LU Decomposition class.

Decompose a general n x n matrix A into P A = L U

where P is a permutation matrix, L is unit lower triangular and U is upper triangular. L is stored in the strict lower triangular part of the matrix fLU. The diagonal elements of L are unity and are not stored. U is stored in the diagonal and upper triangular part of the matrix fU. P is stored in the index array fIndex : j = fIndex[i] indicates that row j and row i should be swapped .

fSign gives the sign of the permutation, (-1)^n, where n is the number of interchanges in the permutation.

fLU has the same indexing range as matrix A .

The decomposition fails if a diagonal element of abs(fLU) is == 0, The matrix fUL is made invalid .

Definition at line 23 of file TDecompLU.h.

Public Member Functions
	TDecompLU ()
	Default constructor. More...

	TDecompLU (Int_t nrows)
	Constructor for (nrows x nrows) matrix. More...

	TDecompLU (Int_t row_lwb, Int_t row_upb)
	Constructor for ([row_lwb..row_upb] x [row_lwb..row_upb]) matrix. More...

	TDecompLU (const TMatrixD &m, Double_t tol=0.0, Int_t implicit=1)
	Constructor for matrix a. More...

	TDecompLU (const TDecompLU &another)
	Copy constructor. More...

virtual	~TDecompLU ()

virtual Bool_t	Decompose ()
	Matrix A is decomposed in components U and L so that P * A = U * L If the decomposition succeeds, bit kDecomposed is set , otherwise kSingular. More...

virtual void	Det (Double_t &d1, Double_t &d2)
	Calculate determinant det = d1*TMath::Power(2.,d2) More...

const TMatrixD &	GetLU ()

const TMatrixD	GetMatrix ()
	Reconstruct the original matrix using the decomposition parts. More...

virtual Int_t	GetNcols () const

virtual Int_t	GetNrows () const

Bool_t	Invert (TMatrixD &inv)
	For a matrix A(m,m), its inverse A_inv is defined as A * A_inv = A_inv * A = unit (m x m) Ainv is returned . More...

TMatrixD	Invert (Bool_t &status)
	For a matrix A(m,n), its inverse A_inv is defined as A * A_inv = A_inv * A = unit (n x m) Ainv is returned . More...

TMatrixD	Invert ()

TDecompLU &	operator= (const TDecompLU &source)
	assignment operator More...

void	Print (Option_t *opt="") const
	Print internals of this object. More...

virtual void	SetMatrix (const TMatrixD &a)
	Set matrix to be decomposed. More...

virtual Bool_t	Solve (TVectorD &b)
	Solve Ax=b assuming the LU form of A is stored in fLU, but assume b has not been transformed. More...

virtual TVectorD	Solve (const TVectorD &b, Bool_t &ok)

virtual Bool_t	Solve (TMatrixDColumn &b)
	Solve Ax=b assuming the LU form of A is stored in fLU, but assume b has not been transformed. More...

virtual Bool_t	TransSolve (TVectorD &b)
	Solve A^T x=b assuming the LU form of A^T is stored in fLU, but assume b has not been transformed. More...

virtual TVectorD	TransSolve (const TVectorD &b, Bool_t &ok)

virtual Bool_t	TransSolve (TMatrixDColumn &b)
	Solve A^T x=b assuming the LU form of A^T is stored in fLU, but assume b has not been transformed. More...

Public Member Functions inherited from TDecompBase
	TDecompBase ()
	Default constructor. More...

	TDecompBase (const TDecompBase &another)
	Copy constructor. More...

virtual	~TDecompBase ()

virtual Double_t	Condition ()
	Matrix condition number. More...

Int_t	GetColLwb () const

Double_t	GetCondition () const

Double_t	GetDet1 () const

Double_t	GetDet2 () const

Int_t	GetRowLwb () const

Double_t	GetTol () const

virtual Bool_t	MultiSolve (TMatrixD &B)
	Solve set of equations with RHS in columns of B. More...

TDecompBase &	operator= (const TDecompBase &source)
	Assignment operator. More...

void	Print (Option_t *opt="") const
	Print class members. More...

Double_t	SetTol (Double_t tol)

Static Public Member Functions
static Bool_t	InvertLU (TMatrixD &a, Double_t tol, Double_t *det=0)
	Calculate matrix inversion through in place forward/backward substitution. More...

Protected Member Functions
virtual const TMatrixDBase &	GetDecompMatrix () const

Protected Member Functions inherited from TDecompBase
Int_t	Hager (Double_t &est, Int_t iter=5)

void	ResetStatus ()

Static Protected Member Functions
static Bool_t	DecomposeLUCrout (TMatrixD &lu, Int_t *index, Double_t &sign, Double_t tol, Int_t &nrZeros)
	Crout/Doolittle algorithm of LU decomposing a square matrix, with implicit partial pivoting. More...

static Bool_t	DecomposeLUGauss (TMatrixD &lu, Int_t *index, Double_t &sign, Double_t tol, Int_t &nrZeros)
	LU decomposition using Gaussian Elimination with partial pivoting (See Golub & Van Loan, Matrix Computations, Algorithm 3.4.1) of a square matrix . More...

Static Protected Member Functions inherited from TDecompBase
static void	DiagProd (const TVectorD &diag, Double_t tol, Double_t &d1, Double_t &d2)

Protected Attributes
Int_t	fImplicitPivot

Int_t *	fIndex

TMatrixD	fLU

Int_t	fNIndex

Double_t	fSign

Protected Attributes inherited from TDecompBase
Int_t	fColLwb

Double_t	fCondition

Double_t	fDet1

Double_t	fDet2

Int_t	fRowLwb

Double_t	fTol

Additional Inherited Members
Protected Types inherited from TDecompBase
enum	{ kWorkMax = 100 }

enum	EMatrixDecompStat { kInit = BIT(14), kPatternSet = BIT(15), kValuesSet = BIT(16), kMatrixSet = BIT(17), kDecomposed = BIT(18), kDetermined = BIT(19), kCondition = BIT(20), kSingular = BIT(21) }

#include <TDecompLU.h>

Inheritance diagram for TDecompLU:

[legend]

Constructor & Destructor Documentation

◆ TDecompLU() [1/5]

TDecompLU::TDecompLU ( )

Default constructor.

Definition at line 45 of file TDecompLU.cxx.

◆ TDecompLU() [2/5]

TDecompLU::TDecompLU ( Int_t nrows )

explicit

Constructor for (nrows x nrows) matrix.

Definition at line 56 of file TDecompLU.cxx.

◆ TDecompLU() [3/5]

TDecompLU::TDecompLU	(	Int_t	row_lwb,
		Int_t	row_upb
	)

Constructor for ([row_lwb..row_upb] x [row_lwb..row_upb]) matrix.

Definition at line 69 of file TDecompLU.cxx.

◆ TDecompLU() [4/5]

TDecompLU::TDecompLU	(	const TMatrixD &	m,
		Double_t	tol = `0.0`,
		Int_t	implicit = `1`
	)

Constructor for matrix a.

Definition at line 85 of file TDecompLU.cxx.

◆ TDecompLU() [5/5]

TDecompLU::TDecompLU ( const TDecompLU & another )

Copy constructor.

Definition at line 115 of file TDecompLU.cxx.

◆ ~TDecompLU()

virtual TDecompLU::~TDecompLU ( )

inlinevirtual

Definition at line 47 of file TDecompLU.h.

Member Function Documentation

◆ Decompose()

Bool_t TDecompLU::Decompose ( )

virtual

Matrix A is decomposed in components U and L so that P * A = U * L If the decomposition succeeds, bit kDecomposed is set , otherwise kSingular.

Implements TDecompBase.

Definition at line 126 of file TDecompLU.cxx.

◆ DecomposeLUCrout()

Bool_t TDecompLU::DecomposeLUCrout	(	TMatrixD &	lu,
		Int_t *	index,
		Double_t &	sign,
		Double_t	tol,
		Int_t &	nrZeros
	)

staticprotected

Crout/Doolittle algorithm of LU decomposing a square matrix, with implicit partial pivoting.

The decomposition is stored in fLU: U is explicit in the upper triag and L is in multiplier form in the subdiagionals . Row permutations are mapped out in fIndex. fSign, used for calculating the determinant, is +/- 1 for even/odd row permutations. .

Definition at line 599 of file TDecompLU.cxx.

◆ DecomposeLUGauss()

Bool_t TDecompLU::DecomposeLUGauss	(	TMatrixD &	lu,
		Int_t *	index,
		Double_t &	sign,
		Double_t	tol,
		Int_t &	nrZeros
	)

staticprotected

LU decomposition using Gaussian Elimination with partial pivoting (See Golub & Van Loan, Matrix Computations, Algorithm 3.4.1) of a square matrix .

The decomposition is stored in fLU: U is explicit in the upper triag and L is in multiplier form in the subdiagionals . Row permutations are mapped out in fIndex. fSign, used for calculating the determinant, is +/- 1 for even/odd row permutations. Since this algorithm uses partial pivoting without scaling like in Crout/Doolitle. it is somewhat faster but less precise .

Definition at line 708 of file TDecompLU.cxx.

◆ Det()

void TDecompLU::Det	(	Double_t &	d1,
		Double_t &	d2
	)

virtual

Calculate determinant det = d1*TMath::Power(2.,d2)

Reimplemented from TDecompBase.

Definition at line 509 of file TDecompLU.cxx.

◆ GetDecompMatrix()

virtual const TMatrixDBase& TDecompLU::GetDecompMatrix ( ) const

inlineprotectedvirtual

Implements TDecompBase.

Definition at line 38 of file TDecompLU.h.

◆ GetLU()

const TMatrixD& TDecompLU::GetLU ( )

inline

Definition at line 52 of file TDecompLU.h.

◆ GetMatrix()

const TMatrixD TDecompLU::GetMatrix ( )

Reconstruct the original matrix using the decomposition parts.

Definition at line 151 of file TDecompLU.cxx.

◆ GetNcols()

virtual Int_t TDecompLU::GetNcols ( ) const

inlinevirtual

Implements TDecompBase.

Definition at line 51 of file TDecompLU.h.

◆ GetNrows()

virtual Int_t TDecompLU::GetNrows ( ) const

inlinevirtual

Implements TDecompBase.

Definition at line 50 of file TDecompLU.h.

◆ Invert() [1/3]

Bool_t TDecompLU::Invert ( TMatrixD & inv )

For a matrix A(m,m), its inverse A_inv is defined as A * A_inv = A_inv * A = unit (m x m) Ainv is returned .

Definition at line 526 of file TDecompLU.cxx.

◆ Invert() [2/3]

TMatrixD TDecompLU::Invert ( Bool_t & status )

For a matrix A(m,n), its inverse A_inv is defined as A * A_inv = A_inv * A = unit (n x m) Ainv is returned .

Definition at line 544 of file TDecompLU.cxx.

◆ Invert() [3/3]

TMatrixD TDecompLU::Invert ( )

inline

Definition at line 69 of file TDecompLU.h.

◆ InvertLU()

Bool_t TDecompLU::InvertLU	(	TMatrixD &	a,
		Double_t	tol,
		Double_t *	det = `0`
	)

static

Calculate matrix inversion through in place forward/backward substitution.

Definition at line 775 of file TDecompLU.cxx.

◆ operator=()

TDecompLU & TDecompLU::operator= ( const TDecompLU & source )

assignment operator

Definition at line 573 of file TDecompLU.cxx.

◆ Print()

void TDecompLU::Print ( Option_t * opt = "" ) const

Print internals of this object.

Definition at line 559 of file TDecompLU.cxx.

◆ SetMatrix()

void TDecompLU::SetMatrix ( const TMatrixD & a )

virtual

Set matrix to be decomposed.

Definition at line 202 of file TDecompLU.cxx.

◆ Solve() [1/3]

Bool_t TDecompLU::Solve ( TVectorD & b )

virtual

Solve Ax=b assuming the LU form of A is stored in fLU, but assume b has not been transformed.

Solution returned in b.

Implements TDecompBase.

Definition at line 233 of file TDecompLU.cxx.

◆ Solve() [2/3]

virtual TVectorD TDecompLU::Solve	(	const TVectorD &	b,
		Bool_t &	ok
	)

inlinevirtual

Implements TDecompBase.

Definition at line 59 of file TDecompLU.h.

◆ Solve() [3/3]

Bool_t TDecompLU::Solve ( TMatrixDColumn & cb )

virtual

Solve Ax=b assuming the LU form of A is stored in fLU, but assume b has not been transformed.

Solution returned in b.

Implements TDecompBase.

Definition at line 299 of file TDecompLU.cxx.

◆ TransSolve() [1/3]

Bool_t TDecompLU::TransSolve ( TVectorD & b )

virtual

Solve A^T x=b assuming the LU form of A^T is stored in fLU, but assume b has not been transformed.

Solution returned in b.

Implements TDecompBase.

Definition at line 371 of file TDecompLU.cxx.

◆ TransSolve() [2/3]

virtual TVectorD TDecompLU::TransSolve	(	const TVectorD &	b,
		Bool_t &	ok
	)

inlinevirtual

Implements TDecompBase.

Definition at line 62 of file TDecompLU.h.

◆ TransSolve() [3/3]

Bool_t TDecompLU::TransSolve ( TMatrixDColumn & cb )

virtual

Solve A^T x=b assuming the LU form of A^T is stored in fLU, but assume b has not been transformed.

Solution returned in b.

Implements TDecompBase.

Definition at line 440 of file TDecompLU.cxx.

Member Data Documentation

◆ fImplicitPivot

Int_t TDecompLU::fImplicitPivot

protected

Definition at line 27 of file TDecompLU.h.

◆ fIndex

Int_t* TDecompLU::fIndex

protected

Definition at line 30 of file TDecompLU.h.

◆ fLU

TMatrixD TDecompLU::fLU

protected

Definition at line 32 of file TDecompLU.h.

◆ fNIndex

Int_t TDecompLU::fNIndex

protected

Definition at line 29 of file TDecompLU.h.

◆ fSign

Double_t TDecompLU::fSign

protected

Definition at line 31 of file TDecompLU.h.

Libraries for TDecompLU:

[legend]

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

math/matrix/inc/TDecompLU.h
math/matrix/src/TDecompLU.cxx

Public Member Functions

Static Public Member Functions

Protected Member Functions

Static Protected Member Functions

Protected Attributes

Additional Inherited Members

Constructor & Destructor Documentation

◆ TDecompLU() [1/5]

◆ TDecompLU() [2/5]

◆ TDecompLU() [3/5]

◆ TDecompLU() [4/5]

◆ TDecompLU() [5/5]

◆ ~TDecompLU()

Member Function Documentation

◆ Decompose()

◆ DecomposeLUCrout()

◆ DecomposeLUGauss()

◆ Det()

◆ GetDecompMatrix()

◆ GetLU()

◆ GetMatrix()

◆ GetNcols()

◆ GetNrows()

◆ Invert() [1/3]

◆ Invert() [2/3]

◆ Invert() [3/3]

◆ InvertLU()

◆ operator=()

◆ Print()

◆ SetMatrix()

◆ Solve() [1/3]

◆ Solve() [2/3]

◆ Solve() [3/3]

◆ TransSolve() [1/3]

◆ TransSolve() [2/3]

◆ TransSolve() [3/3]

Member Data Documentation

◆ fImplicitPivot

◆ fIndex

◆ fLU

◆ fNIndex

◆ fSign