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maths/polynomial_evaluation.py
54 строки
2 KB
Caeden Perelli-Harris
Remove useless code in doctests (#7733)
27 окт 2022, 23:52
Не верифицирован
27 окт 2022, 23:52
61eedc1
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from collections.abc import Sequence def evaluate_poly(poly: Sequence[float], x: float) -> float: """Evaluate a polynomial f(x) at specified point x and return the value. Arguments: poly -- the coefficients of a polynomial as an iterable in order of ascending degree x -- the point at which to evaluate the polynomial >>> evaluate_poly((0.0, 0.0, 5.0, 9.3, 7.0), 10.0) 79800.0 """ return sum(c * (x**i) for i, c in enumerate(poly)) def horner(poly: Sequence[float], x: float) -> float: """Evaluate a polynomial at specified point using Horner's method. In terms of computational complexity, Horner's method is an efficient method of evaluating a polynomial. It avoids the use of expensive exponentiation, and instead uses only multiplication and addition to evaluate the polynomial in O(n), where n is the degree of the polynomial. https://en.wikipedia.org/wiki/Horner's_method Arguments: poly -- the coefficients of a polynomial as an iterable in order of ascending degree x -- the point at which to evaluate the polynomial >>> horner((0.0, 0.0, 5.0, 9.3, 7.0), 10.0) 79800.0 """ result = 0.0 for coeff in reversed(poly): result = result * x + coeff return result if __name__ == "__main__": """ Example: >>> poly = (0.0, 0.0, 5.0, 9.3, 7.0) # f(x) = 7.0x^4 + 9.3x^3 + 5.0x^2 >>> x = -13.0 >>> # f(-13) = 7.0(-13)^4 + 9.3(-13)^3 + 5.0(-13)^2 = 180339.9 >>> evaluate_poly(poly, x) 180339.9 """ poly = (0.0, 0.0, 5.0, 9.3, 7.0) x = 10.0 print(evaluate_poly(poly, x)) print(horner(poly, x))