Lagrange interpolation

lagrange-interpolation.py

# Python3 program for implementation
# of Lagrange's Interpolation

# To represent a data point corresponding to x and y = f(x)
class Data:
	def __init__(self, x, y):
		self.x = x
		self.y = y

# function to interpolate the given data points
# using Lagrange's formula
# xi -> corresponds to the new data point
# whose value is to be obtained
# n -> represents the number of known data points
def interpolate(f: list, xi: int, n: int) -> float:

	# Initialize result
	result = 0.0
	for i in range(n):

		# Compute individual terms of above formula
		term = f[i].y
		for j in range(n):
			if j != i:
				term = term * (xi - f[j].x) / (f[i].x - f[j].x)

		# Add current term to result
		result += term

	return result

# Driver Code
if __name__ == "__main__":

	# creating an array of 4 known data points
	f = [Data(0, 2), Data(1, 3), Data(2, 12), Data(5, 147)]

	# Using the interpolate function to obtain a data point
	# corresponding to x=3
	print("Value of f(3) is :", interpolate(f, 3, 4))

# This code is contributed by
# sanjeev2552