待拟合函数 y = alpha * pow(x, beta)

输入： x数组，y数组

输出： alpha，beta，相关系数R2

from scipy.optimize import leastsq
from pylab import *
import numpy as np

xdata = np.array([4.79616, 11.63, 37.5534, 105.414])

ydata = np.array([1.33921, 0.755319, 0.34085, 0.0554339])

Define function for calculating a power law

powerlaw = lambda x, alpha, beta: alpha * (x ** beta)
logx = log10(xdata)
logy = log10(ydata)

define our (line) fitting function

fitfunc = lambda p, x: p[0] + p[1] * x
errfunc = lambda p, x, y: (y - fitfunc(p, x))

pinit = [1.0, -1.0]
out, cov, infodict, mesg, ier = leastsq(errfunc, pinit,
args = (logx, logy), full_output=1)

beta = out[1]
alpha = 10.0 ** out[0]

ss_err = (infodict['fvec'] ** 2).sum()
ss_tot = ((ydata - ydata.mean()) ** 2).sum()
r2 = 1 - (ss_err / ss_tot)

print('Alpha: %f, Beta: %f' % (alpha, beta))
print ('R2: %f' % r2)