def test_pseudodet_pinv():
# Make sure that pseudo-inverse and pseudo-det agree on cutoff
# Assemble random covariance matrix with large and small eigenvalues
np.random.seed(1234)
n = 7
x = np.random.randn(n, n)
cov = np.dot(x, x.T)
s, u = scipy.linalg.eigh(cov)
s = 0.5 * np.ones(n)
s[0] = 1.0
s[-1] = 1e-7
cov = np.dot(u, np.dot(np.diag(s), u.T))
# Set cond so that the lowest eigenvalue is below the cutoff
cond = 1e-5
psd = _PSD(cov, cond=cond)
psd_pinv = _PSD(psd.pinv, cond=cond)
# Check that the log pseudo-determinant agrees with the sum
# of the logs of all but the smallest eigenvalue
assert_allclose(psd.log_pdet, np.sum(np.log(s[:-1])))
# Check that the pseudo-determinant of the pseudo-inverse
# agrees with 1 / pseudo-determinant
assert_allclose(-psd.log_pdet, psd_pinv.log_pdet)
def test_pseudodet_pinv():
# Make sure that pseudo-inverse and pseudo-det agree on cutoff
# Assemble random covariance matrix with large and small eigenvalues
np.random.seed(1234)
n = 7
x = np.random.randn(n, n)
cov = np.dot(x, x.T)
s, u = scipy.linalg.eigh(cov)
s = 0.5 * np.ones(n)
s[0] = 1.0
s[-1] = 1e-7
cov = np.dot(u, np.dot(np.diag(s), u.T))
# Set cond so that the lowest eigenvalue is below the cutoff
cond = 1e-5
psd = _PSD(cov, cond=cond)
psd_pinv = _PSD(psd.pinv, cond=cond)
# Check that the log pseudo-determinant agrees with the sum
# of the logs of all but the smallest eigenvalue
assert_allclose(psd.log_pdet, np.sum(np.log(s[:-1])))
# Check that the pseudo-determinant of the pseudo-inverse
# agrees with 1 / pseudo-determinant
assert_allclose(-psd.log_pdet, psd_pinv.log_pdet)
def test_large_pseudo_determinant():
# Check that large pseudo-determinants are handled appropriately.
# Construct a singular diagonal covariance matrix
# whose pseudo determinant overflows double precision.
large_total_log = 1000.0
npos = 100
nzero = 2
large_entry = np.exp(large_total_log / npos)
n = npos + nzero
cov = np.zeros((n, n), dtype=float)
np.fill_diagonal(cov, large_entry)
cov[-nzero:, -nzero:] = 0
# Check some determinants.
assert_equal(scipy.linalg.det(cov), 0)
assert_equal(scipy.linalg.det(cov[:npos, :npos]), np.inf)
# np.linalg.slogdet is only available in numpy 1.6+
# but scipy currently supports numpy 1.5.1.
# assert_allclose(np.linalg.slogdet(cov[:npos, :npos]),
# (1, large_total_log))
# Check the pseudo-determinant.
psd = _PSD(cov)
assert_allclose(psd.log_pdet, large_total_log)
def test_large_pseudo_determinant():
# Check that large pseudo-determinants are handled appropriately.
# Construct a singular diagonal covariance matrix
# whose pseudo determinant overflows double precision.
large_total_log = 1000.0
npos = 100
nzero = 2
large_entry = np.exp(large_total_log / npos)
n = npos + nzero
cov = np.zeros((n, n), dtype=float)
np.fill_diagonal(cov, large_entry)
cov[-nzero:, -nzero:] = 0
# Check some determinants.
assert_equal(scipy.linalg.det(cov), 0)
assert_equal(scipy.linalg.det(cov[:npos, :npos]), np.inf)
# np.linalg.slogdet is only available in numpy 1.6+
# but scipy currently supports numpy 1.5.1.
# assert_allclose(np.linalg.slogdet(cov[:npos, :npos]),
# (1, large_total_log))
# Check the pseudo-determinant.
psd = _PSD(cov)
assert_allclose(psd.log_pdet, large_total_log)
