lagrange.py

import numpy as np
import matplotlib.pyplot as plt

def lagrange_interpolation(x_data, y_data, x_val):
  """
  This function performs Lagrange polynomial interpolation for a given set of data points.

  Args:
      x_data: A list or numpy array containing the x-coordinates of the data points.
      y_data: A list or numpy array containing the corresponding y-values of the data points.
      x_val: The value at which to evaluate the interpolated polynomial.

  Returns:
      The interpolated value of the function at x_val.
  """
  n = len(x_data)
  result = 0
  for i in range(n):
    basis_poly = 1
    for j in range(n):
      if j != i:
        basis_poly *= (x_val - x_data[j]) / (x_data[i] - x_data[j])
    result += y_data[i] * basis_poly
  return result

def plot_interpolation(x_data, y_data, x_range):
  """
  This function plots the original data points and the interpolated polynomial.

  Args:
      x_data: A list or numpy array containing the x-coordinates of the data points.
      y_data: A list or numpy array containing the corresponding y-values of the data points.
      x_range: A tuple containing the minimum and maximum values for the x-axis.
  """
  # Generate interpolated points
  x_interp = np.linspace(x_range[0], x_range[1], 100)  # Adjust number of points as needed
  y_interp = [lagrange_interpolation(x_data, y_data, x) for x in x_interp]

  # Plot data points and interpolated function
  plt.plot(x_data, y_data, 'o', label='Data Points')
  plt.plot(x_interp, y_interp, label='Interpolated Polynomial')

  # Set labels and title
  plt.xlabel("X")
  plt.ylabel("Y")
  plt.title("Lagrange Polynomial Interpolation")
  plt.legend()
  plt.grid(True)
  plt.show()

# Example usage
x_data = np.array([0, 0.5, 1, 1.5, 2, 2.5, 3, 3.5, 4, 4.5, 5, 5.5, 6, 6.5, 7, 7.5, 8, 8.5, 9, 9.5, 10, 10.5, 11, 11.5, 12, 12.5, 13, 13.5, 14, 14.5, 14.875])  # Replace with your data points
y_data = np.array([0.44, 1.5, 2.875, 4.125, 5.5, 6.875, 8.25, 9.25, 9.375, 9.25, 8.75, 8, 7.375, 6.875, 6.375, 6.375, 6.625, 7.25, 8, 8.25, 7.5, 5.625, 5.25, 5, 5, 5.125, 5.625, 6.375, 7, 7.5, 8.25])  # Replace with your function values at x_data points

# Define x-axis range for plotting
x_range = (min(x_data), max(x_data))

# Calculate interpolated points and plot
plot_interpolation(x_data, y_data, x_range)