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TDecompSVD.h
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1 // @(#)root/matrix:$Id$
2 // Authors: Fons Rademakers, Eddy Offermann Dec 2003
3 
4 /*************************************************************************
5  * Copyright (C) 1995-2000, Rene Brun and Fons Rademakers. *
6  * All rights reserved. *
7  * *
8  * For the licensing terms see $ROOTSYS/LICENSE. *
9  * For the list of contributors see $ROOTSYS/README/CREDITS. *
10  *************************************************************************/
11 
12 #ifndef ROOT_TDecompSVD
13 #define ROOT_TDecompSVD
14 
15 ///////////////////////////////////////////////////////////////////////////
16 // //
17 // Single Value Decomposition class //
18 // //
19 ///////////////////////////////////////////////////////////////////////////
20 
21 #include "TDecompBase.h"
22 
23 class TDecompSVD : public TDecompBase
24 {
25 protected :
26 
27  // A = fU fSig fV^T
28  TMatrixD fU; // orthogonal matrix
29  TMatrixD fV; // orthogonal matrix
30  TVectorD fSig; // diagonal of diagonal matrix
31 
32  static Bool_t Bidiagonalize(TMatrixD &v,TMatrixD &u,TVectorD &sDiag,TVectorD &oDiag);
33  static Bool_t Diagonalize (TMatrixD &v,TMatrixD &u,TVectorD &sDiag,TVectorD &oDiag);
34  static void Diag_1 (TMatrixD &v,TVectorD &sDiag,TVectorD &oDiag,Int_t k);
35  static void Diag_2 (TVectorD &sDiag,TVectorD &oDiag,Int_t k,Int_t l);
36  static void Diag_3 (TMatrixD &v,TMatrixD &u,TVectorD &sDiag,TVectorD &oDiag,Int_t k,Int_t l);
37  static void SortSingular (TMatrixD &v,TMatrixD &u,TVectorD &sDiag);
38 
39  virtual const TMatrixDBase &GetDecompMatrix() const { return fU; }
40 
41 public :
42 
43  enum {kWorkMax = 100}; // size of work array
44 
45  TDecompSVD(): fU(), fV(), fSig() {}
46  TDecompSVD(Int_t nrows,Int_t ncols);
47  TDecompSVD(Int_t row_lwb,Int_t row_upb,Int_t col_lwb,Int_t col_upb);
48  TDecompSVD(const TMatrixD &m,Double_t tol = 0.0);
49  TDecompSVD(const TDecompSVD &another);
50  virtual ~TDecompSVD() {}
51 
52  const TMatrixD GetMatrix ();
53  virtual Int_t GetNrows () const;
54  virtual Int_t GetNcols () const;
55  const TMatrixD &GetU () { if ( !TestBit(kDecomposed) ) Decompose();
56  return fU; }
57  const TMatrixD &GetV () { if ( !TestBit(kDecomposed) ) Decompose();
58  return fV; }
59  const TVectorD &GetSig () { if ( !TestBit(kDecomposed) ) Decompose();
60  return fSig; }
61 
62  virtual void SetMatrix (const TMatrixD &a);
63 
64  virtual Bool_t Decompose ();
65  virtual Bool_t Solve ( TVectorD &b);
66  virtual TVectorD Solve (const TVectorD& b,Bool_t &ok) { TVectorD x = b; ok = Solve(x);
67  const Int_t rowLwb = GetRowLwb();
68  x.ResizeTo(rowLwb,rowLwb+GetNcols()-1);
69  return x; }
70  virtual Bool_t Solve ( TMatrixDColumn &b);
71  virtual Bool_t TransSolve ( TVectorD &b);
72  virtual TVectorD TransSolve (const TVectorD& b,Bool_t &ok) { TVectorD x = b; ok = TransSolve(x);
73  const Int_t rowLwb = GetRowLwb();
74  x.ResizeTo(rowLwb,rowLwb+GetNcols()-1);
75  return x; }
76  virtual Bool_t TransSolve ( TMatrixDColumn &b);
77  virtual Double_t Condition ();
78  virtual void Det (Double_t &d1,Double_t &d2);
79 
81  TMatrixD Invert (Bool_t &status);
82  TMatrixD Invert () {Bool_t status; return Invert(status); }
83 
84  void Print(Option_t *opt ="") const; // *MENU*
85 
86  TDecompSVD &operator= (const TDecompSVD &source);
87 
88  ClassDef(TDecompSVD,1) // Matrix Decompositition SVD
89 };
90 
91 #endif
const TVectorD & GetSig()
Definition: TDecompSVD.h:59
virtual void Det(Double_t &d1, Double_t &d2)
Matrix determinant det = d1*TMath::Power(2.,d2)
Definition: TDecompSVD.cxx:846
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 ap...
Definition: TDecompSVD.cxx:192
static void Diag_3(TMatrixD &v, TMatrixD &u, TVectorD &sDiag, TVectorD &oDiag, Int_t k, Int_t l)
Step 3 in the matrix diagonalization.
Definition: TDecompSVD.cxx:416
auto * m
Definition: textangle.C:8
virtual Bool_t TransSolve(TVectorD &b)
Solve A^T x=b assuming the SVD form of A is stored . Solution returned in b.
Definition: TDecompSVD.cxx:723
Int_t GetRowLwb() const
Definition: TDecompBase.h:73
const char Option_t
Definition: RtypesCore.h:62
Decomposition Base class.
Definition: TDecompBase.h:33
R__ALWAYS_INLINE Bool_t TestBit(UInt_t f) const
Definition: TObject.h:172
int Int_t
Definition: RtypesCore.h:41
bool Bool_t
Definition: RtypesCore.h:59
virtual ~TDecompSVD()
Definition: TDecompSVD.h:50
virtual void SetMatrix(const TMatrixD &a)
Set matrix to be decomposed.
Definition: TDecompSVD.cxx:582
TMatrixD fV
Definition: TDecompSVD.h:29
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...
Definition: TDecompSVD.cxx:307
Single Value Decomposition class.
Definition: TDecompSVD.h:23
Double_t x[n]
Definition: legend1.C:17
#define ClassDef(name, id)
Definition: Rtypes.h:326
virtual TVectorD Solve(const TVectorD &b, Bool_t &ok)
Definition: TDecompSVD.h:66
const TMatrixD & GetU()
Definition: TDecompSVD.h:55
virtual Bool_t Decompose()
SVD decomposition of matrix If the decomposition succeeds, bit kDecomposed is set ...
Definition: TDecompSVD.cxx:123
static void SortSingular(TMatrixD &v, TMatrixD &u, TVectorD &sDiag)
Perform a permutation transformation on the diagonal matrix S', so that matrix S'' = U''^T ...
Definition: TDecompSVD.cxx:497
virtual Int_t GetNcols() const
Definition: TDecompSVD.cxx:870
void inv(rsa_NUMBER *, rsa_NUMBER *, rsa_NUMBER *)
Definition: rsaaux.cxx:949
auto * a
Definition: textangle.C:12
virtual TVectorD TransSolve(const TVectorD &b, Bool_t &ok)
Definition: TDecompSVD.h:72
virtual const TMatrixDBase & GetDecompMatrix() const
Definition: TDecompSVD.h:39
TMatrixD fU
Definition: TDecompSVD.h:28
Linear Algebra Package.
virtual Bool_t Solve(TVectorD &b)
Solve Ax=b assuming the SVD form of A is stored .
Definition: TDecompSVD.cxx:615
static void Diag_1(TMatrixD &v, TVectorD &sDiag, TVectorD &oDiag, Int_t k)
Step 1 in the matrix diagonalization.
Definition: TDecompSVD.cxx:374
double Double_t
Definition: RtypesCore.h:55
virtual Int_t GetNrows() const
Definition: TDecompSVD.cxx:865
const TMatrixD GetMatrix()
Reconstruct the original matrix using the decomposition parts.
Definition: TDecompSVD.cxx:557
TMatrixD Invert()
Definition: TDecompSVD.h:82
auto * l
Definition: textangle.C:4
you should not use this method at all Int_t Int_t Double_t Double_t Double_t Int_t Double_t Double_t Double_t Double_t b
Definition: TRolke.cxx:630
TVectorD fSig
Definition: TDecompSVD.h:30
const TMatrixD & GetV()
Definition: TDecompSVD.h:57
virtual Double_t Condition()
Matrix condition number.
Definition: TDecompSVD.cxx:823
TDecompSVD & operator=(const TDecompSVD &source)
Assignment operator.
Definition: TDecompSVD.cxx:930
static void Diag_2(TVectorD &sDiag, TVectorD &oDiag, Int_t k, Int_t l)
Step 2 in the matrix diagonalization.
Definition: TDecompSVD.cxx:398
void Print(Option_t *opt="") const
Print class members.
Definition: TDecompSVD.cxx:919