mathlib-fp 1.7.0

Released 2026-07-30.

Version 1.7.0 completes the numerical-modelling and optimisation milestone on the 1.5/1.6 typed dense engine. It provides end-to-end interpolation, fitting, integration, nonlinear-equation, adaptive ODE, derivative, LP/QP, cone-constrained, and nonlinear-optimisation workflows with inspectable outcomes.

User-visible additions

• NumericsLib.Interpolation: barycentric/rational interpolation, monotonicity-preserving PCHIP, Akima curves, derivatives/antiderivatives, bilinear/bicubic grids, and small scattered IDW/RBF/thin-plate methods.
• NumericsLib.Differentiation: scale-aware gradients, Jacobians, Hessians, dual-number forward AD, and analytic-gradient checks.
• NumericsLib.Modelling: adaptive Gauss-Kronrod finite/improper integration, deterministic Halton integration, weighted QR polynomial/linear-basis fitting, bounded robust Levenberg-Marquardt, vector Newton equations, and adaptive vector Dormand-Prince ODEs with dense output and events.
• MathBase.Iteration: a common status vocabulary distinguishing convergence, acceptable limits, stagnation, breakdown, infeasibility, unboundedness, iteration exhaustion, and cancellation.
• OptimizationLib.Convex: dense positive-semidefinite QP with explicit projection and feasible-start affine second-order-cone optimisation.

The numerical modelling guide and convex optimisation guide contain 60-second examples, selection advice, API contracts, diagnostics, and limitations. Runnable cross-domain examples are 17_numerical_modelling.pas and 18_convex_optimization.pas.

Diagnostics and derivative paths

Iterative 1.7 results retain the best finite iterate and a TIterationStatus. Analytic, central-difference, and forward-AD derivatives are compared on smooth reference problems. CheckGradient and nonlinear fit Jacobian checking identify the mismatching variable or matrix element before a long solve.

Adaptive integration reports an embedded-pair error estimate. Fits report parameters, residuals, rank, degrees of freedom, justified covariance, RSS, R-squared, iterations, evaluations, and gradient scale. Vector roots report residual/step norms. ODE results report accepted/rejected steps, dense output, and event state. Convex results report objective, optimality scale, feasibility, iterations, evaluations, and status.

Compatibility and migration

This release is additive. TNumericsKit, TOptimizationKit, existing result fields, and all 1.6 typed dense APIs remain source compatible. Callers can migrate one workflow at a time.

The old PenaltyMethod and Maximize implementations no longer use unit-global callback adapters or locks. Their signatures and numerical intent are unchanged, while independent calls are now reentrant.

Accuracy evidence

Checked reference workflows include polynomial knot reproduction, monotone PCHIP bounds, planar grid interpolation, exact RBF nodes, the sine and Gaussian integrals, exact linear fits, bounded nonlinear residual fits, a two-equation system, exponential ODE dense output and event time, a constrained convex quadratic, and the scalar unit-cone optimum.

The 1.7 qualification report lists configurations and exact gates. Accuracy statements are workload-specific; they are not universal worst-case proofs.

Known limitations

• Adaptive ODE integration is non-stiff; stiff methods and mass matrices are not claimed.
• RBF/thin-plate construction is dense and intended for small data sets.
• Forward AD targets scalar and small-to-medium parameter problems; reverse mode is absent.
• The convex APIs are dense continuous QP/SOCP solvers. Sparse, semidefinite, integer/mixed-integer, and general non-convex models are not claimed.
• The SOCP solver requires a strictly feasible initial point and does not provide a general infeasibility certificate.

No persistence/interchange, expression-evaluation, parallel/SIMD, large-data, or other 1.8.0 feature was added.