Cholesky Decomposition class.

Decompose a symmetric, positive definite matrix A = U^T * U

where U is a upper triangular matrix

The decomposition fails if a diagonal element of fU is <= 0, the matrix is not positive negative . The matrix fU is made invalid .

fU has the same index range as A .

Definition at line 24 of file TDecompChol.h.

Public Member Functions
	TDecompChol ()

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

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

	TDecompChol (const TMatrixDSym &a, Double_t tol=0.0)
	Constructor for symmetric matrix A . Matrix should be positive definite. More...

	TDecompChol (const TMatrixD &a, Double_t tol=0.0)
	Constructor for general matrix A . Matrix should be symmetric positive definite. More...

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

virtual	~TDecompChol ()

virtual Bool_t	Decompose ()
	Matrix A is decomposed in component U so that A = U^T * U If the decomposition succeeds, bit kDecomposed is set , otherwise kSingular. More...

virtual void	Det (Double_t &d1, Double_t &d2)
	Matrix determinant det = d1*TMath::Power(2.,d2) is square of diagProd of cholesky factor. More...

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

virtual Int_t	GetNcols () const

virtual Int_t	GetNrows () const

const TMatrixD &	GetU () const

Bool_t	Invert (TMatrixDSym &inv)
	For a symmetric matrix A(m,m), its inverse A_inv(m,m) is returned . More...

TMatrixDSym	Invert (Bool_t &status)
	For a symmetric matrix A(m,m), its inverse A_inv(m,m) is returned . More...

TMatrixDSym	Invert ()

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

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

virtual void	SetMatrix (const TMatrixDSym &a)
	Set the matrix to be decomposed, decomposition status is reset. More...

virtual Bool_t	Solve (TVectorD &b)
	Solve equations Ax=b assuming A has been factored by Cholesky. More...

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

virtual Bool_t	Solve (TMatrixDColumn &b)
	Solve equations Ax=b assuming A has been factored by Cholesky. More...

virtual Bool_t	TransSolve (TVectorD &b)

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

virtual Bool_t	TransSolve (TMatrixDColumn &b)

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)

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 ()

Protected Attributes
TMatrixD	fU

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) }

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

#include <TDecompChol.h>

Inheritance diagram for TDecompChol:

[legend]

Constructor & Destructor Documentation

◆ TDecompChol() [1/6]

TDecompChol::TDecompChol ( )

inline

Definition at line 34 of file TDecompChol.h.

◆ TDecompChol() [2/6]

TDecompChol::TDecompChol ( Int_t nrows )

explicit

Constructor for (nrows x nrows) matrix.

Definition at line 35 of file TDecompChol.cxx.

◆ TDecompChol() [3/6]

TDecompChol::TDecompChol	(	Int_t	row_lwb,
		Int_t	row_upb
	)

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

Definition at line 43 of file TDecompChol.cxx.

◆ TDecompChol() [4/6]

TDecompChol::TDecompChol	(	const TMatrixDSym &	a,
		Double_t	tol = `0.0`
	)

Constructor for symmetric matrix A . Matrix should be positive definite.

Definition at line 54 of file TDecompChol.cxx.

◆ TDecompChol() [5/6]

TDecompChol::TDecompChol	(	const TMatrixD &	a,
		Double_t	tol = `0.0`
	)

Constructor for general matrix A . Matrix should be symmetric positive definite.

Definition at line 73 of file TDecompChol.cxx.

◆ TDecompChol() [6/6]

TDecompChol::TDecompChol ( const TDecompChol & another )

Copy constructor.

Definition at line 97 of file TDecompChol.cxx.

◆ ~TDecompChol()

virtual TDecompChol::~TDecompChol ( )

inlinevirtual

Definition at line 40 of file TDecompChol.h.

Member Function Documentation

◆ Decompose()

Bool_t TDecompChol::Decompose ( )

virtual

Matrix A is decomposed in component U so that A = U^T * U If the decomposition succeeds, bit kDecomposed is set , otherwise kSingular.

Implements TDecompBase.

Definition at line 106 of file TDecompChol.cxx.

◆ Det()

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

virtual

Matrix determinant det = d1*TMath::Power(2.,d2) is square of diagProd of cholesky factor.

Reimplemented from TDecompBase.

Definition at line 323 of file TDecompChol.cxx.

◆ GetDecompMatrix()

virtual const TMatrixDBase& TDecompChol::GetDecompMatrix ( ) const

inlineprotectedvirtual

Implements TDecompBase.

Definition at line 30 of file TDecompChol.h.

◆ GetMatrix()

const TMatrixDSym TDecompChol::GetMatrix ( )

Reconstruct the original matrix using the decomposition parts.

Definition at line 160 of file TDecompChol.cxx.

◆ GetNcols()

virtual Int_t TDecompChol::GetNcols ( ) const

inlinevirtual

Implements TDecompBase.

Definition at line 44 of file TDecompChol.h.

◆ GetNrows()

virtual Int_t TDecompChol::GetNrows ( ) const

inlinevirtual

Implements TDecompBase.

Definition at line 43 of file TDecompChol.h.

◆ GetU()

const TMatrixD& TDecompChol::GetU ( ) const

inline

Definition at line 45 of file TDecompChol.h.

◆ Invert() [1/3]

Bool_t TDecompChol::Invert ( TMatrixDSym & inv )

For a symmetric matrix A(m,m), its inverse A_inv(m,m) is returned .

Definition at line 341 of file TDecompChol.cxx.

◆ Invert() [2/3]

TMatrixDSym TDecompChol::Invert ( Bool_t & status )

For a symmetric matrix A(m,m), its inverse A_inv(m,m) is returned .

Definition at line 364 of file TDecompChol.cxx.

◆ Invert() [3/3]

TMatrixDSym TDecompChol::Invert ( )

inline

Definition at line 60 of file TDecompChol.h.

◆ operator=()

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

Assignment operator.

Definition at line 388 of file TDecompChol.cxx.

◆ Print()

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

Print class members .

Definition at line 379 of file TDecompChol.cxx.

◆ SetMatrix()

void TDecompChol::SetMatrix ( const TMatrixDSym & a )

virtual

Set the matrix to be decomposed, decomposition status is reset.

Definition at line 179 of file TDecompChol.cxx.

◆ Solve() [1/3]

Bool_t TDecompChol::Solve ( TVectorD & b )

virtual

Solve equations Ax=b assuming A has been factored by Cholesky.

The factor U is assumed to be in upper triang of fU. fTol is used to determine if diagonal element is zero. The solution is returned in b.

Implements TDecompBase.

Definition at line 203 of file TDecompChol.cxx.

◆ Solve() [2/3]

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

inlinevirtual

Implements TDecompBase.

Definition at line 51 of file TDecompChol.h.

◆ Solve() [3/3]

Bool_t TDecompChol::Solve ( TMatrixDColumn & cb )

virtual

Solve equations Ax=b assuming A has been factored by Cholesky.

The factor U is assumed to be in upper triang of fU. fTol is used to determine if diagonal element is zero. The solution is returned in b.

Implements TDecompBase.

Definition at line 261 of file TDecompChol.cxx.

◆ TransSolve() [1/3]

virtual Bool_t TDecompChol::TransSolve ( TVectorD & b )

inlinevirtual

Implements TDecompBase.

Definition at line 53 of file TDecompChol.h.

◆ TransSolve() [2/3]

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

inlinevirtual

Implements TDecompBase.

Definition at line 54 of file TDecompChol.h.

◆ TransSolve() [3/3]

virtual Bool_t TDecompChol::TransSolve ( TMatrixDColumn & b )

inlinevirtual

Implements TDecompBase.

Definition at line 55 of file TDecompChol.h.

Member Data Documentation

◆ fU

TMatrixD TDecompChol::fU

protected

Definition at line 28 of file TDecompChol.h.

Libraries for TDecompChol:

[legend]

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

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

Public Member Functions

Protected Member Functions

Protected Attributes

Additional Inherited Members

Constructor & Destructor Documentation

◆ TDecompChol() [1/6]

◆ TDecompChol() [2/6]

◆ TDecompChol() [3/6]

◆ TDecompChol() [4/6]

◆ TDecompChol() [5/6]

◆ TDecompChol() [6/6]

◆ ~TDecompChol()

Member Function Documentation

◆ Decompose()

◆ Det()

◆ GetDecompMatrix()

◆ GetMatrix()

◆ GetNcols()

◆ GetNrows()

◆ GetU()

◆ Invert() [1/3]

◆ Invert() [2/3]

◆ Invert() [3/3]

◆ operator=()

◆ Print()

◆ SetMatrix()

◆ Solve() [1/3]

◆ Solve() [2/3]

◆ Solve() [3/3]

◆ TransSolve() [1/3]

◆ TransSolve() [2/3]

◆ TransSolve() [3/3]

Member Data Documentation

◆ fU