def test_random_problems_without_slack_variables_and_down_rectangular_matrix(
self):
cntr_ok = 0
cntr_fail = 0
cnt_experiments = 20
for _ in range(cnt_experiments):
cnt_rows = np.random.randint(5, 25)
A = np.random.rand(cnt_rows, np.random.randint(2,
cnt_rows - 1)) * 10
b = np.random.rand(A.shape[0], 1) * 10
c = -np.random.rand(A.shape[1], 1)
Q = sparse.random(A.shape[1], A.shape[1], 0.9).A
Q = Q @ Q.T
tol = 1e-5
ip_res = ipsolver.optimize(
[Q, c], [A, b],
method=ipsolver.REGULARIZED_MEHROTRA_METHOD_QP,
tol=tol)
if ip_res.success:
cntr_ok += 1
else:
cntr_fail += 1
print(
"{} - Percentage when Jacobian is not rank-deficient: {:.2f}%".
format(
self.
test_random_problems_without_slack_variables_and_down_rectangular_matrix
.__name__, cntr_ok / cnt_experiments * 100))
def test_random_rank_deficient_problems(self):
cntr_ok = 0
cntr_fail = 0
cnt_experiments = 20
for _ in range(cnt_experiments):
A = np.random.rand(np.random.randint(3, 25),
np.random.randint(3, 25)) * 10
cnt_rows = A.shape[0]
b = np.random.rand(cnt_rows, 1) * 10
A = np.r_[A, A[0:int(cnt_rows * 0.4), :]]
b = np.r_[b, b[0:int(cnt_rows * 0.4), :]]
c = -np.random.rand(A.shape[1], 1)
Q = sparse.random(A.shape[1], A.shape[1], 0.9).A
Q = Q @ Q.T
tol = 1e-7
ip_res = ipsolver.optimize(
[Q, c], [A, b],
method=ipsolver.REGULARIZED_MEHROTRA_METHOD_QP,
tol=tol)
if ip_res.success:
cntr_ok += 1
else:
cntr_fail += 1
print("{} - Percentage when Jacobian is not rank-deficient: {:.2f}%".
format(self.test_random_rank_deficient_problems.__name__,
cntr_ok / cnt_experiments * 100))
def test_initial(self):
A = np.array([[1, 1, 0], [1, 3, 2], [0, 2, 3]], dtype=np.float64)
I = np.eye(A.shape[0])
A = np.c_[A, I]
b = np.array([[7], [15], [9]], dtype=np.float64)
c = -np.array([[3], [13], [13], [0], [0], [0]], dtype=np.float64)
tol = 1e-7
ip_res = ipsolver.optimize([c], [A, b],
method=ipsolver.MEHROTRA_METHOD_LP,
tol=tol)
lp_res = linprog(c, A_eq=A, b_eq=b, bounds=((0, None), ) * c.shape[0])
self.assertTrue(np.allclose(ip_res.x, lp_res.x))
def test_rank_deficient(self):
A = np.array([[1, -1, 0, 5, 3], [-4, 3, 2, 0, 4], [0, 2, -3, 1, 2],
[0, 2, -3, 1, 2]],
dtype=np.float64)
I = np.eye(A.shape[0])
A = np.c_[A, I]
b = np.array([[7], [15], [9], [9]], dtype=np.float64)
c = -np.array([[3], [13], [13], [-5], [9], [0], [0], [0], [0]],
dtype=np.float64)
tol = 1e-7
ip_res = ipsolver.optimize([c], [A, b],
method=ipsolver.MEHROTRA_METHOD_LP,
tol=tol)
self.assertFalse(ip_res.success)
def test_20_random_rank_deficient_problems(self):
for _ in range(20):
A = np.random.rand(np.random.randint(3, 25),
np.random.randint(3, 25)) * 10
cnt_rows = A.shape[0]
b = np.random.rand(cnt_rows, 1) * 10
A = np.r_[A, A[0:int(cnt_rows * 0.4), :]]
b = np.r_[b, b[0:int(cnt_rows * 0.4), :]]
c = -np.random.rand(A.shape[1], 1)
tol = 1e-7
ip_res = ipsolver.optimize([c], [A, b],
method=ipsolver.MEHROTRA_METHOD_LP,
tol=tol)
self.assertFalse(ip_res.success)
def test_10_random_problems_with_slack_variables(self):
for _ in range(10):
A = np.random.rand(np.random.randint(3, 25),
np.random.randint(3, 25)) * 10
I = np.eye(A.shape[0])
A = np.c_[A, I]
b = np.random.rand(A.shape[0], 1) * 10
c = -np.random.rand(A.shape[1], 1)
tol = 1e-7
ip_res = ipsolver.optimize([c], [A, b],
method=ipsolver.MEHROTRA_METHOD_LP,
tol=tol)
lp_res = linprog(c,
A_eq=A,
b_eq=b,
bounds=((0, None), ) * c.shape[0])
self.assertTrue(np.allclose(ip_res.x, lp_res.x))
def test_random_problems_without_slack_variables_and_right_rectangular_matrix(
self):
cntr_ok = 0
cntr_fail = 0
cnt_experiments = 20
primal_resid = 0
for _ in range(cnt_experiments):
cnt_rows = np.random.randint(5, 25)
A = np.random.rand(cnt_rows, np.random.randint(cnt_rows, 26)) * 10
b = np.random.rand(A.shape[0], 1) * 10
c = -np.random.rand(A.shape[1], 1)
tol = 1e-4
ip_res = ipsolver.optimize(
[c], [A, b],
method=ipsolver.REGULARIZED_MEHROTRA_METHOD_LP,
tol=tol)
if ip_res.success:
lp_res = linprog(c,
A_eq=A,
b_eq=b,
bounds=((0, None), ) * c.shape[0])
primal_resid += np.linalg.norm(A @ ip_res.x -
b) / ip_res.x.shape[0]
if (ip_res.f <= lp_res.fun
and np.linalg.norm(A @ ip_res.x - b, np.inf) <
np.linalg.norm(A @ lp_res.x - b, np.inf)):
cntr_ok += 1
else:
cntr_fail += 1
print(
"{} - Percentage when IP is better then LINPROG: {:.2f}, Percentage of fails: {:.2f}%, Mean primal residual: {:.4f}"
.format(
self.
test_random_problems_without_slack_variables_and_right_rectangular_matrix
.__name__, cntr_ok / cnt_experiments * 100,
cntr_fail / cnt_experiments * 100,
primal_resid / cnt_experiments))
def test_random_problems_without_slack_variables_and_right_rectangular_matrix(
self):
cntr_ok = 0
cntr_fail = 0
cnt_experiments = 20
primal_resid = 0
for _ in range(cnt_experiments):
cnt_rows = np.random.randint(5, 25)
A = np.random.rand(cnt_rows, np.random.randint(cnt_rows, 26)) * 10
b = np.random.rand(A.shape[0], 1) * 10
c = -np.random.rand(A.shape[1], 1)
tol = 1e-4
Q = sparse.random(A.shape[1], A.shape[1], 0.9).A
Q = Q @ Q.T
ip_res = ipsolver.optimize(
[Q, c], [A, b],
method=ipsolver.REGULARIZED_MEHROTRA_METHOD_QP,
tol=tol)
if ip_res.success:
qp_res = solveqp(Q, c, A, b)
qp_res.fun = (qp_res.x.T @ Q @ qp_res.x + qp_res.x @ c)[0]
primal_resid += np.linalg.norm(A @ ip_res.x -
b) / ip_res.x.shape[0]
if (ip_res.f <= qp_res.fun
and np.linalg.norm(A @ ip_res.x - b, np.inf) <
np.linalg.norm(A @ qp_res.x - b, np.inf)):
cntr_ok += 1
else:
cntr_fail += 1
print(
"{} - Percentage when IP is better then SLSQP: {:.2f}, Percentage of fails: {:.2f}%, Mean primal residual: {:.4f}"
.format(
self.
test_random_problems_without_slack_variables_and_right_rectangular_matrix
.__name__, cntr_ok / cnt_experiments * 100,
cntr_fail / cnt_experiments * 100,
primal_resid / cnt_experiments))
def test_random_rank_deficient_problems(self):
cntr_ok = 0
cntr_fail = 0
cnt_experiments = 20
for _ in range(cnt_experiments):
A = np.random.rand(np.random.randint(3, 25),
np.random.randint(3, 25)) * 10
cnt_rows = A.shape[0]
b = np.random.rand(cnt_rows, 1) * 10
A = np.r_[A, A[0:int(cnt_rows * 0.4), :]]
b = np.r_[b, b[0:int(cnt_rows * 0.4), :]]
c = -np.random.rand(A.shape[1], 1)
tol = 1e-7
ip_res = ipsolver.optimize(
[c], [A, b],
method=ipsolver.REGULARIZED_MEHROTRA_METHOD_LP,
tol=tol)
if ip_res.success:
lp_res = linprog(c,
A_eq=A,
b_eq=b,
bounds=((0, None), ) * c.shape[0])
if (ip_res.f <= lp_res.fun
and np.linalg.norm(A @ ip_res.x - b, np.inf) <
np.linalg.norm(A @ lp_res.x - b, np.inf)):
cntr_ok += 1
else:
cntr_fail += 1
print(
"{} - Percentage when IP is better then LINPROG: {:.2f}, Percentage of fails: {:.2f}%"
.format(self.test_random_rank_deficient_problems.__name__,
cntr_ok / cnt_experiments * 100,
cntr_fail / cnt_experiments * 100))