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55 lines
1.6 KiB
Python
55 lines
1.6 KiB
Python
from typing import Sequence
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def evaluate_poly(poly: Sequence[float], x: float) -> float:
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"""Evaluate a polynomial f(x) at specified point x and return the value.
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Arguments:
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poly -- the coefficients of a polynomial as an iterable in order of
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ascending degree
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x -- the point at which to evaluate the polynomial
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>>> evaluate_poly((0.0, 0.0, 5.0, 9.3, 7.0), 10.0)
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79800.0
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"""
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return sum(c * (x**i) for i, c in enumerate(poly))
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def horner(poly: Sequence[float], x: float) -> float:
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"""Evaluate a polynomial at specified point using Horner's method.
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In terms of computational complexity, Horner's method is an efficient method
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of evaluating a polynomial. It avoids the use of expensive exponentiation,
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and instead uses only multiplication and addition to evaluate the polynomial
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in O(n), where n is the degree of the polynomial.
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https://en.wikipedia.org/wiki/Horner's_method
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Arguments:
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poly -- the coefficients of a polynomial as an iterable in order of
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ascending degree
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x -- the point at which to evaluate the polynomial
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>>> horner((0.0, 0.0, 5.0, 9.3, 7.0), 10.0)
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79800.0
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"""
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result = 0.0
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for coeff in reversed(poly):
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result = result * x + coeff
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return result
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if __name__ == "__main__":
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"""
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Example:
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>>> poly = (0.0, 0.0, 5.0, 9.3, 7.0) # f(x) = 7.0x^4 + 9.3x^3 + 5.0x^2
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>>> x = -13.0
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>>> # f(-13) = 7.0(-13)^4 + 9.3(-13)^3 + 5.0(-13)^2 = 180339.9
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>>> print(evaluate_poly(poly, x))
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180339.9
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"""
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poly = (0.0, 0.0, 5.0, 9.3, 7.0)
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x = 10.0
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print(evaluate_poly(poly, x))
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print(horner(poly, x))
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