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class TDecompChol: public TDecompBase


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 .

Function Members (Methods)

public:

	TDecompChol()
	TDecompChol(Int_t nrows)
	TDecompChol(const TDecompChol& another)
	TDecompChol(Int_t row_lwb, Int_t row_upb)
	TDecompChol(const TMatrixDSym& a, Double_t tol = 0.0)
	TDecompChol(const TMatrixD& a, Double_t tol = 0.0)
virtual	~TDecompChol()
void	TObject::AbstractMethod(const char* method) const
virtual void	TObject::AppendPad(Option_t* option = "")
virtual void	TObject::Browse(TBrowser* b)
static TClass*	Class()
virtual const char*	TObject::ClassName() const
virtual void	TObject::Clear(Option_t* = "")
virtual TObject*	TObject::Clone(const char* newname = "") const
virtual Int_t	TObject::Compare(const TObject* obj) const
virtual Double_t	TDecompBase::Condition()
virtual void	TObject::Copy(TObject& object) const
virtual Bool_t	Decompose()
virtual void	TObject::Delete(Option_t* option = "")MENU
virtual void	Det(Double_t& d1, Double_t& d2)
virtual Int_t	TObject::DistancetoPrimitive(Int_t px, Int_t py)
virtual void	TObject::Draw(Option_t* option = "")
virtual void	TObject::DrawClass() constMENU
virtual TObject*	TObject::DrawClone(Option_t* option = "") constMENU
virtual void	TObject::Dump() constMENU
virtual void	TObject::Error(const char* method, const char* msgfmt) const
virtual void	TObject::Execute(const char* method, const char* params, Int_t* error = 0)
virtual void	TObject::Execute(TMethod* method, TObjArray* params, Int_t* error = 0)
virtual void	TObject::ExecuteEvent(Int_t event, Int_t px, Int_t py)
virtual void	TObject::Fatal(const char* method, const char* msgfmt) const
virtual TObject*	TObject::FindObject(const char* name) const
virtual TObject*	TObject::FindObject(const TObject* obj) const
Int_t	TDecompBase::GetColLwb() const
Double_t	TDecompBase::GetCondition() const
Double_t	TDecompBase::GetDet1() const
Double_t	TDecompBase::GetDet2() const
virtual Option_t*	TObject::GetDrawOption() const
static Long_t	TObject::GetDtorOnly()
virtual const char*	TObject::GetIconName() const
const TMatrixDSym	GetMatrix()
virtual const char*	TObject::GetName() const
virtual Int_t	GetNcols() const
virtual Int_t	GetNrows() const
virtual char*	TObject::GetObjectInfo(Int_t px, Int_t py) const
static Bool_t	TObject::GetObjectStat()
virtual Option_t*	TObject::GetOption() const
Int_t	TDecompBase::GetRowLwb() const
virtual const char*	TObject::GetTitle() const
Double_t	TDecompBase::GetTol() const
const TMatrixD&	GetU() const
virtual UInt_t	TObject::GetUniqueID() const
virtual Bool_t	TObject::HandleTimer(TTimer* timer)
virtual ULong_t	TObject::Hash() const
virtual void	TObject::Info(const char* method, const char* msgfmt) const
virtual Bool_t	TObject::InheritsFrom(const char* classname) const
virtual Bool_t	TObject::InheritsFrom(const TClass* cl) const
virtual void	TObject::Inspect() constMENU
TMatrixDSym	Invert()
Bool_t	Invert(TMatrixDSym& inv)
TMatrixDSym	Invert(Bool_t& status)
void	TObject::InvertBit(UInt_t f)
virtual TClass*	IsA() const
virtual Bool_t	TObject::IsEqual(const TObject* obj) const
virtual Bool_t	TObject::IsFolder() const
Bool_t	TObject::IsOnHeap() const
virtual Bool_t	TObject::IsSortable() const
Bool_t	TObject::IsZombie() const
virtual void	TObject::ls(Option_t* option = "") const
void	TObject::MayNotUse(const char* method) const
virtual Bool_t	TDecompBase::MultiSolve(TMatrixD& B)
virtual Bool_t	TObject::Notify()
void	TObject::Obsolete(const char* method, const char* asOfVers, const char* removedFromVers) const
static void	TObject::operator delete(void* ptr)
static void	TObject::operator delete(void* ptr, void* vp)
static void	TObject::operator delete[](void* ptr)
static void	TObject::operator delete[](void* ptr, void* vp)
void*	TObject::operator new(size_t sz)
void*	TObject::operator new(size_t sz, void* vp)
void*	TObject::operator new[](size_t sz)
void*	TObject::operator new[](size_t sz, void* vp)
TDecompChol&	operator=(const TDecompChol& source)
virtual void	TObject::Paint(Option_t* option = "")
virtual void	TObject::Pop()
virtual void	Print(Option_t* opt = "") constMENU
virtual Int_t	TObject::Read(const char* name)
virtual void	TObject::RecursiveRemove(TObject* obj)
void	TObject::ResetBit(UInt_t f)
virtual void	TObject::SaveAs(const char* filename = "", Option_t* option = "") constMENU
virtual void	TObject::SavePrimitive(ostream& out, Option_t* option = "")
void	TObject::SetBit(UInt_t f)
void	TObject::SetBit(UInt_t f, Bool_t set)
virtual void	TObject::SetDrawOption(Option_t* option = "")MENU
static void	TObject::SetDtorOnly(void* obj)
virtual void	SetMatrix(const TMatrixDSym& a)
static void	TObject::SetObjectStat(Bool_t stat)
Double_t	TDecompBase::SetTol(Double_t newTol)
virtual void	TObject::SetUniqueID(UInt_t uid)
virtual void	ShowMembers(TMemberInspector& insp)
virtual Bool_t	Solve(TVectorD& b)
virtual Bool_t	Solve(TMatrixDColumn& b)
virtual TVectorD	Solve(const TVectorD& b, Bool_t& ok)
virtual void	Streamer(TBuffer& b)
void	StreamerNVirtual(TBuffer& b)
virtual void	TObject::SysError(const char* method, const char* msgfmt) const
Bool_t	TObject::TestBit(UInt_t f) const
Int_t	TObject::TestBits(UInt_t f) const
virtual Bool_t	TransSolve(TVectorD& b)
virtual Bool_t	TransSolve(TMatrixDColumn& b)
virtual TVectorD	TransSolve(const TVectorD& b, Bool_t& ok)
virtual void	TObject::UseCurrentStyle()
virtual void	TObject::Warning(const char* method, const char* msgfmt) const
virtual Int_t	TObject::Write(const char* name = 0, Int_t option = 0, Int_t bufsize = 0)
virtual Int_t	TObject::Write(const char* name = 0, Int_t option = 0, Int_t bufsize = 0) const

protected:

static void	TDecompBase::DiagProd(const TVectorD& diag, Double_t tol, Double_t& d1, Double_t& d2)
virtual void	TObject::DoError(int level, const char* location, const char* fmt, va_list va) const
virtual const TMatrixDBase&	GetDecompMatrix() const
Int_t	TDecompBase::Hager(Double_t& est, Int_t iter = 5)
void	TObject::MakeZombie()
void	TDecompBase::ResetStatus()

Data Members

public:

enum TDecompBase::EMatrixDecompStat {	kInit
	kPatternSet
	kValuesSet
	kMatrixSet
	kDecomposed
	kDetermined
	kCondition
	kSingular
};
enum TDecompBase::[unnamed] {	kWorkMax
};
enum TObject::EStatusBits {	kCanDelete
	kMustCleanup
	kObjInCanvas
	kIsReferenced
	kHasUUID
	kCannotPick
	kNoContextMenu
	kInvalidObject
};
enum TObject::[unnamed] {	kIsOnHeap
	kNotDeleted
	kZombie
	kBitMask
	kSingleKey
	kOverwrite
	kWriteDelete
};

protected:

Int_t	TDecompBase::fColLwb	Column lower bound of decomposed matrix
Double_t	TDecompBase::fCondition	matrix condition number
Double_t	TDecompBase::fDet1	determinant mantissa
Double_t	TDecompBase::fDet2	determinant exponent for powers of 2
Int_t	TDecompBase::fRowLwb	Row lower bound of decomposed matrix
Double_t	TDecompBase::fTol	sqrt(epsilon); epsilon is smallest number number so that 1+epsilon > 1
TMatrixD	fU	decomposed matrix fU so that a = fU^T fU

Class Charts

Inheritance Inherited Members Includes Libraries

Function documentation

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(const TMatrixDSym& a, Double_t tol = 0.0)

 Constructor for symmetric matrix A . Matrix should be positive definite

TDecompChol(const TMatrixD& a, Double_t tol = 0.0)

 Constructor for general matrix A . Matrix should be symmetric positive definite

TDecompChol(const TDecompChol& another)

 Copy constructor

Bool_t Decompose()

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

const TMatrixDSym GetMatrix()

 Reconstruct the original matrix using the decomposition parts

void SetMatrix(const TMatrixDSym& a)

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

Bool_t Solve(TVectorD& b)

 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.

Bool_t Solve(TMatrixDColumn& b)

 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.

void Det(Double_t& d1, Double_t& d2)

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

Bool_t Invert(TMatrixDSym& inv)

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

TMatrixDSym Invert(Bool_t& status)

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

void Print(Option_t* opt = "") const

 Print class members .

TDecompChol & operator=(const TDecompChol& source)

 Assignment operator

const TMatrixDBase & GetDecompMatrix() const

{ return fU; }

TDecompChol()

{}

virtual ~TDecompChol()

{}

Int_t GetNrows() const

{ return fU.GetNrows(); }

Int_t GetNcols() const

{ return fU.GetNcols(); }

const TMatrixD & GetU() const

{ return fU; }

Bool_t Solve(TVectorD& b)

Bool_t TransSolve(TVectorD& b)

{ return Solve(b); }

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

{ TVectorD x = b; ok = Solve(x); return x; }

Bool_t TransSolve(TMatrixDColumn& b)

{ return Solve(b); }

Bool_t Invert(TMatrixDSym& inv)