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Reference Guide
TDecompQRH Class Reference

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

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 thw 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,
  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)
}
 

Public Member Functions

 TDecompQRH ()
 
 TDecompQRH (const TDecompQRH &another)
 Copy constructor. More...
 
 TDecompQRH (const TMatrixD &m, Double_t tol=0.0)
 Constructor for general matrix A . More...
 
 TDecompQRH (Int_t nrows, Int_t ncols)
 Constructor for (nrows x ncols) matrix. More...
 
 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. More...
 
virtual ~TDecompQRH ()
 
virtual Bool_t Decompose ()
 QR decomposition of matrix a by Householder transformations, see Golub & Loan first edition p41 & Sec 6.2. More...
 
virtual void Det (Double_t &d1, Double_t &d2)
 This routine calculates the absolute (!) value of the determinant |det| = d1*TMath::Power(2.,d2) More...
 
virtual Int_t GetNcols () const
 
virtual Int_t GetNrows () const
 
TMatrixD GetOrthogonalMatrix () const
 For a matrix A(m,n), return the OtrhogonalMatrix Q such as A = Q * R. More...
 
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 . More...
 
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 . More...
 
TDecompQRHoperator= (const TDecompQRH &source)
 Assignment operator. More...
 
void Print (Option_t *opt="") const
 Print the class members. More...
 
virtual void SetMatrix (const TMatrixD &a)
 Set matrix to be decomposed. More...
 
virtual TVectorD Solve (const TVectorD &b, Bool_t &ok)
 
virtual 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. More...
 
virtual 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. More...
 
virtual TVectorD TransSolve (const TVectorD &b, Bool_t &ok)
 
virtual 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. More...
 
virtual 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. More...
 
- Public Member Functions inherited from TDecompBase
 TDecompBase ()
 Default constructor. More...
 
 TDecompBase (const TDecompBase &another)
 Copy constructor. More...
 
virtual ~TDecompBase ()
 
virtual Double_t Condition ()
 Matrix condition number. More...
 
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. More...
 
TDecompBaseoperator= (const TDecompBase &source)
 Assignment operator. More...
 
Double_t SetTol (Double_t tol)
 
- 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=0)
 Execute method on this object with the given parameter string, e.g. More...
 
virtual void Execute (TMethod *method, TObjArray *params, Int_t *error=0)
 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 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...
 
voidoperator new (size_t sz)
 
voidoperator new (size_t sz, void *vp)
 
voidoperator new[] (size_t sz)
 
voidoperator 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 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 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=0, Int_t option=0, Int_t bufsize=0)
 Write this object to the current directory. More...
 
virtual Int_t Write (const char *name=0, Int_t option=0, Int_t bufsize=0) const
 Write this object to the current directory. More...
 

Protected Member Functions

virtual const TMatrixDBaseGetDecompMatrix () 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). More...
 
void MakeZombie ()
 

Static Protected Member Functions

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

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
 

Additional Inherited Members

- Static Public Member Functions inherited from TObject
static Long_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 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)
}
 

#include <TDecompQRH.h>

Inheritance diagram for TDecompQRH:
[legend]

Member Enumeration Documentation

◆ anonymous enum

anonymous enum
Enumerator
kWorkMax 

Definition at line 47 of file TDecompQRH.h.

Constructor & Destructor Documentation

◆ TDecompQRH() [1/5]

TDecompQRH::TDecompQRH ( )
inline

Definition at line 49 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()

virtual TDecompQRH::~TDecompQRH ( )
inlinevirtual

Definition at line 54 of file TDecompQRH.h.

Member Function Documentation

◆ Decompose()

Bool_t TDecompQRH::Decompose ( )
virtual

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 
)
virtual

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()

virtual const TMatrixDBase& TDecompQRH::GetDecompMatrix ( ) const
inlineprotectedvirtual

Implements TDecompBase.

Definition at line 43 of file TDecompQRH.h.

◆ GetNcols()

virtual Int_t TDecompQRH::GetNcols ( ) const
inlinevirtual

Implements TDecompBase.

Definition at line 57 of file TDecompQRH.h.

◆ GetNrows()

virtual Int_t TDecompQRH::GetNrows ( ) const
inlinevirtual

Implements TDecompBase.

Definition at line 56 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 58 of file TDecompQRH.h.

◆ GetR()

virtual const TMatrixD& TDecompQRH::GetR ( )
inlinevirtual

Definition at line 60 of file TDecompQRH.h.

◆ GetTriangularMatrix()

const TMatrixD& TDecompQRH::GetTriangularMatrix ( ) const
inline

Definition at line 68 of file TDecompQRH.h.

◆ GetUp()

virtual const TVectorD& TDecompQRH::GetUp ( )
inlinevirtual

Definition at line 62 of file TDecompQRH.h.

◆ GetW()

virtual const TVectorD& TDecompQRH::GetW ( )
inlinevirtual

Definition at line 64 of file TDecompQRH.h.

◆ Invert() [1/3]

TMatrixD TDecompQRH::Invert ( )
inline

Definition at line 83 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.

◆ 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
virtual

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]

virtual TVectorD TDecompQRH::Solve ( const TVectorD b,
Bool_t ok 
)
inlinevirtual

Implements TDecompBase.

Definition at line 74 of file TDecompQRH.h.

◆ Solve() [2/3]

Bool_t TDecompQRH::Solve ( TMatrixDColumn cb)
virtual

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)
virtual

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.

◆ TransSolve() [1/3]

virtual TVectorD TDecompQRH::TransSolve ( const TVectorD b,
Bool_t ok 
)
inlinevirtual

Implements TDecompBase.

Definition at line 77 of file TDecompQRH.h.

◆ TransSolve() [2/3]

Bool_t TDecompQRH::TransSolve ( TMatrixDColumn cb)
virtual

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)
virtual

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.

Member Data Documentation

◆ fQ

TMatrixD TDecompQRH::fQ
protected

Definition at line 36 of file TDecompQRH.h.

◆ fR

TMatrixD TDecompQRH::fR
protected

Definition at line 37 of file TDecompQRH.h.

◆ fUp

TVectorD TDecompQRH::fUp
protected

Definition at line 38 of file TDecompQRH.h.

◆ fW

TVectorD TDecompQRH::fW
protected

Definition at line 39 of file TDecompQRH.h.

Libraries for TDecompQRH:
[legend]

The documentation for this class was generated from the following files:
m
auto * m
Definition: textangle.C:8
n
const Int_t n
Definition: legend1.C:16
TGeant4Unit::s
static constexpr double s
Definition: TGeant4SystemOfUnits.h:168
x
Double_t x[n]
Definition: legend1.C:17
ROOT::Math::beta
double beta(double x, double y)
Calculates the beta function.
Definition: SpecFuncMathCore.cxx:111
TDecompQRH::fQ
TMatrixD fQ
Definition: TDecompQRH.h:36
TDecompQRH::fW
TVectorD fW
Definition: TDecompQRH.h:39
ROOT::Math::Cephes::Q
static double Q[]
Definition: SpecFuncCephes.cxx:294