Closure to create an interpolator function

lagrange.py

"""
Closure to create an interpolator function.
Bruce Wernick
13 August 2025
"""

def lagrange(xp, yp):
  n = len(xp)
  def inner(x):
    value = 0.0
    for j in range(n):
      L = 1.0
      for k in range(n):
        if k != j:
          L *= (x - xp[k]) / (xp[j] - xp[k])
      value += yp[j] * L
    return value
  return inner

# given a sample data set X and Y.
X = [1,2,3,4,5]
Y = [2,4,6,8,10]
f = lagrange(X, Y)  # get the interp function.

# Now, we can just call y = f(x)
# like any other function
x = 2.2
y = f(x)
print(f"x = {x}\ny = f({x}) = {y}")


# Plot the interpolated values with matplotlib
import matplotlib.pyplot as plt
import numpy as np
x = np.linspace(1, 5, 20)
#y = f(x)  # <-- use the interp function f(x)
plt.plot(x, f(x))  # use y or f(x) directly.
plt.show()