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Use HessenbergDecomposition in EigenSolver.

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This commit is contained in:
Jitse Niesen 2010-03-31 21:50:18 +01:00
parent 1b3f7f2fee
commit 8cfa672fe0
1 changed files with 5 additions and 68 deletions
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73
Eigen/src/Eigenvalues/EigenSolver.h
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@ -25,6 +25,8 @@
#ifndef EIGEN_EIGENSOLVER_H #ifndef EIGEN_EIGENSOLVER_H
#define EIGEN_EIGENSOLVER_H #define EIGEN_EIGENSOLVER_H
#include "./HessenbergDecomposition.h"
/** \eigenvalues_module \ingroup Eigenvalues_Module /** \eigenvalues_module \ingroup Eigenvalues_Module
* \nonstableyet * \nonstableyet
* *
@ -310,13 +312,11 @@ EigenSolver<MatrixType>& EigenSolver<MatrixType>::compute(const MatrixType& matr
assert(matrix.cols() == matrix.rows()); assert(matrix.cols() == matrix.rows());
int n = matrix.cols(); int n = matrix.cols();
m_eivalues.resize(n,1); m_eivalues.resize(n,1);
m_eivec.resize(n,n);
MatrixType matH = matrix;
RealVectorType ort(n);
// Reduce to Hessenberg form. // Reduce to Hessenberg form.
orthes(matH, ort); HessenbergDecomposition<MatrixType> hd(matrix);
MatrixType matH = hd.matrixH();
m_eivec = hd.matrixQ();
// Reduce Hessenberg to real Schur form. // Reduce Hessenberg to real Schur form.
hqr2(matH); hqr2(matH);
@ -325,69 +325,6 @@ EigenSolver<MatrixType>& EigenSolver<MatrixType>::compute(const MatrixType& matr
return *this; return *this;
} }
// Nonsymmetric reduction to Hessenberg form.
template<typename MatrixType>
void EigenSolver<MatrixType>::orthes(MatrixType& matH, RealVectorType& ort)
{
// This is derived from the Algol procedures orthes and ortran,
// by Martin and Wilkinson, Handbook for Auto. Comp.,
// Vol.ii-Linear Algebra, and the corresponding
// Fortran subroutines in EISPACK.
int n = m_eivec.cols();
int low = 0;
int high = n-1;
for (int m = low+1; m <= high-1; ++m)
{
// Scale column.
RealScalar scale = matH.block(m, m-1, high-m+1, 1).cwiseAbs().sum();
if (scale != 0.0)
{
// Compute Householder transformation.
RealScalar h = 0.0;
// FIXME could be rewritten, but this one looks better wrt cache
for (int i = high; i >= m; i--)
{
ort.coeffRef(i) = matH.coeff(i,m-1)/scale;
h += ort.coeff(i) * ort.coeff(i);
}
RealScalar g = ei_sqrt(h);
if (ort.coeff(m) > 0)
g = -g;
h = h - ort.coeff(m) * g;
ort.coeffRef(m) = ort.coeff(m) - g;
// Apply Householder similarity transformation
// H = (I-u*u'/h)*H*(I-u*u')/h)
int bSize = high-m+1;
matH.block(m, m, bSize, n-m).noalias() -= ((ort.segment(m, bSize)/h)
* (ort.segment(m, bSize).transpose() * matH.block(m, m, bSize, n-m)));
matH.block(0, m, high+1, bSize).noalias() -= ((matH.block(0, m, high+1, bSize) * ort.segment(m, bSize))
* (ort.segment(m, bSize)/h).transpose());
ort.coeffRef(m) = scale*ort.coeff(m);
matH.coeffRef(m,m-1) = scale*g;
}
}
// Accumulate transformations (Algol's ortran).
m_eivec.setIdentity();
for (int m = high-1; m >= low+1; m--)
{
if (matH.coeff(m,m-1) != 0.0)
{
ort.segment(m+1, high-m) = matH.col(m-1).segment(m+1, high-m);
int bSize = high-m+1;
m_eivec.block(m, m, bSize, bSize).noalias() += ( (ort.segment(m, bSize) / (matH.coeff(m,m-1) * ort.coeff(m)))
* (ort.segment(m, bSize).transpose() * m_eivec.block(m, m, bSize, bSize)) );
}
}
}
// Complex scalar division. // Complex scalar division.
template<typename Scalar> template<typename Scalar>
std::complex<Scalar> cdiv(Scalar xr, Scalar xi, Scalar yr, Scalar yi) std::complex<Scalar> cdiv(Scalar xr, Scalar xi, Scalar yr, Scalar yi)