How to use curvefit in python

问题

I am studying nonlinear curvefit with python.
I made example like below.
But the optimized plot is not drawn well

plt.plot(basketCont, fittedData)

I guess the optimized parametes are not good also.
Could you give some recommends? Thank you.

import matplotlib
matplotlib.use('Qt4Agg')
import matplotlib.pyplot as plt
from matplotlib.pyplot import cm
import numpy as np
from scipy.optimize import curve_fit 

def func(x, a, b, c):
    return a - b* np.exp(c * x) 

baskets = np.array([475, 108, 2, 38, 320])
scaling_factor = np.array([95.5, 57.7, 1.4, 21.9, 88.8])

popt,pcov = curve_fit(func, baskets, scaling_factor)

print (popt)
print (pcov)

basketCont=np.linspace(min(baskets),max(baskets),50)
fittedData=[func(x, *popt) for x in basketCont]

fig1 = plt.figure(1)

plt.scatter(baskets, scaling_factor, s=5)
plt.plot(basketCont, fittedData)

plt.grid()

plt.show()

回答1:

I personally could not get a good fit to your data using the equation you posted, however the Hill sigmoidal equation gave a good fit. Here is the Python code for the graphical fitter I used.

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


baskets = numpy.array([475.0, 108.0, 2.0, 38.0, 320.0])
scaling_factor = numpy.array([95.5, 57.7, 1.4, 21.9, 88.8])

# rename data for simpler code re-use later
xData = baskets
yData = scaling_factor


def func(x, a, b, c): # Hill sigmoidal equation from zunzun.com
    return  a * numpy.power(x, b) / (numpy.power(c, b) + numpy.power(x, b)) 


# these are the same as the scipy defaults
initialParameters = numpy.array([1.0, 1.0, 1.0])

# do not print unnecessary warnings during curve_fit()
warnings.filterwarnings("ignore")

# curve fit the test data
fittedParameters, pcov = curve_fit(func, xData, yData, initialParameters)

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('Parameters:', fittedParameters)
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)

来源：https://stackoverflow.com/questions/55078451/how-to-use-curvefit-in-python