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Add support for Schur decomposition of matrices in Hessenberg form

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Desire NUENTSA 2013-01-11 17:36:45 +01:00
parent 0f94e96342
commit 33febdb48b
2 changed files with 34 additions and 4 deletions
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32
Eigen/src/Eigenvalues/ComplexSchur.h
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@ -187,6 +187,26 @@ template<typename _MatrixType> class ComplexSchur
* \sa compute(const MatrixType&, bool, Index) * \sa compute(const MatrixType&, bool, Index)
*/ */
ComplexSchur& compute(const MatrixType& matrix, bool computeU = true); ComplexSchur& compute(const MatrixType& matrix, bool computeU = true);
/** \brief Compute Schur decomposition from a given Hessenberg matrix
* \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>
ComplexSchur& computeFromHessenberg(const HessMatrixType& matrixH, const OrthMatrixType& matrixQ, bool computeU=true);
/** \brief Reports whether previous computation was successful. /** \brief Reports whether previous computation was successful.
* *
@ -309,10 +329,20 @@ ComplexSchur<MatrixType>& ComplexSchur<MatrixType>::compute(const MatrixType& ma
} }
internal::complex_schur_reduce_to_hessenberg<MatrixType, NumTraits<Scalar>::IsComplex>::run(*this, matrix, computeU); internal::complex_schur_reduce_to_hessenberg<MatrixType, NumTraits<Scalar>::IsComplex>::run(*this, matrix, computeU);
reduceToTriangularForm(computeU); computeFromHessenberg(m_matT, m_matU, computeU);
return *this; return *this;
} }
template<typename MatrixType>
template<typename HessMatrixType, typename OrthMatrixType>
ComplexSchur<MatrixType>& ComplexSchur<MatrixType>::computeFromHessenberg(const HessMatrixType& matrixH, const OrthMatrixType& matrixQ, bool computeU)
{
m_matT = matrixH;
if(computeU)
m_matU = matrixQ;
reduceToTriangularForm(computeU);
return *this;
}
namespace internal { namespace internal {
/* Reduce given matrix to Hessenberg form */ /* Reduce given matrix to Hessenberg form */

6
Eigen/src/Eigenvalues/RealSchur.h
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@ -185,7 +185,7 @@ template<typename _MatrixType> class RealSchur
* \sa compute(const MatrixType&, bool) * \sa compute(const MatrixType&, bool)
*/ */
template<typename HessMatrixType, typename OrthMatrixType> template<typename HessMatrixType, typename OrthMatrixType>
RealSchur& computeHessenberg(const HessMatrixType& matrixH, const OrthMatrixType& matrixQ, bool computeU); RealSchur& computeFromHessenberg(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.
@ -254,13 +254,13 @@ RealSchur<MatrixType>& RealSchur<MatrixType>::compute(const MatrixType& matrix,
m_hess.compute(matrix); m_hess.compute(matrix);
// Step 2. Reduce to real Schur form // Step 2. Reduce to real Schur form
computeHessenberg(m_hess.matrixH(), m_hess.matrixQ(), computeU); computeFromHessenberg(m_hess.matrixH(), m_hess.matrixQ(), computeU);
return *this; return *this;
} }
template<typename MatrixType> template<typename MatrixType>
template<typename HessMatrixType, typename OrthMatrixType> template<typename HessMatrixType, typename OrthMatrixType>
RealSchur<MatrixType>& RealSchur<MatrixType>::computeHessenberg(const HessMatrixType& matrixH, const OrthMatrixType& matrixQ, bool computeU) RealSchur<MatrixType>& RealSchur<MatrixType>::computeFromHessenberg(const HessMatrixType& matrixH, const OrthMatrixType& matrixQ, bool computeU)
{ {
m_matT = matrixH; m_matT = matrixH;
if(computeU) if(computeU)