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