From 8c0d6f0e1f721ac5a6490bb6203657de062018d9 Mon Sep 17 00:00:00 2001
From: Patrick Kidger <33688385+patrick-kidger@users.noreply.github.com>
Date: Fri, 28 Jul 2023 15:53:59 -0700
Subject: [PATCH] Added test for grad-of-discontinuous-forcing

---
 test/test_adaptive_stepsize_controller.py | 45 +++++++++++++++++++++++
 1 file changed, 45 insertions(+)

diff --git a/test/test_adaptive_stepsize_controller.py b/test/test_adaptive_stepsize_controller.py
index 6f4dd494..997dc4ae 100644
--- a/test/test_adaptive_stepsize_controller.py
+++ b/test/test_adaptive_stepsize_controller.py
@@ -1,8 +1,11 @@
 import diffrax
 import equinox as eqx
+import jax
 import jax.numpy as jnp
 import jax.tree_util as jtu
 
+from .helpers import shaped_allclose
+
 
 def test_step_ts():
     term = diffrax.ODETerm(lambda t, y, args: -0.2 * y)
@@ -90,3 +93,45 @@ def run(ys, controller, state):
         ys = (y0, y1_candidate, y_error)
         grads = run(ys, stepsize_controller, state)
         assert not any(jnp.isnan(grad).any() for grad in grads)
+
+
+def test_grad_of_discontinuous_forcing():
+    def vector_field(t, y, forcing):
+        y, _ = y
+        dy = -y + forcing(t)
+        dsum = y
+        return dy, dsum
+
+    def run(t):
+        term = diffrax.ODETerm(vector_field)
+        solver = diffrax.Tsit5()
+        t0 = 0
+        t1 = 1
+        dt0 = None
+        y0 = 1.0
+        stepsize_controller = diffrax.PIDController(
+            rtol=1e-8, atol=1e-8, step_ts=t[None]
+        )
+
+        def forcing(s):
+            return jnp.where(s < t, 0, 1)
+
+        sol = diffrax.diffeqsolve(
+            term,
+            solver,
+            t0,
+            t1,
+            dt0,
+            (y0, 0),
+            args=forcing,
+            stepsize_controller=stepsize_controller,
+        )
+        _, sum = sol.ys
+        (sum,) = sum
+        return sum
+
+    r = jax.jit(run)
+    eps = 1e-5
+    finite_diff = (r(0.5) - r(0.5 - eps)) / eps
+    autodiff = jax.jit(jax.grad(run))(0.5)
+    assert shaped_allclose(finite_diff, autodiff)