def __init__(self, budget_membership_mat, rhs_vec):
"""
BudgetSet constructor
Args:
budget_membership_mat: A matrix with 0-1 entries to designate which uncertain parameters participate in each budget constraint. Here, each row is associated with a separate budget constraint.
rhs_vec: Vector (``list``) of right-hand side values for the budget constraints.
"""
# === Non-zero number of columns
mat = np.asarray(budget_membership_mat)
rhs = np.asarray(rhs_vec)
if len(mat.shape) == 1:
cols = mat.shape
else:
cols = mat.shape[1]
if cols == 0:
raise AttributeError(
"Budget membership matrix must have non-zero number of columns."
)
# === Assert is valid matrix (same number of columns across all rows
if not all(len(row) == cols for row in budget_membership_mat):
raise AttributeError(
"Budget membership matrix must be a valid matrix, "
"e.g. same number of column entries across rows.")
# === Matrix dimension compatibility
if mat.shape[0] != rhs.shape[0]:
raise AttributeError(
"Rows of lhs_coefficients_mat matrix must equal rows of rhs_vec lists."
)
# === Ensure a 0-1 matrix
if any(not np.isclose(elem, 0) and not np.isclose(elem, 1)
for row in budget_membership_mat for elem in row):
raise AttributeError(
"Budget membership matrix must be a matrix of 0's and 1's.")
# === No all zero rows
if all(elem == 0 for row in budget_membership_mat for elem in row):
raise AttributeError(
"All zero rows are not permitted in the budget membership matrix."
)
# === Ensure 0 <= rhs_i for all i
if any(rhs_vec[i] < 0 for i in range(len(rhs_vec))):
raise AttributeError("RHS vector entries must be >= 0.")
# === Non-emptiness is implied by the set
# === Add constraints such that uncertain params are >= 0
# === This adds >=0 bound on all parameters in the set
cols = mat.shape[1]
identity = np.identity(cols) * -1
for row in identity:
budget_membership_mat.append(row.tolist())
for i in range(identity.shape[0]):
rhs_vec.append(0)
self.coefficients_mat = budget_membership_mat
self.rhs_vec = rhs_vec
self.type = "budget"
def __init__(self, lhs_coefficients_mat, rhs_vec):
"""
PolyhedralSet constructor
Args:
lhs_coefficients_mat: Matrix of left-hand side coefficients for the linear inequality constraints defining the polyhedral set.
rhs_vec: Vector (``list``) of right-hand side values for the linear inequality constraints defining the polyhedral set.
"""
# === Real valued data
mat = np.asarray(lhs_coefficients_mat)
if not all(
isinstance(elem, (int, float)) for row in lhs_coefficients_mat
for elem in row):
raise AttributeError(
"Matrix lhs_coefficients_mat must be real-valued and numeric.")
if not all(isinstance(elem, (int, float)) for elem in rhs_vec):
raise AttributeError(
"Vector rhs_vec must be real-valued and numeric.")
# === Check columns of A must be same length as rhs
if mat.shape[0] != len(rhs_vec):
raise AttributeError(
"Rows of lhs_coefficients_mat matrix must equal length of rhs_vec list."
)
# === Columns are non-zero
if mat.shape[1] == 0:
raise AttributeError(
"Columns of lhs_coefficients_mat must be non-zero.")
# === Matrix is not all zeros
if all(
np.isclose(elem, 0) for row in lhs_coefficients_mat
for elem in row):
raise AttributeError(
"Matrix lhs_coefficients_mat cannot be all zeroes.")
# === Non-emptiness
res = sp.optimize.linprog(c=np.zeros(mat.shape[1]),
A_ub=mat,
b_ub=rhs_vec,
method="simplex")
if not res.success:
raise AttributeError(
"User-defined PolyhedralSet was determined to be empty. "
"Please check the set of constraints supplied during set construction."
)
# === Boundedness
if res.status == 3:
# scipy linprog status == 3 indicates unboundedness
raise AttributeError(
"User-defined PolyhedralSet was determined to be unbounded. "
"Please augment the set of constraints supplied during set construction."
)
self.coefficients_mat = lhs_coefficients_mat
self.rhs_vec = rhs_vec
self.type = "polyhedral"
def __init__(self, origin, number_of_factors, psi_mat, beta):
"""
FactorModelSet constructor
Args:
origin: Vector (``list``) of uncertain parameter values around which deviations are restrained.
number_of_factors: Natural number representing the dimensionality of the space to which the set projects.
psi: Matrix with non-negative entries designating each uncertain parameter's contribution to each factor. Here, each row is associated with a separate uncertain parameter and each column with a separate factor.
beta: Number in [0,1] representing the fraction of the independent factors that can simultaneously attain their extreme values. Setting 'beta = 0' will enforce that as many factors will be above 0 as there will be below 0 (i.e., "zero-net-alpha" model). Setting 'beta = 1' produces the hyper-rectangle [origin - psi e, origin + psi e], where 'e' is the vector of ones.
"""
mat = np.asarray(psi_mat)
# === Numeric valued arrays
if not all(isinstance(elem, (int, float)) for elem in origin):
raise AttributeError(
"All elements of origin vector must be numeric.")
if not all(
isinstance(elem, (int, float)) for row in psi_mat
for elem in row):
raise AttributeError(
"All elements of psi_mat vector must be numeric.")
if not isinstance(beta, (int, float)):
raise AttributeError("Beta parameter must be numeric.")
if not isinstance(number_of_factors, (int)):
raise AttributeError("number_of_factors must be integer.")
# === Ensure dimensions of psi are n x F
if mat.shape != (len(origin), number_of_factors):
raise AttributeError(
"Psi matrix must be of dimensions n x F where n is dim(uncertain_params)"
"and F is number_of_factors.")
# === Ensure beta in [0,1]
if beta > 1 or beta < 0:
raise AttributeError("Beta parameter must be in [0,1].")
# === No all zero columns of psi_mat
for idx in range(mat.shape[1]):
if all(np.isclose(elem, 0) for elem in mat[:, idx]):
raise AttributeError(
"Psi matrix cannot have all zero columns.")
# === Psi must be strictly positive entries
for idx in range(mat.shape[1]):
if any(elem < 0 for elem in mat[:, idx]):
raise AttributeError(
"Psi matrix cannot have any negative entries. All factors must be non-negative."
)
self.origin = origin
self.number_of_factors = number_of_factors
self.psi_mat = psi_mat
self.beta = beta
self.type = "factor_model"