TFEL adaptors: call the TiledLUpp solvers directly on the tfel::math objects (matrices, vectors, views) instead of raw pointers. More...

#include <cstddef>
#include <type_traits>
#include <tdls/core/macros.hpp>
#include <tdls/solvers/tiled_lupp/solver_dynamic.hpp>
#include <tdls/solvers/tiled_lupp/solver_static.hpp>

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Classes
struct	tdls::detail::has_data< T, typename >
	Detects a data() member returning a pointer. More...

struct	tdls::detail::has_data< T, std::void_t< decltype(std::declval< const T & >().data())> >

struct	tdls::detail::has_pair_data< T, typename >
	Detects a data() member returning a (pointer, stride) pair: the shape of strided views, whose data pointer must not be mistaken for contiguous storage. More...

struct	tdls::detail::has_pair_data< T, std::void_t< decltype(std::declval< const T & >().data().first), decltype(std::declval< const T & >().data().second)> >

struct	tdls::detail::const_data_pointer< T, bool >
	Element pointer type of a dense object, const flavour. More...

struct	tdls::detail::const_data_pointer< T, true >
	Element pointer type of a dense object whose data() returns a (pointer, stride) pair, const flavour. More...

struct	tdls::detail::mutable_data_pointer< T, bool >
	Element pointer type of a dense object, mutable flavour. More...

struct	tdls::detail::mutable_data_pointer< T, true >
	Element pointer type of a dense object whose data() returns a (pointer, stride) pair, mutable flavour. More...

struct	tdls::detail::has_stride< T, typename >
	Detects a stride() member. More...

struct	tdls::detail::has_stride< T, std::void_t< decltype(std::declval< const T & >().stride())> >

struct	tdls::detail::has_get_stride< T, typename >
	Detects a getStride() member. More...

struct	tdls::detail::has_get_stride< T, std::void_t< decltype(std::declval< const T & >().getStride())> >

struct	tdls::detail::has_indexing_policy< T, typename >
	Detects a nested indexing_policy type. More...

struct	tdls::detail::has_indexing_policy< T, std::void_t< typename T::indexing_policy > >

struct	tdls::storage_traits< DenseType, std::enable_if_t< detail::is_dense_v< DenseType > > >
	Storage description of dense objects matching the structural contract: a data() member (plain pointer or (pointer, stride) pair) and an indexing_policy type with constexpr extents. More...

struct	tdls::detail::has_storage_traits< T, typename >
	Detects a complete storage_traits: the structural contract or a user specialization. More...

struct	tdls::detail::has_storage_traits< T, std::void_t< typename storage_traits< T >::value_type > >

struct	tdls::detail::matrix_scalar_of< MatrixType >
	Scalar type of a dense matrix argument, read from its storage description; a matrix argument without storage_traits is rejected here with an explicit message. More...

struct	tdls::detail::is_solver_config< ConfigType >
	Detects the configuration value types accepted by the entry points. Only the TiledLUpp family exists today; a specialization per family can join when another one lands. More...

struct	tdls::detail::is_solver_config< TiledLUppConfig< Scalar > >
	TiledLUppConfig values are accepted. More...

struct	tdls::detail::adaptor_context< MatrixType, Config >
	Common compile-time context of the adaptor entry points: resolves the scalar type, the dimension and the TiledLUpp solvers from the matrix argument and the configuration value. More...

struct	tdls::detail::pivot_access< PivotType, N >
	Pivot argument unwrapping: accepts a raw int pointer/array (treated as contiguous caller-local storage) or any int object with storage_traits, vector-like and of the system dimension when both are fixed-size. More...

Concepts
concept	tdls::detail::solver_config
	Concept gating the explicit-configuration entry points.

Typedefs
template<typename MatrixType >
using	tdls::detail::matrix_scalar = typename matrix_scalar_of<MatrixType>::type
	Scalar type of a dense matrix argument, see matrix_scalar_of.

Functions
template<typename MatrixType , auto UserConfig>
consteval auto	tdls::detail::checked_config ()
	Validates a user configuration value against the matrix scalar type and returns it with its concrete type.

template<typename VectorType , typename Scalar , int N>
TDLS_HOST_DEVICE TDLS_FORCEINLINE constexpr void	tdls::detail::check_vector ()
	Checks that a vector-like argument matches the system: arity 1, extent N, same scalar type. The extent is only checkable when both the matrix and the vector are fixed-size; when either side is runtime-sized (N == 0, or a runtime-sized vector), the extent match is an unchecked precondition, as everywhere in the raw API.

template<typename RhsType , typename SolutionType >
TDLS_HOST_DEVICE TDLS_FORCEINLINE constexpr void	tdls::detail::check_rhs_pair ()
	Checks that the right-hand side and the solution share one residency and one compile-time stride: the raw API carries a single rhs_stride for both. Their extents must match whenever both are fixed-size. With runtime-strided views, both must be mapped on the same batch (equal runtime strides), which is the caller's responsibility.

template<typename RhsType , typename SolutionType , typename Scalar , int N>
TDLS_HOST_DEVICE TDLS_FORCEINLINE constexpr void	tdls::detail::check_multirhs_pair ()
	Checks a matrix-like right-hand-side block pair (B, X): matching scalar, matching extents where compile-time knowledge allows, one shared layout. On any runtime-sized side the extents are unchecked preconditions, as everywhere in the raw API: B and X must have N rows and the same column count.

template<typename Ctx , int pass_width, bool inplace, typename MatrixType , typename PivotType , typename RhsType , typename SolutionType >
TDLS_HOST_DEVICE TDLS_FORCEINLINE constexpr void	tdls::detail::substitute_multirhs_dispatch (const MatrixType &A, const PivotType &piv, const RhsType &b, SolutionType &x)
	Shared translator of the matrix right-hand-side entry points: reduces the dense objects to raw arguments and forwards to the _multirhs entry points, which do the pass cutting themselves. Matrix right-hand sides are always routed through the external addressing of the raw API: the register convention of its internal mode is not the row-major layout of dense matrix objects.

template<auto UserConfig, bool oot_diagnostics, typename MatrixType , typename PivotType >
TDLS_HOST_DEVICE TDLS_FORCEINLINE constexpr bool	tdls::detail::factorize_dispatch (MatrixType &A, PivotType &piv, int &oot_count)
	Shared engine of the factorize entry points: reduces the dense objects to raw arguments and forwards to the raw factorize, with or without the out-of-tile counter.

template<auto UserConfig, int pass_width, bool oot_diagnostics, typename MatrixType , typename PivotType , typename RhsType , typename SolutionType >
TDLS_HOST_DEVICE TDLS_FORCEINLINE constexpr bool	tdls::detail::solve_dispatch (MatrixType &A, PivotType &piv, const RhsType &b, SolutionType &x, int &oot_count)
	Shared engine of the solve entry points: factorize + substitute on dense objects, with or without the out-of-tile counter.

template<auto UserConfig, int pass_width, bool oot_diagnostics, typename MatrixType , typename PivotType , typename VectorType >
TDLS_HOST_DEVICE TDLS_FORCEINLINE constexpr bool	tdls::detail::solve_inplace_dispatch (MatrixType &A, PivotType &piv, VectorType &y, int &oot_count)
	Shared engine of the solve_inplace entry points: fused factorization on dense objects, with or without the out-of-tile counter.

template<detail::solver_config auto UserConfig, typename MatrixType , typename PivotType >
TDLS_HOST_DEVICE TDLS_FORCEINLINE constexpr bool	tdls::factorize (MatrixType &A, PivotType &piv)
	Factor a dense matrix object in place, A := PLU.

template<typename MatrixType , typename PivotType >
TDLS_HOST_DEVICE TDLS_FORCEINLINE constexpr bool	tdls::factorize (MatrixType &A, PivotType &piv)
	Default-configuration overload of factorize.

template<detail::solver_config auto UserConfig, typename MatrixType , typename PivotType >
TDLS_HOST_DEVICE TDLS_FORCEINLINE constexpr bool	tdls::factorize (MatrixType &A, PivotType &piv, int &oot_count)
	Counting overload of factorize: also reports the number of columns whose best in-tile pivot fell below oot_threshold.

template<typename MatrixType , typename PivotType >
TDLS_HOST_DEVICE TDLS_FORCEINLINE constexpr bool	tdls::factorize (MatrixType &A, PivotType &piv, int &oot_count)
	Default-configuration counting overload of factorize.

template<detail::solver_config auto UserConfig, int pass_width = 0, typename MatrixType , typename PivotType , typename RhsType , typename SolutionType >
TDLS_HOST_DEVICE TDLS_FORCEINLINE constexpr bool	tdls::solve (MatrixType &A, PivotType &piv, const RhsType &b, SolutionType &x)
	Solve A x = b on dense objects: factorize + substitute.

template<int pass_width = 0, typename MatrixType , typename PivotType , typename RhsType , typename SolutionType >
TDLS_HOST_DEVICE TDLS_FORCEINLINE constexpr bool	tdls::solve (MatrixType &A, PivotType &piv, const RhsType &b, SolutionType &x)
	Default-configuration overload of solve.

template<detail::solver_config auto UserConfig, int pass_width = 0, typename MatrixType , typename PivotType , typename RhsType , typename SolutionType >
TDLS_HOST_DEVICE TDLS_FORCEINLINE constexpr bool	tdls::solve (MatrixType &A, PivotType &piv, const RhsType &b, SolutionType &x, int &oot_count)
	Counting overload of solve: also reports the number of columns whose best in-tile pivot fell below oot_threshold.

template<int pass_width = 0, typename MatrixType , typename PivotType , typename RhsType , typename SolutionType >
TDLS_HOST_DEVICE TDLS_FORCEINLINE constexpr bool	tdls::solve (MatrixType &A, PivotType &piv, const RhsType &b, SolutionType &x, int &oot_count)
	Default-configuration counting overload of solve.

template<detail::solver_config auto UserConfig, int pass_width = 0, typename MatrixType , typename PivotType , typename VectorType >
TDLS_HOST_DEVICE TDLS_FORCEINLINE constexpr bool	tdls::solve_inplace (MatrixType &A, PivotType &piv, VectorType &y)
	Solve A y = y on dense objects with the fused factorization (forward substitution folded into factorize, backward pass after).

template<int pass_width = 0, typename MatrixType , typename PivotType , typename VectorType >
TDLS_HOST_DEVICE TDLS_FORCEINLINE constexpr bool	tdls::solve_inplace (MatrixType &A, PivotType &piv, VectorType &y)
	Default-configuration overload of solve_inplace.

template<detail::solver_config auto UserConfig, int pass_width = 0, typename MatrixType , typename PivotType , typename VectorType >
TDLS_HOST_DEVICE TDLS_FORCEINLINE constexpr bool	tdls::solve_inplace (MatrixType &A, PivotType &piv, VectorType &y, int &oot_count)
	Counting overload of solve_inplace: also reports the number of columns whose best in-tile pivot fell below oot_threshold.

template<int pass_width = 0, typename MatrixType , typename PivotType , typename VectorType >
TDLS_HOST_DEVICE TDLS_FORCEINLINE constexpr bool	tdls::solve_inplace (MatrixType &A, PivotType &piv, VectorType &y, int &oot_count)
	Default-configuration counting overload of solve_inplace.

template<detail::solver_config auto UserConfig, int pass_width = 0, typename MatrixType , typename PivotType , typename RhsType , typename SolutionType >
TDLS_HOST_DEVICE TDLS_FORCEINLINE constexpr void	tdls::substitute (const MatrixType &A, const PivotType &piv, const RhsType &b, SolutionType &x)
	Solve x := U^-1 L^-1 P b on dense objects, from a prior factorize. b and x must not alias.

template<int pass_width = 0, typename MatrixType , typename PivotType , typename RhsType , typename SolutionType >
TDLS_HOST_DEVICE TDLS_FORCEINLINE constexpr void	tdls::substitute (const MatrixType &A, const PivotType &piv, const RhsType &b, SolutionType &x)
	Default-configuration overload of substitute.

template<detail::solver_config auto UserConfig, int pass_width = 0, typename MatrixType , typename PivotType , typename SolutionType >
TDLS_HOST_DEVICE TDLS_FORCEINLINE constexpr void	tdls::substitute_inplace (const MatrixType &A, const PivotType &piv, SolutionType &x)
	Solve in place on dense objects: x holds the unpermuted right-hand side on entry and the solution on exit.

template<int pass_width = 0, typename MatrixType , typename PivotType , typename SolutionType >
TDLS_HOST_DEVICE TDLS_FORCEINLINE constexpr void	tdls::substitute_inplace (const MatrixType &A, const PivotType &piv, SolutionType &x)
	Default-configuration overload of substitute_inplace.

template<detail::solver_config auto UserConfig, int pass_width = 0, typename MatrixType , typename PivotType , typename SolutionType >
TDLS_HOST_DEVICE TDLS_FORCEINLINE constexpr void	tdls::substitute_canonical (const MatrixType &A, const PivotType &piv, const int col, SolutionType &x)
	Solve A x = e_col on dense objects, from a prior factorize: the consistent-tangent-operator path.

template<int pass_width = 0, typename MatrixType , typename PivotType , typename SolutionType >
TDLS_HOST_DEVICE TDLS_FORCEINLINE constexpr void	tdls::substitute_canonical (const MatrixType &A, const PivotType &piv, const int col, SolutionType &x)
	Default-configuration overload of substitute_canonical.

Variables
template<typename T >
constexpr bool	tdls::detail::is_dense_v
	A type is "dense" when it exposes both a data pointer and an indexing policy, the structural core of the TFEL protocol.

Detailed Description

TFEL adaptors: call the TiledLUpp solvers directly on the tfel::math objects (matrices, vectors, views) instead of raw pointers.

Author: Tristan Chenaille

Copyright: Copyright (C) 2026 CEA. All rights reserved. This project is publicly released under the BSD 3-Clause License (see the LICENSE file). CEA may also distribute it under specific licensing conditions.

The adaptors are designed for the TFEL math types, recognized STRUCTURALLY: TFEL is never named or included, so the library stays dependency-free, and any type following the TFEL protocol is accepted. Three families are recognized:

contiguous fixed-size objects and views, tfel::math tmatrix / tvector / View: expose data() and an indexing_policy type whose extents are constexpr;
element-strided views, tfel::math StridedCoalescedView, i.e. the map_strided SoA views: expose their runtime stride through a data() member returning a (pointer, stride) pair, or through a stride() / getStride() member next to a plain data();
runtime-sized objects, tfel::math matrix / vector: their indexing policy carries its extents as data members, so its default-constructed instance reports a zero extent. They also expose getIndexingPolicy(), from which the dimension is read at run time.

A fixed-size matrix resolves the compile-time TiledLUpp solver, with the dimension deduced from the indexing policy and the residency template booleans of the raw API inferred from the argument types (contiguous object -> internal, strided view -> external), mixed freely. A runtime-sized matrix resolves the runtime TiledLUpp solver, every argument reduced to its (pointer, stride) pair. On that path the extents cannot be checked at compile time: the matrix must be square and every vector extent must match its dimension. These are unchecked preconditions, exactly as in the raw API.

solve, solve_inplace, substitute and substitute_inplace also accept a matrix-like right-hand side holding one right-hand side per column: A X = B, every column solved against the one factorization through the multirhs entry points of the raw API. substitute_canonical accepts a matrix-like x the same way: its columns receive the consecutive canonical columns e_col .. e{col+M-1}. On all five, the template parameter pass_width cuts the substitution into passes (0, the default, means all columns in one pass; the last pass takes the remainder).

Two families are rejected at compile time with an explicit message: row-strided matrix views (sub-matrix views, whose stride between rows is unrelated to the column count) cannot be expressed by the TiledLUpp solvers' single-stride addressing, and gather views holding one pointer per element expose no data() at all.

TFEL stores matrices row-major and the adaptors follow that convention: a configuration selecting the column-major layout is rejected at compile time.

The detection can be overridden for non-TFEL types by specializing tdls::storage_traits.

Every entry point comes in two overloads: a default-configuration form, and an explicit-configuration form taking a constexpr TiledLUppConfig value of the matrix scalar type as its first template argument. Only the TiledLUpp family exists today; a configuration value of another family can select it when one lands.

factorize, solve and solve_inplace also come in counting overloads taking a trailing int& out-parameter: the out-of-tile search counter of the raw API. Without it the diagnostic is compiled out.

Typedef Documentation

◆ matrix_scalar

template<typename MatrixType >

using tdls::detail::matrix_scalar = typename matrix_scalar_of<MatrixType>::type

Scalar type of a dense matrix argument, see matrix_scalar_of.

Template Parameters

MatrixType dense matrix type

Function Documentation

◆ check_multirhs_pair()

template<typename RhsType , typename SolutionType , typename Scalar , int N>

TDLS_HOST_DEVICE TDLS_FORCEINLINE constexpr void tdls::detail::check_multirhs_pair ( )

constexpr

Checks a matrix-like right-hand-side block pair (B, X): matching scalar, matching extents where compile-time knowledge allows, one shared layout. On any runtime-sized side the extents are unchecked preconditions, as everywhere in the raw API: B and X must have N rows and the same column count.

Template Parameters

RhsType	right-hand-side block type
SolutionType	solution block type
Scalar	scalar type of the system
N	system dimension (0 on the runtime path)

◆ check_rhs_pair()

template<typename RhsType , typename SolutionType >

TDLS_HOST_DEVICE TDLS_FORCEINLINE constexpr void tdls::detail::check_rhs_pair ( )

constexpr

Checks that the right-hand side and the solution share one residency and one compile-time stride: the raw API carries a single rhs_stride for both. Their extents must match whenever both are fixed-size. With runtime-strided views, both must be mapped on the same batch (equal runtime strides), which is the caller's responsibility.

Template Parameters

RhsType	right-hand-side type
SolutionType	solution type

◆ check_vector()

template<typename VectorType , typename Scalar , int N>

TDLS_HOST_DEVICE TDLS_FORCEINLINE constexpr void tdls::detail::check_vector ( )

constexpr

Checks that a vector-like argument matches the system: arity 1, extent N, same scalar type. The extent is only checkable when both the matrix and the vector are fixed-size; when either side is runtime-sized (N == 0, or a runtime-sized vector), the extent match is an unchecked precondition, as everywhere in the raw API.

Template Parameters

VectorType	dense vector type
Scalar	scalar type of the system
N	system dimension (0 on the runtime path)

◆ checked_config()

template<typename MatrixType , auto UserConfig>

auto tdls::detail::checked_config ( )

consteval

Validates a user configuration value against the matrix scalar type and returns it with its concrete type.

Template Parameters

MatrixType	dense matrix type
UserConfig	user configuration value

Returns: the configuration value

◆ factorize() [1/4]

template<detail::solver_config auto UserConfig, typename MatrixType , typename PivotType >

TDLS_HOST_DEVICE TDLS_FORCEINLINE constexpr bool tdls::factorize	(	MatrixType &	A,
		PivotType &	piv )

nodiscardconstexpr

Factor a dense matrix object in place, A := P*L*U.

Template Parameters

UserConfig compile-time knobs, a constexpr TiledLUppConfig value of the matrix scalar type

Parameters

[in,out]	A	matrix-like object (factored in place)
[in,out]	piv	pivot storage: int pointer/array or dense int object

Returns: false on a singular matrix.

◆ factorize() [2/4]

template<typename MatrixType , typename PivotType >

TDLS_HOST_DEVICE TDLS_FORCEINLINE constexpr bool tdls::factorize	(	MatrixType &	A,
		PivotType &	piv )

nodiscardconstexpr

Default-configuration overload of factorize.

Parameters

[in,out]	A	matrix-like object (factored in place)
[in,out]	piv	pivot storage: int pointer/array or dense int object

Returns: false on a singular matrix.

◆ factorize() [3/4]

template<detail::solver_config auto UserConfig, typename MatrixType , typename PivotType >

TDLS_HOST_DEVICE TDLS_FORCEINLINE constexpr bool tdls::factorize	(	MatrixType &	A,
		PivotType &	piv,
		int &	oot_count )

nodiscardconstexpr

Counting overload of factorize: also reports the number of columns whose best in-tile pivot fell below oot_threshold.

Template Parameters

UserConfig compile-time knobs, a constexpr TiledLUppConfig value of the matrix scalar type

Parameters

[in,out]	A	matrix-like object (factored in place)
[in,out]	piv	pivot storage: int pointer/array or dense int object
[out]	oot_count	number of columns whose best in-tile pivot fell below oot_threshold

Returns: false on a singular matrix.

◆ factorize() [4/4]

template<typename MatrixType , typename PivotType >

TDLS_HOST_DEVICE TDLS_FORCEINLINE constexpr bool tdls::factorize	(	MatrixType &	A,
		PivotType &	piv,
		int &	oot_count )

nodiscardconstexpr

Default-configuration counting overload of factorize.

Parameters

[in,out]	A	matrix-like object (factored in place)
[in,out]	piv	pivot storage: int pointer/array or dense int object
[out]	oot_count	number of columns whose best in-tile pivot fell below oot_threshold

Returns: false on a singular matrix.

◆ factorize_dispatch()

template<auto UserConfig, bool oot_diagnostics, typename MatrixType , typename PivotType >

TDLS_HOST_DEVICE TDLS_FORCEINLINE constexpr bool tdls::detail::factorize_dispatch	(	MatrixType &	A,
		PivotType &	piv,
		int &	oot_count )

nodiscardconstexpr

Shared engine of the factorize entry points: reduces the dense objects to raw arguments and forwards to the raw factorize, with or without the out-of-tile counter.

Template Parameters

UserConfig	configuration value, validated by checked_config
oot_diagnostics	compile the out-of-tile counter in or out

Parameters

[in,out]	A	matrix-like object (factored in place)
[in,out]	piv	pivot storage
[out]	oot_count	out-of-tile search counter (oot_diagnostics)

Returns: false on a singular matrix.

◆ solve() [1/4]

template<detail::solver_config auto UserConfig, int pass_width = 0, typename MatrixType , typename PivotType , typename RhsType , typename SolutionType >

TDLS_HOST_DEVICE TDLS_FORCEINLINE constexpr bool tdls::solve	(	MatrixType &	A,
		PivotType &	piv,
		const RhsType &	b,
		SolutionType &	x )

nodiscardconstexpr

Solve A x = b on dense objects: factorize + substitute.

With a matrix-like b (and x), all its columns are solved against the one factorization: A X = B. pass_width then cuts the substitution into passes (0 = all columns in one pass; the last pass takes the remainder). The forward pass is not folded into the factorization on that path (see the raw solve_multirhs).

Template Parameters

UserConfig	compile-time knobs, a constexpr TiledLUppConfig value of the matrix scalar type
pass_width	columns per substitution pass for a matrix-like b (0 = all at once; must be 0 for a vector-like b)

Parameters

[in,out]	A	matrix-like object (factored in place)
[in,out]	piv	pivot storage: int pointer/array or dense int object
[in]	b	right-hand side, in original order: vector-like, or matrix-like holding one right-hand side per column
[out]	x	solution, of the same shape as b

Returns: false on a singular matrix.

◆ solve() [2/4]

template<int pass_width = 0, typename MatrixType , typename PivotType , typename RhsType , typename SolutionType >

TDLS_HOST_DEVICE TDLS_FORCEINLINE constexpr bool tdls::solve	(	MatrixType &	A,
		PivotType &	piv,
		const RhsType &	b,
		SolutionType &	x )

nodiscardconstexpr

Default-configuration overload of solve.

Template Parameters

pass_width columns per substitution pass for a matrix-like b (0 = all at once; must be 0 for a vector-like b)

Parameters

[in,out]	A	matrix-like object (factored in place)
[in,out]	piv	pivot storage: int pointer/array or dense int object
[in]	b	right-hand side, in original order: vector-like, or matrix-like holding one right-hand side per column
[out]	x	solution, of the same shape as b

Returns: false on a singular matrix.

◆ solve() [3/4]

template<detail::solver_config auto UserConfig, int pass_width = 0, typename MatrixType , typename PivotType , typename RhsType , typename SolutionType >

TDLS_HOST_DEVICE TDLS_FORCEINLINE constexpr bool tdls::solve	(	MatrixType &	A,
		PivotType &	piv,
		const RhsType &	b,
		SolutionType &	x,
		int &	oot_count )

nodiscardconstexpr

Counting overload of solve: also reports the number of columns whose best in-tile pivot fell below oot_threshold.

Template Parameters

UserConfig	compile-time knobs, a constexpr TiledLUppConfig value of the matrix scalar type
pass_width	columns per substitution pass for a matrix-like b (0 = all at once; must be 0 for a vector-like b)

Parameters

[in,out]	A	matrix-like object (factored in place)
[in,out]	piv	pivot storage: int pointer/array or dense int object
[in]	b	right-hand side, in original order
[out]	x	solution, of the same shape as b
[out]	oot_count	number of columns whose best in-tile pivot fell below oot_threshold

Returns: false on a singular matrix.

◆ solve() [4/4]

template<int pass_width = 0, typename MatrixType , typename PivotType , typename RhsType , typename SolutionType >

TDLS_HOST_DEVICE TDLS_FORCEINLINE constexpr bool tdls::solve	(	MatrixType &	A,
		PivotType &	piv,
		const RhsType &	b,
		SolutionType &	x,
		int &	oot_count )

nodiscardconstexpr

Default-configuration counting overload of solve.

Template Parameters

pass_width columns per substitution pass for a matrix-like b (0 = all at once; must be 0 for a vector-like b)

Parameters

[in,out]	A	matrix-like object (factored in place)
[in,out]	piv	pivot storage: int pointer/array or dense int object
[in]	b	right-hand side, in original order
[out]	x	solution, of the same shape as b
[out]	oot_count	number of columns whose best in-tile pivot fell below oot_threshold

Returns: false on a singular matrix.

◆ solve_dispatch()

template<auto UserConfig, int pass_width, bool oot_diagnostics, typename MatrixType , typename PivotType , typename RhsType , typename SolutionType >

TDLS_HOST_DEVICE TDLS_FORCEINLINE constexpr bool tdls::detail::solve_dispatch	(	MatrixType &	A,
		PivotType &	piv,
		const RhsType &	b,
		SolutionType &	x,
		int &	oot_count )

nodiscardconstexpr

Shared engine of the solve entry points: factorize + substitute on dense objects, with or without the out-of-tile counter.

Template Parameters

UserConfig	configuration value, validated by checked_config
pass_width	columns per substitution pass for a matrix-like b
oot_diagnostics	compile the out-of-tile counter in or out

Parameters

[in,out]	A	matrix-like object (factored in place)
[in,out]	piv	pivot storage
[in]	b	right-hand side
[out]	x	solution
[out]	oot_count	out-of-tile search counter (oot_diagnostics)

Returns: false on a singular matrix.

◆ solve_inplace() [1/4]

template<detail::solver_config auto UserConfig, int pass_width = 0, typename MatrixType , typename PivotType , typename VectorType >

TDLS_HOST_DEVICE TDLS_FORCEINLINE constexpr bool tdls::solve_inplace	(	MatrixType &	A,
		PivotType &	piv,
		VectorType &	y )

nodiscardconstexpr

Solve A y = y on dense objects with the fused factorization (forward substitution folded into factorize, backward pass after).

With a matrix-like y, all its columns are overwritten by the solutions against the one factorization. pass_width then cuts the substitution into passes (0 = all columns in one pass; the last pass takes the remainder). The forward pass is not folded into the factorization on that path (see the raw solve_inplace_multirhs).

Template Parameters

UserConfig	compile-time knobs, a constexpr TiledLUppConfig value of the matrix scalar type
pass_width	columns per substitution pass for a matrix-like y (0 = all at once; must be 0 for a vector-like y)

Parameters

[in,out]	A	matrix-like object (factored in place)
[in,out]	piv	pivot storage: int pointer/array or dense int object
[in,out]	y	right-hand side on entry, solution on exit: vector-like, or matrix-like holding one right-hand side per column

Returns: false on a singular matrix (y left partially updated with a vector-like y, untouched with a matrix-like y).

◆ solve_inplace() [2/4]

template<int pass_width = 0, typename MatrixType , typename PivotType , typename VectorType >

TDLS_HOST_DEVICE TDLS_FORCEINLINE constexpr bool tdls::solve_inplace	(	MatrixType &	A,
		PivotType &	piv,
		VectorType &	y )

nodiscardconstexpr

Default-configuration overload of solve_inplace.

Template Parameters

pass_width columns per substitution pass for a matrix-like y (0 = all at once; must be 0 for a vector-like y)

Parameters

[in,out]	A	matrix-like object (factored in place)
[in,out]	piv	pivot storage: int pointer/array or dense int object
[in,out]	y	right-hand side on entry, solution on exit: vector-like, or matrix-like holding one right-hand side per column

Returns: false on a singular matrix (y left partially updated with a vector-like y, untouched with a matrix-like y).

◆ solve_inplace() [3/4]

template<detail::solver_config auto UserConfig, int pass_width = 0, typename MatrixType , typename PivotType , typename VectorType >

TDLS_HOST_DEVICE TDLS_FORCEINLINE constexpr bool tdls::solve_inplace	(	MatrixType &	A,
		PivotType &	piv,
		VectorType &	y,
		int &	oot_count )

nodiscardconstexpr

Counting overload of solve_inplace: also reports the number of columns whose best in-tile pivot fell below oot_threshold.

Template Parameters

UserConfig	compile-time knobs, a constexpr TiledLUppConfig value of the matrix scalar type
pass_width	columns per substitution pass for a matrix-like y (0 = all at once; must be 0 for a vector-like y)

Parameters

[in,out]	A	matrix-like object (factored in place)
[in,out]	piv	pivot storage: int pointer/array or dense int object
[in,out]	y	right-hand side on entry, solution on exit
[out]	oot_count	number of columns whose best in-tile pivot fell below oot_threshold

Returns: false on a singular matrix (y left partially updated with a vector-like y, untouched with a matrix-like y).

◆ solve_inplace() [4/4]

template<int pass_width = 0, typename MatrixType , typename PivotType , typename VectorType >

TDLS_HOST_DEVICE TDLS_FORCEINLINE constexpr bool tdls::solve_inplace	(	MatrixType &	A,
		PivotType &	piv,
		VectorType &	y,
		int &	oot_count )

nodiscardconstexpr

Default-configuration counting overload of solve_inplace.

Template Parameters

pass_width columns per substitution pass for a matrix-like y (0 = all at once; must be 0 for a vector-like y)

Parameters

[in,out]	A	matrix-like object (factored in place)
[in,out]	piv	pivot storage: int pointer/array or dense int object
[in,out]	y	right-hand side on entry, solution on exit
[out]	oot_count	number of columns whose best in-tile pivot fell below oot_threshold

Returns: false on a singular matrix (y left partially updated with a vector-like y, untouched with a matrix-like y).

◆ solve_inplace_dispatch()

template<auto UserConfig, int pass_width, bool oot_diagnostics, typename MatrixType , typename PivotType , typename VectorType >

TDLS_HOST_DEVICE TDLS_FORCEINLINE constexpr bool tdls::detail::solve_inplace_dispatch	(	MatrixType &	A,
		PivotType &	piv,
		VectorType &	y,
		int &	oot_count )

nodiscardconstexpr

Shared engine of the solve_inplace entry points: fused factorization on dense objects, with or without the out-of-tile counter.

Template Parameters

UserConfig	configuration value, validated by checked_config
pass_width	columns per substitution pass for a matrix-like y
oot_diagnostics	compile the out-of-tile counter in or out

Parameters

[in,out]	A	matrix-like object (factored in place)
[in,out]	piv	pivot storage
[in,out]	y	right-hand side on entry, solution on exit
[out]	oot_count	out-of-tile search counter (oot_diagnostics)

Returns: false on a singular matrix.

◆ substitute() [1/2]

template<detail::solver_config auto UserConfig, int pass_width = 0, typename MatrixType , typename PivotType , typename RhsType , typename SolutionType >

TDLS_HOST_DEVICE TDLS_FORCEINLINE constexpr void tdls::substitute	(	const MatrixType &	A,
		const PivotType &	piv,
		const RhsType &	b,
		SolutionType &	x )

constexpr

Solve x := U^-1 L^-1 P b on dense objects, from a prior factorize. b and x must not alias.

With a matrix-like b (and x), every column of b is solved into the matching column of x. pass_width then cuts the substitution into passes (0 = all columns in one pass; the last pass takes the remainder).

Template Parameters

UserConfig	compile-time knobs, a constexpr TiledLUppConfig value of the matrix scalar type
pass_width	columns per substitution pass for a matrix-like b (0 = all at once; must be 0 for a vector-like b)

Parameters

[in]	A	factored matrix-like object
[in]	piv	pivot storage produced by factorize
[in]	b	right-hand side, in original order: vector-like, or matrix-like holding one right-hand side per column
[out]	x	solution, of the same shape as b

◆ substitute() [2/2]

template<int pass_width = 0, typename MatrixType , typename PivotType , typename RhsType , typename SolutionType >

TDLS_HOST_DEVICE TDLS_FORCEINLINE constexpr void tdls::substitute	(	const MatrixType &	A,
		const PivotType &	piv,
		const RhsType &	b,
		SolutionType &	x )

constexpr

Default-configuration overload of substitute.

Template Parameters

pass_width columns per substitution pass for a matrix-like b (0 = all at once; must be 0 for a vector-like b)

Parameters

[in]	A	factored matrix-like object
[in]	piv	pivot storage produced by factorize
[in]	b	right-hand side, in original order: vector-like, or matrix-like holding one right-hand side per column
[out]	x	solution, of the same shape as b

◆ substitute_canonical() [1/2]

template<detail::solver_config auto UserConfig, int pass_width = 0, typename MatrixType , typename PivotType , typename SolutionType >

TDLS_HOST_DEVICE TDLS_FORCEINLINE constexpr void tdls::substitute_canonical	(	const MatrixType &	A,
		const PivotType &	piv,
		const int	col,
		SolutionType &	x )

constexpr

Solve A x = e_col on dense objects, from a prior factorize: the consistent-tangent-operator path.

With a matrix-like x, its columns receive the solutions of the consecutive canonical columns e_col .. e_{col+M-1}, M being the column count of x, every L/U tile loaded once for the block. M is read from x: at compile time on the fixed-size path, at run time for a runtime-sized x, which the runtime-sized matrix path accepts exactly as substitute does for its right-hand-side block. pass_width then cuts the substitution into passes (0 = all columns in one pass; the last pass takes the remainder).

Template Parameters

UserConfig	compile-time knobs, a constexpr TiledLUppConfig value of the matrix scalar type
pass_width	columns per substitution pass for a matrix-like x (0 = all at once; must be 0 for a vector-like x)

Parameters

[in]	A	factored matrix-like object
[in]	piv	pivot storage produced by factorize
[in]	col	index of the canonical column e_col (the first one with a matrix-like x)
[out]	x	vector-like solution, or matrix-like holding one solution per canonical column

◆ substitute_canonical() [2/2]

template<int pass_width = 0, typename MatrixType , typename PivotType , typename SolutionType >

TDLS_HOST_DEVICE TDLS_FORCEINLINE constexpr void tdls::substitute_canonical	(	const MatrixType &	A,
		const PivotType &	piv,
		const int	col,
		SolutionType &	x )

constexpr

Default-configuration overload of substitute_canonical.

Template Parameters

pass_width columns per substitution pass for a matrix-like x (0 = all at once; must be 0 for a vector-like x)

Parameters

[in]	A	factored matrix-like object
[in]	piv	pivot storage produced by factorize
[in]	col	index of the canonical column e_col (the first one with a matrix-like x)
[out]	x	vector-like solution, or matrix-like holding one solution per canonical column

◆ substitute_inplace() [1/2]

template<detail::solver_config auto UserConfig, int pass_width = 0, typename MatrixType , typename PivotType , typename SolutionType >

TDLS_HOST_DEVICE TDLS_FORCEINLINE constexpr void tdls::substitute_inplace	(	const MatrixType &	A,
		const PivotType &	piv,
		SolutionType &	x )

constexpr

Solve in place on dense objects: x holds the unpermuted right-hand side on entry and the solution on exit.

With a matrix-like x, every column is overwritten by its solution. pass_width then cuts the substitution into passes (0 = all columns in one pass; the last pass takes the remainder).

Template Parameters

UserConfig	compile-time knobs, a constexpr TiledLUppConfig value of the matrix scalar type
pass_width	columns per substitution pass for a matrix-like x (0 = all at once; must be 0 for a vector-like x)

Parameters

[in]	A	factored matrix-like object
[in]	piv	pivot storage produced by factorize
[in,out]	x	right-hand side, then solution: vector-like, or matrix-like holding one right-hand side per column

◆ substitute_inplace() [2/2]

template<int pass_width = 0, typename MatrixType , typename PivotType , typename SolutionType >

TDLS_HOST_DEVICE TDLS_FORCEINLINE constexpr void tdls::substitute_inplace	(	const MatrixType &	A,
		const PivotType &	piv,
		SolutionType &	x )

constexpr

Default-configuration overload of substitute_inplace.

Template Parameters

pass_width columns per substitution pass for a matrix-like x (0 = all at once; must be 0 for a vector-like x)

Parameters

[in]	A	factored matrix-like object
[in]	piv	pivot storage produced by factorize
[in,out]	x	right-hand side, then solution: vector-like, or matrix-like holding one right-hand side per column

◆ substitute_multirhs_dispatch()

template<typename Ctx , int pass_width, bool inplace, typename MatrixType , typename PivotType , typename RhsType , typename SolutionType >

TDLS_HOST_DEVICE TDLS_FORCEINLINE constexpr void tdls::detail::substitute_multirhs_dispatch	(	const MatrixType &	A,
		const PivotType &	piv,
		const RhsType &	b,
		SolutionType &	x )

constexpr

Shared translator of the matrix right-hand-side entry points: reduces the dense objects to raw arguments and forwards to the _multirhs entry points, which do the pass cutting themselves. Matrix right-hand sides are always routed through the external addressing of the raw API: the register convention of its internal mode is not the row-major layout of dense matrix objects.

Template Parameters

Ctx	adaptor context of the entry point
pass_width	columns per substitution pass (0 = all at once)
inplace	false: read B, write X; true: overwrite X in place (b is then ignored and may alias x)

Variable Documentation

◆ is_dense_v

template<typename T >

bool tdls::detail::is_dense_v

inlineconstexpr

Initial value:

=

(has_data<T>::value || has_pair_data<T>::value) && has_indexing_policy<T>::value

A type is "dense" when it exposes both a data pointer and an indexing policy, the structural core of the TFEL protocol.

Classes

Concepts

Typedefs

Functions

Variables

Detailed Description

Typedef Documentation

◆ matrix_scalar

Function Documentation

◆ check_multirhs_pair()

◆ check_rhs_pair()

◆ check_vector()

◆ checked_config()

◆ factorize() [1/4]

◆ factorize() [2/4]

◆ factorize() [3/4]

◆ factorize() [4/4]

◆ factorize_dispatch()

◆ solve() [1/4]

◆ solve() [2/4]

◆ solve() [3/4]

◆ solve() [4/4]

◆ solve_dispatch()

◆ solve_inplace() [1/4]

◆ solve_inplace() [2/4]

◆ solve_inplace() [3/4]

◆ solve_inplace() [4/4]

◆ solve_inplace_dispatch()

◆ substitute() [1/2]

◆ substitute() [2/2]

◆ substitute_canonical() [1/2]

◆ substitute_canonical() [2/2]

◆ substitute_inplace() [1/2]

◆ substitute_inplace() [2/2]

◆ substitute_multirhs_dispatch()

Variable Documentation

◆ is_dense_v