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 = (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
	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.

	~TDecompSVD () override

Double_t	Condition () override
	Matrix condition number.

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

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

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

Int_t	GetNcols () const override

Int_t	GetNrows () const override

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 .

TClass *	IsA () const override

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

void	Print (Option_t *opt="") const override
	Print 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 SVD form of A is stored .

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

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 SVD form of A is stored . Solution returned in b.

Bool_t	TransSolve (TVectorD &b) override
	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.

	~TDecompBase () override

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)

void	StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b)

Public Member Functions inherited from TObject
	TObject ()
	TObject constructor.

	TObject (const TObject &object) noexcept
	TObject copy ctor.

virtual	~TObject ()
	TObject destructor.

void	AbstractMethod (const char *method) const
	Call this function within a function that you don't want to define as purely virtual, in order not to force all users deriving from that class to implement that maybe (on their side) unused function; but at the same time, emit a run-time warning if they try to call it, telling that it is not implemented in the derived class: action must thus be taken on the user side to override it.

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 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 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 (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 *, size_t)
	Operator delete for sized deallocation.

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 *, size_t)
	Operator delete [] for sized deallocation.

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)

TObject &	operator= (const TObject &rhs) noexcept
	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 TClass *	Class ()

static const char *	Class_Name ()

static constexpr Version_t	Class_Version ()

static const char *	DeclFileName ()

Static Public Member Functions inherited from TDecompBase
static TClass *	Class ()

static const char *	Class_Name ()

static constexpr Version_t	Class_Version ()

static const char *	DeclFileName ()

Static Public Member Functions inherited from TObject
static TClass *	Class ()

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 TMatrixDBase &	GetDecompMatrix () 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	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)

Static Protected Member Functions inherited from TObject
static void	SavePrimitiveConstructor (std::ostream &out, TClass cl, const char variable_name, const char *constructor_agrs="", Bool_t empty_line=kTRUE)
	Save object constructor in the output stream "out".

static void	SavePrimitiveDraw (std::ostream &out, const char variable_name, Option_t option=nullptr)
	Save invocation of primitive Draw() method Skipped if option contains "nodraw" string.

static TString	SavePrimitiveVector (std::ostream &out, const char prefix, Int_t len, Double_t arr, Bool_t empty_line=kFALSE)
	Save array in the output stream "out" as vector.

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
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 <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 51 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 65 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 84 of file TDecompSVD.cxx.

◆ TDecompSVD() [5/5]

TDecompSVD::TDecompSVD ( const TDecompSVD & another )

Copy constructor.

Definition at line 113 of file TDecompSVD.cxx.

◆ ~TDecompSVD()

TDecompSVD::~TDecompSVD ( )

inlineoverride

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 191 of file TDecompSVD.cxx.

◆ Class()

static TClass * TDecompSVD::Class ( )

static

Returns: TClass describing this class

◆ Class_Name()

static const char * TDecompSVD::Class_Name ( )

static

Returns: Name of this class

◆ Class_Version()

static constexpr Version_t TDecompSVD::Class_Version ( )

inlinestaticconstexpr

Returns: Version of this class

Definition at line 88 of file TDecompSVD.h.

◆ Condition()

Double_t TDecompSVD::Condition ( )

overridevirtual

Matrix condition number.

Reimplemented from TDecompBase.

Definition at line 822 of file TDecompSVD.cxx.

◆ DeclFileName()

static const char * TDecompSVD::DeclFileName ( )

inlinestatic

Returns: Name of the file containing the class declaration

Definition at line 88 of file TDecompSVD.h.

◆ Decompose()

Bool_t TDecompSVD::Decompose ( )

overridevirtual

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

Implements TDecompBase.

Definition at line 122 of file TDecompSVD.cxx.

◆ Det()

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

overridevirtual

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

Reimplemented from TDecompBase.

Definition at line 845 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 373 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 397 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 415 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 306 of file TDecompSVD.cxx.

◆ GetDecompMatrix()

const TMatrixDBase & TDecompSVD::GetDecompMatrix ( ) const

inlineoverrideprotectedvirtual

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 556 of file TDecompSVD.cxx.

◆ GetNcols()

Int_t TDecompSVD::GetNcols ( ) const

overridevirtual

Implements TDecompBase.

Definition at line 869 of file TDecompSVD.cxx.

◆ GetNrows()

Int_t TDecompSVD::GetNrows ( ) const

overridevirtual

Implements TDecompBase.

Definition at line 864 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 902 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 880 of file TDecompSVD.cxx.

◆ IsA()

TClass * TDecompSVD::IsA ( ) const

inlineoverridevirtual

Returns: TClass describing current object

Reimplemented from TDecompBase.

Definition at line 88 of file TDecompSVD.h.

◆ operator=()

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

Assignment operator.

Definition at line 929 of file TDecompSVD.cxx.

◆ Print()

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

overridevirtual

Print class members.

Reimplemented from TDecompBase.

Definition at line 918 of file TDecompSVD.cxx.

◆ SetMatrix()

void TDecompSVD::SetMatrix ( const TMatrixD & a )

virtual

Set matrix to be decomposed.

Definition at line 581 of file TDecompSVD.cxx.

◆ Solve() [1/3]

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

inlineoverridevirtual

Implements TDecompBase.

Definition at line 66 of file TDecompSVD.h.

◆ Solve() [2/3]

Bool_t TDecompSVD::Solve ( TMatrixDColumn & cb )

overridevirtual

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 669 of file TDecompSVD.cxx.

◆ Solve() [3/3]

Bool_t TDecompSVD::Solve ( TVectorD & b )

overridevirtual

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 614 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 496 of file TDecompSVD.cxx.

◆ Streamer()

void TDecompSVD::Streamer ( TBuffer & R__b )

overridevirtual

Stream an object of class TObject.

Reimplemented from TDecompBase.

◆ StreamerNVirtual()

void TDecompSVD::StreamerNVirtual ( TBuffer & ClassDef_StreamerNVirtual_b )

inline

Definition at line 88 of file TDecompSVD.h.

◆ TransSolve() [1/3]

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

inlineoverridevirtual

Implements TDecompBase.

Definition at line 72 of file TDecompSVD.h.

◆ TransSolve() [2/3]

Bool_t TDecompSVD::TransSolve ( TMatrixDColumn & b )

overridevirtual

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

Implements TDecompBase.

Definition at line 771 of file TDecompSVD.cxx.

◆ TransSolve() [3/3]

Bool_t TDecompSVD::TransSolve ( TVectorD & b )

overridevirtual

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

Implements TDecompBase.

Definition at line 722 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:

[legend]

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

Static 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()

◆ Class()

◆ Class_Name()

◆ Class_Version()

◆ Condition()

◆ DeclFileName()

◆ 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]

◆ IsA()

◆ operator=()

◆ Print()

◆ SetMatrix()

◆ Solve() [1/3]

◆ Solve() [2/3]

◆ Solve() [3/3]

◆ SortSingular()

◆ Streamer()

◆ StreamerNVirtual()

◆ TransSolve() [1/3]

◆ TransSolve() [2/3]

◆ TransSolve() [3/3]

Member Data Documentation

◆ fSig

◆ fU

◆ fV