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class TDecompQRH: public TDecompBase


QR Decomposition class

Decompose  a general (m x n) matrix A into A = fQ fR H   where

fQ : (m x n) - orthogonal matrix
fR : (n x n) - upper triangular matrix
H  : HouseHolder matrix which is stored through
fUp: (n) - vector with Householder up's
fW : (n) - vector with Householder beta's

If row/column index of A starts at (rowLwb,colLwb) then
the decomposed matrices start from :
fQ  : (rowLwb,0)
fR  : (0,colLwb)
and the decomposed vectors start from :
fUp : (0)
fW  : (0)

Errors arise from formation of reflectors i.e. singularity .
Note it attempts to handle the cases where the nRow <= nCol .

Function Members (Methods)

public:

virtual	~TDecompQRH()
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
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
virtual const TMatrixD&	GetQ()
virtual const TMatrixD&	GetR()
Int_t	TDecompBase::GetRowLwb() const
virtual const char*	TObject::GetTitle() const
Double_t	TDecompBase::GetTol() const
virtual UInt_t	TObject::GetUniqueID() const
virtual const TVectorD&	GetUp()
virtual const TVectorD&	GetW()
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
TMatrixD	Invert()
Bool_t	Invert(TMatrixD& inv)
TMatrixD	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
void	TObject::operator delete(void* ptr)
void	TObject::operator delete(void* ptr, void* vp)
void	TObject::operator delete[](void* ptr)
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)
TDecompQRH&	operator=(const TDecompQRH& 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 TMatrixD& a)
static void	TObject::SetObjectStat(Bool_t stat)
Double_t	TDecompBase::SetTol(Double_t tol)
virtual void	TObject::SetUniqueID(UInt_t uid)
virtual void	ShowMembers(TMemberInspector& insp) const
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&)
void	StreamerNVirtual(TBuffer& ClassDef_StreamerNVirtual_b)
virtual void	TObject::SysError(const char* method, const char* msgfmt) const
	TDecompQRH()
	TDecompQRH(const TDecompQRH& another)
	TDecompQRH(Int_t nrows, Int_t ncols)
	TDecompQRH(const TMatrixD& m, Double_t tol = 0.)
	TDecompQRH(Int_t row_lwb, Int_t row_upb, Int_t col_lwb, Int_t col_upb)
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()
static Bool_t	QRH(TMatrixD& q, TVectorD& diagR, TVectorD& up, TVectorD& w, Double_t tol)
void	TDecompBase::ResetStatus()

Data Members

public:

static TObject::(anonymous)	TObject::kBitMask
static TObject::EStatusBits	TObject::kCanDelete
static TObject::EStatusBits	TObject::kCannotPick
static TObject::EStatusBits	TObject::kHasUUID
static TObject::EStatusBits	TObject::kInvalidObject
static TObject::(anonymous)	TObject::kIsOnHeap
static TObject::EStatusBits	TObject::kIsReferenced
static TObject::EStatusBits	TObject::kMustCleanup
static TObject::EStatusBits	TObject::kNoContextMenu
static TObject::(anonymous)	TObject::kNotDeleted
static TObject::EStatusBits	TObject::kObjInCanvas
static TObject::(anonymous)	TObject::kOverwrite
static TObject::(anonymous)	TObject::kSingleKey
static TDecompQRH::(anonymous)	kWorkMax
static TObject::(anonymous)	TObject::kWriteDelete
static TObject::(anonymous)	TObject::kZombie

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
TMatrixD	fQ	(m x n) - orthogonal matrix
TMatrixD	fR	(n x n) - upper triangular matrix
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
TVectorD	fUp	(n) - vector with Householder up's
TVectorD	fW	(n) - vector with Householder beta's
static TDecompBase::EMatrixDecompStat	TDecompBase::kCondition
static TDecompBase::EMatrixDecompStat	TDecompBase::kDecomposed
static TDecompBase::EMatrixDecompStat	TDecompBase::kDetermined
static TDecompBase::EMatrixDecompStat	TDecompBase::kInit
static TDecompBase::EMatrixDecompStat	TDecompBase::kMatrixSet
static TDecompBase::EMatrixDecompStat	TDecompBase::kPatternSet
static TDecompBase::EMatrixDecompStat	TDecompBase::kSingular
static TDecompBase::EMatrixDecompStat	TDecompBase::kValuesSet
static TDecompBase::(anonymous)	TDecompBase::kWorkMax

Class Charts

Inheritance Inherited Members Includes Libraries

Function documentation

TDecompQRH(Int_t nrows, Int_t ncols)

 Constructor for (nrows x ncols) matrix

TDecompQRH(Int_t row_lwb, Int_t row_upb, Int_t col_lwb, Int_t col_upb)

 Constructor for ([row_lwb..row_upb] x [col_lwb..col_upb]) matrix

TDecompQRH(const TMatrixD& m, Double_t tol = 0.)

 Constructor for general matrix A .

TDecompQRH(const TDecompQRH& another)

 Copy constructor

Bool_t Decompose()

 QR decomposition of matrix a by Householder transformations,
  see Golub & Loan first edition p41 & Sec 6.2.
 First fR is returned in upper triang of fQ and diagR. fQ returned in
 'u-form' in lower triang of fQ and fW, the latter containing the
  "Householder betas".
 If the decomposition succeeds, bit kDecomposed is set , otherwise kSingular

Bool_t QRH(TMatrixD& q, TVectorD& diagR, TVectorD& up, TVectorD& w, Double_t tol)

 Decomposition function .

void SetMatrix(const TMatrixD& a)

 Set matrix to be decomposed

Bool_t Solve(TVectorD& b)

 Solve Ax=b assuming the QR form of A is stored in fR,fQ and fW, but assume b
 has *not* been transformed.  Solution returned in b.

Bool_t Solve(TMatrixDColumn& b)

 Solve Ax=b assuming the QR form of A is stored in fR,fQ and fW, but assume b
 has *not* been transformed.  Solution returned in b.

Bool_t TransSolve(TVectorD& b)

 Solve A^T x=b assuming the QR form of A is stored in fR,fQ and fW, but assume b
 has *not* been transformed.  Solution returned in b.

Bool_t TransSolve(TMatrixDColumn& b)

 Solve A^T x=b assuming the QR form of A is stored in fR,fQ and fW, but assume b
 has *not* been transformed.  Solution returned in b.

void Det(Double_t& d1, Double_t& d2)

 This routine calculates the absolute (!) value of the determinant
 |det| = d1*TMath::Power(2.,d2)

Bool_t Invert(TMatrixD& inv)

 For a matrix A(m,n), its inverse A_inv is defined as A * A_inv = A_inv * A = unit
 The user should always supply a matrix of size (m x m) !
 If m > n , only the (n x m) part of the returned (pseudo inverse) matrix
 should be used .

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 .

void Print(Option_t* opt = "") const

 Print the class members

TDecompQRH & operator=(const TDecompQRH& source)

 Assignment operator

const TMatrixDBase & GetDecompMatrix() const

{ return fR; }

TDecompQRH()

{}

virtual ~TDecompQRH()

{}

Int_t GetNrows() const

{ return fQ.GetNrows(); }

Int_t GetNcols() const

{ return fQ.GetNcols(); }

const TMatrixD & GetQ()

const TMatrixD & GetR()

const TVectorD & GetUp()

const TVectorD & GetW()

Bool_t Solve(TVectorD& b)

Bool_t TransSolve(TVectorD& b)

Bool_t Invert(TMatrixD& inv)