Python 使用numpy/scipy进行六次曲线拟合

我对使用6次多项式插值非线性数据有一个非常具体的要求。我见过numpy/scipy例程（scipy.interpolate.InterpolatedUnivariateSpline），它只允许5次以内的插值

即使没有直接函数来实现这一点，有没有办法在Python中复制Excel的LINEST线性回归算法？LINEST允许6次曲线拟合，但我不想使用Excel进行任何操作，因为此计算是更大Python脚本的一部分

任何帮助都将不胜感激

您可以使用它（在合理的范围内）将您想要的任何函数适配到您的数据中。此函数的签名是

curve_fit(f, xdata, ydata, p0=None, sigma=None, **kw)

它使用非线性最小二乘拟合将函数

f

拟合到数据

ydata（xdata）

。在你的情况下，我会尝试以下方法：

import numpy
from scipy.optimize import curve_fit
import matplotlib.pyplot as plt

def _polynomial(x, *p):
    """Polynomial fitting function of arbitrary degree."""
    poly = 0.
    for i, n in enumerate(p):
        poly += n * x**i
    return poly

# Define some test data:
x = numpy.linspace(0., numpy.pi)
y = numpy.cos(x) + 0.05 * numpy.random.normal(size=len(x))

# p0 is the initial guess for the fitting coefficients, set the length
# of this to be the order of the polynomial you want to fit. Here I
# have set all the initial guesses to 1., you may have a better idea of
# what values to expect based on your data.
p0 = numpy.ones(6,)

coeff, var_matrix = curve_fit(_polynomial, x, y, p0=p0)

yfit = [_polynomial(xx, *tuple(coeff)) for xx in x] # I'm sure there is a better
                                                    # way of doing this

plt.plot(x, y, label='Test data')
plt.plot(x, yfit, label='fitted data')

plt.show()

这会给你一些类似的东西：

import numpy
from scipy.optimize import curve_fit
import matplotlib.pyplot as plt

def _polynomial(x, *p):
    """Polynomial fitting function of arbitrary degree."""
    poly = 0.
    for i, n in enumerate(p):
        poly += n * x**i
    return poly

# Define some test data:
x = numpy.linspace(0., numpy.pi)
y = numpy.cos(x) + 0.05 * numpy.random.normal(size=len(x))

# p0 is the initial guess for the fitting coefficients, set the length
# of this to be the order of the polynomial you want to fit. Here I
# have set all the initial guesses to 1., you may have a better idea of
# what values to expect based on your data.
p0 = numpy.ones(6,)

coeff, var_matrix = curve_fit(_polynomial, x, y, p0=p0)

yfit = [_polynomial(xx, *tuple(coeff)) for xx in x] # I'm sure there is a better
                                                    # way of doing this

plt.plot(x, y, label='Test data')
plt.plot(x, yfit, label='fitted data')

plt.show()

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使用numpys polyfit例行程序

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我不敢相信我以前没有想到这一点！谢谢：）+1我简直不敢相信我写出了一个不必要的复杂示例，竟然忘记了

polyfit

例程！您可以使用

yfit=_多项式（xx，*coeff）

，还请注意，对于0次多项式，p0的长度至少应为1。