mathlib-fp 1.7.0

Release date: 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.