"""
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')

##############################################################################
# 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')

##############################################################################
# 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')

##############################################################################
# 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')