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Uni20
Asynchronous tensor and runtime library.
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This document inventories dense BLAS/LAPACK components that were developed for projected Krylov problems and broader dense linear-algebra experiments. It is a provider/wrapper coverage survey, not the Krylov algorithm contract.
Most broad utility rows below are retained in dense_subspace_unused.hpp. That header is quarantined from the default Krylov API and is not used by the maintained projected-problem path. Dedicated ordinary-precision and optional MPLAPACK binary128 regression sources still compile and exercise the inventory; this coverage does not make those helpers a supported linalg API. Rows explicitly described as dispatched are supported linalg operations and lower through the dense linalg layer; the maintained Krylov path uses the subset required by its algorithms.
Keep this inventory synchronized with provider declarations and with any helpers promoted from the quarantined survey into operation-tag linalg backends.
The optional MPFR/MPC provider uses explicit-precision provider arrays. It supplies real/complex GEMM through BlasBackend, and square solves, reusable LU/log determinants, LU condition estimates, QR/LQ, QR and SVD least squares, self-adjoint eigensystems, SVD and general eigensystems through LapackBackend.
| MPFR/MPC operation | Real provider | Complex provider |
|---|---|---|
| GEMM | Rgemm | Cgemm |
| LU and square solve | Rgetrf, Rgetrs | Cgetrf, Cgetrs |
| LU reciprocal condition estimate (one/infinity norm) | Rgecon | Cgecon |
| Three-precision LU refinement | Reuses Rgetrf/Rgetrs; host residual/update arithmetic | Reuses Cgetrf/Cgetrs; host residual/update arithmetic |
| Rank-aware minimum-norm least squares | Rgelss | Cgelss |
| Reduced QR | Rgeqrf, Rorgqr | Cgeqrf, Cungqr |
| Full-column-rank least squares | Reduced QR above, then scalar triangular solve | Reduced QR above, then scalar triangular solve |
| Reduced LQ | Rgelqf, Rorglq | Cgelqf, Cunglq |
| Self-adjoint eigensystem | Rsyev | Cheev |
| SVD, including values-only and one-sided factors | Rgesvd | Cgesvd |
| General eigenvalues/right eigenvectors | Rgeev | Cgeev |
Operation acceptance remains specific to these kernels. This coverage does not imply MPFR Schur, tridiagonal, other surveyed routines or projected Krylov support. Native float32/64 and binary128 also have active real/complex GELSS and GECON operation adapters, and support complex QR/LQ through their geqrf/ungqr and gelqf/unglq provider wrappers.
The optional binary80 adapter covers real and complex GEMM through BlasBackend and real LU/solve, QR/LQ, self-adjoint/general eigensystems and all SVD forms, GELSS and GECON through LapackBackend. Its decomposition routines match the MPFR table above. Complex LU and decompositions require a long double provider; they are disabled for distinct _Float64x because its generic complex division can silently overflow. This does not extend the broad raw-wrapper BLAS/LAPACK scalar traits, Schur/tridiagonal or projected coverage.
CUDA provider coverage is currently narrower: cuBLAS S/D/C/ZGEMM, conjugate dot products, and Euclidean norms have checked provider wrappers and a Tensor-facing CublasBackend. Ordinary async gemm, assign_product, and add_product resolve CudaTensor operands through their deferred mdspec() descriptors. Their CudaTask awaits a provider-handle/stream execution lease from the device resource set before invoking the prepared provider leaf. Ordinary direct Tensor GEMM stages the same BLAS-compatible layouts and blocks for resource admission. Both paths open synchronized buffer access and enqueue the provider call. Column- and row-major outputs are supported. The optimized cuBLAS path accepts zero-inner-dimension GEMM with null zero-sized input buffers and applies C = beta*C directly.
The Tensor-level GEMM conformance suite applies one shared semantic matrix to every statically eligible host backend and to cuBLAS. It covers all four ordinary scalar families, canonical and mixed row/column layouts, padded leading dimensions, and lazy conjugation. CUDA-specific cases additionally cover nonzero buffer offsets, transpose and conjugate-transpose subviews, clean unsupported-layout decline before resource admission, cross-device rejection, and exact or partial output/input alias rejection.
Full CUDA inner products and norms accept exhaustive raw CUDA mdspecs for all four ordinary scalar families and return host scalars. The provider stream is synchronized before return. Packed BlockTensor tests cover nonzero descriptor offsets. General strided reductions and accessor transformations remain for a CUDA reference reduction backend.
The optional cuSOLVER backend provides blocking exact SVD through cusolverDnSgesvd and cusolverDnDgesvd. Its first operation accepts destructive tall column-major CUDA-buffer matrices, real float or double, and reduced or full left and right vectors. It acquires a device-local handle/stream lease, allocates stream-ordered workspace, checks devInfo on host, and synchronizes the operation stream before return. Complex scalars, wide matrices, other SVD forms, and asynchronous completion remain outside this checkpoint.
Fixed-output dense Tensor contraction has direct and residual-axis host BLAS lowerings for s/d/c/z scalars. They jointly merge the logical M, N, and K stride groups, project directly representable slices to rank-two mdspecs, and reuse ordinary GEMM dispatch. The looped path currently accepts one residual M or N descriptor and leaves K unlooped. Multiple residual dimensions, residual-K accumulation, unsupported accessors or matrix layouts, and packed plans remain on the accessor-respecting CPU reference path.
LAPACK-style scalar tags are used throughout. Complex scalar spellings follow the project Scalar Policy:
| tag | scalar type |
|---|---|
s | float |
d | double |
c | uni20::complex<float> |
z | uni20::complex<double> |
f128 | optional uni20::float128 |
cf128 | optional uni20::complex<uni20::float128> |
| component | s | d | c | z | role |
|---|---|---|---|---|---|
| Dense vector and matrix primitives | yes | yes | yes | yes | Local BLAS-like operations over Krylov subspace data. |
| Dense matrix norms | yes | yes | yes | yes | Active matrix_norm_op dispatch covers general maximum-entry, induced one/infinity, and Frobenius norms. LAPACK lange handles direct real layouts and complex Frobenius norms; the accessor-respecting CPU backend preserves mathematical complex-magnitude semantics for the remaining complex forms. Quarantined projected helpers additionally survey lansy/lanhe and lantr. |
| Dense general linear solve | yes | yes | yes | yes | Active destructive linear_solve_op dispatch uses LAPACK getrf/getrs for compatible column-major workspaces and accessor-respecting pivoted Gaussian elimination as the native CPU fallback; runtime MPFR/MPC uses the shared CPU LU factor/solve implementation without MPLAPACK. solve preserves inputs; solve_inplace is strict and destructive; solve_inplace_with_info reports recoverable numerical failures. See square solves. |
| Dense real refined linear solve | yes | yes | n/a | n/a | Dense projected utility solve through LAPACK getrf/getrs followed by gerfs, returning forward/backward error estimates. |
| Dense real expert linear solve | yes | yes | n/a | n/a | Dense projected utility solve through LAPACK gesvx, returning condition estimates, forward/backward error bounds, equilibration, and condition diagnostics. |
| Dense real equilibration | yes | yes | n/a | n/a | Dense projected row/column scaling diagnostics through LAPACK geequ. |
| Dense LU factorization and solve | yes | yes | yes | yes | Active lu_factor_op/lu_solve_op dispatch exposes owning reusable LU through LAPACK getrf/getrs, with a CPU reference fallback for native and MPFR/MPC scalars. Runtime CPU factorization and solves convert values to finite working precision and require no MPLAPACK. slogdet reduces these factors without forming the determinant product; see LU. |
| Dense real general-band factorization and solve | yes | yes | n/a | n/a | Dense projected reusable general-band LU solve through LAPACK gbtrf/gbtrs. |
| Dense real general-band refined solve | yes | yes | n/a | n/a | Dense projected general-band solve through LAPACK gbtrf/gbtrs followed by gbrfs, returning forward/backward error estimates. |
| Dense real general-band expert solve | yes | yes | n/a | n/a | Dense projected general-band expert solve with condition and forward/backward error diagnostics through LAPACK gbsvx. |
| Dense real general-band equilibration | yes | yes | n/a | n/a | Dense projected general-band row/column scaling diagnostics through LAPACK gbequ/gbequb. |
| Dense real general-band reciprocal condition estimate | yes | yes | n/a | n/a | Dense projected general-band one-norm reciprocal condition estimate through LAPACK gbtrf/gbcon. |
| Dense real general tridiagonal solve, condition, and refinement | yes | yes | n/a | n/a | Dense projected reusable general tridiagonal LU solve plus diagnostics through LAPACK gtsv/gttrf/gttrs/gtcon/gtrfs/gtsvx. |
| Dense general reciprocal condition estimate | yes | yes | yes | yes | Active lu_rcond_op provides one-/infinity-norm estimates from reusable factors through gecon; the older dense projected helper exposes one-norm only. |
| Dense real triangular solve | yes | yes | n/a | n/a | Dense projected triangular solve through LAPACK trtrs. |
| Dense real triangular refined solve | yes | yes | n/a | n/a | Dense projected triangular solve through LAPACK trtrs followed by trrfs, returning forward/backward error estimates. |
| Dense real triangular inverse | yes | yes | n/a | n/a | Dense projected triangular inverse through LAPACK trtri. |
| Dense real triangular reciprocal condition estimate | yes | yes | n/a | n/a | Dense projected triangular one-norm reciprocal condition estimate through LAPACK trcon. |
| Dense real Sylvester equation solve | yes | yes | n/a | n/a | Dense projected Sylvester equation solve through LAPACK trsyl, returning LAPACK's scale factor and perturbation diagnostic. |
| Dense general inverse | yes | yes | yes | yes | Dense projected utility inverse through LAPACK getrf/getri. |
| Dense real least-squares solve | yes | yes | n/a | n/a | Dense projected least-squares/minimum-norm solve through LAPACK gels. |
| Dense SVD least-squares solve | yes | yes | yes | yes | Active svd_least_squares_op calls gelss with working-precision epsilon as the default relative cutoff, reporting rank and optional singular values. The quarantined real projected helper retains its separate 100 * epsilon() policy. |
| Dense real divide-and-conquer SVD least-squares solve | yes | yes | n/a | n/a | Dense projected least-squares solve with singular values and rank through LAPACK gelsd; default rank threshold is 100 * uni20::numeric_limits<Scalar>::epsilon(). |
| Dense real rank-revealing least-squares solve | yes | yes | n/a | n/a | Dense projected least-squares solve with column pivoting through LAPACK gelsy; default rank threshold is 100 * uni20::numeric_limits<Scalar>::epsilon(). |
| Dense real symmetric positive definite solve | yes | yes | n/a | n/a | Dense projected SPD solve through LAPACK potrf/potrs. |
| Dense real symmetric positive definite factorization and solve | yes | yes | n/a | n/a | Dense projected reusable SPD Cholesky solve through LAPACK potrf/potrs. |
| Dense real symmetric positive definite band solve, condition, and refinement | yes | yes | n/a | n/a | Dense projected reusable SPD band Cholesky solve plus diagnostics through LAPACK pbsv/pbtrf/pbtrs/pbcon/pbrfs/pbsvx. |
| Dense real symmetric positive definite tridiagonal solve, condition, and refinement | yes | yes | n/a | n/a | Dense projected reusable SPD tridiagonal solve plus diagnostics through LAPACK ptsv/pttrf/pttrs/ptcon/ptrfs/ptsvx. |
| Dense real symmetric positive definite refined solve | yes | yes | n/a | n/a | Dense projected SPD solve through LAPACK potrf/potrs followed by porfs, returning forward/backward error estimates. |
| Dense real symmetric positive definite expert solve | yes | yes | n/a | n/a | Dense projected SPD expert solve with condition and forward/backward error diagnostics through LAPACK posvx. |
| Dense real symmetric positive definite equilibration | yes | yes | n/a | n/a | Dense projected SPD symmetric scaling diagnostics through LAPACK poequ. |
| Dense real symmetric positive definite reciprocal condition estimate | yes | yes | n/a | n/a | Dense projected SPD one-norm reciprocal condition estimate through LAPACK potrf/pocon. |
| Dense real symmetric positive definite factorized reciprocal condition estimate | yes | yes | n/a | n/a | Dense projected SPD one-norm reciprocal condition estimate from reusable Cholesky factors through LAPACK pocon. |
| Dense real symmetric positive definite inverse | yes | yes | n/a | n/a | Dense projected SPD inverse through LAPACK potrf/potri. |
| Dense real pivoted Cholesky factorization | yes | yes | n/a | n/a | Dense projected positive-semidefinite rank-revealing Cholesky factorization through LAPACK pstrf. |
| Dense real symmetric indefinite solve | yes | yes | n/a | n/a | Dense projected symmetric indefinite solve through LAPACK sytrf/sytrs. |
| Dense real symmetric indefinite factorization and solve | yes | yes | n/a | n/a | Dense projected reusable Bunch-Kaufman solve through LAPACK sytrf/sytrs. |
| Dense real symmetric indefinite refined solve | yes | yes | n/a | n/a | Dense projected symmetric indefinite solve through LAPACK sytrf/sytrs followed by syrfs, returning forward/backward error estimates. |
| Dense real symmetric indefinite inverse | yes | yes | n/a | n/a | Dense projected symmetric indefinite inverse through LAPACK sytrf/sytri. |
| Dense real symmetric indefinite expert solve | yes | yes | n/a | n/a | Dense projected symmetric indefinite expert solve with condition and forward/backward error diagnostics through LAPACK sysvx. |
| Dense real symmetric indefinite reciprocal condition estimate | yes | yes | n/a | n/a | Dense projected symmetric indefinite one-norm reciprocal condition estimate through LAPACK sytrf/sycon. |
| Dense real symmetric indefinite factorized reciprocal condition estimate | yes | yes | n/a | n/a | Dense projected symmetric indefinite one-norm reciprocal condition estimate from reusable Bunch-Kaufman factors through LAPACK sycon. |
| Dense real compact QR factor application | yes | yes | n/a | n/a | Dense projected Householder QR factor application through LAPACK ormqr. |
| Dense real/complex QR factorization | yes | yes | yes | yes | Active qr_op dispatch computes reduced QR through LAPACK geqrf and orgqr/ungqr. qr_factorization exposes destructive workspace semantics; qr preserves its input and returns owning column-major factors. |
| Dense real compact LQ factor application | yes | yes | n/a | n/a | Dense projected Householder LQ factor application through LAPACK ormlq. |
| Dense real/complex LQ factorization | yes | yes | yes | yes | Active lq_op dispatch computes reduced LQ through LAPACK gelqf and orglq/unglq. lq_factorization exposes destructive workspace semantics; lq preserves its input and returns owning column-major factors. |
| Dense real compact QL factor application | yes | yes | n/a | n/a | Dense projected Householder QL factor application through LAPACK ormql. |
| Dense real QL factorization | yes | yes | n/a | n/a | Dense projected reduced QL through LAPACK geqlf/orgql. |
| Dense real compact RQ factor application | yes | yes | n/a | n/a | Dense projected Householder RQ factor application through LAPACK ormrq. |
| Dense real RQ factorization | yes | yes | n/a | n/a | Dense projected reduced RQ through LAPACK gerqf/orgrq. |
| Dense real bidiagonal reduction | yes | yes | n/a | n/a | Dense projected bidiagonal reduction and orthogonal-factor materialization through LAPACK gebrd/orgbr. |
| Dense real bidiagonal orthogonal-factor application | yes | yes | n/a | n/a | Dense projected bidiagonal Householder factor application through LAPACK ormbr. |
| Dense real bidiagonal singular values | yes | yes | n/a | n/a | Dense projected bidiagonal singular values through LAPACK bdsqr. |
| Dense real bidiagonal divide-and-conquer singular value decomposition | yes | yes | n/a | n/a | Dense projected bidiagonal SVD through LAPACK bdsdc, with optional explicit singular vectors. |
| Dense selected real bidiagonal singular value decomposition | yes | yes | n/a | n/a | Dense projected selected bidiagonal SVD through LAPACK bdsvdx, using 0-based inclusive decreasing singular-value index ranges. |
| Dense real pivoted QR factorization | yes | yes | n/a | n/a | Dense projected reduced QR with column pivoting through LAPACK geqp3 and orgqr. |
| Dense real Hessenberg reduction | yes | yes | n/a | n/a | Dense projected orthogonal Hessenberg reduction through LAPACK gehrd/orghr. |
| Dense real Hessenberg orthogonal-factor application | yes | yes | n/a | n/a | Dense projected Hessenberg Householder factor application through LAPACK ormhr. |
| Dense real symmetric tridiagonal reduction | yes | yes | n/a | n/a | Dense projected symmetric tridiagonal reduction and Householder factor application through LAPACK sytrd/orgtr/ormtr. |
| Dense symmetric tridiagonal eigenvalues | yes | yes | n/a | n/a | Dense projected symmetric tridiagonal eigenvalues through LAPACK sterf. |
| Dense symmetric tridiagonal divide-and-conquer eigensystem | yes | yes | n/a | n/a | Dense projected symmetric tridiagonal eigensystem through LAPACK stevd. |
| Dense selected symmetric tridiagonal eigensystem | yes | yes | n/a | n/a | Dense projected symmetric tridiagonal eigensystem through LAPACK stevr using 0-based inclusive index ranges. |
| Dense singular value decomposition | yes | yes | yes | yes | Dispatched exact Tensor SVD through LAPACK gesvd, with singular-values-only, left-only, right-only, and complete APIs. truncated_svd is a separate dense policy layer with rank, cutoff, and discarded-weight criteria, rank-zero support, stable same-precision statistics, and preserving/consuming synchronous and Async forms. Reduced consuming exact factors may adopt the input allocation through LAPACK overwrite jobs. Complex singular values use the underlying real scalar type. |
| Dense divide-and-conquer singular value decomposition | yes | yes | yes | yes | Dense projected utility SVD through LAPACK gesdd. Complex singular values use the underlying real scalar type. |
| Dense selected singular value decomposition | yes | yes | yes | yes | Dense projected selected SVD through LAPACK gesvdx, using 0-based inclusive decreasing singular-value index ranges. Complex singular values use the underlying real scalar type. |
| Dense real symmetric eigensystem | yes | yes | n/a | n/a | Dense projected Hermitian reference or utility problem. |
| Dense real divide-and-conquer symmetric eigensystem | yes | yes | n/a | n/a | Dense projected Hermitian reference or utility problem through LAPACK syevd. |
| Dense real selected symmetric eigensystem | yes | yes | n/a | n/a | Dense projected Hermitian reference or utility problem through LAPACK syevr using 0-based inclusive index ranges. |
| Dense generalized real symmetric eigensystem | yes | yes | n/a | n/a | Dense type-1 generalized Hermitian utility problem through LAPACK sygv. |
| Dense generalized real divide-and-conquer symmetric eigensystem | yes | yes | n/a | n/a | Dense type-1 generalized Hermitian utility problem through LAPACK sygvd. |
| Dense generalized real selected symmetric eigensystem | yes | yes | n/a | n/a | Dense type-1 generalized Hermitian utility problem through LAPACK sygvx using 0-based inclusive index ranges. |
| Dense complex Hermitian eigensystem | n/a | n/a | yes | yes | Dense projected Hermitian reference or utility problem through LAPACK heev. |
| Dense complex divide-and-conquer Hermitian eigensystem | n/a | n/a | yes | yes | Dense projected Hermitian reference or utility problem through LAPACK heevd. |
| Dense complex selected Hermitian eigensystem | n/a | n/a | yes | yes | Dense projected Hermitian reference or utility problem through LAPACK heevr using 0-based inclusive index ranges. |
| Dense generalized complex Hermitian eigensystem | n/a | n/a | yes | yes | Dense type-1 generalized Hermitian utility problem through LAPACK hegv. |
| Dense generalized complex divide-and-conquer Hermitian eigensystem | n/a | n/a | yes | yes | Dense type-1 generalized Hermitian utility problem through LAPACK hegvd. |
| Dense generalized complex selected Hermitian eigensystem | n/a | n/a | yes | yes | Dense type-1 generalized Hermitian utility problem through LAPACK hegvx using 0-based inclusive index ranges. |
| Symmetric tridiagonal eigensystem | yes | yes | n/a | n/a | Dispatched Lanczos projected eigensystem through LAPACK sterf for eigenvalues-only and steqr for eigenvectors. |
| Real nonsymmetric eigensystem | yes | yes | n/a | n/a | Dispatched Arnoldi Ritz extraction through LAPACK geev, including complex-pair unpacking. |
| Real nonsymmetric expert eigensystem | yes | yes | n/a | n/a | Dense projected real nonsymmetric eigensystem through LAPACK geevx, returning balancing data and reciprocal eigenvalue/eigenvector condition estimates. |
| Real nonsymmetric balancing and right-vector backtransform | yes | yes | n/a | n/a | Dense projected real nonsymmetric balancing helpers through LAPACK gebal and gebak. |
| Generalized real nonsymmetric eigensystem | yes | yes | n/a | n/a | Dense projected real nonsymmetric matrix pencil through LAPACK ggev, preserving alpha/beta data and finite ratios. |
| Generalized real nonsymmetric expert eigensystem | yes | yes | n/a | n/a | Dense projected real nonsymmetric matrix pencil through LAPACK ggevx, preserving alpha/beta data and returning balancing data and reciprocal condition estimates. |
| Generalized real nonsymmetric balancing and right-vector backtransform | yes | yes | n/a | n/a | Dense projected real nonsymmetric pencil balancing helpers through LAPACK ggbal and ggbak. |
| Generalized real Hessenberg reduction | yes | yes | n/a | n/a | Dense projected real QZ building block through LAPACK gghrd, assuming the second matrix is already upper triangular. |
| Generalized real Hessenberg Schur factorization | yes | yes | n/a | n/a | Dense projected real QZ iteration through LAPACK hgeqz, assuming generalized Hessenberg/upper-triangular input. |
| Generalized real Schur factorization | yes | yes | n/a | n/a | Dense projected real generalized Schur/QZ factorization through LAPACK gges, preserving alpha/beta data and finite ratios. |
| Generalized real Schur reordering | yes | yes | n/a | n/a | Dense projected real generalized Schur/QZ block reordering through LAPACK tgexc, preserving aligned alpha/beta data. |
| Generalized real Schur selected subspace condition estimates | yes | yes | n/a | n/a | Dense projected real generalized Schur/QZ selected deflating subspace through LAPACK tgsen, returning PL, PR, and F-norm DIF estimates. |
| Generalized real Schur right eigenvectors | yes | yes | n/a | n/a | Dense projected real generalized Schur/QZ eigenvector extraction through LAPACK tgevc, unpacked into complex columns. |
| Generalized real Schur eigenpair condition estimates | yes | yes | n/a | n/a | Dense projected real generalized Schur/QZ eigenvalue/eigenvector conditioning through LAPACK tgsna. |
| Real Schur factorization and reordering | yes | yes | n/a | n/a | Dispatched real nonsymmetric implicit restart through LAPACK gees and trexc. |
| Real Hessenberg Schur factorization | yes | yes | n/a | n/a | Dispatched projected upper-Hessenberg-to-real-Schur factorization through LAPACK hseqr. |
| Real Schur selected subspace condition estimates | yes | yes | n/a | n/a | Dense projected real Schur block selection through LAPACK trsen, returning reciprocal eigenvalue-cluster and invariant-subspace condition estimates. |
| Real Schur right eigenvectors | yes | yes | n/a | n/a | Dense projected real Schur eigenvector extraction through LAPACK trevc, unpacked into complex columns. |
| Real Schur eigenpair condition estimates | yes | yes | n/a | n/a | Dense projected real Schur eigenvalue/eigenvector conditioning through LAPACK trsna. |
| Complex nonsymmetric eigensystem | n/a | n/a | yes | yes | Dispatched Arnoldi Ritz extraction through LAPACK geev. |
| Complex Schur factorization and reordering | n/a | n/a | yes | yes | Dispatched complex nonsymmetric implicit restart through LAPACK gees and trexc. |
These rows are available only when UNI20_ENABLE_FLOAT128=ON and UNI20_BACKEND_MPLAPACK=ON and the configured MPLAPACK package provides a real binary128 type. This table covers dense provider/helper support; algorithm-level binary128 coverage remains in Krylov Algorithms.
| component or entry point | f128 | cf128 | notes |
|---|---|---|---|
| Dense vector and matrix primitives | yes | yes | Scalar-generic Krylov host-side helpers. |
| MPBLAS wrapper surface | yes | yes | Current wrapper surface covers projected gemm, gemv, rank-update, symmetric-rank, and Hermitian-rank operations used by active paths. |
| Checked LAPACK norms, core LU, orthogonal factorizations, and SVD wrappers | yes | yes | Provider wrappers cover lange, lansy/lanhe, lantr, gesv, getrf, getrs, getri, gecon, real geqrf/orgqr and gelqf/orglq, plus gesvd, gesdd, and gesvdx. |
| Dispatched SVD least squares and LU conditioning | yes | yes | svd_least_squares_op uses Rgelss/Cgelss; lu_rcond_op uses Rgecon/Cgecon, with shared precision probes. |
| Tensor/linalg CPU helper probes | yes | n/a | Current probes cover dispatched real one-norm evaluation, dense solve, reduced QR/LQ, tensor reductions, and matrix-exponential prescaling in binary128 over uni20::DenseMatrix. |
| Broad dense projected real helper inventory | regression | n/a | Quarantined API inventory exercised by the optional MPLAPACK binary128 regression target. |
| Dense projected complex eigensystem and Schur helper inventory | n/a | regression | Quarantined API inventory exercised by the optional MPLAPACK binary128 regression target. |
| Symmetric tridiagonal projected eigensystem | yes | n/a | Uses MPLAPACK Rsterf/Rsteqr; this is the projected problem behind real and complex Hermitian Lanczos. |
| Real nonsymmetric projected eigensystem and Schur kernels | yes | n/a | Active wrapper surface covers Rgeev, Rgees, Rhseqr, and Rtrexc. |
| Complex nonsymmetric projected eigensystem and Schur kernels | n/a | yes | Active wrapper surface covers Cgeev, Cgees, and Ctrexc. |
1.9.8