assignments_to_experiments: convert values that ramp with time, via a rate rule - #557

#557 was rebased onto main (with the pandas fix #571), so #559 conflicted
with its base. The result is the same tree as #559 rebased onto #557.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

#557 was squash-merged into main, so #559 conflicted with main. The
result is the same tree as before, since main now has exactly #557's
content.

Co-Authored-By: Claude Opus 5.5 <noreply@anthropic.com>

…#559)

A v2 period's `time` overrides the model's initial time, so an
experiment starts at its first period after pre-equilibration.
`assignments_to_experiments` dropped that period whenever nothing
changed there. Either it was redundant, because the model already holds
the value before the switch, or its condition only set symbols that the
conversion replaced, so the condition was emptied and removed. The
experiment then started at its first switch, and measurements before the
switch were simulated from the wrong start.

For example, `k1 := piecewise(1, time < 5, 2)` converted to
`default_experiment` with a single period at t = 5. The existing
`test_assignments_to_experiments` asserted that shape: one period at t =
10, beside a measurement at t = 0.

## Changes

- Every converted experiment keeps the period that starts it, without
conditions if none are left. For `default_experiment`, and for an
experiment that only pre-equilibrates, that is the period at t = 0 the
converter already adds. The `or experiment.periods[:1]` fallback goes,
since the start period is never dropped.
- A switch therefore never becomes an experiment's first period, and
`CheckInitialChangeSymbols` only checks the first period. A start value
that equals the model's value is no longer set just because a switch
refers to symbols outside the parameter table. For `level * piecewise(0,
time < 10, 1)`, the experiment now has an empty period at 0 and `k1 =
level` at 10, where it had `k1 = 0` at 0 and `k1 = level` at 10. A start
value that refers to parameter table symbols is still set at the start
(as since #556), since the model only holds a number for it.

## Tests

- `test_assignments_to_experiments`, `_nested`, `_condition_specific`,
`_several_switches` and `_fixed_switching_time` now expect the empty
period at t = 0.
- New `test_assignments_to_experiments_simulate_before_switch` covers
both cases: no experiment, and a condition at t = 0 that only sets the
switching time. It converts the problem, turns both the original and the
converted problem into SBML events with `ExperimentsToSbmlConverter`,
simulates them in BasiCO at t = 0, 1, 2, 4, 6 and 10, and compares the
results. They match to 3e-11 relative (the test asserts 1e-6). Without
this fix, the converted problem is off by up to 45% before the switch.
- The benchmark problems that convert (Brannmark_JBC2010,
Fujita_SciSignal2010, Isensee_JCB2018, Raimundez_PCB2020) give the same
experiment table, condition table and SBML with and without this change.

## Relation to #557

Stacked on #557; #556 is merged. The bug has been on main since #527. On
main the change merges cleanly as text, but main's
`test_assignments_to_experiments_several_switches` and
`_fixed_switching_time` assert the old shape, with no period at t = 0,
and #557 reworks the `redundant` block that this change simplifies. This
PR's base moves to main once #557 merges.

🤖 Generated with [Claude Code](https://claude.com/claude-code)

---------

Co-authored-by: Claude Opus 5.5 <noreply@anthropic.com>
Co-authored-by: Fabian Fröhlich <frohlif@login006.nemo.thecrick.org>

Follows #559. A refactor of `assignments_to_experiments` that does not
change its behaviour. The fixes for bugs found while reviewing and
stress-testing it are in #574, stacked on this PR.

## Slimming down `assignments_to_experiments`

The function had grown to 340 lines, most of them one loop body passing
around the parsed assignment, its switches, its value before every
switch, the switching times' fixed values and the slope parameter of a
ramp. It is now about 75 lines (plus its docstring) that run the steps
in order:

- `_add_start_periods`: give every experiment the period that starts it,
and find the periods that may be dropped;
- for each time-dependent assignment rule, a `_PiecewiseAssignment`:
- its constructor checks that the assignment is supported and works out
the value before every switch, the switching times' fixed values and
whether the value ramps;
- `replace_in_model()` replaces the rule in the model (the slope
parameter and rate rule for a ramp, the target's value);
- `changes(experiment)` returns the condition changes that replace it in
an experiment. The old module-level `_changes` and `_value_from` became
its methods.
- `_drop_changes` / `_add_conditions`: replace the condition changes the
new conditions cover;
- drop empty periods, add the default experiment, lint.

The `redundant` / `after_preequilibration` double negative became one
decision per period: one branch for the first period, one for the later
ones.

On the review comment on #557 about not turning this into a class:
`assignments_to_experiments` stays a function. `_PiecewiseAssignment`
only holds the values of one assignment that the old loop body passed
between its parts. If you would rather not have it, it can become a few
free functions that take those values.

No change in behaviour: on all 40 conversions in the tests, the old and
new implementations give the same experiment table, condition table,
measurement table, SBML, errors and warnings. The benchmark problems
Brannmark_JBC2010, Fujita_SciSignal2010, Isensee_JCB2018,
Raimundez_PCB2020 (and Oliveira_NatCommun2021's error) also convert
identically.

## Checked

- `pytest tests/v2 tests/v1/test_petab.py`: 244 passed; pre-commit
clean.

🤖 Generated with [Claude Code](https://claude.com/claude-code)

---------

Co-authored-by: Claude Opus 5.5 <noreply@anthropic.com>
Co-authored-by: Fabian Fröhlich <frohlif@login006.nemo.thecrick.org>