Overview

Transpose, Uplo, Side, Diag, Backend and the scalar concepts that constrain every template.

String conversions and other helpers: Enumerations: helpers.

Types

◆ float_t

template<typename T>

using batchlas::float_t = typename base_type<T>::type

Shorthand for base_type<T>::type: the precision of T (tolerances, norms, eigenvalues).

Definition at line 41 of file enums.hh.

Enumerations

◆ MatrixFormat

enum class batchlas::MatrixFormat

strong

Storage format of a Matrix / MatrixView, used as a template argument.

Only Dense and CSR have storage implementations; the other enumerators name formats and are not instantiated by the library.

See also: Matrix model

Enumerator
Dense	Column-major dense storage with leading dimension and batch stride.
CSR	Compressed Sparse Row.
CSC	Compressed Sparse Column.
COO	Coordinate.
SELL	Sliced ELLPACK.
BSR	Blocked Sparse Row.
BLOCKED_ELL	Blocked ELLPACK.

Definition at line 72 of file enums.hh.

◆ Backend

enum class batchlas::Backend

strong

Library family an entry point dispatches to, used as a template argument.

Callers normally do not spell it: the queue-taking entry points take the backend from the batchlas::Queue (Queue::backend(), Queue::set_backend()). Only the backends compiled into the build (BATCHLAS_HAS_*_BACKEND) are available; Queue::backend_available() reports which.

Enumerator
AUTO	A request, not a backend: the Queue resolves it from its device on first query.
CUDA	NVIDIA GPU: cuBLAS / cuSOLVER / cuSPARSE and the native SYCL kernels.
ROCM	AMD GPU: rocBLAS / rocSOLVER / rocSPARSE and the native SYCL kernels.
MKL	Reserved; no dispatch target, never available.
MAGMA	Reserved; no dispatch target, never available.
SYCL	Native SYCL kernels on a GPU with no vendor library (AdaptiveCpp Metal); float and complex<float> only unless the build has device fp64 (BATCHLAS_HAS_DEVICE_FP64).
NETLIB	Host CBLAS / LAPACKE; the fallback for any device.

Definition at line 111 of file enums.hh.

◆ BackendLibrary

enum class batchlas::BackendLibrary

strong

A vendor library inside a Backend; selects library-specific type and handle mappings.

Enumerator
CUBLAS	Backend::CUDA.
CUSPARSE	Backend::CUDA.
CUSOLVER	Backend::CUDA.
ROCBLAS	Backend::ROCM.
ROCSPARSE	Backend::ROCM.
ROCSOLVER	Backend::ROCM.
MAGMA	Backend::MAGMA.
MKL	Backend::MKL.
CBLAS	Backend::NETLIB.
LAPACKE	Backend::NETLIB.

Definition at line 139 of file enums.hh.

◆ Transpose

enum class batchlas::Transpose

strong

The operator op() applied to an operand: op(A) = A, A^T or A^H.

Enumerator
NoTrans	op(A) = A.
Trans	op(A) = A^T.
ConjTrans	op(A) = A^H (the same as Trans for real scalars).

Definition at line 171 of file enums.hh.

◆ JobType

enum class batchlas::JobType

strong

Whether an eigensolver computes eigenvectors (LAPACK jobz).

Enumerator
EigenVectors	Eigenvalues and eigenvectors (jobz = 'V').
NoEigenVectors	Eigenvalues only (jobz = 'N').

Definition at line 189 of file enums.hh.

◆ SvdVectors

enum class batchlas::SvdVectors

strong

Which singular vectors gesvd computes for one factor (LAPACK jobu / jobvt).

For an m x n input with k = min(m, n):

Value	LAPACK	U	V^H
None	'N'	not computed; its MatrixView is not touched	same
All	'A'	m x m	n x n
Thin	'S'	m x k, the first k left vectors	k x n, the first k right vectors, conjugated

Thin and All differ on at most one side: for m <= n a thin U is the full U, for m >= n a thin V^H is the full V^H, and for square input they coincide on both. Entry points canonicalise with canonical_jobu() / canonical_jobvh(). LAPACK's 'O' (overwrite A) is not offered.

See also: gesvd design

Enumerator
None	Do not compute this factor.
All	Full square factor (LAPACK 'A').
Thin	Economy factor with k = min(m, n) vectors (LAPACK 'S').

Definition at line 220 of file enums.hh.

◆ Uplo

enum class batchlas::Uplo

strong

Which triangle of a symmetric, Hermitian or triangular operand is referenced.

Trap: In an option struct write PotrfOptions{}, never a bare {}: {} can select the positional overload, whose Uplo{} is Upper.

Enumerator
Upper	The upper triangle (i <= j).
Lower	The lower triangle (i >= j).

Definition at line 287 of file enums.hh.

◆ Diag

enum class batchlas::Diag

strong

Whether a triangular operand's diagonal is read or assumed to be one.

Enumerator
NonUnit	The stored diagonal is used.
Unit	The diagonal is taken as 1 and not read.

Definition at line 303 of file enums.hh.

◆ Side

enum class batchlas::Side

strong

Side on which a special operand multiplies: op(A) * B or B * op(A).

Enumerator
Left	The special operand is on the left.
Right	The special operand is on the right.

Definition at line 319 of file enums.hh.

◆ SortOrder

enum class batchlas::SortOrder

strong

Order in which eigenvalues (and their vectors) are returned.

Enumerator
Ascending	Smallest first.
Descending	Largest first.

Definition at line 335 of file enums.hh.

◆ ApplyOrder

enum class batchlas::ApplyOrder

strong

Order in which a sequence of plane rotations is applied (steqr sweeps).

Enumerator
Forward	First rotation first (a QR sweep).
Backward	Last rotation first (a QL sweep).

Definition at line 351 of file enums.hh.

◆ SyevxAlgorithm

enum class batchlas::SyevxAlgorithm

strong

Algorithm family of the partial symmetric/Hermitian eigensolver syevx.

Auto picks on matrix format, n, batch size and jobz; the number of requested eigenpairs enters no threshold (syevx_select_algorithm). Set per call through SyevxParams::method, or process-wide through BATCHLAS_SYEVX_ALGORITHM (auto|direct|direct_subset|filtered|lobpcg). The environment variable wins over SyevxParams::method, as a BATCHLAS_<OP>_ROUTE kernel pin does for the other ops, so a whole application can be forced onto one algorithm for diagnosis.

A choice the input cannot use degrades instead of failing: DirectSubset on complex or sparse input runs Direct (dense) or LOBPCG (CSR), and Direct or DirectSubset on CSR runs LOBPCG. A non-extremal SyevxSelect range is never degraded to a different part of the spectrum: on CSR input, or with an explicit LOBPCG or Filtered, it throws batchlas::invalid_argument (under the environment override the dense case runs Direct instead). syevx and syevx_buffer_size resolve the choice identically.

See also: SYEVX for the routing thresholds, syevx: design of the partial symmetric eigensolver for the tiers.

Enumerator
Auto	Heuristic selection on format, n, batch size and jobz (the default).
Direct	Full syev on a copy of A, then select the requested eigenpairs.
DirectSubset	Two-stage reduction, bisection + inverse iteration on the subset (real, dense).
Filtered	Chebyshev-filtered subspace iteration (dense and CSR); only when asked for.
LOBPCG	Locally Optimal Block Preconditioned Conjugate Gradient; the CSR default.

Definition at line 383 of file enums.hh.

◆ SyevxSelect

enum class batchlas::SyevxSelect

strong

Which part of the spectrum syevx returns.

Extremal (the default) returns neigs eigenpairs from one end, chosen by SyevxParams::find_largest: descending for the largest, ascending for the smallest. It is the Index range [n-neigs, n-1] or [0, neigs-1] and is normalised to one internally.

Note: Deliberately not EigenRangeType, whose natural default All means "every eigenvalue"; that type stays the tridiagonal-layer vocabulary.

See also: syevx range selection: design record

Enumerator
Extremal	neigs eigenpairs from one end; SyevxParams::find_largest picks the end.
Index	SyevxParams::il .. iu inclusive, 0-based in the ascending spectrum.
Value	Every eigenvalue in the half-open interval (vl, vu].

Definition at line 414 of file enums.hh.

◆ OrthoAlgorithm

enum class batchlas::OrthoAlgorithm

strong

Algorithm used by ortho to orthonormalise the columns of a batch of blocks.

Enumerator
Chol2	CholeskyQR applied twice; the default.
Cholesky	One CholeskyQR pass; rarely accurate enough on its own.
ShiftChol3	Shifted CholeskyQR3; more robust than Chol2 on ill-conditioned blocks.
Householder	Householder QR.
CGS2	Classical Gram-Schmidt with one reorthogonalisation pass.
SVQB	SVQB (orthonormalisation through the Gram matrix's eigendecomposition).
SVQB2	SVQB applied twice.
NUM_ALGORITHMS	Count of the enumerators above, not an algorithm.

Definition at line 471 of file enums.hh.

◆ ComputePrecision

enum class batchlas::ComputePrecision

strong

Internal compute precision of a GEMM (the cuBLAS cublasComputeType_t).

Anything but Default is served only by the vendor library: the native GEMM kernels do not support it. On cuBLAS, a single-precision scalar accepts F32, F16, BF16 and TF32, a double-precision scalar only F64; any other combination throws batchlas::unsupported.

Enumerator
Default	The precision of the scalar type.
F32	32-bit float accumulation.
F64	64-bit float accumulation.
F16	Half-precision inputs, 32-bit accumulation (CUBLAS_COMPUTE_32F_FAST_16F).
BF16	bfloat16 inputs, 32-bit accumulation (CUBLAS_COMPUTE_32F_FAST_16BF).
TF32	TensorFloat-32 inputs, 32-bit accumulation (CUBLAS_COMPUTE_32F_FAST_TF32).

Definition at line 505 of file enums.hh.

◆ VectorOrientation

enum class batchlas::VectorOrientation

strong

How a VectorView is reinterpreted as a MatrixView: 1 x n or n x 1.

Enumerator
Row	A 1 x n matrix; ld is the vector's inc.
Column	An n x 1 matrix; requires inc == 1.

Definition at line 529 of file enums.hh.

◆ NormType

enum class batchlas::NormType

strong

Matrix norm computed by norm and used by the condition estimators.

Enumerator
Frobenius	sqrt(sum \|a_ij\|^2).
One	Maximum absolute column sum.
Inf	Maximum absolute row sum.
Max	Maximum absolute entry (not a consistent norm).
Spectral	Largest singular value; symmetric/Hermitian input only.

Definition at line 545 of file enums.hh.

◆ Layout

enum class batchlas::Layout

strong

Storage order argument of the host CBLAS / LAPACKE calls.

BatchLAS matrices are always column-major; this only labels host-library calls.

See also: Matrix model

Enumerator
RowMajor	Row-major (CblasRowMajor).
ColMajor	Column-major (CblasColMajor).

Definition at line 570 of file enums.hh.

Variables

◆ is_std_complex_v

template<typename T>

bool batchlas::is_std_complex_v = is_std_complex<T>::value

inlineconstexpr

Value of is_std_complex<T>.

Definition at line 53 of file enums.hh.

Topics
	Enumerations: helpers
	String conversions and shape helpers for the enumerations.

Concepts
concept	batchlas::RealScalar
	A real floating-point scalar (float, double).
concept	batchlas::ComplexScalar
	A std::complex scalar (std::complex<float>, std::complex<double>).
concept	batchlas::FloatingOrComplexScalar
	Any scalar the numerical entry points accept: real or complex floating point.
concept	batchlas::DenseMatrixFormat
	Constrains a member or overload to dense storage.
concept	batchlas::CsrMatrixFormat
	Constrains a member or overload to CSR storage.

Classes
struct	batchlas::base_type< T >
	Real type underlying a scalar: T itself for a real T, R for std::complex<R>. More...
struct	batchlas::base_type< std::complex< T > >
	Specialisation that strips std::complex. More...
struct	batchlas::is_std_complex< T >
	True for std::complex<R>, false otherwise. More...
struct	batchlas::is_std_complex< std::complex< T > >
	Specialisation for std::complex<R>. More...

Overview

Types

◆ float_t

Enumerations

◆ MatrixFormat

◆ Backend

◆ BackendLibrary

◆ Transpose

◆ JobType

◆ SvdVectors

◆ Uplo

◆ Diag

◆ Side

◆ SortOrder

◆ ApplyOrder

◆ SyevxAlgorithm

◆ SyevxSelect

◆ OrthoAlgorithm

◆ ComputePrecision

◆ VectorOrientation

◆ NormType

◆ Layout

Variables

◆ is_std_complex_v

Topics

Concepts

Classes