我希望对数函数适合对数的数据。
不幸的是,我收到以下错误:无法估计参数的协方差
如何防止这种情况?
import numpy as np
import scipy.optimize as opt
import matplotlib.pyplot as plt
x = [0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0, 11.0, 12.0, 13.0, 14.0]
y = [0.073, 2.521, 15.879, 48.365, 72.68, 90.298, 92.111, 93.44, 93.439, 93.389, 93.381, 93.367, 93.94, 93.269, 96.376]
def f(x, a, b, c, d):
return a / (1. + np.exp(-c * (x - d))) + b
(a_, b_, c_, d_), _ = opt.curve_fit(f, x, y)
y_fit = f(x, a_, b_, c_, d_)
fig, ax = plt.subplots(1, 1, figsize=(6, 4))
ax.plot(x, y, 'o')
ax.plot(x, y_fit, '-')
答案 0 :(得分:2)
这是您数据和方程式的图形拟合器,使用scipy的差异进化遗传算法进行初始参数估计。 scipy实现使用Latin Hypercube算法来确保对参数空间进行彻底的搜索,这需要在搜索范围内进行搜索-从代码中可以看到,这些范围可以很宽泛,并且更容易为初始参数估计值比要给出特定值。
import numpy, scipy, matplotlib
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit
from scipy.optimize import differential_evolution
import warnings
xData = numpy.array([0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0, 7.0, 8.0, 9.0, 10.0, 11.0, 12.0, 13.0, 14.0])
yData = numpy.array([0.073, 2.521, 15.879, 48.365, 72.68, 90.298, 92.111, 93.44, 93.439, 93.389, 93.381, 93.367, 93.94, 93.269, 96.376])
def func(x, a, b, c, d):
return a / (1.0 + numpy.exp(-c * (x - d))) + b
# function for genetic algorithm to minimize (sum of squared error)
def sumOfSquaredError(parameterTuple):
warnings.filterwarnings("ignore") # do not print warnings by genetic algorithm
val = func(xData, *parameterTuple)
return numpy.sum((yData - val) ** 2.0)
def generate_Initial_Parameters():
parameterBounds = []
parameterBounds.append([0.0, 100.0]) # search bounds for a
parameterBounds.append([-10.0, 0.0]) # search bounds for b
parameterBounds.append([0.0, 10.0]) # search bounds for c
parameterBounds.append([0.0, 10.0]) # search bounds for d
# "seed" the numpy random number generator for repeatable results
result = differential_evolution(sumOfSquaredError, parameterBounds, seed=3)
return result.x
# by default, differential_evolution completes by calling curve_fit() using parameter bounds
geneticParameters = generate_Initial_Parameters()
# now call curve_fit without passing bounds from the genetic algorithm,
# just in case the best fit parameters are aoutside those bounds
fittedParameters, pcov = curve_fit(func, xData, yData, geneticParameters)
print('Fitted parameters:', fittedParameters)
print()
modelPredictions = func(xData, *fittedParameters)
absError = modelPredictions - yData
SE = numpy.square(absError) # squared errors
MSE = numpy.mean(SE) # mean squared errors
RMSE = numpy.sqrt(MSE) # Root Mean Squared Error, RMSE
Rsquared = 1.0 - (numpy.var(absError) / numpy.var(yData))
print()
print('RMSE:', RMSE)
print('R-squared:', Rsquared)
print()
##########################################################
# graphics output section
def ModelAndScatterPlot(graphWidth, graphHeight):
f = plt.figure(figsize=(graphWidth/100.0, graphHeight/100.0), dpi=100)
axes = f.add_subplot(111)
# first the raw data as a scatter plot
axes.plot(xData, yData, 'D')
# create data for the fitted equation plot
xModel = numpy.linspace(min(xData), max(xData))
yModel = func(xModel, *fittedParameters)
# now the model as a line plot
axes.plot(xModel, yModel)
axes.set_xlabel('X Data') # X axis data label
axes.set_ylabel('Y Data') # Y axis data label
plt.show()
plt.close('all') # clean up after using pyplot
graphWidth = 800
graphHeight = 600
ModelAndScatterPlot(graphWidth, graphHeight)
答案 1 :(得分:1)
经过几次尝试,我发现与您的数据的协方差的计算存在问题。我尝试删除0.0,以防万一,但这不是原因。
我发现的唯一选择是将计算方法从lm更改为trf:
x = np.array(x)
y = np.array(y)
popt, pcov = opt.curve_fit(f, x, y, method="trf")
y_fit = f(x, *popt)
fig, ax = plt.subplots(1, 1, figsize=(6, 4))
ax.plot(x, y, 'o')
ax.plot(x, y_fit, '-')
plt.show()
并且曲线与这些参数[96.2823169 -2.38876852 1.39927921 2.98341838]
答案 2 :(得分:0)
我在Python2.7内核下尝试了您的代码。我没有收到您提到的错误。对于x的所有值,唯一的事情是y_fit = 71.50186844。