def parameter_bounds(self):
"""
Bounds on the realizations of the uncertain parameters, as inferred from the uncertainty set.
"""
scale = self.scale
nom_value = self.center
P = self.shape_matrix
parameter_bounds = [(nom_value[i] - np.power(1.0 / P[i][i], 0.5) * scale,
nom_value[i] + np.power(1.0 / P[i][i], 0.5) * scale) for i in range(self.dim)]
return parameter_bounds
def __init__(self, center, shape_matrix, scale=1):
"""
EllipsoidalSet constructor
Args:
center: Vector (``list``) of uncertain parameter values around which deviations are restrained.
shape_matrix: Positive semi-definite matrix, effectively a covariance matrix for
constraint and bounds determination.
scale: Right-hand side value for the ellipsoid.
"""
# === Valid data in lists/matrixes
if not all(isinstance(elem, (int, float)) for row in shape_matrix for elem in row):
raise AttributeError("Matrix shape_matrix must be real-valued and numeric.")
if not all(isinstance(elem, (int, float)) for elem in center):
raise AttributeError("Vector center must be real-valued and numeric.")
if not isinstance(scale, (int, float)):
raise AttributeError("Ellipse scale must be a real-valued numeric.")
# === Valid matrix dimensions
num_cols = len(shape_matrix[0])
if not all(len(row) == num_cols for row in shape_matrix):
raise AttributeError("Shape matrix must have valid matrix dimensions.")
# === Ensure shape_matrix is a square matrix
array_shape_mat = np.asarray(shape_matrix)
if array_shape_mat.shape[0] != array_shape_mat.shape[1]:
raise AttributeError("Shape matrix must be square.")
# === Ensure dimensions of shape_matrix are same as dimensions of uncertain_params
if array_shape_mat.shape[1] != len(center):
raise AttributeError("Shape matrix must be "
"same dimensions as vector of uncertain parameters.")
# === Symmetric shape_matrix
if not np.all(np.abs(array_shape_mat-array_shape_mat.T) < 1e-8):
raise AttributeError("Shape matrix must be symmetric.")
# === Ensure scale is non-negative
if scale < 0:
raise AttributeError("Scale of ellipse (rhs) must be non-negative.")
# === Check if shape matrix is invertible
try:
np.linalg.inv(shape_matrix)
except np.linalg.LinAlgError as err:
raise("Error with shape matrix supplied to EllipsoidalSet object being singular. %s" % err)
# === Check is shape matrix is positive semidefinite
if not all(np.linalg.eigvals(shape_matrix) >= 0):
raise("Non positive-semidefinite shape matrix.")
# === Ensure matrix is not degenerate, for determining inferred bounds
try:
for i in range(len(shape_matrix)):
np.power(shape_matrix[i][i], 0.5)
except:
raise AttributeError("Shape matrix must be non-degenerate.")
self.center = center
self.shape_matrix = shape_matrix
self.scale = scale
self.type = "ellipsoidal"