def test_feasible_problem_with_box_constr(self):
H = csc_matrix([[6, 2, 1, 3],
[2, 5, 2, 4],
[1, 2, 4, 5],
[3, 4, 5, 7]])
A = csc_matrix([[1, 0, 1, 0],
[0, 1, 1, 1]])
c = np.array([-2, -3, -3, 1])
b = -np.array([3, 0])
trust_radius = 3
lb = np.array([-1, -0.7, -1, -1.5])
ub = np.array([1.9, np.inf, np.inf, np.inf])
Z, _, Y = projections(A)
x_n, x_t, info = qp_subproblem(H, c, A, Z, Y, b,
trust_radius,
lb, ub,
tr_factor=1,
box_factor=1)
x_pcg, info_pcg = projected_cg(H, c, Z, Y, b,
trust_radius, lb, ub)
x = x_n + x_t
r = A.dot(x_n) + b
assert_array_almost_equal(r, np.zeros(2))
assert_array_almost_equal(x, x_pcg)
assert_equal(info["hits_boundary"], info_pcg["hits_boundary"])
assert_equal(info, info_pcg)
assert_array_almost_equal(A.dot(x)+b, r)
assert_(np.linalg.norm(x) <= trust_radius)
assert_(inside_box_boundaries(x, lb, ub))
def test_nocedal_example(self):
H = csc_matrix([[6, 2, 1],
[2, 5, 2],
[1, 2, 4]])
A = csc_matrix([[1, 0, 1],
[0, 1, 1]])
c = np.array([-8, -3, -3])
b = -np.array([3, 0])
Z, _, Y = projections(A)
x, info = projected_cg(H, c, Z, Y, b)
assert_equal(info["stop_cond"], 4)
assert_equal(info["hits_boundary"], False)
assert_array_almost_equal(x, [2, -1, 1])
def test_compare_with_direct_fact(self):
H = csc_matrix([[6, 2, 1, 3],
[2, 5, 2, 4],
[1, 2, 4, 5],
[3, 4, 5, 7]])
A = csc_matrix([[1, 0, 1, 0],
[0, 1, 1, 1]])
c = np.array([-2, -3, -3, 1])
b = -np.array([3, 0])
Z, _, Y = projections(A)
x, info = projected_cg(H, c, Z, Y, b, tol=0)
x_kkt, _ = eqp_kktfact(H, c, A, b)
assert_equal(info["stop_cond"], 1)
assert_equal(info["hits_boundary"], False)
assert_array_almost_equal(x, x_kkt)
def test_negative_curvature(self):
H = csc_matrix([[1, 2, 1, 3],
[2, 0, 2, 4],
[1, 2, 0, 2],
[3, 4, 2, 0]])
A = csc_matrix([[1, 0, 1, 0],
[0, 1, 0, 1]])
c = np.array([-2, -3, -3, 1])
b = -np.array([3, 0])
Z, _, Y = projections(A)
trust_radius = 1000
x, info = projected_cg(H, c, Z, Y, b,
tol=0,
trust_radius=trust_radius)
assert_equal(info["stop_cond"], 3)
assert_equal(info["hits_boundary"], True)
assert_array_almost_equal(np.linalg.norm(x), trust_radius)
def test_hits_boundary(self):
H = csc_matrix([[6, 2, 1, 3],
[2, 5, 2, 4],
[1, 2, 4, 5],
[3, 4, 5, 7]])
A = csc_matrix([[1, 0, 1, 0],
[0, 1, 1, 1]])
c = np.array([-2, -3, -3, 1])
b = -np.array([3, 0])
trust_radius = 3
Z, _, Y = projections(A)
x, info = projected_cg(H, c, Z, Y, b,
tol=0,
trust_radius=trust_radius)
assert_equal(info["stop_cond"], 2)
assert_equal(info["hits_boundary"], True)
assert_array_almost_equal(np.linalg.norm(x), trust_radius)
def test_trust_region_barely_feasible(self):
H = csc_matrix([[6, 2, 1, 3],
[2, 5, 2, 4],
[1, 2, 4, 5],
[3, 4, 5, 7]])
A = csc_matrix([[1, 0, 1, 0],
[0, 1, 1, 1]])
c = np.array([-2, -3, -3, 1])
b = -np.array([3, 0])
trust_radius = 2.32379000772445021283
Z, _, Y = projections(A)
x, info = projected_cg(H, c, Z, Y, b,
tol=0,
trust_radius=trust_radius)
assert_equal(info["stop_cond"], 2)
assert_equal(info["hits_boundary"], True)
assert_array_almost_equal(np.linalg.norm(x), trust_radius)
assert_array_almost_equal(x, -Y.dot(b))
def test_active_box_constraints_hits_boundaries_infeasible_iter(self):
H = csc_matrix([[6, 2, 1, 3],
[2, 5, 2, 4],
[1, 2, 4, 5],
[3, 4, 5, 7]])
A = csc_matrix([[1, 0, 1, 0],
[0, 1, 1, 1]])
c = np.array([-2, -3, -3, 1])
b = -np.array([3, 0])
trust_radius = 4
Z, _, Y = projections(A)
x, info = projected_cg(H, c, Z, Y, b,
tol=0,
ub=[np.inf, 0.1, np.inf, np.inf],
trust_radius=trust_radius,
return_all=True)
assert_equal(info["stop_cond"], 2)
assert_equal(info["hits_boundary"], True)
assert_array_almost_equal(x[1], 0.1)
def test_active_box_constraints_maximum_iterations_reached(self):
H = csc_matrix([[6, 2, 1, 3],
[2, 5, 2, 4],
[1, 2, 4, 5],
[3, 4, 5, 7]])
A = csc_matrix([[1, 0, 1, 0],
[0, 1, 1, 1]])
c = np.array([-2, -3, -3, 1])
b = -np.array([3, 0])
Z, _, Y = projections(A)
x, info = projected_cg(H, c, Z, Y, b,
tol=0,
lb=[0.8, -np.inf,
-np.inf, -np.inf],
return_all=True)
assert_equal(info["stop_cond"], 1)
assert_equal(info["hits_boundary"], True)
assert_array_almost_equal(A.dot(x), -b)
assert_array_almost_equal(x[0], 0.8)
def test_inactive_box_constraints(self):
H = csc_matrix([[6, 2, 1, 3],
[2, 5, 2, 4],
[1, 2, 4, 5],
[3, 4, 5, 7]])
A = csc_matrix([[1, 0, 1, 0],
[0, 1, 1, 1]])
c = np.array([-2, -3, -3, 1])
b = -np.array([3, 0])
Z, _, Y = projections(A)
x, info = projected_cg(H, c, Z, Y, b,
tol=0,
lb=[0.5, -np.inf,
-np.inf, -np.inf],
return_all=True)
x_kkt, _ = eqp_kktfact(H, c, A, b)
assert_equal(info["stop_cond"], 1)
assert_equal(info["hits_boundary"], False)
assert_array_almost_equal(x, x_kkt)
def test_feasible_problem(self):
H = csc_matrix([[6, 2, 1, 3],
[2, 5, 2, 4],
[1, 2, 4, 5],
[3, 4, 5, 7]])
A = csc_matrix([[1, 0, 1, 0],
[0, 1, 1, 1]])
c = np.array([-2, -3, -3, 1])
b = -np.array([3, 0])
trust_radius = 3
Z, _, Y = projections(A)
x_n, x_t, info = qp_subproblem(H, c, A, Z, Y, b,
trust_radius,
tr_factor=1)
x_pcg, info_pcg = projected_cg(H, c, Z, Y, b,
trust_radius)
x = x_n + x_t
r = A.dot(x_n) + b
assert_array_almost_equal(r, np.zeros(2))
assert_array_almost_equal(x, x_pcg)
assert_equal(info["hits_boundary"], info_pcg["hits_boundary"])
assert_equal(info, info_pcg)
assert_array_almost_equal(np.linalg.norm(x) - trust_radius, 0)
assert_array_almost_equal(A.dot(x)+b, r)