LDLTMgr Class Reference

LDLT factorization. More...

#include <ldlt_mgr.hpp>

Public Member Functions
	LDLTMgr (size_t N)
	Construct a new ldlt ext object.
	LDLTMgr (const LDLTMgr &)=delete
LDLTMgr &	operator= (const LDLTMgr &)=delete
	LDLTMgr (LDLTMgr &&)=default
LDLTMgr &	operator= (LDLTMgr &&)=delete
	~LDLTMgr ()=default
template<typename Mat >
auto	factorize (const Mat &A) -> bool
	Perform LDLT Factorization.
template<typename Fn >
auto	factor (Fn get_matrix_elem) -> bool
	Perform LDLT Factorization (Lazy evaluation)
template<typename Fn >
auto	factor_with_allow_semidefinite (Fn get_matrix_elem) -> bool
	Perform LDLT Factorization (Lazy evaluation)
constexpr auto	is_spd () const noexcept -> bool
	Check if the matrix is symmetric positive definite.
auto	witness () -> double
	witness that certifies $A$ is not symmetric positive definite (spd)
template<typename Arr036 >
auto	set_witness_vec (Arr036 &v) const -> void
	Set the witness vec object.
template<typename Mat >
auto	sym_quad (const Mat &A) const -> double
	Calculate v'*{A}(pos,pos)*v.
template<typename Mat >
auto	sqrt (Mat &M) -> void
	Return upper triangular matrix $R$ where $A = R^T R$.

Public Attributes
Rng	pos {0U, 0U}
	the rows where the process starts and stops
Vec	witness_vec
	witness vector
size_t	_n
	dimension

Detailed Description

LDLT factorization.

LDLTMgr is a class that performs the LDLT factorization for a given symmetric matrix. The LDLT factorization decomposes a symmetric matrix A into the product of a lower triangular matrix L, a diagonal matrix D, and the transpose of L. This factorization is useful for solving linear systems and eigenvalue problems. The class provides methods to perform the factorization, check if the matrix is positive definite, calculate a witness vector if it is not positive definite, and calculate the symmetric quadratic form.

• LDL^T square-root-free version
• Option allow semidefinite
• A matrix A in R^{m x m} is positive definite iff v' A v > 0 for all v in R^n.
• O(pos^2) per iteration, independent of N

Constructor & Destructor Documentation

LDLTMgr() [1/3]

LDLTMgr::LDLTMgr ( size_t  N )

inlineexplicit

Construct a new ldlt ext object.

Parameters

[in]

N

dimension

LDLTMgr() [2/3]

LDLTMgr::LDLTMgr ( const LDLTMgr &  )

delete

LDLTMgr() [3/3]

LDLTMgr::LDLTMgr ( LDLTMgr &&  )

default

~LDLTMgr()

LDLTMgr::~LDLTMgr ( )

default

Member Function Documentation

factor()

template<typename Fn >

auto LDLTMgr::factor ( Fn  get_matrix_elem ) -> bool

inline

Perform LDLT Factorization (Lazy evaluation)

Template Parameters

Fn	callable type with signature double(size_t, size_t)

Parameters

[in]

get_matrix_elem

function to access the elements of A

Returns

bool true if factorization was successful, false otherwise

See also: factorize()

factor_with_allow_semidefinite()

template<typename Fn >

auto LDLTMgr::factor_with_allow_semidefinite ( Fn  get_matrix_elem ) -> bool

inline

Perform LDLT Factorization (Lazy evaluation)

Template Parameters

Fn	callable type with signature double(size_t, size_t)

Parameters

[in]

get_matrix_elem

function to access the elements of A

Returns

bool true if factorization was successful, false otherwise

See also: factorize()

factorize()

template<typename Mat >

auto LDLTMgr::factorize ( const Mat &  A ) -> bool

inline

Perform LDLT Factorization.

The factorize function is a template function that takes a symmetric matrix A as input and performs the LDLT factorization on it. It calls the factor function with a lambda function as an argument. The lambda function takes the indices i and j and returns the element A(i, j) of the matrix A. The factor function performs the actual factorization using the provided lambda function. The factorize function returns a boolean value indicating whether the factorization was successful or not.

Parameters

[in]

A

Symmetric Matrix

is_spd()

constexpr auto LDLTMgr::is_spd ( ) const -> bool

inlineconstexprnoexcept

Check if the matrix is symmetric positive definite.

Returns

bool True if the matrix is SPD, false otherwise.

operator=() [1/2]

LDLTMgr & LDLTMgr::operator= ( const LDLTMgr &  )

delete

operator=() [2/2]

LDLTMgr & LDLTMgr::operator= ( LDLTMgr &&  )

delete

set_witness_vec()

template<typename Arr036 >

auto LDLTMgr::set_witness_vec ( Arr036 &  v ) const -> void

inline

Set the witness vec object.

Template Parameters

Arr036

Parameters

[in]

v

sqrt()

template<typename Mat >

auto LDLTMgr::sqrt ( Mat &  M ) -> void

inline

Return upper triangular matrix $R$ where $A = R^T R$.

The sqrt function calculates the square root of a symmetric positive definite matrix M. It assumes that M is a zero matrix and calculates the upper triangular matrix R such that M = R^T * R.

Template Parameters

Mat

Parameters

[in,out]

M

sym_quad()

template<typename Mat >

auto LDLTMgr::sym_quad ( const Mat &  A ) const -> double

inline

Calculate v'*{A}(pos,pos)*v.

Template Parameters

Mat

Parameters

[in]

A

Returns

double

witness()

auto LDLTMgr::witness

(

)

-> double

witness that certifies $A$ is not symmetric positive definite (spd)

The witness() function calculates a witness that certifies that the matrix A is not symmetric positive definite (spd). It returns a double value that represents the witness.

Returns

double

Member Data Documentation

_n

size_t LDLTMgr::_n

dimension

pos

Rng LDLTMgr::pos {0U, 0U}

the rows where the process starts and stops

witness_vec

Vec LDLTMgr::witness_vec

witness vector

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

• ellalgo/oracles/ldlt_mgr.hpp