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

bpp-core 2.2.0

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 throw (BadIntegerException, ZeroDivisionException)
	Solve A*X = B. More...

Real	solve (const std::vector< Real > &b, std::vector< Real > &x) const throw (BadIntegerException, ZeroDivisionException)
	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 70 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 195 of file LUDecomposition.h.

References bpp::LUDecomposition< Real >::LU, bpp::LUDecomposition< Real >::m, bpp::LUDecomposition< Real >::n, bpp::LUDecomposition< Real >::piv, 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 313 of file LUDecomposition.h.

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

◆ getL()

template<class Real >

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

inline

Return lower triangular factor.

Returns: L

Definition at line 250 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 302 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 278 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 82 of file LUDecomposition.h.

References bpp::LUDecomposition< Real >::piv, and 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 97 of file LUDecomposition.h.

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

◆ solve() [1/2]

template<class Real >

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

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 338 of file LUDecomposition.h.

References bpp::LUDecomposition< Real >::LU, bpp::LUDecomposition< Real >::m, bpp::LUDecomposition< Real >::n, bpp::LUDecomposition< Real >::permuteCopy(), bpp::LUDecomposition< Real >::piv, 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
throw	(	BadIntegerException,
		ZeroDivisionException
	)

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 412 of file LUDecomposition.h.

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

Member Data Documentation

◆ L_

template<class Real >

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

private

Definition at line 75 of file LUDecomposition.h.

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

◆ LU

template<class Real >

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

private

Definition at line 74 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 77 of file LUDecomposition.h.

Referenced by bpp::LUDecomposition< Real >::det(), 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 77 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 79 of file LUDecomposition.h.

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

◆ pivsign

template<class Real >

int bpp::LUDecomposition< Real >::pivsign

private

Definition at line 78 of file LUDecomposition.h.

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

◆ U_

template<class Real >

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

private

Definition at line 76 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
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