TDecompQRH

class TDecompQRH : public TDecompBase

    protected:

      virtual const TMatrixDBase& GetDecompMatrix() const
                    static Bool_t QRH(TMatrixD& q, TVectorD& diagR, TVectorD& up, TVectorD& w, Double_t tol)

    public:

                              TDecompQRH()
                              TDecompQRH(Int_t nrows, Int_t ncols)
                              TDecompQRH(Int_t row_lwb, Int_t row_upb, Int_t col_lwb, Int_t col_upb)
                              TDecompQRH(const TMatrixD& m, Double_t tol = 0.0)
                              TDecompQRH(const TDecompQRH& another)
                      virtual ~TDecompQRH()
               static TClass* Class()
               virtual Bool_t Decompose()
                 virtual void Det(Double_t& d1, Double_t& d2)
                virtual Int_t GetNcols() const
                virtual Int_t GetNrows() const
      virtual const TMatrixD& GetQ() const
      virtual const TMatrixD& GetR() const
      virtual const TVectorD& GetUp() const
      virtual const TVectorD& GetW() const
                         void Invert(TMatrixD& inv)
                     TMatrixD Invert()
              virtual TClass* IsA() const
                  TDecompQRH& operator=(const TDecompQRH& source)
                 virtual void Print(Option_t* opt = "") const
                 virtual void SetMatrix(const TMatrixD& a)
                 virtual void ShowMembers(TMemberInspector& insp, char* parent)
               virtual Bool_t Solve(TVectorD& b)
             virtual TVectorD Solve(const TVectorD& b, Bool_t& ok)
               virtual Bool_t Solve(TMatrixDColumn& b)
                 virtual void Streamer(TBuffer& b)
                         void StreamerNVirtual(TBuffer& b)
               virtual Bool_t TransSolve(TVectorD& b)
             virtual TVectorD TransSolve(const TVectorD& b, Bool_t& ok)
               virtual Bool_t TransSolve(TMatrixDColumn& b)

Data Members

    protected:

      TMatrixD fQ   (m x n) - orthogonal matrix
      TMatrixD fR   (n x n) - upper triangular matrix
      TVectorD fUp  (n) - vector with Householder up's
      TVectorD fW   (n) - vector with Householder beta's

    public:

      static const enum TDecompQRH:: kWorkMax  

Class Description

                                                                       
 QR Decomposition class                                                
                                                                       
 Decompose  a general (m x n) matrix A into A = fQ fR H   where        
                                                                       
  fQ : (m x n) - orthogonal matrix                                     
  fR : (n x n) - upper triangular matrix                               
  H  : HouseHolder matrix which is stored through                      
  fUp: (n) - vector with Householder up's                              
  fW : (n) - vector with Householder beta's                            
                                                                       
  If row/column index of A starts at (rowLwb,colLwb) then              
  the decomposed matrices start from :                                 
  fQ  : (rowLwb,0)                                                     
  fR  : (0,colLwb)                                                     
  and the decomposed vectors start from :                              
  fUp : (0)                                                            
  fW  : (0)                                                            
                                                                       
 Errors arise from formation of reflectors i.e. singularity .          
 Note it attempts to handle the cases where the nRow <= nCol .         
                                                                       

 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".

 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.

 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.

 This routine calculates the absolute (!) value of the determinant

 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 .

 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 .

Inline Functions

                       void ~TDecompQRH()
        const TMatrixDBase& GetDecompMatrix() const
                 TDecompQRH TDecompQRH(const TDecompQRH& another)
                      Int_t GetNrows() const
                      Int_t GetNcols() const
            const TMatrixD& GetQ() const
            const TMatrixD& GetR() const
            const TVectorD& GetUp() const
            const TVectorD& GetW() const
                     Bool_t Solve(TMatrixDColumn& b)
                     Bool_t TransSolve(TMatrixDColumn& b)
                TDecompQRH& operator=(const TDecompQRH& source)
                    TClass* Class()
                    TClass* IsA() const
                       void ShowMembers(TMemberInspector& insp, char* parent)
                       void Streamer(TBuffer& b)
                       void StreamerNVirtual(TBuffer& b)