Complex histograms

Shows how spectrum of random matrices with complex eigenvalues is plotted.

# Author: Alejandro Santorum Varela
# License: BSD 3-Clause

from skrmt.ensemble import CircularEnsemble

Several ensembles have symmetric or hermitian matrices, so their eigenvalues are real. However, there are some cases where random matrices are not symmetric either hermitian. Therefore, their eigenvalues can be complex.

This is the case of Circular Unitary Ensemble (CUE) and Circular Symplectic Ensemble (CSE).

scikit-rmt takes into account this possibility and uses histograms in 2D in order to represent spectrum distribution of given ensembles.

In this example, eigenvalue spectrum of CUE random matrix is shown.

cue = CircularEnsemble(beta=2, n=1000)
cue.plot_eigval_hist(bins=80)

And the eigenvalue spectrum of CSE.

cse = CircularEnsemble(beta=4, n=1000)
cse.plot_eigval_hist(bins=80)

The provided heatmap gives an illustration of the eigenvalue accumulation.