def test_thrust_jacobian(self):
'''Test thrust_jacobian
i.e. test that
jac(thrust_matrix(alpha) * u) * delta_alpha
+ thrust_matrix(alpha_0) * u_0
[jacobian evaluated at alpha = alpha_0, u = u_0]
is close to thrust_matrix(delta_alpha + alpha_0)
In English: That the implemented jacobian suffices to do a higher dimensional
first-order Taylor approximation of the nonlinear behavior of the thrust_matrix
'''
max_error = 0.2
tests = [
{
'u_0': (10, 10),
'alpha_0': (0.01, 0.01),
'delta_angle': (0.1, 0.1),
},
{
'u_0': (10, 10),
'alpha_0': (0.1, 0.1),
'delta_angle': (0.05, 0.05),
},
{
'u_0': (25, 10),
'alpha_0': (0.5, 0.3),
'delta_angle': (0.08, 0.05),
},
]
for test in tests:
u_0 = np.array(test['u_0'])
alpha_0 = np.array(test['alpha_0'])
delta_angle = np.array(test['delta_angle'])
jacobian = Azi_Drive.thrust_jacobian(alpha_0, u_0)
initial_thrust_matrix = Azi_Drive.thrust_matrix(alpha_0)
linear_estimate = np.dot(initial_thrust_matrix, u_0) + np.dot(jacobian, delta_angle)
true_thrust_matrix = Azi_Drive.thrust_matrix(alpha_0 + delta_angle)
nonlinear_estimate = np.dot(true_thrust_matrix, u_0)
error = np.linalg.norm(nonlinear_estimate - linear_estimate)
self.assertLess(
error,
max_error,
msg='error of {} exceeds maximum of {}\n Estimates: nonlinear {}, linear {}'.format(
error,
max_error,
nonlinear_estimate,
linear_estimate,
)
)
# jBa_u = Azi_Drive.thrust_jacobian(a_0, u_0)
a_min = -3 * np.pi / 2
a_max = 3 * np.pi / 2
u_min = -100.0
u_max = 100.
da_max = 0.1
tau = np.array([200.0, 200.0, 0.0]).astype(np.double)
Q = np.diag([10., 10., 30.]).astype(np.double)
Ohm = np.diag([0., 0.]).astype(np.double)
tic = time()
for k in range(200):
Ba = Azi_Drive.thrust_matrix(a_0).astype(np.double)
jBa_u = Azi_Drive.thrust_jacobian(a_0, u_0).astype(np.double)
soln = cvxbind.ksolve(
u_0.flatten(),
a_0.flatten(),
Ohm.flatten(),
Q.flatten(),
Ba.transpose().flatten(),
jBa_u.transpose().A1,
u_max,
u_min,
a_min,
a_max,
da_max,
tau.flatten(),
)
# jBa_u = Azi_Drive.thrust_jacobian(a_0, u_0)
a_min = -3 * np.pi / 2
a_max = 3 * np.pi / 2
u_min = -100.0
u_max = 100.
da_max = 0.1
tau = np.array([200.0, 200.0, 0.0]).astype(np.double)
Q = np.diag([10., 10., 30.]).astype(np.double)
Ohm = np.diag([0., 0.]).astype(np.double)
tic = time()
for k in range(200):
Ba = Azi_Drive.thrust_matrix(a_0).astype(np.double)
jBa_u = Azi_Drive.thrust_jacobian(a_0, u_0).astype(np.double)
soln = cvxbind.ksolve(
u_0.flatten(),
a_0.flatten(),
Ohm.flatten(),
Q.flatten(),
Ba.transpose().flatten(),
jBa_u.transpose().A1,
u_max,
u_min,
a_min,
a_max,
da_max,
tau.flatten(),
)
def test_thrust_jacobian(self):
'''Test thrust_jacobian
i.e. test that
jac(thrust_matrix(alpha) * u) * delta_alpha
+ thrust_matrix(alpha_0) * u_0
[jacobian evaluated at alpha = alpha_0, u = u_0]
is close to thrust_matrix(delta_alpha + alpha_0)
In English: That the implemented jacobian suffices to do a higher dimensional
first-order Taylor approximation of the nonlinear behavior of the thrust_matrix
'''
max_error = 0.2
tests = [
{
'u_0': (10, 10),
'alpha_0': (0.01, 0.01),
'delta_angle': (0.1, 0.1),
},
{
'u_0': (10, 10),
'alpha_0': (0.1, 0.1),
'delta_angle': (0.05, 0.05),
},
{
'u_0': (25, 10),
'alpha_0': (0.5, 0.3),
'delta_angle': (0.08, 0.05),
},
]
for test in tests:
u_0 = np.array(test['u_0'])
alpha_0 = np.array(test['alpha_0'])
delta_angle = np.array(test['delta_angle'])
jacobian = Azi_Drive.thrust_jacobian(alpha_0, u_0)
initial_thrust_matrix = Azi_Drive.thrust_matrix(alpha_0)
linear_estimate = np.dot(initial_thrust_matrix, u_0) + np.dot(
jacobian, delta_angle)
true_thrust_matrix = Azi_Drive.thrust_matrix(alpha_0 + delta_angle)
nonlinear_estimate = np.dot(true_thrust_matrix, u_0)
error = np.linalg.norm(nonlinear_estimate - linear_estimate)
self.assertLess(
error,
max_error,
msg=
'error of {} exceeds maximum of {}\n Estimates: nonlinear {}, linear {}'
.format(
error,
max_error,
nonlinear_estimate,
linear_estimate,
))
