Tidy up some internals in the adaptive solver (#826)

* Keyword arguments in AdaState

* Rename extrapolation to strategy according to the rest of the code

* All adaptive_solver.extraction methods have the same signature

* Leave TODOs

* Adaptive solver gets 'eps' to make 'small values' consistent

* Recover old default for adaptive_solver.eps

* Remove unnecessary function call nesting

* Call solve_and_save_at in solve_and_save_terminal_values

* Initial condition returns an IVPSolution object now

* Delete outdated comments

Author: pnkraemer

probdiffeq/ivpsolve.py

@@ -4,7 +4,6 @@
 from probdiffeq.backend import (
     containers,
     control_flow,
-    functools,
     linalg,
     tree_array_util,
     tree_util,
@@ -89,42 +88,21 @@ def solve_adaptive_terminal_values(
     vector_field, initial_condition, t0, t1, adaptive_solver, dt0, *, ssm
 ) -> IVPSolution:
     """Simulate the terminal values of an initial value problem."""
-    save_at = np.asarray([t1])
-    (_t, solution_save_at), _, num_steps = _solve_adaptive_save_at(
-        tree_util.Partial(vector_field),
-        t0,
+    save_at = np.asarray([t0, t1])
+    solution = solve_adaptive_save_at(
+        vector_field,
         initial_condition,
         save_at=save_at,
         adaptive_solver=adaptive_solver,
         dt0=dt0,
-    )
-    # "squeeze"-type functionality (there is only a single state!)
-    squeeze_fun = functools.partial(np.squeeze_along_axis, axis=0)
-    solution_save_at = tree_util.tree_map(squeeze_fun, solution_save_at)
-    num_steps = tree_util.tree_map(squeeze_fun, num_steps)
-
-    # I think the user expects marginals, so we compute them here
-    # todo: do this in IVPSolution.* methods?
-    posterior, output_scale = solution_save_at
-    marginals = posterior.init if isinstance(posterior, stats.MarkovSeq) else posterior
-
-    u = ssm.stats.qoi_from_sample(marginals.mean)
-    std = ssm.stats.standard_deviation(marginals)
-    u_std = ssm.stats.qoi_from_sample(std)
-    return IVPSolution(
-        t=t1,
-        u=u,
-        u_std=u_std,
         ssm=ssm,
-        marginals=marginals,
-        posterior=posterior,
-        output_scale=output_scale,
-        num_steps=num_steps,
+        warn=False,  # Turn off warnings because any solver goes for terminal values
     )
+    return tree_util.tree_map(lambda s: s[-1], solution)
 
 
 def solve_adaptive_save_at(
-    vector_field, initial_condition, save_at, adaptive_solver, dt0, *, ssm
+    vector_field, initial_condition, save_at, adaptive_solver, dt0, *, ssm, warn=True
 ) -> IVPSolution:
     r"""Solve an initial value problem and return the solution at a pre-determined grid.
 
@@ -152,7 +130,7 @@ def solve_adaptive_save_at(
         }
         ```
     """
-    if not adaptive_solver.solver.is_suitable_for_save_at:
+    if not adaptive_solver.solver.is_suitable_for_save_at and warn:
         msg = (
             f"Strategy {adaptive_solver.solver} should not "
             f"be used in solve_adaptive_save_at. "
@@ -170,7 +148,7 @@ def solve_adaptive_save_at(
 
     # I think the user expects the initial condition to be part of the state
     # (as well as marginals), so we compute those things here
-    posterior_t0, *_ = initial_condition
+    posterior_t0 = initial_condition.posterior
     posterior_save_at, output_scale = solution_save_at
     _tmp = _userfriendly_output(
         posterior=posterior_save_at, posterior_t0=posterior_t0, ssm=ssm
@@ -194,41 +172,37 @@ def solve_adaptive_save_at(
 def _solve_adaptive_save_at(
     vector_field, t, initial_condition, *, save_at, adaptive_solver, dt0
 ):
-    advance_func = functools.partial(
-        _advance_and_interpolate,
-        vector_field=vector_field,
-        adaptive_solver=adaptive_solver,
-    )
-
-    state = adaptive_solver.init(t, initial_condition, dt=dt0, num_steps=0.0)
-    _, solution = control_flow.scan(advance_func, init=state, xs=save_at, reverse=False)
-    return solution
-
-
-def _advance_and_interpolate(state, t_next, *, vector_field, adaptive_solver):
-    # Advance until accepted.t >= t_next.
-    # Note: This could already be the case and we may not loop (just interpolate)
-    def cond_fun(s):
-        # Terminate the loop if
-        # the difference from s.t to t_next is smaller than a constant factor
-        # (which is a "small" multiple of the current machine precision)
-        # or if s.t > t_next holds.
-        return s.step_from.t + 10 * np.finfo_eps(float) < t_next
+    def advance(state, t_next):
+        # Advance until accepted.t >= t_next.
+        # Note: This could already be the case and we may not loop (just interpolate)
+        def cond_fun(s):
+            # Terminate the loop if
+            # the difference from s.t to t_next is smaller than a constant factor
+            # (which is a "small" multiple of the current machine precision)
+            # or if s.t > t_next holds.
+            return s.step_from.t + adaptive_solver.eps < t_next
+
+        def body_fun(s):
+            return adaptive_solver.rejection_loop(
+                s, vector_field=vector_field, t1=t_next
+            )
 
-    def body_fun(s):
-        return adaptive_solver.rejection_loop(s, vector_field=vector_field, t1=t_next)
+        state = control_flow.while_loop(cond_fun, body_fun, init=state)
 
-    state = control_flow.while_loop(cond_fun, body_fun, init=state)
+        # Either interpolate (t > t_next) or "finalise" (t == t_next)
+        is_after_t1 = state.step_from.t > t_next + adaptive_solver.eps
+        state, solution = control_flow.cond(
+            is_after_t1,
+            adaptive_solver.extract_after_t1,
+            adaptive_solver.extract_at_t1,
+            state,
+            t_next,
+        )
+        return state, solution
 
-    # Either interpolate (t > t_next) or "finalise" (t == t_next)
-    state, solution = control_flow.cond(
-        state.step_from.t > t_next + 10 * np.finfo_eps(float),
-        adaptive_solver.extract_after_t1_via_interpolation,
-        lambda s, _t: adaptive_solver.extract_at_t1(s),
-        state,
-        t_next,
-    )
-    return state, solution
+    state = adaptive_solver.init(t, initial_condition, dt=dt0, num_steps=0.0)
+    _, solution = control_flow.scan(advance, init=state, xs=save_at, reverse=False)
+    return solution
 
 
 def solve_adaptive_save_every_step(
@@ -264,7 +238,7 @@ def solve_adaptive_save_every_step(
     t = np.concatenate((np.atleast_1d(t0), t))
 
     # I think the user expects marginals, so we compute them here
-    posterior_t0, *_ = initial_condition
+    posterior_t0 = initial_condition.posterior
     posterior, output_scale = solution_every_step
     _tmp = _userfriendly_output(posterior=posterior, posterior_t0=posterior_t0, ssm=ssm)
     marginals, posterior = _tmp
@@ -292,15 +266,16 @@ def _solution_generator(
     while state.step_from.t < t1:
         state = adaptive_solver.rejection_loop(state, vector_field=vector_field, t1=t1)
 
-        if state.step_from.t < t1:
-            solution = adaptive_solver.extract_before_t1(state)
+        if state.step_from.t + adaptive_solver.eps < t1:
+            _, solution = adaptive_solver.extract_before_t1(state, t=t1)
             yield solution
 
     # Either interpolate (t > t_next) or "finalise" (t == t_next)
-    if state.step_from.t > t1:
-        _, solution = adaptive_solver.extract_after_t1_via_interpolation(state, t=t1)
+    is_after_t1 = state.step_from.t > t1 + adaptive_solver.eps
+    if is_after_t1:
+        _, solution = adaptive_solver.extract_after_t1(state, t=t1)
     else:
-        _, solution = adaptive_solver.extract_at_t1(state)
+        _, solution = adaptive_solver.extract_at_t1(state, t=t1)
 
     yield solution
 
@@ -321,7 +296,7 @@ def body_fn(s, dt):
     _t, (posterior, output_scale) = solver.extract(result_state)
 
     # I think the user expects marginals, so we compute them here
-    posterior_t0, *_ = initial_condition
+    posterior_t0 = initial_condition.posterior
     _tmp = _userfriendly_output(posterior=posterior, posterior_t0=posterior_t0, ssm=ssm)
     marginals, posterior = _tmp