scipy.optimize.curve_fit产生无意义的曲线拟合

Question

我正在尝试将曲线拟合到一些生成的数据，这些数据在绘制时类似于指数函数。我正在使用scipy.optimize.curve_fit，因为它似乎是这项工作中最好的（并且有据可查）。每次运行代码时，都会生成新的实际数据，但这是一个示例集：

import pandas
import scipy.optimize as opt

x1 = [0.4145392937447818, 0.7807888116968482, 0.7903528929788539, 
1.5081613036989836, -0.295895237606155, -0.0855307279546107, 
1.0523973736479486, -0.6967509832843239, -0.30499200990688413, 
1.1990545631966807, -1.270460772249312, 0.9531042718153095, 1.5747175535222993, 
-0.6483709650867473, 0.47820180254528477, 1.14266851615097, 0.6237953640100202, 
0.0664027559951128, 0.877280002485417, 0.9432317053343211, 1.0367424879878504, 
-0.6410400513164749, 1.667835241401498, -0.20484029870424125, 
2.887026948755316]

y1 = [0.718716626591187, 0.579938466590508, 0.722005637974309, 
1.61842778379047, 0.331301712743162, 0.342649242449043, 1.14950611092907, 
0.299221762023701, 0.345063839940754, 1.08398125906313, 0.315433168226251, 
1.3343730617376, 1.32514210008176, 0.308702648499771, 0.495749985226691, 
0.406025683910759, 0.445087968405107, 0.423578575247177, 0.816264419038205, 
1.16110461165631, 1.81572974380867, 0.420890068255763, 0.821468286117842, 
0.416275933630732, 4.7877353794036]

data = pandas.DataFrame({"Pi_values": x1, 
                         "CO2_at_solubility": y1})

然后，我从事曲线拟合业务...

##Define curve fitting
def func(x, m, c, c0):
    return c0 + m**x * c

#draw the figure
fig, ax1 = plt.subplots()
plt.xlabel('Pi Parameter')
plt.ylabel('CO2 wt%')

#plot generated data
#tried converting pandas columns to np arrays based on an issue another user was having, but it does not help
x1 = data["Pi_values"].values
y1 = data["CO2_at_solubility"].values

# Curve fitting with scipy.optimize.curve_fit
popt, pcov = opt.curve_fit(func, x1, y1)
# Use the optimized parameters to plot the best fit
plt.plot(x1, y1, 'o', x1, func(x1, *popt))

这是非常奇怪的结果。无论我尝试哪种形式的方程式，如果它能够拟合任何“曲线”，则看起来像是一团糟：

或者这很混乱...

有什么想法吗？我还找不到其他这样的例子。我正在jupyter笔记本中运行python3.5。

我尝试过的其他无效的方法：等式的其他形式；其他方程式；更改初始猜测值；如果y值太小，则缩放比例值。

Answer 1

您只需要对x值进行排序

data.sort_values(by='Pi_values', ascending=True, inplace=True)

在curve_fit之前：

x1 = data["Pi_values"].values
y1 = data["CO2_at_solubility"].values
# Curve fitting with scipy.optimize.curve_fit
popt, pcov = opt.curve_fit(func, x1, y1)
# Use the optimized parameters to plot the best fit
plt.plot(x1, y1, 'o', x1, func(x1, *popt))

Answer 2

在绘制时需要对x轴的元素进行排序。

示例：

x1, y1 = zip(*sorted(zip(x1, y1)))
# Curve fitting with scipy.optimize.curve_fit
popt, pcov = opt.curve_fit(func, x1, y1)
# Use the optimized parameters to plot the best fit
plt.plot(x1, y1, 'o', x1, func(x1, *popt))

结果为：