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 .

Definition at line 25 of file TDecompQRH.h.

Public Types
enum	{ kWorkMax = 100 }

Public Member Functions
	TDecompQRH ()

	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...

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

	TDecompQRH (const TDecompQRH &another)
	Copy constructor. 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

virtual const TMatrixD &	GetQ ()

virtual const TMatrixD &	GetR ()

virtual const TVectorD &	GetUp ()

virtual const TVectorD &	GetW ()

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...

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...

TMatrixD	Invert ()

TDecompQRH &	operator= (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 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	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	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...

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...

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...

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

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

Double_t	SetTol (Double_t tol)

Protected Member Functions
virtual const TMatrixDBase &	GetDecompMatrix () const

Protected Member Functions inherited from TDecompBase
Int_t	Hager (Double_t &est, Int_t iter=5)

void	ResetStatus ()

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
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 41 of file TDecompQRH.h.

Constructor & Destructor Documentation

◆ 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 48 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 69 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 96 of file TDecompQRH.cxx.

◆ TDecompQRH() [5/5]

TDecompQRH::TDecompQRH ( const TDecompQRH & another )

Copy constructor.

Definition at line 130 of file TDecompQRH.cxx.

◆ ~TDecompQRH()

virtual TDecompQRH::~TDecompQRH ( )

inlinevirtual

Definition at line 48 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 143 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 486 of file TDecompQRH.cxx.

◆ GetDecompMatrix()

virtual const TMatrixDBase& TDecompQRH::GetDecompMatrix ( ) const

inlineprotectedvirtual

Implements TDecompBase.

Definition at line 37 of file TDecompQRH.h.

◆ GetNcols()

virtual Int_t TDecompQRH::GetNcols ( ) const

inlinevirtual

Implements TDecompBase.

Definition at line 51 of file TDecompQRH.h.

◆ GetNrows()

virtual Int_t TDecompQRH::GetNrows ( ) const

inlinevirtual

Implements TDecompBase.

Definition at line 50 of file TDecompQRH.h.

◆ 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.

◆ 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]

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 508 of file TDecompQRH.cxx.

◆ 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 526 of file TDecompQRH.cxx.

◆ Invert() [3/3]

TMatrixD TDecompQRH::Invert ( )

inline

Definition at line 74 of file TDecompQRH.h.

◆ operator=()

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

Assignment operator.

Definition at line 554 of file TDecompQRH.cxx.

◆ Print()

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

Print the class members.

Definition at line 542 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 182 of file TDecompQRH.cxx.

◆ SetMatrix()

void TDecompQRH::SetMatrix ( const TMatrixD & a )

virtual

Set matrix to be decomposed.

Definition at line 215 of file TDecompQRH.cxx.

◆ Solve() [1/3]

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 249 of file TDecompQRH.cxx.

◆ Solve() [2/3]

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

inlinevirtual

Implements TDecompBase.

Definition at line 65 of file TDecompQRH.h.

◆ Solve() [3/3]

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 304 of file TDecompQRH.cxx.

◆ TransSolve() [1/3]

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 363 of file TDecompQRH.cxx.

◆ TransSolve() [2/3]

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

inlinevirtual

Implements TDecompBase.

Definition at line 68 of file TDecompQRH.h.

◆ TransSolve() [3/3]

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 423 of file TDecompQRH.cxx.

Member Data Documentation

◆ 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:

[legend]

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

math/matrix/inc/TDecompQRH.h
math/matrix/src/TDecompQRH.cxx

Public Types

Public Member Functions

Protected Member Functions

Static Protected Member Functions

Protected Attributes

Additional Inherited Members

Member Enumeration Documentation

◆ anonymous enum

Constructor & Destructor Documentation

◆ TDecompQRH() [1/5]

◆ TDecompQRH() [2/5]

◆ TDecompQRH() [3/5]

◆ TDecompQRH() [4/5]

◆ TDecompQRH() [5/5]

◆ ~TDecompQRH()

Member Function Documentation

◆ Decompose()

◆ Det()

◆ GetDecompMatrix()

◆ GetNcols()

◆ GetNrows()

◆ GetQ()

◆ GetR()

◆ GetUp()

◆ GetW()

◆ Invert() [1/3]

◆ Invert() [2/3]

◆ Invert() [3/3]

◆ operator=()

◆ Print()

◆ QRH()

◆ SetMatrix()

◆ Solve() [1/3]

◆ Solve() [2/3]

◆ Solve() [3/3]

◆ TransSolve() [1/3]

◆ TransSolve() [2/3]

◆ TransSolve() [3/3]

Member Data Documentation

◆ fQ

◆ fR

◆ fUp

◆ fW