将指数拟合到范围并绘制结果并拟合

Question

我有两个数据帧，对应于我从文件 (Pos10.csv) 中获取的强度与时间的关系。

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt

csv_file="Pos10.csv"
df=pd.read_csv(csv_file)
df_01=df.iloc[:,0]
df_time=df_01*10
df_02=df.iloc[:,2]
df_intensity=df_02
plt.scatter(df_time,df_intensity)#scatter plot
plt.xlabel("Time (min)")
plt.ylabel("Normalized intensity")
plt.title("Kinetic exponential decay")
plt.show

This is how my data is looking after running the code above

df_intensity和df_time对应的值可以从下面得到。

df_intensity [2.80816437e-04 4.68942336e-03 1.86014497e-03 4.91956615e-03 1.71023544e-03 1.27739808e-03 2.69837148e-03 3.03619576e-03 2.93695988e-03 1.00000000e+00 9.86672832e-01 9.35505121e-01 9.10113403e-01 8.63508432e-01 8.13620231e-01 7.95973135e-01 7.86302914e-01 7.65104440e-01 7.51126961e-01 7.23412701e-01 6.78247705e-01 6.94902443e-01 6.83302401e-01 6.61177022e-01 6.58689791e-01 6.40576075e-01 6.31106438e-01 6.36152688e-01 6.24960147e-01 6.03523085e-01 5.75500561e-01 5.79641019e-01 5.79132172e-01 5.63659819e-01 5.61770115e-01 5.59135085e-01 5.48466172e-01 5.32841799e-01 5.28933594e-01 5.22816863e-01 5.11256939e-01 5.06882114e-01 5.00026393e-01 4.97034536e-01 4.89032323e-01 4.82624219e-01 4.79193191e-01 4.73355165e-01 4.61712896e-01 4.59367128e-01 4.59443139e-01 4.51200226e-01 4.44606319e-01 4.46339779e-01 4.39093449e-01 4.30048203e-01 4.29030508e-01 4.28589225e-01 4.19683332e-01 4.13034528e-01 4.14086006e-01 4.11921819e-01 4.04496019e-01 3.96624713e-01 3.98299055e-01 3.89500844e-01 3.82822480e-01 3.81116467e-01 3.85759440e-01 3.83958414e-01 3.75875968e-01 3.75905527e-01 3.75681719e-01 3.69588213e-01 3.65200720e-01 3.66254310e-01 3.66418999e-01 3.61814032e-01 3.55682521e-01 3.56459517e-01 3.54392455e-01 3.48763458e-01 3.47853443e-01 3.49859275e-01 3.48366514e-01 3.40265065e-01 3.41580469e-01 3.40355856e-01 3.37516020e-01 3.33388230e-01]

df_time [ 20. 30. 40. 50. 60. 70. 80. 90. 100. 110. 120. 130. 140. 150. 160. 170. 180. 190. 200. 210. 220. 230. 240. 250. 260. 270. 280. 290. 300. 310. 320. 330. 340. 350. 360. 370. 380. 390. 400. 410. 420. 430. 440. 450. 460. 470. 480. 490. 500. 510. 520. 530. 540. 550. 560. 570. 580. 590. 600. 610. 620. 630. 640. 650. 660. 670. 680. 690. 700. 710. 720. 730. 740. 750. 760. 770. 780. 790. 800. 810. 820. 830. 840. 850. 860. 870. 880. 890. 900. 910.]

有了这些数据...我想： 1) 拟合从最大强度点（y=1，与 x 位置 y=1 的位置无关，因为它因迹线而异）到迹线末端的指数衰减。 2）用拟合绘制我的数据并从拟合中获得系数。

我对 python 非常缺乏经验......到目前为止，我已经设法合并以下代码来拟合我的数据，但我还没有设法将拟合限制在范围内（从最大值点到曲线的末端或绘制它）

from pylab import *
from scipy.optimize import curve_fit
def func(x, a, c, d):
  return a*np.exp(-c*x)+d

popt, pcov = curve_fit(func, df_time, df_intensity)

Answer 1

正如您所说，您需要将第一个点与指数衰减开始的点分开。在这里，我通过使用最大强度点作为衰减的第一个点来做到这一点。

import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
from scipy.optimize import curve_fit

def func(x, a, c, d):
    return a*np.exp(-c*x)+d

df_intensity = '2.80816437e-04 4.68942336e-03 1.86014497e-03 4.91956615e-03 1.71023544e-03 1.27739808e-03 2.69837148e-03 3.03619576e-03 2.93695988e-03 1.00000000e+00 9.86672832e-01 9.35505121e-01 9.10113403e-01 8.63508432e-01 8.13620231e-01 7.95973135e-01 7.86302914e-01 7.65104440e-01 7.51126961e-01 7.23412701e-01 6.78247705e-01 6.94902443e-01 6.83302401e-01 6.61177022e-01 6.58689791e-01 6.40576075e-01 6.31106438e-01 6.36152688e-01 6.24960147e-01 6.03523085e-01 5.75500561e-01 5.79641019e-01 5.79132172e-01 5.63659819e-01 5.61770115e-01 5.59135085e-01 5.48466172e-01 5.32841799e-01 5.28933594e-01 5.22816863e-01 5.11256939e-01 5.06882114e-01 5.00026393e-01 4.97034536e-01 4.89032323e-01 4.82624219e-01 4.79193191e-01 4.73355165e-01 4.61712896e-01 4.59367128e-01 4.59443139e-01 4.51200226e-01 4.44606319e-01 4.46339779e-01 4.39093449e-01 4.30048203e-01 4.29030508e-01 4.28589225e-01 4.19683332e-01 4.13034528e-01 4.14086006e-01 4.11921819e-01 4.04496019e-01 3.96624713e-01 3.98299055e-01 3.89500844e-01 3.82822480e-01 3.81116467e-01 3.85759440e-01 3.83958414e-01 3.75875968e-01 3.75905527e-01 3.75681719e-01 3.69588213e-01 3.65200720e-01 3.66254310e-01 3.66418999e-01 3.61814032e-01 3.55682521e-01 3.56459517e-01 3.54392455e-01 3.48763458e-01 3.47853443e-01 3.49859275e-01 3.48366514e-01 3.40265065e-01 3.41580469e-01 3.40355856e-01 3.37516020e-01 3.33388230e-01'
df_time = '20. 30. 40. 50. 60. 70. 80. 90. 100. 110. 120. 130. 140. 150. 160. 170. 180. 190. 200. 210. 220. 230. 240. 250. 260. 270. 280. 290. 300. 310. 320. 330. 340. 350. 360. 370. 380. 390. 400. 410. 420. 430. 440. 450. 460. 470. 480. 490. 500. 510. 520. 530. 540. 550. 560. 570. 580. 590. 600. 610. 620. 630. 640. 650. 660. 670. 680. 690. 700. 710. 720. 730. 740. 750. 760. 770. 780. 790. 800. 810. 820. 830. 840. 850. 860. 870. 880. 890. 900. 910.'
df_intensity = np.array([float(i) for i in df_intensity.split(' ')])
df_time = np.array([float(i) for i in df_time.split(' ')])

# starting point for the decay to fit
decay_start = np.argmax(df_intensity)

# use only decay points in the fit
guess = [1, 0.001, 0]
popt, pcov = curve_fit(func, df_time[decay_start:],
                       df_intensity[decay_start:],
                       p0=guess)

# get the fit curve
fit = func(df_time[decay_start:], *popt)

# plot the fit and data
plt.plot(df_time[decay_start:], fit, label='fit', c='r')
plt.scatter(df_time, df_intensity, label='data')
plt.legend()
plt.show()

print('Fit parameters: {}'.format(popt))

返回

Fit parameters: [0.99347494 0.00407874 0.32579395]