Intermediate saved values are sometimes `inf`

[dkweiss31]

Hi Patrick! I've run into an issue over in dynamiqs/dynamiqs#666 when t0=t1 and I try to save intermediate values. It seems to be independent of the stepsize_controller that I use (adaptive or constant). Here is a minimal example using constant steps.

import diffrax as dx
import jax.numpy as jnp

term = dx.ODETerm(lambda t, y, _: y)
y0 = jnp.array([1.0])
ts = jnp.array([0.0, 0.0])
saveat = dx.SaveAt(subs=[dx.SubSaveAt(ts=ts), dx.SubSaveAt(t1=True)])

solution = dx.diffeqsolve(
    term,
    dx.Tsit5(),
    ts[0],
    ts[-1],
    0.1,
    y0,
    saveat=saveat,
)
print(solution.ys[0])  # [[inf] [inf]]
print(solution.ys[1])  # [[1.]]

[patrick-kidger]

Ah! Good catch. It seems that we don't try to fill in SaveAt(ts=...) in the t0=t1 case. This case means that we never enter our integration loop and so we never trigger any of the code for saving SaveAt(ts=...):

diffrax/diffrax/_integrate.py

Lines 408 to 456 in 7384bfa

	interpolator = solver.interpolation_cls(
	t0=state.tprev, t1=state.tnext, **dense_info
	)
	save_state = state.save_state
	dense_ts = state.dense_ts
	dense_infos = state.dense_infos
	dense_save_index = state.dense_save_index
	def save_ts(subsaveat: SubSaveAt, save_state: SaveState) -> SaveState:
	if subsaveat.ts is not None:
	save_state = save_ts_impl(subsaveat.ts, subsaveat.fn, save_state)
	return save_state
	def save_ts_impl(ts, fn, save_state: SaveState) -> SaveState:
	def _cond_fun(_save_state):
	return (
	keep_step
	& (ts[_save_state.saveat_ts_index] <= state.tnext)
	& (_save_state.saveat_ts_index < len(ts))
	)
	def _body_fun(_save_state):
	_t = ts[_save_state.saveat_ts_index]
	_y = interpolator.evaluate(_t)
	_ts = _save_state.ts.at[_save_state.save_index].set(_t)
	_ys = jtu.tree_map(
	lambda __y, __ys: __ys.at[_save_state.save_index].set(__y),
	fn(_t, _y, args),
	_save_state.ys,
	)
	return SaveState(
	saveat_ts_index=_save_state.saveat_ts_index + 1,
	ts=_ts,
	ys=_ys,
	save_index=_save_state.save_index + 1,
	)
	return inner_while_loop(
	_cond_fun,
	_body_fun,
	save_state,
	max_steps=len(ts),
	buffers=_inner_buffers,
	checkpoints=len(ts),
	)
	save_state = jtu.tree_map(
	save_ts, saveat.subs, save_state, is_leaf=_is_subsaveat
	)

I suppose we should add a special case in our integration loop that explicitly handles this case. (Something like ys = lax.cond(t0 == t1, lambda: jnp.full(ts, y0), ...) ?)

I'd be happy to take a PR on this.

[dkweiss31]

Gotcha! Nice I'd be happy to give this a go. I've been meaning to learn about while loops and buffers so no time like the present!

[patrick-kidger]

Great!
And the good news is that I think this gets to happen before/after the loop (I mispoke a little above), so there won't be any need to change the integration loop itself.