iframe-proxy | Sunbelt Computer Software

History

103 lines (89 loc) · 3.84 KB

Raw

100

101

102

103

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

>>> points_to_polynomial([])

Traceback (most recent call last):

...

ValueError: The program cannot work out a fitting polynomial.

>>> points_to_polynomial([[]])

Traceback (most recent call last):

...

ValueError: The program cannot work out a fitting polynomial.

>>> points_to_polynomial([[1, 0], [2, 0], [3, 0]])

'f(x)=x^2*0.0+x^1*-0.0+x^0*0.0'

>>> points_to_polynomial([[1, 1], [2, 1], [3, 1]])

'f(x)=x^2*0.0+x^1*-0.0+x^0*1.0'

>>> points_to_polynomial([[1, 3], [2, 3], [3, 3]])

'f(x)=x^2*0.0+x^1*-0.0+x^0*3.0'

>>> points_to_polynomial([[1, 1], [2, 2], [3, 3]])

'f(x)=x^2*0.0+x^1*1.0+x^0*0.0'

>>> points_to_polynomial([[1, 1], [2, 4], [3, 9]])

'f(x)=x^2*1.0+x^1*-0.0+x^0*0.0'

>>> points_to_polynomial([[1, 3], [2, 6], [3, 11]])

'f(x)=x^2*1.0+x^1*-0.0+x^0*2.0'

>>> points_to_polynomial([[1, -3], [2, -6], [3, -11]])

'f(x)=x^2*-1.0+x^1*-0.0+x^0*-2.0'

>>> points_to_polynomial([[1, 5], [2, 2], [3, 9]])

'f(x)=x^2*5.0+x^1*-18.0+x^0*18.0'

>>> points_to_polynomial([[1, 1], [1, 2], [1, 3]])

'x=1'

>>> points_to_polynomial([[1, 1], [2, 2], [2, 2]])

Traceback (most recent call last):

...

ValueError: The program cannot work out a fitting polynomial.

"""

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]]))

Sunbelt Computer Software

PL/B Language Development and Support

Navigation Menu

Sunbelt Computer Software

PL/B Language Development and Support

FilesExpand file tree

polynom_for_points.py

Latest commit

History

polynom_for_points.py

File metadata and controls