The Bunch-Kaufman diagonal pivoting method decomposes a real symmetric matrix A using.
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
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. | |
TDecompBK (const TDecompBK &another) | |
Copy constructor. | |
TDecompBK (const TMatrixDSym &m, Double_t tol=0.0) | |
Constructor for symmetric matrix A. | |
TDecompBK (Int_t nrows) | |
Constructor for (nrows x nrows) symmetric matrix. | |
TDecompBK (Int_t row_lwb, Int_t row_upb) | |
Constructor for ([row_lwb..row_upb] x [row_lwb..row_upb]) symmetric matrix. | |
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. | |
virtual void | Det (Double_t &, Double_t &) |
Matrix determinant det = d1*TMath::Power(2.,d2) | |
virtual Int_t | GetNcols () const |
virtual Int_t | GetNrows () const |
const TMatrixD & | GetU () |
TMatrixDSym | Invert () |
TMatrixDSym | Invert (Bool_t &status) |
For a symmetric matrix A(m,m), its inverse A_inv(m,m) is returned . | |
Bool_t | Invert (TMatrixDSym &inv) |
For a symmetric matrix A(m,m), its inverse A_inv(m,m) is returned . | |
TDecompBK & | operator= (const TDecompBK &source) |
Assignment operator. | |
void | Print (Option_t *opt="") const |
Print the class members. | |
virtual void | SetMatrix (const TMatrixDSym &a) |
Set the matrix to be decomposed, decomposition status is reset. | |
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. | |
virtual Bool_t | Solve (TVectorD &b) |
Solve Ax=b assuming the BK form of A is stored in fU . Solution returned in b. | |
virtual TVectorD | TransSolve (const TVectorD &b, Bool_t &ok) |
virtual Bool_t | TransSolve (TMatrixDColumn &b) |
virtual Bool_t | TransSolve (TVectorD &b) |
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TDecompBase () | |
Default constructor. | |
TDecompBase (const TDecompBase &another) | |
Copy constructor. | |
virtual | ~TDecompBase () |
virtual Double_t | Condition () |
Matrix condition number. | |
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) |
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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 |
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Int_t | Hager (Double_t &est, Int_t iter=5) |
void | ResetStatus () |
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virtual void | DoError (int level, const char *location, const char *fmt, va_list va) const |
Interface to ErrorHandler (protected). | |
void | MakeZombie () |
Protected Attributes | |
Int_t * | fIpiv |
Int_t | fNIpiv |
TMatrixD | fU |
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Int_t | fColLwb |
Double_t | fCondition |
Double_t | fDet1 |
Double_t | fDet2 |
Int_t | fRowLwb |
Double_t | fTol |
Additional Inherited Members | |
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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) } |
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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. | |
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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) } |
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enum | { kOnlyPrepStep = BIT(3) } |
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static void | DiagProd (const TVectorD &diag, Double_t tol, Double_t &d1, Double_t &d2) |
#include <TDecompBK.h>
TDecompBK::TDecompBK | ( | ) |
Default constructor.
Definition at line 64 of file TDecompBK.cxx.
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explicit |
Constructor for (nrows x nrows) symmetric matrix.
Definition at line 73 of file TDecompBK.cxx.
Constructor for ([row_lwb..row_upb] x [row_lwb..row_upb]) symmetric matrix.
Definition at line 84 of file TDecompBK.cxx.
TDecompBK::TDecompBK | ( | const TMatrixDSym & | m, |
Double_t | tol = 0.0 |
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) |
Constructor for symmetric matrix A.
Definition at line 97 of file TDecompBK.cxx.
TDecompBK::TDecompBK | ( | const TDecompBK & | another | ) |
Copy constructor.
Definition at line 120 of file TDecompBK.cxx.
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inlinevirtual |
Definition at line 43 of file TDecompBK.h.
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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.
Matrix determinant det = d1*TMath::Power(2.,d2)
Reimplemented from TDecompBase.
Definition at line 59 of file TDecompBK.h.
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inlineprotectedvirtual |
Implements TDecompBase.
Definition at line 34 of file TDecompBK.h.
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inlinevirtual |
Implements TDecompBase.
Definition at line 46 of file TDecompBK.h.
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inlinevirtual |
Implements TDecompBase.
Definition at line 45 of file TDecompBK.h.
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inline |
Definition at line 47 of file TDecompBK.h.
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inline |
Definition at line 64 of file TDecompBK.h.
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.
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.
Assignment operator.
Definition at line 660 of file TDecompBK.cxx.
Print the class members.
Reimplemented from TDecompBase.
Definition at line 648 of file TDecompBK.cxx.
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virtual |
Set the matrix to be decomposed, decomposition status is reset.
Definition at line 314 of file TDecompBK.cxx.
Implements TDecompBase.
Definition at line 54 of file TDecompBK.h.
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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 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.
Implements TDecompBase.
Definition at line 57 of file TDecompBK.h.
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inlinevirtual |
Implements TDecompBase.
Definition at line 58 of file TDecompBK.h.
Implements TDecompBase.
Definition at line 56 of file TDecompBK.h.
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protected |
Definition at line 31 of file TDecompBK.h.
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protected |
Definition at line 30 of file TDecompBK.h.
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protected |
Definition at line 32 of file TDecompBK.h.