def test_infeasible_m_lt_n():
m, n = 9, 10
A0 = np.random.rand(m, n)
b0 = np.random.rand(m)
A0[-1, :] = np.arange(m - 1).dot(A0[:-1])
A1, b1, status, message = _remove_redundancy(A0, b0)
assert_equal(status, 2)
def test_infeasible_m_lt_n():
m, n = 9, 10
A0 = np.random.rand(m, n)
b0 = np.random.rand(m)
A0[-1, :] = np.arange(m - 1).dot(A0[:-1])
A1, b1, status, message = _remove_redundancy(A0, b0)
assert_equal(status, 2)
def test_infeasible_m_eq_n():
m, n = 10, 10
A0 = np.random.rand(m, n)
b0 = np.random.rand(m)
A0[-1, :] = 2 * A0[-2, :]
A1, b1, status, message = _remove_redundancy(A0, b0)
assert_equal(status, 2)
def test_infeasible_m_eq_n():
m, n = 10, 10
A0 = np.random.rand(m, n)
b0 = np.random.rand(m)
A0[-1, :] = 2 * A0[-2, :]
A1, b1, status, message = _remove_redundancy(A0, b0)
assert_equal(status, 2)
def test_no_redundancy():
m, n = 10, 10
A0 = np.random.rand(m, n)
b0 = np.random.rand(m)
A1, b1, status, message = _remove_redundancy(A0, b0)
assert_allclose(A0, A1)
assert_allclose(b0, b1)
assert_equal(status, 0)
def test_no_redundancy():
m, n = 10, 10
A0 = np.random.rand(m, n)
b0 = np.random.rand(m)
A1, b1, status, message = _remove_redundancy(A0, b0)
assert_allclose(A0, A1)
assert_allclose(b0, b1)
assert_equal(status, 0)
def test_m_gt_n_rank_deficient():
m, n = 20, 10
A0 = np.zeros((m, n))
A0[:, 0] = 1
b0 = np.ones(m)
A1, b1, status, message = _remove_redundancy(A0, b0)
assert_equal(status, 0)
assert_allclose(A1, A0[0:1, :])
assert_allclose(b1, b0[0])
def test_remove_zero_row():
A = np.eye(3)
A[1, :] = 0
b = np.random.rand(3)
b[1] = 0
A1, b1, status, message = _remove_redundancy(A, b)
assert_equal(status, 0)
assert_allclose(A1, A[[0, 2], :])
assert_allclose(b1, b[[0, 2]])
def test_dense2():
A = np.eye(6)
A[-2, -1] = 1
A[-1, :] = 1
b = np.zeros(A.shape[0])
A1, b1, status, message = _remove_redundancy(A, b)
assert_allclose(A1, A[:-1, :])
assert_allclose(b1, b[:-1])
assert_equal(status, 0)
def test_remove_zero_row():
A = np.eye(3)
A[1, :] = 0
b = np.random.rand(3)
b[1] = 0
A1, b1, status, message = _remove_redundancy(A, b)
assert_equal(status, 0)
assert_allclose(A1, A[[0, 2], :])
assert_allclose(b1, b[[0, 2]])
def test_dense2():
A = np.eye(6)
A[-2, -1] = 1
A[-1, :] = 1
b = np.zeros(A.shape[0])
A1, b1, status, message = _remove_redundancy(A, b)
assert_allclose(A1, A[:-1, :])
assert_allclose(b1, b[:-1])
assert_equal(status, 0)
def test_m_gt_n_rank_deficient():
m, n = 20, 10
A0 = np.zeros((m, n))
A0[:, 0] = 1
b0 = np.ones(m)
A1, b1, status, message = _remove_redundancy(A0, b0)
assert_equal(status, 0)
assert_allclose(A1, A0[0:1, :])
assert_allclose(b1, b0[0])
def test_m_lt_n_rank_deficient():
m, n = 9, 10
A0 = np.random.rand(m, n)
b0 = np.random.rand(m)
A0[-1, :] = np.arange(m - 1).dot(A0[:-1])
b0[-1] = np.arange(m - 1).dot(b0[:-1])
A1, b1, status, message = _remove_redundancy(A0, b0)
assert_equal(status, 0)
assert_equal(A1.shape[0], 8)
assert_equal(np.linalg.matrix_rank(A1), 8)
def test_m_gt_n():
m, n = 20, 10
A0 = np.random.rand(m, n)
b0 = np.random.rand(m)
x = np.linalg.solve(A0[:n, :], b0[:n])
b0[n:] = A0[n:, :].dot(x)
A1, b1, status, message = _remove_redundancy(A0, b0)
assert_equal(status, 0)
assert_equal(A1.shape[0], n)
assert_equal(np.linalg.matrix_rank(A1), n)
def test_m_gt_n():
m, n = 20, 10
A0 = np.random.rand(m, n)
b0 = np.random.rand(m)
x = np.linalg.solve(A0[:n, :], b0[:n])
b0[n:] = A0[n:, :].dot(x)
A1, b1, status, message = _remove_redundancy(A0, b0)
assert_equal(status, 0)
assert_equal(A1.shape[0], n)
assert_equal(np.linalg.matrix_rank(A1), n)
def test_m_lt_n_rank_deficient():
m, n = 9, 10
A0 = np.random.rand(m, n)
b0 = np.random.rand(m)
A0[-1, :] = np.arange(m - 1).dot(A0[:-1])
b0[-1] = np.arange(m - 1).dot(b0[:-1])
A1, b1, status, message = _remove_redundancy(A0, b0)
assert_equal(status, 0)
assert_equal(A1.shape[0], 8)
assert_equal(np.linalg.matrix_rank(A1), 8)
def test_m_eq_n_sparse():
np.random.seed(2017)
m, n = 100, 100
p = 0.01
A = np.random.rand(m, n)
A[np.random.rand(m, n) > p] = 0
rank = np.linalg.matrix_rank(A)
b = np.zeros(A.shape[0])
A1, b1, status, message = _remove_redundancy(A, b)
assert_equal(status, 0)
assert_equal(A1.shape[0], rank)
assert_equal(np.linalg.matrix_rank(A1), rank)
def test_m_eq_n_sparse():
np.random.seed(2017)
m, n = 100, 100
p = 0.01
A = np.random.rand(m, n)
A[np.random.rand(m, n) > p] = 0
rank = np.linalg.matrix_rank(A)
b = np.zeros(A.shape[0])
A1, b1, status, message = _remove_redundancy(A, b)
assert_equal(status, 0)
assert_equal(A1.shape[0], rank)
assert_equal(np.linalg.matrix_rank(A1), rank)
def test_dense1():
A = np.ones((6, 6))
A[0, :3] = 0
A[1, 3:] = 0
A[3:, ::2] = -1
A[3, :2] = 0
A[4, 2:] = 0
b = np.zeros(A.shape[0])
A2 = A[[0, 1, 3, 4], :]
b2 = np.zeros(4)
A1, b1, status, message = _remove_redundancy(A, b)
assert_allclose(A1, A2)
assert_allclose(b1, b2)
assert_equal(status, 0)
def test_dense1():
A = np.ones((6, 6))
A[0, :3] = 0
A[1, 3:] = 0
A[3:, ::2] = -1
A[3, :2] = 0
A[4, 2:] = 0
b = np.zeros(A.shape[0])
A2 = A[[0, 1, 3, 4], :]
b2 = np.zeros(4)
A1, b1, status, message = _remove_redundancy(A, b)
assert_allclose(A1, A2)
assert_allclose(b1, b2)
assert_equal(status, 0)
def rr(self, A, b):
return _remove_redundancy(A, b)
def test_infeasible_m_gt_n():
m, n = 20, 10
A0 = np.random.rand(m, n)
b0 = np.random.rand(m)
A1, b1, status, message = _remove_redundancy(A0, b0)
assert_equal(status, 2)
def test_infeasible_zero_row():
A = np.eye(3)
A[1, :] = 0
b = np.random.rand(3)
A1, b1, status, message = _remove_redundancy(A, b)
assert_equal(status, 2)
def test_magic_square2():
A, b, c, numbers = magic_square(4)
A1, b1, status, message = _remove_redundancy(A, b)
assert_equal(status, 0)
assert_equal(A1.shape[0], 39)
assert_equal(np.linalg.matrix_rank(A1), 39)
def test_magic_square2():
A, b, c, numbers = magic_square(4)
A1, b1, status, message = _remove_redundancy(A, b)
assert_equal(status, 0)
assert_equal(A1.shape[0], 39)
assert_equal(np.linalg.matrix_rank(A1), 39)
def test_infeasible_zero_row():
A = np.eye(3)
A[1, :] = 0
b = np.random.rand(3)
A1, b1, status, message = _remove_redundancy(A, b)
assert_equal(status, 2)
def test_infeasible_m_gt_n():
m, n = 20, 10
A0 = np.random.rand(m, n)
b0 = np.random.rand(m)
A1, b1, status, message = _remove_redundancy(A0, b0)
assert_equal(status, 2)
def remove_redundant_lin_contrs(A_eq, b_eq, verbose=False):
"""
Removes redundant linear equality constraints
A_eq x = b_eq
Code is borrowed from scipy.optimize._linprog_util
Parameters
----------
A_eq: array-like (n_constr, n_vars)
b_eq: array-like, (n_constr, )
verbose: bool
Output
------
A_eq, b_eq, status, message
A_eq: array-like (n_constr_non_redundant, n_vars)
b_eq: array-like, (n_constr_non_redundant, )
"""
status = None
message = None
# remove redundant (linearly dependent) rows from equality constraints
n_rows_A = A_eq.shape[0]
redundancy_warning = ("A_eq does not appear to be of full row rank. To "
"improve performance, check the problem formulation "
"for redundant equality constraints.")
if (sps.issparse(A_eq)):
if A_eq.size > 0: # TODO: Fast sparse rank check?
A_eq, b_eq, status, message = _remove_redundancy_sparse(A_eq, b_eq)
if A_eq.shape[0] < n_rows_A and verbose:
warn(redundancy_warning, OptimizeWarning, stacklevel=1)
return A_eq, b_eq, status, message
# This is a wild guess for which redundancy removal algorithm will be
# faster. More testing would be good.
small_nullspace = 5
if A_eq.size > 0:
try: # TODO: instead use results of first SVD in _remove_redundancy
rank = np.linalg.matrix_rank(A_eq)
except Exception: # oh well, we'll have to go with _remove_redundancy_dense
rank = 0
if A_eq.size > 0 and rank < A_eq.shape[0]:
if verbose:
warn(redundancy_warning, OptimizeWarning, stacklevel=3)
dim_row_nullspace = A_eq.shape[0] - rank
if dim_row_nullspace <= small_nullspace:
A_eq, b_eq, status, message = _remove_redundancy(A_eq, b_eq)
if dim_row_nullspace > small_nullspace or status == 4:
A_eq, b_eq, status, message = _remove_redundancy_dense(A_eq, b_eq)
if A_eq.shape[0] < rank:
message = ("Due to numerical issues, redundant equality "
"constraints could not be removed automatically. "
"Try providing your constraint matrices as sparse "
"matrices to activate sparse presolve, try turning "
"off redundancy removal, or try turning off presolve "
"altogether.")
status = 4
return A_eq, b_eq, status, message