bpp-core3: bpp::LUDecomposition< Real > Class Template Reference

bpp-core3 3.0.0

LU Decomposition. More...

#include <Bpp/Numeric/Matrix/LUDecomposition.h>

Collaboration diagram for bpp::LUDecomposition< Real >:

Public Member Functions
	LUDecomposition (const Matrix< Real > &A)
	LU Decomposition. More...

const RowMatrix< Real > &	getL ()
	Return lower triangular factor. More...

const RowMatrix< Real > &	getU ()
	Return upper triangular factor. More...

std::vector< size_t >	getPivot () const
	Return pivot permutation vector. More...

Real	det () const
	Compute determinant using LU factors. More...

Real	solve (const Matrix< Real > &B, Matrix< Real > &X) const
	Solve A*X = B. More...

Real	solve (const std::vector< Real > &b, std::vector< Real > &x) const
	Solve A*x = b, where x and b are vectors of length equal to the number of rows in A. More...

Static Private Member Functions
static void	permuteCopy (const Matrix< Real > &A, const std::vector< size_t > &piv, size_t j0, size_t j1, Matrix< Real > &X)

static void	permuteCopy (const std::vector< Real > &A, const std::vector< size_t > &piv, std::vector< Real > &X)

Private Attributes
RowMatrix< Real >	LU

RowMatrix< Real >	L_

RowMatrix< Real >	U_

size_t	m

size_t	n

int	pivsign

std::vector< size_t >	piv

Detailed Description

template<class Real>
class bpp::LUDecomposition< Real >

LU Decomposition.

[This class and its documentation is adpated from the C++ port of the JAMA library.]

For an m-by-n matrix A with m >= n, the LU decomposition is an m-by-n unit lower triangular matrix L, an n-by-n upper triangular matrix U, and a permutation vector piv of length m so that A(piv,:) = L*U. If m < n, then L is m-by-m and U is m-by-n.

The LU decompostion with pivoting always exists, even if the matrix is singular, so the constructor will never fail. The primary use of the LU decomposition is in the solution of square systems of simultaneous linear equations. This will fail if isNonsingular() returns false.

Definition at line 36 of file LUDecomposition.h.

Constructor & Destructor Documentation

◆ LUDecomposition()

template<class Real >

bpp::LUDecomposition< Real >::LUDecomposition ( const Matrix< Real > & A )

inline

LU Decomposition.

Parameters

A	Rectangular matrix

Returns: LU Decomposition object to access L, U and piv.

Definition at line 161 of file LUDecomposition.h.

References bpp::LUDecomposition< Real >::LU, bpp::LUDecomposition< Real >::m, bpp::LUDecomposition< Real >::n, and bpp::LUDecomposition< Real >::pivsign.

Member Function Documentation

◆ det()

template<class Real >

Real bpp::LUDecomposition< Real >::det ( ) const

inline

Compute determinant using LU factors.

Returns: determinant of A, or 0 if A is not square.

Definition at line 279 of file LUDecomposition.h.

References bpp::LUDecomposition< Real >::LU, and bpp::LUDecomposition< Real >::n.

◆ getL()

template<class Real >

const RowMatrix<Real>& bpp::LUDecomposition< Real >::getL ( )

inline

Return lower triangular factor.

Returns: L

Definition at line 216 of file LUDecomposition.h.

References bpp::LUDecomposition< Real >::L_, bpp::LUDecomposition< Real >::LU, bpp::LUDecomposition< Real >::m, and bpp::LUDecomposition< Real >::n.

◆ getPivot()

template<class Real >

std::vector<size_t> bpp::LUDecomposition< Real >::getPivot ( ) const

inline

Return pivot permutation vector.

Returns: piv

Definition at line 268 of file LUDecomposition.h.

References bpp::LUDecomposition< Real >::piv.

◆ getU()

template<class Real >

const RowMatrix<Real>& bpp::LUDecomposition< Real >::getU ( )

inline

Return upper triangular factor.

Returns: U portion of LU factorization.

Definition at line 244 of file LUDecomposition.h.

References bpp::LUDecomposition< Real >::LU, bpp::LUDecomposition< Real >::n, and bpp::LUDecomposition< Real >::U_.

◆ permuteCopy() [1/2]

template<class Real >

static void bpp::LUDecomposition< Real >::permuteCopy	(	const Matrix< Real > &	A,
		const std::vector< size_t > &	piv,
		size_t	j0,
		size_t	j1,
		Matrix< Real > &	X
	)

inlinestaticprivate

Definition at line 48 of file LUDecomposition.h.

References bpp::Matrix< Scalar >::resize().

Referenced by bpp::LUDecomposition< Real >::solve().

◆ permuteCopy() [2/2]

template<class Real >

static void bpp::LUDecomposition< Real >::permuteCopy	(	const std::vector< Real > &	A,
		const std::vector< size_t > &	piv,
		std::vector< Real > &	X
	)

inlinestaticprivate

Definition at line 63 of file LUDecomposition.h.

◆ solve() [1/2]

template<class Real >

Real bpp::LUDecomposition< Real >::solve	(	const Matrix< Real > &	B,
		Matrix< Real > &	X
	)		const

inline

Solve A*X = B.

Parameters

B	[in] A Matrix with as many rows as A and any number of columns.
X	[out] A RowMatrix that will be changed such that LUX = B(piv,:).

Returns: the lowest diagonal term (in absolute value), for further checkings of non-singularity of LU.

If B is nonconformant or LU is singular, an Exception is raised.

Definition at line 304 of file LUDecomposition.h.

References bpp::Matrix< Scalar >::getNumberOfColumns(), bpp::Matrix< Scalar >::getNumberOfRows(), bpp::LUDecomposition< Real >::LU, bpp::LUDecomposition< Real >::m, bpp::LUDecomposition< Real >::n, bpp::LUDecomposition< Real >::permuteCopy(), and bpp::NumConstants::SMALL().

◆ solve() [2/2]

template<class Real >

Real bpp::LUDecomposition< Real >::solve	(	const std::vector< Real > &	b,
		std::vector< Real > &	x
	)		const

inline

Solve A*x = b, where x and b are vectors of length equal to the number of rows in A.

Parameters

b	[in] a vector (Array1D> of length equal to the first dimension of A.
x	[out] a vector that will be changed so that so that LUx = b(piv).

Returns: the lowest diagonal term (in absolute value), for further checkings of non-singularity of LU.

If B is nonconformant or LU is singular, an Exception is raised.

Definition at line 378 of file LUDecomposition.h.

References bpp::LUDecomposition< Real >::LU, bpp::LUDecomposition< Real >::m, bpp::LUDecomposition< Real >::n, bpp::LUDecomposition< Real >::permuteCopy(), and bpp::NumConstants::SMALL().

Member Data Documentation

◆ L_

template<class Real >

RowMatrix<Real> bpp::LUDecomposition< Real >::L_

private

Definition at line 41 of file LUDecomposition.h.

Referenced by bpp::LUDecomposition< Real >::getL().

◆ LU

template<class Real >

RowMatrix<Real> bpp::LUDecomposition< Real >::LU

private

Definition at line 40 of file LUDecomposition.h.

Referenced by bpp::LUDecomposition< Real >::det(), bpp::LUDecomposition< Real >::getL(), bpp::LUDecomposition< Real >::getU(), bpp::LUDecomposition< Real >::LUDecomposition(), and bpp::LUDecomposition< Real >::solve().

◆ m

template<class Real >

size_t bpp::LUDecomposition< Real >::m

private

Definition at line 43 of file LUDecomposition.h.

Referenced by bpp::LUDecomposition< Real >::getL(), bpp::LUDecomposition< Real >::LUDecomposition(), and bpp::LUDecomposition< Real >::solve().

◆ n

template<class Real >

size_t bpp::LUDecomposition< Real >::n

private

Definition at line 43 of file LUDecomposition.h.

Referenced by bpp::LUDecomposition< Real >::det(), bpp::LUDecomposition< Real >::getL(), bpp::LUDecomposition< Real >::getU(), bpp::LUDecomposition< Real >::LUDecomposition(), and bpp::LUDecomposition< Real >::solve().

◆ piv

template<class Real >

std::vector<size_t> bpp::LUDecomposition< Real >::piv

private

Definition at line 45 of file LUDecomposition.h.

Referenced by bpp::LUDecomposition< Real >::getPivot().

◆ pivsign

template<class Real >

int bpp::LUDecomposition< Real >::pivsign

private

Definition at line 44 of file LUDecomposition.h.

Referenced by bpp::LUDecomposition< Real >::LUDecomposition().

◆ U_

template<class Real >

RowMatrix<Real> bpp::LUDecomposition< Real >::U_

private

Definition at line 42 of file LUDecomposition.h.

Referenced by bpp::LUDecomposition< Real >::getU().

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

Bpp/Numeric/Matrix/LUDecomposition.h

bpp
LUDecomposition
Generated on Wed Jul 3 2024 10:53:58 for bpp-core3 by 1.8.13