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, np.full(3, 0.40807330))
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, np.full(3, 0.7498195))
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, np.full(3, 0.573936265))
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, np.full(3, 0.4478827364))
assert_array_almost_equal(x[1], 1)
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_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_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)