mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-11-23 21:11:08 +00:00
cecf43d648
* Pyupgrade to Python 3.9
* updating DIRECTORY.md
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>
58 lines
1.3 KiB
Python
58 lines
1.3 KiB
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()
|