maximzayats / approximation

Approximation of points by a polynomial of arbitrary power

approximation

Approximation of points by a polynomial of arbitrary power

Usage

Main functions:

1. approximate

   • Arguments:

     1. x: list — coordinates of points on the x-axis
     2. y: list — coordinates of points on the x-axis
     3. p: int — power of the polynomial

   • Returns:

     1. polynomial_coefficients: list
        The obtained coefficients are from the smallest to the largest power.
        Example:
        If you get these coefficients: [2.0, 3.0, 4.0]
        This means that the polynom will look like this:
        2x^0 + 3x^1 + 4x^2
        

   • Notes:

     1. len(x) == len(y) must be True.
        Else you will get an error!
2. create_polynom

   • Argument:

     1. polynomial_coefficients: list coefficients of the polynom.
        Obtained from the approximate

   • Returns:

     1. A polynom.
        Example: 4x^2 + 3x^1 + 2

Code Example:

from approximation import create_polynom, approximate


if __name__ == "__main__":
    print("Some example cases:")

    x = [1, 2, 3]
    y = [2, 5, 10]
    p = 2
    print(f"\nCase 1:\nx = {x},\ny = {y},\np = {p}\nPolynom: {create_polynom( approximate(x, y, p) )}")

    x = [-2, -1, 0, 1, 2]
    y = [0, 5, 0, 10, 4]
    p = 4
    print(f"\nCase 2:\nx = {x},\ny = {y},\np = {p}\nPolynom: {create_polynom( approximate(x, y, p) )}")

    x = [-3, -2, -1, 0, 1, 2]
    y = [-10, 0, 5, 0, 10, 4]
    p = 5
    print(f"\nCase 3:\nx = {x},\ny = {y},\np = {p}\nPolynom: {create_polynom( approximate(x, y, p) )}")