def remove_redundant_rows(data):
"""Remove redundant constraints from A and G.
Parameters
----------
data : dict
All the problem data.
Returns
-------
str
A status indicating if infeasibility was detected.
"""
# Extract data.
dims = data[s.DIMS]
A = data[s.A]
G = data[s.G]
b = data[s.B]
h = data[s.H]
# Remove redundant rows in A.
if A is not None:
# The pivoting improves robustness.
Q, R, P = scipy.linalg.qr(A.todense(), pivoting=True)
rows_to_keep = []
for i in range(R.shape[0]):
if np.linalg.norm(R[i, :]) > 1e-10:
rows_to_keep.append(i)
R = R[rows_to_keep, :]
Q = Q[:, rows_to_keep]
# Invert P from col -> var to var -> col.
Pinv = np.zeros(P.size, dtype='int')
for i in range(P.size):
Pinv[P[i]] = i
# Rearrage R.
R = R[:, Pinv]
A = R
b_old = b
b = Q.T.dot(b)
# If b is not in the range of Q,
# the problem is infeasible.
if not np.allclose(b_old, Q.dot(b)):
return s.INFEASIBLE
dims[s.EQ_DIM] = int(b.shape[0])
data["Q"] = intf.dense2cvxopt(Q)
# Remove obviously redundant rows in G's <= constraints.
if G is not None:
G = G.tocsr()
G_leq = G[:dims[s.LEQ_DIM], :]
h_leq = h[:dims[s.LEQ_DIM]].ravel()
G_other = G[dims[s.LEQ_DIM]:, :]
h_other = h[dims[s.LEQ_DIM]:].ravel()
G_leq, h_leq, P_leq = compress_matrix(G_leq, h_leq)
dims[s.LEQ_DIM] = int(h_leq.shape[0])
data["P_leq"] = intf.sparse2cvxopt(P_leq)
G = sp.vstack([G_leq, G_other])
h = np.hstack([h_leq, h_other])
# Convert A, b, G, h to CVXOPT matrices.
data[s.A] = A
data[s.G] = G
data[s.B] = b
data[s.H] = h
return s.OPTIMAL
def remove_redundant_rows(data):
"""Check if A has redundant rows. If it does, remove redundant constraints
from A, and apply a presolve procedure for G.
Parameters
----------
data : dict
All the problem data.
Returns
-------
str
A status indicating if infeasibility was detected.
"""
# Extract data.
dims = data[s.DIMS]
A = data[s.A]
G = data[s.G]
b = data[s.B]
h = data[s.H]
if A is None:
return s.OPTIMAL
TOL = 1e-10
#
# Use a gram matrix approach to skip dense QR factorization, if possible.
#
gram = A @ A.T
if gram.shape[0] == 1:
gram = gram.toarray().item() # we only have one equality constraint.
if gram > 0:
return s.OPTIMAL
elif not b.item() == 0.0:
return s.INFEASIBLE
else:
data[s.A] = None
data[s.B] = None
return s.OPTIMAL
eig = eigsh(gram, k=1, which='SM', return_eigenvectors=False)
if eig > TOL:
return s.OPTIMAL
#
# Redundant constraints exist, up to numerical tolerance;
# reformulate equality constraints to remove this redundancy.
#
Q, R, P = scipy.linalg.qr(A.todense(), pivoting=True) # pivoting helps robustness
rows_to_keep = []
for i in range(R.shape[0]):
if np.linalg.norm(R[i, :]) > TOL:
rows_to_keep.append(i)
R = R[rows_to_keep, :]
Q = Q[:, rows_to_keep]
# Invert P from col -> var to var -> col.
Pinv = np.zeros(P.size, dtype='int')
for i in range(P.size):
Pinv[P[i]] = i
# Rearrage R.
R = R[:, Pinv]
A = R
b_old = b
b = Q.T.dot(b)
# If b is not in the range of Q, the problem is infeasible.
if not np.allclose(b_old, Q.dot(b)):
return s.INFEASIBLE
dims[s.EQ_DIM] = int(b.shape[0])
data["Q"] = intf.dense2cvxopt(Q)
#
# Since we're applying nontrivial presolve to A, apply to G as well.
#
if G is not None:
G = G.tocsr()
G_leq = G[:dims[s.LEQ_DIM], :]
h_leq = h[:dims[s.LEQ_DIM]].ravel()
G_other = G[dims[s.LEQ_DIM]:, :]
h_other = h[dims[s.LEQ_DIM]:].ravel()
G_leq, h_leq, P_leq = compress_matrix(G_leq, h_leq)
dims[s.LEQ_DIM] = int(h_leq.shape[0])
data["P_leq"] = intf.sparse2cvxopt(P_leq)
G = sp.vstack([G_leq, G_other])
h = np.hstack([h_leq, h_other])
# Record changes, and return.
data[s.A] = A
data[s.G] = G
data[s.B] = b
data[s.H] = h
return s.OPTIMAL
