Create app.py

app.py

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+import gradio as gr
+import numpy as np
+import matplotlib.pyplot as plt
+
+def linear_interpolation(x, y, x_interp):
+    return np.interp(x_interp, x, y)
+
+def quadratic_interpolation(x, y, x_interp):
+    coeffs = np.polyfit(x, y, 2)
+    return np.polyval(coeffs, x_interp)
+
+def lagrange_interpolation(x, y, x_interp):
+    n = len(x)
+    y_interp = np.zeros_like(x_interp, dtype=float)
+    
+    for i in range(n):
+        p = y[i]
+        for j in range(n):
+            if i != j:
+                p = p * (x_interp - x[j]) / (x[i] - x[j])
+        y_interp += p
+    
+    return y_interp
+
+def interpolate_and_plot(x_input, y_input, x_predict):
+    x = np.array([float(val.strip()) for val in x_input.split(',')])
+    y = np.array([float(val.strip()) for val in y_input.split(',')])
+    
+    if len(x) != len(y):
+        return "Error: Number of x and y values must be the same.", None
+    
+    x_interp = np.linspace(min(x), max(x), 100)
+    
+    if len(x) == 2:
+        y_interp = linear_interpolation(x, y, x_interp)
+        method = "Linear"
+    elif len(x) == 3:
+        y_interp = quadratic_interpolation(x, y, x_interp)
+        method = "Quadratic"
+    else:
+        y_interp = lagrange_interpolation(x, y, x_interp)
+        method = "Lagrange"
+    
+    plt.figure(figsize=(10, 6))
+    plt.scatter(x, y, color='red', label='Input points')
+    plt.plot(x_interp, y_interp, label=f'{method} interpolant')
+    plt.xlabel('x')
+    plt.ylabel('y')
+    plt.title(f'{method} Interpolation')
+    plt.legend()
+    plt.grid(True)
+    
+    # Predict y value for given x
+    if x_predict is not None:
+        if x_predict < min(x) or x_predict > max(x):
+            return plt, f"Error: Prediction x value must be between {min(x)} and {max(x)}."
+        
+        if len(x) == 2:
+            y_predict = linear_interpolation(x, y, [x_predict])[0]
+        elif len(x) == 3:
+            y_predict = quadratic_interpolation(x, y, [x_predict])[0]
+        else:
+            y_predict = lagrange_interpolation(x, y, [x_predict])[0]
+        
+        plt.scatter([x_predict], [y_predict], color='green', s=100, label='Predicted point')
+        plt.legend()
+        
+        return plt, f"Predicted y value for x = {x_predict}: {y_predict:.4f}"
+    
+    return plt, None
+
+iface = gr.Interface(
+    fn=interpolate_and_plot,
+    inputs=[
+        gr.Textbox(label="X values (comma-separated)"),
+        gr.Textbox(label="Y values (comma-separated)"),
+        gr.Number(label="X value to predict (optional)")
+    ],
+    outputs=[
+        gr.Plot(label="Interpolation Plot"),
+        gr.Textbox(label="Predicted Y value")
+    ],
+    title="Interpolation App",
+    description="Enter x and y values to see the interpolation graph. The method will be chosen based on the number of points:\n2 points: Linear, 3 points: Quadratic, >3 points: Lagrange.\n Optionally, enter an x value (between min and max of input x values) to predict its corresponding y value."
+)
+
+iface.launch()