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 (const TDecompChol &another)
	Copy constructor.

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

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

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

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

	~TDecompChol () override

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

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

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

Int_t	GetNcols () const override

Int_t	GetNrows () const override

const TMatrixD &	GetU () const

TMatrixDSym	Invert ()

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

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

TClass *	IsA () const override

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

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

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

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

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

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

void	Streamer (TBuffer &) override
	Stream an object of class TObject.

void	StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b)

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

Bool_t	TransSolve (TMatrixDColumn &b) override

Bool_t	TransSolve (TVectorD &b) override

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

	TDecompBase (const TDecompBase &another)
	Copy constructor.

	~TDecompBase () override

virtual Double_t	Condition ()
	Matrix condition number.

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.

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

Double_t	SetTol (Double_t tol)

void	StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b)

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

	TObject (const TObject &object)
	TObject copy ctor.

virtual	~TObject ()
	TObject destructor.

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

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

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

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.

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

virtual void	Clear (Option_t *="")

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

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

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

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

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

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

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

virtual TObject *	DrawClone (Option_t *option="") const
	Draw a clone of this object in the current selected pad with: `gROOT->SetSelectedPad(c1)`.

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

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

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

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

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

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

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

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

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

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

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

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

virtual Option_t *	GetOption () const

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

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

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

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

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.

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

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

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

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

void	InvertBit (UInt_t f)

Bool_t	IsDestructed () const
	IsDestructed.

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

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

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.

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).

virtual Bool_t	Notify ()
	This method must be overridden to handle object notification (the base implementation is no-op).

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

void	operator delete (void *ptr)
	Operator delete.

void	operator delete (void ptr, void vp)
	Only called by placement new when throwing an exception.

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

void	operator delete[] (void ptr, void vp)
	Only called by placement new[] when throwing an exception.

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.

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

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

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

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

void	ResetBit (UInt_t f)

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

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

void	SetBit (UInt_t f)

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

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

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

void	StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b)

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

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.

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

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

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

Static Public Member Functions
static TClass *	Class ()

static const char *	Class_Name ()

static constexpr Version_t	Class_Version ()

static const char *	DeclFileName ()

Static Public Member Functions inherited from TDecompBase
static TClass *	Class ()

static const char *	Class_Name ()

static constexpr Version_t	Class_Version ()

static const char *	DeclFileName ()

Static Public Member Functions inherited from TObject
static TClass *	Class ()

static const char *	Class_Name ()

static constexpr Version_t	Class_Version ()

static const char *	DeclFileName ()

static Longptr_t	GetDtorOnly ()
	Return destructor only flag.

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

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

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

Protected Member Functions
const TMatrixDBase &	GetDecompMatrix () const override

Protected Member Functions inherited from TDecompBase
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).

void	MakeZombie ()

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

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

enum	EDeprecatedStatusBits { kObjInCanvas = (1ULL << ( 3 )) }

enum	EStatusBits { kCanDelete = (1ULL << ( 0 )) , kMustCleanup = (1ULL << ( 3 )) , kIsReferenced = (1ULL << ( 4 )) , kHasUUID = (1ULL << ( 5 )) , kCannotPick = (1ULL << ( 6 )) , kNoContextMenu = (1ULL << ( 8 )) , kInvalidObject = (1ULL << ( 13 )) }

Protected Types inherited from TDecompBase
enum	{ kWorkMax = 100 }

enum	EMatrixDecompStat { kInit = (1ULL << ( 14 )) , kPatternSet = (1ULL << ( 15 )) , kValuesSet = (1ULL << ( 16 )) , kMatrixSet = (1ULL << ( 17 )) , kDecomposed = (1ULL << ( 18 )) , kDetermined = (1ULL << ( 19 )) , kCondition = (1ULL << ( 20 )) , kSingular = (1ULL << ( 21 )) }

Protected Types inherited from TObject
enum	{ kOnlyPrepStep = (1ULL << ( 3 )) }

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()

TDecompChol::~TDecompChol ( )

inlineoverride

Definition at line 40 of file TDecompChol.h.

Member Function Documentation

◆ Class()

static TClass * TDecompChol::Class ( )

static

Returns: TClass describing this class

◆ Class_Name()

static const char * TDecompChol::Class_Name ( )

static

Returns: Name of this class

◆ Class_Version()

static constexpr Version_t TDecompChol::Class_Version ( )

inlinestaticconstexpr

Returns: Version of this class

Definition at line 66 of file TDecompChol.h.

◆ DeclFileName()

static const char * TDecompChol::DeclFileName ( )

inlinestatic

Returns: Name of the file containing the class declaration

Definition at line 66 of file TDecompChol.h.

◆ Decompose()

Bool_t TDecompChol::Decompose ( )

overridevirtual

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
	)

overridevirtual

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

Reimplemented from TDecompBase.

Definition at line 324 of file TDecompChol.cxx.

◆ GetDecompMatrix()

const TMatrixDBase & TDecompChol::GetDecompMatrix ( ) const

inlineoverrideprotectedvirtual

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 161 of file TDecompChol.cxx.

◆ GetNcols()

Int_t TDecompChol::GetNcols ( ) const

inlineoverridevirtual

Implements TDecompBase.

Definition at line 44 of file TDecompChol.h.

◆ GetNrows()

Int_t TDecompChol::GetNrows ( ) const

inlineoverridevirtual

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]

TMatrixDSym TDecompChol::Invert ( )

inline

Definition at line 60 of file TDecompChol.h.

◆ 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 365 of file TDecompChol.cxx.

◆ Invert() [3/3]

Bool_t TDecompChol::Invert ( TMatrixDSym & inv )

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

Definition at line 342 of file TDecompChol.cxx.

◆ IsA()

TClass * TDecompChol::IsA ( ) const

inlineoverridevirtual

Returns: TClass describing current object

Reimplemented from TDecompBase.

Definition at line 66 of file TDecompChol.h.

◆ operator=()

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

Assignment operator.

Definition at line 389 of file TDecompChol.cxx.

◆ Print()

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

overridevirtual

Print class members .

Reimplemented from TDecompBase.

Definition at line 380 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 180 of file TDecompChol.cxx.

◆ Solve() [1/3]

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

inlineoverridevirtual

Implements TDecompBase.

Definition at line 51 of file TDecompChol.h.

◆ Solve() [2/3]

Bool_t TDecompChol::Solve ( TMatrixDColumn & cb )

overridevirtual

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 262 of file TDecompChol.cxx.

◆ Solve() [3/3]

Bool_t TDecompChol::Solve ( TVectorD & b )

overridevirtual

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 204 of file TDecompChol.cxx.

◆ Streamer()

void TDecompChol::Streamer ( TBuffer & R__b )

overridevirtual

Stream an object of class TObject.

Reimplemented from TDecompBase.

◆ StreamerNVirtual()

void TDecompChol::StreamerNVirtual ( TBuffer & ClassDef_StreamerNVirtual_b )

inline

Definition at line 66 of file TDecompChol.h.

◆ TransSolve() [1/3]

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

inlineoverridevirtual

Implements TDecompBase.

Definition at line 54 of file TDecompChol.h.

◆ TransSolve() [2/3]

Bool_t TDecompChol::TransSolve ( TMatrixDColumn & b )

inlineoverridevirtual

Implements TDecompBase.

Definition at line 55 of file TDecompChol.h.

◆ TransSolve() [3/3]

Bool_t TDecompChol::TransSolve ( TVectorD & b )

inlineoverridevirtual

Implements TDecompBase.

Definition at line 53 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

Static 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

◆ Class()

◆ Class_Name()

◆ Class_Version()

◆ DeclFileName()

◆ Decompose()

◆ Det()

◆ GetDecompMatrix()

◆ GetMatrix()

◆ GetNcols()

◆ GetNrows()

◆ GetU()

◆ Invert() [1/3]

◆ Invert() [2/3]

◆ Invert() [3/3]

◆ IsA()

◆ operator=()

◆ Print()

◆ SetMatrix()

◆ Solve() [1/3]

◆ Solve() [2/3]

◆ Solve() [3/3]

◆ Streamer()

◆ StreamerNVirtual()

◆ TransSolve() [1/3]

◆ TransSolve() [2/3]

◆ TransSolve() [3/3]

Member Data Documentation

◆ fU