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

A = U*D*U^T

static double A[]

ROOT::Math::Chebyshev::T

double T(double x)

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

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

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 ()

TMatrixDSym	Invert ()

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

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

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 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	Solve (TVectorD &b)
	Solve Ax=b assuming the BK form of A is stored in fU . Solution returned in b. More...

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

virtual Bool_t	TransSolve (TMatrixDColumn &b)

virtual Bool_t	TransSolve (TVectorD &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...

virtual Bool_t	Decompose ()=0

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

Int_t	GetColLwb () const

Double_t	GetCondition () const

Double_t	GetDet1 () const

Double_t	GetDet2 () const

virtual Int_t	GetNcols () const =0

virtual Int_t	GetNrows () const =0

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)

virtual TVectorD	Solve (const TVectorD &b, Bool_t &ok)=0

virtual Bool_t	Solve (TMatrixDColumn &b)=0

virtual Bool_t	Solve (TVectorD &b)=0

virtual TVectorD	TransSolve (const TVectorD &b, Bool_t &ok)=0

virtual Bool_t	TransSolve (TMatrixDColumn &b)=0

virtual Bool_t	TransSolve (TVectorD &b)=0

Public Member Functions inherited from TObject
	TObject ()
	TObject constructor. More...

	TObject (const TObject &object)
	TObject copy ctor. More...

virtual	~TObject ()
	TObject destructor. More...

void	AbstractMethod (const char *method) const
	Use this method to implement an "abstract" method that you don't want to leave purely abstract. More...

virtual void	AppendPad (Option_t *option="")
	Append graphics object to current pad. More...

virtual void	Browse (TBrowser *b)
	Browse object. May be overridden for another default action. More...

ULong_t	CheckedHash ()
	Check and record whether this class has a consistent Hash/RecursiveRemove setup (*) and then return the regular Hash value for this object. More...

virtual const char *	ClassName () const
	Returns name of class to which the object belongs. More...

virtual void	Clear (Option_t *="")

virtual TObject *	Clone (const char *newname="") const
	Make a clone of an object using the Streamer facility. More...

virtual Int_t	Compare (const TObject *obj) const
	Compare abstract method. More...

virtual void	Copy (TObject &object) const
	Copy this to obj. More...

virtual void	Delete (Option_t *option="")
	Delete this object. More...

virtual Int_t	DistancetoPrimitive (Int_t px, Int_t py)
	Computes distance from point (px,py) to the object. More...

virtual void	Draw (Option_t *option="")
	Default Draw method for all objects. More...

virtual void	DrawClass () const
	Draw class inheritance tree of the class to which this object belongs. More...

virtual TObject *	DrawClone (Option_t *option="") const
	Draw a clone of this object in the current selected pad for instance with: `gROOT->SetSelectedPad(gPad)`. More...

virtual void	Dump () const
	Dump contents of object on stdout. More...

virtual void	Error (const char method, const char msgfmt,...) const
	Issue error message. More...

virtual void	Execute (const char method, const char params, Int_t *error=0)
	Execute method on this object with the given parameter string, e.g. More...

virtual void	Execute (TMethod method, TObjArray params, Int_t *error=0)
	Execute method on this object with parameters stored in the TObjArray. More...

virtual void	ExecuteEvent (Int_t event, Int_t px, Int_t py)
	Execute action corresponding to an event at (px,py). More...

virtual void	Fatal (const char method, const char msgfmt,...) const
	Issue fatal error message. More...

virtual TObject *	FindObject (const char *name) const
	Must be redefined in derived classes. More...

virtual TObject *	FindObject (const TObject *obj) const
	Must be redefined in derived classes. More...

virtual Option_t *	GetDrawOption () const
	Get option used by the graphics system to draw this object. More...

virtual const char *	GetIconName () const
	Returns mime type name of object. More...

virtual const char *	GetName () const
	Returns name of object. More...

virtual char *	GetObjectInfo (Int_t px, Int_t py) const
	Returns string containing info about the object at position (px,py). More...

virtual Option_t *	GetOption () const

virtual const char *	GetTitle () const
	Returns title of object. More...

virtual UInt_t	GetUniqueID () const
	Return the unique object id. More...

virtual Bool_t	HandleTimer (TTimer *timer)
	Execute action in response of a timer timing out. More...

virtual ULong_t	Hash () const
	Return hash value for this object. More...

Bool_t	HasInconsistentHash () const
	Return true is the type of this object is known to have an inconsistent setup for Hash and RecursiveRemove (i.e. More...

virtual void	Info (const char method, const char msgfmt,...) const
	Issue info message. More...

virtual Bool_t	InheritsFrom (const char *classname) const
	Returns kTRUE if object inherits from class "classname". More...

virtual Bool_t	InheritsFrom (const TClass *cl) const
	Returns kTRUE if object inherits from TClass cl. More...

virtual void	Inspect () const
	Dump contents of this object in a graphics canvas. More...

void	InvertBit (UInt_t f)

virtual Bool_t	IsEqual (const TObject *obj) const
	Default equal comparison (objects are equal if they have the same address in memory). More...

virtual Bool_t	IsFolder () const
	Returns kTRUE in case object contains browsable objects (like containers or lists of other objects). More...

R__ALWAYS_INLINE Bool_t	IsOnHeap () const

virtual Bool_t	IsSortable () const

R__ALWAYS_INLINE Bool_t	IsZombie () const

virtual void	ls (Option_t *option="") const
	The ls function lists the contents of a class on stdout. More...

void	MayNotUse (const char *method) const
	Use this method to signal that a method (defined in a base class) may not be called in a derived class (in principle against good design since a child class should not provide less functionality than its parent, however, sometimes it is necessary). More...

virtual Bool_t	Notify ()
	This method must be overridden to handle object notification. More...

void	Obsolete (const char method, const char asOfVers, const char *removedFromVers) const
	Use this method to declare a method obsolete. More...

void	operator delete (void *ptr)
	Operator delete. More...

void	operator delete[] (void *ptr)
	Operator delete []. More...

void *	operator new (size_t sz)

void *	operator new (size_t sz, void *vp)

void *	operator new[] (size_t sz)

void *	operator new[] (size_t sz, void *vp)

TObject &	operator= (const TObject &rhs)
	TObject assignment operator. More...

virtual void	Paint (Option_t *option="")
	This method must be overridden if a class wants to paint itself. More...

virtual void	Pop ()
	Pop on object drawn in a pad to the top of the display list. More...

virtual void	Print (Option_t *option="") const
	This method must be overridden when a class wants to print itself. More...

virtual Int_t	Read (const char *name)
	Read contents of object with specified name from the current directory. More...

virtual void	RecursiveRemove (TObject *obj)
	Recursively remove this object from a list. More...

void	ResetBit (UInt_t f)

virtual void	SaveAs (const char filename="", Option_t option="") const
	Save this object in the file specified by filename. More...

virtual void	SavePrimitive (std::ostream &out, Option_t *option="")
	Save a primitive as a C++ statement(s) on output stream "out". More...

void	SetBit (UInt_t f)

void	SetBit (UInt_t f, Bool_t set)
	Set or unset the user status bits as specified in f. More...

virtual void	SetDrawOption (Option_t *option="")
	Set drawing option for object. More...

virtual void	SetUniqueID (UInt_t uid)
	Set the unique object id. More...

virtual void	SysError (const char method, const char msgfmt,...) const
	Issue system error message. More...

R__ALWAYS_INLINE Bool_t	TestBit (UInt_t f) const

Int_t	TestBits (UInt_t f) const

virtual void	UseCurrentStyle ()
	Set current style settings in this object This function is called when either TCanvas::UseCurrentStyle or TROOT::ForceStyle have been invoked. More...

virtual void	Warning (const char method, const char msgfmt,...) const
	Issue warning message. More...

virtual Int_t	Write (const char *name=0, Int_t option=0, Int_t bufsize=0)
	Write this object to the current directory. More...

virtual Int_t	Write (const char *name=0, Int_t option=0, Int_t bufsize=0) const
	Write this object to the current directory. More...

Protected Member Functions
virtual const TMatrixDBase &	GetDecompMatrix () const

Protected Member Functions inherited from TDecompBase
virtual const TMatrixDBase &	GetDecompMatrix () const =0

Int_t	Hager (Double_t &est, Int_t iter=5)

void	ResetStatus ()

Protected Member Functions inherited from TObject
virtual void	DoError (int level, const char location, const char fmt, va_list va) const
	Interface to ErrorHandler (protected). More...

void	MakeZombie ()

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
Public Types inherited from TObject
enum	{ kIsOnHeap = 0x01000000 , kNotDeleted = 0x02000000 , kZombie = 0x04000000 , kInconsistent = 0x08000000 , kBitMask = 0x00ffffff }

enum	{ kSingleKey = BIT(0) , kOverwrite = BIT(1) , kWriteDelete = BIT(2) }

enum	EDeprecatedStatusBits { kObjInCanvas = BIT(3) }

enum	EStatusBits { kCanDelete = BIT(0) , kMustCleanup = BIT(3) , kIsReferenced = BIT(4) , kHasUUID = BIT(5) , kCannotPick = BIT(6) , kNoContextMenu = BIT(8) , kInvalidObject = BIT(13) }

Static Public Member Functions inherited from TObject
static Long_t	GetDtorOnly ()
	Return destructor only flag. More...

static Bool_t	GetObjectStat ()
	Get status of object stat flag. More...

static void	SetDtorOnly (void *obj)
	Set destructor only flag. More...

static void	SetObjectStat (Bool_t stat)
	Turn on/off tracking of objects in the TObjectTable. More...

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]

TMatrixDSym TDecompBK::Invert ( )

inline

Definition at line 64 of file TDecompBK.h.

◆ 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]

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.

◆ 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

virtual

Print the class members.

Reimplemented from TDecompBase.

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]

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

inlinevirtual

Implements TDecompBase.

Definition at line 54 of file TDecompBK.h.

◆ Solve() [2/3]

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.

◆ Solve() [3/3]

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.

◆ TransSolve() [1/3]

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

inlinevirtual

Implements TDecompBase.

Definition at line 57 of file TDecompBK.h.

◆ TransSolve() [2/3]

virtual Bool_t TDecompBK::TransSolve ( TMatrixDColumn & b )

inlinevirtual

Implements TDecompBase.

Definition at line 58 of file TDecompBK.h.

◆ TransSolve() [3/3]

virtual Bool_t TDecompBK::TransSolve ( TVectorD & b )

inlinevirtual

Implements TDecompBase.

Definition at line 56 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]

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