library: libMatrix #include "TDecompBK.h"

# TDecompBK

class description - source file - inheritance tree (.pdf)

## class TDecompBK : public TDecompBase

| Inheritance Chart:
`TObject`
| <- | `TDecompBase`
| <- | `TDecompBK` |

        protected:

          virtual const TMatrixDBase& GetDecompMatrix() const

        public:

                           TDecompBK()
                           TDecompBK(Int_t nrows)
                           TDecompBK(Int_t row_lwb, Int_t row_upb)
                           TDecompBK(const TMatrixDSym& m, Double_t tol = 0.0)
                           TDecompBK(const TDecompBK& another)
                   virtual ~TDecompBK()
            static TClass* Class()
            virtual Bool_t Decompose()
              virtual void Det(Double_t&, Double_t&)
             virtual Int_t GetNcols() const
             virtual Int_t GetNrows() const
           const TMatrixD& GetU() const
                      void Invert(TMatrixDSym& inv)
               TMatrixDSym Invert()
           virtual TClass* IsA() const
                TDecompBK& operator=(const TDecompBK& source)
              virtual void Print(Option_t* opt = "") const
              virtual void SetMatrix(const TMatrixDSym& 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:

             Int_t fNIpiv  size of row permutation index
            Int_t* fIpiv   [fNIpiv] row permutation index
          TMatrixD fU      decomposed matrix so that a = u d u^T

## Class Description

     The Bunch-Kaufman diagonal pivoting method decomposes a real
     symmetric matrix A using

         A = U*D*U^T

      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

                 (   I    v    0   )   k-s
         U(k) =  (   0    I    0   )   s
                 (   0    0    I   )   n-k
                    k-s   s   n-k

      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.

TDecompBK()

TDecompBK(Int_t nrows)

TDecompBK(Int_t row_lwb,Int_t row_upb)

TDecompBK(const TMatrixDSym &a,Double_t tol)

TDecompBK(const TDecompBK &another) : TDecompBase(another)

Bool_t Decompose()

void SetMatrix(const TMatrixDSym &a)

Bool_t Solve(TVectorD &b)

     Solve Ax=b assuming the BK form of A is stored in fU . Solution returned in b.

Bool_t Solve(TMatrixDColumn &cb)

     Solve Ax=b assuming the BK form of A is stored in fU . Solution returned in b.

void Invert(TMatrixDSym &inv)

     For a symmetric matrix A(m,m), its inverse A_inv(m,m) is returned .

TMatrixDSym Invert()

     For a symmetric matrix A(m,m), its inverse A_inv(m,m) is returned .

void Print(Option_t *opt) const

### Inline Functions

                           void ~TDecompBK()
            const TMatrixDBase& GetDecompMatrix() const
                          Int_t GetNrows() const
                          Int_t GetNcols() const
                const TMatrixD& GetU() const
                         Bool_t Solve(TMatrixDColumn& b)
                         Bool_t TransSolve(TVectorD& b)
                       TVectorD TransSolve(const TVectorD& b, Bool_t& ok)
                         Bool_t TransSolve(TMatrixDColumn& b)
                           void Det(Double_t&, Double_t&)
                     TDecompBK& operator=(const TDecompBK& source)
                        TClass* Class()
                        TClass* IsA() const
                           void ShowMembers(TMemberInspector& insp, char* parent)
                           void Streamer(TBuffer& b)
                           void StreamerNVirtual(TBuffer& b)

Last update: root/matrix:$Name: $:$Id: TDecompBK.cxx,v 1.2 2005/02/15 16:17:09 brun Exp $
Copyright (C) 1995-2000, Rene Brun and Fons Rademakers. *