TDecompLU

class TDecompLU : public TDecompBase

    protected:

                    static Bool_t DecomposeLUCrout(TMatrixD& lu, Int_t* index, Double_t& sign, Double_t tol, Int_t& nrZeros)
                    static Bool_t DecomposeLUGauss(TMatrixD& lu, Int_t* index, Double_t& sign, Double_t tol, Int_t& nrZeros)
      virtual const TMatrixDBase& GetDecompMatrix() const

    public:

                       TDecompLU()
                       TDecompLU(Int_t nrows)
                       TDecompLU(Int_t row_lwb, Int_t row_upb)
                       TDecompLU(const TMatrixD& m, Double_t tol = 0.0, Int_t implicit = 1)
                       TDecompLU(const TDecompLU& another)
               virtual ~TDecompLU()
        static TClass* Class()
        virtual Bool_t Decompose()
          virtual void Det(Double_t& d1, Double_t& d2)
       const TMatrixD& GetLU() const
        const TMatrixD GetMatrix() const
         virtual Int_t GetNcols() const
         virtual Int_t GetNrows() const
                  void Invert(TMatrixD& inv)
              TMatrixD Invert()
         static Bool_t InvertLU(TMatrixD& a, Double_t tol, Double_t* det = 0)
       virtual TClass* IsA() const
            TDecompLU& operator=(const TDecompLU& 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:

         Int_t fImplicitPivot  control to determine implicit row scale before
         Int_t fNIndex         size of row permutation index
        Int_t* fIndex          [fNIndex] row permutation index
      Double_t fSign           = +/- 1 reflecting even/odd row permutations, resp.
      TMatrixD fLU             decomposed matrix so that a = l u where

Class Description

                                                                       
 LU Decomposition class                                                
                                                                       
 Decompose  a general n x n matrix A into P A = L U                    
                                                                       
 where P is a permutation matrix, L is unit lower triangular and U     
 is upper triangular.                                                  
 L is stored in the strict lower triangular part of the matrix fLU.    
 The diagonal elements of L are unity and are not stored.              
 U is stored in the diagonal and upper triangular part of the matrix   
 fU.                                                                   
 P is stored in the index array fIndex : j = fIndex[i] indicates that  
 row j and row i should be swapped .                                   
                                                                       
 fSign gives the sign of the permutation, (-1)^n, where n is the       
 number of interchanges in the permutation.                            
                                                                       
 fLU has the same indexing range as matrix A .                         
                                                                       
 The decomposition fails if a diagonal element of abs(fLU) is == 0,    
 The matrix fUL is made invalid .                                      
                                                                       

 Reconstruct the original matrix using the decomposition parts

 Solve Ax=b assuming the LU form of A is stored in fLU, but assume b has *not*
 been transformed.  Solution returned in b.

 Solve Ax=b assuming the LU form of A is stored in fLU, but assume b has *not*
 been transformed.  Solution returned in b.

 Solve A^T x=b assuming the LU form of A^T is stored in fLU, but assume b has *not*
 been transformed.  Solution returned in b.

 Solve A^T x=b assuming the LU form of A^T is stored in fLU, but assume b has *not*
 been transformed.  Solution returned in b.

 For a matrix A(m,m), its inverse A_inv is defined as A * A_inv = A_inv * A = unit
 (m x m) Ainv is returned .

 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 .

 Crout/Doolittle algorithm of LU decomposing a square matrix, with implicit partial
 pivoting.  The decomposition is stored in fLU: U is explicit in the upper triag
 and L is in multiplier form in the subdiagionals .
 Row permutations are mapped out in fIndex. fSign, used for calculating the
 determinant, is +/- 1 for even/odd row permutations. .

 LU decomposition using Gaussain Elimination with partial pivoting (See Golub &
 Van Loan, Matrix Computations, Algorithm 3.4.1) of a square matrix .
 The decomposition is stored in fLU: U is explicit in the upper triag and L is in
 multiplier form in the subdiagionals . Row permutations are mapped out in fIndex.
 fSign, used for calculating the determinant, is +/- 1 for even/odd row permutations.
 Since this algorithm uses partial pivoting without scaling like in Crout/Doolitle.
 it is somewhat faster but less precise .

 Calculate matrix inversion through in place forward/backward substitution

Inline Functions

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