Piecewise exponential fit: misleading dead bound computation and non-optimisable x_center

[PierreRaybaut]

Summary

DoubleExponentialFitComputer has two structural problems and one piece of dead code.

1. amp_bound / rate_bound look like bounds but are not

compute_initial_params() derives amp_bound and rate_bound and uses them only to clip the seed. compute_bounds() is not overridden, so the optimisation runs unbounded.

Do not "fix" this by applying them. Measured on the shipped reference dataset piecewiseexponential_fit.txt:

Strategy	residual RMS	a_right
clip seed, unbounded (current)	1.8965	22480
clip seed, bounds applied	16.3272	301 (pinned on the bound)
raw seed, unbounded	1.8982	22358

rate_bound = 5 / x_range = 0.5 is half the true rate (≈ 1.0) and amp_bound = 301 is two orders of magnitude below the true amplitude. The bounds are miscalibrated; enforcing them pins three parameters on their limits.

Resolution applied on fix/fitting-audit: keep the fit unbounded, reword the misleading comment so the clamp is documented as a seed sanitiser, and record the measurement in the class docstring. Deriving genuinely usable bounds remains open.

2. x_center is not optimisable

y[x < x_center]  = a_left  * np.exp(b_left  * x[x < x_center]) + y0
y[x >= x_center] = a_right * np.exp(b_right * x[x >= x_center]) + y0

x_center only enters through boolean masks, so the model is piecewise constant in x_center and its numerical derivative is zero almost everywhere. curve_fit cannot move it: the junction stays frozen on the (very rough) initial estimate. Documented on the branch; making the junction differentiable (smooth blend) is a model change that needs a separate decision.

3. Dead code

y0 = 0.0 is assigned then immediately overwritten; x_range is computed twice. Removed on the branch.

[PierreRaybaut]

Status after fix/fitting-audit

Commit 12665d8 on fix/fitting-audit addresses only the documentation and the dead code:

• both .. note:: blocks added to the DoubleExponentialFitComputer class docstring (bounds miscalibration with the measured 1.90 → 16.33 RMS regression, and the zero-gradient x_center);
• the amp_bound/rate_bound comment reworded so the clamp is unambiguously described as a seed sanitiser rather than as optimisation bounds;
• dead code removed (y0 = 0.0 immediately overwritten, x_range computed twice).

The two structural problems are untouched. Here is what is left.

1. Decide what to do with x_center

x_center enters the model only through boolean masks, so the model is piecewise constant with respect to it and curve_fit cannot move it. It is nevertheless listed in PARAMS_NAMES, so it is exposed as an adjustable parameter and reported back to the user as a fit result, when in practice it always equals the initial argmax estimate.

Two mutually exclusive options:

• Make the junction differentiable — replace the hard split with a smooth blend (for instance a logistic transition with a width parameter). This changes the model and its signature, therefore FIT_PARAMS_VERSION and the stored fit_params.
• Accept that it is frozen — remove x_center from the free parameters so the API stops advertising something the optimiser never optimises, and expose it as a fixed input instead.

2. Improve the x_center seed

Because x_center is frozen, the entire quality of the fit hinges on self.x[np.argmax(self.y)], which the code itself flags as "very rough". A cheap and measurable improvement would be a small 1D search over candidate junction positions, keeping the one that minimises the residual. This is worth benchmarking against the current behaviour on the reference dataset before committing to it.

3. Derive bounds that actually work, or state that there are none

The fit is currently unbounded, so nothing protects it from diverging on a pathological dataset. The existing expressions cannot be reused (see the measurement in the issue body). Either usable bounds are derived and validated, or the absence of bounds is accepted as a deliberate design decision.

Note also that the seed clamp itself is not empirically justified: on the reference dataset the clamped seed gives an RMS of 1.8965 against 1.8982 for the raw seed, which is within noise. It may be protecting against a failure mode that no longer exists.

Side effect in DataLab

The interactive fit dialog exposes an x_center slider that the automatic optimiser ignores: moving it manually changes the curve, but pressing Fit always returns it to its initial value. This is confusing and is not covered by any existing ticket.