def test_primal_and_dual_infeasible_problem(self):
self.n = 2
self.m = 4
self.P = sparse.csc_matrix((2, 2))
self.q = np.array([-1., -1.])
self.A = sparse.csc_matrix([[1., -1.], [-1., 1.], [1., 0.], [0., 1.]])
self.l = np.array([1., 1., 0., 0.])
self.u = np.inf * np.ones(self.m)
self.model = osqp.OSQP()
self.model.setup(P=self.P,
q=self.q,
A=self.A,
l=self.l,
u=self.u,
**self.opts)
# Warm start to avoid infeasibility detection at first step
x0 = 25. * np.ones(self.n)
y0 = -2. * np.ones(self.m)
self.model.warm_start(x=x0, y=y0)
# Solve
res = self.model.solve()
# Assert close
self.assertIn(res.info.status_val, [
constant('OSQP_PRIMAL_INFEASIBLE'),
constant('OSQP_DUAL_INFEASIBLE')
])
def test_primal_and_dual_infeasible_problem(self):
self.n = 2
self.m = 4
self.P = sparse.csc_matrix((2, 2))
self.q = np.array([-1., -1.])
self.A = sparse.csc_matrix([[1., -1.], [-1., 1.], [1., 0.], [0., 1.]])
self.l = np.array([1., 1., 0., 0.])
self.u = np.inf * np.ones(self.m)
self.model = osqp.OSQP()
self.model.setup(P=self.P,
q=self.q,
A=self.A,
l=self.l,
u=self.u,
**self.opts)
res = self.model.solve()
# Assert close
self.assertIn(res.info.status_val, [
constant('OSQP_PRIMAL_INFEASIBLE'),
constant('OSQP_DUAL_INFEASIBLE')
])
def linsys_solver_str_to_int(settings):
linsys_solver_str = settings.pop('linsys_solver', '')
if not isinstance(linsys_solver_str, str):
raise TypeError("Setting linsys_solver " +
"is required to be a string.")
linsys_solver_str = linsys_solver_str.lower()
if linsys_solver_str == 'cuda pcg':
settings['linsys_solver'] = _osqp.constant('CUDA_PCG_SOLVER')
# Default solver: CUDA PCG
elif linsys_solver_str == '':
settings['linsys_solver'] = _osqp.constant('CUDA_PCG_SOLVER')
else: # default solver: CUDA PCG
warn("Linear system solver not recognized. " +
"Using default solver CUDA PCG.")
settings['linsys_solver'] = _osqp.constant('CUDA_PCG_SOLVER')
return settings
def test_primal_infeasible_problem(self):
# Set random seed for reproducibility
rg = Generator(PCG64(1))
self.n = 50
self.m = 500
# Generate random Matrices
Pt = sparse.random(self.n, self.n, random_state=rg)
self.P = sparse.triu(Pt.T.dot(Pt), format='csc')
self.q = rg.standard_normal(self.n)
self.A = sparse.random(self.m, self.n, random_state=rg).tolil() # Lil for efficiency
self.u = 3 + rg.standard_normal(self.m)
self.l = -3 + rg.standard_normal(self.m)
# Make random problem primal infeasible
self.A[int(self.n/2), :] = self.A[int(self.n/2)+1, :]
self.l[int(self.n/2)] = self.u[int(self.n/2)+1] + 10 * rg.random()
self.u[int(self.n/2)] = self.l[int(self.n/2)] + 0.5
# Convert A to csc
self.A = self.A.tocsc()
self.model = osqp.OSQP()
self.model.setup(self.P, self.q, self.A, self.l, self.u, **self.opts)
# Solve problem with OSQP
res = self.model.solve()
# Assert close
self.assertEqual(res.info.status_val, constant('OSQP_PRIMAL_INFEASIBLE'))
def test_non_convex(self):
# Setup workspace with new sigma
opts = {'verbose': False, 'sigma': 5}
self.model.setup(P=self.P, q=self.q, A=self.A, l=self.l, u=self.u, **opts)
# Solve problem
res = self.model.solve()
# Assert close
self.assertEqual(res.info.status_val, constant('OSQP_NON_CVX'))
nptest.assert_approx_equal(res.info.obj_val, np.nan)
def test_dual_infeasible_qp(self):
# Dual infeasible example
self.P = sparse.diags([4., 0.], format='csc')
self.q = np.array([0, 2])
self.A = sparse.csc_matrix([[1., 1.], [-1., 1.]])
self.l = np.array([-np.inf, -np.inf])
self.u = np.array([2., 3.])
self.model = osqp.OSQP()
self.model.setup(P=self.P,
q=self.q,
A=self.A,
l=self.l,
u=self.u,
**self.opts)
# Solve problem with OSQP
res = self.model.solve()
# Assert close
self.assertEqual(res.info.status_val, constant('OSQP_DUAL_INFEASIBLE'))
def test_dual_infeasible_lp(self):
# Dual infeasible example
self.P = sparse.csc_matrix((2, 2))
self.q = np.array([2, -1])
self.A = sparse.eye(2, format='csc')
self.l = np.array([0., 0.])
self.u = np.array([np.inf, np.inf])
self.model = osqp.OSQP()
self.model.setup(P=self.P,
q=self.q,
A=self.A,
l=self.l,
u=self.u,
**self.opts)
# Solve problem with OSQP
res = self.model.solve()
# Assert close
self.assertEqual(res.info.status_val, constant('OSQP_DUAL_INFEASIBLE'))
def test_primal_infeasible_problem(self):
# Simple QP problem
sp.random.seed(4)
self.n = 50
self.m = 500
# Generate random Matrices
Pt = sparse.random(self.n, self.n)
self.P = sparse.triu(Pt.T.dot(Pt), format='csc')
self.q = sp.randn(self.n)
self.A = sparse.random(self.m, self.n).tolil() # Lil for efficiency
self.u = 3 + sp.randn(self.m)
self.l = -3 + sp.randn(self.m)
# Make random problem primal infeasible
self.A[int(self.n / 2), :] = self.A[int(self.n / 2) + 1, :]
self.l[int(self.n / 2)] = self.u[int(self.n / 2) + 1] + 10 * sp.rand()
self.u[int(self.n / 2)] = self.l[int(self.n / 2)] + 0.5
# Convert A to csc
self.A = self.A.tocsc()
self.model = osqp.OSQP()
self.model.setup(P=self.P,
q=self.q,
A=self.A,
l=self.l,
u=self.u,
**self.opts)
# Solve problem with OSQP
res = self.model.solve()
# Assert close
self.assertEqual(res.info.status_val,
constant('OSQP_PRIMAL_INFEASIBLE'))
def prepare_data(P=None, q=None, A=None, l=None, u=None, **settings):
"""
Prepare problem data of the form
minimize 1/2 x' * P * x + q' * x
subject to l <= A * x <= u
solver settings can be specified as additional keyword arguments
"""
#
# Get problem dimensions
#
if P is None:
if q is not None:
n = len(q)
elif A is not None:
n = A.shape[1]
else:
raise ValueError("The problem does not have any variables")
else:
n = P.shape[0]
if A is None:
m = 0
else:
m = A.shape[0]
#
# Create parameters if they are None
#
if (A is None and (l is not None or u is not None)) or \
(A is not None and (l is None and u is None)):
raise ValueError("A must be supplied together " +
"with at least one bound l or u")
# Add infinity bounds in case they are not specified
if A is not None and l is None:
l = -np.inf * np.ones(A.shape[0])
if A is not None and u is None:
u = np.inf * np.ones(A.shape[0])
# Create elements if they are not specified
if P is None:
P = sparse.csc_matrix((np.zeros((0,), dtype=np.double),
np.zeros((0,), dtype=np.int),
np.zeros((n+1,), dtype=np.int)),
shape=(n, n))
if q is None:
q = np.zeros(n)
if A is None:
A = sparse.csc_matrix((np.zeros((0,), dtype=np.double),
np.zeros((0,), dtype=np.int),
np.zeros((n+1,), dtype=np.int)),
shape=(m, n))
l = np.zeros(A.shape[0])
u = np.zeros(A.shape[0])
#
# Check vector dimensions (not checked from C solver)
#
# Check if second dimension of A is correct
# if A.shape[1] != n:
# raise ValueError("Dimension n in A and P does not match")
if len(q) != n:
raise ValueError("Incorrect dimension of q")
if len(l) != m:
raise ValueError("Incorrect dimension of l")
if len(u) != m:
raise ValueError("Incorrect dimension of u")
#
# Check or Sparsify Matrices
#
if not sparse.issparse(P) and isinstance(P, np.ndarray) and \
len(P.shape) == 2:
raise TypeError("P is required to be a sparse matrix")
if not sparse.issparse(A) and isinstance(A, np.ndarray) and \
len(A.shape) == 2:
raise TypeError("A is required to be a sparse matrix")
# If P is not triu, then convert it to triu
if sparse.tril(P, -1).data.size > 0:
P = sparse.triu(P, format='csc')
# Convert matrices in CSC form and to individual pointers
if not sparse.isspmatrix_csc(P):
warn("Converting sparse P to a CSC " +
"(compressed sparse column) matrix. (It may take a while...)")
P = P.tocsc()
if not sparse.isspmatrix_csc(A):
warn("Converting sparse A to a CSC " +
"(compressed sparse column) matrix. (It may take a while...)")
A = A.tocsc()
# Check if P an A have sorted indices
if not P.has_sorted_indices:
P.sort_indices()
if not A.has_sorted_indices:
A.sort_indices()
# Convert infinity values to OSQP Infinity
u = np.minimum(u, _osqp.constant('OSQP_INFTY'))
l = np.maximum(l, -_osqp.constant('OSQP_INFTY'))
# Convert linsys_solver string to integer
settings = linsys_solver_str_to_int(settings)
return ((n, m), P.data, P.indices, P.indptr, q,
A.data, A.indices, A.indptr,
l, u), settings
def update(self,
q=None,
l=None,
u=None,
Px=None,
Px_idx=np.array([]),
Ax=None,
Ax_idx=np.array([])):
"""
Update OSQP problem arguments
"""
# get problem dimensions
(n, m) = self._model.dimensions()
# check consistency of the input arguments
if q is not None and len(q) != n:
raise ValueError("q must have length n")
if l is not None:
if not isinstance(l, np.ndarray):
raise TypeError("l must be numpy.ndarray, not %s" %
type(l).__name__)
elif len(l) != m:
raise ValueError("l must have length m")
# Convert values to -OSQP_INFTY
l = np.maximum(l, -_osqp.constant('OSQP_INFTY'))
if u is not None:
if not isinstance(u, np.ndarray):
raise TypeError("u must be numpy.ndarray, not %s" %
type(u).__name__)
elif len(u) != m:
raise ValueError("u must have length m")
# Convert values to OSQP_INFTY
u = np.minimum(u, _osqp.constant('OSQP_INFTY'))
if Ax is None:
if len(Ax_idx) > 0:
raise ValueError("Vector Ax has not been specified")
else:
if len(Ax_idx) > 0 and len(Ax) != len(Ax_idx):
raise ValueError("Ax and Ax_idx must have the same lengths")
if Px is None:
if len(Px_idx) > 0:
raise ValueError("Vector Px has not been specified")
else:
if len(Px_idx) > 0 and len(Px) != len(Px_idx):
raise ValueError("Px and Px_idx must have the same lengths")
if q is None and l is None and u is None and Px is None and Ax is None:
raise ValueError("No updatable data has been specified")
# update linear cost
if q is not None:
self._model.update_lin_cost(q)
# update lower bound
if l is not None and u is None:
self._model.update_bounds(l, np.array([]))
# update upper bound
if u is not None and l is None:
self._model.update_bounds(np.array([]), u)
# update bounds
if l is not None and u is not None:
self._model.update_bounds(l, u)
# update matrix P
if Px is not None and Ax is None:
self._model.update_P(Px, Px_idx, len(Px))
# update matrix A
if Ax is not None and Px is None:
self._model.update_A(Ax, Ax_idx, len(Ax))
# update matrices P and A
if Px is not None and Ax is not None:
self._model.update_P_A(Px, Px_idx, len(Px), Ax, Ax_idx, len(Ax))