def test_phi_2d_linear(self):
C_0, C_1 = symbols('C_0 C_1')
state_vector = [C_0, C_1]
time_symbol = Symbol('t')
input_fluxes = {}
output_fluxes = {0: C_0, 1: C_1}
internal_fluxes = {}
srm = SmoothReservoirModel(state_vector, time_symbol, input_fluxes,
output_fluxes, internal_fluxes)
start_values = np.array([1, 2])
t_0 = 0
t_max = 4
nt = 200
times = np.linspace(t_0, t_max, nt)
smr = SmoothModelRun(srm, {}, start_values, times)
smr.initialize_state_transition_operator_cache(lru_maxsize=None,
size=2)
nr_pools = srm.nr_pools
def baseVector(i):
e_i = np.zeros((nr_pools, 1))
e_i[i] = 1
return e_i
bvs = [baseVector(i) for i in range(nr_pools)]
for s in np.linspace(t_0, t_max, 5):
for t in np.linspace(s, t_max, 5):
phi_ref = np.eye(2) * np.exp(-(t - s))
# test the matrix valued results
with self.subTest():
self.assertTrue(
np.allclose(smr.Phi(t, s), phi_ref, rtol=1e-2))
# test the vectored valued results
for x in bvs:
for phi_x in [
smr._state_transition_operator(t, s, x),
smr._state_transition_operator_for_linear_systems(
t, s, x)
]:
with self.subTest():
self.assertTrue(
np.allclose(phi_x,
np.matmul(phi_ref,
x).reshape(nr_pools, ),
rtol=1e-2))
def test_phi_2d_non_linear(self):
k_0_val = 1
k_1_val = 2
x0_0 = np.float(0.5)
x0_1 = np.float(1.5)
x_0, x_1, k_0, k_1, t, u = symbols("x_0 x_1 k_0 k_1 t u")
inputs = {0: u, 1: u * t}
outputs = {0: k_0 * x_0**2, 1: k_1 * x_1}
internal_fluxes = {}
svec = Matrix([x_0, x_1])
srm = SmoothReservoirModel(state_vector=svec,
time_symbol=t,
input_fluxes=inputs,
output_fluxes=outputs,
internal_fluxes=internal_fluxes)
t_0 = 0
t_max = 4
nt = 20000
times = np.linspace(t_0, t_max, nt)
parameter_dict = {k_0: k_0_val, k_1: k_1_val, u: 1}
func_dict = {}
# make it a column vector for later use
start_x = np.array([x0_0, x0_1])
# create the model run
smr = SmoothModelRun(
model=srm,
parameter_dict=parameter_dict,
start_values=start_x,
times=times,
func_set=func_dict,
)
smr.initialize_state_transition_operator_cache(lru_maxsize=None,
size=4)
nr_pools = srm.nr_pools
def baseVector(i):
e_i = np.zeros((nr_pools, 1))
e_i[i] = 1
return e_i
bvs = [baseVector(i) for i in range(nr_pools)]
smrl = smr.linearize_old()
for s in np.linspace(t_0, t_max, 5):
for t in np.linspace(s, t_max, 5):
for x in bvs:
with self.subTest():
self.assertTrue(
np.allclose(
smr._state_transition_operator(t, s, x),
smrl.
_state_transition_operator_for_linear_systems(
t, s, x), # noqa: E501
rtol=1.5 * 1e-2))
for t in np.linspace(t_0, t_max, 6):
for phi_mat in [smr.Phi(t, t_0), smrl.Phi(t, t_0)]:
for x in bvs:
with self.subTest():
self.assertTrue(
np.allclose(np.matmul(phi_mat,
x).reshape(nr_pools, ),
smr._state_transition_operator(
t, t_0, x),
rtol=1.5 * 1e-2))