拟合单指数衰减误差 python

Question

我有两个 arrays，这将导致 df_intensity_01 与 df_time 的 plot。

df_time
[[  0  10  20  30  40  50  60  70  80  90 100 110 120 130 140 150 160 170
  180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350
  360 370 380 390 400 410 420 430 440 450 460 470 480 490 500 510 520 530
  540 550 560 570 580 590 600 610 620 630 640 650 660 670 680 690 700 710
  720 730 740 750 760 770 780 790 800]]

df_intensity_01
[1.         0.98666909 0.935487   0.91008815 0.86347009 0.81356788
 0.79591582 0.78624289 0.76503846 0.75105705 0.72333501 0.67815733
 0.69481674 0.68321344 0.66108185 0.65859392 0.64047511 0.63100282
 0.63605049 0.6248548  0.60341172 0.57538132 0.57952294 0.57901395
 0.56353725 0.56164702 0.55901125 0.54833934 0.53271058 0.52880127
 0.52268282 0.51111965 0.5067436  0.49988595 0.49689326 0.48888879
 0.48247889 0.4790469  0.47320723 0.46156169 0.45921527 0.4592913
 0.45104607 0.44445031 0.44618426 0.43893589 0.42988811 0.42887013
 0.42842872 0.41952032 0.41286965 0.41392143 0.41175663 0.40432874
 0.39645523 0.39813004 0.38932936 0.38264912 0.38094263 0.3855869
 0.38378537 0.37570065 0.37573022 0.37550635 0.36941113 0.36502241
 0.36607629 0.36624103 0.36163477 0.35550154 0.35627875 0.35421111
 0.34858053 0.34767026 0.34967665 0.34818347 0.34007975 0.34139552
 0.34017057 0.33732993 0.33320098]

我试图将数据拟合到单个指数衰减 function ，其中我提供了拟合的初始系数。

def func(x, a, b, c):
    return a * np.exp(-b * x) + c
xdata = df_time
guess=[1,0.001,0]
ydata = df_intensity
plt.plot(xdata, ydata, 'b-', label='data')
popt, pcov = curve_fit(func, xdata, ydata,p0=guess)
popt

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

我收到一个我真的不知道如何解决的错误：

---------------------------------------------------------------------------
ValueError                                Traceback (most recent call last)
ValueError: object too deep for desired array

---------------------------------------------------------------------------
error                                     Traceback (most recent call last)
<ipython-input-62-97bcc77fc6c7> in <module>
      5 ydata = df_intensity
      6 plt.plot(xdata, ydata, 'b-', label='data')
----> 7 popt, pcov = curve_fit(func, xdata, ydata,p0=guess)
      8 popt
      9 

/anaconda3/lib/python3.7/site-packages/scipy/optimize/minpack.py in curve_fit(f, xdata, ydata, p0, sigma, absolute_sigma, check_finite, bounds, method, jac, **kwargs)
    749         # Remove full_output from kwargs, otherwise we're passing it in twice.
    750         return_full = kwargs.pop('full_output', False)
--> 751         res = leastsq(func, p0, Dfun=jac, full_output=1, **kwargs)
    752         popt, pcov, infodict, errmsg, ier = res
    753         cost = np.sum(infodict['fvec'] ** 2)

/anaconda3/lib/python3.7/site-packages/scipy/optimize/minpack.py in leastsq(func, x0, args, Dfun, full_output, col_deriv, ftol, xtol, gtol, maxfev, epsfcn, factor, diag)
    392         with _MINPACK_LOCK:
    393             retval = _minpack._lmdif(func, x0, args, full_output, ftol, xtol,
--> 394                                      gtol, maxfev, epsfcn, factor, diag)
    395     else:
    396         if col_deriv:

error: Result from function call is not a proper array of floats.

Answer 1

首先，您需要两个输入都是 1D arrays （只有一组大括号： [ ] ）。 目前看起来df_time是一个二维数组，这似乎是您发布的错误的来源。

然后，当您 plot 数据时，请记住您需要为每个x值评估 function ，以便您的x和y arrays 的长度相同。 您可以通过列表理解来做到这一点，记住将您的x值转换为float ，以便您可以将它们传递给您的 function：

plt.plot(xdata, [func(float(x), *popt) for x in xdata], 'r-',
         label='fit: a=%5.3f, b=%5.3f, c=%5.3f' % tuple(popt))

整个工作代码如下所示：

df_time = ['0', '10', '20', '30', '40', '50', '60', '70', '80', '90', '100',
           '110', '120', '130', '140', '150', '160', '170', '180', '190', '200',
           '210', '220', '230', '240', '250', '260', '270', '280', '290', '300',
           '310', '320', '330', '340', '350', '360', '370', '380', '390', '400',
           '410', '420', '430', '440', '450', '460', '470', '480', '490', '500',
           '510', '520', '530', '540', '550', '560', '570', '580', '590', '600',
           '610', '620', '630', '640', '650', '660', '670', '680', '690', '700',
           '710', '720', '730', '740', '750', '760', '770', '780', '790', '800']

df_intensity = ['1.', '0.98666909', '0.935487', '0.91008815', '0.86347009', '0.81356788',
                '0.79591582', '0.78624289', '0.76503846', '0.75105705', '0.72333501', '0.67815733',
                '0.69481674', '0.68321344', '0.66108185', '0.65859392', '0.64047511', '0.63100282',
                '0.63605049', '0.6248548', '0.60341172', '0.57538132', '0.57952294', '0.57901395',
                '0.56353725', '0.56164702', '0.55901125', '0.54833934', '0.53271058', '0.52880127',
                '0.52268282', '0.51111965', '0.5067436', '0.49988595', '0.49689326', '0.48888879',
                '0.48247889', '0.4790469', '0.47320723', '0.46156169', '0.45921527', '0.4592913',
                '0.45104607', '0.44445031', '0.44618426', '0.43893589', '0.42988811', '0.42887013',
                '0.42842872', '0.41952032', '0.41286965', '0.41392143', '0.41175663', '0.40432874',
                '0.39645523', '0.39813004', '0.38932936', '0.38264912', '0.38094263', '0.3855869',
                '0.38378537', '0.37570065', '0.37573022', '0.37550635', '0.36941113', '0.36502241',
                '0.36607629', '0.36624103', '0.36163477', '0.35550154', '0.35627875', '0.35421111',
                '0.34858053', '0.34767026', '0.34967665', '0.34818347', '0.34007975', '0.34139552',
                '0.34017057', '0.33732993', '0.33320098']

from scipy.optimize import curve_fit

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

xdata = [float(x) for x in df_time]
guess=[1,0.001,0]
ydata = df_intensity
plt.plot(xdata, ydata, 'b-', label='data')

popt, pcov = curve_fit(func, xdata, ydata,p0=guess)

fig = plt.figure()  # created a 2nd figure for 2nd plot

plt.plot(xdata, [func(float(x), *popt) for x in xdata], 'r-',
         label='fit: a=%5.3f, b=%5.3f, c=%5.3f' % tuple(popt))
plt.xlabel('x')
plt.ylabel('y');