求解已知y的多项式的x值

Question

我正在尝试求解已知y的x值。我能够得到适合我的数据的多项式，现在我想知道所选y在曲线上的x值。

import numpy as np
x = [50, 25, 12.5, 6.25, 0.625, 0.0625, 0.01]
y = [0.00, 0.50, 0.68, 0.77, 0.79, 0.90, 1.00]
poly_coeffs = np.polyfit(x, y, 3)
f = np.poly1d(poly_coeffs)

我想用0.5 = f求出x的值

我可以解决这个问题在WolframAlpha输入:

0.5 = -9.1e-6*x^3 + 5.9e-4*x^2 - 2.5e-2*x + 9.05e-1

实际x值为~26

Answer 1

In [1]: from numpy.polynomial import Polynomial as P
In [2]: x = [50, 25, 12.5, 6.25, 0.625, 0.0625, 0.01]
In [3]: y = [0.00, 0.50, 0.68, 0.77, 0.79, 0.90, 1.00]
In [4]: p = P.fit(x, y, 3)
In [5]: (p - .5).roots()
Out[5]: 
array([ 19.99806935-37.92449551j,  19.99806935+37.92449551j,
        25.36882693 +0.j        ])

看起来你想要的根是25.36882693

Answer 2

可以用np.roots来解方程f(x) - y = 0。考虑以下函数:

def solve_for_y(poly_coeffs, y):
    pc = poly_coeffs.copy()
    pc[-1] -= y
    return np.roots(pc)

然后你可以用它来解你想要的任何y的多项式:

>>> print solve_for_y(poly_coeffs, 0.5)
[ 19.99806935+37.92449551j  19.99806935-37.92449551j  25.36882693 +0.j        ]
>>> print solve_for_y(poly_coeffs, 1.)
[ 40.85615395+50.1936152j  40.85615395-50.1936152j -16.34734226 +0.j       ]