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* decouple the generalized selfadjoint eigenvalue problem to the standard one

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* uses named values instead of bools
This commit is contained in:
Gael Guennebaud
2010-06-16 23:48:16 +02:00
parent 197ce96c00
commit 74006a9fe9
5 changed files with 244 additions and 112 deletions
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129
Eigen/src/Eigenvalues/SelfAdjointEigenSolver.h
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@@ -57,10 +57,6 @@
*
* Only the \b lower \b triangular \b part of the input matrix is referenced.
*
* This class can also be used to solve the generalized eigenvalue problem
* \f$ Av = \lambda Bv \f$. In this case, the matrix \f$ A \f$ should be
* selfadjoint and the matrix \f$ B \f$ should be positive definite.
*
* Call the function compute() to compute the eigenvalues and eigenvectors of
* a given matrix. Alternatively, you can use the
* SelfAdjointEigenSolver(const MatrixType&, bool) constructor which computes
@@ -70,6 +66,9 @@
*
* The documentation for SelfAdjointEigenSolver(const MatrixType&, bool)
* contains an example of the typical use of this class.
*
* To solve the \em generalized eigenvalue problem \f$ Av = \lambda Bv \f$ and
* the like see the class GeneralizedSelfAdjointEigenSolver.
*
* \sa MatrixBase::eigenvalues(), class EigenSolver, class ComplexEigenSolver
*/
@@ -147,13 +146,11 @@ template<typename _MatrixType> class SelfAdjointEigenSolver
*
* \param[in] matrix Selfadjoint matrix whose eigendecomposition is to
* be computed. Only the lower triangular part of the matrix is referenced.
* \param[in] computeEigenvectors If true, both the eigenvectors and the
* eigenvalues are computed; if false, only the eigenvalues are
* computed.
* \param[in] options Can be ComputeEigenvectors (default) or EigenvaluesOnly.
*
* This constructor calls compute(const MatrixType&, bool) to compute the
* eigenvalues of the matrix \p matrix. The eigenvectors are computed if
* \p computeEigenvectors is true.
* \p options equals ComputeEigenvectors.
*
* Example: \include SelfAdjointEigenSolver_SelfAdjointEigenSolver_MatrixType.cpp
* Output: \verbinclude SelfAdjointEigenSolver_SelfAdjointEigenSolver_MatrixType.out
@@ -161,60 +158,25 @@ template<typename _MatrixType> class SelfAdjointEigenSolver
* \sa compute(const MatrixType&, bool),
* SelfAdjointEigenSolver(const MatrixType&, const MatrixType&, bool)
*/
SelfAdjointEigenSolver(const MatrixType& matrix, bool computeEigenvectors = true)
SelfAdjointEigenSolver(const MatrixType& matrix, int options = ComputeEigenvectors)
: m_eivec(matrix.rows(), matrix.cols()),
m_eivalues(matrix.cols()),
m_subdiag(matrix.rows() > 1 ? matrix.rows() - 1 : 1),
m_isInitialized(false)
{
compute(matrix, computeEigenvectors);
}
/** \brief Constructor; computes generalized eigendecomposition of given matrix pencil.
*
* \param[in] matA Selfadjoint matrix in matrix pencil.
* Only the lower triangular part of the matrix is referenced.
* \param[in] matB Positive-definite matrix in matrix pencil.
* Only the lower triangular part of the matrix is referenced.
* \param[in] computeEigenvectors If true, both the eigenvectors and the
* eigenvalues are computed; if false, only the eigenvalues are
* computed.
*
* This constructor calls compute(const MatrixType&, const MatrixType&, bool)
* to compute the eigenvalues and (if requested) the eigenvectors of the
* generalized eigenproblem \f$ Ax = \lambda B x \f$ with \a matA the
* selfadjoint matrix \f$ A \f$ and \a matB the positive definite matrix
* \f$ B \f$. Each eigenvector \f$ x \f$ satisfies the property
* \f$ x^* B x = 1 \f$. The eigenvectors are computed if
* \a computeEigenvectors is true.
*
* Example: \include SelfAdjointEigenSolver_SelfAdjointEigenSolver_MatrixType2.cpp
* Output: \verbinclude SelfAdjointEigenSolver_SelfAdjointEigenSolver_MatrixType2.out
*
* \sa compute(const MatrixType&, const MatrixType&, bool),
* SelfAdjointEigenSolver(const MatrixType&, bool)
*/
SelfAdjointEigenSolver(const MatrixType& matA, const MatrixType& matB, bool computeEigenvectors = true)
: m_eivec(matA.rows(), matA.cols()),
m_eivalues(matA.cols()),
m_subdiag(matA.rows() > 1 ? matA.rows() - 1 : 1),
m_isInitialized(false)
{
compute(matA, matB, computeEigenvectors);
compute(matrix, options);
}
/** \brief Computes eigendecomposition of given matrix.
*
* \param[in] matrix Selfadjoint matrix whose eigendecomposition is to
* be computed. Only the lower triangular part of the matrix is referenced.
* \param[in] computeEigenvectors If true, both the eigenvectors and the
* eigenvalues are computed; if false, only the eigenvalues are
* computed.
* \param[in] options Can be ComputeEigenvectors (default) or EigenvaluesOnly.
* \returns Reference to \c *this
*
* This function computes the eigenvalues of \p matrix. The eigenvalues()
* function can be used to retrieve them. If \p computeEigenvectors is
* true, then the eigenvectors are also computed and can be retrieved by
* function can be used to retrieve them. If \p options equals ComputeEigenvectors,
* then the eigenvectors are also computed and can be retrieved by
* calling eigenvectors().
*
* This implementation uses a symmetric QR algorithm. The matrix is first
@@ -235,44 +197,7 @@ template<typename _MatrixType> class SelfAdjointEigenSolver
*
* \sa SelfAdjointEigenSolver(const MatrixType&, bool)
*/
SelfAdjointEigenSolver& compute(const MatrixType& matrix, bool computeEigenvectors = true);
/** \brief Computes generalized eigendecomposition of given matrix pencil.
*
* \param[in] matA Selfadjoint matrix in matrix pencil.
* Only the lower triangular part of the matrix is referenced.
* \param[in] matB Positive-definite matrix in matrix pencil.
* Only the lower triangular part of the matrix is referenced.
* \param[in] computeEigenvectors If true, both the eigenvectors and the
* eigenvalues are computed; if false, only the eigenvalues are
* computed.
* \returns Reference to \c *this
*
* This function computes eigenvalues and (if requested) the eigenvectors
* of the generalized eigenproblem \f$ Ax = \lambda B x \f$ with \a matA
* the selfadjoint matrix \f$ A \f$ and \a matB the positive definite
* matrix \f$ B \f$. In addition, each eigenvector \f$ x \f$
* satisfies the property \f$ x^* B x = 1 \f$.
*
* The eigenvalues() function can be used to retrieve
* the eigenvalues. If \p computeEigenvectors is true, then the
* eigenvectors are also computed and can be retrieved by calling
* eigenvectors().
*
* The implementation uses LLT to compute the Cholesky decomposition
* \f$ B = LL^* \f$ and calls compute(const MatrixType&, bool) to compute
* the eigendecomposition \f$ L^{-1} A (L^*)^{-1} \f$. This solves the
* generalized eigenproblem, because any solution of the generalized
* eigenproblem \f$ Ax = \lambda B x \f$ corresponds to a solution
* \f$ L^{-1} A (L^*)^{-1} (L^* x) = \lambda (L^* x) \f$ of the
* eigenproblem for \f$ L^{-1} A (L^*)^{-1} \f$.
*
* Example: \include SelfAdjointEigenSolver_compute_MatrixType2.cpp
* Output: \verbinclude SelfAdjointEigenSolver_compute_MatrixType2.out
*
* \sa SelfAdjointEigenSolver(const MatrixType&, const MatrixType&, bool)
*/
SelfAdjointEigenSolver& compute(const MatrixType& matA, const MatrixType& matB, bool computeEigenvectors = true);
SelfAdjointEigenSolver& compute(const MatrixType& matrix, int options = ComputeEigenvectors);
/** \brief Returns the eigenvectors of given matrix (pencil).
*
@@ -414,9 +339,14 @@ template<typename RealScalar, typename Scalar, typename Index>
static void ei_tridiagonal_qr_step(RealScalar* diag, RealScalar* subdiag, Index start, Index end, Scalar* matrixQ, Index n);
template<typename MatrixType>
SelfAdjointEigenSolver<MatrixType>& SelfAdjointEigenSolver<MatrixType>::compute(const MatrixType& matrix, bool computeEigenvectors)
SelfAdjointEigenSolver<MatrixType>& SelfAdjointEigenSolver<MatrixType>
::compute(const MatrixType& matrix, int options)
{
assert(matrix.cols() == matrix.rows());
ei_assert(matrix.cols() == matrix.rows());
ei_assert((options&~(EigVecMask|GenEigMask))==0
&& (options&EigVecMask)!=EigVecMask
&& "invalid option parameter");
bool computeEigenvectors = (options&ComputeEigenvectors)==ComputeEigenvectors;
Index n = matrix.cols();
m_eivalues.resize(n,1);
@@ -497,29 +427,6 @@ SelfAdjointEigenSolver<MatrixType>& SelfAdjointEigenSolver<MatrixType>::compute(
return *this;
}
template<typename MatrixType>
SelfAdjointEigenSolver<MatrixType>& SelfAdjointEigenSolver<MatrixType>::
compute(const MatrixType& matA, const MatrixType& matB, bool computeEigenvectors)
{
ei_assert(matA.cols()==matA.rows() && matB.rows()==matA.rows() && matB.cols()==matB.rows());
// Compute the cholesky decomposition of matB = L L' = U'U
LLT<MatrixType> cholB(matB);
// compute C = inv(L) A inv(L')
MatrixType matC = matA.template selfadjointView<Lower>();
cholB.matrixL().template solveInPlace<OnTheLeft>(matC);
cholB.matrixU().template solveInPlace<OnTheRight>(matC);
compute(matC, computeEigenvectors);
// transform back the eigen vectors: evecs = inv(U) * evecs
if(computeEigenvectors)
cholB.matrixU().solveInPlace(m_eivec);
return *this;
}
template<typename RealScalar, typename Scalar, typename Index>
static void ei_tridiagonal_qr_step(RealScalar* diag, RealScalar* subdiag, Index start, Index end, Scalar* matrixQ, Index n)
{