PLUQ factorisation. More...

#include <factorized-matrix.h>

Public Types
typedef Field::Element	Element

typedef BlasMatrix< Field, typename Vector< Field >::Dense >	matrixType

typedef TriangularBlasMatrix< matrixType >	TriangularMatrix

Public Member Functions
template<class _Rep>
	PLUQMatrix (const BlasMatrix< Field, _Rep > &A)
	Contruction of PLUQ factorization of A (making a copy of A)

template<class _Rep>
	PLUQMatrix (BlasMatrix< Field, _Rep > &A)
	Contruction of PLUQ factorization of A (in-place in A)

template<class _Rep>
	PLUQMatrix (const BlasMatrix< Field, _Rep > &A, BlasPermutation< size_t > &P, BlasPermutation< size_t > &Q)
	Contruction of PLUQ factorization of A (making a copy of A).

template<class _Rep>
	PLUQMatrix (BlasMatrix< Field, _Rep > &A, BlasPermutation< size_t > &P, BlasPermutation< size_t > &Q)
	Contruction of PLUQ factorization of A (in-place in A).

	~PLUQMatrix ()
	destructor.

Field &	field ()
	get the field on which the factorization is done

size_t	rowdim () const
	get row dimension

size_t	coldim () const
	get column dimension

size_t	getRank () const
	get the rank of matrix

const BlasPermutation< size_t > &	getQ () const
	get the permutation Q.

BlasPermutation< size_t > &	getQ (BlasPermutation< size_t > &Q) const
	get the permutation Q.

const BlasPermutation< size_t > &	getP () const
	Get the transpose of the permutation `P`.

BlasPermutation< size_t > &	getP (BlasPermutation< size_t > &PT) const
	get the permutation P^T.

TriangularMatrix &	getL (TriangularMatrix &L, bool _QLUP=false) const
	get the Matrix `L`.

TriangularMatrix &	getU (TriangularMatrix &U) const
	get the matrix `U`.

Element *	getPointer () const
	get the matrix S.

size_t	getStride () const

template<class Operand>
Operand &	left_solve (Operand &X, const Operand &B) const
	Solvers with matrices or vectors Operand can be a BlasMatrix<Field,_Rep> or a std::vector<Element>

template<class Operand>
Operand &	left_solve (Operand &B) const

template<class Operand>
Operand &	right_solve (Operand &X, const Operand &B) const

template<class Operand>
Operand &	right_solve (Operand &B) const

template<class Operand>
Operand &	left_Lsolve (Operand &X, const Operand &B) const

template<class Operand>
Operand &	left_Lsolve (Operand &B) const

template<class Operand>
Operand &	right_Lsolve (Operand &X, const Operand &B) const

template<class Operand>
Operand &	right_Lsolve (Operand &B) const

template<class Operand>
Operand &	left_Usolve (Operand &X, const Operand &B) const

template<class Operand>
Operand &	rleft_Usolve (Operand &B) const

template<class Operand>
Operand &	right_Usolve (Operand &X, const Operand &B) const

template<class Operand>
Operand &	right_Usolve (Operand &B) const

Protected Attributes
Field	_field

BlasMatrix< Field, typename Vector< Field >::Dense > &	_factLU

BlasPermutation< size_t > &	_permP

BlasPermutation< size_t > &	_permQ

size_t	_m

size_t	_n

size_t	_rank

bool	_alloc

bool	_plloc

Detailed Description

template<class Field>
class LinBox::PLUQMatrix< Field >

PLUQ factorisation.

This is a class to ease the use LU factorisation (see FFPACK::PLUQ

The factorisation is \( A = P L U P \) with L lower unit triangular, U upper non-unit triangular, P and Q permutations.

There are two kind of contructors (with and without permutations) and they build a PLUQ factorisation of a BlasMatrix/BlasBlackbox on a finite field. There are methods for retrieving P L,U and Q matrices and methods for solving systems.

Bug: Should really be tempalted by Matrix and be a (sub)domain

Member Typedef Documentation

◆ Element

template<class Field>

typedef Field::Element Element

◆ matrixType

template<class Field>

typedef BlasMatrix<Field,typename Vector<Field>::Dense > matrixType

◆ TriangularMatrix

template<class Field>

typedef TriangularBlasMatrix<matrixType> TriangularMatrix

Constructor & Destructor Documentation

◆ PLUQMatrix() [1/4]

template<class Field>

template<class _Rep>

PLUQMatrix ( const BlasMatrix< Field, _Rep > & A )

Contruction of PLUQ factorization of A (making a copy of A)

◆ PLUQMatrix() [2/4]

template<class Field>

template<class _Rep>

PLUQMatrix ( BlasMatrix< Field, _Rep > & A )

Contruction of PLUQ factorization of A (in-place in A)

◆ PLUQMatrix() [3/4]

template<class Field>

template<class _Rep>

PLUQMatrix	(	const BlasMatrix< Field, _Rep > &	A,
		BlasPermutation< size_t > &	P,
		BlasPermutation< size_t > &	Q )

Contruction of PLUQ factorization of A (making a copy of A).

P and Q are arguments !

◆ PLUQMatrix() [4/4]

template<class Field>

template<class _Rep>

PLUQMatrix	(	BlasMatrix< Field, _Rep > &	A,
		BlasPermutation< size_t > &	P,
		BlasPermutation< size_t > &	Q )

Contruction of PLUQ factorization of A (in-place in A).

P and Q are arguments !

Bug: in place ?

◆ ~PLUQMatrix()

template<class Field>

~PLUQMatrix ( )

destructor.

Member Function Documentation

◆ field()

template<class Field>

Field & field ( )

get the field on which the factorization is done

◆ rowdim()

template<class Field>

size_t rowdim ( ) const

get row dimension

◆ coldim()

template<class Field>

size_t coldim ( ) const

get column dimension

◆ getRank()

template<class Field>

size_t getRank ( ) const

get the rank of matrix

◆ getQ() [1/2]

template<class Field>

const BlasPermutation< size_t > & getQ ( ) const

get the permutation Q.

(no copy)

◆ getQ() [2/2]

template<class Field>

BlasPermutation< size_t > & getQ ( BlasPermutation< size_t > & Q ) const

get the permutation Q.

(copy)

◆ getP() [1/2]

template<class Field>

const BlasPermutation< size_t > & getP ( ) const

Get the transpose of the permutation P.

Warning: This does not return P itself! (because it is more difficult to compute) If needed, P can be obtained as a TransposedBlasMatrix from the return value. One reason this confusion exists is that left-multiplying by a permuation matrix corresponds to a row permuation \(\pi \in S_n\), while right-multiplying by the same matrix corresponds to the inverse column permutation \(\pi^{-1}\)! Usually this is handled intelligently (eg by applyP) but you must be careful with getP().

◆ getP() [2/2]

template<class Field>

BlasPermutation< size_t > & getP ( BlasPermutation< size_t > & PT ) const

get the permutation P^T.

(copy)

Warning: see PLUQMatrix::getP()

◆ getL()

template<class Field>

PLUQMatrix< Field >::TriangularMatrix & getL	(	TriangularMatrix &	L,
		bool	_QLUP = false ) const

inline

get the Matrix L.

Parameters

[out]	L
	_QLUP	if true then `L` form `QLUP` decomposition, else `L` is form `PLUQ` decomposition.

Precondition: L has unit diagonal

◆ getU()

template<class Field>

PLUQMatrix< Field >::TriangularMatrix & getU ( TriangularMatrix & U ) const

inline

get the matrix U.

Precondition: U has non-unit diagonal

◆ getPointer()

template<class Field>

Field::Element * getPointer ( ) const

get the matrix S.

from the LSP factorization of A deduced from PLUQ)

get a pointer to the begin of storage.

◆ getStride()

template<class Field>

size_t getStride ( ) const

get the stride in _factLU

◆ left_solve() [1/2]

template<class Field>

template<class Operand>

Operand & left_solve	(	Operand &	X,
		const Operand &	B ) const

Solvers with matrices or vectors Operand can be a BlasMatrix<Field,_Rep> or a std::vector<Element>

◆ left_solve() [2/2]

template<class Field>

template<class Operand>

Operand & left_solve ( Operand & B ) const

◆ right_solve() [1/2]

template<class Field>

template<class Operand>

Operand & right_solve	(	Operand &	X,
		const Operand &	B ) const

◆ right_solve() [2/2]

template<class Field>

template<class Operand>

Operand & right_solve ( Operand & B ) const

◆ left_Lsolve() [1/2]

template<class Field>

template<class Operand>

Operand & left_Lsolve	(	Operand &	X,
		const Operand &	B ) const

◆ left_Lsolve() [2/2]

template<class Field>

template<class Operand>

Operand & left_Lsolve ( Operand & B ) const

◆ right_Lsolve() [1/2]

template<class Field>

template<class Operand>

Operand & right_Lsolve	(	Operand &	X,
		const Operand &	B ) const

◆ right_Lsolve() [2/2]

template<class Field>

template<class Operand>

Operand & right_Lsolve ( Operand & B ) const

◆ left_Usolve()

template<class Field>

template<class Operand>

Operand & left_Usolve	(	Operand &	X,
		const Operand &	B ) const

◆ rleft_Usolve()

template<class Field>

template<class Operand>

Operand & rleft_Usolve ( Operand & B ) const

◆ right_Usolve() [1/2]

template<class Field>

template<class Operand>

Operand & right_Usolve	(	Operand &	X,
		const Operand &	B ) const

◆ right_Usolve() [2/2]

template<class Field>

template<class Operand>

Operand & right_Usolve ( Operand & B ) const

Field Documentation

◆ _field

template<class Field>

Field _field

protected

◆ _factLU

template<class Field>

BlasMatrix<Field,typename Vector<Field>::Dense >& _factLU

protected

◆ _permP

template<class Field>

BlasPermutation<size_t>& _permP

protected

◆ _permQ

template<class Field>

BlasPermutation<size_t>& _permQ

protected

◆ _m

template<class Field>

size_t _m

protected

◆ _n

template<class Field>

size_t _n

protected

◆ _rank

template<class Field>

size_t _rank

protected

◆ _alloc

template<class Field>

bool _alloc

protected

◆ _plloc

template<class Field>

bool _plloc

protected

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

Public Types

Public Member Functions

Protected Attributes

Detailed Description

Member Typedef Documentation

◆ Element

◆ matrixType

◆ TriangularMatrix

Constructor & Destructor Documentation

◆ PLUQMatrix() [1/4]

◆ PLUQMatrix() [2/4]

◆ PLUQMatrix() [3/4]

◆ PLUQMatrix() [4/4]

◆ ~PLUQMatrix()

Member Function Documentation

◆ field()

◆ rowdim()

◆ coldim()

◆ getRank()

◆ getQ() [1/2]

◆ getQ() [2/2]

◆ getP() [1/2]

◆ getP() [2/2]

◆ getL()

◆ getU()

◆ getPointer()

◆ getStride()

◆ left_solve() [1/2]

◆ left_solve() [2/2]

◆ right_solve() [1/2]

◆ right_solve() [2/2]

◆ left_Lsolve() [1/2]

◆ left_Lsolve() [2/2]

◆ right_Lsolve() [1/2]

◆ right_Lsolve() [2/2]

◆ left_Usolve()

◆ rleft_Usolve()

◆ right_Usolve() [1/2]

◆ right_Usolve() [2/2]

Field Documentation

◆ _field

◆ _factLU

◆ _permP

◆ _permQ

◆ _m

◆ _n

◆ _rank

◆ _alloc

◆ _plloc