labplan: exact measurement planning, calibration and audit trails for any lab model

Abstract

Fixed Model.jacobian (used by information, design and fit) took its finite-difference step as 1e-6 * max(|theta|, 1e-3). For a parameter smaller than 1e-3 in its own units the step, 1e-9, was too coarse; for a time constant of 1e-9 s it was the size of the parameter itself. The planned error bars then depended on the units the parameter was written in, a noiseless fit could stop away from the truth (V0 = 0.987 and tau = 0.938 ns instead of 1 and 1 ns in the new test's RC model), and a model that divides by such a parameter was refused as "non-finite". The step is now 1e-6 * |theta|. When that step changes the predictions by less than 1e-8 of their size (always for a parameter that is exactly zero, and for one that is tiny next to the rest of the prediction, such as a slope of 1e-12 beside an offset of 1), the 0.1.0 step 1e-6 * max(|theta|, 1e-3) is used instead: a purely relative step would there be lost in floating-point rounding and give wrong slopes, wrong error bars and false "cannot tell the parameters apart" refusals. Results for parameters of size 1e-3 or more are unchanged. Tests New test_small_parameters_unit_invariant: the same RC model with tau in seconds and in nanoseconds gives the same planned error bars (to 1 part in 10^6) and the same noiseless fit, and the slopes of a model that divides by a 1e-9 parameter are finite and exact to 1 part in 10^6. It fails on 0.1.0. New test_near_zero_parameter_keeps_a_resolvable_step: for a straight line with slope 1e-12, 1e-300 or 0, the slopes match the exact ones to 1 part in 10^6, and a noiseless fit of a flat line returns the textbook covariance. It guards the fallback above. The CI matrix now includes Python 3.10, which the classifiers claim but CI did not run, and a new oldest-dependencies job runs the suite on Python 3.9 with NumPy 1.22.0 and pytest 7.0.0, the lowest versions pyproject.toml allows. Changed README rewritten in plain language, with worked examples whose printed output is checked, a list of the actual refusals, and each test described with the tolerance it really uses. Corrections to the v0.1.0 notes "the recomputed greedy rule": no test recomputes the greedy selection step by step. The tests check that the picks are distinct, that they beat 30 random subsets, and that the two-point pick equals the best pair found by exhaustion. "linear-model covariance equals the textbook closed form exactly, planner and fit agree as one matrix": the tests assert this to a relative tolerance of 1e-6, not exactly. Full history: CHANGELOG.md