mirror of
https://hub.njuu.cf/TheAlgorithms/Python.git
synced 2023-10-11 13:06:12 +08:00
4f2a346c27
* Reduce the complexity of linear_algebra/src/polynom_for_points.py * updating DIRECTORY.md * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * Fix * Fix review issues --------- Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com> Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com>
98 lines
3.7 KiB
Python
98 lines
3.7 KiB
Python
def points_to_polynomial(coordinates: list[list[int]]) -> str:
|
|
"""
|
|
coordinates is a two dimensional matrix: [[x, y], [x, y], ...]
|
|
number of points you want to use
|
|
|
|
>>> print(points_to_polynomial([]))
|
|
Traceback (most recent call last):
|
|
...
|
|
ValueError: The program cannot work out a fitting polynomial.
|
|
>>> print(points_to_polynomial([[]]))
|
|
Traceback (most recent call last):
|
|
...
|
|
ValueError: The program cannot work out a fitting polynomial.
|
|
>>> print(points_to_polynomial([[1, 0], [2, 0], [3, 0]]))
|
|
f(x)=x^2*0.0+x^1*-0.0+x^0*0.0
|
|
>>> print(points_to_polynomial([[1, 1], [2, 1], [3, 1]]))
|
|
f(x)=x^2*0.0+x^1*-0.0+x^0*1.0
|
|
>>> print(points_to_polynomial([[1, 3], [2, 3], [3, 3]]))
|
|
f(x)=x^2*0.0+x^1*-0.0+x^0*3.0
|
|
>>> print(points_to_polynomial([[1, 1], [2, 2], [3, 3]]))
|
|
f(x)=x^2*0.0+x^1*1.0+x^0*0.0
|
|
>>> print(points_to_polynomial([[1, 1], [2, 4], [3, 9]]))
|
|
f(x)=x^2*1.0+x^1*-0.0+x^0*0.0
|
|
>>> print(points_to_polynomial([[1, 3], [2, 6], [3, 11]]))
|
|
f(x)=x^2*1.0+x^1*-0.0+x^0*2.0
|
|
>>> print(points_to_polynomial([[1, -3], [2, -6], [3, -11]]))
|
|
f(x)=x^2*-1.0+x^1*-0.0+x^0*-2.0
|
|
>>> print(points_to_polynomial([[1, 5], [2, 2], [3, 9]]))
|
|
f(x)=x^2*5.0+x^1*-18.0+x^0*18.0
|
|
"""
|
|
if len(coordinates) == 0 or not all(len(pair) == 2 for pair in coordinates):
|
|
raise ValueError("The program cannot work out a fitting polynomial.")
|
|
|
|
if len({tuple(pair) for pair in coordinates}) != len(coordinates):
|
|
raise ValueError("The program cannot work out a fitting polynomial.")
|
|
|
|
set_x = {x for x, _ in coordinates}
|
|
if len(set_x) == 1:
|
|
return f"x={coordinates[0][0]}"
|
|
|
|
if len(set_x) != len(coordinates):
|
|
raise ValueError("The program cannot work out a fitting polynomial.")
|
|
|
|
x = len(coordinates)
|
|
|
|
# put the x and x to the power values in a matrix
|
|
matrix: list[list[float]] = [
|
|
[
|
|
coordinates[count_of_line][0] ** (x - (count_in_line + 1))
|
|
for count_in_line in range(x)
|
|
]
|
|
for count_of_line in range(x)
|
|
]
|
|
|
|
# put the y values into a vector
|
|
vector: list[float] = [coordinates[count_of_line][1] for count_of_line in range(x)]
|
|
|
|
for count in range(x):
|
|
for number in range(x):
|
|
if count == number:
|
|
continue
|
|
fraction = matrix[number][count] / matrix[count][count]
|
|
for counting_columns, item in enumerate(matrix[count]):
|
|
# manipulating all the values in the matrix
|
|
matrix[number][counting_columns] -= item * fraction
|
|
# manipulating the values in the vector
|
|
vector[number] -= vector[count] * fraction
|
|
|
|
# make solutions
|
|
solution: list[str] = [
|
|
str(vector[count] / matrix[count][count]) for count in range(x)
|
|
]
|
|
|
|
solved = "f(x)="
|
|
|
|
for count in range(x):
|
|
remove_e: list[str] = solution[count].split("E")
|
|
if len(remove_e) > 1:
|
|
solution[count] = f"{remove_e[0]}*10^{remove_e[1]}"
|
|
solved += f"x^{x - (count + 1)}*{solution[count]}"
|
|
if count + 1 != x:
|
|
solved += "+"
|
|
|
|
return solved
|
|
|
|
|
|
if __name__ == "__main__":
|
|
print(points_to_polynomial([]))
|
|
print(points_to_polynomial([[]]))
|
|
print(points_to_polynomial([[1, 0], [2, 0], [3, 0]]))
|
|
print(points_to_polynomial([[1, 1], [2, 1], [3, 1]]))
|
|
print(points_to_polynomial([[1, 3], [2, 3], [3, 3]]))
|
|
print(points_to_polynomial([[1, 1], [2, 2], [3, 3]]))
|
|
print(points_to_polynomial([[1, 1], [2, 4], [3, 9]]))
|
|
print(points_to_polynomial([[1, 3], [2, 6], [3, 11]]))
|
|
print(points_to_polynomial([[1, -3], [2, -6], [3, -11]]))
|
|
print(points_to_polynomial([[1, 5], [2, 2], [3, 9]]))
|