Python 用 numpy 拟合数据
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fitting data with numpy
提问by ezitoc
Let me start by telling that what I get may not be what I expect and perhaps you can help me here. I have the following data:
让我首先告诉我我得到的可能不是我所期望的，也许你可以在这里帮助我。我有以下数据：
>>> x
array([ 3.08, 3.1 , 3.12, 3.14, 3.16, 3.18, 3.2 , 3.22, 3.24,
3.26, 3.28, 3.3 , 3.32, 3.34, 3.36, 3.38, 3.4 , 3.42,
3.44, 3.46, 3.48, 3.5 , 3.52, 3.54, 3.56, 3.58, 3.6 ,
3.62, 3.64, 3.66, 3.68])
>>> y
array([ 0.000857, 0.001182, 0.001619, 0.002113, 0.002702, 0.003351,
0.004062, 0.004754, 0.00546 , 0.006183, 0.006816, 0.007362,
0.007844, 0.008207, 0.008474, 0.008541, 0.008539, 0.008445,
0.008251, 0.007974, 0.007608, 0.007193, 0.006752, 0.006269,
0.005799, 0.005302, 0.004822, 0.004339, 0.00391 , 0.003481,
0.003095])
Now, I want to fit these data with, say, a 4 degree polynomial. So I do:
现在，我想用 4 度多项式拟合这些数据。所以我这样做：
>>> coefs = np.polynomial.polynomial.polyfit(x, y, 4)
>>> ffit = np.poly1d(coefs)
Now I create a new grid for x values to evaluate the fitting function ffit:
现在我为 x 值创建一个新网格来评估拟合函数ffit：
>>> x_new = np.linspace(x[0], x[-1], num=len(x)*10)
When I do all the plotting (data set and fitting curve) with the command:
当我使用以下命令进行所有绘图（数据集和拟合曲线）时：
>>> fig1 = plt.figure()
>>> ax1 = fig1.add_subplot(111)
>>> ax1.scatter(x, y, facecolors='None')
>>> ax1.plot(x_new, ffit(x_new))
>>> plt.show()
I get the following:
我得到以下信息：
What I expect is the fitting function to fit correctly (at least near the maximum value of the data). What am I doing wrong?
我期望的是拟合函数正确拟合（至少接近数据的最大值）。我究竟做错了什么？
Thanks in advance.
提前致谢。
采纳答案by askewchan
Unfortunately, np.polynomial.polynomial.polyfitreturns the coefficients in the opposite order of that for np.polyfitand np.polyval(or, as you used np.poly1d). To illustrate:
不幸的是，np.polynomial.polynomial.polyfit返回系数的顺序与 fornp.polyfit和np.polyval（或，如您使用的那样np.poly1d）的顺序相反。为了显示：
In [40]: np.polynomial.polynomial.polyfit(x, y, 4)
Out[40]:
array([ 84.29340848, -100.53595376, 44.83281408, -8.85931101,
0.65459882])
In [41]: np.polyfit(x, y, 4)
Out[41]:
array([ 0.65459882, -8.859311 , 44.83281407, -100.53595375,
84.29340846])
In general: np.polynomial.polynomial.polyfitreturns coefficients [A, B, C]to A + Bx + Cx^2 + ..., while np.polyfitreturns: ... + Ax^2 + Bx + C.
通常：np.polynomial.polynomial.polyfit将系数返回[A, B, C]到A + Bx + Cx^2 + ...，而np.polyfit返回：... + Ax^2 + Bx + C。
So if you want to use this combination of functions, you must reverse the order of coefficients, as in:
因此，如果要使用这种函数组合，则必须颠倒系数的顺序，如下所示：
ffit = np.polyval(coefs[::-1], x_new)
However, the documentationstates clearly to avoid np.polyfit, np.polyval, and np.poly1d, and instead to use only the new(er) package.
但是，文档明确指出要避免np.polyfit,np.polyval和np.poly1d, 而是仅使用 new(er) 包。
You're safest to use only the polynomial package:
只使用 polynomial 包是最安全的：
import numpy.polynomial.polynomial as poly
coefs = poly.polyfit(x, y, 4)
ffit = poly.polyval(x_new, coefs)
plt.plot(x_new, ffit)
Or, to create the polynomial function:
或者，创建多项式函数：
ffit = poly.Polynomial(coefs) # instead of np.poly1d
plt.plot(x_new, ffit(x_new))
回答by Charles Harris
Note that you can use the Polynomial class directly to do the fitting and return a Polynomial instance.
请注意，您可以直接使用 Polynomial 类进行拟合并返回 Polynomial 实例。
from numpy.polynomial import Polynomial
p = Polynomial.fit(x, y, 4)
plt.plot(*p.linspace())
puses scaled and shifted x values for numerical stability. If you need the usual form of the coefficients, you will need to follow with
p使用缩放和移位的 x 值来保证数值稳定性。如果您需要系数的通常形式，则需要遵循
pnormal = p.convert(domain=(-1, 1))
