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
N, M_1, M_2 = [
self.params[key] for key in ['size_N', 'size_M1', 'size_M2']
]
fig, ax = plt.subplots(1, 1)
# Title
str_ratio = r'with ratios $M_1/N \approx {:.3f}, M_2/N \approx {:.3f}$'.format(
M_1 / N, M_2 / 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 Beta(a,b) reference measure
a, b = [self.params[key] for key in ['a', 'b']]
x = np.linspace(0, 1, 100)
ax.plot(x,
sp_beta.pdf(x, a=a, b=b),
'r-',
lw=2,
alpha=0.6,
label=r'$\operatorname{{Beta}}({},{})$'.format(a, b))
else: # self.beta > 0
if normalization:
# Display the limiting distribution: Wachter law
eps = 5e-3
x = np.linspace(eps, 1.0 - eps, 500)
ax.plot(x,
rm.wachter_law(x, M_1, M_2, N),
'r-',
lw=2,
alpha=0.6,
label=r'$f_{Wachter}$')
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_wachter_for_jacobi_ensemble_banded_model(self):
"""
"""
M_1, M_2 = 2 * self.N, 4 * self.N
a, b = M_1 / self.N, M_2 / self.N
supp = ((np.sqrt(a * (a + b - 1)) + np.array([-1, 1]) * np.sqrt(b)) /
(a + b))**2
tol = 1e-2
bins = np.linspace(supp[0] + tol, supp[1] - tol, 20)
f_theo = [
quad(lambda x: rm.wachter_law(x, M_1, M_2, self.N), a, b)[0]
for a, b in zip(bins[:-1], bins[1:])
]
for beta in (1, 2, 4):
je = be.JacobiEnsemble(beta)
for _ in range(self.nb_samples):
je.sample_banded_model(size_N=self.N, size_M1=M_1, size_M2=M_2)
vals, _ =\
np.histogram(je.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.wachter_law(x, M_1, M_2, N)