OMD Namespace Reference
Optimal Mode Decomposition. More...
Classes | |
| class | DataStore |
| interface to internal representation of OMD data More... | |
| class | LineSearchFunctor |
| Functor for linesearch along geodesic. More... | |
Enumerations | |
| enum | ImplementationType { kDirect, kPrecondQR } |
| defines how the method is implemented More... | |
Functions | |
| template<ImplementationType T> | |
| int | compute (std::ostream &out, Eigen::Ref< Eigen::MatrixXd > L, Eigen::Ref< Eigen::MatrixXd > M, const Eigen::Ref< const Eigen::MatrixXd > S, const Eigen::Index r, const GrManifold::CGOptions< double > *opt) |
| compute OMD matrices L and M The Optimal Mode Decomposition computes iteratively the solution to More... | |
| template<> | |
| int | compute< kPrecondQR > (std::ostream &out, Eigen::Ref< Eigen::MatrixXd > L, Eigen::Ref< Eigen::MatrixXd > M, const Eigen::Ref< const Eigen::MatrixXd > S, const Eigen::Index r, const GrManifold::CGOptions< double > *opt) |
| computes OMD for given data set More... | |
| template<> | |
| int | compute< kDirect > (std::ostream &out, Eigen::Ref< Eigen::MatrixXd > L, Eigen::Ref< Eigen::MatrixXd > M, const Eigen::Ref< const Eigen::MatrixXd > S, const Eigen::Index r, const GrManifold::CGOptions< double > *opt) |
| directly computes OMD for given data set More... | |
Detailed Description
Optimal Mode Decomposition.
Enumeration Type Documentation
◆ ImplementationType
Function Documentation
◆ compute()
template<ImplementationType T>
| int OMD::compute | ( | std::ostream & | out, |
| Eigen::Ref< Eigen::MatrixXd > | L, | ||
| Eigen::Ref< Eigen::MatrixXd > | M, | ||
| const Eigen::Ref< const Eigen::MatrixXd > | S, | ||
| const Eigen::Index | r, | ||
| const GrManifold::CGOptions< double > * | opt | ||
| ) |
compute OMD matrices L and M The Optimal Mode Decomposition computes iteratively the solution to
![\[ \begin{aligned} \min_{L,M} & \Vert Y - L M L^\top X \Vert_F \\ \mathrm{s.t.}\,L^\top L = I, \,&\, X = [s_0 \cdots s_{m-2}], Y = [s_1 \cdots s_{m-1}] \end{aligned} \]](form_25.png)
on the Grassmann manifold
- Template Parameters
-
T declares implementation type
- Warning
- Find the explicit specializations for the implementation types below. This template does not have a generic implementation.
- Parameters
-
out reference to output stream L resulting orthonormal bases [n x r] M resulting system matrix [r x r] S snapshot matrix [n x m] r reduced system dimension opt optional set of options
- Returns
- o on success
◆ compute< kDirect >()
template<>
| int OMD::compute< kDirect > | ( | std::ostream & | out, |
| Eigen::Ref< Eigen::MatrixXd > | L, | ||
| Eigen::Ref< Eigen::MatrixXd > | M, | ||
| const Eigen::Ref< const Eigen::MatrixXd > | S, | ||
| const Eigen::Index | r, | ||
| const GrManifold::CGOptions< double > * | opt | ||
| ) |
directly computes OMD for given data set
- Warning
- aborts if no initial subspace is supplied in opt
- Parameters
-
out reference to output stream L resulting orthonormal bases M resulting system matrix S snapshot data r system dimension opt necessary set of options (uses intial subspace)
- Returns
- 0 on success
◆ compute< kPrecondQR >()
template<>
| int OMD::compute< kPrecondQR > | ( | std::ostream & | out, |
| Eigen::Ref< Eigen::MatrixXd > | L, | ||
| Eigen::Ref< Eigen::MatrixXd > | M, | ||
| const Eigen::Ref< const Eigen::MatrixXd > | S, | ||
| const Eigen::Index | r, | ||
| const GrManifold::CGOptions< double > * | opt | ||
| ) |
computes OMD for given data set
- Note
- decomposes data set by QR (usually more efficient), then calls OMD::compute<kDirect>()
- Parameters
-
out reference to output stream L resulting orthonormal bases M resulting system matrix S snapshot data r system dimension opt (optional) set of options
- Returns
- 0 on success
