ROOT   Reference Guide

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. More...

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

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

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

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

~TDecompLU () override

Bool_t Decompose () override
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. More...

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

const TMatrixDGetLU ()

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

Int_t GetNcols () const override

Int_t GetNrows () const override

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 . More...

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 . More...

TClassIsA () const override

TDecompLUoperator= (const TDecompLU &source)
assignment operator More...

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

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

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

Bool_t Solve (TMatrixDColumn &b) override
Solve Ax=b assuming the LU form of A is stored in fLU, but assume b has not been transformed. More...

Bool_t Solve (TVectorD &b) override
Solve Ax=b assuming the LU form of A is stored in fLU, but assume b has not been transformed. More...

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

void StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b)

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

Bool_t TransSolve (TMatrixDColumn &b) override
Solve A^T x=b assuming the LU form of A^T is stored in fLU, but assume b has not been transformed. More...

Bool_t TransSolve (TVectorD &b) override
Solve A^T x=b assuming the LU form of A^T is stored in fLU, but assume b has not been transformed. More...

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

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

~TDecompBase () override

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

TClassIsA () const override

virtual Bool_t MultiSolve (TMatrixD &B)
Solve set of equations with RHS in columns of B. More...

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

void Print (Option_t *opt="") const override
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

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

void StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b)

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 TObjectClone (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 TObjectDrawClone (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=nullptr)
Execute method on this object with the given parameter string, e.g. More...

virtual void Execute (TMethod *method, TObjArray *params, Int_t *error=nullptr)
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 TObjectFindObject (const char *name) const
Must be redefined in derived classes. More...

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

virtual Option_tGetDrawOption () 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_tGetOption () 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 TClassIsA () const

Bool_t IsDestructed () const
IsDestructed. More...

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)

TObjectoperator= (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 Streamer (TBuffer &)
Stream an object of class TObject. More...

void StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b)

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

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

## Static Public Member Functions

static TClassClass ()

static const char * Class_Name ()

static constexpr Version_t Class_Version ()

static const char * DeclFileName ()

static Bool_t InvertLU (TMatrixD &a, Double_t tol, Double_t *det=nullptr)
Calculate matrix inversion through in place forward/backward substitution. More...

Static Public Member Functions inherited from TDecompBase
static TClassClass ()

static const char * Class_Name ()

static constexpr Version_t Class_Version ()

static const char * DeclFileName ()

Static Public Member Functions inherited from TObject
static TClassClass ()

static const char * Class_Name ()

static constexpr Version_t Class_Version ()

static const char * DeclFileName ()

static Longptr_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 Member Functions

const TMatrixDBaseGetDecompMatrix () const override

Protected Member Functions inherited from TDecompBase
virtual const TMatrixDBaseGetDecompMatrix () 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 ()

## 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. More...

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 . More...

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_tfIndex

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 ,
}

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 )) }

#include <TDecompLU.h>

Inheritance diagram for TDecompLU:
[legend]

## ◆ 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()

 TDecompLU::~TDecompLU ( )
inlineoverride

Definition at line 47 of file TDecompLU.h.

## ◆ Class()

 static TClass * TDecompLU::Class ( )
static
Returns
TClass describing this class

## ◆ Class_Name()

 static const char * TDecompLU::Class_Name ( )
static
Returns
Name of this class

## ◆ Class_Version()

 static constexpr Version_t TDecompLU::Class_Version ( )
inlinestaticconstexpr
Returns
Version of this class

Definition at line 75 of file TDecompLU.h.

## ◆ DeclFileName()

 static const char * TDecompLU::DeclFileName ( )
inlinestatic
Returns
Name of the file containing the class declaration

Definition at line 75 of file TDecompLU.h.

## ◆ Decompose()

 Bool_t TDecompLU::Decompose ( )
overridevirtual

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 )
overridevirtual

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

Reimplemented from TDecompBase.

Definition at line 509 of file TDecompLU.cxx.

## ◆ GetDecompMatrix()

 const TMatrixDBase & TDecompLU::GetDecompMatrix ( ) const
inlineoverrideprotectedvirtual

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()

 Int_t TDecompLU::GetNcols ( ) const
inlineoverridevirtual

Implements TDecompBase.

Definition at line 51 of file TDecompLU.h.

## ◆ GetNrows()

 Int_t TDecompLU::GetNrows ( ) const
inlineoverridevirtual

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 = nullptr )
static

Calculate matrix inversion through in place forward/backward substitution.

Definition at line 775 of file TDecompLU.cxx.

## ◆ IsA()

 TClass * TDecompLU::IsA ( ) const
inlineoverridevirtual
Returns
TClass describing current object

Reimplemented from TDecompBase.

Definition at line 75 of file TDecompLU.h.

## ◆ 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
overridevirtual

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]

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

Implements TDecompBase.

Definition at line 59 of file TDecompLU.h.

## ◆ Solve() [2/3]

 Bool_t TDecompLU::Solve ( TMatrixDColumn & cb )
overridevirtual

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 )
overridevirtual

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.

## ◆ Streamer()

 void TDecompLU::Streamer ( TBuffer & R__b )
overridevirtual

Stream an object of class TObject.

Reimplemented from TDecompBase.

## ◆ StreamerNVirtual()

 void TDecompLU::StreamerNVirtual ( TBuffer & ClassDef_StreamerNVirtual_b )
inline

Definition at line 75 of file TDecompLU.h.

## ◆ TransSolve() [1/3]

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

Implements TDecompBase.

Definition at line 62 of file TDecompLU.h.

## ◆ TransSolve() [2/3]

 Bool_t TDecompLU::TransSolve ( TMatrixDColumn & cb )
overridevirtual

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 )
overridevirtual

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.

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