def matrix_is_psd(M):
err = True
s, u = eigh(M, lower=True, check_finite=True)
eps = _multivariate._eigvalsh_to_eps(s, None, None)
if np.min(s) < -eps:
err = False
return err
def matrix_is_not_singular(M):
err = True
s, u = eigh(M, lower=True, check_finite=True)
eps = _multivariate._eigvalsh_to_eps(s, None, None)
d = s[s > eps]
if len(d) < len(s):
err = False
return err
def matrix_is_well_conditioned(M):
err = True
s, u = eigh(M, lower=True, check_finite=True)
eps = _multivariate._eigvalsh_to_eps(s, None, None)
if np.min(s) < -eps:
err = False
d = s[s > eps]
if len(d) < len(s):
err = False
return err
def is_valid_covariance_matrix(cov_matrix):
""" Checks if valid covariance matrix.
Computes the eigenvalues and checks for negative ones. Also checks
if the matrix is singular.
Args:
cov_matrix: a matrix to be checked.
Returns:
True if the array is valid covariance matrix and False otherwise.
"""
# Check for complex elements
if np.sum(np.where(np.iscomplex(cov_matrix))) > 0:
return False
# Check eigenvalues
try:
eig_values = eigh(cov_matrix, lower=True, check_finite=True)[0]
eps = _eigvalsh_to_eps(eig_values, None, None)
except ValueError:
print(cov_matrix)
return False
# Singular matrix (too small eigenvalues)
if np.min(eig_values) < -eps:
return False
large_eig_values = eig_values[eig_values > eps]
if len(large_eig_values) < len(eig_values):
return False
# Negative eigenvalues
if np.min(eig_values) < 0.0:
return False
return True
def problematic_hessian(hessian,
check_pd=True,
check_sing=True,
verbose=False):
""" Checks if the Hessian (covariance matrix) is problematic.
Computes the eigenvalues and checks for negative ones. Also checks
if the matrix is singular.
Args:
hessian: a matrix to be checked.
Returns:
True if the array is valid covariance matrix and False otherwise.
"""
if hessian is None:
return True
# Check for nan and inf
if np.isnan(hessian).any():
if verbose:
print("Warning: some Hessian elements are not finite...")
return True
# Check for nan and inf
if not np.all(np.isfinite(hessian)):
if verbose:
print("Warning: some Hessian elements are not finite...")
return True
# Check for nan and inf
if np.any(np.isnan(hessian)):
if verbose:
print("Warning: some Hessian elements are NaN...")
return True
# Check for complex elements
if np.any(np.iscomplex(hessian)):
if verbose:
print("Warning: some Hessian elements are complex...")
return True
# Check for large elements
if np.any(np.diag(hessian) > 1e20):
if verbose:
print("Warning: some Hessian elements are too large...")
return True
# Singular matrix (too small eigenvalues)
# Negative eigenvalues
flag = False
try:
eig_values = eigh(hessian, lower=True, check_finite=True)[0]
eps = _eigvalsh_to_eps(eig_values, None, None)
if check_sing and (np.abs(eig_values) < eps).any():
flag = True
if verbose:
print(
"Warning: Hessian has very small eigenvalues: {}.".format(
np.min(eig_values)))
large_eig_values = eig_values[np.abs(eig_values) > eps]
if check_sing and len(large_eig_values) < len(eig_values):
if verbose:
print("Warning: Hessian is illconditioned with eigenvalues:")
print(eig_values)
flag = True
if check_pd and np.min(eig_values) < 0.0:
if verbose:
neg_eig_values = eig_values[eig_values < 0.0]
print("Warning: Hessian has negative eigenvalues: {}".format(
neg_eig_values))
flag = True
except Exception as e:
print(e)
raise Warning(
"Numerical issues in eigenvalue computations, rejecting.")
flag = True
return flag