vnl_generalized_eigensystem.h

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#ifndef vnl_generalized_eigensystem_h_
#define vnl_generalized_eigensystem_h_

//:
//  \file
//  \brief  Solves the generalized eigenproblem Ax=La
//  \author Andrew W. Fitzgibbon, Oxford RRG, 29 Aug 96
//
//  Modifications
//  dac (Manchester) 28/03/2001: tidied up documentation
//

#include <vnl/vnl_diag_matrix.h>

//: Solves the generalized eigenproblem Ax=La
//  Solves the generalized eigenproblem of @{ $A x = \lambda B x$ @},
//  with $A$ symmetric and $B$ positive definite.
//  See Golub and van Loan, Section 8.7.

class vnl_generalized_eigensystem {
public:
// Public data members because they're unique.
  int n;

//: @{ Solve real generalized eigensystem $A x = \lambda B x$ for
//  $\lambda$ and $x$, where $A$ symmetric, $B$ positive definite.
//  Initializes storage for the matrix $V = [ x_0 x_1 .. x_n ]$ and
//  the vnl_diag_matrix $D = [ \lambda_0 \lambda_1 ... \lambda_n ]$.
//  The eigenvalues are sorted into increasing order (of value, not
//  absolute value).
//  \par
//  Uses vnl_cholesky decomposition $C^\top C = B$, to convert to 
//  $C^{-\top} A C^{-1} x = \lambda x$ and then uses the
//  Symmetric eigensystem code.   It will print a verbose warning
//  if $B$ is not positive definite.
//  @}
  vnl_generalized_eigensystem(const vnl_matrix<double>& A, 
        const vnl_matrix<double>& B);

//: Public eigenvectors.  After construction, this contains the matrix of
// eigenvectors.
  vnl_matrix<double> V;

//: Public eigenvalues.  After construction, this contains the diagonal
// matrix of eigenvalues, stored as a vector.
  vnl_diag_matrix<double> D;
};

#endif // vnl_generalized_eigensystem_h_

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