import scipy.integrate
import autograd.numpy as np
from autograd.extend import primitive, defvjp_argnums
from autograd import make_vjp
from autograd.misc import flatten
from autograd.builtins import tuple
odeint = primitive(scipy.integrate.odeint)
def grad_odeint_all(yt, func, y0, t, func_args, **kwargs):
T,D = np.shape(yt)
flat_args, unflatten = flatten(func_args)
def flat_func(y, t, flat_args):
return func(y, t, *unflatten(flat_args))
def unpack(x):
# y , vjp_y , vjp_t , vjp_args
return x[0:D], x[D:2 * D], x[2 * D], x[2 * D + 1:]
def augmented_dynamics(augmented_state, t, flat_args):
# Orginal system augmented with vjp_y , vjp_t and vjp_args .
y, vjp_y, _, _ = unpack(augmented_state)
vjp_all, dy_dt = make_vjp(flat_func, (0, 1, 2))(y, t, flat_args)
vjp_y, vjp_t, vjp_args = vjp_all((vjp_y))
return np.hstack((dy_dt, vjp_y, vjp_t, vjp_args))
def vjp_all(g, **kwargs):
vjp_y = g[-1, :]
vjp_t0 = 0
time_vjp_list = []
vjp_args = np.zeros(np.size(flat_args))
for i in range(T - 1, 0, -1):
# Compute e f f e c t o f moving c u r r e n t tim e .
vjp_cur_t = np.dot(func(yt[i, :], t[i], *func_args), g[i, :])
time_vjp_list.append(vjp_cur_t)
vjp_t0 = vjp_t0 - vjp_cur_t
# Run a u gme nte d s y st em b a c kw a r d s t o t h e p r e v i o u s o b s e r v a t i o n .
aug_y0 = np.hstack((yt[i, :], vjp_y, vjp_t0, vjp_args))
aug_ans = odeint(augmented_dynamics, aug_y0, np.array([t[i], t[i - 1]]), tuple((flat_args,)), **kwargs)
_, vjp_y, vjp_t0, vjp_args = unpack(aug_ans[1])
# Add g r a d i e n t f rom c u r r e n t o u t p u t .
vjp_y = vjp_y + g[i - 1, :]
time_vjp_list.append(vjp_t0)
vjp_times = np.hstack(time_vjp_list)[:: -1]
return None, vjp_y, vjp_times, unflatten(vjp_args)
return vjp_all
def grad_argnums_wrapper(all_vjp_builder):
def build_
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