Factors a real symmetric matrix as A = L D L^T without pivoting. More...

#include <ldl.hpp>

Inheritance diagram for linalg::LDL< Mat >:

Public Types
using	SymmetricBase = SymmetricOperator< Mat, LDL< Mat > >
	alias for symmetric matrix

Public Types inherited from linalg::SymmetricOperator< Mat, LDL< Mat > >
using	OperatorBase = Endomorphism< Mat, SymmetricOperator< Mat, LDL< Mat > > >
	alias to extract base types

Public Types inherited from linalg::Endomorphism< Mat, Derived >
using	T = matrix_scalar_t< Mat >
	alias helpers for types

using	ScalarT = real_type_t< T >

using	ComplexT = std::complex< ScalarT >

Public Member Functions
constexpr	LDL (const Mat &A)
	Factor a symmetric matrix as A = L D L^T.

constexpr	LDL (const Mat &A, const config::FactorConfig< T > &config_in)
	Factor a symmetric matrix with explicit pivot tolerance.

constexpr auto	D () const
	Reconstruct the diagonal factor.

constexpr auto	L () const
	Reconstruct the unit lower-triangular factor.

constexpr auto	solve (const Vector< T, N > &b) const
	Solve A x = b using the stored LDL^T factors.

constexpr T	det () const
	Compute the determinant from the diagonal pivots.

template<linalg::MatrixContainer MatIn> requires (std::same_as<linalg::matrix_scalar_t<MatIn>, T>)
constexpr auto	apply (const MatIn &Y) const
	Solve A X = Y one column at a time.

Public Member Functions inherited from linalg::SymmetricOperator< Mat, LDL< Mat > >
constexpr	SymmetricOperator (const Mat &A)
	CTOR.

constexpr auto	operator() (std::size_t i, std::size_t j) const
	get element at (i,j) index

constexpr std::size_t	index (std::size_t i, std::size_t j) const
	index from (row, col)

constexpr bool	is_pd () const
	is pd check

constexpr bool	is_nd () const
	is nd check

constexpr bool	is_psd () const
	is psd check

constexpr bool	is_nsd () const
	is nsd check

constexpr bool	is_ind () const
	is indefinite

constexpr bool	is_valid () const
	is valid

constexpr void	compute_definiteness (const Vector< DiagT, N > &diag, const ScalarT &tol)
	compute definiteness

constexpr const LDL< Mat > &	self () const
	self

Public Member Functions inherited from linalg::Endomorphism< Mat, Derived >
constexpr const T &	operator() (std::size_t i, std::size_t j) const
	get element at (i,j) index

constexpr T &	operator() (std::size_t i, std::size_t j)
	get element at (i,j) index

constexpr Derived &	self ()
	self

constexpr const Derived &	self () const
	self

Additional Inherited Members
Public Attributes inherited from linalg::SymmetricOperator< Mat, LDL< Mat > >
SymmetricOperatorType	type
	member variables

Vector< T, DIM >	svec

Static Public Attributes inherited from linalg::SymmetricOperator< Mat, LDL< Mat > >
static constexpr std::size_t	DIM
	helpers to get DIM from mat

Static Public Attributes inherited from linalg::Endomorphism< Mat, Derived >
static constexpr std::size_t	N = mat_rows_v<Mat>
	helper to extract N

Detailed Description

template<SquareMatrix Mat>
struct linalg::LDL< Mat >

Factors a real symmetric matrix as A = L D L^T without pivoting.

forward declaration of LDL^T operator

Template Parameters

Mat	Square symmetric matrix type.

Definition at line 22 of file ldl.hpp.

Member Typedef Documentation

◆ SymmetricBase

template<SquareMatrix Mat>

using linalg::LDL< Mat >::SymmetricBase = SymmetricOperator<Mat, LDL<Mat> >

alias for symmetric matrix

Definition at line 24 of file ldl.hpp.

Constructor & Destructor Documentation

◆ LDL() [1/2]

template<SquareMatrix Mat>

constexpr linalg::LDL< Mat >::LDL ( const Mat & A )

inlineexplicitconstexpr

Factor a symmetric matrix as A = L D L^T.

Parameters

[in] A Square symmetric input matrix.

Definition at line 40 of file ldl.hpp.

References linalg::mat_rows_v.

◆ LDL() [2/2]

template<SquareMatrix Mat>

constexpr linalg::LDL< Mat >::LDL	(	const Mat &	A,
		const config::FactorConfig< T > &	config_in
	)

inlineexplicitconstexpr

Factor a symmetric matrix with explicit pivot tolerance.

Parameters

[in]	A	Square symmetric input matrix.
[in]	config_in	Factorization settings, including pivot tolerance.

Definition at line 48 of file ldl.hpp.

References linalg::mat_rows_v.

Member Function Documentation

◆ apply()

template<SquareMatrix Mat>

template<linalg::MatrixContainer MatIn>
requires (std::same_as<linalg::matrix_scalar_t<MatIn>, T>)

constexpr auto linalg::LDL< Mat >::apply ( const MatIn & Y ) const

inlineconstexpr

Solve A X = Y one column at a time.

Template Parameters

MatIn Matrix type sharing the factorization scalar type.

Parameters

[in] Y Right-hand-side matrix with N rows.

Returns: Tuple (solution matrix X, NumericalEvent event); X = A^-1 Y on success.

Definition at line 106 of file ldl.hpp.

References linalg::get_col(), linalg::is_fatal_event(), linalg::mat_rows_v, linalg::Endomorphism< Mat, Derived >::N, linalg::NONE, and linalg::LDL< Mat >::solve().

◆ D()

template<SquareMatrix Mat>

constexpr auto linalg::LDL< Mat >::D ( ) const

inlineconstexpr

Reconstruct the diagonal factor.

Returns: Matrix<T, N, N> containing D.

Definition at line 58 of file ldl.hpp.

References linalg::make_diag().

◆ det()

template<SquareMatrix Mat>

constexpr T linalg::LDL< Mat >::det ( ) const

inlineconstexpr

Compute the determinant from the diagonal pivots.

Returns: Scalar T equal to the product of the entries of D.

Definition at line 90 of file ldl.hpp.

References linalg::mat_rows_v.

◆ L()

template<SquareMatrix Mat>

constexpr auto linalg::LDL< Mat >::L ( ) const

inlineconstexpr

Reconstruct the unit lower-triangular factor.

Returns: Matrix<T, N, N> containing L.

Definition at line 65 of file ldl.hpp.

References linalg::mat_rows_v.

Referenced by linalg::LDL< Mat >::solve().

◆ solve()

template<SquareMatrix Mat>

constexpr auto linalg::LDL< Mat >::solve ( const Vector< T, N > & b ) const

inlineconstexpr

Solve A x = b using the stored LDL^T factors.

Solve L y = b, D z = y, then L^T x = z.

Parameters

[in] b Right-hand side with N entries.

Returns: Tuple (Vector<T, N> x, NumericalEvent event).

Definition at line 75 of file ldl.hpp.

References linalg::is_fatal_event(), linalg::LDL< Mat >::L(), linalg::mat_rows_v, linalg::NONE, and linalg::transpose().

Referenced by linalg::LDL< Mat >::apply().

The documentation for this struct was generated from the following file:

include/akreon/linalg/operator/ldl.hpp

Public Types

Public Member Functions

Additional Inherited Members

Detailed Description

Member Typedef Documentation

◆ SymmetricBase

Constructor & Destructor Documentation

◆ LDL() [1/2]

◆ LDL() [2/2]

Member Function Documentation

◆ apply()

◆ D()

◆ det()

◆ L()

◆ solve()