https://codingforchemistsbook.com/book_material/chapter-11/index.html Data Download Data for Chapter 11 Alternatively, individual files can be found in the Data section. Code from chapter ''' A quick test of the accuracty of linear and cubic spline interpolation Written by: myself (email@domain.com) Changelog: 240606 - v1.0.0 - initial version ''' import numpy as np import scipy.interpolate as spi # Define a function that returns the y-values for a Gaussian function def Gaussian(x, A, x0, sigma): return A * np.exp(-1 * (x - x0)**2 / (2 * sigma**2)) # Define the parameters of the Gaussian A = 1 x0 = 0 sigma = 2 # Create the x- and y-values for the fake data x_data = np.linspace(-5, 5, 8) y_data = Gaussian(x_data, A, x0, sigma) # Create the x- and (exact) y-values for the points at which we would like interpolation x_interp = np.linspace(-5, 5, 1000) y_interp_exact = Gaussian(x_interp, A, x0, sigma) # Do the interpolation. First we will do a linear interpolation y_interp_linear = np.interp(x_interp, x_data, y_data) # Do the cubic spline interpolation - first create the cubic spline object cs = spi.CubicSpline(x_data, y_data) # Now generate the array of interpolated points using the cubic spline object y_interp_cubic = cs(x_interp) # Compute and print the RMSE print(f"Linear Interpolation RMSE: {np.sqrt(np.sum((y_interp_linear - y_interp_exact)**2)):4.2f}") print(f" Cubic Interpolation RMSE: {np.sqrt(np.sum((y_interp_cubic - y_interp_exact)**2)):4.2f}") ''' Produce an interpolated 785 nm raman spectrum with data points that match an old 532 nm spectrum Requires: one 532 nm and one 785 nm Raman spectrum Written by: Chris Johnson and Ben Lear (authors@codechembook.com) v1.0.0 - 250304 - initial version ''' import numpy as np from plotly.subplots import make_subplots from codechembook.quickTools import quickSelectFolder, quickPopupMessage from codechembook.symbols.chem import wavenumber as wn # Scaling factor for 532 data scale_532 = 2.95 # Get the folder containing the files to process quickPopupMessage(message = 'Select the folder with the Raman spectra.') folder_name = quickSelectFolder() # Read the data: 785 is the new data that has a contaminant, 532 is the old data x532, y532 = np.genfromtxt(folder_name/'oldNPs.csv', delimiter = ',', skip_header = 2, unpack = True) x785, y785 = np.genfromtxt(folder_name/'newNPs.csv', delimiter = ',', skip_header = 2, unpack = True) # Interpolate to the 532 spectrum because 785 has the larger span of x points y785_interp = np.interp(x532, x785, y785) # Normalize the 532 data and subtract it from the 785 data y_delta = y785_interp - scale_532 * y532 # Plot the 785 spectrum, the 532 spectrum, and the difference spectrum fig = make_subplots(2, 1) fig.add_scatter(x = x532, y = y785_interp, name = '785 nm', row = 1, col = 1) fig.add_scatter(x = x532, y = scale_532 * y532, name = '532 nm', row=1, col=1) fig.add_scatter(x = x532, y = y_delta, name = 'Subtracted', showlegend = False, row = 2, col = 1) fig.update_xaxes(title = f'wavenumber /{wn}') fig.update_yaxes(title = 'intensity') fig.update_layout(template = 'simple_white', font_size = 18, width = 3 * 300, height = 3 * 300, margin = dict(b = 10, t = 30, l = 10, r = 10)) fig.show('png') fig.write_image('raman.png') Solutions to Exercises Targeted exercises Implementing linear interpolation using numpy.interp Exercise 1 Consider a Gaussian distribution with $x_0 = 0$, $\sigma = 2$, and amplitude of 1. Hugo en-us authors@codingforchemistsbook.com (Benjamin Lear and Christopher Johnson) authors@codingforchemistsbook.com (Benjamin Lear and Christopher Johnson)