Base class of SVD algorithms. More...
#include <ForwardDeclarations.h>
Public Member Functions | |
| template<typename RhsType , typename DstType > | |
| void | _solve_impl (const RhsType &rhs, DstType &dst) const |
| template<bool Conjugate, typename RhsType , typename DstType > | |
| void | _solve_impl_transposed (const RhsType &rhs, DstType &dst) const |
| Index | cols () const |
| bool | computeU () const |
| bool | computeV () const |
| Derived & | derived () |
| const Derived & | derived () const |
| EIGEN_DEVICE_FUNC ComputationInfo | info () const |
| Reports whether previous computation was successful. More... | |
| const MatrixUType & | matrixU () const |
| const MatrixVType & | matrixV () const |
| Index | nonzeroSingularValues () const |
| Index | rank () const |
| Index | rows () const |
| Derived & | setThreshold (const RealScalar &threshold) |
| Derived & | setThreshold (Default_t) |
| const SingularValuesType & | singularValues () const |
| RealScalar | threshold () const |
Protected Member Functions | |
| void | _check_compute_assertions () const |
| template<bool Transpose_, typename Rhs > | |
| void | _check_solve_assertion (const Rhs &b) const |
| bool | allocate (Index rows, Index cols, unsigned int computationOptions) |
| SVDBase () | |
| Default Constructor. More... | |
Static Protected Member Functions | |
| static void | check_template_parameters () |
Protected Attributes | |
| Index | m_cols |
| unsigned int | m_computationOptions |
| bool | m_computeFullU |
| bool | m_computeFullV |
| bool | m_computeThinU |
| bool | m_computeThinV |
| Index | m_diagSize |
| ComputationInfo | m_info |
| bool | m_isAllocated |
| bool | m_isInitialized |
| MatrixUType | m_matrixU |
| MatrixVType | m_matrixV |
| Index | m_nonzeroSingularValues |
| RealScalar | m_prescribedThreshold |
| Index | m_rows |
| SingularValuesType | m_singularValues |
| bool | m_usePrescribedThreshold |
Friends | |
| template<typename Derived_ > | |
| struct | internal::solve_assertion |
Detailed Description
Base class of SVD algorithms.
- Template Parameters
-
Derived the type of the actual SVD decomposition
SVD decomposition consists in decomposing any n-by-p matrix A as a product
![\[ A = U S V^* \]](form_236.png)
where U is a n-by-n unitary, V is a p-by-p unitary, and S is a n-by-p real positive matrix which is zero outside of its main diagonal; the diagonal entries of S are known as the singular values of A and the columns of U and V are known as the left and right singular vectors of A respectively.
Singular values are always sorted in decreasing order.
You can ask for only thin U or V to be computed, meaning the following. In case of a rectangular n-by-p matrix, letting m be the smaller value among n and p, there are only m singular vectors; the remaining columns of U and V do not correspond to actual singular vectors. Asking for thin U or V means asking for only their m first columns to be formed. So U is then a n-by-m matrix, and V is then a p-by-m matrix. Notice that thin U and V are all you need for (least squares) solving.
The status of the computation can be retrived using the info() method. Unless info() returns Success, the results should be not considered well defined.
If the input matrix has inf or nan coefficients, the result of the computation is undefined, and info() will return InvalidInput, but the computation is guaranteed to terminate in finite (and reasonable) time.
Definition at line 277 of file ForwardDeclarations.h.
Member Typedef Documentation
◆ Index
| typedef Eigen::Index Eigen::SVDBase::Index |
- Deprecated:
- since Eigen 3.3
◆ MatrixType
| typedef internal::traits<Derived>::MatrixType Eigen::SVDBase::MatrixType |
◆ MatrixUType
◆ MatrixVType
◆ RealScalar
| typedef NumTraits<typename MatrixType::Scalar>::Real Eigen::SVDBase::RealScalar |
◆ Scalar
| typedef MatrixType::Scalar Eigen::SVDBase::Scalar |
◆ SingularValuesType
◆ StorageIndex
Member Enumeration Documentation
◆ anonymous enum
| anonymous enum |
Constructor & Destructor Documentation
◆ SVDBase()
|
inlineprotected |
Member Function Documentation
◆ _check_compute_assertions()
|
inlineprotected |
◆ _check_solve_assertion()
|
inlineprotected |
◆ _solve_impl()
| void Eigen::SVDBase::_solve_impl | ( | const RhsType & | rhs, |
| DstType & | dst | ||
| ) | const |
◆ _solve_impl_transposed()
| void Eigen::SVDBase::_solve_impl_transposed | ( | const RhsType & | rhs, |
| DstType & | dst | ||
| ) | const |
◆ allocate()
◆ check_template_parameters()
|
inlinestaticprotected |
◆ cols()
◆ computeU()
|
inline |
◆ computeV()
|
inline |
◆ derived() [1/2]
◆ derived() [2/2]
◆ info()
|
inline |
◆ matrixU()
|
inline |
- Returns
- the U matrix.
For the SVD decomposition of a n-by-p matrix, letting m be the minimum of n and p, the U matrix is n-by-n if you asked for ComputeFullU , and is n-by-m if you asked for ComputeThinU .
The m first columns of U are the left singular vectors of the matrix being decomposed.
This method asserts that you asked for U to be computed.
◆ matrixV()
|
inline |
- Returns
- the V matrix.
For the SVD decomposition of a n-by-p matrix, letting m be the minimum of n and p, the V matrix is p-by-p if you asked for ComputeFullV , and is p-by-m if you asked for ComputeThinV .
The m first columns of V are the right singular vectors of the matrix being decomposed.
This method asserts that you asked for V to be computed.
◆ nonzeroSingularValues()
|
inline |
◆ rank()
|
inline |
- Returns
- the rank of the matrix of which
*thisis the SVD.
- Note
- This method has to determine which singular values should be considered nonzero. For that, it uses the threshold value that you can control by calling setThreshold(const RealScalar&).
◆ rows()
◆ setThreshold() [1/2]
|
inline |
Allows to prescribe a threshold to be used by certain methods, such as rank() and solve(), which need to determine when singular values are to be considered nonzero. This is not used for the SVD decomposition itself.
When it needs to get the threshold value, Eigen calls threshold(). The default is NumTraits<Scalar>::epsilon()
- Parameters
-
threshold The new value to use as the threshold.
A singular value will be considered nonzero if its value is strictly greater than 
.
If you want to come back to the default behavior, call setThreshold(Default_t)
◆ setThreshold() [2/2]
|
inline |
Allows to come back to the default behavior, letting Eigen use its default formula for determining the threshold.
You should pass the special object Eigen::Default as parameter here.
See the documentation of setThreshold(const RealScalar&).
◆ singularValues()
|
inline |
◆ threshold()
|
inline |
Returns the threshold that will be used by certain methods such as rank().
See the documentation of setThreshold(const RealScalar&).
Friends And Related Function Documentation
◆ internal::solve_assertion
|
friend |
Member Data Documentation
◆ m_cols
◆ m_computationOptions
|
protected |
◆ m_computeFullU
◆ m_computeFullV
◆ m_computeThinU
◆ m_computeThinV
◆ m_diagSize
◆ m_info
|
protected |
◆ m_isAllocated
◆ m_isInitialized
◆ m_matrixU
|
protected |
◆ m_matrixV
|
protected |
◆ m_nonzeroSingularValues
◆ m_prescribedThreshold
|
protected |
◆ m_rows
◆ m_singularValues
|
protected |
◆ m_usePrescribedThreshold
The documentation for this class was generated from the following files: