How can I determine the x-value of a maximum of a data set within a certain range?

For context, these records the datasets look like this:

• value['Wavelength']:

  PixelNo
  0       1167.467506
  1       1167.219570
  2       1166.971628
  3       1166.723680
  4       1166.475725
             ...     
  3635     233.904486
  3636     233.641110
  3637     233.377731
  3638     233.114350
  3639     232.850967
  Name: Wavelength, Length: 3640, dtype: float64
  

• value['Calib_1']:

  PixelNo
  0       1.000000e 00
  1       5.500000e 01
  2       3.500000e 01
  3       1.000000e-07
  4       4.600000e 01
              ...     
  3635    4.000000e 01
  3636    7.400000e 01
  3637    1.000000e-07
  3638    3.000000e 00
  3639    1.600000e 01
  Name: Calib_1, Length: 3640, dtype: float64
  

This is an example of the corresponding plot of all data sets.

CodePudding user response：

You can use argmax method which returns the index of the maximum value.
Let's suppose you have a curve like this:

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


value = pd.DataFrame({'Wavelength': np.linspace(250, 600, 10000)})
value['Calib_1'] = (np.sin(2*np.pi/20*value['Wavelength'])*np.exp(-(value['Wavelength']-455)**2/20/(600-250)))**2

fig, ax = plt.subplots()

ax.plot(value['Wavelength'], value['Calib_1'], color = 'blue')

ax.set_xlabel('Wavelength')
ax.set_ylabel('Calib_1')

plt.show()

The above curve is designed to have a maximum in 455.
You can find the index of the maximum with:

value['Calib_1'].argmax()
# 5857

and use it to get the corresponding x axis value through loc method:

value.loc[value['Calib_1'].argmax(), 'Wavelength']
# 455.015501550155

As you can see, it returns a value approximately close to the exact value of 455. The error is to be addressed to the x axis discretization with numpy.linspace.
You can plot the maximum on the above plot with:

id_max = value['Calib_1'].argmax()
x_max = value.loc[id_max, 'Wavelength']
y_max = value.loc[id_max, 'Calib_1']


fig, ax = plt.subplots()

ax.plot(value['Wavelength'], value['Calib_1'], color = 'blue')
ax.plot(x_max, y_max, marker = 'o', color = 'red')

ax.set_xlabel('Wavelength')
ax.set_ylabel('Calib_1')

plt.show()

If you need a maximum only on a specific range, let's say [500, 550], then first of all you have to filter the dataframe, then compute the index of the maximum:

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


value = pd.DataFrame({'Wavelength': np.linspace(250, 600, 10000)})
value['Calib_1'] = (np.sin(2*np.pi/20*value['Wavelength'])*np.exp(-(value['Wavelength']-455)**2/20/(600-250)))**2

value_filt = value[(value['Wavelength'] >= 500) & (value['Wavelength'] <= 550)].reset_index()
id_max = value_filt['Calib_1'].argmax()
x_max = value_filt.loc[id_max, 'Wavelength']
y_max = value_filt.loc[id_max, 'Calib_1']


fig, ax = plt.subplots()

ax.plot(value['Wavelength'], value['Calib_1'], color = 'blue')
ax.plot(x_max, y_max, marker = 'o', color = 'red')

ax.axvline(x = 500, color = 'black', linestyle = '--')
ax.axvline(x = 550, color = 'black', linestyle = '--')

ax.set_xlabel('Wavelength')
ax.set_ylabel('Calib_1')

plt.show()