OriginalWLS

OriginalWLS

CLI: --model original_wls. Class: loqculate.compat.wls.OriginalWLS. Registered on MODEL_REGISTRY when you import loqculate.

Port of old/calculate-loq.py process_peptide(model='piecewise'). I keep it so a rewrite can still be compared to the paper script. It is not a drop-in for PiecewiseCF: the LOQ rule is different, and LOD guards are different.

The original script used lmfit. This class uses scipy.optimize.least_squares(..., method="trf") with the same $(a, b, c-b)$ bounds. CHANGELOG 0.2.2 already records that 2 of 27 demo peptides can land in a different local optimum than lmfit.

Fit

• At least 3 observations and at least 2 unique $x$, else ValueError.
• Weights: min(1/(sqrt(x)+eps), 1000), same cap as inverse_sqrt_weights.
• Init: _initialize_params_legacy (top-two concentrations).
• Solver: TRF, max_nfev=5000. Unlike PiecewiseWLS, a solver failure is not caught; result.x is used as returned.
• LOD and bootstrap LOQ are computed inside fit(), not lazily.

lod(std_mult) and loq(cv_thresh) after fit ignore those arguments and return the values stored at fit time. Constructor std_mult and cv_thresh (defaults 2 and 0.20) are the ones that matter. The CLI passes --std_mult / --cv_thresh into lod() / loq() after fit, so those CLI flags do not change OriginalWLS output. --bootreps is also not forwarded (name does not start with piecewise).

LOD

_calculate_lod_legacy:

1. $a \le 0$ $\to$ $\infty$.
2. $x_{\mathrm{int}} = (c-b)/a$.
3. $\sigma$ from all $y$ with $x < x_{\mathrm{int}}$, ddof=1, if at least one such point; otherwise $\sigma=\infty$.
4. $\mathrm{LOD} = (c + \mathrm{std_mult}\cdot\sigma - b)/a$.
5. If $\mathrm{LOD} > \max(x)$, $\infty$.
6. Let inner_points be unique $x$ with the global min and max removed. If that set is empty, or $\mathrm{LOD} < \min(\mathrm{inner_points})$, $\infty$.

min_noise_points and min_linear_points are accepted on the constructor and passed into this function. They are not read in the function body.

LOQ

Bootstrap predictions on np.linspace(LOD, max(x), 100). Per-replicate seed SeedSequence(i) for i in range(n_boot), matching the original _bootstrap_once. CV is std/mean with ddof=1 on the bootstrap matrix.

Single-point rule, strict inequality:

$$\mathrm{LOQ} = \min{ x_{\mathrm{grid}} : x_{\mathrm{grid}} > \mathrm{LOD},\ \mathrm{CV}(x_{\mathrm{grid}}) < \tau }$$

No sliding window. If none, or the min is $\le 0$ or $\ge \max(x_{\mathrm{grid}})$, $\infty$.

This is not find_loq_threshold, and it is not <=.