ROOT   Reference Guide
TDecompBK Class Reference

The Bunch-Kaufman diagonal pivoting method decomposes a real symmetric matrix A using.

A = U*D*U^T
static double A[]
double T(double x)
Definition: ChebyshevPol.h:34

where U is a product of permutation and unit upper triangular matrices, U^T is the transpose of U, and D is symmetric and block diagonal with 1-by-1 and 2-by-2 diagonal blocks.

U = P(n-1)*U(n-1)* ... P(k)U(k) ..., i.e., U is a product of terms P(k)*U(k), where k decreases from n-1 to 0 in steps of 1 or 2, and D is a block diagonal matrix with 1-by-1 and 2-by-2 diagonal blocks D(k). P(k) is a permutation matrix as defined by IPIV(k), and U(k) is a unit upper triangular matrix, such that if the diagonal block D(k) is of order s (s = 1 or 2), then

( I v 0 ) k-s
U(k) = ( 0 I 0 ) s
( 0 0 I ) n-k
k-s s n-k
const Int_t n
Definition: legend1.C:16
#define I(x, y, z)
static constexpr double s

If s = 1, D(k) overwrites A(k,k), and v overwrites A(0:k-1,k). If s = 2, the upper triangle of D(k) overwrites A(k-1,k-1), A(k-1,k), and A(k,k), and v overwrites A(0:k-2,k-1:k).

fU contains on entry the symmetric matrix A of which only the upper triangular part is referenced . On exit fU contains the block diagonal matrix D and the multipliers used to obtain the factor U, see above .

fIpiv if dimension n contains details of the interchanges and the the block structure of D . If (fIPiv(k) > 0, then rows and columns k and fIPiv(k) were interchanged and D(k,k) is a 1-by-1 diagonal block. If IPiv(k) = fIPiv(k-1) < 0, rows and columns k-1 and -IPiv(k) were interchanged and D(k-1:k,k-1:k) is a 2-by-2 diagonal block.

Definition at line 26 of file TDecompBK.h.

## Public Member Functions

TDecompBK ()
Default constructor. More...

TDecompBK (const TDecompBK &another)
Copy constructor. More...

TDecompBK (const TMatrixDSym &m, Double_t tol=0.0)
Constructor for symmetric matrix A. More...

TDecompBK (Int_t nrows)
Constructor for (nrows x nrows) symmetric matrix. More...

TDecompBK (Int_t row_lwb, Int_t row_upb)
Constructor for ([row_lwb..row_upb] x [row_lwb..row_upb]) symmetric matrix. More...

virtual ~TDecompBK ()

virtual Bool_t Decompose ()
Matrix A is decomposed in components U and D so that A = U*D*U^T If the decomposition succeeds, bit kDecomposed is set , otherwise kSingular. More...

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

virtual Int_t GetNcols () const

virtual Int_t GetNrows () const

const TMatrixDGetU ()

TMatrixDSym Invert ()

TMatrixDSym Invert (Bool_t &status)
For a symmetric matrix A(m,m), its inverse A_inv(m,m) is returned . More...

Bool_t Invert (TMatrixDSym &inv)
For a symmetric matrix A(m,m), its inverse A_inv(m,m) is returned . More...

TDecompBKoperator= (const TDecompBK &source)
Assignment operator. More...

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

virtual void SetMatrix (const TMatrixDSym &a)
Set the matrix to be decomposed, decomposition status is reset. More...

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

virtual Bool_t Solve (TMatrixDColumn &b)
Solve Ax=b assuming the BK form of A is stored in fU . Solution returned in b. More...

virtual Bool_t Solve (TVectorD &b)
Solve Ax=b assuming the BK form of A is stored in fU . Solution returned in b. More...

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

virtual Bool_t TransSolve (TMatrixDColumn &b)

virtual Bool_t TransSolve (TVectorD &b)

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...

virtual Bool_t Decompose ()=0

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

Int_t GetColLwb () const

Double_t GetCondition () const

Double_t GetDet1 () const

Double_t GetDet2 () const

virtual Int_t GetNcols () const =0

virtual Int_t GetNrows () const =0

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...

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

Double_t SetTol (Double_t tol)

virtual TVectorD Solve (const TVectorD &b, Bool_t &ok)=0

virtual Bool_t Solve (TMatrixDColumn &b)=0

virtual Bool_t Solve (TVectorD &b)=0

virtual TVectorD TransSolve (const TVectorD &b, Bool_t &ok)=0

virtual Bool_t TransSolve (TMatrixDColumn &b)=0

virtual Bool_t TransSolve (TVectorD &b)=0

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...

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 void Print (Option_t *option="") const
This method must be overridden when a class wants to print itself. 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
virtual const TMatrixDBaseGetDecompMatrix () const =0

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 ()

## Protected Attributes

Int_tfIpiv

Int_t fNIpiv

TMatrixD fU

Protected Attributes inherited from TDecompBase
Int_t fColLwb

Double_t fCondition

Double_t fDet1

Double_t fDet2

Int_t fRowLwb

Double_t fTol

Public Types inherited from TObject
enum  {
kIsOnHeap = 0x01000000 , kNotDeleted = 0x02000000 , kZombie = 0x04000000 , kInconsistent = 0x08000000 ,
}

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)
}

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)
}

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

#include <TDecompBK.h>

Inheritance diagram for TDecompBK:
[legend]

## ◆ TDecompBK() [1/5]

 TDecompBK::TDecompBK ( )

Default constructor.

Definition at line 64 of file TDecompBK.cxx.

## ◆ TDecompBK() [2/5]

 TDecompBK::TDecompBK ( Int_t nrows )
explicit

Constructor for (nrows x nrows) symmetric matrix.

Definition at line 73 of file TDecompBK.cxx.

## ◆ TDecompBK() [3/5]

 TDecompBK::TDecompBK ( Int_t row_lwb, Int_t row_upb )

Constructor for ([row_lwb..row_upb] x [row_lwb..row_upb]) symmetric matrix.

Definition at line 84 of file TDecompBK.cxx.

## ◆ TDecompBK() [4/5]

 TDecompBK::TDecompBK ( const TMatrixDSym & m, Double_t tol = 0.0 )

Constructor for symmetric matrix A.

Definition at line 97 of file TDecompBK.cxx.

## ◆ TDecompBK() [5/5]

 TDecompBK::TDecompBK ( const TDecompBK & another )

Copy constructor.

Definition at line 120 of file TDecompBK.cxx.

## ◆ ~TDecompBK()

 virtual TDecompBK::~TDecompBK ( )
inlinevirtual

Definition at line 43 of file TDecompBK.h.

## ◆ Decompose()

 Bool_t TDecompBK::Decompose ( )
virtual

Matrix A is decomposed in components U and D so that A = U*D*U^T If the decomposition succeeds, bit kDecomposed is set , otherwise kSingular.

Implements TDecompBase.

Definition at line 131 of file TDecompBK.cxx.

## ◆ Det()

 virtual void TDecompBK::Det ( Double_t & d1, Double_t & d2 )
inlinevirtual

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

Reimplemented from TDecompBase.

Definition at line 59 of file TDecompBK.h.

## ◆ GetDecompMatrix()

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

Implements TDecompBase.

Definition at line 34 of file TDecompBK.h.

## ◆ GetNcols()

 virtual Int_t TDecompBK::GetNcols ( ) const
inlinevirtual

Implements TDecompBase.

Definition at line 46 of file TDecompBK.h.

## ◆ GetNrows()

 virtual Int_t TDecompBK::GetNrows ( ) const
inlinevirtual

Implements TDecompBase.

Definition at line 45 of file TDecompBK.h.

## ◆ GetU()

 const TMatrixD & TDecompBK::GetU ( )
inline

Definition at line 47 of file TDecompBK.h.

## ◆ Invert() [1/3]

 TMatrixDSym TDecompBK::Invert ( )
inline

Definition at line 64 of file TDecompBK.h.

## ◆ Invert() [2/3]

 TMatrixDSym TDecompBK::Invert ( Bool_t & status )

For a symmetric matrix A(m,m), its inverse A_inv(m,m) is returned .

Definition at line 633 of file TDecompBK.cxx.

## ◆ Invert() [3/3]

 Bool_t TDecompBK::Invert ( TMatrixDSym & inv )

For a symmetric matrix A(m,m), its inverse A_inv(m,m) is returned .

Definition at line 610 of file TDecompBK.cxx.

## ◆ operator=()

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

Assignment operator.

Definition at line 660 of file TDecompBK.cxx.

## ◆ Print()

 void TDecompBK::Print ( Option_t * opt = "" ) const
virtual

Print the class members.

Reimplemented from TDecompBase.

Definition at line 648 of file TDecompBK.cxx.

## ◆ SetMatrix()

 void TDecompBK::SetMatrix ( const TMatrixDSym & a )
virtual

Set the matrix to be decomposed, decomposition status is reset.

Definition at line 314 of file TDecompBK.cxx.

## ◆ Solve() [1/3]

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

Implements TDecompBase.

Definition at line 54 of file TDecompBK.h.

## ◆ Solve() [2/3]

 Bool_t TDecompBK::Solve ( TMatrixDColumn & b )
virtual

Solve Ax=b assuming the BK form of A is stored in fU . Solution returned in b.

Implements TDecompBase.

Definition at line 473 of file TDecompBK.cxx.

## ◆ Solve() [3/3]

 Bool_t TDecompBK::Solve ( TVectorD & b )
virtual

Solve Ax=b assuming the BK form of A is stored in fU . Solution returned in b.

Implements TDecompBase.

Definition at line 339 of file TDecompBK.cxx.

## ◆ TransSolve() [1/3]

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

Implements TDecompBase.

Definition at line 57 of file TDecompBK.h.

## ◆ TransSolve() [2/3]

 virtual Bool_t TDecompBK::TransSolve ( TMatrixDColumn & b )
inlinevirtual

Implements TDecompBase.

Definition at line 58 of file TDecompBK.h.

## ◆ TransSolve() [3/3]

 virtual Bool_t TDecompBK::TransSolve ( TVectorD & b )
inlinevirtual

Implements TDecompBase.

Definition at line 56 of file TDecompBK.h.

## ◆ fIpiv

 Int_t* TDecompBK::fIpiv
protected

Definition at line 31 of file TDecompBK.h.

## ◆ fNIpiv

 Int_t TDecompBK::fNIpiv
protected

Definition at line 30 of file TDecompBK.h.

## ◆ fU

 TMatrixD TDecompBK::fU
protected

Definition at line 32 of file TDecompBK.h.

Libraries for TDecompBK:
[legend]

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