Example of singular value decomposition applied or real spectral data, ready to be copied&pasted into https://github.com/FilipDominec/plotcommander

SVD_for_plotcommander.py

plotstyle = "basis"
#plotstyle = "amplitude"
decimatex = 20
ncomponents = 5
a = ys[:, ::decimatex]
xs = xs[:, ::decimatex]
U, s, V = np.linalg.svd(a, full_matrices=True)

if plotstyle=="basis":
  for x, y, label in         zip(xs[:ncomponents], V[:ncomponents], range(ncomponents)):
    ax.plot(x, y, label="SVD component %d" % (label+1), lw=5*.5**label)
    ax.set_xlabel(xlabelsdedup)
    ax.set_ylabel(ylabelsdedup)

if plotstyle=="amplitude":
  for y, label in         zip(np.dot(U,np.diag(s)).T, range(ncomponents)):
    ax.plot(range(U.shape[0]), y, marker='s', label="SVD component %d" % (label+1), lw=5*.5**label)
    ax.set_xlabel('dataset number')
    ax.set_ylabel('SVD component amplitude')

ax.set_title('')
ax.legend(loc='best', prop={'size':10})

Scientific data are often measured as a function of one or more parameters. In this case, I irradiated a semiconductor sample with an electron beam in a SEM and registered the optical emission spectra. The plots are overlapping and are quite hard to understand:

However, there is clearly some complex dependence on the voltage! I could set up some fitting to determine how the spectral peaks grow, shift and/or broaden, but SVD can do a similar job, and it is fully automatic requiring no prior knowledge of how the data should look like. In a nutshell, SVD finds the optimum basis functions for the whole dataset, orders them starting from the most prominent basis function, and expresses each of the spectral curves as a sum of these. The first five basis functions are as such:

Now one can change the code as such:

#plotstyle = "basis"
plotstyle = "amplitude"

to retrieve the respective amplitudes of each basis function and for each data file. From the dependence of first three amplitudes on the acceleration voltage, it is easy to show how

• the main spectral peak grows (blue, component 1)
• how it shifts (orange, component 2)
• how it gets narrower and how another peak emerges at shorter wavelength when electron acceleration voltage exceeds 15 kV (green, component 3) etc.
• Higher numbered components tend to enable less physical interpretation and are mostly noise.

The presented code is just a snippet of python code; to use it, either select your data files in plotcommander (https://github.com/FilipDominec/plotcommander), or write a simple standalone python script that loads the data arrays into the xs and ys variables.