https://codingforchemistsbook.com/book_material/chapter-9/index.html Data Download Data for Chapter 9 Alternatively, individual files can be found in the Data section. Code from chapter ''' A quick test script to check the accuracy of numerical integration Written by: Chris Johnson and Ben Lear (authors@codechembook.com) v1.0.0 - 250220 - initial version ''' import numpy as np import scipy.integrate as spi # Gaussian parameters for the simulation A = 1 # amplitude x0 = 0 # center sigma = 1 # width # Create the test data and calculate the analytical value of integral xdata = np.linspace(-10, 10, 11) ydata = A * np.exp(-1 * (xdata - x0)**2 / (2 * sigma**2)) area = A * sigma * np.sqrt(2 * np.pi) # Compute the area using the rectangle rule, the trapezoid rule, or Simpson's rule area_rect = np.sum(ydata[:-1] * (xdata[1:] - xdata[:-1])) # height * width area_trap = spi.trapezoid(ydata, x = xdata) area_simp = spi.simpson(ydata, x = xdata) # Print the error print(f'Area = {area:8.6f}') print( 'Errors: Absolute --> % Diff') print(f'Rectangle: {area - area_rect:8.6f} --> {100*(area - area_rect)/area:4.1f}%') print(f'Trapezoid: {area - area_trap:8.6f} --> {100*(area - area_trap)/area:4.1f}%') print(f"Simpson's: {area - area_simp:8.6f} --> {100*(area - area_simp)/area:4.1f}%") ''' Integrate the intensities of azide peaks in an FTIR and produce a kinetics plot Requires: FTIR spectra in .csv format for each time point filename must include the time the spectrum was taken Written by: Chris Johnson and Ben Lear (authors@codechembook.com) v1.0.0 - 250220 - initial version ''' import numpy as np from plotly.subplots import make_subplots from codechembook.quickTools import quickOpenFilenames, quickPopupMessage from codechembook.quickPlots import customColorList from codechembook.symbols.chem import wavenumber as wn from codechembook.numericalTools import integrateRange # Get and sort the spectrum file names quickPopupMessage(message = 'Select CSV files containing the FTIR spectra.') data_files = sorted(quickOpenFilenames(filetypes = 'CSV files, *.csv')) # Set the upper and lower wavenumbers for the integration integration_limits = np.array([1950, 2150]) # Make a color scale for the different traces in the figure colors = customColorList(len(data_files)) # Get samples of a continuously changing color scale # Loop through files, read data and times, put them in a dict, and add to the plot data = [] fig = make_subplots(rows = 1, cols = 3) for c, file in zip(colors, data_files): wavenumber, absorption = np.genfromtxt(file, delimiter = ',', unpack = True) time = float(file.stem.split('_')[1]) # get the time from the file name # Create a dictionary with everything we need for this file, add it to the list data.append(dict(wavenumber = wavenumber, absorption = absorption, time = time)) # Add the trace to the plot fig.add_scatter(x = wavenumber, y = absorption, line = dict(color = c), name = time, row = 1, col = 1) # Loop through the spectra to background subtract and integrate for c, spec in zip(colors, data): # Find the indicies of the points at the limits of integration xmin_index = np.argmin(abs(spec['wavenumber'] - integration_limits[0])) xmax_index = np.argmin(abs(spec['wavenumber'] - integration_limits[1])) # Calculate line that connects the x and y values at the limits of integration m = (spec['absorption'][xmax_index] - spec['absorption'][xmin_index]) / (spec['wavenumber'][xmax_index] - spec['wavenumber'][xmin_index]) b = spec['absorption'][xmin_index] - m * spec['wavenumber'][xmin_index] # Subtract the baseline from the data and add it to the figure spec['back corr'] = spec['absorption'] - (m * spec['wavenumber'] + b) fig.add_scatter(x = spec['wavenumber'], y = spec['back corr'], line = dict(color = c), showlegend = False, row = 1, col = 2) # Integrate the baseline-corrected data and store it in the dict spec['integral'] = integrateRange(spec['back corr'], spec['wavenumber'], integration_limits) # Calculate the maximum y value for this spectrum section spec['ymax'] = np.max(spec['back corr'][xmin_index:xmax_index]) # Find the max y height to determine the zoom range for the y-axis ymax = max([spec['ymax'] for spec in data]) # Plot the kinetic trace tdata = np.array([spec['time'] for spec in data]) # get array of times intdata = np.array([spec['integral'] for spec in data]) # get array of integrals fig.add_scatter(x = tdata, y = intdata, name = 'kinetic trace', line = dict(color = 'black'), row = 1, col = 3) # Format the plot fig.update_xaxes(title = f'wavenumber / {wn}', row = 1, col = 1) fig.update_yaxes(title = 'absorption', row = 1, col = 1) fig.update_xaxes(title = f'wavenumber / {wn}', range = integration_limits, row = 1, col = 2) fig.update_yaxes(title = 'absorption', range = [-0.1 * ymax, 1.1 * ymax], row = 1, col = 2) fig.update_xaxes(title = 'time /s', row = 1, col = 3) fig.update_yaxes(title = f'intensity / AU{wn}', row = 1, col = 3) fig.update_layout(template = 'simple_white') fig.show('browser') # format for the static plot fig.update_layout(template = 'simple_white', showlegend = False, width = 4 * 300, height = 1.2 * 300, margin = {'b': 10, 't': 30, 'l': 10, 'r': 10}) fig.show('png') fig.write_image(format = 'png', file = 'IntegrateAzide.png') Solutions to Exercises Targeted exercises Integrating data using scipy.integrate Exercise 0 The cumulative integral is the integral from the beginning of the data up to a given data point, plotted against the value of the last data point integrated. Write a code that plots the cumulative integral of a Gaussian function with an amplitude of 1, a center of 5, and a width of 1, from 0 to 10 with 100 points on the $x$-axis. Hugo en-us authors@codingforchemistsbook.com (Benjamin Lear and Christopher Johnson) authors@codingforchemistsbook.com (Benjamin Lear and Christopher Johnson)