Creation

app.py

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+import numpy as np
+import gradio as gr
+import matplotlib.pyplot as plt
+
+# Define functions and classes
+def true_fun(x):
+    return x ** 2 - np.cos(np.pi * x)
+
+def euclid_dist(x, xk):
+    return np.sqrt((x.reshape(-1, 1) - xk.reshape(1, -1)) ** 2)
+
+def rbf(radius, eps):
+    return np.exp(-(eps * radius) ** 2)
+
+class RBFInt:
+    def __init__(self, eps):
+        self.eps = eps
+
+    def fit(self, x, y):
+        self.xk_ = x
+        transf = rbf(euclid_dist(x, x), self.eps)
+        self.w_ = np.linalg.solve(transf, y)
+
+    def __call__(self, xn):
+        transf = rbf(euclid_dist(xn, self.xk_), self.eps)
+        return transf.dot(self.w_)
+
+def rbf_interpolation(eps, num_points):
+    # Generate random points
+    np.random.seed(42)
+    xk = np.linspace(0, 1, num_points)
+    yk = true_fun(xk) + np.random.randn(num_points) * 0.1
+
+    # Fit the RBF model
+    rbf_model = RBFInt(eps)
+    rbf_model.fit(xk, yk)
+
+    # Interpolate over a range of x values
+    x = np.linspace(0, 1, 100)
+    y_true = true_fun(x)
+    y_interp = rbf_model(x)
+
+    # Plot the results
+    fig, ax = plt.subplots()
+    ax.plot(x, y_true, label="True function")
+    ax.plot(x, y_interp, label="RBF Interpolation")
+    ax.scatter(xk, yk, color="red", label="Data points")
+    ax.legend()
+    plt.close(fig)  # Close the figure to avoid display issues in some environments
+    return fig
+
+# Gradio UI
+iface = gr.Interface(
+    fn=rbf_interpolation,
+    inputs=[
+        gr.Slider(0.1, 10.0, step=0.1, label="Epsilon (eps)"),
+        gr.Slider(1, 20, step=1, label="Number of points")
+    ],
+    outputs=gr.Plot(label="RBF Interpolation"),
+    live=True
+)
+
+iface.launch()