def test_midpoint(self):
""" A_numerical should be approximately equal to A_analytical """
self.parameters["method"] = "MIDPOINT"
self.parameters["total_steps"] = 50
stepper = Stepper(**self.parameters)
A_numerical = stepper(self.A_initial)
assert_equal(A_numerical, 0.71663952968427402)
self.parameters["total_steps"] = 500
stepper = Stepper(**self.parameters)
A_numerical = stepper(self.A_initial)
assert_equal(A_numerical, 0.71669512731047913)
def test_bs(self):
""" A_numerical should be approximately equal to A_analytical """
self.parameters["method"] = "BS"
self.parameters["total_steps"] = 50
stepper = Stepper(**self.parameters)
A_numerical = stepper(self.A_initial)
assert_equal(A_numerical, 0.71669591977945657)
self.parameters["total_steps"] = 500
stepper = Stepper(**self.parameters)
A_numerical = stepper(self.A_initial)
assert_equal(A_numerical, 0.71669567831028291)
def test_euler(self):
""" A_numerical should be approximately equal to A_analytical """
self.parameters["method"] = "EULER"
self.parameters["total_steps"] = 50
stepper = Stepper(**self.parameters)
A_numerical = stepper(self.A_initial)
assert_equal(A_numerical, 0.72152686293820223)
self.parameters["total_steps"] = 500
stepper = Stepper(**self.parameters)
A_numerical = stepper(self.A_initial)
assert_equal(A_numerical, 0.71717199224362427)
def test_dp(self):
""" A_numerical should be approximately equal to A_analytical """
self.parameters["method"] = "DP"
self.parameters["total_steps"] = 50
stepper = Stepper(**self.parameters)
A_numerical = stepper(self.A_initial)
assert_almost_equal(A_numerical, self.A_analytical)
assert_equal(A_numerical, 0.71669567807314427)
self.parameters["total_steps"] = 500
stepper = Stepper(**self.parameters)
A_numerical = stepper(self.A_initial)
assert_almost_equal(A_numerical, self.A_analytical)
assert_equal(A_numerical, 0.71669567807368462)
def test_rk4(self):
""" A_numerical should be approximately equal to A_analytical """
self.parameters["method"] = "RK4"
self.parameters["total_steps"] = 50
stepper = Stepper(**self.parameters)
A_numerical = stepper(self.A_initial)
assert_almost_equal(A_numerical, self.A_analytical)
assert_equal(A_numerical, 0.71669567757603803)
self.parameters["total_steps"] = 500
stepper = Stepper(**self.parameters)
A_numerical = stepper(self.A_initial)
assert_almost_equal(A_numerical, self.A_analytical)
assert_equal(A_numerical, 0.71669567807363854)
def test_rk4ip(self):
""" Test Runge-kutta in the interaction picture. """
self.parameters["method"] = "RK4IP"
stepper = Stepper(**self.parameters)
A_out = stepper(self.A_in)
assert_almost_equal(max(np.abs(A_out) ** 2), self.P_analytical, 5)
def test_ss_sym_rk4(self):
""" Test symmetric splitstep with Runge-Kutta method. """
self.parameters["method"] = "SS_SYM_RK4"
stepper = Stepper(**self.parameters)
A_out = stepper(self.A_in)
assert_almost_equal(max(np.abs(A_out) ** 2), self.P_analytical, 3)
def test_ss_sym_midpoint(self):
""" Test symmetric splitstep with midpoint method. """
self.parameters["method"] = "SS_SYM_MIDPOINT"
stepper = Stepper(**self.parameters)
A_out = stepper(self.A_in)
assert_almost_equal(max(np.abs(A_out) ** 2), self.P_analytical, 2)
def test_ss_agrawal(self):
""" Test splitstep Agrawal method. """
self.parameters["method"] = "SS_AGRAWAL"
stepper = Stepper(**self.parameters)
A_out = stepper(self.A_in)
assert_almost_equal(max(np.abs(A_out) ** 2), self.P_analytical, 4)
def test_ss_reduced(self):
""" Test reduced splitstep method. """
self.parameters["method"] = "SS_REDUCED"
stepper = Stepper(**self.parameters)
A_out = stepper(self.A_in)
assert_almost_equal(max(np.abs(A_out) ** 2), self.P_analytical, 3)
def test_ss_symmetric(self):
""" Test symmetric splitstep method. """
self.parameters["method"] = "SS_SYMMETRIC"
stepper = Stepper(**self.parameters)
A_out = stepper(self.A_in)
assert_almost_equal(max(np.abs(A_out) ** 2), self.P_analytical, 0)
def test_ss_simple(self):
""" Test simple splitstep method. """
self.parameters["method"] = "SS_SIMPLE"
stepper = Stepper(**self.parameters)
A_out = stepper(self.A_in)
assert_almost_equal(max(np.abs(A_out) ** 2), self.P_analytical, 3)
def test_default(self):
""" Should use default values (except for f) """
stepper = Stepper(f=self.default_function)
self.assertEqual(stepper.traces, 1)
self.assertEqual(stepper.local_error, 1e-6)
self.assertEqual(stepper.method, "RK4")
self.assertEqual(stepper.length, 1.0)
self.assertEqual(stepper.total_steps, 100)
self.assertEqual(stepper.adaptive, False)