numpy 曲线拟合的np.exp函数中的溢出错误

我尝试使用以下代码拟合一个组合高斯：

def curve_f(x,a,b,c,d,e,f):
  return (a*np.exp(((x-b)**2)/(2*-c**2)))+(d*np.exp(((x-e)**2)/(2*f**2)))

问题是，当我把这个函数放在scipy.optimize.curve_fit中使用我的数据时，我得到以下警告：

<ipython-input-27-1baee2b89bf1>:2: RuntimeWarning: overflow encountered in exp
  return (a*np.exp(((x-b)**2)/(2*-c**2)))+(d*np.exp(((x-e)**2)/(2*f**2)))
/usr/local/lib/python3.10/dist-packages/scipy/optimize/_minpack_py.py:862: RuntimeWarning: overflow encountered in square
cost = np.sum(infodict['fvec'] ** 2)

我试着把我的数据放在float 128中，但它不起作用。
这是我的数据看起来像什么。

下面是一个数据样本（这是y轴）：[ 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 5 5 7 3 10 3 11 10 4 16 13 32 23 21 23 37 42 42 43 56 62 41 56 71 59 61 84 82 76 73 78 73 69 84 85 74 65 75 59 74 73 76 74 60 95 63 91 85 82 73 72 76 82 71 85 71 60 53 71 84 95 83 50 88 63 76 68 81 73 80 60 89 78 76 86 73 99 91 94 104 98 114 117 110 122 104 106 121 135 130 161 146 133 172 145 186 202 222 216 205 200 234 219 231 265 269 266 296 286 304 303 325 319 381 328 362 370 339 360 423 405 368 400 411 416 448 454 453 468 480 427 433 490 471 505 500 442 483 482 462 436 457 483 435 431 432 416 410 438 402 422 387 403 366 371 369 339 341 306 327 331 310 296 277 259 268 228 214 225 234 204 208 205 205 176 168 190 192 142 161 126 107 122 112 86 107 92 90 89 78 82 59 69 67 57 34 42 46 44 35 36 37 29 28 29 25 20 20 18 20 17 8 22 12 9 9 7 13 8 11 5 14 5 3 6 4 6 9 2 5 5 2 4 5 8 7 5 1 4 3 2 6 - 1 3 3 2 3 2 3 1 1 2 0 1 2 3 0 1 0 5 3 2 1 1 2 2 0 4 3 1 2 2 4 2 4 0 4 1 2 1 1 1 1 0 2 - 1 2 1 1 1 1 4 0 4 2 3 0 - 1 1 3 1 2 0 2 1 1 1 1 0 1 1 1 1 0 1 2 0 3 2 1 1 1 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 1 2 1 0 1 1 1 0]

工作正常。如StackOverflow高斯拟合问题中所示（一遍又一遍），添加好的边界和初始猜测。

import numpy as np
from matplotlib import pyplot as plt
from scipy.optimize import curve_fit, Bounds

def curve_f(x: np.ndarray, a: float, b: float, c: float, d: float, e: float, f: float, g: float) -> np.ndarray:
    return (
        1/np.sqrt(2*np.pi) *
        (
            + a/c * np.exp(-0.5*((x - b)/c)**2)
            + d/f * np.exp(-0.5*((x - e)/f)**2)
        )
        + g
    )

y = np.array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -110, 1290, 33, 0, 0, 0, 0, 0, -1, 1, 1, 2, 2, 0, -1, -2, -1, 1, 1, 1, 2, 2, 2, 4, -3, 5,
              5, 7, 3, 10, 3, 11, 10, 4, 16, 13, 32, 23, 21, 23, 37, 42, 42, 43, 56, 62, 41, 56, 71, 59, 61, 84, 82, 76, 73, 78, 73, 69, 84, 85, 74, 65, 75, 59, 74, 73, 76, 74,
              60, 95, 63, 91, 85, 82, 73, 72, 76, 82, 71, 85, 71, 60, 53, 71, 84, 95, 83, 50, 88, 63, 76, 68, 81, 73, 80, 60, 89, 78, 76, 86, 73, 99, 91, 94, 104, 98, 114, 117,
              110, 122, 104, 106, 121, 135, 130, 161, 146, 133, 172, 145, 186, 202, 222, 216, 205, 200, 234, 219, 231, 265, 269, 266, 296, 286, 304, 303, 325, 319, 381, 328,
              362, 370, 339, 360, 423, 405, 368, 400, 411, 416, 448, 454, 453, 468, 480, 427, 433, 490, 471, 505, 500, 442, 483, 482, 462, 436, 457, 483, 435, 431, 432, 416,
              410, 438, 402, 422, 387, 403, 366, 371, 369, 339, 341, 306, 327, 331, 310, 296, 277, 259, 268, 228, 214, 225, 234, 204, 208, 205, 205, 176, 168, 190, 192, 142,
              161, 126, 107, 122, 112, 86, 107, 92, 90, 89, 78, 82, 59, 69, 67, 57, 34, 42, 46, 44, 35, 36, 37, 29, 28, 29, 25, 20, 20, 18, 20, 17, 8, 22, 12, 9, 9, 7, 13, 8,
              11, 5, 5, 14, 5, 3, 6, 4, 6, 9, 2, 5, 5, 2, 4, 5, 8, 7, 5, 1, 4, 3, 2, 6, -1, 3, 3, 3, 2, 3, 2, 3, 1, 1, 2, 0, 1, 2, 3, 0, 1, 0, 5, 3, 2, 1, 1, 2, 2, 0, 4, 3, 1,
              2, 2, 4, 2, 4, 0, 4, 1, 2, 1, 1, 1, 1, 0, 2, -1, 2, 1, 1, 1, 4, 0, 4, 2, 3, 0, -1, 1, 3, 1, 2, 0, 2, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 2, 2, 0, 3, 2, 1,
              1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 0, 1, -1, 2, 1, 1, 2, 1, 0, 1, 1, 0])

# Ignore massive spike at beginning
y = y[30:]

x = np.arange(len(y))
x0 = [5000, 50, 25, 25000, 150, 25, 0]
popt, *_ = curve_fit(
    f=curve_f,
    xdata=x,
    ydata=y,
    p0=x0,
    bounds=Bounds(
        lb=[1e-2,   0, 1e-2, 1e-2,   0, 1e-2, -1000],
        ub=[1e+6, 400, 1000, 1e+6, 400, 1000,  1000],
    )
)
print(popt)

plt.scatter(x, y, label='experiment', marker='+', color='green')
plt.plot(x, curve_f(x, *x0), label='guess')
plt.plot(x, curve_f(x, *popt), label='fit')
plt.legend()
plt.show()

或者不是PDF格式：

import numpy as np
from matplotlib import pyplot as plt
from scipy.optimize import curve_fit, Bounds

def curve_f(x: np.ndarray, a: float, b: float, c: float, d: float, e: float, f: float) -> np.ndarray:
    return (
        + a * np.exp(-0.5*((x - b)/c)**2)
        + d * np.exp(-0.5*((x - e)/f)**2)
    )

y = np.array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, -110, 1290, 33, 0, 0, 0, 0, 0, -1, 1, 1, 2, 2, 0, -1, -2, -1, 1, 1, 1, 2, 2, 2, 4, -3, 5,
              5, 7, 3, 10, 3, 11, 10, 4, 16, 13, 32, 23, 21, 23, 37, 42, 42, 43, 56, 62, 41, 56, 71, 59, 61, 84, 82, 76, 73, 78, 73, 69, 84, 85, 74, 65, 75, 59, 74, 73, 76, 74,
              60, 95, 63, 91, 85, 82, 73, 72, 76, 82, 71, 85, 71, 60, 53, 71, 84, 95, 83, 50, 88, 63, 76, 68, 81, 73, 80, 60, 89, 78, 76, 86, 73, 99, 91, 94, 104, 98, 114, 117,
              110, 122, 104, 106, 121, 135, 130, 161, 146, 133, 172, 145, 186, 202, 222, 216, 205, 200, 234, 219, 231, 265, 269, 266, 296, 286, 304, 303, 325, 319, 381, 328,
              362, 370, 339, 360, 423, 405, 368, 400, 411, 416, 448, 454, 453, 468, 480, 427, 433, 490, 471, 505, 500, 442, 483, 482, 462, 436, 457, 483, 435, 431, 432, 416,
              410, 438, 402, 422, 387, 403, 366, 371, 369, 339, 341, 306, 327, 331, 310, 296, 277, 259, 268, 228, 214, 225, 234, 204, 208, 205, 205, 176, 168, 190, 192, 142,
              161, 126, 107, 122, 112, 86, 107, 92, 90, 89, 78, 82, 59, 69, 67, 57, 34, 42, 46, 44, 35, 36, 37, 29, 28, 29, 25, 20, 20, 18, 20, 17, 8, 22, 12, 9, 9, 7, 13, 8,
              11, 5, 5, 14, 5, 3, 6, 4, 6, 9, 2, 5, 5, 2, 4, 5, 8, 7, 5, 1, 4, 3, 2, 6, -1, 3, 3, 3, 2, 3, 2, 3, 1, 1, 2, 0, 1, 2, 3, 0, 1, 0, 5, 3, 2, 1, 1, 2, 2, 0, 4, 3, 1,
              2, 2, 4, 2, 4, 0, 4, 1, 2, 1, 1, 1, 1, 0, 2, -1, 2, 1, 1, 1, 4, 0, 4, 2, 3, 0, -1, 1, 3, 1, 2, 0, 2, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1, 1, 0, 0, 1, 2, 2, 0, 3, 2, 1,
              1, 1, 0, 0, 1, 1, 1, 1, 1, 1, 2, 2, 1, 2, 0, 1, -1, 2, 1, 1, 2, 1, 0, 1, 1, 0])

# Ignore massive spike at beginning
y = y[30:]

x = np.arange(len(y))
x0 = [80, 50, 20, 500, 150, 30]
popt, *_ = curve_fit(
    f=curve_f,
    xdata=x,
    ydata=y,
    p0=x0,
    bounds=Bounds(
        lb=[1e-2,   0, 1e-2, 1e-2,   0, 1e-2],
        ub=[1e+6, 400, 1000, 1e+6, 400, 1000],
    )
)
print(popt)

plt.scatter(x, y, label='experiment', marker='+', color='green')
plt.plot(x, curve_f(x, *x0), label='guess')
plt.plot(x, curve_f(x, *popt), label='fit')
plt.legend()
plt.show()

numpy 曲线拟合的np.exp函数中的溢出错误

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