Python/arithmetic_analysis/newton_forward_interpolation.py
Christian Clauss cecf43d648
Pyupgrade to Python 3.9 (#4718)
* Pyupgrade to Python 3.9

* updating DIRECTORY.md

Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
2021-09-07 13:37:03 +02:00

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Python

# https://www.geeksforgeeks.org/newton-forward-backward-interpolation/
from __future__ import annotations
import math
# for calculating u value
def ucal(u: float, p: int) -> float:
"""
>>> ucal(1, 2)
0
>>> ucal(1.1, 2)
0.11000000000000011
>>> ucal(1.2, 2)
0.23999999999999994
"""
temp = u
for i in range(1, p):
temp = temp * (u - i)
return temp
def main() -> None:
n = int(input("enter the numbers of values: "))
y: list[list[float]] = []
for i in range(n):
y.append([])
for i in range(n):
for j in range(n):
y[i].append(j)
y[i][j] = 0
print("enter the values of parameters in a list: ")
x = list(map(int, input().split()))
print("enter the values of corresponding parameters: ")
for i in range(n):
y[i][0] = float(input())
value = int(input("enter the value to interpolate: "))
u = (value - x[0]) / (x[1] - x[0])
# for calculating forward difference table
for i in range(1, n):
for j in range(n - i):
y[j][i] = y[j + 1][i - 1] - y[j][i - 1]
summ = y[0][0]
for i in range(1, n):
summ += (ucal(u, i) * y[0][i]) / math.factorial(i)
print(f"the value at {value} is {summ}")
if __name__ == "__main__":
main()