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RealShur for a already Hessenberg matrix

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Desire NUENTSA 2012-10-09 12:16:54 +02:00
parent a67eea05c1
commit 23e2de3cb6
1 changed files with 34 additions and 3 deletions
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37
Eigen/src/Eigenvalues/RealSchur.h
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@ -167,6 +167,25 @@ template<typename _MatrixType> class RealSchur
*/ */
RealSchur& compute(const MatrixType& matrix, bool computeU = true); RealSchur& compute(const MatrixType& matrix, bool computeU = true);
/** \brief Computes Schur decomposition of a Hessenberg matrix H = Z T Z^T
* \param[in] matrixH Matrix in Hessenberg form H
* \param[in] matrixQ orthogonal matrix Q that transform a matrix A to H : A = Q H Q^T
* \param computeU Computes the matriX U of the Schur vectors
* \return Reference to \c *this
*
* This routine assumes that the matrix is already reduced in Hessenberg form matrixH
* using either the class HessenbergDecomposition or another mean.
* It computes the upper quasi-triangular matrix T of the Schur decomposition of H
* When computeU is true, this routine computes the matrix U such that
* A = U T U^T = (QZ) T (QZ)^T = Q H Q^T where A is the initial matrix
*
* NOTE Q is referenced if computeU is true; so, if the initial orthogonal matrix
* is not available, the user should give an identity matrix (Q.setIdentity())
*
* \sa compute(const MatrixType&, bool)
*/
template<typename HessMatrixType, typename OrthMatrixType>
RealSchur& computeHessenberg(const HessMatrixType& matrixH, const OrthMatrixType& matrixQ, bool computeU);
/** \brief Reports whether previous computation was successful. /** \brief Reports whether previous computation was successful.
* *
* \returns \c Success if computation was succesful, \c NoConvergence otherwise. * \returns \c Success if computation was succesful, \c NoConvergence otherwise.
@ -233,11 +252,23 @@ RealSchur<MatrixType>& RealSchur<MatrixType>::compute(const MatrixType& matrix,
// Step 1. Reduce to Hessenberg form // Step 1. Reduce to Hessenberg form
m_hess.compute(matrix); m_hess.compute(matrix);
m_matT = m_hess.matrixH();
if (computeU)
m_matU = m_hess.matrixQ();
// Step 2. Reduce to real Schur form // Step 2. Reduce to real Schur form
computeHessenberg(m_hess.matrixH(), m_hess.matrixQ(), computeU);
return *this;
}
template<typename MatrixType>
template<typename HessMatrixType, typename OrthMatrixType>
RealSchur<MatrixType>& RealSchur<MatrixType>::computeHessenberg(const HessMatrixType& matrixH, const OrthMatrixType& matrixQ, bool computeU)
{
m_matT = matrixH;
if(computeU)
m_matU = matrixQ;
Index maxIters = m_maxIters;
if (maxIters == -1)
maxIters = m_maxIterationsPerRow * matrixH.rows();
m_workspaceVector.resize(m_matT.cols()); m_workspaceVector.resize(m_matT.cols());
Scalar* workspace = &m_workspaceVector.coeffRef(0); Scalar* workspace = &m_workspaceVector.coeffRef(0);