def __display_and_normalization(self, display_type, normalization):
if not self.list_of_samples:
raise ValueError(
'Empty attribute `list_of_samples`, sample first!')
else:
points = self.list_of_samples[-1].copy() # Pick last sample
if normalization:
points = self.normalize_points(points)
N, M = [self.params[key] for key in ['size_N', 'size_M']]
fig, ax = plt.subplots(1, 1)
# Title
str_ratio = r'with ratio $M/N \approx {:.3f}$'.format(M / N)
# Answers Issue #33 raised by @adrienhardy
str_beta = '' if self.beta > 0 else 'with i.i.d. draws'
title = '\n'.join([self._str_title(), ' '.join([str_ratio, str_beta])])
plt.title(title)
if self.beta == 0:
if normalization:
# Display Gamma(k,2) reference measure of the full matrix model
k, theta = self.params['shape'], 2
x = np.linspace(0, np.max(points) + 4, 100)
ax.plot(x,
sp_gamma.pdf(x, a=k, loc=0.0, scale=theta),
'r-',
lw=2,
alpha=0.6,
label=r'$\Gamma({},{})$'.format(k, theta))
else: # self.beta > 0
if normalization:
# Display the limiting distribution: Marcenko Pastur
x = np.linspace(1e-2, np.max(points) + 0.3, 100)
ax.plot(x,
rm.marcenko_pastur_law(x, M, N),
'r-',
lw=2,
alpha=0.6,
label=r'$f_{Marcenko-Pastur}$')
if display_type == 'scatter':
ax.scatter(points,
np.zeros(points.shape[0]),
c='blue',
label='sample')
elif display_type == 'hist':
ax.hist(points,
bins=30,
density=1,
facecolor='blue',
alpha=0.5,
label='hist')
else:
pass
plt.legend(loc='best', frameon=False)
def test_marcenko_pastur_for_laguerre_ensemble_full_model(self):
"""
"""
M = 2 * self.N
supp = (1 + np.array([-1, 1]) * np.sqrt(self.N / M))**2
tol = 1e-2
bins = np.linspace(supp[0] + tol, supp[1] - tol, 20)
f_theo = [
quad(lambda x: rm.marcenko_pastur_law(x, M, self.N), a, b)[0]
for a, b in zip(bins[:-1], bins[1:])
]
for beta in (1, 2, 4):
le = be.LaguerreEnsemble(beta)
for _ in range(self.nb_samples):
le.sample_full_model(size_N=self.N, size_M=M)
vals, _ =\
np.histogram(le.normalize_points(le.list_of_samples[-1]),
bins=bins,
density=True)
f_emp = vals * np.diff(bins)
print(f_emp)
self.assertTrue(self.adequation(f_emp, f_theo))
def limiting_distribution(x):
return rm.marcenko_pastur_law(x, M, N)