我正在嘗試experimental data (x and y)使用 a來適應一些custom function (Srt)并使用scipy.optimize.curve_fit()：
讀取資料并定義函式，使用 Km 和 Vmax（將使用曲線擬合確定）的虛擬值 (10,10) 作業正常，只要我使用np.asarray()：
from scipy.special import lambertw
from scipy.optimize import curve_fit
import numpy as np
import scipy
def Srt(t,s,Km,Vmax):
print("t",type(t))
print("t",t)
print("last element of t:",t[-1])
print("s",type(s))
print("s",s)
print("last element of s:",s[-1])
Smax = s[-1] # Substrate concentration at end of reaction
t0 = t[0] # time=0 (beginning of reaction)
s0 = s[0] # Substrate concentration at time = 0 (beginning of reaction)
E = np.exp(((Smax - s0) - Vmax*(t t0))/Km)
L = lambertw(((Smax - s0)/Km)*E)
y = Smax - Km*L
return y
x=[2.780000e-03,2.778000e-02,5.278000e-02,7.778000e-02,1.027800e-01
,1.277800e-01,1.527800e-01,1.777800e-01,2.027800e-01,2.277800e-01
,2.527800e-01,2.777800e-01,3.027800e-01,3.277800e-01,3.527800e-01]
y=[0.44236,0.4308,0.42299,0.41427,0.40548,0.39908,0.39039,0.3845,0.37882
,0.37411,0.36759,0.36434,0.35864,0.35508,0.35138]
xdata = np.asarray(x)
ydata = np.asarray(y)
Srt(xdata, ydata,10,10)
如果我不使用np.asarray，我會收到“型別錯誤”：
Srt(x, y,10,10)
當我繼續使用 curve_fit 來擬合 Vmax 和 Km 時：
parameters, covariance = scipy.optimize.curve_fit(Srt, xdata, ydata)
我遇到了麻煩：
如果我正確理解錯誤訊息，出于某種原因，ydata當它作為s?!?讀入時，該陣列不再是陣列。
我必須在代碼中更改什么才能使用我的函式Srt和curve_fit？
編輯：代碼的完整輸出：
t <class 'numpy.ndarray'>
t [0.00278 0.02778 0.05278 0.07778 0.10278 0.12778 0.15278 0.17778 0.20278
0.22778 0.25278 0.27778 0.30278 0.32778 0.35278]
last element of t: 0.35278
s <class 'numpy.ndarray'>
s [0.44236 0.4308 0.42299 0.41427 0.40548 0.39908 0.39039 0.3845 0.37882
0.37411 0.36759 0.36434 0.35864 0.35508 0.35138]
last element of s: 0.35138
t <class 'numpy.ndarray'>
t [0.00278 0.02778 0.05278 0.07778 0.10278 0.12778 0.15278 0.17778 0.20278
0.22778 0.25278 0.27778 0.30278 0.32778 0.35278]
last element of t: 0.35278
s <class 'numpy.float64'>
s 1.0
---------------------------------------------------------------------------
IndexError Traceback (most recent call last)
<ipython-input-23-5ce34d06b849> in <module>
33 #then the problems start
34
---> 35 parameters, covariance = scipy.optimize.curve_fit(Srt, xdata, ydata)
~\anaconda3\lib\site-packages\scipy\optimize\minpack.py in curve_fit(f, xdata, ydata, p0, sigma, absolute_sigma, check_finite, bounds, method, jac, **kwargs)
761 # Remove full_output from kwargs, otherwise we're passing it in twice.
762 return_full = kwargs.pop('full_output', False)
--> 763 res = leastsq(func, p0, Dfun=jac, full_output=1, **kwargs)
764 popt, pcov, infodict, errmsg, ier = res
765 ysize = len(infodict['fvec'])
~\anaconda3\lib\site-packages\scipy\optimize\minpack.py in leastsq(func, x0, args, Dfun, full_output, col_deriv, ftol, xtol, gtol, maxfev, epsfcn, factor, diag)
386 if not isinstance(args, tuple):
387 args = (args,)
--> 388 shape, dtype = _check_func('leastsq', 'func', func, x0, args, n)
389 m = shape[0]
390
~\anaconda3\lib\site-packages\scipy\optimize\minpack.py in _check_func(checker, argname, thefunc, x0, args, numinputs, output_shape)
24 def _check_func(checker, argname, thefunc, x0, args, numinputs,
25 output_shape=None):
---> 26 res = atleast_1d(thefunc(*((x0[:numinputs],) args)))
27 if (output_shape is not None) and (shape(res) != output_shape):
28 if (output_shape[0] != 1):
~\anaconda3\lib\site-packages\scipy\optimize\minpack.py in func_wrapped(params)
461 if transform is None:
462 def func_wrapped(params):
--> 463 return func(xdata, *params) - ydata
464 elif transform.ndim == 1:
465 def func_wrapped(params):
<ipython-input-23-5ce34d06b849> in Srt(t, s, Km, Vmax)
10 print("s",type(s))
11 print("s",s)
---> 12 print("last element of s:",s[-1])
13 Smax = s[-1] # Substrate concentration at end of reaction
14 t0 = t[0] # time=0 (beginning of reaction)
IndexError: invalid index to scalar variable.
編輯 2 完全功能代碼，感謝 Jonathan Weine。由于“壞”的實驗資料，擬合不是最佳的，我現在正在使用我的完整資料集：D
from scipy.special import lambertw
from scipy.optimize import curve_fit
import numpy as np
import scipy
def Srt(t, Smax: float, s0: float, Km: float, Vmax: float):
t0 = t[0] # time=0 (beginning of reaction)
E = np.exp(((Smax - s0) - Vmax*(t t0))/Km)
# L = lambertw(((Smax - s0)/Km)*E) # this apparently can be complex which causes another Error
L = np.abs(lambertw(((Smax - s0)/Km)*E))
y = Smax Km*L
return y
y = [0.44236,0.4308,0.42299,0.41427,0.40548,0.39908,0.39039,0.3845,0.37882
,0.37411,0.36759,0.36434,0.35864,0.35508,0.35138,0.34748,0.34437,0.34143
,0.3391,0.3348,0.33345,0.31404,0.30212,0.29043,0.28026,0.27331,0.26672
,0.26187,0.25645,0.25208,0.24736,0.244,0.24056,0.23798,0.23359,0.23138
,0.22845,0.22566,0.22384,0.22112,0.21894,0.21672,0.21466,0.21316,0.21209
,0.20941,0.20823,0.20687,0.2056,0.20324,0.20266,0.20095,0.19935,0.19895
,0.19746,0.19616,0.19486,0.19419,0.19382,0.19301,0.19085,0.19108,0.19024
,0.18933,0.18839,0.18706,0.18643,0.18623,0.18569,0.18469,0.18381,0.18341
,0.18331,0.18324,0.18222,0.18106,0.18039,0.18022,0.17906,0.17935,0.17842
,0.17834,0.1781,0.17731,0.17704,0.1766,0.17654,0.1761,0.17568,0.1744
,0.17453,0.17393,0.17325,0.17329,0.17302,0.17347,0.17344,0.17233,0.17228
,0.17208,0.17177,0.1712,0.17076,0.171,0.17043,0.17057,0.17003,0.16965
,0.16923,0.16944,0.16898,0.16879,0.16809,0.16821,0.16794,0.16831,0.16779
,0.16805,0.16765,0.16762,0.16695,0.16694,0.1669,0.16642,0.16583,0.166
,0.16625,0.16575,0.1658,0.16553,0.16565,0.1654,0.16419,0.16487,0.16467
,0.16452,0.16433,0.16468,0.16423,0.16427,0.16372,0.16388,0.16388,0.16394
,0.16382,0.1631,0.16353,0.1638,0.16304,0.163,0.16296,0.16295,0.16284
,0.16275,0.16214,0.16243,0.16211,0.16207,0.16185,0.16187,0.16176,0.16168
,0.16195,0.16138,0.16177,0.16121,0.16163,0.16121,0.161,0.16114,0.16122
,0.16096,0.16105,0.16102,0.16068,0.16031,0.16028,0.16051,0.16045,0.16017
,0.15977,0.15927,0.16007,0.15953,0.15933,0.1596,0.15911,0.15903,0.15884
,0.15856,0.15889,0.15888,0.15861,0.15849,0.158,0.15822,0.15776,0.15759
,0.15734,0.15757,0.15718,0.15699,0.15747,0.15692,0.15701,0.15715,0.15675
,0.15732,0.15687,0.15659,0.15664,0.15635,0.15633,0.15591]
#csvFile.iloc[0:500,9]
x = [2.780000e-03,2.778000e-02,5.278000e-02,7.778000e-02,1.027800e-01
,1.277800e-01,1.527800e-01,1.777800e-01,2.027800e-01,2.277800e-01
,2.527800e-01,2.777800e-01,3.027800e-01,3.277800e-01,3.527800e-01
,3.777800e-01,4.027800e-01,4.277800e-01,4.527800e-01,4.777800e-01
,5.027800e-01,7.538900e-01,1.003890e 00,1.253890e 00,1.503890e 00
,1.753890e 00,2.003890e 00,2.253890e 00,2.503890e 00,2.753890e 00
,3.003890e 00,3.253890e 00,3.503890e 00,3.753890e 00,4.003890e 00
,4.253890e 00,4.503890e 00,4.753890e 00,5.003890e 00,5.253890e 00
,5.503890e 00,5.753890e 00,6.003890e 00,6.253890e 00,6.503890e 00
,6.753890e 00,7.003890e 00,7.253890e 00,7.503890e 00,7.753890e 00
,8.003890e 00,8.253890e 00,8.503890e 00,8.753890e 00,9.003890e 00
,9.253890e 00,9.503890e 00,9.753890e 00,1.000389e 01,1.025389e 01
,1.050389e 01,1.075389e 01,1.100389e 01,1.125389e 01,1.150389e 01
,1.175389e 01,1.200389e 01,1.225389e 01,1.250389e 01,1.275389e 01
,1.300389e 01,1.325389e 01,1.350389e 01,1.375389e 01,1.400389e 01
,1.425389e 01,1.450389e 01,1.475389e 01,1.500389e 01,1.525389e 01
,1.550389e 01,1.575389e 01,1.600389e 01,1.625389e 01,1.650389e 01
,1.675389e 01,1.700389e 01,1.725389e 01,1.750389e 01,1.775389e 01
,1.800389e 01,1.825389e 01,1.850389e 01,1.875389e 01,1.900389e 01
,1.925389e 01,1.950389e 01,1.975389e 01,2.000389e 01,2.025389e 01
,2.050389e 01,2.075389e 01,2.100389e 01,2.125389e 01,2.150389e 01
,2.175389e 01,2.200389e 01,2.225389e 01,2.250389e 01,2.275389e 01
,2.300389e 01,2.325389e 01,2.350389e 01,2.375389e 01,2.400389e 01
,2.425389e 01,2.450389e 01,2.475389e 01,2.500389e 01,2.525389e 01
,2.550389e 01,2.575389e 01,2.600389e 01,2.625389e 01,2.650389e 01
,2.675389e 01,2.700389e 01,2.725389e 01,2.750389e 01,2.775389e 01
,2.800389e 01,2.825389e 01,2.850389e 01,2.875389e 01,2.900389e 01
,2.925389e 01,2.950389e 01,2.975389e 01,3.000389e 01,3.025389e 01
,3.050389e 01,3.075389e 01,3.100389e 01,3.125389e 01,3.150389e 01
,3.175389e 01,3.200389e 01,3.225389e 01,3.250389e 01,3.275389e 01
,3.300389e 01,3.325389e 01,3.350389e 01,3.375389e 01,3.400389e 01
,3.425389e 01,3.450389e 01,3.475389e 01,3.500389e 01,3.525389e 01
,3.550389e 01,3.575389e 01,3.600389e 01,3.625389e 01,3.650389e 01
,3.675389e 01,3.700389e 01,3.725389e 01,3.750389e 01,3.775389e 01
,3.800389e 01,3.825389e 01,3.850389e 01,3.875389e 01,3.900389e 01
,3.925389e 01,3.950389e 01,3.975389e 01,4.000389e 01,4.025389e 01
,4.050389e 01,4.075389e 01,4.100389e 01,4.125389e 01,4.150389e 01
,4.175389e 01,4.200389e 01,4.225389e 01,4.250389e 01,4.275389e 01
,4.300389e 01,4.325389e 01,4.350389e 01,4.375389e 01,4.400389e 01
,4.425389e 01,4.450389e 01,4.475389e 01,4.500389e 01,4.525389e 01
,4.550389e 01,4.575389e 01,4.600389e 01,4.625389e 01,4.650389e 01
,4.675389e 01,4.700389e 01,4.725389e 01,4.750389e 01,4.775389e 01
,4.800389e 01,4.825389e 01,4.850389e 01,4.875389e 01]
# csvFile.iloc[0:500,0]
xdata = np.array(x)
ydata = np.array(y)
parameters, covariance = scipy.optimize.curve_fit(Srt, xdata, ydata)
Km = parameters[1]
Vmax = parameters[0]
fit_y = Srt(xdata, ydata[-1],ydata[0], Km, Vmax)
print("Km: ", parameters[1], "Vmax: ", parameters[0])
plt.plot(xdata, fit_y, '-', color="green",linewidth=1)
plt.plot(xdata, ydata, 'o', color="red")
uj5u.com熱心網友回復：
請仔細查看該 函式的檔案curve_fit。它指出ydata必須名義上是 的結果func(xdata... )。因此，您交給的 ydatacurve_fit永遠不會Srt作為您在手動呼叫中指示的呼叫的引數傳遞。
此外，要估計的引數必須具有相同的形狀，這意味著您必須定義Smax和s0作為浮動輸入。我修改了您的示例，使其實際運行：
from scipy.special import lambertw
from scipy.optimize import curve_fit
import numpy as np
import scipy
def Srt(t, Smax: float, s0: float, Km: float, Vmax: float):
t0 = t[0] # time=0 (beginning of reaction)
E = np.exp(((Smax - s0) - Vmax*(t t0))/Km)
# L = lambertw(((Smax - s0)/Km)*E) # this apparently can be complex which causes another Error
L = np.abs(lambertw(((Smax - s0)/Km)*E))
y = Smax - Km*L
return y
x=[2.780000e-03,2.778000e-02,5.278000e-02,7.778000e-02,1.027800e-01
,1.277800e-01,1.527800e-01,1.777800e-01,2.027800e-01,2.277800e-01
,2.527800e-01,2.777800e-01,3.027800e-01,3.277800e-01,3.527800e-01]
y=[0.44236,0.4308,0.42299,0.41427,0.40548,0.39908,0.39039,0.3845,0.37882
,0.37411,0.36759,0.36434,0.35864,0.35508,0.35138]
xdata = np.array(x)
ydata = np.array(y)
parameters, covariance = scipy.optimize.curve_fit(Srt, xdata, ydata)
注：
該np.abs內部的功能沒有意義，但對復雜的結果lambertw顯然會很復雜。在這種情況下，由于沒有安全的轉換規則，會引發錯誤，導致曲線擬合中止。
uj5u.com熱心網友回復：
您的第一個錯誤是由t t0運算式產生的。它t是一個 list x，這是一個串列“連接”運算式，它適用于[1,2,3] [4,5]但不適用于[1,2,3] 5. 這就是為什么x并且y必須陣列。
在第二個錯誤中，
print("s",type(s))
print("s",s)
展示？顯然s不是陣列，甚至不是串列。
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