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from __future__ import absolute_import
from builtins import range
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(yt, func, y0, t, func_args, **kwargs):
# Extended from "Scalable Inference of Ordinary Differential
# Equation Models of Biochemical Processes", Sec. 2.4.2
# Fabian Froehlich, Carolin Loos, Jan Hasenauer, 2017
# https://arxiv.org/abs/1711.08079
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, argnum=(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):
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 effect of moving measurement time.
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 augmented system backwards to the previous observation.
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 gradient from current output.
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 argnums_unpack(all_vjp_builder):
# A generic autograd helper function. Takes a function that
# builds vjps for all arguments, and wraps it to return only required vjps.
def build_selected_vjps(argnums, ans, combined_args, kwargs):
vjp_func = all_vjp_builder(ans, *combined_args, **kwargs)
def chosen_vjps(g): # Returns whichever vjps were asked for.
all_vjps = vjp_func(g)
return [all_vjps[argnum] for argnum in argnums]
return chosen_vjps
return build_selected_vjps
defvjp_argnums(odeint, argnums_unpack(grad_odeint))