Utilities and Enumerations

Core utilities for LAPACK++ including error handling, enumerations, and type conversions.

Error Handling

class Error : public std::exception

Exception class for LAPACK errors.

Thrown by LAPACK++ wrapper functions when error conditions are detected. Error checking behavior can be controlled at compile time:

• Default: Throws exceptions (recommended)

• LAPACK_ERROR_ASSERT: Aborts on error

• LAPACK_ERROR_NDEBUG: Disables error checking

Public Functions

inline Error()

Constructs LAPACK error.

inline Error(std::string const &msg)

Constructs BLAS error with message.

inline Error(const char *msg, const char *func)

Constructs LAPACK error with message: “func: msg”.

inline virtual const char *what() const noexcept override

Returns LAPACK error message.

Enumerations

LAPACK++ provides type-safe enumerations for function parameters. All enumerations include: - Conversion functions: to_char(), to_string(), from_string() - Character-based values matching LAPACK Fortran conventions

Sides - Extended side specification (Left, Right, Both)

Values: Left, Right, Both

Used in: trevc (eigenvector computation)

Norm - Matrix/vector norm types

Values: - One (1-norm): Maximum absolute column sum - Two (2-norm): Spectral norm (largest singular value) - Inf (infinity-norm): Maximum absolute row sum - Fro (Frobenius): Square root of sum of squares - Max: Maximum absolute element

Used in: lange, lansy, lanhe, gecon

Job - Eigenvector/singular vector computation options

Values: - NoVec: Compute eigenvalues only - Vec: Compute eigenvectors - UpdateVec: Update eigenvectors - AllVec: Compute all singular vectors - SomeVec: Compute some singular vectors - OverwriteVec: Overwrite with singular vectors - CompactVec: Compact representation - SomeVecTol: Some vectors with tolerance - VecJacobi: Jacobi method vectors - Workspace: Workspace query

Used in: geev, syev, gesvd, gesdd, gejsv, gesvj

JobSchur - Schur decomposition options

Values: - Eigenvalues: Compute eigenvalues only - Schur: Compute full Schur form

Used in: hseqr

Sort - Eigenvalue sorting

Values: - NotSorted: Keep original order - Sorted: Sort eigenvalues

Used in: gees, gges

Range - Eigenvalue/singular value selection

Values: - All: Compute all values - Value: Compute values in (vl, vu] - Index: Compute values with indices [il, iu]

Used in: syevx, gesvdx, stebz

Vect - Orthogonal vector generation

Values: - Q: Generate Q vectors - P: Generate P vectors - None: Don’t generate vectors - Both: Generate both Q and P

Used in: orgbr, ormbr, gbbrd

Direction - Block reflector direction

Values: - Forward: Apply reflectors forward - Backward: Apply reflectors backward

Used in: larfb, larft

StoreV - Reflector storage format

Values: - Columnwise: Reflectors stored in columns - Rowwise: Reflectors stored in rows

Used in: larfb

MatrixType - Matrix structure for scaling

Values: - General: Full matrix - Lower: Lower triangular - Upper: Upper triangular - Hessenberg: Upper Hessenberg - LowerBand: Lower banded - UpperBand: Upper banded - Band: Full band

Used in: lascl, laset

HowMany - Eigenvector selection

Values: - All: Compute all eigenvectors - Backtransform: Backtransform eigenvectors - Select: Compute selected eigenvectors

Used in: trevc

Equed - Equilibration status

Values: - None: No equilibration - Row: Row equilibration - Col: Column equilibration - Both: Row and column equilibration - Yes: Equilibrated (porfsx)

Used in: gesvx, posvx, sysvx

Factored - Factorization status

Values: - Factored: Matrix already factored - NotFactored: Need factorization - Equilibrate: Equilibrate then factor

Used in: gesvx, posvx, sysvx

Sense - Condition number computation

Values: - None: Don’t compute condition numbers - Eigenvalues: Condition numbers for eigenvalues - Subspace: Condition numbers for invariant subspace - Both: Both eigenvalues and subspace

Used in: geesx, trsen

JobCond - Singular/eigenvector condition numbers

Values: - EigenVec: Eigenvector condition numbers - LeftSingularVec: Left singular vector conditions - RightSingularVec: Right singular vector conditions

Used in: disna

Balance - Matrix balancing options

Values: - None: No balancing - Permute: Permute only - Scale: Scale only - Both: Permute and scale

Used in: gebal, ggbal, gebak, ggbak

Order - Eigenvalue ordering for tridiagonal solvers

Values: - Block: By block - Entire: For entire matrix

Used in: stebz, larrd, stein

RowCol - Row/column orientation

Values: - Col: Column-oriented - Row: Row-oriented

Used in: LAPACK testing utilities

Pivot - Pivoting strategy

Values: - Variable: Algorithm-chosen pivots - Top: Pivot at top - Bottom: Pivot at bottom

Used in: geqp3 (rank-revealing QR)

Version Information

LAPACK++ provides version query functions:

lapackpp_version() - Returns version as integer (YYYYMMDD format, e.g., 20250528)

lapackpp_id() - Returns version string with git commit (e.g., “2025.05.28.id123abc”)

These functions are defined in lapack.hh.