def test_trust_region_infeasible(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 = 1
     Z, _, Y = projections(A)
     with pytest.raises(ValueError):
         projected_cg(H, c, Z, Y, b, trust_radius=trust_radius)
 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_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_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_3d_example(self):
        A = np.array([[1, 8, 1], [4, 2, 2]])
        b = np.array([-16, 2])
        Z, LS, Y = projections(A)

        newton_point = np.array([-1.37090909, 2.23272727, -0.49090909])
        cauchy_point = np.array([0.11165723, 1.73068711, 0.16748585])
        origin = np.zeros_like(newton_point)

        # newton_point inside boundaries
        x = modified_dogleg(A, Y, b, 3, [-np.inf, -np.inf, -np.inf],
                            [np.inf, np.inf, np.inf])
        assert_array_almost_equal(x, newton_point)

        # line between cauchy_point and newton_point contains best point
        # (spherical constrain is active).
        x = modified_dogleg(A, Y, b, 2, [-np.inf, -np.inf, -np.inf],
                            [np.inf, np.inf, np.inf])
        z = cauchy_point
        d = newton_point - cauchy_point
        t = ((x - z) / (d))
        assert_array_almost_equal(t, 0.40807330 * np.ones(3))
        assert_array_almost_equal(np.linalg.norm(x), 2)

        # line between cauchy_point and newton_point contains best point
        # (box constrain is active).
        x = modified_dogleg(A, Y, b, 5, [-1, -np.inf, -np.inf],
                            [np.inf, np.inf, np.inf])
        z = cauchy_point
        d = newton_point - cauchy_point
        t = ((x - z) / (d))
        assert_array_almost_equal(t, 0.7498195 * np.ones(3))
        assert_array_almost_equal(x[0], -1)

        # line between origin and cauchy_point contains best point
        # (spherical constrain is active).
        x = modified_dogleg(A, Y, b, 1, [-np.inf, -np.inf, -np.inf],
                            [np.inf, np.inf, np.inf])
        z = origin
        d = cauchy_point
        t = ((x - z) / (d))
        assert_array_almost_equal(t, 0.573936265 * np.ones(3))
        assert_array_almost_equal(np.linalg.norm(x), 1)

        # line between origin and newton_point contains best point
        # (box constrain is active).
        x = modified_dogleg(A, Y, b, 2, [-np.inf, -np.inf, -np.inf],
                            [np.inf, 1, np.inf])
        z = origin
        d = newton_point
        t = ((x - z) / (d))
        assert_array_almost_equal(t, 0.4478827364 * np.ones(3))
        assert_array_almost_equal(x[1], 1)
 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_rowspace_dense(self):
        A = np.array([[1, 2, 3, 4, 0, 5, 0, 7], [0, 8, 7, 0, 1, 5, 9, 0],
                      [1, 0, 0, 0, 0, 1, 2, 3]])
        test_points = ([1, 2, 3], [1, 10, 3], [1.12, 10, 0])

        for method in available_dense_methods:
            _, _, Y = projections(A, method)
            for z in test_points:
                # Test if x is solution of A x = z
                x = Y.matvec(z)
                assert_array_almost_equal(A.dot(x), z)
                # Test if x is in the return row space of A
                A_ext = np.vstack((A, x))
                assert_equal(np.linalg.matrix_rank(A),
                             np.linalg.matrix_rank(A_ext))
    def test_iterative_refinements_dense(self):
        A = np.array([[1, 2, 3, 4, 0, 5, 0, 7], [0, 8, 7, 0, 1, 5, 9, 0],
                      [1, 0, 0, 0, 0, 1, 2, 3]])
        test_points = ([1, 2, 3, 4, 5, 6, 7,
                        8], [1, 10, 3, 0, 1, 6, 7,
                             8], [1, 0, 0, 0, 0, 1, 2, 3 + 1e-10])

        for method in available_dense_methods:
            Z, LS, _ = projections(A, method, orth_tol=1e-18, max_refin=10)
            for z in test_points:
                # Test if x is in the null_space
                x = Z.matvec(z)
                assert_array_almost_equal(A.dot(x), 0, decimal=14)
                # Test orthogonality
                assert_array_almost_equal(orthogonality(A, x), 0, decimal=16)
    def test_cauchypoint_equalsto_newtonpoint(self):
        A = np.array([[1, 8]])
        b = np.array([-16])
        _, _, Y = projections(A)
        newton_point = np.array([0.24615385, 1.96923077])

        # Newton point inside boundaries
        x = modified_dogleg(A, Y, b, 2, [-np.inf, -np.inf], [np.inf, np.inf])
        assert_array_almost_equal(x, newton_point)

        # Spherical constraint active
        x = modified_dogleg(A, Y, b, 1, [-np.inf, -np.inf], [np.inf, np.inf])
        assert_array_almost_equal(x,
                                  newton_point / np.linalg.norm(newton_point))

        # Box Constraints active
        x = modified_dogleg(A, Y, b, 2, [-np.inf, -np.inf], [0.1, np.inf])
        assert_array_almost_equal(x, (newton_point / newton_point[0]) * 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_nullspace_and_least_squares_dense(self):
        A = np.array([[1, 2, 3, 4, 0, 5, 0, 7], [0, 8, 7, 0, 1, 5, 9, 0],
                      [1, 0, 0, 0, 0, 1, 2, 3]])
        At = A.T
        test_points = ([1, 2, 3, 4, 5, 6, 7,
                        8], [1, 10, 3, 0, 1, 6, 7,
                             8], [1.12, 10, 0, 0, 100000, 6, 0.7, 8])

        for method in available_dense_methods:
            Z, LS, _ = projections(A, method)
            for z in test_points:
                # Test if x is in the null_space
                x = Z.matvec(z)
                assert_array_almost_equal(A.dot(x), 0)
                # Test orthogonality
                assert_array_almost_equal(orthogonality(A, x), 0)
                # Test if x is the least square solution
                x = LS.matvec(z)
                x2 = scipy.linalg.lstsq(At, z)[0]
                assert_array_almost_equal(x, x2)
 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)