Class of matrices connected with LAPACK.

It is build as an interface on the library Lapack. The main functionalities that are exported are resolution of systems by LU-decomposition or Least-square methods, QR-decomposition, LU-decomposition, reduction by another matrix, computation of eigenvalues and eigenvectors:

  Vector<XXCOEFF>& solve_LU(const Vector<XXCOEFF> &);
  Vector<XXCOEFF>& solve_LS(const Vector<XXCOEFF> &);

  unsigned int diagRank();
  integer dcmp_QR();
  integer dcmp_LU(unsigned int *);

  void LeftMult_QR(const MatrixLa<XXCOEFF> & M, 
               char *trans, XXCOEFF *tau);
  void ReduceBy(const MatrixLa<XXCOEFF> & K);

  Vector  <AlgClos<XXCOEFF>::TYPE> & eigval(void);
  MatrixLa<AlgClos<XXCOEFF>::TYPE> & leigvct(void);
  MatrixLa<AlgClos<XXCOEFF>::TYPE> & 
       leigvct(Vector<AlgClos<XXCOEFF>::TYPE> *);
  MatrixLa<AlgClos<XXCOEFF>::TYPE> & reigvct(void);
  MatrixLa<AlgClos<XXCOEFF>::TYPE> & 
       reigvct(Vector<AlgClos<XXCOEFF>::TYPE> *);

Note the type of the coefficients in the results of the eigencomputations is in the "algebraic closure" of the input coefficients. If we deal with double, we obtain complex<double> and if we deal with complex<double> we still obtain complex<double> values. This is implemented with traits, in the class AlgClos<XXCOEFF> .