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WPILibC++ 2023.4.3
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WPILibC++ 2023.4.3
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\eigenvalues_module More...
Public Types | |
| typedef _MatrixType | MatrixType |
 Public Types inherited from Eigen::SelfAdjointEigenSolver< _MatrixType > | |
| enum | { Size = MatrixType::RowsAtCompileTime , ColsAtCompileTime = MatrixType::ColsAtCompileTime , Options = MatrixType::Options , MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime } |
| typedef _MatrixType | MatrixType |
| typedef MatrixType::Scalar | Scalar |
Scalar type for matrices of type _MatrixType. More... | |
| typedef Eigen::Index | Index |
| typedef Matrix< Scalar, Size, Size, ColMajor, MaxColsAtCompileTime, MaxColsAtCompileTime > | EigenvectorsType |
| typedef NumTraits< Scalar >::Real | RealScalar |
Real scalar type for _MatrixType. More... | |
| typedef internal::plain_col_type< MatrixType, RealScalar >::type | RealVectorType |
| Type for vector of eigenvalues as returned by eigenvalues(). More... | |
| typedef Tridiagonalization< MatrixType > | TridiagonalizationType |
| typedef TridiagonalizationType::SubDiagonalType | SubDiagonalType |
Public Member Functions | |
| GeneralizedSelfAdjointEigenSolver () | |
| Default constructor for fixed-size matrices. More... | |
| GeneralizedSelfAdjointEigenSolver (Index size) | |
| Constructor, pre-allocates memory for dynamic-size matrices. More... | |
| GeneralizedSelfAdjointEigenSolver (const MatrixType &matA, const MatrixType &matB, int options=ComputeEigenvectors|Ax_lBx) | |
| Constructor; computes generalized eigendecomposition of given matrix pencil. More... | |
| GeneralizedSelfAdjointEigenSolver & | compute (const MatrixType &matA, const MatrixType &matB, int options=ComputeEigenvectors|Ax_lBx) |
| Computes generalized eigendecomposition of given matrix pencil. More... | |
| Public Member Functions inherited from Eigen::SelfAdjointEigenSolver< _MatrixType > | |
| EIGEN_DEVICE_FUNC | SelfAdjointEigenSolver () |
| Default constructor for fixed-size matrices. More... | |
| EIGEN_DEVICE_FUNC | SelfAdjointEigenSolver (Index size) |
| Constructor, pre-allocates memory for dynamic-size matrices. More... | |
| template<typename InputType > | |
| EIGEN_DEVICE_FUNC | SelfAdjointEigenSolver (const EigenBase< InputType > &matrix, int options=ComputeEigenvectors) |
| Constructor; computes eigendecomposition of given matrix. More... | |
| template<typename InputType > | |
| EIGEN_DEVICE_FUNC SelfAdjointEigenSolver & | compute (const EigenBase< InputType > &matrix, int options=ComputeEigenvectors) |
| Computes eigendecomposition of given matrix. More... | |
| EIGEN_DEVICE_FUNC SelfAdjointEigenSolver & | computeDirect (const MatrixType &matrix, int options=ComputeEigenvectors) |
| Computes eigendecomposition of given matrix using a closed-form algorithm. More... | |
| SelfAdjointEigenSolver & | computeFromTridiagonal (const RealVectorType &diag, const SubDiagonalType &subdiag, int options=ComputeEigenvectors) |
| Computes the eigen decomposition from a tridiagonal symmetric matrix. More... | |
| EIGEN_DEVICE_FUNC const EigenvectorsType & | eigenvectors () const |
| Returns the eigenvectors of given matrix. More... | |
| EIGEN_DEVICE_FUNC const RealVectorType & | eigenvalues () const |
| Returns the eigenvalues of given matrix. More... | |
| EIGEN_DEVICE_FUNC MatrixType | operatorSqrt () const |
| Computes the positive-definite square root of the matrix. More... | |
| EIGEN_DEVICE_FUNC MatrixType | operatorInverseSqrt () const |
| Computes the inverse square root of the matrix. More... | |
| EIGEN_DEVICE_FUNC ComputationInfo | info () const |
| Reports whether previous computation was successful. More... | |
| template<typename InputType > | |
| EIGEN_DEVICE_FUNC SelfAdjointEigenSolver< MatrixType > & | compute (const EigenBase< InputType > &a_matrix, int options) |
Additional Inherited Members | |
| Static Public Attributes inherited from Eigen::SelfAdjointEigenSolver< _MatrixType > | |
| static const int | m_maxIterations = 30 |
| Maximum number of iterations. More... | |
| Static Protected Member Functions inherited from Eigen::SelfAdjointEigenSolver< _MatrixType > | |
| static EIGEN_DEVICE_FUNC void | check_template_parameters () |
| Protected Attributes inherited from Eigen::SelfAdjointEigenSolver< _MatrixType > | |
| EigenvectorsType | m_eivec |
| RealVectorType | m_eivalues |
| TridiagonalizationType::SubDiagonalType | m_subdiag |
| TridiagonalizationType::CoeffVectorType | m_hcoeffs |
| ComputationInfo | m_info |
| bool | m_isInitialized |
| bool | m_eigenvectorsOk |
\eigenvalues_module
Computes eigenvalues and eigenvectors of the generalized selfadjoint eigen problem
| _MatrixType | the type of the matrix of which we are computing the eigendecomposition; this is expected to be an instantiation of the Matrix class template. |
This class solves the generalized eigenvalue problem \( Av = \lambda Bv \). In this case, the matrix \( A \) should be selfadjoint and the matrix \( B \) should be positive definite.
Only the lower triangular part of the input matrix is referenced.
Call the function compute() to compute the eigenvalues and eigenvectors of a given matrix. Alternatively, you can use the GeneralizedSelfAdjointEigenSolver(const MatrixType&, const MatrixType&, int) constructor which computes the eigenvalues and eigenvectors at construction time. Once the eigenvalue and eigenvectors are computed, they can be retrieved with the eigenvalues() and eigenvectors() functions.
The documentation for GeneralizedSelfAdjointEigenSolver(const MatrixType&, const MatrixType&, int) contains an example of the typical use of this class.
| typedef _MatrixType Eigen::GeneralizedSelfAdjointEigenSolver< _MatrixType >::MatrixType |
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inline |
Default constructor for fixed-size matrices.
The default constructor is useful in cases in which the user intends to perform decompositions via compute(). This constructor can only be used if _MatrixType is a fixed-size matrix; use GeneralizedSelfAdjointEigenSolver(Index) for dynamic-size matrices.
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inlineexplicit |
Constructor, pre-allocates memory for dynamic-size matrices.
| [in] | size | Positive integer, size of the matrix whose eigenvalues and eigenvectors will be computed. |
This constructor is useful for dynamic-size matrices, when the user intends to perform decompositions via compute(). The size parameter is only used as a hint. It is not an error to give a wrong size, but it may impair performance.
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inline |
Constructor; computes generalized eigendecomposition of given matrix pencil.
| [in] | matA | Selfadjoint matrix in matrix pencil. Only the lower triangular part of the matrix is referenced. |
| [in] | matB | Positive-definite matrix in matrix pencil. Only the lower triangular part of the matrix is referenced. |
| [in] | options | A or-ed set of flags {ComputeEigenvectors,EigenvaluesOnly} | {Ax_lBx,ABx_lx,BAx_lx}. Default is ComputeEigenvectors|Ax_lBx. |
This constructor calls compute(const MatrixType&, const MatrixType&, int) to compute the eigenvalues and (if requested) the eigenvectors of the generalized eigenproblem \( Ax = \lambda B x \) with matA the selfadjoint matrix \( A \) and matB the positive definite matrix \( B \). Each eigenvector \( x \) satisfies the property \( x^* B x = 1 \). The eigenvectors are computed if options contains ComputeEigenvectors.
In addition, the two following variants can be solved via options:
ABx_lx: \( ABx = \lambda x \)BAx_lx: \( BAx = \lambda x \)Example:
Output:
| GeneralizedSelfAdjointEigenSolver< MatrixType > & Eigen::GeneralizedSelfAdjointEigenSolver< MatrixType >::compute | ( | const MatrixType & | matA, |
| const MatrixType & | matB, | ||
| int | options = ComputeEigenvectors|Ax_lBx |
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| ) |
Computes generalized eigendecomposition of given matrix pencil.
| [in] | matA | Selfadjoint matrix in matrix pencil. Only the lower triangular part of the matrix is referenced. |
| [in] | matB | Positive-definite matrix in matrix pencil. Only the lower triangular part of the matrix is referenced. |
| [in] | options | A or-ed set of flags {ComputeEigenvectors,EigenvaluesOnly} | {Ax_lBx,ABx_lx,BAx_lx}. Default is ComputeEigenvectors|Ax_lBx. |
*this According to options, this function computes eigenvalues and (if requested) the eigenvectors of one of the following three generalized eigenproblems:
Ax_lBx: \( Ax = \lambda B x \)ABx_lx: \( ABx = \lambda x \)BAx_lx: \( BAx = \lambda x \) with matA the selfadjoint matrix \( A \) and matB the positive definite matrix \( B \). In addition, each eigenvector \( x \) satisfies the property \( x^* B x = 1 \).The eigenvalues() function can be used to retrieve the eigenvalues. If options contains ComputeEigenvectors, then the eigenvectors are also computed and can be retrieved by calling eigenvectors().
The implementation uses LLT to compute the Cholesky decomposition \( B = LL^* \) and computes the classical eigendecomposition of the selfadjoint matrix \( L^{-1} A (L^*)^{-1} \) if options contains Ax_lBx and of \( L^{*} A L \) otherwise. This solves the generalized eigenproblem, because any solution of the generalized eigenproblem \( Ax = \lambda B x \) corresponds to a solution \( L^{-1} A (L^*)^{-1} (L^* x) = \lambda (L^* x) \) of the eigenproblem for \( L^{-1} A (L^*)^{-1} \). Similar statements can be made for the two other variants.
Example:
Output:
1.9.4