Single Value Decomposition class.

For an (m x n) matrix A with m >= n, the singular value decomposition is an (m x m) orthogonal matrix fU, an (m x n) diagonal matrix fS, and an (n x n) orthogonal matrix fV so that A = U*S*V'.

If the row/column index of A starts at (rowLwb,colLwb) then the decomposed matrices/vectors start at :

fU   : (rowLwb,colLwb)
fV   : (colLwb,colLwb)
fSig : (colLwb)

The diagonal matrix fS is stored in the singular values vector fSig . The singular values, fSig[k] = S[k][k], are ordered so that fSig[0] >= fSig[1] >= ... >= fSig[n-1].

The singular value decomposition always exists, so the decomposition will (as long as m >=n) never fail. If m < n, the user should add sufficient zero rows to A , so that m == n

Here fTol is used to set the threshold on the minimum allowed value of the singular values: min_singular = fTol*max(fSig[i])

Definition at line 23 of file TDecompSVD.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
	TDecompSVD ()

	TDecompSVD (const TDecompSVD &another)
	Copy constructor.

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

	TDecompSVD (Int_t nrows, Int_t ncols)
	Constructor for (nrows x ncols) matrix.

	TDecompSVD (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.

virtual	~TDecompSVD ()

virtual Double_t	Condition ()
	Matrix condition number.

virtual Bool_t	Decompose ()
	SVD decomposition of matrix If the decomposition succeeds, bit kDecomposed is set , otherwise kSingular.

virtual void	Det (Double_t &d1, Double_t &d2)
	Matrix determinant det = d1*TMath::Power(2.,d2)

const TMatrixD	GetMatrix ()
	Reconstruct the original matrix using the decomposition parts.

virtual Int_t	GetNcols () const

virtual Int_t	GetNrows () const

const TVectorD &	GetSig ()

const TMatrixD &	GetU ()

const TMatrixD &	GetV ()

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 .

TDecompSVD &	operator= (const TDecompSVD &source)
	Assignment operator.

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

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

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

virtual Bool_t	Solve (TMatrixDColumn &b)
	Solve Ax=b assuming the SVD form of A is stored .

virtual Bool_t	Solve (TVectorD &b)
	Solve Ax=b assuming the SVD form of A is stored .

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

virtual Bool_t	TransSolve (TMatrixDColumn &b)
	Solve A^T x=b assuming the SVD form of A is stored . Solution returned in b.

virtual Bool_t	TransSolve (TVectorD &b)
	Solve A^T x=b assuming the SVD form of A is stored . Solution returned in b.

Public Member Functions inherited from TDecompBase
	TDecompBase ()
	Default constructor.

	TDecompBase (const TDecompBase &another)
	Copy constructor.

virtual	~TDecompBase ()

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.

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

Double_t	SetTol (Double_t tol)

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.

virtual void	AppendPad (Option_t *option="")
	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 TObject *	Clone (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 TObject *	DrawClone (Option_t *option="") const
	Draw a clone of this object in the current selected pad for instance with: `gROOT->SetSelectedPad(gPad)`.

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=0)
	Execute method on this object with the given parameter string, e.g.

virtual void	Execute (TMethod method, TObjArray params, Int_t *error=0)
	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 TObject *	FindObject (const char *name) const
	Must be redefined in derived classes.

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

virtual Option_t *	GetDrawOption () 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_t *	GetOption () 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.

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)
	Operator delete [].

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)

TObject &	operator= (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.

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=0, Int_t option=0, Int_t bufsize=0)
	Write this object to the current directory.

virtual Int_t	Write (const char *name=0, Int_t option=0, Int_t bufsize=0) const
	Write this object to the current directory.

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 ()

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	Bidiagonalize (TMatrixD &v, TMatrixD &u, TVectorD &sDiag, TVectorD &oDiag)
	Bidiagonalize the (m x n) - matrix a (stored in v) through a series of Householder transformations applied to the left (Q^T) and to the right (H) of a , so that A = Q .

static void	Diag_1 (TMatrixD &v, TVectorD &sDiag, TVectorD &oDiag, Int_t k)
	Step 1 in the matrix diagonalization.

static void	Diag_2 (TVectorD &sDiag, TVectorD &oDiag, Int_t k, Int_t l)
	Step 2 in the matrix diagonalization.

static void	Diag_3 (TMatrixD &v, TMatrixD &u, TVectorD &sDiag, TVectorD &oDiag, Int_t k, Int_t l)
	Step 3 in the matrix diagonalization.

static Bool_t	Diagonalize (TMatrixD &v, TMatrixD &u, TVectorD &sDiag, TVectorD &oDiag)
	Diagonalizes in an iterative fashion the bidiagonal matrix C as described through sDiag and oDiag, so that S' = U'^T .

static void	SortSingular (TMatrixD &v, TMatrixD &u, TVectorD &sDiag)
	Perform a permutation transformation on the diagonal matrix S', so that matrix S'' = U''^T .

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

Protected Attributes
TVectorD	fSig

TMatrixD	fU

TMatrixD	fV

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 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 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) }

Protected Types inherited from TObject
enum	{ kOnlyPrepStep = BIT(3) }

#include <TDecompSVD.h>

Inheritance diagram for TDecompSVD:

[legend]

Member Enumeration Documentation

◆ anonymous enum

anonymous enum

Enumerator
kWorkMax

Definition at line 43 of file TDecompSVD.h.

Constructor & Destructor Documentation

◆ TDecompSVD() [1/5]

TDecompSVD::TDecompSVD ( )

inline

Definition at line 45 of file TDecompSVD.h.

◆ TDecompSVD() [2/5]

TDecompSVD::TDecompSVD	(	Int_t	nrows,
		Int_t	ncols
	)

Constructor for (nrows x ncols) matrix.

Definition at line 52 of file TDecompSVD.cxx.

◆ TDecompSVD() [3/5]

TDecompSVD::TDecompSVD	(	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 66 of file TDecompSVD.cxx.

◆ TDecompSVD() [4/5]

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

Constructor for general matrix A .

Definition at line 85 of file TDecompSVD.cxx.

◆ TDecompSVD() [5/5]

TDecompSVD::TDecompSVD ( const TDecompSVD & another )

Copy constructor.

Definition at line 114 of file TDecompSVD.cxx.

◆ ~TDecompSVD()

virtual TDecompSVD::~TDecompSVD ( )

inlinevirtual

Definition at line 50 of file TDecompSVD.h.

Member Function Documentation

◆ Bidiagonalize()

Bool_t TDecompSVD::Bidiagonalize	(	TMatrixD &	v,
		TMatrixD &	u,
		TVectorD &	sDiag,
		TVectorD &	oDiag
	)

staticprotected

Bidiagonalize the (m x n) - matrix a (stored in v) through a series of Householder transformations applied to the left (Q^T) and to the right (H) of a , so that A = Q .

C . H^T with matrix C bidiagonal. Q and H are orthogonal matrices .

Output: v - (n x n) - matrix H in the (n x n) part of v u - (m x m) - matrix Q^T sDiag - diagonal of the (m x n) C oDiag - off-diagonal elements of matrix C

Test code for the output:

const Int_t nRow = v.GetNrows();
const Int_t nCol = v.GetNcols();
TMatrixD H(v); H.ResizeTo(nCol,nCol);
TMatrixD E1(nCol,nCol); E1.UnitMatrix();
TMatrixD Ht(TMatrixDBase::kTransposed,H);
Bool_t ok = kTRUE;
ok &= VerifyMatrixIdentity(Ht * H,E1,kTRUE,1.0e-13);
ok &= VerifyMatrixIdentity(H * Ht,E1,kTRUE,1.0e-13);
TMatrixD E2(nRow,nRow); E2.UnitMatrix();
TMatrixD Qt(u);
TMatrixD Q(TMatrixDBase::kTransposed,Qt);
ok &= VerifyMatrixIdentity(Q * Qt,E2,kTRUE,1.0e-13);
TMatrixD C(nRow,nCol);
TMatrixDDiag(C) = sDiag;
for (Int_t i = 0; i < nCol-1; i++)
  C(i,i+1) = oDiag(i+1);
TMatrixD A = Q*C*Ht;
ok &= VerifyMatrixIdentity(A,a,kTRUE,1.0e-13);

Definition at line 192 of file TDecompSVD.cxx.

◆ Condition()

Double_t TDecompSVD::Condition ( )

virtual

Matrix condition number.

Reimplemented from TDecompBase.

Definition at line 823 of file TDecompSVD.cxx.

◆ Decompose()

Bool_t TDecompSVD::Decompose ( )

virtual

SVD decomposition of matrix If the decomposition succeeds, bit kDecomposed is set , otherwise kSingular.

Implements TDecompBase.

Definition at line 123 of file TDecompSVD.cxx.

◆ Det()

void TDecompSVD::Det	(	Double_t &	d1,
		Double_t &	d2
	)

virtual

Matrix determinant det = d1*TMath::Power(2.,d2)

Reimplemented from TDecompBase.

Definition at line 846 of file TDecompSVD.cxx.

◆ Diag_1()

void TDecompSVD::Diag_1	(	TMatrixD &	v,
		TVectorD &	sDiag,
		TVectorD &	oDiag,
		Int_t	k
	)

staticprotected

Step 1 in the matrix diagonalization.

Definition at line 374 of file TDecompSVD.cxx.

◆ Diag_2()

void TDecompSVD::Diag_2	(	TVectorD &	sDiag,
		TVectorD &	oDiag,
		Int_t	k,
		Int_t	l
	)

staticprotected

Step 2 in the matrix diagonalization.

Definition at line 398 of file TDecompSVD.cxx.

◆ Diag_3()

void TDecompSVD::Diag_3	(	TMatrixD &	v,
		TMatrixD &	u,
		TVectorD &	sDiag,
		TVectorD &	oDiag,
		Int_t	k,
		Int_t	l
	)

staticprotected

Step 3 in the matrix diagonalization.

Definition at line 416 of file TDecompSVD.cxx.

◆ Diagonalize()

Bool_t TDecompSVD::Diagonalize	(	TMatrixD &	v,
		TMatrixD &	u,
		TVectorD &	sDiag,
		TVectorD &	oDiag
	)

staticprotected

Diagonalizes in an iterative fashion the bidiagonal matrix C as described through sDiag and oDiag, so that S' = U'^T .

C . V' is diagonal. U' and V' are orthogonal matrices .

Output:

v - (n x n) - matrix H . V' in the (n x n) part of v
u - (m x m) - matrix U'^T . Q^T
sDiag - diagonal of the (m x n) S'

return convergence flag: 0 -> no convergence 1 -> convergence

Test code for the output:

const Int_t nRow = v.GetNrows();
const Int_t nCol = v.GetNcols();
TMatrixD tmp = v; tmp.ResizeTo(nCol,nCol);
TMatrixD Vprime  = Ht*tmp;
TMatrixD Vprimet(TMatrixDBase::kTransposed,Vprime);
TMatrixD Uprimet = u*Q;
TMatrixD Uprime(TMatrixDBase::kTransposed,Uprimet);
TMatrixD Sprime(nRow,nCol);
TMatrixDDiag(Sprime) = sDiag;
ok &= VerifyMatrixIdentity(Uprimet * C * Vprime,Sprime,kTRUE,1.0e-13);
ok &= VerifyMatrixIdentity(Q*Uprime * Sprime * Vprimet * Ht,a,kTRUE,1.0e-13);

Definition at line 307 of file TDecompSVD.cxx.

◆ GetDecompMatrix()

virtual const TMatrixDBase & TDecompSVD::GetDecompMatrix ( ) const

inlineprotectedvirtual

Implements TDecompBase.

Definition at line 39 of file TDecompSVD.h.

◆ GetMatrix()

const TMatrixD TDecompSVD::GetMatrix ( )

Reconstruct the original matrix using the decomposition parts.

Definition at line 557 of file TDecompSVD.cxx.

◆ GetNcols()

Int_t TDecompSVD::GetNcols ( ) const

virtual

Implements TDecompBase.

Definition at line 870 of file TDecompSVD.cxx.

◆ GetNrows()

Int_t TDecompSVD::GetNrows ( ) const

virtual

Implements TDecompBase.

Definition at line 865 of file TDecompSVD.cxx.

◆ GetSig()

const TVectorD & TDecompSVD::GetSig ( )

inline

Definition at line 59 of file TDecompSVD.h.

◆ GetU()

const TMatrixD & TDecompSVD::GetU ( )

inline

Definition at line 55 of file TDecompSVD.h.

◆ GetV()

const TMatrixD & TDecompSVD::GetV ( )

inline

Definition at line 57 of file TDecompSVD.h.

◆ Invert() [1/3]

TMatrixD TDecompSVD::Invert ( )

inline

Definition at line 82 of file TDecompSVD.h.

◆ Invert() [2/3]

TMatrixD TDecompSVD::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 903 of file TDecompSVD.cxx.

◆ Invert() [3/3]

Bool_t TDecompSVD::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 881 of file TDecompSVD.cxx.

◆ operator=()

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

Assignment operator.

Definition at line 930 of file TDecompSVD.cxx.

◆ Print()

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

virtual

Print class members.

Reimplemented from TDecompBase.

Definition at line 919 of file TDecompSVD.cxx.

◆ SetMatrix()

void TDecompSVD::SetMatrix ( const TMatrixD & a )

virtual

Set matrix to be decomposed.

Definition at line 582 of file TDecompSVD.cxx.

◆ Solve() [1/3]

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

inlinevirtual

Implements TDecompBase.

Definition at line 66 of file TDecompSVD.h.

◆ Solve() [2/3]

Bool_t TDecompSVD::Solve ( TMatrixDColumn & cb )

virtual

Solve Ax=b assuming the SVD form of A is stored .

Solution returned in the matrix column cb b. If A is of size (m x n), input vector b should be of size (m), however, the solution, returned in b, will be in the first (n) elements .

For m > n , x is the least-squares solution of min(A . x - b)

Implements TDecompBase.

Definition at line 670 of file TDecompSVD.cxx.

◆ Solve() [3/3]

Bool_t TDecompSVD::Solve ( TVectorD & b )

virtual

Solve Ax=b assuming the SVD form of A is stored .

Solution returned in b. If A is of size (m x n), input vector b should be of size (m), however, the solution, returned in b, will be in the first (n) elements .

For m > n , x is the least-squares solution of min(A . x - b)

Implements TDecompBase.

Definition at line 615 of file TDecompSVD.cxx.

◆ SortSingular()

void TDecompSVD::SortSingular	(	TMatrixD &	v,
		TMatrixD &	u,
		TVectorD &	sDiag
	)

staticprotected

Perform a permutation transformation on the diagonal matrix S', so that matrix S'' = U''^T .

S' . V'' has diagonal elements ordered such that they do not increase.

Output:

v - (n x n) - matrix H . V' . V'' in the (n x n) part of v
u - (m x m) - matrix U''^T . U'^T . Q^T
sDiag - diagonal of the (m x n) S''

Definition at line 497 of file TDecompSVD.cxx.

◆ TransSolve() [1/3]

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

inlinevirtual

Implements TDecompBase.

Definition at line 72 of file TDecompSVD.h.

◆ TransSolve() [2/3]

Bool_t TDecompSVD::TransSolve ( TMatrixDColumn & b )

virtual

Solve A^T x=b assuming the SVD form of A is stored . Solution returned in b.

Implements TDecompBase.

Definition at line 772 of file TDecompSVD.cxx.

◆ TransSolve() [3/3]

Bool_t TDecompSVD::TransSolve ( TVectorD & b )

virtual

Solve A^T x=b assuming the SVD form of A is stored . Solution returned in b.

Implements TDecompBase.

Definition at line 723 of file TDecompSVD.cxx.

Member Data Documentation

◆ fSig

TVectorD TDecompSVD::fSig

protected

Definition at line 30 of file TDecompSVD.h.

◆ fU

TMatrixD TDecompSVD::fU

protected

Definition at line 28 of file TDecompSVD.h.

◆ fV

TMatrixD TDecompSVD::fV

protected

Definition at line 29 of file TDecompSVD.h.

Libraries for TDecompSVD:

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

math/matrix/inc/TDecompSVD.h
math/matrix/src/TDecompSVD.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

◆ TDecompSVD() [1/5]

◆ TDecompSVD() [2/5]

◆ TDecompSVD() [3/5]

◆ TDecompSVD() [4/5]

◆ TDecompSVD() [5/5]

◆ ~TDecompSVD()

Member Function Documentation

◆ Bidiagonalize()

◆ Condition()

◆ Decompose()

◆ Det()

◆ Diag_1()

◆ Diag_2()

◆ Diag_3()

◆ Diagonalize()

◆ GetDecompMatrix()

◆ GetMatrix()

◆ GetNcols()

◆ GetNrows()

◆ GetSig()

◆ GetU()

◆ GetV()

◆ Invert() [1/3]

◆ Invert() [2/3]

◆ Invert() [3/3]

◆ operator=()

◆ Print()

◆ SetMatrix()

◆ Solve() [1/3]

◆ Solve() [2/3]

◆ Solve() [3/3]

◆ SortSingular()

◆ TransSolve() [1/3]

◆ TransSolve() [2/3]

◆ TransSolve() [3/3]

Member Data Documentation

◆ fSig

◆ fU

◆ fV