def f(it,V):
X = V[0:9]
co2 = V[9]
npp = npp_func(it,X)
B = B_func(it,X)
X_new = X + npp * b + B@X
# we also compute the respired co2 in every (daily) timestep
# and use this part of the solution later to sum up the monthly amount
co2_new = respiration_from_compartmental_matrix(B,X)
V_new = np.concatenate((X_new,np.array([co2_new]).reshape(1,1)), axis=0)
return V_new
def test_respiration(self):
# The respiration is a function of the Matrix B = A*K
# here we test that this leads to the same result as yuanyuan's original version
# which computes it directly from the parameters
def respiration_from_params(pa, X):
lig_leaf = pa.lig_leaf
f41 = pa.f_leaf2metlit
f42 = pa.f_root2metlit
f51 = 1 - f41
f52 = 1 - f42
f63 = 1
f74 = 0.45
f75 = 0.45 * (1 - lig_leaf)
f85 = 0.7 * lig_leaf
f86 = 0.4 * (1 - pa.lig_wood)
f96 = 0.7 * pa.lig_wood
f87 = (0.85 - 0.68 *
(pa.clay + pa.silt)) * (0.997 - 0.032 * pa.clay)
f97 = (0.85 - 0.68 *
(pa.clay + pa.silt)) * (0.003 + 0.032 * pa.clay)
f98 = 0.45 * (0.003 + 0.009 * pa.clay)
temp = [
pa.k_leaf, pa.k_root, pa.k_wood, pa.k_metlit,
pa.k_metlit / (5.75 * np.exp(-3 * pa.lig_leaf)),
pa.k_metlit / 20.6, pa.k_mic, pa.k_slowsom, pa.k_passsom
]
K = np.zeros(81).reshape([9, 9])
for i in range(0, 9):
K[i][i] = temp[i]
co2_rate = np.array([
0, 0, 0, (1 - f74) * K[3, 3], (1 - f75 - f85) * K[4, 4],
(1 - f86 - f96) * K[5, 5], (1 - f87 - f97) * K[6, 6],
(1 - f98) * K[7, 7], K[8, 8]
]) #.reshape(9,1)
return np.sum(co2_rate * X.reshape(1, 9))
Xnt = self.x_init
X = np.array(Xnt).reshape(9, 1)
orh = respiration_from_params(self.mpa, X)
B_func = make_compartmental_matrix_func(self.mpa)
B = B_func(0, self.x_init)
nrh = respiration_from_compartmental_matrix(B, X)
self.assertTrue(np.allclose(orh - nrh, np.zeros((9, 1))))