def forward_model(m=None, sim_info=None):
assert m is not None, "Please define parameters."
m = np.exp(m)
assert sim_info is not None, "Please define simulation parameters."
Nt = sim_info['Nt']
h = sim_info['h']
sampling_rate = sim_info['sampling_rate']
u = np.zeros((5, Nt))
_, drugs, u[:, 0] = model_Rong_init()
for i in range(1, Nt):
x_old = u[:, i - 1] + h * f_Rong(u[:, i - 1], p=m, drugs=drugs)
x_new = Newton(x_old, u[:, i - 1], p=m, drugs=drugs, h=h)
k = 0
dev = np.abs(x_old - x_new)
while dev[0] > tol and dev[1] > tol and dev[2] > tol:
x_old = x_new
x_new = Newton(x_old, u[:, i - 1], p=m, drugs=drugs, h=h)
dev = np.abs(x_old - x_new)
k += 1
u[:, i] = x_new
if not (i % 10000):
print('Solved at time ', str(i), ' after ', str(k),
' Newton iterations.')
idx_obs = np.where(t % sampling_rate == 0)[0].astype(int)[:-1]
return u[:, idx_obs], u[0, idx_obs] + u[1, idx_obs] + u[3, idx_obs], u[
2, idx_obs] + u[4, idx_obs]
def Newton(x_old, u_old, p=para):
J_old = Dg(h, Df_Rong(x_old, p=para))
g_old = g(u_old, x_old, h, f_Rong(x_old, p=para))
return x_old - np.dot(np.linalg.pinv(J_old), g_old)
return np.identity(5) - h * Df
for idx, eps in enumerate(epsilon_RT_alpha_02):
print('Solving for epsilon_RT = ', str(eps))
para, u[:, 0] = model_Rong_init()
para[8] = eps
@numba.jit(nopython=True)
def Newton(x_old, u_old, p=para):
J_old = Dg(h, Df_Rong(x_old, p=para))
g_old = g(u_old, x_old, h, f_Rong(x_old, p=para))
return x_old - np.dot(np.linalg.pinv(J_old), g_old)
for i in range(1, Nt):
guess = u[:, i - 1] + h * f_Rong(u[:, i - 1])
x_old = guess
x_new = Newton(x_old, u[:, i - 1], p=para)
k = 0
dev = np.abs(x_old - x_new)
while dev[0] > tol and dev[1] > tol and dev[2] > tol:
x_old = x_new
x_new = Newton(x_old, u[:, i - 1], p=para)
dev = np.abs(x_old - x_new)
k += 1
u[:, i] = x_new
if not (i % 10000):
print('Solved at time ', str(i), ' after ', str(k),
' Newton iterations.')