def test_1():
random = np.random.RandomState(0)
p = 100
sigma = scipy.stats.wishart(scale=np.eye(p), seed=random).rvs()
Ns = [int(x) for x in [p / 10, p / 2, 2 * p, 10 * p]]
x = np.arange(p)
plt.figure(figsize=(8, 8))
for i, N in enumerate(Ns):
X = random.multivariate_normal(mean=np.zeros(p), cov=sigma, size=N)
S1 = np.cov(X.T)
S2 = cov_shrink_ss(X)[0]
S3 = cov_shrink_rblw(np.cov(X.T), len(X))[0]
plt.subplot(3, 2, i + 1)
plt.title('p/n = %.1f' % (p / N))
plt.plot(x,
sorted(np.linalg.eigvalsh(S2), reverse=True),
'b',
lw=2,
label='cov_shrink_ss')
plt.plot(x,
sorted(np.linalg.eigvalsh(S3), reverse=True),
'g',
alpha=0.7,
lw=2,
label='cov_shrink_rblw')
plt.plot(x,
sorted(np.linalg.eigvalsh(sigma), reverse=True),
'k--',
lw=2,
label='true')
plt.plot(x,
sorted(np.linalg.eigvalsh(S1), reverse=True),
'r--',
lw=2,
label='sample covariance')
if i == 1:
plt.legend(fontsize=10)
# plt.ylim(max(plt.ylim()[0], 1e-4), plt.ylim()[1])
plt.figtext(
.05, .05,
"""Ordered eigenvalues of the sample covariance matrix (red),
cov_shrink_ss()-estimated covariance matrix (blue),
cov_shrink_rblw()-estimated covariance matrix (green), and
true eigenvalues (dashed black). The data generated by sampling
from a p-variate normal distribution for p=100 and various
ratios of p/n. Note that for the larger value of p/n, the
cov_shrink_rblw() estimator is identical to the sample
covariance matrix.""")
# plt.yscale('log')
plt.ylabel('Eigenvalue')
plt.tight_layout()
plt.savefig('%s/test_2.png' % DIRNAME, dpi=300)
def test_1():
for X in [np.random.randn(10,3), np.random.randn(100,3)]:
r_result = corpcor.cov_shrink(X, lambda_var=0, verbose=False)
py_result = cov_shrink_ss(X)
np.testing.assert_array_almost_equal(r_result, py_result[0])
np.testing.assert_almost_equal(r.attr(r_result, 'lambda')[0], py_result[1])
def test_1():
random = np.random.RandomState(0)
p = 100
sigma = scipy.stats.wishart(scale=np.eye(p), seed=random).rvs()
Ns = [int(x) for x in [p/10, p/2, 2*p, 10*p]]
x = np.arange(p)
plt.figure(figsize=(8,8))
for i, N in enumerate(Ns):
X = random.multivariate_normal(mean=np.zeros(p), cov=sigma, size=N)
S1 = np.cov(X.T)
S2 = cov_shrink_ss(X)[0]
S3 = cov_shrink_rblw(np.cov(X.T), len(X))[0]
plt.subplot(3,2,i+1)
plt.title('p/n = %.1f' % (p/N))
plt.plot(x, sorted(np.linalg.eigvalsh(S2), reverse=True), 'b', lw=2, label='cov_shrink_ss')
plt.plot(x, sorted(np.linalg.eigvalsh(S3), reverse=True), 'g', alpha=0.7, lw=2, label='cov_shrink_rblw')
plt.plot(x, sorted(np.linalg.eigvalsh(sigma), reverse=True), 'k--', lw=2, label='true')
plt.plot(x, sorted(np.linalg.eigvalsh(S1), reverse=True), 'r--', lw=2, label='sample covariance')
if i == 1:
plt.legend(fontsize=10)
# plt.ylim(max(plt.ylim()[0], 1e-4), plt.ylim()[1])
plt.figtext(.05, .05,
"""Ordered eigenvalues of the sample covariance matrix (red),
cov_shrink_ss()-estimated covariance matrix (blue),
cov_shrink_rblw()-estimated covariance matrix (green), and
true eigenvalues (dashed black). The data generated by sampling
from a p-variate normal distribution for p=100 and various
ratios of p/n. Note that for the larger value of p/n, the
cov_shrink_rblw() estimator is identical to the sample
covariance matrix.""")
# plt.yscale('log')
plt.ylabel('Eigenvalue')
plt.tight_layout()
plt.savefig('%s/test_2.png' % DIRNAME, dpi=300)
def covariance(H_estimates, m, cov_mode):
"""Covariance estimation for H-vector with different methods"""
if cov_mode == 'ledoit_wolf':
cov, _ = ledoit_wolf(H_estimates.T)
elif cov_mode == 'empirical':
cov = np.cov(H_estimates)
elif cov_mode == 'shrink_ss':
cov, _ = covar.cov_shrink_ss(H_estimates.T)
elif cov_mode == "shrink_rblw":
S = np.cov(H_estimates)
cov, _ = covar.cov_shrink_rblw(S, H_estimates.shape[1])
else: # default: 'oas'
cov, _ = oas(H_estimates.T)
cov = cov / m
return cov
