
+        st.session_state.iteration = 0
+        st.session_state.final_minimum = False
+        st.session_state.x_values = [start_point]
+        st.session_state.loss_values = [func(start_point)]
+        st.session_state.gradients = []
+
+    col1, col2 = st.columns([2, 1])
+
+    with col1:
+        st.subheader(f"🔍 Gradient Descent Visualization for: $f(x) = {user_function}$")
+        st.markdown(f"**Gradient (f'(x)):**  $f'(x) = {gradient_str}$")
+
+        fig, ax = plt.subplots(figsize=(10, 6))
+        x_range = np.linspace(-10, 10, 500)
+        y_range = func(x_range)
+
+        ax.plot(x_range, y_range, label="Function: f(x)", color='#0077b6', linewidth=2)
+
+        for i in range(st.session_state.iteration + 1):
+            x = st.session_state.x_values[i]
+            y = func(x)
+            ax.scatter(x, y, color="#d90429", s=60, zorder=5, label="Descent Point" if i == 0 else "")
+
+        if st.session_state.iteration < len(st.session_state.x_values):
+            x = st.session_state.x_values[st.session_state.iteration]
+            y = func(x)
+            grad = gradient(x)
+            tangent = grad * (x_range - x) + y
+            ax.plot(x_range, tangent, color="#ffb703", linestyle="--", linewidth=1.5, alpha=0.8, label="Tangent Line")
+
+        ax.set_xlim([-10, 10])
+        ax.set_ylim([min(func(x_range)) - 1, max(func(x_range)) + 1])
+        ax.set_xlabel("x", fontsize=12, labelpad=10)
+        ax.set_ylabel("f(x)", fontsize=12, labelpad=10)
+        ax.set_title("Gradient Descent with Tangent Lines", fontsize=14, fontweight="bold", color="#4a4e69")
+        ax.legend(loc="upper right", frameon=True, fontsize=10)
+        ax.grid(alpha=0.3)
+        st.pyplot(fig)
+
+    with col2:
+        st.subheader("📊 Progress")
+        for i, (x, loss) in enumerate(zip(st.session_state.x_values, st.session_state.loss_values)):
+            st.write(f"Iteration {i}: x = {x:.4f}, f(x) = {loss:.4f}")
+
+        current_gradient = gradient(st.session_state.x_values[-1])
+        if abs(current_gradient) < 1e-6 and not st.session_state.final_minimum:
+            st.success(f"🎯 Final Minimum Reached: $x = {st.session_state.x_values[-1]:.4f}, f(x) = {st.session_state.loss_values[-1]:.4f}$")
+            st.session_state.final_minimum = True
+
+    def next_iteration():
+        if not st.session_state.final_minimum:
+            new_x, new_loss, grad = gradient_descent_step(st.session_state.x_values[-1], learning_rate, func, gradient)
+            st.session_state.x_values.append(new_x)
+            st.session_state.loss_values.append(new_loss)
+            st.session_state.gradients.append(grad)
+            st.session_state.iteration += 1
+
+    st.sidebar.button("⏭ Next Iteration", on_click=next_iteration)
+
+    if st.session_state.final_minimum:
+        st.info("The gradient is close to zero. Further iterations may not improve the result.")