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Reference Guide
TDecompBK Class Reference

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

A = U*D*U^T

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

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...
 
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 ()
 

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
 

Additional Inherited Members

- 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)
}
 
- 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]

Constructor & Destructor Documentation

◆ 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 49 of file TDecompBK.h.

Member Function Documentation

◆ 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 65 of file TDecompBK.h.

◆ GetDecompMatrix()

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

Implements TDecompBase.

Definition at line 40 of file TDecompBK.h.

◆ GetNcols()

virtual Int_t TDecompBK::GetNcols ( ) const
inlinevirtual

Implements TDecompBase.

Definition at line 52 of file TDecompBK.h.

◆ GetNrows()

virtual Int_t TDecompBK::GetNrows ( ) const
inlinevirtual

Implements TDecompBase.

Definition at line 51 of file TDecompBK.h.

◆ GetU()

const TMatrixD& TDecompBK::GetU ( )
inline

Definition at line 53 of file TDecompBK.h.

◆ Invert() [1/3]

TMatrixDSym TDecompBK::Invert ( )
inline

Definition at line 70 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 60 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 63 of file TDecompBK.h.

◆ TransSolve() [2/3]

virtual Bool_t TDecompBK::TransSolve ( TMatrixDColumn b)
inlinevirtual

Implements TDecompBase.

Definition at line 64 of file TDecompBK.h.

◆ TransSolve() [3/3]

virtual Bool_t TDecompBK::TransSolve ( TVectorD b)
inlinevirtual

Implements TDecompBase.

Definition at line 62 of file TDecompBK.h.

Member Data Documentation

◆ fIpiv

Int_t* TDecompBK::fIpiv
protected

Definition at line 37 of file TDecompBK.h.

◆ fNIpiv

Int_t TDecompBK::fNIpiv
protected

Definition at line 36 of file TDecompBK.h.

◆ fU

TMatrixD TDecompBK::fU
protected

Definition at line 38 of file TDecompBK.h.

Libraries for TDecompBK:
[legend]

The documentation for this class was generated from the following files:
n
const Int_t n
Definition: legend1.C:16
TGeant4Unit::s
static constexpr double s
Definition: TGeant4SystemOfUnits.h:168
ROOT::Math::Cephes::A
static double A[]
Definition: SpecFuncCephes.cxx:170
v
@ v
Definition: rootcling_impl.cxx:3635
ROOT::Math::Chebyshev::T
double T(double x)
Definition: ChebyshevPol.h:52
I
#define I(x, y, z)