devtools/eigen
1
0
Fork 0
mirror of https://gitlab.com/libeigen/eigen.git synced 2026-04-10 11:34:33 +08:00
Code Issues Packages Projects Releases Wiki Activity

Fixes in Eigensolver:

Browse Source 
* eigenvectors => pseudoEigenvectors
 * added pseudoEigenvalueMatrix
 * clear the documentation
 * added respective unit test
Still missing: a proper eigenvectors() function.
This commit is contained in:
Gael Guennebaud
2008-10-01 10:17:08 +00:00
parent 618de17bf7
commit d907cd4410
2 changed files with 104 additions and 15 deletions
Download Patch File Download Diff File Expand all files Collapse all files

64
Eigen/src/QR/EigenSolver.h
View File

@@ -58,9 +58,50 @@ template<typename _MatrixType> class EigenSolver
compute(matrix);
}
MatrixType eigenvectors(void) const { return m_eivec; }
// TODO compute the complex eigen vectors
// MatrixType eigenvectors(void) const { return m_eivec; }
EigenvalueType eigenvalues(void) const { return m_eivalues; }
/** \returns a real matrix V of pseudo eigenvectors.
*
* Let D be the block diagonal matrix with the real eigenvalues in 1x1 blocks,
* and any complex values u+iv in 2x2 blocks [u v ; -v u]. Then, the matrices D
* and V satisfy A*V = V*D.
*
* More precisely, if the diagonal matrix of the eigen values is:\n
* \f$
* \left[ \begin{array}{cccccc}
* u+iv & & & & & \\
* & u-iv & & & & \\
* & & a+ib & & & \\
* & & & a-ib & & \\
* & & & & x & \\
* & & & & & y \\
* \end{array} \right]
* \f$ \n
* then, we have:\n
* \f$
* D =\left[ \begin{array}{cccccc}
* u & v & & & & \\
* -v & u & & & & \\
* & & a & b & & \\
* & & -b & a & & \\
* & & & & x & \\
* & & & & & y \\
* \end{array} \right]
* \f$
*
* \sa pseudoEigenvalueMatrix()
*/
const MatrixType& pseudoEigenvectors() const { return m_eivec; }
/** \returns the real block diagonal matrix D of the eigenvalues.
*
* See pseudoEigenvectors() for the details.
*/
MatrixType pseudoEigenvalueMatrix() const;
/** \returns the eigenvalues as a column vector */
EigenvalueType eigenvalues() const { return m_eivalues; }
void compute(const MatrixType& matrix);
@@ -74,6 +115,25 @@ template<typename _MatrixType> class EigenSolver
EigenvalueType m_eivalues;
};
template<typename MatrixType>
MatrixType EigenSolver<MatrixType>::pseudoEigenvalueMatrix() const
{
int n = m_eivec.cols();
MatrixType matD = MatrixType::Zero(n,n);
for (int i=0; i<n; i++)
{
if (ei_isMuchSmallerThan(ei_imag(m_eivalues.coeff(i)), ei_real(m_eivalues.coeff(i))))
matD.coeffRef(i,i) = ei_real(m_eivalues.coeff(i));
else
{
matD.template block<2,2>(i,i) << ei_real(m_eivalues.coeff(i)), ei_imag(m_eivalues.coeff(i)),
-ei_imag(m_eivalues.coeff(i)), ei_real(m_eivalues.coeff(i));
i++;
}
}
return matD;
}
template<typename MatrixType>
void EigenSolver<MatrixType>::compute(const MatrixType& matrix)
{