Numerical validation policy#
Validation is layered. Many public scalar helpers reject nonfinite inputs and impossible physical ranges before division, logarithms or square roots. Geometric/distribution/matrix routines validate ordering, shape or integer indices where needed. Domain guides distinguish enforced bounds from assumptions that cannot be inferred from the arguments. Passing validation does not certify that a physical model applies to a particular apparatus.
Independent benchmark matrix#
Domain |
Independent evidence |
|---|---|
Structural |
Beam equilibrium/curvature, support values, bar reaction balance, energy derivative, three-moment equation, moment distribution and frame stiffness against one another, method of joints against direct stiffness, mechanism work minimum, Engesser residual, Macaulay beams against handbook cases and superposition, Gauss-quadrature stress resultants of the flexure formula, Jourawski stress integrating to the shear force, Lamé equilibrium residual, stress-tensor invariants, rosette round trip, unit-load against stiffness deflection, slope-deflection against moment distribution, cable arc length by quadrature, Hibbeler and Gere-Goodno worked examples |
Electrical |
Closed-form transient current, charge integral, RC and RL energy accounting, resonance, RLC step against SciPy, mesh against nodal analysis, diode load line against Lambert W, Newton-Raphson against Gauss-Seidel load flow, swing-curve energy and equal areas, Glover-Overbye-Sarma worked examples |
Controls |
Analytic scalar LQR/Kalman, matrix Riccati residuals and shape/weight failures, Ogata textbook values |
Thermodynamics |
Integrated P dV, T delta_S, four-state cycle balances and COP identities, IF97 verification tables (regions 1 to 5) and Gibbs relations, van der Waals critical inflection and isenthalpic throttle, Curzon-Ahlborn power maximum, Rankine and Brayton plant energy balances and Çengel and Boles plants, Ericsson limit, Stirling and dual four-process balances, Peng-Robinson critical inflection, equal-area rule, Clapeyron slope and R-134a tables, Maxwell relation and Joule-Thomson throttle on IF97 steam, Dalton mixing entropy against isothermal expansions, psychrometric mass and energy balances, Hess heating values, flame-temperature energy balance and JANAF enthalpies, Çengel-Boles and Moran et al. worked examples |
Fluids |
Integrated parabolic profile and wall pressure, laminar Darcy equivalence, Colebrook residual and limits, Hardy Cross against Newton, Pi-group null space, White and Munson et al. worked examples |
Heat transfer |
Interface Q*R drops, thin-wall limit, exchanger limits, Planck integral, plane-wall series and finite-difference energy, Blasius-Pohlhausen similarity solution, Graetz eigenvalue, exact crossflow series, effectiveness-NTU against F-LMTD, cylinder and sphere lumped and fixed-surface limits and energy balance, 2-D Fourier series and second-order convergence, shape-factor identities, two- and three-surface radiation networks, Incropera et al. worked examples |
Materials |
Isotropic modulus identities, elastic strain-energy triangle, offset yield, Griffith-Irwin agreement, Paris life against closed form and quadrature, composite bounds, strain-life transition, Fick’s second law, Callister and Shigley textbook values, Neuber’s product, Halpin-Tsai limits, laminate ABD closed forms, Weibull size effect |
Mechanical |
Undamped energy, damping dissipation, critical solution, gear power, forced equilibrium, simulated forced steady state, modal superposition against direct integration, double-pendulum energy, Rayleigh-Dunkerley bracket, Castigliano spring rate, integrated pressure cone, balancing residuals, finite-difference linkage and cam derivatives, Shigley and Rao worked examples |
Aerodynamics |
Normal and oblique shock mass/momentum/energy balances, sonic and infinite-wing limits, Prandtl-Meyer and Fanno ODE quadrature, Rayleigh-line conservation, exact elliptic lifting line, panel method against the exact cylinder and Kutta-Joukowski lift, built-up moment slope at the neutral point, integrated take-off roll and time-stepped propeller cruise, Anderson worked examples |
Signals |
Parseval, periodogram integral, cutoff gain, sinc nodes, ADC error bounds, FFT and Welch against NumPy and SciPy, Gibbs limit, Haar energy, Wiener and LMS system identification, Chebyshev and elliptic ripple bounds and orders, bilinear transform and prewarping, Parks-McClellan alternation, overlap-add against direct convolution, interpolation and decimation, Hilbert transform, DCT orthonormality, Levinson-Durbin against a Toeplitz solve, cepstral echo, Oppenheim-Schafer and Proakis-Manolakis worked examples |
Communications |
Analytic FM phase, unsigned bit handling, linear/log link budgets and noise limits, Haykin worked examples |
Reliability |
Survival integral, SciPy distributions, exhaustive independent system states, sensitivities, Monte Carlo fault trees, interference and Kaplan-Meier, Markov matrix exponential, beta-median ranks, SciPy and censored-likelihood Weibull fits, flood-fill network states, simulated standby, Monte Carlo against FORM, numerical gamma-Poisson posterior, NIST e-Handbook worked examples |
Tests use analytical values, invariants, independent quadrature and established SciPy distributions. Where a governing-equation residual is checked, it verifies the numerical solve but does not independently prove the equation’s physics. Most assertions use tight tolerances for algebraic identities; integrations allow appropriate quadrature/discretization error. Source coverage excludes tests and is a diagnostic, not a proof of correctness.
Behavior fixed in 0.1.0#
SeriesRLC returns current, correcting the previous charge/current mismatch. FM integration starts at zero modulation phase and supports nonuniform grids. Unsigned BPSK/QPSK input is converted before subtraction. Physical range errors raise ValueError instead of propagating NaNs or divisions by zero. Colebrook transition inputs are rejected. Rare-failure PFD and empirical Oswald estimates now enforce their documented implementation ranges. NumPy 1.24 remains supported by using SciPy trapezoid for stress-strain integration.
Coverage gate#
The test suite covers all executable production statements and branches: every
if and loop is seen taking each way out. Coverage excludes only test code;
production validation, plotting, constants and unit helpers are included, and no
production code carries a coverage-ignore pragma. The report’s fail_under=100
gate fails on any missed statement or branch. An executed branch can still
contain an error or rely on an invalid model assumption, so analytical
benchmarks and the domain guides remain essential.
Reproducing the checks#
CI runs these on every push. On 2026-10-31, 1730 tests pass (and 33
expected failures, xfail) in about 10 s, covering all 10683 production
statements and 1856 branches.
python -m pip install -e '.[dev]'
ruff check .
ruff format --check .
python -m mypy
MPLBACKEND=Agg pytest --cov=engineeringkit --cov-report=term-missing
make -C docs html
python -m build