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Program 1

Interpolation

import numpy as np
from scipy.interpolate import interp1d
import matplotlib.pyplot as plt

# Define the x and y data directly in the script (lists of length 20)
x = np.array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19])
y = np.array([0, 1.5, 2.5, 3.8, 5.2, 7.5, 9.0, 12.1, 14.8, 15.6, 16.5, 18.3, 19.0, 20.5, 22.1, 23.4, 24.8, 25.2, 26.9, 28.1])

# Create an interpolating function (cubic interpolation)
interp_func = interp1d(x, y, kind='linear')
interp_func1 = interp1d(x, y, kind='cubic')

# Generate new x values for interpolation
x_new = np.linspace(min(x), max(x), 100)

# Use the interpolating function to estimate y values at new x values
y_new = interp_func(x_new)
y_new1 = interp_func1(x_new)

# Plot the original data points and the interpolated curve
plt.scatter(x, y, color='red', label='Original Data (20 points)')
plt.plot(x_new, y_new, label='Linear Interpolation', color='blue')
plt.plot(x_new, y_new1, '--', label='Cubic Interpolation', color='red')
plt.legend()
plt.xlabel('x')
plt.ylabel('y')
plt.title('Interpolation with 20 Data Points')
plt.show()

Output 1

Introduction to Scipy

Interpolation