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a8b6bda993
* Remove eval from arithmetic_analysis/newton_raphson.py
* Relocate contents of arithmetic_analysis/
Delete the arithmetic_analysis/ directory and relocate its files because
the purpose of the directory was always ill-defined. "Arithmetic
analysis" isn't a field of math, and the directory's files contained
algorithms for linear algebra, numerical analysis, and physics.
Relocated the directory's linear algebra algorithms to linear_algebra/,
its numerical analysis algorithms to a new subdirectory called
maths/numerical_analysis/, and its single physics algorithm to physics/.
* 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/
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from __future__ import annotations
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import math
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# for calculating u value
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def ucal(u: float, p: int) -> float:
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"""
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>>> ucal(1, 2)
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0
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>>> ucal(1.1, 2)
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0.11000000000000011
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>>> ucal(1.2, 2)
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0.23999999999999994
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"""
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temp = u
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for i in range(1, p):
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temp = temp * (u - i)
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return temp
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def main() -> None:
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n = int(input("enter the numbers of values: "))
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y: list[list[float]] = []
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for _ in range(n):
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y.append([])
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for i in range(n):
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for j in range(n):
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y[i].append(j)
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y[i][j] = 0
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print("enter the values of parameters in a list: ")
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x = list(map(int, input().split()))
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print("enter the values of corresponding parameters: ")
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for i in range(n):
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y[i][0] = float(input())
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value = int(input("enter the value to interpolate: "))
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u = (value - x[0]) / (x[1] - x[0])
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# for calculating forward difference table
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for i in range(1, n):
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for j in range(n - i):
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y[j][i] = y[j + 1][i - 1] - y[j][i - 1]
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summ = y[0][0]
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for i in range(1, n):
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summ += (ucal(u, i) * y[0][i]) / math.factorial(i)
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print(f"the value at {value} is {summ}")
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if __name__ == "__main__":
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main()
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