{ "schema_version": 1, "release": "2.3.1", "inventory": "docs/reference/capabilities.json", "inventory_release": "2.3.1", "families": [ { "family": "bessel_elliptic_exponential_integral", "status": "qualified", "risk": "standard", "input_domain": "Finite real double inputs within each function's documented validated domain, including stated endpoint limits and exclusions.", "budget": { "kind": "relative_error", "metric": "Absolute difference from independent reference values, with the test's 5e-13 absolute floor and 5e-12 relative allowance", "limit": 5e-12, "unit": "function output units" }, "reference": { "method": "120-digit decimal reference corpora, independent quadrature for E1 values, and documented mathematical identities", "source": "Repository-generated reference include files cite NIST DLMF; reference generators use decimal arithmetic and Gauss-Legendre quadrature", "precision": "At least 120 decimal digits during reference generation, rounded to IEEE-754 binary64 literals", "parameters": "Bessel small and large arguments; modified Bessel domain and scale cases; incomplete and complete elliptic integrals including Pi; Jacobi quarter periods; Ei/E1 tails; convergent 2F1 parameter and argument fixtures", "license": "Repository-authored generators and fixtures under MIT; mathematical reference material is cited from NIST DLMF", "regeneration": "Run the generate_*_data.py tools referenced by each include header, then run the cited special-function test units" }, "tests": [ { "path": "tests/TestSpecialFunctions.pas", "assertions": [ "procedure TTestBessel.TestJReferenceCorpus;", "procedure TTestBessel.TestYReferenceCorpus;", "Y0 negative domain" ], "kind": "independent decimal references, identities, and domain edges" }, { "path": "tests/TestModifiedBessel.pas", "assertions": [ "procedure TTestModifiedBessel.TestReferenceCorpus;", "I/K Wronskian", "K0 negative domain" ], "kind": "independent decimal references, identities, and domain edges" }, { "path": "tests/TestEllipticIntegrals.pas", "assertions": [ "procedure TTestEllipticIntegrals.TestIncompleteReferenceCorpus;", "procedure TTestEllipticIntegrals.TestThirdKindReferenceValues;", "F(phi, 0)" ], "kind": "decimal/quadrature references and endpoint/domain checks" }, { "path": "tests/TestJacobiElliptic.pas", "assertions": [ "procedure TTestJacobiElliptic.TestIndependentReferences;", "sn(K,m)=1", "infinite parameter" ], "kind": "independent decimal references, quarter-period identities, and domain edges" }, { "path": "tests/TestExponentialIntegrals.pas", "assertions": [ "procedure TTestExponentialIntegrals.TestEiReferenceCorpus;", "procedure TTestExponentialIntegrals.TestE1ReferenceCorpus;", "Ei below validated range" ], "kind": "independent decimal/quadrature references and pole/domain checks" }, { "path": "tests/TestGaussHypergeometric.pas", "assertions": [ "procedure TTestGaussHypergeometric.TestReferenceCorpus;", "F(1,1;2;0.5) identity", "X above range" ], "kind": "independent decimal references, identities, and convergence-domain checks" } ], "edge_cases": [ "Function-specific poles and finite endpoint limits are checked explicitly.", "NaN, infinity, and out-of-domain values follow the documented rejection behavior.", "Elliptic Pi principal-value poles, unsupported characteristics, and hypergeometric analytic continuation are excluded." ], "documentation": "docs/guides/domains/math-base.md" }, { "family": "remaining_advanced_spectral_linear_algebra", "status": "qualified", "risk": "standard", "input_domain": "Finite real or complex double dense matrices and regular real or complex matrix pencils in documented supported dimensions.", "budget": { "kind": "residual", "metric": "Normalized reconstruction, orthogonality/unitarity, and generalized eigenpair residuals; maximum explicit generalized residual fixture threshold", "limit": 1e-07, "unit": "dimensionless normalized residual" }, "reference": { "method": "Independently reconstructed Schur factorizations, known eigenvalue fixtures, orthogonality/unitarity checks, and normalized homogeneous generalized-eigenpair residuals", "source": "Repository-authored fixtures and independently computed residuals in TestDenseDecompositions", "precision": "IEEE-754 binary64 real and complex arithmetic", "parameters": "Real/complex Hessenberg and Schur factors, nonsymmetric real eigenpairs, finite and infinite generalized eigenvalues, and real/complex 3x3 pencils", "license": "Repository-authored tests under MIT; no third-party reference data", "regeneration": "Run TestDenseDecompositions; recompute the stated factor reconstructions and normalized homogeneous eigenpair residuals from the fixtures" }, "tests": [ { "path": "tests/TestDenseDecompositions.pas", "assertions": [ "real generalized Schur reconstructs A", "finite generalized eigenpair residual is small", "3x3 generalized eigenvectors report small residuals" ], "kind": "factor reconstruction and normalized eigenpair residual" }, { "path": "tests/TestDenseDecompositions.pas", "assertions": [ "complex generalized Schur reconstructs A", "complex generalized eigenpair residual is small", "3x3 complex generalized eigenpair residual is small" ], "kind": "complex factor reconstruction and normalized eigenpair residual" } ], "edge_cases": [ "Singular B produces projective infinite generalized eigenvalues where supported.", "Empty inputs, invalid dimensions, non-finite entries, and bounded-iteration failures have explicit tests.", "Repeated or clustered eigenvalues may rotate their eigenvector basis; polynomial and interior-target workflows are outside this family." ], "documentation": "docs/guides/domains/dense-linear-algebra.md" }, { "family": "stiff_ode_integration", "status": "qualified", "risk": "standard", "input_domain": "Finite real-double explicit-form initial-value systems with smooth right-hand sides over the integration interval, dense state Jacobians, and tolerances for which the bounded step and Newton iteration converges.", "budget": { "kind": "absolute_error", "metric": "Fixture-specific endpoint, interpolation, and event bounds; the Robertson endpoint uses 20*(rtol*abs(reference)+10*atol) per component (maximum allowed state deviation 2.2e-3).", "limit": 0.0022, "unit": "state units; event-time bounds are separately asserted" }, "reference": { "method": "Closed-form forced-stiff scalar solution and published Robertson kinetics endpoint values", "source": "The repository spec cites the SUNDIALS cvRoberts_dns.c example: https://github.com/LLNL/sundials/blob/main/examples/cvode/serial/cvRoberts_dns.c", "precision": "IEEE-754 binary64; published Robertson decimal values are represented as binary64 literals", "parameters": "Forced equation y'=-1000*(y-cos(t))-sin(t), y(0)=0; Robertson system at t=4e10 with y0=[1,0,0], rtol=1e-4 and atols=[1e-8,1e-14,1e-6]", "license": "Repository-authored test fixture under the project license; upstream SUNDIALS source is cited and no third-party implementation code is copied", "regeneration": "Run TestNumericalModelling. Review the cited SUNDIALS endpoint fixture and evaluate the forced-problem identity y(t)=cos(t)-exp(-1000*t); no network access is needed at test time." }, "tests": [ { "path": "tests/TestNumericalModelling.pas", "assertions": [ "procedure TTestNumericalModelling.TestStiffODEJacobianModesAndEvents;", "tighter tolerances reduce endpoint error", "stiff event found", "analytic Jacobian endpoint", "automatic Jacobian endpoint", "backward integration endpoint", "non-stiff result agrees with explicit solver" ], "kind": "closed-form stiff endpoint and dense-output accuracy, tolerance refinement, event location, analytic/automatic/finite-difference Jacobians, backward integration, and non-stiff comparison" }, { "path": "tests/TestNumericalModelling.pas", "assertions": [ "procedure TTestNumericalModelling.TestStiffODERobertsonReference;", "Robertson stiff status", "Robertson integration accepted steps", "Robertson component %d reference: expected %.16g, got %.16g" ], "kind": "published Robertson reference endpoint with per-component absolute/relative tolerance weighting" }, { "path": "tests/TestNumericalModelling.pas", "assertions": [ "procedure TTestNumericalModelling.TestStiffODEValidation;", "missing analytic Jacobian is rejected", "wrong Jacobian dimensions are rejected", "step limit is reported", "Newton failure is reported as breakdown", "non-finite derivative output is rejected", "nested stiff integration is reentrant" ], "kind": "invalid-input, iteration-limit, Newton-breakdown, non-finite-output, and reentrancy checks" } ], "edge_cases": [ "Forward and backward integration, scalar and component tolerances, interpolation, and directional event localization are covered.", "Finite-difference, analytic, and automatic Jacobian modes are tested against the same forced-stiff reference.", "Missing or malformed Jacobians, zero combined tolerance, non-finite or wrong-dimension derivatives, step exhaustion, and Newton failure have explicit outcomes.", "The Robertson kinetics system exercises a three-component stiff trajectory at t=4e10; sparse Jacobians, mass matrices, DAEs, and large-scale solves are outside the supported domain." ], "documentation": "docs/guides/domains/numerical-modelling.md" } ], "carried_forward_from": "2.3.0", "carry_forward_reason": "The 2.3.1 patch changes documentation and release metadata only; Pascal source, numerical tests, and stable capability scope are unchanged." }