curve_fit：“LinAlgError：SVD 未收敛”

Question

我有数据框

df

，其中包含以下列：

X	是	delta_t
.	.	.
.	.	.
.	.	.
.	.	.
.	.	.

并且我正在尝试使用 python curve_fit (https://docs.scipy) 拟合指数函数： Y/X = a x Exp(-(b_1 - b_2) x

 c 

x delta_t) .org/doc/scipy/reference/ generated/scipy.optimize.curve_fit.html）

我遇到一个问题

"LinAlgError: SVD did not converge"

。

如何克服这个问题？

有关数据框和变量的一些详细信息：

• df.shape = (4592, 92)

• df['Y'].describe()

  ： |统计|数字| |------|-------------| |计数| 3537.000000 | |意思是| 19.985690 | |标准| 22.486308 | |分钟 | 0.582168 | |25% | 5.446700| |50% | 10.997200| |75% | 25.789900| |最大| 121.417000|

• df['X'].describe()

  ： |统计|数字| |------|-------------| |计数| 3537.000000| |意思是| 5.686478| |标准| 5.564841| |分钟| 0.265318| | 25% | 1.928670| | 50% | 3.581990| | 75% | 6.938480| |最大 |26.451900 |

df['delta_t'].describe()

： |统计|数字| |------|-------------| |计数| 1318.000000| |意思是| 10.666609| |标准| 5.854462| |分钟| -6.644779| |25% | 6.354654| |50% | 9.811106| |75% | 14.335943| |最大| 46.353073|

代码如下：

b_2 = 0.83e-12
c = 2.5e6
df.dropna(subset=['Y / X'], inplace=True)

Q1 = df['Y / X'].quantile(0.25)
Q3 = df['Y / X'].quantile(0.75)
IQR = Q3 - Q1
lower_bound = Q1 - 1.5 * IQR
upper_bound = Q3 + 1.5 * IQR
dfsum_copy2 = df[(df['Y / X'] >= lower_bound) & (df['Y / X'] <= upper_bound)]

x_data = df['c']
y_data = df['Y / X']

def fitting_function(delta_t, a, b_2):
return a * np.exp(-(b_1 - b_2) * c* delta_t)

x_data_normalized = (x_data - x_data.mean()) / x_data.std()
y_data_normalized = (y_data - y_data.mean()) / y_data.std()

initial_guess = [0.22, 1.25e-12]
fit_params, pcov = curve_fit(fitting_function, x_data_normalized, y_data_normalized, p0=initial_guess, method='lm')

a_fit, b_1_fit = fit_params

x_curve = np.linspace(min(x_data), max(x_data), 1000)
y_curve = fitting_function(x_curve, a_fit, b_1_fit)

plt.scatter(x_data, y_data, label='Data')
plt.plot(x_curve, y_curve, 'r-', label='Fitted Curve')
plt.xlabel('delta_t')
plt.ylabel('Y/ X')
plt.legend()
plt.grid(True)
plt.show()

a_fit, b_1_fit = fit_params
print("Fitted Parameters:")
print("a =", a_fit)
print("b_1 =", b_1)

收敛性测试

当我尝试检查它的收敛性时：

np.linalg.cond（pcov）

显示以下错误：

LinAlgError Traceback (most recent call last)
Cell In[202], line 1
----> 1 np.linalg.cond(pcov)
File <array_function internals>:200, in cond(*args, **kwargs)
File /usr/local/lib/python3.11/site-packages/numpy/linalg/linalg.py:1747, in cond(x, p)
1745 raise LinAlgError("cond is not defined on empty arrays")
1746 if p is None or p == 2 or p == -2:
-> 1747 s = svd(x, compute_uv=False)
1748 with errstate(all='ignore'):
1749 if p == -2:
File <array_function internals>:200, in svd(*args, **kwargs)
File /usr/local/lib/python3.11/site-packages/numpy/linalg/linalg.py:1654, in svd(a, full_matrices, compute_uv, hermitian)
1651 gufunc = _umath_linalg.svd_n
1653 signature = 'D->d' if isComplexType(t) else 'd->d'
-> 1654 s = gufunc(a, signature=signature, extobj=extobj)
1655 s = s.astype(_realType(result_t), copy=False)
1656 return s
File /usr/local/lib/python3.11/site-packages/numpy/linalg/linalg.py:98, in _raise_linalgerror_svd_nonconvergence(err, flag)
97 def _raise_linalgerror_svd_nonconvergence(err, flag):
---> 98 raise LinAlgError("SVD did not converge")
LinAlgError: SVD did not converge

请帮我解决问题。

提前致谢。

问候 阿伦