正确使用 scipy.optimize.leastsq

Question

所以基于对问题的回答 [python nonlinear least squares fitting

我调整了答案来估计三个参数kd,p0,l0

    N = 10
    kd_guess = 7.0  # <-- You have to supply a guess for kd
    p0_guess = 8.0
    l0_guess = 15.0
    p0 = np.linspace(0,10,N)
    l0 = np.linspace(0,10,N)

    PLP = func(4.0,5.0,6.0)+(np.random.random(N)-0.5)*2.0
    # The target should be (4.0,5.0,6.0)

    kd,p0,l0,cov = scp.optimize.leastsq(residuals,[kd_guess,p0_guess,l0_guess,PLP])

我想避免以下错误，

Traceback (most recent call last):
  File "Main.py", line 40, in <module>
    kd,p0,l0,cov = scp.optimize.leastsq(residuals,[kd_guess,p0_guess,l0_guess,PLP])
  File "/home/arvaldez/anaconda3/lib/python3.6/site-packages/scipy/optimize/minpack.py", line 380, in leastsq
    x0 = asarray(x0).flatten()
  File "/home/arvaldez/anaconda3/lib/python3.6/site-packages/numpy/core/numeric.py", line 501, in asarray
    return array(a, dtype, copy=False, order=order)
ValueError: setting an array element with a sequence.

Answer 1

这是一个使用 scipy 的 curve_fit() 例程的图形示例，它调用了 minimumsq() - 我个人发现 scipy curve_fit 例程比 leastsq 更容易使用。

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

xData = numpy.array([1.1, 2.2, 3.3, 4.4, 5.0, 6.6, 7.7])
yData = numpy.array([1.1, 20.2, 30.3, 60.4, 50.0, 60.6, 70.7])


def func(x, a, b, c): # simple quadratic example
    return (a * numpy.square(x)) + b * x + c


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

# 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)