The Bunch-Kaufman diagonal pivoting method decomposes a real symmetric matrix A using.

A = U*D*U^T

where U is a product of permutation and unit upper triangular matrices, U^T is the transpose of U, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.

U = P(n-1)*U(n-1)* ... P(k)U(k) ..., i.e., U is a product of terms P(k)*U(k), where k decreases from n-1 to 0 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as defined by IPIV(k), and U(k) is a unit upper triangular matrix, such that if the diagonal block D(k) is of order s (s = 1 or 2), then

        (   I    v    0   )   k-s
U(k) =  (   0    I    0   )   s
        (   0    0    I   )   n-k
           k-s   s   n-k

If s = 1, D(k) overwrites A(k,k), and v overwrites A(0:k-1,k). If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k), and A(k,k), and v overwrites A(0:k-2,k-1:k).

fU contains on entry the symmetric matrix A of which only the upper triangular part is referenced . On exit fU contains the block diagonal matrix D and the multipliers used to obtain the factor U, see above .

fIpiv if dimension n contains details of the interchanges and the the block structure of D . If (fIPiv(k) > 0, then rows and columns k and fIPiv(k) were interchanged and D(k,k) is a 1-by-1 diagonal block. If IPiv(k) = fIPiv(k-1) < 0, rows and columns k-1 and -IPiv(k) were interchanged and D(k-1:k,k-1:k) is a 2-by-2 diagonal block.

Definition at line 26 of file TDecompBK.h.

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

	TDecompBK (Int_t nrows)
	Constructor for (nrows x nrows) symmetric matrix. More...

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

	TDecompBK (const TMatrixDSym &m, Double_t tol=0.0)
	Constructor for symmetric matrix A. More...

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

virtual	~TDecompBK ()

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

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

virtual Int_t	GetNcols () const

virtual Int_t	GetNrows () const

const TMatrixD &	GetU ()

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 ()

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

void	Print (Option_t *opt="") const
	Print the 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 Ax=b assuming the BK form of A is stored in fU . Solution returned in b. More...

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

virtual Bool_t	Solve (TMatrixDColumn &b)
	Solve Ax=b assuming the BK form of A is stored in fU . Solution returned in b. 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
Int_t *	fIpiv

Int_t	fNIpiv

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 <TDecompBK.h>

Inheritance diagram for TDecompBK:

[legend]

Constructor & Destructor Documentation

◆ TDecompBK() [1/5]

TDecompBK::TDecompBK ( )

Default constructor.

Definition at line 64 of file TDecompBK.cxx.

◆ TDecompBK() [2/5]

TDecompBK::TDecompBK ( Int_t nrows )

explicit

Constructor for (nrows x nrows) symmetric matrix.

Definition at line 73 of file TDecompBK.cxx.

◆ TDecompBK() [3/5]

TDecompBK::TDecompBK	(	Int_t	row_lwb,
		Int_t	row_upb
	)

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

Definition at line 84 of file TDecompBK.cxx.

◆ TDecompBK() [4/5]

TDecompBK::TDecompBK	(	const TMatrixDSym &	m,
		Double_t	tol = `0.0`
	)

Constructor for symmetric matrix A.

Definition at line 97 of file TDecompBK.cxx.

◆ TDecompBK() [5/5]

TDecompBK::TDecompBK ( const TDecompBK & another )

Copy constructor.

Definition at line 120 of file TDecompBK.cxx.

◆ ~TDecompBK()

virtual TDecompBK::~TDecompBK ( )

inlinevirtual

Definition at line 43 of file TDecompBK.h.

Member Function Documentation

◆ Decompose()

Bool_t TDecompBK::Decompose ( )

virtual

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

Implements TDecompBase.

Definition at line 131 of file TDecompBK.cxx.

◆ Det()

virtual void TDecompBK::Det	(	Double_t &	d1,
		Double_t &	d2
	)

inlinevirtual

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

Reimplemented from TDecompBase.

Definition at line 59 of file TDecompBK.h.

◆ GetDecompMatrix()

virtual const TMatrixDBase& TDecompBK::GetDecompMatrix ( ) const

inlineprotectedvirtual

Implements TDecompBase.

Definition at line 34 of file TDecompBK.h.

◆ GetNcols()

virtual Int_t TDecompBK::GetNcols ( ) const

inlinevirtual

Implements TDecompBase.

Definition at line 46 of file TDecompBK.h.

◆ GetNrows()

virtual Int_t TDecompBK::GetNrows ( ) const

inlinevirtual

Implements TDecompBase.

Definition at line 45 of file TDecompBK.h.

◆ GetU()

const TMatrixD& TDecompBK::GetU ( )

inline

Definition at line 47 of file TDecompBK.h.

◆ Invert() [1/3]

Bool_t TDecompBK::Invert ( TMatrixDSym & inv )

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

Definition at line 610 of file TDecompBK.cxx.

◆ Invert() [2/3]

TMatrixDSym TDecompBK::Invert ( Bool_t & status )

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

Definition at line 633 of file TDecompBK.cxx.

◆ Invert() [3/3]

TMatrixDSym TDecompBK::Invert ( )

inline

Definition at line 64 of file TDecompBK.h.

◆ operator=()

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

Assignment operator.

Definition at line 660 of file TDecompBK.cxx.

◆ Print()

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

Print the class members.

Definition at line 648 of file TDecompBK.cxx.

◆ SetMatrix()

void TDecompBK::SetMatrix ( const TMatrixDSym & a )

virtual

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

Definition at line 314 of file TDecompBK.cxx.

◆ Solve() [1/3]

Bool_t TDecompBK::Solve ( TVectorD & b )

virtual

Solve Ax=b assuming the BK form of A is stored in fU . Solution returned in b.

Implements TDecompBase.

Definition at line 339 of file TDecompBK.cxx.

◆ Solve() [2/3]

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

inlinevirtual

Implements TDecompBase.

Definition at line 54 of file TDecompBK.h.

◆ Solve() [3/3]

Bool_t TDecompBK::Solve ( TMatrixDColumn & b )

virtual

Solve Ax=b assuming the BK form of A is stored in fU . Solution returned in b.

Implements TDecompBase.

Definition at line 473 of file TDecompBK.cxx.

◆ TransSolve() [1/3]

virtual Bool_t TDecompBK::TransSolve ( TVectorD & b )

inlinevirtual

Implements TDecompBase.

Definition at line 56 of file TDecompBK.h.

◆ TransSolve() [2/3]

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

inlinevirtual

Implements TDecompBase.

Definition at line 57 of file TDecompBK.h.

◆ TransSolve() [3/3]

virtual Bool_t TDecompBK::TransSolve ( TMatrixDColumn & b )

inlinevirtual

Implements TDecompBase.

Definition at line 58 of file TDecompBK.h.

Member Data Documentation

◆ fIpiv

Int_t* TDecompBK::fIpiv

protected

Definition at line 31 of file TDecompBK.h.

◆ fNIpiv

Int_t TDecompBK::fNIpiv

protected

Definition at line 30 of file TDecompBK.h.

◆ fU

TMatrixD TDecompBK::fU

protected

Definition at line 32 of file TDecompBK.h.

Libraries for TDecompBK:

[legend]

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

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

Public Member Functions

Protected Member Functions

Protected Attributes

Additional Inherited Members

Constructor & Destructor Documentation

◆ TDecompBK() [1/5]

◆ TDecompBK() [2/5]

◆ TDecompBK() [3/5]

◆ TDecompBK() [4/5]

◆ TDecompBK() [5/5]

◆ ~TDecompBK()

Member Function Documentation

◆ Decompose()

◆ Det()

◆ GetDecompMatrix()

◆ 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

◆ fIpiv

◆ fNIpiv

◆ fU