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eigenvalues: documentation fixes

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This commit is contained in:
Gael Guennebaud 2010-06-17 14:34:10 +02:00
parent 9196b6b659
commit ab6a044d0d
4 changed files with 15 additions and 15 deletions
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24
Eigen/src/Eigenvalues/GeneralizedSelfAdjointEigenSolver.h
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@ -141,16 +141,14 @@ class GeneralizedSelfAdjointEigenSolver : public SelfAdjointEigenSolver<_MatrixT
* *
* \returns Reference to \c *this * \returns Reference to \c *this
* *
* If \p options contains Ax_lBx (the default), this function computes eigenvalues * Accoring to \p options, this function computes eigenvalues and (if requested)
* and (if requested) the eigenvectors of the generalized eigenproblem * the eigenvectors of one of the following three generalized eigenproblems:
* \f$ Ax = \lambda B x \f$ with \a matA the selfadjoint * - \c Ax_lBx: \f$ Ax = \lambda B x \f$
* 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$.
*
* In addition, the two following variants can be solved via \p options:
* - \c ABx_lx: \f$ ABx = \lambda x \f$ * - \c ABx_lx: \f$ ABx = \lambda x \f$
* - \c BAx_lx: \f$ BAx = \lambda x \f$ * - \c BAx_lx: \f$ BAx = \lambda 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$.
* *
* The eigenvalues() function can be used to retrieve * The eigenvalues() function can be used to retrieve
* the eigenvalues. If \p options contains ComputeEigenvectors, then the * the eigenvalues. If \p options contains ComputeEigenvectors, then the
@ -158,17 +156,19 @@ class GeneralizedSelfAdjointEigenSolver : public SelfAdjointEigenSolver<_MatrixT
* eigenvectors(). * eigenvectors().
* *
* The implementation uses LLT to compute the Cholesky decomposition * The implementation uses LLT to compute the Cholesky decomposition
* \f$ B = LL^* \f$ and calls compute(const MatrixType&, bool) to compute * \f$ B = LL^* \f$ and computes the classical eigendecomposition
* the eigendecomposition \f$ L^{-1} A (L^*)^{-1} \f$. This solves the * of the selfadjoint matrix \f$ L^{-1} A (L^*)^{-1} \f$ if \p options contains Ax_lBx
* and of \f$ L^{*} A L \f$ otherwise. This solves the
* generalized eigenproblem, because any solution of the generalized * generalized eigenproblem, because any solution of the generalized
* eigenproblem \f$ Ax = \lambda B x \f$ corresponds to a solution * 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 * \f$ L^{-1} A (L^*)^{-1} (L^* x) = \lambda (L^* x) \f$ of the
* eigenproblem for \f$ L^{-1} A (L^*)^{-1} \f$. * eigenproblem for \f$ L^{-1} A (L^*)^{-1} \f$. Similar statements
* can be made for the two other variants.
* *
* Example: \include SelfAdjointEigenSolver_compute_MatrixType2.cpp * Example: \include SelfAdjointEigenSolver_compute_MatrixType2.cpp
* Output: \verbinclude SelfAdjointEigenSolver_compute_MatrixType2.out * Output: \verbinclude SelfAdjointEigenSolver_compute_MatrixType2.out
* *
* \sa SelfAdjointEigenSolver(const MatrixType&, const MatrixType&, int) * \sa GeneralizedSelfAdjointEigenSolver(const MatrixType&, const MatrixType&, int)
*/ */
GeneralizedSelfAdjointEigenSolver& compute(const MatrixType& matA, const MatrixType& matB, GeneralizedSelfAdjointEigenSolver& compute(const MatrixType& matA, const MatrixType& matB,
int options = ComputeEigenvectors|Ax_lBx); int options = ComputeEigenvectors|Ax_lBx);

2
Eigen/src/Eigenvalues/SelfAdjointEigenSolver.h
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@ -68,7 +68,7 @@
* contains an example of the typical use of this class. * contains an example of the typical use of this class.
* *
* To solve the \em generalized eigenvalue problem \f$ Av = \lambda Bv \f$ and * To solve the \em generalized eigenvalue problem \f$ Av = \lambda Bv \f$ and
* the like see the class GeneralizedSelfAdjointEigenSolver. * the likes, see the class GeneralizedSelfAdjointEigenSolver.
* *
* \sa MatrixBase::eigenvalues(), class EigenSolver, class ComplexEigenSolver * \sa MatrixBase::eigenvalues(), class EigenSolver, class ComplexEigenSolver
*/ */

2
doc/snippets/SelfAdjointEigenSolver_SelfAdjointEigenSolver_MatrixType2.cpp
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@ -5,7 +5,7 @@ X = MatrixXd::Random(5,5);
MatrixXd B = X * X.transpose(); MatrixXd B = X * X.transpose();
cout << "and a random postive-definite matrix, B:" << endl << B << endl << endl; cout << "and a random postive-definite matrix, B:" << endl << B << endl << endl;
SelfAdjointEigenSolver<MatrixXd> es(A,B); GeneralizedSelfAdjointEigenSolver<MatrixXd> es(A,B);
cout << "The eigenvalues of the pencil (A,B) are:" << endl << es.eigenvalues() << endl; cout << "The eigenvalues of the pencil (A,B) are:" << endl << es.eigenvalues() << endl;
cout << "The matrix of eigenvectors, V, is:" << endl << es.eigenvectors() << endl << endl; cout << "The matrix of eigenvectors, V, is:" << endl << es.eigenvectors() << endl << endl;

2
doc/snippets/SelfAdjointEigenSolver_compute_MatrixType2.cpp
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@ -3,7 +3,7 @@ MatrixXd A = X * X.transpose();
X = MatrixXd::Random(5,5); X = MatrixXd::Random(5,5);
MatrixXd B = X * X.transpose(); MatrixXd B = X * X.transpose();
SelfAdjointEigenSolver<MatrixXd> es(A,B,false); GeneralizedSelfAdjointEigenSolver<MatrixXd> es(A,B,EigenvaluesOnly);
cout << "The eigenvalues of the pencil (A,B) are:" << endl << es.eigenvalues() << endl; cout << "The eigenvalues of the pencil (A,B) are:" << endl << es.eigenvalues() << endl;
es.compute(B,A,false); es.compute(B,A,false);
cout << "The eigenvalues of the pencil (B,A) are:" << endl << es.eigenvalues() << endl; cout << "The eigenvalues of the pencil (B,A) are:" << endl << es.eigenvalues() << endl;