fit exponential to range and plot results and fit

Question

I have two dataframes corresponding to intensity versus time that I have taken from a file (Pos10.csv).

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

The values corresponding to the df_intensity and df_time can be obtained from below.

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.]

With this data...I would like to: 1) fit an exponential decay from the maximum intensity point (y=1, independently of in which x position y=1 is because it varies from trace to trace) to the end of the trace. 2) plot my data with the fit and obtain the coefficients from the fit.

I am quite inexperienced with python...and so far I have managed to incorporate the followign code for fitting my data but I havent managed to limit the fit to the range (from maximun point to the end of the curve or to plot it)

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

Like you said, you need to separate the first points from the points where your exponential decay starts. Here I did this by using the maximum intensity point as your first point of the decay.

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))

Returns

Fit parameters: [0.99347494 0.00407874 0.32579395]