我有一个尝试过的curve_fit函数用于多个变量。我遇到了“ sigma形状不正确”的问题。我尝试了以下代码。谁能解释为什么我会收到此错误？ 这里的x和y是我的自变量，而p，q，r是我要拟合的参数
xdata = [214.737191559, -5.64912101538e-36, 36.1372453686, 189.459700978, 233.562136902, 201.230228832, -5.59364882619e-36, -36.3232002416, -188.192199081, -212.837139143, -232.342545403, -200.699429716]
ydata = [-5.88273617837e-37, -211.536123799, -186.67108047, -35.9497006815, 200.282998159, 232.085860035, 213.44274878, 187.945919272, 35.7227474297, -6.00785257974e-37, -199.746844708, -230.856058666]
xdata = np.array(xdata)
ydata = np.array(ydata)
def func1(X,a,b,c):
x,y = X
n = 8
# % A = ydata
# % B = -xdata
# % C = xdata. - ydata
# % H = zdata
g = np.subtract(x,y)
I_0 = np.subtract(x,y) # x-y = C
I_1 = np.multiply(I_0,c) # c(x-y) = cC
I_2 = np.multiply(b,-x) #b(-x) = bB
I_3 = np.multiply(a,y) # aA
I3_0 = np.subtract(I_1,I_2) # cC-bB
I3_1 = np.subtract(I_3,I_1) # aA-cC
I3_2 = np.subtract(I_2,I_3) # bB-aA
I3_00 = np.multiply(I3_0,I3_1) # (cC-bB)(aA-cC)
I3_01 = np.multiply(I3_00,I3_2) # (cC-bB)(aA-cC)(bB-aA)
I3 = np.divide(I3_01,54) # (cC-bB)(aA-cC)(bB-aA)/54
I2_0 = np.power((I3_1),2) # (aA-cC)^2
I2_1 = np.power((I3_0),2) # (cC-bB)^2
I2_2 = np.power((I3_2),2) # (bB-aA)^2
I2_00 = np.add(I2_0,I2_1) # (aA-cC)^2 + (cC-bB)^2
I2_01 = np.add(I2_00,I2_2) # (aA-cC)^2 + (cC-bB)^2 + (bB-aA)^2
I2 = np.divide(I2_01,54) # ((aA-cC)^2 + (cC-bB)^2 + (bB-aA)^2)/54
th_0 = np.divide(I3,(np.power(I2,(3/2)))) # I3/(I2^(3/2))
th = np.arccos(np.clip((th_0),-1,1)) # arccos(I3/(I2^(3/2)))
ans_0 = np.divide(np.add((2*th),(np.pi)),6) # (2*th + pi)/6
ans_1 = np.divide(np.add((2*th),(3*np.pi)),6) # (2*th + 3*pi)/6
ans_2 = np.divide(np.add((2*th),(5*np.pi)),6) # (2*th + 5*pi)/6
ans_00 = np.multiply(np.cos(ans_0),2) # 2*cos((2*th + pi)/6)
ans_11 = np.multiply(np.cos(ans_1),2) # 2*cos((2*th + 3*pi)/6)
ans_22 = np.multiply(np.cos(ans_2),2) # 2*cos((2*th + 5*pi)/6)
ans_000 = np.power(np.absolute(ans_00),n) # (abs(2*cos((2*th + pi)/6)))^n
ans_111 = np.power(np.absolute(ans_11),n) # (abs(2*cos((2*th + 3*pi)/6)))^n
ans_222 = np.power(np.absolute(ans_22),n) # (abs(2*cos((2*th + 5*pi)/6)))^n
ans_0000 = np.add((np.power(np.absolute(ans_00),n)),(np.power(np.absolute(ans_11),n))) # (abs(2*cos((2*th + pi)/6)))^n + (abs(2*cos((2*th + 3*pi)/6)))^n
ans_1111 = np.add((ans_0000),(np.power(np.absolute(ans_22),n))) # (abs(2*cos((2*th + pi)/6)))^n + (abs(2*cos((2*th + 3*pi)/6)))^n + (abs(2*cos((2*th + 5*pi)/6)))^n
sna_0 = np.power(np.multiply(3,I2),(n/2)) # (3*I2)^(n/2) !!
sna_1 = 2*(np.power(190,n)) # 2*(sigma^n) !!
sna_00 = np.multiply(sna_0,ans_1111)
sna_11 = np.subtract(sna_00,sna_1)
return sna_11
a, b, c = 10., 4., 6.
z = func1((xdata,ydata), a, b, c) * 1 + np.random.random(12) / 100
# initial guesses for a,b,c:
a, b, c = 1, 1, 1
p0 = np.array([a, b, c])
# p0 = 8., 2., 7.
popt,pcov = (curve_fit(func1, (xdata,ydata),z, p0))
popt
运行此命令时，出现以下错误
---------------------------------------------------------------------------
ValueError Traceback (most recent call last)
<ipython-input-13-484bc542850b> in <module>()
6 p0 = np.array([a, b, c])
7 # p0 = 8., 2., 7.
----> 8 popt,pcov = (curve_fit(func1, (xdata,ydata), p0))
9 popt
~/.conda/envs/ML/lib/python3.6/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)
~/.conda/envs/ML/lib/python3.6/site-packages/scipy/optimize/minpack.py in leastsq(func, x0, args, Dfun, full_output, col_deriv, ftol, xtol, gtol, maxfev, epsfcn, factor, diag)
381 if not isinstance(args, tuple):
382 args = (args,)
--> 383 shape, dtype = _check_func('leastsq', 'func', func, x0, args, n)
384 m = shape[0]
385 if n > m:
~/.conda/envs/ML/lib/python3.6/site-packages/scipy/optimize/minpack.py in _check_func(checker, argname, thefunc, x0, args, numinputs, output_shape)
25 def _check_func(checker, argname, thefunc, x0, args, numinputs,
26 output_shape=None):
---> 27 res = atleast_1d(thefunc(*((x0[:numinputs],) + args)))
28 if (output_shape is not None) and (shape(res) != output_shape):
29 if (output_shape[0] != 1):
~/.conda/envs/ML/lib/python3.6/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):
ValueError: operands could not be broadcast together with shapes (12,) (3,)
答案 0 :(得分：1)
您收到ValueError: ``sigma`` has incorrect shape.的错误与curve_fit的错误调用以及函数所期望的内容和要提供的内容之间的差异有关。这是正确呼叫的示例：
p, q, r = 1, 1, 1
p0 = np.array([p, q, r])
cfit = curve_fit(func, xdata, ydata, p0)
print(cfit)
不幸的是，这并不是代码中唯一的问题。您的func1将需要您进行一些编辑。您可以参考此post on how to use curve_fit。
更新：
我缩短了代码并优化了一些代码行，如注释中所述，您需要一个输出变量，因此我生成了一些自定义zdata，以后可以将其替换为数据。
import numpy as np
from scipy.optimize import curve_fit
xdata = [214.737, -5.649e-36, 36.137, 189.459, 233.562, 201.230, -5.593e-36, -36.323, -188.192, -212.837, -232.342, -200.699]
ydata = [-5.882e-37, -211.536, -186.671, -35.949, 200.282, 232.085, 213.442, 187.945, 35.722, -6.007, -199.746, -230.856]
def func(X, p, q, r):
x = np.array(X[0])
y = np.array(X[1])
n = 8
a1 = (p * y) - (r * (x-y))
b1 = (q * -1 * x) - (p * y)
c1 = (r * (x - y)) - (q * -1 * x)
I3 = (a1 * b1 * c1) / 54
I2 = (a1**2 + b1**2 + c1**2) / 54
th = np.arccos( I3 / (I2**(3/2)) )
an1 = (np.abs(2 * np.cos((2 * th + 1 * np.pi) /6)))**n
an2 = (np.abs(2 * np.cos((2 * th + 3 * np.pi) /6)))**n
an3 = (np.abs(2 * np.cos((2 * th + 5 * np.pi) /6)))**n
res = ( (3 * I2)**(n/2) ) * (an1 + an2 + an3) - (2 * (189.32)**8)
return res
# init
p, q, r = 1, 1, 1
p0 = np.array([p, q, r])
# artificial zdata
zdata = func((xdata, ydata), p, q, r) + np.random.random(np.array(xdata).shape)
cfit = curve_fit(func, (xdata, ydata), zdata, p0)
# print output
print(cfit)
我仍然无法完全了解func内部的内容，由于RuntimeWarning:而导致invalid value encountered in arccos，这也是为什么我也编辑了您提供的数据的原因。