ROOT 6.18/05 Reference Guide |
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 :
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 = 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) } |
Public Member Functions | |
TDecompSVD () | |
TDecompSVD (const TDecompSVD &another) | |
Copy constructor. More... | |
TDecompSVD (const TMatrixD &m, Double_t tol=0.0) | |
Constructor for general matrix A . More... | |
TDecompSVD (Int_t nrows, Int_t ncols) | |
Constructor for (nrows x ncols) matrix. More... | |
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. More... | |
virtual | ~TDecompSVD () |
virtual Double_t | Condition () |
Matrix condition number. More... | |
virtual Bool_t | Decompose () |
SVD decomposition of matrix If the decomposition succeeds, bit kDecomposed is set , otherwise kSingular. More... | |
virtual void | Det (Double_t &d1, Double_t &d2) |
Matrix determinant det = d1*TMath::Power(2.,d2) More... | |
const TMatrixD | GetMatrix () |
Reconstruct the original matrix using the decomposition parts. More... | |
virtual Int_t | GetNcols () const |
virtual Int_t | GetNrows () const |
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 . More... | |
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 . More... | |
TDecompSVD & | operator= (const TDecompSVD &source) |
Assignment operator. More... | |
void | Print (Option_t *opt="") const |
Print class members. More... | |
virtual void | SetMatrix (const TMatrixD &a) |
Set matrix to be decomposed. More... | |
virtual TVectorD | Solve (const TVectorD &b, Bool_t &ok) |
virtual Bool_t | Solve (TMatrixDColumn &b) |
Solve Ax=b assuming the SVD form of A is stored . More... | |
virtual Bool_t | Solve (TVectorD &b) |
Solve Ax=b assuming the SVD form of A is stored . More... | |
virtual TVectorD | TransSolve (const TVectorD &b, Bool_t &ok) |
virtual Bool_t | TransSolve (TMatrixDColumn &b) |
Solve A^T x=b assuming the SVD form of A is stored . Solution returned in b. More... | |
virtual Bool_t | TransSolve (TVectorD &b) |
Solve A^T x=b assuming the SVD form of A is stored . Solution returned in b. More... | |
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... | |
TDecompBase & | operator= (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... | |
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 TObject * | Clone (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 TObject * | DrawClone (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 TObject * | FindObject (const char *name) const |
Must be redefined in derived classes. More... | |
virtual TObject * | FindObject (const TObject *obj) const |
Must be redefined in derived classes. More... | |
virtual Option_t * | GetDrawOption () 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_t * | GetOption () 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... | |
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. 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 TMatrixDBase & | GetDecompMatrix () const |
Protected Member Functions inherited from TDecompBase | |
virtual const TMatrixDBase & | GetDecompMatrix () 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 () |
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 . More... | |
static void | Diag_1 (TMatrixD &v, TVectorD &sDiag, TVectorD &oDiag, Int_t k) |
Step 1 in the matrix diagonalization. More... | |
static void | Diag_2 (TVectorD &sDiag, TVectorD &oDiag, Int_t k, Int_t l) |
Step 2 in the matrix diagonalization. More... | |
static void | Diag_3 (TMatrixD &v, TMatrixD &u, TVectorD &sDiag, TVectorD &oDiag, Int_t k, Int_t l) |
Step 3 in the matrix diagonalization. More... | |
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 . More... | |
static void | SortSingular (TMatrixD &v, TMatrixD &u, TVectorD &sDiag) |
Perform a permutation transformation on the diagonal matrix S', so that matrix S'' = U''^T . More... | |
Static Protected Member Functions inherited from TDecompBase | |
static void | DiagProd (const TVectorD &diag, Double_t tol, Double_t &d1, Double_t &d2) |
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 | |
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) } |
#include <TDecompSVD.h>
anonymous enum |
Enumerator | |
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kWorkMax |
Definition at line 43 of file TDecompSVD.h.
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inline |
Definition at line 45 of file TDecompSVD.h.
Constructor for (nrows x ncols) matrix.
Definition at line 52 of file TDecompSVD.cxx.
Constructor for ([row_lwb..row_upb] x [col_lwb..col_upb]) matrix.
Definition at line 66 of file TDecompSVD.cxx.
Constructor for general matrix A .
Definition at line 85 of file TDecompSVD.cxx.
TDecompSVD::TDecompSVD | ( | const TDecompSVD & | another | ) |
Copy constructor.
Definition at line 114 of file TDecompSVD.cxx.
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inlinevirtual |
Definition at line 50 of file TDecompSVD.h.
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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:
Definition at line 192 of file TDecompSVD.cxx.
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Matrix condition number.
Reimplemented from TDecompBase.
Definition at line 823 of file TDecompSVD.cxx.
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SVD decomposition of matrix If the decomposition succeeds, bit kDecomposed is set , otherwise kSingular.
Implements TDecompBase.
Definition at line 123 of file TDecompSVD.cxx.
Matrix determinant det = d1*TMath::Power(2.,d2)
Reimplemented from TDecompBase.
Definition at line 846 of file TDecompSVD.cxx.
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staticprotected |
Step 1 in the matrix diagonalization.
Definition at line 374 of file TDecompSVD.cxx.
Step 2 in the matrix diagonalization.
Definition at line 398 of file TDecompSVD.cxx.
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staticprotected |
Step 3 in the matrix diagonalization.
Definition at line 416 of file TDecompSVD.cxx.
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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:
sDiag - diagonal of the (m x n) S'
return convergence flag: 0 -> no convergence 1 -> convergence
Test code for the output:
Definition at line 307 of file TDecompSVD.cxx.
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inlineprotectedvirtual |
Implements TDecompBase.
Definition at line 39 of file TDecompSVD.h.
const TMatrixD TDecompSVD::GetMatrix | ( | ) |
Reconstruct the original matrix using the decomposition parts.
Definition at line 557 of file TDecompSVD.cxx.
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virtual |
Implements TDecompBase.
Definition at line 870 of file TDecompSVD.cxx.
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virtual |
Implements TDecompBase.
Definition at line 865 of file TDecompSVD.cxx.
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inline |
Definition at line 59 of file TDecompSVD.h.
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inline |
Definition at line 55 of file TDecompSVD.h.
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inline |
Definition at line 57 of file TDecompSVD.h.
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inline |
Definition at line 82 of file TDecompSVD.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 903 of file TDecompSVD.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 881 of file TDecompSVD.cxx.
TDecompSVD & TDecompSVD::operator= | ( | const TDecompSVD & | source | ) |
Assignment operator.
Definition at line 930 of file TDecompSVD.cxx.
Set matrix to be decomposed.
Definition at line 582 of file TDecompSVD.cxx.
Implements TDecompBase.
Definition at line 66 of file TDecompSVD.h.
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virtual |
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 670 of file TDecompSVD.cxx.
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 615 of file TDecompSVD.cxx.
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:
Definition at line 497 of file TDecompSVD.cxx.
Implements TDecompBase.
Definition at line 72 of file TDecompSVD.h.
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Solve A^T x=b assuming the SVD form of A is stored . Solution returned in b.
Implements TDecompBase.
Definition at line 772 of file TDecompSVD.cxx.
Solve A^T x=b assuming the SVD form of A is stored . Solution returned in b.
Implements TDecompBase.
Definition at line 723 of file TDecompSVD.cxx.
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protected |
Definition at line 30 of file TDecompSVD.h.
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Definition at line 28 of file TDecompSVD.h.
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Definition at line 29 of file TDecompSVD.h.