Boosting density representation

Describes how speed up histogram representation of ensemble spectral density.

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

import time

from skrmt.ensemble import GaussianEnsemble, WishartEnsemble

We can sample a random matrix of the Gaussian Ensemble with a relatively large size and plot its spectral density.

goe = GaussianEnsemble(beta=1, n=5000)

t1 = time.time()
goe.plot_eigval_hist(bins=60, density=False, normalize=False)
t2 = time.time()

The time needed to compute the previous histogram is:

print(t2-t1, 'seconds')

7.273745059967041 seconds

We can speed up this procedure using the tridiagonal form of Gaussian Ensemble random matrices: tridiagonal_form=True.

goe_tridiag = GaussianEnsemble(beta=1, n=5000, tridiagonal_form=True)

t1 = time.time()
goe_tridiag.plot_eigval_hist(bins=60, density=False, normalize=False)
t2 = time.time()

The time needed to compute the previous histogram is:

print(t2-t1, 'seconds')

0.2736492156982422 seconds

This boosting trick can be used with Wishart Ensemble too

wre = WishartEnsemble(beta=1, p=5000, n=10000)

t1 = time.time()
wre.plot_eigval_hist(bins=60, density=False, normalize=False)
t2 = time.time()

The time needed to compute the previous histogram is:

print(t2-t1, 'seconds')

7.242355823516846 seconds

Using tridiagonal form of the Wishart Ensemble by setting tridiagonal_form=True.

wre_tridiag = WishartEnsemble(beta=1, p=5000, n=10000, tridiagonal_form=True)

t1 = time.time()
wre_tridiag.plot_eigval_hist(bins=60, density=False, normalize=False)
t2 = time.time()

The time needed to compute the previous histogram is:

print(t2-t1, 'seconds')

0.2683908939361572 seconds