如何在python中将生成的函数返回到数学表达式的形式并对其进行求导等操作？
使用scipy中的curve_fitting后，对散点数据进行高斯近似拟合，代码如下：
x = np.linspace(1,len(y),len(y))
n = len(x)
mean = sum(x*y)/n
sigma = np.sqrt(sum(y*(x-mean)**2)/n)
def gaus(x,a,x0,sigma):
return a*np.exp(-(x-x0)**2/(2*sigma**2))/(sigma*np.sqrt(2*np.pi))
popt,pcov = curve_fit(gaus,x,y,maxfev = 200000)
当我调用它时，生成的p1只是一个与x对应的数组：
p1 = gaus(x,*popt) < /代码> ，返回的数组为：
[0.09933219 0.10139629 0.10350315 0.10565368 0.10784877 0.11008935
0.11237635 0.11471073 0.11709347 0.11952557 0.12200806 0.12454196
0.12712835 0.1297683 0.13246293 0.13521337 0.13802076 0.14088628
0.14381113 0.14679655 0.14984377 0.15295407 0.15612876 0.15936917
0.16267665 0.16605259 0.1694984 0.17301552 0.17660543 0.18026962
0.18400963 0.18782703 0.19172341 0.19570039 0.19975966 0.20390289
0.20813183 0.21244823 0.21685392 0.22135072 0.22594052 0.23062523
0.23540682 0.24028728 0.24526864 0.250353 0.25554246 0.26083921
0.26624545 0.27176344 0.27739549 0.28314393 0.28901118 0.29499968
0.30111193 0.30735049 0.31371794 0.32021696 0.32685025 0.33362057
0.34053076 0.34758369 0.3547823 0.36212959 0.36962863 0.37728255
0.38509452 0.39306781 0.40120574 0.4095117 0.41798914 0.42664161
0.4354727 0.4444861 0.45368554 0.46307487 0.472658 0.4824389
0.49242166 0.50261042 0.51300944 0.52362302 0.53445559 0.54551166
0.55679582]
这种情况下，如何求出生成函数的一阶导数表达式、二阶导数等？
After using curve_fitting from scipy,the scatter data is fitted by Gaussian approximation,the code is as follows:
x = np.linspace(1,len(y),len(y))
n = len(x)
mean = sum(x*y)/n
sigma = np.sqrt(sum(y*(x-mean)**2)/n)
def gaus(x,a,x0,sigma):
return a*np.exp(-(x-x0)**2/(2*sigma**2))/(sigma*np.sqrt(2*np.pi))
popt,pcov = curve_fit(gaus,x,y,maxfev = 200000)
When I call it, the generated p1 is just an array corresponding to x：
p1 = gaus(x,*popt)
,The returned array is：
[0.09933219 0.10139629 0.10350315 0.10565368 0.10784877 0.11008935
0.11237635 0.11471073 0.11709347 0.11952557 0.12200806 0.12454196
0.12712835 0.1297683 0.13246293 0.13521337 0.13802076 0.14088628
0.14381113 0.14679655 0.14984377 0.15295407 0.15612876 0.15936917
0.16267665 0.16605259 0.1694984 0.17301552 0.17660543 0.18026962
0.18400963 0.18782703 0.19172341 0.19570039 0.19975966 0.20390289
0.20813183 0.21244823 0.21685392 0.22135072 0.22594052 0.23062523
0.23540682 0.24028728 0.24526864 0.250353 0.25554246 0.26083921
0.26624545 0.27176344 0.27739549 0.28314393 0.28901118 0.29499968
0.30111193 0.30735049 0.31371794 0.32021696 0.32685025 0.33362057
0.34053076 0.34758369 0.3547823 0.36212959 0.36962863 0.37728255
0.38509452 0.39306781 0.40120574 0.4095117 0.41798914 0.42664161
0.4354727 0.4444861 0.45368554 0.46307487 0.472658 0.4824389
0.49242166 0.50261042 0.51300944 0.52362302 0.53445559 0.54551166
0.55679582]
In this case, how can I find it's first derivative expression, the second derivative and so on for the generated function?
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这可以使用 scipy.interpolate.InterpolatedUnivariateSpline 来实现。
首先，您需要创建数据的样条线，如下所示：
然后，您可以使用
spl对象传递x和n（数字的导数），在x处获得一个新的样条线作为np.ndarray，其第 n 个导数为：This can be achieved using
scipy.interpolate.InterpolatedUnivariateSpline.First, you need to create a spline of your data as:
Afterward, you can use the
splobject to passxandn(the number of derivative), to get a new spline asnp.ndarrayatxwith its nth derivative as: