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.