TMatrixDEigen

class TMatrixDEigen

    protected:

      static void MakeHessenBerg(TMatrixD& v, TVectorD& ortho, TMatrixD& H)
      static void MakeSchurr(TMatrixD& v, TVectorD& d, TVectorD& e, TMatrixD& H)
      static void Sort(TMatrixD& v, TVectorD& d, TVectorD& e)

    public:

                      TMatrixDEigen()
                      TMatrixDEigen(const TMatrixD& a)
                      TMatrixDEigen(const TMatrixDEigen& another)
              virtual ~TMatrixDEigen()
       static TClass* Class()
       const TMatrixD GetEigenValues() const
      const TVectorD& GetEigenValuesIm() const
      const TVectorD& GetEigenValuesRe() const
      const TMatrixD& GetEigenVectors() const
      virtual TClass* IsA() const
       TMatrixDEigen& operator=(const TMatrixDEigen& source)
         virtual void ShowMembers(TMemberInspector& insp, char* parent)
         virtual void Streamer(TBuffer& b)
                 void StreamerNVirtual(TBuffer& b)

Data Members

    protected:

      TMatrixD fEigenVectors   Eigen-vectors of matrix
      TVectorD fEigenValuesRe  Eigen-values
      TVectorD fEigenValuesIm  Eigen-values

    public:

      static const enum TMatrixDEigen:: kWorkMax  

Class Description

                                                                      
 TMatrixDEigen                                                        
                                                                      
 Eigenvalues and eigenvectors of a real matrix.                       
                                                                      
 If A is not symmetric, then the eigenvalue matrix D is block         
 diagonal with the real eigenvalues in 1-by-1 blocks and any complex  
 eigenvalues, a + i*b, in 2-by-2 blocks, [a, b; -b, a].  That is, if  
 the complex eigenvalues look like                                    
                                                                      
     u + iv     .        .          .      .    .                     
       .      u - iv     .          .      .    .                     
       .        .      a + ib       .      .    .                     
       .        .        .        a - ib   .    .                     
       .        .        .          .      x    .                     
       .        .        .          .      .    y                     
                                                                      
 then D looks like                                                    
                                                                      
       u        v        .          .      .    .                     
      -v        u        .          .      .    .                     
       .        .        a          b      .    .                     
       .        .       -b          a      .    .                     
       .        .        .          .      x    .                     
       .        .        .          .      .    y                     
                                                                      
 This keeps V a real matrix in both symmetric and non-symmetric       
 cases, and A*V = V*D.                                                
                                                                      

 Nonsymmetric reduction to Hessenberg form.
 This is derived from the Algol procedures orthes and ortran, by Martin and Wilkinson,
 Handbook for Auto. Comp., Vol.ii-Linear Algebra, and the corresponding
 Fortran subroutines in EISPACK.

 Nonsymmetric reduction from Hessenberg to real Schur form.
 This is derived from the Algol procedure hqr2, by Martin and Wilkinson,
 Handbook for Auto. Comp., Vol.ii-Linear Algebra, and the corresponding
 Fortran subroutine in EISPACK.

 Sort eigenvalues and corresponding vectors in descending order of Re^2+Im^2
 of the complex eigenvalues .

 Computes the block diagonal eigenvalue matrix.
 If the original matrix A is not symmetric, then the eigenvalue
 matrix D is block diagonal with the real eigenvalues in 1-by-1
 blocks and any complex eigenvalues,
    a + i*b, in 2-by-2 blocks, [a, b; -b, a].
  That is, if the complex eigenvalues look like

     u + iv     .        .          .      .    .
       .      u - iv     .          .      .    .
       .        .      a + ib       .      .    .
       .        .        .        a - ib   .    .
       .        .        .          .      x    .
       .        .        .          .      .    y

 then D looks like

     u        v        .          .      .    .
    -v        u        .          .      .    .
     .        .        a          b      .    .
     .        .       -b          a      .    .
     .        .        .          .      x    .
     .        .        .          .      .    y

 This keeps V a real matrix in both symmetric and non-symmetric
 cases, and A*V = V*D.

 Indexing:
  If matrix A has the index/shape (rowLwb,rowUpb,rowLwb,rowUpb)
  each eigen-vector must have the shape (rowLwb,rowUpb) .
  For convinience, the column index of the eigen-vector matrix
  also runs from rowLwb to rowUpb so that the returned matrix
  has also index/shape (rowLwb,rowUpb,rowLwb,rowUpb) .

Inline Functions

                   void ~TMatrixDEigen()
          TMatrixDEigen TMatrixDEigen(const TMatrixDEigen& another)
        const TMatrixD& GetEigenVectors() const
        const TVectorD& GetEigenValuesRe() const
        const TVectorD& GetEigenValuesIm() const
         TMatrixDEigen& operator=(const TMatrixDEigen& source)
                TClass* Class()
                TClass* IsA() const
                   void ShowMembers(TMemberInspector& insp, char* parent)
                   void Streamer(TBuffer& b)
                   void StreamerNVirtual(TBuffer& b)