Principal Component Analysis of azimuthal flow in intermediate-energy heavy-ion reactions

Principal Component Analysis (PCA) via Singular Value Decomposition (SVD) of large datasets is an adaptive exploratory method to uncover natural patterns underlying the data. Several recent applications PCA-SVD event-by-event single-particle azimuthal angle distribution matrices in ultra-relativistic heavy-ion collisions at RHIC-LHC energies indicate that sine and cosine functions chosen {\it a priori} traditional Fourier analysis are naturally most optimal basis for flow studies according data itself. We perform analyses mid-central Au+Au $E_{\rm beam}/A$=1.23 GeV simulated using isospin-dependent Boltzmann-Uehling-Uhlenbeck (IBUU) transport model address following two questions: (1) if principal components covariance matrix nucleon distributions reactions around 1 GeV/nucleon and/or (2) what any advantages may have over expansion studying EOS dense nuclear matter. find none our come out as functions, while both eigenvectors eigenvalues appreciably dependent, has no apparent advantage matter collective collisions.