def test_circular():
rng = ensure_rng(10)
n = 6
sy = np.kron(np.identity(n // 2), [[0, 1j], [-1j, 0]])
for sym in rmt.sym_list:
if rmt.t(sym) == -1 or rmt.p(sym) == -1:
raises(ValueError, rmt.circular, 5, sym)
s = rmt.circular(n, sym, rng=rng)
assert_allclose(np.dot(s, s.T.conj()),
np.identity(n),
atol=1e-9,
err_msg='Unitarity broken in ' + sym)
if rmt.t(sym):
s1 = np.copy(
s.T if rmt.p(sym) != -1 else np.dot(sy, np.dot(s.T, sy)))
s1 *= rmt.t(sym) * (-1 if rmt.p(sym) == -1 else 1)
assert_allclose(s, s1, atol=1e-9, err_msg='TRS broken in ' + sym)
if rmt.p(sym):
s1 = np.copy(s.conj() if rmt.p(sym) != -1 else np.
dot(sy, np.dot(s.conj(), sy)))
if sym in ('DIII', 'CI'):
s1 *= -1
assert_allclose(s, s1, atol=1e-9, err_msg='PHS broken in ' + sym)
if rmt.c(sym):
assert_allclose(s,
s.T.conj(),
atol=1e-9,
err_msg='SLS broken in ' + sym)
# Check for distribution properties if the ensemble is a symmetric group.
f = lambda x: x[0] / np.linalg.norm(x)
for sym in ('A', 'C'):
sample_distr = np.apply_along_axis(f, 0, rng.randn(2 * n, 1000))
s_sample = np.array(
[rmt.circular(n, sym, rng=rng) for i in range(1000)])
assert stats.ks_2samp(sample_distr, s_sample[:, 0, 0].real)[1] > 0.1, \
'Noncircular distribution in ' + sym
assert stats.ks_2samp(sample_distr, s_sample[:, 3, 2].real)[1] > 0.1, \
'Noncircular distribution in ' + sym
assert stats.ks_2samp(sample_distr, s_sample[:, 1, 1].imag)[1] > 0.1, \
'Noncircular distribution in ' + sym
assert stats.ks_2samp(sample_distr, s_sample[:, 2, 3].imag)[1] > 0.1, \
'Noncircular distribution in ' + sym
sample_distr = np.apply_along_axis(f, 0, rng.randn(n, 500))
s_sample = np.array([rmt.circular(n, 'D', rng=rng) for i in range(500)])
ks = stats.ks_2samp(sample_distr, s_sample[:, 0, 0])
assert ks[1] > 0.1, 'Noncircular distribution in D ' + str(ks)
ks = stats.ks_2samp(sample_distr, s_sample[:, 3, 2])
assert ks[1] > 0.1, 'Noncircular distribution in D ' + str(ks)
def test_gaussian_symmetries():
rng = ensure_rng(10)
for n in (5, 8, 100, 200):
for sym in rmt.sym_list:
if sym not in ('A', 'D', 'AI') and n % 2:
raises(ValueError, rmt.gaussian, 5, sym)
continue
h = rmt.gaussian(n, sym, rng=rng)
if rmt.t(sym):
t_mat = np.array(rmt.h_t_matrix[sym])
t_mat = np.kron(np.identity(n // len(t_mat)), t_mat)
assert_allclose(h,
np.dot(t_mat, np.dot(h.conj(), t_mat)),
err_msg='TRS broken in ' + sym)
if rmt.p(sym):
p_mat = np.array(rmt.h_p_matrix[sym])
p_mat = np.kron(np.identity(n // len(p_mat)), p_mat)
assert_allclose(h,
-np.dot(p_mat, np.dot(h.conj(), p_mat)),
err_msg='PHS broken in ' + sym)
if rmt.c(sym):
sz = np.kron(np.identity(n // 2), np.diag([1, -1]))
assert_allclose(h,
-np.dot(sz, np.dot(h, sz)),
err_msg='SLS broken in ' + sym)
def test_circular():
np.random.seed(10)
n = 6
sy = np.kron(np.identity(n / 2), [[0, 1j], [-1j, 0]])
for sym in rmt.sym_list:
if rmt.t(sym) == -1 or rmt.p(sym) == -1:
assert_raises(ValueError, rmt.circular, 5, sym)
s = rmt.circular(n, sym)
assert_allclose(np.dot(s, s.T.conj()), np.identity(n), atol=1e-9,
err_msg='Unitarity broken in ' + sym)
if rmt.t(sym):
s1 = np.copy(s.T if rmt.p(sym) != -1
else np.dot(sy, np.dot(s.T, sy)))
s1 *= rmt.t(sym) * (-1 if rmt.p(sym) == -1 else 1)
assert_allclose(s, s1, atol=1e-9, err_msg='TRS broken in ' + sym)
if rmt.p(sym):
s1 = np.copy(s.conj() if rmt.p(sym) != -1
else np.dot(sy, np.dot(s.conj(), sy)))
if sym in ('DIII', 'CI'):
s1 *= -1
assert_allclose(s, s1, atol=1e-9, err_msg='PHS broken in ' + sym)
if rmt.c(sym):
assert_allclose(s, s.T.conj(), atol=1e-9,
err_msg='SLS broken in ' + sym)
# Check for distribution properties if the ensemble is a symmetric group.
f = lambda x: x[0] / np.linalg.norm(x)
for sym in ('A', 'C'):
sample_distr = np.apply_along_axis(f, 0, np.random.randn(2 * n, 1000))
s_sample = np.array([rmt.circular(n, sym)
for i in range(1000)])
assert stats.ks_2samp(sample_distr, s_sample[:, 0, 0].real)[1] > 0.1, \
'Noncircular distribution in ' + sym
assert stats.ks_2samp(sample_distr, s_sample[:, 3, 2].real)[1] > 0.1, \
'Noncircular distribution in ' + sym
assert stats.ks_2samp(sample_distr, s_sample[:, 1, 1].imag)[1] > 0.1, \
'Noncircular distribution in ' + sym
assert stats.ks_2samp(sample_distr, s_sample[:, 2, 3].imag)[1] > 0.1, \
'Noncircular distribution in ' + sym
sample_distr = np.apply_along_axis(f, 0, np.random.randn(n, 500))
s_sample = np.array([rmt.circular(n, 'D') for i in range(500)])
ks = stats.ks_2samp(sample_distr, s_sample[:, 0, 0])
assert ks[1] > 0.1, 'Noncircular distribution in D ' + str(ks)
ks = stats.ks_2samp(sample_distr, s_sample[:, 3, 2])
assert ks[1] > 0.1, 'Noncircular distribution in D ' + str(ks)
def test_gaussian_symmetries():
np.random.seed(10)
for n in (5, 8, 100, 200):
for sym in rmt.sym_list:
if sym not in ('A', 'D', 'AI') and n % 2:
assert_raises(ValueError, rmt.gaussian, 5, sym)
continue
h = rmt.gaussian(n, sym)
if rmt.t(sym):
t_mat = np.array(rmt.h_t_matrix[sym])
t_mat = np.kron(np.identity(n / len(t_mat)), t_mat)
assert_allclose(h, np.dot(t_mat, np.dot(h.conj(), t_mat)),
err_msg='TRS broken in ' + sym)
if rmt.p(sym):
p_mat = np.array(rmt.h_p_matrix[sym])
p_mat = np.kron(np.identity(n / len(p_mat)), p_mat)
assert_allclose(h, -np.dot(p_mat, np.dot(h.conj(), p_mat)),
err_msg='PHS broken in ' + sym)
if rmt.c(sym):
sz = np.kron(np.identity(n / 2), np.diag([1, -1]))
assert_allclose(h, -np.dot(sz, np.dot(h, sz)),
err_msg='SLS broken in ' + sym)