谢谢!我正在尝试对一些数据拟合S形曲线,下面是我的代码
import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit
====== some code in between =======
plt.scatter(drag[0].w,drag[0].s, s = 10, label = 'drag%d'%0)
def sigmoid(x,x0,k):
y = 1.0/(1.0+np.exp(-x0*(x-k)))
return y
popt,pcov = curve_fit(sigmoid, drag[0].w, drag[0].s)
xx = np.linspace(10,1000,10)
yy = sigmoid(xx, *popt)
plt.plot(xx,yy,'r-', label='fit')
plt.legend(loc='upper left')
plt.xlabel('weight(kg)', fontsize=12)
plt.ylabel('wing span(m)', fontsize=12)
plt.show()
这现在显示下面的图形,它不太正确fitting curve is the red one at bottom
可能的解决方案是什么?
我也乐于接受其他在这组数据上拟合逻辑曲线的方法
再次感谢!
答案 0 :(得分:0)
这是一个示例图形拟合器,该方程式将您的方程式与幅度缩放因子一起用于我的测试数据。此代码使用scipy的差异进化遗传算法为curve_fit()提供初始参数估计,因为所有1.0的scipy默认初始参数估计都不总是最优的。差分进化的科学实现使用Latin Hypercube算法来确保对参数空间的彻底搜索,这需要在搜索范围内进行。在此示例中,这些边界取自我提供的示例数据,当使用您自己的数据时,请检查边界是否合理。请注意,参数的范围比初始参数估计的特定值要容易得多。
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([19.1647, 18.0189, 16.9550, 15.7683, 14.7044, 13.6269, 12.6040, 11.4309, 10.2987, 9.23465, 8.18440, 7.89789, 7.62498, 7.36571, 7.01106, 6.71094, 6.46548, 6.27436, 6.16543, 6.05569, 5.91904, 5.78247, 5.53661, 4.85425, 4.29468, 3.74888, 3.16206, 2.58882, 1.93371, 1.52426, 1.14211, 0.719035, 0.377708, 0.0226971, -0.223181, -0.537231, -0.878491, -1.27484, -1.45266, -1.57583, -1.61717])
yData = numpy.array([0.644557, 0.641059, 0.637555, 0.634059, 0.634135, 0.631825, 0.631899, 0.627209, 0.622516, 0.617818, 0.616103, 0.613736, 0.610175, 0.606613, 0.605445, 0.603676, 0.604887, 0.600127, 0.604909, 0.588207, 0.581056, 0.576292, 0.566761, 0.555472, 0.545367, 0.538842, 0.529336, 0.518635, 0.506747, 0.499018, 0.491885, 0.484754, 0.475230, 0.464514, 0.454387, 0.444861, 0.437128, 0.415076, 0.401363, 0.390034, 0.378698])
def sigmoid(x, amplitude, x0, k):
return amplitude * 1.0/(1.0+numpy.exp(-x0*(x-k)))
# function for genetic algorithm to minimize (sum of squared error)
def sumOfSquaredError(parameterTuple):
warnings.filterwarnings("ignore") # do not print warnings by genetic algorithm
val = sigmoid(xData, *parameterTuple)
return numpy.sum((yData - val) ** 2.0)
def generate_Initial_Parameters():
# min and max used for bounds
maxX = max(xData)
minX = min(xData)
maxY = max(yData)
minY = min(yData)
parameterBounds = []
parameterBounds.append([minY, maxY]) # search bounds for amplitude
parameterBounds.append([minX, maxX]) # search bounds for x0
parameterBounds.append([minX, maxX]) # search bounds for k
# "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(sigmoid, xData, yData, geneticParameters)
print('Fitted parameters:', fittedParameters)
print()
modelPredictions = sigmoid(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 = sigmoid(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)