LQUP factorisation. More...

#include <factorized-matrix.h>

Public Member Functions
	LQUPMatrix (const Field &F, const BlasMatrix< Element > &A)
	Contruction of LQUP factorization of A (making a copy of A)
	LQUPMatrix (const Field &F, BlasMatrix< Element > &A)
	Contruction of LQUP factorization of A (in-place in A)
	LQUPMatrix (const BlasBlackbox< Field > &A)
	Contruction of LQUP factorization of A (making a copy of A)
	LQUPMatrix (BlasBlackbox< Field > &A)
	Contruction of LQUP factorization of A (in-place in A)
	LQUPMatrix (const Field &F, const BlasMatrix< Element > &A, BlasPermutation< size_t > &P, BlasPermutation< size_t > &Q)
	Contruction of LQUP factorization of A (making a copy of A).
	LQUPMatrix (const Field &F, BlasMatrix< Element > &A, BlasPermutation< size_t > &P, BlasPermutation< size_t > &Q)
	Contruction of LQUP factorization of A (in-place in A).
	LQUPMatrix (const BlasBlackbox< Field > &A, BlasPermutation< size_t > &P, BlasPermutation< size_t > &Q)
	Contruction of LQUP factorization of A (making a copy of A).
	LQUPMatrix (BlasBlackbox< Field > &A, BlasPermutation< size_t > &P, BlasPermutation< size_t > &Q)
	Contruction of LQUP factorization of A (in-place in A).
	~LQUPMatrix ()
	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 > &	getP () const
	get the permutation P.
BlasPermutation< size_t > &	getP (BlasPermutation< size_t > &P) const
	get the permutation P.
const BlasPermutation< size_t > &	getQ () const
	Get the transpose of the permutation `Q`.
BlasPermutation< size_t > &	getQ (BlasPermutation< size_t > &Qt) const
	get the permutation Qt.
TriangularBlasMatrix< Element > &	getL (TriangularBlasMatrix< Element > &L, bool _QLUP=false) const
	get the Matrix `L`.
TriangularBlasMatrix< Element > &	getU (TriangularBlasMatrix< Element > &U) const
	get the matrix `U`.
BlasMatrix< Element > &	getS (BlasMatrix< Element > &S) const
	get the matrix S.

template<class Operand >
Operand &	left_solve (Operand &X, const Operand &B) const
	Solvers with matrices or vectors Operand can be a BlasMatrix<Element> or a std::vector<Element>
template<class Operand >
Operand &	left_solve (Operand &B) const
	Solvers with matrices or vectors Operand can be a BlasMatrix<Element> or a std::vector<Element>
template<class Operand >
Operand &	right_solve (Operand &X, const Operand &B) const
	Solvers with matrices or vectors Operand can be a BlasMatrix<Element> or a std::vector<Element>
template<class Operand >
Operand &	right_solve (Operand &B) const
	Solvers with matrices or vectors Operand can be a BlasMatrix<Element> or a std::vector<Element>
template<class Operand >
Operand &	left_Lsolve (Operand &X, const Operand &B) const
	Solvers with matrices or vectors Operand can be a BlasMatrix<Element> or a std::vector<Element>
template<class Operand >
Operand &	left_Lsolve (Operand &B) const
	Solvers with matrices or vectors Operand can be a BlasMatrix<Element> or a std::vector<Element>
template<class Operand >
Operand &	right_Lsolve (Operand &X, const Operand &B) const
	Solvers with matrices or vectors Operand can be a BlasMatrix<Element> or a std::vector<Element>
template<class Operand >
Operand &	right_Lsolve (Operand &B) const
	Solvers with matrices or vectors Operand can be a BlasMatrix<Element> or a std::vector<Element>
template<class Operand >
Operand &	left_Usolve (Operand &X, const Operand &B) const
	Solvers with matrices or vectors Operand can be a BlasMatrix<Element> or a std::vector<Element>
template<class Operand >
Operand &	rleft_Usolve (Operand &B) const
	Solvers with matrices or vectors Operand can be a BlasMatrix<Element> or a std::vector<Element>
template<class Operand >
Operand &	right_Usolve (Operand &X, const Operand &B) const
	Solvers with matrices or vectors Operand can be a BlasMatrix<Element> or a std::vector<Element>
template<class Operand >
Operand &	right_Usolve (Operand &B) const
	Solvers with matrices or vectors Operand can be a BlasMatrix<Element> or a std::vector<Element>

Detailed Description

template<class Field>
class LinBox::LQUPMatrix< Field >

LQUP factorisation.

This is a class to ease the use LU factorisation (see LUdivine in FFPACK)

The factorisation is $ A = L Q 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 LQUP factorisation of a BlasMatrix/BlasBlackbox on a finite field. There are methods for retrieving L,Q,U and P matrices and methods for solving systems.

Constructor & Destructor Documentation

LQUPMatrix	(	const Field &	F,
		const BlasMatrix< Element > &	A,
		BlasPermutation< size_t > &	P,
		BlasPermutation< size_t > &	Q
	)		`[inline]`

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

P and Q are arguments !

LQUPMatrix	(	const Field &	F,
		BlasMatrix< Element > &	A,
		BlasPermutation< size_t > &	P,
		BlasPermutation< size_t > &	Q
	)		`[inline]`

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

P and Q are arguments !

LQUPMatrix	(	const BlasBlackbox< Field > &	A,
		BlasPermutation< size_t > &	P,
		BlasPermutation< size_t > &	Q
	)		`[inline]`

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

P and Q are arguments !

LQUPMatrix	(	BlasBlackbox< Field > &	A,
		BlasPermutation< size_t > &	P,
		BlasPermutation< size_t > &	Q
	)		`[inline]`

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

P and Q are arguments !

Member Function Documentation

const BlasPermutation<size_t>& getP ( ) const [inline]

get the permutation P.

(no copy)

BlasPermutation<size_t>& getP ( BlasPermutation< size_t > & P ) const [inline]

get the permutation P.

(copy)

const BlasPermutation<size_t>& getQ ( ) const [inline]

Get the transpose of the permutation Q.

Warning:: This does not return Q itself! (because it is more difficult to compute) If needed, Q 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 getQ().

BlasPermutation<size_t>& getQ ( BlasPermutation< size_t > & Qt ) const [inline]

get the permutation Qt.

(copy)

Warning:: see LQUPMatrix::getQ()

TriangularBlasMatrix< typename Field::Element > & getL	(	TriangularBlasMatrix< Element > &	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 `LQUP` decomposition.

Precondition:: L has unit diagonal

TriangularBlasMatrix< typename Field::Element > & getU ( TriangularBlasMatrix< Element > & U ) const [inline]

get the matrix U.

Precondition:: U has non-unit diagonal

BlasMatrix< typename Field::Element > & getS ( BlasMatrix< Element > & S ) const [inline]

get the matrix S.

from the LSP factorization of A deduced from LQUP)

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

factorized-matrix.h
factorized-matrix.inl

Public Member Functions

Detailed Description

template<class Field> class LinBox::LQUPMatrix< Field >

Constructor & Destructor Documentation

Member Function Documentation

template<class Field>
class LinBox::LQUPMatrix< Field >