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QR Decomposition class.

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

fQ : (m x n) - internal Q' matrix (not orthoginal)
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
TMatrixD fQ
Definition TDecompQRH.h:30
TVectorD fW
Definition TDecompQRH.h:33
Double_t x[n]
Definition legend1.C:17
const Int_t n
Definition legend1.C:16
TMarker m
Definition textangle.C:8

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)

In order to get the QR dcomposition of A (i.e. A = QR ) The orthoginal matrix Q needs to be computed from the internal Q' and the up's and beta's vector defining the Householder transformation

The orthogonal Q matrix is returned to the user by calling the function TDecompQRH::GetOrthogonalMatrix()

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

Definition at line 25 of file TDecompQRH.h.

## Public Types

enum  { kWorkMax = 100 }

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 ))
}

## Public Member Functions

TDecompQRH ()

TDecompQRH (const TDecompQRH &another)
Copy constructor.

TDecompQRH (const TMatrixD &m, Double_t tol=0.0)
Constructor for general matrix A .

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 () override

Bool_t Decompose () override
QR decomposition of matrix a by Householder transformations, see Golub & Loan first edition p41 & Sec 6.2.

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

Int_t GetNcols () const override

Int_t GetNrows () const override

TMatrixD GetOrthogonalMatrix () const
For a matrix A(m,n), return the OtrhogonalMatrix Q such as A = Q * R.

virtual const TMatrixDGetQ ()

virtual const TMatrixDGetR ()

const TMatrixDGetTriangularMatrix () const

virtual const TVectorDGetUp ()

virtual const TVectorDGetW ()

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,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 .

TClassIsA () const override

TDecompQRHoperator= (const TDecompQRH &source)
Assignment operator.

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

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

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

Bool_t Solve (TMatrixDColumn &b) override
Solve Ax=b assuming the QR form of A is stored in fR,fQ and fW, but assume b has not been transformed.

Bool_t Solve (TVectorD &b) override
Solve Ax=b assuming the QR form of A is stored in fR,fQ and fW, but assume b has not been transformed.

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
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.

Bool_t TransSolve (TVectorD &b) override
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.

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.

TDecompBaseoperator= (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.

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 TObjectClone (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 TObjectDrawClone (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 TObjectFindObject (const char *name) const
Must be redefined in derived classes.

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

virtual Option_tGetDrawOption () 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_tGetOption () 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)

TObjectoperator= (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 TClassClass ()

static const char * Class_Name ()

static constexpr Version_t Class_Version ()

static const char * DeclFileName ()

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.

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 TMatrixDBaseGetDecompMatrix () 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 ()

## Static Protected Member Functions

static Bool_t QRH (TMatrixD &q, TVectorD &diagR, TVectorD &up, TVectorD &w, Double_t tol)
Decomposition function .

Static Protected Member Functions inherited from TDecompBase
static void DiagProd (const TVectorD &diag, Double_t tol, Double_t &d1, Double_t &d2)

## Protected Attributes

TMatrixD fQ

TMatrixD fR

TVectorD fUp

TVectorD fW

Protected Attributes inherited from TDecompBase
Int_t fColLwb

Double_t fCondition

Double_t fDet1

Double_t fDet2

Int_t fRowLwb

Double_t fTol

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 <TDecompQRH.h>

Inheritance diagram for TDecompQRH:
[legend]

## ◆ anonymous enum

 anonymous enum
Enumerator
kWorkMax

Definition at line 41 of file TDecompQRH.h.

## ◆ TDecompQRH() [1/5]

 TDecompQRH::TDecompQRH ( )
inline

Definition at line 43 of file TDecompQRH.h.

## ◆ TDecompQRH() [2/5]

 TDecompQRH::TDecompQRH ( Int_t nrows, Int_t ncols )

Constructor for (nrows x ncols) matrix.

Definition at line 55 of file TDecompQRH.cxx.

## ◆ TDecompQRH() [3/5]

 TDecompQRH::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.

Definition at line 76 of file TDecompQRH.cxx.

## ◆ TDecompQRH() [4/5]

 TDecompQRH::TDecompQRH ( const TMatrixD & m, Double_t tol = 0.0 )

Constructor for general matrix A .

Definition at line 103 of file TDecompQRH.cxx.

## ◆ TDecompQRH() [5/5]

 TDecompQRH::TDecompQRH ( const TDecompQRH & another )

Copy constructor.

Definition at line 137 of file TDecompQRH.cxx.

## ◆ ~TDecompQRH()

 TDecompQRH::~TDecompQRH ( )
inlineoverride

Definition at line 48 of file TDecompQRH.h.

## ◆ Class()

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

## ◆ Class_Name()

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

## ◆ Class_Version()

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

Definition at line 83 of file TDecompQRH.h.

## ◆ DeclFileName()

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

Definition at line 83 of file TDecompQRH.h.

## ◆ Decompose()

 Bool_t TDecompQRH::Decompose ( )
overridevirtual

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

Implements TDecompBase.

Definition at line 150 of file TDecompQRH.cxx.

## ◆ Det()

 void TDecompQRH::Det ( Double_t & d1, Double_t & d2 )
overridevirtual

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

Reimplemented from TDecompBase.

Definition at line 493 of file TDecompQRH.cxx.

## ◆ GetDecompMatrix()

 const TMatrixDBase & TDecompQRH::GetDecompMatrix ( ) const
inlineoverrideprotectedvirtual

Implements TDecompBase.

Definition at line 37 of file TDecompQRH.h.

## ◆ GetNcols()

 Int_t TDecompQRH::GetNcols ( ) const
inlineoverridevirtual

Implements TDecompBase.

Definition at line 51 of file TDecompQRH.h.

## ◆ GetNrows()

 Int_t TDecompQRH::GetNrows ( ) const
inlineoverridevirtual

Implements TDecompBase.

Definition at line 50 of file TDecompQRH.h.

## ◆ GetOrthogonalMatrix()

 TMatrixD TDecompQRH::GetOrthogonalMatrix ( ) const

For a matrix A(m,n), return the OtrhogonalMatrix Q such as A = Q * R.

Note that this Q is not th einternal fQ matrix obtained in the QRH decomposition, but can be computed from the fQ and the up and beta vector's defining the Householder transformation

Definition at line 516 of file TDecompQRH.cxx.

## ◆ GetQ()

 virtual const TMatrixD & TDecompQRH::GetQ ( )
inlinevirtual

Definition at line 52 of file TDecompQRH.h.

## ◆ GetR()

 virtual const TMatrixD & TDecompQRH::GetR ( )
inlinevirtual

Definition at line 54 of file TDecompQRH.h.

## ◆ GetTriangularMatrix()

 const TMatrixD & TDecompQRH::GetTriangularMatrix ( ) const
inline

Definition at line 62 of file TDecompQRH.h.

## ◆ GetUp()

 virtual const TVectorD & TDecompQRH::GetUp ( )
inlinevirtual

Definition at line 56 of file TDecompQRH.h.

## ◆ GetW()

 virtual const TVectorD & TDecompQRH::GetW ( )
inlinevirtual

Definition at line 58 of file TDecompQRH.h.

## ◆ Invert() [1/3]

 TMatrixD TDecompQRH::Invert ( )
inline

Definition at line 77 of file TDecompQRH.h.

## ◆ Invert() [2/3]

 TMatrixD TDecompQRH::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 565 of file TDecompQRH.cxx.

## ◆ Invert() [3/3]

 Bool_t TDecompQRH::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 .

Definition at line 547 of file TDecompQRH.cxx.

## ◆ IsA()

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

Reimplemented from TDecompBase.

Definition at line 83 of file TDecompQRH.h.

## ◆ operator=()

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

Assignment operator.

Definition at line 593 of file TDecompQRH.cxx.

## ◆ Print()

 void TDecompQRH::Print ( Option_t * opt = "" ) const
overridevirtual

Print the class members.

Reimplemented from TDecompBase.

Definition at line 581 of file TDecompQRH.cxx.

## ◆ QRH()

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

Decomposition function .

Definition at line 189 of file TDecompQRH.cxx.

## ◆ SetMatrix()

 void TDecompQRH::SetMatrix ( const TMatrixD & a )
virtual

Set matrix to be decomposed.

Definition at line 222 of file TDecompQRH.cxx.

## ◆ Solve() [1/3]

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

Implements TDecompBase.

Definition at line 68 of file TDecompQRH.h.

## ◆ Solve() [2/3]

 Bool_t TDecompQRH::Solve ( TMatrixDColumn & cb )
overridevirtual

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.

Implements TDecompBase.

Definition at line 311 of file TDecompQRH.cxx.

## ◆ Solve() [3/3]

 Bool_t TDecompQRH::Solve ( TVectorD & b )
overridevirtual

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.

Implements TDecompBase.

Definition at line 256 of file TDecompQRH.cxx.

## ◆ Streamer()

 void TDecompQRH::Streamer ( TBuffer & R__b )
overridevirtual

Stream an object of class TObject.

Reimplemented from TDecompBase.

## ◆ StreamerNVirtual()

 void TDecompQRH::StreamerNVirtual ( TBuffer & ClassDef_StreamerNVirtual_b )
inline

Definition at line 83 of file TDecompQRH.h.

## ◆ TransSolve() [1/3]

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

Implements TDecompBase.

Definition at line 71 of file TDecompQRH.h.

## ◆ TransSolve() [2/3]

 Bool_t TDecompQRH::TransSolve ( TMatrixDColumn & cb )
overridevirtual

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.

Implements TDecompBase.

Definition at line 430 of file TDecompQRH.cxx.

## ◆ TransSolve() [3/3]

 Bool_t TDecompQRH::TransSolve ( TVectorD & b )
overridevirtual

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.

Implements TDecompBase.

Definition at line 370 of file TDecompQRH.cxx.

## ◆ fQ

 TMatrixD TDecompQRH::fQ
protected

Definition at line 30 of file TDecompQRH.h.

## ◆ fR

 TMatrixD TDecompQRH::fR
protected

Definition at line 31 of file TDecompQRH.h.

## ◆ fUp

 TVectorD TDecompQRH::fUp
protected

Definition at line 32 of file TDecompQRH.h.

## ◆ fW

 TVectorD TDecompQRH::fW
protected

Definition at line 33 of file TDecompQRH.h.

Libraries for TDecompQRH:

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