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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() |