Compute the largest eigenvalues and the associated principle eigenvector via power iteration. More...
#include <pinocchio/math/lanczos-decomposition.hpp>

Public Types | |
| enum | { Options = _Matrix::Options } |
| typedef _Matrix | PlainMatrix |
| typedef _Matrix::Scalar | Scalar |
| typedef TridiagonalSymmetricMatrixTpl< Scalar, Options > | TridiagonalMatrix |
| typedef PlainMatrix::ColXpr | Vector |
Public Member Functions | |
| template<typename MatrixLikeType > | |
| LanczosDecompositionTpl (const MatrixLikeType &mat, const Eigen::DenseIndex decomposition_size) | |
| Default constructor for the Lanczos decomposition from an input matrix. | |
| template<typename MatrixLikeType > | |
| void | compute (const MatrixLikeType &A) |
| Computes the Lanczos decomposition of the input matrix A. | |
| template<typename MatrixLikeType > | |
| PlainMatrix | computeDecompositionResidual (const MatrixLikeType &A) const |
| Computes the residual associated with the decomposition, namely, the quantity \( A
Q_s - Q_s T_s \). | |
| bool | operator!= (const LanczosDecompositionTpl &other) const |
| bool | operator== (const LanczosDecompositionTpl &other) const |
| PlainMatrix & | Qs () |
| Returns the orthogonal basis associated with the Lanczos decomposition. | |
| const PlainMatrix & | Qs () const |
| Returns the orthogonal basis associated with the Lanczos decomposition. | |
| Eigen::DenseIndex | rank () const |
| Returns the rank of the decomposition. | |
| TridiagonalMatrix & | Ts () |
| Returns the tridiagonal matrix associated with the Lanczos decomposition. | |
| const TridiagonalMatrix & | Ts () const |
| Returns the tridiagonal matrix associated with the Lanczos decomposition. | |
Protected Attributes | |
| Vector | m_A_times_q |
| PlainMatrix | m_Qs |
| Eigen::DenseIndex | m_rank |
| TridiagonalMatrix | m_Ts |
Compute the largest eigenvalues and the associated principle eigenvector via power iteration.
Definition at line 18 of file lanczos-decomposition.hpp.
Definition at line 22 of file lanczos-decomposition.hpp.
Definition at line 24 of file lanczos-decomposition.hpp.
| typedef TridiagonalSymmetricMatrixTpl<Scalar, Options> TridiagonalMatrix |
Definition at line 29 of file lanczos-decomposition.hpp.
Definition at line 23 of file lanczos-decomposition.hpp.
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Default constructor for the Lanczos decomposition from an input matrix.
Definition at line 33 of file lanczos-decomposition.hpp.
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Computes the Lanczos decomposition of the input matrix A.
| [in] | A | The matrix to decompose |
Definition at line 67 of file lanczos-decomposition.hpp.
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Computes the residual associated with the decomposition, namely, the quantity \( A Q_s - Q_s T_s \).
| [in] | A | the matrix that have been decomposed. |
Definition at line 123 of file lanczos-decomposition.hpp.
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Definition at line 56 of file lanczos-decomposition.hpp.
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Definition at line 49 of file lanczos-decomposition.hpp.
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Returns the orthogonal basis associated with the Lanczos decomposition.
Definition at line 162 of file lanczos-decomposition.hpp.
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Returns the orthogonal basis associated with the Lanczos decomposition.
Definition at line 157 of file lanczos-decomposition.hpp.
Returns the rank of the decomposition.
Definition at line 168 of file lanczos-decomposition.hpp.
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Returns the tridiagonal matrix associated with the Lanczos decomposition.
Definition at line 151 of file lanczos-decomposition.hpp.
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Returns the tridiagonal matrix associated with the Lanczos decomposition.
Definition at line 146 of file lanczos-decomposition.hpp.
Definition at line 176 of file lanczos-decomposition.hpp.
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Definition at line 174 of file lanczos-decomposition.hpp.
Definition at line 177 of file lanczos-decomposition.hpp.
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Definition at line 175 of file lanczos-decomposition.hpp.