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.

	TDecompLU (const TDecompLU &another)
	Copy constructor.

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

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

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

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.

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

const TMatrixD &	GetLU ()

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

virtual Int_t	GetNcols () const

virtual Int_t	GetNrows () const

TMatrixD	Invert ()

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 .

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 .

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

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

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

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.

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.

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.

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.

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

	TDecompBase (const TDecompBase &another)
	Copy constructor.

virtual	~TDecompBase ()

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)

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 for instance with: `gROOT->SetSelectedPad(gPad)`.

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=0)
	Execute method on this object with the given parameter string, e.g.

virtual void	Execute (TMethod method, TObjArray params, Int_t *error=0)
	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)

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.

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)
	Operator delete [].

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.

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=0, Int_t option=0, Int_t bufsize=0)
	Write this object to the current directory.

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

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.

Static Public Member Functions inherited from TObject
static Long_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
virtual const TMatrixDBase &	GetDecompMatrix () const

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 ()

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.

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 .

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
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) }

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) }

Protected Types inherited from TObject
enum	{ kOnlyPrepStep = BIT(3) }

#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]

TMatrixD TDecompLU::Invert ( )

inline

Definition at line 69 of file TDecompLU.h.

◆ 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]

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.

◆ 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

virtual

Print internals of this object.

Reimplemented from TDecompBase.

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]

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

inlinevirtual

Implements TDecompBase.

Definition at line 59 of file TDecompLU.h.

◆ Solve() [2/3]

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.

◆ Solve() [3/3]

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.

◆ TransSolve() [1/3]

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

inlinevirtual

Implements TDecompBase.

Definition at line 62 of file TDecompLU.h.

◆ TransSolve() [2/3]

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.

◆ TransSolve() [3/3]

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.

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