QR Decomposition class.
Decompose a general (m x n) matrix A into A = fQ' fR H where
If row/column index of A starts at (rowLwb,colLwb) then the decomposed matrices start from :
In order to get thw QR dcomposition of A (i.e. A = QR ) The orthoginal matrix Q needs to be computed from the internal Q' and the up's and beta's vector defining the Householder transformation
The orthogonal Q matrix is returned to the user by calling the function TDecompQRH::GetOrthogonalMatrix()
Errors arise from formation of reflectors i.e. singularity . Note it attempts to handle the cases where the nRow <= nCol .
Definition at line 25 of file TDecompQRH.h.
Public Types | |
enum | { kWorkMax = 100 } |
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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 | |
TDecompQRH () | |
TDecompQRH (const TDecompQRH &another) | |
Copy constructor. | |
TDecompQRH (const TMatrixD &m, Double_t tol=0.0) | |
Constructor for general matrix A . | |
TDecompQRH (Int_t nrows, Int_t ncols) | |
Constructor for (nrows x ncols) matrix. | |
TDecompQRH (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. | |
~TDecompQRH () override | |
Bool_t | Decompose () override |
QR decomposition of matrix a by Householder transformations, see Golub & Loan first edition p41 & Sec 6.2. | |
void | Det (Double_t &d1, Double_t &d2) override |
This routine calculates the absolute (!) value of the determinant |det| = d1*TMath::Power(2.,d2) | |
Int_t | GetNcols () const override |
Int_t | GetNrows () const override |
TMatrixD | GetOrthogonalMatrix () const |
For a matrix A(m,n), return the OtrhogonalMatrix Q such as A = Q * R. | |
virtual const TMatrixD & | GetQ () |
virtual const TMatrixD & | GetR () |
const TMatrixD & | GetTriangularMatrix () const |
virtual const TVectorD & | GetUp () |
virtual const TVectorD & | GetW () |
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 |
TDecompQRH & | operator= (const TDecompQRH &source) |
Assignment operator. | |
void | Print (Option_t *opt="") const override |
Print the 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 QR form of A is stored in fR,fQ and fW, but assume b has not been transformed. | |
Bool_t | Solve (TVectorD &b) override |
Solve Ax=b assuming the QR form of A is stored in fR,fQ and fW, but assume b has not been transformed. | |
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 QR form of A is stored in fR,fQ and fW, but assume b has not been transformed. | |
Bool_t | TransSolve (TVectorD &b) override |
Solve A^T x=b assuming the QR form of A is stored in fR,fQ and fW, but assume b has not been transformed. | |
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TDecompBase () | |
Default constructor. | |
TDecompBase (const TDecompBase &another) | |
Copy constructor. | |
~TDecompBase () override | |
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) |
void | StreamerNVirtual (TBuffer &ClassDef_StreamerNVirtual_b) |
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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 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. | |
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. | |
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 () |
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static TClass * | Class () |
static const char * | Class_Name () |
static constexpr Version_t | Class_Version () |
static const char * | DeclFileName () |
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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 |
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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 () |
Static Protected Member Functions | |
static Bool_t | QRH (TMatrixD &q, TVectorD &diagR, TVectorD &up, TVectorD &w, Double_t tol) |
Decomposition function . | |
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static void | DiagProd (const TVectorD &diag, Double_t tol, Double_t &d1, Double_t &d2) |
Protected Attributes | |
TMatrixD | fQ |
TMatrixD | fR |
TVectorD | fUp |
TVectorD | fW |
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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 | { 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 )) } |
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enum | { kOnlyPrepStep = (1ULL << ( 3 )) } |
#include <TDecompQRH.h>
anonymous enum |
Enumerator | |
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kWorkMax |
Definition at line 41 of file TDecompQRH.h.
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inline |
Definition at line 43 of file TDecompQRH.h.
Constructor for (nrows x ncols) matrix.
Definition at line 55 of file TDecompQRH.cxx.
Constructor for ([row_lwb..row_upb] x [col_lwb..col_upb]) matrix.
Definition at line 76 of file TDecompQRH.cxx.
Constructor for general matrix A .
Definition at line 103 of file TDecompQRH.cxx.
TDecompQRH::TDecompQRH | ( | const TDecompQRH & | another | ) |
Copy constructor.
Definition at line 137 of file TDecompQRH.cxx.
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inlineoverride |
Definition at line 48 of file TDecompQRH.h.
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inlinestaticconstexpr |
Definition at line 83 of file TDecompQRH.h.
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inlinestatic |
Definition at line 83 of file TDecompQRH.h.
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overridevirtual |
QR decomposition of matrix a by Householder transformations, see Golub & Loan first edition p41 & Sec 6.2.
First fR is returned in upper triang of fQ and diagR. fQ returned in 'u-form' in lower triang of fQ and fW, the latter containing the "Householder betas". If the decomposition succeeds, bit kDecomposed is set , otherwise kSingular
Implements TDecompBase.
Definition at line 150 of file TDecompQRH.cxx.
This routine calculates the absolute (!) value of the determinant |det| = d1*TMath::Power(2.,d2)
Reimplemented from TDecompBase.
Definition at line 493 of file TDecompQRH.cxx.
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inlineoverrideprotectedvirtual |
Implements TDecompBase.
Definition at line 37 of file TDecompQRH.h.
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inlineoverridevirtual |
Implements TDecompBase.
Definition at line 51 of file TDecompQRH.h.
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inlineoverridevirtual |
Implements TDecompBase.
Definition at line 50 of file TDecompQRH.h.
TMatrixD TDecompQRH::GetOrthogonalMatrix | ( | ) | const |
For a matrix A(m,n), return the OtrhogonalMatrix Q such as A = Q * R.
Note that this Q is not th einternal fQ matrix obtained in the QRH decomposition, but can be computed from the fQ and the up and beta vector's defining the Householder transformation
Definition at line 516 of file TDecompQRH.cxx.
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inlinevirtual |
Definition at line 52 of file TDecompQRH.h.
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inlinevirtual |
Definition at line 54 of file TDecompQRH.h.
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inline |
Definition at line 62 of file TDecompQRH.h.
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inlinevirtual |
Definition at line 56 of file TDecompQRH.h.
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inlinevirtual |
Definition at line 58 of file TDecompQRH.h.
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inline |
Definition at line 77 of file TDecompQRH.h.
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 565 of file TDecompQRH.cxx.
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 547 of file TDecompQRH.cxx.
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inlineoverridevirtual |
Reimplemented from TDecompBase.
Definition at line 83 of file TDecompQRH.h.
TDecompQRH & TDecompQRH::operator= | ( | const TDecompQRH & | source | ) |
Assignment operator.
Definition at line 593 of file TDecompQRH.cxx.
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overridevirtual |
Print the class members.
Reimplemented from TDecompBase.
Definition at line 581 of file TDecompQRH.cxx.
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staticprotected |
Decomposition function .
Definition at line 189 of file TDecompQRH.cxx.
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virtual |
Set matrix to be decomposed.
Definition at line 222 of file TDecompQRH.cxx.
Implements TDecompBase.
Definition at line 68 of file TDecompQRH.h.
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overridevirtual |
Solve Ax=b assuming the QR form of A is stored in fR,fQ and fW, but assume b has not been transformed.
Solution returned in b.
Implements TDecompBase.
Definition at line 311 of file TDecompQRH.cxx.
Solve Ax=b assuming the QR form of A is stored in fR,fQ and fW, but assume b has not been transformed.
Solution returned in b.
Implements TDecompBase.
Definition at line 256 of file TDecompQRH.cxx.
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overridevirtual |
Stream an object of class TObject.
Reimplemented from TDecompBase.
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inline |
Definition at line 83 of file TDecompQRH.h.
Implements TDecompBase.
Definition at line 71 of file TDecompQRH.h.
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overridevirtual |
Solve A^T x=b assuming the QR form of A is stored in fR,fQ and fW, but assume b has not been transformed.
Solution returned in b.
Implements TDecompBase.
Definition at line 430 of file TDecompQRH.cxx.
Solve A^T x=b assuming the QR form of A is stored in fR,fQ and fW, but assume b has not been transformed.
Solution returned in b.
Implements TDecompBase.
Definition at line 370 of file TDecompQRH.cxx.
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protected |
Definition at line 30 of file TDecompQRH.h.
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Definition at line 31 of file TDecompQRH.h.
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Definition at line 32 of file TDecompQRH.h.
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Definition at line 33 of file TDecompQRH.h.