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Change return type of matrixH() method to HouseholderSequence.

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This method is a member of Tridiagonalization and HessenbergDecomposition.
This commit is contained in:
Jitse Niesen
2010-05-24 17:35:54 +01:00
parent 76dd0e5314
commit eb3ca68684
5 changed files with 92 additions and 81 deletions
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61
Eigen/src/Eigenvalues/ComplexSchur.h
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@@ -3,6 +3,7 @@
//
// Copyright (C) 2009 Claire Maurice
// Copyright (C) 2009 Gael Guennebaud <g.gael@free.fr>
// Copyright (C) 2010 Jitse Niesen <jitse@maths.leeds.ac.uk>
//
// Eigen is free software; you can redistribute it and/or
// modify it under the terms of the GNU Lesser General Public
@@ -26,6 +27,8 @@
#ifndef EIGEN_COMPLEX_SCHUR_H
#define EIGEN_COMPLEX_SCHUR_H
template<typename MatrixType, bool IsComplex> struct ei_complex_schur_reduce_to_hessenberg;
/** \eigenvalues_module \ingroup Eigenvalues_Module
* \nonstableyet
*
@@ -50,6 +53,8 @@
* decomposition is computed, you can use the matrixU() and matrixT()
* functions to retrieve the matrices U and V in the decomposition.
*
* \note This code is inspired from Jampack
*
* \sa class RealSchur, class EigenSolver, class ComplexEigenSolver
*/
template<typename _MatrixType> class ComplexSchur
@@ -194,6 +199,8 @@ template<typename _MatrixType> class ComplexSchur
private:
bool subdiagonalEntryIsNeglegible(int i);
ComplexScalar computeShift(int iu, int iter);
void reduceToTriangularForm(bool skipU);
friend struct ei_complex_schur_reduce_to_hessenberg<MatrixType, NumTraits<Scalar>::IsComplex>;
};
/** Computes the principal value of the square root of the complex \a z. */
@@ -290,12 +297,10 @@ typename ComplexSchur<MatrixType>::ComplexScalar ComplexSchur<MatrixType>::compu
template<typename MatrixType>
void ComplexSchur<MatrixType>::compute(const MatrixType& matrix, bool skipU)
{
// this code is inspired from Jampack
m_matUisUptodate = false;
ei_assert(matrix.cols() == matrix.rows());
int n = matrix.cols();
if(n==1)
if(matrix.cols() == 1)
{
m_matU = ComplexMatrixType::Identity(1,1);
if(!skipU) m_matT = matrix.template cast<ComplexScalar>();
@@ -304,15 +309,49 @@ void ComplexSchur<MatrixType>::compute(const MatrixType& matrix, bool skipU)
return;
}
// Reduce to Hessenberg form
// TODO skip Q if skipU = true
m_hess.compute(matrix);
ei_complex_schur_reduce_to_hessenberg<MatrixType, NumTraits<Scalar>::IsComplex>::run(*this, matrix, skipU);
reduceToTriangularForm(skipU);
}
m_matT = m_hess.matrixH().template cast<ComplexScalar>();
if(!skipU) m_matU = m_hess.matrixQ().template cast<ComplexScalar>();
/* Reduce given matrix to Hessenberg form */
template<typename MatrixType, bool IsComplex>
struct ei_complex_schur_reduce_to_hessenberg
{
// this is the implementation for the case IsComplex = true
static void run(ComplexSchur<MatrixType>& _this, const MatrixType& matrix, bool skipU)
{
// TODO skip Q if skipU = true
_this.m_hess.compute(matrix);
_this.m_matT = _this.m_hess.matrixH();
if(!skipU) _this.m_matU = _this.m_hess.matrixQ();
}
};
// Reduce the Hessenberg matrix m_matT to triangular form by QR iteration.
template<typename MatrixType>
struct ei_complex_schur_reduce_to_hessenberg<MatrixType, false>
{
static void run(ComplexSchur<MatrixType>& _this, const MatrixType& matrix, bool skipU)
{
typedef typename ComplexSchur<MatrixType>::ComplexScalar ComplexScalar;
typedef typename ComplexSchur<MatrixType>::ComplexMatrixType ComplexMatrixType;
// Note: m_hess is over RealScalar; m_matT and m_matU is over ComplexScalar
// TODO skip Q if skipU = true
_this.m_hess.compute(matrix);
_this.m_matT = _this.m_hess.matrixH().template cast<ComplexScalar>();
if(!skipU)
{
// This may cause an allocation which seems to be avoidable
MatrixType Q = _this.m_hess.matrixQ();
_this.m_matU = Q.template cast<ComplexScalar>();
}
}
};
// Reduce the Hessenberg matrix m_matT to triangular form by QR iteration.
template<typename MatrixType>
void ComplexSchur<MatrixType>::reduceToTriangularForm(bool skipU)
{
// The matrix m_matT is divided in three parts.
// Rows 0,...,il-1 are decoupled from the rest because m_matT(il,il-1) is zero.
// Rows il,...,iu is the part we are working on (the active submatrix).
@@ -352,7 +391,7 @@ void ComplexSchur<MatrixType>::compute(const MatrixType& matrix, bool skipU)
ComplexScalar shift = computeShift(iu, iter);
PlanarRotation<ComplexScalar> rot;
rot.makeGivens(m_matT.coeff(il,il) - shift, m_matT.coeff(il+1,il));
m_matT.rightCols(n-il).applyOnTheLeft(il, il+1, rot.adjoint());
m_matT.rightCols(m_matT.cols()-il).applyOnTheLeft(il, il+1, rot.adjoint());
m_matT.topRows(std::min(il+2,iu)+1).applyOnTheRight(il, il+1, rot);
if(!skipU) m_matU.applyOnTheRight(il, il+1, rot);
@@ -360,7 +399,7 @@ void ComplexSchur<MatrixType>::compute(const MatrixType& matrix, bool skipU)
{
rot.makeGivens(m_matT.coeffRef(i,i-1), m_matT.coeffRef(i+1,i-1), &m_matT.coeffRef(i,i-1));
m_matT.coeffRef(i+1,i-1) = ComplexScalar(0);
m_matT.rightCols(n-i).applyOnTheLeft(i, i+1, rot.adjoint());
m_matT.rightCols(m_matT.cols()-i).applyOnTheLeft(i, i+1, rot.adjoint());
m_matT.topRows(std::min(i+2,iu)+1).applyOnTheRight(i, i+1, rot);
if(!skipU) m_matU.applyOnTheRight(i, i+1, rot);
}