mirror of
https://github.com/TheAlgorithms/Python.git
synced 2024-12-22 11:10:14 +00:00
4700297b3e
* Enable ruff RUF002 rule * Fix --------- Co-authored-by: Christian Clauss <cclauss@me.com>
56 lines
1.8 KiB
Python
56 lines
1.8 KiB
Python
"""
|
|
Python program to show how to interpolate and evaluate a polynomial
|
|
using Neville's method.
|
|
Neville's method evaluates a polynomial that passes through a
|
|
given set of x and y points for a particular x value (x0) using the
|
|
Newton polynomial form.
|
|
Reference:
|
|
https://rpubs.com/aaronsc32/nevilles-method-polynomial-interpolation
|
|
"""
|
|
|
|
|
|
def neville_interpolate(x_points: list, y_points: list, x0: int) -> list:
|
|
"""
|
|
Interpolate and evaluate a polynomial using Neville's method.
|
|
Arguments:
|
|
x_points, y_points: Iterables of x and corresponding y points through
|
|
which the polynomial passes.
|
|
x0: The value of x to evaluate the polynomial for.
|
|
Return Value: A list of the approximated value and the Neville iterations
|
|
table respectively.
|
|
>>> import pprint
|
|
>>> neville_interpolate((1,2,3,4,6), (6,7,8,9,11), 5)[0]
|
|
10.0
|
|
>>> pprint.pprint(neville_interpolate((1,2,3,4,6), (6,7,8,9,11), 99)[1])
|
|
[[0, 6, 0, 0, 0],
|
|
[0, 7, 0, 0, 0],
|
|
[0, 8, 104.0, 0, 0],
|
|
[0, 9, 104.0, 104.0, 0],
|
|
[0, 11, 104.0, 104.0, 104.0]]
|
|
>>> neville_interpolate((1,2,3,4,6), (6,7,8,9,11), 99)[0]
|
|
104.0
|
|
>>> neville_interpolate((1,2,3,4,6), (6,7,8,9,11), '')
|
|
Traceback (most recent call last):
|
|
...
|
|
TypeError: unsupported operand type(s) for -: 'str' and 'int'
|
|
"""
|
|
n = len(x_points)
|
|
q = [[0] * n for i in range(n)]
|
|
for i in range(n):
|
|
q[i][1] = y_points[i]
|
|
|
|
for i in range(2, n):
|
|
for j in range(i, n):
|
|
q[j][i] = (
|
|
(x0 - x_points[j - i + 1]) * q[j][i - 1]
|
|
- (x0 - x_points[j]) * q[j - 1][i - 1]
|
|
) / (x_points[j] - x_points[j - i + 1])
|
|
|
|
return [q[n - 1][n - 1], q]
|
|
|
|
|
|
if __name__ == "__main__":
|
|
import doctest
|
|
|
|
doctest.testmod()
|