Public Types | Public Member Functions | Protected Member Functions | Static Protected Member Functions | Protected Attributes | List of all members
Eigen::SVDBase< Derived > Class Template Reference

Base class of SVD algorithms. More...

#include <SVDBase.h>

Public Types

enum  {
  RowsAtCompileTime = MatrixType::RowsAtCompileTime, ColsAtCompileTime = MatrixType::ColsAtCompileTime, DiagSizeAtCompileTime = EIGEN_SIZE_MIN_PREFER_DYNAMIC(RowsAtCompileTime,ColsAtCompileTime), MaxRowsAtCompileTime = MatrixType::MaxRowsAtCompileTime,
  MaxColsAtCompileTime = MatrixType::MaxColsAtCompileTime, MaxDiagSizeAtCompileTime = EIGEN_SIZE_MIN_PREFER_FIXED(MaxRowsAtCompileTime,MaxColsAtCompileTime), MatrixOptions = MatrixType::Options
}
 
typedef Eigen::Index Index
 
typedef internal::traits< Derived >::MatrixType MatrixType
 
typedef Matrix< Scalar, RowsAtCompileTime, RowsAtCompileTime, MatrixOptions, MaxRowsAtCompileTime, MaxRowsAtCompileTimeMatrixUType
 
typedef Matrix< Scalar, ColsAtCompileTime, ColsAtCompileTime, MatrixOptions, MaxColsAtCompileTime, MaxColsAtCompileTimeMatrixVType
 
typedef NumTraits< typename MatrixType::Scalar >::Real RealScalar
 
typedef MatrixType::Scalar Scalar
 
typedef internal::plain_diag_type< MatrixType, RealScalar >::type SingularValuesType
 
typedef MatrixType::StorageIndex StorageIndex
 

Public Member Functions

template<typename RhsType , typename DstType >
EIGEN_DEVICE_FUNC void _solve_impl (const RhsType &rhs, DstType &dst) const
 
template<typename RhsType , typename DstType >
void _solve_impl (const RhsType &rhs, DstType &dst) const
 
Index cols () const
 
bool computeU () const
 
bool computeV () const
 
Derived & derived ()
 
const Derived & derived () const
 
const MatrixUTypematrixU () const
 
const MatrixVTypematrixV () const
 
Index nonzeroSingularValues () const
 
Index rank () const
 
Index rows () const
 
Derived & setThreshold (const RealScalar &threshold)
 
Derived & setThreshold (Default_t)
 
const SingularValuesTypesingularValues () const
 
template<typename Rhs >
const Solve< Derived, Rhs > solve (const MatrixBase< Rhs > &b) const
 
RealScalar threshold () const
 

Protected Member Functions

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
 
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
 

Detailed Description

template<typename Derived>
class Eigen::SVDBase< Derived >

Base class of SVD algorithms.

Template Parameters
Derivedthe type of the actual SVD decomposition

SVD decomposition consists in decomposing any n-by-p matrix A as a product

\[ A = U S V^* \]

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.

If the input matrix has inf or nan coefficients, the result of the computation is undefined, but the computation is guaranteed to terminate in finite (and reasonable) time.

See also
class BDCSVD, class JacobiSVD

Definition at line 48 of file SVDBase.h.

Member Typedef Documentation

template<typename Derived>
typedef Eigen::Index Eigen::SVDBase< Derived >::Index
Deprecated:
since Eigen 3.3

Definition at line 56 of file SVDBase.h.

template<typename Derived>
typedef internal::traits<Derived>::MatrixType Eigen::SVDBase< Derived >::MatrixType

Definition at line 52 of file SVDBase.h.

Definition at line 67 of file SVDBase.h.

Definition at line 68 of file SVDBase.h.

template<typename Derived>
typedef NumTraits<typename MatrixType::Scalar>::Real Eigen::SVDBase< Derived >::RealScalar

Definition at line 54 of file SVDBase.h.

template<typename Derived>
typedef MatrixType::Scalar Eigen::SVDBase< Derived >::Scalar

Definition at line 53 of file SVDBase.h.

template<typename Derived>
typedef internal::plain_diag_type<MatrixType, RealScalar>::type Eigen::SVDBase< Derived >::SingularValuesType

Definition at line 69 of file SVDBase.h.

template<typename Derived>
typedef MatrixType::StorageIndex Eigen::SVDBase< Derived >::StorageIndex

Definition at line 55 of file SVDBase.h.

Member Enumeration Documentation

template<typename Derived>
anonymous enum
Enumerator
RowsAtCompileTime 
ColsAtCompileTime 
DiagSizeAtCompileTime 
MaxRowsAtCompileTime 
MaxColsAtCompileTime 
MaxDiagSizeAtCompileTime 
MatrixOptions 

Definition at line 57 of file SVDBase.h.

Constructor & Destructor Documentation

template<typename Derived>
Eigen::SVDBase< Derived >::SVDBase ( )
inlineprotected

Default Constructor.

Default constructor of SVDBase

Definition at line 245 of file SVDBase.h.

Member Function Documentation

template<typename Derived>
template<typename RhsType , typename DstType >
EIGEN_DEVICE_FUNC void Eigen::SVDBase< Derived >::_solve_impl ( const RhsType &  rhs,
DstType &  dst 
) const
template<typename Derived>
template<typename RhsType , typename DstType >
void Eigen::SVDBase< Derived >::_solve_impl ( const RhsType &  rhs,
DstType &  dst 
) const

Definition at line 261 of file SVDBase.h.

template<typename MatrixType >
bool Eigen::SVDBase< MatrixType >::allocate ( Index  rows,
Index  cols,
unsigned int  computationOptions 
)
protected

Definition at line 277 of file SVDBase.h.

template<typename Derived>
static void Eigen::SVDBase< Derived >::check_template_parameters ( )
inlinestaticprotected

Definition at line 223 of file SVDBase.h.

template<typename Derived>
Index Eigen::SVDBase< Derived >::cols ( void  ) const
inline

Definition at line 195 of file SVDBase.h.

template<typename Derived>
bool Eigen::SVDBase< Derived >::computeU ( ) const
inline
Returns
true if U (full or thin) is asked for in this SVD decomposition

Definition at line 190 of file SVDBase.h.

template<typename Derived>
bool Eigen::SVDBase< Derived >::computeV ( ) const
inline
Returns
true if V (full or thin) is asked for in this SVD decomposition

Definition at line 192 of file SVDBase.h.

template<typename Derived>
Derived& Eigen::SVDBase< Derived >::derived ( )
inline

Definition at line 71 of file SVDBase.h.

template<typename Derived>
const Derived& Eigen::SVDBase< Derived >::derived ( ) const
inline

Definition at line 72 of file SVDBase.h.

template<typename Derived>
const MatrixUType& Eigen::SVDBase< Derived >::matrixU ( ) const
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.

Definition at line 83 of file SVDBase.h.

template<typename Derived>
const MatrixVType& Eigen::SVDBase< Derived >::matrixV ( ) const
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.

Definition at line 99 of file SVDBase.h.

template<typename Derived>
Index Eigen::SVDBase< Derived >::nonzeroSingularValues ( ) const
inline
Returns
the number of singular values that are not exactly 0

Definition at line 118 of file SVDBase.h.

template<typename Derived>
Index Eigen::SVDBase< Derived >::rank ( ) const
inline
Returns
the rank of the matrix of which *this is 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&).

Definition at line 130 of file SVDBase.h.

template<typename Derived>
Index Eigen::SVDBase< Derived >::rows ( void  ) const
inline

Definition at line 194 of file SVDBase.h.

template<typename Derived>
Derived& Eigen::SVDBase< Derived >::setThreshold ( const RealScalar threshold)
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
thresholdThe new value to use as the threshold.

A singular value will be considered nonzero if its value is strictly greater than $ \vert singular value \vert \leqslant threshold \times \vert max singular value \vert $.

If you want to come back to the default behavior, call setThreshold(Default_t)

Definition at line 155 of file SVDBase.h.

template<typename Derived>
Derived& Eigen::SVDBase< Derived >::setThreshold ( Default_t  )
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.

svd.setThreshold(Eigen::Default);

See the documentation of setThreshold(const RealScalar&).

Definition at line 170 of file SVDBase.h.

template<typename Derived>
const SingularValuesType& Eigen::SVDBase< Derived >::singularValues ( ) const
inline
Returns
the vector of singular values.

For the SVD decomposition of a n-by-p matrix, letting m be the minimum of n and p, the returned vector has size m. Singular values are always sorted in decreasing order.

Definition at line 111 of file SVDBase.h.

template<typename Derived>
template<typename Rhs >
const Solve<Derived, Rhs> Eigen::SVDBase< Derived >::solve ( const MatrixBase< Rhs > &  b) const
inline
Returns
a (least squares) solution of $ A x = b $ using the current SVD decomposition of A.
Parameters
bthe right-hand-side of the equation to solve.
Note
Solving requires both U and V to be computed. Thin U and V are enough, there is no need for full U or V.
SVD solving is implicitly least-squares. Thus, this method serves both purposes of exact solving and least-squares solving. In other words, the returned solution is guaranteed to minimize the Euclidean norm $ \Vert A x - b \Vert $.

Definition at line 208 of file SVDBase.h.

template<typename Derived>
RealScalar Eigen::SVDBase< Derived >::threshold ( ) const
inline

Returns the threshold that will be used by certain methods such as rank().

See the documentation of setThreshold(const RealScalar&).

Definition at line 180 of file SVDBase.h.

Member Data Documentation

template<typename Derived>
Index Eigen::SVDBase< Derived >::m_cols
protected

Definition at line 238 of file SVDBase.h.

template<typename Derived>
unsigned int Eigen::SVDBase< Derived >::m_computationOptions
protected

Definition at line 237 of file SVDBase.h.

template<typename Derived>
bool Eigen::SVDBase< Derived >::m_computeFullU
protected

Definition at line 235 of file SVDBase.h.

template<typename Derived>
bool Eigen::SVDBase< Derived >::m_computeFullV
protected

Definition at line 236 of file SVDBase.h.

template<typename Derived>
bool Eigen::SVDBase< Derived >::m_computeThinU
protected

Definition at line 235 of file SVDBase.h.

template<typename Derived>
bool Eigen::SVDBase< Derived >::m_computeThinV
protected

Definition at line 236 of file SVDBase.h.

template<typename Derived>
Index Eigen::SVDBase< Derived >::m_diagSize
protected

Definition at line 238 of file SVDBase.h.

template<typename Derived>
bool Eigen::SVDBase< Derived >::m_isAllocated
protected

Definition at line 234 of file SVDBase.h.

template<typename Derived>
bool Eigen::SVDBase< Derived >::m_isInitialized
protected

Definition at line 234 of file SVDBase.h.

template<typename Derived>
MatrixUType Eigen::SVDBase< Derived >::m_matrixU
protected

Definition at line 231 of file SVDBase.h.

template<typename Derived>
MatrixVType Eigen::SVDBase< Derived >::m_matrixV
protected

Definition at line 232 of file SVDBase.h.

template<typename Derived>
Index Eigen::SVDBase< Derived >::m_nonzeroSingularValues
protected

Definition at line 238 of file SVDBase.h.

template<typename Derived>
RealScalar Eigen::SVDBase< Derived >::m_prescribedThreshold
protected

Definition at line 239 of file SVDBase.h.

template<typename Derived>
Index Eigen::SVDBase< Derived >::m_rows
protected

Definition at line 238 of file SVDBase.h.

template<typename Derived>
SingularValuesType Eigen::SVDBase< Derived >::m_singularValues
protected

Definition at line 233 of file SVDBase.h.

template<typename Derived>
bool Eigen::SVDBase< Derived >::m_usePrescribedThreshold
protected

Definition at line 234 of file SVDBase.h.


The documentation for this class was generated from the following file:


gtsam
Author(s):
autogenerated on Sat May 8 2021 02:55:09