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Move computation of eigenvalues from RealSchur to EigenSolver.

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This commit is contained in:
Jitse Niesen
2010-04-12 18:54:15 +01:00
parent 73d3a27667
commit 574ad9efbd
2 changed files with 33 additions and 34 deletions
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38
Eigen/src/Eigenvalues/EigenSolver.h
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@@ -68,7 +68,9 @@
* The documentation for EigenSolver(const MatrixType&) contains an example of
* the typical use of this class.
*
* \note this code was adapted from JAMA (public domain)
* \note The implementation is adapted from
* <a href="http://math.nist.gov/javanumerics/jama/">JAMA</a> (public domain).
* Their code is based on EISPACK.
*
* \sa MatrixBase::eigenvalues(), class ComplexEigenSolver, class SelfAdjointEigenSolver
*/
@@ -232,12 +234,13 @@ template<typename _MatrixType> class EigenSolver
* The eigenvalues() and eigenvectors() functions can be used to retrieve
* the computed eigendecomposition.
*
* The matrix is first reduced to Schur form. The Schur decomposition is
* then used to compute the eigenvalues and eigenvectors.
* The matrix is first reduced to real Schur form using the RealSchur
* class. The Schur decomposition is then used to compute the eigenvalues
* and eigenvectors.
*
* The cost of the computation is dominated by the cost of the Schur
* decomposition, which is \f$ O(n^3) \f$ where \f$ n \f$ is the size of
* the matrix.
* decomposition, which is very approximately \f$ 25n^3 \f$ where
* \f$ n \f$ is the size of the matrix.
*
* This method reuses of the allocated data in the EigenSolver object.
*
@@ -311,12 +314,31 @@ EigenSolver<MatrixType>& EigenSolver<MatrixType>::compute(const MatrixType& matr
// Reduce to real Schur form.
RealSchur<MatrixType> rs(matrix);
MatrixType matH = rs.matrixT();
MatrixType matT = rs.matrixT();
m_eivec = rs.matrixU();
m_eivalues = rs.eigenvalues();
// Compute eigenvalues from matT
m_eivalues.resize(matrix.cols());
int i = 0;
while (i < matrix.cols())
{
if (i == matrix.cols() - 1 || matT.coeff(i+1, i) == Scalar(0))
{
m_eivalues.coeffRef(i) = matT.coeff(i, i);
++i;
}
else
{
Scalar p = Scalar(0.5) * (matT.coeff(i, i) - matT.coeff(i+1, i+1));
Scalar z = ei_sqrt(ei_abs(p * p + matT.coeff(i+1, i) * matT.coeff(i, i+1)));
m_eivalues.coeffRef(i) = ComplexScalar(matT.coeff(i+1, i+1) + p, z);
m_eivalues.coeffRef(i+1) = ComplexScalar(matT.coeff(i+1, i+1) + p, -z);
i += 2;
}
}
// Compute eigenvectors.
hqr2_step2(matH);
hqr2_step2(matT);
m_isInitialized = true;
return *this;