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generalized eigendecomposition doc

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Gael Guennebaud 2010-06-10 09:44:52 +02:00
parent 41e5625f96
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1 changed files with 9 additions and 5 deletions
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14
Eigen/src/Eigenvalues/SelfAdjointEigenSolver.h
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@ -171,7 +171,7 @@ template<typename _MatrixType> class SelfAdjointEigenSolver
compute(matrix, computeEigenvectors); compute(matrix, computeEigenvectors);
} }
/** \brief Constructor; computes eigendecomposition of given matrix pencil. /** \brief Constructor; computes generalized eigendecomposition of given matrix pencil.
* *
* \param[in] matA Selfadjoint matrix in matrix pencil. * \param[in] matA Selfadjoint matrix in matrix pencil.
* \param[in] matB Positive-definite matrix in matrix pencil. * \param[in] matB Positive-definite matrix in matrix pencil.
@ -183,8 +183,9 @@ template<typename _MatrixType> class SelfAdjointEigenSolver
* to compute the eigenvalues and (if requested) the eigenvectors of the * to compute the eigenvalues and (if requested) the eigenvectors of the
* generalized eigenproblem \f$ Ax = \lambda B x \f$ with \a matA 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 * selfadjoint matrix \f$ A \f$ and \a matB the positive definite matrix
* \f$ B \f$ . The eigenvectors are computed if \a computeEigenvectors is * \f$ B \f$. Each eigenvector \f$ x \f$ satisfies the property
* true. * \f$ x^* B x = 1 \f$. The eigenvectors are computed if
* \a computeEigenvectors is true.
* *
* Example: \include SelfAdjointEigenSolver_SelfAdjointEigenSolver_MatrixType2.cpp * Example: \include SelfAdjointEigenSolver_SelfAdjointEigenSolver_MatrixType2.cpp
* Output: \verbinclude SelfAdjointEigenSolver_SelfAdjointEigenSolver_MatrixType2.out * Output: \verbinclude SelfAdjointEigenSolver_SelfAdjointEigenSolver_MatrixType2.out
@ -236,7 +237,7 @@ template<typename _MatrixType> class SelfAdjointEigenSolver
*/ */
SelfAdjointEigenSolver& compute(const MatrixType& matrix, bool computeEigenvectors = true); SelfAdjointEigenSolver& compute(const MatrixType& matrix, bool computeEigenvectors = true);
/** \brief Computes eigendecomposition of given matrix pencil. /** \brief Computes generalized eigendecomposition of given matrix pencil.
* *
* \param[in] matA Selfadjoint matrix in matrix pencil. * \param[in] matA Selfadjoint matrix in matrix pencil.
* \param[in] matB Positive-definite matrix in matrix pencil. * \param[in] matB Positive-definite matrix in matrix pencil.
@ -248,7 +249,10 @@ template<typename _MatrixType> class SelfAdjointEigenSolver
* This function computes eigenvalues and (if requested) the eigenvectors * This function computes eigenvalues and (if requested) the eigenvectors
* of the generalized eigenproblem \f$ Ax = \lambda B x \f$ with \a matA * 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 * the selfadjoint matrix \f$ A \f$ and \a matB the positive definite
* matrix \f$ B \f$. The eigenvalues() function can be used to retrieve * matrix \f$ 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 * the eigenvalues. If \p computeEigenvectors is true, then the
* eigenvectors are also computed and can be retrieved by calling * eigenvectors are also computed and can be retrieved by calling
* eigenvectors(). * eigenvectors().