def test_run_adjoint2(trajectory_implicit):
u, f, fu, fs, J, Ju, Js = trajectory_implicit
w_tmn, vst_tmn = adjoint_terminal_condition(M, f[-1])
w, vst = segment.get_wvst(w_tmn, vst_tmn, fu, Ju,
lorenz.adjoint_step_implicit)
assert w.shape[0] == vst.shape[0]
assert w.shape[2] == vst.shape[1]
# test if w remains orthorgonal to f
_ = (w[:, :-1] * f[:, np.newaxis, :]).sum(axis=-1)
assert np.allclose(_, np.zeros(_.shape))
def test_run_adjoint(trajectory):
u, f, fu, fs, J, Ju, Js = trajectory
w_tmn, vst_tmn = adjoint_terminal_condition(M, f[-1])
w, vst = lorenz.run_adjoint(w_tmn, vst_tmn, fu, Ju, dt,
lorenz.adjoint_step_explicit)
assert w.shape[0] == vst.shape[0] == nstep + 1
assert w.shape[1] == M
assert w.shape[2] == vst.shape[1] == m
# test if w remains orthorgonal to f
_ = (w * f[:, np.newaxis, :]).sum(axis=-1)
assert np.allclose(_, np.zeros(_.shape))
def test_terminal_condition_function():
M_modes = 3
m = 5
f_tmn = np.random.rand(m)
w_tmn, vst_tmn = adjoint_terminal_condition(M_modes, f_tmn)
# check shape
assert w_tmn.shape == (M_modes, m)
assert vst_tmn.shape == f_tmn.shape == (m, )
# check if w_tmn is orthogonal to f_tmn
assert np.allclose(np.dot(w_tmn[:-1], f_tmn), np.zeros(M_modes - 1))
# check the last column of w is f_tmn
assert np.allclose(w_tmn[-1], f_tmn / np.linalg.norm(f_tmn))
# check vst_tmn is zero
assert np.allclose(vst_tmn, np.zeros(m))