6度曲线拟合与numpy / scipy

Question

我对使用6次多项式插值非线性数据有非常具体的要求。我见过numpy / scipy例程（scipy.interpolate.InterpolatedUnivariateSpline），只允许插入5度。

即使没有直接的功能，有没有办法在Python中复制Excel的LINEST线性回归算法？ LINEST允许6度曲线拟合，但我不想将Excel用于任何事情，因为这个计算是更大的Python脚本的一部分。

任何帮助将不胜感激！

Answer 1

您可以使用scipy.optimize.curve_fit使您想要的任何功能（在合理范围内）适合您的数据。该功能的签名是

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

并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()

应该给你类似的东西：

Answer 2

使用numpys polyfit例程。

http://docs.scipy.org/doc/numpy-1.3.x/reference/generated/numpy.polyfit.html