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Added a Hessenberg decomposition class for both real and complex matrices.

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This is the first step towards a non-selfadjoint eigen solver.
Notes:
 - We might consider merging Tridiagonalization and Hessenberg toghether ?
 - Or we could factorize some code into a Householder class (could also be shared with QR)
This commit is contained in:
Gael Guennebaud
2008-06-08 15:03:23 +00:00
parent 4dd57b585d
commit e3fac69f19
6 changed files with 287 additions and 5 deletions
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24
Eigen/src/QR/Tridiagonalization.h
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@@ -29,7 +29,7 @@
*
* \brief Trigiagonal decomposition of a selfadjoint matrix
*
* \param MatrixType the type of the matrix of which we are computing the eigen decomposition
* \param MatrixType the type of the matrix of which we are performing the tridiagonalization
*
* This class performs a tridiagonal decomposition of a selfadjoint matrix \f$ A \f$ such that:
* \f$ A = Q T Q^* \f$ where \f$ Q \f$ is unitatry and \f$ T \f$ a real symmetric tridiagonal matrix
@@ -81,7 +81,7 @@ template<typename _MatrixType> class Tridiagonalization
void compute(const MatrixType& matrix)
{
m_matrix = matrix;
m_hCoeffs.resize(matrix.rows()-1);
m_hCoeffs.resize(matrix.rows()-1, 1);
_compute(m_matrix, m_hCoeffs);
}
@@ -111,6 +111,7 @@ template<typename _MatrixType> class Tridiagonalization
const MatrixType& packedMatrix(void) const { return m_matrix; }
MatrixType matrixQ(void) const;
MatrixType matrixT(void) const;
const DiagonalReturnType diagonal(void) const;
const SubDiagonalReturnType subDiagonal(void) const;
@@ -252,6 +253,25 @@ Tridiagonalization<MatrixType>::subDiagonal(void) const
.nestByValue().diagonal().nestByValue().real();
}
/** constructs and returns the tridiagonal matrix T.
* Note that the matrix T is equivalent to the diagonal and sub-diagonal of the packed matrix.
* Therefore, it might be often sufficient to directly use the packed matrix, or the vector
* expressions returned by diagonal() and subDiagonal() instead of creating a new matrix.
*/
template<typename MatrixType>
typename Tridiagonalization<MatrixType>::MatrixType
Tridiagonalization<MatrixType>::matrixT(void) const
{
// FIXME should this function (and other similar) rather take a matrix as argument
// and fill it (avoids temporaries)
int n = m_matrix.rows();
MatrixType matT = m_matrix;
matT.corner(TopRight,n-1, n-1).diagonal() = subDiagonal().conjugate();
matT.corner(TopRight,n-2, n-2).template part<Upper>().setZero();
matT.corner(BottomLeft,n-2, n-2).template part<Lower>().setZero();
return matT;
}
/** Performs a full decomposition in place */
template<typename MatrixType>
void Tridiagonalization<MatrixType>::decomposeInPlace(MatrixType& mat, DiagonalType& diag, SubDiagonalType& subdiag, bool extractQ)