如何使用Scipy优化曲线与熊猫df拟合

Question

这是我在这里的第一篇文章，我花了数小时来寻找答案，但似乎无法弄清楚。我使用了熊猫将.csv传递给np矩阵。从那里，我尝试应用简单的曲线拟合，但是我得到的输出始终是错误的。代码将绘制错误的拟合，并且不会绘制数据。

import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit

df = pd.read_csv("Results.csv")
xdata = df['Frame'].as_matrix()
ydata = df['Area'].as_matrix()

def func(x, a, b, c):
    return (a*np.sin(b*x))+(c * np.exp(x))
popt, pcov = curve_fit(func, xdata, ydata)

plt.plot(xdata, func(xdata, *popt), 'r-',
        label='fit: a=%5.3f, b=%5.3f, c=%5.3f' % tuple(popt))
popt, pcov = curve_fit(func, xdata, ydata)

plt.plot(xdata, func(xdata, *popt), 'g--',
          label='fit: a=%5.3f, b=%5.3f, c=%5.3f' % tuple(popt))
plt.xlabel('x')
plt.ylabel('y')
plt.legend()
plt.show()

数据如下所示：

预先感谢您的帮助。

Answer 1

Your model contains "exp(x)" and the data file contains x values of 1000, and this is giving math overflow errors no matter the starting values - the optimizer cannot find a way out of that problem, and you must change the equation to fit this data set. I can suggest other equations, but this data set cannot be fit to the posted equation.

EDIT: Per your comment on dividing by 100, here is code using scipy's Differential Evolution genetic algorithm module to find initial parameter estimates, which uses the Latin Hypercube algorithm to ensure a thorough search of parameter space - that algorithm requires bounds within which to search, and ranges on parameters are much easier to find than exact initial parameter values. Here I tried a few ranges and got what is probably the best fit you can get here from what I can see.

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


df = pd.read_csv("Results.csv")
xData = df['Frame'].as_matrix() / 100.0
yData = df['Area'].as_matrix()

def func(x, a, b, c):
    return (a*numpy.sin(b*x))+(c * numpy.exp(x))


# 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([0.0, 1.0]) # search bounds for b
    parameterBounds.append([0.0, 1.0]) # search bounds for c

    # "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)