def test_rotation_matrix_3d(self):
z_rot_vec = np.array([0, 0, 1])
z_rot_theta = np.pi / 4
trans_matrix = cde.rotation_matrix_3d(z_rot_vec, z_rot_theta)
vec_to_rotate = np.array([1, 0, 0])
r2 = np.sqrt(2.0)
self.assertTrue(
np.equal(trans_matrix.dot(vec_to_rotate), [1 / r2, 1 / r2, 0]).all)
x_rot_vec = np.array([1, 0, 0])
x_rot_theta = np.pi / 4
trans_matrix = cde.rotation_matrix_3d(x_rot_vec, x_rot_theta)
vec_to_rotate = np.array([0, 0, 1])
self.assertTrue(
np.equal(trans_matrix.dot(vec_to_rotate),
[0, -1 / r2, 1 / r2]).all)
rot_vec = np.array([1, 1, 1])
rot_theta = np.pi * 2 / 3
trans_matrix = cde.rotation_matrix_3d(rot_vec, rot_theta)
vec_to_rotate = np.array([0, 0, 1])
try:
goo = cde.rotation_matrix_3d(np.array([0, 0, 0]), np.pi / 3)
self.assertTrue(False)
except:
self.assertTrue(True)
self.assertTrue(
np.equal(trans_matrix.dot(vec_to_rotate), [1, 0, 0]).all)
def test_rotation_matrix_3d(self): z_rot_vec = np.array([0, 0, 1]) z_rot_theta = np.pi / 4 trans_matrix = cde.rotation_matrix_3d(z_rot_vec, z_rot_theta) vec_to_rotate = np.array([1, 0, 0]) r2 = np.sqrt(2.0) self.assertTrue(np.equal(trans_matrix.dot(vec_to_rotate), [1 / r2, 1 / r2, 0]).all) x_rot_vec = np.array([1, 0, 0]) x_rot_theta = np.pi / 4 trans_matrix = cde.rotation_matrix_3d(x_rot_vec, x_rot_theta) vec_to_rotate = np.array([0, 0, 1]) self.assertTrue(np.equal(trans_matrix.dot(vec_to_rotate), [0, - 1 / r2, 1 / r2]).all) rot_vec = np.array([1, 1, 1]) rot_theta = np.pi * 2 / 3 trans_matrix = cde.rotation_matrix_3d(rot_vec, rot_theta) vec_to_rotate = np.array([0, 0, 1]) try: goo = cde.rotation_matrix_3d(np.array([0,0,0]), np.pi/3) self.assertTrue(False) except: self.assertTrue(True) self.assertTrue(np.equal(trans_matrix.dot(vec_to_rotate), [1, 0, 0]).all)
def test_rk4_stepper(self): earth_vel = cde.earth_omega * cde.AU start_coords_1 = np.array([[cde.AU, 0.0, 0.0], [0.0, earth_vel, 0.0]]).T dt = cde.year / 360 #let's go forward one degree! one_deg = 2 * np.pi / 360. rot_coords_1 = np.dot(cde.rotation_matrix_3d( np.array([0, 0, 1.0]), one_deg), start_coords_1) int_coords = cde.rk4_stepper(start_coords_1, .5 * dt) final_coords = cde.rk4_stepper(int_coords, .5 * dt) final_coords_2 = cde.rk4_stepper(start_coords_1, dt) rot_mags = np.array([rot_coords_1[:,0].dot(rot_coords_1[:,0]), rot_coords_1[:,1].dot(rot_coords_1[:,1])]) log_diff_coords = (rot_coords_1 - final_coords_2) / rot_mags pos_err = np.sqrt(np.dot(log_diff_coords[:,0], log_diff_coords[:,0])) vel_err = np.sqrt(np.dot(log_diff_coords[:,1], log_diff_coords[:,1])) max_err = max(pos_err, vel_err)
def test_orbital_step_time_simple(self): earth_vel = cde.earth_omega * cde.AU start_coords_1 = np.array([[cde.AU, 0.0, 0.0], [0.0, earth_vel, 0.0]]).T dt = cde.year / 360 #let's go forward one degree! one_deg = 2 * np.pi / 360. rot_coords = np.dot(cde.rotation_matrix_3d( np.array([0, 0, 1.0]), one_deg), start_coords_1) final_coords = cde.orbital_step_time_simple(start_coords_1, dt) final_mags = np.array([final_coords[:,0].dot(final_coords[:,0]), final_coords[:,1].dot(final_coords[:,1])]) diff_coords = (rot_coords - final_coords) / final_mags diff_coords_max = np.sqrt( max(np.dot(diff_coords[:,0], diff_coords[:,0]), np.dot(diff_coords[:,1], diff_coords[:,1]))) #Check to see if it's off by not more than a linear amount self.assertTrue(diff_coords_max < 1.0 / 360.0)
def test_rk4_stepper(self):
earth_vel = cde.earth_omega * cde.AU
start_coords_1 = np.array([[cde.AU, 0.0, 0.0], [0.0, earth_vel,
0.0]]).T
dt = cde.year / 360 #let's go forward one degree!
one_deg = 2 * np.pi / 360.
rot_coords_1 = np.dot(
cde.rotation_matrix_3d(np.array([0, 0, 1.0]), one_deg),
start_coords_1)
int_coords = cde.rk4_stepper(start_coords_1, .5 * dt)
final_coords = cde.rk4_stepper(int_coords, .5 * dt)
final_coords_2 = cde.rk4_stepper(start_coords_1, dt)
rot_mags = np.array([
rot_coords_1[:, 0].dot(rot_coords_1[:, 0]),
rot_coords_1[:, 1].dot(rot_coords_1[:, 1])
])
log_diff_coords = (rot_coords_1 - final_coords_2) / rot_mags
pos_err = np.sqrt(np.dot(log_diff_coords[:, 0], log_diff_coords[:, 0]))
vel_err = np.sqrt(np.dot(log_diff_coords[:, 1], log_diff_coords[:, 1]))
max_err = max(pos_err, vel_err)
def test_orbital_step_time_simple(self):
earth_vel = cde.earth_omega * cde.AU
start_coords_1 = np.array([[cde.AU, 0.0, 0.0], [0.0, earth_vel,
0.0]]).T
dt = cde.year / 360 #let's go forward one degree!
one_deg = 2 * np.pi / 360.
rot_coords = np.dot(
cde.rotation_matrix_3d(np.array([0, 0, 1.0]), one_deg),
start_coords_1)
final_coords = cde.orbital_step_time_simple(start_coords_1, dt)
final_mags = np.array([
final_coords[:, 0].dot(final_coords[:, 0]),
final_coords[:, 1].dot(final_coords[:, 1])
])
diff_coords = (rot_coords - final_coords) / final_mags
diff_coords_max = np.sqrt(
max(np.dot(diff_coords[:, 0], diff_coords[:, 0]),
np.dot(diff_coords[:, 1], diff_coords[:, 1])))
#Check to see if it's off by not more than a linear amount
self.assertTrue(diff_coords_max < 1.0 / 360.0)