|
Uni20
Asynchronous tensor and runtime library.
|
This note records which native Krylov precision paths are implemented and covered by tests. LAPACK-style precision names are used. Complex scalar spellings follow the project scalar policy in Scalar Policy:
For the full algorithm inventory, public parameters, defaults, and internal tuning values, see Krylov Algorithms.
| tag | scalar |
|---|---|
s | float |
d | double |
c | uni20::complex<float> |
z | uni20::complex<double> |
f128 | uni20::float128, when UNI20_HAS_FLOAT128=1 |
cf128 | uni20::complex<uni20::float128>, also spelled uni20::complex256, when UNI20_HAS_FLOAT128=1 |
Binary128 validation is gated by UNI20_ENABLE_FLOAT128=ON and UNI20_BACKEND_MPLAPACK=ON. CMake resolves an installed MPLAPACK 3.0.0 or newer package with the binary128 component, or fetches the pinned 3.0.0 release. The optional validation currently covers scalar aliases and I/O, BLAS/LAPACK wrapper surfaces, tensor linear algebra probes, broad dense projected helper coverage, real and complex matrix-free eigensolvers, and projected exponential action. The gated probes also check that selected scalar-generic helpers use Uni20's real scalar traits rather than relying only on std::floating_point.
Most ordinary Krylov tests are typed through tests/krylov/krylov_test_types.hpp. In a normal build those aliases expand to the s, d, c, and z paths. The MPLAPACK-enabled binary128 coverage is kept in separate MplapackBinary128* targets. The broad dense-subspace wrappers are retained and tested there, but are not pulled into the ordinary typed solver matrix.
This table records the ordinary default-build coverage for s, d, c, and z. Optional binary128 probes are listed separately below.
| algorithm | s | d | c | z | tests |
|---|---|---|---|---|---|
| Dense vector/matrix primitives | yes | yes | yes | yes | KrylovDenseLinalgTypedTest |
| Dense real matrix norms | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.ComputesDenseReal*MatrixNorms |
| Dense matrix exponential, including complex multipliers | yes | yes | yes | yes | MatrixExponentialTypedTest, MatrixExponentialTest.RealMatrixWithComplexMultiplierPromotesToComplex, MatrixExponentialTest.ComplexMatrixWithComplexMultiplierUsesComplexTime |
| Dense real linear solve | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.SolvesDenseRealLinearSystemWithPivoting |
| Dense real refined linear solve | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.RefinesDenseRealLinearSystemWithDiagnostics |
| Dense real expert linear solve | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.SolvesDenseRealExpertLinearSystemWithDiagnostics |
| Dense real equilibration | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.ComputesDenseRealEquilibration |
| Dense real LU factorization and solve | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.SolvesFromDenseRealLuFactorization |
| Dense real general-band norm, equilibration, solve, refined/expert solve, and condition estimate | yes | yes | n/a | n/a | ordinary s/d dense-subspace tests; binary128 coverage is listed in the optional table below |
| Dense real general tridiagonal solve, condition, and refinement | yes | yes | n/a | n/a | ordinary s/d dense-subspace tests; binary128 coverage is listed in the optional table below |
| Dense real reciprocal condition estimate | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.EstimatesDenseRealReciprocalConditionNumber |
| Dense real triangular solve | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.SolvesDenseRealTriangularSystem |
| Dense real triangular refined solve | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.RefinesDenseRealTriangularSystemWithDiagnostics |
| Dense real triangular inverse | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.InvertsDenseRealTriangularMatrix |
| Dense real triangular reciprocal condition estimate | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.EstimatesDenseRealTriangularReciprocalConditionNumber |
| Dense real Sylvester equation solve | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.SolvesDenseRealSylvesterEquation |
| Dense real inverse | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.InvertsDenseRealMatrix |
| Dense real least-squares solve | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.SolvesDenseRealLeastSquaresProblem |
| Dense real SVD least-squares solve | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.SolvesDenseSvdLeastSquaresProblem |
| Dense real divide-and-conquer SVD least-squares solve | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.SolvesDenseDivideAndConquerSvdLeastSquaresProblem |
| Dense real rank-revealing least-squares solve | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.SolvesDenseRankRevealingLeastSquaresProblem |
| Dense real symmetric positive definite solve | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.SolvesDenseSymmetricPositiveDefiniteSystem |
| Dense real symmetric positive definite factorization and solve | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.SolvesDenseSymmetricPositiveDefiniteSystemFromFactorization |
| Dense real symmetric positive definite band solve, condition, and refinement | yes | yes | n/a | n/a | ordinary s/d dense-subspace tests; binary128 coverage is listed in the optional table below |
| Dense real symmetric positive definite tridiagonal solve, condition, and refinement | yes | yes | n/a | n/a | ordinary s/d dense-subspace tests; binary128 coverage is listed in the optional table below |
| Dense real symmetric positive definite refined solve | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.RefinesDenseSymmetricPositiveDefiniteSystemWithDiagnostics |
| Dense real symmetric positive definite expert solve | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.SolvesDenseSymmetricPositiveDefiniteExpertSystemWithDiagnostics |
| Dense real symmetric positive definite equilibration | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.ComputesDenseSymmetricPositiveDefiniteEquilibration |
| Dense real symmetric positive definite reciprocal condition estimate | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.EstimatesDenseSymmetricPositiveDefiniteReciprocalConditionNumber |
| Dense real symmetric positive definite factorized reciprocal condition estimate | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.EstimatesDenseSymmetricPositiveDefiniteFactorizedReciprocalConditionNumber |
| Dense real symmetric positive definite inverse | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.InvertsDenseSymmetricPositiveDefiniteMatrix |
| Dense real pivoted Cholesky factorization | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.ComputesDensePivotedCholeskyFactorization, ReportsRankDeficientPivotedCholeskyFactorization |
| Dense real symmetric indefinite solve | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.SolvesDenseSymmetricIndefiniteSystem |
| Dense real symmetric indefinite factorization and solve | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.SolvesDenseSymmetricIndefiniteSystemFromFactorization |
| Dense real symmetric indefinite refined solve | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.RefinesDenseSymmetricIndefiniteSystemWithDiagnostics |
| Dense real symmetric indefinite inverse | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.InvertsDenseSymmetricIndefiniteMatrix |
| Dense real symmetric indefinite expert solve | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.SolvesDenseSymmetricIndefiniteExpertSystemWithDiagnostics |
| Dense real symmetric indefinite reciprocal condition estimate | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.EstimatesDenseSymmetricIndefiniteReciprocalConditionNumber |
| Dense real symmetric indefinite factorized reciprocal condition estimate | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.EstimatesDenseSymmetricIndefiniteFactorizedReciprocalConditionNumber |
| Dense real compact QR factor application | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.AppliesCompactRealQrFactorization |
| Dense real QR factorization | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.ComputesReducedRealQrFactorization |
| Dense real compact LQ factor application | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.AppliesCompactRealLqFactorization |
| Dense real LQ factorization | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.ComputesReducedRealLqFactorization |
| Dense real compact QL factor application | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.AppliesCompactRealQlFactorization |
| Dense real QL factorization | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.ComputesReducedRealQlFactorization |
| Dense real compact RQ factor application | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.AppliesCompactRealRqFactorization |
| Dense real RQ factorization | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.ComputesReducedRealRqFactorization |
| Dense real bidiagonal reduction | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.ComputesRealBidiagonalReduction* |
| Dense real bidiagonal orthogonal-factor application | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.AppliesRealBidiagonalOrthogonalFactors |
| Dense real bidiagonal singular values | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.ComputesRealBidiagonalSingularValues |
| Dense real bidiagonal divide-and-conquer singular value decomposition | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.ComputesRealBidiagonalDivideAndConquerSvd |
| Dense selected real bidiagonal singular value decomposition | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.ComputesSelectedRealBidiagonalSvd |
| Dense real pivoted QR factorization | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.ComputesReducedRealPivotedQrFactorization |
| Dense real Hessenberg reduction | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.ComputesRealHessenbergReductionAndOrthogonalFactor |
| Dense real Hessenberg orthogonal-factor application | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.AppliesRealHessenbergOrthogonalFactor |
| Dense real symmetric tridiagonal reduction | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.ComputesRealSymmetricTridiagonalReductionAndOrthogonalFactor |
| Dense symmetric tridiagonal eigenvalues | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.SolvesSymmetricTridiagonalEigenvalues |
| Dense symmetric tridiagonal divide-and-conquer eigensystem | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.SolvesSymmetricTridiagonalDivideAndConquerEigensystem |
| Dense selected symmetric tridiagonal eigensystem | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.SolvesSelectedSymmetricTridiagonalEigenvectors |
| Dense real singular value decomposition | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.ComputesDenseRealSingularValueDecomposition |
| Dense real divide-and-conquer singular value decomposition | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.ComputesDenseRealDivideAndConquerSingularValueDecomposition |
| Dense selected real singular value decomposition | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.ComputesSelectedDenseRealSingularValueDecomposition |
| Dense real symmetric eigensystem | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.SolvesDenseRealSymmetric* |
| Dense real divide-and-conquer symmetric eigensystem | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.SolvesDenseRealSymmetricDivideAndConquerEigenvectors |
| Dense real selected symmetric eigensystem | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.SolvesSelectedDenseRealSymmetricEigenvectors |
| Dense generalized real symmetric eigensystem | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.SolvesDenseGeneralizedRealSymmetricEigenvectors |
| Dense generalized real divide-and-conquer symmetric eigensystem | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.SolvesDenseGeneralizedRealSymmetricDivideAndConquerEigenvectors |
| Dense generalized real selected symmetric eigensystem | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.SolvesSelectedDenseGeneralizedRealSymmetricEigenvectors |
| Dense complex Hermitian eigensystem | n/a | n/a | yes | yes | KrylovDenseSubspaceComplexTypedTest.SolvesDenseComplexHermitianEigenvectors |
| Dense complex divide-and-conquer Hermitian eigensystem | n/a | n/a | yes | yes | KrylovDenseSubspaceComplexTypedTest.SolvesDenseComplexHermitianDivideAndConquerEigenvectors |
| Dense complex selected Hermitian eigensystem | n/a | n/a | yes | yes | KrylovDenseSubspaceComplexTypedTest.SolvesSelectedDenseComplexHermitianEigenvectors |
| Dense generalized complex Hermitian eigensystem | n/a | n/a | yes | yes | KrylovDenseSubspaceComplexTypedTest.SolvesDenseGeneralizedComplexHermitianEigenvectors |
| Dense generalized complex divide-and-conquer Hermitian eigensystem | n/a | n/a | yes | yes | KrylovDenseSubspaceComplexTypedTest.SolvesDenseGeneralizedComplexHermitianDivideAndConquerEigenvectors |
| Dense generalized complex selected Hermitian eigensystem | n/a | n/a | yes | yes | KrylovDenseSubspaceComplexTypedTest.SolvesSelectedDenseGeneralizedComplexHermitianEigenvectors |
| Dense symmetric tridiagonal eigensystem | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.SolvesSymmetricTridiagonal* |
| Dense real nonsymmetric eigensystem | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.SolvesRealNonsymmetric* |
| Dense real nonsymmetric expert eigensystem | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.SolvesRealNonsymmetricExpertEigenvectorsWithDiagnostics |
| Dense real nonsymmetric balancing and right-vector backtransform | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.BalancesRealNonsymmetricMatrixAndBacktransformsRightVectors |
| Dense generalized real nonsymmetric eigensystem | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.SolvesRealGeneralizedNonsymmetricDiagonalEigenvectors |
| Dense generalized real nonsymmetric expert eigensystem | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.SolvesRealGeneralizedNonsymmetricExpertEigenvectorsWithDiagnostics |
| Dense generalized real nonsymmetric balancing and right-vector backtransform | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.BalancesRealGeneralizedNonsymmetricPencilAndBacktransformsRightVectors |
| Dense generalized real Hessenberg reduction | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.ComputesRealGeneralizedHessenbergReduction |
| Dense generalized real Hessenberg Schur factorization | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.ComputesRealGeneralizedHessenbergSchurDecomposition |
| Dense generalized real Schur factorization | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.ComputesRealGeneralizedSchurDecomposition |
| Dense generalized real Schur reordering | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.ReordersRealGeneralizedSchurBlocks |
| Dense generalized real Schur selected subspace condition estimates | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.SelectsRealGeneralizedSchurSubspaceWithConditionEstimates |
| Dense generalized real Schur right eigenvectors | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.ComputesRealGeneralizedSchurRightEigenvectors |
| Dense generalized real Schur eigenpair condition estimates | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.EstimatesRealGeneralizedSchurEigenpairConditioning |
| Dense real Schur and reordering | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.ComputesRealSchur*, ReordersRealSchur* |
| Dense real Hessenberg Schur factorization | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.ComputesRealHessenbergSchurDecomposition |
| Dense real Schur selected subspace condition estimates | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.SelectsRealSchurSubspaceWithConditionEstimates |
| Dense real Schur right eigenvectors | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.ComputesRealSchurRightEigenvectors |
| Dense real Schur eigenpair condition estimates | yes | yes | n/a | n/a | KrylovDenseSubspaceTypedTest.EstimatesRealSchurEigenpairConditioning |
| Dense complex nonsymmetric eigensystem | n/a | n/a | yes | yes | KrylovDenseSubspaceComplexTypedTest.SolvesComplexNonsymmetricEigenvalues |
| Dense complex Schur and reordering | n/a | n/a | yes | yes | KrylovDenseSubspaceComplexTypedTest.ComputesComplexSchur*, ReordersComplexSchur* |
| Symmetric/Hermitian Lanczos, full projection | yes | yes | yes | yes | KrylovSymmetricLanczosRealTypedTest.SolvesDiagonalLargestAlgebraicProblem, KrylovHermitianLanczosComplexTypedTest.SolvesImaginaryOffDiagonalHermitianProblem |
| Symmetric/Hermitian Lanczos, restarted regular mode | yes | yes | yes | yes | KrylovSymmetricLanczosRealTypedTest.RestartedSolveConvergesOnDiagonalLargestAlgebraicProblem, KrylovHermitianLanczosComplexTypedTest.RestartedSolveConvergesOnPhaseTwistedLaplacian |
| Symmetric/Hermitian Lanczos, transformed shift-invert mapping | yes | yes | yes | yes | KrylovSymmetricLanczosRealTypedTest.ShiftInvertSmallestAlgebraicSelectorActsInTransformedSpace, KrylovHermitianLanczosComplexTypedTest.ShiftInvertSelectorMapsComplexHermitianVectorPath |
Symmetric/Hermitian generalized Lanczos with B metric | yes | yes | yes | yes | KrylovSymmetricLanczosRealTypedTest.GeneralizedRegularModeUsesBMetric, KrylovHermitianLanczosComplexTypedTest.GeneralizedRegularModeUsesComplexBMetricPath |
| Real nonsymmetric Arnoldi, full projection | yes | yes | n/a | n/a | KrylovNonsymmetricArnoldiRealTypedTest.SolvesNonrestartedRealNonsymmetricDiagonalProblem |
| Real nonsymmetric Arnoldi, real Schur restart | yes | yes | n/a | n/a | KrylovNonsymmetricArnoldiRealTypedTest.RestartedSolveConvergesOnRealNonsymmetricDiagonalProblem |
| Complex nonsymmetric Arnoldi, full projection | n/a | n/a | yes | yes | KrylovNonsymmetricArnoldiComplexTypedTest.SolvesNonrestartedComplexNonsymmetricDiagonalProblem |
| Complex nonsymmetric Arnoldi, complex Schur restart | n/a | n/a | yes | yes | KrylovNonsymmetricArnoldiComplexTypedTest.RestartedSolveConvergesOnComplexNonsymmetricDiagonalProblem, RestartedSolveConvergesOnTransferLikeClusteredSpectrum |
| Hermitian Krylov exponential action, fixed subspace | yes | yes | yes | yes | KrylovExponentialRealTypedTest.HermitianFullSubspaceMatchesDiagonalExponential, KrylovExponentialComplexTypedTest.HermitianZeroVectorReturnsZeroWithoutMatvec, KrylovExponentialComplexTypedTest.HermitianActionAcceptsComplexTime |
| Nonsymmetric Krylov exponential action, fixed subspace | yes | yes | yes | yes | KrylovExponentialRealTypedTest.NonsymmetricFullSubspaceMatchesJordanExponential, KrylovExponentialComplexTypedTest.NonsymmetricFullSubspaceMatchesComplexDiagonalExponential, KrylovExponentialComplexTypedTest.NonsymmetricActionAcceptsComplexTime |
| Taylor exponential action, scaled Taylor validation path | yes | yes | yes | yes | KrylovExponentialRealTypedTest.TaylorActionMatchesDiagonalExponential, KrylovExponentialRealTypedTest.TaylorActionMatchesJordanExponential, KrylovExponentialComplexTypedTest.TaylorActionAcceptsComplexTime, KrylovExponentialComplexTypedTest.TaylorZeroVectorReturnsZeroWithoutMatvec, KrylovExponentialTaylorAction.ThrowsWhenTaylorDegreeCannotMeetTolerance |
| Lanczos-vs-Taylor exponential probe example | yes | yes | yes | yes | KrylovExponentialProbeExample.Float, KrylovExponentialProbeExample.Double |
| Lanczos exponential orthogonality-floor example | yes | yes | n/a | n/a | KrylovExponentialOrthogonalityExample.Float |
| TDVP Matrix Market exponential probe example | n/a | n/a | yes | yes | KrylovExponentialMatrixMarketProbeExample.TdvpFloat, KrylovExponentialMatrixMarketProbeExample.TdvpDouble |
DenseHostVectorOps also has compile-time KrylovMatrixFreeOperator assertions for s, d, c, and z.
The numerical precision matrix now runs common gap, residual, and accuracy probes across float32/64/80/128 and MPFR at 128/256 bits, with real and complex cases. Unavailable configurations and unsupported operations remain visible in the coverage report with reasons; they are not registered as executable tests. Missing expected probes fail the registry check or report instead of becoming skips. NumericalKrylov/* covers projected tridiagonal eigensystems, Lanczos, Arnoldi, and Hermitian exponential action for the supported native and binary128 types. Float80 and MPFR/MPC support for those eigensolver/exponential paths remains unsupported; runtime Ritz-reality helpers do not certify those solvers.
GmresRotationAndSolve, GmresAccuracyImprovesWithPrecision, and GmresMixedRefinement cover the new GMRES paths across all twelve configured real/complex cases. These do not need projected LAPACK. The accuracy probe uses an independent 512-bit oracle when MPFR is configured; its unavailable status is recorded otherwise. Mixed refinement uses float32 inner corrections and checks recovery of the selected working precision. A separate runtime test uses 40-bit inner, 128-bit working and 256-bit residual MPFR spaces. GmresErrorDiagnostics verifies the optional 2-norm error formulas and retention of precision in their arithmetic for the same twelve real/complex cases. GmresDiagnostics.* covers partial information, supplied-bound provenance, zero RHS, invalid inputs, and representable estimates whose intermediate products or ratios would overflow/underflow without scaling.
Gmres.* and GmresRefinement.* exercise restarts, initial guesses, breakdown, nonfinite publication, tiny residual conversion and independent precision contexts. BlockTensorVectorOpsTest.GmresPreservesU1BlocksAndBoundaries checks the block-sparse integration. GPU/distributed GMRES execution is not certified by these host tests.
This table records the UNI20_ENABLE_FLOAT128=ON and UNI20_BACKEND_MPLAPACK=ON probes. The entries are not part of the ordinary default test matrix. They check that the scalar-generic paths genuinely operate at the configured binary128 precision and do not silently collapse to double precision.
The native solver entry points are intended to mirror the ordinary precision coverage where the scalar category makes sense: real solver paths gain f128, complex solver paths gain cf128, and Hermitian paths gain both. The broad dense projected helper inventory remains quarantined in dense_subspace_unused.hpp, but its dedicated regression source is compiled in the optional MPLAPACK binary128 test executable. See Dense BLAS/LAPACK Wrapper Coverage for that provider/helper inventory.
| algorithm or surface | f128 | cf128 | tests |
|---|---|---|---|
| Scalar aliases, numeric limits, scalar concepts, and scalar I/O | yes | yes | MplapackBinary128Test.Uni20NumericLimitsSeesBackendScalar, Uni20ScalarConceptsSeeBackendScalar, Uni20ScalarIo* |
| MPBLAS wrapper surface | yes | yes | MplapackBinary128Test.LinksMpblasTransitively, Uni20BlasWrappersPreserveBinary128OnlyIncrements |
| Dense one-norm and linear solve through CPU helpers | yes | yes | NumericalLinalg/{Real,Complex}Float128.CpuMatrixOneNormRetainsIncrement, CpuSolvePreservesExtendedExponentRange |
| Tensor reductions through the CPU reference backend | yes | yes | NumericalLinalg/{Real,Complex}Float128.CpuReductionsRetainIncrement |
| Dense matrix exponential prescaling | yes | no | MplapackBinary128CpuOpsTest.MatrixExponentialPrescalesWithinBinary128 |
| Exact Tensor SVD | yes | yes | MplapackBinary128CpuOpsTest.ExactSvdPreservesRealAndComplexBinary128Values, AsyncSvdTest.SupportsConfiguredFloat128Backend |
| Reduced Tensor QR and LQ | yes | n/a | MplapackBinary128CpuOpsTest.ReducedQrAndLqPreserveBinary128Values |
| BlockTensor SVD and finite two-site DMRG | yes | yes | SpinHalfHeisenbergDmrgFloat128Example, SpinHalfHeisenbergDmrgComplexFloat128Example; the analytic four-site energy check requires fp128 agreement beyond double precision. |
| Broad dense projected real helper inventory | regression | n/a | Quarantined API inventory exercised by MplapackBinary128DenseSubspaceTest.*. |
| Dense projected complex eigensystem and Schur helper inventory | n/a | regression | Quarantined API inventory exercised by MplapackBinary128DenseSubspaceTest.*. |
| Symmetric tridiagonal projected eigensystem | yes | n/a | NumericalKrylov/RealFloat128.ProjectedTridiagonalResolvesGap |
| Symmetric/Hermitian Lanczos, full projection | yes | yes | NumericalKrylov/{Real,Complex}Float128.LanczosResolvesGapAndResidual |
| Real nonsymmetric projected Schur kernels | yes | n/a | MplapackBinary128KrylovSolversTest.RealSchurAndReorderUseBinary128ProjectedLAPACK, RealHessenbergSchurUsesBinary128ProjectedLAPACK |
| Real nonsymmetric Arnoldi, full projection | yes | n/a | MplapackBinary128KrylovSolversTest.RealArnoldiResolvesTriangularGapBelowDoublePrecision |
| Complex nonsymmetric projected Schur kernels | n/a | yes | MplapackBinary128KrylovSolversTest.ComplexSchurAndReorderUseBinary128ProjectedLAPACK |
| Complex nonsymmetric Arnoldi, full projection | n/a | yes | NumericalKrylov/ComplexFloat128.ArnoldiResolvesGap |
| Hermitian Krylov exponential action, fixed subspace | yes | yes | NumericalKrylov/{Real,Complex}Float128.ExponentialActionRetainsIncrement |
no in this optional table means no dedicated binary128 probe exists yet. It does not necessarily mean the templated implementation cannot instantiate once the corresponding dense projected kernel and matrix-free operation are covered.
During development, the native Krylov paths were compared against vendored ARPACK-NG adapters for the upstream double-precision routines:
| ARPACK path | covered precision |
|---|---|
symmetric dsaupd/dseupd | d |
real nonsymmetric dnaupd/dneupd | d |
complex nonsymmetric znaupd/zneupd | z |
Those oracle adapters are not part of the core Uni20 API or build. Future ARPACK comparisons should live in the separate validation and benchmarking repository.
Precision-specific hardening remains future work. The validation matrix proves that the solver paths instantiate and solve simple representative problems for their supported scalar tags; stress thresholds, breakdown floors, and Matrix Market reliability tests still need type-specific tuning.
The Krylov exponential action tests currently validate exact full-subspace projection cases, small analytic Taylor-action cases, diagonal Lanczos-vs-Taylor-vs-exact probe examples, and the TDVP harmonic-oscillator Matrix Market stress fixture. The probe examples now report several published exponential-action error indicators; see Krylov Exponential Estimators. Adaptive Lanczos time stepping, restart/error control, Al-Mohy/Higham-style norm estimation for the Taylor reference path, and broader matrix-free exponential stress tests remain future work.
With UNI20_ENABLE_MPREAL=ON, KrylovMatrixFreeInterface.RitzRealityUsesRuntimePrecision checks the standalone Ritz-reality classifier at 80 and 256 bits, including all three classifications, precision-dependent classification of the same numerical value, and exact inputs with and without an explicit finite-precision tolerance. MPFR/MPC eigensolver support is not part of this helper validation; GMRES coverage is described above.
1.9.8